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'6.19623599985866653147637043862910', '6.65392230687402623552823791409787', '6.78985885669453201253627076053427', '7.35302866930895167404280226921352', '7.45142130696493152047355657719390', '7.55092493200683228694329383045937', '7.88427259289301532109579215506574', '8.233415677265477648799570996711407', '8.301024455810803340374157015044063', '8.509573331427482567706864236629686'], 'prelabel': '6-2254e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.532142262083806, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3e3-0', 'trace_hash': 1008309891666664456, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70250433787796759767131451223', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.18183834997668096735039076969', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.49039631562347948871697109185', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2352122.5610521585, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 11451483064, 'conductor_radical': 322, 'degree': 6, 'dirichlet_coefficients': [1, -6, 3, 24, -8, -18, 0, -80, -42, 48, 6, 72, -13, 0, -24, 240, -20, 252, 12, -192, 0, -36, -69, -240, -177, 78, -163, 0, -67, 144, -41, -672, 18, 120, 0, -1008, -36, -72, -39, 640, -273, 0, 564, 144, 336, 414, -1145, 720, 0, 1062, -60, -312, 632, 978, -48, 0, 36, 402, 128, -576, -266, 246, 0, 1792, 104, -108, 1128, -480, -207, 0, 1075, 3360, -59, 216, -531, 288, 0, 234, -744, -1920, 624, 1638, -2708, 0, 160, -3384, -201, -480, -448, -2016, 0, -1656, -123, 6870, -96, -2016, 1322, 0, -252, -4248], 'euler11': [1, -6, 3477, -15820, 4627887, -10629366, 2357947691], 'euler13': [1, 13, 5743, 48890, 12617371, 62748517, 10604499373], 'euler17': [1, 20, 14337, 197288, 70437681, 482751380, 118587876497], 'euler19': [1, -12, 7653, -524904, 52491927, -564550572, 322687697779], 'euler2': [1, 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119851595982618319], [1, 2708, 3903245, 3586323960, 2231824748815, 885354531083252, 186940255267540403], [1, 448, 1612617, 707661976, 1136844993873, 222647618350528, 350356403707485209], [1, -1322, 1040633, -1001644904, 949757642009, -1101188990516138, 760231058654565217]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2254/4/a/h'], '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': '6-2254e3-1.1-c3e3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'prelabel': '6-2254e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.532142262083806, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 1008309891666664456, 'z1': {'__RealLiteral__': 0, 'data': '0.70250433787796759767131451223', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '890530045573940496551326756548,1498158093720679873551332427253,1889301784078045407067399927261', 'Lhash_array': ['890530045573940496551326756548', '1498158093720679873551332427253', '1889301784078045407067399927261'], 'factors': ['2-2254-1.1-c3-0-69', '2-2254-1.1-c3-0-153', '2-2254-1.1-c3-0-194'], 'label': '6-2254e3-1.1-c3e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2254/4/a/h'}