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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': 1, 'Lhash': '1687789348631169854063965908017', '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': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.401922408716853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]]], 'bad_primes': [2, 3], 'central_character': '147456.1', 'coefficient_field': '1.1.1.1', 'conductor': 147456, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 4, 10, 20, 25], [1, 0, -6, 0, 49], [1, 0, 6, 0, 121], [1, 0, 22, 0, 169], [1, -4, 22, -68, 289], [1, 0, -26, 0, 361], [1, 0, -18, 0, 529], [1, 12, 90, 348, 841], [1, 0, -38, 0, 961], [1, -8, 86, -296, 1369], [1, 12, 102, 492, 1681], [1, 0, 22, 0, 1849], [1, 0, 14, 0, 2209], [1, -4, 106, -212, 2809], [1, 0, 6, 0, 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-1.7148750116118152, -3.331707783690432, -5.0024629390371675, -6.520759707830282], 'positive_zeros': ['1.33143103338356653338127828980718', '2.45114369135953411393145166600080', '3.40344343984727589960638657042330', '3.76158828313533998837190908075491', '4.17714412925507901551595555107345', '4.92287886477545098024644591549814', '5.45353694848573023074846106301876', '6.04809798742748541923440855847860', '6.77764414569881643520752481603618', '7.27031221195864598570739877553153', '7.69448116604158071714543108364295', '7.915918038780357399751626349437981', '8.462555862017482523279707127431140', '9.016055594667838105100327165227740'], 'prelabel': '4-384e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1425781280900771869, 'z1': {'__RealLiteral__': 0, 'data': '1.33143103338356653338127828980718', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.45114369135953411393145166600080', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.40344343984727589960638657042330', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.401922408716853, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 147456, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -12, 0, 0, 0, -4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -16, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, -4, 22, -68, 289], 'euler19': [1, 0, -26, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -18, 0, 529], 'euler29': [1, 12, 90, 348, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -38, 0, 961], 'euler37': [1, -8, 86, -296, 1369], 'euler41': [1, 12, 102, 492, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, 14, 0, 2209], 'euler5': [1, 4, 10, 20, 25], 'euler53': [1, -4, 106, -212, 2809], 'euler59': [1, 0, 6, 0, 3481], 'euler61': [1, 8, 102, 488, 3721], 'euler67': [1, 0, -106, 0, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, 0, -114, 0, 5041], 'euler73': [1, -12, 118, -876, 5329], 'euler79': [1, 0, 58, 0, 6241], 'euler83': [1, 0, -42, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, 12, 166, 1164, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 4, 10, 20, 25], [1, 0, -6, 0, 49], [1, 0, 6, 0, 121], [1, 0, 22, 0, 169], [1, -4, 22, -68, 289], [1, 0, -26, 0, 361], [1, 0, -18, 0, 529], [1, 12, 90, 348, 841], [1, 0, -38, 0, 961], [1, -8, 86, -296, 1369], [1, 12, 102, 492, 1681], [1, 0, 22, 0, 1849], [1, 0, 14, 0, 2209], [1, -4, 106, -212, 2809], [1, 0, 6, 0, 3481], [1, 8, 102, 488, 3721], [1, 0, -106, 0, 4489], [1, 0, -114, 0, 5041], [1, -12, 118, -876, 5329], [1, 0, 58, 0, 6241], [1, 0, -42, 0, 6889], [1, 12, 214, 1068, 7921], [1, 12, 166, 1164, 9409]], 'index': 29, 'instance_types': ['BMF', 'BMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/9216.1/e', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/9216.1/b', 'EllipticCurve/2.0.4.1/9216.1/b', 'EllipticCurve/2.0.4.1/9216.1/e'], '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': '4-384e2-1.1-c1e2-0-29', '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': '4-384e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1425781280900771869, 'z1': {'__RealLiteral__': 0, 'data': '1.33143103338356653338127828980718', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9773991
{'Lhash': '1687789348631169854063965908017', 'Lhash_array': ['1687789348631169854063965908017'], 'label': '4-384e2-1.1-c1e2-0-29', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/9216.1/e'}
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id: 9773990
{'Lhash': '1687789348631169854063965908017', 'Lhash_array': ['1687789348631169854063965908017'], 'label': '4-384e2-1.1-c1e2-0-29', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/9216.1/b'}
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id: 9773816
{'Lhash': '1687789348631169854063965908017', 'Lhash_array': ['1687789348631169854063965908017'], 'label': '4-384e2-1.1-c1e2-0-29', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/9216.1/b'}
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id: 9773749
{'Lhash': '1687789348631169854063965908017', 'Lhash_array': ['1687789348631169854063965908017'], 'label': '4-384e2-1.1-c1e2-0-29', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/9216.1/e'}