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lfunc_lfunctions • Show schema
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{'Lhash': '675504524449644159593424741410,3007207058928643896007988372682', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 32, 'a5': 0, 'a6': 0, 'a7': -211, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 102.09446657181874, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, 211, 16807]]], 'bad_primes': [3, 7], 'central_character': '63.1', 'coefficient_field': '1.1.1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 4, 'euler_factors': [[1, 0, -32, 0, 1024], [1], [1, 0, -3125, 0, 9765625], [1, 211, 16807], [1, 0, -161051, 0, 25937424601], [1, 854, 924915, 317084222, 137858491849], [1, 0, -1419857, 0, 2015993900449], [1, 3143, 7402350, 7782379157, 6131066257801], [1, 0, -6436343, 0, 41426511213649], [1, 0, 41022298, 0, 420707233300201], [1, 2723, -21214422, 77957178173, 819628286980801], [1, -6661, -24975036, -461900097577, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, -44950, 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{'algebraic': True, 'analytic_conductor': 102.09446657181874, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 32, 0, 0, -211, 0, 0, 0, 0, 0, -854, 0, 0, 0, 0, 0, -3143, 0, 0, 0, 0, 0, 3125, 0, 0, -6752, 0, 0, -2723, 0, 0, 0, 0, 0, 6661, 0, 0, 0, 0, 0, 44950, 0, 0, 0, 0, 0, 27714, 0, 0, -27328, 0, 0, 0, 0, 0, 0, 0, 0, 38626, 0, 0, -32768, 0, 0, 37939, 0, 0, 0, 0, 0, 78127, 0, 0, -100576, 0, 0, -90857, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180194, 0, 0, 0, 0, 0, -268772, 0, 0, 100000], 'euler11': [1, 0, -161051, 0, 25937424601], 'euler13': [1, 854, 924915, 317084222, 137858491849], 'euler17': [1, 0, -1419857, 0, 2015993900449], 'euler19': [1, 3143, 7402350, 7782379157, 6131066257801], 'euler2': [1, 0, -32, 0, 1024], 'euler23': [1, 0, -6436343, 0, 41426511213649], 'euler29': [1, 0, 41022298, 0, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 2723, -21214422, 77957178173, 819628286980801], 'euler37': [1, -6661, -24975036, -461900097577, 4808584372417849], 'euler41': [1, 0, 231712402, 0, 13422659310152401], 'euler43': [1, -44950, 799142511, -6608029512850, 21611482313284249], 'euler47': [1, 0, -229345007, 0, 52599132235830049], 'euler5': [1, 0, -3125, 0, 9765625], 'euler53': [1, 0, -418195493, 0, 174887470365513049], 'euler59': [1, 0, -714924299, 0, 511116753300641401], 'euler61': [1, -38626, 647371575, -32623376722426, 713342911662882601], 'euler67': [1, -37939, 89242614, -51222396434473, 1822837804551761449], 'euler7': [1, 211, 16807, 0, 0], 'euler71': [1, 0, 3608458702, 0, 3255243551009881201], 'euler73': [1, -78127, 4030756536, -161962864346311, 4297625829703557649], 'euler79': [1, 90857, 5177938050, 279572113243943, 9468276082626847201], 'euler83': [1, 0, 7878081286, 0, 15516041187205853449], 'euler89': [1, 0, -5584059449, 0, 31181719929966183601], 'euler97': [1, 268772, 35234277510, 2308036615554404, 73742412689492826049], 'euler_factors': [[1, 0, -32, 0, 1024], [1, 0, 0, 0, 0], [1, 0, -3125, 0, 9765625], [1, 211, 16807, 0, 0], [1, 0, -161051, 0, 25937424601], [1, 854, 924915, 317084222, 137858491849], [1, 0, -1419857, 0, 2015993900449], [1, 3143, 7402350, 7782379157, 6131066257801], [1, 0, -6436343, 0, 41426511213649], [1, 0, 41022298, 0, 420707233300201], [1, 2723, -21214422, 77957178173, 819628286980801], [1, -6661, -24975036, -461900097577, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, -44950, 799142511, -6608029512850, 21611482313284249], [1, 0, -229345007, 0, 52599132235830049], [1, 0, -418195493, 0, 174887470365513049], [1, 0, -714924299, 0, 511116753300641401], [1, -38626, 647371575, -32623376722426, 713342911662882601], [1, -37939, 89242614, -51222396434473, 1822837804551761449], [1, 0, 3608458702, 0, 3255243551009881201], [1, -78127, 4030756536, -161962864346311, 4297625829703557649], [1, 90857, 5177938050, 279572113243943, 9468276082626847201], [1, 0, 7878081286, 0, 15516041187205853449], [1, 0, -5584059449, 0, 31181719929966183601], [1, 268772, 35234277510, 2308036615554404, 73742412689492826049]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/63/6/e/b'], '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': '4-63e2-1.1-c5e2-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-63e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.178707386378586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 691163857172378441, 'z1': {'__RealLiteral__': 0, 'data': '0.53287911063823539317724046957', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '675504524449644159593424741410,3007207058928643896007988372682', 'Lhash_array': ['675504524449644159593424741410', '3007207058928643896007988372682'], 'label': '4-63e2-1.1-c5e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/63/6/e/b'}