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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4031.4', 'a10': [0.8225573016153944, -0.568682236015159], 'a2': [0.8577808539338085, 0.5140155704106503], 'a3': [0.9536354202855305, -0.3009642589691335], 'a4': [0.4715759867508277, 0.8818254298442426], 'a5': [0.41326238066140636, -0.910611994611353], 'a6': [0.9727105204012866, 0.2320220754597679], 'a7': [-0.8708623580174888, -0.49152696099829474], 'a8': [-0.04876314871420185, 0.9988103700540342], 'a9': [0.8188410296463207, -0.5740203551859057], 'algebraic': True, 'analytic_conductor': 18.71988529995465, 'analytic_normalization': 0, 'bad_lfactors': [[29, [1]], [139, [1]]], 'bad_primes': [29, 139], 'central_character': '4031.4', 'coeff_info': ['x^966 - 1', '0.999978846903185 + 0.00650428675380408*I', '\\\\zeta_{966}'], 'conductor': 4031, 'conductor_radical': 4031, 'conjugate': 'dirichlet_L_4031.1008', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^83', 'a^919', 'a^166', 'a^790', 'a^36', 'a^562', 'a^249', 'a^872', 'a^873', 'a^857', 'a^119', 'a^206', 'a^645', 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'193.020213708770922248522893003019', '193.56308962165043814576333753236', '194.15443588749056912753217109544', '194.91485752944832072486841633355', '195.16903901932689018255653756268', '195.84272253581032742186656437187', '196.48954985209343452467146978988', '196.718808266769289082586865521554', '197.13460112206421999616369537383', '197.73039423858249488085709560406', '198.04296277591239823505359325748', '198.688661393843462179900479016424', '199.39041656567674113258586172725'], 'prelabel': '1-4031-4031.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.71988529995465, 'root_angle': -0.09694504660814823, 'root_number': '0.953978435592356293176481457153-0.299875214755672189406543692353*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(966)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.51873342965083299596229867528+0.0219042157034757833431045235437*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.890948588989', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.81756488447', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.69745583792', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.71988529995465, 'bad_primes': [29, 139], 'central_character': '4031.4', 'conductor': 4031, 'conductor_radical': 4031, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4031/4'], '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': '1-4031-4031.4-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': '1-4031-4031.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.71988529995465, 'root_angle': -0.04847252330407412, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.890948588989', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4031.4', 'Lhash_array': ['dirichlet_L_4031.4'], 'label': '1-4031-4031.4-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4031/4'}