time c = ChowHeegner2('58a', '58b'); v1 = c.point_on_E_target_cardinality2(CDF(.1)); v2 = c.point_on_E_target_cardinality2(CDF(.2)); [f(v['P']) for v in [v1,v2]] def f(P): P = v['P'].best_approx(); print str(P).replace(' ','').replace(':',','), ' ', index_in_mw(P) def f(P): m = P.close_points(200, 1e-5) if len(m) != 1: print "nope!" else: P = m[0] print str(P).replace(' ','').replace(':',','), ' ', index_in_mw(P) Below done with: deg1 = 500, min_imag = 0.0001 ['37a1', {'degE': 2, 'degF': 2, 'F': '37b1'}] (6,14,1) 6 ['57a1', {'degE': 4, 'degF': 3, 'F': '57b1'}] (-1976/7569,-1408510/658503,1) 16 ['57a1', {'degE': 4, 'degF': 12, 'F': '57c1'}] (13/9,1/27,1) 8 ['58a1', {'degE': 4, 'degF': 4, 'F': '58b1'}] (15,-64,1) 8 ['77a1', {'degE': 4, 'degF': 20, 'F': '77b1'}] (3202868484180682218187009/178920312037400355533056,5712176166885965668811017269131209343/75681454554646576096389911416631296,1) 24 ['77a1', {'degE': 4, 'degF': 6, 'F': '77c1'}] (4,8,1) 4 ['89a1', {'degE': 2, 'degF': 5, 'F': '89b1'}] (3/4,-15/8,1) 4 ? ['91a1', {'degE': 4, 'degF': 4, 'F': '91b1'}] (-2/9 : -17/27 : 1) 4 via time v = c.point_on_E_fiber_cardinality2() ? ['91b1', {'degE': 4, 'degF': 4, 'F': '91a1'}] (1,-1,1) 0 *** another stabilize prob with 2 versus 4 *** (1,-1) = 3-torsion ['92b1', {'degE': 6, 'degF': 2, 'F': '92a1'}] 0 0 ['99a1', {'degE': 4, 'degF': 12, 'F': '99b1'}] (105/64,-897/512,1) 4 ['99a1', {'degE': 4, 'degF': 12, 'F': '99c1'}] 0 0 ['99a1', {'degE': 4, 'degF': 6, 'F': '99d1'}] (3,-6,1) 2 ? ['102a1', {'degE': 8, 'degF': 16, 'F': '102b1'}] (1,-1,1) 2 ** stabilize 4 versus 16 ** (really "(6889/3249,415415/185193,1) 8") ['102a1', {'degE': 8, 'degF': 24, 'F': '102c1'}] (4818774633289091395456101011786326209831535810587124503006450409/309488543223695809439572961112765055377212200068433537784110929,-388731550993541842956884558115764053727442750345435516546013972052557536999650553824262181523720/5444611111408433256088622027913856710052115762586261539987133723345421783044230078364666927783,1) 32 ['106b1', {'degE': 8, 'degF': 6, 'F': '106a1'}] (-1,4,1) 4 ['106b1', {'degE': 8, 'degF': 48, 'F': '106c1'}] (5383971196031101818014683387586966104438288145245055971863291611949053360577292485170067582329143431125657719938865709958205639640150642628075197400646879532236462186385900180756027607622016033503945659841601283337427828631573772879/1398401344234597179231469502211420540599956949608361174943486579942432554268939057411521876343920050769425759670792437572656919734691636231679050398149266367941109486646770265260346436217874341694428712241855060183973457449681666609,282358898767923963904252573555482079382535911525290324492500230823510282709413301145310808144257218711991289114153975355990759669959034537241421372199815179258585785589558701668689141274620256984110088688885942016128145066213639755163250181709853225525725847254948512175809731564566333855500622272331904415233545131679274131568546408153505632549980/52293504701395016926691868730714213477297584534466985274326989404664835898357828803152733088011829421011791160157734388398300650069549100890864328907908038555238201763756625625924540118742713586273943926842828942249099789807962551656861687584208206979057890491923411352159489739999336029595602582532303139682238835633840066029813430981804208944727,1) 88 ['106b1', {'degE': 8, 'degF': 10, 'F': '106d1'}] (19729/16384,-2017095/2097152,1) 12 ['112a1', {'degE': 8, 'degF': 4, 'F': '112b1'}] 0 0 ['112a1', {'degE': 8, 'degF': 8, 'F': '112c1'}] 0 9 ** stabilize 2 versus guess of 4 ** ['118a1', {'degE': 4, 'degF': 12, 'F': '118b1'}] (35/169,2248/2197,1) 8 ** default params find only 4; defaulty wrong.; using this works fine though: v = c.point_on_E_target_cardinality2(CDF(.1), min_imag=1e-5, deg1=1000) # 39 seconds Also, this works: v = c.point_on_E_target_cardinality2(CDF(.05), min_imag=1e-5, deg1=1000) ; but using CDF(.2) does not!? ** This gets it in 13 seconds! v = c.point_on_E_2(deg1=800,min_imag=1e-4/2) ** ['118a1', {'degE': 4, 'degF': 6, 'F': '118c1'}] (3,-8,1) 4 ['118a1', {'degE': 4, 'degF': 38, 'F': '118d1'}] (728502982837043292165033754595/119577288065983419158347477969,-817392833630493674138073028128419528696198803/41349765363959915899138703583595648675574297,1) 28 ['121b1', {'degE': 4, 'degF': 6, 'F': '121a1'}] (-2,3,1) 4 ['121b1', {'degE': 4, 'degF': 6, 'F': '121c1'}] (-2,3,1) 4 ?? ['121b1', {'degE': 4, 'degF': 24, 'F': '121d1'}] (5119618196719040281826668897646/2400031463588621904697520887009,-4419314062651116306628268621639347274360019948/3718137127371596955926444367615869737571602223,1) 28 ** default params no good; stab at 18 (instead of 24) sage: time v = c.point_on_E_target_cardinality2(CDF(.15), min_imag=(1e-4)/2, deg1=2000) # for above gets to 22, but not 24 sage: time v = c.point_on_E_target_cardinality2(CDF(.1), min_imag=1e-5, deg1=3000) modular degree of F = 24 target number of points on E = 24 ** deg1 = 3000, min_imag = 0.0000100000000000000, len(w) = 0, target = 24 len(v) = 320 deg(second f) = 749700 found 261 double prec roots that refined in 46.1902258396 seconds ** found 24 new points in 260.29 seconds *** W00t! found all needed points *** Time: CPU 260.30 s, Wall: 261.04 s ... and finally. Same *exact* result from: sage: time v = c.point_on_E_fiber_cardinality2(CDF(0.1), deg1=3000, min_imag=1e-5, equiv_prec=20) ?? ['123a1', {'degE': 20, 'degF': 4, 'F': '123b1'}] 0 0 ** stab 2 versus guess of 4 ** really is 2! ['123b1', {'degE': 4, 'degF': 20, 'F': '123a1'}] (79/81,-692/729,1) 4 -- interesting since both curves have rank 1, but point is nonzero! ['124a1', {'degE': 6, 'degF': 6, 'F': '124b1'}] 0 0 ** stab at 2 instead of 6 ** sage: time v = c.point_on_E_target_cardinality2(CDF(.05), min_imag=1e-5, deg1=1000) # still stabilize at 2 ['128a1', {'degE': 4, 'degF': 8, 'F': '128b1'}] 0 0 ** stab at 4 instead of 8 ** ['128a1', {'degE': 4, 'degF': 4, 'F': '128c1'}] (-1,0,1) 0 ** stab 2 instead of 4 *** -- answer is 2-torsion ['128a1', {'degE': 4, 'degF': 8, 'F': '128d1'}] 0 0 ** stab 4 instead of 8 ** ['129a1', {'degE': 8, 'degF': 15, 'F': '129b1'}] (247281540631/89433893025,-1149193748352104/26745652878591375,1) 16 ['130a1', {'degE': 24, 'degF': 8, 'F': '130b1'}] 0 0 ** stab 4 instead of 8 ** -- note .2 one took too long to do something at end (mod param?), so used just .1 -- ['130a1', {'degE': 24, 'degF': 80, 'F': '130c1'}] 0 0 ** stab at 40 instead of 80 ** ['135a1', {'degE': 12, 'degF': 36, 'F': '135b1'}] 0 0 ** stab at 6 instead of 18 ** -- very interesting; looks like really is 6 sage: time v = c.point_on_E_target_cardinality2(CDF(.1), min_imag=1e-5, deg1=3000) modular degree of F = 36 target number of points on E = 18 ** deg1 = 3000, min_imag = 0.0000100000000000000, len(w) = 0, target = 18 len(v) = 305 deg(second f) = 749699 found 281 double prec roots that refined in 28.341078043 seconds ** found 6 new points in 275.36 seconds z (=1.08333565468) |--> 1.08333565468 ** deg1 = 3000, min_imag = 0.0000100000000000000, len(w) = 6, target = 18 # maybe really is 6! Looks like it! sage: time v = c.point_on_E_fiber_cardinality2() # quick sage: m = [NumericalPoint(c.E.elliptic_exponential(z),1e-4) for z in c.fE(v['fiber'])] sage: sage: len(set(m)) 6 ** WAIT ** -- but result is definitely not 0 0!!!! sage: time v = c.point_on_E_fiber_cardinality2(ComplexField(100)(0), equiv_prec=10) # 56 seconds sage: f(v['P']) (58473328848645495781173417569542705175708085309924358188134569872529168860609371374760645947223752497833242517286636765149776951530537730059640305092088337531173534719125300467791389782241391584686506666330299944138942636048184615804087728543555400154055617415336753438455137111365844137097903912084527221863370301932053433708270756029606278309235734834352139357133031640731932289576398479248176474076388855469517493908071255363548337092812566142752204616152631790451053381/42705741347299202560578633595037402493604574960316506298768888424620670238124090710862677878937759792299011899625734977010432009085005281052649906461724794187876861342290381130189536278228168791877078359715113462534620825983737341020352438254505175487018677032300654982909913891775004472135457225705408522269707584929354656214590937230975431212368109804217089278975867995353202099285464876808144063968522385503835202354119853669601696157664508937239147323516188347457982025,10113721304419266398065400449791719058823694907730659296228399353884953973656897236161023342025725441153001948845437258915877305082663418814473833050183828570792370542293176339825190393759005171001738245379726902533243995131515689580507013978299959330372060288336713980815175344573538548526014421352225904387720548044233444304242325331091437374595955183639044187234236252603671642841588575267171474869302217864446680139873830607520224486763416602159527680745528188901934969392283287975626502250832065526477144186006610218029990756134928511375375360457346136098854632310873636750619483198019515070309577925367073783952377582203542664821139651682955769182615635254270575109978489884844308391150108416516345551846/8825298388502785128074939454563931093921645832645440712959079661938938892517713518362243793790276457766575492996572084379441372702329311253992117410900968236610821904307347789173523740379079655700640499633508332497085641469029240518148818901012168786193949566671974405672784350815185754490133300145972289338097890127994056246810846938640296393356415609761133792479970114839383115911050978645893135839179925561335062858541521466644652620249523991470735245408404170351250064774460364404035075865818655799810009521198494349405175564108876833948766278515993212236653917051373676895893400023016508672535481518171316396417020679297301786289469812712230412111616222845018152624695924533611355682099538045990795165125,1) 192 # clearly right! sage: P = v['P'] sage: Q = P.close_points(200)[0] sage: float(Q[0]) 1.3692147005040451 sage: P (1.3692147005040451624969352233 - 9.8845171153593294329600049959e-29*I : 1.1459919947403685073245150570 - 7.8795678802094049107484407138e-29*I : 1.0000000000000000000000000000) This example is incredible. Crazy. sage: m = [NumericalPoint(c.E.elliptic_exponential(z),1e-4) for z in c.fE(v['fiber'])] sage: set(m) set([(13.000000000000000000000000000 + 1.1635082045023765407771718361e-28*I : -47.000000000000000000000000002 - 6.3054638149009653260768337752e-28*I : 1.0000000000000000000000000000)]) sage: len(set(m)) 1 sage: len(v['fiber']) 24 sage: c.fE.cusps_over_torsion() {1: [0, 1/45, 1/27, 2/45, 1/15, 1/9, 2/15, 1/5, 2/9, 1/3, 2/3, Infinity]} sage: len(c.fE.cusps_over_torsion()[1]) 12 sage: len(m) 24 Thus the picture is that over the point 0 on E, we have 12 cusps, so 0 is not ramified, since mod deg of E is 12. Then we have 12 cuspidal points and 24 noncusp points in fiber over 0 on F. Every single one of those 24 distinct noncuspidal points map to the same point (13,-47) on E. So there are exactly **2 points** in phi_E(phi_F^(-1)(0)). Generically, we were finding only 6 in phi_F^(-1)(anything random) and many in phi_E(phi_F^(-1)(anything random)) -- at least 34 --, which all map to 6 points, which strongly suggests get only 6. How to explain 6? ['136a1', {'degE': 8, 'degF': 8, 'F': '136b1'}] 0 0 ** stab at 2 instead of 8 ** ** It turns out that all points over F(0) are cusps! So this one is trivial by pure thought. Nice. ** sage: c = ChowHeegner2('136a', '136b') sage: time v = c.point_on_E_fiber_cardinality2(CDF(0)) modular degree of F (target fiber size) = 8 reducing target by 8 cusps to 0 (TODO *** result may be off by torsion! *** ) mapping them to E... mapped to E in 0.0 seconds Time: CPU 0.28 s, Wall: 0.32 s sage: v['P'] (0 : 1 : 0) ['138a1', {'degE': 8, 'degF': 16, 'F': '138b1'}] (36252351627402736231/16336278881691201225,189731720137534689494414505899/66028238020321085452416949125,1) 16 ['138a1', {'degE': 8, 'degF': 8, 'F': '138c1'}] (-56729/38025,-4832554/7414875,1) 8 ['141a1', {'degE': 28, 'degF': 12, 'F': '141b1'}] 0 0 ['141a1', {'degE': 28, 'degF': 6, 'F': '141c1'}] 0 0 ['141a1', {'degE': 28, 'degF': 4, 'F': '141d1'}] 0 0 again, all are cusps! sage: c = ChowHeegner2('141a', '141d') sage: time v = c.point_on_E_fiber_cardinality2(CDF(0)) modular degree of F (target fiber size) = 4 reducing target by 4 cusps to 0 (TODO *** result may be off by torsion! *** ) mapping them to E... mapped to E in 0.0 seconds Time: CPU 1.02 s, Wall: 1.07 s This also works: sage: time v = c.point_on_E_fiber_cardinality2() ['141a1', {'degE': 28, 'degF': 12, 'F': '141e1'}] 0 0 ['141d1', {'degE': 4, 'degF': 28, 'F': '141a1'}] (2561529134017/127894925376,3967963841584030337/45738294792666624,1) 12 # -- interesting symmetry! ['141d1', {'degE': 4, 'degF': 12, 'F': '141b1'}] (22/9,55/27,1) 4 time v = c.point_on_E_fiber_cardinality2() # no prob; fast. ['141d1', {'degE': 4, 'degF': 6, 'F': '141c1'}] (22/9,55/27,1) 4 ['141d1', {'degE': 4, 'degF': 12, 'F': '141e1'}] (22/9,55/27,1) 4 ['142a1', {'degE': 36, 'degF': 4, 'F': '142b1'}] 0 0 ['142a1', {'degE': 36, 'degF': 9, 'F': '142c1'}] 0 0 ['142a1', {'degE': 36, 'degF': 4, 'F': '142d1'}] 0 0 ['142a1', {'degE': 36, 'degF': 324, 'F': '142e1'}] 0 0 ** a challenge!** This seems to peter out with around 214 points: sage: time v = c.point_on_E_fiber_cardinality2() as does this: sage: time v = c.point_on_E_target_cardinality2() Probably just needs big precision. Amazingly, the following *worked* sage: time v = c.point_on_E_fiber_cardinality2(CDF(0.1), deg1=3000, min_imag=1e-5, equiv_prec=15) sage: v['P'] (1.14832318821430e24 - 6.72399507466805e23*I : -1.07541890794230e36 + 1.09537085207921e36*I : 1.00000000000000) Time: CPU 5784.15 s, Wall: 5800.56 s ['142b1', {'degE': 4, 'degF': 36, 'F': '142a1'}] (17,64,1) 4 ['142b1', {'degE': 4, 'degF': 9, 'F': '142c1'}] (84241/21025,-33269824/3048625,1) 8 ['142b1', {'degE': 4, 'degF': 4, 'F': '142d1'}] (17,64,1) 4 ['142b1', {'degE': 4, 'degF': 324, 'F': '142e1'}] HARD ['152a1', {'degE': 8, 'degF': 8, 'F': '152b1'}] 0 0 ['153a1', {'degE': 8, 'degF': 16, 'F': '153b1'}] (85,-784,1) 8 ['153a1', {'degE': 8, 'degF': 8, 'F': '153c1'}] (85,-784,1) 8 ['153a1', {'degE': 8, 'degF': 24, 'F': '153d1'}] 0 0 ['153b1', {'degE': 16, 'degF': 8, 'F': '153a1'}] 0 0 ['153b1', {'degE': 16, 'degF': 8, 'F': '153c1'}] 0 0 ['153b1', {'degE': 16, 'degF': 24, 'F': '153d1'}] 0 0 ['154a1', {'degE': 24, 'degF': 24, 'F': '154b1'}] (-16155785573482351722495636282077180405744532919963789361801855/4660202655539870928671535987824948296020237767597037582434304,127116296439023445325249725237653852845575849831723997770548180457743556541761684967841662849/10060213662446814590472450763213421418871161850997556652766817218519428083811293651856785408,1) 24 ['154a1', {'degE': 24, 'degF': 16, 'F': '154c1'}] (805974612186514548196821595/556342388583220854261139689,60492681033403602659321855107827276698239/13122398618044987672493491411410448308363,1) 16 ['155a1', {'degE': 20, 'degF': 8, 'F': '155b1'}] ['155a1', {'degE': 20, 'degF': 4, 'F': '155c1'}] ['155c1', {'degE': 4, 'degF': 20, 'F': '155a1'}] ['155c1', {'degE': 4, 'degF': 8, 'F': '155b1'}] ['156a1', {'degE': 12, 'degF': 12, 'F': '156b1'}] ['158a1', {'degE': 32, 'degF': 8, 'F': '158b1'}] ['158a1', {'degE': 32, 'degF': 48, 'F': '158c1'}] ['158a1', {'degE': 32, 'degF': 40, 'F': '158d1'}] ['158a1', {'degE': 32, 'degF': 6, 'F': '158e1'}] ['158b1', {'degE': 8, 'degF': 32, 'F': '158a1'}] ['158b1', {'degE': 8, 'degF': 48, 'F': '158c1'}] ['158b1', {'degE': 8, 'degF': 40, 'F': '158d1'}] ['158b1', {'degE': 8, 'degF': 6, 'F': '158e1'}] ['160a1', {'degE': 8, 'degF': 8, 'F': '160b1'}] ['162a1', {'degE': 12, 'degF': 6, 'F': '162b1'}] ['162a1', {'degE': 12, 'degF': 6, 'F': '162c1'}] ['162a1', {'degE': 12, 'degF': 12, 'F': '162d1'}] ['170a1', {'degE': 16, 'degF': 160, 'F': '170b1'}] fails with min_imag=1e-4 and deg1=500, so time v = c.point_on_E_fiber_cardinality2(min_imag=1e-4/3,deg1=1000) ['170a1', {'degE': 16, 'degF': 84, 'F': '170c1'}] 0 0 v=c.point_on_E_target_cardinality2() ['170a1', {'degE': 16, 'degF': 12, 'F': '170d1'}] ['170a1', {'degE': 16, 'degF': 20, 'F': '170e1'}] ['171b1', {'degE': 8, 'degF': 12, 'F': '171a1'}] ['171b1', {'degE': 8, 'degF': 96, 'F': '171c1'}] ['171b1', {'degE': 8, 'degF': 32, 'F': '171d1'}] ['175a1', {'degE': 8, 'degF': 16, 'F': '175b1'}] ['175a1', {'degE': 8, 'degF': 40, 'F': '175c1'}] ['175b1', {'degE': 16, 'degF': 8, 'F': '175a1'}] ['175b1', {'degE': 16, 'degF': 40, 'F': '175c1'}] ['176c1', {'degE': 8, 'degF': 16, 'F': '176a1'}] ['176c1', {'degE': 8, 'degF': 8, 'F': '176b1'}] ['184a1', {'degE': 8, 'degF': 8, 'F': '184b1'}] ['184a1', {'degE': 8, 'degF': 12, 'F': '184c1'}] ['184a1', {'degE': 8, 'degF': 24, 'F': '184d1'}] ['184b1', {'degE': 8, 'degF': 8, 'F': '184a1'}] ['184b1', {'degE': 8, 'degF': 12, 'F': '184c1'}] ['184b1', {'degE': 8, 'degF': 24, 'F': '184d1'}] ['185a1', {'degE': 48, 'degF': 8, 'F': '185b1'}] ['185a1', {'degE': 48, 'degF': 6, 'F': '185c1'}] ['185b1', {'degE': 8, 'degF': 48, 'F': '185a1'}] ['185b1', {'degE': 8, 'degF': 6, 'F': '185c1'}] ['185c1', {'degE': 6, 'degF': 48, 'F': '185a1'}] ['185c1', {'degE': 6, 'degF': 8, 'F': '185b1'}] ['189a1', {'degE': 12, 'degF': 12, 'F': '189b1'}] ['189a1', {'degE': 12, 'degF': 12, 'F': '189c1'}] ['189a1', {'degE': 12, 'degF': 36, 'F': '189d1'}] ['189b1', {'degE': 12, 'degF': 12, 'F': '189a1'}] ['189b1', {'degE': 12, 'degF': 12, 'F': '189c1'}] ['189b1', {'degE': 12, 'degF': 36, 'F': '189d1'}] ['190a1', {'degE': 88, 'degF': 8, 'F': '190b1'}] ['190a1', {'degE': 88, 'degF': 24, 'F': '190c1'}] 0 0 FAIL because too low precision to recognize point or something?!: v = c.point_on_E_fiber_cardinality2(0) Doing v = c.point_on_E_fiber_cardinality2(ComplexField(150)(0)) shows in fact two equal points were considered different to double precision... Need more points... or just use a generic fiber? Tried with various bigger precisions, but starting to get really slow... so went for the image and in 14 seconds got 0... consistent with different fibers. ['190b1', {'degE': 8, 'degF': 88, 'F': '190a1'}] (-236785238928473/265847774815921,5006699395017249635943/4334605166881846541719,1) 16 Above just works easily with "v = c.point_on_E_target_cardinality2()", since Atkin-Lehner's knock things down so much. ['190b1', {'degE': 8, 'degF': 24, 'F': '190c1'}] ['192a1', {'degE': 8, 'degF': 8, 'F': '192b1'}] ['192a1', {'degE': 8, 'degF': 8, 'F': '192c1'}] ['192a1', {'degE': 8, 'degF': 8, 'F': '192d1'}] ['196a1', {'degE': 6, 'degF': 42, 'F': '196b1'}] ['198a1', {'degE': 32, 'degF': 32, 'F': '198b1'}] ['198a1', {'degE': 32, 'degF': 32, 'F': '198c1'}] ['198a1', {'degE': 32, 'degF': 32, 'F': '198d1'}] ['198a1', {'degE': 32, 'degF': 160, 'F': '198e1'}] ['200b1', {'degE': 8, 'degF': 120, 'F': '200a1'}] ['200b1', {'degE': 8, 'degF': 24, 'F': '200c1'}] ['200b1', {'degE': 8, 'degF': 40, 'F': '200d1'}] ['200b1', {'degE': 8, 'degF': 24, 'F': '200e1'}] ['201a1', {'degE': 12, 'degF': 12, 'F': '201b1'}] ['201a1', {'degE': 12, 'degF': 60, 'F': '201c1'}] ['201b1', {'degE': 12, 'degF': 12, 'F': '201a1'}] ['201b1', {'degE': 12, 'degF': 60, 'F': '201c1'}] ['201c1', {'degE': 60, 'degF': 12, 'F': '201a1'}] ['201c1', {'degE': 60, 'degF': 12, 'F': '201b1'}] ['203b1', {'degE': 8, 'degF': 48, 'F': '203a1'}] ['203b1', {'degE': 8, 'degF': 12, 'F': '203c1'}] ['205a1', {'degE': 12, 'degF': 16, 'F': '205b1'}] ['205a1', {'degE': 12, 'degF': 8, 'F': '205c1'}] ['208a1', {'degE': 16, 'degF': 16, 'F': '208b1'}] ['208a1', {'degE': 16, 'degF': 12, 'F': '208c1'}] ['208a1', {'degE': 16, 'degF': 48, 'F': '208d1'}] ['208b1', {'degE': 16, 'degF': 16, 'F': '208a1'}] ['208b1', {'degE': 16, 'degF': 12, 'F': '208c1'}] ['208b1', {'degE': 16, 'degF': 48, 'F': '208d1'}] ['210d1', {'degE': 16, 'degF': 48, 'F': '210a1'}] ['210d1', {'degE': 16, 'degF': 96, 'F': '210b1'}] ['210d1', {'degE': 16, 'degF': 32, 'F': '210c1'}] ['210d1', {'degE': 16, 'degF': 128, 'F': '210e1'}] ['212a1', {'degE': 12, 'degF': 21, 'F': '212b1'}] ['214a1', {'degE': 28, 'degF': 12, 'F': '214b1'}] ['214a1', {'degE': 28, 'degF': 60, 'F': '214c1'}] ['214a1', {'degE': 28, 'degF': 12, 'F': '214d1'}] ['214b1', {'degE': 12, 'degF': 28, 'F': '214a1'}] ['214b1', {'degE': 12, 'degF': 60, 'F': '214c1'}] ['214b1', {'degE': 12, 'degF': 12, 'F': '214d1'}] ['214c1', {'degE': 60, 'degF': 28, 'F': '214a1'}] ['214c1', {'degE': 60, 'degF': 12, 'F': '214b1'}] ['214c1', {'degE': 60, 'degF': 12, 'F': '214d1'}] ['216a1', {'degE': 24, 'degF': 24, 'F': '216b1'}] ['216a1', {'degE': 24, 'degF': 72, 'F': '216c1'}] ['216a1', {'degE': 24, 'degF': 72, 'F': '216d1'}] ['219a1', {'degE': 12, 'degF': 12, 'F': '219b1'}] ['219a1', {'degE': 12, 'degF': 60, 'F': '219c1'}] ['219b1', {'degE': 12, 'degF': 12, 'F': '219a1'}] ['219b1', {'degE': 12, 'degF': 60, 'F': '219c1'}] ['219c1', {'degE': 60, 'degF': 12, 'F': '219a1'}] ['219c1', {'degE': 60, 'degF': 12, 'F': '219b1'}] ['220a1', {'degE': 36, 'degF': 12, 'F': '220b1'}] ['224a1', {'degE': 8, 'degF': 8, 'F': '224b1'}] ['225a1', {'degE': 8, 'degF': 40, 'F': '225b1'}] ['225a1', {'degE': 8, 'degF': 48, 'F': '225c1'}] ['225a1', {'degE': 8, 'degF': 48, 'F': '225d1'}] ['225a1', {'degE': 8, 'degF': 48, 'F': '225e1'}] ['225e1', {'degE': 48, 'degF': 8, 'F': '225a1'}] ['225e1', {'degE': 48, 'degF': 40, 'F': '225b1'}] ['225e1', {'degE': 48, 'degF': 48, 'F': '225c1'}] ['225e1', {'degE': 48, 'degF': 48, 'F': '225d1'}] ['228b1', {'degE': 24, 'degF': 18, 'F': '228a1'}] ['232a1', {'degE': 16, 'degF': 16, 'F': '232b1'}] ['234c1', {'degE': 16, 'degF': 28, 'F': '234a1'}] ['234c1', {'degE': 16, 'degF': 48, 'F': '234b1'}] ['234c1', {'degE': 16, 'degF': 320, 'F': '234d1'}] ['234c1', {'degE': 16, 'degF': 20, 'F': '234e1'}] ['235a1', {'degE': 12, 'degF': 108, 'F': '235b1'}] ['235a1', {'degE': 12, 'degF': 18, 'F': '235c1'}] ['236a1', {'degE': 6, 'degF': 14, 'F': '236b1'}] ['238a1', {'degE': 112, 'degF': 8, 'F': '238b1'}] ['238a1', {'degE': 112, 'degF': 16, 'F': '238c1'}] ['238a1', {'degE': 112, 'degF': 16, 'F': '238d1'}] ['238a1', {'degE': 112, 'degF': 80, 'F': '238e1'}] ['238b1', {'degE': 8, 'degF': 112, 'F': '238a1'}] ['238b1', {'degE': 8, 'degF': 16, 'F': '238c1'}] ['238b1', {'degE': 8, 'degF': 16, 'F': '238d1'}] ['238b1', {'degE': 8, 'degF': 80, 'F': '238e1'}] ['240c1', {'degE': 16, 'degF': 16, 'F': '240a1'}] ['240c1', {'degE': 16, 'degF': 48, 'F': '240b1'}] ['240c1', {'degE': 16, 'degF': 16, 'F': '240d1'}] ['242a1', {'degE': 16, 'degF': 176, 'F': '242b1'}] ['243a1', {'degE': 6, 'degF': 9, 'F': '243b1'}] ['245a1', {'degE': 48, 'degF': 336, 'F': '245b1'}] ['245a1', {'degE': 48, 'degF': 32, 'F': '245c1'}] ['245c1', {'degE': 32, 'degF': 48, 'F': '245a1'}] ['245c1', {'degE': 32, 'degF': 336, 'F': '245b1'}] ['246d1', {'degE': 48, 'degF': 84, 'F': '246a1'}] ['246d1', {'degE': 48, 'degF': 300, 'F': '246b1'}] ['246d1', {'degE': 48, 'degF': 1680, 'F': '246c1'}] ['246d1', {'degE': 48, 'degF': 24, 'F': '246e1'}] ['246d1', {'degE': 48, 'degF': 20, 'F': '246f1'}] ['246d1', {'degE': 48, 'degF': 44, 'F': '246g1'}] ['248a1', {'degE': 8, 'degF': 16, 'F': '248b1'}] ['248a1', {'degE': 8, 'degF': 8, 'F': '248c1'}] ['248c1', {'degE': 8, 'degF': 8, 'F': '248a1'}] ['248c1', {'degE': 8, 'degF': 16, 'F': '248b1'}] ['249a1', {'degE': 24, 'degF': 8, 'F': '249b1'}] ['249b1', {'degE': 8, 'degF': 24, 'F': '249a1'}] ['252b1', {'degE': 48, 'degF': 48, 'F': '252a1'}] ['254a1', {'degE': 36, 'degF': 16, 'F': '254b1'}] ['254a1', {'degE': 36, 'degF': 12, 'F': '254c1'}] ['254a1', {'degE': 36, 'degF': 24, 'F': '254d1'}] ['254c1', {'degE': 12, 'degF': 36, 'F': '254a1'}] ['254c1', {'degE': 12, 'degF': 16, 'F': '254b1'}] ['254c1', {'degE': 12, 'degF': 24, 'F': '254d1'}] ['256a1', {'degE': 8, 'degF': 8, 'F': '256b1'}] ['256a1', {'degE': 8, 'degF': 8, 'F': '256c1'}] ['256a1', {'degE': 8, 'degF': 8, 'F': '256d1'}] ['256b1', {'degE': 8, 'degF': 8, 'F': '256a1'}] ['256b1', {'degE': 8, 'degF': 8, 'F': '256c1'}] ['256b1', {'degE': 8, 'degF': 8, 'F': '256d1'}] ['258a1', {'degE': 24, 'degF': 196, 'F': '258b1'}] ['258a1', {'degE': 24, 'degF': 40, 'F': '258c1'}] ['258a1', {'degE': 24, 'degF': 60, 'F': '258d1'}] ['258a1', {'degE': 24, 'degF': 760, 'F': '258e1'}] ['258a1', {'degE': 24, 'degF': 168, 'F': '258f1'}] ['258a1', {'degE': 24, 'degF': 12, 'F': '258g1'}] ['258c1', {'degE': 40, 'degF': 24, 'F': '258a1'}] ['258c1', {'degE': 40, 'degF': 196, 'F': '258b1'}] ['258c1', {'degE': 40, 'degF': 60, 'F': '258d1'}] ['258c1', {'degE': 40, 'degF': 760, 'F': '258e1'}] ['258c1', {'degE': 40, 'degF': 168, 'F': '258f1'}] ['258c1', {'degE': 40, 'degF': 12, 'F': '258g1'}] ['262a1', {'degE': 44, 'degF': 12, 'F': '262b1'}] ['262b1', {'degE': 12, 'degF': 44, 'F': '262a1'}] ['272a1', {'degE': 16, 'degF': 16, 'F': '272b1'}] ['272a1', {'degE': 16, 'degF': 16, 'F': '272c1'}] ['272a1', {'degE': 16, 'degF': 48, 'F': '272d1'}] ['272b1', {'degE': 16, 'degF': 16, 'F': '272a1'}] ['272b1', {'degE': 16, 'degF': 16, 'F': '272c1'}] ['272b1', {'degE': 16, 'degF': 48, 'F': '272d1'}] ['273a1', {'degE': 48, 'degF': 672, 'F': '273b1'}] ['274a1', {'degE': 28, 'degF': 132, 'F': '274b1'}] ['274a1', {'degE': 28, 'degF': 12, 'F': '274c1'}] ['274b1', {'degE': 132, 'degF': 28, 'F': '274a1'}] ['274b1', {'degE': 132, 'degF': 12, 'F': '274c1'}] ['274c1', {'degE': 12, 'degF': 28, 'F': '274a1'}] ['274c1', {'degE': 12, 'degF': 132, 'F': '274b1'}] ['275a1', {'degE': 24, 'degF': 28, 'F': '275b1'}] ['278a1', {'degE': 32, 'degF': 272, 'F': '278b1'}] ['280a1', {'degE': 16, 'degF': 240, 'F': '280b1'}] ['280b1', {'degE': 240, 'degF': 16, 'F': '280a1'}] ['282b1', {'degE': 64, 'degF': 48, 'F': '282a1'}] ['285a1', {'degE': 40, 'degF': 24, 'F': '285b1'}] ['285a1', {'degE': 40, 'degF': 72, 'F': '285c1'}] ['285b1', {'degE': 24, 'degF': 40, 'F': '285a1'}] ['285b1', {'degE': 24, 'degF': 72, 'F': '285c1'}] ['286b1', {'degE': 104, 'degF': 60, 'F': '286a1'}] ['286b1', {'degE': 104, 'degF': 24, 'F': '286c1'}] ['286b1', {'degE': 104, 'degF': 120, 'F': '286d1'}] ['286b1', {'degE': 104, 'degF': 60, 'F': '286e1'}] ['286b1', {'degE': 104, 'degF': 12, 'F': '286f1'}] ['286c1', {'degE': 24, 'degF': 60, 'F': '286a1'}] ['286c1', {'degE': 24, 'degF': 104, 'F': '286b1'}] ['286c1', {'degE': 24, 'degF': 120, 'F': '286d1'}] ['286c1', {'degE': 24, 'degF': 60, 'F': '286e1'}] ['286c1', {'degE': 24, 'degF': 12, 'F': '286f1'}] ['288a1', {'degE': 16, 'degF': 32, 'F': '288b1'}] ['288a1', {'degE': 16, 'degF': 32, 'F': '288c1'}] ['288a1', {'degE': 16, 'degF': 16, 'F': '288d1'}] ['288a1', {'degE': 16, 'degF': 48, 'F': '288e1'}] ['288b1', {'degE': 32, 'degF': 16, 'F': '288a1'}] ['288b1', {'degE': 32, 'degF': 32, 'F': '288c1'}] ['288b1', {'degE': 32, 'degF': 16, 'F': '288d1'}] ['288b1', {'degE': 32, 'degF': 48, 'F': '288e1'}] ['291c1', {'degE': 12, 'degF': 1012, 'F': '291a1'}] ['291c1', {'degE': 12, 'degF': 120, 'F': '291b1'}] ['291c1', {'degE': 12, 'degF': 12, 'F': '291d1'}] ['294g1', {'degE': 64, 'degF': 84, 'F': '294a1'}] ['294g1', {'degE': 64, 'degF': 12, 'F': '294b1'}] ['294g1', {'degE': 64, 'degF': 192, 'F': '294c1'}] ['294g1', {'degE': 64, 'degF': 60, 'F': '294d1'}] ['294g1', {'degE': 64, 'degF': 420, 'F': '294e1'}] ['294g1', {'degE': 64, 'degF': 448, 'F': '294f1'}] ['296a1', {'degE': 16, 'degF': 16, 'F': '296b1'}] ['296b1', {'degE': 16, 'degF': 16, 'F': '296a1'}] ['297a1', {'degE': 72, 'degF': 12, 'F': '297b1'}] ['297a1', {'degE': 72, 'degF': 36, 'F': '297c1'}] ['297a1', {'degE': 72, 'degF': 24, 'F': '297d1'}] ['297b1', {'degE': 12, 'degF': 72, 'F': '297a1'}] ['297b1', {'degE': 12, 'degF': 36, 'F': '297c1'}] ['297b1', {'degE': 12, 'degF': 24, 'F': '297d1'}] ['297c1', {'degE': 36, 'degF': 72, 'F': '297a1'}] ['297c1', {'degE': 36, 'degF': 12, 'F': '297b1'}] ['297c1', {'degE': 36, 'degF': 24, 'F': '297d1'}] ['298a1', {'degE': 36, 'degF': 20, 'F': '298b1'}] ['298b1', {'degE': 20, 'degF': 36, 'F': '298a1'}] ['300d1', {'degE': 24, 'degF': 36, 'F': '300a1'}] ['300d1', {'degE': 24, 'degF': 180, 'F': '300b1'}] ['300d1', {'degE': 24, 'degF': 120, 'F': '300c1'}] ['302a1', {'degE': 120, 'degF': 27, 'F': '302b1'}] ['302a1', {'degE': 120, 'degF': 40, 'F': '302c1'}] ['302c1', {'degE': 40, 'degF': 120, 'F': '302a1'}] ['302c1', {'degE': 40, 'degF': 27, 'F': '302b1'}] ['303a1', {'degE': 112, 'degF': 32, 'F': '303b1'}] ['303b1', {'degE': 32, 'degF': 112, 'F': '303a1'}] ['304a1', {'degE': 48, 'degF': 48, 'F': '304b1'}] ['304a1', {'degE': 48, 'degF': 16, 'F': '304c1'}] ['304a1', {'degE': 48, 'degF': 16, 'F': '304d1'}] ['304a1', {'degE': 48, 'degF': 24, 'F': '304e1'}] ['304a1', {'degE': 48, 'degF': 24, 'F': '304f1'}] ['304c1', {'degE': 16, 'degF': 48, 'F': '304a1'}] ['304c1', {'degE': 16, 'degF': 48, 'F': '304b1'}] ['304c1', {'degE': 16, 'degF': 16, 'F': '304d1'}] ['304c1', {'degE': 16, 'degF': 24, 'F': '304e1'}] ['304c1', {'degE': 16, 'degF': 24, 'F': '304f1'}] ['304f1', {'degE': 24, 'degF': 48, 'F': '304a1'}] ['304f1', {'degE': 24, 'degF': 48, 'F': '304b1'}] ['304f1', {'degE': 24, 'degF': 16, 'F': '304c1'}] ['304f1', {'degE': 24, 'degF': 16, 'F': '304d1'}] ['304f1', {'degE': 24, 'degF': 24, 'F': '304e1'}] ['306b1', {'degE': 48, 'degF': 192, 'F': '306a1'}] ['306b1', {'degE': 48, 'degF': 128, 'F': '306c1'}] ['306b1', {'degE': 48, 'degF': 64, 'F': '306d1'}] ['310b1', {'degE': 96, 'degF': 48, 'F': '310a1'}] ['312b1', {'degE': 16, 'degF': 16, 'F': '312a1'}] ['312b1', {'degE': 16, 'degF': 16, 'F': '312c1'}] ['312b1', {'degE': 16, 'degF': 32, 'F': '312d1'}] ['312b1', {'degE': 16, 'degF': 240, 'F': '312e1'}] ['312b1', {'degE': 16, 'degF': 48, 'F': '312f1'}] ['312f1', {'degE': 48, 'degF': 16, 'F': '312a1'}] ['312f1', {'degE': 48, 'degF': 16, 'F': '312b1'}] ['312f1', {'degE': 48, 'degF': 16, 'F': '312c1'}] ['312f1', {'degE': 48, 'degF': 32, 'F': '312d1'}] ['312f1', {'degE': 48, 'degF': 240, 'F': '312e1'}] ['315b1', {'degE': 32, 'degF': 20, 'F': '315a1'}] ['316b1', {'degE': 36, 'degF': 36, 'F': '316a1'}] ['318c1', {'degE': 24, 'degF': 20, 'F': '318a1'}] ['318c1', {'degE': 24, 'degF': 60, 'F': '318b1'}] ['318c1', {'degE': 24, 'degF': 88, 'F': '318d1'}] ['318c1', {'degE': 24, 'degF': 204, 'F': '318e1'}] ['318d1', {'degE': 88, 'degF': 20, 'F': '318a1'}] ['318d1', {'degE': 88, 'degF': 60, 'F': '318b1'}] ['318d1', {'degE': 88, 'degF': 24, 'F': '318c1'}] ['318d1', {'degE': 88, 'degF': 204, 'F': '318e1'}] ['320b1', {'degE': 16, 'degF': 16, 'F': '320a1'}] ['320b1', {'degE': 16, 'degF': 16, 'F': '320c1'}] ['320b1', {'degE': 16, 'degF': 16, 'F': '320d1'}] ['320b1', {'degE': 16, 'degF': 16, 'F': '320e1'}] ['320b1', {'degE': 16, 'degF': 16, 'F': '320f1'}] ['320f1', {'degE': 16, 'degF': 16, 'F': '320a1'}] ['320f1', {'degE': 16, 'degF': 16, 'F': '320b1'}] ['320f1', {'degE': 16, 'degF': 16, 'F': '320c1'}] ['320f1', {'degE': 16, 'degF': 16, 'F': '320d1'}] ['320f1', {'degE': 16, 'degF': 16, 'F': '320e1'}] ['322a1', {'degE': 48, 'degF': 112, 'F': '322b1'}] ['322a1', {'degE': 48, 'degF': 24, 'F': '322c1'}] ['322a1', {'degE': 48, 'degF': 40, 'F': '322d1'}] ['322d1', {'degE': 40, 'degF': 48, 'F': '322a1'}] ['322d1', {'degE': 40, 'degF': 112, 'F': '322b1'}] ['322d1', {'degE': 40, 'degF': 24, 'F': '322c1'}] ['324c1', {'degE': 18, 'degF': 18, 'F': '324a1'}] ['324c1', {'degE': 18, 'degF': 36, 'F': '324b1'}] ['324c1', {'degE': 18, 'degF': 36, 'F': '324d1'}] ['325a1', {'degE': 60, 'degF': 12, 'F': '325b1'}] ['325a1', {'degE': 60, 'degF': 48, 'F': '325c1'}] ['325a1', {'degE': 60, 'degF': 84, 'F': '325d1'}] ['325a1', {'degE': 60, 'degF': 84, 'F': '325e1'}] ['325b1', {'degE': 12, 'degF': 60, 'F': '325a1'}] ['325b1', {'degE': 12, 'degF': 48, 'F': '325c1'}] ['325b1', {'degE': 12, 'degF': 84, 'F': '325d1'}] ['325b1', {'degE': 12, 'degF': 84, 'F': '325e1'}] ['326a1', {'degE': 36, 'degF': 20, 'F': '326b1'}] ['326a1', {'degE': 36, 'degF': 204, 'F': '326c1'}] ['326b1', {'degE': 20, 'degF': 36, 'F': '326a1'}] ['326b1', {'degE': 20, 'degF': 204, 'F': '326c1'}] ['328a1', {'degE': 16, 'degF': 24, 'F': '328b1'}] ['330e1', {'degE': 64, 'degF': 160, 'F': '330a1'}] ['330e1', {'degE': 64, 'degF': 32, 'F': '330b1'}] ['330e1', {'degE': 64, 'degF': 192, 'F': '330c1'}] ['330e1', {'degE': 64, 'degF': 2240, 'F': '330d1'}] ['333a1', {'degE': 20, 'degF': 48, 'F': '333b1'}] ['333a1', {'degE': 20, 'degF': 16, 'F': '333c1'}] ['333a1', {'degE': 20, 'degF': 28, 'F': '333d1'}] ['333b1', {'degE': 48, 'degF': 20, 'F': '333a1'}] ['333b1', {'degE': 48, 'degF': 16, 'F': '333c1'}] ['333b1', {'degE': 48, 'degF': 28, 'F': '333d1'}] ['333c1', {'degE': 16, 'degF': 20, 'F': '333a1'}] ['333c1', {'degE': 16, 'degF': 48, 'F': '333b1'}] ['333c1', {'degE': 16, 'degF': 28, 'F': '333d1'}] ['336e1', {'degE': 32, 'degF': 24, 'F': '336a1'}] ['336e1', {'degE': 32, 'degF': 16, 'F': '336b1'}] ['336e1', {'degE': 32, 'degF': 48, 'F': '336c1'}] ['336e1', {'degE': 32, 'degF': 96, 'F': '336d1'}] ['336e1', {'degE': 32, 'degF': 24, 'F': '336f1'}] ['338a1', {'degE': 12, 'degF': 156, 'F': '338b1'}] ['338a1', {'degE': 12, 'degF': 112, 'F': '338c1'}] ['338a1', {'degE': 12, 'degF': 312, 'F': '338d1'}] ['338a1', {'degE': 12, 'degF': 24, 'F': '338e1'}] ['338a1', {'degE': 12, 'degF': 336, 'F': '338f1'}] ['338e1', {'degE': 24, 'degF': 12, 'F': '338a1'}] ['338e1', {'degE': 24, 'degF': 156, 'F': '338b1'}] ['338e1', {'degE': 24, 'degF': 112, 'F': '338c1'}] ['338e1', {'degE': 24, 'degF': 312, 'F': '338d1'}] ['338e1', {'degE': 24, 'degF': 336, 'F': '338f1'}] ['338f1', {'degE': 336, 'degF': 12, 'F': '338a1'}] ['338f1', {'degE': 336, 'degF': 156, 'F': '338b1'}] ['338f1', {'degE': 336, 'degF': 112, 'F': '338c1'}] ['338f1', {'degE': 336, 'degF': 312, 'F': '338d1'}] ['338f1', {'degE': 336, 'degF': 24, 'F': '338e1'}] ['339a1', {'degE': 72, 'degF': 126, 'F': '339b1'}] ['339a1', {'degE': 72, 'degF': 24, 'F': '339c1'}] ['339c1', {'degE': 24, 'degF': 72, 'F': '339a1'}] ['339c1', {'degE': 24, 'degF': 126, 'F': '339b1'}] ['342c1', {'degE': 96, 'degF': 60, 'F': '342a1'}] ['342c1', {'degE': 96, 'degF': 160, 'F': '342b1'}] ['342c1', {'degE': 96, 'degF': 48, 'F': '342d1'}] ['342c1', {'degE': 96, 'degF': 16, 'F': '342e1'}] ['342c1', {'degE': 96, 'degF': 480, 'F': '342f1'}] ['342c1', {'degE': 96, 'degF': 60, 'F': '342g1'}] ['342e1', {'degE': 16, 'degF': 60, 'F': '342a1'}] ['342e1', {'degE': 16, 'degF': 160, 'F': '342b1'}] ['342e1', {'degE': 16, 'degF': 96, 'F': '342c1'}] ['342e1', {'degE': 16, 'degF': 48, 'F': '342d1'}] ['342e1', {'degE': 16, 'degF': 480, 'F': '342f1'}] ['342e1', {'degE': 16, 'degF': 60, 'F': '342g1'}] ['345b1', {'degE': 16, 'degF': 80, 'F': '345a1'}] ['345b1', {'degE': 16, 'degF': 300, 'F': '345c1'}] ['345b1', {'degE': 16, 'degF': 40, 'F': '345d1'}] ['345b1', {'degE': 16, 'degF': 96, 'F': '345e1'}] ['345b1', {'degE': 16, 'degF': 192, 'F': '345f1'}] ['345f1', {'degE': 192, 'degF': 80, 'F': '345a1'}] ['345f1', {'degE': 192, 'degF': 16, 'F': '345b1'}] ['345f1', {'degE': 192, 'degF': 300, 'F': '345c1'}] ['345f1', {'degE': 192, 'degF': 40, 'F': '345d1'}] ['345f1', {'degE': 192, 'degF': 96, 'F': '345e1'}] ['346b1', {'degE': 28, 'degF': 28, 'F': '346a1'}] ['348a1', {'degE': 12, 'degF': 12, 'F': '348b1'}] ['348a1', {'degE': 12, 'degF': 180, 'F': '348c1'}] ['348a1', {'degE': 12, 'degF': 84, 'F': '348d1'}] ['348d1', {'degE': 84, 'degF': 12, 'F': '348a1'}] ['348d1', {'degE': 84, 'degF': 12, 'F': '348b1'}] ['348d1', {'degE': 84, 'degF': 180, 'F': '348c1'}] ['350c1', {'degE': 24, 'degF': 96, 'F': '350a1'}] ['350c1', {'degE': 24, 'degF': 120, 'F': '350b1'}] ['350c1', {'degE': 24, 'degF': 48, 'F': '350d1'}] ['350c1', {'degE': 24, 'degF': 1320, 'F': '350e1'}] ['350c1', {'degE': 24, 'degF': 264, 'F': '350f1'}] ['350f1', {'degE': 264, 'degF': 96, 'F': '350a1'}] ['350f1', {'degE': 264, 'degF': 120, 'F': '350b1'}] ['350f1', {'degE': 264, 'degF': 24, 'F': '350c1'}] ['350f1', {'degE': 264, 'degF': 48, 'F': '350d1'}] ['350f1', {'degE': 264, 'degF': 1320, 'F': '350e1'}] ['352b1', {'degE': 32, 'degF': 32, 'F': '352a1'}] ['352b1', {'degE': 32, 'degF': 32, 'F': '352c1'}] ['352b1', {'degE': 32, 'degF': 32, 'F': '352d1'}] ['352b1', {'degE': 32, 'degF': 96, 'F': '352e1'}] ['352b1', {'degE': 32, 'degF': 96, 'F': '352f1'}] ['352c1', {'degE': 32, 'degF': 32, 'F': '352a1'}] ['352c1', {'degE': 32, 'degF': 32, 'F': '352b1'}] ['352c1', {'degE': 32, 'degF': 32, 'F': '352d1'}] ['352c1', {'degE': 32, 'degF': 96, 'F': '352e1'}] ['352c1', {'degE': 32, 'degF': 96, 'F': '352f1'}] ['352d1', {'degE': 32, 'degF': 32, 'F': '352a1'}] ['352d1', {'degE': 32, 'degF': 32, 'F': '352b1'}] ['352d1', {'degE': 32, 'degF': 32, 'F': '352c1'}] ['352d1', {'degE': 32, 'degF': 96, 'F': '352e1'}] ['352d1', {'degE': 32, 'degF': 96, 'F': '352f1'}] ['352f1', {'degE': 96, 'degF': 32, 'F': '352a1'}] ['352f1', {'degE': 96, 'degF': 32, 'F': '352b1'}] ['352f1', {'degE': 96, 'degF': 32, 'F': '352c1'}] ['352f1', {'degE': 96, 'degF': 32, 'F': '352d1'}] ['352f1', {'degE': 96, 'degF': 96, 'F': '352e1'}] ['354c1', {'degE': 120, 'degF': 16, 'F': '354a1'}] ['354c1', {'degE': 120, 'degF': 40, 'F': '354b1'}] ['354c1', {'degE': 120, 'degF': 48, 'F': '354d1'}] ['354c1', {'degE': 120, 'degF': 1584, 'F': '354e1'}] ['354c1', {'degE': 120, 'degF': 56, 'F': '354f1'}] ['354f1', {'degE': 56, 'degF': 16, 'F': '354a1'}] ['354f1', {'degE': 56, 'degF': 40, 'F': '354b1'}] ['354f1', {'degE': 56, 'degF': 120, 'F': '354c1'}] ['354f1', {'degE': 56, 'degF': 48, 'F': '354d1'}] ['354f1', {'degE': 56, 'degF': 1584, 'F': '354e1'}] ['357b1', {'degE': 32, 'degF': 544, 'F': '357a1'}] ['357b1', {'degE': 32, 'degF': 48, 'F': '357c1'}] ['357b1', {'degE': 32, 'degF': 112, 'F': '357d1'}] ['357d1', {'degE': 112, 'degF': 544, 'F': '357a1'}] ['357d1', {'degE': 112, 'degF': 32, 'F': '357b1'}] ['357d1', {'degE': 112, 'degF': 48, 'F': '357c1'}] ['359a1', {'degE': 16, 'degF': 8, 'F': '359b1'}] ['359b1', {'degE': 8, 'degF': 16, 'F': '359a1'}] ['360e1', {'degE': 32, 'degF': 64, 'F': '360a1'}] ['360e1', {'degE': 32, 'degF': 32, 'F': '360b1'}] ['360e1', {'degE': 32, 'degF': 96, 'F': '360c1'}] ['360e1', {'degE': 32, 'degF': 64, 'F': '360d1'}] ['361a1', {'degE': 20, 'degF': 120, 'F': '361b1'}] ['362a1', {'degE': 20, 'degF': 28, 'F': '362b1'}] ['362b1', {'degE': 28, 'degF': 20, 'F': '362a1'}] ['364a1', {'degE': 120, 'degF': 24, 'F': '364b1'}] ['364b1', {'degE': 24, 'degF': 120, 'F': '364a1'}] ['366f1', {'degE': 48, 'degF': 48, 'F': '366a1'}] ['366f1', {'degE': 48, 'degF': 60, 'F': '366b1'}] ['366f1', {'degE': 48, 'degF': 228, 'F': '366c1'}] ['366f1', {'degE': 48, 'degF': 364, 'F': '366d1'}] ['366f1', {'degE': 48, 'degF': 52, 'F': '366e1'}] ['366f1', {'degE': 48, 'degF': 80, 'F': '366g1'}] ['366g1', {'degE': 80, 'degF': 48, 'F': '366a1'}] ['366g1', {'degE': 80, 'degF': 60, 'F': '366b1'}] ['366g1', {'degE': 80, 'degF': 228, 'F': '366c1'}] ['366g1', {'degE': 80, 'degF': 364, 'F': '366d1'}] ['366g1', {'degE': 80, 'degF': 52, 'F': '366e1'}] ['366g1', {'degE': 80, 'degF': 48, 'F': '366f1'}] ['368a1', {'degE': 24, 'degF': 120, 'F': '368b1'}] ['368a1', {'degE': 24, 'degF': 16, 'F': '368c1'}] ['368a1', {'degE': 24, 'degF': 16, 'F': '368d1'}] ['368a1', {'degE': 24, 'degF': 8, 'F': '368e1'}] ['368a1', {'degE': 24, 'degF': 24, 'F': '368f1'}] ['368a1', {'degE': 24, 'degF': 48, 'F': '368g1'}] ['368d1', {'degE': 16, 'degF': 24, 'F': '368a1'}] ['368d1', {'degE': 16, 'degF': 120, 'F': '368b1'}] ['368d1', {'degE': 16, 'degF': 16, 'F': '368c1'}] ['368d1', {'degE': 16, 'degF': 8, 'F': '368e1'}] ['368d1', {'degE': 16, 'degF': 24, 'F': '368f1'}] ['368d1', {'degE': 16, 'degF': 48, 'F': '368g1'}] ['368e1', {'degE': 8, 'degF': 24, 'F': '368a1'}] ['368e1', {'degE': 8, 'degF': 120, 'F': '368b1'}] ['368e1', {'degE': 8, 'degF': 16, 'F': '368c1'}] ['368e1', {'degE': 8, 'degF': 16, 'F': '368d1'}] ['368e1', {'degE': 8, 'degF': 24, 'F': '368f1'}] ['368e1', {'degE': 8, 'degF': 48, 'F': '368g1'}] ['368g1', {'degE': 48, 'degF': 24, 'F': '368a1'}] ['368g1', {'degE': 48, 'degF': 120, 'F': '368b1'}] ['368g1', {'degE': 48, 'degF': 16, 'F': '368c1'}] ['368g1', {'degE': 48, 'degF': 16, 'F': '368d1'}] ['368g1', {'degE': 48, 'degF': 8, 'F': '368e1'}] ['368g1', {'degE': 48, 'degF': 24, 'F': '368f1'}] ['369a1', {'degE': 32, 'degF': 160, 'F': '369b1'}] ['370a1', {'degE': 16, 'degF': 44, 'F': '370b1'}] ['370a1', {'degE': 16, 'degF': 108, 'F': '370c1'}] ['370a1', {'degE': 16, 'degF': 96, 'F': '370d1'}] ['371a1', {'degE': 32, 'degF': 60, 'F': '371b1'}] ['372a1', {'degE': 24, 'degF': 30, 'F': '372b1'}] ['372a1', {'degE': 24, 'degF': 360, 'F': '372c1'}] ['372a1', {'degE': 24, 'degF': 48, 'F': '372d1'}] ['372d1', {'degE': 48, 'degF': 24, 'F': '372a1'}] ['372d1', {'degE': 48, 'degF': 30, 'F': '372b1'}] ['372d1', {'degE': 48, 'degF': 360, 'F': '372c1'}] ['378d1', {'degE': 24, 'degF': 36, 'F': '378a1'}] ['378d1', {'degE': 24, 'degF': 36, 'F': '378b1'}] ['378d1', {'degE': 24, 'degF': 72, 'F': '378c1'}] ['378d1', {'degE': 24, 'degF': 72, 'F': '378e1'}] ['378d1', {'degE': 24, 'degF': 72, 'F': '378f1'}] ['378d1', {'degE': 24, 'degF': 1260, 'F': '378g1'}] ['378d1', {'degE': 24, 'degF': 420, 'F': '378h1'}] ['378f1', {'degE': 72, 'degF': 36, 'F': '378a1'}] ['378f1', {'degE': 72, 'degF': 36, 'F': '378b1'}] ['378f1', {'degE': 72, 'degF': 72, 'F': '378c1'}] ['378f1', {'degE': 72, 'degF': 24, 'F': '378d1'}] ['378f1', {'degE': 72, 'degF': 72, 'F': '378e1'}] ['378f1', {'degE': 72, 'degF': 1260, 'F': '378g1'}] ['378f1', {'degE': 72, 'degF': 420, 'F': '378h1'}] ['380a1', {'degE': 24, 'degF': 240, 'F': '380b1'}] ['381a1', {'degE': 20, 'degF': 44, 'F': '381b1'}] ['384d1', {'degE': 16, 'degF': 16, 'F': '384a1'}] ['384d1', {'degE': 16, 'degF': 16, 'F': '384b1'}] ['384d1', {'degE': 16, 'degF': 16, 'F': '384c1'}] ['384d1', {'degE': 16, 'degF': 48, 'F': '384e1'}] ['384d1', {'degE': 16, 'degF': 48, 'F': '384f1'}] ['384d1', {'degE': 16, 'degF': 48, 'F': '384g1'}] ['384d1', {'degE': 16, 'degF': 48, 'F': '384h1'}] ['384h1', {'degE': 48, 'degF': 16, 'F': '384a1'}] ['384h1', {'degE': 48, 'degF': 16, 'F': '384b1'}] ['384h1', {'degE': 48, 'degF': 16, 'F': '384c1'}] ['384h1', {'degE': 48, 'degF': 16, 'F': '384d1'}] ['384h1', {'degE': 48, 'degF': 48, 'F': '384e1'}] ['384h1', {'degE': 48, 'degF': 48, 'F': '384f1'}] ['384h1', {'degE': 48, 'degF': 48, 'F': '384g1'}] ['385a1', {'degE': 64, 'degF': 32, 'F': '385b1'}] ['385b1', {'degE': 32, 'degF': 64, 'F': '385a1'}] ['387b1', {'degE': 48, 'degF': 64, 'F': '387a1'}] ['387b1', {'degE': 48, 'degF': 16, 'F': '387c1'}] 0 0 For this, needed to use "v = c.point_on_E_fiber_cardinality2(ComplexField(150)(0))" ['387b1', {'degE': 48, 'degF': 60, 'F': '387d1'}] ['387b1', {'degE': 48, 'degF': 48, 'F': '387e1'}] ['387c1', {'degE': 16, 'degF': 64, 'F': '387a1'}] ['387c1', {'degE': 16, 'degF': 48, 'F': '387b1'}] ['387c1', {'degE': 16, 'degF': 60, 'F': '387d1'}] ((9889/1024 : 762849/32768 : 1), 8) ['387c1', {'degE': 16, 'degF': 48, 'F': '387e1'}] ((9689733501416065/3599669767573504 : -1155571416592813298781153/215970279763209877716992 : 1), 16) To get the above, I used time v = c.point_on_E_2(deg1=1000,min_imag=1e-4/2)