Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(73\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53607 | −1.08617 | −0.543084 | − | 0.839678i | \(-0.682744\pi\) | ||||
−0.543084 | + | 0.839678i | \(0.682744\pi\) | |||||||
\(3\) | −1.95086 | −1.12633 | −0.563165 | − | 0.826344i | \(-0.690417\pi\) | ||||
−0.563165 | + | 0.826344i | \(0.690417\pi\) | |||||||
\(4\) | 0.359523 | 0.179761 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.99667 | 1.22338 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.51989 | 0.890917 | ||||||||
\(9\) | 0.805862 | 0.268621 | ||||||||
\(10\) | −1.53607 | −0.485749 | ||||||||
\(11\) | −5.97648 | −1.80198 | −0.900988 | − | 0.433845i | \(-0.857157\pi\) | ||||
−0.900988 | + | 0.433845i | \(0.857157\pi\) | |||||||
\(12\) | −0.701380 | −0.202471 | ||||||||
\(13\) | 3.87926 | 1.07591 | 0.537957 | − | 0.842972i | \(-0.319196\pi\) | ||||
0.537957 | + | 0.842972i | \(0.319196\pi\) | |||||||
\(14\) | −1.53607 | −0.410533 | ||||||||
\(15\) | −1.95086 | −0.503710 | ||||||||
\(16\) | −4.58979 | −1.14745 | ||||||||
\(17\) | 3.91503 | 0.949533 | 0.474767 | − | 0.880112i | \(-0.342533\pi\) | ||||
0.474767 | + | 0.880112i | \(0.342533\pi\) | |||||||
\(18\) | −1.23786 | −0.291767 | ||||||||
\(19\) | 8.22848 | 1.88774 | 0.943871 | − | 0.330314i | \(-0.107155\pi\) | ||||
0.943871 | + | 0.330314i | \(0.107155\pi\) | |||||||
\(20\) | 0.359523 | 0.0803918 | ||||||||
\(21\) | −1.95086 | −0.425713 | ||||||||
\(22\) | 9.18031 | 1.95725 | ||||||||
\(23\) | 7.00330 | 1.46029 | 0.730144 | − | 0.683293i | \(-0.239453\pi\) | ||||
0.730144 | + | 0.683293i | \(0.239453\pi\) | |||||||
\(24\) | −4.91597 | −1.00347 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.95884 | −1.16862 | ||||||||
\(27\) | 4.28046 | 0.823775 | ||||||||
\(28\) | 0.359523 | 0.0679435 | ||||||||
\(29\) | 8.04465 | 1.49385 | 0.746927 | − | 0.664906i | \(-0.231528\pi\) | ||||
0.746927 | + | 0.664906i | \(0.231528\pi\) | |||||||
\(30\) | 2.99667 | 0.547114 | ||||||||
\(31\) | −6.18132 | −1.11020 | −0.555099 | − | 0.831784i | \(-0.687320\pi\) | ||||
−0.555099 | + | 0.831784i | \(0.687320\pi\) | |||||||
\(32\) | 2.01047 | 0.355404 | ||||||||
\(33\) | 11.6593 | 2.02962 | ||||||||
\(34\) | −6.01377 | −1.03135 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.289726 | 0.0482877 | ||||||||
\(37\) | 10.7596 | 1.76886 | 0.884432 | − | 0.466670i | \(-0.154546\pi\) | ||||
0.884432 | + | 0.466670i | \(0.154546\pi\) | |||||||
\(38\) | −12.6396 | −2.05041 | ||||||||
\(39\) | −7.56791 | −1.21184 | ||||||||
\(40\) | 2.51989 | 0.398430 | ||||||||
\(41\) | 2.87438 | 0.448903 | 0.224452 | − | 0.974485i | \(-0.427941\pi\) | ||||
0.224452 | + | 0.974485i | \(0.427941\pi\) | |||||||
\(42\) | 2.99667 | 0.462396 | ||||||||
\(43\) | −0.964070 | −0.147019 | −0.0735096 | − | 0.997295i | \(-0.523420\pi\) | ||||
−0.0735096 | + | 0.997295i | \(0.523420\pi\) | |||||||
\(44\) | −2.14868 | −0.323926 | ||||||||
\(45\) | 0.805862 | 0.120131 | ||||||||
\(46\) | −10.7576 | −1.58612 | ||||||||
\(47\) | 6.91503 | 1.00866 | 0.504330 | − | 0.863511i | \(-0.331739\pi\) | ||||
0.504330 | + | 0.863511i | \(0.331739\pi\) | |||||||
\(48\) | 8.95404 | 1.29241 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.53607 | −0.217234 | ||||||||
\(51\) | −7.63767 | −1.06949 | ||||||||
\(52\) | 1.39468 | 0.193408 | ||||||||
\(53\) | −3.53218 | −0.485183 | −0.242591 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242591 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(54\) | −6.57510 | −0.894758 | ||||||||
\(55\) | −5.97648 | −0.805868 | ||||||||
\(56\) | 2.51989 | 0.336735 | ||||||||
\(57\) | −16.0526 | −2.12622 | ||||||||
\(58\) | −12.3572 | −1.62258 | ||||||||
\(59\) | 10.8686 | 1.41498 | 0.707488 | − | 0.706725i | \(-0.249828\pi\) | ||||
0.707488 | + | 0.706725i | \(0.249828\pi\) | |||||||
\(60\) | −0.701380 | −0.0905477 | ||||||||
\(61\) | 0.921656 | 0.118006 | 0.0590030 | − | 0.998258i | \(-0.481208\pi\) | ||||
0.0590030 | + | 0.998258i | \(0.481208\pi\) | |||||||
\(62\) | 9.49497 | 1.20586 | ||||||||
\(63\) | 0.805862 | 0.101529 | ||||||||
\(64\) | 6.09135 | 0.761419 | ||||||||
\(65\) | 3.87926 | 0.481163 | ||||||||
\(66\) | −17.9095 | −2.20451 | ||||||||
\(67\) | −10.6268 | −1.29827 | −0.649133 | − | 0.760675i | \(-0.724868\pi\) | ||||
−0.649133 | + | 0.760675i | \(0.724868\pi\) | |||||||
\(68\) | 1.40754 | 0.170689 | ||||||||
\(69\) | −13.6625 | −1.64477 | ||||||||
\(70\) | −1.53607 | −0.183596 | ||||||||
\(71\) | −6.66462 | −0.790944 | −0.395472 | − | 0.918478i | \(-0.629419\pi\) | ||||
−0.395472 | + | 0.918478i | \(0.629419\pi\) | |||||||
\(72\) | 2.03069 | 0.239319 | ||||||||
\(73\) | 8.63409 | 1.01054 | 0.505272 | − | 0.862960i | \(-0.331392\pi\) | ||||
0.505272 | + | 0.862960i | \(0.331392\pi\) | |||||||
\(74\) | −16.5275 | −1.92128 | ||||||||
\(75\) | −1.95086 | −0.225266 | ||||||||
\(76\) | 2.95833 | 0.339343 | ||||||||
\(77\) | −5.97648 | −0.681083 | ||||||||
\(78\) | 11.6249 | 1.31626 | ||||||||
\(79\) | 7.66741 | 0.862651 | 0.431326 | − | 0.902196i | \(-0.358046\pi\) | ||||
0.431326 | + | 0.902196i | \(0.358046\pi\) | |||||||
\(80\) | −4.58979 | −0.513154 | ||||||||
\(81\) | −10.7682 | −1.19646 | ||||||||
\(82\) | −4.41527 | −0.487584 | ||||||||
\(83\) | 16.2498 | 1.78364 | 0.891822 | − | 0.452386i | \(-0.149427\pi\) | ||||
0.891822 | + | 0.452386i | \(0.149427\pi\) | |||||||
\(84\) | −0.701380 | −0.0765268 | ||||||||
\(85\) | 3.91503 | 0.424644 | ||||||||
\(86\) | 1.48088 | 0.159688 | ||||||||
\(87\) | −15.6940 | −1.68257 | ||||||||
\(88\) | −15.0601 | −1.60541 | ||||||||
\(89\) | −4.24267 | −0.449723 | −0.224861 | − | 0.974391i | \(-0.572193\pi\) | ||||
−0.224861 | + | 0.974391i | \(0.572193\pi\) | |||||||
\(90\) | −1.23786 | −0.130482 | ||||||||
\(91\) | 3.87926 | 0.406657 | ||||||||
\(92\) | 2.51785 | 0.262504 | ||||||||
\(93\) | 12.0589 | 1.25045 | ||||||||
\(94\) | −10.6220 | −1.09558 | ||||||||
\(95\) | 8.22848 | 0.844224 | ||||||||
\(96\) | −3.92214 | −0.400302 | ||||||||
\(97\) | 11.5264 | 1.17033 | 0.585163 | − | 0.810916i | \(-0.301031\pi\) | ||||
0.585163 | + | 0.810916i | \(0.301031\pi\) | |||||||
\(98\) | −1.53607 | −0.155167 | ||||||||
\(99\) | −4.81622 | −0.484048 | ||||||||
\(100\) | 0.359523 | 0.0359523 | ||||||||
\(101\) | 17.4091 | 1.73227 | 0.866133 | − | 0.499814i | \(-0.166598\pi\) | ||||
0.866133 | + | 0.499814i | \(0.166598\pi\) | |||||||
\(102\) | 11.7320 | 1.16164 | ||||||||
\(103\) | 16.9764 | 1.67273 | 0.836365 | − | 0.548173i | \(-0.184677\pi\) | ||||
0.836365 | + | 0.548173i | \(0.184677\pi\) | |||||||
\(104\) | 9.77533 | 0.958550 | ||||||||
\(105\) | −1.95086 | −0.190385 | ||||||||
\(106\) | 5.42570 | 0.526990 | ||||||||
\(107\) | −10.6726 | −1.03176 | −0.515881 | − | 0.856660i | \(-0.672535\pi\) | ||||
−0.515881 | + | 0.856660i | \(0.672535\pi\) | |||||||
\(108\) | 1.53892 | 0.148083 | ||||||||
\(109\) | 2.76910 | 0.265232 | 0.132616 | − | 0.991168i | \(-0.457662\pi\) | ||||
0.132616 | + | 0.991168i | \(0.457662\pi\) | |||||||
\(110\) | 9.18031 | 0.875308 | ||||||||
\(111\) | −20.9904 | −1.99232 | ||||||||
\(112\) | −4.58979 | −0.433694 | ||||||||
\(113\) | −12.3535 | −1.16212 | −0.581060 | − | 0.813860i | \(-0.697362\pi\) | ||||
−0.581060 | + | 0.813860i | \(0.697362\pi\) | |||||||
\(114\) | 24.6580 | 2.30944 | ||||||||
\(115\) | 7.00330 | 0.653061 | ||||||||
\(116\) | 2.89224 | 0.268538 | ||||||||
\(117\) | 3.12615 | 0.289013 | ||||||||
\(118\) | −16.6950 | −1.53690 | ||||||||
\(119\) | 3.91503 | 0.358890 | ||||||||
\(120\) | −4.91597 | −0.448764 | ||||||||
\(121\) | 24.7183 | 2.24711 | ||||||||
\(122\) | −1.41573 | −0.128174 | ||||||||
\(123\) | −5.60753 | −0.505614 | ||||||||
\(124\) | −2.22233 | −0.199571 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.23786 | −0.110278 | ||||||||
\(127\) | 4.79813 | 0.425765 | 0.212883 | − | 0.977078i | \(-0.431715\pi\) | ||||
0.212883 | + | 0.977078i | \(0.431715\pi\) | |||||||
\(128\) | −13.3777 | −1.18243 | ||||||||
\(129\) | 1.88077 | 0.165592 | ||||||||
\(130\) | −5.95884 | −0.522624 | ||||||||
\(131\) | −19.0112 | −1.66101 | −0.830507 | − | 0.557008i | \(-0.811949\pi\) | ||||
−0.830507 | + | 0.557008i | \(0.811949\pi\) | |||||||
\(132\) | 4.19178 | 0.364847 | ||||||||
\(133\) | 8.22848 | 0.713500 | ||||||||
\(134\) | 16.3235 | 1.41013 | ||||||||
\(135\) | 4.28046 | 0.368403 | ||||||||
\(136\) | 9.86545 | 0.845955 | ||||||||
\(137\) | 6.31057 | 0.539149 | 0.269574 | − | 0.962980i | \(-0.413117\pi\) | ||||
0.269574 | + | 0.962980i | \(0.413117\pi\) | |||||||
\(138\) | 20.9866 | 1.78649 | ||||||||
\(139\) | −7.03166 | −0.596417 | −0.298209 | − | 0.954501i | \(-0.596389\pi\) | ||||
−0.298209 | + | 0.954501i | \(0.596389\pi\) | |||||||
\(140\) | 0.359523 | 0.0303852 | ||||||||
\(141\) | −13.4903 | −1.13609 | ||||||||
\(142\) | 10.2373 | 0.859099 | ||||||||
\(143\) | −23.1843 | −1.93877 | ||||||||
\(144\) | −3.69874 | −0.308228 | ||||||||
\(145\) | 8.04465 | 0.668072 | ||||||||
\(146\) | −13.2626 | −1.09762 | ||||||||
\(147\) | −1.95086 | −0.160904 | ||||||||
\(148\) | 3.86831 | 0.317973 | ||||||||
\(149\) | 7.60719 | 0.623205 | 0.311602 | − | 0.950213i | \(-0.399134\pi\) | ||||
0.311602 | + | 0.950213i | \(0.399134\pi\) | |||||||
\(150\) | 2.99667 | 0.244677 | ||||||||
\(151\) | −13.0858 | −1.06490 | −0.532452 | − | 0.846460i | \(-0.678729\pi\) | ||||
−0.532452 | + | 0.846460i | \(0.678729\pi\) | |||||||
\(152\) | 20.7349 | 1.68182 | ||||||||
\(153\) | 3.15497 | 0.255064 | ||||||||
\(154\) | 9.18031 | 0.739770 | ||||||||
\(155\) | −6.18132 | −0.496496 | ||||||||
\(156\) | −2.72084 | −0.217841 | ||||||||
\(157\) | −6.94851 | −0.554551 | −0.277276 | − | 0.960790i | \(-0.589432\pi\) | ||||
−0.277276 | + | 0.960790i | \(0.589432\pi\) | |||||||
\(158\) | −11.7777 | −0.936984 | ||||||||
\(159\) | 6.89080 | 0.546476 | ||||||||
\(160\) | 2.01047 | 0.158941 | ||||||||
\(161\) | 7.00330 | 0.551937 | ||||||||
\(162\) | 16.5407 | 1.29956 | ||||||||
\(163\) | −19.1379 | −1.49900 | −0.749499 | − | 0.662006i | \(-0.769705\pi\) | ||||
−0.749499 | + | 0.662006i | \(0.769705\pi\) | |||||||
\(164\) | 1.03341 | 0.0806955 | ||||||||
\(165\) | 11.6593 | 0.907674 | ||||||||
\(166\) | −24.9609 | −1.93734 | ||||||||
\(167\) | 2.08602 | 0.161421 | 0.0807106 | − | 0.996738i | \(-0.474281\pi\) | ||||
0.0807106 | + | 0.996738i | \(0.474281\pi\) | |||||||
\(168\) | −4.91597 | −0.379275 | ||||||||
\(169\) | 2.04869 | 0.157591 | ||||||||
\(170\) | −6.01377 | −0.461235 | ||||||||
\(171\) | 6.63102 | 0.507087 | ||||||||
\(172\) | −0.346605 | −0.0264284 | ||||||||
\(173\) | −11.4872 | −0.873356 | −0.436678 | − | 0.899618i | \(-0.643845\pi\) | ||||
−0.436678 | + | 0.899618i | \(0.643845\pi\) | |||||||
\(174\) | 24.1072 | 1.82756 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 27.4308 | 2.06767 | ||||||||
\(177\) | −21.2032 | −1.59373 | ||||||||
\(178\) | 6.51706 | 0.488474 | ||||||||
\(179\) | −7.99235 | −0.597377 | −0.298688 | − | 0.954351i | \(-0.596549\pi\) | ||||
−0.298688 | + | 0.954351i | \(0.596549\pi\) | |||||||
\(180\) | 0.289726 | 0.0215949 | ||||||||
\(181\) | 20.1971 | 1.50124 | 0.750618 | − | 0.660736i | \(-0.229756\pi\) | ||||
0.750618 | + | 0.660736i | \(0.229756\pi\) | |||||||
\(182\) | −5.95884 | −0.441698 | ||||||||
\(183\) | −1.79802 | −0.132914 | ||||||||
\(184\) | 17.6476 | 1.30100 | ||||||||
\(185\) | 10.7596 | 0.791060 | ||||||||
\(186\) | −18.5234 | −1.35820 | ||||||||
\(187\) | −23.3981 | −1.71103 | ||||||||
\(188\) | 2.48611 | 0.181318 | ||||||||
\(189\) | 4.28046 | 0.311358 | ||||||||
\(190\) | −12.6396 | −0.916969 | ||||||||
\(191\) | 13.5931 | 0.983565 | 0.491783 | − | 0.870718i | \(-0.336345\pi\) | ||||
0.491783 | + | 0.870718i | \(0.336345\pi\) | |||||||
\(192\) | −11.8834 | −0.857610 | ||||||||
\(193\) | 9.53875 | 0.686614 | 0.343307 | − | 0.939223i | \(-0.388453\pi\) | ||||
0.343307 | + | 0.939223i | \(0.388453\pi\) | |||||||
\(194\) | −17.7054 | −1.27117 | ||||||||
\(195\) | −7.56791 | −0.541949 | ||||||||
\(196\) | 0.359523 | 0.0256802 | ||||||||
\(197\) | −27.2605 | −1.94223 | −0.971115 | − | 0.238611i | \(-0.923308\pi\) | ||||
−0.971115 | + | 0.238611i | \(0.923308\pi\) | |||||||
\(198\) | 7.39806 | 0.525757 | ||||||||
\(199\) | 0.826906 | 0.0586178 | 0.0293089 | − | 0.999570i | \(-0.490669\pi\) | ||||
0.0293089 | + | 0.999570i | \(0.490669\pi\) | |||||||
\(200\) | 2.51989 | 0.178183 | ||||||||
\(201\) | 20.7313 | 1.46228 | ||||||||
\(202\) | −26.7416 | −1.88153 | ||||||||
\(203\) | 8.04465 | 0.564624 | ||||||||
\(204\) | −2.74592 | −0.192253 | ||||||||
\(205\) | 2.87438 | 0.200756 | ||||||||
\(206\) | −26.0769 | −1.81687 | ||||||||
\(207\) | 5.64369 | 0.392264 | ||||||||
\(208\) | −17.8050 | −1.23455 | ||||||||
\(209\) | −49.1773 | −3.40166 | ||||||||
\(210\) | 2.99667 | 0.206790 | ||||||||
\(211\) | −0.152522 | −0.0105000 | −0.00525001 | − | 0.999986i | \(-0.501671\pi\) | ||||
−0.00525001 | + | 0.999986i | \(0.501671\pi\) | |||||||
\(212\) | −1.26990 | −0.0872172 | ||||||||
\(213\) | 13.0017 | 0.890865 | ||||||||
\(214\) | 16.3939 | 1.12067 | ||||||||
\(215\) | −0.964070 | −0.0657490 | ||||||||
\(216\) | 10.7863 | 0.733915 | ||||||||
\(217\) | −6.18132 | −0.419615 | ||||||||
\(218\) | −4.25354 | −0.288086 | ||||||||
\(219\) | −16.8439 | −1.13821 | ||||||||
\(220\) | −2.14868 | −0.144864 | ||||||||
\(221\) | 15.1874 | 1.02162 | ||||||||
\(222\) | 32.2429 | 2.16400 | ||||||||
\(223\) | 16.6683 | 1.11619 | 0.558096 | − | 0.829776i | \(-0.311532\pi\) | ||||
0.558096 | + | 0.829776i | \(0.311532\pi\) | |||||||
\(224\) | 2.01047 | 0.134330 | ||||||||
\(225\) | 0.805862 | 0.0537241 | ||||||||
\(226\) | 18.9759 | 1.26226 | ||||||||
\(227\) | 20.1274 | 1.33591 | 0.667953 | − | 0.744204i | \(-0.267171\pi\) | ||||
0.667953 | + | 0.744204i | \(0.267171\pi\) | |||||||
\(228\) | −5.77129 | −0.382213 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −10.7576 | −0.709334 | ||||||||
\(231\) | 11.6593 | 0.767124 | ||||||||
\(232\) | 20.2717 | 1.33090 | ||||||||
\(233\) | −9.56199 | −0.626427 | −0.313213 | − | 0.949683i | \(-0.601406\pi\) | ||||
−0.313213 | + | 0.949683i | \(0.601406\pi\) | |||||||
\(234\) | −4.80200 | −0.313917 | ||||||||
\(235\) | 6.91503 | 0.451087 | ||||||||
\(236\) | 3.90753 | 0.254358 | ||||||||
\(237\) | −14.9581 | −0.971630 | ||||||||
\(238\) | −6.01377 | −0.389815 | ||||||||
\(239\) | −15.9302 | −1.03044 | −0.515221 | − | 0.857058i | \(-0.672290\pi\) | ||||
−0.515221 | + | 0.857058i | \(0.672290\pi\) | |||||||
\(240\) | 8.95404 | 0.577981 | ||||||||
\(241\) | 20.0192 | 1.28955 | 0.644776 | − | 0.764372i | \(-0.276951\pi\) | ||||
0.644776 | + | 0.764372i | \(0.276951\pi\) | |||||||
\(242\) | −37.9691 | −2.44074 | ||||||||
\(243\) | 8.16584 | 0.523839 | ||||||||
\(244\) | 0.331356 | 0.0212129 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 8.61357 | 0.549181 | ||||||||
\(247\) | 31.9204 | 2.03105 | ||||||||
\(248\) | −15.5763 | −0.989094 | ||||||||
\(249\) | −31.7011 | −2.00897 | ||||||||
\(250\) | −1.53607 | −0.0971498 | ||||||||
\(251\) | 9.07393 | 0.572741 | 0.286371 | − | 0.958119i | \(-0.407551\pi\) | ||||
0.286371 | + | 0.958119i | \(0.407551\pi\) | |||||||
\(252\) | 0.289726 | 0.0182510 | ||||||||
\(253\) | −41.8550 | −2.63140 | ||||||||
\(254\) | −7.37029 | −0.462453 | ||||||||
\(255\) | −7.63767 | −0.478290 | ||||||||
\(256\) | 8.36643 | 0.522902 | ||||||||
\(257\) | −17.5659 | −1.09573 | −0.547866 | − | 0.836566i | \(-0.684560\pi\) | ||||
−0.547866 | + | 0.836566i | \(0.684560\pi\) | |||||||
\(258\) | −2.88900 | −0.179861 | ||||||||
\(259\) | 10.7596 | 0.668567 | ||||||||
\(260\) | 1.39468 | 0.0864947 | ||||||||
\(261\) | 6.48288 | 0.401280 | ||||||||
\(262\) | 29.2026 | 1.80414 | ||||||||
\(263\) | −7.78017 | −0.479746 | −0.239873 | − | 0.970804i | \(-0.577106\pi\) | ||||
−0.239873 | + | 0.970804i | \(0.577106\pi\) | |||||||
\(264\) | 29.3801 | 1.80822 | ||||||||
\(265\) | −3.53218 | −0.216980 | ||||||||
\(266\) | −12.6396 | −0.774981 | ||||||||
\(267\) | 8.27687 | 0.506536 | ||||||||
\(268\) | −3.82056 | −0.233378 | ||||||||
\(269\) | −0.469573 | −0.0286303 | −0.0143152 | − | 0.999898i | \(-0.504557\pi\) | ||||
−0.0143152 | + | 0.999898i | \(0.504557\pi\) | |||||||
\(270\) | −6.57510 | −0.400148 | ||||||||
\(271\) | −19.3442 | −1.17508 | −0.587538 | − | 0.809196i | \(-0.699903\pi\) | ||||
−0.587538 | + | 0.809196i | \(0.699903\pi\) | |||||||
\(272\) | −17.9691 | −1.08954 | ||||||||
\(273\) | −7.56791 | −0.458031 | ||||||||
\(274\) | −9.69351 | −0.585606 | ||||||||
\(275\) | −5.97648 | −0.360395 | ||||||||
\(276\) | −4.91197 | −0.295666 | ||||||||
\(277\) | 24.4319 | 1.46797 | 0.733986 | − | 0.679165i | \(-0.237658\pi\) | ||||
0.733986 | + | 0.679165i | \(0.237658\pi\) | |||||||
\(278\) | 10.8011 | 0.647809 | ||||||||
\(279\) | −4.98129 | −0.298222 | ||||||||
\(280\) | 2.51989 | 0.150592 | ||||||||
\(281\) | −13.7029 | −0.817445 | −0.408723 | − | 0.912659i | \(-0.634026\pi\) | ||||
−0.408723 | + | 0.912659i | \(0.634026\pi\) | |||||||
\(282\) | 20.7220 | 1.23398 | ||||||||
\(283\) | −28.5765 | −1.69870 | −0.849348 | − | 0.527833i | \(-0.823005\pi\) | ||||
−0.849348 | + | 0.527833i | \(0.823005\pi\) | |||||||
\(284\) | −2.39608 | −0.142181 | ||||||||
\(285\) | −16.0526 | −0.950875 | ||||||||
\(286\) | 35.6128 | 2.10583 | ||||||||
\(287\) | 2.87438 | 0.169669 | ||||||||
\(288\) | 1.62016 | 0.0954688 | ||||||||
\(289\) | −1.67258 | −0.0983870 | ||||||||
\(290\) | −12.3572 | −0.725639 | ||||||||
\(291\) | −22.4863 | −1.31817 | ||||||||
\(292\) | 3.10415 | 0.181657 | ||||||||
\(293\) | −12.3659 | −0.722423 | −0.361212 | − | 0.932484i | \(-0.617637\pi\) | ||||
−0.361212 | + | 0.932484i | \(0.617637\pi\) | |||||||
\(294\) | 2.99667 | 0.174769 | ||||||||
\(295\) | 10.8686 | 0.632797 | ||||||||
\(296\) | 27.1130 | 1.57591 | ||||||||
\(297\) | −25.5821 | −1.48442 | ||||||||
\(298\) | −11.6852 | −0.676905 | ||||||||
\(299\) | 27.1676 | 1.57115 | ||||||||
\(300\) | −0.701380 | −0.0404942 | ||||||||
\(301\) | −0.964070 | −0.0555681 | ||||||||
\(302\) | 20.1007 | 1.15667 | ||||||||
\(303\) | −33.9627 | −1.95110 | ||||||||
\(304\) | −37.7670 | −2.16609 | ||||||||
\(305\) | 0.921656 | 0.0527739 | ||||||||
\(306\) | −4.84627 | −0.277043 | ||||||||
\(307\) | −3.52710 | −0.201302 | −0.100651 | − | 0.994922i | \(-0.532093\pi\) | ||||
−0.100651 | + | 0.994922i | \(0.532093\pi\) | |||||||
\(308\) | −2.14868 | −0.122432 | ||||||||
\(309\) | −33.1185 | −1.88405 | ||||||||
\(310\) | 9.49497 | 0.539278 | ||||||||
\(311\) | −3.59366 | −0.203778 | −0.101889 | − | 0.994796i | \(-0.532489\pi\) | ||||
−0.101889 | + | 0.994796i | \(0.532489\pi\) | |||||||
\(312\) | −19.0703 | −1.07964 | ||||||||
\(313\) | −19.5864 | −1.10709 | −0.553544 | − | 0.832820i | \(-0.686725\pi\) | ||||
−0.553544 | + | 0.832820i | \(0.686725\pi\) | |||||||
\(314\) | 10.6734 | 0.602336 | ||||||||
\(315\) | 0.805862 | 0.0454052 | ||||||||
\(316\) | 2.75661 | 0.155071 | ||||||||
\(317\) | −15.8897 | −0.892453 | −0.446227 | − | 0.894920i | \(-0.647232\pi\) | ||||
−0.446227 | + | 0.894920i | \(0.647232\pi\) | |||||||
\(318\) | −10.5848 | −0.593565 | ||||||||
\(319\) | −48.0787 | −2.69189 | ||||||||
\(320\) | 6.09135 | 0.340517 | ||||||||
\(321\) | 20.8208 | 1.16211 | ||||||||
\(322\) | −10.7576 | −0.599497 | ||||||||
\(323\) | 32.2147 | 1.79247 | ||||||||
\(324\) | −3.87141 | −0.215078 | ||||||||
\(325\) | 3.87926 | 0.215183 | ||||||||
\(326\) | 29.3973 | 1.62816 | ||||||||
\(327\) | −5.40213 | −0.298739 | ||||||||
\(328\) | 7.24314 | 0.399936 | ||||||||
\(329\) | 6.91503 | 0.381238 | ||||||||
\(330\) | −17.9095 | −0.985886 | ||||||||
\(331\) | −22.2890 | −1.22511 | −0.612556 | − | 0.790427i | \(-0.709859\pi\) | ||||
−0.612556 | + | 0.790427i | \(0.709859\pi\) | |||||||
\(332\) | 5.84217 | 0.320631 | ||||||||
\(333\) | 8.67074 | 0.475153 | ||||||||
\(334\) | −3.20428 | −0.175331 | ||||||||
\(335\) | −10.6268 | −0.580602 | ||||||||
\(336\) | 8.95404 | 0.488483 | ||||||||
\(337\) | −25.6985 | −1.39989 | −0.699944 | − | 0.714197i | \(-0.746792\pi\) | ||||
−0.699944 | + | 0.714197i | \(0.746792\pi\) | |||||||
\(338\) | −3.14693 | −0.171171 | ||||||||
\(339\) | 24.1000 | 1.30893 | ||||||||
\(340\) | 1.40754 | 0.0763347 | ||||||||
\(341\) | 36.9425 | 2.00055 | ||||||||
\(342\) | −10.1857 | −0.550782 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.42935 | −0.130982 | ||||||||
\(345\) | −13.6625 | −0.735563 | ||||||||
\(346\) | 17.6452 | 0.948612 | ||||||||
\(347\) | 10.5496 | 0.566334 | 0.283167 | − | 0.959071i | \(-0.408615\pi\) | ||||
0.283167 | + | 0.959071i | \(0.408615\pi\) | |||||||
\(348\) | −5.64236 | −0.302462 | ||||||||
\(349\) | 12.3239 | 0.659685 | 0.329842 | − | 0.944036i | \(-0.393004\pi\) | ||||
0.329842 | + | 0.944036i | \(0.393004\pi\) | |||||||
\(350\) | −1.53607 | −0.0821066 | ||||||||
\(351\) | 16.6050 | 0.886311 | ||||||||
\(352\) | −12.0155 | −0.640429 | ||||||||
\(353\) | −16.5244 | −0.879505 | −0.439753 | − | 0.898119i | \(-0.644934\pi\) | ||||
−0.439753 | + | 0.898119i | \(0.644934\pi\) | |||||||
\(354\) | 32.5697 | 1.73106 | ||||||||
\(355\) | −6.66462 | −0.353721 | ||||||||
\(356\) | −1.52534 | −0.0808428 | ||||||||
\(357\) | −7.63767 | −0.404229 | ||||||||
\(358\) | 12.2768 | 0.648851 | ||||||||
\(359\) | −17.9265 | −0.946123 | −0.473061 | − | 0.881029i | \(-0.656851\pi\) | ||||
−0.473061 | + | 0.881029i | \(0.656851\pi\) | |||||||
\(360\) | 2.03069 | 0.107027 | ||||||||
\(361\) | 48.7079 | 2.56357 | ||||||||
\(362\) | −31.0242 | −1.63060 | ||||||||
\(363\) | −48.2219 | −2.53099 | ||||||||
\(364\) | 1.39468 | 0.0731013 | ||||||||
\(365\) | 8.63409 | 0.451929 | ||||||||
\(366\) | 2.76190 | 0.144367 | ||||||||
\(367\) | −1.47462 | −0.0769744 | −0.0384872 | − | 0.999259i | \(-0.512254\pi\) | ||||
−0.0384872 | + | 0.999259i | \(0.512254\pi\) | |||||||
\(368\) | −32.1437 | −1.67560 | ||||||||
\(369\) | 2.31636 | 0.120585 | ||||||||
\(370\) | −16.5275 | −0.859224 | ||||||||
\(371\) | −3.53218 | −0.183382 | ||||||||
\(372\) | 4.33545 | 0.224783 | ||||||||
\(373\) | 9.97684 | 0.516581 | 0.258291 | − | 0.966067i | \(-0.416841\pi\) | ||||
0.258291 | + | 0.966067i | \(0.416841\pi\) | |||||||
\(374\) | 35.9411 | 1.85847 | ||||||||
\(375\) | −1.95086 | −0.100742 | ||||||||
\(376\) | 17.4251 | 0.898633 | ||||||||
\(377\) | 31.2073 | 1.60726 | ||||||||
\(378\) | −6.57510 | −0.338187 | ||||||||
\(379\) | −12.9633 | −0.665878 | −0.332939 | − | 0.942948i | \(-0.608040\pi\) | ||||
−0.332939 | + | 0.942948i | \(0.608040\pi\) | |||||||
\(380\) | 2.95833 | 0.151759 | ||||||||
\(381\) | −9.36049 | −0.479553 | ||||||||
\(382\) | −20.8801 | −1.06832 | ||||||||
\(383\) | −4.28450 | −0.218928 | −0.109464 | − | 0.993991i | \(-0.534913\pi\) | ||||
−0.109464 | + | 0.993991i | \(0.534913\pi\) | |||||||
\(384\) | 26.0980 | 1.33181 | ||||||||
\(385\) | −5.97648 | −0.304589 | ||||||||
\(386\) | −14.6522 | −0.745778 | ||||||||
\(387\) | −0.776907 | −0.0394924 | ||||||||
\(388\) | 4.14399 | 0.210379 | ||||||||
\(389\) | −0.929310 | −0.0471179 | −0.0235589 | − | 0.999722i | \(-0.507500\pi\) | ||||
−0.0235589 | + | 0.999722i | \(0.507500\pi\) | |||||||
\(390\) | 11.6249 | 0.588648 | ||||||||
\(391\) | 27.4181 | 1.38659 | ||||||||
\(392\) | 2.51989 | 0.127274 | ||||||||
\(393\) | 37.0882 | 1.87085 | ||||||||
\(394\) | 41.8741 | 2.10959 | ||||||||
\(395\) | 7.66741 | 0.385789 | ||||||||
\(396\) | −1.73154 | −0.0870132 | ||||||||
\(397\) | 10.8879 | 0.546447 | 0.273224 | − | 0.961951i | \(-0.411910\pi\) | ||||
0.273224 | + | 0.961951i | \(0.411910\pi\) | |||||||
\(398\) | −1.27019 | −0.0636688 | ||||||||
\(399\) | −16.0526 | −0.803636 | ||||||||
\(400\) | −4.58979 | −0.229489 | ||||||||
\(401\) | −31.4024 | −1.56816 | −0.784081 | − | 0.620658i | \(-0.786866\pi\) | ||||
−0.784081 | + | 0.620658i | \(0.786866\pi\) | |||||||
\(402\) | −31.8449 | −1.58828 | ||||||||
\(403\) | −23.9790 | −1.19448 | ||||||||
\(404\) | 6.25895 | 0.311395 | ||||||||
\(405\) | −10.7682 | −0.535075 | ||||||||
\(406\) | −12.3572 | −0.613277 | ||||||||
\(407\) | −64.3043 | −3.18745 | ||||||||
\(408\) | −19.2461 | −0.952825 | ||||||||
\(409\) | 14.7617 | 0.729917 | 0.364958 | − | 0.931024i | \(-0.381083\pi\) | ||||
0.364958 | + | 0.931024i | \(0.381083\pi\) | |||||||
\(410\) | −4.41527 | −0.218054 | ||||||||
\(411\) | −12.3111 | −0.607260 | ||||||||
\(412\) | 6.10339 | 0.300692 | ||||||||
\(413\) | 10.8686 | 0.534811 | ||||||||
\(414\) | −8.66913 | −0.426065 | ||||||||
\(415\) | 16.2498 | 0.797670 | ||||||||
\(416\) | 7.79913 | 0.382384 | ||||||||
\(417\) | 13.7178 | 0.671763 | ||||||||
\(418\) | 75.5400 | 3.69478 | ||||||||
\(419\) | −12.3441 | −0.603051 | −0.301525 | − | 0.953458i | \(-0.597496\pi\) | ||||
−0.301525 | + | 0.953458i | \(0.597496\pi\) | |||||||
\(420\) | −0.701380 | −0.0342238 | ||||||||
\(421\) | −19.2823 | −0.939761 | −0.469881 | − | 0.882730i | \(-0.655703\pi\) | ||||
−0.469881 | + | 0.882730i | \(0.655703\pi\) | |||||||
\(422\) | 0.234285 | 0.0114048 | ||||||||
\(423\) | 5.57256 | 0.270947 | ||||||||
\(424\) | −8.90073 | −0.432258 | ||||||||
\(425\) | 3.91503 | 0.189907 | ||||||||
\(426\) | −19.9716 | −0.967629 | ||||||||
\(427\) | 0.921656 | 0.0446021 | ||||||||
\(428\) | −3.83706 | −0.185471 | ||||||||
\(429\) | 45.2294 | 2.18370 | ||||||||
\(430\) | 1.48088 | 0.0714145 | ||||||||
\(431\) | 15.9503 | 0.768300 | 0.384150 | − | 0.923271i | \(-0.374494\pi\) | ||||
0.384150 | + | 0.923271i | \(0.374494\pi\) | |||||||
\(432\) | −19.6464 | −0.945238 | ||||||||
\(433\) | 31.6376 | 1.52040 | 0.760202 | − | 0.649687i | \(-0.225100\pi\) | ||||
0.760202 | + | 0.649687i | \(0.225100\pi\) | |||||||
\(434\) | 9.49497 | 0.455773 | ||||||||
\(435\) | −15.6940 | −0.752470 | ||||||||
\(436\) | 0.995555 | 0.0476784 | ||||||||
\(437\) | 57.6265 | 2.75665 | ||||||||
\(438\) | 25.8735 | 1.23628 | ||||||||
\(439\) | 38.3967 | 1.83257 | 0.916287 | − | 0.400522i | \(-0.131171\pi\) | ||||
0.916287 | + | 0.400522i | \(0.131171\pi\) | |||||||
\(440\) | −15.0601 | −0.717961 | ||||||||
\(441\) | 0.805862 | 0.0383744 | ||||||||
\(442\) | −23.3290 | −1.10965 | ||||||||
\(443\) | 6.00670 | 0.285387 | 0.142693 | − | 0.989767i | \(-0.454424\pi\) | ||||
0.142693 | + | 0.989767i | \(0.454424\pi\) | |||||||
\(444\) | −7.54655 | −0.358143 | ||||||||
\(445\) | −4.24267 | −0.201122 | ||||||||
\(446\) | −25.6037 | −1.21237 | ||||||||
\(447\) | −14.8406 | −0.701935 | ||||||||
\(448\) | 6.09135 | 0.287789 | ||||||||
\(449\) | 7.92105 | 0.373818 | 0.186909 | − | 0.982377i | \(-0.440153\pi\) | ||||
0.186909 | + | 0.982377i | \(0.440153\pi\) | |||||||
\(450\) | −1.23786 | −0.0583535 | ||||||||
\(451\) | −17.1787 | −0.808913 | ||||||||
\(452\) | −4.44137 | −0.208905 | ||||||||
\(453\) | 25.5285 | 1.19943 | ||||||||
\(454\) | −30.9172 | −1.45102 | ||||||||
\(455\) | 3.87926 | 0.181863 | ||||||||
\(456\) | −40.4509 | −1.89429 | ||||||||
\(457\) | 24.6085 | 1.15114 | 0.575568 | − | 0.817754i | \(-0.304781\pi\) | ||||
0.575568 | + | 0.817754i | \(0.304781\pi\) | |||||||
\(458\) | −1.53607 | −0.0717760 | ||||||||
\(459\) | 16.7581 | 0.782201 | ||||||||
\(460\) | 2.51785 | 0.117395 | ||||||||
\(461\) | 17.2357 | 0.802748 | 0.401374 | − | 0.915914i | \(-0.368533\pi\) | ||||
0.401374 | + | 0.915914i | \(0.368533\pi\) | |||||||
\(462\) | −17.9095 | −0.833226 | ||||||||
\(463\) | −38.6088 | −1.79430 | −0.897152 | − | 0.441721i | \(-0.854368\pi\) | ||||
−0.897152 | + | 0.441721i | \(0.854368\pi\) | |||||||
\(464\) | −36.9233 | −1.71412 | ||||||||
\(465\) | 12.0589 | 0.559218 | ||||||||
\(466\) | 14.6879 | 0.680405 | ||||||||
\(467\) | −17.0671 | −0.789773 | −0.394886 | − | 0.918730i | \(-0.629216\pi\) | ||||
−0.394886 | + | 0.918730i | \(0.629216\pi\) | |||||||
\(468\) | 1.12392 | 0.0519534 | ||||||||
\(469\) | −10.6268 | −0.490698 | ||||||||
\(470\) | −10.6220 | −0.489956 | ||||||||
\(471\) | 13.5556 | 0.624608 | ||||||||
\(472\) | 27.3878 | 1.26063 | ||||||||
\(473\) | 5.76174 | 0.264925 | ||||||||
\(474\) | 22.9767 | 1.05535 | ||||||||
\(475\) | 8.22848 | 0.377548 | ||||||||
\(476\) | 1.40754 | 0.0645146 | ||||||||
\(477\) | −2.84645 | −0.130330 | ||||||||
\(478\) | 24.4700 | 1.11923 | ||||||||
\(479\) | −15.4903 | −0.707770 | −0.353885 | − | 0.935289i | \(-0.615140\pi\) | ||||
−0.353885 | + | 0.935289i | \(0.615140\pi\) | |||||||
\(480\) | −3.92214 | −0.179021 | ||||||||
\(481\) | 41.7392 | 1.90315 | ||||||||
\(482\) | −30.7510 | −1.40067 | ||||||||
\(483\) | −13.6625 | −0.621664 | ||||||||
\(484\) | 8.88678 | 0.403945 | ||||||||
\(485\) | 11.5264 | 0.523385 | ||||||||
\(486\) | −12.5433 | −0.568977 | ||||||||
\(487\) | −25.1005 | −1.13741 | −0.568706 | − | 0.822541i | \(-0.692556\pi\) | ||||
−0.568706 | + | 0.822541i | \(0.692556\pi\) | |||||||
\(488\) | 2.32248 | 0.105134 | ||||||||
\(489\) | 37.3354 | 1.68837 | ||||||||
\(490\) | −1.53607 | −0.0693927 | ||||||||
\(491\) | 7.47426 | 0.337309 | 0.168654 | − | 0.985675i | \(-0.446058\pi\) | ||||
0.168654 | + | 0.985675i | \(0.446058\pi\) | |||||||
\(492\) | −2.01603 | −0.0908898 | ||||||||
\(493\) | 31.4950 | 1.41846 | ||||||||
\(494\) | −49.0322 | −2.20606 | ||||||||
\(495\) | −4.81622 | −0.216473 | ||||||||
\(496\) | 28.3710 | 1.27389 | ||||||||
\(497\) | −6.66462 | −0.298949 | ||||||||
\(498\) | 48.6952 | 2.18208 | ||||||||
\(499\) | 41.4161 | 1.85404 | 0.927020 | − | 0.375013i | \(-0.122362\pi\) | ||||
0.927020 | + | 0.375013i | \(0.122362\pi\) | |||||||
\(500\) | 0.359523 | 0.0160784 | ||||||||
\(501\) | −4.06954 | −0.181814 | ||||||||
\(502\) | −13.9382 | −0.622093 | ||||||||
\(503\) | 4.36969 | 0.194835 | 0.0974174 | − | 0.995244i | \(-0.468942\pi\) | ||||
0.0974174 | + | 0.995244i | \(0.468942\pi\) | |||||||
\(504\) | 2.03069 | 0.0904540 | ||||||||
\(505\) | 17.4091 | 0.774693 | ||||||||
\(506\) | 64.2924 | 2.85815 | ||||||||
\(507\) | −3.99670 | −0.177500 | ||||||||
\(508\) | 1.72504 | 0.0765362 | ||||||||
\(509\) | 16.7762 | 0.743593 | 0.371797 | − | 0.928314i | \(-0.378742\pi\) | ||||
0.371797 | + | 0.928314i | \(0.378742\pi\) | |||||||
\(510\) | 11.7320 | 0.519503 | ||||||||
\(511\) | 8.63409 | 0.381950 | ||||||||
\(512\) | 13.9039 | 0.614473 | ||||||||
\(513\) | 35.2217 | 1.55507 | ||||||||
\(514\) | 26.9826 | 1.19015 | ||||||||
\(515\) | 16.9764 | 0.748067 | ||||||||
\(516\) | 0.676179 | 0.0297671 | ||||||||
\(517\) | −41.3275 | −1.81758 | ||||||||
\(518\) | −16.5275 | −0.726177 | ||||||||
\(519\) | 22.4100 | 0.983688 | ||||||||
\(520\) | 9.77533 | 0.428677 | ||||||||
\(521\) | 10.5619 | 0.462726 | 0.231363 | − | 0.972867i | \(-0.425681\pi\) | ||||
0.231363 | + | 0.972867i | \(0.425681\pi\) | |||||||
\(522\) | −9.95819 | −0.435858 | ||||||||
\(523\) | 14.7817 | 0.646357 | 0.323179 | − | 0.946338i | \(-0.395249\pi\) | ||||
0.323179 | + | 0.946338i | \(0.395249\pi\) | |||||||
\(524\) | −6.83495 | −0.298586 | ||||||||
\(525\) | −1.95086 | −0.0851426 | ||||||||
\(526\) | 11.9509 | 0.521085 | ||||||||
\(527\) | −24.2000 | −1.05417 | ||||||||
\(528\) | −53.5136 | −2.32888 | ||||||||
\(529\) | 26.0462 | 1.13244 | ||||||||
\(530\) | 5.42570 | 0.235677 | ||||||||
\(531\) | 8.75863 | 0.380092 | ||||||||
\(532\) | 2.95833 | 0.128260 | ||||||||
\(533\) | 11.1505 | 0.482981 | ||||||||
\(534\) | −12.7139 | −0.550184 | ||||||||
\(535\) | −10.6726 | −0.461418 | ||||||||
\(536\) | −26.7783 | −1.15665 | ||||||||
\(537\) | 15.5920 | 0.672844 | ||||||||
\(538\) | 0.721298 | 0.0310974 | ||||||||
\(539\) | −5.97648 | −0.257425 | ||||||||
\(540\) | 1.53892 | 0.0662247 | ||||||||
\(541\) | −1.81268 | −0.0779332 | −0.0389666 | − | 0.999241i | \(-0.512407\pi\) | ||||
−0.0389666 | + | 0.999241i | \(0.512407\pi\) | |||||||
\(542\) | 29.7141 | 1.27633 | ||||||||
\(543\) | −39.4017 | −1.69089 | ||||||||
\(544\) | 7.87103 | 0.337468 | ||||||||
\(545\) | 2.76910 | 0.118615 | ||||||||
\(546\) | 11.6249 | 0.497498 | ||||||||
\(547\) | −31.5136 | −1.34742 | −0.673712 | − | 0.738994i | \(-0.735301\pi\) | ||||
−0.673712 | + | 0.738994i | \(0.735301\pi\) | |||||||
\(548\) | 2.26880 | 0.0969182 | ||||||||
\(549\) | 0.742728 | 0.0316988 | ||||||||
\(550\) | 9.18031 | 0.391450 | ||||||||
\(551\) | 66.1953 | 2.82001 | ||||||||
\(552\) | −34.4280 | −1.46535 | ||||||||
\(553\) | 7.66741 | 0.326051 | ||||||||
\(554\) | −37.5292 | −1.59446 | ||||||||
\(555\) | −20.9904 | −0.890995 | ||||||||
\(556\) | −2.52804 | −0.107213 | ||||||||
\(557\) | −2.15836 | −0.0914528 | −0.0457264 | − | 0.998954i | \(-0.514560\pi\) | ||||
−0.0457264 | + | 0.998954i | \(0.514560\pi\) | |||||||
\(558\) | 7.65163 | 0.323919 | ||||||||
\(559\) | −3.73988 | −0.158180 | ||||||||
\(560\) | −4.58979 | −0.193954 | ||||||||
\(561\) | 45.6464 | 1.92719 | ||||||||
\(562\) | 21.0486 | 0.887883 | ||||||||
\(563\) | 25.3264 | 1.06738 | 0.533689 | − | 0.845681i | \(-0.320805\pi\) | ||||
0.533689 | + | 0.845681i | \(0.320805\pi\) | |||||||
\(564\) | −4.85006 | −0.204224 | ||||||||
\(565\) | −12.3535 | −0.519716 | ||||||||
\(566\) | 43.8956 | 1.84507 | ||||||||
\(567\) | −10.7682 | −0.452221 | ||||||||
\(568\) | −16.7941 | −0.704666 | ||||||||
\(569\) | −9.71652 | −0.407338 | −0.203669 | − | 0.979040i | \(-0.565287\pi\) | ||||
−0.203669 | + | 0.979040i | \(0.565287\pi\) | |||||||
\(570\) | 24.6580 | 1.03281 | ||||||||
\(571\) | 13.8527 | 0.579717 | 0.289858 | − | 0.957070i | \(-0.406392\pi\) | ||||
0.289858 | + | 0.957070i | \(0.406392\pi\) | |||||||
\(572\) | −8.33530 | −0.348516 | ||||||||
\(573\) | −26.5183 | −1.10782 | ||||||||
\(574\) | −4.41527 | −0.184290 | ||||||||
\(575\) | 7.00330 | 0.292058 | ||||||||
\(576\) | 4.90879 | 0.204533 | ||||||||
\(577\) | −0.616662 | −0.0256720 | −0.0128360 | − | 0.999918i | \(-0.504086\pi\) | ||||
−0.0128360 | + | 0.999918i | \(0.504086\pi\) | |||||||
\(578\) | 2.56920 | 0.106865 | ||||||||
\(579\) | −18.6088 | −0.773354 | ||||||||
\(580\) | 2.89224 | 0.120094 | ||||||||
\(581\) | 16.2498 | 0.674154 | ||||||||
\(582\) | 34.5407 | 1.43176 | ||||||||
\(583\) | 21.1100 | 0.874287 | ||||||||
\(584\) | 21.7570 | 0.900311 | ||||||||
\(585\) | 3.12615 | 0.129250 | ||||||||
\(586\) | 18.9949 | 0.784673 | ||||||||
\(587\) | 36.5768 | 1.50969 | 0.754843 | − | 0.655906i | \(-0.227713\pi\) | ||||
0.754843 | + | 0.655906i | \(0.227713\pi\) | |||||||
\(588\) | −0.701380 | −0.0289244 | ||||||||
\(589\) | −50.8629 | −2.09577 | ||||||||
\(590\) | −16.6950 | −0.687324 | ||||||||
\(591\) | 53.1815 | 2.18759 | ||||||||
\(592\) | −49.3842 | −2.02968 | ||||||||
\(593\) | 3.03815 | 0.124762 | 0.0623808 | − | 0.998052i | \(-0.480131\pi\) | ||||
0.0623808 | + | 0.998052i | \(0.480131\pi\) | |||||||
\(594\) | 39.2959 | 1.61233 | ||||||||
\(595\) | 3.91503 | 0.160500 | ||||||||
\(596\) | 2.73496 | 0.112028 | ||||||||
\(597\) | −1.61318 | −0.0660231 | ||||||||
\(598\) | −41.7315 | −1.70653 | ||||||||
\(599\) | −30.9082 | −1.26287 | −0.631437 | − | 0.775427i | \(-0.717535\pi\) | ||||
−0.631437 | + | 0.775427i | \(0.717535\pi\) | |||||||
\(600\) | −4.91597 | −0.200693 | ||||||||
\(601\) | 48.4418 | 1.97598 | 0.987991 | − | 0.154509i | \(-0.0493795\pi\) | ||||
0.987991 | + | 0.154509i | \(0.0493795\pi\) | |||||||
\(602\) | 1.48088 | 0.0603563 | ||||||||
\(603\) | −8.56370 | −0.348741 | ||||||||
\(604\) | −4.70463 | −0.191429 | ||||||||
\(605\) | 24.7183 | 1.00494 | ||||||||
\(606\) | 52.1692 | 2.11923 | ||||||||
\(607\) | −31.7716 | −1.28957 | −0.644786 | − | 0.764363i | \(-0.723053\pi\) | ||||
−0.644786 | + | 0.764363i | \(0.723053\pi\) | |||||||
\(608\) | 16.5431 | 0.670911 | ||||||||
\(609\) | −15.6940 | −0.635953 | ||||||||
\(610\) | −1.41573 | −0.0573213 | ||||||||
\(611\) | 26.8252 | 1.08523 | ||||||||
\(612\) | 1.13428 | 0.0458507 | ||||||||
\(613\) | 14.3682 | 0.580324 | 0.290162 | − | 0.956977i | \(-0.406291\pi\) | ||||
0.290162 | + | 0.956977i | \(0.406291\pi\) | |||||||
\(614\) | 5.41788 | 0.218648 | ||||||||
\(615\) | −5.60753 | −0.226117 | ||||||||
\(616\) | −15.0601 | −0.606788 | ||||||||
\(617\) | 18.0237 | 0.725605 | 0.362803 | − | 0.931866i | \(-0.381820\pi\) | ||||
0.362803 | + | 0.931866i | \(0.381820\pi\) | |||||||
\(618\) | 50.8725 | 2.04639 | ||||||||
\(619\) | −24.1259 | −0.969701 | −0.484850 | − | 0.874597i | \(-0.661126\pi\) | ||||
−0.484850 | + | 0.874597i | \(0.661126\pi\) | |||||||
\(620\) | −2.22233 | −0.0892508 | ||||||||
\(621\) | 29.9773 | 1.20295 | ||||||||
\(622\) | 5.52013 | 0.221337 | ||||||||
\(623\) | −4.24267 | −0.169979 | ||||||||
\(624\) | 34.7351 | 1.39052 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 30.0861 | 1.20248 | ||||||||
\(627\) | 95.9381 | 3.83140 | ||||||||
\(628\) | −2.49815 | −0.0996870 | ||||||||
\(629\) | 42.1240 | 1.67959 | ||||||||
\(630\) | −1.23786 | −0.0493177 | ||||||||
\(631\) | 18.8570 | 0.750685 | 0.375343 | − | 0.926886i | \(-0.377525\pi\) | ||||
0.375343 | + | 0.926886i | \(0.377525\pi\) | |||||||
\(632\) | 19.3211 | 0.768551 | ||||||||
\(633\) | 0.297549 | 0.0118265 | ||||||||
\(634\) | 24.4077 | 0.969354 | ||||||||
\(635\) | 4.79813 | 0.190408 | ||||||||
\(636\) | 2.47740 | 0.0982354 | ||||||||
\(637\) | 3.87926 | 0.153702 | ||||||||
\(638\) | 73.8524 | 2.92384 | ||||||||
\(639\) | −5.37076 | −0.212464 | ||||||||
\(640\) | −13.3777 | −0.528800 | ||||||||
\(641\) | −25.9382 | −1.02450 | −0.512249 | − | 0.858837i | \(-0.671187\pi\) | ||||
−0.512249 | + | 0.858837i | \(0.671187\pi\) | |||||||
\(642\) | −31.9823 | −1.26224 | ||||||||
\(643\) | 27.3493 | 1.07855 | 0.539275 | − | 0.842130i | \(-0.318698\pi\) | ||||
0.539275 | + | 0.842130i | \(0.318698\pi\) | |||||||
\(644\) | 2.51785 | 0.0992171 | ||||||||
\(645\) | 1.88077 | 0.0740551 | ||||||||
\(646\) | −49.4842 | −1.94693 | ||||||||
\(647\) | 37.0219 | 1.45548 | 0.727740 | − | 0.685853i | \(-0.240571\pi\) | ||||
0.727740 | + | 0.685853i | \(0.240571\pi\) | |||||||
\(648\) | −27.1347 | −1.06595 | ||||||||
\(649\) | −64.9562 | −2.54975 | ||||||||
\(650\) | −5.95884 | −0.233725 | ||||||||
\(651\) | 12.0589 | 0.472626 | ||||||||
\(652\) | −6.88052 | −0.269462 | ||||||||
\(653\) | −30.8446 | −1.20704 | −0.603522 | − | 0.797347i | \(-0.706236\pi\) | ||||
−0.603522 | + | 0.797347i | \(0.706236\pi\) | |||||||
\(654\) | 8.29807 | 0.324480 | ||||||||
\(655\) | −19.0112 | −0.742828 | ||||||||
\(656\) | −13.1928 | −0.515093 | ||||||||
\(657\) | 6.95789 | 0.271453 | ||||||||
\(658\) | −10.6220 | −0.414088 | ||||||||
\(659\) | 22.9502 | 0.894014 | 0.447007 | − | 0.894531i | \(-0.352490\pi\) | ||||
0.447007 | + | 0.894531i | \(0.352490\pi\) | |||||||
\(660\) | 4.19178 | 0.163165 | ||||||||
\(661\) | −9.29919 | −0.361696 | −0.180848 | − | 0.983511i | \(-0.557884\pi\) | ||||
−0.180848 | + | 0.983511i | \(0.557884\pi\) | |||||||
\(662\) | 34.2375 | 1.33068 | ||||||||
\(663\) | −29.6285 | −1.15068 | ||||||||
\(664\) | 40.9477 | 1.58908 | ||||||||
\(665\) | 8.22848 | 0.319087 | ||||||||
\(666\) | −13.3189 | −0.516097 | ||||||||
\(667\) | 56.3391 | 2.18146 | ||||||||
\(668\) | 0.749973 | 0.0290173 | ||||||||
\(669\) | −32.5175 | −1.25720 | ||||||||
\(670\) | 16.3235 | 0.630631 | ||||||||
\(671\) | −5.50825 | −0.212644 | ||||||||
\(672\) | −3.92214 | −0.151300 | ||||||||
\(673\) | 14.2310 | 0.548564 | 0.274282 | − | 0.961649i | \(-0.411560\pi\) | ||||
0.274282 | + | 0.961649i | \(0.411560\pi\) | |||||||
\(674\) | 39.4749 | 1.52051 | ||||||||
\(675\) | 4.28046 | 0.164755 | ||||||||
\(676\) | 0.736550 | 0.0283288 | ||||||||
\(677\) | −1.43433 | −0.0551256 | −0.0275628 | − | 0.999620i | \(-0.508775\pi\) | ||||
−0.0275628 | + | 0.999620i | \(0.508775\pi\) | |||||||
\(678\) | −37.0194 | −1.42172 | ||||||||
\(679\) | 11.5264 | 0.442341 | ||||||||
\(680\) | 9.86545 | 0.378323 | ||||||||
\(681\) | −39.2659 | −1.50467 | ||||||||
\(682\) | −56.7464 | −2.17293 | ||||||||
\(683\) | 20.0901 | 0.768727 | 0.384364 | − | 0.923182i | \(-0.374421\pi\) | ||||
0.384364 | + | 0.923182i | \(0.374421\pi\) | |||||||
\(684\) | 2.38400 | 0.0911547 | ||||||||
\(685\) | 6.31057 | 0.241115 | ||||||||
\(686\) | −1.53607 | −0.0586476 | ||||||||
\(687\) | −1.95086 | −0.0744300 | ||||||||
\(688\) | 4.42488 | 0.168697 | ||||||||
\(689\) | −13.7023 | −0.522015 | ||||||||
\(690\) | 20.9866 | 0.798945 | ||||||||
\(691\) | −10.4477 | −0.397450 | −0.198725 | − | 0.980055i | \(-0.563680\pi\) | ||||
−0.198725 | + | 0.980055i | \(0.563680\pi\) | |||||||
\(692\) | −4.12992 | −0.156996 | ||||||||
\(693\) | −4.81622 | −0.182953 | ||||||||
\(694\) | −16.2050 | −0.615134 | ||||||||
\(695\) | −7.03166 | −0.266726 | ||||||||
\(696\) | −39.5472 | −1.49903 | ||||||||
\(697\) | 11.2533 | 0.426248 | ||||||||
\(698\) | −18.9305 | −0.716528 | ||||||||
\(699\) | 18.6541 | 0.705564 | ||||||||
\(700\) | 0.359523 | 0.0135887 | ||||||||
\(701\) | 31.7175 | 1.19795 | 0.598976 | − | 0.800767i | \(-0.295574\pi\) | ||||
0.598976 | + | 0.800767i | \(0.295574\pi\) | |||||||
\(702\) | −25.5066 | −0.962683 | ||||||||
\(703\) | 88.5349 | 3.33916 | ||||||||
\(704\) | −36.4048 | −1.37206 | ||||||||
\(705\) | −13.4903 | −0.508073 | ||||||||
\(706\) | 25.3827 | 0.955291 | ||||||||
\(707\) | 17.4091 | 0.654735 | ||||||||
\(708\) | −7.62304 | −0.286492 | ||||||||
\(709\) | −10.4312 | −0.391752 | −0.195876 | − | 0.980629i | \(-0.562755\pi\) | ||||
−0.195876 | + | 0.980629i | \(0.562755\pi\) | |||||||
\(710\) | 10.2373 | 0.384201 | ||||||||
\(711\) | 6.17888 | 0.231726 | ||||||||
\(712\) | −10.6911 | −0.400666 | ||||||||
\(713\) | −43.2896 | −1.62121 | ||||||||
\(714\) | 11.7320 | 0.439060 | ||||||||
\(715\) | −23.1843 | −0.867045 | ||||||||
\(716\) | −2.87343 | −0.107385 | ||||||||
\(717\) | 31.0777 | 1.16062 | ||||||||
\(718\) | 27.5364 | 1.02765 | ||||||||
\(719\) | −25.9836 | −0.969024 | −0.484512 | − | 0.874785i | \(-0.661003\pi\) | ||||
−0.484512 | + | 0.874785i | \(0.661003\pi\) | |||||||
\(720\) | −3.69874 | −0.137844 | ||||||||
\(721\) | 16.9764 | 0.632232 | ||||||||
\(722\) | −74.8189 | −2.78447 | ||||||||
\(723\) | −39.0548 | −1.45246 | ||||||||
\(724\) | 7.26131 | 0.269865 | ||||||||
\(725\) | 8.04465 | 0.298771 | ||||||||
\(726\) | 74.0724 | 2.74909 | ||||||||
\(727\) | −33.5079 | −1.24274 | −0.621369 | − | 0.783518i | \(-0.713423\pi\) | ||||
−0.621369 | + | 0.783518i | \(0.713423\pi\) | |||||||
\(728\) | 9.77533 | 0.362298 | ||||||||
\(729\) | 16.3741 | 0.606448 | ||||||||
\(730\) | −13.2626 | −0.490871 | ||||||||
\(731\) | −3.77436 | −0.139600 | ||||||||
\(732\) | −0.646431 | −0.0238928 | ||||||||
\(733\) | 9.04317 | 0.334017 | 0.167009 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167009 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(734\) | 2.26512 | 0.0836071 | ||||||||
\(735\) | −1.95086 | −0.0719586 | ||||||||
\(736\) | 14.0799 | 0.518992 | ||||||||
\(737\) | 63.5106 | 2.33944 | ||||||||
\(738\) | −3.55810 | −0.130975 | ||||||||
\(739\) | −47.2381 | −1.73768 | −0.868841 | − | 0.495092i | \(-0.835135\pi\) | ||||
−0.868841 | + | 0.495092i | \(0.835135\pi\) | |||||||
\(740\) | 3.86831 | 0.142202 | ||||||||
\(741\) | −62.2724 | −2.28763 | ||||||||
\(742\) | 5.42570 | 0.199184 | ||||||||
\(743\) | 34.4137 | 1.26252 | 0.631258 | − | 0.775573i | \(-0.282539\pi\) | ||||
0.631258 | + | 0.775573i | \(0.282539\pi\) | |||||||
\(744\) | 30.3872 | 1.11405 | ||||||||
\(745\) | 7.60719 | 0.278706 | ||||||||
\(746\) | −15.3252 | −0.561094 | ||||||||
\(747\) | 13.0951 | 0.479124 | ||||||||
\(748\) | −8.41214 | −0.307578 | ||||||||
\(749\) | −10.6726 | −0.389969 | ||||||||
\(750\) | 2.99667 | 0.109423 | ||||||||
\(751\) | 3.29269 | 0.120152 | 0.0600761 | − | 0.998194i | \(-0.480866\pi\) | ||||
0.0600761 | + | 0.998194i | \(0.480866\pi\) | |||||||
\(752\) | −31.7385 | −1.15738 | ||||||||
\(753\) | −17.7020 | −0.645096 | ||||||||
\(754\) | −47.9368 | −1.74575 | ||||||||
\(755\) | −13.0858 | −0.476240 | ||||||||
\(756\) | 1.53892 | 0.0559701 | ||||||||
\(757\) | 15.2624 | 0.554721 | 0.277361 | − | 0.960766i | \(-0.410540\pi\) | ||||
0.277361 | + | 0.960766i | \(0.410540\pi\) | |||||||
\(758\) | 19.9125 | 0.723255 | ||||||||
\(759\) | 81.6534 | 2.96383 | ||||||||
\(760\) | 20.7349 | 0.752134 | ||||||||
\(761\) | −32.9716 | −1.19522 | −0.597609 | − | 0.801787i | \(-0.703883\pi\) | ||||
−0.597609 | + | 0.801787i | \(0.703883\pi\) | |||||||
\(762\) | 14.3784 | 0.520875 | ||||||||
\(763\) | 2.76910 | 0.100248 | ||||||||
\(764\) | 4.88705 | 0.176807 | ||||||||
\(765\) | 3.15497 | 0.114068 | ||||||||
\(766\) | 6.58131 | 0.237792 | ||||||||
\(767\) | 42.1623 | 1.52239 | ||||||||
\(768\) | −16.3218 | −0.588961 | ||||||||
\(769\) | 40.9027 | 1.47499 | 0.737494 | − | 0.675353i | \(-0.236009\pi\) | ||||
0.737494 | + | 0.675353i | \(0.236009\pi\) | |||||||
\(770\) | 9.18031 | 0.330835 | ||||||||
\(771\) | 34.2687 | 1.23416 | ||||||||
\(772\) | 3.42940 | 0.123427 | ||||||||
\(773\) | 20.3229 | 0.730965 | 0.365482 | − | 0.930818i | \(-0.380904\pi\) | ||||
0.365482 | + | 0.930818i | \(0.380904\pi\) | |||||||
\(774\) | 1.19339 | 0.0428954 | ||||||||
\(775\) | −6.18132 | −0.222040 | ||||||||
\(776\) | 29.0452 | 1.04266 | ||||||||
\(777\) | −20.9904 | −0.753028 | ||||||||
\(778\) | 1.42749 | 0.0511779 | ||||||||
\(779\) | 23.6518 | 0.847414 | ||||||||
\(780\) | −2.72084 | −0.0974216 | ||||||||
\(781\) | 39.8309 | 1.42526 | ||||||||
\(782\) | −42.1162 | −1.50607 | ||||||||
\(783\) | 34.4348 | 1.23060 | ||||||||
\(784\) | −4.58979 | −0.163921 | ||||||||
\(785\) | −6.94851 | −0.248003 | ||||||||
\(786\) | −56.9702 | −2.03206 | ||||||||
\(787\) | −27.1546 | −0.967956 | −0.483978 | − | 0.875080i | \(-0.660809\pi\) | ||||
−0.483978 | + | 0.875080i | \(0.660809\pi\) | |||||||
\(788\) | −9.80078 | −0.349138 | ||||||||
\(789\) | 15.1780 | 0.540352 | ||||||||
\(790\) | −11.7777 | −0.419032 | ||||||||
\(791\) | −12.3535 | −0.439240 | ||||||||
\(792\) | −12.1364 | −0.431247 | ||||||||
\(793\) | 3.57535 | 0.126964 | ||||||||
\(794\) | −16.7246 | −0.593534 | ||||||||
\(795\) | 6.89080 | 0.244392 | ||||||||
\(796\) | 0.297292 | 0.0105372 | ||||||||
\(797\) | −16.0833 | −0.569698 | −0.284849 | − | 0.958572i | \(-0.591944\pi\) | ||||
−0.284849 | + | 0.958572i | \(0.591944\pi\) | |||||||
\(798\) | 24.6580 | 0.872884 | ||||||||
\(799\) | 27.0725 | 0.957756 | ||||||||
\(800\) | 2.01047 | 0.0710808 | ||||||||
\(801\) | −3.41901 | −0.120805 | ||||||||
\(802\) | 48.2365 | 1.70329 | ||||||||
\(803\) | −51.6014 | −1.82098 | ||||||||
\(804\) | 7.45339 | 0.262861 | ||||||||
\(805\) | 7.00330 | 0.246834 | ||||||||
\(806\) | 36.8335 | 1.29740 | ||||||||
\(807\) | 0.916071 | 0.0322472 | ||||||||
\(808\) | 43.8690 | 1.54330 | ||||||||
\(809\) | −22.7533 | −0.799964 | −0.399982 | − | 0.916523i | \(-0.630984\pi\) | ||||
−0.399982 | + | 0.916523i | \(0.630984\pi\) | |||||||
\(810\) | 16.5407 | 0.581181 | ||||||||
\(811\) | −26.1261 | −0.917411 | −0.458706 | − | 0.888588i | \(-0.651687\pi\) | ||||
−0.458706 | + | 0.888588i | \(0.651687\pi\) | |||||||
\(812\) | 2.89224 | 0.101498 | ||||||||
\(813\) | 37.7379 | 1.32352 | ||||||||
\(814\) | 98.7762 | 3.46210 | ||||||||
\(815\) | −19.1379 | −0.670372 | ||||||||
\(816\) | 35.0553 | 1.22718 | ||||||||
\(817\) | −7.93283 | −0.277534 | ||||||||
\(818\) | −22.6750 | −0.792812 | ||||||||
\(819\) | 3.12615 | 0.109237 | ||||||||
\(820\) | 1.03341 | 0.0360881 | ||||||||
\(821\) | 11.8963 | 0.415184 | 0.207592 | − | 0.978216i | \(-0.433437\pi\) | ||||
0.207592 | + | 0.978216i | \(0.433437\pi\) | |||||||
\(822\) | 18.9107 | 0.659586 | ||||||||
\(823\) | −51.8008 | −1.80566 | −0.902831 | − | 0.429995i | \(-0.858515\pi\) | ||||
−0.902831 | + | 0.429995i | \(0.858515\pi\) | |||||||
\(824\) | 42.7786 | 1.49026 | ||||||||
\(825\) | 11.6593 | 0.405924 | ||||||||
\(826\) | −16.6950 | −0.580895 | ||||||||
\(827\) | 3.29877 | 0.114709 | 0.0573547 | − | 0.998354i | \(-0.481733\pi\) | ||||
0.0573547 | + | 0.998354i | \(0.481733\pi\) | |||||||
\(828\) | 2.02904 | 0.0705139 | ||||||||
\(829\) | −0.525668 | −0.0182572 | −0.00912860 | − | 0.999958i | \(-0.502906\pi\) | ||||
−0.00912860 | + | 0.999958i | \(0.502906\pi\) | |||||||
\(830\) | −24.9609 | −0.866404 | ||||||||
\(831\) | −47.6633 | −1.65342 | ||||||||
\(832\) | 23.6300 | 0.819221 | ||||||||
\(833\) | 3.91503 | 0.135648 | ||||||||
\(834\) | −21.0715 | −0.729648 | ||||||||
\(835\) | 2.08602 | 0.0721897 | ||||||||
\(836\) | −17.6804 | −0.611488 | ||||||||
\(837\) | −26.4589 | −0.914553 | ||||||||
\(838\) | 18.9615 | 0.655014 | ||||||||
\(839\) | −37.7785 | −1.30426 | −0.652130 | − | 0.758107i | \(-0.726124\pi\) | ||||
−0.652130 | + | 0.758107i | \(0.726124\pi\) | |||||||
\(840\) | −4.91597 | −0.169617 | ||||||||
\(841\) | 35.7165 | 1.23160 | ||||||||
\(842\) | 29.6190 | 1.02074 | ||||||||
\(843\) | 26.7324 | 0.920713 | ||||||||
\(844\) | −0.0548350 | −0.00188750 | ||||||||
\(845\) | 2.04869 | 0.0704770 | ||||||||
\(846\) | −8.55986 | −0.294294 | ||||||||
\(847\) | 24.7183 | 0.849329 | ||||||||
\(848\) | 16.2120 | 0.556722 | ||||||||
\(849\) | 55.7488 | 1.91329 | ||||||||
\(850\) | −6.01377 | −0.206271 | ||||||||
\(851\) | 75.3525 | 2.58305 | ||||||||
\(852\) | 4.67443 | 0.160143 | ||||||||
\(853\) | 32.1194 | 1.09975 | 0.549874 | − | 0.835247i | \(-0.314676\pi\) | ||||
0.549874 | + | 0.835247i | \(0.314676\pi\) | |||||||
\(854\) | −1.41573 | −0.0484453 | ||||||||
\(855\) | 6.63102 | 0.226776 | ||||||||
\(856\) | −26.8939 | −0.919214 | ||||||||
\(857\) | −45.2164 | −1.54456 | −0.772282 | − | 0.635280i | \(-0.780885\pi\) | ||||
−0.772282 | + | 0.635280i | \(0.780885\pi\) | |||||||
\(858\) | −69.4757 | −2.37186 | ||||||||
\(859\) | −26.6135 | −0.908042 | −0.454021 | − | 0.890991i | \(-0.650011\pi\) | ||||
−0.454021 | + | 0.890991i | \(0.650011\pi\) | |||||||
\(860\) | −0.346605 | −0.0118191 | ||||||||
\(861\) | −5.60753 | −0.191104 | ||||||||
\(862\) | −24.5009 | −0.834504 | ||||||||
\(863\) | −0.191721 | −0.00652625 | −0.00326312 | − | 0.999995i | \(-0.501039\pi\) | ||||
−0.00326312 | + | 0.999995i | \(0.501039\pi\) | |||||||
\(864\) | 8.60572 | 0.292773 | ||||||||
\(865\) | −11.4872 | −0.390577 | ||||||||
\(866\) | −48.5976 | −1.65142 | ||||||||
\(867\) | 3.26297 | 0.110816 | ||||||||
\(868\) | −2.22233 | −0.0754307 | ||||||||
\(869\) | −45.8241 | −1.55448 | ||||||||
\(870\) | 24.1072 | 0.817309 | ||||||||
\(871\) | −41.2240 | −1.39682 | ||||||||
\(872\) | 6.97784 | 0.236299 | ||||||||
\(873\) | 9.28866 | 0.314374 | ||||||||
\(874\) | −88.5186 | −2.99418 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −6.05578 | −0.204606 | ||||||||
\(877\) | −30.0240 | −1.01384 | −0.506920 | − | 0.861993i | \(-0.669216\pi\) | ||||
−0.506920 | + | 0.861993i | \(0.669216\pi\) | |||||||
\(878\) | −58.9802 | −1.99048 | ||||||||
\(879\) | 24.1242 | 0.813688 | ||||||||
\(880\) | 27.4308 | 0.924691 | ||||||||
\(881\) | 11.3233 | 0.381490 | 0.190745 | − | 0.981640i | \(-0.438910\pi\) | ||||
0.190745 | + | 0.981640i | \(0.438910\pi\) | |||||||
\(882\) | −1.23786 | −0.0416810 | ||||||||
\(883\) | 50.0640 | 1.68479 | 0.842394 | − | 0.538862i | \(-0.181146\pi\) | ||||
0.842394 | + | 0.538862i | \(0.181146\pi\) | |||||||
\(884\) | 5.46022 | 0.183647 | ||||||||
\(885\) | −21.2032 | −0.712738 | ||||||||
\(886\) | −9.22674 | −0.309978 | ||||||||
\(887\) | −48.4139 | −1.62558 | −0.812790 | − | 0.582557i | \(-0.802052\pi\) | ||||
−0.812790 | + | 0.582557i | \(0.802052\pi\) | |||||||
\(888\) | −52.8937 | −1.77500 | ||||||||
\(889\) | 4.79813 | 0.160924 | ||||||||
\(890\) | 6.51706 | 0.218452 | ||||||||
\(891\) | 64.3557 | 2.15600 | ||||||||
\(892\) | 5.99264 | 0.200648 | ||||||||
\(893\) | 56.9002 | 1.90409 | ||||||||
\(894\) | 22.7962 | 0.762419 | ||||||||
\(895\) | −7.99235 | −0.267155 | ||||||||
\(896\) | −13.3777 | −0.446918 | ||||||||
\(897\) | −53.0003 | −1.76963 | ||||||||
\(898\) | −12.1673 | −0.406029 | ||||||||
\(899\) | −49.7266 | −1.65847 | ||||||||
\(900\) | 0.289726 | 0.00965753 | ||||||||
\(901\) | −13.8286 | −0.460697 | ||||||||
\(902\) | 26.3877 | 0.878615 | ||||||||
\(903\) | 1.88077 | 0.0625880 | ||||||||
\(904\) | −31.1295 | −1.03535 | ||||||||
\(905\) | 20.1971 | 0.671374 | ||||||||
\(906\) | −39.2137 | −1.30279 | ||||||||
\(907\) | −21.2568 | −0.705821 | −0.352910 | − | 0.935657i | \(-0.614808\pi\) | ||||
−0.352910 | + | 0.935657i | \(0.614808\pi\) | |||||||
\(908\) | 7.23628 | 0.240144 | ||||||||
\(909\) | 14.0293 | 0.465322 | ||||||||
\(910\) | −5.95884 | −0.197533 | ||||||||
\(911\) | −14.5109 | −0.480767 | −0.240384 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240384 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(912\) | 73.6782 | 2.43973 | ||||||||
\(913\) | −97.1164 | −3.21408 | ||||||||
\(914\) | −37.8004 | −1.25033 | ||||||||
\(915\) | −1.79802 | −0.0594408 | ||||||||
\(916\) | 0.359523 | 0.0118790 | ||||||||
\(917\) | −19.0112 | −0.627804 | ||||||||
\(918\) | −25.7417 | −0.849602 | ||||||||
\(919\) | 17.4569 | 0.575849 | 0.287925 | − | 0.957653i | \(-0.407035\pi\) | ||||
0.287925 | + | 0.957653i | \(0.407035\pi\) | |||||||
\(920\) | 17.6476 | 0.581823 | ||||||||
\(921\) | 6.88088 | 0.226733 | ||||||||
\(922\) | −26.4754 | −0.871920 | ||||||||
\(923\) | −25.8538 | −0.850988 | ||||||||
\(924\) | 4.19178 | 0.137899 | ||||||||
\(925\) | 10.7596 | 0.353773 | ||||||||
\(926\) | 59.3060 | 1.94892 | ||||||||
\(927\) | 13.6806 | 0.449330 | ||||||||
\(928\) | 16.1735 | 0.530922 | ||||||||
\(929\) | −57.4679 | −1.88546 | −0.942730 | − | 0.333556i | \(-0.891751\pi\) | ||||
−0.942730 | + | 0.333556i | \(0.891751\pi\) | |||||||
\(930\) | −18.5234 | −0.607405 | ||||||||
\(931\) | 8.22848 | 0.269677 | ||||||||
\(932\) | −3.43776 | −0.112607 | ||||||||
\(933\) | 7.01074 | 0.229521 | ||||||||
\(934\) | 26.2164 | 0.857826 | ||||||||
\(935\) | −23.3981 | −0.765198 | ||||||||
\(936\) | 7.87757 | 0.257486 | ||||||||
\(937\) | 32.7997 | 1.07152 | 0.535759 | − | 0.844371i | \(-0.320025\pi\) | ||||
0.535759 | + | 0.844371i | \(0.320025\pi\) | |||||||
\(938\) | 16.3235 | 0.532981 | ||||||||
\(939\) | 38.2103 | 1.24695 | ||||||||
\(940\) | 2.48611 | 0.0810880 | ||||||||
\(941\) | 22.5391 | 0.734754 | 0.367377 | − | 0.930072i | \(-0.380256\pi\) | ||||
0.367377 | + | 0.930072i | \(0.380256\pi\) | |||||||
\(942\) | −20.8224 | −0.678430 | ||||||||
\(943\) | 20.1302 | 0.655528 | ||||||||
\(944\) | −49.8848 | −1.62361 | ||||||||
\(945\) | 4.28046 | 0.139243 | ||||||||
\(946\) | −8.85046 | −0.287753 | ||||||||
\(947\) | −12.1985 | −0.396397 | −0.198198 | − | 0.980162i | \(-0.563509\pi\) | ||||
−0.198198 | + | 0.980162i | \(0.563509\pi\) | |||||||
\(948\) | −5.37777 | −0.174662 | ||||||||
\(949\) | 33.4939 | 1.08726 | ||||||||
\(950\) | −12.6396 | −0.410081 | ||||||||
\(951\) | 30.9986 | 1.00520 | ||||||||
\(952\) | 9.86545 | 0.319741 | ||||||||
\(953\) | −57.0405 | −1.84772 | −0.923861 | − | 0.382728i | \(-0.874985\pi\) | ||||
−0.923861 | + | 0.382728i | \(0.874985\pi\) | |||||||
\(954\) | 4.37236 | 0.141560 | ||||||||
\(955\) | 13.5931 | 0.439864 | ||||||||
\(956\) | −5.72728 | −0.185234 | ||||||||
\(957\) | 93.7949 | 3.03196 | ||||||||
\(958\) | 23.7943 | 0.768758 | ||||||||
\(959\) | 6.31057 | 0.203779 | ||||||||
\(960\) | −11.8834 | −0.383535 | ||||||||
\(961\) | 7.20872 | 0.232540 | ||||||||
\(962\) | −64.1145 | −2.06714 | ||||||||
\(963\) | −8.60067 | −0.277153 | ||||||||
\(964\) | 7.19737 | 0.231812 | ||||||||
\(965\) | 9.53875 | 0.307063 | ||||||||
\(966\) | 20.9866 | 0.675232 | ||||||||
\(967\) | 26.7899 | 0.861504 | 0.430752 | − | 0.902470i | \(-0.358248\pi\) | ||||
0.430752 | + | 0.902470i | \(0.358248\pi\) | |||||||
\(968\) | 62.2874 | 2.00199 | ||||||||
\(969\) | −62.8464 | −2.01892 | ||||||||
\(970\) | −17.7054 | −0.568485 | ||||||||
\(971\) | −6.85367 | −0.219945 | −0.109972 | − | 0.993935i | \(-0.535076\pi\) | ||||
−0.109972 | + | 0.993935i | \(0.535076\pi\) | |||||||
\(972\) | 2.93581 | 0.0941660 | ||||||||
\(973\) | −7.03166 | −0.225425 | ||||||||
\(974\) | 38.5562 | 1.23542 | ||||||||
\(975\) | −7.56791 | −0.242367 | ||||||||
\(976\) | −4.23021 | −0.135406 | ||||||||
\(977\) | −8.22637 | −0.263185 | −0.131592 | − | 0.991304i | \(-0.542009\pi\) | ||||
−0.131592 | + | 0.991304i | \(0.542009\pi\) | |||||||
\(978\) | −57.3500 | −1.83385 | ||||||||
\(979\) | 25.3562 | 0.810389 | ||||||||
\(980\) | 0.359523 | 0.0114845 | ||||||||
\(981\) | 2.23151 | 0.0712467 | ||||||||
\(982\) | −11.4810 | −0.366374 | ||||||||
\(983\) | −15.7839 | −0.503428 | −0.251714 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251714 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(984\) | −14.1304 | −0.450460 | ||||||||
\(985\) | −27.2605 | −0.868592 | ||||||||
\(986\) | −48.3787 | −1.54069 | ||||||||
\(987\) | −13.4903 | −0.429400 | ||||||||
\(988\) | 11.4761 | 0.365104 | ||||||||
\(989\) | −6.75167 | −0.214691 | ||||||||
\(990\) | 7.39806 | 0.235126 | ||||||||
\(991\) | 54.2686 | 1.72390 | 0.861949 | − | 0.506995i | \(-0.169244\pi\) | ||||
0.861949 | + | 0.506995i | \(0.169244\pi\) | |||||||
\(992\) | −12.4273 | −0.394569 | ||||||||
\(993\) | 43.4827 | 1.37988 | ||||||||
\(994\) | 10.2373 | 0.324709 | ||||||||
\(995\) | 0.826906 | 0.0262147 | ||||||||
\(996\) | −11.3973 | −0.361136 | ||||||||
\(997\) | 11.4561 | 0.362818 | 0.181409 | − | 0.983408i | \(-0.441934\pi\) | ||||
0.181409 | + | 0.983408i | \(0.441934\pi\) | |||||||
\(998\) | −63.6182 | −2.01380 | ||||||||
\(999\) | 46.0559 | 1.45715 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8015.2.a.o.1.18 | ✓ | 73 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.o.1.18 | ✓ | 73 | 1.1 | even | 1 | trivial |