-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 2, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '816601611664576313369680890886', 'a10': [0.632455532033676, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.58422300161857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 0, -1]], [5, [1, 2, 1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1216800.1', 'coefficient_field': '1.1.1.1', 'conductor': 1216800, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1, 1], [1, 0, -1], [1, 2, 1], [1, 0, -2, 0, 49], [1, 0, -2, 0, 121], [1, -2, 1], [1, 0, -2, 0, 289], [1, 0, -2, 0, 361], [1, 0, 22, 0, 529], [1, 0, 22, 0, 841], [1, 0, -2, 0, 961], [1, -4, 78, -148, 1369], [1, -12, 118, -492, 1681], [1, 0, -26, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, -98, 0, 3481], [1, -4, -18, -244, 3721], [1, 0, -74, 0, 4489], [1, 0, -2, 0, 5041], [1, -16, 174, -1168, 5329], [1, 0, -50, 0, 6241], [1, 0, -26, 0, 6889], [1, -12, 214, -1068, 7921], [1, 8, 174, 776, 9409], [1, 0, 166, 0, 10201], [1, 0, -170, 0, 10609], [1, 0, 70, 0, 11449], [1, 8, 198, 872, 11881], [1, 0, 190, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 9, 'label': '4-1216800-1.1-c1e2-0-9', 'leading_term': '1.28691146374', '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/2.0.4.1/76050.5/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.2869114637378878, 1.2797061077865877, 1.2580576778569545, 1.221880027799327, 1.17106552790377, 1.1055371709728201, 1.0253179082244488, 0.9306136470322117, 0.8219053997276513, 0.7000452085634143, 0.5663497246588146, 0.42268473518101907, 0.2715335671011866, 0.11604220580782236, -0.03996578892385624, -0.192010855088763, -0.3350207116696462, -0.4634390572258362, -0.5713814114794074, -0.6528374202394005, -0.701916167792059, -0.7131279947148513, -0.6816931400011228, -0.6038643875486779, -0.477248002493828, -0.3011048188757966, -0.07661162331465217, 0.19293779837324068, 0.5020122139234622, 0.8428216717802691, 1.2054108671571648, 1.5778780505222996, 1.9467244390348866, 2.29733194183353, 2.6145589415611474, 2.8834352849836398, 3.0899290221165576, 3.2217493719521, 3.2691435090365215, 3.2256396952729554, 3.088686627860209, 2.8601391559003253, 2.5465441187572964, 2.1591871791576294, 1.7138721384915228, 1.230418050089967, 0.7318759364161356, 0.2434852483070399, -0.20859068410220313, -0.598692326549358, -0.9031800901947339, -1.101950818539142, -1.1798576274292256, -1.1279330781948773, -0.9443193194931265, -0.6348196605720717, -0.21300403167291954, 0.30017460476193086, 0.8772657241235718, 1.4856874880074036, 2.08951704743361, 2.6516133806310824, 3.1359498871165084, 3.510008966804058, 3.7470746039091334, 3.828253635960129, 3.7440633539728654, 3.4954429500984268, 3.094078729533907, 2.561976515737519, 1.9302668493245523, 1.2372860231210294, 0.5260345734303895, -0.1588300494227686, -0.7742630235024341, -1.2821261264309547, -1.6522507145697622, -1.8650159780777773, -1.91321115749692, -1.8029933302301795, -1.5538138226245275, -1.1972625536056307, -0.7748653756380229, -0.33495820836239354, 0.07115386109705284, 0.3934718334770582, 0.587678182076622, 0.6192495189176248, 0.4669442417760647, 0.12533457117475066, -0.3938853542083891, -1.0619942146736026, -1.8348093819636213, -2.6556688498464136, -3.4596480666152134, -4.178712772982171, -4.747410587520984, -5.108635127402142, -5.218964922486199, -5.053090399835497, -4.606897336892166, -3.8988719997340158, -2.969625293342288, -1.8794905868416392, -0.7043194195956007, 0.4702338843220251, 1.5554991068837745, 2.467093362641661, 3.1321153131138124, 3.495589064012349, 3.5255588498647032, 3.2163351921074406, 2.5895432505658906, 1.6928126780593338, 0.596159241520771, -0.6136773392764835, -1.8404778016854388, -2.9867480904350754, -3.96215576083504, -4.691428525905317, -5.120976959350225, -5.223606721347747, -5.000853198588079, -4.482688779827815, -3.7246002270618925, -2.802287114710513, -1.8044669843448355, -0.8244646358400758, 0.0486086461056408, 0.7382298093544424, 1.187571392836988, 1.3646386699651079, 1.2649255435693163, 0.911325144432698, 0.35130872200806884, -0.34833370035700034, -1.1086446810223733, -1.8467981025276083, -2.4846786849710956, -2.9568444049114118, -3.2170382730691585, -3.242570326310218, -3.0361196993747197, -2.6247862378826423, -2.0565211799709777, -1.394353975439959, -0.709075100807625, -0.07120497445485424, 0.4568433037477863, 0.8275245553015984, 1.013088346783207, 1.008128097023537, 0.8294854644706023, 0.5135521291185374, 0.1113165044646875, -0.3182314150971502, -0.7155298992933959, -1.0278045271225098, -1.215461147816234, -1.2567362251767153, -1.1500421848066602, -0.9137299322581038, -0.583311579086447, -0.2065044339014076, 0.1632670566476658, 0.47407651616226826, 0.6824783148928383, 0.7593602407260877, 0.6938969601917574, 0.4950737479108671, 0.1905603064042038, -0.17694203173081943, -0.5554234743182664, -0.8906239226468353, -1.133502735912272, -1.2471263559521677, -1.212039053966102, -1.029365671918797, -0.721182216142178, -0.3280451703158028, 0.09605181735754952, 0.49067413663008747, 0.7969985177039464, 0.9658604551660277, 0.9647093962631292, 0.7825030819120125, 0.4318244584770709, -0.05214012091717526, -0.615708861151111, -1.1934277130077358, -1.7165710788411674, -2.1223181832774625, -2.3623804352081277, -2.409894434551865, -2.2635962894791515, -1.9486332296586972, -1.5138061594664847, -1.0255152954054638, -0.5591365650947572, -0.18892634751795004, 0.02221652302305771, 0.031745429098195915, -0.17603874693166247, -0.5869429569292165, -1.1577961055770198, -1.821305524148345, -2.494302808426046, -3.0883507679016455, -3.521336219470477, -3.728505766955541, -3.671441366296731, -3.3437193029873926, -2.7724213931996333, -2.015216395836663, -1.1533297136584635, -0.2812883689695883, 0.5052139055636129, 1.1217061732887637, 1.5058991949272775, 1.625702309719715, 1.4831749043466702, 1.1138411163011845, 0.5814378113968164, -0.031192489965048063, -0.6338014009646991, -1.1413854523165952, -1.4859956345855152, -1.6260177807363505, -1.5515848243335364, -1.2853297132872428, -0.8783585432558864, -0.4020218919655625, 0.063313258331867, 0.4408313894294148, 0.6692971985257584, 0.712722351028139, 0.5661762395520535, 0.2568054990090692, -0.16016265041344707, -0.6098991658994609, -1.0097051937541155, -1.2822441539391942, -1.368250414365655, -1.236722385555767, -0.8909442326445978, -0.36927921509522377, 0.2595447104367814, 0.9060932575735149, 1.4734825047220148, 1.8722890749832146, 2.0348499133878453, 1.9267067877021684, 1.5533159174238793, 0.960810240450977, 0.23047865256747266, -0.5324142648369278, -1.213947384086592], 'positive_zeros': ['0.64418508658265482350248534270188', '1.23286094969581372261993193711190', '2.22773038890382925548262920399743', '2.64534656414478412609021430765466', '3.41067871091058592233972496042474', '3.92871883184026369104779176326426', '4.18470159024800140960378103774474', '4.90287820927114447450258908945311', '5.36716835253816956204350340048831', '5.99714563622230372484380845210937', '6.30563282675575538526656888796517', '6.89632635082758358357029115131195', '7.23091626527372242959341239046052', '7.66625670460088011141896478036655', '7.993652391521439250723001751174475'], 'prelabel': '4-1216800-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.967859612069989, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 712491240046786781, 'z1': {'__RealLiteral__': 0, 'data': '0.64418508658265482350248534270188', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.23286094969581372261993193711190', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.22773038890382925548262920399743', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 77.58422300161857, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1216800, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, -2, 0, 0, -1, 1, 2, 0, 0, 2, 0, 0, 1, 0, -1, 0, -2, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 4, 0, 0, 2, 12, 0, 0, 0, -2, 0, 0, 0, 2, -3, 0, 2, 12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 1, -4, 0, 0, 0, 0, 0, 0, -1, 16, -4, 0, 0, 0, 0, 0, -2, 1, -12, 0, 0, 0, 0, 0, 0, 12, 2, 0, 0, 0, 0, 0, 0, -8, -2, 0, 3], 'euler11': [1, 0, -2, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, -2, 0, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 22, 0, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 0, -26, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, 2, 1, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, -98, 0, 3481], 'euler61': [1, -4, -18, -244, 3721], 'euler67': [1, 0, -74, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, -16, 174, -1168, 5329], 'euler79': [1, 0, -50, 0, 6241], 'euler83': [1, 0, -26, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 8, 174, 776, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 0, -1, 0, 0], [1, 2, 1, 0, 0], [1, 0, -2, 0, 49], [1, 0, -2, 0, 121], [1, -2, 1, 0, 0], [1, 0, -2, 0, 289], [1, 0, -2, 0, 361], [1, 0, 22, 0, 529], [1, 0, 22, 0, 841], [1, 0, -2, 0, 961], [1, -4, 78, -148, 1369], [1, -12, 118, -492, 1681], [1, 0, -26, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, -98, 0, 3481], [1, -4, -18, -244, 3721], [1, 0, -74, 0, 4489], [1, 0, -2, 0, 5041], [1, -16, 174, -1168, 5329], [1, 0, -50, 0, 6241], [1, 0, -26, 0, 6889], [1, -12, 214, -1068, 7921], [1, 8, 174, 776, 9409]], 'index': 9, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/76050.5/d', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/76050.5/c', 'EllipticCurve/2.0.4.1/76050.5/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/76050.5/d'], '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': '4-1216800-1.1-c1e2-0-9', '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': '4-1216800-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.967859612069989, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 712491240046786781, 'z1': {'__RealLiteral__': 0, 'data': '0.64418508658265482350248534270188', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9745148
{'Lhash': '816601611664576313369680890886', 'Lhash_array': ['816601611664576313369680890886'], 'label': '4-1216800-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/76050.5/d'}
-
id: 9744500
{'Lhash': '816601611664576313369680890886', 'Lhash_array': ['816601611664576313369680890886'], 'label': '4-1216800-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/76050.5/c'}
-
id: 9744100
{'Lhash': '816601611664576313369680890886', 'Lhash_array': ['816601611664576313369680890886'], 'label': '4-1216800-1.1-c1e2-0-9', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/76050.5/c'}
-
id: 9743744
{'Lhash': '816601611664576313369680890886', 'Lhash_array': ['816601611664576313369680890886'], 'label': '4-1216800-1.1-c1e2-0-9', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/76050.5/d'}