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lfunc_lfunctions • Show schema
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{'Lhash': '2339800671979874489344026407812', 'a10': [-1.1010213651430907, 0.0], 'a2': [-0.2995416514108558, 0.0], 'a3': [3.0177434965697425, 0.0], 'a4': [-1.9102747990700573, 0.0], 'a5': [3.675687037035505, 0.0], 'a6': [-0.903939870496871, 0.0], 'a7': [-0.7831557345351897, 0.0], 'a8': [1.1712901707836976, 0.0], 'a9': [6.1067758110889745, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [1.0, 0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [13, 31], 'central_character': '403.1', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '2339800671979874489344026407812', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2995416514108558, 0], [2.0, 0]], [[1.0, 0], [-3.0177434965697425, 0], [3.0, 0]], [[1.0, 0], [-3.675687037035505, 0], [5.0, 0]], [[1.0, 0], [0.7831557345351897, 0], [7.0, 0]], [[1.0, 0], [1.4771667507677397, 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'5.34591239953407421839771722474447', '6.70847664759941524155761044549292', '7.87192162869237479144096174485127', '8.840146597104196439587687571165253', '9.351692807441014053677075641791250', '9.827051263715422338893085395216703', '10.79972994508412708630134820077560'], 'prelabel': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84577727613477550226818928670', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82601134736842073380180582416', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18690033350946735162270303109', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '1.1', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/a/c/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': '2-403-1.1-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-403-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84577727613477550226818928670', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2339800671979874489344026407812', 'Lhash_array': ['2339800671979874489344026407812'], 'label': '2-403-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/a/c/1/3'}