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lfunc_lfunctions • Show schema
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{'Lhash': '851840523002611237383668601533', 'a10': [0, 0], 'a2': [0, 0], 'a3': [7.710480276108493, -13.354943588977616], 'a4': [0, 0], 'a5': [60.26125064294385, -104.37554784122142], 'a6': [0, 0], 'a7': [-1390.3197051168881, 0], 'a8': [0, 0], 'a9': [974.5969878234838, 1688.0514998138603], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.741261936793265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1273.7543568202723, 29870.54215842895]]]], 'bad_primes': [2, 19], 'central_character': '76.49', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '1568217554003029631550883144959', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-7.710480276108493, 13.354943588977616], [-1093.5, -1893.9975580765674]], [[1.0, 0], [-60.26125064294385, 104.37554784122142], [-39062.5, -67658.23467065927]], [[1.0, 0], [1390.3197051168881, 0], [823543.0, 0]], [[1.0, 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'6.02031751638323908569132635999387', '6.79635449992865322526919971844681', '8.527152537314246670860963308309940', '9.811539942458821803749760813805083', '10.31824174480254865065550538867308', '12.05124556640489572732800743486797', '12.90679278942201291223633038424096'], 'prelabel': '2-76-19.11-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8725005835600745, 'root_angle': -0.22085464625633083, 'root_number': '0.7687990157382595 - 0.6394904795224738*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11042732312816543', 'prec': 67}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67198368607978002999732885089846', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.91141992710475424248530433364042', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.94131084739515608792399335324594', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.741261936793265, 'bad_primes': [2, 19], 'central_character': '19.11', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/8/e/a/49/7'], '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': '2-76-19.11-c7-0-3', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-76-19.11-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8725005835600745, 'root_angle': -0.11042732312816542, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67198368607978002999732885089846', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '851840523002611237383668601533', 'Lhash_array': ['851840523002611237383668601533'], 'label': '2-76-19.11-c7-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/8/e/a/49/7'}