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lfunc_lfunctions • Show schema
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{'Lhash': '1533839445841964550441054745186', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.5244379562000208, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.41178332170387, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.1', 'coefficient_field': 'CDF', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.5244379562000208, 0], [7.0, 0]], [[1.0, 0], [-3.102775049096641, 0], [11.0, 0]], [[1.0, 0], [-6.729988054393303, 0], [13.0, 0]], [[1.0, 0], [2.57833709289662, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.57833709289662, 0], [23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 47, 'label': '2-4560-1.1-c1-0-47', 'leading_term': '3.64297780456708035889734393723', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4560/2/a/bv/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [3.64297780456708, 3.6359841632039873, 3.6149192092268265, 3.5795398336471393, 3.529470157750902, 3.4642433465505333, 3.383356114123147, 3.286332414775645, 3.172792447902221, 3.0425230469747775, 2.895545716284918, 2.7321789460999883, 2.5530919016383815, 2.3593470817441684, 2.1524300379526036, 1.9342647129829005, 1.7072133952644728, 1.4740606992529222, 1.2379813813034268, 1.00249219933986, 0.7713884302810952, 0.5486660764263851, 0.3384312198765291, 0.1447984166912846, -0.02821955041356527, -0.17682783422096676, 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'5.48611932564853712236000164267951', '6.09673648229398328550240466066797', '6.97661411185707920819498895303979', '7.60117422152673220125750841729167', '8.612146907409701480637514716343670'], 'prelabel': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20998597371058726737610643989', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73957985921372683655496556478', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90736949869887144200165221752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.41178332170387, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4560/2/a/bv/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': '2-4560-1.1-c1-0-47', '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': '2-4560-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20998597371058726737610643989', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1533839445841964550441054745186', 'Lhash_array': ['1533839445841964550441054745186'], 'label': '2-4560-1.1-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4560/2/a/bv/1/2'}