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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_287.12', 'a10': [0.10452846326765347, 0.9945218953682733], 'a2': [0.20791169081775934, 0.9781476007338057], 'a3': [0.9659258262890683, -0.25881904510252074], 'a4': [-0.9135454576426009, 0.4067366430758002], 'a5': [0.9945218953682733, 0.10452846326765347], 'a6': [0.4539904997395468, 0.8910065241883679], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [0.8660254037844386, -0.5], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.12', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.24', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^115', 'a^52', 'a^2', 'a^21', 0, 'a^78', 'a^110', 'a^28', 'a^43', 'a^47', 'a^51', 0, 'a^117', 'a^104', 'a^13', 'a^16', 'a^29', 'a^54', 0, 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'193.359337541903102725625689870828', '194.02755579002802465770549995330', '194.91017829001046763526530725176', '195.90500610449660772704063370105', '196.25528692691187844756270114345', '196.635429457479542305103451664310', '197.721565122579711656006545738756', '197.85499092689962101822110948272', '198.552204690751240164173645312725', '199.29322968124559111466050557261'], 'prelabel': '1-287-287.12-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.45412605312002613, 'root_number': '0.143618891650424868606457489275+0.989633070365528721583230825087*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.22706302656', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(120)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.40126404435297109906264294930+0.767967117072879130764242975255*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.77337339973', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.99811031879', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.36015435309', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.12', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/12'], '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': '1-287-287.12-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-287-287.12-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.22706302656001306, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77337339973', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_287.12', 'Lhash_array': ['dirichlet_L_287.12'], 'label': '1-287-287.12-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/12'}