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lfunc_lfunctions • Show schema
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{'Lhash': '2589693636594848139000780225592', 'a10': [0.0, 0.0], 'a2': [2.302775637731995, 0.0], 'a3': [-1.3027756377319946, 0.0], 'a4': [3.302775637731995, 0.0], 'a5': [0.0, 0.0], 'a6': [-3.0, 0.0], 'a7': [4.302775637731995, 0.0], 'a8': [3.0, 0.0], 'a9': [-1.3027756377319946, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '275.1', 'coefficient_field': 'CDF', 'conductor': 275, 'conductor_radical': 55, 'conjugate': '2589693636594848139000780225592', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.302775637731995, 0], [2.0, 0]], [[1.0, 0], [1.3027756377319946, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.302775637731995, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.0, 0], [13.0, 0]], [[1.0, 0], [3.908326913195984, 0], [17.0, 0]], [[1.0, 0], [1.0, 0], 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'8.843291587354579709770843927932990', '10.83460400463024479003249245451233', '11.24933123400379278318604389691709', '11.75264289167998397713824240051260'], 'prelabel': '2-275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04290806640930588735681357089', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79894828953799276588994147306', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80175039695978728299343645479', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 275, 'conductor_radical': 55, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/2/a/f/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': '2-275-1.1-c1-0-7', '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': '2-275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04290806640930588735681357089', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2589693636594848139000780225592', 'Lhash_array': ['2589693636594848139000780225592'], 'label': '2-275-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/2/a/f/1/2'}