Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,6,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.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: | \(44.9074695476\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 791x^{3} + 280x^{2} + 24832x + 39040 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(6.54694\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.54694 | 0.355836 | 0.177918 | − | 0.984045i | \(-0.443064\pi\) | ||||
0.177918 | + | 0.984045i | \(0.443064\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −212.231 | −0.873380 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 713.630 | 1.77824 | 0.889122 | − | 0.457670i | \(-0.151316\pi\) | ||||
0.889122 | + | 0.457670i | \(0.151316\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −157.390 | −0.258297 | −0.129148 | − | 0.991625i | \(-0.541224\pi\) | ||||
−0.129148 | + | 0.991625i | \(0.541224\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −138.674 | −0.159135 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1669.06 | −1.40071 | −0.700355 | − | 0.713794i | \(-0.746975\pi\) | ||||
−0.700355 | + | 0.713794i | \(0.746975\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.8324 | 0.0119680 | 0.00598400 | − | 0.999982i | \(-0.498095\pi\) | ||||
0.00598400 | + | 0.999982i | \(0.498095\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −271.800 | −0.134494 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1479.72 | 0.583257 | 0.291628 | − | 0.956532i | \(-0.405803\pi\) | ||||
0.291628 | + | 0.956532i | \(0.405803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2525.14 | −0.666617 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7550.14 | 1.66709 | 0.833547 | − | 0.552449i | \(-0.186307\pi\) | ||||
0.833547 | + | 0.552449i | \(0.186307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6293.24 | 1.17617 | 0.588085 | − | 0.808799i | \(-0.299882\pi\) | ||||
0.588085 | + | 0.808799i | \(0.299882\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3958.46 | 0.632764 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −391.915 | −0.0470639 | −0.0235319 | − | 0.999723i | \(-0.507491\pi\) | ||||
−0.0235319 | + | 0.999723i | \(0.507491\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −873.033 | −0.0919113 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5926.90 | −0.550641 | −0.275320 | − | 0.961353i | \(-0.588784\pi\) | ||||
−0.275320 | + | 0.961353i | \(0.588784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20027.4 | 1.65179 | 0.825893 | − | 0.563827i | \(-0.190672\pi\) | ||||
0.825893 | + | 0.563827i | \(0.190672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5305.79 | 0.390588 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −20388.6 | −1.34630 | −0.673152 | − | 0.739505i | \(-0.735060\pi\) | ||||
−0.673152 | + | 0.739505i | \(0.735060\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9258.15 | −0.498424 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2088.81 | 0.102143 | 0.0510717 | − | 0.998695i | \(-0.483736\pi\) | ||||
0.0510717 | + | 0.998695i | \(0.483736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17840.8 | −0.795255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 104.462 | 0.00425865 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 45077.4 | 1.68589 | 0.842943 | − | 0.538002i | \(-0.180821\pi\) | ||||
0.842943 | + | 0.538002i | \(0.180821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21786.2 | 0.749649 | 0.374824 | − | 0.927096i | \(-0.377703\pi\) | ||||
0.374824 | + | 0.927096i | \(0.377703\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10399.3 | 0.330107 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3934.75 | 0.115514 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 64262.6 | 1.74893 | 0.874463 | − | 0.485093i | \(-0.161214\pi\) | ||||
0.874463 | + | 0.485093i | \(0.161214\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8207.92 | 0.207544 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16333.8 | 0.384541 | 0.192270 | − | 0.981342i | \(-0.438415\pi\) | ||||
0.192270 | + | 0.981342i | \(0.438415\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6540.80 | 0.143656 | 0.0718280 | − | 0.997417i | \(-0.477117\pi\) | ||||
0.0718280 | + | 0.997417i | \(0.477117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3466.84 | 0.0711673 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −34967.9 | −0.672113 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −84587.9 | −1.52490 | −0.762448 | − | 0.647049i | \(-0.776003\pi\) | ||||
−0.762448 | + | 0.647049i | \(0.776003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 37565.4 | 0.636174 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28514.9 | 0.454336 | 0.227168 | − | 0.973856i | \(-0.427053\pi\) | ||||
0.227168 | + | 0.973856i | \(0.427053\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41726.4 | 0.626417 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 41880.2 | 0.593213 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13227.8 | −0.177016 | −0.0885080 | − | 0.996075i | \(-0.528210\pi\) | ||||
−0.0885080 | + | 0.996075i | \(0.528210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7712.11 | 0.0976269 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 34908.2 | 0.418524 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −470.810 | −0.00535226 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 139857. | 1.50923 | 0.754615 | − | 0.656167i | \(-0.227823\pi\) | ||||
0.754615 | + | 0.656167i | \(0.227823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −151455. | −1.55308 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 24058.8 | 0.234677 | 0.117339 | − | 0.993092i | \(-0.462564\pi\) | ||||
0.117339 | + | 0.993092i | \(0.462564\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7378.93 | 0.0685331 | 0.0342666 | − | 0.999413i | \(-0.489090\pi\) | ||||
0.0342666 | + | 0.999413i | \(0.489090\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6795.00 | 0.0601473 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 32937.0 | 0.278115 | 0.139058 | − | 0.990284i | \(-0.455593\pi\) | ||||
0.139058 | + | 0.990284i | \(0.455593\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 213922. | 1.72460 | 0.862301 | − | 0.506395i | \(-0.169022\pi\) | ||||
0.862301 | + | 0.506395i | \(0.169022\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2173.93 | −0.0167470 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12294.4 | 0.0905753 | 0.0452876 | − | 0.998974i | \(-0.485580\pi\) | ||||
0.0452876 | + | 0.998974i | \(0.485580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36993.0 | −0.260840 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33403.1 | 0.225591 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 81783.7 | 0.529419 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 348217. | 2.16215 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −32876.2 | −0.195938 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19972.3 | −0.109880 | −0.0549401 | − | 0.998490i | \(-0.517497\pi\) | ||||
−0.0549401 | + | 0.998490i | \(0.517497\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 111091. | 0.587765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 122192. | 0.622108 | 0.311054 | − | 0.950392i | \(-0.399318\pi\) | ||||
0.311054 | + | 0.950392i | \(0.399318\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −922.788 | −0.00452348 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 63128.5 | 0.298120 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −147736. | −0.672489 | −0.336245 | − | 0.941775i | \(-0.609157\pi\) | ||||
−0.336245 | + | 0.941775i | \(0.609157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −97522.3 | −0.428121 | −0.214061 | − | 0.976820i | \(-0.568669\pi\) | ||||
−0.214061 | + | 0.976820i | \(0.568669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −113094. | −0.479064 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −112318. | −0.459314 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −188753. | −0.745547 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13318.2 | 0.0508338 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 106789. | 0.394057 | 0.197029 | − | 0.980398i | \(-0.436871\pi\) | ||||
0.197029 | + | 0.980398i | \(0.436871\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −374118. | −1.33526 | −0.667631 | − | 0.744492i | \(-0.732692\pi\) | ||||
−0.667631 | + | 0.744492i | \(0.732692\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 354226. | 1.22335 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −157331. | −0.525999 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −385106. | −1.24690 | −0.623449 | − | 0.781864i | \(-0.714269\pi\) | ||||
−0.623449 | + | 0.781864i | \(0.714269\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11586.5 | 0.0363463 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −72506.3 | −0.220450 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −349922. | −1.03158 | −0.515789 | − | 0.856716i | \(-0.672501\pi\) | ||||
−0.515789 | + | 0.856716i | \(0.672501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −98961.6 | −0.282981 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 63417.5 | 0.175962 | 0.0879809 | − | 0.996122i | \(-0.471959\pi\) | ||||
0.0879809 | + | 0.996122i | \(0.471959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −346521. | −0.933283 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3996.83 | −0.0104526 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 469308. | 1.19218 | 0.596091 | − | 0.802917i | \(-0.296720\pi\) | ||||
0.596091 | + | 0.802917i | \(0.296720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 250041. | 0.599900 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 480916. | 1.12186 | 0.560928 | − | 0.827865i | \(-0.310445\pi\) | ||||
0.560928 | + | 0.827865i | \(0.310445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −467752. | −1.06125 | −0.530627 | − | 0.847606i | \(-0.678043\pi\) | ||||
−0.530627 | + | 0.847606i | \(0.678043\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 120847. | 0.266752 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9797.88 | 0.0210476 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.19109e6 | −2.49081 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 123732. | 0.251958 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −523673. | −1.03867 | −0.519334 | − | 0.854572i | \(-0.673820\pi\) | ||||
−0.519334 | + | 0.854572i | \(0.673820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 663432. | 1.28204 | 0.641022 | − | 0.767522i | \(-0.278511\pi\) | ||||
0.641022 | + | 0.767522i | \(0.278511\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 21825.8 | 0.0411040 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 102398. | 0.187987 | 0.0939933 | − | 0.995573i | \(-0.470037\pi\) | ||||
0.0939933 | + | 0.995573i | \(0.470037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −208690. | −0.373567 | −0.186784 | − | 0.982401i | \(-0.559806\pi\) | ||||
−0.186784 | + | 0.982401i | \(0.559806\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 356461. | 0.622331 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −369957. | −0.630102 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 148173. | 0.246254 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −314043. | −0.509405 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13439.4 | 0.0212820 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −238134. | −0.368227 | −0.184114 | − | 0.982905i | \(-0.558941\pi\) | ||||
−0.184114 | + | 0.982905i | \(0.558941\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 90602.8 | 0.136834 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −500685. | −0.738701 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −308369. | −0.444551 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 36281.4 | 0.0511180 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 262692. | 0.361799 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −577920. | −0.778225 | −0.389113 | − | 0.921190i | \(-0.627218\pi\) | ||||
−0.389113 | + | 0.921190i | \(0.627218\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −132645. | −0.174676 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.32560e6 | −1.70745 | −0.853723 | − | 0.520727i | \(-0.825661\pi\) | ||||
−0.853723 | + | 0.520727i | \(0.825661\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.56401e6 | −1.97084 | −0.985420 | − | 0.170137i | \(-0.945579\pi\) | ||||
−0.985420 | + | 0.170137i | \(0.945579\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −193965. | −0.239162 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.35581e6 | −1.63610 | −0.818048 | − | 0.575150i | \(-0.804944\pi\) | ||||
−0.818048 | + | 0.575150i | \(0.804944\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 509715. | 0.602085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −469204. | −0.542614 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 389979. | 0.441618 | 0.220809 | − | 0.975317i | \(-0.429130\pi\) | ||||
0.220809 | + | 0.975317i | \(0.429130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 952265. | 1.05612 | 0.528062 | − | 0.849206i | \(-0.322919\pi\) | ||||
0.528062 | + | 0.849206i | \(0.322919\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 821983. | 0.892991 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −60025.0 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2964.03 | −0.00309129 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 158171. | 0.161669 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.58021e6 | 1.58318 | 0.791591 | − | 0.611052i | \(-0.209253\pi\) | ||||
0.791591 | + | 0.611052i | \(0.209253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.05597e6 | 1.03717 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 231454. | 0.222902 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.52332e6 | 1.43866 | 0.719329 | − | 0.694669i | \(-0.244449\pi\) | ||||
0.719329 | + | 0.694669i | \(0.244449\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19203.8 | 0.0177885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.60238e6 | −1.45601 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −999652. | −0.891168 | −0.445584 | − | 0.895240i | \(-0.647004\pi\) | ||||
−0.445584 | + | 0.895240i | \(0.647004\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −52220.3 | −0.0456799 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −73373.8 | −0.0629887 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.67825e6 | 1.41408 | 0.707041 | − | 0.707172i | \(-0.250030\pi\) | ||||
0.707041 | + | 0.707172i | \(0.250030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −89342.2 | −0.0738981 | −0.0369491 | − | 0.999317i | \(-0.511764\pi\) | ||||
−0.0369491 | + | 0.999317i | \(0.511764\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 42778.6 | 0.0347392 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 446019. | 0.355649 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15650.8 | 0.0122556 | 0.00612782 | − | 0.999981i | \(-0.498049\pi\) | ||||
0.00612782 | + | 0.999981i | \(0.498049\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.33562e6 | −1.02724 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.03527e6 | −0.782145 | −0.391072 | − | 0.920360i | \(-0.627896\pi\) | ||||
−0.391072 | + | 0.920360i | \(0.627896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21123.9 | 0.0156786 | 0.00783932 | − | 0.999969i | \(-0.497505\pi\) | ||||
0.00783932 | + | 0.999969i | \(0.497505\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2611.56 | −0.00190453 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 290418. | 0.208123 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.36589e6 | 0.961991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 775780. | 0.537039 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.05832e6 | −0.720193 | −0.360097 | − | 0.932915i | \(-0.617256\pi\) | ||||
−0.360097 | + | 0.932915i | \(0.617256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.12693e6 | −0.753952 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.80202e6 | −1.18541 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −232893. | −0.150653 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −981343. | −0.624316 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 133453. | 0.0835068 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −544656. | −0.335253 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −921205. | −0.557841 | −0.278920 | − | 0.960314i | \(-0.589977\pi\) | ||||
−0.278920 | + | 0.960314i | \(0.589977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40930.5 | 0.0243866 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −436095. | −0.255670 | −0.127835 | − | 0.991795i | \(-0.540803\pi\) | ||||
−0.127835 | + | 0.991795i | \(0.540803\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.12004e6 | 1.80011 | 0.900057 | − | 0.435773i | \(-0.143525\pi\) | ||||
0.900057 | + | 0.435773i | \(0.143525\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −259984. | −0.147628 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.40017e6 | −1.34151 | −0.670756 | − | 0.741678i | \(-0.734030\pi\) | ||||
−0.670756 | + | 0.741678i | \(0.734030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.38801e6 | 2.96450 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 182700. | 0.0989636 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31432.3 | −0.0167637 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −98368.7 | −0.0516593 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.18661e6 | 0.613676 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 999042. | 0.508855 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.50079e6 | 1.25461 | 0.627303 | − | 0.778776i | \(-0.284159\pi\) | ||||
0.627303 | + | 0.778776i | \(0.284159\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 83176.7 | 0.0411047 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.60656e6 | −0.782143 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.20634e6 | −1.05828 | −0.529138 | − | 0.848536i | \(-0.677484\pi\) | ||||
−0.529138 | + | 0.848536i | \(0.677484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 68196.1 | 0.0322300 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.49105e6 | 2.09152 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −205198. | −0.0928165 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.07193e6 | 0.923745 | 0.461872 | − | 0.886946i | \(-0.347178\pi\) | ||||
0.461872 | + | 0.886946i | \(0.347178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.88623e6 | 1.26843 | 0.634215 | − | 0.773157i | \(-0.281323\pi\) | ||||
0.634215 | + | 0.773157i | \(0.281323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 397432. | 0.172185 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.32386e6 | −0.992598 | −0.496299 | − | 0.868152i | \(-0.665308\pi\) | ||||
−0.496299 | + | 0.868152i | \(0.665308\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −408346. | −0.171972 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 453649. | 0.188387 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.55224e6 | 1.86419 | 0.932093 | − | 0.362219i | \(-0.117981\pi\) | ||||
0.932093 | + | 0.362219i | \(0.117981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47574e6 | −0.999857 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.93154e6 | 0.769373 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −163520. | −0.0642449 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.51918e6 | −0.976324 | −0.488162 | − | 0.872753i | \(-0.662332\pi\) | ||||
−0.488162 | + | 0.872753i | \(0.662332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.25788e6 | 0.480919 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −102352. | −0.0386065 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.35441e6 | 0.876213 | 0.438107 | − | 0.898923i | \(-0.355649\pi\) | ||||
0.438107 | + | 0.898923i | \(0.355649\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −86671.0 | −0.0318270 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.18832e6 | −0.430604 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.74826e6 | 0.625185 | 0.312593 | − | 0.949887i | \(-0.398802\pi\) | ||||
0.312593 | + | 0.949887i | \(0.398802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −110785. | −0.0390994 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.57306e6 | 0.896300 | 0.448150 | − | 0.893958i | \(-0.352083\pi\) | ||||
0.448150 | + | 0.893958i | \(0.352083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 874197. | 0.300578 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.25045e6 | −1.44264 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.22324e6 | 0.744924 | 0.372462 | − | 0.928047i | \(-0.378514\pi\) | ||||
0.372462 | + | 0.928047i | \(0.378514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.46973e6 | −0.816974 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 677794. | 0.221369 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.11470e6 | 0.681955 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.95025e6 | −1.57635 | −0.788173 | − | 0.615454i | \(-0.788973\pi\) | ||||
−0.788173 | + | 0.615454i | \(0.788973\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5118.65 | −0.00160962 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.91241e6 | 1.83613 | 0.918066 | − | 0.396428i | \(-0.129750\pi\) | ||||
0.918066 | + | 0.396428i | \(0.129750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −990493. | −0.303801 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −939136. | −0.284506 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −279683. | −0.0836911 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.28867e6 | −0.972101 | −0.486050 | − | 0.873931i | \(-0.661563\pi\) | ||||
−0.486050 | + | 0.873931i | \(0.661563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −819484. | −0.239296 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.20879e6 | −0.637205 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −712873. | −0.203185 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −540950. | −0.152341 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 917263. | 0.255246 | 0.127623 | − | 0.991823i | \(-0.459265\pi\) | ||||
0.127623 | + | 0.991823i | \(0.459265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00150e6 | −0.550365 | −0.275183 | − | 0.961392i | \(-0.588738\pi\) | ||||
−0.275183 | + | 0.961392i | \(0.588738\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.32710e6 | 1.17583 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.04316e6 | −0.280142 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.06753e6 | −0.283341 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −623022. | −0.163441 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.22623e6 | 1.09587 | 0.547936 | − | 0.836520i | \(-0.315414\pi\) | ||||
0.547936 | + | 0.836520i | \(0.315414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.45557e6 | 1.39836 | 0.699182 | − | 0.714943i | \(-0.253548\pi\) | ||||
0.699182 | + | 0.714943i | \(0.253548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.04700e6 | −0.265293 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27866.7 | 0.00698042 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.43517e6 | 1.09837 | 0.549185 | − | 0.835701i | \(-0.314938\pi\) | ||||
0.549185 | + | 0.835701i | \(0.314938\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −509568. | −0.124769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.18645e6 | 0.529335 | 0.264667 | − | 0.964340i | \(-0.414738\pi\) | ||||
0.264667 | + | 0.964340i | \(0.414738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 330695. | 0.0791640 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 592350. | 0.140220 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.47302e6 | −0.344820 | −0.172410 | − | 0.985025i | \(-0.555155\pi\) | ||||
−0.172410 | + | 0.985025i | \(0.555155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.22962e6 | −0.979174 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.07521e6 | −0.475135 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −192803. | −0.0436601 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.58032e6 | 0.801920 | 0.400960 | − | 0.916096i | \(-0.368677\pi\) | ||||
0.400960 | + | 0.916096i | \(0.368677\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.21460e6 | 0.933738 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.45341e6 | −1.63344 | −0.816719 | − | 0.577035i | \(-0.804210\pi\) | ||||
−0.816719 | + | 0.577035i | \(0.804210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −819161. | −0.177589 | −0.0887947 | − | 0.996050i | \(-0.528301\pi\) | ||||
−0.0887947 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −872706. | −0.187170 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 571988. | 0.121365 | 0.0606827 | − | 0.998157i | \(-0.480672\pi\) | ||||
0.0606827 | + | 0.998157i | \(0.480672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.14887e6 | −0.661032 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.13616e6 | −0.443692 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.42922e7 | 2.93728 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11770.3 | 0.00239360 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −443312. | −0.0892100 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.73825e6 | 0.346157 | 0.173079 | − | 0.984908i | \(-0.444629\pi\) | ||||
0.173079 | + | 0.984908i | \(0.444629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 61683.5 | 0.0121564 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −402188. | −0.0784443 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.49643e6 | −0.674948 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.79360e6 | 1.10694 | 0.553472 | − | 0.832867i | \(-0.313302\pi\) | ||||
0.553472 | + | 0.832867i | \(0.313302\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.94099e6 | −0.367073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.43388e6 | 1.20440 | 0.602198 | − | 0.798347i | \(-0.294292\pi\) | ||||
0.602198 | + | 0.798347i | \(0.294292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.26016e7 | −2.33512 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.78637e6 | 0.694560 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −800358. | −0.145343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.28825e6 | 1.49009 | 0.745043 | − | 0.667017i | \(-0.232429\pi\) | ||||
0.745043 | + | 0.667017i | \(0.232429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 351773. | 0.0626136 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00504e7 | −1.77118 | −0.885590 | − | 0.464468i | \(-0.846245\pi\) | ||||
−0.885590 | + | 0.464468i | \(0.846245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −601471. | −0.104951 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.92213e6 | −0.332096 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.73931e6 | −0.468648 | −0.234324 | − | 0.972159i | \(-0.575288\pi\) | ||||
−0.234324 | + | 0.972159i | \(0.575288\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −320499. | −0.0542969 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −47554.5 | −0.00797808 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −184473. | −0.0306489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.45499e7 | −2.39406 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.60322e6 | 0.424222 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.69300e6 | 0.757454 | 0.378727 | − | 0.925508i | \(-0.376362\pi\) | ||||
0.378727 | + | 0.925508i | \(0.376362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.92425e6 | −1.26679 | −0.633394 | − | 0.773829i | \(-0.718339\pi\) | ||||
−0.633394 | + | 0.773829i | \(0.718339\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −169875. | −0.0268987 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.05038e7 | −1.64747 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.24677e6 | −0.659812 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.56683e6 | −1.47242 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 932835. | 0.142229 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −823426. | −0.124377 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.66761e6 | 0.399197 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.71343e6 | 0.254035 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.60043e6 | 0.969569 | 0.484785 | − | 0.874634i | \(-0.338898\pi\) | ||||
0.484785 | + | 0.874634i | \(0.338898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.59459e6 | −0.377633 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.34805e6 | −0.771266 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.74178e6 | −0.534700 | −0.267350 | − | 0.963600i | \(-0.586148\pi\) | ||||
−0.267350 | + | 0.963600i | \(0.586148\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.62373e6 | −0.654729 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 142187. | 0.0199518 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.14481e6 | 0.576357 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 54348.3 | 0.00748951 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.38624e6 | −0.189322 | −0.0946608 | − | 0.995510i | \(-0.530177\pi\) | ||||
−0.0946608 | + | 0.995510i | \(0.530177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.15211e6 | −0.426650 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.60690e6 | −0.886320 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.05387e7 | 1.40125 | 0.700624 | − | 0.713531i | \(-0.252905\pi\) | ||||
0.700624 | + | 0.713531i | \(0.252905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −307359. | −0.0405065 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.84071e6 | −0.240451 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.89568e6 | −0.245462 | −0.122731 | − | 0.992440i | \(-0.539165\pi\) | ||||
−0.122731 | + | 0.992440i | \(0.539165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.77283e6 | 0.227550 | 0.113775 | − | 0.993507i | \(-0.463706\pi\) | ||||
0.113775 | + | 0.993507i | \(0.463706\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.90478e6 | −0.369596 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 924825. | 0.116651 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.91545e6 | −1.23986 | −0.619930 | − | 0.784657i | \(-0.712839\pi\) | ||||
−0.619930 | + | 0.784657i | \(0.712839\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.68002e6 | 0.456198 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.39723e6 | −0.171723 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.49064e6 | 0.181636 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −835077. | −0.100887 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.50312e6 | −0.898766 | −0.449383 | − | 0.893339i | \(-0.648356\pi\) | ||||
−0.449383 | + | 0.893339i | \(0.648356\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 118517. | 0.0140764 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 567997. | 0.0668924 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.33626e7 | 1.56047 | 0.780235 | − | 0.625487i | \(-0.215100\pi\) | ||||
0.780235 | + | 0.625487i | \(0.215100\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.04459e6 | −0.236763 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.15759e6 | −0.132929 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.67515e6 | 0.532388 | 0.266194 | − | 0.963919i | \(-0.414234\pi\) | ||||
0.266194 | + | 0.963919i | \(0.414234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.29686e7 | 1.46456 | 0.732279 | − | 0.681005i | \(-0.238457\pi\) | ||||
0.732279 | + | 0.681005i | \(0.238457\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.36385e7 | −1.52748 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.70542e6 | −0.966944 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.12171e7 | −1.23569 | −0.617845 | − | 0.786300i | \(-0.711994\pi\) | ||||
−0.617845 | + | 0.786300i | \(0.711994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.05213e6 | −0.224213 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.20896e6 | 0.347745 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.09615e7 | 1.17820 | 0.589102 | − | 0.808059i | \(-0.299482\pi\) | ||||
0.589102 | + | 0.808059i | \(0.299482\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 821905. | 0.0876261 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.20607e6 | −0.973557 | −0.486779 | − | 0.873525i | \(-0.661828\pi\) | ||||
−0.486779 | + | 0.873525i | \(0.661828\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.81664e6 | −0.819962 | −0.409981 | − | 0.912094i | \(-0.634465\pi\) | ||||
−0.409981 | + | 0.912094i | \(0.634465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.73650e6 | −0.388809 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 648162. | 0.0669058 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 74547.4 | 0.00757293 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 654128. | 0.0659229 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.26789e6 | −0.626683 | −0.313341 | − | 0.949641i | \(-0.601448\pi\) | ||||
−0.313341 | + | 0.949641i | \(0.601448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.32092e6 | −0.131029 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 499309. | 0.0491400 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −377893. | −0.0368995 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.46655e6 | −0.335850 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50806e7 | 1.44968 | 0.724840 | − | 0.688917i | \(-0.241914\pi\) | ||||
0.724840 | + | 0.688917i | \(0.241914\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.33403e7 | −1.27245 | −0.636223 | − | 0.771506i | \(-0.719504\pi\) | ||||
−0.636223 | + | 0.771506i | \(0.719504\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.77727e6 | −0.262857 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.94521e6 | −0.182686 | −0.0913431 | − | 0.995819i | \(-0.529116\pi\) | ||||
−0.0913431 | + | 0.995819i | \(0.529116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.21686e7 | 2.99792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.71050e6 | −0.158187 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.04880e6 | −0.188025 | −0.0940125 | − | 0.995571i | \(-0.529969\pi\) | ||||
−0.0940125 | + | 0.995571i | \(0.529969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.05481e6 | −0.278215 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.38816e6 | −0.125466 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.45814e6 | 0.668986 | 0.334493 | − | 0.942398i | \(-0.391435\pi\) | ||||
0.334493 | + | 0.942398i | \(0.391435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.86599e6 | 0.166113 | 0.0830567 | − | 0.996545i | \(-0.473532\pi\) | ||||
0.0830567 | + | 0.996545i | \(0.473532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.45714e6 | 0.128741 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23069.7 | 0.00202296 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.11721e7 | 0.972344 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.20569e6 | −0.276921 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.55473e7 | 1.33306 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.06697e6 | −0.601445 | −0.300722 | − | 0.953712i | \(-0.597228\pi\) | ||||
−0.300722 | + | 0.953712i | \(0.597228\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.57821e6 | −0.133323 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.92223e7 | 1.61189 | 0.805943 | − | 0.591992i | \(-0.201658\pi\) | ||||
0.805943 | + | 0.591992i | \(0.201658\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.85300e6 | −0.570436 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.35301e6 | −0.607572 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.16710e7 | 1.77757 | 0.888786 | − | 0.458322i | \(-0.151549\pi\) | ||||
0.888786 | + | 0.458322i | \(0.151549\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.69340e6 | 0.300746 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.67549e6 | −0.701297 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −328758. | −0.0263833 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.29271e7 | −1.02993 | −0.514964 | − | 0.857212i | \(-0.672195\pi\) | ||||
−0.514964 | + | 0.857212i | \(0.672195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.42128e6 | 0.587011 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.43806e6 | 0.191462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.89233e6 | 0.771288 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.52059e6 | −0.582183 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.46000e7 | −1.12217 | −0.561083 | − | 0.827759i | \(-0.689615\pi\) | ||||
−0.561083 | + | 0.827759i | \(0.689615\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7380.71 | −0.000563261 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.82736e6 | 0.214244 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.17888e6 | −0.0886997 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.34336e7 | −1.00364 | −0.501818 | − | 0.864973i | \(-0.667335\pi\) | ||||
−0.501818 | + | 0.864973i | \(0.667335\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.79522e7 | 1.33182 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.31223e6 | 0.686009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.80795e6 | 0.205412 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.16319e6 | 0.157144 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.10819e7 | 0.799454 | 0.399727 | − | 0.916634i | \(-0.369105\pi\) | ||||
0.399727 | + | 0.916634i | \(0.369105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −361568. | −0.0259031 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.28216e6 | 0.375808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.71884e6 | 0.333419 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.30383e6 | 0.652869 | 0.326434 | − | 0.945220i | \(-0.394153\pi\) | ||||
0.326434 | + | 0.945220i | \(0.394153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.56891e6 | −0.318415 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.34269e7 | −2.31367 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.49677e6 | −0.309130 | −0.154565 | − | 0.987983i | \(-0.549398\pi\) | ||||
−0.154565 | + | 0.987983i | \(0.549398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −332955. | −0.0227336 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.58597e7 | 3.11002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.04581e7 | −0.704434 | −0.352217 | − | 0.935918i | \(-0.614572\pi\) | ||||
−0.352217 | + | 0.935918i | \(0.614572\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16441.3 | −0.00110000 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −285721. | −0.0189876 | −0.00949379 | − | 0.999955i | \(-0.503022\pi\) | ||||
−0.00949379 | + | 0.999955i | \(0.503022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.66971e6 | −0.176228 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.05176e6 | −0.396808 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.61391e6 | −0.105118 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.76200e7 | −1.14000 | −0.570002 | − | 0.821643i | \(-0.693058\pi\) | ||||
−0.570002 | + | 0.821643i | \(0.693058\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.76533e6 | 0.563354 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.35296e6 | 0.597147 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.63145e6 | 0.166899 | 0.0834497 | − | 0.996512i | \(-0.473406\pi\) | ||||
0.0834497 | + | 0.996512i | \(0.473406\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.85742e6 | 0.369064 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.25303e7 | 0.784332 | 0.392166 | − | 0.919894i | \(-0.371726\pi\) | ||||
0.392166 | + | 0.919894i | \(0.371726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.04822e7 | −0.651839 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.85565e6 | −0.547100 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.09472e6 | −0.435459 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.44887e7 | −0.883515 | −0.441757 | − | 0.897135i | \(-0.645645\pi\) | ||||
−0.441757 | + | 0.897135i | \(0.645645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.44976e6 | 0.511927 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.08149e7 | 1.25292 | 0.626462 | − | 0.779452i | \(-0.284502\pi\) | ||||
0.626462 | + | 0.779452i | \(0.284502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.93328e6 | 0.235234 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 106523. | 0.00632979 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −111618. | −0.00659007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.16563e7 | 0.683807 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.90652e7 | −1.11131 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.62765e6 | 0.557630 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.92751e6 | −0.110933 | −0.0554665 | − | 0.998461i | \(-0.517665\pi\) | ||||
−0.0554665 | + | 0.998461i | \(0.517665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.54501e6 | −0.317110 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −602423. | −0.0342342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.42894e6 | −0.193632 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −289663. | −0.0162546 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.00107e7 | 0.558239 | 0.279120 | − | 0.960256i | \(-0.409957\pi\) | ||||
0.279120 | + | 0.960256i | \(0.409957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.40297e7 | 1.88578 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.80735e6 | 0.154602 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.66771e6 | 0.255455 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.81266e6 | 0.0985884 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.30913e6 | 0.503182 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.60552e7 | 1.39966 | 0.699832 | − | 0.714308i | \(-0.253258\pi\) | ||||
0.699832 | + | 0.714308i | \(0.253258\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.84980e7 | −1.52147 | −0.760733 | − | 0.649064i | \(-0.775161\pi\) | ||||
−0.760733 | + | 0.649064i | \(0.775161\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −495576. | −0.0262956 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.74804e6 | 0.461335 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 377164. | 0.0197686 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.63675e6 | −0.0852654 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.20586e7 | 1.14214 | 0.571071 | − | 0.820901i | \(-0.306528\pi\) | ||||
0.571071 | + | 0.820901i | \(0.306528\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.88032e6 | 0.148232 | 0.0741158 | − | 0.997250i | \(-0.476387\pi\) | ||||
0.0741158 | + | 0.997250i | \(0.476387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.47404e6 | 0.126553 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.90804e7 | 1.47855 | 0.739275 | − | 0.673403i | \(-0.235168\pi\) | ||||
0.739275 | + | 0.673403i | \(0.235168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.12006e7 | −1.57680 | −0.788399 | − | 0.615164i | \(-0.789090\pi\) | ||||
−0.788399 | + | 0.615164i | \(0.789090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 86813.8 | 0.00436100 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00740e6 | −0.200102 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.58544e6 | −0.0786925 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.58913e7 | −0.784055 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.36267e6 | −0.164922 | −0.0824612 | − | 0.996594i | \(-0.526278\pi\) | ||||
−0.0824612 | + | 0.996594i | \(0.526278\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.64934e7 | 1.77920 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.74257e6 | −0.278316 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.66304e6 | 0.417377 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.70626e7 | −0.817217 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 117173. | 0.00557903 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −579925. | −0.0274503 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.95962e7 | 0.922144 | 0.461072 | − | 0.887363i | \(-0.347465\pi\) | ||||
0.461072 | + | 0.887363i | \(0.347465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 99920.7 | 0.00467456 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.56996e6 | 0.445101 | 0.222550 | − | 0.974921i | \(-0.428562\pi\) | ||||
0.222550 | + | 0.974921i | \(0.428562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.49323e7 | 1.15287 | 0.576435 | − | 0.817143i | \(-0.304443\pi\) | ||||
0.576435 | + | 0.817143i | \(0.304443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.61093e6 | 0.0740576 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.31911e7 | −0.602913 | −0.301457 | − | 0.953480i | \(-0.597473\pi\) | ||||
−0.301457 | + | 0.953480i | \(0.597473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.17327e7 | −0.533160 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.57651e6 | 0.342311 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.03645e7 | −2.71164 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.01143e7 | −0.451741 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.96821e7 | −1.31813 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.92706e6 | −0.391931 | −0.195965 | − | 0.980611i | \(-0.562784\pi\) | ||||
−0.195965 | + | 0.980611i | \(0.562784\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.87045e6 | −0.256271 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.59013e6 | 0.286058 | 0.143029 | − | 0.989718i | \(-0.454316\pi\) | ||||
0.143029 | + | 0.989718i | \(0.454316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.43558e7 | −1.05124 | −0.525618 | − | 0.850721i | \(-0.676166\pi\) | ||||
−0.525618 | + | 0.850721i | \(0.676166\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.25104e6 | −0.268283 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.49008e6 | −0.276975 | −0.138488 | − | 0.990364i | \(-0.544224\pi\) | ||||
−0.138488 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 978645. | 0.0415308 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.68078e7 | 1.13127 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −383967. | −0.0161126 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.20229e7 | −0.501709 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.29184e6 | −0.0536079 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.75149e7 | 1.96079 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.48635e6 | −0.143073 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.44345e6 | −0.222154 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.16938e7 | 0.474607 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.63222e7 | 1.86970 | 0.934848 | − | 0.355049i | \(-0.115536\pi\) | ||||
0.934848 | + | 0.355049i | \(0.115536\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.10604e6 | −0.204963 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.91803e7 | 0.765701 | 0.382850 | − | 0.923810i | \(-0.374942\pi\) | ||||
0.382850 | + | 0.923810i | \(0.374942\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.03491e7 | 0.807920 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.02118e6 | −0.119295 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.98742e6 | −0.235135 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.93274e7 | −0.754892 | −0.377446 | − | 0.926032i | \(-0.623198\pi\) | ||||
−0.377446 | + | 0.926032i | \(0.623198\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.10987e6 | −0.198500 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.57078e6 | −0.0993255 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −244947. | −0.00941278 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.56604e6 | −0.0598555 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.56658e7 | −0.975697 | −0.487848 | − | 0.872928i | \(-0.662218\pi\) | ||||
−0.487848 | + | 0.872928i | \(0.662218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45216.6 | 0.00170972 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.41899e6 | −0.0909767 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.97772e7 | 1.11392 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.72369e6 | 0.250184 | 0.125092 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125092 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.73067e7 | 0.640546 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.99755e7 | −1.10355 | −0.551775 | − | 0.833993i | \(-0.686049\pi\) | ||||
−0.551775 | + | 0.833993i | \(0.686049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.77016e6 | −0.321165 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.09330e6 | −0.112679 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.10799e7 | −0.763823 | −0.381912 | − | 0.924199i | \(-0.624734\pi\) | ||||
−0.381912 | + | 0.924199i | \(0.624734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.02946e6 | −0.0371058 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.33136e7 | −0.477359 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 231114. | 0.00824318 | 0.00412159 | − | 0.999992i | \(-0.498688\pi\) | ||||
0.00412159 | + | 0.999992i | \(0.498688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.30918e7 | 0.464506 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.98870e7 | 1.05488 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.23907e6 | 0.254177 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.09757e7 | 0.383377 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.99027e6 | −0.242901 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.65858e7 | −0.573348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.67022e7 | −0.574391 | −0.287195 | − | 0.957872i | \(-0.592723\pi\) | ||||
−0.287195 | + | 0.957872i | \(0.592723\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −174353. | −0.00596514 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.46767e7 | −0.839924 | −0.419962 | − | 0.907542i | \(-0.637957\pi\) | ||||
−0.419962 | + | 0.907542i | \(0.637957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.77859e6 | 0.161815 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −545645. | −0.0183823 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.73438e6 | 0.158682 | 0.0793409 | − | 0.996848i | \(-0.474718\pi\) | ||||
0.0793409 | + | 0.996848i | \(0.474718\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.43975e6 | −0.314778 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.54010e7 | −1.50623 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.25544e7 | −1.07455 | −0.537273 | − | 0.843408i | \(-0.680546\pi\) | ||||
−0.537273 | + | 0.843408i | \(0.680546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.55995e6 | −0.0840701 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.54162e6 | 0.181069 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.96349e7 | 0.963415 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.80110e6 | 0.155295 | 0.0776473 | − | 0.996981i | \(-0.475259\pi\) | ||||
0.0776473 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.38717e7 | 0.446434 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.21725e6 | 0.167064 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.58078e6 | −0.145949 | −0.0729745 | − | 0.997334i | \(-0.523249\pi\) | ||||
−0.0729745 | + | 0.997334i | \(0.523249\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 989642. | 0.0313736 |
(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 | 280.6.a.i.1.4 | ✓ | 5 | |
4.3 | odd | 2 | 560.6.a.z.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.i.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
560.6.a.z.1.2 | 5 | 4.3 | odd | 2 |