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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 4, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '634813255736997062', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2166.596928123806, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7537, [1, -1]]], 'bad_primes': [2, 3, 7537], 'central_character': '271332.1', 'coefficient_field': '1.1.1.1', 'conductor': 271332, 'conductor_radical': 45222, 'degree': 2, 'euler_factors': [[1], [1], [1, -4, 5], [1, 4, 7], [1, -2, 11], [1, 2, 13], [1, -8, 17], [1, 6, 19], [1, -5, 23], [1, -6, 29], [1, -3, 31], [1, 10, 37], [1, 0, 41], [1, 10, 43], [1, -9, 47], [1, -11, 53], [1, -10, 59], [1, -11, 61], [1, -3, 67], [1, -12, 71], [1, 13, 73], [1, -8, 79], [1, 10, 83], [1, -14, 89], [1, -4, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-271332-1.1-c1-0-0', 'leading_term': '4.47627998693', '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/271332/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.476279986926195, 3.489325031202005, 1.218055555750379, -0.5384343716322155, -0.1966819934562572, 1.734019143307084, 2.771172406876564, 1.406400884471693, -0.6615640610403812, -0.7062572117718274, 0.9274895788131721, 1.192234107892702, -0.6472256014267231, -1.392578755578946, 0.6147388124361522, 1.590492087643429, -2.123255352683532, -7.04757048937616, -6.744973829493759, -1.792649892525033, 1.0795456612774, -0.2869496394037648, -1.190829839183106, 0.5638991367595376, 1.423167930419478, 0.1132677713829027, -0.01712179541514091, 1.12433977159756, -0.03194209855895361, -1.324999081980147, 3.373715377305477, 11.00030846765964, 11.20037186581726, 3.578598245180455, -1.375495222136369, -0.166713062897292, 0.38762287768854, -1.825896816966884, -1.977249490007354, -0.08579650400942707, 0.0987845911814031, -0.08697000706733617, 0.179017237576505, -4.046526823435639, -11.30782934630427, -10.7935733537208, -1.724540431008124, 2.959458587261048, -0.5933962979424876, -2.487562051018425, 0.01446184315583005, 0.3404994372160986, -0.910940571323823, 0.6098202109468684, 1.30584302587278, -1.089562357072424, -1.110708823541817, 1.103867381640985, 0.008711232395930782, -0.5679813888852276, 4.209175585729345, 6.06951018400353, 0.3504803353845214, -1.948537555617429, 3.396352823116218, 5.49487148609904, 1.668776444779849, -0.06492196178344797, 0.1453951582836535, -0.8897974424653065, 0.8324454075327777, 3.709214163962521, 0.6344308947612814, -3.324995503057139, -0.5179674216276178, 2.274780959975855, 0.1546589428528023, -0.1909114910516266, 0.2076618495551658, -4.55149549986629, -6.488832315118573, 0.1314406777749672, 3.836861203720338, 0.1476281320043074, -1.034204542872209, 0.726940894765133, -0.3717131296981714, -0.3108603172562046, 1.886276865548204, 0.3565162651808695, -1.135166764255755, 1.317497099737106, 0.3250790890655917, -2.956020504603279, -0.05110065656412392, 0.8203149356589783, -8.07736629476881, -12.55147670247904, -5.429721725552082, 0.06458160244164901, -0.1061252632829688, 0.6632092860155059, 0.7638314217426664, -0.2600683313768496, 0.6603030413713529, -1.426519936501736, -5.362080888485796, -1.498510240012289, 3.031017891510727, -2.300402478550448, -5.366525063827331, 0.8339721791917974, 2.485595647157115, -1.602469993242799, -0.694891866276728, 0.984650152523653, -1.118714976036152, -0.8654177913223321, 0.3953510019668631, -0.3873824847404754, 0.2413965826804895], 'positive_zeros': ['0.6457963659198617', '1.031620585260349', '1.905216647813730', '2.363914649422362', '2.921815953379265', '3.438528127216197', '3.892822139741907', '4.854979236915480', '5.215797054634299', '5.683585628108697', '6.273433448636503', '6.503982156573212', '6.996552819326294', '7.367434667388181', '8.385165646228506', '8.770178990725740', '9.054930943783567', '9.766843396441898', '10.03983308182791', '10.28525194926465', '10.53053614473386', '11.55109770806844', '11.96773764863312', '12.49844634726253', '12.80266853811923', '13.18164485229583', '13.64476805901485', '14.11100751245791', '14.50092854603390', '14.79686100904005', '15.51423401690383', '15.86121198639885', '16.67874871438019', '16.79561090944056', '17.04576145953486', '17.43695593845162', '18.02858707185109', '18.52768009911017', '19.01705670410789', '19.28174430693690', '19.52115296745146'], 'prelabel': '2-271332-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.54671769441757, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 634813255736997062, 'z1': {'__RealLiteral__': 0, 'data': '0.6457963659198617', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.031620585260349', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.905216647813730', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2166.596928123806, 'bad_primes': [2, 3, 7537], 'central_character': '1.1', 'conductor': 271332, 'conductor_radical': 45222, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2, 0, -2, 0, 0, 0, 8, 0, -6, 0, 0, 0, 5, 0, 11, 0, 0, 0, 6, 0, 3, 0, 0, 0, -16, 0, -10, 0, 0, 0, 0, 0, -10, 0, 0, 0, 9, 0, 9, 0, 0, 0, 11, 0, 8, 0, 0, 0, 10, 0, 11, 0, 0, 0, -8, 0, 3, 0, 0, 0, 12, 0, -13, 0, 0, 0, -8, 0, 8, 0, 0, 0, -10, 0, 32, 0, 0, 0, 14, 0, 8, 0, 0, 0, -24, 0, 4, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 2, 13], 'euler17': [1, -8, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -5, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -3, 31], 'euler37': [1, 10, 37], 'euler41': [1, 0, 41], 'euler43': [1, 10, 43], 'euler47': [1, -9, 47], 'euler5': [1, -4, 5], 'euler53': [1, -11, 53], 'euler59': [1, -10, 59], 'euler61': [1, -11, 61], 'euler67': [1, -3, 67], 'euler7': [1, 4, 7], 'euler71': [1, -12, 71], 'euler73': [1, 13, 73], 'euler79': [1, -8, 79], 'euler83': [1, 10, 83], 'euler89': [1, -14, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -4, 5], [1, 4, 7], [1, -2, 11], [1, 2, 13], [1, -8, 17], [1, 6, 19], [1, -5, 23], [1, -6, 29], [1, -3, 31], [1, 10, 37], [1, 0, 41], [1, 10, 43], [1, -9, 47], [1, -11, 53], [1, -10, 59], [1, -11, 61], [1, -3, 67], [1, -12, 71], [1, 13, 73], [1, -8, 79], [1, 10, 83], [1, -14, 89], [1, -4, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/271332/b'], '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': '2-271332-1.1-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': '2-271332-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 46.54671769441757, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 634813255736997062, 'z1': {'__RealLiteral__': 0, 'data': '0.6457963659198617', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '634813255736997062', 'Lhash_array': ['634813255736997062'], 'label': '2-271332-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/271332/b'}