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lfunc_lfunctions • Show schema
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{'Lhash': '2284571033679941851585470083281', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.5, -1.5388417685876268], 'a6': [0.0, 0.0], 'a7': [1.3090169943749475, -0.9510565162951535], 'a8': [0.0, 0.0], 'a9': [-0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6688734022447602, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [19, [[1.0, 0], [-0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.303', 'coefficient_field': 'CDF', 'conductor': 3344, 'conductor_radical': 418, 'conjugate': '1482127466535265906585345711100', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.5, 1.5388417685876268], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], 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'root_analytic_conductor': 1.2918488310343281, 'root_angle': 0.49300173434355704, 'root_number': '0.021983928808648741284673760754881 + 0.99975832423348007046960505176677*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.24650086717177852', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80220877367046157813403250965', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61128011374648330496064837222', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01076482370695393060820390116', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6688734022447602, 'bad_primes': [2, 11, 19], 'central_character': '836.303', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/1/bq/b/303/1'], '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': '2-3344-836.303-c0-0-5', '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': '2-3344-836.303-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2918488310343281, 'root_angle': 0.24650086717177852, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80220877367046157813403250965', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2284571033679941851585470083281', 'Lhash_array': ['2284571033679941851585470083281'], 'label': '2-3344-836.303-c0-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/1/bq/b/303/1'}