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lfunc_lfunctions • Show schema
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{'Lhash': '1816360701811574169011777949501', 'a10': [-0.3596249068005759, 0.6228886102458198], 'a2': [0.0, -1.3859525450877728], 'a3': [-1.4128870151086237, 2.447192095522472], 'a4': [0.07913554276472494, 0.0], 'a5': [-0.4494299696288461, -0.25947851394709964], 'a6': [3.3916921131080504, 1.9581943545112634], 'a7': [0.0, 0.0], 'a8': [0.0, -2.8815831970772185], 'a9': [-2.492499434925112, -4.31713565912701], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.426413659428095, 3.311396091106733]]]], 'bad_primes': [7, 13], 'central_character': '637.569', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '839239747305902033557333540453', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.3859525450877728], [-2.0, 0]], [[1.0, 0], [1.4128870151086237, -2.447192095522472], [-1.5, -2.598076211353316]], 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'group': 'GL2', 'index': 24, 'label': '2-637-91.23-c1-0-24', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/637/2/k/g/569/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0373376128996197, 1.1584654344040497, 1.2626219015658091, 1.3463141794760594, 1.4023348142178969, 1.4206195718056713, 1.3895947575970617, 1.2978106261845612, 1.1357175686874057, 0.8974786774417913, 0.5827074163066716, 0.19798771753982172, -0.2420011503254697, -0.7139528495931342, -1.1861871340504757, -1.619840929155197, -1.9710775199467536, -2.1942902153768458, -2.2461500930562392, -2.0902106675176677, -1.7016527751312496, -1.071650598748289, -0.21078495678616088, 0.849059432182956, 2.0547881067005953, 3.334489748321259, 4.602195324194953, 5.7647805060440795, 6.7304797843519095, 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'9.925616980344240788358817943938701', '11.15116867335201152579752772093805'], 'prelabel': '2-637-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.4605878907448029, 'root_number': '0.1235006710623016 + 0.9923444886969248*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.230293945372', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.43285594743895069642754447168', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77665333545400345021126672287', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86147627927550320893575784324', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.23', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/k/g/569/2'], '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': '2-637-91.23-c1-0-24', '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': '2-637-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.23029394537240144, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43285594743895069642754447168', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1816360701811574169011777949501', 'Lhash_array': ['1816360701811574169011777949501'], 'label': '2-637-91.23-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/k/g/569/2'}