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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_6027.1076', 'a10': [0.5998218946879137, 0.8001335480112063], 'a2': [0.28042738930600275, -0.9598752415428891], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8427209586540392, -0.5383506160906824], 'a5': [-0.5998218946879137, 0.8001335480112063], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.753071466003611, 0.6579387259397126], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.989270330644178, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [41, [1]]], 'bad_primes': [3, 7, 41], 'central_character': '6027.1076', 'coeff_info': ['x^210 - 1', '0.999552432283503 + 0.0299154661693985*I', '\\\\zeta_{210}'], 'conductor': 6027, 'conductor_radical': 861, 'conjugate': 'dirichlet_L_6027.857', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^167', 0, 'a^124', 'a^74', 0, 0, 'a^81', 0, 'a^31', 'a^181', 0, 'a^27', 0, 0, 'a^38', 'a^16', 0, 'a^203', 'a^198', 0, 'a^138', 'a^47', 0, 'a^148', 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0.028476065215699085, 'root_number': '0.996001104590713099145443948028+0.0893409181398948119116048174438*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(210)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11253473317864646449665917627-0.288766806549175230492600782105*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.993326835347', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.48048503274', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.67965938676', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.989270330644178, 'bad_primes': [3, 7, 41], 'central_character': '6027.1076', 'conductor': 6027, 'conductor_radical': 861, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6027/1076'], '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': '1-6027-6027.1076-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': '1-6027-6027.1076-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.989270330644178, 'root_angle': 0.014238032607849543, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.993326835347', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_6027.1076', 'Lhash_array': ['dirichlet_L_6027.1076'], 'label': '1-6027-6027.1076-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6027/1076'}