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lfunc_lfunctions • Show schema
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{'Lhash': '1445919304169060170739884938112', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -0.378937381963012], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.397532625703008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.1729', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'conjugate': '834957902787774935230540868214', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 5.0]], [[1.0, 0], [0, 0.378937381963012], [-7.0, 0]], [[1.0, 0], [0, 0], [0, 11.0]], [[1.0, 0], [-2.4641016151377544, 2.4641016151377544], [0, -13.0]], [[1.0, 0], [0, 0], [17.0, 0]], [[1.0, 0], [2.449489742783178, -2.449489742783178], [0, -19.0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [0, 0], [0, -29.0]], [[1.0, 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'8.498541613607827328473377871966265', '8.980454838758594229273635865203723'], 'prelabel': '2-48e2-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.2916666666666667, 'root_number': '0.6087614290087206394160975428981640045163937119624752301 + 0.7933533402912351645797769615012992766286759210519102343*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14583333333333334', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14062921116334031518339444598', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32945836844049919345298260651', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36356506937563210708842703101', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.397532625703008, 'bad_primes': [2, 3], 'central_character': '16.5', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/2/k/g/1729/2'], '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': '2-48e2-16.5-c1-0-25', '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': '2-48e2-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.289234503463644, 'root_angle': 0.14583333333333334, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14062921116334031518339444598', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1445919304169060170739884938112', 'Lhash_array': ['1445919304169060170739884938112'], 'label': '2-48e2-16.5-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/2/k/g/1729/2'}