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lfunc_lfunctions • Show schema
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{'Lhash': '1384213456092563242769813753930', 'a10': [0.0, 0.0], 'a2': [-1.224744871391589, 0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [2.1513358700666244e-79, -1.6802385325461643e-79], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9807890351403867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '3969.3509', 'coefficient_field': 'CDF', 'conductor': 3969, 'conductor_radical': 21, 'conjugate': '745114107268732473279074982909', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.224744871391589, -0.7071067811865476], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 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-0.7294265020600201, -1.401857289102493], 'positive_zeros': ['1.09195187999228471846735585428999', '2.12283783571082670787491667006105', '2.75948145275648521759044180892528', '3.99701773176668348038927274078831', '4.85539147311880201060511145955801', '5.66186782385849580269429033617096', '6.94704489609035353981663165134569', '7.21952114621616392550246030328498', '8.236134793495151317261377067565174', '8.762745365432376273881345224010858'], 'prelabel': '2-63e2-63.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4074050714490078, 'root_angle': 0.0959014616634478, 'root_number': '0.95495645335653963306289494723989 + 0.29674597249617246352945442345290*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0479507308317239', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09195187999228471846735585429', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.12283783571082670787491667006', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75948145275648521759044180893', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9807890351403867, 'bad_primes': [3, 7], 'central_character': '63.2', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3969/1/n/b/3509/1'], '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': '2-63e2-63.2-c0-0-3', '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': '2-63e2-63.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4074050714490078, 'root_angle': 0.0479507308317239, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09195187999228471846735585429', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1384213456092563242769813753930', 'Lhash_array': ['1384213456092563242769813753930'], 'label': '2-63e2-63.2-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3969/1/n/b/3509/1'}