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lfunc_lfunctions • Show schema
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{'Lhash': '1596197784673476583698506243987', 'a10': [0.0, 0.0], 'a2': [-2.292692055459261, 0.0], 'a3': [-1.4828574183460224, 0.0], 'a4': [3.2564368611660104, 0.0], 'a5': [0.0, 0.0], 'a6': [3.399735422420755, 0.0], 'a7': [-1.3913501099173051, 0.0], 'a8': [-2.880622809781482, 0.0], 'a9': [-0.8011338768561695, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.583918217287646, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 43], 'central_character': '1075.1', 'coefficient_field': 'CDF', 'conductor': 1075, 'conductor_radical': 215, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.292692055459261, 0], [2.0, 0]], [[1.0, 0], [1.4828574183460224, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3913501099173051, 0], [7.0, 0]], [[1.0, 0], [-1.8742075282633277, 0], [11.0, 0]], [[1.0, 0], [-2.05757073802218, 0], [13.0, 0]], [[1.0, 0], [2.7493426240301417, 0], [17.0, 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'6.44881657844598981212936898655718', '6.88125527784060315662560806510381', '8.096595392060732911986812215913554', '8.673647323794274397562055488478604', '9.519331950726118059128543128282333'], 'prelabel': '2-1075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.929832455497694, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25917802932929242149759850196', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68539015886119657550498911374', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13237736244766444453514015434', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.583918217287646, 'bad_primes': [5, 43], 'central_character': '1.1', 'conductor': 1075, 'conductor_radical': 215, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1075/2/a/s/1/2'], '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': '2-1075-1.1-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.929832455497694, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25917802932929242149759850196', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1596197784673476583698506243987', 'Lhash_array': ['1596197784673476583698506243987'], 'label': '2-1075-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1075/2/a/s/1/2'}