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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_119.13', 'a10': [-7.040766286173228e-31, 1.0], 'a2': [-1.0, -1.4081532572346456e-30], 'a3': [2.9010907910729803e-30, -1.0], 'a4': [1.0, 0.0], 'a5': [2.9010907910729803e-30, -1.0], 'a6': [-7.040766286173228e-31, 1.0], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 12.788326050560377, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [17, [1]]], 'bad_primes': [7, 17], 'central_character': '119.13', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 119, 'conductor_radical': 119, 'conjugate': 'dirichlet_L_119.55', 'degree': 1, 'dirichlet_coefficients': [1, -1, '-I', 1, '-I', 'I', 0, -1, -1, 'I', '-I', '-I', -1, 0, -1, 1, 0, 1, 1, '-I', 0, 'I', '-I', 'I', -1, 1, 'I', 0, 'I', 1, '-I', -1, -1, 0, 0, -1, 'I', -1, 'I', 'I', 'I', 0, -1, '-I', 'I', 'I', -1, '-I', 0, 1, 0, -1, -1, '-I', -1, 0, '-I', '-I', 1, 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'186.530842606138297673581093105615', '187.44348181096731338504348565383', '188.460920226119545652030624698734', '189.02433331490625739786303227962', '189.2742432709949424824276004770', '190.443304649971270738366400344194', '191.03347678332549776012415068531', '191.62958892651291927409207753798', '192.35694280675945821132613610669', '193.10836176207278626888844185969', '194.10299888033640678829721083122', '195.142428510098069054058874575225', '195.88421078909162810415074249134', '196.52155915747382639711356551145', '197.186158598275391901871694177191', '197.77350674989023972078898069782', '198.97546853721681905182804224168', '199.66414079836804984606539511982'], 'prelabel': '1-119-119.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.788326050560377, 'root_angle': 0.7889895651886847, 'root_number': '-0.788205438016109152217745626790+0.615412209402635684530619439242*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.394494782594', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.453989506289876926200291928312-0.354464295266324729210499347077*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.272423391483', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.4174662183', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.90676188139', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.788326050560377, 'bad_primes': [7, 17], 'central_character': '119.13', 'conductor': 119, 'conductor_radical': 119, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/119/13'], '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': '1-119-119.13-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': '1-119-119.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.788326050560377, 'root_angle': 0.39449478259434234, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.272423391483', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_119.13', 'Lhash_array': ['dirichlet_L_119.13'], 'label': '1-119-119.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/119/13'}