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lfunc_lfunctions • Show schema
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{'Lhash': '1233897058578093941751953306943', 'a10': [24.554603575078982, 0.0], 'a2': [-4.910920715015796, 0.0], 'a3': [0.0, 0.0], 'a4': [16.117142269171257, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-39.86264211640346, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 130.09921156265813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1', 'coefficient_field': 'CDF', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.910920715015796, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [12.002286833970699, 0], [1331.0, 0]], [[1.0, 0], [-46.95400823535836, 0], [2197.0, 0]], [[1.0, 0], [44.70799450216554, 0], [4913.0, 0]], [[1.0, 0], [31.74138338606363, 0], [6859.0, 0]], [[1.0, 0], 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'4.09907671594196140534705611449166', '5.27759087917955294089130096292935', '6.51213399151245181603647577998180', '6.84366525560363363172482914471645', '7.893326562427386680806748335807115', '8.425571162290477388780433527222980'], 'prelabel': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.973373150579459016674029112394', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.97366932482756549266064292955', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99886870079497091349977612725', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 130.09921156265813, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 2205, 'conductor_radical': 105, 'degree': 2, 'index': 105, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2205/4/a/bx/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': '2-2205-1.1-c3-0-105', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2205-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.406104136060573, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.973373150579459016674029112394', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1233897058578093941751953306943', 'Lhash_array': ['1233897058578093941751953306943'], 'label': '2-2205-1.1-c3-0-105', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2205/4/a/bx/1/1'}