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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_29.25', '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': '29.25', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 29, 'conductor_radical': 29, 'conjugate': 'dirichlet_L_29.7', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^6', 'a^1', 'a^4', 'a^3', 'a^6', 'a^5', 'a^5', 'a^1', 'a^2', 'a^0', 'a^2', 'a^3', 'a^3', 'a^2', 'a^0', 'a^2', 'a^1', 'a^5', 'a^5', 'a^6', 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'188.26912429571010295184162549283', '188.78167272614575349994783364299', '190.22128998763998596312612920723', '190.66824534610363191797265637613', '191.75525188049487846215431563925', '191.889255537119754248464461762329', '193.16091994012588668263420880592', '194.427228973145465639790450318270', '195.51300735264683264120216119137', '196.11414253869359010537154494341', '197.42531816806617431298375917718', '198.2487857647012299322118950563', '198.78098539555522088671113563510'], 'prelabel': '1-29-29.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.4273362364042696, 'root_number': '0.226302428235437063117110655777-0.974057088149737175298377063989*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.213668118202', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(7)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.652891995669099506295354381402-0.331600711143738112963114188501*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.61214558537', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.84804476636', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.31352967874', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.25', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/25'], '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': '1-29-29.25-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': '1-29-29.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.2136681182021348, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61214558537', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_29.25', 'Lhash_array': ['dirichlet_L_29.25'], 'label': '1-29-29.25-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/29/25'}
Lfunction data - 1-29-29.25-r0-0-0