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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_79.7', 'a10': [0.5680647467311558, -0.8229838658936564], 'a2': [-0.20002569377604443, -0.9797906520422677], 'a3': [-0.4286925614030542, -0.9034504346103823], 'a4': [-0.9199794436588242, 0.3919666098600751], 'a5': [0.6927243535095994, 0.7212024473438146], 'a6': [-0.7994427634035012, 0.6007422642379789], 'a7': [0.99675730813421, 0.08046656871672588], 'a8': [0.5680647467311558, 0.8229838658936564], 'a9': [-0.6324453755953773, 0.7746049618276546], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.7', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.34', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^56', 'a^53', 'a^34', 'a^10', 'a^31', 'a^1', 'a^12', 'a^28', 'a^66', 'a^16', 'a^9', 'a^8', 'a^57', 'a^63', 'a^68', 'a^21', 'a^6', 'a^58', 'a^44', 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'183.50657020681798362989259152554', '184.714244769137975458834678457784', '185.29963286825997899457370467010', '185.69388855073877863810661990886', '186.586372018583275028961103428', '188.190581993521881913574794216496', '188.80665295561211163903974041192', '189.80626002478607797779655525979', '190.27238928705148481718803579836', '190.714099207755930983431492381224', '191.950699847663757321670236178668', '192.67515852876554202312807297279', '193.373306045750145948964734145600', '194.38900571386378162275143252772', '194.91685260168154416960754214814', '195.48293541573619166271602911616', '196.59456358905109675502954458015', '197.51457086501482433123784633016', '198.591170531477796723298458664691', '199.07077668150226837913350355820'], 'prelabel': '1-79-79.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.11259625337545068, 'root_number': '0.760013054804142191872208303061-0.649907806175057384318144524009*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.112596253375', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.934522568935278308937472040235-0.400939399600889579403219960790*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.45768614528', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.3757594325', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.50418512697', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.7', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/7'], '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': '1-79-79.7-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-79-79.7-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.11259625337545068, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45768614528', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_79.7', 'Lhash_array': ['dirichlet_L_79.7'], 'factors': ['1-79-79.7-r1-0-0'], 'label': '1-79-79.7-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/7'}
Lfunction data - 1-79-79.7-r1-0-0