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lfunc_lfunctions • Show schema
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{'Lhash': '629889693150701246621592276010', 'a10': [1.0694661999564836, 0.0], 'a2': [-0.4498508337888554, 0.0], 'a3': [1.972895758711614, 0.0], 'a4': [-1.7976342273394716, 0.0], 'a5': [-2.377379610367588, 0.0], 'a6': [-0.887508802034916, 0.0], 'a7': [-0.2368970013218793, 0.0], 'a8': [1.708368923593757, 0.0], 'a9': [0.8923176747422752, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4498508337888554, 0], [2.0, 0]], [[1.0, 0], [-1.972895758711614, 0], [3.0, 0]], [[1.0, 0], [2.377379610367588, 0], [5.0, 0]], [[1.0, 0], [0.2368970013218793, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'2.79160336828598752069597803734404', '3.62213676965333629550607038077764', '4.14173051110912394239382875295702', '4.67243062838739999245401033886530', '5.77483985412143987406185176664071', '6.57518243017753395694078137886189', '7.73608076433338210512897510877705', '7.86581884285959628691727583220388'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49689535352824754508801367457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80082430947891189623015469967', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79160336828598752069597803734', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 103, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/33'], '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': '2-8041-1.1-c1-0-103', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49689535352824754508801367457', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '629889693150701246621592276010', 'Lhash_array': ['629889693150701246621592276010'], 'label': '2-8041-1.1-c1-0-103', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/33'}