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lfunc_lfunctions • Show schema
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{'Lhash': '2426393710778959759893800338460', 'a10': [6.393813607309654, 0], 'a2': [0, 2.0], 'a3': [3.0, 0], 'a4': [-4.0, 0], 'a5': [0, -3.196906803654827], 'a6': [0, 6.0], 'a7': [0, -34.68371275574165], 'a8': [0, -8.0], 'a9': [9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.82793674582101, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -2.0]]], [3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '1014.337', 'coefficient_field': 'CDF', 'conductor': 1014, 'conductor_radical': 78, 'conjugate': '368115708286904739051409300692', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 3.196906803654827], [-125.0, 0]], [[1.0, 0], [0, 34.68371275574165], [-343.0, 0]], [[1.0, 0], [0, 63.003005017542044], [-1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [79.6228270885426, 0], [4913.0, 0]], [[1.0, 0], [0, -35.04341352440265], 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['1.91408713910766010580732749279355', '2.30884608212862595087776990522468', '3.34228362858785389469859930357711', '4.63858085906899478183040385900846', '5.30360799889398584258861768556027', '6.60549504705343440885725738888933', '7.42353726623986605627936858021019', '8.681221887215644179749230201585830', '9.056258005074757002914829414787878', '9.709426895669889298333095304613865'], 'prelabel': '2-1014-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.734852082995577, 'root_angle': 0.7568621317591576, 'root_number': '-0.72218511752397428955250087569773938357120758075148748103 + 0.6916998308709374287080491938581327632030041385121643854*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3784310658795788', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91408713910766010580732749279', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30884608212862595087776990522', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34228362858785389469859930358', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.82793674582101, 'bad_primes': [2, 3, 13], 'central_character': '13.12', 'conductor': 1014, 'conductor_radical': 78, 'degree': 2, 'index': 76, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1014/4/b/q/337/9'], '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': '2-1014-13.12-c3-0-76', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1014-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.734852082995577, 'root_angle': 0.3784310658795788, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91408713910766010580732749279', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2426393710778959759893800338460', 'Lhash_array': ['2426393710778959759893800338460'], 'label': '2-1014-13.12-c3-0-76', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1014/4/b/q/337/9'}