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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_547.195', 'a10': [-0.15472933479028125, -0.9879568983287464], 'a2': [-0.6501040936687442, -0.7598451601445788], 'a3': [-0.9009688679024191, 0.4338837391175581], 'a4': [-0.15472933479028125, 0.9879568983287464], 'a5': [0.8512844415843512, 0.524704487799008], 'a6': [0.9154080085253663, 0.40252723873996754], 'a7': [-0.5961324854692254, -0.8028860814388825], 'a8': [0.8512844415843512, -0.524704487799008], 'a9': [0.6234898018587335, -0.7818314824680298], 'algebraic': True, 'analytic_conductor': 2.540257320534655, 'analytic_normalization': 0, 'bad_lfactors': [[547, [1]]], 'bad_primes': [547], 'central_character': '547.195', 'coeff_info': ['x^91 - 1', '0.997617272301248 + 0.0689911444043249*I', '\\\\zeta_{91}'], 'conductor': 547, 'conductor_radical': 547, 'conjugate': 'dirichlet_L_547.216', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^58', 'a^39', 'a^25', 'a^8', 'a^6', 'a^59', 'a^83', 'a^78', 'a^66', 'a^56', 'a^64', 'a^26', 'a^26', 'a^47', 'a^50', 'a^22', 'a^45', 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'198.42523037508488184516223600679', '198.7259876361756148079133288804', '199.52621348692919901166810943580'], 'prelabel': '1-547-547.195-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': 0.8976398022475433, 'root_number': '-0.948739100355804450085678312721+0.316060309839844984565114856923*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.448819901124', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(91)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.467735703125273954213593429048-0.0759096517489922597032785167988*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.00726642540267', 'prec': 54}, 'z2': {'__RealLiteral__': 0, 'data': '1.52153495064', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.78425094649', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.540257320534655, 'bad_primes': [547], 'central_character': '547.195', 'conductor': 547, 'conductor_radical': 547, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/547/195'], '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': '1-547-547.195-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': '1-547-547.195-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': 0.4488199011237716, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.00726642540267', 'prec': 54}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_547.195', 'Lhash_array': ['dirichlet_L_547.195'], 'label': '1-547-547.195-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/547/195'}
Lfunction data - 1-547-547.195-r0-0-0