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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.247', 'a10': [0.9555728057861407, 0.2947551744109042], 'a2': [-0.9009688679024191, 0.4338837391175581], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [-0.7330518718298263, -0.6801727377709194], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.2225209339563144, 0.9749279121818236], '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': '441.247', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.25', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 0, 'a^18', 'a^13', 0, 0, 'a^6', 0, 'a^1', 'a^2', 0, 'a^2', 0, 0, 'a^15', 'a^10', 0, 'a^14', 'a^10', 0, 'a^11', 'a^4', 0, 'a^5', 'a^11', 0, 0, 'a^10', 0, 'a^0', 'a^3', 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'192.44457266584255244306190878095', '192.66309991264150200348940773398', '193.58967091959846843147027225648', '194.75327637772858556592572104078', '195.31485551198550640032095920718', '195.71588131752457758815355548397', '196.54358170715135412288242486487', '197.13639693772860655516833303821', '197.830391060120318415364929235821', '198.38564130132024187896665295443', '199.25262325162428150775531968258', '199.52066117719835252030213907385'], 'prelabel': '1-21e2-441.247-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': 0.14058956916099774, 'root_number': '0.904036878365807391692268002841+0.427454468399391482132161491557*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0702947845805', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(21)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.682686698829697378044068466855+0.0839646385219833763087538914666*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.961195760347', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.11573906758', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.87788325778', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.047995390047135, 'bad_primes': [3, 7], 'central_character': '441.247', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/247'], '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': '1-21e2-441.247-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': '1-21e2-441.247-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': 0.07029478458049887, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.961195760347', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.247', 'Lhash_array': ['dirichlet_L_441.247'], 'label': '1-21e2-441.247-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/247'}
Lfunction data - 1-21e2-441.247-r0-0-0