Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,6,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(85.1638083207\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + \cdots - 14846072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-5.62527\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.62527 | 1.17119 | 0.585597 | − | 0.810602i | \(-0.300860\pi\) | ||||
0.585597 | + | 0.810602i | \(0.300860\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 11.8942 | 0.371695 | ||||||||
\(5\) | 85.2025 | 1.52415 | 0.762074 | − | 0.647490i | \(-0.224181\pi\) | ||||
0.762074 | + | 0.647490i | \(0.224181\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −103.010 | −0.794573 | −0.397287 | − | 0.917695i | \(-0.630048\pi\) | ||||
−0.397287 | + | 0.917695i | \(0.630048\pi\) | |||||||
\(8\) | −133.206 | −0.735867 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 564.490 | 1.78507 | ||||||||
\(11\) | −579.703 | −1.44452 | −0.722260 | − | 0.691622i | \(-0.756897\pi\) | ||||
−0.722260 | + | 0.691622i | \(0.756897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 435.487 | 0.714689 | 0.357344 | − | 0.933973i | \(-0.383682\pi\) | ||||
0.357344 | + | 0.933973i | \(0.383682\pi\) | |||||||
\(14\) | −682.469 | −0.930599 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1263.14 | −1.23354 | ||||||||
\(17\) | −424.138 | −0.355946 | −0.177973 | − | 0.984035i | \(-0.556954\pi\) | ||||
−0.177973 | + | 0.984035i | \(0.556954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1540.54 | 0.979012 | 0.489506 | − | 0.872000i | \(-0.337177\pi\) | ||||
0.489506 | + | 0.872000i | \(0.337177\pi\) | |||||||
\(20\) | 1013.42 | 0.566518 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3840.69 | −1.69181 | ||||||||
\(23\) | 4164.00 | 1.64131 | 0.820656 | − | 0.571423i | \(-0.193609\pi\) | ||||
0.820656 | + | 0.571423i | \(0.193609\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4134.46 | 1.32303 | ||||||||
\(26\) | 2885.22 | 0.837039 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1225.22 | −0.295339 | ||||||||
\(29\) | 8418.14 | 1.85875 | 0.929376 | − | 0.369135i | \(-0.120346\pi\) | ||||
0.929376 | + | 0.369135i | \(0.120346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7073.40 | 1.32198 | 0.660989 | − | 0.750396i | \(-0.270137\pi\) | ||||
0.660989 | + | 0.750396i | \(0.270137\pi\) | |||||||
\(32\) | −4106.07 | −0.708845 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2810.03 | −0.416882 | ||||||||
\(35\) | −8776.70 | −1.21105 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12420.5 | 1.49154 | 0.745769 | − | 0.666205i | \(-0.232082\pi\) | ||||
0.745769 | + | 0.666205i | \(0.232082\pi\) | |||||||
\(38\) | 10206.5 | 1.14661 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11349.5 | −1.12157 | ||||||||
\(41\) | 2421.33 | 0.224954 | 0.112477 | − | 0.993654i | \(-0.464122\pi\) | ||||
0.112477 | + | 0.993654i | \(0.464122\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11711.3 | −0.965905 | −0.482953 | − | 0.875646i | \(-0.660436\pi\) | ||||
−0.482953 | + | 0.875646i | \(0.660436\pi\) | |||||||
\(44\) | −6895.12 | −0.536921 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 27587.6 | 1.92229 | ||||||||
\(47\) | 9436.30 | 0.623099 | 0.311550 | − | 0.950230i | \(-0.399152\pi\) | ||||
0.311550 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6195.96 | −0.368654 | ||||||||
\(50\) | 27391.9 | 1.54952 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5179.79 | 0.265646 | ||||||||
\(53\) | 23764.2 | 1.16207 | 0.581037 | − | 0.813877i | \(-0.302647\pi\) | ||||
0.581037 | + | 0.813877i | \(0.302647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −49392.1 | −2.20166 | ||||||||
\(56\) | 13721.5 | 0.584700 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 55772.5 | 2.17696 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5566.88 | 0.191552 | 0.0957761 | − | 0.995403i | \(-0.469467\pi\) | ||||
0.0957761 | + | 0.995403i | \(0.469467\pi\) | |||||||
\(62\) | 46863.2 | 1.54829 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13216.7 | 0.403343 | ||||||||
\(65\) | 37104.6 | 1.08929 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −57888.7 | −1.57546 | −0.787729 | − | 0.616022i | \(-0.788743\pi\) | ||||
−0.787729 | + | 0.616022i | \(0.788743\pi\) | |||||||
\(68\) | −5044.80 | −0.132304 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −58148.0 | −1.41837 | ||||||||
\(71\) | 11960.0 | 0.281569 | 0.140784 | − | 0.990040i | \(-0.455038\pi\) | ||||
0.140784 | + | 0.990040i | \(0.455038\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 25056.7 | 0.550322 | 0.275161 | − | 0.961398i | \(-0.411269\pi\) | ||||
0.275161 | + | 0.961398i | \(0.411269\pi\) | |||||||
\(74\) | 82289.1 | 1.74688 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 18323.5 | 0.363894 | ||||||||
\(77\) | 59715.1 | 1.14778 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17801.5 | 0.320914 | 0.160457 | − | 0.987043i | \(-0.448703\pi\) | ||||
0.160457 | + | 0.987043i | \(0.448703\pi\) | |||||||
\(80\) | −107623. | −1.88009 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16042.0 | 0.263465 | ||||||||
\(83\) | 2768.37 | 0.0441092 | 0.0220546 | − | 0.999757i | \(-0.492979\pi\) | ||||
0.0220546 | + | 0.999757i | \(0.492979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −36137.6 | −0.542515 | ||||||||
\(86\) | −77590.7 | −1.13126 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 77219.9 | 1.06297 | ||||||||
\(89\) | −17994.8 | −0.240809 | −0.120404 | − | 0.992725i | \(-0.538419\pi\) | ||||
−0.120404 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −44859.5 | −0.567872 | ||||||||
\(92\) | 49527.6 | 0.610067 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 62518.1 | 0.729770 | ||||||||
\(95\) | 131257. | 1.49216 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −166125. | −1.79269 | −0.896346 | − | 0.443355i | \(-0.853788\pi\) | ||||
−0.896346 | + | 0.443355i | \(0.853788\pi\) | |||||||
\(98\) | −41049.9 | −0.431765 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 49176.3 | 0.491763 | ||||||||
\(101\) | 38127.7 | 0.371909 | 0.185954 | − | 0.982558i | \(-0.440462\pi\) | ||||
0.185954 | + | 0.982558i | \(0.440462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 81615.4 | 0.758018 | 0.379009 | − | 0.925393i | \(-0.376265\pi\) | ||||
0.379009 | + | 0.925393i | \(0.376265\pi\) | |||||||
\(104\) | −58009.5 | −0.525916 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 157444. | 1.36101 | ||||||||
\(107\) | −121265. | −1.02395 | −0.511973 | − | 0.859002i | \(-0.671085\pi\) | ||||
−0.511973 | + | 0.859002i | \(0.671085\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −153096. | −1.23424 | −0.617118 | − | 0.786870i | \(-0.711700\pi\) | ||||
−0.617118 | + | 0.786870i | \(0.711700\pi\) | |||||||
\(110\) | −327236. | −2.57857 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 130116. | 0.980136 | ||||||||
\(113\) | 54428.5 | 0.400987 | 0.200494 | − | 0.979695i | \(-0.435745\pi\) | ||||
0.200494 | + | 0.979695i | \(0.435745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 354783. | 2.50160 | ||||||||
\(116\) | 100127. | 0.690889 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −23062.6 | −0.152476 | ||||||||
\(119\) | 43690.4 | 0.282825 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 175004. | 1.08664 | ||||||||
\(122\) | 36882.1 | 0.224345 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 84132.8 | 0.491373 | ||||||||
\(125\) | 86008.6 | 0.492342 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −203111. | −1.11744 | −0.558721 | − | 0.829356i | \(-0.688708\pi\) | ||||
−0.558721 | + | 0.829356i | \(0.688708\pi\) | |||||||
\(128\) | 218959. | 1.18124 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 245828. | 1.27577 | ||||||||
\(131\) | 282282. | 1.43716 | 0.718579 | − | 0.695445i | \(-0.244793\pi\) | ||||
0.718579 | + | 0.695445i | \(0.244793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −158690. | −0.777896 | ||||||||
\(134\) | −383529. | −1.84517 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 56497.7 | 0.261929 | ||||||||
\(137\) | 290437. | 1.32206 | 0.661029 | − | 0.750360i | \(-0.270120\pi\) | ||||
0.661029 | + | 0.750360i | \(0.270120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 429789. | 1.88677 | 0.943383 | − | 0.331705i | \(-0.107624\pi\) | ||||
0.943383 | + | 0.331705i | \(0.107624\pi\) | |||||||
\(140\) | −104392. | −0.450140 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 79238.2 | 0.329772 | ||||||||
\(143\) | −252453. | −1.03238 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 717247. | 2.83301 | ||||||||
\(146\) | 166008. | 0.644534 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 147732. | 0.554397 | ||||||||
\(149\) | 383936. | 1.41675 | 0.708376 | − | 0.705835i | \(-0.249428\pi\) | ||||
0.708376 | + | 0.705835i | \(0.249428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −91551.4 | −0.326755 | −0.163378 | − | 0.986564i | \(-0.552239\pi\) | ||||
−0.163378 | + | 0.986564i | \(0.552239\pi\) | |||||||
\(152\) | −205209. | −0.720422 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 395629. | 1.34427 | ||||||||
\(155\) | 602671. | 2.01489 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18734.2 | −0.0606578 | −0.0303289 | − | 0.999540i | \(-0.509655\pi\) | ||||
−0.0303289 | + | 0.999540i | \(0.509655\pi\) | |||||||
\(158\) | 117940. | 0.375852 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −349847. | −1.08039 | ||||||||
\(161\) | −428933. | −1.30414 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 85172.5 | 0.251091 | 0.125545 | − | 0.992088i | \(-0.459932\pi\) | ||||
0.125545 | + | 0.992088i | \(0.459932\pi\) | |||||||
\(164\) | 28799.9 | 0.0836143 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18341.2 | 0.0516604 | ||||||||
\(167\) | −541622. | −1.50281 | −0.751407 | − | 0.659839i | \(-0.770625\pi\) | ||||
−0.751407 | + | 0.659839i | \(0.770625\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −181644. | −0.489220 | ||||||||
\(170\) | −239421. | −0.635390 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −139297. | −0.359022 | ||||||||
\(173\) | −238752. | −0.606502 | −0.303251 | − | 0.952911i | \(-0.598072\pi\) | ||||
−0.303251 | + | 0.952911i | \(0.598072\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −425890. | −1.05124 | ||||||||
\(176\) | 732247. | 1.78187 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −119221. | −0.282034 | ||||||||
\(179\) | −284533. | −0.663744 | −0.331872 | − | 0.943324i | \(-0.607680\pi\) | ||||
−0.331872 | + | 0.943324i | \(0.607680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −402281. | −0.912711 | −0.456355 | − | 0.889798i | \(-0.650845\pi\) | ||||
−0.456355 | + | 0.889798i | \(0.650845\pi\) | |||||||
\(182\) | −297206. | −0.665089 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −554670. | −1.20779 | ||||||||
\(185\) | 1.05826e6 | 2.27332 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 245874. | 0.514172 | ||||||||
\(188\) | 112238. | 0.231603 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 869617. | 1.74761 | ||||||||
\(191\) | 624305. | 1.23826 | 0.619132 | − | 0.785287i | \(-0.287485\pi\) | ||||
0.619132 | + | 0.785287i | \(0.287485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 835697. | 1.61494 | 0.807469 | − | 0.589910i | \(-0.200837\pi\) | ||||
0.807469 | + | 0.589910i | \(0.200837\pi\) | |||||||
\(194\) | −1.10062e6 | −2.09959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −73696.3 | −0.137027 | ||||||||
\(197\) | 724552. | 1.33016 | 0.665080 | − | 0.746772i | \(-0.268397\pi\) | ||||
0.665080 | + | 0.746772i | \(0.268397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −691882. | −1.23851 | −0.619255 | − | 0.785190i | \(-0.712565\pi\) | ||||
−0.619255 | + | 0.785190i | \(0.712565\pi\) | |||||||
\(200\) | −550736. | −0.973572 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 252606. | 0.435577 | ||||||||
\(203\) | −867152. | −1.47691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 206303. | 0.342863 | ||||||||
\(206\) | 540725. | 0.887786 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −550082. | −0.881595 | ||||||||
\(209\) | −893053. | −1.41420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 249343. | 0.385559 | 0.192779 | − | 0.981242i | \(-0.438250\pi\) | ||||
0.192779 | + | 0.981242i | \(0.438250\pi\) | |||||||
\(212\) | 282657. | 0.431937 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −803416. | −1.19924 | ||||||||
\(215\) | −997833. | −1.47218 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −728630. | −1.05041 | ||||||||
\(218\) | −1.01430e6 | −1.44553 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −587482. | −0.818347 | ||||||||
\(221\) | −184706. | −0.254391 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −542135. | −0.730038 | −0.365019 | − | 0.931000i | \(-0.618938\pi\) | ||||
−0.365019 | + | 0.931000i | \(0.618938\pi\) | |||||||
\(224\) | 422966. | 0.563229 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 360604. | 0.469634 | ||||||||
\(227\) | 480667. | 0.619127 | 0.309563 | − | 0.950879i | \(-0.399817\pi\) | ||||
0.309563 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −623840. | −0.786112 | −0.393056 | − | 0.919514i | \(-0.628582\pi\) | ||||
−0.393056 | + | 0.919514i | \(0.628582\pi\) | |||||||
\(230\) | 2.35053e6 | 2.92986 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.12135e6 | −1.36779 | ||||||||
\(233\) | −645676. | −0.779157 | −0.389579 | − | 0.920993i | \(-0.627379\pi\) | ||||
−0.389579 | + | 0.920993i | \(0.627379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 803996. | 0.949695 | ||||||||
\(236\) | −41403.9 | −0.0483906 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 289461. | 0.331243 | ||||||||
\(239\) | −1.10502e6 | −1.25134 | −0.625669 | − | 0.780089i | \(-0.715174\pi\) | ||||
−0.625669 | + | 0.780089i | \(0.715174\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.44502e6 | 1.60262 | 0.801309 | − | 0.598250i | \(-0.204137\pi\) | ||||
0.801309 | + | 0.598250i | \(0.204137\pi\) | |||||||
\(242\) | 1.15945e6 | 1.27266 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 66213.8 | 0.0711990 | ||||||||
\(245\) | −527911. | −0.561883 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 670883. | 0.699688 | ||||||||
\(248\) | −942220. | −0.972799 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 569830. | 0.576628 | ||||||||
\(251\) | −528809. | −0.529803 | −0.264902 | − | 0.964275i | \(-0.585340\pi\) | ||||
−0.264902 | + | 0.964275i | \(0.585340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.41388e6 | −2.37091 | ||||||||
\(254\) | −1.34567e6 | −1.30874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.02773e6 | 0.980116 | ||||||||
\(257\) | 1.15172e6 | 1.08771 | 0.543856 | − | 0.839179i | \(-0.316964\pi\) | ||||
0.543856 | + | 0.839179i | \(0.316964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.27943e6 | −1.18514 | ||||||||
\(260\) | 441331. | 0.404884 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.87019e6 | 1.68319 | ||||||||
\(263\) | −452277. | −0.403195 | −0.201598 | − | 0.979468i | \(-0.564613\pi\) | ||||
−0.201598 | + | 0.979468i | \(0.564613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.02477e6 | 1.77117 | ||||||||
\(266\) | −1.05137e6 | −0.911067 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −688543. | −0.585590 | ||||||||
\(269\) | 1.71384e6 | 1.44407 | 0.722036 | − | 0.691856i | \(-0.243207\pi\) | ||||
0.722036 | + | 0.691856i | \(0.243207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.32879e6 | 1.09909 | 0.549546 | − | 0.835463i | \(-0.314801\pi\) | ||||
0.549546 | + | 0.835463i | \(0.314801\pi\) | |||||||
\(272\) | 535746. | 0.439073 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.92422e6 | 1.54839 | ||||||||
\(275\) | −2.39676e6 | −1.91114 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.54297e6 | −1.20825 | −0.604126 | − | 0.796889i | \(-0.706478\pi\) | ||||
−0.604126 | + | 0.796889i | \(0.706478\pi\) | |||||||
\(278\) | 2.84747e6 | 2.20977 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.16911e6 | 0.891169 | ||||||||
\(281\) | 5515.62 | 0.00416705 | 0.00208352 | − | 0.999998i | \(-0.499337\pi\) | ||||
0.00208352 | + | 0.999998i | \(0.499337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −944988. | −0.701391 | −0.350696 | − | 0.936489i | \(-0.614055\pi\) | ||||
−0.350696 | + | 0.936489i | \(0.614055\pi\) | |||||||
\(284\) | 142255. | 0.104658 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.67257e6 | −1.20912 | ||||||||
\(287\) | −249421. | −0.178742 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.23996e6 | −0.873302 | ||||||||
\(290\) | 4.75196e6 | 3.31801 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 298031. | 0.204552 | ||||||||
\(293\) | 1.52734e6 | 1.03936 | 0.519681 | − | 0.854361i | \(-0.326051\pi\) | ||||
0.519681 | + | 0.854361i | \(0.326051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −296590. | −0.198427 | ||||||||
\(296\) | −1.65448e6 | −1.09757 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.54368e6 | 1.65929 | ||||||||
\(299\) | 1.81337e6 | 1.17303 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.20638e6 | 0.767482 | ||||||||
\(302\) | −606553. | −0.382694 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.94592e6 | −1.20765 | ||||||||
\(305\) | 474312. | 0.291954 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.82858e6 | −1.71286 | −0.856431 | − | 0.516261i | \(-0.827323\pi\) | ||||
−0.856431 | + | 0.516261i | \(0.827323\pi\) | |||||||
\(308\) | 710266. | 0.426623 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.99286e6 | 2.35983 | ||||||||
\(311\) | −490910. | −0.287806 | −0.143903 | − | 0.989592i | \(-0.545965\pi\) | ||||
−0.143903 | + | 0.989592i | \(0.545965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.05776e6 | 1.76418 | 0.882089 | − | 0.471083i | \(-0.156137\pi\) | ||||
0.882089 | + | 0.471083i | \(0.156137\pi\) | |||||||
\(314\) | −124119. | −0.0710420 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 211735. | 0.119282 | ||||||||
\(317\) | 3.44305e6 | 1.92440 | 0.962199 | − | 0.272348i | \(-0.0878002\pi\) | ||||
0.962199 | + | 0.272348i | \(0.0878002\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.88002e6 | −2.68500 | ||||||||
\(320\) | 1.12610e6 | 0.614754 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.84180e6 | −1.52740 | ||||||||
\(323\) | −653399. | −0.348476 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.80050e6 | 0.945553 | ||||||||
\(326\) | 564291. | 0.294076 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −322536. | −0.165536 | ||||||||
\(329\) | −972032. | −0.495098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.53352e6 | −1.27102 | −0.635512 | − | 0.772091i | \(-0.719211\pi\) | ||||
−0.635512 | + | 0.772091i | \(0.719211\pi\) | |||||||
\(332\) | 32927.7 | 0.0163952 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.58840e6 | −1.76009 | ||||||||
\(335\) | −4.93226e6 | −2.40123 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.44618e6 | −1.17331 | −0.586657 | − | 0.809835i | \(-0.699556\pi\) | ||||
−0.586657 | + | 0.809835i | \(0.699556\pi\) | |||||||
\(338\) | −1.20344e6 | −0.572972 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −429829. | −0.201650 | ||||||||
\(341\) | −4.10047e6 | −1.90962 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.36953e6 | 1.08750 | ||||||||
\(344\) | 1.56002e6 | 0.710778 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.58180e6 | −0.710332 | ||||||||
\(347\) | −92368.8 | −0.0411815 | −0.0205907 | − | 0.999788i | \(-0.506555\pi\) | ||||
−0.0205907 | + | 0.999788i | \(0.506555\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 519444. | 0.228284 | 0.114142 | − | 0.993464i | \(-0.463588\pi\) | ||||
0.114142 | + | 0.993464i | \(0.463588\pi\) | |||||||
\(350\) | −2.82164e6 | −1.23121 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.38030e6 | 1.02394 | ||||||||
\(353\) | 1.65548e6 | 0.707109 | 0.353555 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353555 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.01902e6 | 0.429153 | ||||||||
\(356\) | −214035. | −0.0895074 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.88511e6 | −0.777373 | ||||||||
\(359\) | −2.51488e6 | −1.02987 | −0.514934 | − | 0.857230i | \(-0.672184\pi\) | ||||
−0.514934 | + | 0.857230i | \(0.672184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −102848. | −0.0415361 | ||||||||
\(362\) | −2.66522e6 | −1.06896 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −533570. | −0.211075 | ||||||||
\(365\) | 2.13489e6 | 0.838773 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −792348. | −0.307080 | −0.153540 | − | 0.988142i | \(-0.549067\pi\) | ||||
−0.153540 | + | 0.988142i | \(0.549067\pi\) | |||||||
\(368\) | −5.25972e6 | −2.02462 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.01124e6 | 2.66250 | ||||||||
\(371\) | −2.44795e6 | −0.923352 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 846687. | 0.315102 | 0.157551 | − | 0.987511i | \(-0.449640\pi\) | ||||
0.157551 | + | 0.987511i | \(0.449640\pi\) | |||||||
\(374\) | 1.62898e6 | 0.602195 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.25697e6 | −0.458518 | ||||||||
\(377\) | 3.66599e6 | 1.32843 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.63333e6 | 0.584085 | 0.292043 | − | 0.956405i | \(-0.405665\pi\) | ||||
0.292043 | + | 0.956405i | \(0.405665\pi\) | |||||||
\(380\) | 1.56121e6 | 0.554628 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.13619e6 | 1.45025 | ||||||||
\(383\) | 4.23461e6 | 1.47508 | 0.737541 | − | 0.675302i | \(-0.235987\pi\) | ||||
0.737541 | + | 0.675302i | \(0.235987\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.08787e6 | 1.74938 | ||||||||
\(386\) | 5.53672e6 | 1.89141 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.97593e6 | −0.666335 | ||||||||
\(389\) | −4.32595e6 | −1.44946 | −0.724732 | − | 0.689031i | \(-0.758037\pi\) | ||||
−0.724732 | + | 0.689031i | \(0.758037\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.76611e6 | −0.584219 | ||||||||
\(392\) | 825340. | 0.271280 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.80035e6 | 1.55787 | ||||||||
\(395\) | 1.51673e6 | 0.489120 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.34065e6 | 1.06379 | 0.531894 | − | 0.846811i | \(-0.321480\pi\) | ||||
0.531894 | + | 0.846811i | \(0.321480\pi\) | |||||||
\(398\) | −4.58391e6 | −1.45054 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.22241e6 | −1.63200 | ||||||||
\(401\) | 600538. | 0.186500 | 0.0932502 | − | 0.995643i | \(-0.470274\pi\) | ||||
0.0932502 | + | 0.995643i | \(0.470274\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.08037e6 | 0.944802 | ||||||||
\(404\) | 453500. | 0.138237 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.74512e6 | −1.72975 | ||||||||
\(407\) | −7.20019e6 | −2.15456 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.87846e6 | −0.555256 | −0.277628 | − | 0.960689i | \(-0.589548\pi\) | ||||
−0.277628 | + | 0.960689i | \(0.589548\pi\) | |||||||
\(410\) | 1.36681e6 | 0.401559 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 970754. | 0.281751 | ||||||||
\(413\) | 358577. | 0.103445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 235872. | 0.0672289 | ||||||||
\(416\) | −1.78814e6 | −0.506604 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.91672e6 | −1.65630 | ||||||||
\(419\) | 4.65041e6 | 1.29407 | 0.647033 | − | 0.762462i | \(-0.276010\pi\) | ||||
0.647033 | + | 0.762462i | \(0.276010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.24723e6 | −0.342959 | −0.171479 | − | 0.985188i | \(-0.554855\pi\) | ||||
−0.171479 | + | 0.985188i | \(0.554855\pi\) | |||||||
\(422\) | 1.65196e6 | 0.451564 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.16554e6 | −0.855131 | ||||||||
\(425\) | −1.75358e6 | −0.470927 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −573443. | −0.152202 | ||||||||
\(428\) | −1.44236e6 | −0.380596 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.61092e6 | −1.72421 | ||||||||
\(431\) | −975574. | −0.252969 | −0.126484 | − | 0.991969i | \(-0.540369\pi\) | ||||
−0.126484 | + | 0.991969i | \(0.540369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.56758e6 | 0.658119 | 0.329060 | − | 0.944309i | \(-0.393268\pi\) | ||||
0.329060 | + | 0.944309i | \(0.393268\pi\) | |||||||
\(434\) | −4.82737e6 | −1.23023 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.82096e6 | −0.458760 | ||||||||
\(437\) | 6.41479e6 | 1.60686 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 875156. | 0.216733 | 0.108366 | − | 0.994111i | \(-0.465438\pi\) | ||||
0.108366 | + | 0.994111i | \(0.465438\pi\) | |||||||
\(440\) | 6.57933e6 | 1.62013 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.22373e6 | −0.297941 | ||||||||
\(443\) | −4.39426e6 | −1.06384 | −0.531920 | − | 0.846795i | \(-0.678529\pi\) | ||||
−0.531920 | + | 0.846795i | \(0.678529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.53320e6 | −0.367028 | ||||||||
\(446\) | −3.59180e6 | −0.855016 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.36145e6 | −0.320485 | ||||||||
\(449\) | −2.22268e6 | −0.520308 | −0.260154 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260154 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.40365e6 | −0.324951 | ||||||||
\(452\) | 647386. | 0.149045 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.18455e6 | 0.725118 | ||||||||
\(455\) | −3.82214e6 | −0.865521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.49053e6 | −0.781810 | −0.390905 | − | 0.920431i | \(-0.627838\pi\) | ||||
−0.390905 | + | 0.920431i | \(0.627838\pi\) | |||||||
\(458\) | −4.13311e6 | −0.920690 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.21987e6 | 0.929833 | ||||||||
\(461\) | −341191. | −0.0747732 | −0.0373866 | − | 0.999301i | \(-0.511903\pi\) | ||||
−0.0373866 | + | 0.999301i | \(0.511903\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.72986e6 | −1.45899 | −0.729497 | − | 0.683984i | \(-0.760246\pi\) | ||||
−0.729497 | + | 0.683984i | \(0.760246\pi\) | |||||||
\(464\) | −1.06333e7 | −2.29284 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.27778e6 | −0.912544 | ||||||||
\(467\) | 2.11594e6 | 0.448964 | 0.224482 | − | 0.974478i | \(-0.427931\pi\) | ||||
0.224482 | + | 0.974478i | \(0.427931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.96311e6 | 1.25182 | ||||||||
\(470\) | 5.32669e6 | 1.11228 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 463691. | 0.0958017 | ||||||||
\(473\) | 6.78908e6 | 1.39527 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.36929e6 | 1.29526 | ||||||||
\(476\) | 519664. | 0.105125 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.32105e6 | −1.46556 | ||||||||
\(479\) | 8.71672e6 | 1.73586 | 0.867929 | − | 0.496688i | \(-0.165451\pi\) | ||||
0.867929 | + | 0.496688i | \(0.165451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.40896e6 | 1.06599 | ||||||||
\(482\) | 9.57363e6 | 1.87698 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.08154e6 | 0.403898 | ||||||||
\(485\) | −1.41543e7 | −2.73233 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.19716e6 | −1.56618 | −0.783089 | − | 0.621910i | \(-0.786357\pi\) | ||||
−0.783089 | + | 0.621910i | \(0.786357\pi\) | |||||||
\(488\) | −741542. | −0.140957 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.49756e6 | −0.658074 | ||||||||
\(491\) | 6.65738e6 | 1.24623 | 0.623117 | − | 0.782128i | \(-0.285866\pi\) | ||||
0.623117 | + | 0.782128i | \(0.285866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.57045e6 | −0.661616 | ||||||||
\(494\) | 4.44479e6 | 0.819471 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.93472e6 | −1.63071 | ||||||||
\(497\) | −1.23200e6 | −0.223727 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.16723e6 | −0.389630 | −0.194815 | − | 0.980840i | \(-0.562411\pi\) | ||||
−0.194815 | + | 0.980840i | \(0.562411\pi\) | |||||||
\(500\) | 1.02301e6 | 0.183001 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.50351e6 | −0.620503 | ||||||||
\(503\) | 3.01053e6 | 0.530547 | 0.265273 | − | 0.964173i | \(-0.414538\pi\) | ||||
0.265273 | + | 0.964173i | \(0.414538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.24857e6 | 0.566844 | ||||||||
\(506\) | −1.59926e7 | −2.77679 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.41586e6 | −0.415348 | ||||||||
\(509\) | −8.34439e6 | −1.42758 | −0.713790 | − | 0.700360i | \(-0.753023\pi\) | ||||
−0.713790 | + | 0.700360i | \(0.753023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.58109e6 | −0.437271 | ||||||||
\(512\) | −197715. | −0.0333322 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.63045e6 | 1.27392 | ||||||||
\(515\) | 6.95384e6 | 1.15533 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.47025e6 | −0.900079 | ||||||||
\(518\) | −8.47659e6 | −1.38802 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.94256e6 | −0.801573 | ||||||||
\(521\) | −7.03207e6 | −1.13498 | −0.567491 | − | 0.823380i | \(-0.692086\pi\) | ||||
−0.567491 | + | 0.823380i | \(0.692086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.76023e6 | 0.760982 | 0.380491 | − | 0.924785i | \(-0.375755\pi\) | ||||
0.380491 | + | 0.924785i | \(0.375755\pi\) | |||||||
\(524\) | 3.35753e6 | 0.534185 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.99646e6 | −0.472220 | ||||||||
\(527\) | −3.00010e6 | −0.470553 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.09025e7 | 1.69390 | ||||||||
\(530\) | 1.34146e7 | 2.07439 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.88750e6 | −0.289140 | ||||||||
\(533\) | 1.05446e6 | 0.160772 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.03321e7 | −1.56065 | ||||||||
\(536\) | 7.71113e6 | 1.15933 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.13546e7 | 1.69129 | ||||||||
\(539\) | 3.59182e6 | 0.532528 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.92671e6 | 0.283024 | 0.141512 | − | 0.989937i | \(-0.454804\pi\) | ||||
0.141512 | + | 0.989937i | \(0.454804\pi\) | |||||||
\(542\) | 8.80362e6 | 1.28725 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.74154e6 | 0.252311 | ||||||||
\(545\) | −1.30442e7 | −1.88116 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.45466e6 | 0.350771 | 0.175385 | − | 0.984500i | \(-0.443883\pi\) | ||||
0.175385 | + | 0.984500i | \(0.443883\pi\) | |||||||
\(548\) | 3.45453e6 | 0.491403 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.58792e7 | −2.23832 | ||||||||
\(551\) | 1.29685e7 | 1.81974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.83373e6 | −0.254989 | ||||||||
\(554\) | −1.02226e7 | −1.41510 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.11201e6 | 0.701302 | ||||||||
\(557\) | −7.38777e6 | −1.00896 | −0.504482 | − | 0.863422i | \(-0.668316\pi\) | ||||
−0.504482 | + | 0.863422i | \(0.668316\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.10013e6 | −0.690322 | ||||||||
\(560\) | 1.10862e7 | 1.49387 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 36542.5 | 0.00488042 | ||||||||
\(563\) | −2.38312e6 | −0.316866 | −0.158433 | − | 0.987370i | \(-0.550644\pi\) | ||||
−0.158433 | + | 0.987370i | \(0.550644\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.63745e6 | 0.611164 | ||||||||
\(566\) | −6.26081e6 | −0.821465 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.59314e6 | −0.207197 | ||||||||
\(569\) | 7.30870e6 | 0.946367 | 0.473184 | − | 0.880964i | \(-0.343105\pi\) | ||||
0.473184 | + | 0.880964i | \(0.343105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.52181e6 | 0.323684 | 0.161842 | − | 0.986817i | \(-0.448256\pi\) | ||||
0.161842 | + | 0.986817i | \(0.448256\pi\) | |||||||
\(572\) | −3.00274e6 | −0.383731 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.65248e6 | −0.209342 | ||||||||
\(575\) | 1.72159e7 | 2.17150 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −758503. | −0.0948457 | −0.0474229 | − | 0.998875i | \(-0.515101\pi\) | ||||
−0.0474229 | + | 0.998875i | \(0.515101\pi\) | |||||||
\(578\) | −8.21510e6 | −1.02281 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.53111e6 | 1.05302 | ||||||||
\(581\) | −285169. | −0.0350480 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.37762e7 | −1.67864 | ||||||||
\(584\) | −3.33771e6 | −0.404964 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.01190e7 | 1.21729 | ||||||||
\(587\) | −4.83844e6 | −0.579576 | −0.289788 | − | 0.957091i | \(-0.593585\pi\) | ||||
−0.289788 | + | 0.957091i | \(0.593585\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.08968e7 | 1.29423 | ||||||||
\(590\) | −1.96499e6 | −0.232397 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.56888e7 | −1.83987 | ||||||||
\(593\) | 3.38920e6 | 0.395785 | 0.197893 | − | 0.980224i | \(-0.436590\pi\) | ||||
0.197893 | + | 0.980224i | \(0.436590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.72253e6 | 0.431068 | ||||||||
\(596\) | 4.56663e6 | 0.526600 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.20141e7 | 1.37384 | ||||||||
\(599\) | −7.50330e6 | −0.854447 | −0.427224 | − | 0.904146i | \(-0.640508\pi\) | ||||
−0.427224 | + | 0.904146i | \(0.640508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43644e7 | 1.62219 | 0.811095 | − | 0.584915i | \(-0.198872\pi\) | ||||
0.811095 | + | 0.584915i | \(0.198872\pi\) | |||||||
\(602\) | 7.99261e6 | 0.898871 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.08893e6 | −0.121453 | ||||||||
\(605\) | 1.49108e7 | 1.65620 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.75401e6 | −0.854191 | −0.427095 | − | 0.904207i | \(-0.640463\pi\) | ||||
−0.427095 | + | 0.904207i | \(0.640463\pi\) | |||||||
\(608\) | −6.32555e6 | −0.693968 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.14244e6 | 0.341935 | ||||||||
\(611\) | 4.10939e6 | 0.445322 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.52805e6 | 0.271728 | 0.135864 | − | 0.990727i | \(-0.456619\pi\) | ||||
0.135864 | + | 0.990727i | \(0.456619\pi\) | |||||||
\(614\) | −1.87401e7 | −2.00609 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.95442e6 | −0.844611 | ||||||||
\(617\) | −8.69599e6 | −0.919615 | −0.459808 | − | 0.888018i | \(-0.652082\pi\) | ||||
−0.459808 | + | 0.888018i | \(0.652082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.01187e6 | −0.106145 | −0.0530723 | − | 0.998591i | \(-0.516901\pi\) | ||||
−0.0530723 | + | 0.998591i | \(0.516901\pi\) | |||||||
\(620\) | 7.16832e6 | 0.748925 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.25241e6 | −0.337077 | ||||||||
\(623\) | 1.85364e6 | 0.191340 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.59205e6 | −0.572626 | ||||||||
\(626\) | 2.02585e7 | 2.06619 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −222829. | −0.0225462 | ||||||||
\(629\) | −5.26800e6 | −0.530907 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.14790e7 | 1.14771 | 0.573854 | − | 0.818958i | \(-0.305448\pi\) | ||||
0.573854 | + | 0.818958i | \(0.305448\pi\) | |||||||
\(632\) | −2.37126e6 | −0.236150 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.28111e7 | 2.25384 | ||||||||
\(635\) | −1.73056e7 | −1.70315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.69826e6 | −0.263473 | ||||||||
\(638\) | −3.23315e7 | −3.14466 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.86558e7 | 1.80038 | ||||||||
\(641\) | −1.67427e7 | −1.60946 | −0.804728 | − | 0.593643i | \(-0.797689\pi\) | ||||
−0.804728 | + | 0.593643i | \(0.797689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.05866e6 | −0.768662 | −0.384331 | − | 0.923195i | \(-0.625568\pi\) | ||||
−0.384331 | + | 0.923195i | \(0.625568\pi\) | |||||||
\(644\) | −5.10183e6 | −0.484743 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.32895e6 | −0.408132 | ||||||||
\(647\) | −3.80079e6 | −0.356955 | −0.178477 | − | 0.983944i | \(-0.557117\pi\) | ||||
−0.178477 | + | 0.983944i | \(0.557117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.01794e6 | 0.188060 | ||||||||
\(650\) | 1.19288e7 | 1.10743 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.01306e6 | 0.0933291 | ||||||||
\(653\) | 7.58623e6 | 0.696215 | 0.348107 | − | 0.937455i | \(-0.386824\pi\) | ||||
0.348107 | + | 0.937455i | \(0.386824\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.40511e7 | 2.19044 | ||||||||
\(656\) | −3.05848e6 | −0.277489 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.43998e6 | −0.579856 | ||||||||
\(659\) | −1.09734e7 | −0.984299 | −0.492149 | − | 0.870511i | \(-0.663789\pi\) | ||||
−0.492149 | + | 0.870511i | \(0.663789\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.85236e6 | −0.520988 | −0.260494 | − | 0.965476i | \(-0.583885\pi\) | ||||
−0.260494 | + | 0.965476i | \(0.583885\pi\) | |||||||
\(662\) | −1.67852e7 | −1.48862 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −368764. | −0.0324585 | ||||||||
\(665\) | −1.35208e7 | −1.18563 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.50531e7 | 3.05079 | ||||||||
\(668\) | −6.44219e6 | −0.558589 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.26776e7 | −2.81231 | ||||||||
\(671\) | −3.22713e6 | −0.276701 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.43218e6 | 0.547420 | 0.273710 | − | 0.961812i | \(-0.411749\pi\) | ||||
0.273710 | + | 0.961812i | \(0.411749\pi\) | |||||||
\(674\) | −1.62066e7 | −1.37418 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.16052e6 | −0.181841 | ||||||||
\(677\) | 2.35723e7 | 1.97665 | 0.988325 | − | 0.152363i | \(-0.0486882\pi\) | ||||
0.988325 | + | 0.152363i | \(0.0486882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.71125e7 | 1.42442 | ||||||||
\(680\) | 4.81375e6 | 0.399219 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.71667e7 | −2.23654 | ||||||||
\(683\) | −2.00530e7 | −1.64486 | −0.822428 | − | 0.568870i | \(-0.807381\pi\) | ||||
−0.822428 | + | 0.568870i | \(0.807381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.47460e7 | 2.01501 | ||||||||
\(686\) | 1.56988e7 | 1.27367 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.47931e7 | 1.19148 | ||||||||
\(689\) | 1.03490e7 | 0.830520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.03136e7 | 1.61842 | 0.809211 | − | 0.587518i | \(-0.199895\pi\) | ||||
0.809211 | + | 0.587518i | \(0.199895\pi\) | |||||||
\(692\) | −2.83978e6 | −0.225434 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −611969. | −0.0482315 | ||||||||
\(695\) | 3.66191e7 | 2.87571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.02698e6 | −0.0800716 | ||||||||
\(698\) | 3.44146e6 | 0.267365 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.06564e6 | −0.390742 | ||||||||
\(701\) | −1.59318e7 | −1.22453 | −0.612265 | − | 0.790653i | \(-0.709741\pi\) | ||||
−0.612265 | + | 0.790653i | \(0.709741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.91342e7 | 1.46023 | ||||||||
\(704\) | −7.66178e6 | −0.582637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.09680e7 | 0.828162 | ||||||||
\(707\) | −3.92753e6 | −0.295509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.13021e7 | 1.59150 | 0.795749 | − | 0.605626i | \(-0.207077\pi\) | ||||
0.795749 | + | 0.605626i | \(0.207077\pi\) | |||||||
\(710\) | 6.75129e6 | 0.502621 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.39702e6 | 0.177203 | ||||||||
\(713\) | 2.94536e7 | 2.16978 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.15096e7 | −1.57350 | ||||||||
\(716\) | −3.38431e6 | −0.246710 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.66618e7 | −1.20618 | ||||||||
\(719\) | 1.46154e7 | 1.05436 | 0.527180 | − | 0.849753i | \(-0.323249\pi\) | ||||
0.527180 | + | 0.849753i | \(0.323249\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.40720e6 | −0.602300 | ||||||||
\(722\) | −681393. | −0.0486469 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.78483e6 | −0.339250 | ||||||||
\(725\) | 3.48045e7 | 2.45918 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.13626e6 | −0.430594 | −0.215297 | − | 0.976549i | \(-0.569072\pi\) | ||||
−0.215297 | + | 0.976549i | \(0.569072\pi\) | |||||||
\(728\) | 5.97556e6 | 0.417878 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.41443e7 | 0.982365 | ||||||||
\(731\) | 4.96721e6 | 0.343810 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.06072e7 | 0.729190 | 0.364595 | − | 0.931166i | \(-0.381207\pi\) | ||||
0.364595 | + | 0.931166i | \(0.381207\pi\) | |||||||
\(734\) | −5.24953e6 | −0.359650 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.70977e7 | −1.16344 | ||||||||
\(737\) | 3.35582e7 | 2.27578 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −75441.2 | −0.00508156 | −0.00254078 | − | 0.999997i | \(-0.500809\pi\) | ||||
−0.00254078 | + | 0.999997i | \(0.500809\pi\) | |||||||
\(740\) | 1.25872e7 | 0.844984 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.62183e7 | −1.08142 | ||||||||
\(743\) | 3.43706e6 | 0.228410 | 0.114205 | − | 0.993457i | \(-0.463568\pi\) | ||||
0.114205 | + | 0.993457i | \(0.463568\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.27123e7 | 2.15934 | ||||||||
\(746\) | 5.60953e6 | 0.369045 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.92448e6 | 0.191115 | ||||||||
\(749\) | 1.24915e7 | 0.813600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.47000e6 | 0.548004 | 0.274002 | − | 0.961729i | \(-0.411653\pi\) | ||||
0.274002 | + | 0.961729i | \(0.411653\pi\) | |||||||
\(752\) | −1.19194e7 | −0.768616 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.42882e7 | 1.55585 | ||||||||
\(755\) | −7.80040e6 | −0.498023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.70756e6 | −0.615702 | −0.307851 | − | 0.951435i | \(-0.599610\pi\) | ||||
−0.307851 | + | 0.951435i | \(0.599610\pi\) | |||||||
\(758\) | 1.08213e7 | 0.684077 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.74843e7 | −1.09803 | ||||||||
\(761\) | 4.60781e6 | 0.288425 | 0.144212 | − | 0.989547i | \(-0.453935\pi\) | ||||
0.144212 | + | 0.989547i | \(0.453935\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.57704e7 | 0.980691 | ||||||||
\(764\) | 7.42564e6 | 0.460257 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.80554e7 | 1.72761 | ||||||||
\(767\) | −1.51593e6 | −0.0930445 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.09236e7 | −0.666114 | −0.333057 | − | 0.942907i | \(-0.608080\pi\) | ||||
−0.333057 | + | 0.942907i | \(0.608080\pi\) | |||||||
\(770\) | 3.37086e7 | 2.04887 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.93999e6 | 0.600265 | ||||||||
\(773\) | −6.36770e6 | −0.383295 | −0.191648 | − | 0.981464i | \(-0.561383\pi\) | ||||
−0.191648 | + | 0.981464i | \(0.561383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.92447e7 | 1.74901 | ||||||||
\(776\) | 2.21289e7 | 1.31918 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.86606e7 | −1.69760 | ||||||||
\(779\) | 3.73014e6 | 0.220233 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.93323e6 | −0.406732 | ||||||||
\(782\) | −1.17009e7 | −0.684233 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.82638e6 | 0.454748 | ||||||||
\(785\) | −1.59620e6 | −0.0924514 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.17413e7 | −1.25126 | −0.625631 | − | 0.780119i | \(-0.715159\pi\) | ||||
−0.625631 | + | 0.780119i | \(0.715159\pi\) | |||||||
\(788\) | 8.61799e6 | 0.494414 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.00487e7 | 0.572854 | ||||||||
\(791\) | −5.60668e6 | −0.318614 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.42430e6 | 0.136900 | ||||||||
\(794\) | 2.21328e7 | 1.24590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.22942e6 | −0.460348 | ||||||||
\(797\) | 1.29730e7 | 0.723424 | 0.361712 | − | 0.932290i | \(-0.382192\pi\) | ||||
0.361712 | + | 0.932290i | \(0.382192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00229e6 | −0.221790 | ||||||||
\(800\) | −1.69764e7 | −0.937822 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.97873e6 | 0.218428 | ||||||||
\(803\) | −1.45254e7 | −0.794951 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.65461e7 | −1.98770 | ||||||||
\(806\) | 2.04083e7 | 1.10655 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.07884e6 | −0.273675 | ||||||||
\(809\) | 1.50725e7 | 0.809682 | 0.404841 | − | 0.914387i | \(-0.367327\pi\) | ||||
0.404841 | + | 0.914387i | \(0.367327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.99366e6 | −0.533547 | −0.266773 | − | 0.963759i | \(-0.585958\pi\) | ||||
−0.266773 | + | 0.963759i | \(0.585958\pi\) | |||||||
\(812\) | −1.03141e7 | −0.548962 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.77032e7 | −2.52340 | ||||||||
\(815\) | 7.25691e6 | 0.382699 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.80417e7 | −0.945633 | ||||||||
\(818\) | −1.24453e7 | −0.650312 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.45382e6 | 0.127441 | ||||||||
\(821\) | −2.35975e7 | −1.22182 | −0.610912 | − | 0.791698i | \(-0.709197\pi\) | ||||
−0.610912 | + | 0.791698i | \(0.709197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.42657e6 | −0.382198 | −0.191099 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191099 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(824\) | −1.08717e7 | −0.557800 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.37567e6 | 0.121154 | ||||||||
\(827\) | 2.03546e7 | 1.03490 | 0.517451 | − | 0.855713i | \(-0.326881\pi\) | ||||
0.517451 | + | 0.855713i | \(0.326881\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.84957e7 | 0.934725 | 0.467362 | − | 0.884066i | \(-0.345204\pi\) | ||||
0.467362 | + | 0.884066i | \(0.345204\pi\) | |||||||
\(830\) | 1.56272e6 | 0.0787381 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.75572e6 | 0.288264 | ||||||||
\(833\) | 2.62794e6 | 0.131221 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.61476e7 | −2.29051 | ||||||||
\(836\) | −1.06222e7 | −0.525652 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.08103e7 | 1.51560 | ||||||||
\(839\) | −4.89142e6 | −0.239900 | −0.119950 | − | 0.992780i | \(-0.538273\pi\) | ||||
−0.119950 | + | 0.992780i | \(0.538273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.03540e7 | 2.45496 | ||||||||
\(842\) | −8.26325e6 | −0.401671 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.96574e6 | 0.143310 | ||||||||
\(845\) | −1.54765e7 | −0.745644 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.80272e7 | −0.863413 | ||||||||
\(848\) | −3.00176e7 | −1.43346 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.16179e7 | −0.551547 | ||||||||
\(851\) | 5.17189e7 | 2.44808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.49648e7 | −1.17478 | −0.587389 | − | 0.809305i | \(-0.699844\pi\) | ||||
−0.587389 | + | 0.809305i | \(0.699844\pi\) | |||||||
\(854\) | −3.79922e6 | −0.178258 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.61533e7 | 0.753488 | ||||||||
\(857\) | 4.44419e6 | 0.206700 | 0.103350 | − | 0.994645i | \(-0.467044\pi\) | ||||
0.103350 | + | 0.994645i | \(0.467044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.83513e7 | −1.31096 | −0.655480 | − | 0.755212i | \(-0.727534\pi\) | ||||
−0.655480 | + | 0.755212i | \(0.727534\pi\) | |||||||
\(860\) | −1.18685e7 | −0.547203 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.46345e6 | −0.296276 | ||||||||
\(863\) | −1.98739e7 | −0.908358 | −0.454179 | − | 0.890911i | \(-0.650067\pi\) | ||||
−0.454179 | + | 0.890911i | \(0.650067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.03423e7 | −0.924400 | ||||||||
\(866\) | 1.70109e7 | 0.770785 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.66651e6 | −0.390431 | ||||||||
\(869\) | −1.03196e7 | −0.463566 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.52098e7 | −1.12596 | ||||||||
\(872\) | 2.03934e7 | 0.908234 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.24997e7 | 1.88195 | ||||||||
\(875\) | −8.85973e6 | −0.391202 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.39535e7 | 1.05165 | 0.525823 | − | 0.850594i | \(-0.323757\pi\) | ||||
0.525823 | + | 0.850594i | \(0.323757\pi\) | |||||||
\(878\) | 5.79815e6 | 0.253836 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.23893e7 | 2.71583 | ||||||||
\(881\) | −1.44336e7 | −0.626522 | −0.313261 | − | 0.949667i | \(-0.601421\pi\) | ||||
−0.313261 | + | 0.949667i | \(0.601421\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.96597e7 | −0.848547 | −0.424274 | − | 0.905534i | \(-0.639471\pi\) | ||||
−0.424274 | + | 0.905534i | \(0.639471\pi\) | |||||||
\(884\) | −2.19694e6 | −0.0945558 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.91131e7 | −1.24596 | ||||||||
\(887\) | −430936. | −0.0183909 | −0.00919547 | − | 0.999958i | \(-0.502927\pi\) | ||||
−0.00919547 | + | 0.999958i | \(0.502927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.09225e7 | 0.887889 | ||||||||
\(890\) | −1.01579e7 | −0.429861 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.44829e6 | −0.271352 | ||||||||
\(893\) | 1.45370e7 | 0.610021 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.42430e7 | −1.01164 | ||||||||
\(896\) | −2.25549e7 | −0.938580 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.47258e7 | −0.609381 | ||||||||
\(899\) | 5.95449e7 | 2.45723 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.00793e7 | −0.413636 | ||||||||
\(902\) | −9.29956e6 | −0.380580 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.25021e6 | −0.295073 | ||||||||
\(905\) | −3.42753e7 | −1.39111 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.15056e7 | −0.464398 | −0.232199 | − | 0.972668i | \(-0.574592\pi\) | ||||
−0.232199 | + | 0.972668i | \(0.574592\pi\) | |||||||
\(908\) | 5.71717e6 | 0.230126 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.53227e7 | −1.01369 | ||||||||
\(911\) | −3.19861e7 | −1.27693 | −0.638463 | − | 0.769653i | \(-0.720429\pi\) | ||||
−0.638463 | + | 0.769653i | \(0.720429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.60483e6 | −0.0637166 | ||||||||
\(914\) | −2.31257e7 | −0.915652 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.42011e6 | −0.292194 | ||||||||
\(917\) | −2.90778e7 | −1.14193 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.83417e7 | 1.49756 | 0.748778 | − | 0.662821i | \(-0.230641\pi\) | ||||
0.748778 | + | 0.662821i | \(0.230641\pi\) | |||||||
\(920\) | −4.72593e7 | −1.84085 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.26049e6 | −0.0875739 | ||||||||
\(923\) | 5.20842e6 | 0.201234 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.13520e7 | 1.97335 | ||||||||
\(926\) | −4.45872e7 | −1.70877 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.45655e7 | −1.31757 | ||||||||
\(929\) | −3.81222e7 | −1.44923 | −0.724617 | − | 0.689151i | \(-0.757984\pi\) | ||||
−0.724617 | + | 0.689151i | \(0.757984\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.54510e6 | −0.360916 | ||||||||
\(932\) | −7.67983e6 | −0.289609 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.40187e7 | 0.525824 | ||||||||
\(935\) | 2.09490e7 | 0.783674 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.63559e7 | −0.608591 | −0.304295 | − | 0.952578i | \(-0.598421\pi\) | ||||
−0.304295 | + | 0.952578i | \(0.598421\pi\) | |||||||
\(938\) | 3.95072e7 | 1.46612 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.56293e6 | 0.352997 | ||||||||
\(941\) | −1.57758e7 | −0.580789 | −0.290395 | − | 0.956907i | \(-0.593787\pi\) | ||||
−0.290395 | + | 0.956907i | \(0.593787\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.00824e7 | 0.369220 | ||||||||
\(944\) | 4.39700e6 | 0.160593 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.49795e7 | 1.63413 | ||||||||
\(947\) | 2.76570e7 | 1.00214 | 0.501072 | − | 0.865405i | \(-0.332939\pi\) | ||||
0.501072 | + | 0.865405i | \(0.332939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.09119e7 | 0.393309 | ||||||||
\(950\) | 4.21983e7 | 1.51700 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.81982e6 | −0.208122 | ||||||||
\(953\) | −1.15464e6 | −0.0411825 | −0.0205912 | − | 0.999788i | \(-0.506555\pi\) | ||||
−0.0205912 | + | 0.999788i | \(0.506555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.31923e7 | 1.88730 | ||||||||
\(956\) | −1.31434e7 | −0.465116 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.77507e7 | 2.03303 | ||||||||
\(959\) | −2.99179e7 | −1.05047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.14039e7 | 0.747625 | ||||||||
\(962\) | 3.58358e7 | 1.24848 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.71874e7 | 0.595686 | ||||||||
\(965\) | 7.12035e7 | 2.46140 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.77090e7 | −1.64072 | −0.820360 | − | 0.571848i | \(-0.806227\pi\) | ||||
−0.820360 | + | 0.571848i | \(0.806227\pi\) | |||||||
\(968\) | −2.33116e7 | −0.799621 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.37759e7 | −3.20009 | ||||||||
\(971\) | −3.61364e7 | −1.22998 | −0.614988 | − | 0.788537i | \(-0.710839\pi\) | ||||
−0.614988 | + | 0.788537i | \(0.710839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.42725e7 | −1.49917 | ||||||||
\(974\) | −5.43084e7 | −1.83430 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.03176e6 | −0.236287 | ||||||||
\(977\) | −2.58953e7 | −0.867930 | −0.433965 | − | 0.900930i | \(-0.642886\pi\) | ||||
−0.433965 | + | 0.900930i | \(0.642886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.04316e7 | 0.347853 | ||||||||
\(980\) | −6.27911e6 | −0.208849 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.41070e7 | 1.45958 | ||||||||
\(983\) | 3.78204e7 | 1.24837 | 0.624183 | − | 0.781278i | \(-0.285432\pi\) | ||||
0.624183 | + | 0.781278i | \(0.285432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.17336e7 | 2.02736 | ||||||||
\(986\) | −2.36552e7 | −0.774880 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.97965e6 | 0.260071 | ||||||||
\(989\) | −4.87659e7 | −1.58535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.64574e7 | −1.17924 | −0.589619 | − | 0.807681i | \(-0.700722\pi\) | ||||
−0.589619 | + | 0.807681i | \(0.700722\pi\) | |||||||
\(992\) | −2.90439e7 | −0.937077 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.16232e6 | −0.262028 | ||||||||
\(995\) | −5.89501e7 | −1.88767 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.17735e6 | 0.0375119 | 0.0187559 | − | 0.999824i | \(-0.494029\pi\) | ||||
0.0187559 | + | 0.999824i | \(0.494029\pi\) | |||||||
\(998\) | −1.43585e7 | −0.456333 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.6.a.b.1.8 | 11 | ||
3.2 | odd | 2 | 177.6.a.a.1.4 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.a.1.4 | ✓ | 11 | 3.2 | odd | 2 | ||
531.6.a.b.1.8 | 11 | 1.1 | even | 1 | trivial |