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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1003.353', 'a10': [-7.040766286173228e-31, 1.0], 'a2': [1.0, 0.0], 'a3': [-7.040766286173228e-31, 1.0], 'a4': [1.0, 0.0], 'a5': [-7.040766286173228e-31, 1.0], 'a6': [-7.040766286173228e-31, 1.0], 'a7': [2.9010907910729803e-30, -1.0], 'a8': [1.0, 0.0], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 107.7873195690089, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]], [59, [1]]], 'bad_primes': [17, 59], 'central_character': '1003.353', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 1003, 'conductor_radical': 1003, 'conjugate': 'dirichlet_L_1003.412', 'degree': 1, 'dirichlet_coefficients': [1, 1, 'I', 1, 'I', 'I', '-I', 1, -1, 'I', 'I', 'I', -1, '-I', -1, 1, 0, -1, -1, 'I', 1, 'I', 'I', 'I', -1, -1, '-I', '-I', 'I', -1, '-I', 1, -1, 0, 1, -1, '-I', -1, '-I', 'I', '-I', 1, 1, 'I', '-I', 'I', -1, 'I', -1, -1, 0, -1, -1, '-I', -1, '-I', '-I', 'I', 0, -1, 'I', '-I', 'I', 1, 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'195.480290377885580230003432211675', '196.08885985911140888026842698419', '196.8680661665475009591088748193', '197.61171387939679609351109578196', '197.92736524049867775064705848892', '198.5491543343641260857309416809', '198.719708651472025822592929337451', '199.945545573713042171689978615942'], 'prelabel': '1-1003-1003.353-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 107.7873195690089, 'root_angle': -0.7110104348113153, 'root_number': '-0.615412209402635684530619439242-0.788205438016109152217745626790*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.355505217406', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.32378696429953650682934158478+0.728345793998903402326760812455*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.9219048224', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.81906209171', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.79161954125', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 107.7873195690089, 'bad_primes': [17, 59], 'central_character': '1003.353', 'conductor': 1003, 'conductor_radical': 1003, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1003/353'], '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': '1-1003-1003.353-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': '1-1003-1003.353-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 107.7873195690089, 'root_angle': -0.35550521740565766, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.9219048224', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1003.353', 'Lhash_array': ['dirichlet_L_1003.353'], 'label': '1-1003-1003.353-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1003/353'}