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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_29.23', 'a10': [-0.9009688679024191, 0.4338837391175581], 'a2': [-0.2225209339563144, -0.9749279121818236], 'a3': [-0.9009688679024191, -0.4338837391175581], 'a4': [-0.9009688679024191, 0.4338837391175581], 'a5': [-0.2225209339563144, -0.9749279121818236], 'a6': [-0.2225209339563144, 0.9749279121818236], 'a7': [-0.9009688679024191, -0.4338837391175581], 'a8': [0.6234898018587335, 0.7818314824680298], 'a9': [0.6234898018587335, 0.7818314824680298], 'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'analytic_normalization': 0, 'bad_lfactors': [[29, [1]]], 'bad_primes': [29], 'central_character': '29.23', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 29, 'conductor_radical': 29, 'conjugate': 'dirichlet_L_29.24', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^4', 'a^3', 'a^5', 'a^2', 'a^4', 'a^1', 'a^1', 'a^3', 'a^6', 'a^0', 'a^6', 'a^2', 'a^2', 'a^6', 'a^0', 'a^6', 'a^3', 'a^1', 'a^1', 'a^4', 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'188.931065838325577103116018728114', '189.70130710558823838511366995082', '190.41702109338739210268739222970', '191.67874542684405662150964246924', '192.14751378456076790587983029850', '193.41740226985461502923757324560', '194.22484949266023723693770225069', '194.7711618889127765679856770294', '195.89939443528974935288682187064', '196.69214220722629066412583713908', '198.13986090431580195584351622974', '199.40649231957283084567645228643', '199.99885277121641949478590640900'], 'prelabel': '1-29-29.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.4067598392337177, 'root_number': '-0.833245064723243481280900843207-0.552903845270005136886904849331*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.406759839234', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(7)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.406028623194271420557388703572-0.438747345593106869682265863231*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.00015516298', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.84734117536', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.7613853355', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.23', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/23'], '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': '1-29-29.23-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': '1-29-29.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.4067598392337177, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00015516298', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_29.23', 'Lhash_array': ['dirichlet_L_29.23'], 'factors': ['1-29-29.23-r0-0-0'], 'label': '1-29-29.23-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/29/23'}
Lfunction data - 1-29-29.23-r0-0-0