Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,6,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(157.657294876\) |
Analytic rank: | \(0\) |
Dimension: | \(218\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.86337 | −1.74361 | −0.871807 | − | 0.489849i | \(-0.837052\pi\) | ||||
−0.871807 | + | 0.489849i | \(0.837052\pi\) | |||||||
\(3\) | −14.1514 | −0.907814 | −0.453907 | − | 0.891049i | \(-0.649970\pi\) | ||||
−0.453907 | + | 0.891049i | \(0.649970\pi\) | |||||||
\(4\) | 65.2861 | 2.04019 | ||||||||
\(5\) | 8.97631 | 0.160573 | 0.0802865 | − | 0.996772i | \(-0.474416\pi\) | ||||
0.0802865 | + | 0.996772i | \(0.474416\pi\) | |||||||
\(6\) | 139.581 | 1.58288 | ||||||||
\(7\) | −99.2905 | −0.765883 | −0.382942 | − | 0.923772i | \(-0.625089\pi\) | ||||
−0.382942 | + | 0.923772i | \(0.625089\pi\) | |||||||
\(8\) | −328.313 | −1.81369 | ||||||||
\(9\) | −42.7375 | −0.175875 | ||||||||
\(10\) | −88.5367 | −0.279977 | ||||||||
\(11\) | 111.541 | 0.277942 | 0.138971 | − | 0.990296i | \(-0.455620\pi\) | ||||
0.138971 | + | 0.990296i | \(0.455620\pi\) | |||||||
\(12\) | −923.891 | −1.85211 | ||||||||
\(13\) | −531.103 | −0.871607 | −0.435804 | − | 0.900042i | \(-0.643536\pi\) | ||||
−0.435804 | + | 0.900042i | \(0.643536\pi\) | |||||||
\(14\) | 979.339 | 1.33541 | ||||||||
\(15\) | −127.027 | −0.145770 | ||||||||
\(16\) | 1149.12 | 1.12219 | ||||||||
\(17\) | 1571.26 | 1.31864 | 0.659320 | − | 0.751862i | \(-0.270844\pi\) | ||||
0.659320 | + | 0.751862i | \(0.270844\pi\) | |||||||
\(18\) | 421.536 | 0.306657 | ||||||||
\(19\) | −264.968 | −0.168387 | −0.0841937 | − | 0.996449i | \(-0.526831\pi\) | ||||
−0.0841937 | + | 0.996449i | \(0.526831\pi\) | |||||||
\(20\) | 586.028 | 0.327600 | ||||||||
\(21\) | 1405.10 | 0.695279 | ||||||||
\(22\) | −1100.18 | −0.484624 | ||||||||
\(23\) | −3900.63 | −1.53750 | −0.768750 | − | 0.639550i | \(-0.779121\pi\) | ||||
−0.768750 | + | 0.639550i | \(0.779121\pi\) | |||||||
\(24\) | 4646.10 | 1.64650 | ||||||||
\(25\) | −3044.43 | −0.974216 | ||||||||
\(26\) | 5238.47 | 1.51975 | ||||||||
\(27\) | 4043.59 | 1.06747 | ||||||||
\(28\) | −6482.29 | −1.56255 | ||||||||
\(29\) | −66.6159 | −0.0147090 | −0.00735449 | − | 0.999973i | \(-0.502341\pi\) | ||||
−0.00735449 | + | 0.999973i | \(0.502341\pi\) | |||||||
\(30\) | 1252.92 | 0.254167 | ||||||||
\(31\) | −9708.03 | −1.81437 | −0.907187 | − | 0.420727i | \(-0.861775\pi\) | ||||
−0.907187 | + | 0.420727i | \(0.861775\pi\) | |||||||
\(32\) | −828.191 | −0.142974 | ||||||||
\(33\) | −1578.47 | −0.252320 | ||||||||
\(34\) | −15498.0 | −2.29920 | ||||||||
\(35\) | −891.262 | −0.122980 | ||||||||
\(36\) | −2790.17 | −0.358818 | ||||||||
\(37\) | −8340.98 | −1.00164 | −0.500821 | − | 0.865551i | \(-0.666969\pi\) | ||||
−0.500821 | + | 0.865551i | \(0.666969\pi\) | |||||||
\(38\) | 2613.48 | 0.293603 | ||||||||
\(39\) | 7515.86 | 0.791257 | ||||||||
\(40\) | −2947.04 | −0.291230 | ||||||||
\(41\) | 886.529 | 0.0823632 | 0.0411816 | − | 0.999152i | \(-0.486888\pi\) | ||||
0.0411816 | + | 0.999152i | \(0.486888\pi\) | |||||||
\(42\) | −13859.0 | −1.21230 | ||||||||
\(43\) | −8108.75 | −0.668780 | −0.334390 | − | 0.942435i | \(-0.608530\pi\) | ||||
−0.334390 | + | 0.942435i | \(0.608530\pi\) | |||||||
\(44\) | 7282.11 | 0.567055 | ||||||||
\(45\) | −383.625 | −0.0282407 | ||||||||
\(46\) | 38473.3 | 2.68081 | ||||||||
\(47\) | 14909.8 | 0.984523 | 0.492262 | − | 0.870447i | \(-0.336170\pi\) | ||||
0.492262 | + | 0.870447i | \(0.336170\pi\) | |||||||
\(48\) | −16261.7 | −1.01874 | ||||||||
\(49\) | −6948.39 | −0.413422 | ||||||||
\(50\) | 30028.3 | 1.69866 | ||||||||
\(51\) | −22235.6 | −1.19708 | ||||||||
\(52\) | −34673.7 | −1.77825 | ||||||||
\(53\) | 9636.89 | 0.471246 | 0.235623 | − | 0.971845i | \(-0.424287\pi\) | ||||
0.235623 | + | 0.971845i | \(0.424287\pi\) | |||||||
\(54\) | −39883.4 | −1.86126 | ||||||||
\(55\) | 1001.23 | 0.0446300 | ||||||||
\(56\) | 32598.4 | 1.38908 | ||||||||
\(57\) | 3749.67 | 0.152864 | ||||||||
\(58\) | 657.057 | 0.0256468 | ||||||||
\(59\) | 15352.7 | 0.574190 | 0.287095 | − | 0.957902i | \(-0.407310\pi\) | ||||
0.287095 | + | 0.957902i | \(0.407310\pi\) | |||||||
\(60\) | −8293.13 | −0.297400 | ||||||||
\(61\) | 23017.1 | 0.792002 | 0.396001 | − | 0.918250i | \(-0.370398\pi\) | ||||
0.396001 | + | 0.918250i | \(0.370398\pi\) | |||||||
\(62\) | 95753.9 | 3.16357 | ||||||||
\(63\) | 4243.43 | 0.134699 | ||||||||
\(64\) | −28603.2 | −0.872899 | ||||||||
\(65\) | −4767.35 | −0.139957 | ||||||||
\(66\) | 15569.0 | 0.439948 | ||||||||
\(67\) | 48328.1 | 1.31526 | 0.657631 | − | 0.753340i | \(-0.271559\pi\) | ||||
0.657631 | + | 0.753340i | \(0.271559\pi\) | |||||||
\(68\) | 102582. | 2.69028 | ||||||||
\(69\) | 55199.4 | 1.39576 | ||||||||
\(70\) | 8790.85 | 0.214430 | ||||||||
\(71\) | −82166.5 | −1.93441 | −0.967206 | − | 0.253995i | \(-0.918255\pi\) | ||||
−0.967206 | + | 0.253995i | \(0.918255\pi\) | |||||||
\(72\) | 14031.3 | 0.318982 | ||||||||
\(73\) | −33236.7 | −0.729979 | −0.364990 | − | 0.931012i | \(-0.618927\pi\) | ||||
−0.364990 | + | 0.931012i | \(0.618927\pi\) | |||||||
\(74\) | 82270.2 | 1.74648 | ||||||||
\(75\) | 43082.9 | 0.884407 | ||||||||
\(76\) | −17298.7 | −0.343543 | ||||||||
\(77\) | −11075.0 | −0.212871 | ||||||||
\(78\) | −74131.8 | −1.37965 | ||||||||
\(79\) | −21080.5 | −0.380025 | −0.190013 | − | 0.981782i | \(-0.560853\pi\) | ||||
−0.190013 | + | 0.981782i | \(0.560853\pi\) | |||||||
\(80\) | 10314.9 | 0.180193 | ||||||||
\(81\) | −46837.3 | −0.793194 | ||||||||
\(82\) | −8744.17 | −0.143610 | ||||||||
\(83\) | −73614.2 | −1.17291 | −0.586457 | − | 0.809980i | \(-0.699478\pi\) | ||||
−0.586457 | + | 0.809980i | \(0.699478\pi\) | |||||||
\(84\) | 91733.6 | 1.41850 | ||||||||
\(85\) | 14104.1 | 0.211738 | ||||||||
\(86\) | 79979.7 | 1.16609 | ||||||||
\(87\) | 942.709 | 0.0133530 | ||||||||
\(88\) | −36620.6 | −0.504102 | ||||||||
\(89\) | 74582.2 | 0.998068 | 0.499034 | − | 0.866583i | \(-0.333688\pi\) | ||||
0.499034 | + | 0.866583i | \(0.333688\pi\) | |||||||
\(90\) | 3783.84 | 0.0492409 | ||||||||
\(91\) | 52733.5 | 0.667549 | ||||||||
\(92\) | −254657. | −3.13679 | ||||||||
\(93\) | 137382. | 1.64711 | ||||||||
\(94\) | −147061. | −1.71663 | ||||||||
\(95\) | −2378.44 | −0.0270385 | ||||||||
\(96\) | 11720.1 | 0.129793 | ||||||||
\(97\) | 3359.59 | 0.0362541 | 0.0181271 | − | 0.999836i | \(-0.494230\pi\) | ||||
0.0181271 | + | 0.999836i | \(0.494230\pi\) | |||||||
\(98\) | 68534.6 | 0.720849 | ||||||||
\(99\) | −4767.01 | −0.0488830 | ||||||||
\(100\) | −198759. | −1.98759 | ||||||||
\(101\) | −148108. | −1.44469 | −0.722345 | − | 0.691533i | \(-0.756936\pi\) | ||||
−0.722345 | + | 0.691533i | \(0.756936\pi\) | |||||||
\(102\) | 219318. | 2.08725 | ||||||||
\(103\) | −14922.1 | −0.138592 | −0.0692958 | − | 0.997596i | \(-0.522075\pi\) | ||||
−0.0692958 | + | 0.997596i | \(0.522075\pi\) | |||||||
\(104\) | 174368. | 1.58083 | ||||||||
\(105\) | 12612.6 | 0.111643 | ||||||||
\(106\) | −95052.2 | −0.821670 | ||||||||
\(107\) | −50031.3 | −0.422457 | −0.211229 | − | 0.977437i | \(-0.567746\pi\) | ||||
−0.211229 | + | 0.977437i | \(0.567746\pi\) | |||||||
\(108\) | 263990. | 2.17785 | ||||||||
\(109\) | 20239.2 | 0.163165 | 0.0815827 | − | 0.996667i | \(-0.474003\pi\) | ||||
0.0815827 | + | 0.996667i | \(0.474003\pi\) | |||||||
\(110\) | −9875.51 | −0.0778176 | ||||||||
\(111\) | 118037. | 0.909305 | ||||||||
\(112\) | −114097. | −0.859467 | ||||||||
\(113\) | −59127.0 | −0.435602 | −0.217801 | − | 0.975993i | \(-0.569888\pi\) | ||||
−0.217801 | + | 0.975993i | \(0.569888\pi\) | |||||||
\(114\) | −36984.4 | −0.266537 | ||||||||
\(115\) | −35013.2 | −0.246881 | ||||||||
\(116\) | −4349.09 | −0.0300092 | ||||||||
\(117\) | 22698.0 | 0.153294 | ||||||||
\(118\) | −151430. | −1.00117 | ||||||||
\(119\) | −156012. | −1.00993 | ||||||||
\(120\) | 41704.8 | 0.264383 | ||||||||
\(121\) | −148610. | −0.922748 | ||||||||
\(122\) | −227026. | −1.38095 | ||||||||
\(123\) | −12545.6 | −0.0747704 | ||||||||
\(124\) | −633800. | −3.70167 | ||||||||
\(125\) | −55378.7 | −0.317006 | ||||||||
\(126\) | −41854.5 | −0.234864 | ||||||||
\(127\) | 34082.9 | 0.187511 | 0.0937556 | − | 0.995595i | \(-0.470113\pi\) | ||||
0.0937556 | + | 0.995595i | \(0.470113\pi\) | |||||||
\(128\) | 308626. | 1.66497 | ||||||||
\(129\) | 114750. | 0.607127 | ||||||||
\(130\) | 47022.1 | 0.244030 | ||||||||
\(131\) | −227377. | −1.15763 | −0.578814 | − | 0.815460i | \(-0.696484\pi\) | ||||
−0.578814 | + | 0.815460i | \(0.696484\pi\) | |||||||
\(132\) | −103052. | −0.514781 | ||||||||
\(133\) | 26308.8 | 0.128965 | ||||||||
\(134\) | −476678. | −2.29331 | ||||||||
\(135\) | 36296.5 | 0.171408 | ||||||||
\(136\) | −515867. | −2.39161 | ||||||||
\(137\) | −392429. | −1.78632 | −0.893162 | − | 0.449736i | \(-0.851518\pi\) | ||||
−0.893162 | + | 0.449736i | \(0.851518\pi\) | |||||||
\(138\) | −544452. | −2.43367 | ||||||||
\(139\) | −4264.18 | −0.0187197 | −0.00935985 | − | 0.999956i | \(-0.502979\pi\) | ||||
−0.00935985 | + | 0.999956i | \(0.502979\pi\) | |||||||
\(140\) | −58187.1 | −0.250903 | ||||||||
\(141\) | −210994. | −0.893764 | ||||||||
\(142\) | 810439. | 3.37287 | ||||||||
\(143\) | −59240.1 | −0.242256 | ||||||||
\(144\) | −49110.6 | −0.197365 | ||||||||
\(145\) | −597.965 | −0.00236187 | ||||||||
\(146\) | 327826. | 1.27280 | ||||||||
\(147\) | 98329.6 | 0.375311 | ||||||||
\(148\) | −544550. | −2.04354 | ||||||||
\(149\) | −329553. | −1.21607 | −0.608036 | − | 0.793909i | \(-0.708043\pi\) | ||||
−0.608036 | + | 0.793909i | \(0.708043\pi\) | |||||||
\(150\) | −424943. | −1.54206 | ||||||||
\(151\) | −215741. | −0.770000 | −0.385000 | − | 0.922917i | \(-0.625799\pi\) | ||||
−0.385000 | + | 0.922917i | \(0.625799\pi\) | |||||||
\(152\) | 86992.6 | 0.305403 | ||||||||
\(153\) | −67151.9 | −0.231915 | ||||||||
\(154\) | 109237. | 0.371166 | ||||||||
\(155\) | −87142.3 | −0.291340 | ||||||||
\(156\) | 490682. | 1.61432 | ||||||||
\(157\) | 253368. | 0.820357 | 0.410179 | − | 0.912005i | \(-0.365466\pi\) | ||||
0.410179 | + | 0.912005i | \(0.365466\pi\) | |||||||
\(158\) | 207924. | 0.662617 | ||||||||
\(159\) | −136376. | −0.427803 | ||||||||
\(160\) | −7434.10 | −0.0229577 | ||||||||
\(161\) | 387295. | 1.17755 | ||||||||
\(162\) | 461974. | 1.38302 | ||||||||
\(163\) | −46194.6 | −0.136183 | −0.0680914 | − | 0.997679i | \(-0.521691\pi\) | ||||
−0.0680914 | + | 0.997679i | \(0.521691\pi\) | |||||||
\(164\) | 57878.0 | 0.168037 | ||||||||
\(165\) | −14168.8 | −0.0405158 | ||||||||
\(166\) | 726084. | 2.04511 | ||||||||
\(167\) | −129478. | −0.359256 | −0.179628 | − | 0.983735i | \(-0.557489\pi\) | ||||
−0.179628 | + | 0.983735i | \(0.557489\pi\) | |||||||
\(168\) | −461314. | −1.26102 | ||||||||
\(169\) | −89222.1 | −0.240301 | ||||||||
\(170\) | −139114. | −0.369190 | ||||||||
\(171\) | 11324.1 | 0.0296151 | ||||||||
\(172\) | −529389. | −1.36444 | ||||||||
\(173\) | −81131.0 | −0.206097 | −0.103048 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103048 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(174\) | −9298.29 | −0.0232825 | ||||||||
\(175\) | 302283. | 0.746136 | ||||||||
\(176\) | 128175. | 0.311904 | ||||||||
\(177\) | −217263. | −0.521258 | ||||||||
\(178\) | −735632. | −1.74025 | ||||||||
\(179\) | −303006. | −0.706836 | −0.353418 | − | 0.935466i | \(-0.614981\pi\) | ||||
−0.353418 | + | 0.935466i | \(0.614981\pi\) | |||||||
\(180\) | −25045.4 | −0.0576165 | ||||||||
\(181\) | −109800. | −0.249119 | −0.124560 | − | 0.992212i | \(-0.539752\pi\) | ||||
−0.124560 | + | 0.992212i | \(0.539752\pi\) | |||||||
\(182\) | −520131. | −1.16395 | ||||||||
\(183\) | −325725. | −0.718990 | ||||||||
\(184\) | 1.28063e6 | 2.78855 | ||||||||
\(185\) | −74871.2 | −0.160837 | ||||||||
\(186\) | −1.35505e6 | −2.87193 | ||||||||
\(187\) | 175261. | 0.366506 | ||||||||
\(188\) | 973400. | 2.00862 | ||||||||
\(189\) | −401490. | −0.817561 | ||||||||
\(190\) | 23459.4 | 0.0471447 | ||||||||
\(191\) | −432893. | −0.858612 | −0.429306 | − | 0.903159i | \(-0.641242\pi\) | ||||
−0.429306 | + | 0.903159i | \(0.641242\pi\) | |||||||
\(192\) | 404775. | 0.792430 | ||||||||
\(193\) | −595297. | −1.15038 | −0.575189 | − | 0.818021i | \(-0.695071\pi\) | ||||
−0.575189 | + | 0.818021i | \(0.695071\pi\) | |||||||
\(194\) | −33136.9 | −0.0632132 | ||||||||
\(195\) | 67464.7 | 0.127055 | ||||||||
\(196\) | −453634. | −0.843461 | ||||||||
\(197\) | 944989. | 1.73485 | 0.867423 | − | 0.497571i | \(-0.165775\pi\) | ||||
0.867423 | + | 0.497571i | \(0.165775\pi\) | |||||||
\(198\) | 47018.8 | 0.0852331 | ||||||||
\(199\) | −96047.7 | −0.171931 | −0.0859655 | − | 0.996298i | \(-0.527397\pi\) | ||||
−0.0859655 | + | 0.996298i | \(0.527397\pi\) | |||||||
\(200\) | 999526. | 1.76693 | ||||||||
\(201\) | −683910. | −1.19401 | ||||||||
\(202\) | 1.46084e6 | 2.51898 | ||||||||
\(203\) | 6614.33 | 0.0112654 | ||||||||
\(204\) | −1.45168e6 | −2.44227 | ||||||||
\(205\) | 7957.75 | 0.0132253 | ||||||||
\(206\) | 147182. | 0.241650 | ||||||||
\(207\) | 166703. | 0.270407 | ||||||||
\(208\) | −610303. | −0.978109 | ||||||||
\(209\) | −29554.9 | −0.0468020 | ||||||||
\(210\) | −124403. | −0.194663 | ||||||||
\(211\) | −547771. | −0.847018 | −0.423509 | − | 0.905892i | \(-0.639202\pi\) | ||||
−0.423509 | + | 0.905892i | \(0.639202\pi\) | |||||||
\(212\) | 629155. | 0.961431 | ||||||||
\(213\) | 1.16277e6 | 1.75608 | ||||||||
\(214\) | 493478. | 0.736602 | ||||||||
\(215\) | −72786.7 | −0.107388 | ||||||||
\(216\) | −1.32757e6 | −1.93607 | ||||||||
\(217\) | 963916. | 1.38960 | ||||||||
\(218\) | −199627. | −0.284497 | ||||||||
\(219\) | 470346. | 0.662685 | ||||||||
\(220\) | 65366.5 | 0.0910538 | ||||||||
\(221\) | −834503. | −1.14934 | ||||||||
\(222\) | −1.16424e6 | −1.58548 | ||||||||
\(223\) | −831358. | −1.11950 | −0.559752 | − | 0.828660i | \(-0.689104\pi\) | ||||
−0.559752 | + | 0.828660i | \(0.689104\pi\) | |||||||
\(224\) | 82231.5 | 0.109501 | ||||||||
\(225\) | 130111. | 0.171340 | ||||||||
\(226\) | 583192. | 0.759522 | ||||||||
\(227\) | −1.06213e6 | −1.36808 | −0.684041 | − | 0.729444i | \(-0.739779\pi\) | ||||
−0.684041 | + | 0.729444i | \(0.739779\pi\) | |||||||
\(228\) | 244802. | 0.311873 | ||||||||
\(229\) | 336960. | 0.424609 | 0.212304 | − | 0.977204i | \(-0.431903\pi\) | ||||
0.212304 | + | 0.977204i | \(0.431903\pi\) | |||||||
\(230\) | 345349. | 0.430465 | ||||||||
\(231\) | 156727. | 0.193248 | ||||||||
\(232\) | 21870.9 | 0.0266776 | ||||||||
\(233\) | −1.05063e6 | −1.26782 | −0.633912 | − | 0.773405i | \(-0.718552\pi\) | ||||
−0.633912 | + | 0.773405i | \(0.718552\pi\) | |||||||
\(234\) | −223879. | −0.267285 | ||||||||
\(235\) | 133835. | 0.158088 | ||||||||
\(236\) | 1.00232e6 | 1.17146 | ||||||||
\(237\) | 298318. | 0.344992 | ||||||||
\(238\) | 1.53880e6 | 1.76092 | ||||||||
\(239\) | −713976. | −0.808517 | −0.404258 | − | 0.914645i | \(-0.632470\pi\) | ||||
−0.404258 | + | 0.914645i | \(0.632470\pi\) | |||||||
\(240\) | −145970. | −0.163582 | ||||||||
\(241\) | −1.39830e6 | −1.55081 | −0.775406 | − | 0.631463i | \(-0.782455\pi\) | ||||
−0.775406 | + | 0.631463i | \(0.782455\pi\) | |||||||
\(242\) | 1.46579e6 | 1.60892 | ||||||||
\(243\) | −319779. | −0.347403 | ||||||||
\(244\) | 1.50270e6 | 1.61583 | ||||||||
\(245\) | −62370.9 | −0.0663845 | ||||||||
\(246\) | 123742. | 0.130371 | ||||||||
\(247\) | 140726. | 0.146768 | ||||||||
\(248\) | 3.18728e6 | 3.29072 | ||||||||
\(249\) | 1.04174e6 | 1.06479 | ||||||||
\(250\) | 546220. | 0.552736 | ||||||||
\(251\) | 1.10081e6 | 1.10288 | 0.551439 | − | 0.834215i | \(-0.314079\pi\) | ||||
0.551439 | + | 0.834215i | \(0.314079\pi\) | |||||||
\(252\) | 277037. | 0.274813 | ||||||||
\(253\) | −435082. | −0.427336 | ||||||||
\(254\) | −336172. | −0.326947 | ||||||||
\(255\) | −199593. | −0.192219 | ||||||||
\(256\) | −2.12879e6 | −2.03017 | ||||||||
\(257\) | 1.59543e6 | 1.50676 | 0.753380 | − | 0.657585i | \(-0.228422\pi\) | ||||
0.753380 | + | 0.657585i | \(0.228422\pi\) | |||||||
\(258\) | −1.13183e6 | −1.05860 | ||||||||
\(259\) | 828180. | 0.767142 | ||||||||
\(260\) | −311242. | −0.285538 | ||||||||
\(261\) | 2847.00 | 0.00258694 | ||||||||
\(262\) | 2.24271e6 | 2.01846 | ||||||||
\(263\) | −1.49855e6 | −1.33592 | −0.667962 | − | 0.744195i | \(-0.732833\pi\) | ||||
−0.667962 | + | 0.744195i | \(0.732833\pi\) | |||||||
\(264\) | 518233. | 0.457631 | ||||||||
\(265\) | 86503.7 | 0.0756693 | ||||||||
\(266\) | −259494. | −0.224866 | ||||||||
\(267\) | −1.05544e6 | −0.906059 | ||||||||
\(268\) | 3.15515e6 | 2.68339 | ||||||||
\(269\) | 455961. | 0.384191 | 0.192096 | − | 0.981376i | \(-0.438472\pi\) | ||||
0.192096 | + | 0.981376i | \(0.438472\pi\) | |||||||
\(270\) | −358006. | −0.298869 | ||||||||
\(271\) | 871573. | 0.720909 | 0.360454 | − | 0.932777i | \(-0.382622\pi\) | ||||
0.360454 | + | 0.932777i | \(0.382622\pi\) | |||||||
\(272\) | 1.80557e6 | 1.47977 | ||||||||
\(273\) | −746254. | −0.606010 | ||||||||
\(274\) | 3.87068e6 | 3.11466 | ||||||||
\(275\) | −339580. | −0.270776 | ||||||||
\(276\) | 3.60375e6 | 2.84762 | ||||||||
\(277\) | 505821. | 0.396094 | 0.198047 | − | 0.980193i | \(-0.436540\pi\) | ||||
0.198047 | + | 0.980193i | \(0.436540\pi\) | |||||||
\(278\) | 42059.2 | 0.0326399 | ||||||||
\(279\) | 414897. | 0.319102 | ||||||||
\(280\) | 292613. | 0.223048 | ||||||||
\(281\) | 917159. | 0.692913 | 0.346457 | − | 0.938066i | \(-0.387385\pi\) | ||||
0.346457 | + | 0.938066i | \(0.387385\pi\) | |||||||
\(282\) | 2.08111e6 | 1.55838 | ||||||||
\(283\) | 97454.2 | 0.0723326 | 0.0361663 | − | 0.999346i | \(-0.488485\pi\) | ||||
0.0361663 | + | 0.999346i | \(0.488485\pi\) | |||||||
\(284\) | −5.36433e6 | −3.94657 | ||||||||
\(285\) | 33658.2 | 0.0245459 | ||||||||
\(286\) | 584307. | 0.422402 | ||||||||
\(287\) | −88023.9 | −0.0630806 | ||||||||
\(288\) | 35394.8 | 0.0251454 | ||||||||
\(289\) | 1.04901e6 | 0.738814 | ||||||||
\(290\) | 5897.95 | 0.00411819 | ||||||||
\(291\) | −47543.0 | −0.0329120 | ||||||||
\(292\) | −2.16989e6 | −1.48930 | ||||||||
\(293\) | 1.03378e6 | 0.703493 | 0.351746 | − | 0.936095i | \(-0.385588\pi\) | ||||
0.351746 | + | 0.936095i | \(0.385588\pi\) | |||||||
\(294\) | −969861. | −0.654397 | ||||||||
\(295\) | 137811. | 0.0921995 | ||||||||
\(296\) | 2.73846e6 | 1.81667 | ||||||||
\(297\) | 451028. | 0.296696 | ||||||||
\(298\) | 3.25050e6 | 2.12036 | ||||||||
\(299\) | 2.07164e6 | 1.34010 | ||||||||
\(300\) | 2.81272e6 | 1.80436 | ||||||||
\(301\) | 805122. | 0.512207 | ||||||||
\(302\) | 2.12794e6 | 1.34258 | ||||||||
\(303\) | 2.09593e6 | 1.31151 | ||||||||
\(304\) | −304481. | −0.188963 | ||||||||
\(305\) | 206609. | 0.127174 | ||||||||
\(306\) | 662344. | 0.404371 | ||||||||
\(307\) | 718916. | 0.435344 | 0.217672 | − | 0.976022i | \(-0.430154\pi\) | ||||
0.217672 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(308\) | −723045. | −0.434298 | ||||||||
\(309\) | 211169. | 0.125815 | ||||||||
\(310\) | 859517. | 0.507984 | ||||||||
\(311\) | −878326. | −0.514938 | −0.257469 | − | 0.966287i | \(-0.582888\pi\) | ||||
−0.257469 | + | 0.966287i | \(0.582888\pi\) | |||||||
\(312\) | −2.46756e6 | −1.43510 | ||||||||
\(313\) | 1.26268e6 | 0.728502 | 0.364251 | − | 0.931301i | \(-0.381325\pi\) | ||||
0.364251 | + | 0.931301i | \(0.381325\pi\) | |||||||
\(314\) | −2.49907e6 | −1.43039 | ||||||||
\(315\) | 38090.3 | 0.0216291 | ||||||||
\(316\) | −1.37626e6 | −0.775324 | ||||||||
\(317\) | 2.19292e6 | 1.22567 | 0.612837 | − | 0.790209i | \(-0.290028\pi\) | ||||
0.612837 | + | 0.790209i | \(0.290028\pi\) | |||||||
\(318\) | 1.34512e6 | 0.745924 | ||||||||
\(319\) | −7430.43 | −0.00408825 | ||||||||
\(320\) | −256751. | −0.140164 | ||||||||
\(321\) | 708014. | 0.383512 | ||||||||
\(322\) | −3.82004e6 | −2.05319 | ||||||||
\(323\) | −416335. | −0.222043 | ||||||||
\(324\) | −3.05783e6 | −1.61827 | ||||||||
\(325\) | 1.61691e6 | 0.849134 | ||||||||
\(326\) | 455635. | 0.237450 | ||||||||
\(327\) | −286414. | −0.148124 | ||||||||
\(328\) | −291059. | −0.149382 | ||||||||
\(329\) | −1.48040e6 | −0.754030 | ||||||||
\(330\) | 139752. | 0.0706439 | ||||||||
\(331\) | −2.67827e6 | −1.34365 | −0.671823 | − | 0.740711i | \(-0.734489\pi\) | ||||
−0.671823 | + | 0.740711i | \(0.734489\pi\) | |||||||
\(332\) | −4.80599e6 | −2.39297 | ||||||||
\(333\) | 356473. | 0.176163 | ||||||||
\(334\) | 1.27709e6 | 0.626404 | ||||||||
\(335\) | 433807. | 0.211196 | ||||||||
\(336\) | 1.61463e6 | 0.780235 | ||||||||
\(337\) | −597512. | −0.286597 | −0.143299 | − | 0.989680i | \(-0.545771\pi\) | ||||
−0.143299 | + | 0.989680i | \(0.545771\pi\) | |||||||
\(338\) | 880031. | 0.418992 | ||||||||
\(339\) | 836731. | 0.395445 | ||||||||
\(340\) | 920805. | 0.431986 | ||||||||
\(341\) | −1.08285e6 | −0.504291 | ||||||||
\(342\) | −111694. | −0.0516373 | ||||||||
\(343\) | 2.35869e6 | 1.08252 | ||||||||
\(344\) | 2.66221e6 | 1.21296 | ||||||||
\(345\) | 495487. | 0.224122 | ||||||||
\(346\) | 800225. | 0.359354 | ||||||||
\(347\) | 3.47608e6 | 1.54976 | 0.774882 | − | 0.632106i | \(-0.217809\pi\) | ||||
0.774882 | + | 0.632106i | \(0.217809\pi\) | |||||||
\(348\) | 61545.8 | 0.0272427 | ||||||||
\(349\) | −2.84825e6 | −1.25174 | −0.625871 | − | 0.779926i | \(-0.715256\pi\) | ||||
−0.625871 | + | 0.779926i | \(0.715256\pi\) | |||||||
\(350\) | −2.98153e6 | −1.30097 | ||||||||
\(351\) | −2.14756e6 | −0.930419 | ||||||||
\(352\) | −92377.7 | −0.0397384 | ||||||||
\(353\) | −2.74391e6 | −1.17201 | −0.586007 | − | 0.810306i | \(-0.699301\pi\) | ||||
−0.586007 | + | 0.810306i | \(0.699301\pi\) | |||||||
\(354\) | 2.14294e6 | 0.908872 | ||||||||
\(355\) | −737551. | −0.310614 | ||||||||
\(356\) | 4.86918e6 | 2.03625 | ||||||||
\(357\) | 2.20778e6 | 0.916824 | ||||||||
\(358\) | 2.98866e6 | 1.23245 | ||||||||
\(359\) | −2.96720e6 | −1.21510 | −0.607549 | − | 0.794282i | \(-0.707847\pi\) | ||||
−0.607549 | + | 0.794282i | \(0.707847\pi\) | |||||||
\(360\) | 125949. | 0.0512200 | ||||||||
\(361\) | −2.40589e6 | −0.971646 | ||||||||
\(362\) | 1.08300e6 | 0.434368 | ||||||||
\(363\) | 2.10303e6 | 0.837683 | ||||||||
\(364\) | 3.44277e6 | 1.36193 | ||||||||
\(365\) | −298343. | −0.117215 | ||||||||
\(366\) | 3.21274e6 | 1.25364 | ||||||||
\(367\) | 1.23117e6 | 0.477150 | 0.238575 | − | 0.971124i | \(-0.423320\pi\) | ||||
0.238575 | + | 0.971124i | \(0.423320\pi\) | |||||||
\(368\) | −4.48230e6 | −1.72537 | ||||||||
\(369\) | −37888.0 | −0.0144856 | ||||||||
\(370\) | 738483. | 0.280437 | ||||||||
\(371\) | −956852. | −0.360919 | ||||||||
\(372\) | 8.96916e6 | 3.36043 | ||||||||
\(373\) | 583045. | 0.216985 | 0.108493 | − | 0.994097i | \(-0.465398\pi\) | ||||
0.108493 | + | 0.994097i | \(0.465398\pi\) | |||||||
\(374\) | −1.72866e6 | −0.639045 | ||||||||
\(375\) | 783686. | 0.287782 | ||||||||
\(376\) | −4.89508e6 | −1.78562 | ||||||||
\(377\) | 35379.9 | 0.0128205 | ||||||||
\(378\) | 3.96005e6 | 1.42551 | ||||||||
\(379\) | −4.59556e6 | −1.64339 | −0.821695 | − | 0.569928i | \(-0.806971\pi\) | ||||
−0.821695 | + | 0.569928i | \(0.806971\pi\) | |||||||
\(380\) | −155279. | −0.0551637 | ||||||||
\(381\) | −482321. | −0.170225 | ||||||||
\(382\) | 4.26978e6 | 1.49709 | ||||||||
\(383\) | 150837. | 0.0525424 | 0.0262712 | − | 0.999655i | \(-0.491637\pi\) | ||||
0.0262712 | + | 0.999655i | \(0.491637\pi\) | |||||||
\(384\) | −4.36749e6 | −1.51149 | ||||||||
\(385\) | −99412.7 | −0.0341814 | ||||||||
\(386\) | 5.87164e6 | 2.00581 | ||||||||
\(387\) | 346548. | 0.117621 | ||||||||
\(388\) | 219335. | 0.0739653 | ||||||||
\(389\) | 3.83980e6 | 1.28657 | 0.643286 | − | 0.765626i | \(-0.277570\pi\) | ||||
0.643286 | + | 0.765626i | \(0.277570\pi\) | |||||||
\(390\) | −665430. | −0.221534 | ||||||||
\(391\) | −6.12891e6 | −2.02741 | ||||||||
\(392\) | 2.28125e6 | 0.749821 | ||||||||
\(393\) | 3.21771e6 | 1.05091 | ||||||||
\(394\) | −9.32078e6 | −3.02490 | ||||||||
\(395\) | −189225. | −0.0610218 | ||||||||
\(396\) | −311219. | −0.0997306 | ||||||||
\(397\) | −3.29694e6 | −1.04987 | −0.524934 | − | 0.851143i | \(-0.675910\pi\) | ||||
−0.524934 | + | 0.851143i | \(0.675910\pi\) | |||||||
\(398\) | 947354. | 0.299781 | ||||||||
\(399\) | −372307. | −0.117076 | ||||||||
\(400\) | −3.49842e6 | −1.09326 | ||||||||
\(401\) | −806095. | −0.250337 | −0.125169 | − | 0.992135i | \(-0.539947\pi\) | ||||
−0.125169 | + | 0.992135i | \(0.539947\pi\) | |||||||
\(402\) | 6.74566e6 | 2.08190 | ||||||||
\(403\) | 5.15597e6 | 1.58142 | ||||||||
\(404\) | −9.66939e6 | −2.94744 | ||||||||
\(405\) | −420426. | −0.127366 | ||||||||
\(406\) | −65239.6 | −0.0196425 | ||||||||
\(407\) | −930365. | −0.278399 | ||||||||
\(408\) | 7.30024e6 | 2.17114 | ||||||||
\(409\) | 1.88559e6 | 0.557363 | 0.278682 | − | 0.960384i | \(-0.410103\pi\) | ||||
0.278682 | + | 0.960384i | \(0.410103\pi\) | |||||||
\(410\) | −78490.3 | −0.0230598 | ||||||||
\(411\) | 5.55343e6 | 1.62165 | ||||||||
\(412\) | −974207. | −0.282754 | ||||||||
\(413\) | −1.52438e6 | −0.439763 | ||||||||
\(414\) | −1.64426e6 | −0.471486 | ||||||||
\(415\) | −660783. | −0.188338 | ||||||||
\(416\) | 439855. | 0.124617 | ||||||||
\(417\) | 60344.2 | 0.0169940 | ||||||||
\(418\) | 291511. | 0.0816046 | ||||||||
\(419\) | 1.71269e6 | 0.476590 | 0.238295 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238295 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(420\) | 823429. | 0.227773 | ||||||||
\(421\) | 5.62613e6 | 1.54705 | 0.773526 | − | 0.633765i | \(-0.218491\pi\) | ||||
0.773526 | + | 0.633765i | \(0.218491\pi\) | |||||||
\(422\) | 5.40287e6 | 1.47687 | ||||||||
\(423\) | −637206. | −0.173153 | ||||||||
\(424\) | −3.16392e6 | −0.854695 | ||||||||
\(425\) | −4.78359e6 | −1.28464 | ||||||||
\(426\) | −1.14689e7 | −3.06193 | ||||||||
\(427\) | −2.28538e6 | −0.606581 | ||||||||
\(428\) | −3.26635e6 | −0.861893 | ||||||||
\(429\) | 838331. | 0.219924 | ||||||||
\(430\) | 717922. | 0.187243 | ||||||||
\(431\) | −2.32510e6 | −0.602905 | −0.301452 | − | 0.953481i | \(-0.597471\pi\) | ||||
−0.301452 | + | 0.953481i | \(0.597471\pi\) | |||||||
\(432\) | 4.64658e6 | 1.19791 | ||||||||
\(433\) | −3.55174e6 | −0.910377 | −0.455189 | − | 0.890395i | \(-0.650428\pi\) | ||||
−0.455189 | + | 0.890395i | \(0.650428\pi\) | |||||||
\(434\) | −9.50746e6 | −2.42293 | ||||||||
\(435\) | 8462.04 | 0.00214413 | ||||||||
\(436\) | 1.32134e6 | 0.332889 | ||||||||
\(437\) | 1.03354e6 | 0.258896 | ||||||||
\(438\) | −4.63920e6 | −1.15547 | ||||||||
\(439\) | 5.81929e6 | 1.44115 | 0.720574 | − | 0.693378i | \(-0.243878\pi\) | ||||
0.720574 | + | 0.693378i | \(0.243878\pi\) | |||||||
\(440\) | −328717. | −0.0809452 | ||||||||
\(441\) | 296957. | 0.0727105 | ||||||||
\(442\) | 8.23102e6 | 2.00400 | ||||||||
\(443\) | −5.26135e6 | −1.27376 | −0.636880 | − | 0.770963i | \(-0.719775\pi\) | ||||
−0.636880 | + | 0.770963i | \(0.719775\pi\) | |||||||
\(444\) | 7.70616e6 | 1.85516 | ||||||||
\(445\) | 669472. | 0.160263 | ||||||||
\(446\) | 8.20000e6 | 1.95198 | ||||||||
\(447\) | 4.66364e6 | 1.10397 | ||||||||
\(448\) | 2.84002e6 | 0.668539 | ||||||||
\(449\) | 4.43910e6 | 1.03915 | 0.519576 | − | 0.854424i | \(-0.326090\pi\) | ||||
0.519576 | + | 0.854424i | \(0.326090\pi\) | |||||||
\(450\) | −1.28334e6 | −0.298751 | ||||||||
\(451\) | 98884.7 | 0.0228922 | ||||||||
\(452\) | −3.86017e6 | −0.888711 | ||||||||
\(453\) | 3.05304e6 | 0.699016 | ||||||||
\(454\) | 1.04762e7 | 2.38541 | ||||||||
\(455\) | 473352. | 0.107190 | ||||||||
\(456\) | −1.23107e6 | −0.277249 | ||||||||
\(457\) | −540340. | −0.121025 | −0.0605127 | − | 0.998167i | \(-0.519274\pi\) | ||||
−0.0605127 | + | 0.998167i | \(0.519274\pi\) | |||||||
\(458\) | −3.32356e6 | −0.740354 | ||||||||
\(459\) | 6.35354e6 | 1.40762 | ||||||||
\(460\) | −2.28588e6 | −0.503684 | ||||||||
\(461\) | 1.56355e6 | 0.342657 | 0.171329 | − | 0.985214i | \(-0.445194\pi\) | ||||
0.171329 | + | 0.985214i | \(0.445194\pi\) | |||||||
\(462\) | −1.54586e6 | −0.336949 | ||||||||
\(463\) | 5.64955e6 | 1.22479 | 0.612395 | − | 0.790552i | \(-0.290206\pi\) | ||||
0.612395 | + | 0.790552i | \(0.290206\pi\) | |||||||
\(464\) | −76549.8 | −0.0165063 | ||||||||
\(465\) | 1.23319e6 | 0.264482 | ||||||||
\(466\) | 1.03627e7 | 2.21060 | ||||||||
\(467\) | 8.59103e6 | 1.82286 | 0.911430 | − | 0.411456i | \(-0.134980\pi\) | ||||
0.911430 | + | 0.411456i | \(0.134980\pi\) | |||||||
\(468\) | 1.48187e6 | 0.312748 | ||||||||
\(469\) | −4.79852e6 | −1.00734 | ||||||||
\(470\) | −1.32006e6 | −0.275644 | ||||||||
\(471\) | −3.58552e6 | −0.744732 | ||||||||
\(472\) | −5.04051e6 | −1.04140 | ||||||||
\(473\) | −904462. | −0.185882 | ||||||||
\(474\) | −2.94242e6 | −0.601533 | ||||||||
\(475\) | 806676. | 0.164046 | ||||||||
\(476\) | −1.01854e7 | −2.06044 | ||||||||
\(477\) | −411857. | −0.0828801 | ||||||||
\(478\) | 7.04221e6 | 1.40974 | ||||||||
\(479\) | −3.22040e6 | −0.641315 | −0.320658 | − | 0.947195i | \(-0.603904\pi\) | ||||
−0.320658 | + | 0.947195i | \(0.603904\pi\) | |||||||
\(480\) | 105203. | 0.0208413 | ||||||||
\(481\) | 4.42992e6 | 0.873039 | ||||||||
\(482\) | 1.37920e7 | 2.70402 | ||||||||
\(483\) | −5.48078e6 | −1.06899 | ||||||||
\(484\) | −9.70214e6 | −1.88258 | ||||||||
\(485\) | 30156.7 | 0.00582143 | ||||||||
\(486\) | 3.15409e6 | 0.605737 | ||||||||
\(487\) | 5.76818e6 | 1.10209 | 0.551044 | − | 0.834476i | \(-0.314230\pi\) | ||||
0.551044 | + | 0.834476i | \(0.314230\pi\) | |||||||
\(488\) | −7.55683e6 | −1.43645 | ||||||||
\(489\) | 653719. | 0.123629 | ||||||||
\(490\) | 615187. | 0.115749 | ||||||||
\(491\) | −6.36396e6 | −1.19131 | −0.595654 | − | 0.803241i | \(-0.703107\pi\) | ||||
−0.595654 | + | 0.803241i | \(0.703107\pi\) | |||||||
\(492\) | −819056. | −0.152546 | ||||||||
\(493\) | −104671. | −0.0193959 | ||||||||
\(494\) | −1.38803e6 | −0.255906 | ||||||||
\(495\) | −42790.1 | −0.00784929 | ||||||||
\(496\) | −1.11557e7 | −2.03607 | ||||||||
\(497\) | 8.15835e6 | 1.48153 | ||||||||
\(498\) | −1.02751e7 | −1.85658 | ||||||||
\(499\) | 4.12358e6 | 0.741349 | 0.370675 | − | 0.928763i | \(-0.379126\pi\) | ||||
0.370675 | + | 0.928763i | \(0.379126\pi\) | |||||||
\(500\) | −3.61546e6 | −0.646753 | ||||||||
\(501\) | 1.83229e6 | 0.326138 | ||||||||
\(502\) | −1.08577e7 | −1.92299 | ||||||||
\(503\) | 4.25725e6 | 0.750256 | 0.375128 | − | 0.926973i | \(-0.377599\pi\) | ||||
0.375128 | + | 0.926973i | \(0.377599\pi\) | |||||||
\(504\) | −1.39318e6 | −0.244303 | ||||||||
\(505\) | −1.32946e6 | −0.231978 | ||||||||
\(506\) | 4.29137e6 | 0.745109 | ||||||||
\(507\) | 1.26262e6 | 0.218149 | ||||||||
\(508\) | 2.22514e6 | 0.382559 | ||||||||
\(509\) | 3.04625e6 | 0.521160 | 0.260580 | − | 0.965452i | \(-0.416086\pi\) | ||||
0.260580 | + | 0.965452i | \(0.416086\pi\) | |||||||
\(510\) | 1.96866e6 | 0.335155 | ||||||||
\(511\) | 3.30009e6 | 0.559079 | ||||||||
\(512\) | 1.11210e7 | 1.87486 | ||||||||
\(513\) | −1.07142e6 | −0.179749 | ||||||||
\(514\) | −1.57363e7 | −2.62721 | ||||||||
\(515\) | −133945. | −0.0222541 | ||||||||
\(516\) | 7.49160e6 | 1.23866 | ||||||||
\(517\) | 1.66306e6 | 0.273641 | ||||||||
\(518\) | −8.16865e6 | −1.33760 | ||||||||
\(519\) | 1.14812e6 | 0.187098 | ||||||||
\(520\) | 1.56518e6 | 0.253838 | ||||||||
\(521\) | −1.05140e7 | −1.69696 | −0.848480 | − | 0.529227i | \(-0.822482\pi\) | ||||
−0.848480 | + | 0.529227i | \(0.822482\pi\) | |||||||
\(522\) | −28081.0 | −0.00451062 | ||||||||
\(523\) | 1.12338e7 | 1.79586 | 0.897932 | − | 0.440134i | \(-0.145069\pi\) | ||||
0.897932 | + | 0.440134i | \(0.145069\pi\) | |||||||
\(524\) | −1.48446e7 | −2.36178 | ||||||||
\(525\) | −4.27773e6 | −0.677353 | ||||||||
\(526\) | 1.47808e7 | 2.32934 | ||||||||
\(527\) | −1.52539e7 | −2.39251 | ||||||||
\(528\) | −1.81385e6 | −0.283151 | ||||||||
\(529\) | 8.77856e6 | 1.36390 | ||||||||
\(530\) | −853218. | −0.131938 | ||||||||
\(531\) | −656138. | −0.100985 | ||||||||
\(532\) | 1.71760e6 | 0.263114 | ||||||||
\(533\) | −470839. | −0.0717884 | ||||||||
\(534\) | 1.04102e7 | 1.57982 | ||||||||
\(535\) | −449097. | −0.0678352 | ||||||||
\(536\) | −1.58668e7 | −2.38548 | ||||||||
\(537\) | 4.28796e6 | 0.641675 | ||||||||
\(538\) | −4.49732e6 | −0.669881 | ||||||||
\(539\) | −775034. | −0.114908 | ||||||||
\(540\) | 2.36966e6 | 0.349705 | ||||||||
\(541\) | 2.97668e6 | 0.437259 | 0.218629 | − | 0.975808i | \(-0.429841\pi\) | ||||
0.218629 | + | 0.975808i | \(0.429841\pi\) | |||||||
\(542\) | −8.59665e6 | −1.25699 | ||||||||
\(543\) | 1.55383e6 | 0.226154 | ||||||||
\(544\) | −1.30131e6 | −0.188531 | ||||||||
\(545\) | 181674. | 0.0262000 | ||||||||
\(546\) | 7.36058e6 | 1.05665 | ||||||||
\(547\) | −5.53177e6 | −0.790488 | −0.395244 | − | 0.918576i | \(-0.629340\pi\) | ||||
−0.395244 | + | 0.918576i | \(0.629340\pi\) | |||||||
\(548\) | −2.56202e7 | −3.64444 | ||||||||
\(549\) | −983694. | −0.139293 | ||||||||
\(550\) | 3.34940e6 | 0.472129 | ||||||||
\(551\) | 17651.1 | 0.00247681 | ||||||||
\(552\) | −1.81227e7 | −2.53149 | ||||||||
\(553\) | 2.09309e6 | 0.291055 | ||||||||
\(554\) | −4.98911e6 | −0.690635 | ||||||||
\(555\) | 1.05953e6 | 0.146010 | ||||||||
\(556\) | −278392. | −0.0381918 | ||||||||
\(557\) | −1.09629e7 | −1.49723 | −0.748613 | − | 0.663007i | \(-0.769280\pi\) | ||||
−0.748613 | + | 0.663007i | \(0.769280\pi\) | |||||||
\(558\) | −4.09229e6 | −0.556392 | ||||||||
\(559\) | 4.30659e6 | 0.582913 | ||||||||
\(560\) | −1.02417e6 | −0.138007 | ||||||||
\(561\) | −2.48019e6 | −0.332719 | ||||||||
\(562\) | −9.04628e6 | −1.20817 | ||||||||
\(563\) | −2.26278e6 | −0.300865 | −0.150433 | − | 0.988620i | \(-0.548067\pi\) | ||||
−0.150433 | + | 0.988620i | \(0.548067\pi\) | |||||||
\(564\) | −1.37750e7 | −1.82345 | ||||||||
\(565\) | −530742. | −0.0699459 | ||||||||
\(566\) | −961227. | −0.126120 | ||||||||
\(567\) | 4.65050e6 | 0.607494 | ||||||||
\(568\) | 2.69764e7 | 3.50843 | ||||||||
\(569\) | −286044. | −0.0370385 | −0.0185192 | − | 0.999829i | \(-0.505895\pi\) | ||||
−0.0185192 | + | 0.999829i | \(0.505895\pi\) | |||||||
\(570\) | −331984. | −0.0427986 | ||||||||
\(571\) | −5.52774e6 | −0.709508 | −0.354754 | − | 0.934960i | \(-0.615435\pi\) | ||||
−0.354754 | + | 0.934960i | \(0.615435\pi\) | |||||||
\(572\) | −3.86755e6 | −0.494250 | ||||||||
\(573\) | 6.12604e6 | 0.779459 | ||||||||
\(574\) | 868213. | 0.109988 | ||||||||
\(575\) | 1.18752e7 | 1.49786 | ||||||||
\(576\) | 1.22243e6 | 0.153521 | ||||||||
\(577\) | −334668. | −0.0418480 | −0.0209240 | − | 0.999781i | \(-0.506661\pi\) | ||||
−0.0209240 | + | 0.999781i | \(0.506661\pi\) | |||||||
\(578\) | −1.03468e7 | −1.28821 | ||||||||
\(579\) | 8.42429e6 | 1.04433 | ||||||||
\(580\) | −39038.8 | −0.00481866 | ||||||||
\(581\) | 7.30919e6 | 0.898316 | ||||||||
\(582\) | 468934. | 0.0573858 | ||||||||
\(583\) | 1.07491e6 | 0.130979 | ||||||||
\(584\) | 1.09120e7 | 1.32396 | ||||||||
\(585\) | 203745. | 0.0246148 | ||||||||
\(586\) | −1.01966e7 | −1.22662 | ||||||||
\(587\) | 1.56616e7 | 1.87604 | 0.938020 | − | 0.346582i | \(-0.112658\pi\) | ||||
0.938020 | + | 0.346582i | \(0.112658\pi\) | |||||||
\(588\) | 6.41956e6 | 0.765705 | ||||||||
\(589\) | 2.57232e6 | 0.305518 | ||||||||
\(590\) | −1.35928e6 | −0.160760 | ||||||||
\(591\) | −1.33729e7 | −1.57492 | ||||||||
\(592\) | −9.58481e6 | −1.12403 | ||||||||
\(593\) | 7.06151e6 | 0.824634 | 0.412317 | − | 0.911040i | \(-0.364720\pi\) | ||||
0.412317 | + | 0.911040i | \(0.364720\pi\) | |||||||
\(594\) | −4.44866e6 | −0.517324 | ||||||||
\(595\) | −1.40041e6 | −0.162167 | ||||||||
\(596\) | −2.15152e7 | −2.48102 | ||||||||
\(597\) | 1.35921e6 | 0.156081 | ||||||||
\(598\) | −2.04333e7 | −2.33661 | ||||||||
\(599\) | 4.87247e6 | 0.554858 | 0.277429 | − | 0.960746i | \(-0.410518\pi\) | ||||
0.277429 | + | 0.960746i | \(0.410518\pi\) | |||||||
\(600\) | −1.41447e7 | −1.60404 | ||||||||
\(601\) | 1.08737e6 | 0.122798 | 0.0613990 | − | 0.998113i | \(-0.480444\pi\) | ||||
0.0613990 | + | 0.998113i | \(0.480444\pi\) | |||||||
\(602\) | −7.94122e6 | −0.893092 | ||||||||
\(603\) | −2.06542e6 | −0.231321 | ||||||||
\(604\) | −1.40849e7 | −1.57095 | ||||||||
\(605\) | −1.33396e6 | −0.148168 | ||||||||
\(606\) | −2.06730e7 | −2.28677 | ||||||||
\(607\) | −1.18003e6 | −0.129993 | −0.0649966 | − | 0.997885i | \(-0.520704\pi\) | ||||
−0.0649966 | + | 0.997885i | \(0.520704\pi\) | |||||||
\(608\) | 219444. | 0.0240749 | ||||||||
\(609\) | −93602.0 | −0.0102269 | ||||||||
\(610\) | −2.03786e6 | −0.221743 | ||||||||
\(611\) | −7.91862e6 | −0.858117 | ||||||||
\(612\) | −4.38409e6 | −0.473152 | ||||||||
\(613\) | −1.06660e7 | −1.14643 | −0.573217 | − | 0.819404i | \(-0.694305\pi\) | ||||
−0.573217 | + | 0.819404i | \(0.694305\pi\) | |||||||
\(614\) | −7.09094e6 | −0.759072 | ||||||||
\(615\) | −112613. | −0.0120061 | ||||||||
\(616\) | 3.63608e6 | 0.386083 | ||||||||
\(617\) | −1.26485e7 | −1.33760 | −0.668799 | − | 0.743443i | \(-0.733191\pi\) | ||||
−0.668799 | + | 0.743443i | \(0.733191\pi\) | |||||||
\(618\) | −2.08284e6 | −0.219374 | ||||||||
\(619\) | 1.18606e7 | 1.24417 | 0.622083 | − | 0.782951i | \(-0.286286\pi\) | ||||
0.622083 | + | 0.782951i | \(0.286286\pi\) | |||||||
\(620\) | −5.68918e6 | −0.594389 | ||||||||
\(621\) | −1.57725e7 | −1.64124 | ||||||||
\(622\) | 8.66325e6 | 0.897853 | ||||||||
\(623\) | −7.40530e6 | −0.764403 | ||||||||
\(624\) | 8.63665e6 | 0.887940 | ||||||||
\(625\) | 9.01674e6 | 0.923314 | ||||||||
\(626\) | −1.24542e7 | −1.27023 | ||||||||
\(627\) | 418244. | 0.0424875 | ||||||||
\(628\) | 1.65414e7 | 1.67369 | ||||||||
\(629\) | −1.31059e7 | −1.32081 | ||||||||
\(630\) | −375699. | −0.0377128 | ||||||||
\(631\) | 9.66478e6 | 0.966314 | 0.483157 | − | 0.875534i | \(-0.339490\pi\) | ||||
0.483157 | + | 0.875534i | \(0.339490\pi\) | |||||||
\(632\) | 6.92100e6 | 0.689249 | ||||||||
\(633\) | 7.75173e6 | 0.768934 | ||||||||
\(634\) | −2.16296e7 | −2.13710 | ||||||||
\(635\) | 305938. | 0.0301092 | ||||||||
\(636\) | −8.90344e6 | −0.872800 | ||||||||
\(637\) | 3.69032e6 | 0.360342 | ||||||||
\(638\) | 73289.1 | 0.00712833 | ||||||||
\(639\) | 3.51159e6 | 0.340214 | ||||||||
\(640\) | 2.77032e6 | 0.267350 | ||||||||
\(641\) | −8.00413e6 | −0.769430 | −0.384715 | − | 0.923035i | \(-0.625700\pi\) | ||||
−0.384715 | + | 0.923035i | \(0.625700\pi\) | |||||||
\(642\) | −6.98341e6 | −0.668697 | ||||||||
\(643\) | −5.13318e6 | −0.489619 | −0.244810 | − | 0.969571i | \(-0.578725\pi\) | ||||
−0.244810 | + | 0.969571i | \(0.578725\pi\) | |||||||
\(644\) | 2.52850e7 | 2.40242 | ||||||||
\(645\) | 1.03003e6 | 0.0974883 | ||||||||
\(646\) | 4.10646e6 | 0.387157 | ||||||||
\(647\) | 1.08589e7 | 1.01982 | 0.509910 | − | 0.860228i | \(-0.329679\pi\) | ||||
0.509910 | + | 0.860228i | \(0.329679\pi\) | |||||||
\(648\) | 1.53773e7 | 1.43861 | ||||||||
\(649\) | 1.71247e6 | 0.159592 | ||||||||
\(650\) | −1.59481e7 | −1.48056 | ||||||||
\(651\) | −1.36408e7 | −1.26150 | ||||||||
\(652\) | −3.01587e6 | −0.277839 | ||||||||
\(653\) | −8.01399e6 | −0.735472 | −0.367736 | − | 0.929930i | \(-0.619867\pi\) | ||||
−0.367736 | + | 0.929930i | \(0.619867\pi\) | |||||||
\(654\) | 2.82501e6 | 0.258271 | ||||||||
\(655\) | −2.04101e6 | −0.185884 | ||||||||
\(656\) | 1.01873e6 | 0.0924272 | ||||||||
\(657\) | 1.42045e6 | 0.128385 | ||||||||
\(658\) | 1.46017e7 | 1.31474 | ||||||||
\(659\) | −1.11015e7 | −0.995792 | −0.497896 | − | 0.867237i | \(-0.665894\pi\) | ||||
−0.497896 | + | 0.867237i | \(0.665894\pi\) | |||||||
\(660\) | −925028. | −0.0826599 | ||||||||
\(661\) | −134707. | −0.0119918 | −0.00599592 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599592 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(662\) | 2.64168e7 | 2.34280 | ||||||||
\(663\) | 1.18094e7 | 1.04338 | ||||||||
\(664\) | 2.41685e7 | 2.12731 | ||||||||
\(665\) | 236156. | 0.0207083 | ||||||||
\(666\) | −3.51603e6 | −0.307161 | ||||||||
\(667\) | 259844. | 0.0226151 | ||||||||
\(668\) | −8.45311e6 | −0.732951 | ||||||||
\(669\) | 1.17649e7 | 1.01630 | ||||||||
\(670\) | −4.27880e6 | −0.368244 | ||||||||
\(671\) | 2.56736e6 | 0.220131 | ||||||||
\(672\) | −1.16369e6 | −0.0994066 | ||||||||
\(673\) | 1.43311e7 | 1.21967 | 0.609834 | − | 0.792529i | \(-0.291236\pi\) | ||||
0.609834 | + | 0.792529i | \(0.291236\pi\) | |||||||
\(674\) | 5.89348e6 | 0.499715 | ||||||||
\(675\) | −1.23104e7 | −1.03995 | ||||||||
\(676\) | −5.82497e6 | −0.490260 | ||||||||
\(677\) | 9.12082e6 | 0.764825 | 0.382413 | − | 0.923992i | \(-0.375093\pi\) | ||||
0.382413 | + | 0.923992i | \(0.375093\pi\) | |||||||
\(678\) | −8.25299e6 | −0.689504 | ||||||||
\(679\) | −333576. | −0.0277664 | ||||||||
\(680\) | −4.63058e6 | −0.384028 | ||||||||
\(681\) | 1.50306e7 | 1.24196 | ||||||||
\(682\) | 1.06805e7 | 0.879290 | ||||||||
\(683\) | 7.63895e6 | 0.626587 | 0.313294 | − | 0.949656i | \(-0.398568\pi\) | ||||
0.313294 | + | 0.949656i | \(0.398568\pi\) | |||||||
\(684\) | 739306. | 0.0604204 | ||||||||
\(685\) | −3.52257e6 | −0.286835 | ||||||||
\(686\) | −2.32646e7 | −1.88749 | ||||||||
\(687\) | −4.76845e6 | −0.385466 | ||||||||
\(688\) | −9.31795e6 | −0.750498 | ||||||||
\(689\) | −5.11819e6 | −0.410741 | ||||||||
\(690\) | −4.88717e6 | −0.390782 | ||||||||
\(691\) | 2.36484e7 | 1.88411 | 0.942056 | − | 0.335455i | \(-0.108890\pi\) | ||||
0.942056 | + | 0.335455i | \(0.108890\pi\) | |||||||
\(692\) | −5.29673e6 | −0.420477 | ||||||||
\(693\) | 473318. | 0.0374387 | ||||||||
\(694\) | −3.42858e7 | −2.70219 | ||||||||
\(695\) | −38276.6 | −0.00300588 | ||||||||
\(696\) | −309504. | −0.0242183 | ||||||||
\(697\) | 1.39297e6 | 0.108608 | ||||||||
\(698\) | 2.80934e7 | 2.18256 | ||||||||
\(699\) | 1.48679e7 | 1.15095 | ||||||||
\(700\) | 1.97349e7 | 1.52226 | ||||||||
\(701\) | −2.04164e7 | −1.56922 | −0.784609 | − | 0.619991i | \(-0.787136\pi\) | ||||
−0.784609 | + | 0.619991i | \(0.787136\pi\) | |||||||
\(702\) | 2.11822e7 | 1.62229 | ||||||||
\(703\) | 2.21009e6 | 0.168664 | ||||||||
\(704\) | −3.19044e6 | −0.242616 | ||||||||
\(705\) | −1.89395e6 | −0.143514 | ||||||||
\(706\) | 2.70642e7 | 2.04354 | ||||||||
\(707\) | 1.47057e7 | 1.10646 | ||||||||
\(708\) | −1.41843e7 | −1.06347 | ||||||||
\(709\) | 1.44443e7 | 1.07915 | 0.539575 | − | 0.841938i | \(-0.318585\pi\) | ||||
0.539575 | + | 0.841938i | \(0.318585\pi\) | |||||||
\(710\) | 7.27474e6 | 0.541592 | ||||||||
\(711\) | 900927. | 0.0668368 | ||||||||
\(712\) | −2.44863e7 | −1.81019 | ||||||||
\(713\) | 3.78674e7 | 2.78960 | ||||||||
\(714\) | −2.17762e7 | −1.59859 | ||||||||
\(715\) | −531757. | −0.0388999 | ||||||||
\(716\) | −1.97821e7 | −1.44208 | ||||||||
\(717\) | 1.01038e7 | 0.733982 | ||||||||
\(718\) | 2.92666e7 | 2.11866 | ||||||||
\(719\) | −2.54689e7 | −1.83733 | −0.918667 | − | 0.395032i | \(-0.870733\pi\) | ||||
−0.918667 | + | 0.395032i | \(0.870733\pi\) | |||||||
\(720\) | −440832. | −0.0316914 | ||||||||
\(721\) | 1.48162e6 | 0.106145 | ||||||||
\(722\) | 2.37302e7 | 1.69418 | ||||||||
\(723\) | 1.97880e7 | 1.40785 | ||||||||
\(724\) | −7.16845e6 | −0.508251 | ||||||||
\(725\) | 202807. | 0.0143297 | ||||||||
\(726\) | −2.07430e7 | −1.46060 | ||||||||
\(727\) | −3.13310e6 | −0.219856 | −0.109928 | − | 0.993940i | \(-0.535062\pi\) | ||||
−0.109928 | + | 0.993940i | \(0.535062\pi\) | |||||||
\(728\) | −1.73131e7 | −1.21073 | ||||||||
\(729\) | 1.59068e7 | 1.10857 | ||||||||
\(730\) | 2.94266e6 | 0.204378 | ||||||||
\(731\) | −1.27410e7 | −0.881880 | ||||||||
\(732\) | −2.12653e7 | −1.46688 | ||||||||
\(733\) | 7.30024e6 | 0.501854 | 0.250927 | − | 0.968006i | \(-0.419265\pi\) | ||||
0.250927 | + | 0.968006i | \(0.419265\pi\) | |||||||
\(734\) | −1.21435e7 | −0.831965 | ||||||||
\(735\) | 882636. | 0.0602648 | ||||||||
\(736\) | 3.23047e6 | 0.219822 | ||||||||
\(737\) | 5.39058e6 | 0.365567 | ||||||||
\(738\) | 373704. | 0.0252573 | ||||||||
\(739\) | −2.06051e6 | −0.138792 | −0.0693958 | − | 0.997589i | \(-0.522107\pi\) | ||||
−0.0693958 | + | 0.997589i | \(0.522107\pi\) | |||||||
\(740\) | −4.88805e6 | −0.328138 | ||||||||
\(741\) | −1.99146e6 | −0.133238 | ||||||||
\(742\) | 9.43779e6 | 0.629304 | ||||||||
\(743\) | −8.21654e6 | −0.546031 | −0.273015 | − | 0.962010i | \(-0.588021\pi\) | ||||
−0.273015 | + | 0.962010i | \(0.588021\pi\) | |||||||
\(744\) | −4.51045e7 | −2.98736 | ||||||||
\(745\) | −2.95817e6 | −0.195269 | ||||||||
\(746\) | −5.75079e6 | −0.378339 | ||||||||
\(747\) | 3.14609e6 | 0.206286 | ||||||||
\(748\) | 1.14421e7 | 0.747743 | ||||||||
\(749\) | 4.96764e6 | 0.323553 | ||||||||
\(750\) | −7.72979e6 | −0.501781 | ||||||||
\(751\) | −2.81267e7 | −1.81978 | −0.909889 | − | 0.414852i | \(-0.863833\pi\) | ||||
−0.909889 | + | 0.414852i | \(0.863833\pi\) | |||||||
\(752\) | 1.71331e7 | 1.10482 | ||||||||
\(753\) | −1.55780e7 | −1.00121 | ||||||||
\(754\) | −348965. | −0.0223539 | ||||||||
\(755\) | −1.93656e6 | −0.123641 | ||||||||
\(756\) | −2.62117e7 | −1.66798 | ||||||||
\(757\) | 2.57239e6 | 0.163154 | 0.0815770 | − | 0.996667i | \(-0.474004\pi\) | ||||
0.0815770 | + | 0.996667i | \(0.474004\pi\) | |||||||
\(758\) | 4.53277e7 | 2.86544 | ||||||||
\(759\) | 6.15702e6 | 0.387941 | ||||||||
\(760\) | 780872. | 0.0490395 | ||||||||
\(761\) | 1.65869e7 | 1.03825 | 0.519127 | − | 0.854697i | \(-0.326257\pi\) | ||||
0.519127 | + | 0.854697i | \(0.326257\pi\) | |||||||
\(762\) | 4.75731e6 | 0.296807 | ||||||||
\(763\) | −2.00956e6 | −0.124966 | ||||||||
\(764\) | −2.82619e7 | −1.75173 | ||||||||
\(765\) | −602776. | −0.0372394 | ||||||||
\(766\) | −1.48776e6 | −0.0916136 | ||||||||
\(767\) | −8.15389e6 | −0.500468 | ||||||||
\(768\) | 3.01254e7 | 1.84302 | ||||||||
\(769\) | −2.57160e7 | −1.56815 | −0.784075 | − | 0.620666i | \(-0.786862\pi\) | ||||
−0.784075 | + | 0.620666i | \(0.786862\pi\) | |||||||
\(770\) | 980544. | 0.0595992 | ||||||||
\(771\) | −2.25776e7 | −1.36786 | ||||||||
\(772\) | −3.88646e7 | −2.34699 | ||||||||
\(773\) | 5.61581e6 | 0.338036 | 0.169018 | − | 0.985613i | \(-0.445940\pi\) | ||||
0.169018 | + | 0.985613i | \(0.445940\pi\) | |||||||
\(774\) | −3.41813e6 | −0.205086 | ||||||||
\(775\) | 2.95554e7 | 1.76759 | ||||||||
\(776\) | −1.10300e6 | −0.0657538 | ||||||||
\(777\) | −1.17199e7 | −0.696422 | ||||||||
\(778\) | −3.78734e7 | −2.24329 | ||||||||
\(779\) | −234902. | −0.0138689 | ||||||||
\(780\) | 4.40451e6 | 0.259216 | ||||||||
\(781\) | −9.16497e6 | −0.537655 | ||||||||
\(782\) | 6.04517e7 | 3.53502 | ||||||||
\(783\) | −269367. | −0.0157015 | ||||||||
\(784\) | −7.98455e6 | −0.463939 | ||||||||
\(785\) | 2.27431e6 | 0.131727 | ||||||||
\(786\) | −3.17375e7 | −1.83238 | ||||||||
\(787\) | 3.01795e7 | 1.73690 | 0.868451 | − | 0.495775i | \(-0.165116\pi\) | ||||
0.868451 | + | 0.495775i | \(0.165116\pi\) | |||||||
\(788\) | 6.16946e7 | 3.53942 | ||||||||
\(789\) | 2.12066e7 | 1.21277 | ||||||||
\(790\) | 1.86639e6 | 0.106399 | ||||||||
\(791\) | 5.87075e6 | 0.333620 | ||||||||
\(792\) | 1.56507e6 | 0.0886587 | ||||||||
\(793\) | −1.22245e7 | −0.690314 | ||||||||
\(794\) | 3.25189e7 | 1.83056 | ||||||||
\(795\) | −1.22415e6 | −0.0686936 | ||||||||
\(796\) | −6.27058e6 | −0.350772 | ||||||||
\(797\) | −4.92765e6 | −0.274785 | −0.137393 | − | 0.990517i | \(-0.543872\pi\) | ||||
−0.137393 | + | 0.990517i | \(0.543872\pi\) | |||||||
\(798\) | 3.67220e6 | 0.204136 | ||||||||
\(799\) | 2.34272e7 | 1.29823 | ||||||||
\(800\) | 2.52137e6 | 0.139287 | ||||||||
\(801\) | −3.18746e6 | −0.175535 | ||||||||
\(802\) | 7.95082e6 | 0.436492 | ||||||||
\(803\) | −3.70727e6 | −0.202892 | ||||||||
\(804\) | −4.46499e7 | −2.43601 | ||||||||
\(805\) | 3.47648e6 | 0.189082 | ||||||||
\(806\) | −5.08553e7 | −2.75739 | ||||||||
\(807\) | −6.45250e6 | −0.348774 | ||||||||
\(808\) | 4.86258e7 | 2.62022 | ||||||||
\(809\) | 2.11048e7 | 1.13373 | 0.566864 | − | 0.823811i | \(-0.308156\pi\) | ||||
0.566864 | + | 0.823811i | \(0.308156\pi\) | |||||||
\(810\) | 4.14682e6 | 0.222076 | ||||||||
\(811\) | −1.10101e7 | −0.587814 | −0.293907 | − | 0.955834i | \(-0.594956\pi\) | ||||
−0.293907 | + | 0.955834i | \(0.594956\pi\) | |||||||
\(812\) | 431824. | 0.0229835 | ||||||||
\(813\) | −1.23340e7 | −0.654451 | ||||||||
\(814\) | 9.17654e6 | 0.485420 | ||||||||
\(815\) | −414657. | −0.0218673 | ||||||||
\(816\) | −2.55514e7 | −1.34335 | ||||||||
\(817\) | 2.14856e6 | 0.112614 | ||||||||
\(818\) | −1.85983e7 | −0.971827 | ||||||||
\(819\) | −2.25370e6 | −0.117405 | ||||||||
\(820\) | 519531. | 0.0269822 | ||||||||
\(821\) | 2.92979e7 | 1.51698 | 0.758488 | − | 0.651687i | \(-0.225938\pi\) | ||||
0.758488 | + | 0.651687i | \(0.225938\pi\) | |||||||
\(822\) | −5.47755e7 | −2.82753 | ||||||||
\(823\) | −3.59573e7 | −1.85050 | −0.925248 | − | 0.379364i | \(-0.876143\pi\) | ||||
−0.925248 | + | 0.379364i | \(0.876143\pi\) | |||||||
\(824\) | 4.89913e6 | 0.251363 | ||||||||
\(825\) | 4.80553e6 | 0.245814 | ||||||||
\(826\) | 1.50355e7 | 0.766777 | ||||||||
\(827\) | −2.08172e7 | −1.05842 | −0.529211 | − | 0.848490i | \(-0.677512\pi\) | ||||
−0.529211 | + | 0.848490i | \(0.677512\pi\) | |||||||
\(828\) | 1.08834e7 | 0.551682 | ||||||||
\(829\) | 1.14738e6 | 0.0579857 | 0.0289929 | − | 0.999580i | \(-0.490770\pi\) | ||||
0.0289929 | + | 0.999580i | \(0.490770\pi\) | |||||||
\(830\) | 6.51755e6 | 0.328390 | ||||||||
\(831\) | −7.15809e6 | −0.359579 | ||||||||
\(832\) | 1.51912e7 | 0.760825 | ||||||||
\(833\) | −1.09178e7 | −0.545156 | ||||||||
\(834\) | −595197. | −0.0296310 | ||||||||
\(835\) | −1.16223e6 | −0.0576869 | ||||||||
\(836\) | −1.92953e6 | −0.0954850 | ||||||||
\(837\) | −3.92553e7 | −1.93680 | ||||||||
\(838\) | −1.68929e7 | −0.830989 | ||||||||
\(839\) | −3.34395e7 | −1.64004 | −0.820021 | − | 0.572333i | \(-0.806038\pi\) | ||||
−0.820021 | + | 0.572333i | \(0.806038\pi\) | |||||||
\(840\) | −4.14089e6 | −0.202486 | ||||||||
\(841\) | −2.05067e7 | −0.999784 | ||||||||
\(842\) | −5.54927e7 | −2.69746 | ||||||||
\(843\) | −1.29791e7 | −0.629036 | ||||||||
\(844\) | −3.57618e7 | −1.72808 | ||||||||
\(845\) | −800885. | −0.0385859 | ||||||||
\(846\) | 6.28500e6 | 0.301911 | ||||||||
\(847\) | 1.47555e7 | 0.706718 | ||||||||
\(848\) | 1.10740e7 | 0.528827 | ||||||||
\(849\) | −1.37911e6 | −0.0656645 | ||||||||
\(850\) | 4.71824e7 | 2.23992 | ||||||||
\(851\) | 3.25351e7 | 1.54003 | ||||||||
\(852\) | 7.59129e7 | 3.58275 | ||||||||
\(853\) | 2.30119e7 | 1.08288 | 0.541441 | − | 0.840739i | \(-0.317879\pi\) | ||||
0.541441 | + | 0.840739i | \(0.317879\pi\) | |||||||
\(854\) | 2.25416e7 | 1.05764 | ||||||||
\(855\) | 101648. | 0.00475538 | ||||||||
\(856\) | 1.64260e7 | 0.766207 | ||||||||
\(857\) | 1.97851e7 | 0.920207 | 0.460103 | − | 0.887865i | \(-0.347812\pi\) | ||||
0.460103 | + | 0.887865i | \(0.347812\pi\) | |||||||
\(858\) | −8.26877e6 | −0.383462 | ||||||||
\(859\) | 3.01949e7 | 1.39621 | 0.698104 | − | 0.715997i | \(-0.254027\pi\) | ||||
0.698104 | + | 0.715997i | \(0.254027\pi\) | |||||||
\(860\) | −4.75196e6 | −0.219092 | ||||||||
\(861\) | 1.24566e6 | 0.0572654 | ||||||||
\(862\) | 2.29333e7 | 1.05123 | ||||||||
\(863\) | −3.53884e7 | −1.61746 | −0.808731 | − | 0.588178i | \(-0.799845\pi\) | ||||
−0.808731 | + | 0.588178i | \(0.799845\pi\) | |||||||
\(864\) | −3.34887e6 | −0.152621 | ||||||||
\(865\) | −728257. | −0.0330936 | ||||||||
\(866\) | 3.50321e7 | 1.58735 | ||||||||
\(867\) | −1.48450e7 | −0.670705 | ||||||||
\(868\) | 6.29303e7 | 2.83505 | ||||||||
\(869\) | −2.35135e6 | −0.105625 | ||||||||
\(870\) | −83464.3 | −0.00373854 | ||||||||
\(871\) | −2.56672e7 | −1.14639 | ||||||||
\(872\) | −6.64482e6 | −0.295932 | ||||||||
\(873\) | −143581. | −0.00637618 | ||||||||
\(874\) | −1.01942e7 | −0.451414 | ||||||||
\(875\) | 5.49858e6 | 0.242790 | ||||||||
\(876\) | 3.07071e7 | 1.35200 | ||||||||
\(877\) | −1.51182e7 | −0.663745 | −0.331872 | − | 0.943324i | \(-0.607680\pi\) | ||||
−0.331872 | + | 0.943324i | \(0.607680\pi\) | |||||||
\(878\) | −5.73978e7 | −2.51281 | ||||||||
\(879\) | −1.46295e7 | −0.638640 | ||||||||
\(880\) | 1.15054e6 | 0.0500834 | ||||||||
\(881\) | 2.69041e7 | 1.16783 | 0.583913 | − | 0.811816i | \(-0.301521\pi\) | ||||
0.583913 | + | 0.811816i | \(0.301521\pi\) | |||||||
\(882\) | −2.92900e6 | −0.126779 | ||||||||
\(883\) | 2.44399e6 | 0.105487 | 0.0527434 | − | 0.998608i | \(-0.483203\pi\) | ||||
0.0527434 | + | 0.998608i | \(0.483203\pi\) | |||||||
\(884\) | −5.44815e7 | −2.34487 | ||||||||
\(885\) | −1.95022e6 | −0.0836999 | ||||||||
\(886\) | 5.18946e7 | 2.22095 | ||||||||
\(887\) | −1.21459e6 | −0.0518347 | −0.0259174 | − | 0.999664i | \(-0.508251\pi\) | ||||
−0.0259174 | + | 0.999664i | \(0.508251\pi\) | |||||||
\(888\) | −3.87530e7 | −1.64920 | ||||||||
\(889\) | −3.38411e6 | −0.143612 | ||||||||
\(890\) | −6.60325e6 | −0.279436 | ||||||||
\(891\) | −5.22430e6 | −0.220462 | ||||||||
\(892\) | −5.42762e7 | −2.28400 | ||||||||
\(893\) | −3.95061e6 | −0.165781 | ||||||||
\(894\) | −4.59992e7 | −1.92489 | ||||||||
\(895\) | −2.71987e6 | −0.113499 | ||||||||
\(896\) | −3.06436e7 | −1.27518 | ||||||||
\(897\) | −2.93166e7 | −1.21656 | ||||||||
\(898\) | −4.37845e7 | −1.81188 | ||||||||
\(899\) | 646709. | 0.0266876 | ||||||||
\(900\) | 8.49446e6 | 0.349566 | ||||||||
\(901\) | 1.51421e7 | 0.621404 | ||||||||
\(902\) | −975337. | −0.0399152 | ||||||||
\(903\) | −1.13936e7 | −0.464989 | ||||||||
\(904\) | 1.94122e7 | 0.790048 | ||||||||
\(905\) | −985602. | −0.0400019 | ||||||||
\(906\) | −3.01133e7 | −1.21882 | ||||||||
\(907\) | −1.06834e7 | −0.431212 | −0.215606 | − | 0.976480i | \(-0.569173\pi\) | ||||
−0.215606 | + | 0.976480i | \(0.569173\pi\) | |||||||
\(908\) | −6.93422e7 | −2.79115 | ||||||||
\(909\) | 6.32976e6 | 0.254084 | ||||||||
\(910\) | −4.66885e6 | −0.186899 | ||||||||
\(911\) | 1.24982e7 | 0.498944 | 0.249472 | − | 0.968382i | \(-0.419743\pi\) | ||||
0.249472 | + | 0.968382i | \(0.419743\pi\) | |||||||
\(912\) | 4.30883e6 | 0.171543 | ||||||||
\(913\) | −8.21103e6 | −0.326002 | ||||||||
\(914\) | 5.32957e6 | 0.211022 | ||||||||
\(915\) | −2.92380e6 | −0.115450 | ||||||||
\(916\) | 2.19988e7 | 0.866283 | ||||||||
\(917\) | 2.25764e7 | 0.886608 | ||||||||
\(918\) | −6.26674e7 | −2.45434 | ||||||||
\(919\) | −1.94664e7 | −0.760322 | −0.380161 | − | 0.924920i | \(-0.624131\pi\) | ||||
−0.380161 | + | 0.924920i | \(0.624131\pi\) | |||||||
\(920\) | 1.14953e7 | 0.447766 | ||||||||
\(921\) | −1.01737e7 | −0.395211 | ||||||||
\(922\) | −1.54219e7 | −0.597462 | ||||||||
\(923\) | 4.36389e7 | 1.68605 | ||||||||
\(924\) | 1.02321e7 | 0.394262 | ||||||||
\(925\) | 2.53935e7 | 0.975817 | ||||||||
\(926\) | −5.57236e7 | −2.13556 | ||||||||
\(927\) | 637734. | 0.0243748 | ||||||||
\(928\) | 55170.7 | 0.00210300 | ||||||||
\(929\) | 2.43227e7 | 0.924638 | 0.462319 | − | 0.886714i | \(-0.347017\pi\) | ||||
0.462319 | + | 0.886714i | \(0.347017\pi\) | |||||||
\(930\) | −1.21634e7 | −0.461155 | ||||||||
\(931\) | 1.84110e6 | 0.0696152 | ||||||||
\(932\) | −6.85914e7 | −2.58661 | ||||||||
\(933\) | 1.24295e7 | 0.467467 | ||||||||
\(934\) | −8.47366e7 | −3.17836 | ||||||||
\(935\) | 1.57320e6 | 0.0588510 | ||||||||
\(936\) | −7.45208e6 | −0.278027 | ||||||||
\(937\) | 1.22842e7 | 0.457088 | 0.228544 | − | 0.973534i | \(-0.426604\pi\) | ||||
0.228544 | + | 0.973534i | \(0.426604\pi\) | |||||||
\(938\) | 4.73296e7 | 1.75641 | ||||||||
\(939\) | −1.78686e7 | −0.661344 | ||||||||
\(940\) | 8.73754e6 | 0.322530 | ||||||||
\(941\) | −9.16247e6 | −0.337317 | −0.168659 | − | 0.985675i | \(-0.553944\pi\) | ||||
−0.168659 | + | 0.985675i | \(0.553944\pi\) | |||||||
\(942\) | 3.53653e7 | 1.29852 | ||||||||
\(943\) | −3.45802e6 | −0.126633 | ||||||||
\(944\) | 1.76422e7 | 0.644350 | ||||||||
\(945\) | −3.60390e6 | −0.131278 | ||||||||
\(946\) | 8.92105e6 | 0.324107 | ||||||||
\(947\) | 1.96327e7 | 0.711386 | 0.355693 | − | 0.934603i | \(-0.384245\pi\) | ||||
0.355693 | + | 0.934603i | \(0.384245\pi\) | |||||||
\(948\) | 1.94760e7 | 0.703850 | ||||||||
\(949\) | 1.76521e7 | 0.636255 | ||||||||
\(950\) | −7.95655e6 | −0.286033 | ||||||||
\(951\) | −3.10330e7 | −1.11268 | ||||||||
\(952\) | 5.12207e7 | 1.83169 | ||||||||
\(953\) | 2.96559e7 | 1.05774 | 0.528870 | − | 0.848703i | \(-0.322616\pi\) | ||||
0.528870 | + | 0.848703i | \(0.322616\pi\) | |||||||
\(954\) | 4.06230e6 | 0.144511 | ||||||||
\(955\) | −3.88578e6 | −0.137870 | ||||||||
\(956\) | −4.66127e7 | −1.64953 | ||||||||
\(957\) | 105151. | 0.00371137 | ||||||||
\(958\) | 3.17640e7 | 1.11821 | ||||||||
\(959\) | 3.89645e7 | 1.36812 | ||||||||
\(960\) | 3.63339e6 | 0.127243 | ||||||||
\(961\) | 6.56167e7 | 2.29196 | ||||||||
\(962\) | −4.36940e7 | −1.52224 | ||||||||
\(963\) | 2.13821e6 | 0.0742995 | ||||||||
\(964\) | −9.12899e7 | −3.16395 | ||||||||
\(965\) | −5.34357e6 | −0.184720 | ||||||||
\(966\) | 5.40589e7 | 1.86391 | ||||||||
\(967\) | 1.72509e7 | 0.593260 | 0.296630 | − | 0.954992i | \(-0.404137\pi\) | ||||
0.296630 | + | 0.954992i | \(0.404137\pi\) | |||||||
\(968\) | 4.87905e7 | 1.67358 | ||||||||
\(969\) | 5.89172e6 | 0.201573 | ||||||||
\(970\) | −297447. | −0.0101503 | ||||||||
\(971\) | −120921. | −0.00411578 | −0.00205789 | − | 0.999998i | \(-0.500655\pi\) | ||||
−0.00205789 | + | 0.999998i | \(0.500655\pi\) | |||||||
\(972\) | −2.08771e7 | −0.708769 | ||||||||
\(973\) | 423393. | 0.0143371 | ||||||||
\(974\) | −5.68937e7 | −1.92162 | ||||||||
\(975\) | −2.28815e7 | −0.770855 | ||||||||
\(976\) | 2.64495e7 | 0.888776 | ||||||||
\(977\) | −9.07671e6 | −0.304223 | −0.152112 | − | 0.988363i | \(-0.548607\pi\) | ||||
−0.152112 | + | 0.988363i | \(0.548607\pi\) | |||||||
\(978\) | −6.44788e6 | −0.215561 | ||||||||
\(979\) | 8.31900e6 | 0.277405 | ||||||||
\(980\) | −4.07195e6 | −0.135437 | ||||||||
\(981\) | −864975. | −0.0286966 | ||||||||
\(982\) | 6.27701e7 | 2.07718 | ||||||||
\(983\) | 966289. | 0.0318950 | ||||||||
\(984\) | 4.11890e6 | 0.135611 | ||||||||
\(985\) | 8.48251e6 | 0.278570 | ||||||||
\(986\) | 1.03241e6 | 0.0338189 | ||||||||
\(987\) | 2.09497e7 | 0.684519 | ||||||||
\(988\) | 9.18742e6 | 0.299434 | ||||||||
\(989\) | 3.16292e7 | 1.02825 | ||||||||
\(990\) | 422055. | 0.0136861 | ||||||||
\(991\) | 1.11150e7 | 0.359523 | 0.179761 | − | 0.983710i | \(-0.442467\pi\) | ||||
0.179761 | + | 0.983710i | \(0.442467\pi\) | |||||||
\(992\) | 8.04011e6 | 0.259408 | ||||||||
\(993\) | 3.79014e7 | 1.21978 | ||||||||
\(994\) | −8.04689e7 | −2.58322 | ||||||||
\(995\) | −862153. | −0.0276075 | ||||||||
\(996\) | 6.80115e7 | 2.17237 | ||||||||
\(997\) | −2.67032e7 | −0.850794 | −0.425397 | − | 0.905007i | \(-0.639866\pi\) | ||||
−0.425397 | + | 0.905007i | \(0.639866\pi\) | |||||||
\(998\) | −4.06724e7 | −1.29263 | ||||||||
\(999\) | −3.37275e7 | −1.06923 |
(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 | 983.6.a.b.1.16 | ✓ | 218 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.6.a.b.1.16 | ✓ | 218 | 1.1 | even | 1 | trivial |