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lfunc_lfunctions • Show schema
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{'Lhash': '3419383036341424405049956058087', 'a10': [2.302775637731995, 0.0], 'a2': [-1.0, 0.0], 'a3': [3.302775637731995, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.302775637731995, 0.0], 'a6': [-3.302775637731995, 0.0], 'a7': [-2.605551275463989, 0.0], 'a8': [-1.0, 0.0], 'a9': [7.908326913195984, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 37], 'central_character': '74.1', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3419383036341424405049956058087', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.302775637731995, 0], [3.0, 0]], [[1.0, 0], [2.302775637731995, 0], [5.0, 0]], [[1.0, 0], [2.605551275463989, 0], [7.0, 0]], [[1.0, 0], [2.302775637731995, 0], [11.0, 0]], [[1.0, 0], [-1.3027756377319946, 0], [13.0, 0]], [[1.0, 0], [6.0, 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'11.00558376992052385392883780627012', '12.72332663292485060593600802017617', '13.45578658411617519237182903232250', '14.85715955519318499835389416333048'], 'prelabel': '2-74-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, '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': '2.69741759734566796341285138193', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93060845224348257138198386426', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.96682723610503755952759087238', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/a/a/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': '2-74-1.1-c1-0-2', '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': '2-74-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.69741759734566796341285138193', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3419383036341424405049956058087', 'Lhash_array': ['3419383036341424405049956058087'], 'label': '2-74-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/a/a/1/2'}