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lfunc_lfunctions • Show schema
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{'Lhash': '2174957313690914278426498956170', 'a10': [-264.34733635431996, -6.858241482228649e-60], 'a2': [-2.0, 3.4641016151377544], 'a3': [15.514472348096666, 1.5169534469270742], 'a4': [-8.0, -13.856406460551018], 'a5': [33.043417044289995, 57.23287717639769], 'a6': [-36.283825581782196, 50.709801825197545], 'a7': [-57.09519051471994, 98.89177083931958], 'a8': [64.0, 0.0], 'a9': [238.39770447971213, 47.06946461140003], '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], [-15.514472348096666, -1.5169534469270742]]]], 'bad_primes': [2, 3], 'central_character': '18.7', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '3645355332307696872090057559598', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, -3.4641016151377544]], [[1.0, 0], [-15.514472348096666, -1.5169534469270742]], 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'7.35859196614345558665499002618079', '9.191918292527484390043958788067253', '9.836308933444155697069781855300451', '12.18808942070390514921159856707414', '13.29475160753135191812451146276876', '14.41991161420366995179511261573854', '16.42291179109022691283834270905722', '17.38545921243229792090258146964789'], 'prelabel': '2-18-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': -0.3823951175399174, 'root_number': '0.36111810955688034 - 0.9325200860839754*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19119755877', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71573879529527477054922217364', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20451398805836135541476945585', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.35859196614345558665499002618', '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': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/6/c/b/7/3'], '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-c5-0-1', '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': -0.1911975587699587, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.71573879529527477054922217364', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2174957313690914278426498956170', 'Lhash_array': ['2174957313690914278426498956170'], 'label': '2-18-9.7-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/c/b/7/3'}