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lfunc_lfunctions • Show schema
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{'Lhash': '1501141157980543295156765440472', 'a10': [-17.655644370746373, 0.0], 'a2': [-3.531128874149275, 0.0], 'a3': [3.0, 0.0], 'a4': [4.468871125850725, 0.0], 'a5': [5.0, 0.0], 'a6': [-10.593386622447824, 0.0], 'a7': [-7.0, 0.0], 'a8': [12.468871125850725, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.195200550602768, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [7, [[1.0, 0], [7.0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.1', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '1501141157980543295156765440472', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.531128874149275, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [2.9377422517014504, 0], [1331.0, 0]], [[1.0, 0], [19.06225774829855, 0], [2197.0, 0]], [[1.0, 0], [-122.4980619863884, 0], 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'5.17693363736470717283113350431378', '7.02876736555687686837865597329411', '7.920982822273216246053602816815908', '9.153033322238177666395213432805539', '9.750487568024786448080816428638023', '10.67678270051248069312468546548277', '12.18250555097709804072936119577021', '13.40546592608703245871921898326225'], 'prelabel': '2-105-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18419157274904927371218082605', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.08354544168682833867216834671', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.17693363736470717283113350431', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.195200550602768, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/4/a/f/1/1'], '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': '2-105-1.1-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-105-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18419157274904927371218082605', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1501141157980543295156765440472', 'Lhash_array': ['1501141157980543295156765440472'], 'label': '2-105-1.1-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/4/a/f/1/1'}