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lfunc_lfunctions • Show schema
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{'Lhash': '2778794368790519849854060435673', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -3.116122749720017], 'a4': [0, 0], 'a5': [0, -1.0], 'a6': [0, 0], 'a7': [1.3840719421511398, 0], 'a8': [0, 0], 'a9': [-6.71022099132264, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]], [23, [[1.0, 0], [0.2870392159809587, -4.787233907852116]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1471', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'conjugate': '281381008172369691226899271311', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.116122749720017], [-3.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.3840719421511398, 0], [7.0, 0]], [[1.0, 0], [5.135212773269853, 0], [11.0, 0]], [[1.0, 0], [-5.71022099132264, 0], [13.0, 0]], [[1.0, 0], [0, 4.71022099132264], [-17.0, 0]], 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'4.18162948637782822785880487014105', '4.58660581216957190366418749228808', '5.88886084369113895803251805550036', '6.07611889604319801297382426892967', '7.74253791022267588499824482852760', '8.493384964489617213133227679029219', '8.858296305273361935265550515192819', '10.06212622620167216992096081148093'], 'prelabel': '2-1840-92.91-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': -0.6476038497502088, 'root_number': '-0.4472704452975649407724216466108422947623195221604483881 - 0.8943987638426821796990692521933879310558578069149578648*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32380192487510445', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19208224118713960449067571079', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22280917829305931924619417762', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18162948637782822785880487014', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '92.91', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/i/a/1471/1'], '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': '2-1840-92.91-c1-0-46', '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': '2-1840-92.91-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': -0.3238019248751044, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.19208224118713960449067571079', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2778794368790519849854060435673', 'Lhash_array': ['2778794368790519849854060435673'], 'label': '2-1840-92.91-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/i/a/1471/1'}