Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + \cdots - 22888100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 7^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-9.33424\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.3342 | 1.82685 | 0.913426 | − | 0.407005i | \(-0.133427\pi\) | ||||
0.913426 | + | 0.407005i | \(0.133427\pi\) | |||||||
\(3\) | 10.7786 | 0.691451 | 0.345725 | − | 0.938336i | \(-0.387633\pi\) | ||||
0.345725 | + | 0.938336i | \(0.387633\pi\) | |||||||
\(4\) | 74.7964 | 2.33739 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 111.389 | 1.26318 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 442.268 | 2.44321 | ||||||||
\(9\) | −126.821 | −0.521896 | ||||||||
\(10\) | 258.356 | 0.816993 | ||||||||
\(11\) | −262.917 | −0.655145 | −0.327572 | − | 0.944826i | \(-0.606231\pi\) | ||||
−0.327572 | + | 0.944826i | \(0.606231\pi\) | |||||||
\(12\) | 806.204 | 1.61619 | ||||||||
\(13\) | 688.927 | 1.13061 | 0.565307 | − | 0.824880i | \(-0.308758\pi\) | ||||
0.565307 | + | 0.824880i | \(0.308758\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 269.466 | 0.309226 | ||||||||
\(16\) | 2177.02 | 2.12600 | ||||||||
\(17\) | 1678.08 | 1.40828 | 0.704141 | − | 0.710060i | \(-0.251332\pi\) | ||||
0.704141 | + | 0.710060i | \(0.251332\pi\) | |||||||
\(18\) | −1310.60 | −0.953427 | ||||||||
\(19\) | 925.109 | 0.587907 | 0.293954 | − | 0.955820i | \(-0.405029\pi\) | ||||
0.293954 | + | 0.955820i | \(0.405029\pi\) | |||||||
\(20\) | 1869.91 | 1.04531 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2717.05 | −1.19685 | ||||||||
\(23\) | 4608.33 | 1.81645 | 0.908226 | − | 0.418480i | \(-0.137437\pi\) | ||||
0.908226 | + | 0.418480i | \(0.137437\pi\) | |||||||
\(24\) | 4767.06 | 1.68936 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 7119.53 | 2.06547 | ||||||||
\(27\) | −3986.17 | −1.05232 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3413.30 | −0.753666 | −0.376833 | − | 0.926281i | \(-0.622987\pi\) | ||||
−0.376833 | + | 0.926281i | \(0.622987\pi\) | |||||||
\(30\) | 2784.73 | 0.564910 | ||||||||
\(31\) | −5534.34 | −1.03434 | −0.517168 | − | 0.855884i | \(-0.673014\pi\) | ||||
−0.517168 | + | 0.855884i | \(0.673014\pi\) | |||||||
\(32\) | 8345.25 | 1.44067 | ||||||||
\(33\) | −2833.89 | −0.453000 | ||||||||
\(34\) | 17341.7 | 2.57272 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9485.74 | −1.21987 | ||||||||
\(37\) | −14971.8 | −1.79791 | −0.898956 | − | 0.438038i | \(-0.855674\pi\) | ||||
−0.898956 | + | 0.438038i | \(0.855674\pi\) | |||||||
\(38\) | 9560.29 | 1.07402 | ||||||||
\(39\) | 7425.70 | 0.781764 | ||||||||
\(40\) | 11056.7 | 1.09264 | ||||||||
\(41\) | 14959.7 | 1.38983 | 0.694916 | − | 0.719091i | \(-0.255442\pi\) | ||||
0.694916 | + | 0.719091i | \(0.255442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19652.7 | −1.62088 | −0.810442 | − | 0.585818i | \(-0.800773\pi\) | ||||
−0.810442 | + | 0.585818i | \(0.800773\pi\) | |||||||
\(44\) | −19665.3 | −1.53133 | ||||||||
\(45\) | −3170.52 | −0.233399 | ||||||||
\(46\) | 47623.6 | 3.31839 | ||||||||
\(47\) | −11299.0 | −0.746096 | −0.373048 | − | 0.927812i | \(-0.621687\pi\) | ||||
−0.373048 | + | 0.927812i | \(0.621687\pi\) | |||||||
\(48\) | 23465.3 | 1.47002 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6458.90 | 0.365370 | ||||||||
\(51\) | 18087.4 | 0.973758 | ||||||||
\(52\) | 51529.3 | 2.64269 | ||||||||
\(53\) | −21380.7 | −1.04552 | −0.522759 | − | 0.852480i | \(-0.675097\pi\) | ||||
−0.522759 | + | 0.852480i | \(0.675097\pi\) | |||||||
\(54\) | −41194.0 | −1.92243 | ||||||||
\(55\) | −6572.93 | −0.292990 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9971.42 | 0.406509 | ||||||||
\(58\) | −35273.8 | −1.37684 | ||||||||
\(59\) | −3476.31 | −0.130014 | −0.0650068 | − | 0.997885i | \(-0.520707\pi\) | ||||
−0.0650068 | + | 0.997885i | \(0.520707\pi\) | |||||||
\(60\) | 20155.1 | 0.722782 | ||||||||
\(61\) | −22396.1 | −0.770633 | −0.385317 | − | 0.922784i | \(-0.625908\pi\) | ||||
−0.385317 | + | 0.922784i | \(0.625908\pi\) | |||||||
\(62\) | −57193.2 | −1.88958 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 16577.2 | 0.505895 | ||||||||
\(65\) | 17223.2 | 0.505626 | ||||||||
\(66\) | −29286.1 | −0.827564 | ||||||||
\(67\) | 44935.8 | 1.22294 | 0.611470 | − | 0.791267i | \(-0.290578\pi\) | ||||
0.611470 | + | 0.791267i | \(0.290578\pi\) | |||||||
\(68\) | 125514. | 3.29170 | ||||||||
\(69\) | 49671.6 | 1.25599 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10904.9 | 0.256729 | 0.128365 | − | 0.991727i | \(-0.459027\pi\) | ||||
0.128365 | + | 0.991727i | \(0.459027\pi\) | |||||||
\(72\) | −56088.8 | −1.27510 | ||||||||
\(73\) | −9209.41 | −0.202267 | −0.101133 | − | 0.994873i | \(-0.532247\pi\) | ||||
−0.101133 | + | 0.994873i | \(0.532247\pi\) | |||||||
\(74\) | −154722. | −3.28452 | ||||||||
\(75\) | 6736.65 | 0.138290 | ||||||||
\(76\) | 69194.8 | 1.37417 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 76738.9 | 1.42817 | ||||||||
\(79\) | −3355.92 | −0.0604984 | −0.0302492 | − | 0.999542i | \(-0.509630\pi\) | ||||
−0.0302492 | + | 0.999542i | \(0.509630\pi\) | |||||||
\(80\) | 54425.5 | 0.950775 | ||||||||
\(81\) | −12148.1 | −0.205728 | ||||||||
\(82\) | 154597. | 2.53902 | ||||||||
\(83\) | 45537.7 | 0.725565 | 0.362782 | − | 0.931874i | \(-0.381827\pi\) | ||||
0.362782 | + | 0.931874i | \(0.381827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41951.9 | 0.629803 | ||||||||
\(86\) | −203096. | −2.96112 | ||||||||
\(87\) | −36790.7 | −0.521123 | ||||||||
\(88\) | −116280. | −1.60066 | ||||||||
\(89\) | −52889.1 | −0.707768 | −0.353884 | − | 0.935289i | \(-0.615139\pi\) | ||||
−0.353884 | + | 0.935289i | \(0.615139\pi\) | |||||||
\(90\) | −32764.9 | −0.426386 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 344687. | 4.24575 | ||||||||
\(93\) | −59652.7 | −0.715193 | ||||||||
\(94\) | −116766. | −1.36301 | ||||||||
\(95\) | 23127.7 | 0.262920 | ||||||||
\(96\) | 89950.5 | 0.996152 | ||||||||
\(97\) | −164527. | −1.77545 | −0.887725 | − | 0.460375i | \(-0.847715\pi\) | ||||
−0.887725 | + | 0.460375i | \(0.847715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33343.4 | 0.341917 | ||||||||
\(100\) | 46747.8 | 0.467478 | ||||||||
\(101\) | 24003.0 | 0.234132 | 0.117066 | − | 0.993124i | \(-0.462651\pi\) | ||||
0.117066 | + | 0.993124i | \(0.462651\pi\) | |||||||
\(102\) | 186920. | 1.77891 | ||||||||
\(103\) | −110339. | −1.02479 | −0.512394 | − | 0.858750i | \(-0.671241\pi\) | ||||
−0.512394 | + | 0.858750i | \(0.671241\pi\) | |||||||
\(104\) | 304690. | 2.76233 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −220953. | −1.91001 | ||||||||
\(107\) | 90804.3 | 0.766738 | 0.383369 | − | 0.923595i | \(-0.374764\pi\) | ||||
0.383369 | + | 0.923595i | \(0.374764\pi\) | |||||||
\(108\) | −298151. | −2.45967 | ||||||||
\(109\) | 141520. | 1.14091 | 0.570454 | − | 0.821330i | \(-0.306767\pi\) | ||||
0.570454 | + | 0.821330i | \(0.306767\pi\) | |||||||
\(110\) | −67926.2 | −0.535249 | ||||||||
\(111\) | −161375. | −1.24317 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −116848. | −0.860845 | −0.430423 | − | 0.902627i | \(-0.641636\pi\) | ||||
−0.430423 | + | 0.902627i | \(0.641636\pi\) | |||||||
\(114\) | 103047. | 0.742631 | ||||||||
\(115\) | 115208. | 0.812342 | ||||||||
\(116\) | −255303. | −1.76161 | ||||||||
\(117\) | −87370.2 | −0.590063 | ||||||||
\(118\) | −35925.0 | −0.237516 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 119176. | 0.755505 | ||||||||
\(121\) | −91925.6 | −0.570785 | ||||||||
\(122\) | −231447. | −1.40783 | ||||||||
\(123\) | 161245. | 0.961000 | ||||||||
\(124\) | −413949. | −2.41765 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −147879. | −0.813574 | −0.406787 | − | 0.913523i | \(-0.633351\pi\) | ||||
−0.406787 | + | 0.913523i | \(0.633351\pi\) | |||||||
\(128\) | −95735.8 | −0.516475 | ||||||||
\(129\) | −211830. | −1.12076 | ||||||||
\(130\) | 177988. | 0.923704 | ||||||||
\(131\) | −73626.8 | −0.374850 | −0.187425 | − | 0.982279i | \(-0.560014\pi\) | ||||
−0.187425 | + | 0.982279i | \(0.560014\pi\) | |||||||
\(132\) | −211965. | −1.05884 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 464377. | 2.23413 | ||||||||
\(135\) | −99654.2 | −0.470610 | ||||||||
\(136\) | 742161. | 3.44073 | ||||||||
\(137\) | 338575. | 1.54118 | 0.770589 | − | 0.637332i | \(-0.219962\pi\) | ||||
0.770589 | + | 0.637332i | \(0.219962\pi\) | |||||||
\(138\) | 513318. | 2.29450 | ||||||||
\(139\) | 372518. | 1.63535 | 0.817675 | − | 0.575680i | \(-0.195263\pi\) | ||||
0.817675 | + | 0.575680i | \(0.195263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −121788. | −0.515889 | ||||||||
\(142\) | 112694. | 0.469006 | ||||||||
\(143\) | −181131. | −0.740716 | ||||||||
\(144\) | −276091. | −1.10955 | ||||||||
\(145\) | −85332.4 | −0.337050 | ||||||||
\(146\) | −95172.2 | −0.369511 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.11983e6 | −4.20242 | ||||||||
\(149\) | −155353. | −0.573263 | −0.286632 | − | 0.958041i | \(-0.592536\pi\) | ||||
−0.286632 | + | 0.958041i | \(0.592536\pi\) | |||||||
\(150\) | 69618.2 | 0.252636 | ||||||||
\(151\) | 220907. | 0.788439 | 0.394219 | − | 0.919016i | \(-0.371015\pi\) | ||||
0.394219 | + | 0.919016i | \(0.371015\pi\) | |||||||
\(152\) | 409146. | 1.43638 | ||||||||
\(153\) | −212815. | −0.734977 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −138359. | −0.462569 | ||||||||
\(156\) | 555416. | 1.82729 | ||||||||
\(157\) | 543726. | 1.76048 | 0.880240 | − | 0.474529i | \(-0.157382\pi\) | ||||
0.880240 | + | 0.474529i | \(0.157382\pi\) | |||||||
\(158\) | −34680.9 | −0.110522 | ||||||||
\(159\) | −230455. | −0.722925 | ||||||||
\(160\) | 208631. | 0.644287 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −125541. | −0.375835 | ||||||||
\(163\) | 11753.3 | 0.0346490 | 0.0173245 | − | 0.999850i | \(-0.494485\pi\) | ||||
0.0173245 | + | 0.999850i | \(0.494485\pi\) | |||||||
\(164\) | 1.11893e6 | 3.24858 | ||||||||
\(165\) | −70847.3 | −0.202588 | ||||||||
\(166\) | 470598. | 1.32550 | ||||||||
\(167\) | 38571.8 | 0.107023 | 0.0535117 | − | 0.998567i | \(-0.482959\pi\) | ||||
0.0535117 | + | 0.998567i | \(0.482959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 103327. | 0.278289 | ||||||||
\(170\) | 433541. | 1.15056 | ||||||||
\(171\) | −117323. | −0.306826 | ||||||||
\(172\) | −1.46996e6 | −3.78864 | ||||||||
\(173\) | 26934.3 | 0.0684213 | 0.0342106 | − | 0.999415i | \(-0.489108\pi\) | ||||
0.0342106 | + | 0.999415i | \(0.489108\pi\) | |||||||
\(174\) | −380204. | −0.952015 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −572376. | −1.39284 | ||||||||
\(177\) | −37469.9 | −0.0898979 | ||||||||
\(178\) | −546568. | −1.29299 | ||||||||
\(179\) | 261941. | 0.611041 | 0.305521 | − | 0.952185i | \(-0.401170\pi\) | ||||
0.305521 | + | 0.952185i | \(0.401170\pi\) | |||||||
\(180\) | −237144. | −0.545544 | ||||||||
\(181\) | 447956. | 1.01634 | 0.508170 | − | 0.861257i | \(-0.330322\pi\) | ||||
0.508170 | + | 0.861257i | \(0.330322\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −241400. | −0.532855 | ||||||||
\(184\) | 2.03812e6 | 4.43798 | ||||||||
\(185\) | −374294. | −0.804051 | ||||||||
\(186\) | −616465. | −1.30655 | ||||||||
\(187\) | −441195. | −0.922629 | ||||||||
\(188\) | −845124. | −1.74392 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 239007. | 0.480316 | ||||||||
\(191\) | −159526. | −0.316409 | −0.158204 | − | 0.987406i | \(-0.550570\pi\) | ||||
−0.158204 | + | 0.987406i | \(0.550570\pi\) | |||||||
\(192\) | 178679. | 0.349801 | ||||||||
\(193\) | 348995. | 0.674413 | 0.337207 | − | 0.941431i | \(-0.390518\pi\) | ||||
0.337207 | + | 0.941431i | \(0.390518\pi\) | |||||||
\(194\) | −1.70026e6 | −3.24348 | ||||||||
\(195\) | 185642. | 0.349616 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −459058. | −0.842755 | −0.421378 | − | 0.906885i | \(-0.638453\pi\) | ||||
−0.421378 | + | 0.906885i | \(0.638453\pi\) | |||||||
\(198\) | 344578. | 0.624633 | ||||||||
\(199\) | 1.02765e6 | 1.83955 | 0.919776 | − | 0.392444i | \(-0.128370\pi\) | ||||
0.919776 | + | 0.392444i | \(0.128370\pi\) | |||||||
\(200\) | 276418. | 0.488642 | ||||||||
\(201\) | 484347. | 0.845603 | ||||||||
\(202\) | 248052. | 0.427725 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.35287e6 | 2.27605 | ||||||||
\(205\) | 373992. | 0.621552 | ||||||||
\(206\) | −1.14026e6 | −1.87214 | ||||||||
\(207\) | −584432. | −0.947999 | ||||||||
\(208\) | 1.49981e6 | 2.40368 | ||||||||
\(209\) | −243227. | −0.385164 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −854033. | −1.32059 | −0.660296 | − | 0.751006i | \(-0.729569\pi\) | ||||
−0.660296 | + | 0.751006i | \(0.729569\pi\) | |||||||
\(212\) | −1.59920e6 | −2.44378 | ||||||||
\(213\) | 117540. | 0.177515 | ||||||||
\(214\) | 938393. | 1.40072 | ||||||||
\(215\) | −491319. | −0.724882 | ||||||||
\(216\) | −1.76296e6 | −2.57103 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.46250e6 | 2.08427 | ||||||||
\(219\) | −99264.9 | −0.139857 | ||||||||
\(220\) | −491632. | −0.684831 | ||||||||
\(221\) | 1.15607e6 | 1.59222 | ||||||||
\(222\) | −1.66769e6 | −2.27108 | ||||||||
\(223\) | 274209. | 0.369249 | 0.184625 | − | 0.982809i | \(-0.440893\pi\) | ||||
0.184625 | + | 0.982809i | \(0.440893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −79263.0 | −0.104379 | ||||||||
\(226\) | −1.20753e6 | −1.57264 | ||||||||
\(227\) | −1.32207e6 | −1.70290 | −0.851450 | − | 0.524435i | \(-0.824276\pi\) | ||||
−0.851450 | + | 0.524435i | \(0.824276\pi\) | |||||||
\(228\) | 745827. | 0.950169 | ||||||||
\(229\) | 163985. | 0.206640 | 0.103320 | − | 0.994648i | \(-0.467053\pi\) | ||||
0.103320 | + | 0.994648i | \(0.467053\pi\) | |||||||
\(230\) | 1.19059e6 | 1.48403 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.50959e6 | −1.84137 | ||||||||
\(233\) | −1.10695e6 | −1.33579 | −0.667895 | − | 0.744256i | \(-0.732804\pi\) | ||||
−0.667895 | + | 0.744256i | \(0.732804\pi\) | |||||||
\(234\) | −902904. | −1.07796 | ||||||||
\(235\) | −282475. | −0.333664 | ||||||||
\(236\) | −260016. | −0.303892 | ||||||||
\(237\) | −36172.3 | −0.0418316 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 576115. | 0.652401 | 0.326200 | − | 0.945301i | \(-0.394232\pi\) | ||||
0.326200 | + | 0.945301i | \(0.394232\pi\) | |||||||
\(240\) | 586633. | 0.657414 | ||||||||
\(241\) | −1.01805e6 | −1.12908 | −0.564541 | − | 0.825405i | \(-0.690947\pi\) | ||||
−0.564541 | + | 0.825405i | \(0.690947\pi\) | |||||||
\(242\) | −949980. | −1.04274 | ||||||||
\(243\) | 837699. | 0.910065 | ||||||||
\(244\) | −1.67515e6 | −1.80127 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.66634e6 | 1.75561 | ||||||||
\(247\) | 637332. | 0.664696 | ||||||||
\(248\) | −2.44767e6 | −2.52710 | ||||||||
\(249\) | 490835. | 0.501692 | ||||||||
\(250\) | 161472. | 0.163399 | ||||||||
\(251\) | −44770.6 | −0.0448548 | −0.0224274 | − | 0.999748i | \(-0.507139\pi\) | ||||
−0.0224274 | + | 0.999748i | \(0.507139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.21161e6 | −1.19004 | ||||||||
\(254\) | −1.52822e6 | −1.48628 | ||||||||
\(255\) | 452185. | 0.435478 | ||||||||
\(256\) | −1.51983e6 | −1.44942 | ||||||||
\(257\) | 300025. | 0.283351 | 0.141676 | − | 0.989913i | \(-0.454751\pi\) | ||||
0.141676 | + | 0.989913i | \(0.454751\pi\) | |||||||
\(258\) | −2.18910e6 | −2.04747 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.28823e6 | 1.18184 | ||||||||
\(261\) | 432877. | 0.393336 | ||||||||
\(262\) | −760877. | −0.684796 | ||||||||
\(263\) | −151046. | −0.134654 | −0.0673271 | − | 0.997731i | \(-0.521447\pi\) | ||||
−0.0673271 | + | 0.997731i | \(0.521447\pi\) | |||||||
\(264\) | −1.25334e6 | −1.10677 | ||||||||
\(265\) | −534517. | −0.467570 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −570073. | −0.489387 | ||||||||
\(268\) | 3.36104e6 | 2.85849 | ||||||||
\(269\) | 1.18347e6 | 0.997191 | 0.498595 | − | 0.866835i | \(-0.333849\pi\) | ||||
0.498595 | + | 0.866835i | \(0.333849\pi\) | |||||||
\(270\) | −1.02985e6 | −0.859735 | ||||||||
\(271\) | −1.43453e6 | −1.18655 | −0.593276 | − | 0.804999i | \(-0.702166\pi\) | ||||
−0.593276 | + | 0.804999i | \(0.702166\pi\) | |||||||
\(272\) | 3.65321e6 | 2.99400 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.49891e6 | 2.81551 | ||||||||
\(275\) | −164323. | −0.131029 | ||||||||
\(276\) | 3.71526e6 | 2.93573 | ||||||||
\(277\) | −485316. | −0.380036 | −0.190018 | − | 0.981781i | \(-0.560855\pi\) | ||||
−0.190018 | + | 0.981781i | \(0.560855\pi\) | |||||||
\(278\) | 3.84969e6 | 2.98754 | ||||||||
\(279\) | 701870. | 0.539816 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 110465. | 0.0834564 | 0.0417282 | − | 0.999129i | \(-0.486714\pi\) | ||||
0.0417282 | + | 0.999129i | \(0.486714\pi\) | |||||||
\(282\) | −1.25858e6 | −0.942452 | ||||||||
\(283\) | 324717. | 0.241012 | 0.120506 | − | 0.992713i | \(-0.461548\pi\) | ||||
0.120506 | + | 0.992713i | \(0.461548\pi\) | |||||||
\(284\) | 815646. | 0.600076 | ||||||||
\(285\) | 249286. | 0.181796 | ||||||||
\(286\) | −1.87185e6 | −1.35318 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.05835e6 | −0.751880 | ||||||||
\(289\) | 1.39609e6 | 0.983259 | ||||||||
\(290\) | −881846. | −0.615740 | ||||||||
\(291\) | −1.77338e6 | −1.22764 | ||||||||
\(292\) | −688831. | −0.472776 | ||||||||
\(293\) | 1.30456e6 | 0.887758 | 0.443879 | − | 0.896087i | \(-0.353602\pi\) | ||||
0.443879 | + | 0.896087i | \(0.353602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −86907.8 | −0.0581438 | ||||||||
\(296\) | −6.62154e6 | −4.39268 | ||||||||
\(297\) | 1.04803e6 | 0.689419 | ||||||||
\(298\) | −1.60545e6 | −1.04727 | ||||||||
\(299\) | 3.17480e6 | 2.05371 | ||||||||
\(300\) | 503878. | 0.323238 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.28291e6 | 1.44036 | ||||||||
\(303\) | 258720. | 0.161891 | ||||||||
\(304\) | 2.01398e6 | 1.24989 | ||||||||
\(305\) | −559903. | −0.344638 | ||||||||
\(306\) | −2.19928e6 | −1.34269 | ||||||||
\(307\) | −774592. | −0.469058 | −0.234529 | − | 0.972109i | \(-0.575355\pi\) | ||||
−0.234529 | + | 0.972109i | \(0.575355\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.18930e6 | −0.708590 | ||||||||
\(310\) | −1.42983e6 | −0.845046 | ||||||||
\(311\) | 3.06756e6 | 1.79842 | 0.899211 | − | 0.437515i | \(-0.144141\pi\) | ||||
0.899211 | + | 0.437515i | \(0.144141\pi\) | |||||||
\(312\) | 3.28415e6 | 1.91001 | ||||||||
\(313\) | 949654. | 0.547904 | 0.273952 | − | 0.961743i | \(-0.411669\pi\) | ||||
0.273952 | + | 0.961743i | \(0.411669\pi\) | |||||||
\(314\) | 5.61899e6 | 3.21614 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −251011. | −0.141408 | ||||||||
\(317\) | 2.31477e6 | 1.29378 | 0.646889 | − | 0.762584i | \(-0.276070\pi\) | ||||
0.646889 | + | 0.762584i | \(0.276070\pi\) | |||||||
\(318\) | −2.38157e6 | −1.32068 | ||||||||
\(319\) | 897415. | 0.493761 | ||||||||
\(320\) | 414429. | 0.226243 | ||||||||
\(321\) | 978747. | 0.530161 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.55240e6 | 0.827939 | ||||||||
\(324\) | −908631. | −0.480867 | ||||||||
\(325\) | 430579. | 0.226123 | ||||||||
\(326\) | 121461. | 0.0632986 | ||||||||
\(327\) | 1.52539e6 | 0.788881 | ||||||||
\(328\) | 6.61619e6 | 3.39565 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −732153. | −0.370098 | ||||||||
\(331\) | −300877. | −0.150945 | −0.0754726 | − | 0.997148i | \(-0.524047\pi\) | ||||
−0.0754726 | + | 0.997148i | \(0.524047\pi\) | |||||||
\(332\) | 3.40606e6 | 1.69593 | ||||||||
\(333\) | 1.89873e6 | 0.938324 | ||||||||
\(334\) | 398610. | 0.195516 | ||||||||
\(335\) | 1.12339e6 | 0.546916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −484462. | −0.232373 | −0.116186 | − | 0.993227i | \(-0.537067\pi\) | ||||
−0.116186 | + | 0.993227i | \(0.537067\pi\) | |||||||
\(338\) | 1.06780e6 | 0.508394 | ||||||||
\(339\) | −1.25946e6 | −0.595232 | ||||||||
\(340\) | 3.13786e6 | 1.47209 | ||||||||
\(341\) | 1.45507e6 | 0.677640 | ||||||||
\(342\) | −1.21244e6 | −0.560527 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.69179e6 | −3.96016 | ||||||||
\(345\) | 1.24179e6 | 0.561694 | ||||||||
\(346\) | 278346. | 0.124996 | ||||||||
\(347\) | 3.02605e6 | 1.34912 | 0.674562 | − | 0.738218i | \(-0.264332\pi\) | ||||
0.674562 | + | 0.738218i | \(0.264332\pi\) | |||||||
\(348\) | −2.75182e6 | −1.21807 | ||||||||
\(349\) | −2.48201e6 | −1.09079 | −0.545393 | − | 0.838181i | \(-0.683619\pi\) | ||||
−0.545393 | + | 0.838181i | \(0.683619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.74618e6 | −1.18976 | ||||||||
\(352\) | −2.19411e6 | −0.943847 | ||||||||
\(353\) | 3.77106e6 | 1.61075 | 0.805373 | − | 0.592768i | \(-0.201965\pi\) | ||||
0.805373 | + | 0.592768i | \(0.201965\pi\) | |||||||
\(354\) | −387223. | −0.164230 | ||||||||
\(355\) | 272622. | 0.114813 | ||||||||
\(356\) | −3.95591e6 | −1.65433 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.70696e6 | 1.11628 | ||||||||
\(359\) | 199028. | 0.0815039 | 0.0407519 | − | 0.999169i | \(-0.487025\pi\) | ||||
0.0407519 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(360\) | −1.40222e6 | −0.570243 | ||||||||
\(361\) | −1.62027e6 | −0.654365 | ||||||||
\(362\) | 4.62929e6 | 1.85670 | ||||||||
\(363\) | −990833. | −0.394670 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −230235. | −0.0904564 | ||||||||
\(366\) | −2.49468e6 | −0.973447 | ||||||||
\(367\) | 2.68132e6 | 1.03916 | 0.519581 | − | 0.854421i | \(-0.326088\pi\) | ||||
0.519581 | + | 0.854421i | \(0.326088\pi\) | |||||||
\(368\) | 1.00324e7 | 3.86177 | ||||||||
\(369\) | −1.89720e6 | −0.725348 | ||||||||
\(370\) | −3.86804e6 | −1.46888 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.46181e6 | −1.67168 | ||||||||
\(373\) | −550183. | −0.204755 | −0.102378 | − | 0.994746i | \(-0.532645\pi\) | ||||
−0.102378 | + | 0.994746i | \(0.532645\pi\) | |||||||
\(374\) | −4.55942e6 | −1.68551 | ||||||||
\(375\) | 168416. | 0.0618452 | ||||||||
\(376\) | −4.99718e6 | −1.82287 | ||||||||
\(377\) | −2.35151e6 | −0.852106 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 939596. | 0.336003 | 0.168002 | − | 0.985787i | \(-0.446269\pi\) | ||||
0.168002 | + | 0.985787i | \(0.446269\pi\) | |||||||
\(380\) | 1.72987e6 | 0.614546 | ||||||||
\(381\) | −1.59394e6 | −0.562546 | ||||||||
\(382\) | −1.64858e6 | −0.578032 | ||||||||
\(383\) | −4.48212e6 | −1.56130 | −0.780650 | − | 0.624969i | \(-0.785112\pi\) | ||||
−0.780650 | + | 0.624969i | \(0.785112\pi\) | |||||||
\(384\) | −1.03190e6 | −0.357117 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.60660e6 | 1.23205 | ||||||||
\(387\) | 2.49238e6 | 0.845933 | ||||||||
\(388\) | −1.23060e7 | −4.14992 | ||||||||
\(389\) | −5.21921e6 | −1.74876 | −0.874381 | − | 0.485241i | \(-0.838732\pi\) | ||||
−0.874381 | + | 0.485241i | \(0.838732\pi\) | |||||||
\(390\) | 1.91847e6 | 0.638696 | ||||||||
\(391\) | 7.73314e6 | 2.55808 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −793598. | −0.259190 | ||||||||
\(394\) | −4.74401e6 | −1.53959 | ||||||||
\(395\) | −83898.0 | −0.0270557 | ||||||||
\(396\) | 2.49396e6 | 0.799194 | ||||||||
\(397\) | 1.06864e6 | 0.340294 | 0.170147 | − | 0.985419i | \(-0.445576\pi\) | ||||
0.170147 | + | 0.985419i | \(0.445576\pi\) | |||||||
\(398\) | 1.06200e7 | 3.36059 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.36064e6 | 0.425199 | ||||||||
\(401\) | 464941. | 0.144390 | 0.0721950 | − | 0.997391i | \(-0.477000\pi\) | ||||
0.0721950 | + | 0.997391i | \(0.477000\pi\) | |||||||
\(402\) | 5.00536e6 | 1.54479 | ||||||||
\(403\) | −3.81276e6 | −1.16944 | ||||||||
\(404\) | 1.79534e6 | 0.547258 | ||||||||
\(405\) | −303701. | −0.0920045 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.93633e6 | 1.17789 | ||||||||
\(408\) | 7.99949e6 | 2.37910 | ||||||||
\(409\) | 4.46546e6 | 1.31995 | 0.659976 | − | 0.751286i | \(-0.270566\pi\) | ||||
0.659976 | + | 0.751286i | \(0.270566\pi\) | |||||||
\(410\) | 3.86492e6 | 1.13548 | ||||||||
\(411\) | 3.64938e6 | 1.06565 | ||||||||
\(412\) | −8.25293e6 | −2.39533 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.03966e6 | −1.73185 | ||||||||
\(415\) | 1.13844e6 | 0.324482 | ||||||||
\(416\) | 5.74927e6 | 1.62884 | ||||||||
\(417\) | 4.01525e6 | 1.13076 | ||||||||
\(418\) | −2.51356e6 | −0.703638 | ||||||||
\(419\) | 6.25416e6 | 1.74034 | 0.870170 | − | 0.492751i | \(-0.164009\pi\) | ||||
0.870170 | + | 0.492751i | \(0.164009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.01694e6 | 1.37954 | 0.689768 | − | 0.724030i | \(-0.257712\pi\) | ||||
0.689768 | + | 0.724030i | \(0.257712\pi\) | |||||||
\(422\) | −8.82578e6 | −2.41253 | ||||||||
\(423\) | 1.43295e6 | 0.389385 | ||||||||
\(424\) | −9.45600e6 | −2.55442 | ||||||||
\(425\) | 1.04880e6 | 0.281656 | ||||||||
\(426\) | 1.21468e6 | 0.324294 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.79183e6 | 1.79216 | ||||||||
\(429\) | −1.95234e6 | −0.512169 | ||||||||
\(430\) | −5.07740e6 | −1.32425 | ||||||||
\(431\) | −4.52767e6 | −1.17404 | −0.587018 | − | 0.809574i | \(-0.699698\pi\) | ||||
−0.587018 | + | 0.809574i | \(0.699698\pi\) | |||||||
\(432\) | −8.67797e6 | −2.23722 | ||||||||
\(433\) | −1.88959e6 | −0.484338 | −0.242169 | − | 0.970234i | \(-0.577859\pi\) | ||||
−0.242169 | + | 0.970234i | \(0.577859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −919768. | −0.233053 | ||||||||
\(436\) | 1.05852e7 | 2.66674 | ||||||||
\(437\) | 4.26321e6 | 1.06791 | ||||||||
\(438\) | −1.02583e6 | −0.255499 | ||||||||
\(439\) | 5.31281e6 | 1.31572 | 0.657859 | − | 0.753141i | \(-0.271462\pi\) | ||||
0.657859 | + | 0.753141i | \(0.271462\pi\) | |||||||
\(440\) | −2.90700e6 | −0.715835 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.19471e7 | 2.90876 | ||||||||
\(443\) | 3.37858e6 | 0.817946 | 0.408973 | − | 0.912546i | \(-0.365887\pi\) | ||||
0.408973 | + | 0.912546i | \(0.365887\pi\) | |||||||
\(444\) | −1.20703e7 | −2.90577 | ||||||||
\(445\) | −1.32223e6 | −0.316524 | ||||||||
\(446\) | 2.83374e6 | 0.674564 | ||||||||
\(447\) | −1.67450e6 | −0.396383 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.32305e6 | −0.309714 | −0.154857 | − | 0.987937i | \(-0.549492\pi\) | ||||
−0.154857 | + | 0.987937i | \(0.549492\pi\) | |||||||
\(450\) | −819122. | −0.190685 | ||||||||
\(451\) | −3.93315e6 | −0.910541 | ||||||||
\(452\) | −8.73981e6 | −2.01213 | ||||||||
\(453\) | 2.38108e6 | 0.545166 | ||||||||
\(454\) | −1.36626e7 | −3.11095 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.41004e6 | 0.993187 | ||||||||
\(457\) | −664.505 | −0.000148836 0 | −7.44179e−5 | − | 1.00000i | \(-0.500024\pi\) | ||||
−7.44179e−5 | 1.00000i | \(0.500024\pi\) | ||||||||
\(458\) | 1.69466e6 | 0.377501 | ||||||||
\(459\) | −6.68910e6 | −1.48196 | ||||||||
\(460\) | 8.61717e6 | 1.89876 | ||||||||
\(461\) | −381694. | −0.0836495 | −0.0418247 | − | 0.999125i | \(-0.513317\pi\) | ||||
−0.0418247 | + | 0.999125i | \(0.513317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.44698e6 | −0.747284 | −0.373642 | − | 0.927573i | \(-0.621891\pi\) | ||||
−0.373642 | + | 0.927573i | \(0.621891\pi\) | |||||||
\(464\) | −7.43082e6 | −1.60229 | ||||||||
\(465\) | −1.49132e6 | −0.319844 | ||||||||
\(466\) | −1.14395e7 | −2.44029 | ||||||||
\(467\) | −3.77979e6 | −0.802002 | −0.401001 | − | 0.916078i | \(-0.631338\pi\) | ||||
−0.401001 | + | 0.916078i | \(0.631338\pi\) | |||||||
\(468\) | −6.53498e6 | −1.37921 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.91916e6 | −0.609555 | ||||||||
\(471\) | 5.86063e6 | 1.21728 | ||||||||
\(472\) | −1.53746e6 | −0.317651 | ||||||||
\(473\) | 5.16704e6 | 1.06191 | ||||||||
\(474\) | −373813. | −0.0764202 | ||||||||
\(475\) | 578193. | 0.117581 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.71151e6 | 0.545652 | ||||||||
\(478\) | 5.95371e6 | 1.19184 | ||||||||
\(479\) | −3.31921e6 | −0.660992 | −0.330496 | − | 0.943807i | \(-0.607216\pi\) | ||||
−0.330496 | + | 0.943807i | \(0.607216\pi\) | |||||||
\(480\) | 2.24876e6 | 0.445493 | ||||||||
\(481\) | −1.03144e7 | −2.03275 | ||||||||
\(482\) | −1.05207e7 | −2.06267 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.87570e6 | −1.33415 | ||||||||
\(485\) | −4.11318e6 | −0.794005 | ||||||||
\(486\) | 8.65698e6 | 1.66255 | ||||||||
\(487\) | −2.61900e6 | −0.500394 | −0.250197 | − | 0.968195i | \(-0.580495\pi\) | ||||
−0.250197 | + | 0.968195i | \(0.580495\pi\) | |||||||
\(488\) | −9.90509e6 | −1.88282 | ||||||||
\(489\) | 126685. | 0.0239581 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.05614e7 | −1.97706 | −0.988528 | − | 0.151035i | \(-0.951739\pi\) | ||||
−0.988528 | + | 0.151035i | \(0.951739\pi\) | |||||||
\(492\) | 1.20606e7 | 2.24623 | ||||||||
\(493\) | −5.72778e6 | −1.06138 | ||||||||
\(494\) | 6.58634e6 | 1.21430 | ||||||||
\(495\) | 833584. | 0.152910 | ||||||||
\(496\) | −1.20484e7 | −2.19900 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.07241e6 | 0.916517 | ||||||||
\(499\) | −605466. | −0.108852 | −0.0544262 | − | 0.998518i | \(-0.517333\pi\) | ||||
−0.0544262 | + | 0.998518i | \(0.517333\pi\) | |||||||
\(500\) | 1.16869e6 | 0.209062 | ||||||||
\(501\) | 415752. | 0.0740014 | ||||||||
\(502\) | −462670. | −0.0819431 | ||||||||
\(503\) | 511276. | 0.0901023 | 0.0450511 | − | 0.998985i | \(-0.485655\pi\) | ||||
0.0450511 | + | 0.998985i | \(0.485655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 600074. | 0.104707 | ||||||||
\(506\) | −1.25211e7 | −2.17403 | ||||||||
\(507\) | 1.11372e6 | 0.192423 | ||||||||
\(508\) | −1.10608e7 | −1.90164 | ||||||||
\(509\) | 6.53778e6 | 1.11850 | 0.559250 | − | 0.828999i | \(-0.311089\pi\) | ||||
0.559250 | + | 0.828999i | \(0.311089\pi\) | |||||||
\(510\) | 4.67299e6 | 0.795553 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.26427e7 | −2.13140 | ||||||||
\(513\) | −3.68764e6 | −0.618664 | ||||||||
\(514\) | 3.10053e6 | 0.517641 | ||||||||
\(515\) | −2.75846e6 | −0.458299 | ||||||||
\(516\) | −1.58441e7 | −2.61966 | ||||||||
\(517\) | 2.97070e6 | 0.488801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 290316. | 0.0473099 | ||||||||
\(520\) | 7.61726e6 | 1.23535 | ||||||||
\(521\) | −4.28064e6 | −0.690899 | −0.345449 | − | 0.938437i | \(-0.612273\pi\) | ||||
−0.345449 | + | 0.938437i | \(0.612273\pi\) | |||||||
\(522\) | 4.47345e6 | 0.718566 | ||||||||
\(523\) | −5.42616e6 | −0.867438 | −0.433719 | − | 0.901048i | \(-0.642799\pi\) | ||||
−0.433719 | + | 0.901048i | \(0.642799\pi\) | |||||||
\(524\) | −5.50702e6 | −0.876171 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.56095e6 | −0.245993 | ||||||||
\(527\) | −9.28706e6 | −1.45664 | ||||||||
\(528\) | −6.16944e6 | −0.963077 | ||||||||
\(529\) | 1.48004e7 | 2.29950 | ||||||||
\(530\) | −5.52383e6 | −0.854182 | ||||||||
\(531\) | 440868. | 0.0678536 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.03061e7 | 1.57136 | ||||||||
\(534\) | −5.89127e6 | −0.894037 | ||||||||
\(535\) | 2.27011e6 | 0.342896 | ||||||||
\(536\) | 1.98737e7 | 2.98790 | ||||||||
\(537\) | 2.82337e6 | 0.422505 | ||||||||
\(538\) | 1.22303e7 | 1.82172 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.45378e6 | −1.10000 | ||||||||
\(541\) | −6.45696e6 | −0.948495 | −0.474248 | − | 0.880392i | \(-0.657280\pi\) | ||||
−0.474248 | + | 0.880392i | \(0.657280\pi\) | |||||||
\(542\) | −1.48248e7 | −2.16766 | ||||||||
\(543\) | 4.82836e6 | 0.702749 | ||||||||
\(544\) | 1.40040e7 | 2.02887 | ||||||||
\(545\) | 3.53799e6 | 0.510229 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.38834e6 | 0.769993 | 0.384996 | − | 0.922918i | \(-0.374203\pi\) | ||||
0.384996 | + | 0.922918i | \(0.374203\pi\) | |||||||
\(548\) | 2.53242e7 | 3.60233 | ||||||||
\(549\) | 2.84029e6 | 0.402191 | ||||||||
\(550\) | −1.69815e6 | −0.239370 | ||||||||
\(551\) | −3.15767e6 | −0.443086 | ||||||||
\(552\) | 2.19682e7 | 3.06864 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.01537e6 | −0.694270 | ||||||||
\(555\) | −4.03438e6 | −0.555962 | ||||||||
\(556\) | 2.78631e7 | 3.82245 | ||||||||
\(557\) | 1.09891e7 | 1.50080 | 0.750400 | − | 0.660984i | \(-0.229861\pi\) | ||||
0.750400 | + | 0.660984i | \(0.229861\pi\) | |||||||
\(558\) | 7.25329e6 | 0.986164 | ||||||||
\(559\) | −1.35393e7 | −1.83260 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.75549e6 | −0.637952 | ||||||||
\(562\) | 1.14157e6 | 0.152462 | ||||||||
\(563\) | 2.71099e6 | 0.360460 | 0.180230 | − | 0.983625i | \(-0.442316\pi\) | ||||
0.180230 | + | 0.983625i | \(0.442316\pi\) | |||||||
\(564\) | −9.10929e6 | −1.20583 | ||||||||
\(565\) | −2.92120e6 | −0.384982 | ||||||||
\(566\) | 3.35571e6 | 0.440294 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.82288e6 | 0.627243 | ||||||||
\(569\) | 9.28980e6 | 1.20289 | 0.601444 | − | 0.798915i | \(-0.294592\pi\) | ||||
0.601444 | + | 0.798915i | \(0.294592\pi\) | |||||||
\(570\) | 2.57618e6 | 0.332115 | ||||||||
\(571\) | 2.93605e6 | 0.376854 | 0.188427 | − | 0.982087i | \(-0.439661\pi\) | ||||
0.188427 | + | 0.982087i | \(0.439661\pi\) | |||||||
\(572\) | −1.35479e7 | −1.73134 | ||||||||
\(573\) | −1.71947e6 | −0.218781 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.88021e6 | 0.363290 | ||||||||
\(576\) | −2.10233e6 | −0.264024 | ||||||||
\(577\) | −5.47983e6 | −0.685217 | −0.342608 | − | 0.939478i | \(-0.611310\pi\) | ||||
−0.342608 | + | 0.939478i | \(0.611310\pi\) | |||||||
\(578\) | 1.44275e7 | 1.79627 | ||||||||
\(579\) | 3.76170e6 | 0.466324 | ||||||||
\(580\) | −6.38256e6 | −0.787817 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.83265e7 | −2.24271 | ||||||||
\(583\) | 5.62135e6 | 0.684966 | ||||||||
\(584\) | −4.07303e6 | −0.494180 | ||||||||
\(585\) | −2.18426e6 | −0.263884 | ||||||||
\(586\) | 1.34816e7 | 1.62180 | ||||||||
\(587\) | −3.99203e6 | −0.478188 | −0.239094 | − | 0.970996i | \(-0.576850\pi\) | ||||
−0.239094 | + | 0.970996i | \(0.576850\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.11987e6 | −0.608094 | ||||||||
\(590\) | −898125. | −0.106220 | ||||||||
\(591\) | −4.94802e6 | −0.582724 | ||||||||
\(592\) | −3.25938e7 | −3.82236 | ||||||||
\(593\) | −5.63897e6 | −0.658511 | −0.329256 | − | 0.944241i | \(-0.606798\pi\) | ||||
−0.329256 | + | 0.944241i | \(0.606798\pi\) | |||||||
\(594\) | 1.08306e7 | 1.25947 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.16199e7 | −1.33994 | ||||||||
\(597\) | 1.10767e7 | 1.27196 | ||||||||
\(598\) | 3.28091e7 | 3.75182 | ||||||||
\(599\) | 2.96431e6 | 0.337565 | 0.168782 | − | 0.985653i | \(-0.446017\pi\) | ||||
0.168782 | + | 0.985653i | \(0.446017\pi\) | |||||||
\(600\) | 2.97941e6 | 0.337872 | ||||||||
\(601\) | 9.79673e6 | 1.10636 | 0.553178 | − | 0.833063i | \(-0.313415\pi\) | ||||
0.553178 | + | 0.833063i | \(0.313415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.69879e6 | −0.638248 | ||||||||
\(604\) | 1.65231e7 | 1.84289 | ||||||||
\(605\) | −2.29814e6 | −0.255263 | ||||||||
\(606\) | 2.67367e6 | 0.295751 | ||||||||
\(607\) | 9.37747e6 | 1.03303 | 0.516516 | − | 0.856277i | \(-0.327229\pi\) | ||||
0.516516 | + | 0.856277i | \(0.327229\pi\) | |||||||
\(608\) | 7.72027e6 | 0.846980 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.78616e6 | −0.629602 | ||||||||
\(611\) | −7.78417e6 | −0.843547 | ||||||||
\(612\) | −1.59178e7 | −1.71793 | ||||||||
\(613\) | −772746. | −0.0830588 | −0.0415294 | − | 0.999137i | \(-0.513223\pi\) | ||||
−0.0415294 | + | 0.999137i | \(0.513223\pi\) | |||||||
\(614\) | −8.00481e6 | −0.856900 | ||||||||
\(615\) | 4.03112e6 | 0.429772 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.62192e6 | 0.594528 | 0.297264 | − | 0.954795i | \(-0.403926\pi\) | ||||
0.297264 | + | 0.954795i | \(0.403926\pi\) | |||||||
\(618\) | −1.22905e7 | −1.29449 | ||||||||
\(619\) | 7.31530e6 | 0.767371 | 0.383685 | − | 0.923464i | \(-0.374655\pi\) | ||||
0.383685 | + | 0.923464i | \(0.374655\pi\) | |||||||
\(620\) | −1.03487e7 | −1.08120 | ||||||||
\(621\) | −1.83696e7 | −1.91148 | ||||||||
\(622\) | 3.17009e7 | 3.28545 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.61659e7 | 1.66203 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 9.81395e6 | 1.00094 | ||||||||
\(627\) | −2.62166e6 | −0.266322 | ||||||||
\(628\) | 4.06688e7 | 4.11493 | ||||||||
\(629\) | −2.51238e7 | −2.53197 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.13464e6 | 0.113444 | 0.0567222 | − | 0.998390i | \(-0.481935\pi\) | ||||
0.0567222 | + | 0.998390i | \(0.481935\pi\) | |||||||
\(632\) | −1.48422e6 | −0.147810 | ||||||||
\(633\) | −9.20532e6 | −0.913124 | ||||||||
\(634\) | 2.39214e7 | 2.36354 | ||||||||
\(635\) | −3.69697e6 | −0.363841 | ||||||||
\(636\) | −1.72372e7 | −1.68976 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.27409e6 | 0.902028 | ||||||||
\(639\) | −1.38297e6 | −0.133986 | ||||||||
\(640\) | −2.39340e6 | −0.230975 | ||||||||
\(641\) | −1.53233e7 | −1.47301 | −0.736506 | − | 0.676431i | \(-0.763526\pi\) | ||||
−0.736506 | + | 0.676431i | \(0.763526\pi\) | |||||||
\(642\) | 1.01146e7 | 0.968526 | ||||||||
\(643\) | −3.65136e6 | −0.348279 | −0.174139 | − | 0.984721i | \(-0.555714\pi\) | ||||
−0.174139 | + | 0.984721i | \(0.555714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.29575e6 | −0.501220 | ||||||||
\(646\) | 1.60429e7 | 1.51252 | ||||||||
\(647\) | 3.97508e6 | 0.373324 | 0.186662 | − | 0.982424i | \(-0.440233\pi\) | ||||
0.186662 | + | 0.982424i | \(0.440233\pi\) | |||||||
\(648\) | −5.37270e6 | −0.502638 | ||||||||
\(649\) | 913982. | 0.0851777 | ||||||||
\(650\) | 4.44971e6 | 0.413093 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 879105. | 0.0809882 | ||||||||
\(653\) | −6.29637e6 | −0.577840 | −0.288920 | − | 0.957353i | \(-0.593296\pi\) | ||||
−0.288920 | + | 0.957353i | \(0.593296\pi\) | |||||||
\(654\) | 1.57637e7 | 1.44117 | ||||||||
\(655\) | −1.84067e6 | −0.167638 | ||||||||
\(656\) | 3.25675e7 | 2.95478 | ||||||||
\(657\) | 1.16794e6 | 0.105562 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.26507e7 | 1.13476 | 0.567378 | − | 0.823457i | \(-0.307958\pi\) | ||||
0.567378 | + | 0.823457i | \(0.307958\pi\) | |||||||
\(660\) | −5.29912e6 | −0.473526 | ||||||||
\(661\) | −7.73188e6 | −0.688306 | −0.344153 | − | 0.938914i | \(-0.611834\pi\) | ||||
−0.344153 | + | 0.938914i | \(0.611834\pi\) | |||||||
\(662\) | −3.10934e6 | −0.275755 | ||||||||
\(663\) | 1.24609e7 | 1.10094 | ||||||||
\(664\) | 2.01399e7 | 1.77271 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.96219e7 | 1.71418 | ||||||||
\(667\) | −1.57296e7 | −1.36900 | ||||||||
\(668\) | 2.88503e6 | 0.250155 | ||||||||
\(669\) | 2.95560e6 | 0.255318 | ||||||||
\(670\) | 1.16094e7 | 0.999134 | ||||||||
\(671\) | 5.88832e6 | 0.504876 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.97858e7 | −1.68390 | −0.841948 | − | 0.539558i | \(-0.818591\pi\) | ||||
−0.841948 | + | 0.539558i | \(0.818591\pi\) | |||||||
\(674\) | −5.00655e6 | −0.424511 | ||||||||
\(675\) | −2.49135e6 | −0.210463 | ||||||||
\(676\) | 7.72849e6 | 0.650471 | ||||||||
\(677\) | −9.72065e6 | −0.815124 | −0.407562 | − | 0.913178i | \(-0.633621\pi\) | ||||
−0.407562 | + | 0.913178i | \(0.633621\pi\) | |||||||
\(678\) | −1.30156e7 | −1.08740 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.85540e7 | 1.53874 | ||||||||
\(681\) | −1.42501e7 | −1.17747 | ||||||||
\(682\) | 1.50371e7 | 1.23795 | ||||||||
\(683\) | 3.48276e6 | 0.285675 | 0.142837 | − | 0.989746i | \(-0.454377\pi\) | ||||
0.142837 | + | 0.989746i | \(0.454377\pi\) | |||||||
\(684\) | −8.77534e6 | −0.717173 | ||||||||
\(685\) | 8.46437e6 | 0.689236 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.76753e6 | 0.142881 | ||||||||
\(688\) | −4.27844e7 | −3.44600 | ||||||||
\(689\) | −1.47297e7 | −1.18208 | ||||||||
\(690\) | 1.28329e7 | 1.02613 | ||||||||
\(691\) | 5.55426e6 | 0.442518 | 0.221259 | − | 0.975215i | \(-0.428983\pi\) | ||||
0.221259 | + | 0.975215i | \(0.428983\pi\) | |||||||
\(692\) | 2.01459e6 | 0.159927 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.12719e7 | 2.46465 | ||||||||
\(695\) | 9.31296e6 | 0.731351 | ||||||||
\(696\) | −1.62714e7 | −1.27321 | ||||||||
\(697\) | 2.51035e7 | 1.95728 | ||||||||
\(698\) | −2.56496e7 | −1.99270 | ||||||||
\(699\) | −1.19314e7 | −0.923632 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.82510e6 | −0.524583 | −0.262291 | − | 0.964989i | \(-0.584478\pi\) | ||||
−0.262291 | + | 0.964989i | \(0.584478\pi\) | |||||||
\(702\) | −2.83796e7 | −2.17352 | ||||||||
\(703\) | −1.38505e7 | −1.05701 | ||||||||
\(704\) | −4.35842e6 | −0.331434 | ||||||||
\(705\) | −3.04469e6 | −0.230712 | ||||||||
\(706\) | 3.89711e7 | 2.94259 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.80262e6 | −0.210126 | ||||||||
\(709\) | −7.64382e6 | −0.571077 | −0.285539 | − | 0.958367i | \(-0.592172\pi\) | ||||
−0.285539 | + | 0.958367i | \(0.592172\pi\) | |||||||
\(710\) | 2.81734e6 | 0.209746 | ||||||||
\(711\) | 425600. | 0.0315739 | ||||||||
\(712\) | −2.33912e7 | −1.72923 | ||||||||
\(713\) | −2.55041e7 | −1.87882 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.52827e6 | −0.331258 | ||||||||
\(716\) | 1.95922e7 | 1.42824 | ||||||||
\(717\) | 6.20974e6 | 0.451103 | ||||||||
\(718\) | 2.05680e6 | 0.148896 | ||||||||
\(719\) | −1.15186e7 | −0.830954 | −0.415477 | − | 0.909604i | \(-0.636385\pi\) | ||||
−0.415477 | + | 0.909604i | \(0.636385\pi\) | |||||||
\(720\) | −6.90228e6 | −0.496206 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.67443e7 | −1.19543 | ||||||||
\(723\) | −1.09732e7 | −0.780705 | ||||||||
\(724\) | 3.35055e7 | 2.37558 | ||||||||
\(725\) | −2.13331e6 | −0.150733 | ||||||||
\(726\) | −1.02395e7 | −0.721004 | ||||||||
\(727\) | −2.26458e7 | −1.58910 | −0.794550 | − | 0.607199i | \(-0.792293\pi\) | ||||
−0.794550 | + | 0.607199i | \(0.792293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.19812e7 | 0.834993 | ||||||||
\(730\) | −2.37930e6 | −0.165251 | ||||||||
\(731\) | −3.29788e7 | −2.28266 | ||||||||
\(732\) | −1.80558e7 | −1.24549 | ||||||||
\(733\) | −1.46343e7 | −1.00603 | −0.503015 | − | 0.864278i | \(-0.667776\pi\) | ||||
−0.503015 | + | 0.864278i | \(0.667776\pi\) | |||||||
\(734\) | 2.77094e7 | 1.89839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.84577e7 | 2.61691 | ||||||||
\(737\) | −1.18144e7 | −0.801203 | ||||||||
\(738\) | −1.96061e7 | −1.32510 | ||||||||
\(739\) | −1.76251e7 | −1.18719 | −0.593596 | − | 0.804763i | \(-0.702292\pi\) | ||||
−0.593596 | + | 0.804763i | \(0.702292\pi\) | |||||||
\(740\) | −2.79959e7 | −1.87938 | ||||||||
\(741\) | 6.86958e6 | 0.459605 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.03747e7 | 1.35400 | 0.677002 | − | 0.735981i | \(-0.263279\pi\) | ||||
0.677002 | + | 0.735981i | \(0.263279\pi\) | |||||||
\(744\) | −2.63825e7 | −1.74737 | ||||||||
\(745\) | −3.88383e6 | −0.256371 | ||||||||
\(746\) | −5.68572e6 | −0.374057 | ||||||||
\(747\) | −5.77513e6 | −0.378669 | ||||||||
\(748\) | −3.29998e7 | −2.15654 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.74045e6 | 0.112982 | ||||||||
\(751\) | 1.21784e7 | 0.787935 | 0.393967 | − | 0.919124i | \(-0.371102\pi\) | ||||
0.393967 | + | 0.919124i | \(0.371102\pi\) | |||||||
\(752\) | −2.45981e7 | −1.58620 | ||||||||
\(753\) | −482567. | −0.0310149 | ||||||||
\(754\) | −2.43011e7 | −1.55667 | ||||||||
\(755\) | 5.52269e6 | 0.352601 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.83013e6 | 0.623476 | 0.311738 | − | 0.950168i | \(-0.399089\pi\) | ||||
0.311738 | + | 0.950168i | \(0.399089\pi\) | |||||||
\(758\) | 9.71001e6 | 0.613828 | ||||||||
\(759\) | −1.30595e7 | −0.822853 | ||||||||
\(760\) | 1.02287e7 | 0.642369 | ||||||||
\(761\) | 1.49014e7 | 0.932749 | 0.466375 | − | 0.884587i | \(-0.345560\pi\) | ||||
0.466375 | + | 0.884587i | \(0.345560\pi\) | |||||||
\(762\) | −1.64721e7 | −1.02769 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.19320e7 | −0.739570 | ||||||||
\(765\) | −5.32038e6 | −0.328692 | ||||||||
\(766\) | −4.63193e7 | −2.85226 | ||||||||
\(767\) | −2.39492e6 | −0.146995 | ||||||||
\(768\) | −1.63817e7 | −1.00220 | ||||||||
\(769\) | 3.08958e7 | 1.88401 | 0.942004 | − | 0.335600i | \(-0.108939\pi\) | ||||
0.942004 | + | 0.335600i | \(0.108939\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.23387e6 | 0.195923 | ||||||||
\(772\) | 2.61036e7 | 1.57637 | ||||||||
\(773\) | 3.80951e6 | 0.229308 | 0.114654 | − | 0.993405i | \(-0.463424\pi\) | ||||
0.114654 | + | 0.993405i | \(0.463424\pi\) | |||||||
\(774\) | 2.57568e7 | 1.54540 | ||||||||
\(775\) | −3.45896e6 | −0.206867 | ||||||||
\(776\) | −7.27652e7 | −4.33780 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.39365e7 | −3.19473 | ||||||||
\(779\) | 1.38393e7 | 0.817092 | ||||||||
\(780\) | 1.38854e7 | 0.817187 | ||||||||
\(781\) | −2.86708e6 | −0.168195 | ||||||||
\(782\) | 7.99160e7 | 4.67323 | ||||||||
\(783\) | 1.36060e7 | 0.793095 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.35932e7 | 0.787311 | ||||||||
\(786\) | −8.20123e6 | −0.473503 | ||||||||
\(787\) | 3.11509e7 | 1.79281 | 0.896405 | − | 0.443237i | \(-0.146170\pi\) | ||||
0.896405 | + | 0.443237i | \(0.146170\pi\) | |||||||
\(788\) | −3.43359e7 | −1.96985 | ||||||||
\(789\) | −1.62807e6 | −0.0931068 | ||||||||
\(790\) | −867021. | −0.0494268 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.47467e7 | 0.835377 | ||||||||
\(793\) | −1.54293e7 | −0.871289 | ||||||||
\(794\) | 1.10436e7 | 0.621667 | ||||||||
\(795\) | −5.76137e6 | −0.323302 | ||||||||
\(796\) | 7.68644e7 | 4.29975 | ||||||||
\(797\) | −1.85777e7 | −1.03597 | −0.517983 | − | 0.855391i | \(-0.673317\pi\) | ||||
−0.517983 | + | 0.855391i | \(0.673317\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.89606e7 | −1.05071 | ||||||||
\(800\) | 5.21578e6 | 0.288134 | ||||||||
\(801\) | 6.70743e6 | 0.369381 | ||||||||
\(802\) | 4.80481e6 | 0.263779 | ||||||||
\(803\) | 2.42131e6 | 0.132514 | ||||||||
\(804\) | 3.62274e7 | 1.97650 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.94019e7 | −2.13639 | ||||||||
\(807\) | 1.27563e7 | 0.689508 | ||||||||
\(808\) | 1.06158e7 | 0.572035 | ||||||||
\(809\) | −7.53243e6 | −0.404635 | −0.202318 | − | 0.979320i | \(-0.564847\pi\) | ||||
−0.202318 | + | 0.979320i | \(0.564847\pi\) | |||||||
\(810\) | −3.13852e6 | −0.168079 | ||||||||
\(811\) | 9.91517e6 | 0.529356 | 0.264678 | − | 0.964337i | \(-0.414734\pi\) | ||||
0.264678 | + | 0.964337i | \(0.414734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.54623e7 | −0.820442 | ||||||||
\(814\) | 4.06790e7 | 2.15184 | ||||||||
\(815\) | 293833. | 0.0154955 | ||||||||
\(816\) | 3.93767e7 | 2.07021 | ||||||||
\(817\) | −1.81809e7 | −0.952930 | ||||||||
\(818\) | 4.61472e7 | 2.41136 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.79732e7 | 1.45281 | ||||||||
\(821\) | −1.33726e7 | −0.692402 | −0.346201 | − | 0.938160i | \(-0.612528\pi\) | ||||
−0.346201 | + | 0.938160i | \(0.612528\pi\) | |||||||
\(822\) | 3.77135e7 | 1.94678 | ||||||||
\(823\) | 225760. | 0.0116184 | 0.00580921 | − | 0.999983i | \(-0.498151\pi\) | ||||
0.00580921 | + | 0.999983i | \(0.498151\pi\) | |||||||
\(824\) | −4.87993e7 | −2.50377 | ||||||||
\(825\) | −1.77118e6 | −0.0906000 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.75070e7 | 1.90699 | 0.953495 | − | 0.301409i | \(-0.0974570\pi\) | ||||
0.953495 | + | 0.301409i | \(0.0974570\pi\) | |||||||
\(828\) | −4.37134e7 | −2.21584 | ||||||||
\(829\) | 2.38271e6 | 0.120416 | 0.0602082 | − | 0.998186i | \(-0.480824\pi\) | ||||
0.0602082 | + | 0.998186i | \(0.480824\pi\) | |||||||
\(830\) | 1.17649e7 | 0.592781 | ||||||||
\(831\) | −5.23105e6 | −0.262776 | ||||||||
\(832\) | 1.14204e7 | 0.571972 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.14945e7 | 2.06574 | ||||||||
\(835\) | 964296. | 0.0478624 | ||||||||
\(836\) | −1.81925e7 | −0.900278 | ||||||||
\(837\) | 2.20608e7 | 1.08845 | ||||||||
\(838\) | 6.46320e7 | 3.17934 | ||||||||
\(839\) | −1.72260e7 | −0.844848 | −0.422424 | − | 0.906398i | \(-0.638821\pi\) | ||||
−0.422424 | + | 0.906398i | \(0.638821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.86055e6 | −0.431987 | ||||||||
\(842\) | 5.18462e7 | 2.52021 | ||||||||
\(843\) | 1.19066e6 | 0.0577059 | ||||||||
\(844\) | −6.38786e7 | −3.08674 | ||||||||
\(845\) | 2.58317e6 | 0.124455 | ||||||||
\(846\) | 1.48084e7 | 0.711348 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.65462e7 | −2.22277 | ||||||||
\(849\) | 3.50001e6 | 0.166648 | ||||||||
\(850\) | 1.08385e7 | 0.514545 | ||||||||
\(851\) | −6.89948e7 | −3.26582 | ||||||||
\(852\) | 8.79156e6 | 0.414923 | ||||||||
\(853\) | 7.69238e6 | 0.361983 | 0.180992 | − | 0.983485i | \(-0.442069\pi\) | ||||
0.180992 | + | 0.983485i | \(0.442069\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.93307e6 | −0.137217 | ||||||||
\(856\) | 4.01599e7 | 1.87330 | ||||||||
\(857\) | −3.27783e7 | −1.52452 | −0.762262 | − | 0.647269i | \(-0.775911\pi\) | ||||
−0.762262 | + | 0.647269i | \(0.775911\pi\) | |||||||
\(858\) | −2.01760e7 | −0.935656 | ||||||||
\(859\) | 1.42531e7 | 0.659062 | 0.329531 | − | 0.944145i | \(-0.393109\pi\) | ||||
0.329531 | + | 0.944145i | \(0.393109\pi\) | |||||||
\(860\) | −3.67489e7 | −1.69433 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.67900e7 | −2.14479 | ||||||||
\(863\) | −5.53788e6 | −0.253114 | −0.126557 | − | 0.991959i | \(-0.540393\pi\) | ||||
−0.126557 | + | 0.991959i | \(0.540393\pi\) | |||||||
\(864\) | −3.32656e7 | −1.51604 | ||||||||
\(865\) | 673359. | 0.0305989 | ||||||||
\(866\) | −1.95275e7 | −0.884814 | ||||||||
\(867\) | 1.50479e7 | 0.679875 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 882329. | 0.0396352 | ||||||||
\(870\) | −9.50510e6 | −0.425754 | ||||||||
\(871\) | 3.09575e7 | 1.38267 | ||||||||
\(872\) | 6.25896e7 | 2.78748 | ||||||||
\(873\) | 2.08655e7 | 0.926600 | ||||||||
\(874\) | 4.40570e7 | 1.95090 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.42466e6 | −0.326901 | ||||||||
\(877\) | 1.95012e7 | 0.856173 | 0.428086 | − | 0.903738i | \(-0.359188\pi\) | ||||
0.428086 | + | 0.903738i | \(0.359188\pi\) | |||||||
\(878\) | 5.49038e7 | 2.40362 | ||||||||
\(879\) | 1.40614e7 | 0.613841 | ||||||||
\(880\) | −1.43094e7 | −0.622895 | ||||||||
\(881\) | 609895. | 0.0264737 | 0.0132369 | − | 0.999912i | \(-0.495786\pi\) | ||||
0.0132369 | + | 0.999912i | \(0.495786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.55781e7 | 1.10399 | 0.551996 | − | 0.833847i | \(-0.313866\pi\) | ||||
0.551996 | + | 0.833847i | \(0.313866\pi\) | |||||||
\(884\) | 8.64701e7 | 3.72165 | ||||||||
\(885\) | −936748. | −0.0402036 | ||||||||
\(886\) | 3.49150e7 | 1.49427 | ||||||||
\(887\) | 3.29071e7 | 1.40436 | 0.702182 | − | 0.711997i | \(-0.252209\pi\) | ||||
0.702182 | + | 0.711997i | \(0.252209\pi\) | |||||||
\(888\) | −7.13712e7 | −3.03732 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.36642e7 | −0.578242 | ||||||||
\(891\) | 3.19393e6 | 0.134782 | ||||||||
\(892\) | 2.05099e7 | 0.863079 | ||||||||
\(893\) | −1.04528e7 | −0.438635 | ||||||||
\(894\) | −1.73046e7 | −0.724133 | ||||||||
\(895\) | 6.54852e6 | 0.273266 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.42201e7 | 1.42004 | ||||||||
\(898\) | −1.36727e7 | −0.565802 | ||||||||
\(899\) | 1.88904e7 | 0.779545 | ||||||||
\(900\) | −5.92859e6 | −0.243975 | ||||||||
\(901\) | −3.58784e7 | −1.47239 | ||||||||
\(902\) | −4.06461e7 | −1.66342 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.16782e7 | −2.10323 | ||||||||
\(905\) | 1.11989e7 | 0.454521 | ||||||||
\(906\) | 2.46067e7 | 0.995938 | ||||||||
\(907\) | 2.76339e7 | 1.11538 | 0.557692 | − | 0.830048i | \(-0.311687\pi\) | ||||
0.557692 | + | 0.830048i | \(0.311687\pi\) | |||||||
\(908\) | −9.88860e7 | −3.98034 | ||||||||
\(909\) | −3.04407e6 | −0.122193 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.20633e7 | −0.880796 | −0.440398 | − | 0.897803i | \(-0.645163\pi\) | ||||
−0.440398 | + | 0.897803i | \(0.645163\pi\) | |||||||
\(912\) | 2.17080e7 | 0.864236 | ||||||||
\(913\) | −1.19727e7 | −0.475350 | ||||||||
\(914\) | −6867.15 | −0.000271901 0 | ||||||||
\(915\) | −6.03499e6 | −0.238300 | ||||||||
\(916\) | 1.22655e7 | 0.482998 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.91267e7 | −2.70732 | ||||||||
\(919\) | 5.70536e6 | 0.222841 | 0.111420 | − | 0.993773i | \(-0.464460\pi\) | ||||
0.111420 | + | 0.993773i | \(0.464460\pi\) | |||||||
\(920\) | 5.09530e7 | 1.98472 | ||||||||
\(921\) | −8.34905e6 | −0.324331 | ||||||||
\(922\) | −3.94452e6 | −0.152815 | ||||||||
\(923\) | 7.51266e6 | 0.290262 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.35735e6 | −0.359583 | ||||||||
\(926\) | −3.56219e7 | −1.36518 | ||||||||
\(927\) | 1.39932e7 | 0.534833 | ||||||||
\(928\) | −2.84848e7 | −1.08578 | ||||||||
\(929\) | −2.49645e7 | −0.949038 | −0.474519 | − | 0.880245i | \(-0.657378\pi\) | ||||
−0.474519 | + | 0.880245i | \(0.657378\pi\) | |||||||
\(930\) | −1.54116e7 | −0.584307 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.27959e7 | −3.12226 | ||||||||
\(933\) | 3.30641e7 | 1.24352 | ||||||||
\(934\) | −3.90612e7 | −1.46514 | ||||||||
\(935\) | −1.10299e7 | −0.412612 | ||||||||
\(936\) | −3.86411e7 | −1.44165 | ||||||||
\(937\) | −3.62569e7 | −1.34909 | −0.674546 | − | 0.738233i | \(-0.735661\pi\) | ||||
−0.674546 | + | 0.738233i | \(0.735661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.02360e7 | 0.378849 | ||||||||
\(940\) | −2.11281e7 | −0.779903 | ||||||||
\(941\) | −2.08967e7 | −0.769314 | −0.384657 | − | 0.923060i | \(-0.625680\pi\) | ||||
−0.384657 | + | 0.923060i | \(0.625680\pi\) | |||||||
\(942\) | 6.05652e7 | 2.22380 | ||||||||
\(943\) | 6.89391e7 | 2.52456 | ||||||||
\(944\) | −7.56800e6 | −0.276408 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.33975e7 | 1.93996 | ||||||||
\(947\) | 5.27033e7 | 1.90969 | 0.954845 | − | 0.297104i | \(-0.0960209\pi\) | ||||
0.954845 | + | 0.297104i | \(0.0960209\pi\) | |||||||
\(948\) | −2.70556e6 | −0.0977768 | ||||||||
\(949\) | −6.34461e6 | −0.228686 | ||||||||
\(950\) | 5.97518e6 | 0.214804 | ||||||||
\(951\) | 2.49501e7 | 0.894584 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.95159e7 | −0.696077 | −0.348039 | − | 0.937480i | \(-0.613152\pi\) | ||||
−0.348039 | + | 0.937480i | \(0.613152\pi\) | |||||||
\(954\) | 2.80214e7 | 0.996826 | ||||||||
\(955\) | −3.98815e6 | −0.141502 | ||||||||
\(956\) | 4.30913e7 | 1.52491 | ||||||||
\(957\) | 9.67292e6 | 0.341411 | ||||||||
\(958\) | −3.43015e7 | −1.20753 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.46698e6 | 0.156436 | ||||||||
\(961\) | 1.99980e6 | 0.0698519 | ||||||||
\(962\) | −1.06592e8 | −3.71353 | ||||||||
\(963\) | −1.15159e7 | −0.400157 | ||||||||
\(964\) | −7.61463e7 | −2.63910 | ||||||||
\(965\) | 8.72488e6 | 0.301607 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.66033e7 | 1.60269 | 0.801347 | − | 0.598200i | \(-0.204117\pi\) | ||||
0.801347 | + | 0.598200i | \(0.204117\pi\) | |||||||
\(968\) | −4.06558e7 | −1.39455 | ||||||||
\(969\) | 1.67328e7 | 0.572479 | ||||||||
\(970\) | −4.25066e7 | −1.45053 | ||||||||
\(971\) | 9.65070e6 | 0.328481 | 0.164241 | − | 0.986420i | \(-0.447483\pi\) | ||||
0.164241 | + | 0.986420i | \(0.447483\pi\) | |||||||
\(972\) | 6.26569e7 | 2.12718 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.70653e7 | −0.914146 | ||||||||
\(975\) | 4.64106e6 | 0.156353 | ||||||||
\(976\) | −4.87568e7 | −1.63836 | ||||||||
\(977\) | −1.00843e7 | −0.337994 | −0.168997 | − | 0.985617i | \(-0.554053\pi\) | ||||
−0.168997 | + | 0.985617i | \(0.554053\pi\) | |||||||
\(978\) | 1.30919e6 | 0.0437679 | ||||||||
\(979\) | 1.39054e7 | 0.463691 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.79476e7 | −0.595435 | ||||||||
\(982\) | −1.09144e8 | −3.61179 | ||||||||
\(983\) | 1.49185e7 | 0.492427 | 0.246213 | − | 0.969216i | \(-0.420814\pi\) | ||||
0.246213 | + | 0.969216i | \(0.420814\pi\) | |||||||
\(984\) | 7.13136e7 | 2.34793 | ||||||||
\(985\) | −1.14764e7 | −0.376892 | ||||||||
\(986\) | −5.91922e7 | −1.93898 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.76702e7 | 1.55365 | ||||||||
\(989\) | −9.05663e7 | −2.94426 | ||||||||
\(990\) | 8.61445e6 | 0.279344 | ||||||||
\(991\) | −1.33955e7 | −0.433285 | −0.216642 | − | 0.976251i | \(-0.569511\pi\) | ||||
−0.216642 | + | 0.976251i | \(0.569511\pi\) | |||||||
\(992\) | −4.61855e7 | −1.49014 | ||||||||
\(993\) | −3.24305e6 | −0.104371 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.56912e7 | 0.822672 | ||||||||
\(996\) | 3.67127e7 | 1.17265 | ||||||||
\(997\) | 3.28464e7 | 1.04653 | 0.523263 | − | 0.852171i | \(-0.324715\pi\) | ||||
0.523263 | + | 0.852171i | \(0.324715\pi\) | |||||||
\(998\) | −6.25703e6 | −0.198857 | ||||||||
\(999\) | 5.96800e7 | 1.89197 |
(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 | 245.6.a.m.1.10 | yes | 10 | |
7.6 | odd | 2 | 245.6.a.l.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.6.a.l.1.10 | ✓ | 10 | 7.6 | odd | 2 | ||
245.6.a.m.1.10 | yes | 10 | 1.1 | even | 1 | trivial |