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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4033.48', 'a10': [0.39607976603915684, -0.918216106880274], 'a2': [-0.766044443118978, -0.6427876096865394], 'a3': [-0.993238357741943, 0.11609291412523023], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.28680323271109026, 0.9579895123154889], 'a6': [0.8354878114129364, 0.549508978070806], 'a7': [-0.6862416378687336, 0.7273736415730487], 'a8': [0.5, -0.8660254037844386], 'a9': [0.9730448705798238, -0.23061587074244017], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.48', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.3949', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^33', 'a^26', 'a^12', 'a^11', 'a^5', 'a^20', 'a^45', 'a^52', 'a^44', 'a^10', 'a^38', 'a^47', 'a^53', 'a^37', 'a^24', 'a^51', 'a^31', 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[]], 'index': 0, 'label': '1-4033-4033.48-r0-0-0', 'leading_term': '0.750502048439086391167096305315+0.324490127235982380548514664567*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/4033/48', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8176473368053552, 0.8838637557328063, 0.32732442494945757, -0.8621270530658316, -1.638064025499441, -0.9624800018822607, 0.7205608370399397, 1.6160784395190233, 0.612389262502494, -1.0800175520261461, -1.1100270945222084, 0.9276932862526046, 2.4098109361434146, 0.6620537708380962, -3.257183258137579, -5.113028930678889, -2.4601689335774957, 2.063163682442119, 3.7548795577091107, 1.6402906271967916, -0.6130405796360826, 0.0354906083379196, 1.8694553911902927, 1.3056333345415387, -1.3998452402375134, -2.141397257682053, 1.069968515945624, 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'193.26116771172860312011158147951', '193.590945202169025500306122495126', '194.07568965340747561854677125039', '194.53487560397617071308797507958', '194.91717420937415557834923441741', '195.87550273651771905757674756784', '196.32025722971754282932422482763', '196.938405603989952705482598804507', '197.653048694497475848630979304610', '198.24264651114891176769000561670', '198.52962462338684210129460804216', '199.16618106031448151220475796141', '199.53209829144427823519866827712'], 'prelabel': '1-4033-4033.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.2597991289709103, 'root_number': '0.685006988854668524262887969291+0.728536495462142261636813834283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.601140749393668042550675403871+0.0518177770022043194996879768357*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.72047232688', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.74486545613', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.60482175914', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.48', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/48'], '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': '1-4033-4033.48-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': '1-4033-4033.48-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.12989956448545514, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72047232688', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4033.48', 'Lhash_array': ['dirichlet_L_4033.48'], 'label': '1-4033-4033.48-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/48'}