-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4428626703199502682403446394539', 'a10': [0.17844793394610473, 0.08593599576708644], 'a2': [0.2225209339563144, -0.9749279121818236], 'a3': [0.5, -0.24078730940376433], 'a4': [-0.9009688679024191, -0.4338837391175581], 'a5': [-0.04407300001020968, 0.1930964297137938], 'a6': [-0.12348980185873352, -0.5410441730642654], 'a7': [-0.09903113209758087, 0.047690879689970524], 'a8': [-0.6234898018587335, 0.7818314824680298], 'a9': [-1.6784479339461047, 2.1047071380003253], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.2225209339563144, 0.9749279121818236]]], [29, [[1.0, 0], [1.3949280753373532, 5.201362866079969]]]], 'bad_primes': [2, 29], 'central_character': '58.25', 'coefficient_field': 'CDF', 'conductor': 58, 'conductor_radical': 58, 'conjugate': '3185189534067210261406136693950', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [-0.5, 0.24078730940376433], [1.8704694055762006, -2.3454944474040893]], [[1.0, 0], [0.04407300001020968, -0.1930964297137938], [-4.504844339512096, -2.1694186955877908]], [[1.0, 0], [0.09903113209758087, -0.047690879689970524], [4.3644286130111345, -5.472820377276209]], [[1.0, 0], [0.8324371981310568, 1.043843230051415], [-2.4477302735194586, 10.72420703400006]], [[1.0, 0], [-2.4559269999897904, -3.079635050182149], [-2.8927721414320873, 12.674062858363706]], [[1.0, 0], [2.9118539999795807, 0], [17.0, 0]], [[1.0, 0], [1.1675628018689432, 0.5622686112438864], [11.846306235315938, 14.854798166892566]], [[1.0, 0], [1.733406066033476, 7.594548193174028], [-20.72228396175564, 9.979325999703837]], [[1.0, 0], [1.3949280753373532, 5.201362866079969]], [[1.0, 0], [-2.0794168018485237, 9.110520278420118], [-27.930034904974992, -13.450395912644302]], [[1.0, 0], [1.8873953302184279, -2.3667188855837105], [-8.233274556383632, -36.072332750727476]], [[1.0, 0], [-3.762709075306724, 0], [41.0, 0]], [[1.0, 0], [-1.4830740753577727, -6.497772080101915], [-38.741661319804024, 18.657000782055]], [[1.0, 0], [-0.5, -0.6269801688313519], [-10.458483895946777, 45.82161187254571]], [[1.0, 0], [1.8547399339869435, -8.12614660262544], [-47.75134999882821, -22.99583817323058]], [[1.0, 0], [5.088146000020419, 0], [59.0, 0]], [[1.0, 0], [-9.963459745108716, 4.798149328754886], [38.03287791338275, -47.69172043054982]], [[1.0, 0], [6.858387820446069, -8.600146307148329], [-14.908902575073066, -65.32017011618218]], [[1.0, 0], [-6.8263964055659905, -8.560030341742998], [-15.798986310898323, 69.21988176490947]], [[1.0, 0], [1.7687498678717901, 7.749399506810707], [-65.77072735687659, 31.673512955581742]], [[1.0, 0], [-3.0489173395223053, 3.8232214165730625], [-17.579153782548836, -77.01930506236407]], [[1.0, 0], [-10.518417877196086, -5.065403079669], [51.749653554274886, 64.89201304484648]], [[1.0, 0], [-2.557646537694201, 11.205781652807588], [-80.1862292433153, -38.61565278146267]], [[1.0, 0], [-9.54287654695724, -4.595607135428238], [60.47851078029715, 75.8376537993989]], [[1.0, 0], [1.3290848111728206, 5.823101031580592], [-90.99785565814433, 43.82225765087337]], [[1.0, 0], [8.974344877185876, 11.25347253249756], [-22.919656197500384, 100.41757495472783]], [[1.0, 0], [10.28232340555578, -12.89362572958785], [-23.80973993332564, -104.31728660345513]], [[1.0, 0], [2.559802471599467, -1.2327358994830828], [67.96038840260195, -85.21963158901525]], [[1.0, 0], [14.122293348805764, -6.800938036139232], [70.45434761003689, -88.34695751888736]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-58-29.25-c1-0-2', '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/58/2/d/a/25/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9320722129728914, 0.9621465095742374, 1.008001196633242, 1.069682942532292, 1.1465487160236219, 1.2373911349984306, 1.3405456710156631, 1.4539505480519033, 1.575159927618008, 1.7013274723753038, 1.829181008955108, 1.9550059974005103, 2.074650837444814, 2.1835629123273748, 2.276861098103658, 2.3494479499057443, 2.39616250464451, 2.4119723073042394, 2.3922007170066015, 2.3327827496044273, 2.230539736998502, 2.0834600790603757, 1.8909705412771525, 1.6541801627661785, 1.3760771639919707, 1.0616585662080569, 0.7179728227168124, 0.3540578388635931, -0.01923952573950011, -0.3895709725819595, -0.7435227762436017, -1.0671733596277229, -1.3467560755999315, -1.5694009422213386, -1.7239193926318959, -1.80158742043162, -1.7968756904457668, -1.708071111585872, -1.5377338319920337, -1.2929372626129005, -0.985246971150332, -0.6304072025940701, -0.2477210797946253, 0.14086850465568448, 0.5119668350284893, 0.8421292953499615, 1.10939898577171, 1.2948814245204467, 1.3842426836565247, 1.3690096003284455, 1.2475520510095492, 1.0256388340295775, 0.7164808837253623, 0.3402078389381826, -0.07723508850325783, -0.5057359592128132, -0.9131269466963184, -1.2676251797816447, -1.5404293599272134, -1.7082663612474092, -1.7556653564904152, -1.6767386115230485, -1.4762699984872765, -1.1699548372578474, -0.7836962669361928, -0.3519402948190756, 0.08488166721818824, 0.483644865333051, 0.80231678900595, 1.0039267506598382, 1.0603644939329138, 0.9556373663152692, 0.6882346919018559, 0.27230332109345246, -0.26257198236343815, -0.8730712761006223, -1.5052753953120082, -2.099040098954653, -2.593275189974501, -2.9316790737559524, -3.0683988445079784, -2.9730531863980363, -2.634577794917121, -2.063433095167195, -1.2918481800202568, -0.37195333215269516, 0.628139264002735, 1.6300309880319175, 2.5520306948807456, 3.3168042506779223, 3.858929661459361, 4.1315745000963595, 4.111562025959268, 3.8022253277499916, 3.2336558170227545, 2.460215079493133, 1.5554712904742598, 0.605011638836482, -0.30216299808048996, -1.082767161059228, -1.6678949242013708, -2.0102448658967114, -2.089060260663106, -1.912172296221248, -1.5148502040822915, -0.9555271707363434, -0.30884296006232503, 0.34322185325570204, 0.921092342871151, 1.3570624370444477, 1.6033138823976176, 1.6374783502543586, 1.465011791316037, 1.1180352759207282, 0.6507401130884887, 0.13190198411866796, -0.36455925366039854, -0.7697547397548227, -1.0293864022215387, -1.1113860165849614, -1.0105509907307573, -0.7494726525499724, -0.3755419084887121, 0.04564529689129892, 0.4396465015425347, 0.7340416722706709, 0.8693010864804058, 0.8080859025020344, 0.5415809017083614, 0.09183195292387461, -0.4904023187475109, -1.1321436700588767, -1.7482517016915118, -2.253710007035876, -2.576419521861453, -2.6686258192675956, -2.515223338038151, -2.1375601392957946, -1.5919689269280772, -0.9629958615801972, -0.3520848129977056, 0.1368136797020235, 0.41271209853485014, 0.4118825017479494, 0.10879698923068841, -0.4780723340469059, -1.2866937146619184, -2.218374698616863, -3.1503828734440127, -3.9526637920445795, -4.506348422271155, -4.721377227008566, -4.550590478554602, -3.9980585383523026, -3.12020449416538, -2.0193009502329478, -0.830055777564662, 0.29893140847107047, 1.2262261525485911, 1.8380499668777786, 2.0651182175269645, 1.893205094213139, 1.3657010472097189, 0.5776084801151173, -0.3382777531167557, -1.2310375072903634, -1.9542260521842179, -2.387979867539253, -2.457211113818365, -2.143025781538567, -1.485517998834914, -0.5774257155684045, 0.45042546523294263, 1.4496434243908356, 2.2775271378235153, 2.8193568333731744, 3.0061324513841283, 2.8248839274576563, 2.31986780114035, 1.5844507899170581, 0.745020082771769, -0.06040476838004982, -0.7052809722006721, -1.0954858894591122, -1.1845548003158946, -0.9806282680716293, -0.5439339211956229, 0.0247442714452854, 0.6025883394067905, 1.06700670728885, 1.3177035772138819, 1.2946385491010353, 0.9886639654901637, 0.4429160553028247, -0.2553133768354641, -0.9907755972739262, -1.6416008584810544, -2.1018672943362113, -2.301227664910091, -2.217912648545077, -1.8826134590656194, -1.3724173479207444, -0.7958280186474566, -0.27160707192403605, 0.0946006212991495, 0.2313883075985296, 0.11631533684489197, -0.21877213932071138, -0.6931081936332547, -1.192312541471472, -1.5909361512994769, -1.7780554446961223, -1.6809863557503457, -1.282375953576735, -0.627036413619493, 0.1832649678423906, 1.0065824443717328, 1.6863982448232926, 2.0814995519678736, 2.0945479712536845, 1.6937739669172294, 0.9233061034161831, -0.10037628762560591, -1.2058422791442434, -2.195305600679194, -2.8795375470252087, -3.1128335898025927, -2.821524318636217, -2.0204968611253156, -0.8142455009376549, 0.6182556816564966, 2.0525743540939603, 3.2568055306342187, 4.031801373525057, 4.24635458935663, 3.860831558875804, 2.9347773324549817, 1.6169208526578809, 0.11925881802377497, -1.320123625957191, -2.478701966342429, -3.187968842893208, -3.3616166968664474, -3.008301060010093, -2.226769029183441, -1.1845017901590411, -0.0841664514744661, 0.8755159690871218, 1.53686131723494, 1.8111282594196332, 1.6919865973952872, 1.2522217761818037, 0.6247274478391335, -0.02801281615887564, -0.5494718702183043, -0.8222229047806507, -0.7918332894103125], 'positive_zeros': ['3.49357046997190486475942377953672', '5.32943593020712940336867539765750', '6.72739288050964183111280694596820', '8.225239511846850158540244353264179', '9.191521501729499755706783795967853', '10.67215851392972238258172563527554', '12.20694610435273642423391662469227', '13.30837238118236334187272276554622', '14.40694218610462715111579306293834', '15.36146466461543118137215038524422'], 'prelabel': '2-58-29.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': 0.13625213555845356, 'root_number': '0.6553900363987342 + 0.755290606448449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.136252135558', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.49357046997190486475942377954', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.32943593020712940336867539766', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.72739288050964183111280694597', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.46313233172342644, 'bad_primes': [2, 29], 'central_character': '29.25', 'conductor': 58, 'conductor_radical': 58, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/58/2/d/a/25/1'], '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': '2-58-29.25-c1-0-2', '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': '2-58-29.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6805382661712907, 'root_angle': 0.13625213555845356, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.49357046997190486475942377954', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4428626703199502682403446394539', 'Lhash_array': ['4428626703199502682403446394539'], 'factors': ['2-58-29.25-c1-0-2'], 'label': '2-58-29.25-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/58/2/d/a/25/1'}