-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -1, 'A4': -3, 'A5': 0, 'A6': 0, 'A7': 8, 'A8': 0, 'A9': 1, 'Lhash': '403871582455362642,2152338429622007325', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 0], 'a4': [-1.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [3.0237157840738176, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.536929273438037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1, 0, -1]], [19, [1, 2, 1]]], 'bad_primes': [3, 5, 19], 'central_character': '243675.1', 'coefficient_field': '1.1.1.1', 'conductor': 243675, 'conductor_radical': 285, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, 1], [1, 0, -1], [1, -8, 30, -56, 49], [1, 0, 6, 0, 121], [1, -4, 30, -52, 169], [1, 0, 30, 0, 289], [1, 2, 1], [1, 0, 30, 0, 529], [1, 0, 54, 0, 841], [1, 0, 62, 0, 961], [1, 12, 110, 444, 1369], [1, 0, 46, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -50, 0, 2209], [1, 0, -90, 0, 2809], [1, 0, 102, 0, 3481], [1, -28, 318, -1708, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, 28, 342, 2044, 5329], [1, -32, 414, -2528, 6241], [1, 0, 166, 0, 6889], [1, 0, 142, 0, 7921], [1, 20, 294, 1940, 9409], [1, 0, 102, 0, 10201], [1, -32, 462, -3296, 10609], [1, 0, 70, 0, 11449], [1, 4, 222, 436, 11881], [1, 0, 126, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 1, 'label': '4-243675-1.1-c1e2-0-1', 'leading_term': '1.53314747542', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.0.3.1/27075.2/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.052734375', 'prec': 37}, 'plot_values': [1.5331474754240417, 1.5294741083956804, 1.518311019956822, 1.4992387663391376, 1.4715898374709027, 1.4344954079062595, 1.3869495429778795, 1.3278894850696688, 1.2562900822291871, 1.171269758371685, 1.0722046674111618, 0.9588468442631791, 0.8314413012414543, 0.6908361721624027, 0.538579246220356, 0.3769936390626047, 0.20922500715319356, 0.039252713925959366, -0.12814221082677899, -0.28745853777549407, -0.4326104489578458, -0.5571199180319131, -0.6543658087310849, -0.7178864302378007, -0.7417286425627827, -0.7208326730248638, -0.6514377861085144, -0.5314900888635105, -0.361030335379392, -0.14253692343544866, 0.11880233285897793, 0.41491632120379035, 0.7347999410997539, 1.0646087333666459, 1.387915876532117, 1.6861416269123077, 1.9391565704217566, 2.1260499065392753, 2.2260428485018733, 2.219515691538052, 2.089105888115039, 1.8208243804307318, 1.4051293241467966, 0.8378910293424517, 0.12118020330412908, -0.7361859825501806, -1.718398464275948, -2.8027582432543676, -3.960156265556712, -5.155941606257532, -6.351165171762505, -7.504161206831542, -8.572403763404154, -9.514551716727222, -10.292575760034756, -10.873845896781834, -11.233049921244037, -11.35381354136143, -11.229901980073894, -10.86590131897708, -10.27730505646724, -9.489966145415655, -8.538915239892786, -7.46658946427115, -6.320559670193146, -5.150884517077545, -4.007253398000138, -2.936104060743373, -1.9779120877371061, -1.1648463375555373, -0.5189661845924437, -0.051103293107181244, 0.239475621414422, 0.36458515026718896, 0.34583959199225045, 0.21266051541624628, -0.0002791899851017838, -0.25597666931716967, -0.5181513958412519, -0.7541760747918468, -0.9376371702936378, -1.0503015750228957, -1.083312608495076, -1.0375033142012051, -0.9227929772523982, -0.7567173632063579, -0.5622267612996866, -0.36496044693557683, -0.1902639271562821, -0.060249675459942406, 0.00879177439766425, 0.008347825483626614, -0.0612214305178062, -0.19059757850611744, -0.3624750839646397, -0.5535262625848203, -0.7371862795725781, -0.8869854464410604, -0.9800799047372023, -1.0005880002067777, -0.9423351286214784, -0.8106478104685267, -0.6229171997085587, -0.40776764318245723, -0.20280753009182656, -0.05109422352031937, 0.003403312938166152, -0.0790719682996291, -0.3288692708535651, -0.7622248265918596, -1.377603269842955, -2.153573312820859, -3.04858010276314, -4.002803019327275, -4.942081055769658, -5.7836681981269695, -6.443371084508515, -6.843443950446096, -6.920492738217236, -6.632588115870818, -5.964816257677408, -4.93260864169821, -3.582380926595691, -1.9892605048237435, -0.2519693148044293, 1.5147758442934578, 3.1897103218130027, 4.6554612695778905, 5.808985681372756, 6.57097200259977, 6.89323809000992, 6.763331627612112, 6.205803847875115, 5.279958361998938, 4.07424028903178, 2.697787771182806, 1.2699785296934454, -0.09096786669567525, -1.279154121158621, -2.210768007057861, -2.8314163166743187, -3.120260225629398, -3.0905312632828092, -2.7864091207895023, -2.276652211465469, -1.645741443810887, -0.983582653579116, -0.3749779961746377, 0.10990075381204102, 0.4229290236408618, 0.5424885073745539, 0.4744863415919727, 0.2498802975485065, -0.08090603965327062, -0.45590094453743013, -0.8107602691692869, -1.0879641292095859, -1.2447941386040704, -1.2590100299037716, -1.1314490130307808, -0.8851841884262425, -0.5613476051021029, -0.2121880019674613, 0.1076694915555113, 0.35051979153161483, 0.48407729496839624, 0.49789752355950306, 0.40669221932890603, 0.24991251234092893, 0.08747959004830806, -0.00791700562161414, 0.03897035988166689, 0.29454846304519966, 0.8053452478040194, 1.5889078650620305, 2.6280210598022515, 3.869240962163065, 5.226196912739806, 6.587486592500405, 7.828359961798069, 8.824841382338912, 9.468554634036366, 9.680350915690058, 9.420925818477333, 8.69694481446632, 7.561740954058839, 6.110335879780184, 4.469276599733891, 2.782476045682567, 1.194798795332219, -0.16453522552530886, -1.1965979444890065, -1.8435496271634495, -2.094175240581417, -1.983443758224284, -1.5861740662473927, -1.0056903008244849, -0.35903529524006383, 0.23921499178053932, 0.6923009978726993, 0.9336792778453236, 0.9347806767221621, 0.707101479932326, 0.2984197240683652, -0.21621877866289518, -0.7473370233645587, -1.2057176267454344, -1.516706682715179, -1.6319489441194783, -1.5367601598843013, -1.2520046405583862, -0.8301873718645745, -0.34636559950125273, 0.11470071139511469, 0.47313283644245613, 0.667922070143284, 0.6680480705440186, 0.4788623362347697, 0.1425839756146446, -0.2673362052565422, -0.6572577940821068, -0.9281930790032532, -0.9921919456878456, -0.7876968794034276, -0.29137605960142354, 0.4755831145543429, 1.4479324492901744, 2.5237659118629185, 3.577978618082967, 4.479918200454652, 5.112651089398614, 5.3909327062572805, 5.275080114707352, 4.778493517092086, 3.9674855909040785, 2.9532224289952063, 1.876784319848739, 0.889432553623531, 0.13094883994967632, -0.2907316896439302, -0.3155091049516219, 0.05974022298313682, 0.7803309097274621, 1.741454660243005, 2.803294709319462, 3.8113300222620983, 4.618778076854541, 5.107780462648834, 5.206119116099682, 4.89693953593921, 4.220046428486823, 3.2646568456026426, 2.154836645524507, 1.0299927513859743, 0.02355998267182379, -0.7567190816498464, -1.2438143884721622], 'positive_zeros': ['0.908717833826787650120905118137922', '1.55903104009719190466896724013967', '2.32830304228468473527730093463634', '3.75150945152824378664368493386498', '4.00775128266596845974693279238704', '4.73512523477553586192350141458174', '4.80915338219819536204131275847356', '5.57442263951836682011583202205038', '5.59885321084019164088416378697550', '6.54655367252788500605108631347664', '7.22090991652715915706448156970866', '7.79111029211693930669614606595379', '8.056447043933612031171269197879576', '8.576861436588155713465515075006391', '8.956131697052494305782515642843365'], 'prelabel': '4-243675-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9853692777947534, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 250367002863676016, 'z1': {'__RealLiteral__': 0, 'data': '0.908717833826787650120905118137922', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.55903104009719190466896724013967', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.32830304228468473527730093463634', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.536929273438037, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 243675, 'conductor_radical': 285, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -3, 0, 0, 8, 0, 1, 0, 0, 3, 4, 0, 0, 5, 0, 0, -2, 0, -8, 0, 0, 0, 1, 0, -1, -24, 0, 0, 0, 0, 0, 0, 0, -3, -12, 0, -4, 0, 0, 0, 16, 0, 0, 0, 0, -5, 34, 0, 0, -12, 0, 0, 0, 0, 2, 0, 0, 0, 28, 0, 8, -3, 0, 0, -8, 0, 0, 0, 0, 0, -28, 0, -1, 6, 0, 0, 32, 0, 1, 0, 0, 24, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -20, 0, 0, -3], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, 30, 0, 289], 'euler19': [1, 2, 1, 0, 0], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 0, 54, 0, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 12, 110, 444, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, -90, 0, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, -28, 318, -1708, 3721], 'euler67': [1, 8, 150, 536, 4489], 'euler7': [1, -8, 30, -56, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 28, 342, 2044, 5329], 'euler79': [1, -32, 414, -2528, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 20, 294, 1940, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 1, 0, 0, 0], [1, 0, -1, 0, 0], [1, -8, 30, -56, 49], [1, 0, 6, 0, 121], [1, -4, 30, -52, 169], [1, 0, 30, 0, 289], [1, 2, 1, 0, 0], [1, 0, 30, 0, 529], [1, 0, 54, 0, 841], [1, 0, 62, 0, 961], [1, 12, 110, 444, 1369], [1, 0, 46, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, -50, 0, 2209], [1, 0, -90, 0, 2809], [1, 0, 102, 0, 3481], [1, -28, 318, -1708, 3721], [1, 8, 150, 536, 4489], [1, 0, 142, 0, 5041], [1, 28, 342, 2044, 5329], [1, -32, 414, -2528, 6241], [1, 0, 166, 0, 6889], [1, 0, 142, 0, 7921], [1, 20, 294, 1940, 9409]], 'index': 1, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/27075.2/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/27075.2/b'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-243675-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-243675-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9853692777947534, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 250367002863676016, 'z1': {'__RealLiteral__': 0, 'data': '0.908717833826787650120905118137922', 'prec': 117}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9748709
{'Lhash': '403871582455362642,2152338429622007325', 'Lhash_array': ['403871582455362642', '2152338429622007325'], 'label': '4-243675-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/27075.2/b'}
-
id: 9748708
{'Lhash': '403871582455362642,2152338429622007325', 'Lhash_array': ['403871582455362642', '2152338429622007325'], 'label': '4-243675-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/27075.2/b'}