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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1225.72', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.7017979028839914, 0.7123760969513449], 'a3': [0.6117242991150064, -0.7910710346563412], 'a4': [-0.01495940701526362, -0.9998881018102734], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.1342332658176555, 0.9909497617679347], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.7227948638273916, 0.6910626489868646], 'a9': [-0.2515867637445085, -0.9678347484506665], 'algebraic': True, 'analytic_conductor': 131.64453287341564, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]]], 'bad_primes': [5, 7], 'central_character': '1225.72', 'coeff_info': ['x^420 - 1', '0.999888101810273 + 0.0149594070152636*I', '\\\\zeta_{420}'], 'conductor': 1225, 'conductor_radical': 35, 'conjugate': 'dirichlet_L_1225.1208', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^157', 'a^359', 'a^314', 0, 'a^96', 0, 'a^51', 'a^298', 0, 'a^332', 'a^253', 'a^3', 0, 0, 'a^208', 'a^281', 'a^35', 'a^406', 0, 0, 'a^69', 'a^307', 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'primitive': True, 'rational': False, 'root_analytic_conductor': 131.64453287341564, 'root_angle': -0.5356462585034014, 'root_number': '-0.111752103549485665278866777070-0.993736115551943212845237744961*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.267823129252', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(420)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02285727173983479948173031917-0.256980577921009954770240395887*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.582021931664', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.11136605938', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.36881404799', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 131.64453287341564, 'bad_primes': [5, 7], 'central_character': '1225.72', 'conductor': 1225, 'conductor_radical': 35, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1225/72'], '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': '1-35e2-1225.72-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': '1-35e2-1225.72-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 131.64453287341564, 'root_angle': -0.2678231292517007, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.582021931664', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1225.72', 'Lhash_array': ['dirichlet_L_1225.72'], 'label': '1-35e2-1225.72-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1225/72'}