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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_69.2', 'a10': [-0.14231483827328514, 0.9898214418809327], 'a2': [-0.41541501300188644, -0.9096319953545183], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [-0.8412535328311812, -0.5406408174555976], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.14231483827328514, -0.9898214418809327], 'a8': [0.9594929736144974, 0.28173255684142967], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 7.415079810829127, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]]], 'bad_primes': [3, 23], 'central_character': '69.2', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 69, 'conductor_radical': 69, 'conjugate': 'dirichlet_L_69.35', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 0, 'a^8', 'a^13', 0, 'a^16', 'a^1', 0, 'a^6', 'a^7', 0, 'a^6', 'a^9', 0, 'a^16', 'a^3', 0, 'a^8', 'a^21', 0, 'a^0', 0, 0, 'a^4', 'a^21', 0, 'a^2', 'a^3', 0, 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'193.83641388379960201229376190060', '194.469003058489672262796876529361', '195.3968804057559157286485237245', '195.98781623708344184428887241834', '197.32940208536833480481095148223', '198.2644596266109199893129166032', '198.80659997337192883087026013041', '199.65510046541264730898697276275'], 'prelabel': '1-69-69.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.415079810829127, 'root_angle': 0.3765228911482685, 'root_number': '0.378258949294250814005877835767+0.925699825688008537834359561624*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.188261445574', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.546492849959045707274308234439-0.173864089069625766102195820041*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.56636609866', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.67657999812', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.6254202035', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.415079810829127, 'bad_primes': [3, 23], 'central_character': '69.2', 'conductor': 69, 'conductor_radical': 69, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/69/2'], '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': '1-69-69.2-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': '1-69-69.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.415079810829127, 'root_angle': 0.18826144557413424, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56636609866', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_69.2', 'Lhash_array': ['dirichlet_L_69.2'], 'label': '1-69-69.2-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/69/2'}