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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.1982', 'a10': [-0.7741416106390825, -0.6330124538088704], 'a2': [0.5644432188667692, -0.825471896962774], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [-0.362807705350641, -0.9318640292114523], 'a5': [0.08557500847883974, -0.9963317308626913], 'a6': [0.9418443636395247, -0.33604939321543015], 'a7': [0.8707460771197771, -0.49173292464560375], 'a8': [-0.9740119169423335, -0.22649676742576438], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1982', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2712', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^93', 'a^11', 'a^76', 'a^84', 'a^104', 'a^101', 'a^59', 'a^22', 'a^67', 0, 'a^87', 'a^54', 'a^84', 'a^95', 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'193.22694961036522063695748773095', '193.87936655649437634233391159966', '194.409197884642100998921550055969', '195.141917408437712738313595676872', '195.65825519984004304065500013229', '196.11805687185541630416776408818', '196.418631463135133972975453200817', '197.26952082749258304918898100863', '197.624396665565275984239689322411', '198.53075830470796078365287301228', '198.703495555290496149588782025926', '199.478242831332419073687916330194'], 'prelabel': '1-3751-3751.1982-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.4971791758576331, 'root_number': '-0.999842938263025878149577783275+0.0177228328875217455346535488352*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(110)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.26721862976808473770058737031-1.04879414345806388128490772824*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.432274297482', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.53777765257', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.21262833242', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.1982', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1982'], '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': '1-3751-3751.1982-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': '1-3751-3751.1982-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.4971791758576331, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.432274297482', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.1982', 'Lhash_array': ['dirichlet_L_3751.1982'], 'factors': ['1-3751-3751.1982-r0-0-0'], 'label': '1-3751-3751.1982-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1982'}
Lfunction data - 1-3751-3751.1982-r0-0-0