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lfunc_lfunctions • Show schema
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{'Lhash': '1552417965735953822215804697624', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.7071067811865476, 0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1200.1007', 'coefficient_field': 'CDF', 'conductor': 1200, 'conductor_radical': 30, 'conjugate': '1302820154547009200972227983474', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.224744871391589, 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'8.696971499392248197459982456699450', '9.325262658929576262135558019632966', '10.08507196645866072445573421240173'], 'prelabel': '2-1200-60.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': 0.20841136706739585, 'root_number': '0.79320407846348717581587558542018 + 0.60895590144844649487054104111660*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10420568353369791', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22464184173182622059227492847', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26709994203518284727793812159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89028868211495220529802022498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5988780151596029, 'bad_primes': [2, 3, 5], 'central_character': '60.47', 'conductor': 1200, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1200/1/bj/b/1007/2'], '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': '2-1200-60.47-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1200-60.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7738720922475515, 'root_angle': 0.10420568353369793, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22464184173182622059227492847', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1552417965735953822215804697624', 'Lhash_array': ['1552417965735953822215804697624'], 'label': '2-1200-60.47-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1200/1/bj/b/1007/2'}