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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 0, 'Lhash': '18950087430636185,111470209756918388', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.3867215545988, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '209952.1', 'coefficient_field': '1.1.1.1', 'conductor': 209952, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, -1], [1], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 0, 13, 0, 121], [1, -4, 30, -52, 169], [1, 6, 43, 102, 289], [1, 0, 37, 0, 361], [1, 0, 10, 0, 529], [1, -12, 94, -348, 841], [1, 0, 46, 0, 961], [1, 8, 90, 296, 1369], [1, -18, 163, -738, 1681], [1, 0, 85, 0, 1849], [1, 0, 58, 0, 2209], [1, -24, 250, -1272, 2809], [1, 0, 109, 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1.440616820135067, 1.1369842907970702, 0.7342619052660058, 0.30824261955698634, -0.06632164715327063], 'positive_zeros': ['0.967496248641159004586773303228891', '2.19879385611801234222671009190633', '2.48468545989121014995168597574860', '3.57376731663222433353058317816872', '3.94847330019587176084970982030586', '4.39002474802971059462229776672348', '5.13805326110939411578475614906574', '5.57014449737897797729246275254926', '6.25936593777468405983226275094273', '6.48609808834188223043361623015051', '6.97337389606279696915121240098517', '7.63671497466111343831458484772724', '8.131333319129826356153375895616386', '8.543319215757720981308384286559420', '8.982636192572195812922115743561356'], 'prelabel': '4-209952-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9127955710377982, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 130420297187554573, 'z1': {'__RealLiteral__': 0, 'data': '0.967496248641159004586773303228891', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.19879385611801234222671009190633', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.48468545989121014995168597574860', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.3867215545988, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 209952, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 1, -6, 0, 0, 0, 0, 0, 0, 0, -10, 4, 0, 0, 12, 0, 0, 1, 0, -6, 0, 0, -8, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, -10, -10, 0, 4, 24, 0, 0, 0, 0, 12, 0, 0, 16, 0, 0, 1, 0, 0, 0, -6, 0, 0, 0, 0, 22, -8, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 10, -10, 0, -10], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 6, 43, 102, 289], 'euler19': [1, 0, 37, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, -12, 94, -348, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 8, 90, 296, 1369], 'euler41': [1, -18, 163, -738, 1681], 'euler43': [1, 0, 85, 0, 1849], 'euler47': [1, 0, 58, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, -24, 250, -1272, 2809], 'euler59': [1, 0, 109, 0, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 0, 109, 0, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, -10, 219, -970, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, 0, 10, 0, 49], [1, 0, 13, 0, 121], [1, -4, 30, -52, 169], [1, 6, 43, 102, 289], [1, 0, 37, 0, 361], [1, 0, 10, 0, 529], [1, -12, 94, -348, 841], [1, 0, 46, 0, 961], [1, 8, 90, 296, 1369], [1, -18, 163, -738, 1681], [1, 0, 85, 0, 1849], [1, 0, 58, 0, 2209], [1, -24, 250, -1272, 2809], [1, 0, 109, 0, 3481], [1, -16, 186, -976, 3721], [1, 0, 109, 0, 4489], [1, 0, -2, 0, 5041], [1, -22, 267, -1606, 5329], [1, 0, 142, 0, 6241], [1, 0, 22, 0, 6889], [1, -12, 214, -1068, 7921], [1, -10, 219, -970, 9409]], 'index': 5, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/13122.1/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/13122.1/c'], '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': '4-209952-1.1-c1e2-0-5', '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': '4-209952-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9127955710377982, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 130420297187554573, 'z1': {'__RealLiteral__': 0, 'data': '0.967496248641159004586773303228891', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9651050
{'Lhash': '18950087430636185,111470209756918388', 'Lhash_array': ['18950087430636185', '111470209756918388'], 'label': '4-209952-1.1-c1e2-0-5', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/13122.1/c'}
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id: 9650600
{'Lhash': '18950087430636185,111470209756918388', 'Lhash_array': ['18950087430636185', '111470209756918388'], 'label': '4-209952-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/13122.1/c'}