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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_967.15', 'a10': [-0.7757112907044198, 0.6310879443260528], 'a2': [0.6132667502837162, 0.7898758718915586], 'a3': [-0.7757112907044198, 0.6310879443260528], 'a4': [-0.2478077859928999, 0.9688092181649064], 'a5': [0.022763197856105682, 0.9997408848413492], 'a6': [-0.9741990826734791, -0.22569037932121064], 'a7': [-0.9989636736467276, -0.045514599132963594], 'a8': [-0.917211301505453, 0.39840108984624145], 'a9': [0.20345601305263378, -0.9790840876823229], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.15', 'coeff_info': ['x^69 - 1', '0.995856842531531 + 0.0909348623088469*I', '\\\\zeta_{69}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.129', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^10', 'a^27', 'a^20', 'a^17', 'a^37', 'a^35', 'a^30', 'a^54', 'a^27', 'a^54', 'a^47', 'a^38', 'a^45', 'a^44', 'a^40', 'a^48', 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'0.957661424500449623879079500072+0.287896849624600138417662024065*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0464780147037', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(69)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.670112571628491794706550984202+0.490177094138527026517402305155*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.300436520161', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.88081547537', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.26023961228', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.15', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/15'], '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': '1-967-967.15-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': '1-967-967.15-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.04647801470373707, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.300436520161', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_967.15', 'Lhash_array': ['dirichlet_L_967.15'], 'label': '1-967-967.15-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/15'}