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lfunc_lfunctions • Show schema
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{'Lhash': '999635660659751810247089643884', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.114907541476756, 0.7260620434954195], 'a6': [0.0, 0.0], 'a7': [0.0, 4.057046976053768], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [-2.114907541476756, -0.7260620434954195]]]], 'bad_primes': [2, 3, 5], 'central_character': '480.49', 'coefficient_field': 'CDF', 'conductor': 480, 'conductor_radical': 30, 'conjugate': '2429259259762640963325874442878', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.114907541476756, -0.7260620434954195]], [[1.0, 0], [0, -4.057046976053768], [-7.0, 0]], [[1.0, 0], [0, 0.985938793316794], [-11.0, 0]], [[1.0, 0], [4.945667817990511, 0], [13.0, 0]], [[1.0, 0], [0, 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'4.95931229340575094338685669196575', '6.14503190504333502210334240580742', '7.08900096895442126730275693543599', '7.81067370261997413161506546217517', '9.349628622178159898479507360808818', '10.02190843560214306704268834138933', '10.53042622649115316451913972648448'], 'prelabel': '2-480-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': -0.4676291719288548, 'root_number': '0.10152075520897064 - 0.9948334213634965*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.233814585964', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78857349215925599222326520489', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44669549968000715208754961176', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.27143611009554372742365879392', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8328192970214605, 'bad_primes': [2, 3, 5], 'central_character': '40.29', 'conductor': 480, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/480/2/d/a/49/6'], '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': '2-480-40.29-c1-0-1', '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': '2-480-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9577587433137569, 'root_angle': -0.2338145859644274, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78857349215925599222326520489', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '999635660659751810247089643884', 'Lhash_array': ['999635660659751810247089643884'], 'label': '2-480-40.29-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/480/2/d/a/49/6'}