Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.13459 | −1.26123 | −0.630615 | − | 0.776096i | \(-0.717197\pi\) | ||||
−0.630615 | + | 0.776096i | \(0.717197\pi\) | |||||||
\(3\) | −23.4497 | −1.50430 | −0.752150 | − | 0.658991i | \(-0.770983\pi\) | ||||
−0.752150 | + | 0.658991i | \(0.770983\pi\) | |||||||
\(4\) | 18.9024 | 0.590701 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 167.304 | 1.89727 | ||||||||
\(7\) | −10.1832 | −0.0785489 | −0.0392745 | − | 0.999228i | \(-0.512505\pi\) | ||||
−0.0392745 | + | 0.999228i | \(0.512505\pi\) | |||||||
\(8\) | 93.4458 | 0.516220 | ||||||||
\(9\) | 306.890 | 1.26292 | ||||||||
\(10\) | 178.365 | 0.564039 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −443.257 | −0.888592 | ||||||||
\(13\) | −724.498 | −1.18899 | −0.594496 | − | 0.804099i | \(-0.702648\pi\) | ||||
−0.594496 | + | 0.804099i | \(0.702648\pi\) | |||||||
\(14\) | 72.6532 | 0.0990682 | ||||||||
\(15\) | 586.243 | 0.672744 | ||||||||
\(16\) | −1271.58 | −1.24177 | ||||||||
\(17\) | 1368.41 | 1.14840 | 0.574201 | − | 0.818714i | \(-0.305313\pi\) | ||||
0.574201 | + | 0.818714i | \(0.305313\pi\) | |||||||
\(18\) | −2189.53 | −1.59283 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | −472.561 | −0.264170 | ||||||||
\(21\) | 238.794 | 0.118161 | ||||||||
\(22\) | −863.286 | −0.380275 | ||||||||
\(23\) | 2972.81 | 1.17178 | 0.585892 | − | 0.810389i | \(-0.300744\pi\) | ||||
0.585892 | + | 0.810389i | \(0.300744\pi\) | |||||||
\(24\) | −2191.28 | −0.776550 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 5169.00 | 1.49959 | ||||||||
\(27\) | −1498.20 | −0.395512 | ||||||||
\(28\) | −192.488 | −0.0463989 | ||||||||
\(29\) | −1773.14 | −0.391514 | −0.195757 | − | 0.980652i | \(-0.562716\pi\) | ||||
−0.195757 | + | 0.980652i | \(0.562716\pi\) | |||||||
\(30\) | −4182.61 | −0.848485 | ||||||||
\(31\) | −6189.60 | −1.15680 | −0.578400 | − | 0.815753i | \(-0.696323\pi\) | ||||
−0.578400 | + | 0.815753i | \(0.696323\pi\) | |||||||
\(32\) | 6081.91 | 1.04994 | ||||||||
\(33\) | −2837.42 | −0.453564 | ||||||||
\(34\) | −9763.06 | −1.44840 | ||||||||
\(35\) | 254.581 | 0.0351281 | ||||||||
\(36\) | 5800.97 | 0.746009 | ||||||||
\(37\) | −9314.71 | −1.11858 | −0.559288 | − | 0.828974i | \(-0.688925\pi\) | ||||
−0.559288 | + | 0.828974i | \(0.688925\pi\) | |||||||
\(38\) | −2575.59 | −0.289346 | ||||||||
\(39\) | 16989.3 | 1.78860 | ||||||||
\(40\) | −2336.14 | −0.230861 | ||||||||
\(41\) | 12420.1 | 1.15389 | 0.576946 | − | 0.816782i | \(-0.304244\pi\) | ||||
0.576946 | + | 0.816782i | \(0.304244\pi\) | |||||||
\(42\) | −1703.70 | −0.149028 | ||||||||
\(43\) | −22399.2 | −1.84740 | −0.923702 | − | 0.383113i | \(-0.874852\pi\) | ||||
−0.923702 | + | 0.383113i | \(0.874852\pi\) | |||||||
\(44\) | 2287.20 | 0.178103 | ||||||||
\(45\) | −7672.25 | −0.564795 | ||||||||
\(46\) | −21209.8 | −1.47789 | ||||||||
\(47\) | −14672.3 | −0.968842 | −0.484421 | − | 0.874835i | \(-0.660970\pi\) | ||||
−0.484421 | + | 0.874835i | \(0.660970\pi\) | |||||||
\(48\) | 29818.1 | 1.86800 | ||||||||
\(49\) | −16703.3 | −0.993830 | ||||||||
\(50\) | −4459.12 | −0.252246 | ||||||||
\(51\) | −32088.9 | −1.72754 | ||||||||
\(52\) | −13694.8 | −0.702339 | ||||||||
\(53\) | 16934.8 | 0.828116 | 0.414058 | − | 0.910250i | \(-0.364111\pi\) | ||||
0.414058 | + | 0.910250i | \(0.364111\pi\) | |||||||
\(54\) | 10689.0 | 0.498832 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | −951.579 | −0.0405485 | ||||||||
\(57\) | −8465.35 | −0.345110 | ||||||||
\(58\) | 12650.6 | 0.493789 | ||||||||
\(59\) | −14147.6 | −0.529119 | −0.264560 | − | 0.964369i | \(-0.585227\pi\) | ||||
−0.264560 | + | 0.964369i | \(0.585227\pi\) | |||||||
\(60\) | 11081.4 | 0.397391 | ||||||||
\(61\) | −49335.1 | −1.69759 | −0.848793 | − | 0.528726i | \(-0.822670\pi\) | ||||
−0.848793 | + | 0.528726i | \(0.822670\pi\) | |||||||
\(62\) | 44160.3 | 1.45899 | ||||||||
\(63\) | −3125.13 | −0.0992011 | ||||||||
\(64\) | −2701.56 | −0.0824450 | ||||||||
\(65\) | 18112.5 | 0.531733 | ||||||||
\(66\) | 20243.8 | 0.572048 | ||||||||
\(67\) | 49933.3 | 1.35895 | 0.679475 | − | 0.733699i | \(-0.262208\pi\) | ||||
0.679475 | + | 0.733699i | \(0.262208\pi\) | |||||||
\(68\) | 25866.3 | 0.678363 | ||||||||
\(69\) | −69711.6 | −1.76272 | ||||||||
\(70\) | −1816.33 | −0.0443047 | ||||||||
\(71\) | 3606.70 | 0.0849111 | 0.0424556 | − | 0.999098i | \(-0.486482\pi\) | ||||
0.0424556 | + | 0.999098i | \(0.486482\pi\) | |||||||
\(72\) | 28677.6 | 0.651945 | ||||||||
\(73\) | −37981.1 | −0.834181 | −0.417090 | − | 0.908865i | \(-0.636950\pi\) | ||||
−0.417090 | + | 0.908865i | \(0.636950\pi\) | |||||||
\(74\) | 66456.7 | 1.41078 | ||||||||
\(75\) | −14656.1 | −0.300860 | ||||||||
\(76\) | 6823.78 | 0.135516 | ||||||||
\(77\) | −1232.17 | −0.0236834 | ||||||||
\(78\) | −121212. | −2.25584 | ||||||||
\(79\) | 51992.1 | 0.937281 | 0.468641 | − | 0.883389i | \(-0.344744\pi\) | ||||
0.468641 | + | 0.883389i | \(0.344744\pi\) | |||||||
\(80\) | 31789.4 | 0.555338 | ||||||||
\(81\) | −39441.9 | −0.667951 | ||||||||
\(82\) | −88612.3 | −1.45532 | ||||||||
\(83\) | 110613. | 1.76242 | 0.881209 | − | 0.472726i | \(-0.156730\pi\) | ||||
0.881209 | + | 0.472726i | \(0.156730\pi\) | |||||||
\(84\) | 4513.79 | 0.0697980 | ||||||||
\(85\) | −34210.3 | −0.513581 | ||||||||
\(86\) | 159809. | 2.33000 | ||||||||
\(87\) | 41579.6 | 0.588955 | ||||||||
\(88\) | 11306.9 | 0.155646 | ||||||||
\(89\) | 72518.5 | 0.970451 | 0.485226 | − | 0.874389i | \(-0.338737\pi\) | ||||
0.485226 | + | 0.874389i | \(0.338737\pi\) | |||||||
\(90\) | 54738.4 | 0.712337 | ||||||||
\(91\) | 7377.73 | 0.0933940 | ||||||||
\(92\) | 56193.4 | 0.692174 | ||||||||
\(93\) | 145144. | 1.74018 | ||||||||
\(94\) | 104681. | 1.22193 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | −142619. | −1.57943 | ||||||||
\(97\) | 29912.4 | 0.322791 | 0.161395 | − | 0.986890i | \(-0.448401\pi\) | ||||
0.161395 | + | 0.986890i | \(0.448401\pi\) | |||||||
\(98\) | 119171. | 1.25345 | ||||||||
\(99\) | 37133.7 | 0.380785 | ||||||||
\(100\) | 11814.0 | 0.118140 | ||||||||
\(101\) | −8365.38 | −0.0815985 | −0.0407992 | − | 0.999167i | \(-0.512990\pi\) | ||||
−0.0407992 | + | 0.999167i | \(0.512990\pi\) | |||||||
\(102\) | 228941. | 2.17883 | ||||||||
\(103\) | 136335. | 1.26623 | 0.633117 | − | 0.774056i | \(-0.281775\pi\) | ||||
0.633117 | + | 0.774056i | \(0.281775\pi\) | |||||||
\(104\) | −67701.3 | −0.613781 | ||||||||
\(105\) | −5969.85 | −0.0528433 | ||||||||
\(106\) | −120823. | −1.04444 | ||||||||
\(107\) | 112954. | 0.953767 | 0.476883 | − | 0.878967i | \(-0.341766\pi\) | ||||
0.476883 | + | 0.878967i | \(0.341766\pi\) | |||||||
\(108\) | −28319.6 | −0.233630 | ||||||||
\(109\) | 135933. | 1.09587 | 0.547936 | − | 0.836520i | \(-0.315414\pi\) | ||||
0.547936 | + | 0.836520i | \(0.315414\pi\) | |||||||
\(110\) | 21582.1 | 0.170064 | ||||||||
\(111\) | 218427. | 1.68267 | ||||||||
\(112\) | 12948.7 | 0.0975399 | ||||||||
\(113\) | −186974. | −1.37748 | −0.688739 | − | 0.725009i | \(-0.741835\pi\) | ||||
−0.688739 | + | 0.725009i | \(0.741835\pi\) | |||||||
\(114\) | 60396.9 | 0.435263 | ||||||||
\(115\) | −74320.3 | −0.524038 | ||||||||
\(116\) | −33516.6 | −0.231268 | ||||||||
\(117\) | −222341. | −1.50160 | ||||||||
\(118\) | 100938. | 0.667341 | ||||||||
\(119\) | −13934.8 | −0.0902058 | ||||||||
\(120\) | 54782.0 | 0.347284 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 351986. | 2.14105 | ||||||||
\(123\) | −291248. | −1.73580 | ||||||||
\(124\) | −116999. | −0.683323 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 22296.5 | 0.125115 | ||||||||
\(127\) | −28581.6 | −0.157245 | −0.0786224 | − | 0.996904i | \(-0.525052\pi\) | ||||
−0.0786224 | + | 0.996904i | \(0.525052\pi\) | |||||||
\(128\) | −175347. | −0.945960 | ||||||||
\(129\) | 525256. | 2.77905 | ||||||||
\(130\) | −129225. | −0.670638 | ||||||||
\(131\) | 45167.0 | 0.229955 | 0.114978 | − | 0.993368i | \(-0.463320\pi\) | ||||
0.114978 | + | 0.993368i | \(0.463320\pi\) | |||||||
\(132\) | −53634.1 | −0.267921 | ||||||||
\(133\) | −3676.14 | −0.0180204 | ||||||||
\(134\) | −356254. | −1.71395 | ||||||||
\(135\) | 37455.0 | 0.176879 | ||||||||
\(136\) | 127872. | 0.592828 | ||||||||
\(137\) | 290883. | 1.32409 | 0.662045 | − | 0.749465i | \(-0.269689\pi\) | ||||
0.662045 | + | 0.749465i | \(0.269689\pi\) | |||||||
\(138\) | 497364. | 2.22319 | ||||||||
\(139\) | −356868. | −1.56665 | −0.783323 | − | 0.621615i | \(-0.786477\pi\) | ||||
−0.783323 | + | 0.621615i | \(0.786477\pi\) | |||||||
\(140\) | 4812.19 | 0.0207502 | ||||||||
\(141\) | 344061. | 1.45743 | ||||||||
\(142\) | −25732.4 | −0.107092 | ||||||||
\(143\) | −87664.3 | −0.358495 | ||||||||
\(144\) | −390234. | −1.56826 | ||||||||
\(145\) | 44328.4 | 0.175090 | ||||||||
\(146\) | 270980. | 1.05209 | ||||||||
\(147\) | 391688. | 1.49502 | ||||||||
\(148\) | −176071. | −0.660744 | ||||||||
\(149\) | 8184.78 | 0.0302024 | 0.0151012 | − | 0.999886i | \(-0.495193\pi\) | ||||
0.0151012 | + | 0.999886i | \(0.495193\pi\) | |||||||
\(150\) | 104565. | 0.379454 | ||||||||
\(151\) | −412405. | −1.47191 | −0.735956 | − | 0.677029i | \(-0.763267\pi\) | ||||
−0.735956 | + | 0.677029i | \(0.763267\pi\) | |||||||
\(152\) | 33733.9 | 0.118429 | ||||||||
\(153\) | 419951. | 1.45034 | ||||||||
\(154\) | 8791.03 | 0.0298702 | ||||||||
\(155\) | 154740. | 0.517337 | ||||||||
\(156\) | 321139. | 1.05653 | ||||||||
\(157\) | 243063. | 0.786991 | 0.393496 | − | 0.919326i | \(-0.371266\pi\) | ||||
0.393496 | + | 0.919326i | \(0.371266\pi\) | |||||||
\(158\) | −370943. | −1.18213 | ||||||||
\(159\) | −397117. | −1.24574 | ||||||||
\(160\) | −152048. | −0.469548 | ||||||||
\(161\) | −30272.8 | −0.0920424 | ||||||||
\(162\) | 281402. | 0.842440 | ||||||||
\(163\) | 333447. | 0.983010 | 0.491505 | − | 0.870875i | \(-0.336447\pi\) | ||||
0.491505 | + | 0.870875i | \(0.336447\pi\) | |||||||
\(164\) | 234770. | 0.681605 | ||||||||
\(165\) | 70935.4 | 0.202840 | ||||||||
\(166\) | −789175. | −2.22282 | ||||||||
\(167\) | 100210. | 0.278049 | 0.139024 | − | 0.990289i | \(-0.455603\pi\) | ||||
0.139024 | + | 0.990289i | \(0.455603\pi\) | |||||||
\(168\) | 22314.3 | 0.0609972 | ||||||||
\(169\) | 153605. | 0.413702 | ||||||||
\(170\) | 244076. | 0.647744 | ||||||||
\(171\) | 110787. | 0.289734 | ||||||||
\(172\) | −423400. | −1.09126 | ||||||||
\(173\) | 712310. | 1.80948 | 0.904740 | − | 0.425964i | \(-0.140065\pi\) | ||||
0.904740 | + | 0.425964i | \(0.140065\pi\) | |||||||
\(174\) | −296654. | −0.742808 | ||||||||
\(175\) | −6364.51 | −0.0157098 | ||||||||
\(176\) | −153861. | −0.374409 | ||||||||
\(177\) | 331758. | 0.795955 | ||||||||
\(178\) | −517390. | −1.22396 | ||||||||
\(179\) | −785407. | −1.83215 | −0.916077 | − | 0.401002i | \(-0.868662\pi\) | ||||
−0.916077 | + | 0.401002i | \(0.868662\pi\) | |||||||
\(180\) | −145024. | −0.333625 | ||||||||
\(181\) | −181159. | −0.411021 | −0.205510 | − | 0.978655i | \(-0.565885\pi\) | ||||
−0.205510 | + | 0.978655i | \(0.565885\pi\) | |||||||
\(182\) | −52637.1 | −0.117791 | ||||||||
\(183\) | 1.15690e6 | 2.55368 | ||||||||
\(184\) | 277797. | 0.604898 | ||||||||
\(185\) | 232868. | 0.500242 | ||||||||
\(186\) | −1.03555e6 | −2.19476 | ||||||||
\(187\) | 165578. | 0.346256 | ||||||||
\(188\) | −277342. | −0.572296 | ||||||||
\(189\) | 15256.5 | 0.0310671 | ||||||||
\(190\) | 64389.7 | 0.129399 | ||||||||
\(191\) | 316299. | 0.627356 | 0.313678 | − | 0.949529i | \(-0.398439\pi\) | ||||
0.313678 | + | 0.949529i | \(0.398439\pi\) | |||||||
\(192\) | 63350.8 | 0.124022 | ||||||||
\(193\) | 608517. | 1.17592 | 0.587962 | − | 0.808888i | \(-0.299930\pi\) | ||||
0.587962 | + | 0.808888i | \(0.299930\pi\) | |||||||
\(194\) | −213413. | −0.407114 | ||||||||
\(195\) | −424732. | −0.799887 | ||||||||
\(196\) | −315733. | −0.587057 | ||||||||
\(197\) | −461024. | −0.846366 | −0.423183 | − | 0.906044i | \(-0.639087\pi\) | ||||
−0.423183 | + | 0.906044i | \(0.639087\pi\) | |||||||
\(198\) | −264934. | −0.480258 | ||||||||
\(199\) | −101657. | −0.181972 | −0.0909862 | − | 0.995852i | \(-0.529002\pi\) | ||||
−0.0909862 | + | 0.995852i | \(0.529002\pi\) | |||||||
\(200\) | 58403.6 | 0.103244 | ||||||||
\(201\) | −1.17092e6 | −2.04427 | ||||||||
\(202\) | 59683.6 | 0.102914 | ||||||||
\(203\) | 18056.3 | 0.0307530 | ||||||||
\(204\) | −606558. | −1.02046 | ||||||||
\(205\) | −310502. | −0.516036 | ||||||||
\(206\) | −972694. | −1.59701 | ||||||||
\(207\) | 912325. | 1.47987 | ||||||||
\(208\) | 921255. | 1.47646 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | 42592.4 | 0.0666475 | ||||||||
\(211\) | 104595. | 0.161735 | 0.0808675 | − | 0.996725i | \(-0.474231\pi\) | ||||
0.0808675 | + | 0.996725i | \(0.474231\pi\) | |||||||
\(212\) | 320110. | 0.489169 | ||||||||
\(213\) | −84576.2 | −0.127732 | ||||||||
\(214\) | −805881. | −1.20292 | ||||||||
\(215\) | 559980. | 0.826184 | ||||||||
\(216\) | −140000. | −0.204171 | ||||||||
\(217\) | 63030.1 | 0.0908654 | ||||||||
\(218\) | −969829. | −1.38215 | ||||||||
\(219\) | 890646. | 1.25486 | ||||||||
\(220\) | −57179.9 | −0.0796501 | ||||||||
\(221\) | −991411. | −1.36544 | ||||||||
\(222\) | −1.55839e6 | −2.12224 | ||||||||
\(223\) | 408179. | 0.549653 | 0.274827 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274827 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(224\) | −61933.5 | −0.0824718 | ||||||||
\(225\) | 191806. | 0.252584 | ||||||||
\(226\) | 1.33398e6 | 1.73732 | ||||||||
\(227\) | 196271. | 0.252808 | 0.126404 | − | 0.991979i | \(-0.459656\pi\) | ||||
0.126404 | + | 0.991979i | \(0.459656\pi\) | |||||||
\(228\) | −160016. | −0.203857 | ||||||||
\(229\) | 570260. | 0.718595 | 0.359297 | − | 0.933223i | \(-0.383016\pi\) | ||||
0.359297 | + | 0.933223i | \(0.383016\pi\) | |||||||
\(230\) | 530245. | 0.660932 | ||||||||
\(231\) | 28894.1 | 0.0356269 | ||||||||
\(232\) | −165692. | −0.202107 | ||||||||
\(233\) | 785003. | 0.947287 | 0.473643 | − | 0.880717i | \(-0.342939\pi\) | ||||
0.473643 | + | 0.880717i | \(0.342939\pi\) | |||||||
\(234\) | 1.58631e6 | 1.89387 | ||||||||
\(235\) | 366807. | 0.433279 | ||||||||
\(236\) | −267425. | −0.312551 | ||||||||
\(237\) | −1.21920e6 | −1.40995 | ||||||||
\(238\) | 99419.4 | 0.113770 | ||||||||
\(239\) | 802419. | 0.908671 | 0.454336 | − | 0.890831i | \(-0.349877\pi\) | ||||
0.454336 | + | 0.890831i | \(0.349877\pi\) | |||||||
\(240\) | −745453. | −0.835395 | ||||||||
\(241\) | −25488.4 | −0.0282683 | −0.0141341 | − | 0.999900i | \(-0.504499\pi\) | ||||
−0.0141341 | + | 0.999900i | \(0.504499\pi\) | |||||||
\(242\) | −104458. | −0.114657 | ||||||||
\(243\) | 1.28896e6 | 1.40031 | ||||||||
\(244\) | −932554. | −1.00277 | ||||||||
\(245\) | 417583. | 0.444454 | ||||||||
\(246\) | 2.07793e6 | 2.18924 | ||||||||
\(247\) | −261544. | −0.272774 | ||||||||
\(248\) | −578392. | −0.597163 | ||||||||
\(249\) | −2.59383e6 | −2.65121 | ||||||||
\(250\) | 111478. | 0.112808 | ||||||||
\(251\) | −678835. | −0.680111 | −0.340055 | − | 0.940405i | \(-0.610446\pi\) | ||||
−0.340055 | + | 0.940405i | \(0.610446\pi\) | |||||||
\(252\) | −59072.5 | −0.0585982 | ||||||||
\(253\) | 359710. | 0.353306 | ||||||||
\(254\) | 203918. | 0.198322 | ||||||||
\(255\) | 802222. | 0.772581 | ||||||||
\(256\) | 1.33748e6 | 1.27552 | ||||||||
\(257\) | −929690. | −0.878022 | −0.439011 | − | 0.898482i | \(-0.644671\pi\) | ||||
−0.439011 | + | 0.898482i | \(0.644671\pi\) | |||||||
\(258\) | −3.74749e6 | −3.50502 | ||||||||
\(259\) | 94853.8 | 0.0878629 | ||||||||
\(260\) | 342370. | 0.314096 | ||||||||
\(261\) | −544158. | −0.494451 | ||||||||
\(262\) | −322248. | −0.290026 | ||||||||
\(263\) | 413965. | 0.369041 | 0.184520 | − | 0.982829i | \(-0.440927\pi\) | ||||
0.184520 | + | 0.982829i | \(0.440927\pi\) | |||||||
\(264\) | −265145. | −0.234139 | ||||||||
\(265\) | −423371. | −0.370345 | ||||||||
\(266\) | 26227.8 | 0.0227278 | ||||||||
\(267\) | −1.70054e6 | −1.45985 | ||||||||
\(268\) | 943861. | 0.802733 | ||||||||
\(269\) | 994735. | 0.838159 | 0.419080 | − | 0.907949i | \(-0.362353\pi\) | ||||
0.419080 | + | 0.907949i | \(0.362353\pi\) | |||||||
\(270\) | −267226. | −0.223085 | ||||||||
\(271\) | −512272. | −0.423719 | −0.211859 | − | 0.977300i | \(-0.567952\pi\) | ||||
−0.211859 | + | 0.977300i | \(0.567952\pi\) | |||||||
\(272\) | −1.74004e6 | −1.42606 | ||||||||
\(273\) | −173006. | −0.140493 | ||||||||
\(274\) | −2.07533e6 | −1.66998 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | −1.31772e6 | −1.04124 | ||||||||
\(277\) | −708677. | −0.554944 | −0.277472 | − | 0.960734i | \(-0.589496\pi\) | ||||
−0.277472 | + | 0.960734i | \(0.589496\pi\) | |||||||
\(278\) | 2.54611e6 | 1.97590 | ||||||||
\(279\) | −1.89952e6 | −1.46095 | ||||||||
\(280\) | 23789.5 | 0.0181338 | ||||||||
\(281\) | 1.28836e6 | 0.973356 | 0.486678 | − | 0.873582i | \(-0.338209\pi\) | ||||
0.486678 | + | 0.873582i | \(0.338209\pi\) | |||||||
\(282\) | −2.45474e6 | −1.83815 | ||||||||
\(283\) | −1.35284e6 | −1.00411 | −0.502055 | − | 0.864836i | \(-0.667423\pi\) | ||||
−0.502055 | + | 0.864836i | \(0.667423\pi\) | |||||||
\(284\) | 68175.5 | 0.0501571 | ||||||||
\(285\) | 211634. | 0.154338 | ||||||||
\(286\) | 625449. | 0.452144 | ||||||||
\(287\) | −126477. | −0.0906369 | ||||||||
\(288\) | 1.86648e6 | 1.32599 | ||||||||
\(289\) | 452692. | 0.318829 | ||||||||
\(290\) | −316265. | −0.220829 | ||||||||
\(291\) | −701437. | −0.485575 | ||||||||
\(292\) | −717935. | −0.492751 | ||||||||
\(293\) | −267652. | −0.182139 | −0.0910693 | − | 0.995845i | \(-0.529028\pi\) | ||||
−0.0910693 | + | 0.995845i | \(0.529028\pi\) | |||||||
\(294\) | −2.79453e6 | −1.88556 | ||||||||
\(295\) | 353691. | 0.236629 | ||||||||
\(296\) | −870421. | −0.577431 | ||||||||
\(297\) | −181282. | −0.119251 | ||||||||
\(298\) | −58395.1 | −0.0380922 | ||||||||
\(299\) | −2.15380e6 | −1.39324 | ||||||||
\(300\) | −277036. | −0.177718 | ||||||||
\(301\) | 228096. | 0.145111 | ||||||||
\(302\) | 2.94234e6 | 1.85642 | ||||||||
\(303\) | 196166. | 0.122749 | ||||||||
\(304\) | −459039. | −0.284882 | ||||||||
\(305\) | 1.23338e6 | 0.759183 | ||||||||
\(306\) | −2.99618e6 | −1.82922 | ||||||||
\(307\) | 590360. | 0.357496 | 0.178748 | − | 0.983895i | \(-0.442795\pi\) | ||||
0.178748 | + | 0.983895i | \(0.442795\pi\) | |||||||
\(308\) | −23291.0 | −0.0139898 | ||||||||
\(309\) | −3.19702e6 | −1.90480 | ||||||||
\(310\) | −1.10401e6 | −0.652481 | ||||||||
\(311\) | −1.15358e6 | −0.676309 | −0.338155 | − | 0.941091i | \(-0.609803\pi\) | ||||
−0.338155 | + | 0.941091i | \(0.609803\pi\) | |||||||
\(312\) | 1.58758e6 | 0.923312 | ||||||||
\(313\) | −869231. | −0.501504 | −0.250752 | − | 0.968051i | \(-0.580678\pi\) | ||||
−0.250752 | + | 0.968051i | \(0.580678\pi\) | |||||||
\(314\) | −1.73416e6 | −0.992577 | ||||||||
\(315\) | 78128.2 | 0.0443641 | ||||||||
\(316\) | 982778. | 0.553653 | ||||||||
\(317\) | 1.38504e6 | 0.774128 | 0.387064 | − | 0.922053i | \(-0.373489\pi\) | ||||
0.387064 | + | 0.922053i | \(0.373489\pi\) | |||||||
\(318\) | 2.83327e6 | 1.57116 | ||||||||
\(319\) | −214550. | −0.118046 | ||||||||
\(320\) | 67538.9 | 0.0368705 | ||||||||
\(321\) | −2.64874e6 | −1.43475 | ||||||||
\(322\) | 215984. | 0.116087 | ||||||||
\(323\) | 493996. | 0.263462 | ||||||||
\(324\) | −745547. | −0.394560 | ||||||||
\(325\) | −452811. | −0.237798 | ||||||||
\(326\) | −2.37901e6 | −1.23980 | ||||||||
\(327\) | −3.18760e6 | −1.64852 | ||||||||
\(328\) | 1.16061e6 | 0.595662 | ||||||||
\(329\) | 149411. | 0.0761015 | ||||||||
\(330\) | −506096. | −0.255828 | ||||||||
\(331\) | −2.31804e6 | −1.16292 | −0.581462 | − | 0.813573i | \(-0.697519\pi\) | ||||
−0.581462 | + | 0.813573i | \(0.697519\pi\) | |||||||
\(332\) | 2.09085e6 | 1.04106 | ||||||||
\(333\) | −2.85859e6 | −1.41267 | ||||||||
\(334\) | −714959. | −0.350683 | ||||||||
\(335\) | −1.24833e6 | −0.607741 | ||||||||
\(336\) | −303644. | −0.146729 | ||||||||
\(337\) | −388169. | −0.186186 | −0.0930928 | − | 0.995657i | \(-0.529675\pi\) | ||||
−0.0930928 | + | 0.995657i | \(0.529675\pi\) | |||||||
\(338\) | −1.09591e6 | −0.521774 | ||||||||
\(339\) | 4.38448e6 | 2.07214 | ||||||||
\(340\) | −646658. | −0.303373 | ||||||||
\(341\) | −748941. | −0.348788 | ||||||||
\(342\) | −790422. | −0.365421 | ||||||||
\(343\) | 341243. | 0.156613 | ||||||||
\(344\) | −2.09311e6 | −0.953666 | ||||||||
\(345\) | 1.74279e6 | 0.788311 | ||||||||
\(346\) | −5.08204e6 | −2.28217 | ||||||||
\(347\) | 1.84083e6 | 0.820710 | 0.410355 | − | 0.911926i | \(-0.365405\pi\) | ||||
0.410355 | + | 0.911926i | \(0.365405\pi\) | |||||||
\(348\) | 785956. | 0.347896 | ||||||||
\(349\) | 426759. | 0.187551 | 0.0937755 | − | 0.995593i | \(-0.470106\pi\) | ||||
0.0937755 | + | 0.995593i | \(0.470106\pi\) | |||||||
\(350\) | 45408.2 | 0.0198136 | ||||||||
\(351\) | 1.08544e6 | 0.470261 | ||||||||
\(352\) | 735911. | 0.316569 | ||||||||
\(353\) | −3.30384e6 | −1.41118 | −0.705590 | − | 0.708621i | \(-0.749318\pi\) | ||||
−0.705590 | + | 0.708621i | \(0.749318\pi\) | |||||||
\(354\) | −2.36696e6 | −1.00388 | ||||||||
\(355\) | −90167.6 | −0.0379734 | ||||||||
\(356\) | 1.37078e6 | 0.573247 | ||||||||
\(357\) | 326768. | 0.135697 | ||||||||
\(358\) | 5.60356e6 | 2.31077 | ||||||||
\(359\) | 3.47865e6 | 1.42454 | 0.712271 | − | 0.701905i | \(-0.247667\pi\) | ||||
0.712271 | + | 0.701905i | \(0.247667\pi\) | |||||||
\(360\) | −716939. | −0.291559 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 1.29250e6 | 0.518392 | ||||||||
\(363\) | −343327. | −0.136755 | ||||||||
\(364\) | 139457. | 0.0551680 | ||||||||
\(365\) | 949527. | 0.373057 | ||||||||
\(366\) | −8.25398e6 | −3.22078 | ||||||||
\(367\) | −1.60279e6 | −0.621170 | −0.310585 | − | 0.950546i | \(-0.600525\pi\) | ||||
−0.310585 | + | 0.950546i | \(0.600525\pi\) | |||||||
\(368\) | −3.78015e6 | −1.45509 | ||||||||
\(369\) | 3.81160e6 | 1.45727 | ||||||||
\(370\) | −1.66142e6 | −0.630920 | ||||||||
\(371\) | −172451. | −0.0650476 | ||||||||
\(372\) | 2.74358e6 | 1.02792 | ||||||||
\(373\) | −3.65780e6 | −1.36128 | −0.680640 | − | 0.732618i | \(-0.738298\pi\) | ||||
−0.680640 | + | 0.732618i | \(0.738298\pi\) | |||||||
\(374\) | −1.18133e6 | −0.436709 | ||||||||
\(375\) | 366402. | 0.134549 | ||||||||
\(376\) | −1.37106e6 | −0.500136 | ||||||||
\(377\) | 1.28463e6 | 0.465507 | ||||||||
\(378\) | −108849. | −0.0391827 | ||||||||
\(379\) | 4.71626e6 | 1.68655 | 0.843276 | − | 0.537481i | \(-0.180624\pi\) | ||||
0.843276 | + | 0.537481i | \(0.180624\pi\) | |||||||
\(380\) | −170595. | −0.0606047 | ||||||||
\(381\) | 670230. | 0.236544 | ||||||||
\(382\) | −2.25666e6 | −0.791241 | ||||||||
\(383\) | 1.46343e6 | 0.509770 | 0.254885 | − | 0.966971i | \(-0.417962\pi\) | ||||
0.254885 | + | 0.966971i | \(0.417962\pi\) | |||||||
\(384\) | 4.11183e6 | 1.42301 | ||||||||
\(385\) | 30804.3 | 0.0105915 | ||||||||
\(386\) | −4.34152e6 | −1.48311 | ||||||||
\(387\) | −6.87409e6 | −2.33312 | ||||||||
\(388\) | 565417. | 0.190673 | ||||||||
\(389\) | −5.25615e6 | −1.76114 | −0.880569 | − | 0.473918i | \(-0.842839\pi\) | ||||
−0.880569 | + | 0.473918i | \(0.842839\pi\) | |||||||
\(390\) | 3.03029e6 | 1.00884 | ||||||||
\(391\) | 4.06803e6 | 1.34568 | ||||||||
\(392\) | −1.56085e6 | −0.513035 | ||||||||
\(393\) | −1.05915e6 | −0.345922 | ||||||||
\(394\) | 3.28922e6 | 1.06746 | ||||||||
\(395\) | −1.29980e6 | −0.419165 | ||||||||
\(396\) | 701917. | 0.224930 | ||||||||
\(397\) | −1.54470e6 | −0.491889 | −0.245944 | − | 0.969284i | \(-0.579098\pi\) | ||||
−0.245944 | + | 0.969284i | \(0.579098\pi\) | |||||||
\(398\) | 725283. | 0.229509 | ||||||||
\(399\) | 86204.6 | 0.0271080 | ||||||||
\(400\) | −794735. | −0.248355 | ||||||||
\(401\) | 5.97875e6 | 1.85673 | 0.928366 | − | 0.371666i | \(-0.121213\pi\) | ||||
0.928366 | + | 0.371666i | \(0.121213\pi\) | |||||||
\(402\) | 8.35406e6 | 2.57829 | ||||||||
\(403\) | 4.48435e6 | 1.37543 | ||||||||
\(404\) | −158126. | −0.0482003 | ||||||||
\(405\) | 986047. | 0.298717 | ||||||||
\(406\) | −128824. | −0.0387866 | ||||||||
\(407\) | −1.12708e6 | −0.337263 | ||||||||
\(408\) | −2.99857e6 | −0.891792 | ||||||||
\(409\) | 4.14833e6 | 1.22621 | 0.613105 | − | 0.790001i | \(-0.289920\pi\) | ||||
0.613105 | + | 0.790001i | \(0.289920\pi\) | |||||||
\(410\) | 2.21531e6 | 0.650840 | ||||||||
\(411\) | −6.82113e6 | −1.99183 | ||||||||
\(412\) | 2.57706e6 | 0.747966 | ||||||||
\(413\) | 144068. | 0.0415617 | ||||||||
\(414\) | −6.50907e6 | −1.86646 | ||||||||
\(415\) | −2.76531e6 | −0.788178 | ||||||||
\(416\) | −4.40634e6 | −1.24837 | ||||||||
\(417\) | 8.36846e6 | 2.35671 | ||||||||
\(418\) | −311646. | −0.0872411 | ||||||||
\(419\) | −3.20310e6 | −0.891324 | −0.445662 | − | 0.895201i | \(-0.647032\pi\) | ||||
−0.445662 | + | 0.895201i | \(0.647032\pi\) | |||||||
\(420\) | −112845. | −0.0312146 | ||||||||
\(421\) | −1.09464e6 | −0.301000 | −0.150500 | − | 0.988610i | \(-0.548088\pi\) | ||||
−0.150500 | + | 0.988610i | \(0.548088\pi\) | |||||||
\(422\) | −746242. | −0.203985 | ||||||||
\(423\) | −4.50277e6 | −1.22357 | ||||||||
\(424\) | 1.58249e6 | 0.427490 | ||||||||
\(425\) | 855257. | 0.229681 | ||||||||
\(426\) | 603417. | 0.161099 | ||||||||
\(427\) | 502391. | 0.133343 | ||||||||
\(428\) | 2.13511e6 | 0.563391 | ||||||||
\(429\) | 2.05570e6 | 0.539284 | ||||||||
\(430\) | −3.99523e6 | −1.04201 | ||||||||
\(431\) | 4.49794e6 | 1.16633 | 0.583163 | − | 0.812355i | \(-0.301815\pi\) | ||||
0.583163 | + | 0.812355i | \(0.301815\pi\) | |||||||
\(432\) | 1.90507e6 | 0.491137 | ||||||||
\(433\) | 3.87599e6 | 0.993488 | 0.496744 | − | 0.867897i | \(-0.334529\pi\) | ||||
0.496744 | + | 0.867897i | \(0.334529\pi\) | |||||||
\(434\) | −449694. | −0.114602 | ||||||||
\(435\) | −1.03949e6 | −0.263389 | ||||||||
\(436\) | 2.56947e6 | 0.647333 | ||||||||
\(437\) | 1.07318e6 | 0.268826 | ||||||||
\(438\) | −6.35440e6 | −1.58267 | ||||||||
\(439\) | −386368. | −0.0956842 | −0.0478421 | − | 0.998855i | \(-0.515234\pi\) | ||||
−0.0478421 | + | 0.998855i | \(0.515234\pi\) | |||||||
\(440\) | −282673. | −0.0696071 | ||||||||
\(441\) | −5.12607e6 | −1.25513 | ||||||||
\(442\) | 7.07332e6 | 1.72214 | ||||||||
\(443\) | −2.92841e6 | −0.708961 | −0.354481 | − | 0.935063i | \(-0.615342\pi\) | ||||
−0.354481 | + | 0.935063i | \(0.615342\pi\) | |||||||
\(444\) | 4.12881e6 | 0.993957 | ||||||||
\(445\) | −1.81296e6 | −0.433999 | ||||||||
\(446\) | −2.91219e6 | −0.693239 | ||||||||
\(447\) | −191931. | −0.0454335 | ||||||||
\(448\) | 27510.6 | 0.00647596 | ||||||||
\(449\) | −5.59637e6 | −1.31006 | −0.655029 | − | 0.755604i | \(-0.727343\pi\) | ||||
−0.655029 | + | 0.755604i | \(0.727343\pi\) | |||||||
\(450\) | −1.36846e6 | −0.318567 | ||||||||
\(451\) | 1.50283e6 | 0.347911 | ||||||||
\(452\) | −3.53426e6 | −0.813678 | ||||||||
\(453\) | 9.67079e6 | 2.21420 | ||||||||
\(454\) | −1.40031e6 | −0.318850 | ||||||||
\(455\) | −184443. | −0.0417671 | ||||||||
\(456\) | −791051. | −0.178153 | ||||||||
\(457\) | −179779. | −0.0402669 | −0.0201335 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201335 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(458\) | −4.06857e6 | −0.906313 | ||||||||
\(459\) | −2.05015e6 | −0.454208 | ||||||||
\(460\) | −1.40483e6 | −0.309550 | ||||||||
\(461\) | −2.89395e6 | −0.634217 | −0.317109 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317109 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(462\) | −206147. | −0.0449338 | ||||||||
\(463\) | 4.62210e6 | 1.00205 | 0.501023 | − | 0.865434i | \(-0.332957\pi\) | ||||
0.501023 | + | 0.865434i | \(0.332957\pi\) | |||||||
\(464\) | 2.25468e6 | 0.486172 | ||||||||
\(465\) | −3.62861e6 | −0.778230 | ||||||||
\(466\) | −5.60068e6 | −1.19475 | ||||||||
\(467\) | −548881. | −0.116463 | −0.0582313 | − | 0.998303i | \(-0.518546\pi\) | ||||
−0.0582313 | + | 0.998303i | \(0.518546\pi\) | |||||||
\(468\) | −4.20279e6 | −0.886999 | ||||||||
\(469\) | −508482. | −0.106744 | ||||||||
\(470\) | −2.61702e6 | −0.546465 | ||||||||
\(471\) | −5.69976e6 | −1.18387 | ||||||||
\(472\) | −1.32204e6 | −0.273142 | ||||||||
\(473\) | −2.71031e6 | −0.557013 | ||||||||
\(474\) | 8.69851e6 | 1.77827 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | −263402. | −0.0532847 | ||||||||
\(477\) | 5.19713e6 | 1.04585 | ||||||||
\(478\) | −5.72494e6 | −1.14604 | ||||||||
\(479\) | 5.56572e6 | 1.10836 | 0.554182 | − | 0.832396i | \(-0.313031\pi\) | ||||
0.554182 | + | 0.832396i | \(0.313031\pi\) | |||||||
\(480\) | 3.56548e6 | 0.706342 | ||||||||
\(481\) | 6.74849e6 | 1.32998 | ||||||||
\(482\) | 181849. | 0.0356528 | ||||||||
\(483\) | 709889. | 0.138459 | ||||||||
\(484\) | 276751. | 0.0537001 | ||||||||
\(485\) | −747809. | −0.144357 | ||||||||
\(486\) | −9.19623e6 | −1.76612 | ||||||||
\(487\) | 4.22188e6 | 0.806648 | 0.403324 | − | 0.915057i | \(-0.367855\pi\) | ||||
0.403324 | + | 0.915057i | \(0.367855\pi\) | |||||||
\(488\) | −4.61016e6 | −0.876327 | ||||||||
\(489\) | −7.81924e6 | −1.47874 | ||||||||
\(490\) | −2.97928e6 | −0.560559 | ||||||||
\(491\) | 6.35541e6 | 1.18971 | 0.594853 | − | 0.803835i | \(-0.297210\pi\) | ||||
0.594853 | + | 0.803835i | \(0.297210\pi\) | |||||||
\(492\) | −5.50529e6 | −1.02534 | ||||||||
\(493\) | −2.42638e6 | −0.449616 | ||||||||
\(494\) | 1.86601e6 | 0.344030 | ||||||||
\(495\) | −928342. | −0.170292 | ||||||||
\(496\) | 7.87054e6 | 1.43648 | ||||||||
\(497\) | −36727.9 | −0.00666968 | ||||||||
\(498\) | 1.85060e7 | 3.34378 | ||||||||
\(499\) | −8.86729e6 | −1.59419 | −0.797094 | − | 0.603856i | \(-0.793630\pi\) | ||||
−0.797094 | + | 0.603856i | \(0.793630\pi\) | |||||||
\(500\) | −295351. | −0.0528339 | ||||||||
\(501\) | −2.34990e6 | −0.418269 | ||||||||
\(502\) | 4.84321e6 | 0.857776 | ||||||||
\(503\) | 7.66117e6 | 1.35013 | 0.675064 | − | 0.737759i | \(-0.264116\pi\) | ||||
0.675064 | + | 0.737759i | \(0.264116\pi\) | |||||||
\(504\) | −292030. | −0.0512096 | ||||||||
\(505\) | 209134. | 0.0364919 | ||||||||
\(506\) | −2.56639e6 | −0.445600 | ||||||||
\(507\) | −3.60199e6 | −0.622333 | ||||||||
\(508\) | −540261. | −0.0928848 | ||||||||
\(509\) | −5.46044e6 | −0.934185 | −0.467093 | − | 0.884208i | \(-0.654699\pi\) | ||||
−0.467093 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(510\) | −5.72353e6 | −0.974402 | ||||||||
\(511\) | 386770. | 0.0655240 | ||||||||
\(512\) | −3.93126e6 | −0.662762 | ||||||||
\(513\) | −540850. | −0.0907368 | ||||||||
\(514\) | 6.63296e6 | 1.10739 | ||||||||
\(515\) | −3.40837e6 | −0.566277 | ||||||||
\(516\) | 9.92861e6 | 1.64159 | ||||||||
\(517\) | −1.77535e6 | −0.292117 | ||||||||
\(518\) | −676743. | −0.110815 | ||||||||
\(519\) | −1.67035e7 | −2.72200 | ||||||||
\(520\) | 1.69253e6 | 0.274491 | ||||||||
\(521\) | −6.66984e6 | −1.07652 | −0.538259 | − | 0.842779i | \(-0.680918\pi\) | ||||
−0.538259 | + | 0.842779i | \(0.680918\pi\) | |||||||
\(522\) | 3.88235e6 | 0.623617 | ||||||||
\(523\) | −7.64901e6 | −1.22279 | −0.611394 | − | 0.791326i | \(-0.709391\pi\) | ||||
−0.611394 | + | 0.791326i | \(0.709391\pi\) | |||||||
\(524\) | 853767. | 0.135835 | ||||||||
\(525\) | 149246. | 0.0236322 | ||||||||
\(526\) | −2.95347e6 | −0.465446 | ||||||||
\(527\) | −8.46991e6 | −1.32847 | ||||||||
\(528\) | 3.60799e6 | 0.563223 | ||||||||
\(529\) | 2.40126e6 | 0.373078 | ||||||||
\(530\) | 3.02058e6 | 0.467090 | ||||||||
\(531\) | −4.34176e6 | −0.668236 | ||||||||
\(532\) | −69488.1 | −0.0106446 | ||||||||
\(533\) | −8.99833e6 | −1.37197 | ||||||||
\(534\) | 1.21327e7 | 1.84121 | ||||||||
\(535\) | −2.82385e6 | −0.426537 | ||||||||
\(536\) | 4.66606e6 | 0.701517 | ||||||||
\(537\) | 1.84176e7 | 2.75611 | ||||||||
\(538\) | −7.09703e6 | −1.05711 | ||||||||
\(539\) | −2.02110e6 | −0.299651 | ||||||||
\(540\) | 707990. | 0.104482 | ||||||||
\(541\) | 7.74562e6 | 1.13779 | 0.568896 | − | 0.822409i | \(-0.307371\pi\) | ||||
0.568896 | + | 0.822409i | \(0.307371\pi\) | |||||||
\(542\) | 3.65486e6 | 0.534407 | ||||||||
\(543\) | 4.24813e6 | 0.618299 | ||||||||
\(544\) | 8.32256e6 | 1.20576 | ||||||||
\(545\) | −3.39833e6 | −0.490089 | ||||||||
\(546\) | 1.23433e6 | 0.177194 | ||||||||
\(547\) | −4.59792e6 | −0.657042 | −0.328521 | − | 0.944497i | \(-0.606550\pi\) | ||||
−0.328521 | + | 0.944497i | \(0.606550\pi\) | |||||||
\(548\) | 5.49840e6 | 0.782141 | ||||||||
\(549\) | −1.51404e7 | −2.14392 | ||||||||
\(550\) | −539554. | −0.0760550 | ||||||||
\(551\) | −640103. | −0.0898195 | ||||||||
\(552\) | −6.51426e6 | −0.909949 | ||||||||
\(553\) | −529447. | −0.0736224 | ||||||||
\(554\) | 5.05612e6 | 0.699911 | ||||||||
\(555\) | −5.46069e6 | −0.752514 | ||||||||
\(556\) | −6.74568e6 | −0.925420 | ||||||||
\(557\) | 1.01353e7 | 1.38420 | 0.692099 | − | 0.721803i | \(-0.256686\pi\) | ||||
0.692099 | + | 0.721803i | \(0.256686\pi\) | |||||||
\(558\) | 1.35523e7 | 1.84259 | ||||||||
\(559\) | 1.62282e7 | 2.19655 | ||||||||
\(560\) | −323719. | −0.0436212 | ||||||||
\(561\) | −3.88275e6 | −0.520874 | ||||||||
\(562\) | −9.19193e6 | −1.22763 | ||||||||
\(563\) | −5.95706e6 | −0.792065 | −0.396032 | − | 0.918236i | \(-0.629613\pi\) | ||||
−0.396032 | + | 0.918236i | \(0.629613\pi\) | |||||||
\(564\) | 6.50359e6 | 0.860906 | ||||||||
\(565\) | 4.67434e6 | 0.616027 | ||||||||
\(566\) | 9.65199e6 | 1.26641 | ||||||||
\(567\) | 401645. | 0.0524669 | ||||||||
\(568\) | 337031. | 0.0438328 | ||||||||
\(569\) | 1.37133e6 | 0.177567 | 0.0887836 | − | 0.996051i | \(-0.471702\pi\) | ||||
0.0887836 | + | 0.996051i | \(0.471702\pi\) | |||||||
\(570\) | −1.50992e6 | −0.194656 | ||||||||
\(571\) | −1.40265e7 | −1.80035 | −0.900176 | − | 0.435526i | \(-0.856563\pi\) | ||||
−0.900176 | + | 0.435526i | \(0.856563\pi\) | |||||||
\(572\) | −1.65707e6 | −0.211763 | ||||||||
\(573\) | −7.41712e6 | −0.943733 | ||||||||
\(574\) | 902359. | 0.114314 | ||||||||
\(575\) | 1.85801e6 | 0.234357 | ||||||||
\(576\) | −829080. | −0.104121 | ||||||||
\(577\) | 7.32574e6 | 0.916035 | 0.458018 | − | 0.888943i | \(-0.348560\pi\) | ||||
0.458018 | + | 0.888943i | \(0.348560\pi\) | |||||||
\(578\) | −3.22977e6 | −0.402117 | ||||||||
\(579\) | −1.42696e7 | −1.76894 | ||||||||
\(580\) | 837915. | 0.103426 | ||||||||
\(581\) | −1.12639e6 | −0.138436 | ||||||||
\(582\) | 5.00447e6 | 0.612422 | ||||||||
\(583\) | 2.04911e6 | 0.249686 | ||||||||
\(584\) | −3.54917e6 | −0.430621 | ||||||||
\(585\) | 5.55853e6 | 0.671537 | ||||||||
\(586\) | 1.90959e6 | 0.229719 | ||||||||
\(587\) | 6.69340e6 | 0.801773 | 0.400887 | − | 0.916128i | \(-0.368702\pi\) | ||||
0.400887 | + | 0.916128i | \(0.368702\pi\) | |||||||
\(588\) | 7.40386e6 | 0.883110 | ||||||||
\(589\) | −2.23445e6 | −0.265388 | ||||||||
\(590\) | −2.52344e6 | −0.298444 | ||||||||
\(591\) | 1.08109e7 | 1.27319 | ||||||||
\(592\) | 1.18444e7 | 1.38902 | ||||||||
\(593\) | 4.85520e6 | 0.566983 | 0.283492 | − | 0.958975i | \(-0.408507\pi\) | ||||
0.283492 | + | 0.958975i | \(0.408507\pi\) | |||||||
\(594\) | 1.29337e6 | 0.150404 | ||||||||
\(595\) | 348371. | 0.0403413 | ||||||||
\(596\) | 154712. | 0.0178406 | ||||||||
\(597\) | 2.38383e6 | 0.273741 | ||||||||
\(598\) | 1.53665e7 | 1.75720 | ||||||||
\(599\) | −1.30661e7 | −1.48791 | −0.743957 | − | 0.668227i | \(-0.767053\pi\) | ||||
−0.743957 | + | 0.668227i | \(0.767053\pi\) | |||||||
\(600\) | −1.36955e6 | −0.155310 | ||||||||
\(601\) | −8.60041e6 | −0.971255 | −0.485627 | − | 0.874166i | \(-0.661409\pi\) | ||||
−0.485627 | + | 0.874166i | \(0.661409\pi\) | |||||||
\(602\) | −1.62737e6 | −0.183019 | ||||||||
\(603\) | 1.53240e7 | 1.71625 | ||||||||
\(604\) | −7.79547e6 | −0.869460 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | −1.39956e6 | −0.154814 | ||||||||
\(607\) | 960299. | 0.105788 | 0.0528938 | − | 0.998600i | \(-0.483156\pi\) | ||||
0.0528938 | + | 0.998600i | \(0.483156\pi\) | |||||||
\(608\) | 2.19557e6 | 0.240873 | ||||||||
\(609\) | −423414. | −0.0462618 | ||||||||
\(610\) | −8.79965e6 | −0.957505 | ||||||||
\(611\) | 1.06300e7 | 1.15195 | ||||||||
\(612\) | 7.93811e6 | 0.856719 | ||||||||
\(613\) | 1.37066e7 | 1.47325 | 0.736626 | − | 0.676300i | \(-0.236418\pi\) | ||||
0.736626 | + | 0.676300i | \(0.236418\pi\) | |||||||
\(614\) | −4.21198e6 | −0.450885 | ||||||||
\(615\) | 7.28119e6 | 0.776274 | ||||||||
\(616\) | −115141. | −0.0122258 | ||||||||
\(617\) | −1.05006e7 | −1.11046 | −0.555229 | − | 0.831697i | \(-0.687369\pi\) | ||||
−0.555229 | + | 0.831697i | \(0.687369\pi\) | |||||||
\(618\) | 2.28094e7 | 2.40239 | ||||||||
\(619\) | 1.16029e7 | 1.21713 | 0.608567 | − | 0.793503i | \(-0.291745\pi\) | ||||
0.608567 | + | 0.793503i | \(0.291745\pi\) | |||||||
\(620\) | 2.92496e6 | 0.305591 | ||||||||
\(621\) | −4.45386e6 | −0.463455 | ||||||||
\(622\) | 8.23030e6 | 0.852982 | ||||||||
\(623\) | −738472. | −0.0762279 | ||||||||
\(624\) | −2.16032e7 | −2.22104 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 6.20161e6 | 0.632512 | ||||||||
\(627\) | −1.02431e6 | −0.104055 | ||||||||
\(628\) | 4.59449e6 | 0.464877 | ||||||||
\(629\) | −1.27464e7 | −1.28457 | ||||||||
\(630\) | −557413. | −0.0559533 | ||||||||
\(631\) | −6.57254e6 | −0.657143 | −0.328572 | − | 0.944479i | \(-0.606567\pi\) | ||||
−0.328572 | + | 0.944479i | \(0.606567\pi\) | |||||||
\(632\) | 4.85845e6 | 0.483843 | ||||||||
\(633\) | −2.45272e6 | −0.243298 | ||||||||
\(634\) | −9.88167e6 | −0.976354 | ||||||||
\(635\) | 714539. | 0.0703221 | ||||||||
\(636\) | −7.50648e6 | −0.735858 | ||||||||
\(637\) | 1.21015e7 | 1.18166 | ||||||||
\(638\) | 1.53072e6 | 0.148883 | ||||||||
\(639\) | 1.10686e6 | 0.107236 | ||||||||
\(640\) | 4.38367e6 | 0.423046 | ||||||||
\(641\) | 8.79244e6 | 0.845210 | 0.422605 | − | 0.906314i | \(-0.361116\pi\) | ||||
0.422605 | + | 0.906314i | \(0.361116\pi\) | |||||||
\(642\) | 1.88977e7 | 1.80955 | ||||||||
\(643\) | 1.57144e7 | 1.49890 | 0.749448 | − | 0.662063i | \(-0.230319\pi\) | ||||
0.749448 | + | 0.662063i | \(0.230319\pi\) | |||||||
\(644\) | −572230. | −0.0543695 | ||||||||
\(645\) | −1.31314e7 | −1.24283 | ||||||||
\(646\) | −3.52446e6 | −0.332286 | ||||||||
\(647\) | −1.88098e6 | −0.176654 | −0.0883272 | − | 0.996092i | \(-0.528152\pi\) | ||||
−0.0883272 | + | 0.996092i | \(0.528152\pi\) | |||||||
\(648\) | −3.68568e6 | −0.344810 | ||||||||
\(649\) | −1.71186e6 | −0.159535 | ||||||||
\(650\) | 3.23063e6 | 0.299919 | ||||||||
\(651\) | −1.47804e6 | −0.136689 | ||||||||
\(652\) | 6.30296e6 | 0.580665 | ||||||||
\(653\) | 6.22718e6 | 0.571490 | 0.285745 | − | 0.958306i | \(-0.407759\pi\) | ||||
0.285745 | + | 0.958306i | \(0.407759\pi\) | |||||||
\(654\) | 2.27422e7 | 2.07916 | ||||||||
\(655\) | −1.12918e6 | −0.102839 | ||||||||
\(656\) | −1.57931e7 | −1.43287 | ||||||||
\(657\) | −1.16560e7 | −1.05350 | ||||||||
\(658\) | −1.06599e6 | −0.0959815 | ||||||||
\(659\) | 1.32051e7 | 1.18448 | 0.592241 | − | 0.805761i | \(-0.298243\pi\) | ||||
0.592241 | + | 0.805761i | \(0.298243\pi\) | |||||||
\(660\) | 1.34085e6 | 0.119818 | ||||||||
\(661\) | 1.56980e7 | 1.39746 | 0.698731 | − | 0.715384i | \(-0.253748\pi\) | ||||
0.698731 | + | 0.715384i | \(0.253748\pi\) | |||||||
\(662\) | 1.65383e7 | 1.46671 | ||||||||
\(663\) | 2.32483e7 | 2.05404 | ||||||||
\(664\) | 1.03363e7 | 0.909795 | ||||||||
\(665\) | 91903.6 | 0.00805895 | ||||||||
\(666\) | 2.03949e7 | 1.78170 | ||||||||
\(667\) | −5.27120e6 | −0.458770 | ||||||||
\(668\) | 1.89422e6 | 0.164244 | ||||||||
\(669\) | −9.57170e6 | −0.826844 | ||||||||
\(670\) | 8.90635e6 | 0.766501 | ||||||||
\(671\) | −5.96955e6 | −0.511841 | ||||||||
\(672\) | 1.45232e6 | 0.124062 | ||||||||
\(673\) | 1.98667e7 | 1.69078 | 0.845392 | − | 0.534146i | \(-0.179367\pi\) | ||||
0.845392 | + | 0.534146i | \(0.179367\pi\) | |||||||
\(674\) | 2.76943e6 | 0.234823 | ||||||||
\(675\) | −936374. | −0.0791025 | ||||||||
\(676\) | 2.90350e6 | 0.244374 | ||||||||
\(677\) | −1.07136e7 | −0.898384 | −0.449192 | − | 0.893435i | \(-0.648288\pi\) | ||||
−0.449192 | + | 0.893435i | \(0.648288\pi\) | |||||||
\(678\) | −3.12815e7 | −2.61345 | ||||||||
\(679\) | −304604. | −0.0253549 | ||||||||
\(680\) | −3.19681e6 | −0.265121 | ||||||||
\(681\) | −4.60250e6 | −0.380300 | ||||||||
\(682\) | 5.34339e6 | 0.439902 | ||||||||
\(683\) | −7.82645e6 | −0.641967 | −0.320984 | − | 0.947085i | \(-0.604013\pi\) | ||||
−0.320984 | + | 0.947085i | \(0.604013\pi\) | |||||||
\(684\) | 2.09415e6 | 0.171146 | ||||||||
\(685\) | −7.27208e6 | −0.592151 | ||||||||
\(686\) | −2.43463e6 | −0.197525 | ||||||||
\(687\) | −1.33724e7 | −1.08098 | ||||||||
\(688\) | 2.84823e7 | 2.29406 | ||||||||
\(689\) | −1.22693e7 | −0.984623 | ||||||||
\(690\) | −1.24341e7 | −0.994241 | ||||||||
\(691\) | −1.76929e7 | −1.40963 | −0.704814 | − | 0.709392i | \(-0.748970\pi\) | ||||
−0.704814 | + | 0.709392i | \(0.748970\pi\) | |||||||
\(692\) | 1.34644e7 | 1.06886 | ||||||||
\(693\) | −378140. | −0.0299102 | ||||||||
\(694\) | −1.31336e7 | −1.03510 | ||||||||
\(695\) | 8.92171e6 | 0.700625 | ||||||||
\(696\) | 3.88544e6 | 0.304030 | ||||||||
\(697\) | 1.69958e7 | 1.32513 | ||||||||
\(698\) | −3.04475e6 | −0.236545 | ||||||||
\(699\) | −1.84081e7 | −1.42500 | ||||||||
\(700\) | −120305. | −0.00927979 | ||||||||
\(701\) | 1.48548e7 | 1.14175 | 0.570874 | − | 0.821037i | \(-0.306604\pi\) | ||||
0.570874 | + | 0.821037i | \(0.306604\pi\) | |||||||
\(702\) | −7.74419e6 | −0.593108 | ||||||||
\(703\) | −3.36261e6 | −0.256619 | ||||||||
\(704\) | −326888. | −0.0248581 | ||||||||
\(705\) | −8.60153e6 | −0.651782 | ||||||||
\(706\) | 2.35716e7 | 1.77982 | ||||||||
\(707\) | 85186.5 | 0.00640947 | ||||||||
\(708\) | 6.27104e6 | 0.470171 | ||||||||
\(709\) | −1.65746e7 | −1.23831 | −0.619153 | − | 0.785271i | \(-0.712524\pi\) | ||||
−0.619153 | + | 0.785271i | \(0.712524\pi\) | |||||||
\(710\) | 643309. | 0.0478932 | ||||||||
\(711\) | 1.59559e7 | 1.18371 | ||||||||
\(712\) | 6.77655e6 | 0.500966 | ||||||||
\(713\) | −1.84005e7 | −1.35552 | ||||||||
\(714\) | −2.33136e6 | −0.171145 | ||||||||
\(715\) | 2.19161e6 | 0.160324 | ||||||||
\(716\) | −1.48461e7 | −1.08226 | ||||||||
\(717\) | −1.88165e7 | −1.36691 | ||||||||
\(718\) | −2.48188e7 | −1.79667 | ||||||||
\(719\) | −6.21856e6 | −0.448609 | −0.224304 | − | 0.974519i | \(-0.572011\pi\) | ||||
−0.224304 | + | 0.974519i | \(0.572011\pi\) | |||||||
\(720\) | 9.75584e6 | 0.701348 | ||||||||
\(721\) | −1.38833e6 | −0.0994613 | ||||||||
\(722\) | −929787. | −0.0663805 | ||||||||
\(723\) | 597695. | 0.0425240 | ||||||||
\(724\) | −3.42435e6 | −0.242790 | ||||||||
\(725\) | −1.10821e6 | −0.0783028 | ||||||||
\(726\) | 2.44950e6 | 0.172479 | ||||||||
\(727\) | −1.25697e7 | −0.882042 | −0.441021 | − | 0.897497i | \(-0.645384\pi\) | ||||
−0.441021 | + | 0.897497i | \(0.645384\pi\) | |||||||
\(728\) | 689418. | 0.0482119 | ||||||||
\(729\) | −2.06415e7 | −1.43854 | ||||||||
\(730\) | −6.77449e6 | −0.470511 | ||||||||
\(731\) | −3.06513e7 | −2.12156 | ||||||||
\(732\) | 2.18681e7 | 1.50846 | ||||||||
\(733\) | −2.66588e7 | −1.83265 | −0.916327 | − | 0.400430i | \(-0.868861\pi\) | ||||
−0.916327 | + | 0.400430i | \(0.868861\pi\) | |||||||
\(734\) | 1.14352e7 | 0.783438 | ||||||||
\(735\) | −9.79220e6 | −0.668593 | ||||||||
\(736\) | 1.80804e7 | 1.23031 | ||||||||
\(737\) | 6.04193e6 | 0.409739 | ||||||||
\(738\) | −2.71942e7 | −1.83796 | ||||||||
\(739\) | −5.21068e6 | −0.350981 | −0.175490 | − | 0.984481i | \(-0.556151\pi\) | ||||
−0.175490 | + | 0.984481i | \(0.556151\pi\) | |||||||
\(740\) | 4.40177e6 | 0.295494 | ||||||||
\(741\) | 6.13313e6 | 0.410333 | ||||||||
\(742\) | 1.23037e6 | 0.0820400 | ||||||||
\(743\) | 2.04875e7 | 1.36149 | 0.680747 | − | 0.732518i | \(-0.261655\pi\) | ||||
0.680747 | + | 0.732518i | \(0.261655\pi\) | |||||||
\(744\) | 1.35631e7 | 0.898313 | ||||||||
\(745\) | −204620. | −0.0135069 | ||||||||
\(746\) | 2.60969e7 | 1.71689 | ||||||||
\(747\) | 3.39459e7 | 2.22580 | ||||||||
\(748\) | 3.12982e6 | 0.204534 | ||||||||
\(749\) | −1.15024e6 | −0.0749173 | ||||||||
\(750\) | −2.61413e6 | −0.169697 | ||||||||
\(751\) | −7.21719e6 | −0.466948 | −0.233474 | − | 0.972363i | \(-0.575009\pi\) | ||||
−0.233474 | + | 0.972363i | \(0.575009\pi\) | |||||||
\(752\) | 1.86569e7 | 1.20308 | ||||||||
\(753\) | 1.59185e7 | 1.02309 | ||||||||
\(754\) | −9.16535e6 | −0.587112 | ||||||||
\(755\) | 1.03101e7 | 0.658259 | ||||||||
\(756\) | 288385. | 0.0183514 | ||||||||
\(757\) | −2.34446e7 | −1.48697 | −0.743487 | − | 0.668751i | \(-0.766829\pi\) | ||||
−0.743487 | + | 0.668751i | \(0.766829\pi\) | |||||||
\(758\) | −3.36486e7 | −2.12713 | ||||||||
\(759\) | −8.43510e6 | −0.531479 | ||||||||
\(760\) | −843348. | −0.0529630 | ||||||||
\(761\) | −1.03281e6 | −0.0646484 | −0.0323242 | − | 0.999477i | \(-0.510291\pi\) | ||||
−0.0323242 | + | 0.999477i | \(0.510291\pi\) | |||||||
\(762\) | −4.78182e6 | −0.298336 | ||||||||
\(763\) | −1.38424e6 | −0.0860795 | ||||||||
\(764\) | 5.97882e6 | 0.370580 | ||||||||
\(765\) | −1.04988e7 | −0.648613 | ||||||||
\(766\) | −1.04410e7 | −0.642937 | ||||||||
\(767\) | 1.02499e7 | 0.629119 | ||||||||
\(768\) | −3.13635e7 | −1.91876 | ||||||||
\(769\) | 2.44745e7 | 1.49245 | 0.746223 | − | 0.665696i | \(-0.231865\pi\) | ||||
0.746223 | + | 0.665696i | \(0.231865\pi\) | |||||||
\(770\) | −219776. | −0.0133584 | ||||||||
\(771\) | 2.18010e7 | 1.32081 | ||||||||
\(772\) | 1.15025e7 | 0.694620 | ||||||||
\(773\) | 1.08231e7 | 0.651484 | 0.325742 | − | 0.945459i | \(-0.394386\pi\) | ||||
0.325742 | + | 0.945459i | \(0.394386\pi\) | |||||||
\(774\) | 4.90439e7 | 2.94261 | ||||||||
\(775\) | −3.86850e6 | −0.231360 | ||||||||
\(776\) | 2.79518e6 | 0.166631 | ||||||||
\(777\) | −2.22430e6 | −0.132172 | ||||||||
\(778\) | 3.75005e7 | 2.22120 | ||||||||
\(779\) | 4.48365e6 | 0.264721 | ||||||||
\(780\) | −8.02848e6 | −0.472494 | ||||||||
\(781\) | 436411. | 0.0256017 | ||||||||
\(782\) | −2.90237e7 | −1.69721 | ||||||||
\(783\) | 2.65651e6 | 0.154849 | ||||||||
\(784\) | 2.12395e7 | 1.23411 | ||||||||
\(785\) | −6.07658e6 | −0.351953 | ||||||||
\(786\) | 7.55664e6 | 0.436287 | ||||||||
\(787\) | −1.65559e7 | −0.952833 | −0.476417 | − | 0.879220i | \(-0.658065\pi\) | ||||
−0.476417 | + | 0.879220i | \(0.658065\pi\) | |||||||
\(788\) | −8.71448e6 | −0.499949 | ||||||||
\(789\) | −9.70737e6 | −0.555149 | ||||||||
\(790\) | 9.27357e6 | 0.528663 | ||||||||
\(791\) | 1.90400e6 | 0.108199 | ||||||||
\(792\) | 3.46998e6 | 0.196569 | ||||||||
\(793\) | 3.57432e7 | 2.01842 | ||||||||
\(794\) | 1.10208e7 | 0.620385 | ||||||||
\(795\) | 9.92793e6 | 0.557110 | ||||||||
\(796\) | −1.92157e6 | −0.107491 | ||||||||
\(797\) | 2.25936e7 | 1.25991 | 0.629956 | − | 0.776631i | \(-0.283073\pi\) | ||||
0.629956 | + | 0.776631i | \(0.283073\pi\) | |||||||
\(798\) | −615035. | −0.0341895 | ||||||||
\(799\) | −2.00777e7 | −1.11262 | ||||||||
\(800\) | 3.80120e6 | 0.209988 | ||||||||
\(801\) | 2.22552e7 | 1.22560 | ||||||||
\(802\) | −4.26560e7 | −2.34177 | ||||||||
\(803\) | −4.59571e6 | −0.251515 | ||||||||
\(804\) | −2.21333e7 | −1.20755 | ||||||||
\(805\) | 756820. | 0.0411626 | ||||||||
\(806\) | −3.19940e7 | −1.73473 | ||||||||
\(807\) | −2.33263e7 | −1.26084 | ||||||||
\(808\) | −781709. | −0.0421228 | ||||||||
\(809\) | 1.66890e7 | 0.896520 | 0.448260 | − | 0.893903i | \(-0.352044\pi\) | ||||
0.448260 | + | 0.893903i | \(0.352044\pi\) | |||||||
\(810\) | −7.03504e6 | −0.376751 | ||||||||
\(811\) | −3.27766e7 | −1.74990 | −0.874948 | − | 0.484217i | \(-0.839105\pi\) | ||||
−0.874948 | + | 0.484217i | \(0.839105\pi\) | |||||||
\(812\) | 341307. | 0.0181658 | ||||||||
\(813\) | 1.20126e7 | 0.637400 | ||||||||
\(814\) | 8.04126e6 | 0.425366 | ||||||||
\(815\) | −8.33618e6 | −0.439615 | ||||||||
\(816\) | 4.08034e7 | 2.14522 | ||||||||
\(817\) | −8.08612e6 | −0.423823 | ||||||||
\(818\) | −2.95967e7 | −1.54653 | ||||||||
\(819\) | 2.26415e6 | 0.117949 | ||||||||
\(820\) | −5.86925e6 | −0.304823 | ||||||||
\(821\) | −1.60822e7 | −0.832697 | −0.416348 | − | 0.909205i | \(-0.636690\pi\) | ||||
−0.416348 | + | 0.909205i | \(0.636690\pi\) | |||||||
\(822\) | 4.86660e7 | 2.51215 | ||||||||
\(823\) | 2.03558e7 | 1.04758 | 0.523791 | − | 0.851847i | \(-0.324517\pi\) | ||||
0.523791 | + | 0.851847i | \(0.324517\pi\) | |||||||
\(824\) | 1.27399e7 | 0.653655 | ||||||||
\(825\) | −1.77339e6 | −0.0907128 | ||||||||
\(826\) | −1.02787e6 | −0.0524189 | ||||||||
\(827\) | −2.47509e7 | −1.25842 | −0.629211 | − | 0.777234i | \(-0.716622\pi\) | ||||
−0.629211 | + | 0.777234i | \(0.716622\pi\) | |||||||
\(828\) | 1.72452e7 | 0.874162 | ||||||||
\(829\) | 2.98798e7 | 1.51005 | 0.755026 | − | 0.655695i | \(-0.227624\pi\) | ||||
0.755026 | + | 0.655695i | \(0.227624\pi\) | |||||||
\(830\) | 1.97294e7 | 0.994073 | ||||||||
\(831\) | 1.66183e7 | 0.834802 | ||||||||
\(832\) | 1.95727e6 | 0.0980264 | ||||||||
\(833\) | −2.28570e7 | −1.14132 | ||||||||
\(834\) | −5.97056e7 | −2.97235 | ||||||||
\(835\) | −2.50526e6 | −0.124347 | ||||||||
\(836\) | 825677. | 0.0408597 | ||||||||
\(837\) | 9.27325e6 | 0.457529 | ||||||||
\(838\) | 2.28528e7 | 1.12416 | ||||||||
\(839\) | −4.58350e6 | −0.224798 | −0.112399 | − | 0.993663i | \(-0.535853\pi\) | ||||
−0.112399 | + | 0.993663i | \(0.535853\pi\) | |||||||
\(840\) | −557857. | −0.0272788 | ||||||||
\(841\) | −1.73671e7 | −0.846717 | ||||||||
\(842\) | 7.80982e6 | 0.379630 | ||||||||
\(843\) | −3.02117e7 | −1.46422 | ||||||||
\(844\) | 1.97710e6 | 0.0955371 | ||||||||
\(845\) | −3.84012e6 | −0.185013 | ||||||||
\(846\) | 3.21255e7 | 1.54320 | ||||||||
\(847\) | −149093. | −0.00714081 | ||||||||
\(848\) | −2.15339e7 | −1.02833 | ||||||||
\(849\) | 3.17238e7 | 1.51048 | ||||||||
\(850\) | −6.10191e6 | −0.289680 | ||||||||
\(851\) | −2.76909e7 | −1.31073 | ||||||||
\(852\) | −1.59870e6 | −0.0754514 | ||||||||
\(853\) | −2.81267e7 | −1.32357 | −0.661784 | − | 0.749695i | \(-0.730200\pi\) | ||||
−0.661784 | + | 0.749695i | \(0.730200\pi\) | |||||||
\(854\) | −3.58435e6 | −0.168177 | ||||||||
\(855\) | −2.76968e6 | −0.129573 | ||||||||
\(856\) | 1.05551e7 | 0.492353 | ||||||||
\(857\) | −1.32333e7 | −0.615485 | −0.307742 | − | 0.951470i | \(-0.599574\pi\) | ||||
−0.307742 | + | 0.951470i | \(0.599574\pi\) | |||||||
\(858\) | −1.46666e7 | −0.680161 | ||||||||
\(859\) | −1.99257e7 | −0.921365 | −0.460682 | − | 0.887565i | \(-0.652395\pi\) | ||||
−0.460682 | + | 0.887565i | \(0.652395\pi\) | |||||||
\(860\) | 1.05850e7 | 0.488028 | ||||||||
\(861\) | 2.96584e6 | 0.136345 | ||||||||
\(862\) | −3.20909e7 | −1.47101 | ||||||||
\(863\) | 3.60952e7 | 1.64976 | 0.824882 | − | 0.565304i | \(-0.191241\pi\) | ||||
0.824882 | + | 0.565304i | \(0.191241\pi\) | |||||||
\(864\) | −9.11192e6 | −0.415265 | ||||||||
\(865\) | −1.78077e7 | −0.809224 | ||||||||
\(866\) | −2.76536e7 | −1.25302 | ||||||||
\(867\) | −1.06155e7 | −0.479615 | ||||||||
\(868\) | 1.19142e6 | 0.0536743 | ||||||||
\(869\) | 6.29105e6 | 0.282601 | ||||||||
\(870\) | 7.41634e6 | 0.332194 | ||||||||
\(871\) | −3.61766e7 | −1.61578 | ||||||||
\(872\) | 1.27024e7 | 0.565711 | ||||||||
\(873\) | 9.17980e6 | 0.407660 | ||||||||
\(874\) | −7.65674e6 | −0.339051 | ||||||||
\(875\) | 159113. | 0.00702563 | ||||||||
\(876\) | 1.68354e7 | 0.741246 | ||||||||
\(877\) | 2.63968e7 | 1.15892 | 0.579458 | − | 0.815002i | \(-0.303264\pi\) | ||||
0.579458 | + | 0.815002i | \(0.303264\pi\) | |||||||
\(878\) | 2.75658e6 | 0.120680 | ||||||||
\(879\) | 6.27637e6 | 0.273991 | ||||||||
\(880\) | 3.84652e6 | 0.167441 | ||||||||
\(881\) | 2.89523e7 | 1.25673 | 0.628367 | − | 0.777917i | \(-0.283724\pi\) | ||||
0.628367 | + | 0.777917i | \(0.283724\pi\) | |||||||
\(882\) | 3.65725e7 | 1.58301 | ||||||||
\(883\) | −2.41824e7 | −1.04375 | −0.521876 | − | 0.853022i | \(-0.674767\pi\) | ||||
−0.521876 | + | 0.853022i | \(0.674767\pi\) | |||||||
\(884\) | −1.87401e7 | −0.806568 | ||||||||
\(885\) | −8.29395e6 | −0.355962 | ||||||||
\(886\) | 2.08930e7 | 0.894163 | ||||||||
\(887\) | −2.52582e7 | −1.07794 | −0.538968 | − | 0.842326i | \(-0.681186\pi\) | ||||
−0.538968 | + | 0.842326i | \(0.681186\pi\) | |||||||
\(888\) | 2.04111e7 | 0.868629 | ||||||||
\(889\) | 291052. | 0.0123514 | ||||||||
\(890\) | 1.29347e7 | 0.547373 | ||||||||
\(891\) | −4.77247e6 | −0.201395 | ||||||||
\(892\) | 7.71559e6 | 0.324681 | ||||||||
\(893\) | −5.29669e6 | −0.222268 | ||||||||
\(894\) | 1.36935e6 | 0.0573021 | ||||||||
\(895\) | 1.96352e7 | 0.819364 | ||||||||
\(896\) | 1.78559e6 | 0.0743041 | ||||||||
\(897\) | 5.05059e7 | 2.09586 | ||||||||
\(898\) | 3.99278e7 | 1.65228 | ||||||||
\(899\) | 1.09750e7 | 0.452903 | ||||||||
\(900\) | 3.62560e6 | 0.149202 | ||||||||
\(901\) | 2.31738e7 | 0.951011 | ||||||||
\(902\) | −1.07221e7 | −0.438796 | ||||||||
\(903\) | −5.34879e6 | −0.218291 | ||||||||
\(904\) | −1.74719e7 | −0.711081 | ||||||||
\(905\) | 4.52898e6 | 0.183814 | ||||||||
\(906\) | −6.89972e7 | −2.79261 | ||||||||
\(907\) | 3.28410e7 | 1.32556 | 0.662778 | − | 0.748816i | \(-0.269377\pi\) | ||||
0.662778 | + | 0.748816i | \(0.269377\pi\) | |||||||
\(908\) | 3.71000e6 | 0.149334 | ||||||||
\(909\) | −2.56725e6 | −0.103052 | ||||||||
\(910\) | 1.31593e6 | 0.0526779 | ||||||||
\(911\) | −1.45892e7 | −0.582418 | −0.291209 | − | 0.956659i | \(-0.594057\pi\) | ||||
−0.291209 | + | 0.956659i | \(0.594057\pi\) | |||||||
\(912\) | 1.07643e7 | 0.428549 | ||||||||
\(913\) | 1.33841e7 | 0.531389 | ||||||||
\(914\) | 1.28265e6 | 0.0507859 | ||||||||
\(915\) | −2.89224e7 | −1.14204 | ||||||||
\(916\) | 1.07793e7 | 0.424475 | ||||||||
\(917\) | −459946. | −0.0180627 | ||||||||
\(918\) | 1.46270e7 | 0.572860 | ||||||||
\(919\) | −1.90083e7 | −0.742428 | −0.371214 | − | 0.928547i | \(-0.621058\pi\) | ||||
−0.371214 | + | 0.928547i | \(0.621058\pi\) | |||||||
\(920\) | −6.94492e6 | −0.270519 | ||||||||
\(921\) | −1.38438e7 | −0.537782 | ||||||||
\(922\) | 2.06471e7 | 0.799894 | ||||||||
\(923\) | −2.61305e6 | −0.100959 | ||||||||
\(924\) | 546168. | 0.0210449 | ||||||||
\(925\) | −5.82170e6 | −0.223715 | ||||||||
\(926\) | −3.29768e7 | −1.26381 | ||||||||
\(927\) | 4.18398e7 | 1.59915 | ||||||||
\(928\) | −1.07841e7 | −0.411067 | ||||||||
\(929\) | 2.97742e7 | 1.13188 | 0.565941 | − | 0.824446i | \(-0.308513\pi\) | ||||
0.565941 | + | 0.824446i | \(0.308513\pi\) | |||||||
\(930\) | 2.58887e7 | 0.981527 | ||||||||
\(931\) | −6.02989e6 | −0.228000 | ||||||||
\(932\) | 1.48385e7 | 0.559564 | ||||||||
\(933\) | 2.70511e7 | 1.01737 | ||||||||
\(934\) | 3.91605e6 | 0.146886 | ||||||||
\(935\) | −4.13944e6 | −0.154851 | ||||||||
\(936\) | −2.07768e7 | −0.775157 | ||||||||
\(937\) | 3.10909e7 | 1.15687 | 0.578434 | − | 0.815729i | \(-0.303664\pi\) | ||||
0.578434 | + | 0.815729i | \(0.303664\pi\) | |||||||
\(938\) | 3.62781e6 | 0.134629 | ||||||||
\(939\) | 2.03832e7 | 0.754413 | ||||||||
\(940\) | 6.93355e6 | 0.255939 | ||||||||
\(941\) | 1.24141e7 | 0.457025 | 0.228513 | − | 0.973541i | \(-0.426614\pi\) | ||||
0.228513 | + | 0.973541i | \(0.426614\pi\) | |||||||
\(942\) | 4.06655e7 | 1.49313 | ||||||||
\(943\) | 3.69226e7 | 1.35211 | ||||||||
\(944\) | 1.79898e7 | 0.657046 | ||||||||
\(945\) | −381412. | −0.0138936 | ||||||||
\(946\) | 1.93369e7 | 0.702522 | ||||||||
\(947\) | −3.55400e7 | −1.28778 | −0.643891 | − | 0.765117i | \(-0.722681\pi\) | ||||
−0.643891 | + | 0.765117i | \(0.722681\pi\) | |||||||
\(948\) | −2.30459e7 | −0.832861 | ||||||||
\(949\) | 2.75172e7 | 0.991834 | ||||||||
\(950\) | −1.60974e6 | −0.0578692 | ||||||||
\(951\) | −3.24787e7 | −1.16452 | ||||||||
\(952\) | −1.30215e6 | −0.0465660 | ||||||||
\(953\) | 2.63749e7 | 0.940716 | 0.470358 | − | 0.882476i | \(-0.344125\pi\) | ||||
0.470358 | + | 0.882476i | \(0.344125\pi\) | |||||||
\(954\) | −3.70794e7 | −1.31905 | ||||||||
\(955\) | −7.90747e6 | −0.280562 | ||||||||
\(956\) | 1.51677e7 | 0.536753 | ||||||||
\(957\) | 5.03113e6 | 0.177577 | ||||||||
\(958\) | −3.97091e7 | −1.39790 | ||||||||
\(959\) | −2.96213e6 | −0.104006 | ||||||||
\(960\) | −1.58377e6 | −0.0554643 | ||||||||
\(961\) | 9.68198e6 | 0.338186 | ||||||||
\(962\) | −4.81478e7 | −1.67741 | ||||||||
\(963\) | 3.46644e7 | 1.20453 | ||||||||
\(964\) | −481792. | −0.0166981 | ||||||||
\(965\) | −1.52129e7 | −0.525889 | ||||||||
\(966\) | −5.06477e6 | −0.174629 | ||||||||
\(967\) | −5.28241e7 | −1.81663 | −0.908314 | − | 0.418289i | \(-0.862630\pi\) | ||||
−0.908314 | + | 0.418289i | \(0.862630\pi\) | |||||||
\(968\) | 1.36814e6 | 0.0469291 | ||||||||
\(969\) | −1.15841e7 | −0.396326 | ||||||||
\(970\) | 5.33531e6 | 0.182067 | ||||||||
\(971\) | 2.42410e7 | 0.825092 | 0.412546 | − | 0.910937i | \(-0.364640\pi\) | ||||
0.412546 | + | 0.910937i | \(0.364640\pi\) | |||||||
\(972\) | 2.43646e7 | 0.827166 | ||||||||
\(973\) | 3.63407e6 | 0.123058 | ||||||||
\(974\) | −3.01214e7 | −1.01737 | ||||||||
\(975\) | 1.06183e7 | 0.357720 | ||||||||
\(976\) | 6.27334e7 | 2.10802 | ||||||||
\(977\) | −4.50760e7 | −1.51081 | −0.755404 | − | 0.655260i | \(-0.772559\pi\) | ||||
−0.755404 | + | 0.655260i | \(0.772559\pi\) | |||||||
\(978\) | 5.57871e7 | 1.86503 | ||||||||
\(979\) | 8.77474e6 | 0.292602 | ||||||||
\(980\) | 7.89333e6 | 0.262540 | ||||||||
\(981\) | 4.17166e7 | 1.38400 | ||||||||
\(982\) | −4.53433e7 | −1.50049 | ||||||||
\(983\) | 1.19204e7 | 0.393465 | 0.196733 | − | 0.980457i | \(-0.436967\pi\) | ||||
0.196733 | + | 0.980457i | \(0.436967\pi\) | |||||||
\(984\) | −2.72159e7 | −0.896055 | ||||||||
\(985\) | 1.15256e7 | 0.378506 | ||||||||
\(986\) | 1.73112e7 | 0.567069 | ||||||||
\(987\) | −3.50365e6 | −0.114480 | ||||||||
\(988\) | −4.94382e6 | −0.161128 | ||||||||
\(989\) | −6.65886e7 | −2.16476 | ||||||||
\(990\) | 6.62334e6 | 0.214778 | ||||||||
\(991\) | 2.72613e7 | 0.881783 | 0.440892 | − | 0.897560i | \(-0.354662\pi\) | ||||
0.440892 | + | 0.897560i | \(0.354662\pi\) | |||||||
\(992\) | −3.76446e7 | −1.21457 | ||||||||
\(993\) | 5.43575e7 | 1.74939 | ||||||||
\(994\) | 262039. | 0.00841200 | ||||||||
\(995\) | 2.54143e6 | 0.0813805 | ||||||||
\(996\) | −4.90298e7 | −1.56607 | ||||||||
\(997\) | −1.82305e7 | −0.580846 | −0.290423 | − | 0.956898i | \(-0.593796\pi\) | ||||
−0.290423 | + | 0.956898i | \(0.593796\pi\) | |||||||
\(998\) | 6.32645e7 | 2.01064 | ||||||||
\(999\) | 1.39553e7 | 0.442410 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1045.6.a.a.1.8 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.a.1.8 | ✓ | 35 | 1.1 | even | 1 | trivial |