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lfunc_lfunctions • Show schema
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{'Lhash': '1643824299202152630532152635241', 'a10': [-0.28216071122428493, 2.2181941603568895], 'a2': [-0.07133918319923234, 0.9974521146102535], 'a3': [-1.4119752030024275, 0.30715640434412705], 'a4': [-0.9898214418809327, -0.14231483827328514], 'a5': [2.2326715705337503, 0.1231976384934286], 'a6': [-0.20564464734936816, -1.4302899390123365], 'a7': [3.3803514412451032, -1.8458115350045738], 'a8': [0.21256528955297668, -0.9771468659711595], 'a9': [-0.8295670688994217, 0.37885058625107026], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.07133918319923234, -0.9974521146102535]]], [5, [[1.0, 0], [-2.2326715705337503, -0.1231976384934286]]], [23, [[1.0, 0], [-4.167692384982015, 2.372833787723642]]]], 'bad_primes': [2, 5, 23], 'central_character': '230.217', 'coefficient_field': 'CDF', 'conductor': 230, 'conductor_radical': 230, 'conjugate': '2227161732149274663137531841444', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.07133918319923234, -0.9974521146102535]], [[1.0, 0], [1.4119752030024275, -0.30715640434412705], [2.7288959860635553, -1.2462450390056592]], [[1.0, 0], [-2.2326715705337503, -0.1231976384934286]], [[1.0, 0], [-3.3803514412451032, 1.8458115350045738], [3.784485722189183, -5.888774729818268]], [[1.0, 0], [-3.85970288173901, -3.3444515851775263], [1.5654632210061366, 10.88803586069026]], [[1.0, 0], [2.1543072038220443, -3.9453190768506654], [-7.028330626922768, -10.936295926805355]], [[1.0, 0], [3.528551379035673, 2.6414404761361827], [4.7894534663043045, 16.311380551446454]], [[1.0, 0], [0.5969395853626791, -4.151806011716546], [-18.23036649867545, -5.352918579987164]], [[1.0, 0], [-4.167692384982015, 2.372833787723642]], [[1.0, 0], [-5.2990044299911245, 0.7618818168159299], [27.825296234820424, -8.170244148401462]], [[1.0, 0], [-2.1031974664003705, 1.3516429389348203], [12.877865403058479, 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[66.45902909366332, -42.71062457899221]], [[1.0, 0], [-2.018390116697362, 5.4115133257758075], [-62.72721467140344, -54.35344091745866]], [[1.0, 0], [0.3688845001039173, 0.23706767329903486], [36.97193615716789, 80.95724758655213]], [[1.0, 0], [-6.19201138208352, -16.60142498236611], [-73.30770871236305, 63.52149119269265]], [[1.0, 0], [4.217687368704754, 9.235447099643054], [-66.14093412847379, 76.33070700978008]], [[1.0, 0], [12.69818395727116, -0.9081920408573048], [101.95160851373608, -14.658428342148369]], [[1.0, 0], [-1.5916556895446328, 7.316723120761854], [-97.33062350293346, -44.44940639120185]], [[1.0, 0], [-0.12592015485526145, -0.8757939140637165], [-104.58473412398021, 30.708848695715837]], [[1.0, 0], [-0.9143464872584625, 12.78423436185662], [-111.8498229325454, -16.08157672488122]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-230-115.102-c1-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/230/2/l/a/217/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1328210786046482, 1.076159486087924, 1.020569857826471, 0.9617025087138631, 0.8942929370280143, 0.8129437614330108, 0.7128230650438868, 0.5902436408503716, 0.44313633895302007, 0.271439475908925, 0.0774108219763573, -0.13415245129325165, -0.35581674530877183, -0.577576628870573, -0.7871188770045727, -0.9703149805963363, -1.1119553925296393, -1.1967171767188767, -1.2103307791807738, -1.1408833820082418, -0.9801683792875882, -0.7249661121479939, -0.378123626092801, 0.05070563386430037, 0.5447945345488386, 1.0806572455273014, 1.6290174340345351, 2.156446222939341, 2.627619824810942, 3.0080731098439064, 3.267251899230534, 3.3816021188838348, 3.3373873424767604, 3.132906508164727, 2.7797978777413643, 2.303167904368646, 1.7403748814645046, 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'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.19977453463015116, 'root_number': '0.31036398921389197 - 0.9506177960669783*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19977453463', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29674872469290547821606179248', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86125630459363451857361989845', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88274104105306138840273801223', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8365592464894498, 'bad_primes': [2, 5, 23], 'central_character': '115.102', 'conductor': 230, 'conductor_radical': 230, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/230/2/l/a/217/3'], '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': '2-230-115.102-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-230-115.102-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.355197124587213, 'root_angle': -0.19977453463015116, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29674872469290547821606179248', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1643824299202152630532152635241', 'Lhash_array': ['1643824299202152630532152635241'], 'factors': ['2-230-115.102-c1-0-5'], 'label': '2-230-115.102-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/230/2/l/a/217/3'}