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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_6145.1069', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.5761349621863143, 0.8173545774916625], 'a3': [0.453534547898026, -0.8912386963451111], 'a4': [-0.33613701069314844, 0.9418130971919397], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9897551376987948, -0.14277523384270735], 'a7': [-0.3838648995641643, -0.9233892672554701], 'a8': [-0.9634555300765498, 0.26786832878284494], 'a9': [-0.5886128277258663, -0.8084150784322122], 'algebraic': True, 'analytic_conductor': 660.3719628629708, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [1229, [1]]], 'bad_primes': [5, 1229], 'central_character': '6145.1069', 'coeff_info': ['x^1228 - 1', '0.999986910228664 + 0.00511657808795007*I', '\\\\zeta_{1228}'], 'conductor': 6145, 'conductor_radical': 6145, 'conjugate': 'dirichlet_L_6145.1759', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^187', 'a^1013', 'a^374', 0, 'a^1200', 'a^844', 'a^561', 'a^798', 0, 'a^649', 'a^159', 'a^1029', 'a^1031', 0, 'a^748', 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[1, 'a^944'], [1, 'a^520'], [1, 'a^588']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-6145-6145.1069-r1-0-0', 'leading_term': '3.49180376375747107748859555013-0.261159774315729104896495310871*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/6145/1069', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.501556504229439, 2.0791848590153656, -0.25979967636958007, -0.9966139293077649, 1.1809754416252178, 4.681684370889312, 6.153679935213381, 4.028573153094385, 0.48745554798569435, -1.0068960829821254, 0.08050081801837637, 0.9061866522650599, -0.5940574242875062, -2.5982513722324363, -1.9331811394571279, 1.1715543193512943, 3.106366390632629, 1.8910600490016896, -0.17258360633822667, -0.16297177263296972, 1.1765691886961498, 1.1188466696960861, -0.41107569771210517, 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'199.05056067922497861276823921992', '199.66863811368419705037305880706'], 'prelabel': '1-6145-6145.1069-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 660.3719628629708, 'root_angle': -0.04752572366009819, 'root_number': '0.988874480811124550181871668418-0.148752348554666066453478824243*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(1228)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.51356717926169733303380796943+0.0695545126121144603746517963905*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.585247751017', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.12580228703', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.55559564676', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 660.3719628629708, 'bad_primes': [5, 1229], 'central_character': '6145.1069', 'conductor': 6145, 'conductor_radical': 6145, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6145/1069'], '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': '1-6145-6145.1069-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-6145-6145.1069-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 660.3719628629708, 'root_angle': -0.023762861830049095, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.585247751017', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_6145.1069', 'Lhash_array': ['dirichlet_L_6145.1069'], 'label': '1-6145-6145.1069-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6145/1069'}
Lfunction data - 1-6145-6145.1069-r1-0-0