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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': -4, 'A8': 1, 'A9': -5, 'Lhash': '708012337630994629,1592397413044078750', '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': [-1.5118578920369088, 0], 'a8': [0.3535533905932738, 0], 'a9': [-1.6666666666666667, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.863729814002494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [29, [1, 0, -1]]], 'bad_primes': [2, 29], 'central_character': '107648.1', 'coefficient_field': '1.1.1.1', 'conductor': 107648, 'conductor_radical': 58, 'degree': 4, 'euler_factors': [[1, -1], [1, 0, 5, 0, 9], [1, 0, 9, 0, 25], [1, 4, 18, 28, 49], [1, 0, 13, 0, 121], [1, 0, 25, 0, 169], [1, -16, 98, -272, 289], [1, 0, 38, 0, 361], [1, -8, 62, -184, 529], [1, 0, -1], [1, 6, 71, 186, 961], [1, 0, 10, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -35, 0, 1849], [1, -26, 263, 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2300409750675073379, 'z1': {'__RealLiteral__': 0, 'data': '0.907460307275556682567938804358009', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.44287708620897533980700790337455', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.07071881135695746551942332894698', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.863729814002494, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 107648, 'conductor_radical': 58, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -4, 1, -5, 0, 0, 0, 0, -4, 0, 1, 16, -5, 0, 0, 0, 0, 8, 0, -9, 0, 0, -4, 0, 0, -6, 1, 0, 16, 0, -5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 26, 0, -2, -9, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, 20, 1, 0, 0, 0, 16, 0, 0, 4, -5, 8, 0, 0, 0, 0, 0, 30, 0, 16, 4, 0, 0, 0, 0, 0, 0, -20, 0, 0, 8, 0, 26, 0, 0, -4, -2, 0, -9], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, 0, 25, 0, 169], 'euler17': [1, -16, 98, -272, 289], 'euler19': [1, 0, 38, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 0, -1, 0, 0], 'euler3': [1, 0, 5, 0, 9], 'euler31': [1, 6, 71, 186, 961], 'euler37': [1, 0, 10, 0, 1369], 'euler41': [1, -4, 86, -164, 1681], 'euler43': [1, 0, -35, 0, 1849], 'euler47': [1, -26, 263, -1222, 2209], 'euler5': [1, 0, 9, 0, 25], 'euler53': [1, 0, -15, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 0, -10, 0, 4489], 'euler7': [1, 4, 18, 28, 49], 'euler71': [1, -4, 146, -284, 5041], 'euler73': [1, -8, 162, -584, 5329], 'euler79': [1, -30, 383, -2370, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, 20, 278, 1780, 7921], 'euler97': [1, 4, 198, 388, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 5, 0, 9], [1, 0, 9, 0, 25], [1, 4, 18, 28, 49], [1, 0, 13, 0, 121], [1, 0, 25, 0, 169], [1, -16, 98, -272, 289], [1, 0, 38, 0, 361], [1, -8, 62, -184, 529], [1, 0, -1, 0, 0], [1, 6, 71, 186, 961], [1, 0, 10, 0, 1369], [1, -4, 86, -164, 1681], [1, 0, -35, 0, 1849], [1, -26, 263, -1222, 2209], [1, 0, -15, 0, 2809], [1, 0, 118, 0, 3481], [1, 0, 58, 0, 3721], [1, 0, -10, 0, 4489], [1, -4, 146, -284, 5041], [1, -8, 162, -584, 5329], [1, -30, 383, -2370, 6241], [1, 0, 150, 0, 6889], [1, 20, 278, 1780, 7921], [1, 4, 198, 388, 9409]], 'index': 0, 'instance_types': ['ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.8.1/1682.1/a', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-1682.1-a'], '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': '4-107648-1.1-c1e2-0-0', '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': '4-107648-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.618601896325029, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2300409750675073379, 'z1': {'__RealLiteral__': 0, 'data': '0.907460307275556682567938804358009', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9553287
{'Lhash': '708012337630994629,1592397413044078750', 'Lhash_array': ['708012337630994629', '1592397413044078750'], 'label': '4-107648-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-1682.1-a'}
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id: 9552861
{'Lhash': '708012337630994629,1592397413044078750', 'Lhash_array': ['708012337630994629', '1592397413044078750'], 'label': '4-107648-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/1682.1/a'}