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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '2217589956271030732', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 242.7452221446925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, -1]]], 'bad_primes': [2, 5, 19], 'central_character': '30400.1', 'coefficient_field': '1.1.1.1', 'conductor': 30400, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1], [1, 4, 7], [1, 4, 11], [1, 4, 13], [1, -2, 17], [1, -1], [1, 0, 23], [1, 2, 29], [1, -8, 31], [1, -4, 37], [1, -6, 41], [1, 0, 43], [1, 12, 47], [1, 8, 53], [1, 0, 59], [1, 2, 61], [1, 14, 67], [1, -8, 71], [1, 6, 73], [1, 4, 79], [1, -4, 83], [1, -14, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-30400-1.1-c1-0-0', 'leading_term': '0.118845847265', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/30400/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.1188458472647723, -0.1850538484795021, -0.9146527986357922, -1.491104688209433, -1.090320290265732, 0.7602472140283185, 3.492261771859791, 5.511140369045429, 5.308112909820687, 2.92990651094251, 0.2932026928717386, -0.407038281137452, 1.0575692545438, 2.471828041834178, 1.411131797165779, -1.945572705659592, -4.704164292138907, -4.352392554137223, -1.632224596018954, 0.3682896411026383, -0.05667666992653757, -1.371085365386386, -1.213543051070066, 0.2695605102202092, 0.8985992918885634, 0.0203296807491808, -0.3083954171668228, 1.372109855554142, 3.120981916674774, 2.202297027133359, -0.2708023871008845, -0.1736753859001327, 3.438197725111405, 5.852425157546265, 2.710517218810506, -3.478092396805996, -6.171014631458033, -3.444712532230999, 0.01963196534839652, 0.2211510572912051, -0.9807438706441108, -0.2690677449933788, 1.205668663481573, 0.2977056840245156, -2.028216320608913, -1.950801684330631, 0.6099173068838847, 1.720807955352585, 0.1547824207641699, -0.7791749972365299, 0.4824562183316655, 0.9994462185951289, -0.575598030008708, -0.6300798211473765, 2.587969212260189, 4.021198000737057, -0.5141782226145608, -6.025794850630569, -4.980801496016815, 0.726606626415794, 2.636208569474037, -0.9965501501639457, -3.582472113494833, -1.796339571089248, 0.2542056314065938, -0.1527546902679232, -0.172620094900741, 1.498921495787636, 1.632847377537452, -0.4777264939753128, -0.9216785460465232, 0.9376259322020843, 0.6166328935336329, -2.531099413470769, -3.244375682069487, -0.3386017503676866, 0.6928995835495861, -1.561798485394449, -1.444305157152829, 2.09640585051595, 2.18197792708801, -2.803938085682899, -4.624909009015412, 0.4107538548342563, 4.484229293257799, 2.089968235300442, -1.093564939866791, 0.2259767582541013, 2.175223539734753, 0.9473070443711491, -0.337680751045367, 0.4912848899830548, 0.6478789661188831, -0.0214817154657916, 1.675838790051305, 3.857919045342407, 2.056994464330082, -0.5586720214211489, 1.789652938059821, 5.005542839008853, 1.736000955804452, -3.949186373976859, -3.547482590884186, 0.1061015766718581, -0.4904066121352069, -2.559559389599659, -0.2661583343229284, 2.093397657651744, -0.8426811551215811, -3.470639364738614, -0.03715606009856088, 3.887936867564677, 2.503032677874101, -0.09469522826961638, 0.1071830394059767, 0.1943869245234019, -0.861633394318459, -0.1640786873130983, 0.8938561658474764, -0.02317091835046569, 1.607631653686214], 'positive_zeros': ['0.1541146140036195', '1.167690076783917', '2.541961021942302', '2.849738755409346', '3.616127713739708', '4.673604713965254', '4.989185055686299', '5.704810011249430', '6.254857656904135', '6.573798594771729', '7.466353470046430', '7.768184688858123', '8.608846935482575', '9.497592580862592', '9.792071601110367', '10.28851895601953', '10.78198404904434', '11.44267998801282', '12.02067488290074', '12.42431554497342', '12.91901870279024', '13.31559794970556', '13.98018756682862', '14.71591231526304', '15.19394348518764', '15.94078449654834', '16.20727740264966', '16.53421676090647', '17.19430164730904', '17.62918457365566', '18.05709309757820', '18.78022724295514', '19.09312375538721', '19.60840892153284'], 'prelabel': '2-30400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.580283121454901, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2217589956271030732, 'z1': {'__RealLiteral__': 0, 'data': '0.1541146140036195', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.167690076783917', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.541961021942302', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 242.7452221446925, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 30400, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, -4, 0, 1, 0, -4, 0, -4, 0, 0, 0, 2, 0, 1, 0, 8, 0, 0, 0, 0, 0, 4, 0, -2, 0, 8, 0, 8, 0, 0, 0, 4, 0, 8, 0, 6, 0, 0, 0, 0, 0, -12, 0, 9, 0, -4, 0, -8, 0, 0, 0, -2, 0, 0, 0, -2, 0, -4, 0, 0, 0, -14, 0, 0, 0, 8, 0, -6, 0, 0, 0, 16, 0, -4, 0, -11, 0, 4, 0, 0, 0, 4, 0, 14, 0, 16, 0, -16, 0, 0, 0, 12, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 4, 13], 'euler17': [1, -2, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, 2, 3], 'euler31': [1, -8, 31], 'euler37': [1, -4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 0, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 8, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, 14, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, 6, 73], 'euler79': [1, 4, 79], 'euler83': [1, -4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 0, 0], [1, 4, 7], [1, 4, 11], [1, 4, 13], [1, -2, 17], [1, -1, 0], [1, 0, 23], [1, 2, 29], [1, -8, 31], [1, -4, 37], [1, -6, 41], [1, 0, 43], [1, 12, 47], [1, 8, 53], [1, 0, 59], [1, 2, 61], [1, 14, 67], [1, -8, 71], [1, 6, 73], [1, 4, 79], [1, -4, 83], [1, -14, 89], [1, -12, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30400/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-30400-1.1-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-30400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.580283121454901, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2217589956271030732, 'z1': {'__RealLiteral__': 0, 'data': '0.1541146140036195', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2217589956271030732', 'Lhash_array': ['2217589956271030732'], 'label': '2-30400-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30400/d'}