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lfunc_lfunctions • Show schema
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{'Lhash': '401048577870575634892913280023', 'a10': [313.9357993524145, 5.064044465790468e-60], 'a2': [-2.0, 3.4641016151377544], 'a3': [-8.580658306350605, 13.014311469672776], 'a4': [-8.0, -13.856406460551018], 'a5': [-39.24197491905181, -67.96909434914133], 'a6': [-27.921580769298057, -55.752895237319876], 'a7': [-110.56553164997244, 191.50511838361703], 'a8': [64.0, 0.0], 'a9': [-95.74460605931273, -223.34271962736332], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, -3.4641016151377544]]], [3, [[1.0, 0], [8.580658306350605, -13.014311469672776]]]], 'bad_primes': [2, 3], 'central_character': '18.7', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '5788557714178803616600571713821', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, -3.4641016151377544]], [[1.0, 0], [8.580658306350605, -13.014311469672776]], 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'6.66979716421108013218873373970727', '7.82908183812986805363425832654194', '10.53172286475752414027897064340862', '11.06252803263470322855786455431880', '12.81795394538978867927819838011176', '13.85946471812607869170124908439704', '15.91606995175311338214245833677918', '17.30555247170247858523707433007552'], 'prelabel': '2-18-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': 0.9266428346758557, 'root_number': '-0.9735618034217984 + 0.2284237617195186*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.463321417338', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31637154417658173846555528120', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.35908639154472099665748651899', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.66979716421108013218873373971', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/6/c/b/7/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-18-9.7-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-18-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': 0.46332141733792787, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31637154417658173846555528120', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '401048577870575634892913280023', 'Lhash_array': ['401048577870575634892913280023'], 'label': '2-18-9.7-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/c/b/7/1'}