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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1004.167', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9886517447379141, 0.15022558912075706], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.42577929156507266, -0.9048270524660196], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6936533058128049, -0.7203090248879069], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.954864544746643, -0.2970415815770349], 'algebraic': True, 'analytic_conductor': 4.662556398202548, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [251, [1]]], 'bad_primes': [2, 251], 'central_character': '1004.167', 'coeff_info': ['x^250 - 1', '0.999684189283300 + 0.0251300954433375*I', '\\\\zeta_{250}'], 'conductor': 1004, 'conductor_radical': 502, 'conjugate': 'dirichlet_L_1004.499', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^369', 0, 'a^170', 0, 'a^157', 0, 'a^238', 0, 'a^374', 0, 'a^88', 0, 'a^289', 0, 'a^66', 0, 'a^142', 0, 'a^26', 0, 'a^241', 0, 'a^90', 0, 'a^357', 0, 'a^47', 0, 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'191.124883563282732187995260308475', '191.65304249576490994003872401968', '192.32501328792790461974254658990', '193.10233285074059936720472806072', '193.49187065665267285848640769547', '194.16244281013664783302090824401', '194.77155094313641706553255847090', '195.17769924387372776902215233421', '195.96156175562994422473845670854', '196.44084762524379616470190478917', '197.01406156304441552931148144298', '197.82882480047510852798153940697', '198.58463619096945369595693905731', '199.11053804483484246993892063733', '199.5916563232326435674938857775'], 'prelabel': '1-1004-1004.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.662556398202548, 'root_angle': 0.02878808552011299, 'root_number': '0.995913050486288799946663779696+0.0903171958770575200151520721409*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0143940427601', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(250)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.568122331274870906450851512124-0.0608472947246659072107275372796*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.623296250804', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.87366263331', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.42953883194', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.662556398202548, 'bad_primes': [2, 251], 'central_character': '1004.167', 'conductor': 1004, 'conductor_radical': 502, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1004/167'], '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': '1-1004-1004.167-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': '1-1004-1004.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.662556398202548, 'root_angle': 0.014394042760056494, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.623296250804', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1004.167', 'Lhash_array': ['dirichlet_L_1004.167'], 'label': '1-1004-1004.167-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1004/167'}