Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.91265 | −1.75233 | −0.876163 | − | 0.482015i | \(-0.839905\pi\) | ||||
−0.876163 | + | 0.482015i | \(0.839905\pi\) | |||||||
\(3\) | 15.6713 | 1.00532 | 0.502658 | − | 0.864485i | \(-0.332356\pi\) | ||||
0.502658 | + | 0.864485i | \(0.332356\pi\) | |||||||
\(4\) | 66.2607 | 2.07065 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −155.344 | −1.76164 | ||||||||
\(7\) | −122.128 | −0.942041 | −0.471021 | − | 0.882122i | \(-0.656114\pi\) | ||||
−0.471021 | + | 0.882122i | \(0.656114\pi\) | |||||||
\(8\) | −339.614 | −1.87612 | ||||||||
\(9\) | 2.59022 | 0.0106593 | ||||||||
\(10\) | −247.816 | −0.783664 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 1038.39 | 2.08165 | ||||||||
\(13\) | 368.674 | 0.605039 | 0.302520 | − | 0.953143i | \(-0.402172\pi\) | ||||
0.302520 | + | 0.953143i | \(0.402172\pi\) | |||||||
\(14\) | 1210.61 | 1.65076 | ||||||||
\(15\) | 391.783 | 0.449591 | ||||||||
\(16\) | 1246.13 | 1.21693 | ||||||||
\(17\) | −858.004 | −0.720057 | −0.360028 | − | 0.932941i | \(-0.617233\pi\) | ||||
−0.360028 | + | 0.932941i | \(0.617233\pi\) | |||||||
\(18\) | −25.6759 | −0.0186786 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 1656.52 | 0.926021 | ||||||||
\(21\) | −1913.91 | −0.947049 | ||||||||
\(22\) | −1199.43 | −0.528346 | ||||||||
\(23\) | 1759.78 | 0.693646 | 0.346823 | − | 0.937931i | \(-0.387261\pi\) | ||||
0.346823 | + | 0.937931i | \(0.387261\pi\) | |||||||
\(24\) | −5322.20 | −1.88609 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −3654.53 | −1.06023 | ||||||||
\(27\) | −3767.54 | −0.994600 | ||||||||
\(28\) | −8092.28 | −1.95063 | ||||||||
\(29\) | −7399.72 | −1.63388 | −0.816941 | − | 0.576722i | \(-0.804332\pi\) | ||||
−0.816941 | + | 0.576722i | \(0.804332\pi\) | |||||||
\(30\) | −3883.61 | −0.787829 | ||||||||
\(31\) | 1183.72 | 0.221230 | 0.110615 | − | 0.993863i | \(-0.464718\pi\) | ||||
0.110615 | + | 0.993863i | \(0.464718\pi\) | |||||||
\(32\) | −1484.84 | −0.256333 | ||||||||
\(33\) | 1896.23 | 0.303114 | ||||||||
\(34\) | 8505.09 | 1.26177 | ||||||||
\(35\) | −3053.20 | −0.421294 | ||||||||
\(36\) | 171.629 | 0.0220717 | ||||||||
\(37\) | 14337.7 | 1.72177 | 0.860887 | − | 0.508796i | \(-0.169909\pi\) | ||||
0.860887 | + | 0.508796i | \(0.169909\pi\) | |||||||
\(38\) | 3578.47 | 0.402011 | ||||||||
\(39\) | 5777.60 | 0.608255 | ||||||||
\(40\) | −8490.35 | −0.839026 | ||||||||
\(41\) | 19689.2 | 1.82923 | 0.914615 | − | 0.404326i | \(-0.132494\pi\) | ||||
0.914615 | + | 0.404326i | \(0.132494\pi\) | |||||||
\(42\) | 18971.9 | 1.65954 | ||||||||
\(43\) | 8923.31 | 0.735961 | 0.367981 | − | 0.929833i | \(-0.380049\pi\) | ||||
0.367981 | + | 0.929833i | \(0.380049\pi\) | |||||||
\(44\) | 8017.54 | 0.624323 | ||||||||
\(45\) | 64.7554 | 0.00476699 | ||||||||
\(46\) | −17444.0 | −1.21549 | ||||||||
\(47\) | −13532.7 | −0.893594 | −0.446797 | − | 0.894635i | \(-0.647435\pi\) | ||||
−0.446797 | + | 0.894635i | \(0.647435\pi\) | |||||||
\(48\) | 19528.6 | 1.22340 | ||||||||
\(49\) | −1891.76 | −0.112558 | ||||||||
\(50\) | −6195.41 | −0.350465 | ||||||||
\(51\) | −13446.0 | −0.723884 | ||||||||
\(52\) | 24428.6 | 1.25282 | ||||||||
\(53\) | −4747.41 | −0.232149 | −0.116074 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116074 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(54\) | 37346.3 | 1.74286 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | 41476.4 | 1.76738 | ||||||||
\(57\) | −5657.35 | −0.230635 | ||||||||
\(58\) | 73350.9 | 2.86309 | ||||||||
\(59\) | 22266.8 | 0.832776 | 0.416388 | − | 0.909187i | \(-0.363296\pi\) | ||||
0.416388 | + | 0.909187i | \(0.363296\pi\) | |||||||
\(60\) | 25959.8 | 0.930943 | ||||||||
\(61\) | 22138.2 | 0.761759 | 0.380879 | − | 0.924625i | \(-0.375621\pi\) | ||||
0.380879 | + | 0.924625i | \(0.375621\pi\) | |||||||
\(62\) | −11733.8 | −0.387667 | ||||||||
\(63\) | −316.338 | −0.0100415 | ||||||||
\(64\) | −25157.6 | −0.767748 | ||||||||
\(65\) | 9216.84 | 0.270582 | ||||||||
\(66\) | −18796.7 | −0.531155 | ||||||||
\(67\) | 14492.3 | 0.394413 | 0.197206 | − | 0.980362i | \(-0.436813\pi\) | ||||
0.197206 | + | 0.980362i | \(0.436813\pi\) | |||||||
\(68\) | −56851.9 | −1.49098 | ||||||||
\(69\) | 27578.0 | 0.697333 | ||||||||
\(70\) | 30265.3 | 0.738244 | ||||||||
\(71\) | 41494.3 | 0.976884 | 0.488442 | − | 0.872596i | \(-0.337565\pi\) | ||||
0.488442 | + | 0.872596i | \(0.337565\pi\) | |||||||
\(72\) | −879.673 | −0.0199982 | ||||||||
\(73\) | −57928.9 | −1.27230 | −0.636148 | − | 0.771567i | \(-0.719473\pi\) | ||||
−0.636148 | + | 0.771567i | \(0.719473\pi\) | |||||||
\(74\) | −142125. | −3.01711 | ||||||||
\(75\) | 9794.57 | 0.201063 | ||||||||
\(76\) | −23920.1 | −0.475039 | ||||||||
\(77\) | −14777.5 | −0.284036 | ||||||||
\(78\) | −57271.3 | −1.06586 | ||||||||
\(79\) | −76968.9 | −1.38755 | −0.693774 | − | 0.720193i | \(-0.744053\pi\) | ||||
−0.693774 | + | 0.720193i | \(0.744053\pi\) | |||||||
\(80\) | 31153.3 | 0.544226 | ||||||||
\(81\) | −59671.7 | −1.01055 | ||||||||
\(82\) | −195172. | −3.20541 | ||||||||
\(83\) | −33284.7 | −0.530333 | −0.265167 | − | 0.964203i | \(-0.585427\pi\) | ||||
−0.265167 | + | 0.964203i | \(0.585427\pi\) | |||||||
\(84\) | −126817. | −1.96100 | ||||||||
\(85\) | −21450.1 | −0.322019 | ||||||||
\(86\) | −88453.7 | −1.28964 | ||||||||
\(87\) | −115963. | −1.64257 | ||||||||
\(88\) | −41093.3 | −0.565671 | ||||||||
\(89\) | 40140.4 | 0.537163 | 0.268582 | − | 0.963257i | \(-0.413445\pi\) | ||||
0.268582 | + | 0.963257i | \(0.413445\pi\) | |||||||
\(90\) | −641.898 | −0.00835333 | ||||||||
\(91\) | −45025.3 | −0.569972 | ||||||||
\(92\) | 116604. | 1.43629 | ||||||||
\(93\) | 18550.4 | 0.222406 | ||||||||
\(94\) | 134145. | 1.56587 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −23269.4 | −0.257696 | ||||||||
\(97\) | 72189.7 | 0.779015 | 0.389508 | − | 0.921023i | \(-0.372645\pi\) | ||||
0.389508 | + | 0.921023i | \(0.372645\pi\) | |||||||
\(98\) | 18752.4 | 0.197238 | ||||||||
\(99\) | 313.416 | 0.00321391 | ||||||||
\(100\) | 41412.9 | 0.414129 | ||||||||
\(101\) | −26226.8 | −0.255824 | −0.127912 | − | 0.991786i | \(-0.540827\pi\) | ||||
−0.127912 | + | 0.991786i | \(0.540827\pi\) | |||||||
\(102\) | 133286. | 1.26848 | ||||||||
\(103\) | −97439.9 | −0.904990 | −0.452495 | − | 0.891767i | \(-0.649466\pi\) | ||||
−0.452495 | + | 0.891767i | \(0.649466\pi\) | |||||||
\(104\) | −125207. | −1.13513 | ||||||||
\(105\) | −47847.7 | −0.423533 | ||||||||
\(106\) | 47059.4 | 0.406801 | ||||||||
\(107\) | −161675. | −1.36516 | −0.682580 | − | 0.730811i | \(-0.739142\pi\) | ||||
−0.682580 | + | 0.730811i | \(0.739142\pi\) | |||||||
\(108\) | −249640. | −2.05946 | ||||||||
\(109\) | −11322.3 | −0.0912784 | −0.0456392 | − | 0.998958i | \(-0.514532\pi\) | ||||
−0.0456392 | + | 0.998958i | \(0.514532\pi\) | |||||||
\(110\) | −29985.8 | −0.236284 | ||||||||
\(111\) | 224691. | 1.73093 | ||||||||
\(112\) | −152188. | −1.14640 | ||||||||
\(113\) | 4809.56 | 0.0354331 | 0.0177166 | − | 0.999843i | \(-0.494360\pi\) | ||||
0.0177166 | + | 0.999843i | \(0.494360\pi\) | |||||||
\(114\) | 56079.3 | 0.404148 | ||||||||
\(115\) | 43994.4 | 0.310208 | ||||||||
\(116\) | −490311. | −3.38319 | ||||||||
\(117\) | 954.944 | 0.00644931 | ||||||||
\(118\) | −220723. | −1.45929 | ||||||||
\(119\) | 104786. | 0.678323 | ||||||||
\(120\) | −133055. | −0.843486 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −219448. | −1.33485 | ||||||||
\(123\) | 308556. | 1.83895 | ||||||||
\(124\) | 78434.0 | 0.458089 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 3135.75 | 0.0175960 | ||||||||
\(127\) | −254115. | −1.39805 | −0.699023 | − | 0.715099i | \(-0.746382\pi\) | ||||
−0.699023 | + | 0.715099i | \(0.746382\pi\) | |||||||
\(128\) | 296893. | 1.60168 | ||||||||
\(129\) | 139840. | 0.739873 | ||||||||
\(130\) | −91363.3 | −0.474147 | ||||||||
\(131\) | −22841.9 | −0.116293 | −0.0581465 | − | 0.998308i | \(-0.518519\pi\) | ||||
−0.0581465 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(132\) | 125645. | 0.627642 | ||||||||
\(133\) | 44088.2 | 0.216119 | ||||||||
\(134\) | −143657. | −0.691139 | ||||||||
\(135\) | −94188.5 | −0.444798 | ||||||||
\(136\) | 291390. | 1.35091 | ||||||||
\(137\) | −26462.3 | −0.120456 | −0.0602278 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602278 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(138\) | −273371. | −1.22195 | ||||||||
\(139\) | −101775. | −0.446791 | −0.223396 | − | 0.974728i | \(-0.571714\pi\) | ||||
−0.223396 | + | 0.974728i | \(0.571714\pi\) | |||||||
\(140\) | −202307. | −0.872350 | ||||||||
\(141\) | −212075. | −0.898344 | ||||||||
\(142\) | −411319. | −1.71182 | ||||||||
\(143\) | 44609.5 | 0.182426 | ||||||||
\(144\) | 3227.75 | 0.0129716 | ||||||||
\(145\) | −184993. | −0.730694 | ||||||||
\(146\) | 574229. | 2.22948 | ||||||||
\(147\) | −29646.4 | −0.113156 | ||||||||
\(148\) | 950028. | 3.56518 | ||||||||
\(149\) | 39518.6 | 0.145826 | 0.0729132 | − | 0.997338i | \(-0.476770\pi\) | ||||
0.0729132 | + | 0.997338i | \(0.476770\pi\) | |||||||
\(150\) | −97090.2 | −0.352328 | ||||||||
\(151\) | 14475.2 | 0.0516632 | 0.0258316 | − | 0.999666i | \(-0.491777\pi\) | ||||
0.0258316 | + | 0.999666i | \(0.491777\pi\) | |||||||
\(152\) | 122601. | 0.430411 | ||||||||
\(153\) | −2222.41 | −0.00767532 | ||||||||
\(154\) | 146484. | 0.497724 | ||||||||
\(155\) | 29593.0 | 0.0989371 | ||||||||
\(156\) | 382828. | 1.25948 | ||||||||
\(157\) | −470159. | −1.52228 | −0.761142 | − | 0.648585i | \(-0.775361\pi\) | ||||
−0.761142 | + | 0.648585i | \(0.775361\pi\) | |||||||
\(158\) | 762966. | 2.43143 | ||||||||
\(159\) | −74398.1 | −0.233383 | ||||||||
\(160\) | −37121.0 | −0.114636 | ||||||||
\(161\) | −214918. | −0.653443 | ||||||||
\(162\) | 591505. | 1.77081 | ||||||||
\(163\) | 236406. | 0.696929 | 0.348465 | − | 0.937322i | \(-0.386703\pi\) | ||||
0.348465 | + | 0.937322i | \(0.386703\pi\) | |||||||
\(164\) | 1.30462e6 | 3.78769 | ||||||||
\(165\) | 47405.7 | 0.135557 | ||||||||
\(166\) | 329939. | 0.929317 | ||||||||
\(167\) | −295646. | −0.820316 | −0.410158 | − | 0.912015i | \(-0.634526\pi\) | ||||
−0.410158 | + | 0.912015i | \(0.634526\pi\) | |||||||
\(168\) | 649989. | 1.77678 | ||||||||
\(169\) | −235373. | −0.633927 | ||||||||
\(170\) | 212627. | 0.564283 | ||||||||
\(171\) | −935.068 | −0.00244542 | ||||||||
\(172\) | 591264. | 1.52391 | ||||||||
\(173\) | 185379. | 0.470918 | 0.235459 | − | 0.971884i | \(-0.424341\pi\) | ||||
0.235459 | + | 0.971884i | \(0.424341\pi\) | |||||||
\(174\) | 1.14950e6 | 2.87831 | ||||||||
\(175\) | −76330.0 | −0.188408 | ||||||||
\(176\) | 150782. | 0.366917 | ||||||||
\(177\) | 348950. | 0.837202 | ||||||||
\(178\) | −397897. | −0.941285 | ||||||||
\(179\) | −295793. | −0.690010 | −0.345005 | − | 0.938601i | \(-0.612123\pi\) | ||||
−0.345005 | + | 0.938601i | \(0.612123\pi\) | |||||||
\(180\) | 4290.73 | 0.00987076 | ||||||||
\(181\) | 756527. | 1.71644 | 0.858219 | − | 0.513284i | \(-0.171571\pi\) | ||||
0.858219 | + | 0.513284i | \(0.171571\pi\) | |||||||
\(182\) | 446321. | 0.998777 | ||||||||
\(183\) | 346935. | 0.765808 | ||||||||
\(184\) | −597644. | −1.30136 | ||||||||
\(185\) | 358443. | 0.770001 | ||||||||
\(186\) | −183884. | −0.389728 | ||||||||
\(187\) | −103818. | −0.217105 | ||||||||
\(188\) | −896686. | −1.85032 | ||||||||
\(189\) | 460122. | 0.936954 | ||||||||
\(190\) | 89461.7 | 0.179785 | ||||||||
\(191\) | 384626. | 0.762879 | 0.381440 | − | 0.924394i | \(-0.375428\pi\) | ||||
0.381440 | + | 0.924394i | \(0.375428\pi\) | |||||||
\(192\) | −394252. | −0.771829 | ||||||||
\(193\) | −390296. | −0.754225 | −0.377112 | − | 0.926167i | \(-0.623083\pi\) | ||||
−0.377112 | + | 0.926167i | \(0.623083\pi\) | |||||||
\(194\) | −715592. | −1.36509 | ||||||||
\(195\) | 144440. | 0.272020 | ||||||||
\(196\) | −125349. | −0.233068 | ||||||||
\(197\) | −838013. | −1.53846 | −0.769229 | − | 0.638974i | \(-0.779359\pi\) | ||||
−0.769229 | + | 0.638974i | \(0.779359\pi\) | |||||||
\(198\) | −3106.78 | −0.00563181 | ||||||||
\(199\) | 340911. | 0.610252 | 0.305126 | − | 0.952312i | \(-0.401301\pi\) | ||||
0.305126 | + | 0.952312i | \(0.401301\pi\) | |||||||
\(200\) | −212259. | −0.375224 | ||||||||
\(201\) | 227114. | 0.396509 | ||||||||
\(202\) | 259977. | 0.448287 | ||||||||
\(203\) | 903713. | 1.53918 | ||||||||
\(204\) | −890944. | −1.49891 | ||||||||
\(205\) | 492230. | 0.818056 | ||||||||
\(206\) | 965888. | 1.58584 | ||||||||
\(207\) | 4558.20 | 0.00739379 | ||||||||
\(208\) | 459416. | 0.736289 | ||||||||
\(209\) | −43681.0 | −0.0691714 | ||||||||
\(210\) | 474297. | 0.742168 | ||||||||
\(211\) | −167344. | −0.258765 | −0.129382 | − | 0.991595i | \(-0.541299\pi\) | ||||
−0.129382 | + | 0.991595i | \(0.541299\pi\) | |||||||
\(212\) | −314566. | −0.480698 | ||||||||
\(213\) | 650271. | 0.982077 | ||||||||
\(214\) | 1.60263e6 | 2.39221 | ||||||||
\(215\) | 223083. | 0.329132 | ||||||||
\(216\) | 1.27951e6 | 1.86599 | ||||||||
\(217\) | −144565. | −0.208408 | ||||||||
\(218\) | 112234. | 0.159949 | ||||||||
\(219\) | −907822. | −1.27906 | ||||||||
\(220\) | 200438. | 0.279206 | ||||||||
\(221\) | −316323. | −0.435663 | ||||||||
\(222\) | −2.22729e6 | −3.03315 | ||||||||
\(223\) | 958374. | 1.29054 | 0.645272 | − | 0.763953i | \(-0.276744\pi\) | ||||
0.645272 | + | 0.763953i | \(0.276744\pi\) | |||||||
\(224\) | 181341. | 0.241476 | ||||||||
\(225\) | 1618.88 | 0.00213186 | ||||||||
\(226\) | −47675.5 | −0.0620904 | ||||||||
\(227\) | −1.14011e6 | −1.46852 | −0.734261 | − | 0.678867i | \(-0.762471\pi\) | ||||
−0.734261 | + | 0.678867i | \(0.762471\pi\) | |||||||
\(228\) | −374859. | −0.477564 | ||||||||
\(229\) | −305837. | −0.385390 | −0.192695 | − | 0.981259i | \(-0.561723\pi\) | ||||
−0.192695 | + | 0.981259i | \(0.561723\pi\) | |||||||
\(230\) | −436101. | −0.543585 | ||||||||
\(231\) | −231583. | −0.285546 | ||||||||
\(232\) | 2.51305e6 | 3.06536 | ||||||||
\(233\) | 86798.3 | 0.104742 | 0.0523711 | − | 0.998628i | \(-0.483322\pi\) | ||||
0.0523711 | + | 0.998628i | \(0.483322\pi\) | |||||||
\(234\) | −9466.03 | −0.0113013 | ||||||||
\(235\) | −338318. | −0.399627 | ||||||||
\(236\) | 1.47541e6 | 1.72438 | ||||||||
\(237\) | −1.20620e6 | −1.39492 | ||||||||
\(238\) | −1.03871e6 | −1.18864 | ||||||||
\(239\) | 312504. | 0.353884 | 0.176942 | − | 0.984221i | \(-0.443379\pi\) | ||||
0.176942 | + | 0.984221i | \(0.443379\pi\) | |||||||
\(240\) | 488214. | 0.547119 | ||||||||
\(241\) | −433881. | −0.481202 | −0.240601 | − | 0.970624i | \(-0.577345\pi\) | ||||
−0.240601 | + | 0.970624i | \(0.577345\pi\) | |||||||
\(242\) | −145131. | −0.159302 | ||||||||
\(243\) | −19622.6 | −0.0213177 | ||||||||
\(244\) | 1.46689e6 | 1.57733 | ||||||||
\(245\) | −47294.0 | −0.0503374 | ||||||||
\(246\) | −3.05860e6 | −3.22244 | ||||||||
\(247\) | −133091. | −0.138806 | ||||||||
\(248\) | −402007. | −0.415054 | ||||||||
\(249\) | −521615. | −0.533152 | ||||||||
\(250\) | −154885. | −0.156733 | ||||||||
\(251\) | 174142. | 0.174469 | 0.0872347 | − | 0.996188i | \(-0.472197\pi\) | ||||
0.0872347 | + | 0.996188i | \(0.472197\pi\) | |||||||
\(252\) | −20960.7 | −0.0207924 | ||||||||
\(253\) | 212933. | 0.209142 | ||||||||
\(254\) | 2.51896e6 | 2.44983 | ||||||||
\(255\) | −336151. | −0.323731 | ||||||||
\(256\) | −2.13796e6 | −2.03891 | ||||||||
\(257\) | −377892. | −0.356891 | −0.178445 | − | 0.983950i | \(-0.557107\pi\) | ||||
−0.178445 | + | 0.983950i | \(0.557107\pi\) | |||||||
\(258\) | −1.38619e6 | −1.29650 | ||||||||
\(259\) | −1.75104e6 | −1.62198 | ||||||||
\(260\) | 610714. | 0.560279 | ||||||||
\(261\) | −19166.9 | −0.0174161 | ||||||||
\(262\) | 226424. | 0.203783 | ||||||||
\(263\) | −617400. | −0.550399 | −0.275199 | − | 0.961387i | \(-0.588744\pi\) | ||||
−0.275199 | + | 0.961387i | \(0.588744\pi\) | |||||||
\(264\) | −643986. | −0.568678 | ||||||||
\(265\) | −118685. | −0.103820 | ||||||||
\(266\) | −437031. | −0.378711 | ||||||||
\(267\) | 629052. | 0.540019 | ||||||||
\(268\) | 960270. | 0.816688 | ||||||||
\(269\) | 105081. | 0.0885404 | 0.0442702 | − | 0.999020i | \(-0.485904\pi\) | ||||
0.0442702 | + | 0.999020i | \(0.485904\pi\) | |||||||
\(270\) | 933657. | 0.779432 | ||||||||
\(271\) | −831128. | −0.687455 | −0.343728 | − | 0.939069i | \(-0.611690\pi\) | ||||
−0.343728 | + | 0.939069i | \(0.611690\pi\) | |||||||
\(272\) | −1.06919e6 | −0.876257 | ||||||||
\(273\) | −705607. | −0.573002 | ||||||||
\(274\) | 262312. | 0.211077 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 1.82734e6 | 1.44393 | ||||||||
\(277\) | 664598. | 0.520426 | 0.260213 | − | 0.965551i | \(-0.416207\pi\) | ||||
0.260213 | + | 0.965551i | \(0.416207\pi\) | |||||||
\(278\) | 1.00886e6 | 0.782924 | ||||||||
\(279\) | 3066.09 | 0.00235816 | ||||||||
\(280\) | 1.03691e6 | 0.790397 | ||||||||
\(281\) | −1.85375e6 | −1.40051 | −0.700253 | − | 0.713895i | \(-0.746930\pi\) | ||||
−0.700253 | + | 0.713895i | \(0.746930\pi\) | |||||||
\(282\) | 2.10223e6 | 1.57419 | ||||||||
\(283\) | 2.26829e6 | 1.68357 | 0.841787 | − | 0.539810i | \(-0.181504\pi\) | ||||
0.841787 | + | 0.539810i | \(0.181504\pi\) | |||||||
\(284\) | 2.74944e6 | 2.02278 | ||||||||
\(285\) | −141434. | −0.103143 | ||||||||
\(286\) | −442198. | −0.319670 | ||||||||
\(287\) | −2.40460e6 | −1.72321 | ||||||||
\(288\) | −3846.06 | −0.00273234 | ||||||||
\(289\) | −683687. | −0.481518 | ||||||||
\(290\) | 1.83377e6 | 1.28041 | ||||||||
\(291\) | 1.13131e6 | 0.783156 | ||||||||
\(292\) | −3.83841e6 | −2.63447 | ||||||||
\(293\) | 533780. | 0.363239 | 0.181620 | − | 0.983369i | \(-0.441866\pi\) | ||||
0.181620 | + | 0.983369i | \(0.441866\pi\) | |||||||
\(294\) | 293874. | 0.198287 | ||||||||
\(295\) | 556670. | 0.372429 | ||||||||
\(296\) | −4.86929e6 | −3.23025 | ||||||||
\(297\) | −455872. | −0.299883 | ||||||||
\(298\) | −391734. | −0.255535 | ||||||||
\(299\) | 648783. | 0.419683 | ||||||||
\(300\) | 648995. | 0.416330 | ||||||||
\(301\) | −1.08979e6 | −0.693306 | ||||||||
\(302\) | −143487. | −0.0905307 | ||||||||
\(303\) | −411008. | −0.257184 | ||||||||
\(304\) | −449854. | −0.279182 | ||||||||
\(305\) | 553455. | 0.340669 | ||||||||
\(306\) | 22030.0 | 0.0134497 | ||||||||
\(307\) | 852984. | 0.516529 | 0.258265 | − | 0.966074i | \(-0.416849\pi\) | ||||
0.258265 | + | 0.966074i | \(0.416849\pi\) | |||||||
\(308\) | −979166. | −0.588138 | ||||||||
\(309\) | −1.52701e6 | −0.909801 | ||||||||
\(310\) | −293345. | −0.173370 | ||||||||
\(311\) | −1.29944e6 | −0.761824 | −0.380912 | − | 0.924611i | \(-0.624390\pi\) | ||||
−0.380912 | + | 0.924611i | \(0.624390\pi\) | |||||||
\(312\) | −1.96215e6 | −1.14116 | ||||||||
\(313\) | −2.13933e6 | −1.23429 | −0.617144 | − | 0.786850i | \(-0.711711\pi\) | ||||
−0.617144 | + | 0.786850i | \(0.711711\pi\) | |||||||
\(314\) | 4.66052e6 | 2.66754 | ||||||||
\(315\) | −7908.44 | −0.00449071 | ||||||||
\(316\) | −5.10001e6 | −2.87312 | ||||||||
\(317\) | −2.97033e6 | −1.66018 | −0.830092 | − | 0.557627i | \(-0.811712\pi\) | ||||
−0.830092 | + | 0.557627i | \(0.811712\pi\) | |||||||
\(318\) | 737483. | 0.408963 | ||||||||
\(319\) | −895367. | −0.492634 | ||||||||
\(320\) | −628939. | −0.343347 | ||||||||
\(321\) | −2.53366e6 | −1.37242 | ||||||||
\(322\) | 2.13040e6 | 1.14504 | ||||||||
\(323\) | 309739. | 0.165192 | ||||||||
\(324\) | −3.95389e6 | −2.09248 | ||||||||
\(325\) | 230421. | 0.121008 | ||||||||
\(326\) | −2.34341e6 | −1.22125 | ||||||||
\(327\) | −177435. | −0.0917636 | ||||||||
\(328\) | −6.68672e6 | −3.43185 | ||||||||
\(329\) | 1.65272e6 | 0.841802 | ||||||||
\(330\) | −469917. | −0.237540 | ||||||||
\(331\) | 1.92488e6 | 0.965683 | 0.482841 | − | 0.875708i | \(-0.339605\pi\) | ||||
0.482841 | + | 0.875708i | \(0.339605\pi\) | |||||||
\(332\) | −2.20546e6 | −1.09813 | ||||||||
\(333\) | 37137.8 | 0.0183529 | ||||||||
\(334\) | 2.93064e6 | 1.43746 | ||||||||
\(335\) | 362308. | 0.176387 | ||||||||
\(336\) | −2.38498e6 | −1.15249 | ||||||||
\(337\) | 773927. | 0.371215 | 0.185607 | − | 0.982624i | \(-0.440575\pi\) | ||||
0.185607 | + | 0.982624i | \(0.440575\pi\) | |||||||
\(338\) | 2.33317e6 | 1.11085 | ||||||||
\(339\) | 75372.2 | 0.0356215 | ||||||||
\(340\) | −1.42130e6 | −0.666788 | ||||||||
\(341\) | 143230. | 0.0667034 | ||||||||
\(342\) | 9269.00 | 0.00428517 | ||||||||
\(343\) | 2.28364e6 | 1.04808 | ||||||||
\(344\) | −3.03048e6 | −1.38075 | ||||||||
\(345\) | 689450. | 0.311857 | ||||||||
\(346\) | −1.83760e6 | −0.825202 | ||||||||
\(347\) | −3.74600e6 | −1.67011 | −0.835053 | − | 0.550170i | \(-0.814563\pi\) | ||||
−0.835053 | + | 0.550170i | \(0.814563\pi\) | |||||||
\(348\) | −7.68381e6 | −3.40117 | ||||||||
\(349\) | 3.31098e6 | 1.45510 | 0.727549 | − | 0.686055i | \(-0.240659\pi\) | ||||
0.727549 | + | 0.686055i | \(0.240659\pi\) | |||||||
\(350\) | 756632. | 0.330153 | ||||||||
\(351\) | −1.38899e6 | −0.601772 | ||||||||
\(352\) | −179666. | −0.0772874 | ||||||||
\(353\) | −2.79778e6 | −1.19502 | −0.597512 | − | 0.801860i | \(-0.703844\pi\) | ||||
−0.597512 | + | 0.801860i | \(0.703844\pi\) | |||||||
\(354\) | −3.45902e6 | −1.46705 | ||||||||
\(355\) | 1.03736e6 | 0.436876 | ||||||||
\(356\) | 2.65973e6 | 1.11227 | ||||||||
\(357\) | 1.64214e6 | 0.681929 | ||||||||
\(358\) | 2.93209e6 | 1.20912 | ||||||||
\(359\) | 26730.3 | 0.0109463 | 0.00547315 | − | 0.999985i | \(-0.498258\pi\) | ||||
0.00547315 | + | 0.999985i | \(0.498258\pi\) | |||||||
\(360\) | −21991.8 | −0.00894345 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −7.49919e6 | −3.00776 | ||||||||
\(363\) | 229444. | 0.0913923 | ||||||||
\(364\) | −2.98341e6 | −1.18021 | ||||||||
\(365\) | −1.44822e6 | −0.568988 | ||||||||
\(366\) | −3.43904e6 | −1.34194 | ||||||||
\(367\) | 4.12634e6 | 1.59919 | 0.799595 | − | 0.600540i | \(-0.205048\pi\) | ||||
0.799595 | + | 0.600540i | \(0.205048\pi\) | |||||||
\(368\) | 2.19291e6 | 0.844116 | ||||||||
\(369\) | 50999.2 | 0.0194983 | ||||||||
\(370\) | −3.55312e6 | −1.34929 | ||||||||
\(371\) | 579791. | 0.218694 | ||||||||
\(372\) | 1.22916e6 | 0.460524 | ||||||||
\(373\) | −928274. | −0.345465 | −0.172733 | − | 0.984969i | \(-0.555260\pi\) | ||||
−0.172733 | + | 0.984969i | \(0.555260\pi\) | |||||||
\(374\) | 1.02912e6 | 0.380439 | ||||||||
\(375\) | 244864. | 0.0899182 | ||||||||
\(376\) | 4.59590e6 | 1.67649 | ||||||||
\(377\) | −2.72808e6 | −0.988562 | ||||||||
\(378\) | −4.56103e6 | −1.64185 | ||||||||
\(379\) | −2.52172e6 | −0.901778 | −0.450889 | − | 0.892580i | \(-0.648893\pi\) | ||||
−0.450889 | + | 0.892580i | \(0.648893\pi\) | |||||||
\(380\) | −598002. | −0.212444 | ||||||||
\(381\) | −3.98232e6 | −1.40548 | ||||||||
\(382\) | −3.81267e6 | −1.33681 | ||||||||
\(383\) | −1.33224e6 | −0.464072 | −0.232036 | − | 0.972707i | \(-0.574539\pi\) | ||||
−0.232036 | + | 0.972707i | \(0.574539\pi\) | |||||||
\(384\) | 4.65271e6 | 1.61019 | ||||||||
\(385\) | −369437. | −0.127025 | ||||||||
\(386\) | 3.86887e6 | 1.32165 | ||||||||
\(387\) | 23113.3 | 0.00784485 | ||||||||
\(388\) | 4.78334e6 | 1.61306 | ||||||||
\(389\) | −2.97937e6 | −0.998275 | −0.499137 | − | 0.866523i | \(-0.666350\pi\) | ||||
−0.499137 | + | 0.866523i | \(0.666350\pi\) | |||||||
\(390\) | −1.43178e6 | −0.476668 | ||||||||
\(391\) | −1.50989e6 | −0.499464 | ||||||||
\(392\) | 642469. | 0.211172 | ||||||||
\(393\) | −357962. | −0.116911 | ||||||||
\(394\) | 8.30693e6 | 2.69588 | ||||||||
\(395\) | −1.92422e6 | −0.620530 | ||||||||
\(396\) | 20767.2 | 0.00665486 | ||||||||
\(397\) | −1.70619e6 | −0.543316 | −0.271658 | − | 0.962394i | \(-0.587572\pi\) | ||||
−0.271658 | + | 0.962394i | \(0.587572\pi\) | |||||||
\(398\) | −3.37934e6 | −1.06936 | ||||||||
\(399\) | 690920. | 0.217268 | ||||||||
\(400\) | 778833. | 0.243385 | ||||||||
\(401\) | 3.83304e6 | 1.19037 | 0.595186 | − | 0.803588i | \(-0.297078\pi\) | ||||
0.595186 | + | 0.803588i | \(0.297078\pi\) | |||||||
\(402\) | −2.25130e6 | −0.694813 | ||||||||
\(403\) | 436406. | 0.133853 | ||||||||
\(404\) | −1.73780e6 | −0.529721 | ||||||||
\(405\) | −1.49179e6 | −0.451930 | ||||||||
\(406\) | −8.95819e6 | −2.69715 | ||||||||
\(407\) | 1.73487e6 | 0.519134 | ||||||||
\(408\) | 4.56647e6 | 1.35809 | ||||||||
\(409\) | 6.67302e6 | 1.97249 | 0.986243 | − | 0.165303i | \(-0.0528602\pi\) | ||||
0.986243 | + | 0.165303i | \(0.0528602\pi\) | |||||||
\(410\) | −4.87930e6 | −1.43350 | ||||||||
\(411\) | −414700. | −0.121096 | ||||||||
\(412\) | −6.45643e6 | −1.87391 | ||||||||
\(413\) | −2.71940e6 | −0.784509 | ||||||||
\(414\) | −45183.8 | −0.0129563 | ||||||||
\(415\) | −832117. | −0.237172 | ||||||||
\(416\) | −547421. | −0.155092 | ||||||||
\(417\) | −1.59495e6 | −0.449166 | ||||||||
\(418\) | 432995. | 0.121211 | ||||||||
\(419\) | 39601.7 | 0.0110199 | 0.00550996 | − | 0.999985i | \(-0.498246\pi\) | ||||
0.00550996 | + | 0.999985i | \(0.498246\pi\) | |||||||
\(420\) | −3.17042e6 | −0.876987 | ||||||||
\(421\) | −3.25180e6 | −0.894166 | −0.447083 | − | 0.894493i | \(-0.647537\pi\) | ||||
−0.447083 | + | 0.894493i | \(0.647537\pi\) | |||||||
\(422\) | 1.65883e6 | 0.453440 | ||||||||
\(423\) | −35052.6 | −0.00952511 | ||||||||
\(424\) | 1.61229e6 | 0.435539 | ||||||||
\(425\) | −536252. | −0.144011 | ||||||||
\(426\) | −6.44591e6 | −1.72092 | ||||||||
\(427\) | −2.70369e6 | −0.717608 | ||||||||
\(428\) | −1.07127e7 | −2.82676 | ||||||||
\(429\) | 699090. | 0.183396 | ||||||||
\(430\) | −2.21134e6 | −0.576746 | ||||||||
\(431\) | −3.53830e6 | −0.917490 | −0.458745 | − | 0.888568i | \(-0.651701\pi\) | ||||
−0.458745 | + | 0.888568i | \(0.651701\pi\) | |||||||
\(432\) | −4.69486e6 | −1.21036 | ||||||||
\(433\) | 65925.2 | 0.0168978 | 0.00844892 | − | 0.999964i | \(-0.497311\pi\) | ||||
0.00844892 | + | 0.999964i | \(0.497311\pi\) | |||||||
\(434\) | 1.43302e6 | 0.365199 | ||||||||
\(435\) | −2.89909e6 | −0.734578 | ||||||||
\(436\) | −750222. | −0.189005 | ||||||||
\(437\) | −635279. | −0.159133 | ||||||||
\(438\) | 8.99892e6 | 2.24133 | ||||||||
\(439\) | 4.77825e6 | 1.18334 | 0.591668 | − | 0.806182i | \(-0.298470\pi\) | ||||
0.591668 | + | 0.806182i | \(0.298470\pi\) | |||||||
\(440\) | −1.02733e6 | −0.252976 | ||||||||
\(441\) | −4900.07 | −0.00119979 | ||||||||
\(442\) | 3.13560e6 | 0.763423 | ||||||||
\(443\) | −3.56592e6 | −0.863301 | −0.431650 | − | 0.902041i | \(-0.642069\pi\) | ||||
−0.431650 | + | 0.902041i | \(0.642069\pi\) | |||||||
\(444\) | 1.48882e7 | 3.58413 | ||||||||
\(445\) | 1.00351e6 | 0.240227 | ||||||||
\(446\) | −9.50003e6 | −2.26145 | ||||||||
\(447\) | 619309. | 0.146602 | ||||||||
\(448\) | 3.07244e6 | 0.723250 | ||||||||
\(449\) | 971747. | 0.227477 | 0.113738 | − | 0.993511i | \(-0.463717\pi\) | ||||
0.113738 | + | 0.993511i | \(0.463717\pi\) | |||||||
\(450\) | −16047.4 | −0.00373572 | ||||||||
\(451\) | 2.38239e6 | 0.551533 | ||||||||
\(452\) | 318685. | 0.0733694 | ||||||||
\(453\) | 226845. | 0.0519378 | ||||||||
\(454\) | 1.13015e7 | 2.57333 | ||||||||
\(455\) | −1.12563e6 | −0.254899 | ||||||||
\(456\) | 1.92131e6 | 0.432699 | ||||||||
\(457\) | 524697. | 0.117522 | 0.0587609 | − | 0.998272i | \(-0.481285\pi\) | ||||
0.0587609 | + | 0.998272i | \(0.481285\pi\) | |||||||
\(458\) | 3.03165e6 | 0.675329 | ||||||||
\(459\) | 3.23256e6 | 0.716168 | ||||||||
\(460\) | 2.91510e6 | 0.642330 | ||||||||
\(461\) | −2.78946e6 | −0.611319 | −0.305659 | − | 0.952141i | \(-0.598877\pi\) | ||||
−0.305659 | + | 0.952141i | \(0.598877\pi\) | |||||||
\(462\) | 2.29560e6 | 0.500370 | ||||||||
\(463\) | −6.76123e6 | −1.46580 | −0.732898 | − | 0.680339i | \(-0.761833\pi\) | ||||
−0.732898 | + | 0.680339i | \(0.761833\pi\) | |||||||
\(464\) | −9.22104e6 | −1.98831 | ||||||||
\(465\) | 463761. | 0.0994630 | ||||||||
\(466\) | −860401. | −0.183542 | ||||||||
\(467\) | −6.79585e6 | −1.44195 | −0.720977 | − | 0.692959i | \(-0.756307\pi\) | ||||
−0.720977 | + | 0.692959i | \(0.756307\pi\) | |||||||
\(468\) | 63275.2 | 0.0133542 | ||||||||
\(469\) | −1.76992e6 | −0.371553 | ||||||||
\(470\) | 3.35363e6 | 0.700277 | ||||||||
\(471\) | −7.36801e6 | −1.53038 | ||||||||
\(472\) | −7.56212e6 | −1.56239 | ||||||||
\(473\) | 1.07972e6 | 0.221901 | ||||||||
\(474\) | 1.19567e7 | 2.44436 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | 6.94320e6 | 1.40457 | ||||||||
\(477\) | −12296.8 | −0.00247455 | ||||||||
\(478\) | −3.09775e6 | −0.620121 | ||||||||
\(479\) | −7.83424e6 | −1.56012 | −0.780061 | − | 0.625704i | \(-0.784812\pi\) | ||||
−0.780061 | + | 0.625704i | \(0.784812\pi\) | |||||||
\(480\) | −581735. | −0.115245 | ||||||||
\(481\) | 5.28594e6 | 1.04174 | ||||||||
\(482\) | 4.30091e6 | 0.843223 | ||||||||
\(483\) | −3.36804e6 | −0.656916 | ||||||||
\(484\) | 970122. | 0.188240 | ||||||||
\(485\) | 1.80474e6 | 0.348386 | ||||||||
\(486\) | 194512. | 0.0373556 | ||||||||
\(487\) | −1.90142e6 | −0.363291 | −0.181646 | − | 0.983364i | \(-0.558142\pi\) | ||||
−0.181646 | + | 0.983364i | \(0.558142\pi\) | |||||||
\(488\) | −7.51844e6 | −1.42915 | ||||||||
\(489\) | 3.70479e6 | 0.700634 | ||||||||
\(490\) | 468809. | 0.0882076 | ||||||||
\(491\) | 4.88670e6 | 0.914770 | 0.457385 | − | 0.889269i | \(-0.348786\pi\) | ||||
0.457385 | + | 0.889269i | \(0.348786\pi\) | |||||||
\(492\) | 2.04451e7 | 3.80782 | ||||||||
\(493\) | 6.34899e6 | 1.17649 | ||||||||
\(494\) | 1.31929e6 | 0.243233 | ||||||||
\(495\) | 7835.40 | 0.00143730 | ||||||||
\(496\) | 1.47507e6 | 0.269221 | ||||||||
\(497\) | −5.06762e6 | −0.920265 | ||||||||
\(498\) | 5.17058e6 | 0.934257 | ||||||||
\(499\) | −8.97412e6 | −1.61339 | −0.806697 | − | 0.590965i | \(-0.798747\pi\) | ||||
−0.806697 | + | 0.590965i | \(0.798747\pi\) | |||||||
\(500\) | 1.03532e6 | 0.185204 | ||||||||
\(501\) | −4.63317e6 | −0.824676 | ||||||||
\(502\) | −1.72621e6 | −0.305727 | ||||||||
\(503\) | −9.18627e6 | −1.61890 | −0.809449 | − | 0.587190i | \(-0.800234\pi\) | ||||
−0.809449 | + | 0.587190i | \(0.800234\pi\) | |||||||
\(504\) | 107433. | 0.0188391 | ||||||||
\(505\) | −655669. | −0.114408 | ||||||||
\(506\) | −2.11073e6 | −0.366485 | ||||||||
\(507\) | −3.68860e6 | −0.637297 | ||||||||
\(508\) | −1.68378e7 | −2.89486 | ||||||||
\(509\) | 4.47325e6 | 0.765294 | 0.382647 | − | 0.923895i | \(-0.375013\pi\) | ||||
0.382647 | + | 0.923895i | \(0.375013\pi\) | |||||||
\(510\) | 3.33215e6 | 0.567282 | ||||||||
\(511\) | 7.07474e6 | 1.19856 | ||||||||
\(512\) | 1.16922e7 | 1.97116 | ||||||||
\(513\) | 1.36008e6 | 0.228177 | ||||||||
\(514\) | 3.74591e6 | 0.625389 | ||||||||
\(515\) | −2.43600e6 | −0.404724 | ||||||||
\(516\) | 9.26589e6 | 1.53201 | ||||||||
\(517\) | −1.63746e6 | −0.269429 | ||||||||
\(518\) | 1.73574e7 | 2.84224 | ||||||||
\(519\) | 2.90513e6 | 0.473421 | ||||||||
\(520\) | −3.13017e6 | −0.507644 | ||||||||
\(521\) | 4.21769e6 | 0.680739 | 0.340369 | − | 0.940292i | \(-0.389448\pi\) | ||||
0.340369 | + | 0.940292i | \(0.389448\pi\) | |||||||
\(522\) | 189995. | 0.0305186 | ||||||||
\(523\) | −8.62086e6 | −1.37815 | −0.689075 | − | 0.724690i | \(-0.741983\pi\) | ||||
−0.689075 | + | 0.724690i | \(0.741983\pi\) | |||||||
\(524\) | −1.51352e6 | −0.240802 | ||||||||
\(525\) | −1.19619e6 | −0.189410 | ||||||||
\(526\) | 6.12007e6 | 0.964478 | ||||||||
\(527\) | −1.01564e6 | −0.159298 | ||||||||
\(528\) | 2.36295e6 | 0.368868 | ||||||||
\(529\) | −3.33953e6 | −0.518856 | ||||||||
\(530\) | 1.17648e6 | 0.181927 | ||||||||
\(531\) | 57675.8 | 0.00887682 | ||||||||
\(532\) | 2.92131e6 | 0.447506 | ||||||||
\(533\) | 7.25888e6 | 1.10676 | ||||||||
\(534\) | −6.23558e6 | −0.946288 | ||||||||
\(535\) | −4.04188e6 | −0.610518 | ||||||||
\(536\) | −4.92179e6 | −0.739965 | ||||||||
\(537\) | −4.63547e6 | −0.693678 | ||||||||
\(538\) | −1.04163e6 | −0.155152 | ||||||||
\(539\) | −228903. | −0.0339375 | ||||||||
\(540\) | −6.24099e6 | −0.921020 | ||||||||
\(541\) | −4.35985e6 | −0.640440 | −0.320220 | − | 0.947343i | \(-0.603757\pi\) | ||||
−0.320220 | + | 0.947343i | \(0.603757\pi\) | |||||||
\(542\) | 8.23868e6 | 1.20465 | ||||||||
\(543\) | 1.18558e7 | 1.72556 | ||||||||
\(544\) | 1.27400e6 | 0.184574 | ||||||||
\(545\) | −283057. | −0.0408209 | ||||||||
\(546\) | 6.99443e6 | 1.00409 | ||||||||
\(547\) | −1.08483e6 | −0.155022 | −0.0775111 | − | 0.996991i | \(-0.524697\pi\) | ||||
−0.0775111 | + | 0.996991i | \(0.524697\pi\) | |||||||
\(548\) | −1.75341e6 | −0.249421 | ||||||||
\(549\) | 57342.7 | 0.00811983 | ||||||||
\(550\) | −749644. | −0.105669 | ||||||||
\(551\) | 2.67130e6 | 0.374838 | ||||||||
\(552\) | −9.36587e6 | −1.30828 | ||||||||
\(553\) | 9.40006e6 | 1.30713 | ||||||||
\(554\) | −6.58792e6 | −0.911957 | ||||||||
\(555\) | 5.61728e6 | 0.774094 | ||||||||
\(556\) | −6.74369e6 | −0.925146 | ||||||||
\(557\) | −6.27051e6 | −0.856377 | −0.428188 | − | 0.903689i | \(-0.640848\pi\) | ||||
−0.428188 | + | 0.903689i | \(0.640848\pi\) | |||||||
\(558\) | −30393.1 | −0.00413227 | ||||||||
\(559\) | 3.28979e6 | 0.445285 | ||||||||
\(560\) | −3.80469e6 | −0.512684 | ||||||||
\(561\) | −1.62697e6 | −0.218259 | ||||||||
\(562\) | 1.83756e7 | 2.45414 | ||||||||
\(563\) | 4.93153e6 | 0.655708 | 0.327854 | − | 0.944728i | \(-0.393675\pi\) | ||||
0.327854 | + | 0.944728i | \(0.393675\pi\) | |||||||
\(564\) | −1.40523e7 | −1.86015 | ||||||||
\(565\) | 120239. | 0.0158462 | ||||||||
\(566\) | −2.24848e7 | −2.95017 | ||||||||
\(567\) | 7.28758e6 | 0.951976 | ||||||||
\(568\) | −1.40921e7 | −1.83275 | ||||||||
\(569\) | 7.96172e6 | 1.03092 | 0.515461 | − | 0.856913i | \(-0.327621\pi\) | ||||
0.515461 | + | 0.856913i | \(0.327621\pi\) | |||||||
\(570\) | 1.40198e6 | 0.180740 | ||||||||
\(571\) | 1.19086e6 | 0.152852 | 0.0764259 | − | 0.997075i | \(-0.475649\pi\) | ||||
0.0764259 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(572\) | 2.95585e6 | 0.377740 | ||||||||
\(573\) | 6.02760e6 | 0.766934 | ||||||||
\(574\) | 2.38360e7 | 3.01963 | ||||||||
\(575\) | 1.09986e6 | 0.138729 | ||||||||
\(576\) | −65163.5 | −0.00818367 | ||||||||
\(577\) | −2.85119e6 | −0.356523 | −0.178261 | − | 0.983983i | \(-0.557047\pi\) | ||||
−0.178261 | + | 0.983983i | \(0.557047\pi\) | |||||||
\(578\) | 6.77715e6 | 0.843776 | ||||||||
\(579\) | −6.11645e6 | −0.758234 | ||||||||
\(580\) | −1.22578e7 | −1.51301 | ||||||||
\(581\) | 4.06499e6 | 0.499596 | ||||||||
\(582\) | −1.12143e7 | −1.37235 | ||||||||
\(583\) | −574436. | −0.0699956 | ||||||||
\(584\) | 1.96735e7 | 2.38698 | ||||||||
\(585\) | 23873.6 | 0.00288422 | ||||||||
\(586\) | −5.29117e6 | −0.636514 | ||||||||
\(587\) | −7.83586e6 | −0.938623 | −0.469312 | − | 0.883033i | \(-0.655498\pi\) | ||||
−0.469312 | + | 0.883033i | \(0.655498\pi\) | |||||||
\(588\) | −1.96439e6 | −0.234306 | ||||||||
\(589\) | −427323. | −0.0507537 | ||||||||
\(590\) | −5.51808e6 | −0.652616 | ||||||||
\(591\) | −1.31328e7 | −1.54663 | ||||||||
\(592\) | 1.78667e7 | 2.09527 | ||||||||
\(593\) | −4.54441e6 | −0.530690 | −0.265345 | − | 0.964154i | \(-0.585486\pi\) | ||||
−0.265345 | + | 0.964154i | \(0.585486\pi\) | |||||||
\(594\) | 4.51890e6 | 0.525493 | ||||||||
\(595\) | 2.61966e6 | 0.303355 | ||||||||
\(596\) | 2.61853e6 | 0.301955 | ||||||||
\(597\) | 5.34253e6 | 0.613495 | ||||||||
\(598\) | −6.43116e6 | −0.735421 | ||||||||
\(599\) | −8.76221e6 | −0.997807 | −0.498904 | − | 0.866657i | \(-0.666264\pi\) | ||||
−0.498904 | + | 0.866657i | \(0.666264\pi\) | |||||||
\(600\) | −3.32637e6 | −0.377218 | ||||||||
\(601\) | 131994. | 0.0149062 | 0.00745312 | − | 0.999972i | \(-0.497628\pi\) | ||||
0.00745312 | + | 0.999972i | \(0.497628\pi\) | |||||||
\(602\) | 1.08027e7 | 1.21490 | ||||||||
\(603\) | 37538.2 | 0.00420417 | ||||||||
\(604\) | 959134. | 0.106976 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 4.07418e6 | 0.450670 | ||||||||
\(607\) | −1.16973e7 | −1.28859 | −0.644295 | − | 0.764777i | \(-0.722849\pi\) | ||||
−0.644295 | + | 0.764777i | \(0.722849\pi\) | |||||||
\(608\) | 536027. | 0.0588069 | ||||||||
\(609\) | 1.41624e7 | 1.54737 | ||||||||
\(610\) | −5.48620e6 | −0.596963 | ||||||||
\(611\) | −4.98915e6 | −0.540659 | ||||||||
\(612\) | −147259. | −0.0158929 | ||||||||
\(613\) | 1.41538e7 | 1.52133 | 0.760665 | − | 0.649145i | \(-0.224873\pi\) | ||||
0.760665 | + | 0.649145i | \(0.224873\pi\) | |||||||
\(614\) | −8.45533e6 | −0.905128 | ||||||||
\(615\) | 7.71389e6 | 0.822405 | ||||||||
\(616\) | 5.01864e6 | 0.532886 | ||||||||
\(617\) | −4.99655e6 | −0.528393 | −0.264197 | − | 0.964469i | \(-0.585107\pi\) | ||||
−0.264197 | + | 0.964469i | \(0.585107\pi\) | |||||||
\(618\) | 1.51367e7 | 1.59427 | ||||||||
\(619\) | 8.20573e6 | 0.860777 | 0.430389 | − | 0.902644i | \(-0.358377\pi\) | ||||
0.430389 | + | 0.902644i | \(0.358377\pi\) | |||||||
\(620\) | 1.96085e6 | 0.204864 | ||||||||
\(621\) | −6.63002e6 | −0.689900 | ||||||||
\(622\) | 1.28809e7 | 1.33496 | ||||||||
\(623\) | −4.90226e6 | −0.506030 | ||||||||
\(624\) | 7.19966e6 | 0.740203 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.12064e7 | 2.16288 | ||||||||
\(627\) | −684539. | −0.0695391 | ||||||||
\(628\) | −3.11530e7 | −3.15211 | ||||||||
\(629\) | −1.23018e7 | −1.23978 | ||||||||
\(630\) | 78393.6 | 0.00786918 | ||||||||
\(631\) | 1.47441e7 | 1.47416 | 0.737082 | − | 0.675803i | \(-0.236203\pi\) | ||||
0.737082 | + | 0.675803i | \(0.236203\pi\) | |||||||
\(632\) | 2.61397e7 | 2.60320 | ||||||||
\(633\) | −2.62251e6 | −0.260140 | ||||||||
\(634\) | 2.94438e7 | 2.90918 | ||||||||
\(635\) | −6.35288e6 | −0.625225 | ||||||||
\(636\) | −4.92967e6 | −0.483253 | ||||||||
\(637\) | −697442. | −0.0681020 | ||||||||
\(638\) | 8.87546e6 | 0.863255 | ||||||||
\(639\) | 107479. | 0.0104129 | ||||||||
\(640\) | 7.42233e6 | 0.716292 | ||||||||
\(641\) | −6.94288e6 | −0.667413 | −0.333707 | − | 0.942677i | \(-0.608299\pi\) | ||||
−0.333707 | + | 0.942677i | \(0.608299\pi\) | |||||||
\(642\) | 2.51153e7 | 2.40492 | ||||||||
\(643\) | −1.32874e7 | −1.26740 | −0.633700 | − | 0.773579i | \(-0.718465\pi\) | ||||
−0.633700 | + | 0.773579i | \(0.718465\pi\) | |||||||
\(644\) | −1.42406e7 | −1.35305 | ||||||||
\(645\) | 3.49600e6 | 0.330881 | ||||||||
\(646\) | −3.07034e6 | −0.289471 | ||||||||
\(647\) | 9.12095e6 | 0.856603 | 0.428301 | − | 0.903636i | \(-0.359112\pi\) | ||||
0.428301 | + | 0.903636i | \(0.359112\pi\) | |||||||
\(648\) | 2.02653e7 | 1.89590 | ||||||||
\(649\) | 2.69428e6 | 0.251091 | ||||||||
\(650\) | −2.28408e6 | −0.212045 | ||||||||
\(651\) | −2.26553e6 | −0.209516 | ||||||||
\(652\) | 1.56644e7 | 1.44309 | ||||||||
\(653\) | −1.21176e7 | −1.11208 | −0.556039 | − | 0.831156i | \(-0.687679\pi\) | ||||
−0.556039 | + | 0.831156i | \(0.687679\pi\) | |||||||
\(654\) | 1.75885e6 | 0.160800 | ||||||||
\(655\) | −571047. | −0.0520078 | ||||||||
\(656\) | 2.45354e7 | 2.22604 | ||||||||
\(657\) | −150048. | −0.0135618 | ||||||||
\(658\) | −1.63829e7 | −1.47511 | ||||||||
\(659\) | −1.13385e7 | −1.01705 | −0.508525 | − | 0.861047i | \(-0.669809\pi\) | ||||
−0.508525 | + | 0.861047i | \(0.669809\pi\) | |||||||
\(660\) | 3.14114e6 | 0.280690 | ||||||||
\(661\) | −476277. | −0.0423990 | −0.0211995 | − | 0.999775i | \(-0.506749\pi\) | ||||
−0.0211995 | + | 0.999775i | \(0.506749\pi\) | |||||||
\(662\) | −1.90807e7 | −1.69219 | ||||||||
\(663\) | −4.95720e6 | −0.437979 | ||||||||
\(664\) | 1.13039e7 | 0.994969 | ||||||||
\(665\) | 1.10220e6 | 0.0966514 | ||||||||
\(666\) | −368134. | −0.0321603 | ||||||||
\(667\) | −1.30218e7 | −1.13333 | ||||||||
\(668\) | −1.95897e7 | −1.69858 | ||||||||
\(669\) | 1.50190e7 | 1.29740 | ||||||||
\(670\) | −3.59143e6 | −0.309087 | ||||||||
\(671\) | 2.67872e6 | 0.229679 | ||||||||
\(672\) | 2.84184e6 | 0.242760 | ||||||||
\(673\) | 4.96425e6 | 0.422489 | 0.211245 | − | 0.977433i | \(-0.432248\pi\) | ||||
0.211245 | + | 0.977433i | \(0.432248\pi\) | |||||||
\(674\) | −7.67167e6 | −0.650489 | ||||||||
\(675\) | −2.35471e6 | −0.198920 | ||||||||
\(676\) | −1.55960e7 | −1.31264 | ||||||||
\(677\) | 1.87249e7 | 1.57017 | 0.785086 | − | 0.619387i | \(-0.212619\pi\) | ||||
0.785086 | + | 0.619387i | \(0.212619\pi\) | |||||||
\(678\) | −747138. | −0.0624204 | ||||||||
\(679\) | −8.81638e6 | −0.733865 | ||||||||
\(680\) | 7.28475e6 | 0.604147 | ||||||||
\(681\) | −1.78670e7 | −1.47633 | ||||||||
\(682\) | −1.41979e6 | −0.116886 | ||||||||
\(683\) | 7.77676e6 | 0.637892 | 0.318946 | − | 0.947773i | \(-0.396671\pi\) | ||||
0.318946 | + | 0.947773i | \(0.396671\pi\) | |||||||
\(684\) | −61958.2 | −0.00506359 | ||||||||
\(685\) | −661559. | −0.0538694 | ||||||||
\(686\) | −2.26369e7 | −1.83657 | ||||||||
\(687\) | −4.79286e6 | −0.387439 | ||||||||
\(688\) | 1.11196e7 | 0.895611 | ||||||||
\(689\) | −1.75024e6 | −0.140459 | ||||||||
\(690\) | −6.83428e6 | −0.546474 | ||||||||
\(691\) | 2.34197e7 | 1.86589 | 0.932944 | − | 0.360022i | \(-0.117231\pi\) | ||||
0.932944 | + | 0.360022i | \(0.117231\pi\) | |||||||
\(692\) | 1.22833e7 | 0.975104 | ||||||||
\(693\) | −38276.9 | −0.00302763 | ||||||||
\(694\) | 3.71328e7 | 2.92657 | ||||||||
\(695\) | −2.54438e6 | −0.199811 | ||||||||
\(696\) | 3.93828e7 | 3.08165 | ||||||||
\(697\) | −1.68934e7 | −1.31715 | ||||||||
\(698\) | −3.28205e7 | −2.54981 | ||||||||
\(699\) | 1.36024e6 | 0.105299 | ||||||||
\(700\) | −5.05767e6 | −0.390127 | ||||||||
\(701\) | −1.29951e7 | −0.998811 | −0.499406 | − | 0.866368i | \(-0.666448\pi\) | ||||
−0.499406 | + | 0.866368i | \(0.666448\pi\) | |||||||
\(702\) | 1.37686e7 | 1.05450 | ||||||||
\(703\) | −5.17592e6 | −0.395002 | ||||||||
\(704\) | −3.04407e6 | −0.231485 | ||||||||
\(705\) | −5.30189e6 | −0.401752 | ||||||||
\(706\) | 2.77334e7 | 2.09407 | ||||||||
\(707\) | 3.20302e6 | 0.240997 | ||||||||
\(708\) | 2.31217e7 | 1.73355 | ||||||||
\(709\) | −2.42577e7 | −1.81232 | −0.906160 | − | 0.422935i | \(-0.861000\pi\) | ||||
−0.906160 | + | 0.422935i | \(0.861000\pi\) | |||||||
\(710\) | −1.02830e7 | −0.765549 | ||||||||
\(711\) | −199366. | −0.0147903 | ||||||||
\(712\) | −1.36322e7 | −1.00778 | ||||||||
\(713\) | 2.08308e6 | 0.153455 | ||||||||
\(714\) | −1.62779e7 | −1.19496 | ||||||||
\(715\) | 1.11524e6 | 0.0815835 | ||||||||
\(716\) | −1.95994e7 | −1.42877 | ||||||||
\(717\) | 4.89736e6 | 0.355765 | ||||||||
\(718\) | −264968. | −0.0191815 | ||||||||
\(719\) | 4.81309e6 | 0.347218 | 0.173609 | − | 0.984815i | \(-0.444457\pi\) | ||||
0.173609 | + | 0.984815i | \(0.444457\pi\) | |||||||
\(720\) | 80693.9 | 0.00580109 | ||||||||
\(721\) | 1.19001e7 | 0.852538 | ||||||||
\(722\) | −1.29183e6 | −0.0922277 | ||||||||
\(723\) | −6.79948e6 | −0.483760 | ||||||||
\(724\) | 5.01280e7 | 3.55413 | ||||||||
\(725\) | −4.62483e6 | −0.326776 | ||||||||
\(726\) | −2.27440e6 | −0.160149 | ||||||||
\(727\) | 2.76680e7 | 1.94152 | 0.970759 | − | 0.240057i | \(-0.0771662\pi\) | ||||
0.970759 | + | 0.240057i | \(0.0771662\pi\) | |||||||
\(728\) | 1.52912e7 | 1.06934 | ||||||||
\(729\) | 1.41927e7 | 0.989115 | ||||||||
\(730\) | 1.43557e7 | 0.997052 | ||||||||
\(731\) | −7.65623e6 | −0.529934 | ||||||||
\(732\) | 2.29881e7 | 1.58572 | ||||||||
\(733\) | −3.55639e6 | −0.244483 | −0.122242 | − | 0.992500i | \(-0.539008\pi\) | ||||
−0.122242 | + | 0.992500i | \(0.539008\pi\) | |||||||
\(734\) | −4.09030e7 | −2.80230 | ||||||||
\(735\) | −741160. | −0.0506050 | ||||||||
\(736\) | −2.61298e6 | −0.177804 | ||||||||
\(737\) | 1.75357e6 | 0.118920 | ||||||||
\(738\) | −505538. | −0.0341675 | ||||||||
\(739\) | −1.47974e7 | −0.996724 | −0.498362 | − | 0.866969i | \(-0.666065\pi\) | ||||
−0.498362 | + | 0.866969i | \(0.666065\pi\) | |||||||
\(740\) | 2.37507e7 | 1.59440 | ||||||||
\(741\) | −2.08571e6 | −0.139543 | ||||||||
\(742\) | −5.74727e6 | −0.383223 | ||||||||
\(743\) | −1.64371e7 | −1.09233 | −0.546165 | − | 0.837678i | \(-0.683913\pi\) | ||||
−0.546165 | + | 0.837678i | \(0.683913\pi\) | |||||||
\(744\) | −6.29999e6 | −0.417260 | ||||||||
\(745\) | 987966. | 0.0652156 | ||||||||
\(746\) | 9.20166e6 | 0.605367 | ||||||||
\(747\) | −86214.5 | −0.00565299 | ||||||||
\(748\) | −6.87908e6 | −0.449548 | ||||||||
\(749\) | 1.97450e7 | 1.28604 | ||||||||
\(750\) | −2.42725e6 | −0.157566 | ||||||||
\(751\) | −5.47017e6 | −0.353917 | −0.176958 | − | 0.984218i | \(-0.556626\pi\) | ||||
−0.176958 | + | 0.984218i | \(0.556626\pi\) | |||||||
\(752\) | −1.68636e7 | −1.08744 | ||||||||
\(753\) | 2.72903e6 | 0.175397 | ||||||||
\(754\) | 2.70425e7 | 1.73228 | ||||||||
\(755\) | 361879. | 0.0231045 | ||||||||
\(756\) | 3.04880e7 | 1.94010 | ||||||||
\(757\) | 2.48028e6 | 0.157312 | 0.0786559 | − | 0.996902i | \(-0.474937\pi\) | ||||
0.0786559 | + | 0.996902i | \(0.474937\pi\) | |||||||
\(758\) | 2.49970e7 | 1.58021 | ||||||||
\(759\) | 3.33694e6 | 0.210254 | ||||||||
\(760\) | 3.06502e6 | 0.192486 | ||||||||
\(761\) | 7.15291e6 | 0.447735 | 0.223868 | − | 0.974620i | \(-0.428132\pi\) | ||||
0.223868 | + | 0.974620i | \(0.428132\pi\) | |||||||
\(762\) | 3.94754e7 | 2.46285 | ||||||||
\(763\) | 1.38277e6 | 0.0859880 | ||||||||
\(764\) | 2.54856e7 | 1.57965 | ||||||||
\(765\) | −55560.4 | −0.00343251 | ||||||||
\(766\) | 1.32060e7 | 0.813205 | ||||||||
\(767\) | 8.20918e6 | 0.503862 | ||||||||
\(768\) | −3.35046e7 | −2.04975 | ||||||||
\(769\) | 767976. | 0.0468308 | 0.0234154 | − | 0.999726i | \(-0.492546\pi\) | ||||
0.0234154 | + | 0.999726i | \(0.492546\pi\) | |||||||
\(770\) | 3.66210e6 | 0.222589 | ||||||||
\(771\) | −5.92207e6 | −0.358788 | ||||||||
\(772\) | −2.58613e7 | −1.56173 | ||||||||
\(773\) | −2.63575e7 | −1.58656 | −0.793280 | − | 0.608858i | \(-0.791628\pi\) | ||||
−0.793280 | + | 0.608858i | \(0.791628\pi\) | |||||||
\(774\) | −229114. | −0.0137467 | ||||||||
\(775\) | 739824. | 0.0442460 | ||||||||
\(776\) | −2.45166e7 | −1.46153 | ||||||||
\(777\) | −2.74411e7 | −1.63060 | ||||||||
\(778\) | 2.95334e7 | 1.74930 | ||||||||
\(779\) | −7.10780e6 | −0.419654 | ||||||||
\(780\) | 9.57069e6 | 0.563257 | ||||||||
\(781\) | 5.02081e6 | 0.294542 | ||||||||
\(782\) | 1.49670e7 | 0.875224 | ||||||||
\(783\) | 2.78787e7 | 1.62506 | ||||||||
\(784\) | −2.35739e6 | −0.136975 | ||||||||
\(785\) | −1.17540e7 | −0.680786 | ||||||||
\(786\) | 3.54836e6 | 0.204866 | ||||||||
\(787\) | −1.18887e7 | −0.684221 | −0.342110 | − | 0.939660i | \(-0.611142\pi\) | ||||
−0.342110 | + | 0.939660i | \(0.611142\pi\) | |||||||
\(788\) | −5.55273e7 | −3.18560 | ||||||||
\(789\) | −9.67547e6 | −0.553324 | ||||||||
\(790\) | 1.90742e7 | 1.08737 | ||||||||
\(791\) | −587382. | −0.0333795 | ||||||||
\(792\) | −106440. | −0.00602967 | ||||||||
\(793\) | 8.16176e6 | 0.460894 | ||||||||
\(794\) | 1.69129e7 | 0.952066 | ||||||||
\(795\) | −1.85995e6 | −0.104372 | ||||||||
\(796\) | 2.25890e7 | 1.26361 | ||||||||
\(797\) | −2.89357e7 | −1.61357 | −0.806787 | − | 0.590843i | \(-0.798795\pi\) | ||||
−0.806787 | + | 0.590843i | \(0.798795\pi\) | |||||||
\(798\) | −6.84885e6 | −0.380724 | ||||||||
\(799\) | 1.16111e7 | 0.643438 | ||||||||
\(800\) | −928025. | −0.0512666 | ||||||||
\(801\) | 103972. | 0.00572580 | ||||||||
\(802\) | −3.79956e7 | −2.08592 | ||||||||
\(803\) | −7.00940e6 | −0.383612 | ||||||||
\(804\) | 1.50487e7 | 0.821030 | ||||||||
\(805\) | −5.37294e6 | −0.292229 | ||||||||
\(806\) | −4.32594e6 | −0.234554 | ||||||||
\(807\) | 1.64675e6 | 0.0890110 | ||||||||
\(808\) | 8.90697e6 | 0.479956 | ||||||||
\(809\) | 3.57036e7 | 1.91797 | 0.958983 | − | 0.283464i | \(-0.0914837\pi\) | ||||
0.958983 | + | 0.283464i | \(0.0914837\pi\) | |||||||
\(810\) | 1.47876e7 | 0.791928 | ||||||||
\(811\) | −2.11113e7 | −1.12710 | −0.563550 | − | 0.826082i | \(-0.690565\pi\) | ||||
−0.563550 | + | 0.826082i | \(0.690565\pi\) | |||||||
\(812\) | 5.98806e7 | 3.18710 | ||||||||
\(813\) | −1.30249e7 | −0.691110 | ||||||||
\(814\) | −1.71971e7 | −0.909693 | ||||||||
\(815\) | 5.91014e6 | 0.311676 | ||||||||
\(816\) | −1.67556e7 | −0.880915 | ||||||||
\(817\) | −3.22131e6 | −0.168841 | ||||||||
\(818\) | −6.61473e7 | −3.45644 | ||||||||
\(819\) | −116625. | −0.00607552 | ||||||||
\(820\) | 3.26155e7 | 1.69390 | ||||||||
\(821\) | 7.63918e6 | 0.395539 | 0.197769 | − | 0.980249i | \(-0.436630\pi\) | ||||
0.197769 | + | 0.980249i | \(0.436630\pi\) | |||||||
\(822\) | 4.11077e6 | 0.212199 | ||||||||
\(823\) | 2.42232e7 | 1.24661 | 0.623306 | − | 0.781978i | \(-0.285789\pi\) | ||||
0.623306 | + | 0.781978i | \(0.285789\pi\) | |||||||
\(824\) | 3.30920e7 | 1.69787 | ||||||||
\(825\) | 1.18514e6 | 0.0606228 | ||||||||
\(826\) | 2.69565e7 | 1.37472 | ||||||||
\(827\) | −8.31960e6 | −0.422998 | −0.211499 | − | 0.977378i | \(-0.567835\pi\) | ||||
−0.211499 | + | 0.977378i | \(0.567835\pi\) | |||||||
\(828\) | 302029. | 0.0153099 | ||||||||
\(829\) | −3.62770e6 | −0.183335 | −0.0916675 | − | 0.995790i | \(-0.529220\pi\) | ||||
−0.0916675 | + | 0.995790i | \(0.529220\pi\) | |||||||
\(830\) | 8.24848e6 | 0.415603 | ||||||||
\(831\) | 1.04151e7 | 0.523193 | ||||||||
\(832\) | −9.27493e6 | −0.464518 | ||||||||
\(833\) | 1.62314e6 | 0.0810481 | ||||||||
\(834\) | 1.58102e7 | 0.787085 | ||||||||
\(835\) | −7.39115e6 | −0.366856 | ||||||||
\(836\) | −2.89433e6 | −0.143230 | ||||||||
\(837\) | −4.45971e6 | −0.220035 | ||||||||
\(838\) | −392558. | −0.0193105 | ||||||||
\(839\) | 5.97711e6 | 0.293148 | 0.146574 | − | 0.989200i | \(-0.453175\pi\) | ||||
0.146574 | + | 0.989200i | \(0.453175\pi\) | |||||||
\(840\) | 1.62497e7 | 0.794599 | ||||||||
\(841\) | 3.42448e7 | 1.66957 | ||||||||
\(842\) | 3.22339e7 | 1.56687 | ||||||||
\(843\) | −2.90507e7 | −1.40795 | ||||||||
\(844\) | −1.10884e7 | −0.535810 | ||||||||
\(845\) | −5.88432e6 | −0.283501 | ||||||||
\(846\) | 347465. | 0.0166911 | ||||||||
\(847\) | −1.78808e6 | −0.0856401 | ||||||||
\(848\) | −5.91590e6 | −0.282508 | ||||||||
\(849\) | 3.55471e7 | 1.69252 | ||||||||
\(850\) | 5.31568e6 | 0.252355 | ||||||||
\(851\) | 2.52312e7 | 1.19430 | ||||||||
\(852\) | 4.30874e7 | 2.03353 | ||||||||
\(853\) | −3.57598e7 | −1.68276 | −0.841380 | − | 0.540445i | \(-0.818256\pi\) | ||||
−0.841380 | + | 0.540445i | \(0.818256\pi\) | |||||||
\(854\) | 2.68007e7 | 1.25748 | ||||||||
\(855\) | −23376.7 | −0.00109362 | ||||||||
\(856\) | 5.49071e7 | 2.56120 | ||||||||
\(857\) | −2.07247e7 | −0.963911 | −0.481956 | − | 0.876196i | \(-0.660073\pi\) | ||||
−0.481956 | + | 0.876196i | \(0.660073\pi\) | |||||||
\(858\) | −6.92983e6 | −0.321369 | ||||||||
\(859\) | −3.11456e7 | −1.44017 | −0.720084 | − | 0.693887i | \(-0.755897\pi\) | ||||
−0.720084 | + | 0.693887i | \(0.755897\pi\) | |||||||
\(860\) | 1.47816e7 | 0.681515 | ||||||||
\(861\) | −3.76833e7 | −1.73237 | ||||||||
\(862\) | 3.50739e7 | 1.60774 | ||||||||
\(863\) | −3.12886e7 | −1.43008 | −0.715039 | − | 0.699085i | \(-0.753591\pi\) | ||||
−0.715039 | + | 0.699085i | \(0.753591\pi\) | |||||||
\(864\) | 5.59419e6 | 0.254949 | ||||||||
\(865\) | 4.63447e6 | 0.210601 | ||||||||
\(866\) | −653493. | −0.0296105 | ||||||||
\(867\) | −1.07143e7 | −0.484078 | ||||||||
\(868\) | −9.57898e6 | −0.431539 | ||||||||
\(869\) | −9.31324e6 | −0.418361 | ||||||||
\(870\) | 2.87376e7 | 1.28722 | ||||||||
\(871\) | 5.34293e6 | 0.238635 | ||||||||
\(872\) | 3.84521e6 | 0.171249 | ||||||||
\(873\) | 186987. | 0.00830378 | ||||||||
\(874\) | 6.29730e6 | 0.278853 | ||||||||
\(875\) | −1.90825e6 | −0.0842587 | ||||||||
\(876\) | −6.01529e7 | −2.64848 | ||||||||
\(877\) | −1.96807e7 | −0.864053 | −0.432027 | − | 0.901861i | \(-0.642201\pi\) | ||||
−0.432027 | + | 0.901861i | \(0.642201\pi\) | |||||||
\(878\) | −4.73652e7 | −2.07359 | ||||||||
\(879\) | 8.36503e6 | 0.365170 | ||||||||
\(880\) | 3.76955e6 | 0.164090 | ||||||||
\(881\) | 2.26413e7 | 0.982791 | 0.491395 | − | 0.870937i | \(-0.336487\pi\) | ||||
0.491395 | + | 0.870937i | \(0.336487\pi\) | |||||||
\(882\) | 48572.7 | 0.00210243 | ||||||||
\(883\) | 1.58038e7 | 0.682116 | 0.341058 | − | 0.940042i | \(-0.389215\pi\) | ||||
0.341058 | + | 0.940042i | \(0.389215\pi\) | |||||||
\(884\) | −2.09598e7 | −0.902103 | ||||||||
\(885\) | 8.72376e6 | 0.374408 | ||||||||
\(886\) | 3.53477e7 | 1.51278 | ||||||||
\(887\) | −4.26767e7 | −1.82130 | −0.910652 | − | 0.413175i | \(-0.864420\pi\) | ||||
−0.910652 | + | 0.413175i | \(0.864420\pi\) | |||||||
\(888\) | −7.63083e7 | −3.24742 | ||||||||
\(889\) | 3.10346e7 | 1.31702 | ||||||||
\(890\) | −9.94744e6 | −0.420955 | ||||||||
\(891\) | −7.22028e6 | −0.304691 | ||||||||
\(892\) | 6.35025e7 | 2.67226 | ||||||||
\(893\) | 4.88531e6 | 0.205004 | ||||||||
\(894\) | −6.13899e6 | −0.256894 | ||||||||
\(895\) | −7.39483e6 | −0.308582 | ||||||||
\(896\) | −3.62589e7 | −1.50885 | ||||||||
\(897\) | 1.01673e7 | 0.421914 | ||||||||
\(898\) | −9.63259e6 | −0.398614 | ||||||||
\(899\) | −8.75919e6 | −0.361464 | ||||||||
\(900\) | 107268. | 0.00441434 | ||||||||
\(901\) | 4.07329e6 | 0.167160 | ||||||||
\(902\) | −2.36158e7 | −0.966466 | ||||||||
\(903\) | −1.70784e7 | −0.696991 | ||||||||
\(904\) | −1.63339e6 | −0.0664768 | ||||||||
\(905\) | 1.89132e7 | 0.767614 | ||||||||
\(906\) | −2.24863e6 | −0.0910120 | ||||||||
\(907\) | 1.75475e7 | 0.708265 | 0.354133 | − | 0.935195i | \(-0.384776\pi\) | ||||
0.354133 | + | 0.935195i | \(0.384776\pi\) | |||||||
\(908\) | −7.55441e7 | −3.04079 | ||||||||
\(909\) | −67933.0 | −0.00272691 | ||||||||
\(910\) | 1.11580e7 | 0.446667 | ||||||||
\(911\) | −1.97498e7 | −0.788438 | −0.394219 | − | 0.919017i | \(-0.628985\pi\) | ||||
−0.394219 | + | 0.919017i | \(0.628985\pi\) | |||||||
\(912\) | −7.04981e6 | −0.280666 | ||||||||
\(913\) | −4.02744e6 | −0.159902 | ||||||||
\(914\) | −5.20114e6 | −0.205936 | ||||||||
\(915\) | 8.67336e6 | 0.342480 | ||||||||
\(916\) | −2.02649e7 | −0.798007 | ||||||||
\(917\) | 2.78963e6 | 0.109553 | ||||||||
\(918\) | −3.20433e7 | −1.25496 | ||||||||
\(919\) | −1.06858e7 | −0.417366 | −0.208683 | − | 0.977983i | \(-0.566918\pi\) | ||||
−0.208683 | + | 0.977983i | \(0.566918\pi\) | |||||||
\(920\) | −1.49411e7 | −0.581987 | ||||||||
\(921\) | 1.33674e7 | 0.519275 | ||||||||
\(922\) | 2.76509e7 | 1.07123 | ||||||||
\(923\) | 1.52979e7 | 0.591053 | ||||||||
\(924\) | −1.53448e7 | −0.591264 | ||||||||
\(925\) | 8.96108e6 | 0.344355 | ||||||||
\(926\) | 6.70218e7 | 2.56855 | ||||||||
\(927\) | −252390. | −0.00964659 | ||||||||
\(928\) | 1.09874e7 | 0.418818 | ||||||||
\(929\) | 2.27699e7 | 0.865607 | 0.432804 | − | 0.901488i | \(-0.357524\pi\) | ||||
0.432804 | + | 0.901488i | \(0.357524\pi\) | |||||||
\(930\) | −4.59710e6 | −0.174292 | ||||||||
\(931\) | 682926. | 0.0258226 | ||||||||
\(932\) | 5.75131e6 | 0.216884 | ||||||||
\(933\) | −2.03639e7 | −0.765873 | ||||||||
\(934\) | 6.73648e7 | 2.52677 | ||||||||
\(935\) | −2.59546e6 | −0.0970925 | ||||||||
\(936\) | −324312. | −0.0120997 | ||||||||
\(937\) | −2.05541e7 | −0.764803 | −0.382402 | − | 0.923996i | \(-0.624903\pi\) | ||||
−0.382402 | + | 0.923996i | \(0.624903\pi\) | |||||||
\(938\) | 1.75446e7 | 0.651082 | ||||||||
\(939\) | −3.35261e7 | −1.24085 | ||||||||
\(940\) | −2.24172e7 | −0.827487 | ||||||||
\(941\) | 1.76886e7 | 0.651206 | 0.325603 | − | 0.945507i | \(-0.394433\pi\) | ||||
0.325603 | + | 0.945507i | \(0.394433\pi\) | |||||||
\(942\) | 7.30365e7 | 2.68172 | ||||||||
\(943\) | 3.46485e7 | 1.26884 | ||||||||
\(944\) | 2.77474e7 | 1.01343 | ||||||||
\(945\) | 1.15030e7 | 0.419019 | ||||||||
\(946\) | −1.07029e7 | −0.388842 | ||||||||
\(947\) | 4.53179e7 | 1.64208 | 0.821040 | − | 0.570871i | \(-0.193394\pi\) | ||||
0.821040 | + | 0.570871i | \(0.193394\pi\) | |||||||
\(948\) | −7.99239e7 | −2.88839 | ||||||||
\(949\) | −2.13569e7 | −0.769789 | ||||||||
\(950\) | 2.23654e6 | 0.0804022 | ||||||||
\(951\) | −4.65489e7 | −1.66901 | ||||||||
\(952\) | −3.55869e7 | −1.27262 | ||||||||
\(953\) | −5.04177e7 | −1.79825 | −0.899126 | − | 0.437689i | \(-0.855797\pi\) | ||||
−0.899126 | + | 0.437689i | \(0.855797\pi\) | |||||||
\(954\) | 121894. | 0.00433622 | ||||||||
\(955\) | 9.61566e6 | 0.341170 | ||||||||
\(956\) | 2.07067e7 | 0.732769 | ||||||||
\(957\) | −1.40316e7 | −0.495252 | ||||||||
\(958\) | 7.76581e7 | 2.73384 | ||||||||
\(959\) | 3.23179e6 | 0.113474 | ||||||||
\(960\) | −9.85631e6 | −0.345172 | ||||||||
\(961\) | −2.72280e7 | −0.951057 | ||||||||
\(962\) | −5.23977e7 | −1.82547 | ||||||||
\(963\) | −418773. | −0.0145517 | ||||||||
\(964\) | −2.87492e7 | −0.996399 | ||||||||
\(965\) | −9.75740e6 | −0.337300 | ||||||||
\(966\) | 3.33863e7 | 1.15113 | ||||||||
\(967\) | −2.61680e7 | −0.899921 | −0.449960 | − | 0.893049i | \(-0.648562\pi\) | ||||
−0.449960 | + | 0.893049i | \(0.648562\pi\) | |||||||
\(968\) | −4.97229e6 | −0.170556 | ||||||||
\(969\) | 4.85402e6 | 0.166070 | ||||||||
\(970\) | −1.78898e7 | −0.610486 | ||||||||
\(971\) | −2.18018e7 | −0.742068 | −0.371034 | − | 0.928619i | \(-0.620997\pi\) | ||||
−0.371034 | + | 0.928619i | \(0.620997\pi\) | |||||||
\(972\) | −1.30021e6 | −0.0441415 | ||||||||
\(973\) | 1.24296e7 | 0.420896 | ||||||||
\(974\) | 1.88481e7 | 0.636604 | ||||||||
\(975\) | 3.61100e6 | 0.121651 | ||||||||
\(976\) | 2.75871e7 | 0.927005 | ||||||||
\(977\) | −2.98192e7 | −0.999445 | −0.499723 | − | 0.866186i | \(-0.666565\pi\) | ||||
−0.499723 | + | 0.866186i | \(0.666565\pi\) | |||||||
\(978\) | −3.67243e7 | −1.22774 | ||||||||
\(979\) | 4.85698e6 | 0.161961 | ||||||||
\(980\) | −3.13373e6 | −0.104231 | ||||||||
\(981\) | −29327.2 | −0.000972966 0 | ||||||||
\(982\) | −4.84401e7 | −1.60297 | ||||||||
\(983\) | 3.50223e6 | 0.115601 | 0.0578004 | − | 0.998328i | \(-0.481591\pi\) | ||||
0.0578004 | + | 0.998328i | \(0.481591\pi\) | |||||||
\(984\) | −1.04790e8 | −3.45010 | ||||||||
\(985\) | −2.09503e7 | −0.688019 | ||||||||
\(986\) | −6.29353e7 | −2.06159 | ||||||||
\(987\) | 2.59003e7 | 0.846277 | ||||||||
\(988\) | −8.81871e6 | −0.287417 | ||||||||
\(989\) | 1.57030e7 | 0.510496 | ||||||||
\(990\) | −77669.6 | −0.00251862 | ||||||||
\(991\) | 3.23436e7 | 1.04617 | 0.523087 | − | 0.852279i | \(-0.324780\pi\) | ||||
0.523087 | + | 0.852279i | \(0.324780\pi\) | |||||||
\(992\) | −1.75763e6 | −0.0567086 | ||||||||
\(993\) | 3.01655e7 | 0.970816 | ||||||||
\(994\) | 5.02335e7 | 1.61260 | ||||||||
\(995\) | 8.52279e6 | 0.272913 | ||||||||
\(996\) | −3.45625e7 | −1.10397 | ||||||||
\(997\) | 5.98804e7 | 1.90786 | 0.953930 | − | 0.300029i | \(-0.0969963\pi\) | ||||
0.953930 | + | 0.300029i | \(0.0969963\pi\) | |||||||
\(998\) | 8.89573e7 | 2.82719 | ||||||||
\(999\) | −5.40180e7 | −1.71248 |
(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 | 1045.6.a.e.1.4 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.e.1.4 | ✓ | 38 | 1.1 | even | 1 | trivial |