Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, 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("230.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(36.8882785570\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.48374\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −2.48374 | −0.159332 | −0.0796659 | − | 0.996822i | \(-0.525385\pi\) | ||||
−0.0796659 | + | 0.996822i | \(0.525385\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 9.93494 | 0.112665 | ||||||||
\(7\) | −252.275 | −1.94594 | −0.972968 | − | 0.230940i | \(-0.925820\pi\) | ||||
−0.972968 | + | 0.230940i | \(0.925820\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −236.831 | −0.974613 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | −739.487 | −1.84268 | −0.921338 | − | 0.388763i | \(-0.872902\pi\) | ||||
−0.921338 | + | 0.388763i | \(0.872902\pi\) | |||||||
\(12\) | −39.7398 | −0.0796659 | ||||||||
\(13\) | 876.961 | 1.43920 | 0.719601 | − | 0.694387i | \(-0.244325\pi\) | ||||
0.719601 | + | 0.694387i | \(0.244325\pi\) | |||||||
\(14\) | 1009.10 | 1.37598 | ||||||||
\(15\) | −62.0934 | −0.0712553 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1363.74 | −1.14449 | −0.572243 | − | 0.820084i | \(-0.693926\pi\) | ||||
−0.572243 | + | 0.820084i | \(0.693926\pi\) | |||||||
\(18\) | 947.324 | 0.689156 | ||||||||
\(19\) | 1725.29 | 1.09642 | 0.548211 | − | 0.836340i | \(-0.315309\pi\) | ||||
0.548211 | + | 0.836340i | \(0.315309\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | 626.584 | 0.310049 | ||||||||
\(22\) | 2957.95 | 1.30297 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 158.959 | 0.0563323 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −3507.84 | −1.01767 | ||||||||
\(27\) | 1191.77 | 0.314619 | ||||||||
\(28\) | −4036.39 | −0.972968 | ||||||||
\(29\) | 3068.97 | 0.677638 | 0.338819 | − | 0.940852i | \(-0.389973\pi\) | ||||
0.338819 | + | 0.940852i | \(0.389973\pi\) | |||||||
\(30\) | 248.374 | 0.0503851 | ||||||||
\(31\) | −8425.04 | −1.57459 | −0.787295 | − | 0.616576i | \(-0.788519\pi\) | ||||
−0.787295 | + | 0.616576i | \(0.788519\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 1836.69 | 0.293597 | ||||||||
\(34\) | 5454.97 | 0.809273 | ||||||||
\(35\) | −6306.87 | −0.870249 | ||||||||
\(36\) | −3789.30 | −0.487307 | ||||||||
\(37\) | −4041.30 | −0.485308 | −0.242654 | − | 0.970113i | \(-0.578018\pi\) | ||||
−0.242654 | + | 0.970113i | \(0.578018\pi\) | |||||||
\(38\) | −6901.15 | −0.775287 | ||||||||
\(39\) | −2178.14 | −0.229311 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −1633.86 | −0.151794 | −0.0758971 | − | 0.997116i | \(-0.524182\pi\) | ||||
−0.0758971 | + | 0.997116i | \(0.524182\pi\) | |||||||
\(42\) | −2506.33 | −0.219238 | ||||||||
\(43\) | 8735.57 | 0.720477 | 0.360238 | − | 0.932860i | \(-0.382695\pi\) | ||||
0.360238 | + | 0.932860i | \(0.382695\pi\) | |||||||
\(44\) | −11831.8 | −0.921338 | ||||||||
\(45\) | −5920.78 | −0.435860 | ||||||||
\(46\) | 2116.00 | 0.147442 | ||||||||
\(47\) | 18989.0 | 1.25388 | 0.626942 | − | 0.779066i | \(-0.284306\pi\) | ||||
0.626942 | + | 0.779066i | \(0.284306\pi\) | |||||||
\(48\) | −635.836 | −0.0398329 | ||||||||
\(49\) | 46835.5 | 2.78667 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 3387.18 | 0.182353 | ||||||||
\(52\) | 14031.4 | 0.719601 | ||||||||
\(53\) | 18955.0 | 0.926903 | 0.463452 | − | 0.886122i | \(-0.346611\pi\) | ||||
0.463452 | + | 0.886122i | \(0.346611\pi\) | |||||||
\(54\) | −4767.09 | −0.222469 | ||||||||
\(55\) | −18487.2 | −0.824069 | ||||||||
\(56\) | 16145.6 | 0.687992 | ||||||||
\(57\) | −4285.16 | −0.174695 | ||||||||
\(58\) | −12275.9 | −0.479162 | ||||||||
\(59\) | −49726.2 | −1.85975 | −0.929876 | − | 0.367873i | \(-0.880086\pi\) | ||||
−0.929876 | + | 0.367873i | \(0.880086\pi\) | |||||||
\(60\) | −993.494 | −0.0356277 | ||||||||
\(61\) | 19031.8 | 0.654871 | 0.327436 | − | 0.944873i | \(-0.393816\pi\) | ||||
0.327436 | + | 0.944873i | \(0.393816\pi\) | |||||||
\(62\) | 33700.1 | 1.11340 | ||||||||
\(63\) | 59746.5 | 1.89654 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 21924.0 | 0.643631 | ||||||||
\(66\) | −7346.76 | −0.207604 | ||||||||
\(67\) | −9397.24 | −0.255749 | −0.127874 | − | 0.991790i | \(-0.540815\pi\) | ||||
−0.127874 | + | 0.991790i | \(0.540815\pi\) | |||||||
\(68\) | −21819.9 | −0.572243 | ||||||||
\(69\) | 1313.90 | 0.0332230 | ||||||||
\(70\) | 25227.5 | 0.615359 | ||||||||
\(71\) | −28928.8 | −0.681058 | −0.340529 | − | 0.940234i | \(-0.610606\pi\) | ||||
−0.340529 | + | 0.940234i | \(0.610606\pi\) | |||||||
\(72\) | 15157.2 | 0.344578 | ||||||||
\(73\) | 2535.03 | 0.0556770 | 0.0278385 | − | 0.999612i | \(-0.491138\pi\) | ||||
0.0278385 | + | 0.999612i | \(0.491138\pi\) | |||||||
\(74\) | 16165.2 | 0.343164 | ||||||||
\(75\) | −1552.33 | −0.0318663 | ||||||||
\(76\) | 27604.6 | 0.548211 | ||||||||
\(77\) | 186554. | 3.58573 | ||||||||
\(78\) | 8712.56 | 0.162147 | ||||||||
\(79\) | −17637.4 | −0.317956 | −0.158978 | − | 0.987282i | \(-0.550820\pi\) | ||||
−0.158978 | + | 0.987282i | \(0.550820\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 54589.9 | 0.924485 | ||||||||
\(82\) | 6535.44 | 0.107335 | ||||||||
\(83\) | 87609.8 | 1.39591 | 0.697955 | − | 0.716142i | \(-0.254094\pi\) | ||||
0.697955 | + | 0.716142i | \(0.254094\pi\) | |||||||
\(84\) | 10025.3 | 0.155025 | ||||||||
\(85\) | −34093.6 | −0.511829 | ||||||||
\(86\) | −34942.3 | −0.509454 | ||||||||
\(87\) | −7622.51 | −0.107969 | ||||||||
\(88\) | 47327.2 | 0.651484 | ||||||||
\(89\) | 33219.0 | 0.444541 | 0.222270 | − | 0.974985i | \(-0.428653\pi\) | ||||
0.222270 | + | 0.974985i | \(0.428653\pi\) | |||||||
\(90\) | 23683.1 | 0.308200 | ||||||||
\(91\) | −221235. | −2.80060 | ||||||||
\(92\) | −8464.00 | −0.104257 | ||||||||
\(93\) | 20925.6 | 0.250882 | ||||||||
\(94\) | −75956.0 | −0.886630 | ||||||||
\(95\) | 43132.2 | 0.490334 | ||||||||
\(96\) | 2543.35 | 0.0281661 | ||||||||
\(97\) | 41331.2 | 0.446014 | 0.223007 | − | 0.974817i | \(-0.428413\pi\) | ||||
0.223007 | + | 0.974817i | \(0.428413\pi\) | |||||||
\(98\) | −187342. | −1.97047 | ||||||||
\(99\) | 175133. | 1.79590 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −51868.0 | −0.505936 | −0.252968 | − | 0.967475i | \(-0.581407\pi\) | ||||
−0.252968 | + | 0.967475i | \(0.581407\pi\) | |||||||
\(102\) | −13548.7 | −0.128943 | ||||||||
\(103\) | 54330.3 | 0.504602 | 0.252301 | − | 0.967649i | \(-0.418813\pi\) | ||||
0.252301 | + | 0.967649i | \(0.418813\pi\) | |||||||
\(104\) | −56125.5 | −0.508835 | ||||||||
\(105\) | 15664.6 | 0.138658 | ||||||||
\(106\) | −75820.1 | −0.655420 | ||||||||
\(107\) | −106154. | −0.896353 | −0.448176 | − | 0.893945i | \(-0.647926\pi\) | ||||
−0.448176 | + | 0.893945i | \(0.647926\pi\) | |||||||
\(108\) | 19068.4 | 0.157309 | ||||||||
\(109\) | −173904. | −1.40198 | −0.700992 | − | 0.713169i | \(-0.747259\pi\) | ||||
−0.700992 | + | 0.713169i | \(0.747259\pi\) | |||||||
\(110\) | 73948.7 | 0.582705 | ||||||||
\(111\) | 10037.5 | 0.0773249 | ||||||||
\(112\) | −64582.3 | −0.486484 | ||||||||
\(113\) | 262107. | 1.93100 | 0.965501 | − | 0.260399i | \(-0.0838541\pi\) | ||||
0.965501 | + | 0.260399i | \(0.0838541\pi\) | |||||||
\(114\) | 17140.6 | 0.123528 | ||||||||
\(115\) | −13225.0 | −0.0932505 | ||||||||
\(116\) | 49103.5 | 0.338819 | ||||||||
\(117\) | −207692. | −1.40267 | ||||||||
\(118\) | 198905. | 1.31504 | ||||||||
\(119\) | 344038. | 2.22710 | ||||||||
\(120\) | 3973.98 | 0.0251926 | ||||||||
\(121\) | 385790. | 2.39545 | ||||||||
\(122\) | −76127.3 | −0.463064 | ||||||||
\(123\) | 4058.08 | 0.0241856 | ||||||||
\(124\) | −134801. | −0.787295 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −238986. | −1.34105 | ||||||||
\(127\) | 227525. | 1.25176 | 0.625878 | − | 0.779921i | \(-0.284741\pi\) | ||||
0.625878 | + | 0.779921i | \(0.284741\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −21696.8 | −0.114795 | ||||||||
\(130\) | −87696.1 | −0.455116 | ||||||||
\(131\) | 205957. | 1.04857 | 0.524286 | − | 0.851542i | \(-0.324332\pi\) | ||||
0.524286 | + | 0.851542i | \(0.324332\pi\) | |||||||
\(132\) | 29387.0 | 0.146798 | ||||||||
\(133\) | −435246. | −2.13357 | ||||||||
\(134\) | 37589.0 | 0.180842 | ||||||||
\(135\) | 29794.3 | 0.140702 | ||||||||
\(136\) | 87279.6 | 0.404637 | ||||||||
\(137\) | −320648. | −1.45958 | −0.729788 | − | 0.683673i | \(-0.760381\pi\) | ||||
−0.729788 | + | 0.683673i | \(0.760381\pi\) | |||||||
\(138\) | −5255.58 | −0.0234922 | ||||||||
\(139\) | 194736. | 0.854887 | 0.427444 | − | 0.904042i | \(-0.359414\pi\) | ||||
0.427444 | + | 0.904042i | \(0.359414\pi\) | |||||||
\(140\) | −100910. | −0.435125 | ||||||||
\(141\) | −47163.7 | −0.199784 | ||||||||
\(142\) | 115715. | 0.481581 | ||||||||
\(143\) | −648501. | −2.65198 | ||||||||
\(144\) | −60628.8 | −0.243653 | ||||||||
\(145\) | 76724.2 | 0.303049 | ||||||||
\(146\) | −10140.1 | −0.0393696 | ||||||||
\(147\) | −116327. | −0.444004 | ||||||||
\(148\) | −64660.8 | −0.242654 | ||||||||
\(149\) | −393030. | −1.45031 | −0.725155 | − | 0.688586i | \(-0.758232\pi\) | ||||
−0.725155 | + | 0.688586i | \(0.758232\pi\) | |||||||
\(150\) | 6209.34 | 0.0225329 | ||||||||
\(151\) | −5358.24 | −0.0191240 | −0.00956202 | − | 0.999954i | \(-0.503044\pi\) | ||||
−0.00956202 | + | 0.999954i | \(0.503044\pi\) | |||||||
\(152\) | −110418. | −0.387643 | ||||||||
\(153\) | 322977. | 1.11543 | ||||||||
\(154\) | −746215. | −2.53549 | ||||||||
\(155\) | −210626. | −0.704178 | ||||||||
\(156\) | −34850.2 | −0.114655 | ||||||||
\(157\) | 290851. | 0.941721 | 0.470860 | − | 0.882208i | \(-0.343944\pi\) | ||||
0.470860 | + | 0.882208i | \(0.343944\pi\) | |||||||
\(158\) | 70549.7 | 0.224829 | ||||||||
\(159\) | −47079.3 | −0.147685 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | 133453. | 0.405756 | ||||||||
\(162\) | −218360. | −0.653709 | ||||||||
\(163\) | −163365. | −0.481604 | −0.240802 | − | 0.970574i | \(-0.577410\pi\) | ||||
−0.240802 | + | 0.970574i | \(0.577410\pi\) | |||||||
\(164\) | −26141.8 | −0.0758971 | ||||||||
\(165\) | 45917.3 | 0.131300 | ||||||||
\(166\) | −350439. | −0.987058 | ||||||||
\(167\) | −264211. | −0.733094 | −0.366547 | − | 0.930400i | \(-0.619460\pi\) | ||||
−0.366547 | + | 0.930400i | \(0.619460\pi\) | |||||||
\(168\) | −40101.4 | −0.109619 | ||||||||
\(169\) | 397768. | 1.07130 | ||||||||
\(170\) | 136374. | 0.361918 | ||||||||
\(171\) | −408602. | −1.06859 | ||||||||
\(172\) | 139769. | 0.360238 | ||||||||
\(173\) | 341880. | 0.868478 | 0.434239 | − | 0.900798i | \(-0.357017\pi\) | ||||
0.434239 | + | 0.900798i | \(0.357017\pi\) | |||||||
\(174\) | 30490.0 | 0.0763457 | ||||||||
\(175\) | −157672. | −0.389187 | ||||||||
\(176\) | −189309. | −0.460669 | ||||||||
\(177\) | 123507. | 0.296317 | ||||||||
\(178\) | −132876. | −0.314338 | ||||||||
\(179\) | 311766. | 0.727271 | 0.363636 | − | 0.931541i | \(-0.381535\pi\) | ||||
0.363636 | + | 0.931541i | \(0.381535\pi\) | |||||||
\(180\) | −94732.4 | −0.217930 | ||||||||
\(181\) | −263189. | −0.597132 | −0.298566 | − | 0.954389i | \(-0.596508\pi\) | ||||
−0.298566 | + | 0.954389i | \(0.596508\pi\) | |||||||
\(182\) | 884940. | 1.98032 | ||||||||
\(183\) | −47270.0 | −0.104342 | ||||||||
\(184\) | 33856.0 | 0.0737210 | ||||||||
\(185\) | −101033. | −0.217036 | ||||||||
\(186\) | −83702.2 | −0.177400 | ||||||||
\(187\) | 1.00847e6 | 2.10891 | ||||||||
\(188\) | 303824. | 0.626942 | ||||||||
\(189\) | −300654. | −0.612228 | ||||||||
\(190\) | −172529. | −0.346719 | ||||||||
\(191\) | −755404. | −1.49829 | −0.749145 | − | 0.662406i | \(-0.769535\pi\) | ||||
−0.749145 | + | 0.662406i | \(0.769535\pi\) | |||||||
\(192\) | −10173.4 | −0.0199165 | ||||||||
\(193\) | −773822. | −1.49537 | −0.747683 | − | 0.664056i | \(-0.768834\pi\) | ||||
−0.747683 | + | 0.664056i | \(0.768834\pi\) | |||||||
\(194\) | −165325. | −0.315379 | ||||||||
\(195\) | −54453.5 | −0.102551 | ||||||||
\(196\) | 749368. | 1.39333 | ||||||||
\(197\) | 465100. | 0.853848 | 0.426924 | − | 0.904288i | \(-0.359597\pi\) | ||||
0.426924 | + | 0.904288i | \(0.359597\pi\) | |||||||
\(198\) | −700534. | −1.26989 | ||||||||
\(199\) | −601491. | −1.07671 | −0.538353 | − | 0.842720i | \(-0.680953\pi\) | ||||
−0.538353 | + | 0.842720i | \(0.680953\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 23340.3 | 0.0407489 | ||||||||
\(202\) | 207472. | 0.357751 | ||||||||
\(203\) | −774223. | −1.31864 | ||||||||
\(204\) | 54194.8 | 0.0911764 | ||||||||
\(205\) | −40846.5 | −0.0678844 | ||||||||
\(206\) | −217321. | −0.356807 | ||||||||
\(207\) | 125284. | 0.203221 | ||||||||
\(208\) | 224502. | 0.359801 | ||||||||
\(209\) | −1.27583e6 | −2.02035 | ||||||||
\(210\) | −62658.4 | −0.0980462 | ||||||||
\(211\) | −6024.40 | −0.00931553 | −0.00465777 | − | 0.999989i | \(-0.501483\pi\) | ||||
−0.00465777 | + | 0.999989i | \(0.501483\pi\) | |||||||
\(212\) | 303280. | 0.463452 | ||||||||
\(213\) | 71851.4 | 0.108514 | ||||||||
\(214\) | 424618. | 0.633817 | ||||||||
\(215\) | 218389. | 0.322207 | ||||||||
\(216\) | −76273.5 | −0.111234 | ||||||||
\(217\) | 2.12542e6 | 3.06405 | ||||||||
\(218\) | 695615. | 0.991352 | ||||||||
\(219\) | −6296.34 | −0.00887111 | ||||||||
\(220\) | −295795. | −0.412035 | ||||||||
\(221\) | −1.19595e6 | −1.64715 | ||||||||
\(222\) | −40150.1 | −0.0546770 | ||||||||
\(223\) | 1.29198e6 | 1.73978 | 0.869891 | − | 0.493244i | \(-0.164189\pi\) | ||||
0.869891 | + | 0.493244i | \(0.164189\pi\) | |||||||
\(224\) | 258329. | 0.343996 | ||||||||
\(225\) | −148019. | −0.194923 | ||||||||
\(226\) | −1.04843e6 | −1.36542 | ||||||||
\(227\) | 64294.3 | 0.0828148 | 0.0414074 | − | 0.999142i | \(-0.486816\pi\) | ||||
0.0414074 | + | 0.999142i | \(0.486816\pi\) | |||||||
\(228\) | −68562.5 | −0.0873473 | ||||||||
\(229\) | 74653.2 | 0.0940718 | 0.0470359 | − | 0.998893i | \(-0.485022\pi\) | ||||
0.0470359 | + | 0.998893i | \(0.485022\pi\) | |||||||
\(230\) | 52900.0 | 0.0659380 | ||||||||
\(231\) | −463350. | −0.571320 | ||||||||
\(232\) | −196414. | −0.239581 | ||||||||
\(233\) | −163107. | −0.196826 | −0.0984129 | − | 0.995146i | \(-0.531377\pi\) | ||||
−0.0984129 | + | 0.995146i | \(0.531377\pi\) | |||||||
\(234\) | 830767. | 0.991835 | ||||||||
\(235\) | 474725. | 0.560754 | ||||||||
\(236\) | −795619. | −0.929876 | ||||||||
\(237\) | 43806.7 | 0.0506605 | ||||||||
\(238\) | −1.37615e6 | −1.57479 | ||||||||
\(239\) | −458112. | −0.518773 | −0.259386 | − | 0.965774i | \(-0.583520\pi\) | ||||
−0.259386 | + | 0.965774i | \(0.583520\pi\) | |||||||
\(240\) | −15895.9 | −0.0178138 | ||||||||
\(241\) | 1.74728e6 | 1.93785 | 0.968924 | − | 0.247360i | \(-0.0795631\pi\) | ||||
0.968924 | + | 0.247360i | \(0.0795631\pi\) | |||||||
\(242\) | −1.54316e6 | −1.69384 | ||||||||
\(243\) | −425188. | −0.461918 | ||||||||
\(244\) | 304509. | 0.327436 | ||||||||
\(245\) | 1.17089e6 | 1.24624 | ||||||||
\(246\) | −16232.3 | −0.0171018 | ||||||||
\(247\) | 1.51301e6 | 1.57797 | ||||||||
\(248\) | 539202. | 0.556702 | ||||||||
\(249\) | −217600. | −0.222413 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −509792. | −0.510751 | −0.255375 | − | 0.966842i | \(-0.582199\pi\) | ||||
−0.255375 | + | 0.966842i | \(0.582199\pi\) | |||||||
\(252\) | 955944. | 0.948268 | ||||||||
\(253\) | 391189. | 0.384224 | ||||||||
\(254\) | −910100. | −0.885126 | ||||||||
\(255\) | 84679.4 | 0.0815507 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 253793. | 0.239688 | 0.119844 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119844 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(258\) | 86787.4 | 0.0811722 | ||||||||
\(259\) | 1.01952e6 | 0.944378 | ||||||||
\(260\) | 350784. | 0.321816 | ||||||||
\(261\) | −726827. | −0.660435 | ||||||||
\(262\) | −823827. | −0.741452 | ||||||||
\(263\) | −245617. | −0.218962 | −0.109481 | − | 0.993989i | \(-0.534919\pi\) | ||||
−0.109481 | + | 0.993989i | \(0.534919\pi\) | |||||||
\(264\) | −117548. | −0.103802 | ||||||||
\(265\) | 473875. | 0.414524 | ||||||||
\(266\) | 1.74099e6 | 1.50866 | ||||||||
\(267\) | −82507.2 | −0.0708294 | ||||||||
\(268\) | −150356. | −0.127874 | ||||||||
\(269\) | −1.30972e6 | −1.10356 | −0.551782 | − | 0.833989i | \(-0.686052\pi\) | ||||
−0.551782 | + | 0.833989i | \(0.686052\pi\) | |||||||
\(270\) | −119177. | −0.0994911 | ||||||||
\(271\) | 335307. | 0.277345 | 0.138672 | − | 0.990338i | \(-0.455717\pi\) | ||||
0.138672 | + | 0.990338i | \(0.455717\pi\) | |||||||
\(272\) | −349118. | −0.286121 | ||||||||
\(273\) | 549490. | 0.446224 | ||||||||
\(274\) | 1.28259e6 | 1.03208 | ||||||||
\(275\) | −462179. | −0.368535 | ||||||||
\(276\) | 21022.3 | 0.0166115 | ||||||||
\(277\) | 1.24277e6 | 0.973173 | 0.486586 | − | 0.873633i | \(-0.338242\pi\) | ||||
0.486586 | + | 0.873633i | \(0.338242\pi\) | |||||||
\(278\) | −778943. | −0.604497 | ||||||||
\(279\) | 1.99531e6 | 1.53462 | ||||||||
\(280\) | 403639. | 0.307680 | ||||||||
\(281\) | −549120. | −0.414860 | −0.207430 | − | 0.978250i | \(-0.566510\pi\) | ||||
−0.207430 | + | 0.978250i | \(0.566510\pi\) | |||||||
\(282\) | 188655. | 0.141268 | ||||||||
\(283\) | −687675. | −0.510407 | −0.255204 | − | 0.966887i | \(-0.582143\pi\) | ||||
−0.255204 | + | 0.966887i | \(0.582143\pi\) | |||||||
\(284\) | −462860. | −0.340529 | ||||||||
\(285\) | −107129. | −0.0781258 | ||||||||
\(286\) | 2.59401e6 | 1.87524 | ||||||||
\(287\) | 412182. | 0.295382 | ||||||||
\(288\) | 242515. | 0.172289 | ||||||||
\(289\) | 439938. | 0.309847 | ||||||||
\(290\) | −306897. | −0.214288 | ||||||||
\(291\) | −102656. | −0.0710641 | ||||||||
\(292\) | 40560.4 | 0.0278385 | ||||||||
\(293\) | −1.30317e6 | −0.886813 | −0.443406 | − | 0.896321i | \(-0.646230\pi\) | ||||
−0.443406 | + | 0.896321i | \(0.646230\pi\) | |||||||
\(294\) | 465308. | 0.313959 | ||||||||
\(295\) | −1.24315e6 | −0.831706 | ||||||||
\(296\) | 258643. | 0.171582 | ||||||||
\(297\) | −881301. | −0.579740 | ||||||||
\(298\) | 1.57212e6 | 1.02552 | ||||||||
\(299\) | −463912. | −0.300095 | ||||||||
\(300\) | −24837.4 | −0.0159332 | ||||||||
\(301\) | −2.20376e6 | −1.40200 | ||||||||
\(302\) | 21433.0 | 0.0135227 | ||||||||
\(303\) | 128826. | 0.0806117 | ||||||||
\(304\) | 441674. | 0.274105 | ||||||||
\(305\) | 475796. | 0.292867 | ||||||||
\(306\) | −1.29191e6 | −0.788729 | ||||||||
\(307\) | 2.67886e6 | 1.62220 | 0.811099 | − | 0.584909i | \(-0.198870\pi\) | ||||
0.811099 | + | 0.584909i | \(0.198870\pi\) | |||||||
\(308\) | 2.98486e6 | 1.79286 | ||||||||
\(309\) | −134942. | −0.0803991 | ||||||||
\(310\) | 842504. | 0.497929 | ||||||||
\(311\) | 2.66680e6 | 1.56347 | 0.781734 | − | 0.623612i | \(-0.214335\pi\) | ||||
0.781734 | + | 0.623612i | \(0.214335\pi\) | |||||||
\(312\) | 139401. | 0.0810736 | ||||||||
\(313\) | 935722. | 0.539866 | 0.269933 | − | 0.962879i | \(-0.412998\pi\) | ||||
0.269933 | + | 0.962879i | \(0.412998\pi\) | |||||||
\(314\) | −1.16341e6 | −0.665897 | ||||||||
\(315\) | 1.49366e6 | 0.848156 | ||||||||
\(316\) | −282199. | −0.158978 | ||||||||
\(317\) | −1.45385e6 | −0.812592 | −0.406296 | − | 0.913742i | \(-0.633180\pi\) | ||||
−0.406296 | + | 0.913742i | \(0.633180\pi\) | |||||||
\(318\) | 188317. | 0.104429 | ||||||||
\(319\) | −2.26946e6 | −1.24867 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 263660. | 0.142817 | ||||||||
\(322\) | −533813. | −0.286913 | ||||||||
\(323\) | −2.35285e6 | −1.25484 | ||||||||
\(324\) | 873438. | 0.462242 | ||||||||
\(325\) | 548101. | 0.287841 | ||||||||
\(326\) | 653461. | 0.340546 | ||||||||
\(327\) | 431931. | 0.223380 | ||||||||
\(328\) | 104567. | 0.0536674 | ||||||||
\(329\) | −4.79045e6 | −2.43998 | ||||||||
\(330\) | −183669. | −0.0928434 | ||||||||
\(331\) | −13841.3 | −0.00694395 | −0.00347198 | − | 0.999994i | \(-0.501105\pi\) | ||||
−0.00347198 | + | 0.999994i | \(0.501105\pi\) | |||||||
\(332\) | 1.40176e6 | 0.697955 | ||||||||
\(333\) | 957106. | 0.472987 | ||||||||
\(334\) | 1.05684e6 | 0.518376 | ||||||||
\(335\) | −234931. | −0.114374 | ||||||||
\(336\) | 160405. | 0.0775123 | ||||||||
\(337\) | −1.93165e6 | −0.926520 | −0.463260 | − | 0.886222i | \(-0.653320\pi\) | ||||
−0.463260 | + | 0.886222i | \(0.653320\pi\) | |||||||
\(338\) | −1.59107e6 | −0.757527 | ||||||||
\(339\) | −651005. | −0.307670 | ||||||||
\(340\) | −545497. | −0.255915 | ||||||||
\(341\) | 6.23020e6 | 2.90146 | ||||||||
\(342\) | 1.63441e6 | 0.755605 | ||||||||
\(343\) | −7.57543e6 | −3.47674 | ||||||||
\(344\) | −559076. | −0.254727 | ||||||||
\(345\) | 32847.4 | 0.0148578 | ||||||||
\(346\) | −1.36752e6 | −0.614107 | ||||||||
\(347\) | −2.44241e6 | −1.08892 | −0.544458 | − | 0.838788i | \(-0.683265\pi\) | ||||
−0.544458 | + | 0.838788i | \(0.683265\pi\) | |||||||
\(348\) | −121960. | −0.0539846 | ||||||||
\(349\) | 956707. | 0.420451 | 0.210226 | − | 0.977653i | \(-0.432580\pi\) | ||||
0.210226 | + | 0.977653i | \(0.432580\pi\) | |||||||
\(350\) | 630687. | 0.275197 | ||||||||
\(351\) | 1.04514e6 | 0.452800 | ||||||||
\(352\) | 757235. | 0.325742 | ||||||||
\(353\) | 3.71100e6 | 1.58509 | 0.792545 | − | 0.609813i | \(-0.208756\pi\) | ||||
0.792545 | + | 0.609813i | \(0.208756\pi\) | |||||||
\(354\) | −494027. | −0.209528 | ||||||||
\(355\) | −723219. | −0.304578 | ||||||||
\(356\) | 531504. | 0.222270 | ||||||||
\(357\) | −854499. | −0.354847 | ||||||||
\(358\) | −1.24706e6 | −0.514258 | ||||||||
\(359\) | −1.33403e6 | −0.546298 | −0.273149 | − | 0.961972i | \(-0.588065\pi\) | ||||
−0.273149 | + | 0.961972i | \(0.588065\pi\) | |||||||
\(360\) | 378930. | 0.154100 | ||||||||
\(361\) | 500518. | 0.202140 | ||||||||
\(362\) | 1.05275e6 | 0.422236 | ||||||||
\(363\) | −958200. | −0.381671 | ||||||||
\(364\) | −3.53976e6 | −1.40030 | ||||||||
\(365\) | 63375.7 | 0.0248995 | ||||||||
\(366\) | 189080. | 0.0737808 | ||||||||
\(367\) | 2.92197e6 | 1.13243 | 0.566214 | − | 0.824258i | \(-0.308408\pi\) | ||||
0.566214 | + | 0.824258i | \(0.308408\pi\) | |||||||
\(368\) | −135424. | −0.0521286 | ||||||||
\(369\) | 386949. | 0.147941 | ||||||||
\(370\) | 404130. | 0.153468 | ||||||||
\(371\) | −4.78187e6 | −1.80369 | ||||||||
\(372\) | 334809. | 0.125441 | ||||||||
\(373\) | −3.06510e6 | −1.14070 | −0.570352 | − | 0.821401i | \(-0.693193\pi\) | ||||
−0.570352 | + | 0.821401i | \(0.693193\pi\) | |||||||
\(374\) | −4.03388e6 | −1.49123 | ||||||||
\(375\) | −38808.4 | −0.0142511 | ||||||||
\(376\) | −1.21530e6 | −0.443315 | ||||||||
\(377\) | 2.69137e6 | 0.975258 | ||||||||
\(378\) | 1.20262e6 | 0.432910 | ||||||||
\(379\) | 296537. | 0.106043 | 0.0530214 | − | 0.998593i | \(-0.483115\pi\) | ||||
0.0530214 | + | 0.998593i | \(0.483115\pi\) | |||||||
\(380\) | 690115. | 0.245167 | ||||||||
\(381\) | −565112. | −0.199445 | ||||||||
\(382\) | 3.02162e6 | 1.05945 | ||||||||
\(383\) | 2.25387e6 | 0.785113 | 0.392556 | − | 0.919728i | \(-0.371591\pi\) | ||||
0.392556 | + | 0.919728i | \(0.371591\pi\) | |||||||
\(384\) | 40693.5 | 0.0140831 | ||||||||
\(385\) | 4.66385e6 | 1.60359 | ||||||||
\(386\) | 3.09529e6 | 1.05738 | ||||||||
\(387\) | −2.06885e6 | −0.702186 | ||||||||
\(388\) | 661299. | 0.223007 | ||||||||
\(389\) | −956682. | −0.320548 | −0.160274 | − | 0.987073i | \(-0.551238\pi\) | ||||
−0.160274 | + | 0.987073i | \(0.551238\pi\) | |||||||
\(390\) | 217814. | 0.0725144 | ||||||||
\(391\) | 721420. | 0.238642 | ||||||||
\(392\) | −2.99747e6 | −0.985236 | ||||||||
\(393\) | −511542. | −0.167071 | ||||||||
\(394\) | −1.86040e6 | −0.603762 | ||||||||
\(395\) | −440935. | −0.142194 | ||||||||
\(396\) | 2.80214e6 | 0.897948 | ||||||||
\(397\) | 2.14436e6 | 0.682843 | 0.341421 | − | 0.939910i | \(-0.389092\pi\) | ||||
0.341421 | + | 0.939910i | \(0.389092\pi\) | |||||||
\(398\) | 2.40597e6 | 0.761345 | ||||||||
\(399\) | 1.08104e6 | 0.339945 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 702874. | 0.218281 | 0.109141 | − | 0.994026i | \(-0.465190\pi\) | ||||
0.109141 | + | 0.994026i | \(0.465190\pi\) | |||||||
\(402\) | −93361.0 | −0.0288138 | ||||||||
\(403\) | −7.38843e6 | −2.26615 | ||||||||
\(404\) | −829888. | −0.252968 | ||||||||
\(405\) | 1.36475e6 | 0.413442 | ||||||||
\(406\) | 3.09689e6 | 0.932419 | ||||||||
\(407\) | 2.98849e6 | 0.894264 | ||||||||
\(408\) | −216779. | −0.0644715 | ||||||||
\(409\) | 2.71607e6 | 0.802848 | 0.401424 | − | 0.915892i | \(-0.368515\pi\) | ||||
0.401424 | + | 0.915892i | \(0.368515\pi\) | |||||||
\(410\) | 163386. | 0.0480015 | ||||||||
\(411\) | 796404. | 0.232557 | ||||||||
\(412\) | 869284. | 0.252301 | ||||||||
\(413\) | 1.25447e7 | 3.61896 | ||||||||
\(414\) | −501135. | −0.143699 | ||||||||
\(415\) | 2.19025e6 | 0.624270 | ||||||||
\(416\) | −898008. | −0.254418 | ||||||||
\(417\) | −483672. | −0.136211 | ||||||||
\(418\) | 5.10331e6 | 1.42860 | ||||||||
\(419\) | −3.78764e6 | −1.05398 | −0.526992 | − | 0.849870i | \(-0.676680\pi\) | ||||
−0.526992 | + | 0.849870i | \(0.676680\pi\) | |||||||
\(420\) | 250633. | 0.0693291 | ||||||||
\(421\) | −1.72773e6 | −0.475085 | −0.237542 | − | 0.971377i | \(-0.576342\pi\) | ||||
−0.237542 | + | 0.971377i | \(0.576342\pi\) | |||||||
\(422\) | 24097.6 | 0.00658707 | ||||||||
\(423\) | −4.49719e6 | −1.22205 | ||||||||
\(424\) | −1.21312e6 | −0.327710 | ||||||||
\(425\) | −852339. | −0.228897 | ||||||||
\(426\) | −287406. | −0.0767311 | ||||||||
\(427\) | −4.80125e6 | −1.27434 | ||||||||
\(428\) | −1.69847e6 | −0.448176 | ||||||||
\(429\) | 1.61071e6 | 0.422545 | ||||||||
\(430\) | −873557. | −0.227835 | ||||||||
\(431\) | −5.04905e6 | −1.30923 | −0.654615 | − | 0.755962i | \(-0.727169\pi\) | ||||
−0.654615 | + | 0.755962i | \(0.727169\pi\) | |||||||
\(432\) | 305094. | 0.0786546 | ||||||||
\(433\) | 37457.0 | 0.00960093 | 0.00480047 | − | 0.999988i | \(-0.498472\pi\) | ||||
0.00480047 | + | 0.999988i | \(0.498472\pi\) | |||||||
\(434\) | −8.50169e6 | −2.16661 | ||||||||
\(435\) | −190563. | −0.0482853 | ||||||||
\(436\) | −2.78246e6 | −0.700992 | ||||||||
\(437\) | −912677. | −0.228620 | ||||||||
\(438\) | 25185.4 | 0.00627282 | ||||||||
\(439\) | −99673.6 | −0.0246842 | −0.0123421 | − | 0.999924i | \(-0.503929\pi\) | ||||
−0.0123421 | + | 0.999924i | \(0.503929\pi\) | |||||||
\(440\) | 1.18318e6 | 0.291353 | ||||||||
\(441\) | −1.10921e7 | −2.71592 | ||||||||
\(442\) | 4.78380e6 | 1.16471 | ||||||||
\(443\) | −4.60309e6 | −1.11440 | −0.557199 | − | 0.830379i | \(-0.688124\pi\) | ||||
−0.557199 | + | 0.830379i | \(0.688124\pi\) | |||||||
\(444\) | 160600. | 0.0386624 | ||||||||
\(445\) | 830475. | 0.198805 | ||||||||
\(446\) | −5.16793e6 | −1.23021 | ||||||||
\(447\) | 976184. | 0.231080 | ||||||||
\(448\) | −1.03332e6 | −0.243242 | ||||||||
\(449\) | 3.74524e6 | 0.876725 | 0.438363 | − | 0.898798i | \(-0.355559\pi\) | ||||
0.438363 | + | 0.898798i | \(0.355559\pi\) | |||||||
\(450\) | 592078. | 0.137831 | ||||||||
\(451\) | 1.20822e6 | 0.279707 | ||||||||
\(452\) | 4.19371e6 | 0.965501 | ||||||||
\(453\) | 13308.5 | 0.00304707 | ||||||||
\(454\) | −257177. | −0.0585589 | ||||||||
\(455\) | −5.53088e6 | −1.25246 | ||||||||
\(456\) | 274250. | 0.0617639 | ||||||||
\(457\) | 499745. | 0.111933 | 0.0559665 | − | 0.998433i | \(-0.482176\pi\) | ||||
0.0559665 | + | 0.998433i | \(0.482176\pi\) | |||||||
\(458\) | −298613. | −0.0665188 | ||||||||
\(459\) | −1.62527e6 | −0.360076 | ||||||||
\(460\) | −211600. | −0.0466252 | ||||||||
\(461\) | 1.73935e6 | 0.381183 | 0.190592 | − | 0.981669i | \(-0.438959\pi\) | ||||
0.190592 | + | 0.981669i | \(0.438959\pi\) | |||||||
\(462\) | 1.85340e6 | 0.403984 | ||||||||
\(463\) | 866807. | 0.187919 | 0.0939594 | − | 0.995576i | \(-0.470048\pi\) | ||||
0.0939594 | + | 0.995576i | \(0.470048\pi\) | |||||||
\(464\) | 785656. | 0.169409 | ||||||||
\(465\) | 523139. | 0.112198 | ||||||||
\(466\) | 652427. | 0.139177 | ||||||||
\(467\) | −1.52340e6 | −0.323238 | −0.161619 | − | 0.986853i | \(-0.551672\pi\) | ||||
−0.161619 | + | 0.986853i | \(0.551672\pi\) | |||||||
\(468\) | −3.32307e6 | −0.701333 | ||||||||
\(469\) | 2.37069e6 | 0.497671 | ||||||||
\(470\) | −1.89890e6 | −0.396513 | ||||||||
\(471\) | −722398. | −0.150046 | ||||||||
\(472\) | 3.18247e6 | 0.657522 | ||||||||
\(473\) | −6.45984e6 | −1.32760 | ||||||||
\(474\) | −175227. | −0.0358224 | ||||||||
\(475\) | 1.07830e6 | 0.219284 | ||||||||
\(476\) | 5.50461e6 | 1.11355 | ||||||||
\(477\) | −4.48914e6 | −0.903373 | ||||||||
\(478\) | 1.83245e6 | 0.366828 | ||||||||
\(479\) | 9.23081e6 | 1.83824 | 0.919118 | − | 0.393983i | \(-0.128903\pi\) | ||||
0.919118 | + | 0.393983i | \(0.128903\pi\) | |||||||
\(480\) | 63583.6 | 0.0125963 | ||||||||
\(481\) | −3.54407e6 | −0.698456 | ||||||||
\(482\) | −6.98911e6 | −1.37026 | ||||||||
\(483\) | −331463. | −0.0646498 | ||||||||
\(484\) | 6.17264e6 | 1.19773 | ||||||||
\(485\) | 1.03328e6 | 0.199463 | ||||||||
\(486\) | 1.70075e6 | 0.326626 | ||||||||
\(487\) | −1.22749e6 | −0.234529 | −0.117264 | − | 0.993101i | \(-0.537413\pi\) | ||||
−0.117264 | + | 0.993101i | \(0.537413\pi\) | |||||||
\(488\) | −1.21804e6 | −0.231532 | ||||||||
\(489\) | 405756. | 0.0767348 | ||||||||
\(490\) | −4.68355e6 | −0.881222 | ||||||||
\(491\) | −2.99377e6 | −0.560421 | −0.280210 | − | 0.959939i | \(-0.590404\pi\) | ||||
−0.280210 | + | 0.959939i | \(0.590404\pi\) | |||||||
\(492\) | 64929.2 | 0.0120928 | ||||||||
\(493\) | −4.18529e6 | −0.775546 | ||||||||
\(494\) | −6.05204e6 | −1.11580 | ||||||||
\(495\) | 4.37834e6 | 0.803149 | ||||||||
\(496\) | −2.15681e6 | −0.393648 | ||||||||
\(497\) | 7.29799e6 | 1.32529 | ||||||||
\(498\) | 870398. | 0.157270 | ||||||||
\(499\) | −123550. | −0.0222121 | −0.0111061 | − | 0.999938i | \(-0.503535\pi\) | ||||
−0.0111061 | + | 0.999938i | \(0.503535\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 656230. | 0.116805 | ||||||||
\(502\) | 2.03917e6 | 0.361155 | ||||||||
\(503\) | 2.10833e6 | 0.371551 | 0.185775 | − | 0.982592i | \(-0.440520\pi\) | ||||
0.185775 | + | 0.982592i | \(0.440520\pi\) | |||||||
\(504\) | −3.82377e6 | −0.670527 | ||||||||
\(505\) | −1.29670e6 | −0.226262 | ||||||||
\(506\) | −1.56475e6 | −0.271688 | ||||||||
\(507\) | −987950. | −0.170693 | ||||||||
\(508\) | 3.64040e6 | 0.625878 | ||||||||
\(509\) | 1.57302e6 | 0.269116 | 0.134558 | − | 0.990906i | \(-0.457038\pi\) | ||||
0.134558 | + | 0.990906i | \(0.457038\pi\) | |||||||
\(510\) | −338718. | −0.0576650 | ||||||||
\(511\) | −639523. | −0.108344 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 2.05615e6 | 0.344954 | ||||||||
\(514\) | −1.01517e6 | −0.169485 | ||||||||
\(515\) | 1.35826e6 | 0.225665 | ||||||||
\(516\) | −347150. | −0.0573974 | ||||||||
\(517\) | −1.40421e7 | −2.31050 | ||||||||
\(518\) | −4.07807e6 | −0.667776 | ||||||||
\(519\) | −849140. | −0.138376 | ||||||||
\(520\) | −1.40314e6 | −0.227558 | ||||||||
\(521\) | −1.90859e6 | −0.308049 | −0.154024 | − | 0.988067i | \(-0.549223\pi\) | ||||
−0.154024 | + | 0.988067i | \(0.549223\pi\) | |||||||
\(522\) | 2.90731e6 | 0.466998 | ||||||||
\(523\) | 7.33852e6 | 1.17315 | 0.586576 | − | 0.809894i | \(-0.300475\pi\) | ||||
0.586576 | + | 0.809894i | \(0.300475\pi\) | |||||||
\(524\) | 3.29531e6 | 0.524286 | ||||||||
\(525\) | 391615. | 0.0620099 | ||||||||
\(526\) | 982467. | 0.154829 | ||||||||
\(527\) | 1.14896e7 | 1.80210 | ||||||||
\(528\) | 470193. | 0.0733992 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −1.89550e6 | −0.293113 | ||||||||
\(531\) | 1.17767e7 | 1.81254 | ||||||||
\(532\) | −6.96394e6 | −1.06678 | ||||||||
\(533\) | −1.43283e6 | −0.218463 | ||||||||
\(534\) | 330029. | 0.0500840 | ||||||||
\(535\) | −2.65386e6 | −0.400861 | ||||||||
\(536\) | 601423. | 0.0904208 | ||||||||
\(537\) | −774345. | −0.115877 | ||||||||
\(538\) | 5.23887e6 | 0.780337 | ||||||||
\(539\) | −3.46343e7 | −5.13492 | ||||||||
\(540\) | 476709. | 0.0703508 | ||||||||
\(541\) | 1.09412e7 | 1.60721 | 0.803606 | − | 0.595162i | \(-0.202912\pi\) | ||||
0.803606 | + | 0.595162i | \(0.202912\pi\) | |||||||
\(542\) | −1.34123e6 | −0.196112 | ||||||||
\(543\) | 653691. | 0.0951421 | ||||||||
\(544\) | 1.39647e6 | 0.202318 | ||||||||
\(545\) | −4.34760e6 | −0.626986 | ||||||||
\(546\) | −2.19796e6 | −0.315528 | ||||||||
\(547\) | 7.37797e6 | 1.05431 | 0.527155 | − | 0.849769i | \(-0.323259\pi\) | ||||
0.527155 | + | 0.849769i | \(0.323259\pi\) | |||||||
\(548\) | −5.13036e6 | −0.729788 | ||||||||
\(549\) | −4.50733e6 | −0.638246 | ||||||||
\(550\) | 1.84872e6 | 0.260594 | ||||||||
\(551\) | 5.29485e6 | 0.742976 | ||||||||
\(552\) | −84089.4 | −0.0117461 | ||||||||
\(553\) | 4.44947e6 | 0.618722 | ||||||||
\(554\) | −4.97106e6 | −0.688137 | ||||||||
\(555\) | 250938. | 0.0345807 | ||||||||
\(556\) | 3.11577e6 | 0.427444 | ||||||||
\(557\) | 7.81229e6 | 1.06694 | 0.533471 | − | 0.845819i | \(-0.320887\pi\) | ||||
0.533471 | + | 0.845819i | \(0.320887\pi\) | |||||||
\(558\) | −7.98124e6 | −1.08514 | ||||||||
\(559\) | 7.66076e6 | 1.03691 | ||||||||
\(560\) | −1.61456e6 | −0.217562 | ||||||||
\(561\) | −2.50477e6 | −0.336017 | ||||||||
\(562\) | 2.19648e6 | 0.293350 | ||||||||
\(563\) | −9.88567e6 | −1.31442 | −0.657212 | − | 0.753706i | \(-0.728264\pi\) | ||||
−0.657212 | + | 0.753706i | \(0.728264\pi\) | |||||||
\(564\) | −754619. | −0.0998918 | ||||||||
\(565\) | 6.55268e6 | 0.863570 | ||||||||
\(566\) | 2.75070e6 | 0.360913 | ||||||||
\(567\) | −1.37716e7 | −1.79899 | ||||||||
\(568\) | 1.85144e6 | 0.240790 | ||||||||
\(569\) | 3.37792e6 | 0.437390 | 0.218695 | − | 0.975793i | \(-0.429820\pi\) | ||||
0.218695 | + | 0.975793i | \(0.429820\pi\) | |||||||
\(570\) | 428516. | 0.0552433 | ||||||||
\(571\) | 1.44970e7 | 1.86075 | 0.930375 | − | 0.366610i | \(-0.119482\pi\) | ||||
0.930375 | + | 0.366610i | \(0.119482\pi\) | |||||||
\(572\) | −1.03760e7 | −1.32599 | ||||||||
\(573\) | 1.87622e6 | 0.238725 | ||||||||
\(574\) | −1.64873e6 | −0.208866 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | −970060. | −0.121827 | ||||||||
\(577\) | −2.74177e6 | −0.342840 | −0.171420 | − | 0.985198i | \(-0.554836\pi\) | ||||
−0.171420 | + | 0.985198i | \(0.554836\pi\) | |||||||
\(578\) | −1.75975e6 | −0.219095 | ||||||||
\(579\) | 1.92197e6 | 0.238259 | ||||||||
\(580\) | 1.22759e6 | 0.151524 | ||||||||
\(581\) | −2.21017e7 | −2.71635 | ||||||||
\(582\) | 410623. | 0.0502499 | ||||||||
\(583\) | −1.40170e7 | −1.70798 | ||||||||
\(584\) | −162242. | −0.0196848 | ||||||||
\(585\) | −5.19229e6 | −0.627291 | ||||||||
\(586\) | 5.21268e6 | 0.627071 | ||||||||
\(587\) | 2.70287e6 | 0.323765 | 0.161882 | − | 0.986810i | \(-0.448243\pi\) | ||||
0.161882 | + | 0.986810i | \(0.448243\pi\) | |||||||
\(588\) | −1.86123e6 | −0.222002 | ||||||||
\(589\) | −1.45356e7 | −1.72641 | ||||||||
\(590\) | 4.97262e6 | 0.588105 | ||||||||
\(591\) | −1.15518e6 | −0.136045 | ||||||||
\(592\) | −1.03457e6 | −0.121327 | ||||||||
\(593\) | 5.21163e6 | 0.608607 | 0.304303 | − | 0.952575i | \(-0.401576\pi\) | ||||
0.304303 | + | 0.952575i | \(0.401576\pi\) | |||||||
\(594\) | 3.52520e6 | 0.409938 | ||||||||
\(595\) | 8.60095e6 | 0.995987 | ||||||||
\(596\) | −6.28849e6 | −0.725155 | ||||||||
\(597\) | 1.49395e6 | 0.171553 | ||||||||
\(598\) | 1.85565e6 | 0.212199 | ||||||||
\(599\) | 1.51225e7 | 1.72210 | 0.861049 | − | 0.508523i | \(-0.169808\pi\) | ||||
0.861049 | + | 0.508523i | \(0.169808\pi\) | |||||||
\(600\) | 99349.4 | 0.0112665 | ||||||||
\(601\) | 1.54889e7 | 1.74918 | 0.874592 | − | 0.484860i | \(-0.161129\pi\) | ||||
0.874592 | + | 0.484860i | \(0.161129\pi\) | |||||||
\(602\) | 8.81505e6 | 0.991365 | ||||||||
\(603\) | 2.22556e6 | 0.249256 | ||||||||
\(604\) | −85731.8 | −0.00956202 | ||||||||
\(605\) | 9.64475e6 | 1.07128 | ||||||||
\(606\) | −515305. | −0.0570011 | ||||||||
\(607\) | −1.32452e7 | −1.45910 | −0.729551 | − | 0.683926i | \(-0.760271\pi\) | ||||
−0.729551 | + | 0.683926i | \(0.760271\pi\) | |||||||
\(608\) | −1.76669e6 | −0.193822 | ||||||||
\(609\) | 1.92297e6 | 0.210101 | ||||||||
\(610\) | −1.90318e6 | −0.207088 | ||||||||
\(611\) | 1.66526e7 | 1.80459 | ||||||||
\(612\) | 5.16763e6 | 0.557715 | ||||||||
\(613\) | 9.10746e6 | 0.978918 | 0.489459 | − | 0.872026i | \(-0.337194\pi\) | ||||
0.489459 | + | 0.872026i | \(0.337194\pi\) | |||||||
\(614\) | −1.07154e7 | −1.14707 | ||||||||
\(615\) | 101452. | 0.0108161 | ||||||||
\(616\) | −1.19394e7 | −1.26775 | ||||||||
\(617\) | −2.14311e6 | −0.226637 | −0.113319 | − | 0.993559i | \(-0.536148\pi\) | ||||
−0.113319 | + | 0.993559i | \(0.536148\pi\) | |||||||
\(618\) | 539768. | 0.0568507 | ||||||||
\(619\) | 1.74838e7 | 1.83404 | 0.917021 | − | 0.398839i | \(-0.130587\pi\) | ||||
0.917021 | + | 0.398839i | \(0.130587\pi\) | |||||||
\(620\) | −3.37001e6 | −0.352089 | ||||||||
\(621\) | −630448. | −0.0656025 | ||||||||
\(622\) | −1.06672e7 | −1.10554 | ||||||||
\(623\) | −8.38031e6 | −0.865048 | ||||||||
\(624\) | −557604. | −0.0573277 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −3.74289e6 | −0.381743 | ||||||||
\(627\) | 3.16882e6 | 0.321906 | ||||||||
\(628\) | 4.65362e6 | 0.470860 | ||||||||
\(629\) | 5.51130e6 | 0.555427 | ||||||||
\(630\) | −5.97465e6 | −0.599737 | ||||||||
\(631\) | 4.20504e6 | 0.420433 | 0.210216 | − | 0.977655i | \(-0.432583\pi\) | ||||
0.210216 | + | 0.977655i | \(0.432583\pi\) | |||||||
\(632\) | 1.12879e6 | 0.112414 | ||||||||
\(633\) | 14963.0 | 0.00148426 | ||||||||
\(634\) | 5.81541e6 | 0.574589 | ||||||||
\(635\) | 5.68813e6 | 0.559803 | ||||||||
\(636\) | −753268. | −0.0738426 | ||||||||
\(637\) | 4.10729e7 | 4.01058 | ||||||||
\(638\) | 9.07785e6 | 0.882940 | ||||||||
\(639\) | 6.85123e6 | 0.663768 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | 7.83415e6 | 0.753090 | 0.376545 | − | 0.926398i | \(-0.377112\pi\) | ||||
0.376545 | + | 0.926398i | \(0.377112\pi\) | |||||||
\(642\) | −1.05464e6 | −0.100987 | ||||||||
\(643\) | −1.18578e7 | −1.13103 | −0.565517 | − | 0.824737i | \(-0.691323\pi\) | ||||
−0.565517 | + | 0.824737i | \(0.691323\pi\) | |||||||
\(644\) | 2.13525e6 | 0.202878 | ||||||||
\(645\) | −542421. | −0.0513378 | ||||||||
\(646\) | 9.41139e6 | 0.887304 | ||||||||
\(647\) | 5.26318e6 | 0.494297 | 0.247148 | − | 0.968978i | \(-0.420506\pi\) | ||||
0.247148 | + | 0.968978i | \(0.420506\pi\) | |||||||
\(648\) | −3.49375e6 | −0.326855 | ||||||||
\(649\) | 3.67719e7 | 3.42692 | ||||||||
\(650\) | −2.19240e6 | −0.203534 | ||||||||
\(651\) | −5.27899e6 | −0.488201 | ||||||||
\(652\) | −2.61384e6 | −0.240802 | ||||||||
\(653\) | 1.64840e7 | 1.51279 | 0.756397 | − | 0.654113i | \(-0.226958\pi\) | ||||
0.756397 | + | 0.654113i | \(0.226958\pi\) | |||||||
\(654\) | −1.72772e6 | −0.157954 | ||||||||
\(655\) | 5.14892e6 | 0.468935 | ||||||||
\(656\) | −418268. | −0.0379486 | ||||||||
\(657\) | −600373. | −0.0542635 | ||||||||
\(658\) | 1.91618e7 | 1.72533 | ||||||||
\(659\) | −1.73924e7 | −1.56008 | −0.780038 | − | 0.625732i | \(-0.784800\pi\) | ||||
−0.780038 | + | 0.625732i | \(0.784800\pi\) | |||||||
\(660\) | 734676. | 0.0656502 | ||||||||
\(661\) | 1.03745e7 | 0.923553 | 0.461776 | − | 0.886996i | \(-0.347212\pi\) | ||||
0.461776 | + | 0.886996i | \(0.347212\pi\) | |||||||
\(662\) | 55365.2 | 0.00491012 | ||||||||
\(663\) | 2.97042e6 | 0.262443 | ||||||||
\(664\) | −5.60703e6 | −0.493529 | ||||||||
\(665\) | −1.08812e7 | −0.954160 | ||||||||
\(666\) | −3.82842e6 | −0.334453 | ||||||||
\(667\) | −1.62348e6 | −0.141297 | ||||||||
\(668\) | −4.22737e6 | −0.366547 | ||||||||
\(669\) | −3.20895e6 | −0.277202 | ||||||||
\(670\) | 939724. | 0.0808748 | ||||||||
\(671\) | −1.40738e7 | −1.20672 | ||||||||
\(672\) | −641622. | −0.0548095 | ||||||||
\(673\) | −2.69576e6 | −0.229426 | −0.114713 | − | 0.993399i | \(-0.536595\pi\) | ||||
−0.114713 | + | 0.993399i | \(0.536595\pi\) | |||||||
\(674\) | 7.72662e6 | 0.655148 | ||||||||
\(675\) | 744858. | 0.0629237 | ||||||||
\(676\) | 6.36429e6 | 0.535652 | ||||||||
\(677\) | −229429. | −0.0192387 | −0.00961937 | − | 0.999954i | \(-0.503062\pi\) | ||||
−0.00961937 | + | 0.999954i | \(0.503062\pi\) | |||||||
\(678\) | 2.60402e6 | 0.217555 | ||||||||
\(679\) | −1.04268e7 | −0.867914 | ||||||||
\(680\) | 2.18199e6 | 0.180959 | ||||||||
\(681\) | −159690. | −0.0131950 | ||||||||
\(682\) | −2.49208e7 | −2.05164 | ||||||||
\(683\) | 1.09516e7 | 0.898313 | 0.449157 | − | 0.893453i | \(-0.351725\pi\) | ||||
0.449157 | + | 0.893453i | \(0.351725\pi\) | |||||||
\(684\) | −6.53763e6 | −0.534293 | ||||||||
\(685\) | −8.01619e6 | −0.652742 | ||||||||
\(686\) | 3.03017e7 | 2.45843 | ||||||||
\(687\) | −185419. | −0.0149886 | ||||||||
\(688\) | 2.23631e6 | 0.180119 | ||||||||
\(689\) | 1.66228e7 | 1.33400 | ||||||||
\(690\) | −131390. | −0.0105060 | ||||||||
\(691\) | −2.33754e7 | −1.86236 | −0.931181 | − | 0.364558i | \(-0.881220\pi\) | ||||
−0.931181 | + | 0.364558i | \(0.881220\pi\) | |||||||
\(692\) | 5.47008e6 | 0.434239 | ||||||||
\(693\) | −4.41817e7 | −3.49470 | ||||||||
\(694\) | 9.76963e6 | 0.769980 | ||||||||
\(695\) | 4.86839e6 | 0.382317 | ||||||||
\(696\) | 487841. | 0.0381729 | ||||||||
\(697\) | 2.22817e6 | 0.173726 | ||||||||
\(698\) | −3.82683e6 | −0.297304 | ||||||||
\(699\) | 405114. | 0.0313606 | ||||||||
\(700\) | −2.52275e6 | −0.194594 | ||||||||
\(701\) | −285635. | −0.0219542 | −0.0109771 | − | 0.999940i | \(-0.503494\pi\) | ||||
−0.0109771 | + | 0.999940i | \(0.503494\pi\) | |||||||
\(702\) | −4.18056e6 | −0.320178 | ||||||||
\(703\) | −6.97241e6 | −0.532102 | ||||||||
\(704\) | −3.02894e6 | −0.230334 | ||||||||
\(705\) | −1.17909e6 | −0.0893459 | ||||||||
\(706\) | −1.48440e7 | −1.12083 | ||||||||
\(707\) | 1.30850e7 | 0.984520 | ||||||||
\(708\) | 1.97611e6 | 0.148159 | ||||||||
\(709\) | 7.04217e6 | 0.526127 | 0.263064 | − | 0.964778i | \(-0.415267\pi\) | ||||
0.263064 | + | 0.964778i | \(0.415267\pi\) | |||||||
\(710\) | 2.89288e6 | 0.215369 | ||||||||
\(711\) | 4.17709e6 | 0.309884 | ||||||||
\(712\) | −2.12602e6 | −0.157169 | ||||||||
\(713\) | 4.45684e6 | 0.328325 | ||||||||
\(714\) | 3.41800e6 | 0.250915 | ||||||||
\(715\) | −1.62125e7 | −1.18600 | ||||||||
\(716\) | 4.98826e6 | 0.363636 | ||||||||
\(717\) | 1.13783e6 | 0.0826569 | ||||||||
\(718\) | 5.33612e6 | 0.386291 | ||||||||
\(719\) | 1.60147e7 | 1.15531 | 0.577653 | − | 0.816283i | \(-0.303969\pi\) | ||||
0.577653 | + | 0.816283i | \(0.303969\pi\) | |||||||
\(720\) | −1.51572e6 | −0.108965 | ||||||||
\(721\) | −1.37061e7 | −0.981923 | ||||||||
\(722\) | −2.00207e6 | −0.142934 | ||||||||
\(723\) | −4.33978e6 | −0.308761 | ||||||||
\(724\) | −4.21102e6 | −0.298566 | ||||||||
\(725\) | 1.91811e6 | 0.135528 | ||||||||
\(726\) | 3.83280e6 | 0.269882 | ||||||||
\(727\) | 1.09411e7 | 0.767758 | 0.383879 | − | 0.923383i | \(-0.374588\pi\) | ||||
0.383879 | + | 0.923383i | \(0.374588\pi\) | |||||||
\(728\) | 1.41590e7 | 0.990160 | ||||||||
\(729\) | −1.22093e7 | −0.850886 | ||||||||
\(730\) | −253503. | −0.0176066 | ||||||||
\(731\) | −1.19131e7 | −0.824575 | ||||||||
\(732\) | −756321. | −0.0521709 | ||||||||
\(733\) | 1.33642e7 | 0.918718 | 0.459359 | − | 0.888251i | \(-0.348079\pi\) | ||||
0.459359 | + | 0.888251i | \(0.348079\pi\) | |||||||
\(734\) | −1.16879e7 | −0.800748 | ||||||||
\(735\) | −2.90818e6 | −0.198565 | ||||||||
\(736\) | 541696. | 0.0368605 | ||||||||
\(737\) | 6.94914e6 | 0.471262 | ||||||||
\(738\) | −1.54780e6 | −0.104610 | ||||||||
\(739\) | 9.50621e6 | 0.640319 | 0.320159 | − | 0.947364i | \(-0.396264\pi\) | ||||
0.320159 | + | 0.947364i | \(0.396264\pi\) | |||||||
\(740\) | −1.61652e6 | −0.108518 | ||||||||
\(741\) | −3.75792e6 | −0.251421 | ||||||||
\(742\) | 1.91275e7 | 1.27540 | ||||||||
\(743\) | −9.84795e6 | −0.654446 | −0.327223 | − | 0.944947i | \(-0.606113\pi\) | ||||
−0.327223 | + | 0.944947i | \(0.606113\pi\) | |||||||
\(744\) | −1.33924e6 | −0.0887002 | ||||||||
\(745\) | −9.82576e6 | −0.648598 | ||||||||
\(746\) | 1.22604e7 | 0.806599 | ||||||||
\(747\) | −2.07487e7 | −1.36047 | ||||||||
\(748\) | 1.61355e7 | 1.05446 | ||||||||
\(749\) | 2.67801e7 | 1.74425 | ||||||||
\(750\) | 155233. | 0.0100770 | ||||||||
\(751\) | −1.90181e7 | −1.23046 | −0.615230 | − | 0.788348i | \(-0.710937\pi\) | ||||
−0.615230 | + | 0.788348i | \(0.710937\pi\) | |||||||
\(752\) | 4.86119e6 | 0.313471 | ||||||||
\(753\) | 1.26619e6 | 0.0813788 | ||||||||
\(754\) | −1.07655e7 | −0.689612 | ||||||||
\(755\) | −133956. | −0.00855253 | ||||||||
\(756\) | −4.81047e6 | −0.306114 | ||||||||
\(757\) | −1.70495e7 | −1.08136 | −0.540681 | − | 0.841227i | \(-0.681834\pi\) | ||||
−0.540681 | + | 0.841227i | \(0.681834\pi\) | |||||||
\(758\) | −1.18615e6 | −0.0749836 | ||||||||
\(759\) | −971609. | −0.0612191 | ||||||||
\(760\) | −2.76046e6 | −0.173359 | ||||||||
\(761\) | −2.75852e6 | −0.172669 | −0.0863346 | − | 0.996266i | \(-0.527515\pi\) | ||||
−0.0863346 | + | 0.996266i | \(0.527515\pi\) | |||||||
\(762\) | 2.26045e6 | 0.141029 | ||||||||
\(763\) | 4.38715e7 | 2.72817 | ||||||||
\(764\) | −1.20865e7 | −0.749145 | ||||||||
\(765\) | 8.07442e6 | 0.498836 | ||||||||
\(766\) | −9.01548e6 | −0.555158 | ||||||||
\(767\) | −4.36079e7 | −2.67656 | ||||||||
\(768\) | −162774. | −0.00995823 | ||||||||
\(769\) | 1.87467e7 | 1.14316 | 0.571581 | − | 0.820546i | \(-0.306330\pi\) | ||||
0.571581 | + | 0.820546i | \(0.306330\pi\) | |||||||
\(770\) | −1.86554e7 | −1.13391 | ||||||||
\(771\) | −630354. | −0.0381899 | ||||||||
\(772\) | −1.23811e7 | −0.747683 | ||||||||
\(773\) | 1.37482e7 | 0.827553 | 0.413776 | − | 0.910379i | \(-0.364210\pi\) | ||||
0.413776 | + | 0.910379i | \(0.364210\pi\) | |||||||
\(774\) | 8.27542e6 | 0.496521 | ||||||||
\(775\) | −5.26565e6 | −0.314918 | ||||||||
\(776\) | −2.64519e6 | −0.157690 | ||||||||
\(777\) | −2.53221e6 | −0.150469 | ||||||||
\(778\) | 3.82673e6 | 0.226662 | ||||||||
\(779\) | −2.81888e6 | −0.166430 | ||||||||
\(780\) | −871256. | −0.0512754 | ||||||||
\(781\) | 2.13924e7 | 1.25497 | ||||||||
\(782\) | −2.88568e6 | −0.168745 | ||||||||
\(783\) | 3.65752e6 | 0.213197 | ||||||||
\(784\) | 1.19899e7 | 0.696667 | ||||||||
\(785\) | 7.27129e6 | 0.421150 | ||||||||
\(786\) | 2.04617e6 | 0.118137 | ||||||||
\(787\) | 6.89984e6 | 0.397102 | 0.198551 | − | 0.980091i | \(-0.436376\pi\) | ||||
0.198551 | + | 0.980091i | \(0.436376\pi\) | |||||||
\(788\) | 7.44160e6 | 0.426924 | ||||||||
\(789\) | 610047. | 0.0348876 | ||||||||
\(790\) | 1.76374e6 | 0.100547 | ||||||||
\(791\) | −6.61230e7 | −3.75761 | ||||||||
\(792\) | −1.12085e7 | −0.634945 | ||||||||
\(793\) | 1.66902e7 | 0.942493 | ||||||||
\(794\) | −8.57742e6 | −0.482843 | ||||||||
\(795\) | −1.17698e6 | −0.0660468 | ||||||||
\(796\) | −9.62386e6 | −0.538353 | ||||||||
\(797\) | 1.13532e7 | 0.633098 | 0.316549 | − | 0.948576i | \(-0.397476\pi\) | ||||
0.316549 | + | 0.948576i | \(0.397476\pi\) | |||||||
\(798\) | −4.32415e6 | −0.240377 | ||||||||
\(799\) | −2.58961e7 | −1.43505 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −7.86729e6 | −0.433255 | ||||||||
\(802\) | −2.81150e6 | −0.154348 | ||||||||
\(803\) | −1.87462e6 | −0.102595 | ||||||||
\(804\) | 373444. | 0.0203744 | ||||||||
\(805\) | 3.33633e6 | 0.181459 | ||||||||
\(806\) | 2.95537e7 | 1.60241 | ||||||||
\(807\) | 3.25299e6 | 0.175833 | ||||||||
\(808\) | 3.31955e6 | 0.178875 | ||||||||
\(809\) | 2.58652e7 | 1.38946 | 0.694728 | − | 0.719273i | \(-0.255525\pi\) | ||||
0.694728 | + | 0.719273i | \(0.255525\pi\) | |||||||
\(810\) | −5.45899e6 | −0.292348 | ||||||||
\(811\) | 3.88499e6 | 0.207414 | 0.103707 | − | 0.994608i | \(-0.466930\pi\) | ||||
0.103707 | + | 0.994608i | \(0.466930\pi\) | |||||||
\(812\) | −1.23876e7 | −0.659320 | ||||||||
\(813\) | −832815. | −0.0441898 | ||||||||
\(814\) | −1.19540e7 | −0.632340 | ||||||||
\(815\) | −4.08413e6 | −0.215380 | ||||||||
\(816\) | 867117. | 0.0455882 | ||||||||
\(817\) | 1.50714e7 | 0.789946 | ||||||||
\(818\) | −1.08643e7 | −0.567699 | ||||||||
\(819\) | 5.23953e7 | 2.72950 | ||||||||
\(820\) | −653544. | −0.0339422 | ||||||||
\(821\) | −1.98988e7 | −1.03031 | −0.515157 | − | 0.857096i | \(-0.672266\pi\) | ||||
−0.515157 | + | 0.857096i | \(0.672266\pi\) | |||||||
\(822\) | −3.18562e6 | −0.164442 | ||||||||
\(823\) | 3.02715e7 | 1.55788 | 0.778941 | − | 0.627097i | \(-0.215757\pi\) | ||||
0.778941 | + | 0.627097i | \(0.215757\pi\) | |||||||
\(824\) | −3.47714e6 | −0.178404 | ||||||||
\(825\) | 1.14793e6 | 0.0587193 | ||||||||
\(826\) | −5.01786e7 | −2.55899 | ||||||||
\(827\) | 1.36026e7 | 0.691605 | 0.345803 | − | 0.938307i | \(-0.387607\pi\) | ||||
0.345803 | + | 0.938307i | \(0.387607\pi\) | |||||||
\(828\) | 2.00454e6 | 0.101610 | ||||||||
\(829\) | 2.08242e6 | 0.105240 | 0.0526202 | − | 0.998615i | \(-0.483243\pi\) | ||||
0.0526202 | + | 0.998615i | \(0.483243\pi\) | |||||||
\(830\) | −8.76098e6 | −0.441426 | ||||||||
\(831\) | −3.08670e6 | −0.155057 | ||||||||
\(832\) | 3.59203e6 | 0.179900 | ||||||||
\(833\) | −6.38716e7 | −3.18930 | ||||||||
\(834\) | 1.93469e6 | 0.0963155 | ||||||||
\(835\) | −6.60527e6 | −0.327850 | ||||||||
\(836\) | −2.04132e7 | −1.01017 | ||||||||
\(837\) | −1.00407e7 | −0.495395 | ||||||||
\(838\) | 1.51506e7 | 0.745279 | ||||||||
\(839\) | 1.26418e7 | 0.620016 | 0.310008 | − | 0.950734i | \(-0.399668\pi\) | ||||
0.310008 | + | 0.950734i | \(0.399668\pi\) | |||||||
\(840\) | −1.00253e6 | −0.0490231 | ||||||||
\(841\) | −1.10926e7 | −0.540807 | ||||||||
\(842\) | 6.91093e6 | 0.335936 | ||||||||
\(843\) | 1.36387e6 | 0.0661003 | ||||||||
\(844\) | −96390.4 | −0.00465777 | ||||||||
\(845\) | 9.94420e6 | 0.479102 | ||||||||
\(846\) | 1.79887e7 | 0.864122 | ||||||||
\(847\) | −9.73250e7 | −4.66140 | ||||||||
\(848\) | 4.85248e6 | 0.231726 | ||||||||
\(849\) | 1.70800e6 | 0.0813241 | ||||||||
\(850\) | 3.40936e6 | 0.161855 | ||||||||
\(851\) | 2.13785e6 | 0.101194 | ||||||||
\(852\) | 1.14962e6 | 0.0542571 | ||||||||
\(853\) | −2.77167e7 | −1.30427 | −0.652137 | − | 0.758101i | \(-0.726127\pi\) | ||||
−0.652137 | + | 0.758101i | \(0.726127\pi\) | |||||||
\(854\) | 1.92050e7 | 0.901093 | ||||||||
\(855\) | −1.02150e7 | −0.477887 | ||||||||
\(856\) | 6.79389e6 | 0.316909 | ||||||||
\(857\) | −1.68037e7 | −0.781541 | −0.390770 | − | 0.920488i | \(-0.627791\pi\) | ||||
−0.390770 | + | 0.920488i | \(0.627791\pi\) | |||||||
\(858\) | −6.44282e6 | −0.298784 | ||||||||
\(859\) | 6.32943e6 | 0.292672 | 0.146336 | − | 0.989235i | \(-0.453252\pi\) | ||||
0.146336 | + | 0.989235i | \(0.453252\pi\) | |||||||
\(860\) | 3.49423e6 | 0.161104 | ||||||||
\(861\) | −1.02375e6 | −0.0470637 | ||||||||
\(862\) | 2.01962e7 | 0.925766 | ||||||||
\(863\) | −3.58594e7 | −1.63899 | −0.819494 | − | 0.573088i | \(-0.805745\pi\) | ||||
−0.819494 | + | 0.573088i | \(0.805745\pi\) | |||||||
\(864\) | −1.22038e6 | −0.0556172 | ||||||||
\(865\) | 8.54701e6 | 0.388395 | ||||||||
\(866\) | −149828. | −0.00678888 | ||||||||
\(867\) | −1.09269e6 | −0.0493684 | ||||||||
\(868\) | 3.40068e7 | 1.53203 | ||||||||
\(869\) | 1.30426e7 | 0.585890 | ||||||||
\(870\) | 762251. | 0.0341429 | ||||||||
\(871\) | −8.24101e6 | −0.368074 | ||||||||
\(872\) | 1.11298e7 | 0.495676 | ||||||||
\(873\) | −9.78850e6 | −0.434691 | ||||||||
\(874\) | 3.65071e6 | 0.161658 | ||||||||
\(875\) | −3.94179e6 | −0.174050 | ||||||||
\(876\) | −100741. | −0.00443555 | ||||||||
\(877\) | 757238. | 0.0332455 | 0.0166228 | − | 0.999862i | \(-0.494709\pi\) | ||||
0.0166228 | + | 0.999862i | \(0.494709\pi\) | |||||||
\(878\) | 398694. | 0.0174544 | ||||||||
\(879\) | 3.23673e6 | 0.141297 | ||||||||
\(880\) | −4.73272e6 | −0.206017 | ||||||||
\(881\) | 3.19130e6 | 0.138525 | 0.0692625 | − | 0.997598i | \(-0.477935\pi\) | ||||
0.0692625 | + | 0.997598i | \(0.477935\pi\) | |||||||
\(882\) | 4.43684e7 | 1.92045 | ||||||||
\(883\) | 1.92363e7 | 0.830271 | 0.415136 | − | 0.909760i | \(-0.363734\pi\) | ||||
0.415136 | + | 0.909760i | \(0.363734\pi\) | |||||||
\(884\) | −1.91352e7 | −0.823573 | ||||||||
\(885\) | 3.08767e6 | 0.132517 | ||||||||
\(886\) | 1.84124e7 | 0.787999 | ||||||||
\(887\) | −2.68483e7 | −1.14580 | −0.572898 | − | 0.819627i | \(-0.694181\pi\) | ||||
−0.572898 | + | 0.819627i | \(0.694181\pi\) | |||||||
\(888\) | −642402. | −0.0273385 | ||||||||
\(889\) | −5.73988e7 | −2.43584 | ||||||||
\(890\) | −3.32190e6 | −0.140576 | ||||||||
\(891\) | −4.03685e7 | −1.70353 | ||||||||
\(892\) | 2.06717e7 | 0.869891 | ||||||||
\(893\) | 3.27615e7 | 1.37479 | ||||||||
\(894\) | −3.90474e6 | −0.163398 | ||||||||
\(895\) | 7.79415e6 | 0.325246 | ||||||||
\(896\) | 4.13327e6 | 0.171998 | ||||||||
\(897\) | 1.15224e6 | 0.0478146 | ||||||||
\(898\) | −1.49809e7 | −0.619938 | ||||||||
\(899\) | −2.58562e7 | −1.06700 | ||||||||
\(900\) | −2.36831e6 | −0.0974613 | ||||||||
\(901\) | −2.58498e7 | −1.06083 | ||||||||
\(902\) | −4.83287e6 | −0.197783 | ||||||||
\(903\) | 5.47356e6 | 0.223383 | ||||||||
\(904\) | −1.67749e7 | −0.682712 | ||||||||
\(905\) | −6.57971e6 | −0.267046 | ||||||||
\(906\) | −53233.8 | −0.00215460 | ||||||||
\(907\) | 7.62585e6 | 0.307801 | 0.153901 | − | 0.988086i | \(-0.450816\pi\) | ||||
0.153901 | + | 0.988086i | \(0.450816\pi\) | |||||||
\(908\) | 1.02871e6 | 0.0414074 | ||||||||
\(909\) | 1.22839e7 | 0.493092 | ||||||||
\(910\) | 2.21235e7 | 0.885626 | ||||||||
\(911\) | −3.05793e6 | −0.122076 | −0.0610381 | − | 0.998135i | \(-0.519441\pi\) | ||||
−0.0610381 | + | 0.998135i | \(0.519441\pi\) | |||||||
\(912\) | −1.09700e6 | −0.0436737 | ||||||||
\(913\) | −6.47863e7 | −2.57221 | ||||||||
\(914\) | −1.99898e6 | −0.0791485 | ||||||||
\(915\) | −1.18175e6 | −0.0466631 | ||||||||
\(916\) | 1.19445e6 | 0.0470359 | ||||||||
\(917\) | −5.19577e7 | −2.04045 | ||||||||
\(918\) | 6.50109e6 | 0.254612 | ||||||||
\(919\) | −1.40082e7 | −0.547134 | −0.273567 | − | 0.961853i | \(-0.588204\pi\) | ||||
−0.273567 | + | 0.961853i | \(0.588204\pi\) | |||||||
\(920\) | 846400. | 0.0329690 | ||||||||
\(921\) | −6.65358e6 | −0.258468 | ||||||||
\(922\) | −6.95739e6 | −0.269537 | ||||||||
\(923\) | −2.53694e7 | −0.980180 | ||||||||
\(924\) | −7.41361e6 | −0.285660 | ||||||||
\(925\) | −2.52581e6 | −0.0970615 | ||||||||
\(926\) | −3.46723e6 | −0.132879 | ||||||||
\(927\) | −1.28671e7 | −0.491792 | ||||||||
\(928\) | −3.14262e6 | −0.119791 | ||||||||
\(929\) | 1.68894e7 | 0.642061 | 0.321030 | − | 0.947069i | \(-0.395971\pi\) | ||||
0.321030 | + | 0.947069i | \(0.395971\pi\) | |||||||
\(930\) | −2.09256e6 | −0.0793359 | ||||||||
\(931\) | 8.08047e7 | 3.05536 | ||||||||
\(932\) | −2.60971e6 | −0.0984129 | ||||||||
\(933\) | −6.62362e6 | −0.249110 | ||||||||
\(934\) | 6.09362e6 | 0.228564 | ||||||||
\(935\) | 2.52118e7 | 0.943135 | ||||||||
\(936\) | 1.32923e7 | 0.495917 | ||||||||
\(937\) | −7.56415e6 | −0.281457 | −0.140728 | − | 0.990048i | \(-0.544944\pi\) | ||||
−0.140728 | + | 0.990048i | \(0.544944\pi\) | |||||||
\(938\) | −9.48274e6 | −0.351906 | ||||||||
\(939\) | −2.32409e6 | −0.0860178 | ||||||||
\(940\) | 7.59560e6 | 0.280377 | ||||||||
\(941\) | −3.45946e7 | −1.27360 | −0.636802 | − | 0.771027i | \(-0.719743\pi\) | ||||
−0.636802 | + | 0.771027i | \(0.719743\pi\) | |||||||
\(942\) | 2.88959e6 | 0.106099 | ||||||||
\(943\) | 864312. | 0.0316513 | ||||||||
\(944\) | −1.27299e7 | −0.464938 | ||||||||
\(945\) | −7.51636e6 | −0.273797 | ||||||||
\(946\) | 2.58394e7 | 0.938758 | ||||||||
\(947\) | 2.11440e7 | 0.766149 | 0.383074 | − | 0.923717i | \(-0.374865\pi\) | ||||
0.383074 | + | 0.923717i | \(0.374865\pi\) | |||||||
\(948\) | 700907. | 0.0253303 | ||||||||
\(949\) | 2.22312e6 | 0.0801304 | ||||||||
\(950\) | −4.31322e6 | −0.155057 | ||||||||
\(951\) | 3.61099e6 | 0.129472 | ||||||||
\(952\) | −2.20184e7 | −0.787397 | ||||||||
\(953\) | −4.32490e6 | −0.154257 | −0.0771283 | − | 0.997021i | \(-0.524575\pi\) | ||||
−0.0771283 | + | 0.997021i | \(0.524575\pi\) | |||||||
\(954\) | 1.79565e7 | 0.638781 | ||||||||
\(955\) | −1.88851e7 | −0.670056 | ||||||||
\(956\) | −7.32979e6 | −0.259386 | ||||||||
\(957\) | 5.63675e6 | 0.198952 | ||||||||
\(958\) | −3.69232e7 | −1.29983 | ||||||||
\(959\) | 8.08913e7 | 2.84024 | ||||||||
\(960\) | −254335. | −0.00890691 | ||||||||
\(961\) | 4.23521e7 | 1.47933 | ||||||||
\(962\) | 1.41763e7 | 0.493883 | ||||||||
\(963\) | 2.51407e7 | 0.873597 | ||||||||
\(964\) | 2.79565e7 | 0.968924 | ||||||||
\(965\) | −1.93455e7 | −0.668748 | ||||||||
\(966\) | 1.32585e6 | 0.0457143 | ||||||||
\(967\) | −1.38356e7 | −0.475807 | −0.237904 | − | 0.971289i | \(-0.576460\pi\) | ||||
−0.237904 | + | 0.971289i | \(0.576460\pi\) | |||||||
\(968\) | −2.46906e7 | −0.846920 | ||||||||
\(969\) | 5.84385e6 | 0.199936 | ||||||||
\(970\) | −4.13312e6 | −0.141042 | ||||||||
\(971\) | 3.62720e7 | 1.23459 | 0.617296 | − | 0.786731i | \(-0.288228\pi\) | ||||
0.617296 | + | 0.786731i | \(0.288228\pi\) | |||||||
\(972\) | −6.80301e6 | −0.230959 | ||||||||
\(973\) | −4.91269e7 | −1.66356 | ||||||||
\(974\) | 4.90997e6 | 0.165837 | ||||||||
\(975\) | −1.36134e6 | −0.0458621 | ||||||||
\(976\) | 4.87215e6 | 0.163718 | ||||||||
\(977\) | −1.26207e7 | −0.423006 | −0.211503 | − | 0.977377i | \(-0.567836\pi\) | ||||
−0.211503 | + | 0.977377i | \(0.567836\pi\) | |||||||
\(978\) | −1.62302e6 | −0.0542597 | ||||||||
\(979\) | −2.45650e7 | −0.819144 | ||||||||
\(980\) | 1.87342e7 | 0.623118 | ||||||||
\(981\) | 4.11858e7 | 1.36639 | ||||||||
\(982\) | 1.19751e7 | 0.396277 | ||||||||
\(983\) | 3.30183e7 | 1.08986 | 0.544930 | − | 0.838481i | \(-0.316556\pi\) | ||||
0.544930 | + | 0.838481i | \(0.316556\pi\) | |||||||
\(984\) | −259717. | −0.00855091 | ||||||||
\(985\) | 1.16275e7 | 0.381852 | ||||||||
\(986\) | 1.67411e7 | 0.548394 | ||||||||
\(987\) | 1.18982e7 | 0.388766 | ||||||||
\(988\) | 2.42082e7 | 0.788986 | ||||||||
\(989\) | −4.62112e6 | −0.150230 | ||||||||
\(990\) | −1.75133e7 | −0.567912 | ||||||||
\(991\) | 5.10495e7 | 1.65123 | 0.825614 | − | 0.564235i | \(-0.190829\pi\) | ||||
0.825614 | + | 0.564235i | \(0.190829\pi\) | |||||||
\(992\) | 8.62724e6 | 0.278351 | ||||||||
\(993\) | 34378.1 | 0.00110639 | ||||||||
\(994\) | −2.91920e7 | −0.937125 | ||||||||
\(995\) | −1.50373e7 | −0.481517 | ||||||||
\(996\) | −3.48159e6 | −0.111206 | ||||||||
\(997\) | −8.22079e6 | −0.261924 | −0.130962 | − | 0.991387i | \(-0.541807\pi\) | ||||
−0.130962 | + | 0.991387i | \(0.541807\pi\) | |||||||
\(998\) | 494198. | 0.0157063 | ||||||||
\(999\) | −4.81632e6 | −0.152687 |
(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 | 230.6.a.f.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.f.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial |