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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': -3, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 3, 'Lhash': '1653150803884312140,2215180138185436427', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [-1.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.734613728994807, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 1]], [11, [1, 0, -1]], [13, [1, 2, 13]]], 'bad_primes': [3, 11, 13], 'central_character': '184041.1', 'coefficient_field': '1.1.1.1', 'conductor': 184041, 'conductor_radical': 429, 'degree': 4, 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 1], [1, 0, 6, 0, 25], [1, 0, -2, 0, 49], [1, 0, -1], [1, 2, 13], [1, 4, 38, 68, 289], [1, 0, 38, 0, 361], [1, -16, 110, -368, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 78, 0, 1681], [1, 0, 86, 0, 1849], [1, 0, 30, 0, 2209], [1, -12, 142, -636, 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0.609582572002275, 0.6320606444563985, 0.46547984663247627, 0.07624711383482859, -0.5309167063867681], 'positive_zeros': ['1.01190903051797145927138124184629', '2.18490783609343058155048362275765', '3.20967362704724919819221481375048', '4.11432405402007502173846810331508', '4.20407903283329927801590362765999', '5.10830147517302686718916077334095', '5.31622482563829752699303340189764', '5.59092668167682561675172765449897', '6.57112145512025234345666775516045', '6.87625566807413692768701148012213', '7.46995816184461358823952634115962', '7.82831259030341079249655300429044', '8.768985116389244790636560898392406', '8.975261543279013968212899152872650'], 'prelabel': '4-429e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8508328521811284, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1562487932856054616, 'z1': {'__RealLiteral__': 0, 'data': '1.01190903051797145927138124184629', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.18490783609343058155048362275765', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.20967362704724919819221481375048', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.734613728994807, 'bad_primes': [3, 11, 13], 'central_character': '1.1', 'conductor': 184041, 'conductor_radical': 429, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, -3, 0, 0, 0, 0, 3, 0, 0, 6, -2, 0, 0, 5, -4, 0, 0, 0, 0, 0, 16, 0, -6, 0, -4, 0, -12, 0, 0, 0, 0, 0, 0, -9, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -10, 2, 0, 8, 6, 12, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -3, 0, 0, 0, 12, -32, 0, 0, 0, 0, 0, 12, 0, 0, 0, -8, 0, 5, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 18], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, 2, 13, 0, 0], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, 0, 3, 0, 4], 'euler23': [1, -16, 110, -368, 529], 'euler29': [1, 12, 94, 348, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, -2, 0, 961], 'euler37': [1, 0, 38, 0, 1369], 'euler41': [1, 0, 78, 0, 1681], 'euler43': [1, 0, 86, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, 0, -50, 0, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 0, 190, 0, 9409], 'euler_factors': [[1, 0, 3, 0, 4], [1, 2, 1, 0, 0], [1, 0, 6, 0, 25], [1, 0, -2, 0, 49], [1, 0, -1, 0, 0], [1, 2, 13, 0, 0], [1, 4, 38, 68, 289], [1, 0, 38, 0, 361], [1, -16, 110, -368, 529], [1, 12, 94, 348, 841], [1, 0, -2, 0, 961], [1, 0, 38, 0, 1369], [1, 0, 78, 0, 1681], [1, 0, 86, 0, 1849], [1, 0, 30, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 102, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, 118, 0, 4489], [1, 0, 142, 0, 5041], [1, 0, -50, 0, 5329], [1, 8, 174, 632, 6241], [1, 0, 22, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, 190, 0, 9409]], 'index': 2, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1089.1-d', 'EllipticCurve/2.2.13.1/1089.1/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-429e2-1.1-c1e2-0-2', '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': 1, 'prelabel': '4-429e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8508328521811284, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1562487932856054616, 'z1': {'__RealLiteral__': 0, 'data': '1.01190903051797145927138124184629', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9517938
{'Lhash': '1653150803884312140,2215180138185436427', 'Lhash_array': ['1653150803884312140', '2215180138185436427'], 'label': '4-429e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/1089.1/d'}
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id: 9518183
{'Lhash': '1653150803884312140,2215180138185436427', 'Lhash_array': ['1653150803884312140', '2215180138185436427'], 'label': '4-429e2-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1089.1-d'}