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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1849.130', 'a10': [-0.8720494081438076, 0.4894178478110855], 'a2': [0.391104720490156, 0.9203461835691594], 'a3': [-0.9760758775559272, -0.21743017558155697], 'a4': [-0.6940741952206338, 0.7199034737579958], 'a5': [0.10937120837787438, 0.9940009752399459], 'a6': [-0.18163685097943644, -0.9833656768294661], 'a7': [0.957600599908406, 0.2880990993652376], 'a8': [-0.934016108732548, -0.35723088980113277], 'a9': [0.9054482374931466, 0.4244566988758151], 'algebraic': True, 'analytic_conductor': 8.586719900673815, 'analytic_normalization': 0, 'bad_lfactors': [[43, [1]]], 'bad_primes': [43], 'central_character': '1849.130', 'coeff_info': ['x^43 - 1', '0.989343368075110 + 0.145601167735005*I', '\\\\zeta_{43}'], 'conductor': 1849, 'conductor_radical': 43, 'conjugate': 'dirichlet_L_1849.1721', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^23', 'a^16', 'a^10', 'a^31', 'a^2', 'a^24', 'a^3', 'a^18', 'a^37', 'a^39', 'a^12', 'a^10', 'a^33', 'a^32', 'a^13', 'a^11', 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'191.254217383946719340542061606158', '192.38995608701474446047935707343', '192.97600437900641081408319422762', '193.35918981972998095338991663161', '194.09118309653735099939076318458', '194.73594616221337241541167940177', '195.141328417639697058509740711588', '195.1874592666527128350734822965', '196.05935276005002664561123091438', '196.64496706169067791337798789448', '197.409792151853053886562558989752', '197.89387483559256323825016653704', '198.31256877089342586505603236578', '198.97999444676544853731303370919', '199.56134267265810715918489608313', '199.83229681966159188410320933452'], 'prelabel': '1-43e2-1849.130-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.586719900673815, 'root_angle': 0.8263926446727962, 'root_number': '-0.854917991693361903275079271254+0.518763170896883145103685476769*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.413196322336', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(43)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.802934795545816500965772435300+0.763912489314023074669707328913*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.12917493907', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.30886011712', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.57728100334', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.586719900673815, 'bad_primes': [43], 'central_character': '1849.130', 'conductor': 1849, 'conductor_radical': 43, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1849/130'], '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': '1-43e2-1849.130-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': '1-43e2-1849.130-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.586719900673815, 'root_angle': 0.4131963223363981, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12917493907', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1849.130', 'Lhash_array': ['dirichlet_L_1849.130'], 'label': '1-43e2-1849.130-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1849/130'}