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lfunc_lfunctions • Show schema
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{'Lhash': '2498651600260744077257618637596', 'a10': [-1.1222477142024725, -2.6352699294310638], 'a2': [0, -1.2809439904223976], 'a3': [0, -1.0], 'a4': [0.3591824934007443, 0], 'a5': [2.057287398305425, -0.8761099022232859], 'a6': [-1.2809439904223976, 0], 'a7': [0, -1.0], 'a8': [0, -3.0219806372314113], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.222721433457888, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [-2.057287398305425, 0.8761099022232859]]], [7, [[1.0, 0], [0, 1.0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '1155.694', 'coefficient_field': 'CDF', 'conductor': 1155, 'conductor_radical': 1155, 'conjugate': '1173991686834733100282290867596', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.2809439904223976], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-2.057287398305425, 0.8761099022232859]], [[1.0, 0], [0, 1.0]], 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'positive_zeros': ['1.97108856321362031002736671427351', '2.84628019105511542843250963278265', '4.31631900590688207994269160902677', '5.33577067395640060226334428247341', '5.94882734694534761571507988005560', '6.82468373263804928789114098665229', '7.37787488261746491031226228616524', '8.670526645088723377366928528982091', '9.242235013545378725273271331378259', '9.915953305244479486878147944888235'], 'prelabel': '2-1155-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.8718496585197751, 'root_number': '-0.92004689437292318403684049387204790677358112308708393676 + 0.39180825942639229860101921764333793725484705520924314601*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.43592482925988757', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97108856321362031002736671427', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.84628019105511542843250963278', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31631900590688207994269160903', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.222721433457888, 'bad_primes': [3, 5, 7, 11], 'central_character': '5.4', 'conductor': 1155, 'conductor_radical': 1155, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1155/2/c/f/694/7'], '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': '2-1155-5.4-c1-0-51', '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': '2-1155-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.036893385263613, 'root_angle': 0.43592482925988757, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97108856321362031002736671427', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2498651600260744077257618637596', 'Lhash_array': ['2498651600260744077257618637596'], 'label': '2-1155-5.4-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1155/2/c/f/694/7'}