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lfunc_lfunctions • Show schema
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{'Lhash': '1438386919358660363713098723798', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.7622905057289092, 1.5552855637713494], 'a4': [0, 0], 'a5': [0.7054632426477496, 1.2218981791381935], 'a6': [0, 0], 'a7': [1.171234798148486, -2.028638177985856], 'a8': [0, 0], 'a9': [-1.8378263697511277, -2.371158837920267], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7622905057289092, -1.5552855637713494]]]], 'bad_primes': [2, 3], 'central_character': '1152.385', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1254682520857312889874924613202', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7622905057289092, -1.5552855637713494]], [[1.0, 0], [-0.7054632426477496, -1.2218981791381935], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.171234798148486, 2.028638177985856], [-3.5, 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'7.977285399981125173854127503642140', '8.861695304098726656588478068376881', '9.616798388388190806047472163658435'], 'prelabel': '2-1152-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.15432430801370325, 'root_number': '0.8847569357276033560136650923908954102529254967779937265 - 0.4660527488191669749309476585036797273280291213519676010*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07716215400685163', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13468720726333532403441617160', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03527863658142283191770112420', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37341071456529645510869600100', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/i/e/385/2'], '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': '2-1152-9.7-c1-0-25', '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': '2-1152-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.07716215400685163, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13468720726333532403441617160', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1438386919358660363713098723798', 'Lhash_array': ['1438386919358660363713098723798'], 'label': '2-1152-9.7-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/i/e/385/2'}