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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': 0, 'A8': 0, 'A9': 0, 'Lhash': '1910936829524226267,2168192726828383540', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [1.788854381999832, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.392560798782284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 0, -1]]], 'bad_primes': [2, 3, 7], 'central_character': '508032.1', 'coefficient_field': '1.1.1.1', 'conductor': 508032, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, -4, 14, -20, 25], [1, 0, -1], [1, 0, 18, 0, 121], [1, -4, 30, -52, 169], [1, -12, 70, -204, 289], [1, 0, 22, 0, 361], [1, 0, 10, 0, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, -20, 174, -740, 1369], [1, -4, 86, -164, 1681], [1, 0, 70, 0, 1849], [1, 0, 78, 0, 2209], [1, 24, 250, 1272, 2809], [1, 0, -26, 0, 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-2.099048402019841, -0.666157763952306, 0.7128480672390878, 1.899190570665061, 2.7836136612199254, 3.2993246921923545], 'positive_zeros': ['1.23073197938907604520302484273234', '1.38744136941764418419874219847502', '2.45683901738953215093540180119551', '2.88871942698849130206456913366900', '3.60698435135707065201863764201822', '4.10502926185056205242132098715537', '4.88053771103235633099685381109338', '5.50301216544551056360312768488239', '5.73569194086517270564919024712576', '6.18921559649042192845851641510423', '6.32147524527224537125089512132651', '7.16759940438630821447644837255145', '7.79064855464535275520223516341667', '8.016710564482448925343947507212620', '8.348093232759484287064194714284123'], 'prelabel': '4-508032-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3856752259206857, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1773286547138915856, 'z1': {'__RealLiteral__': 0, 'data': '1.23073197938907604520302484273234', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.38744136941764418419874219847502', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.45683901738953215093540180119551', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.392560798782284, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 508032, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0], 'euler11': [1, 0, 18, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, -20, 174, -740, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 78, 0, 2209], 'euler5': [1, -4, 14, -20, 25], 'euler53': [1, 24, 250, 1272, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, -12, 158, -732, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, -54, 0, 5041], 'euler73': [1, 4, 150, 292, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, -90, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 36, 518, 3492, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -4, 14, -20, 25], [1, 0, -1, 0, 0], [1, 0, 18, 0, 121], [1, -4, 30, -52, 169], [1, -12, 70, -204, 289], [1, 0, 22, 0, 361], [1, 0, 10, 0, 529], [1, 0, 58, 0, 841], [1, 0, 46, 0, 961], [1, -20, 174, -740, 1369], [1, -4, 86, -164, 1681], [1, 0, 70, 0, 1849], [1, 0, 78, 0, 2209], [1, 24, 250, 1272, 2809], [1, 0, -26, 0, 3481], [1, -12, 158, -732, 3721], [1, 0, 118, 0, 4489], [1, 0, -54, 0, 5041], [1, 4, 150, 292, 5329], [1, 0, 94, 0, 6241], [1, 0, -90, 0, 6889], [1, 12, 214, 1068, 7921], [1, 36, 518, 3492, 9409]], 'index': 38, 'instance_types': ['BMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/31752.1/i', 'EllipticCurve/2.0.4.1/31752.1/i'], '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': '4-508032-1.1-c1e2-0-38', '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': '4-508032-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3856752259206857, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1773286547138915856, 'z1': {'__RealLiteral__': 0, 'data': '1.23073197938907604520302484273234', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9666667
{'Lhash': '1910936829524226267,2168192726828383540', 'Lhash_array': ['1910936829524226267', '2168192726828383540'], 'label': '4-508032-1.1-c1e2-0-38', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/31752.1/i'}
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id: 9666358
{'Lhash': '1910936829524226267,2168192726828383540', 'Lhash_array': ['1910936829524226267', '2168192726828383540'], 'label': '4-508032-1.1-c1e2-0-38', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/31752.1/i'}