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lfunc_lfunctions • Show schema
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{'Lhash': '1172729629214234144521698851076', 'a10': [0, 0], 'a2': [0, 0], 'a3': [429.4615206811522, -429.4615206811522], 'a4': [0, 0], 'a5': [2473.083165706088, -2473.083165706088], 'a6': [0, 0], 'a7': [-198740.09997071637, 0], 'a8': [0, 0], 'a9': [0, 162566.6045084646], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 116.99120861136457, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '128.95', 'coefficient_field': 'CDF', 'conductor': 128, 'conductor_radical': 2, 'conjugate': '436947060287875596929136791175', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-429.4615206811522, 429.4615206811522], [0, -531441.0]], [[1.0, 0], [-2473.083165706088, 2473.083165706088], [0, -244140625.0]], [[1.0, 0], [198740.09997071637, 0], [13841287201.0, 0]], [[1.0, 0], [-1130312.2427904082, -1130312.2427904082], [0, 3138428376721.0]], [[1.0, 0], [1221424.8848571272, 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'9.997187943393453230284614999671674', '11.20724666781335588786301013833923'], 'prelabel': '2-2e7-16.3-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.816247436674356, 'root_angle': 0.5680921319769524, 'root_number': '-0.2122899626392139858111106972269939656581671714945587066 + 0.9772067190531597701147002965912892381415871571737376335*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2840460659884762', 'prec': 60}, 'spectral_label': 'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.925120556881442278741753055472', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.84473613599358846435420014748', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.32914628394882122199451494610', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 116.99120861136457, 'bad_primes': [2], 'central_character': '16.3', 'conductor': 128, 'conductor_radical': 2, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/128/13/f/b/95/16'], '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': '2-2e7-16.3-c12-0-36', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-2e7-16.3-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.816247436674356, 'root_angle': 0.2840460659884762, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '0.925120556881442278741753055472', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1172729629214234144521698851076', 'Lhash_array': ['1172729629214234144521698851076'], 'label': '2-2e7-16.3-c12-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/128/13/f/b/95/16'}