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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_41.22', 'a10': [0.30901699437494745, -0.9510565162951535], 'a2': [0.5877852522924731, -0.8090169943749475], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [-0.30901699437494745, -0.9510565162951535], 'a5': [0.9510565162951535, -0.30901699437494745], 'a6': [-0.15643446504023087, -0.9876883405951378], 'a7': [-0.15643446504023087, 0.9876883405951378], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 4.406061916579626, 'analytic_normalization': 0, 'bad_lfactors': [[41, [1]]], 'bad_primes': [41], 'central_character': '41.22', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 41, 'conductor_radical': 41, 'conjugate': 'dirichlet_L_41.28', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^35', 'a^28', 'a^38', 'a^29', 'a^11', 'a^22', 'a^30', 'a^32', 'a^7', 'a^23', 'a^19', 'a^5', 'a^33', 'a^16', 'a^37', 'a^24', 'a^21', 'a^26', 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4.406061916579626, 'root_angle': -0.573378571438531, 'root_number': '-0.228489232544655181566052652231-0.973546439884176499791956403453*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.286689285719', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.45280459311829007764605276229-1.11467129689310869447059967151*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.66914631618', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.81765342858', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.06359892797', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.406061916579626, 'bad_primes': [41], 'central_character': '41.22', 'conductor': 41, 'conductor_radical': 41, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/41/22'], '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': '1-41-41.22-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': '1-41-41.22-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.406061916579626, 'root_angle': -0.2866892857192655, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66914631618', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_41.22', 'Lhash_array': ['dirichlet_L_41.22'], 'label': '1-41-41.22-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/41/22'}