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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.142', 'a10': [-0.9888308262251285, 0.14904226617617444], 'a2': [-0.7330518718298263, -0.6801727377709194], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.07473009358642425, 0.9972037971811801], 'a5': [0.6234898018587335, -0.7818314824680298], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.6234898018587335, -0.7818314824680298], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.047995390047135, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.142', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.382', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 0, 'a^5', 'a^18', 0, 0, 'a^18', 0, 'a^10', 'a^6', 0, 'a^13', 0, 0, 'a^10', 'a^16', 0, 'a^14', 'a^2', 0, 'a^19', 'a^12', 0, 'a^15', 'a^5', 0, 0, 'a^2', 0, 'a^14', 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'190.328327823207537307477224881618', '190.866144052761232445189520683842', '191.503322802761576110132172416058', '192.17390767756481486984602739202', '192.875036794606384529365342838358', '193.18666104656225230598324847751', '194.05089298202864107071039928601', '194.41069337862550764980423949487', '195.67745002460652818849804188067', '196.10816039811232139339048392727', '196.80745632461278427788910743872', '197.599290508055108000482965301056', '198.19926794854367939809140074263', '198.97076533639958330245739687601', '199.32678976845028195573707338579'], 'prelabel': '1-21e2-441.142-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': -0.7528344671201814, 'root_number': '-0.713375266152572234601367304998-0.700782226973363478359221144039*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.37641723356', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(21)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.635543598346391935337462094506-0.381030136987260311822075671380*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.54320827123', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.98271689524', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.74204373232', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.047995390047135, 'bad_primes': [3, 7], 'central_character': '441.142', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/142'], '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': '1-21e2-441.142-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': '1-21e2-441.142-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': -0.3764172335600907, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.54320827123', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.142', 'Lhash_array': ['dirichlet_L_441.142'], 'label': '1-21e2-441.142-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/142'}
Lfunction data - 1-21e2-441.142-r0-0-0