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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_751.17', 'a10': [-0.556875616488188, 0.8305958991958127], 'a2': [-0.9957568809385692, 0.09202300833754715], 'a3': [-0.9266599014641722, 0.3759008207205868], 'a4': [0.9830635318730154, -0.18326508751355977], 'a5': [0.6309466603018496, -0.7758262124045193], 'a6': [0.8881364488135445, -0.45957986062148787], 'a7': [-0.8994052515663711, -0.4371157666509329], 'a8': [-0.9620276715860859, 0.2729519355173252], 'a9': [0.7173971459631786, -0.6966644349784807], 'algebraic': True, 'analytic_conductor': 80.7061585207634, 'analytic_normalization': 0, 'bad_lfactors': [[751, [1]]], 'bad_primes': [751], 'central_character': '751.17', 'coeff_info': ['x^750 - 1', '0.999964908278481 + 0.00837748241477061*I', '\\\\zeta_{750}'], 'conductor': 751, 'conductor_radical': 751, 'conjugate': 'dirichlet_L_751.486', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^364', 'a^329', 'a^728', 'a^644', 'a^693', 'a^429', 'a^342', 'a^658', 'a^258', 'a^485', 'a^307', 'a^632', 'a^43', 'a^223', 'a^706', 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'188.9131738261721754243724883938', '189.64078239524335257154866551621', '189.81017922895488671476437368240', '190.57580672747717825945603810574', '191.61639408886672369952632378984', '191.91098217770127401473184441268', '192.57182017174511816001925063092', '193.245258537099139721273775858275', '193.7628649329470972500668575625', '194.39917314449407254266563489870', '194.92540833787142667411782569548', '196.140843302391430696086949507428', '196.48527662293973051226800615604', '197.1479577568001262407841295359', '197.49229054737346650110565047863', '198.54219326442031909433682707019', '198.998471285300241061601938153153', '199.696707630501718909969552617171'], 'prelabel': '1-751-751.17-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 80.7061585207634, 'root_angle': -0.15449910170941297, 'root_number': '0.884500878522630246613035479366-0.466538525625371362781450329798*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0772495508547', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(750)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.515016766859414366817240175513-0.0516980430658029157600693779675*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.514223229773', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.29361603687', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.80556209708', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 80.7061585207634, 'bad_primes': [751], 'central_character': '751.17', 'conductor': 751, 'conductor_radical': 751, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/751/17'], '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': '1-751-751.17-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': '1-751-751.17-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 80.7061585207634, 'root_angle': -0.07724955085470649, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.514223229773', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_751.17', 'Lhash_array': ['dirichlet_L_751.17'], 'label': '1-751-751.17-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/751/17'}
Lfunction data - 1-751-751.17-r1-0-0