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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_29.4', 'a10': [-0.6234898018587335, -0.7818314824680298], 'a2': [0.9009688679024191, 0.4338837391175581], 'a3': [-0.6234898018587335, 0.7818314824680298], 'a4': [0.6234898018587335, 0.7818314824680298], 'a5': [-0.9009688679024191, -0.4338837391175581], 'a6': [-0.9009688679024191, 0.4338837391175581], 'a7': [0.6234898018587335, -0.7818314824680298], 'a8': [0.2225209339563144, 0.9749279121818236], 'a9': [-0.2225209339563144, -0.9749279121818236], 'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'analytic_normalization': 0, 'bad_lfactors': [[29, [1]]], 'bad_primes': [29], 'central_character': '29.4', 'coeff_info': ['x^14 - 1', '0.900968867902419 + 0.433883739117558*I', '\\\\zeta_{14}'], 'conductor': 29, 'conductor_radical': 29, 'conjugate': 'dirichlet_L_29.22', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^5', 'a^2', 'a^8', 'a^6', 'a^12', 'a^3', 'a^10', 'a^9', 'a^11', 'a^7', 'a^4', 'a^13', 'a^13', 'a^4', 'a^7', 'a^11', 'a^9', 'a^10', 'a^3', 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'187.4933526403365490484520850650', '188.16679081415810410698177304171', '188.56679386650063843736327904756', '189.73544260357416462752730409367', '191.27117044961192932762473762649', '192.390250479760941515847043554555', '192.77645957687621956809035858614', '194.19621530776813702988241469095', '194.84697039047612790391735801130', '195.22711104717402216826505818405', '196.392837243886494332310347271619', '197.72031334783323712721881372117', '198.2103947251972316642154882850', '199.21270086336987048073699026398'], 'prelabel': '1-29-29.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.31489225762516976, 'root_number': '0.549305692835098146928991955755+0.835621478792253642684283689757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.157446128813', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(14)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07704926731292402284821988683+0.421596608298028931940575507016*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.89565228478', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.80508075297', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.6985885189', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.4', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/4'], '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': '1-29-29.4-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': '1-29-29.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.15744612881258488, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.89565228478', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_29.4', 'Lhash_array': ['dirichlet_L_29.4'], 'label': '1-29-29.4-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/29/4'}
Lfunction data - 1-29-29.4-r0-0-0