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lfunc_lfunctions • Show schema
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{'Lhash': '1171217770490515426080110013626', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.9980267284282716, 0.06279051952931337], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.12533323356430426, 0.9921147013144779], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.9980267284282716, -0.06279051952931337]]]], 'bad_primes': [2, 5], 'central_character': '4000.513', 'coefficient_field': 'CDF', 'conductor': 4000, 'conductor_radical': 10, 'conjugate': '1688995354652093718057079465105', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.12533323356430426, -0.9921147013144779]], [[1.0, 0], [-0.9980267284282716, -0.06279051952931337]], [[1.0, 0], [0, 0], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [0, 0], [-0.6374239897486897, 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'4.78253412800832602722936549718580', '5.60599373371858127891340378521652', '6.46530090663555683690812610498647', '6.93301279055503909094400413184656', '7.69855555758460980729590990343604', '8.812417774399156650407433007622012'], 'prelabel': '2-4000-125.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.20199999999999999, 'root_number': '0.80530788571112195194530380635271 - 0.59285682016105924552919624078776*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.101', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.923927910640083246920424549825', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.27373952278604018903512389007', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.79742748460050036153195778205', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'bad_primes': [2, 5], 'central_character': '125.13', 'conductor': 4000, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4000/1/cq/a/513/1'], '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': '2-4000-125.13-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-4000-125.13-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.10099999999999999, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.923927910640083246920424549825', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1171217770490515426080110013626', 'Lhash_array': ['1171217770490515426080110013626'], 'label': '2-4000-125.13-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4000/1/cq/a/513/1'}