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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_131.28', 'a10': [-0.9068743608505454, 0.4214011077725291], 'a2': [0.024163745236132288, -0.9997080140801929], 'a3': [-0.16835704134703855, 0.9857260809316509], 'a4': [-0.9988322268323266, -0.048313379525507065], 'a5': [-0.44319154559924134, -0.8964269372957038], 'a6': [0.9813701261394134, 0.19212671735370837], 'a7': [-0.6810158587867972, 0.7322686665977736], 'a8': [-0.07243480016176236, 0.9973731496914912], 'a9': [-0.943311813257743, -0.33190785312852844], 'algebraic': True, 'analytic_conductor': 0.6083614423949539, 'analytic_normalization': 0, 'bad_lfactors': [[131, [1]]], 'bad_primes': [131], 'central_character': '131.28', 'coeff_info': ['x^65 - 1', '0.995331634717649 + 0.0965139209145151*I', '\\\\zeta_{65}'], 'conductor': 131, 'conductor_radical': 131, 'conjugate': 'dirichlet_L_131.117', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^49', 'a^18', 'a^33', 'a^44', 'a^2', 'a^24', 'a^17', 'a^36', 'a^28', 'a^14', 'a^51', 'a^37', 'a^8', 'a^62', 'a^1', 'a^27', 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'189.99550762510526717530866372554', '190.60569221395703002141363212854', '191.566966441434091941982796227616', '192.1156211849773310141717154081', '192.82664726214931232517757150997', '193.42082126113212594036410786727', '193.923516651932486485583862131142', '194.83432105850923901637421377281', '195.88566682315950078723715368228', '196.12774750347448738561853110798', '197.39705814717139376896620363418', '198.55094886690166673113916393560', '198.91085838453117106640027061269', '199.70972999000213000740053396905'], 'prelabel': '1-131-131.28-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6083614423949539, 'root_angle': 0.5991998659358658, 'root_number': '-0.306625354312884766459571835873+0.951830285341088461075818102863*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.299599932968', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(65)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.564972362865492975292120355404+0.0299158993840113556486174381915*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.21689600841', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.7674708255', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.65234245996', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6083614423949539, 'bad_primes': [131], 'central_character': '131.28', 'conductor': 131, 'conductor_radical': 131, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/131/28'], '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': '1-131-131.28-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': '1-131-131.28-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6083614423949539, 'root_angle': 0.2995999329679329, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21689600841', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_131.28', 'Lhash_array': ['dirichlet_L_131.28'], 'label': '1-131-131.28-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/131/28'}