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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_79.75', 'a10': [0.12053668025532305, -0.992708874098054], 'a2': [-0.8451900855437947, 0.5344658261278011], 'a3': [-0.7994427634035012, -0.6007422642379789], 'a4': [0.4286925614030542, -0.9034504346103823], 'a5': [-0.6324453755953773, 0.7746049618276546], 'a6': [0.99675730813421, 0.08046656871672588], 'a7': [0.9199794436588242, -0.3919666098600751], 'a8': [0.12053668025532305, 0.992708874098054], 'a9': [0.27821746391645263, 0.9605181116313724], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.75', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.59', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^32', 'a^47', 'a^64', 'a^28', 'a^1', 'a^73', 'a^18', 'a^16', 'a^60', 'a^76', 'a^33', 'a^38', 'a^27', 'a^75', 'a^50', 'a^51', 'a^48', 'a^22', 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[[1], []], 'index': 0, 'label': '1-79-79.75-r1-0-0', 'leading_term': '0.124111128733017156410300984853-0.241452854276015776355710694658*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/79/75', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.2714830622956401, -0.16923953731797822, -0.6255748839421231, -0.999828830154956, -1.15084326595655, -0.9233845995602391, -0.20798251931898815, 0.9926788646559551, 2.5196830529888987, 4.061987832782422, 5.221597350095807, 5.6303824269613925, 5.084142654210451, 3.642800830035548, 1.6478023865143994, -0.36681520985061816, -1.8508124792752778, -2.4398399347704096, -2.0991218911021896, -1.138368510575078, -0.07788056864930515, 0.5857323351722229, 0.6109816764626813, 0.1264203742418375, -0.437875866184938, -0.5811893173327004, 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'data': '-0.348866763118', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.466457387597664565559704480846+0.00940359844802252035670506899952*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.196521223735', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.93866304664', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.62658929212', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.75', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/75'], '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': '1-79-79.75-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': '1-79-79.75-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': -0.3488667631180574, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.196521223735', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_79.75', 'Lhash_array': ['dirichlet_L_79.75'], 'label': '1-79-79.75-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/75'}
Lfunction data - 1-79-79.75-r1-0-0