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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '704992717552055982,1731115709754361337', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.590782426131276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [5, [1, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '72000.1', 'coefficient_field': '1.1.1.1', 'conductor': 72000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, -1], [1, 0, 14, 0, 49], [1, 8, 38, 88, 121], [1, 0, -10, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 4, 62, 116, 841], [1, 16, 126, 496, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -58, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, 70, 0, 2809], [1, -24, 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1.4773642466139039, 2.371316449628026], 'positive_zeros': ['2.07933314479152275364533906757678', '2.25002432004047770108316173263348', '3.42683606015106566673715003849075', '3.95303834850677407956821293661618', '4.95639818252911756604562729940319', '5.36683559095823513937522588288546', '5.59585158632682227968586342616249', '6.65963768785974737826480192145103', '6.89270810769313104844169224864906', '7.55727707153378484774141976096546', '8.280524075884956092273610432842374', '8.323057177226078640880314002796256', '9.042960162718976648409639393559621', '9.749205121396688870647577836420293'], 'prelabel': '4-72000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4637660753697073, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 130265418092723368, 'z1': {'__RealLiteral__': 0, 'data': '2.07933314479152275364533906757678', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.25002432004047770108316173263348', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.42683606015106566673715003849075', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.590782426131276, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 72000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 1, 0, 0, 0, -14, 0, 0, 0, 0, 0, -8, 0, 0, 0, 24, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 1, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 16, 126, 496, 961], 'euler37': [1, 0, 70, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, -58, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, -1, 0, 0, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, -24, 262, -1416, 3481], 'euler61': [1, -28, 318, -1708, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 0, 110, 0, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -20, 278, -1780, 7921], 'euler97': [1, 0, 190, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, -1, 0, 0, 0], [1, 0, 14, 0, 49], [1, 8, 38, 88, 121], [1, 0, -10, 0, 169], [1, 0, -2, 0, 289], [1, 8, 54, 152, 361], [1, 0, 46, 0, 529], [1, 4, 62, 116, 841], [1, 16, 126, 496, 961], [1, 0, 70, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -58, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, 70, 0, 2809], [1, -24, 262, -1416, 3481], [1, -28, 318, -1708, 3721], [1, 0, 118, 0, 4489], [1, -16, 206, -1136, 5041], [1, 0, 110, 0, 5329], [1, 16, 222, 1264, 6241], [1, 0, 22, 0, 6889], [1, -20, 278, -1780, 7921], [1, 0, 190, 0, 9409]], 'index': 29, 'instance_types': ['HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2880.1-d', 'EllipticCurve/2.2.5.1/2880.1/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': '4-72000-1.1-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': '4-72000-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4637660753697073, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 130265418092723368, 'z1': {'__RealLiteral__': 0, 'data': '2.07933314479152275364533906757678', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9521619
{'Lhash': '704992717552055982,1731115709754361337', 'Lhash_array': ['704992717552055982', '1731115709754361337'], 'label': '4-72000-1.1-c1e2-0-29', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/2880.1/d'}
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id: 9521204
{'Lhash': '704992717552055982,1731115709754361337', 'Lhash_array': ['704992717552055982', '1731115709754361337'], 'label': '4-72000-1.1-c1e2-0-29', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-2880.1-d'}