Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,6,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1075.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(172.412606299\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.29 | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.20077 | 1.27293 | 0.636464 | − | 0.771306i | \(-0.280396\pi\) | ||||
0.636464 | + | 0.771306i | \(0.280396\pi\) | |||||||
\(3\) | −5.47224 | −0.351045 | −0.175522 | − | 0.984475i | \(-0.556161\pi\) | ||||
−0.175522 | + | 0.984475i | \(0.556161\pi\) | |||||||
\(4\) | 19.8511 | 0.620347 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −39.4044 | −0.446855 | ||||||||
\(7\) | 128.650 | 0.992352 | 0.496176 | − | 0.868222i | \(-0.334737\pi\) | ||||
0.496176 | + | 0.868222i | \(0.334737\pi\) | |||||||
\(8\) | −87.4815 | −0.483272 | ||||||||
\(9\) | −213.055 | −0.876768 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 74.6602 | 0.186040 | 0.0930202 | − | 0.995664i | \(-0.470348\pi\) | ||||
0.0930202 | + | 0.995664i | \(0.470348\pi\) | |||||||
\(12\) | −108.630 | −0.217769 | ||||||||
\(13\) | −459.547 | −0.754173 | −0.377087 | − | 0.926178i | \(-0.623074\pi\) | ||||
−0.377087 | + | 0.926178i | \(0.623074\pi\) | |||||||
\(14\) | 926.381 | 1.26319 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1265.17 | −1.23552 | ||||||||
\(17\) | 1157.85 | 0.971691 | 0.485846 | − | 0.874045i | \(-0.338512\pi\) | ||||
0.485846 | + | 0.874045i | \(0.338512\pi\) | |||||||
\(18\) | −1534.16 | −1.11606 | ||||||||
\(19\) | 1010.86 | 0.642404 | 0.321202 | − | 0.947011i | \(-0.395913\pi\) | ||||
0.321202 | + | 0.947011i | \(0.395913\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −704.006 | −0.348360 | ||||||||
\(22\) | 537.611 | 0.236816 | ||||||||
\(23\) | −4235.90 | −1.66965 | −0.834827 | − | 0.550513i | \(-0.814432\pi\) | ||||
−0.834827 | + | 0.550513i | \(0.814432\pi\) | |||||||
\(24\) | 478.720 | 0.169650 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3309.09 | −0.960008 | ||||||||
\(27\) | 2495.64 | 0.658829 | ||||||||
\(28\) | 2553.85 | 0.615602 | ||||||||
\(29\) | −5891.50 | −1.30086 | −0.650430 | − | 0.759566i | \(-0.725411\pi\) | ||||
−0.650430 | + | 0.759566i | \(0.725411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5606.92 | 1.04790 | 0.523950 | − | 0.851749i | \(-0.324458\pi\) | ||||
0.523950 | + | 0.851749i | \(0.324458\pi\) | |||||||
\(32\) | −6310.78 | −1.08945 | ||||||||
\(33\) | −408.559 | −0.0653085 | ||||||||
\(34\) | 8337.38 | 1.23689 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4229.36 | −0.543900 | ||||||||
\(37\) | 13751.4 | 1.65136 | 0.825680 | − | 0.564139i | \(-0.190792\pi\) | ||||
0.825680 | + | 0.564139i | \(0.190792\pi\) | |||||||
\(38\) | 7278.99 | 0.817734 | ||||||||
\(39\) | 2514.75 | 0.264748 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13924.9 | 1.29369 | 0.646846 | − | 0.762621i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762621i | \(0.276088\pi\) | |||||||
\(42\) | −5069.39 | −0.443437 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | 1482.09 | 0.115410 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −30501.8 | −2.12535 | ||||||||
\(47\) | −4559.12 | −0.301048 | −0.150524 | − | 0.988606i | \(-0.548096\pi\) | ||||
−0.150524 | + | 0.988606i | \(0.548096\pi\) | |||||||
\(48\) | 6923.31 | 0.433722 | ||||||||
\(49\) | −256.094 | −0.0152373 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6336.01 | −0.341107 | ||||||||
\(52\) | −9122.50 | −0.467849 | ||||||||
\(53\) | 31988.9 | 1.56426 | 0.782131 | − | 0.623115i | \(-0.214133\pi\) | ||||
0.782131 | + | 0.623115i | \(0.214133\pi\) | |||||||
\(54\) | 17970.5 | 0.838642 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11254.5 | −0.479576 | ||||||||
\(57\) | −5531.69 | −0.225512 | ||||||||
\(58\) | −42423.3 | −1.65590 | ||||||||
\(59\) | −39336.2 | −1.47117 | −0.735585 | − | 0.677433i | \(-0.763092\pi\) | ||||
−0.735585 | + | 0.677433i | \(0.763092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 738.234 | 0.0254021 | 0.0127010 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0127010 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(62\) | 40374.1 | 1.33390 | ||||||||
\(63\) | −27409.5 | −0.870062 | ||||||||
\(64\) | −4957.09 | −0.151278 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2941.94 | −0.0831330 | ||||||||
\(67\) | 37619.4 | 1.02382 | 0.511911 | − | 0.859039i | \(-0.328938\pi\) | ||||
0.511911 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(68\) | 22984.5 | 0.602785 | ||||||||
\(69\) | 23179.9 | 0.586123 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15610.1 | −0.367502 | −0.183751 | − | 0.982973i | \(-0.558824\pi\) | ||||
−0.183751 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(72\) | 18638.3 | 0.423717 | ||||||||
\(73\) | −33418.5 | −0.733972 | −0.366986 | − | 0.930226i | \(-0.619610\pi\) | ||||
−0.366986 | + | 0.930226i | \(0.619610\pi\) | |||||||
\(74\) | 99020.4 | 2.10206 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20066.7 | 0.398513 | ||||||||
\(77\) | 9605.06 | 0.184618 | ||||||||
\(78\) | 18108.1 | 0.337006 | ||||||||
\(79\) | 1653.19 | 0.0298027 | 0.0149013 | − | 0.999889i | \(-0.495257\pi\) | ||||
0.0149013 | + | 0.999889i | \(0.495257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 38115.5 | 0.645489 | ||||||||
\(82\) | 100270. | 1.64678 | ||||||||
\(83\) | −54366.1 | −0.866229 | −0.433115 | − | 0.901339i | \(-0.642585\pi\) | ||||
−0.433115 | + | 0.901339i | \(0.642585\pi\) | |||||||
\(84\) | −13975.3 | −0.216104 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 13314.2 | 0.194120 | ||||||||
\(87\) | 32239.7 | 0.456660 | ||||||||
\(88\) | −6531.38 | −0.0899081 | ||||||||
\(89\) | 75355.5 | 1.00842 | 0.504208 | − | 0.863582i | \(-0.331784\pi\) | ||||
0.504208 | + | 0.863582i | \(0.331784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −59120.8 | −0.748405 | ||||||||
\(92\) | −84087.3 | −1.03576 | ||||||||
\(93\) | −30682.4 | −0.367860 | ||||||||
\(94\) | −32829.2 | −0.383213 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 34534.1 | 0.382446 | ||||||||
\(97\) | 76314.0 | 0.823521 | 0.411761 | − | 0.911292i | \(-0.364914\pi\) | ||||
0.411761 | + | 0.911292i | \(0.364914\pi\) | |||||||
\(98\) | −1844.07 | −0.0193960 | ||||||||
\(99\) | −15906.7 | −0.163114 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 123504. | 1.20470 | 0.602350 | − | 0.798232i | \(-0.294231\pi\) | ||||
0.602350 | + | 0.798232i | \(0.294231\pi\) | |||||||
\(102\) | −45624.2 | −0.434205 | ||||||||
\(103\) | 34077.8 | 0.316503 | 0.158252 | − | 0.987399i | \(-0.449414\pi\) | ||||
0.158252 | + | 0.987399i | \(0.449414\pi\) | |||||||
\(104\) | 40201.8 | 0.364471 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 230345. | 1.99119 | ||||||||
\(107\) | 148390. | 1.25298 | 0.626492 | − | 0.779428i | \(-0.284490\pi\) | ||||
0.626492 | + | 0.779428i | \(0.284490\pi\) | |||||||
\(108\) | 49541.2 | 0.408702 | ||||||||
\(109\) | −41193.2 | −0.332093 | −0.166046 | − | 0.986118i | \(-0.553100\pi\) | ||||
−0.166046 | + | 0.986118i | \(0.553100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −75250.9 | −0.579701 | ||||||||
\(112\) | −162764. | −1.22607 | ||||||||
\(113\) | 166815. | 1.22896 | 0.614482 | − | 0.788931i | \(-0.289365\pi\) | ||||
0.614482 | + | 0.788931i | \(0.289365\pi\) | |||||||
\(114\) | −39832.4 | −0.287061 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −116953. | −0.806984 | ||||||||
\(117\) | 97908.5 | 0.661235 | ||||||||
\(118\) | −283251. | −1.87269 | ||||||||
\(119\) | 148957. | 0.964260 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −155477. | −0.965389 | ||||||||
\(122\) | 5315.85 | 0.0323350 | ||||||||
\(123\) | −76200.2 | −0.454144 | ||||||||
\(124\) | 111303. | 0.650061 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −197370. | −1.10753 | ||||||||
\(127\) | −292468. | −1.60905 | −0.804525 | − | 0.593919i | \(-0.797580\pi\) | ||||
−0.804525 | + | 0.593919i | \(0.797580\pi\) | |||||||
\(128\) | 166250. | 0.896886 | ||||||||
\(129\) | −10118.2 | −0.0535338 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 165082. | 0.840468 | 0.420234 | − | 0.907416i | \(-0.361948\pi\) | ||||
0.420234 | + | 0.907416i | \(0.361948\pi\) | |||||||
\(132\) | −8110.33 | −0.0405139 | ||||||||
\(133\) | 130048. | 0.637491 | ||||||||
\(134\) | 270888. | 1.30325 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −101290. | −0.469591 | ||||||||
\(137\) | 343862. | 1.56525 | 0.782623 | − | 0.622496i | \(-0.213881\pi\) | ||||
0.782623 | + | 0.622496i | \(0.213881\pi\) | |||||||
\(138\) | 166913. | 0.746092 | ||||||||
\(139\) | 396100. | 1.73887 | 0.869436 | − | 0.494045i | \(-0.164482\pi\) | ||||
0.869436 | + | 0.494045i | \(0.164482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24948.6 | 0.105681 | ||||||||
\(142\) | −112405. | −0.467803 | ||||||||
\(143\) | −34309.8 | −0.140307 | ||||||||
\(144\) | 269550. | 1.08326 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −240639. | −0.934294 | ||||||||
\(147\) | 1401.41 | 0.00534899 | ||||||||
\(148\) | 272980. | 1.02442 | ||||||||
\(149\) | −288486. | −1.06453 | −0.532266 | − | 0.846577i | \(-0.678659\pi\) | ||||
−0.532266 | + | 0.846577i | \(0.678659\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 503945. | 1.79863 | 0.899313 | − | 0.437306i | \(-0.144067\pi\) | ||||
0.899313 | + | 0.437306i | \(0.144067\pi\) | |||||||
\(152\) | −88431.8 | −0.310456 | ||||||||
\(153\) | −246684. | −0.851948 | ||||||||
\(154\) | 69163.8 | 0.235005 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 49920.5 | 0.164236 | ||||||||
\(157\) | −279266. | −0.904210 | −0.452105 | − | 0.891965i | \(-0.649327\pi\) | ||||
−0.452105 | + | 0.891965i | \(0.649327\pi\) | |||||||
\(158\) | 11904.2 | 0.0379367 | ||||||||
\(159\) | −175051. | −0.549125 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −544950. | −1.65688 | ||||||||
\(162\) | 274461. | 0.821661 | ||||||||
\(163\) | 81333.7 | 0.239774 | 0.119887 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119887 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(164\) | 276423. | 0.802537 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −391478. | −1.10265 | ||||||||
\(167\) | 369746. | 1.02592 | 0.512959 | − | 0.858413i | \(-0.328549\pi\) | ||||
0.512959 | + | 0.858413i | \(0.328549\pi\) | |||||||
\(168\) | 61587.5 | 0.168352 | ||||||||
\(169\) | −160110. | −0.431223 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −215369. | −0.563239 | ||||||||
\(172\) | 36704.7 | 0.0946020 | ||||||||
\(173\) | 749929. | 1.90504 | 0.952522 | − | 0.304469i | \(-0.0984789\pi\) | ||||
0.952522 | + | 0.304469i | \(0.0984789\pi\) | |||||||
\(174\) | 232151. | 0.581295 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −94457.7 | −0.229856 | ||||||||
\(177\) | 215257. | 0.516446 | ||||||||
\(178\) | 542618. | 1.28364 | ||||||||
\(179\) | 245010. | 0.571546 | 0.285773 | − | 0.958297i | \(-0.407750\pi\) | ||||
0.285773 | + | 0.958297i | \(0.407750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −864861. | −1.96223 | −0.981114 | − | 0.193428i | \(-0.938039\pi\) | ||||
−0.981114 | + | 0.193428i | \(0.938039\pi\) | |||||||
\(182\) | −425715. | −0.952666 | ||||||||
\(183\) | −4039.80 | −0.00891727 | ||||||||
\(184\) | 370563. | 0.806896 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −220937. | −0.468259 | ||||||||
\(187\) | 86445.0 | 0.180774 | ||||||||
\(188\) | −90503.5 | −0.186754 | ||||||||
\(189\) | 321065. | 0.653791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13437.9 | 0.0266531 | 0.0133266 | − | 0.999911i | \(-0.495758\pi\) | ||||
0.0133266 | + | 0.999911i | \(0.495758\pi\) | |||||||
\(192\) | 27126.4 | 0.0531054 | ||||||||
\(193\) | 565162. | 1.09214 | 0.546071 | − | 0.837739i | \(-0.316123\pi\) | ||||
0.546071 | + | 0.837739i | \(0.316123\pi\) | |||||||
\(194\) | 549519. | 1.04828 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5083.74 | −0.00945243 | ||||||||
\(197\) | 225656. | 0.414268 | 0.207134 | − | 0.978313i | \(-0.433586\pi\) | ||||
0.207134 | + | 0.978313i | \(0.433586\pi\) | |||||||
\(198\) | −114540. | −0.207633 | ||||||||
\(199\) | −555552. | −0.994471 | −0.497236 | − | 0.867615i | \(-0.665652\pi\) | ||||
−0.497236 | + | 0.867615i | \(0.665652\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −205862. | −0.359407 | ||||||||
\(202\) | 889327. | 1.53350 | ||||||||
\(203\) | −757943. | −1.29091 | ||||||||
\(204\) | −125777. | −0.211605 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 245386. | 0.402886 | ||||||||
\(207\) | 902478. | 1.46390 | ||||||||
\(208\) | 581404. | 0.931794 | ||||||||
\(209\) | 75471.2 | 0.119513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 772768. | 1.19493 | 0.597465 | − | 0.801895i | \(-0.296175\pi\) | ||||
0.597465 | + | 0.801895i | \(0.296175\pi\) | |||||||
\(212\) | 635014. | 0.970384 | ||||||||
\(213\) | 85422.2 | 0.129010 | ||||||||
\(214\) | 1.06852e6 | 1.59496 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −218323. | −0.318394 | ||||||||
\(217\) | 721332. | 1.03989 | ||||||||
\(218\) | −296623. | −0.422730 | ||||||||
\(219\) | 182874. | 0.257657 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −532084. | −0.732824 | ||||||||
\(222\) | −541864. | −0.737918 | ||||||||
\(223\) | 315027. | 0.424215 | 0.212107 | − | 0.977246i | \(-0.431967\pi\) | ||||
0.212107 | + | 0.977246i | \(0.431967\pi\) | |||||||
\(224\) | −811884. | −1.08112 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.20120e6 | 1.56438 | ||||||||
\(227\) | −1.03800e6 | −1.33700 | −0.668500 | − | 0.743712i | \(-0.733063\pi\) | ||||
−0.668500 | + | 0.743712i | \(0.733063\pi\) | |||||||
\(228\) | −109810. | −0.139896 | ||||||||
\(229\) | 607620. | 0.765673 | 0.382837 | − | 0.923816i | \(-0.374947\pi\) | ||||
0.382837 | + | 0.923816i | \(0.374947\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −52561.2 | −0.0648090 | ||||||||
\(232\) | 515397. | 0.628669 | ||||||||
\(233\) | −170546. | −0.205803 | −0.102901 | − | 0.994692i | \(-0.532813\pi\) | ||||
−0.102901 | + | 0.994692i | \(0.532813\pi\) | |||||||
\(234\) | 705016. | 0.841704 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −780867. | −0.912635 | ||||||||
\(237\) | −9046.66 | −0.0104621 | ||||||||
\(238\) | 1.07261e6 | 1.22743 | ||||||||
\(239\) | 1.51509e6 | 1.71571 | 0.857856 | − | 0.513890i | \(-0.171796\pi\) | ||||
0.857856 | + | 0.513890i | \(0.171796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 565222. | 0.626869 | 0.313434 | − | 0.949610i | \(-0.398520\pi\) | ||||
0.313434 | + | 0.949610i | \(0.398520\pi\) | |||||||
\(242\) | −1.11955e6 | −1.22887 | ||||||||
\(243\) | −815018. | −0.885425 | ||||||||
\(244\) | 14654.7 | 0.0157581 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −548700. | −0.578092 | ||||||||
\(247\) | −464538. | −0.484484 | ||||||||
\(248\) | −490501. | −0.506420 | ||||||||
\(249\) | 297504. | 0.304085 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −193329. | −0.193693 | −0.0968464 | − | 0.995299i | \(-0.530876\pi\) | ||||
−0.0968464 | + | 0.995299i | \(0.530876\pi\) | |||||||
\(252\) | −544109. | −0.539740 | ||||||||
\(253\) | −316253. | −0.310623 | ||||||||
\(254\) | −2.10600e6 | −2.04820 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.35576e6 | 1.29295 | ||||||||
\(257\) | −2.08642e6 | −1.97046 | −0.985232 | − | 0.171225i | \(-0.945228\pi\) | ||||
−0.985232 | + | 0.171225i | \(0.945228\pi\) | |||||||
\(258\) | −72858.7 | −0.0681447 | ||||||||
\(259\) | 1.76912e6 | 1.63873 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.25521e6 | 1.14055 | ||||||||
\(262\) | 1.18872e6 | 1.06986 | ||||||||
\(263\) | 2.22099e6 | 1.97996 | 0.989980 | − | 0.141204i | \(-0.0450975\pi\) | ||||
0.989980 | + | 0.141204i | \(0.0450975\pi\) | |||||||
\(264\) | 35741.3 | 0.0315617 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 936444. | 0.811480 | ||||||||
\(267\) | −412364. | −0.353999 | ||||||||
\(268\) | 746785. | 0.635124 | ||||||||
\(269\) | −767101. | −0.646356 | −0.323178 | − | 0.946338i | \(-0.604751\pi\) | ||||
−0.323178 | + | 0.946338i | \(0.604751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −159729. | −0.132118 | −0.0660588 | − | 0.997816i | \(-0.521043\pi\) | ||||
−0.0660588 | + | 0.997816i | \(0.521043\pi\) | |||||||
\(272\) | −1.46487e6 | −1.20054 | ||||||||
\(273\) | 323524. | 0.262724 | ||||||||
\(274\) | 2.47607e6 | 1.99245 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 460146. | 0.363599 | ||||||||
\(277\) | −484535. | −0.379425 | −0.189712 | − | 0.981840i | \(-0.560756\pi\) | ||||
−0.189712 | + | 0.981840i | \(0.560756\pi\) | |||||||
\(278\) | 2.85222e6 | 2.21346 | ||||||||
\(279\) | −1.19458e6 | −0.918765 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 328209. | 0.247962 | 0.123981 | − | 0.992285i | \(-0.460434\pi\) | ||||
0.123981 | + | 0.992285i | \(0.460434\pi\) | |||||||
\(282\) | 179649. | 0.134525 | ||||||||
\(283\) | 1.03659e6 | 0.769380 | 0.384690 | − | 0.923046i | \(-0.374308\pi\) | ||||
0.384690 | + | 0.923046i | \(0.374308\pi\) | |||||||
\(284\) | −309877. | −0.227978 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −247057. | −0.178600 | ||||||||
\(287\) | 1.79144e6 | 1.28380 | ||||||||
\(288\) | 1.34454e6 | 0.955197 | ||||||||
\(289\) | −79250.4 | −0.0558158 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −417609. | −0.289093 | ||||||||
\(292\) | −663393. | −0.455317 | ||||||||
\(293\) | 546625. | 0.371981 | 0.185990 | − | 0.982552i | \(-0.440451\pi\) | ||||
0.185990 | + | 0.982552i | \(0.440451\pi\) | |||||||
\(294\) | 10091.2 | 0.00680888 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.20299e6 | −0.798055 | ||||||||
\(297\) | 186325. | 0.122569 | ||||||||
\(298\) | −2.07732e6 | −1.35507 | ||||||||
\(299\) | 1.94659e6 | 1.25921 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 237874. | 0.151332 | ||||||||
\(302\) | 3.62879e6 | 2.28952 | ||||||||
\(303\) | −675847. | −0.422904 | ||||||||
\(304\) | −1.27891e6 | −0.793701 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.77632e6 | −1.08447 | ||||||||
\(307\) | −843892. | −0.511024 | −0.255512 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255512 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(308\) | 190671. | 0.114527 | ||||||||
\(309\) | −186482. | −0.111107 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.66748e6 | 1.56387 | 0.781933 | − | 0.623362i | \(-0.214234\pi\) | ||||
0.781933 | + | 0.623362i | \(0.214234\pi\) | |||||||
\(312\) | −219994. | −0.127945 | ||||||||
\(313\) | 211659. | 0.122117 | 0.0610586 | − | 0.998134i | \(-0.480552\pi\) | ||||
0.0610586 | + | 0.998134i | \(0.480552\pi\) | |||||||
\(314\) | −2.01093e6 | −1.15099 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32817.6 | 0.0184880 | ||||||||
\(317\) | −2.76558e6 | −1.54574 | −0.772872 | − | 0.634562i | \(-0.781181\pi\) | ||||
−0.772872 | + | 0.634562i | \(0.781181\pi\) | |||||||
\(318\) | −1.26050e6 | −0.698997 | ||||||||
\(319\) | −439860. | −0.242013 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −812027. | −0.439854 | ||||||||
\(322\) | −3.92406e6 | −2.10909 | ||||||||
\(323\) | 1.17042e6 | 0.624218 | ||||||||
\(324\) | 756634. | 0.400427 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 585665. | 0.305215 | ||||||||
\(327\) | 225419. | 0.116579 | ||||||||
\(328\) | −1.21817e6 | −0.625205 | ||||||||
\(329\) | −586532. | −0.298746 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.10223e6 | 1.05465 | 0.527327 | − | 0.849662i | \(-0.323194\pi\) | ||||
0.527327 | + | 0.849662i | \(0.323194\pi\) | |||||||
\(332\) | −1.07923e6 | −0.537362 | ||||||||
\(333\) | −2.92979e6 | −1.44786 | ||||||||
\(334\) | 2.66246e6 | 1.30592 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 890687. | 0.430404 | ||||||||
\(337\) | 247202. | 0.118570 | 0.0592852 | − | 0.998241i | \(-0.481118\pi\) | ||||
0.0592852 | + | 0.998241i | \(0.481118\pi\) | |||||||
\(338\) | −1.15292e6 | −0.548916 | ||||||||
\(339\) | −912852. | −0.431421 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 418613. | 0.194952 | ||||||||
\(342\) | −1.55082e6 | −0.716963 | ||||||||
\(343\) | −2.19517e6 | −1.00747 | ||||||||
\(344\) | −161753. | −0.0736982 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.40007e6 | 2.42499 | ||||||||
\(347\) | −674766. | −0.300836 | −0.150418 | − | 0.988622i | \(-0.548062\pi\) | ||||
−0.150418 | + | 0.988622i | \(0.548062\pi\) | |||||||
\(348\) | 639993. | 0.283287 | ||||||||
\(349\) | 3.49441e6 | 1.53572 | 0.767858 | − | 0.640620i | \(-0.221323\pi\) | ||||
0.767858 | + | 0.640620i | \(0.221323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.14686e6 | −0.496871 | ||||||||
\(352\) | −471164. | −0.202682 | ||||||||
\(353\) | 3.12311e6 | 1.33398 | 0.666992 | − | 0.745065i | \(-0.267582\pi\) | ||||
0.666992 | + | 0.745065i | \(0.267582\pi\) | |||||||
\(354\) | 1.55002e6 | 0.657399 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.49589e6 | 0.625568 | ||||||||
\(357\) | −815130. | −0.338498 | ||||||||
\(358\) | 1.76426e6 | 0.727537 | ||||||||
\(359\) | 3.02885e6 | 1.24034 | 0.620172 | − | 0.784466i | \(-0.287063\pi\) | ||||
0.620172 | + | 0.784466i | \(0.287063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.45426e6 | −0.587317 | ||||||||
\(362\) | −6.22766e6 | −2.49778 | ||||||||
\(363\) | 850807. | 0.338895 | ||||||||
\(364\) | −1.17361e6 | −0.464271 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −29089.7 | −0.0113510 | ||||||||
\(367\) | −4.62366e6 | −1.79193 | −0.895965 | − | 0.444125i | \(-0.853515\pi\) | ||||
−0.895965 | + | 0.444125i | \(0.853515\pi\) | |||||||
\(368\) | 5.35913e6 | 2.06288 | ||||||||
\(369\) | −2.96675e6 | −1.13427 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.11538e6 | 1.55230 | ||||||||
\(372\) | −609079. | −0.228200 | ||||||||
\(373\) | −1.75855e6 | −0.654461 | −0.327230 | − | 0.944945i | \(-0.606115\pi\) | ||||
−0.327230 | + | 0.944945i | \(0.606115\pi\) | |||||||
\(374\) | 622470. | 0.230112 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 398839. | 0.145488 | ||||||||
\(377\) | 2.70742e6 | 0.981074 | ||||||||
\(378\) | 2.31192e6 | 0.832229 | ||||||||
\(379\) | 3.77525e6 | 1.35004 | 0.675021 | − | 0.737799i | \(-0.264135\pi\) | ||||
0.675021 | + | 0.737799i | \(0.264135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.60046e6 | 0.564848 | ||||||||
\(382\) | 96763.3 | 0.0339275 | ||||||||
\(383\) | −1.85816e6 | −0.647272 | −0.323636 | − | 0.946182i | \(-0.604905\pi\) | ||||
−0.323636 | + | 0.946182i | \(0.604905\pi\) | |||||||
\(384\) | −909762. | −0.314847 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.06960e6 | 1.39022 | ||||||||
\(387\) | −393938. | −0.133706 | ||||||||
\(388\) | 1.51492e6 | 0.510869 | ||||||||
\(389\) | 468713. | 0.157048 | 0.0785241 | − | 0.996912i | \(-0.474979\pi\) | ||||
0.0785241 | + | 0.996912i | \(0.474979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.90452e6 | −1.62239 | ||||||||
\(392\) | 22403.5 | 0.00736377 | ||||||||
\(393\) | −903368. | −0.295042 | ||||||||
\(394\) | 1.62490e6 | 0.527334 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −315765. | −0.101187 | ||||||||
\(397\) | 2.30778e6 | 0.734883 | 0.367442 | − | 0.930047i | \(-0.380234\pi\) | ||||
0.367442 | + | 0.930047i | \(0.380234\pi\) | |||||||
\(398\) | −4.00041e6 | −1.26589 | ||||||||
\(399\) | −711653. | −0.223788 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.86726e6 | 0.890444 | 0.445222 | − | 0.895420i | \(-0.353125\pi\) | ||||
0.445222 | + | 0.895420i | \(0.353125\pi\) | |||||||
\(402\) | −1.48237e6 | −0.457500 | ||||||||
\(403\) | −2.57664e6 | −0.790298 | ||||||||
\(404\) | 2.45170e6 | 0.747332 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.45777e6 | −1.64324 | ||||||||
\(407\) | 1.02668e6 | 0.307220 | ||||||||
\(408\) | 554284. | 0.164847 | ||||||||
\(409\) | −2.17707e6 | −0.643523 | −0.321761 | − | 0.946821i | \(-0.604275\pi\) | ||||
−0.321761 | + | 0.946821i | \(0.604275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.88170e6 | −0.549471 | ||||||||
\(412\) | 676481. | 0.196342 | ||||||||
\(413\) | −5.06062e6 | −1.45992 | ||||||||
\(414\) | 6.49854e6 | 1.86344 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.90010e6 | 0.821636 | ||||||||
\(417\) | −2.16756e6 | −0.610422 | ||||||||
\(418\) | 543451. | 0.152132 | ||||||||
\(419\) | −2.47893e6 | −0.689810 | −0.344905 | − | 0.938638i | \(-0.612089\pi\) | ||||
−0.344905 | + | 0.938638i | \(0.612089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.02419e6 | 0.556605 | 0.278302 | − | 0.960494i | \(-0.410228\pi\) | ||||
0.278302 | + | 0.960494i | \(0.410228\pi\) | |||||||
\(422\) | 5.56452e6 | 1.52106 | ||||||||
\(423\) | 971341. | 0.263950 | ||||||||
\(424\) | −2.79844e6 | −0.755963 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 615106. | 0.164220 | ||||||||
\(427\) | 94974.1 | 0.0252078 | ||||||||
\(428\) | 2.94571e6 | 0.777285 | ||||||||
\(429\) | 187752. | 0.0492539 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.48747e6 | 0.645006 | 0.322503 | − | 0.946568i | \(-0.395476\pi\) | ||||
0.322503 | + | 0.946568i | \(0.395476\pi\) | |||||||
\(432\) | −3.15741e6 | −0.813995 | ||||||||
\(433\) | 1.34938e6 | 0.345871 | 0.172935 | − | 0.984933i | \(-0.444675\pi\) | ||||
0.172935 | + | 0.984933i | \(0.444675\pi\) | |||||||
\(434\) | 5.19414e6 | 1.32370 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −817730. | −0.206012 | ||||||||
\(437\) | −4.28191e6 | −1.07259 | ||||||||
\(438\) | 1.31683e6 | 0.327979 | ||||||||
\(439\) | −4.37772e6 | −1.08414 | −0.542071 | − | 0.840332i | \(-0.682360\pi\) | ||||
−0.542071 | + | 0.840332i | \(0.682360\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 54562.0 | 0.0133596 | ||||||||
\(442\) | −3.83141e6 | −0.932832 | ||||||||
\(443\) | −6.46353e6 | −1.56481 | −0.782403 | − | 0.622772i | \(-0.786006\pi\) | ||||
−0.782403 | + | 0.622772i | \(0.786006\pi\) | |||||||
\(444\) | −1.49381e6 | −0.359615 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.26844e6 | 0.539995 | ||||||||
\(447\) | 1.57866e6 | 0.373698 | ||||||||
\(448\) | −637731. | −0.150121 | ||||||||
\(449\) | 5.49347e6 | 1.28597 | 0.642985 | − | 0.765879i | \(-0.277696\pi\) | ||||
0.642985 | + | 0.765879i | \(0.277696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.03963e6 | 0.240679 | ||||||||
\(452\) | 3.31146e6 | 0.762383 | ||||||||
\(453\) | −2.75771e6 | −0.631398 | ||||||||
\(454\) | −7.47438e6 | −1.70191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 483920. | 0.108984 | ||||||||
\(457\) | −7.91228e6 | −1.77219 | −0.886097 | − | 0.463500i | \(-0.846593\pi\) | ||||
−0.886097 | + | 0.463500i | \(0.846593\pi\) | |||||||
\(458\) | 4.37533e6 | 0.974647 | ||||||||
\(459\) | 2.88957e6 | 0.640179 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.65524e6 | 1.23936 | 0.619682 | − | 0.784853i | \(-0.287262\pi\) | ||||
0.619682 | + | 0.784853i | \(0.287262\pi\) | |||||||
\(462\) | −378481. | −0.0824972 | ||||||||
\(463\) | −7.19442e6 | −1.55971 | −0.779854 | − | 0.625962i | \(-0.784706\pi\) | ||||
−0.779854 | + | 0.625962i | \(0.784706\pi\) | |||||||
\(464\) | 7.45374e6 | 1.60723 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22806e6 | −0.261972 | ||||||||
\(467\) | −5.30058e6 | −1.12468 | −0.562342 | − | 0.826904i | \(-0.690100\pi\) | ||||
−0.562342 | + | 0.826904i | \(0.690100\pi\) | |||||||
\(468\) | 1.94359e6 | 0.410195 | ||||||||
\(469\) | 4.83974e6 | 1.01599 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.52821e6 | 0.317418 | ||||||||
\(472\) | 3.44119e6 | 0.710974 | ||||||||
\(473\) | 138047. | 0.0283709 | ||||||||
\(474\) | −65142.9 | −0.0133175 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.95696e6 | 0.598175 | ||||||||
\(477\) | −6.81537e6 | −1.37149 | ||||||||
\(478\) | 1.09098e7 | 2.18398 | ||||||||
\(479\) | 4.42947e6 | 0.882091 | 0.441045 | − | 0.897485i | \(-0.354608\pi\) | ||||
0.441045 | + | 0.897485i | \(0.354608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.31939e6 | −1.24541 | ||||||||
\(482\) | 4.07004e6 | 0.797959 | ||||||||
\(483\) | 2.98210e6 | 0.581640 | ||||||||
\(484\) | −3.08638e6 | −0.598876 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.86876e6 | −1.12708 | ||||||||
\(487\) | −4.07803e6 | −0.779162 | −0.389581 | − | 0.920992i | \(-0.627380\pi\) | ||||
−0.389581 | + | 0.920992i | \(0.627380\pi\) | |||||||
\(488\) | −64581.8 | −0.0122761 | ||||||||
\(489\) | −445078. | −0.0841713 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.18961e6 | −0.409886 | −0.204943 | − | 0.978774i | \(-0.565701\pi\) | ||||
−0.204943 | + | 0.978774i | \(0.565701\pi\) | |||||||
\(492\) | −1.51266e6 | −0.281726 | ||||||||
\(493\) | −6.82144e6 | −1.26403 | ||||||||
\(494\) | −3.34503e6 | −0.616713 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.09370e6 | −1.29470 | ||||||||
\(497\) | −2.00824e6 | −0.364691 | ||||||||
\(498\) | 2.14226e6 | 0.387079 | ||||||||
\(499\) | −1.03583e7 | −1.86224 | −0.931119 | − | 0.364715i | \(-0.881166\pi\) | ||||
−0.931119 | + | 0.364715i | \(0.881166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.02334e6 | −0.360143 | ||||||||
\(502\) | −1.39212e6 | −0.246557 | ||||||||
\(503\) | 5.77249e6 | 1.01729 | 0.508643 | − | 0.860978i | \(-0.330147\pi\) | ||||
0.508643 | + | 0.860978i | \(0.330147\pi\) | |||||||
\(504\) | 2.39783e6 | 0.420476 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.27727e6 | −0.395401 | ||||||||
\(507\) | 876161. | 0.151378 | ||||||||
\(508\) | −5.80581e6 | −0.998168 | ||||||||
\(509\) | −6.19636e6 | −1.06009 | −0.530044 | − | 0.847970i | \(-0.677825\pi\) | ||||
−0.530044 | + | 0.847970i | \(0.677825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.29930e6 | −0.728359 | ||||||||
\(512\) | 4.44248e6 | 0.748947 | ||||||||
\(513\) | 2.52275e6 | 0.423234 | ||||||||
\(514\) | −1.50238e7 | −2.50826 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −200857. | −0.0332095 | ||||||||
\(517\) | −340385. | −0.0560072 | ||||||||
\(518\) | 1.27390e7 | 2.08599 | ||||||||
\(519\) | −4.10380e6 | −0.668756 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.73637e6 | −1.41006 | −0.705028 | − | 0.709179i | \(-0.749066\pi\) | ||||
−0.705028 | + | 0.709179i | \(0.749066\pi\) | |||||||
\(522\) | 9.03848e6 | 1.45184 | ||||||||
\(523\) | −1.53756e6 | −0.245798 | −0.122899 | − | 0.992419i | \(-0.539219\pi\) | ||||
−0.122899 | + | 0.992419i | \(0.539219\pi\) | |||||||
\(524\) | 3.27705e6 | 0.521381 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.59928e7 | 2.52035 | ||||||||
\(527\) | 6.49194e6 | 1.01824 | ||||||||
\(528\) | 516896. | 0.0806897 | ||||||||
\(529\) | 1.15065e7 | 1.78774 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.38076e6 | 1.28987 | ||||||||
\(532\) | 2.58159e6 | 0.395465 | ||||||||
\(533\) | −6.39912e6 | −0.975668 | ||||||||
\(534\) | −2.96934e6 | −0.450616 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.29100e6 | −0.494784 | ||||||||
\(537\) | −1.34075e6 | −0.200638 | ||||||||
\(538\) | −5.52372e6 | −0.822765 | ||||||||
\(539\) | −19120.0 | −0.00283476 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.59108e6 | 0.380617 | 0.190308 | − | 0.981724i | \(-0.439051\pi\) | ||||
0.190308 | + | 0.981724i | \(0.439051\pi\) | |||||||
\(542\) | −1.15017e6 | −0.168176 | ||||||||
\(543\) | 4.73273e6 | 0.688830 | ||||||||
\(544\) | −7.30691e6 | −1.05861 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.32962e6 | 0.334428 | ||||||||
\(547\) | −1.67024e6 | −0.238677 | −0.119338 | − | 0.992854i | \(-0.538077\pi\) | ||||
−0.119338 | + | 0.992854i | \(0.538077\pi\) | |||||||
\(548\) | 6.82603e6 | 0.970995 | ||||||||
\(549\) | −157284. | −0.0222717 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.95549e6 | −0.835678 | ||||||||
\(552\) | −2.02781e6 | −0.283257 | ||||||||
\(553\) | 212683. | 0.0295747 | ||||||||
\(554\) | −3.48903e6 | −0.482981 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.86301e6 | 1.07870 | ||||||||
\(557\) | −6.91475e6 | −0.944362 | −0.472181 | − | 0.881502i | \(-0.656533\pi\) | ||||
−0.472181 | + | 0.881502i | \(0.656533\pi\) | |||||||
\(558\) | −8.60189e6 | −1.16952 | ||||||||
\(559\) | −849701. | −0.115010 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −473048. | −0.0634597 | ||||||||
\(562\) | 2.36336e6 | 0.315638 | ||||||||
\(563\) | −5.76254e6 | −0.766202 | −0.383101 | − | 0.923706i | \(-0.625144\pi\) | ||||
−0.383101 | + | 0.923706i | \(0.625144\pi\) | |||||||
\(564\) | 495257. | 0.0655591 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.46424e6 | 0.979365 | ||||||||
\(567\) | 4.90357e6 | 0.640553 | ||||||||
\(568\) | 1.36559e6 | 0.177603 | ||||||||
\(569\) | −5.44028e6 | −0.704434 | −0.352217 | − | 0.935918i | \(-0.614572\pi\) | ||||
−0.352217 | + | 0.935918i | \(0.614572\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.87704e6 | 0.882696 | 0.441348 | − | 0.897336i | \(-0.354500\pi\) | ||||
0.441348 | + | 0.897336i | \(0.354500\pi\) | |||||||
\(572\) | −681087. | −0.0870388 | ||||||||
\(573\) | −73535.6 | −0.00935644 | ||||||||
\(574\) | 1.28997e7 | 1.63418 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.05613e6 | 0.132636 | ||||||||
\(577\) | −1.71198e6 | −0.214072 | −0.107036 | − | 0.994255i | \(-0.534136\pi\) | ||||
−0.107036 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(578\) | −570664. | −0.0710495 | ||||||||
\(579\) | −3.09270e6 | −0.383391 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.99421e6 | −0.859604 | ||||||||
\(582\) | −3.00711e6 | −0.367994 | ||||||||
\(583\) | 2.38829e6 | 0.291016 | ||||||||
\(584\) | 2.92350e6 | 0.354708 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.93612e6 | 0.473505 | ||||||||
\(587\) | −9.59837e6 | −1.14975 | −0.574874 | − | 0.818242i | \(-0.694949\pi\) | ||||
−0.574874 | + | 0.818242i | \(0.694949\pi\) | |||||||
\(588\) | 27819.5 | 0.00331823 | ||||||||
\(589\) | 5.66782e6 | 0.673175 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.23485e6 | −0.145427 | ||||||||
\(592\) | −1.73978e7 | −2.04028 | ||||||||
\(593\) | −1.23992e7 | −1.44796 | −0.723982 | − | 0.689818i | \(-0.757690\pi\) | ||||
−0.723982 | + | 0.689818i | \(0.757690\pi\) | |||||||
\(594\) | 1.34168e6 | 0.156021 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.72675e6 | −0.660378 | ||||||||
\(597\) | 3.04012e6 | 0.349104 | ||||||||
\(598\) | 1.40170e7 | 1.60288 | ||||||||
\(599\) | 1.10058e7 | 1.25330 | 0.626648 | − | 0.779303i | \(-0.284426\pi\) | ||||
0.626648 | + | 0.779303i | \(0.284426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.63639e7 | −1.84800 | −0.923998 | − | 0.382397i | \(-0.875099\pi\) | ||||
−0.923998 | + | 0.382397i | \(0.875099\pi\) | |||||||
\(602\) | 1.71288e6 | 0.192635 | ||||||||
\(603\) | −8.01497e6 | −0.897654 | ||||||||
\(604\) | 1.00039e7 | 1.11577 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.86662e6 | −0.538326 | ||||||||
\(607\) | −2.89375e6 | −0.318779 | −0.159390 | − | 0.987216i | \(-0.550953\pi\) | ||||
−0.159390 | + | 0.987216i | \(0.550953\pi\) | |||||||
\(608\) | −6.37933e6 | −0.699868 | ||||||||
\(609\) | 4.14765e6 | 0.453168 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.09513e6 | 0.227043 | ||||||||
\(612\) | −4.89695e6 | −0.528503 | ||||||||
\(613\) | 362110. | 0.0389215 | 0.0194607 | − | 0.999811i | \(-0.493805\pi\) | ||||
0.0194607 | + | 0.999811i | \(0.493805\pi\) | |||||||
\(614\) | −6.07668e6 | −0.650497 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −840265. | −0.0892204 | ||||||||
\(617\) | 3.10076e6 | 0.327911 | 0.163955 | − | 0.986468i | \(-0.447575\pi\) | ||||
0.163955 | + | 0.986468i | \(0.447575\pi\) | |||||||
\(618\) | −1.34281e6 | −0.141431 | ||||||||
\(619\) | −8.22211e6 | −0.862495 | −0.431248 | − | 0.902234i | \(-0.641927\pi\) | ||||
−0.431248 | + | 0.902234i | \(0.641927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.05713e7 | −1.10002 | ||||||||
\(622\) | 1.92079e7 | 1.99069 | ||||||||
\(623\) | 9.69451e6 | 1.00070 | ||||||||
\(624\) | −3.18159e6 | −0.327101 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.52411e6 | 0.155446 | ||||||||
\(627\) | −412997. | −0.0419544 | ||||||||
\(628\) | −5.54374e6 | −0.560923 | ||||||||
\(629\) | 1.59220e7 | 1.60461 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.91402e6 | −0.391336 | −0.195668 | − | 0.980670i | \(-0.562687\pi\) | ||||
−0.195668 | + | 0.980670i | \(0.562687\pi\) | |||||||
\(632\) | −144624. | −0.0144028 | ||||||||
\(633\) | −4.22877e6 | −0.419474 | ||||||||
\(634\) | −1.99143e7 | −1.96762 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.47495e6 | −0.340648 | ||||||||
\(637\) | 117687. | 0.0114916 | ||||||||
\(638\) | −3.16733e6 | −0.308065 | ||||||||
\(639\) | 3.32580e6 | 0.322214 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.88259e6 | 0.180972 | 0.0904859 | − | 0.995898i | \(-0.471158\pi\) | ||||
0.0904859 | + | 0.995898i | \(0.471158\pi\) | |||||||
\(642\) | −5.84722e6 | −0.559902 | ||||||||
\(643\) | −975076. | −0.0930060 | −0.0465030 | − | 0.998918i | \(-0.514808\pi\) | ||||
−0.0465030 | + | 0.998918i | \(0.514808\pi\) | |||||||
\(644\) | −1.08179e7 | −1.02784 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.42795e6 | 0.794585 | ||||||||
\(647\) | 1.46477e7 | 1.37565 | 0.687827 | − | 0.725875i | \(-0.258565\pi\) | ||||
0.687827 | + | 0.725875i | \(0.258565\pi\) | |||||||
\(648\) | −3.33440e6 | −0.311947 | ||||||||
\(649\) | −2.93685e6 | −0.273697 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.94730e6 | −0.365046 | ||||||||
\(652\) | 1.61456e6 | 0.148743 | ||||||||
\(653\) | 1.95004e7 | 1.78962 | 0.894810 | − | 0.446446i | \(-0.147311\pi\) | ||||
0.894810 | + | 0.446446i | \(0.147311\pi\) | |||||||
\(654\) | 1.62319e6 | 0.148397 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.76173e7 | −1.59838 | ||||||||
\(657\) | 7.11996e6 | 0.643523 | ||||||||
\(658\) | −4.22348e6 | −0.380282 | ||||||||
\(659\) | 1.69056e7 | 1.51641 | 0.758206 | − | 0.652015i | \(-0.226076\pi\) | ||||
0.758206 | + | 0.652015i | \(0.226076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.48642e6 | −0.488411 | −0.244206 | − | 0.969723i | \(-0.578527\pi\) | ||||
−0.244206 | + | 0.969723i | \(0.578527\pi\) | |||||||
\(662\) | 1.51377e7 | 1.34250 | ||||||||
\(663\) | 2.91169e6 | 0.257254 | ||||||||
\(664\) | 4.75603e6 | 0.418624 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.10968e7 | −1.84302 | ||||||||
\(667\) | 2.49558e7 | 2.17199 | ||||||||
\(668\) | 7.33987e6 | 0.636425 | ||||||||
\(669\) | −1.72390e6 | −0.148918 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55116.7 | 0.00472582 | ||||||||
\(672\) | 4.44283e6 | 0.379522 | ||||||||
\(673\) | 6.45667e6 | 0.549504 | 0.274752 | − | 0.961515i | \(-0.411404\pi\) | ||||
0.274752 | + | 0.961515i | \(0.411404\pi\) | |||||||
\(674\) | 1.78004e6 | 0.150932 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.17836e6 | −0.267508 | ||||||||
\(677\) | −1.08003e6 | −0.0905658 | −0.0452829 | − | 0.998974i | \(-0.514419\pi\) | ||||
−0.0452829 | + | 0.998974i | \(0.514419\pi\) | |||||||
\(678\) | −6.57324e6 | −0.549168 | ||||||||
\(679\) | 9.81782e6 | 0.817223 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.68018e6 | 0.469347 | ||||||||
\(682\) | 3.01434e6 | 0.248160 | ||||||||
\(683\) | −1.27130e7 | −1.04279 | −0.521395 | − | 0.853315i | \(-0.674588\pi\) | ||||
−0.521395 | + | 0.853315i | \(0.674588\pi\) | |||||||
\(684\) | −4.27531e6 | −0.349403 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.58069e7 | −1.28244 | ||||||||
\(687\) | −3.32505e6 | −0.268785 | ||||||||
\(688\) | −2.33930e6 | −0.188415 | ||||||||
\(689\) | −1.47004e7 | −1.17972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 351123. | 0.0279747 | 0.0139873 | − | 0.999902i | \(-0.495548\pi\) | ||||
0.0139873 | + | 0.999902i | \(0.495548\pi\) | |||||||
\(692\) | 1.48869e7 | 1.18179 | ||||||||
\(693\) | −2.04640e6 | −0.161867 | ||||||||
\(694\) | −4.85884e6 | −0.382943 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.82038e6 | −0.220691 | ||||||||
\(697\) | 1.61228e7 | 1.25707 | ||||||||
\(698\) | 2.51625e7 | 1.95486 | ||||||||
\(699\) | 933268. | 0.0722459 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.65153e6 | 0.741825 | 0.370912 | − | 0.928668i | \(-0.379045\pi\) | ||||
0.370912 | + | 0.928668i | \(0.379045\pi\) | |||||||
\(702\) | −8.25830e6 | −0.632482 | ||||||||
\(703\) | 1.39007e7 | 1.06084 | ||||||||
\(704\) | −370097. | −0.0281439 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.24888e7 | 1.69806 | ||||||||
\(707\) | 1.58889e7 | 1.19549 | ||||||||
\(708\) | 4.27309e6 | 0.320375 | ||||||||
\(709\) | −5.18551e6 | −0.387414 | −0.193707 | − | 0.981059i | \(-0.562051\pi\) | ||||
−0.193707 | + | 0.981059i | \(0.562051\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −352220. | −0.0261300 | ||||||||
\(712\) | −6.59221e6 | −0.487339 | ||||||||
\(713\) | −2.37503e7 | −1.74963 | ||||||||
\(714\) | −5.86957e6 | −0.430884 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.86371e6 | 0.354556 | ||||||||
\(717\) | −8.29096e6 | −0.602292 | ||||||||
\(718\) | 2.18101e7 | 1.57887 | ||||||||
\(719\) | 1.11492e7 | 0.804306 | 0.402153 | − | 0.915572i | \(-0.368262\pi\) | ||||
0.402153 | + | 0.915572i | \(0.368262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.38412e6 | 0.314083 | ||||||||
\(722\) | −1.04718e7 | −0.747613 | ||||||||
\(723\) | −3.09303e6 | −0.220059 | ||||||||
\(724\) | −1.71684e7 | −1.21726 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.12647e6 | 0.431389 | ||||||||
\(727\) | 2.54905e7 | 1.78872 | 0.894361 | − | 0.447347i | \(-0.147631\pi\) | ||||
0.894361 | + | 0.447347i | \(0.147631\pi\) | |||||||
\(728\) | 5.17198e6 | 0.361683 | ||||||||
\(729\) | −4.80208e6 | −0.334666 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.14086e6 | 0.148182 | ||||||||
\(732\) | −80194.4 | −0.00553180 | ||||||||
\(733\) | −1.87850e7 | −1.29137 | −0.645687 | − | 0.763602i | \(-0.723429\pi\) | ||||
−0.645687 | + | 0.763602i | \(0.723429\pi\) | |||||||
\(734\) | −3.32939e7 | −2.28100 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.67319e7 | 1.81901 | ||||||||
\(737\) | 2.80867e6 | 0.190472 | ||||||||
\(738\) | −2.13629e7 | −1.44384 | ||||||||
\(739\) | 8.16688e6 | 0.550104 | 0.275052 | − | 0.961429i | \(-0.411305\pi\) | ||||
0.275052 | + | 0.961429i | \(0.411305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.54207e6 | 0.170075 | ||||||||
\(742\) | 2.96339e7 | 1.97596 | ||||||||
\(743\) | −3.71670e6 | −0.246993 | −0.123497 | − | 0.992345i | \(-0.539411\pi\) | ||||
−0.123497 | + | 0.992345i | \(0.539411\pi\) | |||||||
\(744\) | 2.68414e6 | 0.177776 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.26629e7 | −0.833081 | ||||||||
\(747\) | 1.15829e7 | 0.759482 | ||||||||
\(748\) | 1.71603e6 | 0.112142 | ||||||||
\(749\) | 1.90904e7 | 1.24340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.60827e7 | −1.04054 | −0.520269 | − | 0.854002i | \(-0.674168\pi\) | ||||
−0.520269 | + | 0.854002i | \(0.674168\pi\) | |||||||
\(752\) | 5.76806e6 | 0.371950 | ||||||||
\(753\) | 1.05795e6 | 0.0679948 | ||||||||
\(754\) | 1.94955e7 | 1.24884 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.37349e6 | 0.405577 | ||||||||
\(757\) | 2.47457e7 | 1.56950 | 0.784749 | − | 0.619814i | \(-0.212792\pi\) | ||||
0.784749 | + | 0.619814i | \(0.212792\pi\) | |||||||
\(758\) | 2.71847e7 | 1.71851 | ||||||||
\(759\) | 1.73061e6 | 0.109043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.22532e7 | 1.39294 | 0.696469 | − | 0.717587i | \(-0.254753\pi\) | ||||
0.696469 | + | 0.717587i | \(0.254753\pi\) | |||||||
\(762\) | 1.15245e7 | 0.719011 | ||||||||
\(763\) | −5.29952e6 | −0.329553 | ||||||||
\(764\) | 266757. | 0.0165342 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.33802e7 | −0.823931 | ||||||||
\(767\) | 1.80768e7 | 1.10952 | ||||||||
\(768\) | −7.41903e6 | −0.453883 | ||||||||
\(769\) | −1.98413e7 | −1.20991 | −0.604956 | − | 0.796259i | \(-0.706809\pi\) | ||||
−0.604956 | + | 0.796259i | \(0.706809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.14174e7 | 0.691721 | ||||||||
\(772\) | 1.12191e7 | 0.677507 | ||||||||
\(773\) | −7.62070e6 | −0.458718 | −0.229359 | − | 0.973342i | \(-0.573663\pi\) | ||||
−0.229359 | + | 0.973342i | \(0.573663\pi\) | |||||||
\(774\) | −2.83666e6 | −0.170198 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.67606e6 | −0.397985 | ||||||||
\(777\) | −9.68105e6 | −0.575267 | ||||||||
\(778\) | 3.37509e6 | 0.199911 | ||||||||
\(779\) | 1.40761e7 | 0.831073 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.16545e6 | −0.0683702 | ||||||||
\(782\) | −3.53163e7 | −2.06518 | ||||||||
\(783\) | −1.47031e7 | −0.857045 | ||||||||
\(784\) | 324002. | 0.0188260 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.50495e6 | −0.375567 | ||||||||
\(787\) | 1.94358e7 | 1.11858 | 0.559290 | − | 0.828972i | \(-0.311074\pi\) | ||||
0.559290 | + | 0.828972i | \(0.311074\pi\) | |||||||
\(788\) | 4.47952e6 | 0.256990 | ||||||||
\(789\) | −1.21538e7 | −0.695055 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.14608e7 | 1.21956 | ||||||||
\(792\) | 1.39154e6 | 0.0788285 | ||||||||
\(793\) | −339253. | −0.0191576 | ||||||||
\(794\) | 1.66178e7 | 0.935454 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.10283e7 | −0.616917 | ||||||||
\(797\) | −3.86599e6 | −0.215583 | −0.107792 | − | 0.994174i | \(-0.534378\pi\) | ||||
−0.107792 | + | 0.994174i | \(0.534378\pi\) | |||||||
\(798\) | −5.12445e6 | −0.284866 | ||||||||
\(799\) | −5.27876e6 | −0.292526 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.60548e7 | −0.884147 | ||||||||
\(802\) | 2.06465e7 | 1.13347 | ||||||||
\(803\) | −2.49503e6 | −0.136549 | ||||||||
\(804\) | −4.08659e6 | −0.222957 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.85538e7 | −1.00599 | ||||||||
\(807\) | 4.19776e6 | 0.226900 | ||||||||
\(808\) | −1.08044e7 | −0.582198 | ||||||||
\(809\) | −1.94431e7 | −1.04446 | −0.522232 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522232 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.30552e7 | −0.696995 | −0.348498 | − | 0.937310i | \(-0.613308\pi\) | ||||
−0.348498 | + | 0.937310i | \(0.613308\pi\) | |||||||
\(812\) | −1.50460e7 | −0.800812 | ||||||||
\(813\) | 874077. | 0.0463792 | ||||||||
\(814\) | 7.39288e6 | 0.391069 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.01613e6 | 0.421443 | ||||||||
\(817\) | 1.86908e6 | 0.0979657 | ||||||||
\(818\) | −1.56766e7 | −0.819158 | ||||||||
\(819\) | 1.25960e7 | 0.656178 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.03522e7 | 0.536013 | 0.268006 | − | 0.963417i | \(-0.413635\pi\) | ||||
0.268006 | + | 0.963417i | \(0.413635\pi\) | |||||||
\(822\) | −1.35497e7 | −0.699437 | ||||||||
\(823\) | 2.95055e7 | 1.51846 | 0.759230 | − | 0.650823i | \(-0.225576\pi\) | ||||
0.759230 | + | 0.650823i | \(0.225576\pi\) | |||||||
\(824\) | −2.98118e6 | −0.152957 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.64403e7 | −1.85837 | ||||||||
\(827\) | −2.36807e6 | −0.120401 | −0.0602005 | − | 0.998186i | \(-0.519174\pi\) | ||||
−0.0602005 | + | 0.998186i | \(0.519174\pi\) | |||||||
\(828\) | 1.79152e7 | 0.908124 | ||||||||
\(829\) | −5.54371e6 | −0.280165 | −0.140082 | − | 0.990140i | \(-0.544737\pi\) | ||||
−0.140082 | + | 0.990140i | \(0.544737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.65149e6 | 0.133195 | ||||||||
\(832\) | 2.27801e6 | 0.114090 | ||||||||
\(833\) | −296517. | −0.0148060 | ||||||||
\(834\) | −1.56081e7 | −0.777023 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.49818e6 | 0.0741395 | ||||||||
\(837\) | 1.39929e7 | 0.690387 | ||||||||
\(838\) | −1.78502e7 | −0.878079 | ||||||||
\(839\) | 2.61550e7 | 1.28277 | 0.641386 | − | 0.767218i | \(-0.278360\pi\) | ||||
0.641386 | + | 0.767218i | \(0.278360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.41986e7 | 0.692237 | ||||||||
\(842\) | 1.45758e7 | 0.708518 | ||||||||
\(843\) | −1.79604e6 | −0.0870457 | ||||||||
\(844\) | 1.53403e7 | 0.741271 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.99440e6 | 0.335989 | ||||||||
\(847\) | −2.00021e7 | −0.958006 | ||||||||
\(848\) | −4.04713e7 | −1.93267 | ||||||||
\(849\) | −5.67247e6 | −0.270087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.82494e7 | −2.75720 | ||||||||
\(852\) | 1.69572e6 | 0.0800306 | ||||||||
\(853\) | 1.50861e7 | 0.709911 | 0.354956 | − | 0.934883i | \(-0.384496\pi\) | ||||
0.354956 | + | 0.934883i | \(0.384496\pi\) | |||||||
\(854\) | 683886. | 0.0320877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.29814e7 | −0.605532 | ||||||||
\(857\) | −3.93634e7 | −1.83080 | −0.915398 | − | 0.402550i | \(-0.868124\pi\) | ||||
−0.915398 | + | 0.402550i | \(0.868124\pi\) | |||||||
\(858\) | 1.35196e6 | 0.0626967 | ||||||||
\(859\) | 7.93682e6 | 0.366998 | 0.183499 | − | 0.983020i | \(-0.441258\pi\) | ||||
0.183499 | + | 0.983020i | \(0.441258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.80318e6 | −0.450670 | ||||||||
\(862\) | 1.79117e7 | 0.821047 | ||||||||
\(863\) | −4.07079e7 | −1.86060 | −0.930298 | − | 0.366804i | \(-0.880452\pi\) | ||||
−0.930298 | + | 0.366804i | \(0.880452\pi\) | |||||||
\(864\) | −1.57495e7 | −0.717763 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.71656e6 | 0.440269 | ||||||||
\(867\) | 433678. | 0.0195938 | ||||||||
\(868\) | 1.43192e7 | 0.645089 | ||||||||
\(869\) | 123427. | 0.00554450 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.72878e7 | −0.772139 | ||||||||
\(872\) | 3.60364e6 | 0.160491 | ||||||||
\(873\) | −1.62590e7 | −0.722037 | ||||||||
\(874\) | −3.08331e7 | −1.36533 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.63025e6 | 0.159837 | ||||||||
\(877\) | −1.74592e7 | −0.766523 | −0.383262 | − | 0.923640i | \(-0.625199\pi\) | ||||
−0.383262 | + | 0.923640i | \(0.625199\pi\) | |||||||
\(878\) | −3.15229e7 | −1.38004 | ||||||||
\(879\) | −2.99127e6 | −0.130582 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.98363e7 | 1.72918 | 0.864588 | − | 0.502482i | \(-0.167580\pi\) | ||||
0.864588 | + | 0.502482i | \(0.167580\pi\) | |||||||
\(882\) | 392888. | 0.0170058 | ||||||||
\(883\) | −2.37277e6 | −0.102413 | −0.0512063 | − | 0.998688i | \(-0.516307\pi\) | ||||
−0.0512063 | + | 0.998688i | \(0.516307\pi\) | |||||||
\(884\) | −1.05624e7 | −0.454605 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.65424e7 | −1.99189 | ||||||||
\(887\) | 2.89221e7 | 1.23430 | 0.617150 | − | 0.786846i | \(-0.288287\pi\) | ||||
0.617150 | + | 0.786846i | \(0.288287\pi\) | |||||||
\(888\) | 6.58306e6 | 0.280153 | ||||||||
\(889\) | −3.76261e7 | −1.59674 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.84571e6 | 0.120087 | ||||||||
\(892\) | 6.25363e6 | 0.263160 | ||||||||
\(893\) | −4.60864e6 | −0.193395 | ||||||||
\(894\) | 1.13676e7 | 0.475691 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.13881e7 | 0.890027 | ||||||||
\(897\) | −1.06522e7 | −0.442038 | ||||||||
\(898\) | 3.95572e7 | 1.63695 | ||||||||
\(899\) | −3.30331e7 | −1.36317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.70382e7 | 1.51998 | ||||||||
\(902\) | 7.48615e6 | 0.306367 | ||||||||
\(903\) | −1.30171e6 | −0.0531244 | ||||||||
\(904\) | −1.45932e7 | −0.593923 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.98576e7 | −0.803724 | ||||||||
\(907\) | −3.07512e7 | −1.24120 | −0.620602 | − | 0.784126i | \(-0.713112\pi\) | ||||
−0.620602 | + | 0.784126i | \(0.713112\pi\) | |||||||
\(908\) | −2.06054e7 | −0.829404 | ||||||||
\(909\) | −2.63132e7 | −1.05624 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.59162e6 | 0.382909 | 0.191455 | − | 0.981501i | \(-0.438680\pi\) | ||||
0.191455 | + | 0.981501i | \(0.438680\pi\) | |||||||
\(912\) | 6.99852e6 | 0.278624 | ||||||||
\(913\) | −4.05898e6 | −0.161154 | ||||||||
\(914\) | −5.69745e7 | −2.25588 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.20619e7 | 0.474983 | ||||||||
\(917\) | 2.12378e7 | 0.834040 | ||||||||
\(918\) | 2.08071e7 | 0.814902 | ||||||||
\(919\) | −3.67365e7 | −1.43486 | −0.717429 | − | 0.696631i | \(-0.754681\pi\) | ||||
−0.717429 | + | 0.696631i | \(0.754681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.61799e6 | 0.179392 | ||||||||
\(922\) | 4.07221e7 | 1.57762 | ||||||||
\(923\) | 7.17356e6 | 0.277160 | ||||||||
\(924\) | −1.04340e6 | −0.0402040 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.18053e7 | −1.98540 | ||||||||
\(927\) | −7.26042e6 | −0.277500 | ||||||||
\(928\) | 3.71800e7 | 1.41723 | ||||||||
\(929\) | −7.37467e6 | −0.280352 | −0.140176 | − | 0.990127i | \(-0.544767\pi\) | ||||
−0.140176 | + | 0.990127i | \(0.544767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −258876. | −0.00978852 | ||||||||
\(932\) | −3.38552e6 | −0.127669 | ||||||||
\(933\) | −1.45971e7 | −0.548987 | ||||||||
\(934\) | −3.81682e7 | −1.43164 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.56518e6 | −0.319556 | ||||||||
\(937\) | −3.02596e7 | −1.12594 | −0.562968 | − | 0.826478i | \(-0.690341\pi\) | ||||
−0.562968 | + | 0.826478i | \(0.690341\pi\) | |||||||
\(938\) | 3.48499e7 | 1.29328 | ||||||||
\(939\) | −1.15825e6 | −0.0428686 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.19735e7 | −1.54526 | −0.772629 | − | 0.634858i | \(-0.781059\pi\) | ||||
−0.772629 | + | 0.634858i | \(0.781059\pi\) | |||||||
\(942\) | 1.10043e7 | 0.404050 | ||||||||
\(943\) | −5.89843e7 | −2.16002 | ||||||||
\(944\) | 4.97670e7 | 1.81765 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 994042. | 0.0361141 | ||||||||
\(947\) | −3.18458e7 | −1.15392 | −0.576961 | − | 0.816772i | \(-0.695762\pi\) | ||||
−0.576961 | + | 0.816772i | \(0.695762\pi\) | |||||||
\(948\) | −179586. | −0.00649011 | ||||||||
\(949\) | 1.53574e7 | 0.553542 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.51339e7 | 0.542625 | ||||||||
\(952\) | −1.30310e7 | −0.466000 | ||||||||
\(953\) | −2.50519e7 | −0.893529 | −0.446765 | − | 0.894652i | \(-0.647424\pi\) | ||||
−0.446765 | + | 0.894652i | \(0.647424\pi\) | |||||||
\(954\) | −4.90759e7 | −1.74581 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00762e7 | 1.06434 | ||||||||
\(957\) | 2.40702e6 | 0.0849572 | ||||||||
\(958\) | 3.18956e7 | 1.12284 | ||||||||
\(959\) | 4.42379e7 | 1.55327 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.80835e6 | 0.0980942 | ||||||||
\(962\) | −4.55045e7 | −1.58532 | ||||||||
\(963\) | −3.16152e7 | −1.09858 | ||||||||
\(964\) | 1.12203e7 | 0.388876 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.14734e7 | 0.740386 | ||||||||
\(967\) | −2.06439e7 | −0.709946 | −0.354973 | − | 0.934877i | \(-0.615510\pi\) | ||||
−0.354973 | + | 0.934877i | \(0.615510\pi\) | |||||||
\(968\) | 1.36014e7 | 0.466545 | ||||||||
\(969\) | −6.40484e6 | −0.219128 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.05204e7 | 0.698455 | 0.349227 | − | 0.937038i | \(-0.386444\pi\) | ||||
0.349227 | + | 0.937038i | \(0.386444\pi\) | |||||||
\(972\) | −1.61790e7 | −0.549270 | ||||||||
\(973\) | 5.09584e7 | 1.72557 | ||||||||
\(974\) | −2.93649e7 | −0.991817 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −933991. | −0.0313847 | ||||||||
\(977\) | −2.39254e7 | −0.801904 | −0.400952 | − | 0.916099i | \(-0.631321\pi\) | ||||
−0.400952 | + | 0.916099i | \(0.631321\pi\) | |||||||
\(978\) | −3.20490e6 | −0.107144 | ||||||||
\(979\) | 5.62605e6 | 0.187606 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.77639e6 | 0.291168 | ||||||||
\(982\) | −1.57669e7 | −0.521755 | ||||||||
\(983\) | −3.15675e7 | −1.04197 | −0.520987 | − | 0.853565i | \(-0.674436\pi\) | ||||
−0.520987 | + | 0.853565i | \(0.674436\pi\) | |||||||
\(984\) | 6.66611e6 | 0.219475 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.91196e7 | −1.60903 | ||||||||
\(987\) | 3.20965e6 | 0.104873 | ||||||||
\(988\) | −9.22159e6 | −0.300548 | ||||||||
\(989\) | −7.83218e6 | −0.254620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.05732e7 | −0.341997 | −0.170999 | − | 0.985271i | \(-0.554699\pi\) | ||||
−0.170999 | + | 0.985271i | \(0.554699\pi\) | |||||||
\(992\) | −3.53840e7 | −1.14164 | ||||||||
\(993\) | −1.15039e7 | −0.370231 | ||||||||
\(994\) | −1.44609e7 | −0.464226 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.90579e6 | 0.188638 | ||||||||
\(997\) | 4.35315e7 | 1.38697 | 0.693484 | − | 0.720472i | \(-0.256075\pi\) | ||||
0.693484 | + | 0.720472i | \(0.256075\pi\) | |||||||
\(998\) | −7.45874e7 | −2.37050 | ||||||||
\(999\) | 3.43185e7 | 1.08796 |
(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 | 1075.6.a.j.1.29 | yes | 37 | |
5.4 | even | 2 | 1075.6.a.i.1.9 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1075.6.a.i.1.9 | ✓ | 37 | 5.4 | even | 2 | ||
1075.6.a.j.1.29 | yes | 37 | 1.1 | even | 1 | trivial |