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lfunc_lfunctions • Show schema
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{'Lhash': '1305495096647113547235906212289', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.2602367676030897, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.296110542062616, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 60.94182682264122, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [53, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 53], 'central_character': '7632.1', 'coefficient_field': 'CDF', 'conductor': 7632, 'conductor_radical': 318, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.2602367676030897, 0], [5.0, 0]], [[1.0, 0], [4.296110542062616, 0], [7.0, 0]], [[1.0, 0], [3.929516702047896, 0], [11.0, 0]], [[1.0, 0], [-4.425072339257545, 0], [13.0, 0]], [[1.0, 0], [-3.6853091068606343, 0], [17.0, 0]], [[1.0, 0], [5.022604724783298, 0], [19.0, 0]], [[1.0, 0], 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'5.73254856562844474743495991927435', '6.04101974556905678574004331909811', '6.79340337176560609419927992968871', '7.60686569486752496360971104628387'], 'prelabel': '2-7632-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.806524631527221, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02985404370263428677641485936', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57579863416062185286678446073', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06680886868476216197926825873', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 60.94182682264122, 'bad_primes': [2, 3, 53], 'central_character': '1.1', 'conductor': 7632, 'conductor_radical': 318, 'degree': 2, 'index': 63, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7632/2/a/bu/1/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-7632-1.1-c1-0-63', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-7632-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.806524631527221, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02985404370263428677641485936', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1305495096647113547235906212289', 'Lhash_array': ['1305495096647113547235906212289'], 'factors': ['2-7632-1.1-c1-0-63'], 'label': '2-7632-1.1-c1-0-63', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7632/2/a/bu/1/3'}