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lfunc_lfunctions • Show schema
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{'Lhash': '4257526648818466525273272788692', 'a10': [-2640.0, 0.0], 'a2': [0.0, -11.313708498984761], 'a3': [0.0, 0.0], 'a4': [-128.0, 0.0], 'a5': [0.0, -233.3452377915607], 'a6': [0.0, 0.0], 'a7': [-3532.0, 0.0], 'a8': [0.0, 1448.1546878700494], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.3328149811002925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 11.313708498984761]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '18.17', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '124682310183154776034089696480', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 11.313708498984761]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 233.3452377915607], [-390625.0, 0]], [[1.0, 0], [3532.0, 0], [5764801.0, 0]], [[1.0, 0], [0, -20177.99910793932], [-214358881.0, 0]], [[1.0, 0], [41824.0, 0], [815730721.0, 0]], [[1.0, 0], [0, 94784.83559093195], 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'positive_zeros': ['3.35859632618951633508319508725343', '5.80019996508245135146267048644383', '7.15005099945856710634261426167840', '8.999896508191296451017143115244883', '10.42988872452461900709699907837432', '12.48095525625212537133604321508088', '13.73505940951187823737649356336698', '15.10236266723732315934257461572866', '16.30200561471739735573125992094887', '17.25949815641182139764398727203759'], 'prelabel': '2-18-3.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.707917092730184, 'root_angle': -0.8040867239846964, 'root_number': '-0.8164965809277259 - 0.5773502691896258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.402043361992', 'prec': 50}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.35859632618951633508319508725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.80019996508245135146267048644', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.15005099945856710634261426168', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.3328149811002925, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/9/b/a/17/1'], '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': '2-18-3.2-c8-0-3', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-18-3.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.707917092730184, 'root_angle': -0.4020433619923482, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '3.35859632618951633508319508725', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4257526648818466525273272788692', 'Lhash_array': ['4257526648818466525273272788692'], 'label': '2-18-3.2-c8-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/9/b/a/17/1'}