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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1441.1000', 'a10': [-0.9895063994510511, 0.14448904956922132], 'a2': [-0.8619696668800493, -0.5069598538135904], 'a3': [0.8364701380102267, 0.54801250735467], 'a4': [0.4859834132426061, 0.873968032626518], 'a5': [0.7796743540632224, -0.6261851975383137], 'a6': [-0.44319154559924134, -0.8964269372957038], 'a7': [-0.7155989607441211, -0.698511365248937], 'a8': [0.024163745236132288, -0.9997080140801929], 'a9': [0.39936458356569554, 0.9167921953165824], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.1000', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.1209', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^76', 'a^12', 'a^22', 'a^116', 'a^88', 'a^81', 'a^98', 'a^24', 'a^62', 0, 'a^34', 'a^3', 'a^27', 'a^128', 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'197.16944929014233343011146806443', '197.561368181733831000689037298815', '197.98403302025088647207134918649', '198.70483404211675081085235034622', '199.357910016623048875695988720788', '199.83999964877415281442697182069'], 'prelabel': '1-1441-1441.1000-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.09799898040516887, 'root_number': '0.952980312180248153734156674015-0.303032217093887184597099481216*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0489994902026', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(130)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.10381035111680602700811130811-0.137806164533466342747666893169*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.981412214989', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.86167945449', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.82279583362', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.1000', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/1000'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1441-1441.1000-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1441-1441.1000-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': -0.048999490202584435, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.981412214989', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1441.1000', 'Lhash_array': ['dirichlet_L_1441.1000'], 'label': '1-1441-1441.1000-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/1000'}
Lfunction data - 1-1441-1441.1000-r0-0-0