Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.44400625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.246759\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.246759 | −0.174485 | −0.0872425 | − | 0.996187i | \(-0.527805\pi\) | ||||
−0.0872425 | + | 0.996187i | \(0.527805\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.93911 | −0.969555 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24676 | −0.471231 | −0.235615 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235615 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(8\) | 0.972011 | 0.343658 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56971 | −0.774797 | −0.387398 | − | 0.921912i | \(-0.626626\pi\) | ||||
−0.387398 | + | 0.921912i | \(0.626626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.68126 | −1.29835 | −0.649174 | − | 0.760640i | \(-0.724885\pi\) | ||||
−0.649174 | + | 0.760640i | \(0.724885\pi\) | |||||||
\(14\) | 0.307649 | 0.0822226 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.63837 | 0.909592 | ||||||||
\(17\) | −5.83914 | −1.41620 | −0.708100 | − | 0.706112i | \(-0.750447\pi\) | ||||
−0.708100 | + | 0.706112i | \(0.750447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.16857 | 0.956336 | 0.478168 | − | 0.878268i | \(-0.341301\pi\) | ||||
0.478168 | + | 0.878268i | \(0.341301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.634099 | 0.135190 | ||||||||
\(23\) | −1.60547 | −0.334763 | −0.167382 | − | 0.985892i | \(-0.553531\pi\) | ||||
−0.167382 | + | 0.985892i | \(0.553531\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.15514 | 0.226542 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.41760 | 0.456884 | ||||||||
\(29\) | 3.21573 | 0.597147 | 0.298573 | − | 0.954387i | \(-0.403489\pi\) | ||||
0.298573 | + | 0.954387i | \(0.403489\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.19312 | −1.65113 | −0.825566 | − | 0.564305i | \(-0.809144\pi\) | ||||
−0.825566 | + | 0.564305i | \(0.809144\pi\) | |||||||
\(32\) | −2.84182 | −0.502368 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.44086 | 0.247106 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.27778 | −0.210066 | −0.105033 | − | 0.994469i | \(-0.533495\pi\) | ||||
−0.105033 | + | 0.994469i | \(0.533495\pi\) | |||||||
\(38\) | −1.02863 | −0.166866 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.69592 | −1.35808 | −0.679038 | − | 0.734104i | \(-0.737603\pi\) | ||||
−0.679038 | + | 0.734104i | \(0.737603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.88086 | −0.591825 | −0.295913 | − | 0.955215i | \(-0.595624\pi\) | ||||
−0.295913 | + | 0.955215i | \(0.595624\pi\) | |||||||
\(44\) | 4.98295 | 0.751208 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.396163 | 0.0584111 | ||||||||
\(47\) | 3.20952 | 0.468157 | 0.234079 | − | 0.972218i | \(-0.424793\pi\) | ||||
0.234079 | + | 0.972218i | \(0.424793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.44559 | −0.777942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.07748 | 1.25882 | ||||||||
\(53\) | 13.3343 | 1.83161 | 0.915803 | − | 0.401628i | \(-0.131556\pi\) | ||||
0.915803 | + | 0.401628i | \(0.131556\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.21186 | −0.161942 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.793511 | −0.104193 | ||||||||
\(59\) | 6.39279 | 0.832270 | 0.416135 | − | 0.909303i | \(-0.363384\pi\) | ||||
0.416135 | + | 0.909303i | \(0.363384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.82692 | 0.489986 | 0.244993 | − | 0.969525i | \(-0.421214\pi\) | ||||
0.244993 | + | 0.969525i | \(0.421214\pi\) | |||||||
\(62\) | 2.26848 | 0.288098 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.57549 | −0.821936 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1238 | −1.23682 | −0.618411 | − | 0.785855i | \(-0.712223\pi\) | ||||
−0.618411 | + | 0.785855i | \(0.712223\pi\) | |||||||
\(68\) | 11.3227 | 1.37308 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8791 | −1.64715 | −0.823574 | − | 0.567209i | \(-0.808023\pi\) | ||||
−0.823574 | + | 0.567209i | \(0.808023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3814 | −1.33209 | −0.666045 | − | 0.745912i | \(-0.732014\pi\) | ||||
−0.666045 | + | 0.745912i | \(0.732014\pi\) | |||||||
\(74\) | 0.315305 | 0.0366534 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.08332 | −0.927220 | ||||||||
\(77\) | 3.20381 | 0.365108 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4832 | 1.29196 | 0.645979 | − | 0.763355i | \(-0.276449\pi\) | ||||
0.645979 | + | 0.763355i | \(0.276449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.14580 | 0.236964 | ||||||||
\(83\) | 2.83229 | 0.310884 | 0.155442 | − | 0.987845i | \(-0.450320\pi\) | ||||
0.155442 | + | 0.987845i | \(0.450320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.957636 | 0.103265 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.49779 | −0.266265 | ||||||||
\(89\) | 1.38077 | 0.146362 | 0.0731808 | − | 0.997319i | \(-0.476685\pi\) | ||||
0.0731808 | + | 0.997319i | \(0.476685\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.83641 | 0.611822 | ||||||||
\(92\) | 3.11318 | 0.324571 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.791979 | −0.0816864 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0305081 | 0.00309763 | 0.00154881 | − | 0.999999i | \(-0.499507\pi\) | ||||
0.00154881 | + | 0.999999i | \(0.499507\pi\) | |||||||
\(98\) | 1.34375 | 0.135739 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.2308 | 1.11750 | 0.558751 | − | 0.829336i | \(-0.311281\pi\) | ||||
0.558751 | + | 0.829336i | \(0.311281\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.720983 | −0.0710406 | −0.0355203 | − | 0.999369i | \(-0.511309\pi\) | ||||
−0.0355203 | + | 0.999369i | \(0.511309\pi\) | |||||||
\(104\) | −4.55024 | −0.446187 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.29036 | −0.319588 | ||||||||
\(107\) | −2.11668 | −0.204627 | −0.102313 | − | 0.994752i | \(-0.532624\pi\) | ||||
−0.102313 | + | 0.994752i | \(0.532624\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.23483 | 0.214058 | 0.107029 | − | 0.994256i | \(-0.465866\pi\) | ||||
0.107029 | + | 0.994256i | \(0.465866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.53617 | −0.428628 | ||||||||
\(113\) | 3.14940 | 0.296270 | 0.148135 | − | 0.988967i | \(-0.452673\pi\) | ||||
0.148135 | + | 0.988967i | \(0.452673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.23566 | −0.578967 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.57748 | −0.145219 | ||||||||
\(119\) | 7.28000 | 0.667357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.39659 | −0.399690 | ||||||||
\(122\) | −0.944326 | −0.0854952 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.8265 | 1.60086 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6603 | −1.38962 | −0.694812 | − | 0.719191i | \(-0.744513\pi\) | ||||
−0.694812 | + | 0.719191i | \(0.744513\pi\) | |||||||
\(128\) | 7.30620 | 0.645783 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9564 | 1.30675 | 0.653374 | − | 0.757036i | \(-0.273353\pi\) | ||||
0.653374 | + | 0.757036i | \(0.273353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.19720 | −0.450655 | ||||||||
\(134\) | 2.49814 | 0.215807 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.67571 | −0.486688 | ||||||||
\(137\) | 10.4946 | 0.896611 | 0.448305 | − | 0.893881i | \(-0.352028\pi\) | ||||
0.448305 | + | 0.893881i | \(0.352028\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4508 | 1.05606 | 0.528030 | − | 0.849226i | \(-0.322931\pi\) | ||||
0.528030 | + | 0.849226i | \(0.322931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.42480 | 0.287402 | ||||||||
\(143\) | 12.0295 | 1.00596 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.80846 | 0.232430 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.47776 | 0.203671 | ||||||||
\(149\) | 17.0680 | 1.39826 | 0.699131 | − | 0.714994i | \(-0.253570\pi\) | ||||
0.699131 | + | 0.714994i | \(0.253570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.57516 | −0.128185 | −0.0640923 | − | 0.997944i | \(-0.520415\pi\) | ||||
−0.0640923 | + | 0.997944i | \(0.520415\pi\) | |||||||
\(152\) | 4.05190 | 0.328652 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.790569 | −0.0637059 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.20058 | −0.734286 | −0.367143 | − | 0.930164i | \(-0.619664\pi\) | ||||
−0.367143 | + | 0.930164i | \(0.619664\pi\) | |||||||
\(158\) | −2.83358 | −0.225427 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00163 | 0.157751 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.58076 | −0.358793 | −0.179396 | − | 0.983777i | \(-0.557414\pi\) | ||||
−0.179396 | + | 0.983777i | \(0.557414\pi\) | |||||||
\(164\) | 16.8624 | 1.31673 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.698893 | −0.0542446 | ||||||||
\(167\) | −0.142531 | −0.0110294 | −0.00551469 | − | 0.999985i | \(-0.501755\pi\) | ||||
−0.00551469 | + | 0.999985i | \(0.501755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.91422 | 0.685709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.52541 | 0.573807 | ||||||||
\(173\) | −24.6228 | −1.87203 | −0.936017 | − | 0.351954i | \(-0.885517\pi\) | ||||
−0.936017 | + | 0.351954i | \(0.885517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.34955 | −0.704749 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.340718 | −0.0255379 | ||||||||
\(179\) | 24.1553 | 1.80545 | 0.902726 | − | 0.430216i | \(-0.141563\pi\) | ||||
0.902726 | + | 0.430216i | \(0.141563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.96805 | 0.146284 | 0.0731419 | − | 0.997322i | \(-0.476697\pi\) | ||||
0.0731419 | + | 0.997322i | \(0.476697\pi\) | |||||||
\(182\) | −1.44019 | −0.106754 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.56053 | −0.115044 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0049 | 1.09727 | ||||||||
\(188\) | −6.22362 | −0.453904 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.76854 | 0.562112 | 0.281056 | − | 0.959691i | \(-0.409315\pi\) | ||||
0.281056 | + | 0.959691i | \(0.409315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3458 | 1.03264 | 0.516318 | − | 0.856397i | \(-0.327302\pi\) | ||||
0.516318 | + | 0.856397i | \(0.327302\pi\) | |||||||
\(194\) | −0.00752814 | −0.000540489 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5596 | 0.754257 | ||||||||
\(197\) | −0.163540 | −0.0116517 | −0.00582587 | − | 0.999983i | \(-0.501854\pi\) | ||||
−0.00582587 | + | 0.999983i | \(0.501854\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.96974 | 0.352295 | 0.176148 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176148 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.77129 | −0.194987 | ||||||||
\(203\) | −4.00925 | −0.281394 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.177909 | 0.0123955 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −17.0322 | −1.18097 | ||||||||
\(209\) | −10.7120 | −0.740966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.29381 | 0.226755 | 0.113378 | − | 0.993552i | \(-0.463833\pi\) | ||||
0.113378 | + | 0.993552i | \(0.463833\pi\) | |||||||
\(212\) | −25.8567 | −1.77584 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.522309 | 0.0357043 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4616 | 0.778064 | ||||||||
\(218\) | −0.551465 | −0.0373500 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.3346 | 1.83872 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.7732 | −1.05625 | −0.528127 | − | 0.849166i | \(-0.677105\pi\) | ||||
−0.528127 | + | 0.849166i | \(0.677105\pi\) | |||||||
\(224\) | 3.54307 | 0.236731 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.777142 | −0.0516947 | ||||||||
\(227\) | −13.5406 | −0.898721 | −0.449360 | − | 0.893351i | \(-0.648348\pi\) | ||||
−0.449360 | + | 0.893351i | \(0.648348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.7829 | −0.976879 | −0.488440 | − | 0.872598i | \(-0.662434\pi\) | ||||
−0.488440 | + | 0.872598i | \(0.662434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.12573 | 0.205214 | ||||||||
\(233\) | −0.518980 | −0.0339995 | −0.0169998 | − | 0.999855i | \(-0.505411\pi\) | ||||
−0.0169998 | + | 0.999855i | \(0.505411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.3963 | −0.806932 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.79641 | −0.116444 | ||||||||
\(239\) | −8.23032 | −0.532375 | −0.266188 | − | 0.963921i | \(-0.585764\pi\) | ||||
−0.266188 | + | 0.963921i | \(0.585764\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.28118 | −0.0825280 | −0.0412640 | − | 0.999148i | \(-0.513138\pi\) | ||||
−0.0412640 | + | 0.999148i | \(0.513138\pi\) | |||||||
\(242\) | 1.08490 | 0.0697398 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.42081 | −0.475069 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.5142 | −1.24166 | ||||||||
\(248\) | −8.93581 | −0.567424 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.63494 | −0.292555 | −0.146277 | − | 0.989244i | \(-0.546729\pi\) | ||||
−0.146277 | + | 0.989244i | \(0.546729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.12559 | 0.259373 | ||||||||
\(254\) | 3.86431 | 0.242469 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.3481 | 0.709257 | ||||||||
\(257\) | 18.3001 | 1.14153 | 0.570766 | − | 0.821113i | \(-0.306647\pi\) | ||||
0.570766 | + | 0.821113i | \(0.306647\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.59309 | 0.0989897 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.69063 | −0.228008 | ||||||||
\(263\) | −16.6666 | −1.02771 | −0.513854 | − | 0.857877i | \(-0.671783\pi\) | ||||
−0.513854 | + | 0.857877i | \(0.671783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.28246 | 0.0786324 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.6312 | 1.19917 | ||||||||
\(269\) | −2.63211 | −0.160483 | −0.0802414 | − | 0.996775i | \(-0.525569\pi\) | ||||
−0.0802414 | + | 0.996775i | \(0.525569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.56346 | 0.277210 | 0.138605 | − | 0.990348i | \(-0.455738\pi\) | ||||
0.138605 | + | 0.990348i | \(0.455738\pi\) | |||||||
\(272\) | −21.2449 | −1.28816 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.58963 | −0.156445 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.25926 | 0.0756614 | 0.0378307 | − | 0.999284i | \(-0.487955\pi\) | ||||
0.0378307 | + | 0.999284i | \(0.487955\pi\) | |||||||
\(278\) | −3.07234 | −0.184266 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4167 | −0.800370 | −0.400185 | − | 0.916434i | \(-0.631054\pi\) | ||||
−0.400185 | + | 0.916434i | \(0.631054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0890 | 1.43194 | 0.715971 | − | 0.698130i | \(-0.245984\pi\) | ||||
0.715971 | + | 0.698130i | \(0.245984\pi\) | |||||||
\(284\) | 26.9131 | 1.59700 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.96838 | −0.175524 | ||||||||
\(287\) | 10.8417 | 0.639966 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0956 | 1.00562 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.0697 | 1.29153 | ||||||||
\(293\) | 32.1727 | 1.87955 | 0.939776 | − | 0.341792i | \(-0.111034\pi\) | ||||
0.939776 | + | 0.341792i | \(0.111034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.24202 | −0.0721909 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.21167 | −0.243976 | ||||||||
\(299\) | 7.51561 | 0.434639 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.83849 | 0.278886 | ||||||||
\(302\) | 0.388685 | 0.0223663 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.1668 | 0.869875 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2962 | 1.15837 | 0.579183 | − | 0.815198i | \(-0.303372\pi\) | ||||
0.579183 | + | 0.815198i | \(0.303372\pi\) | |||||||
\(308\) | −6.21254 | −0.353992 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7224 | 1.06165 | 0.530825 | − | 0.847481i | \(-0.321882\pi\) | ||||
0.530825 | + | 0.847481i | \(0.321882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.8839 | 1.40652 | 0.703261 | − | 0.710932i | \(-0.251726\pi\) | ||||
0.703261 | + | 0.710932i | \(0.251726\pi\) | |||||||
\(314\) | 2.27033 | 0.128122 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.2671 | −1.25262 | ||||||||
\(317\) | 25.1880 | 1.41470 | 0.707350 | − | 0.706863i | \(-0.249890\pi\) | ||||
0.707350 | + | 0.706863i | \(0.249890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.26351 | −0.462668 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.493920 | −0.0275251 | ||||||||
\(323\) | −24.3409 | −1.35436 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.13034 | 0.0626039 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.45253 | −0.466713 | ||||||||
\(329\) | −4.00150 | −0.220610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4193 | 1.67199 | 0.835997 | − | 0.548735i | \(-0.184890\pi\) | ||||
0.835997 | + | 0.548735i | \(0.184890\pi\) | |||||||
\(332\) | −5.49212 | −0.301419 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.0351708 | 0.00192446 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.57455 | −0.249192 | −0.124596 | − | 0.992208i | \(-0.539763\pi\) | ||||
−0.124596 | + | 0.992208i | \(0.539763\pi\) | |||||||
\(338\) | −2.19966 | −0.119646 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.6237 | 1.27929 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5167 | 0.837821 | ||||||||
\(344\) | −3.77224 | −0.203385 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.07589 | 0.326642 | ||||||||
\(347\) | 16.8153 | 0.902691 | 0.451346 | − | 0.892349i | \(-0.350944\pi\) | ||||
0.451346 | + | 0.892349i | \(0.350944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.373581 | 0.0199973 | 0.00999866 | − | 0.999950i | \(-0.496817\pi\) | ||||
0.00999866 | + | 0.999950i | \(0.496817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.30266 | 0.389233 | ||||||||
\(353\) | 23.9685 | 1.27572 | 0.637858 | − | 0.770154i | \(-0.279821\pi\) | ||||
0.637858 | + | 0.770154i | \(0.279821\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.67747 | −0.141906 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.96054 | −0.315024 | ||||||||
\(359\) | 4.75020 | 0.250706 | 0.125353 | − | 0.992112i | \(-0.459994\pi\) | ||||
0.125353 | + | 0.992112i | \(0.459994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.62302 | −0.0854221 | ||||||||
\(362\) | −0.485633 | −0.0255243 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.3174 | −0.593195 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.3700 | −0.906706 | −0.453353 | − | 0.891331i | \(-0.649772\pi\) | ||||
−0.453353 | + | 0.891331i | \(0.649772\pi\) | |||||||
\(368\) | −5.84128 | −0.304498 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.6246 | −0.863109 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.10877 | 0.109188 | 0.0545939 | − | 0.998509i | \(-0.482614\pi\) | ||||
0.0545939 | + | 0.998509i | \(0.482614\pi\) | |||||||
\(374\) | −3.70260 | −0.191457 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.11969 | 0.160886 | ||||||||
\(377\) | −15.0537 | −0.775305 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4090 | 0.637405 | 0.318703 | − | 0.947855i | \(-0.396753\pi\) | ||||
0.318703 | + | 0.947855i | \(0.396753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.91696 | −0.0980801 | ||||||||
\(383\) | −33.3056 | −1.70184 | −0.850919 | − | 0.525297i | \(-0.823954\pi\) | ||||
−0.850919 | + | 0.525297i | \(0.823954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.53996 | −0.180179 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0591585 | −0.00300332 | ||||||||
\(389\) | 16.9777 | 0.860802 | 0.430401 | − | 0.902638i | \(-0.358372\pi\) | ||||
0.430401 | + | 0.902638i | \(0.358372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.37455 | 0.474091 | ||||||||
\(392\) | −5.29317 | −0.267346 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.0403549 | 0.00203305 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.866570 | −0.0434919 | −0.0217460 | − | 0.999764i | \(-0.506922\pi\) | ||||
−0.0217460 | + | 0.999764i | \(0.506922\pi\) | |||||||
\(398\) | −1.22633 | −0.0614702 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.68680 | −0.483736 | −0.241868 | − | 0.970309i | \(-0.577760\pi\) | ||||
−0.241868 | + | 0.970309i | \(0.577760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.0354 | 2.14375 | ||||||||
\(404\) | −21.7777 | −1.08348 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.989317 | 0.0490990 | ||||||||
\(407\) | 3.28353 | 0.162759 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.51785 | 0.0750531 | 0.0375265 | − | 0.999296i | \(-0.488052\pi\) | ||||
0.0375265 | + | 0.999296i | \(0.488052\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.39807 | 0.0688778 | ||||||||
\(413\) | −7.97027 | −0.392191 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.3033 | 0.652249 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.64329 | 0.129287 | ||||||||
\(419\) | 30.5620 | 1.49305 | 0.746526 | − | 0.665356i | \(-0.231720\pi\) | ||||
0.746526 | + | 0.665356i | \(0.231720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.97162 | −0.339776 | −0.169888 | − | 0.985463i | \(-0.554341\pi\) | ||||
−0.169888 | + | 0.985463i | \(0.554341\pi\) | |||||||
\(422\) | −0.812777 | −0.0395654 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.9611 | 0.629445 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.77124 | −0.230897 | ||||||||
\(428\) | 4.10447 | 0.198397 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.9472 | −0.527310 | −0.263655 | − | 0.964617i | \(-0.584928\pi\) | ||||
−0.263655 | + | 0.964617i | \(0.584928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.4393 | 0.501683 | 0.250841 | − | 0.968028i | \(-0.419293\pi\) | ||||
0.250841 | + | 0.968028i | \(0.419293\pi\) | |||||||
\(434\) | −2.82825 | −0.135761 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.33359 | −0.207541 | ||||||||
\(437\) | −6.69250 | −0.320146 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.4334 | 0.736594 | 0.368297 | − | 0.929708i | \(-0.379941\pi\) | ||||
0.368297 | + | 0.929708i | \(0.379941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.74505 | −0.320829 | ||||||||
\(443\) | −18.9105 | −0.898463 | −0.449231 | − | 0.893415i | \(-0.648302\pi\) | ||||
−0.449231 | + | 0.893415i | \(0.648302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.89218 | 0.184300 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.19805 | 0.387322 | ||||||||
\(449\) | 11.4152 | 0.538714 | 0.269357 | − | 0.963040i | \(-0.413189\pi\) | ||||
0.269357 | + | 0.963040i | \(0.413189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.3460 | 1.05223 | ||||||||
\(452\) | −6.10703 | −0.287250 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.34126 | 0.156813 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.9739 | −1.58923 | −0.794616 | − | 0.607112i | \(-0.792328\pi\) | ||||
−0.794616 | + | 0.607112i | \(0.792328\pi\) | |||||||
\(458\) | 3.64780 | 0.170451 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6907 | 1.14996 | 0.574981 | − | 0.818167i | \(-0.305009\pi\) | ||||
0.574981 | + | 0.818167i | \(0.305009\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.6315 | −0.633510 | −0.316755 | − | 0.948507i | \(-0.602593\pi\) | ||||
−0.316755 | + | 0.948507i | \(0.602593\pi\) | |||||||
\(464\) | 11.7000 | 0.543160 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.128063 | 0.00593241 | ||||||||
\(467\) | −9.47115 | −0.438272 | −0.219136 | − | 0.975694i | \(-0.570324\pi\) | ||||
−0.219136 | + | 0.975694i | \(0.570324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.6220 | 0.582828 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.21386 | 0.286016 | ||||||||
\(473\) | 9.97268 | 0.458544 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.1167 | −0.647039 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.03091 | 0.0928914 | ||||||||
\(479\) | 25.7286 | 1.17557 | 0.587784 | − | 0.809018i | \(-0.300000\pi\) | ||||
0.587784 | + | 0.809018i | \(0.300000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.98164 | 0.272739 | ||||||||
\(482\) | 0.316142 | 0.0143999 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.52546 | 0.387521 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.4046 | −1.28714 | −0.643568 | − | 0.765389i | \(-0.722547\pi\) | ||||
−0.643568 | + | 0.765389i | \(0.722547\pi\) | |||||||
\(488\) | 3.71980 | 0.168388 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.10299 | 0.275424 | 0.137712 | − | 0.990472i | \(-0.456025\pi\) | ||||
0.137712 | + | 0.990472i | \(0.456025\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.7771 | −0.845679 | ||||||||
\(494\) | 4.81530 | 0.216650 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33.4479 | −1.50186 | ||||||||
\(497\) | 17.3039 | 0.776186 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3163 | −0.909481 | −0.454740 | − | 0.890624i | \(-0.650268\pi\) | ||||
−0.454740 | + | 0.890624i | \(0.650268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.14371 | 0.0510464 | ||||||||
\(503\) | −14.6267 | −0.652171 | −0.326085 | − | 0.945340i | \(-0.605730\pi\) | ||||
−0.326085 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.01803 | −0.0452567 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.3670 | 1.34732 | ||||||||
\(509\) | 4.30584 | 0.190853 | 0.0954265 | − | 0.995436i | \(-0.469578\pi\) | ||||
0.0954265 | + | 0.995436i | \(0.469578\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.1898 | 0.627721 | ||||||||
\(512\) | −17.4127 | −0.769538 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.51572 | −0.199180 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.24755 | −0.362727 | ||||||||
\(518\) | −0.393109 | −0.0172722 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.6413 | 1.73672 | 0.868358 | − | 0.495938i | \(-0.165176\pi\) | ||||
0.868358 | + | 0.495938i | \(0.165176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.2874 | 1.58674 | 0.793369 | − | 0.608741i | \(-0.208325\pi\) | ||||
0.793369 | + | 0.608741i | \(0.208325\pi\) | |||||||
\(524\) | −29.0021 | −1.26696 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.11264 | 0.179320 | ||||||||
\(527\) | 53.6799 | 2.33833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4225 | −0.887934 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.0779 | 0.436934 | ||||||||
\(533\) | 40.7079 | 1.76325 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.84046 | −0.425043 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.649497 | 0.0280018 | ||||||||
\(539\) | 13.9936 | 0.602747 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.6044 | −1.65973 | −0.829866 | − | 0.557962i | \(-0.811583\pi\) | ||||
−0.829866 | + | 0.557962i | \(0.811583\pi\) | |||||||
\(542\) | −1.12607 | −0.0483690 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.5938 | 0.711453 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3620 | 0.443047 | 0.221524 | − | 0.975155i | \(-0.428897\pi\) | ||||
0.221524 | + | 0.975155i | \(0.428897\pi\) | |||||||
\(548\) | −20.3501 | −0.869313 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.4050 | 0.571073 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.3167 | −0.608810 | ||||||||
\(554\) | −0.310733 | −0.0132018 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.1434 | −1.02391 | ||||||||
\(557\) | −12.6830 | −0.537398 | −0.268699 | − | 0.963224i | \(-0.586594\pi\) | ||||
−0.268699 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.1673 | 0.768396 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.31068 | 0.139653 | ||||||||
\(563\) | −13.0892 | −0.551645 | −0.275823 | − | 0.961209i | \(-0.588950\pi\) | ||||
−0.275823 | + | 0.961209i | \(0.588950\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.94417 | −0.249852 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.4906 | −0.566055 | ||||||||
\(569\) | 2.58803 | 0.108496 | 0.0542478 | − | 0.998528i | \(-0.482724\pi\) | ||||
0.0542478 | + | 0.998528i | \(0.482724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5754 | −0.442568 | −0.221284 | − | 0.975209i | \(-0.571025\pi\) | ||||
−0.221284 | + | 0.975209i | \(0.571025\pi\) | |||||||
\(572\) | −23.3265 | −0.975330 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.67529 | −0.111665 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.0142904 | −0.000594917 0 | −0.000297458 | − | 1.00000i | \(-0.500095\pi\) | ||||
−0.000297458 | 1.00000i | \(0.500095\pi\) | ||||||||
\(578\) | −4.21849 | −0.175466 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.53118 | −0.146498 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.2653 | −1.41912 | ||||||||
\(584\) | −11.0628 | −0.457783 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.93891 | −0.327953 | ||||||||
\(587\) | 22.6389 | 0.934408 | 0.467204 | − | 0.884149i | \(-0.345261\pi\) | ||||
0.467204 | + | 0.884149i | \(0.345261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.3222 | −1.57904 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.64905 | −0.191075 | ||||||||
\(593\) | −12.7423 | −0.523264 | −0.261632 | − | 0.965168i | \(-0.584261\pi\) | ||||
−0.261632 | + | 0.965168i | \(0.584261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.0967 | −1.35569 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.85454 | −0.0758380 | ||||||||
\(599\) | 6.83599 | 0.279311 | 0.139656 | − | 0.990200i | \(-0.455400\pi\) | ||||
0.139656 | + | 0.990200i | \(0.455400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.8422 | 1.29887 | 0.649435 | − | 0.760417i | \(-0.275005\pi\) | ||||
0.649435 | + | 0.760417i | \(0.275005\pi\) | |||||||
\(602\) | −1.19394 | −0.0486614 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.05441 | 0.124282 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.7763 | 1.12741 | 0.563703 | − | 0.825977i | \(-0.309376\pi\) | ||||
0.563703 | + | 0.825977i | \(0.309376\pi\) | |||||||
\(608\) | −11.8463 | −0.480432 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0246 | −0.607831 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.61694 | −0.146087 | −0.0730433 | − | 0.997329i | \(-0.523271\pi\) | ||||
−0.0730433 | + | 0.997329i | \(0.523271\pi\) | |||||||
\(614\) | −5.00827 | −0.202117 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.11414 | 0.125472 | ||||||||
\(617\) | −44.6425 | −1.79724 | −0.898621 | − | 0.438727i | \(-0.855430\pi\) | ||||
−0.898621 | + | 0.438727i | \(0.855430\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.5085 | 0.824307 | 0.412153 | − | 0.911115i | \(-0.364777\pi\) | ||||
0.412153 | + | 0.911115i | \(0.364777\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.61992 | −0.185242 | ||||||||
\(623\) | −1.72149 | −0.0689701 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.14033 | −0.245417 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.8409 | 0.711931 | ||||||||
\(629\) | 7.46116 | 0.297496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.7357 | −1.50223 | −0.751117 | − | 0.660169i | \(-0.770485\pi\) | ||||
−0.751117 | + | 0.660169i | \(0.770485\pi\) | |||||||
\(632\) | 11.1618 | 0.443991 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.21537 | −0.246844 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.4922 | 1.01004 | ||||||||
\(638\) | 2.03909 | 0.0807285 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.18606 | 0.362828 | 0.181414 | − | 0.983407i | \(-0.441933\pi\) | ||||
0.181414 | + | 0.983407i | \(0.441933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.42111 | 0.134915 | 0.0674577 | − | 0.997722i | \(-0.478511\pi\) | ||||
0.0674577 | + | 0.997722i | \(0.478511\pi\) | |||||||
\(644\) | −3.88138 | −0.152948 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00633 | 0.236316 | ||||||||
\(647\) | −3.26735 | −0.128453 | −0.0642264 | − | 0.997935i | \(-0.520458\pi\) | ||||
−0.0642264 | + | 0.997935i | \(0.520458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.4276 | −0.644840 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.88259 | 0.347869 | ||||||||
\(653\) | −12.6362 | −0.494494 | −0.247247 | − | 0.968952i | \(-0.579526\pi\) | ||||
−0.247247 | + | 0.968952i | \(0.579526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −31.6390 | −1.23529 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.987407 | 0.0384931 | ||||||||
\(659\) | 9.14896 | 0.356393 | 0.178197 | − | 0.983995i | \(-0.442974\pi\) | ||||
0.178197 | + | 0.983995i | \(0.442974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.39083 | 0.248574 | 0.124287 | − | 0.992246i | \(-0.460336\pi\) | ||||
0.124287 | + | 0.992246i | \(0.460336\pi\) | |||||||
\(662\) | −7.50622 | −0.291738 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.75302 | 0.106838 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.16276 | −0.199903 | ||||||||
\(668\) | 0.276383 | 0.0106936 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.83407 | −0.379640 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.7063 | −1.29928 | −0.649641 | − | 0.760241i | \(-0.725081\pi\) | ||||
−0.649641 | + | 0.760241i | \(0.725081\pi\) | |||||||
\(674\) | 1.12881 | 0.0434802 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.2857 | −0.664833 | ||||||||
\(677\) | −9.20340 | −0.353715 | −0.176858 | − | 0.984236i | \(-0.556593\pi\) | ||||
−0.176858 | + | 0.984236i | \(0.556593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0380362 | −0.00145970 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.82935 | −0.223217 | ||||||||
\(683\) | −27.2216 | −1.04161 | −0.520803 | − | 0.853677i | \(-0.674367\pi\) | ||||
−0.520803 | + | 0.853677i | \(0.674367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.82887 | −0.146187 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.1200 | −0.538320 | ||||||||
\(689\) | −62.4213 | −2.37806 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.8238 | 1.13455 | 0.567276 | − | 0.823528i | \(-0.307997\pi\) | ||||
0.567276 | + | 0.823528i | \(0.307997\pi\) | |||||||
\(692\) | 47.7463 | 1.81504 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.14932 | −0.157506 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.7767 | 1.92331 | ||||||||
\(698\) | −0.0921844 | −0.00348923 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.1081 | 0.721704 | 0.360852 | − | 0.932623i | \(-0.382486\pi\) | ||||
0.360852 | + | 0.932623i | \(0.382486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.32653 | −0.200894 | ||||||||
\(704\) | 16.8971 | 0.636834 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.91445 | −0.222593 | ||||||||
\(707\) | −14.0020 | −0.526601 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.5146 | 0.545107 | 0.272553 | − | 0.962141i | \(-0.412132\pi\) | ||||
0.272553 | + | 0.962141i | \(0.412132\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.34213 | 0.0502983 | ||||||||
\(713\) | 14.7592 | 0.552738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −46.8398 | −1.75048 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.17215 | −0.0437444 | ||||||||
\(719\) | −34.7507 | −1.29598 | −0.647992 | − | 0.761647i | \(-0.724391\pi\) | ||||
−0.647992 | + | 0.761647i | \(0.724391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.898892 | 0.0334765 | ||||||||
\(722\) | 0.400494 | 0.0149049 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.81626 | −0.141830 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.6279 | 1.58098 | 0.790490 | − | 0.612475i | \(-0.209826\pi\) | ||||
0.790490 | + | 0.612475i | \(0.209826\pi\) | |||||||
\(728\) | 5.67305 | 0.210257 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6609 | 0.838143 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.96230 | 0.0724793 | 0.0362397 | − | 0.999343i | \(-0.488462\pi\) | ||||
0.0362397 | + | 0.999343i | \(0.488462\pi\) | |||||||
\(734\) | 4.28620 | 0.158207 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.56245 | 0.168174 | ||||||||
\(737\) | 26.0153 | 0.958286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.3601 | 0.454672 | 0.227336 | − | 0.973816i | \(-0.426998\pi\) | ||||
0.227336 | + | 0.973816i | \(0.426998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.10228 | 0.150599 | ||||||||
\(743\) | −8.63742 | −0.316876 | −0.158438 | − | 0.987369i | \(-0.550646\pi\) | ||||
−0.158438 | + | 0.987369i | \(0.550646\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.520357 | −0.0190516 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.0962 | −1.06386 | ||||||||
\(749\) | 2.63898 | 0.0964264 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3654 | −0.889105 | −0.444552 | − | 0.895753i | \(-0.646637\pi\) | ||||
−0.444552 | + | 0.895753i | \(0.646637\pi\) | |||||||
\(752\) | 11.6774 | 0.425832 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.71463 | 0.135279 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.18352 | −0.188398 | −0.0941991 | − | 0.995553i | \(-0.530029\pi\) | ||||
−0.0941991 | + | 0.995553i | \(0.530029\pi\) | |||||||
\(758\) | −3.06202 | −0.111218 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.2636 | −1.13331 | −0.566653 | − | 0.823957i | \(-0.691762\pi\) | ||||
−0.566653 | + | 0.823957i | \(0.691762\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.78630 | −0.100871 | ||||||||
\(764\) | −15.0641 | −0.544999 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.21846 | 0.296945 | ||||||||
\(767\) | −29.9263 | −1.08058 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.1891 | −1.59350 | −0.796750 | − | 0.604309i | \(-0.793449\pi\) | ||||
−0.796750 | + | 0.604309i | \(0.793449\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.8182 | −1.00120 | ||||||||
\(773\) | 21.5881 | 0.776471 | 0.388236 | − | 0.921560i | \(-0.373085\pi\) | ||||
0.388236 | + | 0.921560i | \(0.373085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.0296542 | 0.00106452 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.18939 | −0.150197 | ||||||||
\(779\) | −36.2496 | −1.29878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.6653 | 1.27621 | ||||||||
\(782\) | −2.31325 | −0.0827218 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.8131 | −0.707610 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4212 | 0.514059 | 0.257029 | − | 0.966404i | \(-0.417256\pi\) | ||||
0.257029 | + | 0.966404i | \(0.417256\pi\) | |||||||
\(788\) | 0.317122 | 0.0112970 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.92654 | −0.139612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.9148 | −0.636173 | ||||||||
\(794\) | 0.213834 | 0.00758868 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.63687 | −0.341570 | ||||||||
\(797\) | 39.4567 | 1.39763 | 0.698814 | − | 0.715304i | \(-0.253712\pi\) | ||||
0.698814 | + | 0.715304i | \(0.253712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.7409 | −0.663004 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.39031 | 0.0844046 | ||||||||
\(803\) | 29.2469 | 1.03210 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.6194 | −0.374051 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.9164 | 0.384038 | ||||||||
\(809\) | 5.96204 | 0.209614 | 0.104807 | − | 0.994493i | \(-0.466577\pi\) | ||||
0.104807 | + | 0.994493i | \(0.466577\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.1764 | −1.37567 | −0.687835 | − | 0.725867i | \(-0.741439\pi\) | ||||
−0.687835 | + | 0.725867i | \(0.741439\pi\) | |||||||
\(812\) | 7.77437 | 0.272827 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.810242 | −0.0283990 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1776 | −0.565984 | ||||||||
\(818\) | −0.374544 | −0.0130956 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.6329 | −0.720092 | −0.360046 | − | 0.932934i | \(-0.617239\pi\) | ||||
−0.360046 | + | 0.932934i | \(0.617239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.0162 | 1.36002 | 0.680009 | − | 0.733203i | \(-0.261976\pi\) | ||||
0.680009 | + | 0.733203i | \(0.261976\pi\) | |||||||
\(824\) | −0.700803 | −0.0244136 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.96673 | 0.0684314 | ||||||||
\(827\) | −19.5976 | −0.681474 | −0.340737 | − | 0.940159i | \(-0.610677\pi\) | ||||
−0.340737 | + | 0.940159i | \(0.610677\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.67511 | −0.301299 | −0.150650 | − | 0.988587i | \(-0.548136\pi\) | ||||
−0.150650 | + | 0.988587i | \(0.548136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 30.7816 | 1.06716 | ||||||||
\(833\) | 31.7976 | 1.10172 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 20.7718 | 0.718407 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.54145 | −0.260515 | ||||||||
\(839\) | 3.85921 | 0.133235 | 0.0666173 | − | 0.997779i | \(-0.478779\pi\) | ||||
0.0666173 | + | 0.997779i | \(0.478779\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.6591 | −0.643416 | ||||||||
\(842\) | 1.72031 | 0.0592858 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.38706 | −0.219852 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.48148 | 0.188346 | ||||||||
\(848\) | 48.5151 | 1.66601 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.05144 | 0.0703224 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.7898 | −1.01998 | −0.509991 | − | 0.860180i | \(-0.670351\pi\) | ||||
−0.509991 | + | 0.860180i | \(0.670351\pi\) | |||||||
\(854\) | 1.17735 | 0.0402880 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.05743 | −0.0703216 | ||||||||
\(857\) | −36.2041 | −1.23671 | −0.618354 | − | 0.785899i | \(-0.712200\pi\) | ||||
−0.618354 | + | 0.785899i | \(0.712200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.6533 | −1.28471 | −0.642357 | − | 0.766406i | \(-0.722043\pi\) | ||||
−0.642357 | + | 0.766406i | \(0.722043\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.70133 | 0.0920077 | ||||||||
\(863\) | 2.49913 | 0.0850715 | 0.0425357 | − | 0.999095i | \(-0.486456\pi\) | ||||
0.0425357 | + | 0.999095i | \(0.486456\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.57600 | −0.0875361 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22.2253 | −0.754376 | ||||||||
\(869\) | −29.5084 | −1.00100 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47.3923 | 1.60583 | ||||||||
\(872\) | 2.17228 | 0.0735628 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.65143 | 0.0558606 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.4491 | −1.09573 | −0.547864 | − | 0.836567i | \(-0.684559\pi\) | ||||
−0.547864 | + | 0.836567i | \(0.684559\pi\) | |||||||
\(878\) | −3.80832 | −0.128525 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.2625 | 1.12064 | 0.560321 | − | 0.828275i | \(-0.310678\pi\) | ||||
0.560321 | + | 0.828275i | \(0.310678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.9730 | −0.369269 | −0.184635 | − | 0.982807i | \(-0.559110\pi\) | ||||
−0.184635 | + | 0.982807i | \(0.559110\pi\) | |||||||
\(884\) | −53.0047 | −1.78274 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.66632 | 0.156768 | ||||||||
\(887\) | 26.0052 | 0.873168 | 0.436584 | − | 0.899664i | \(-0.356188\pi\) | ||||
0.436584 | + | 0.899664i | \(0.356188\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.5246 | 0.654834 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30.5860 | 1.02410 | ||||||||
\(893\) | 13.3791 | 0.447715 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.10907 | −0.304313 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.81679 | −0.0939975 | ||||||||
\(899\) | −29.5626 | −0.985969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.8608 | −2.59392 | ||||||||
\(902\) | −5.51408 | −0.183599 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.06125 | 0.101816 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.0108 | −1.82660 | −0.913302 | − | 0.407283i | \(-0.866476\pi\) | ||||
−0.913302 | + | 0.407283i | \(0.866476\pi\) | |||||||
\(908\) | 26.2567 | 0.871359 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.1075 | 0.401139 | 0.200569 | − | 0.979679i | \(-0.435721\pi\) | ||||
0.200569 | + | 0.979679i | \(0.435721\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.27817 | −0.240872 | ||||||||
\(914\) | 8.38337 | 0.277297 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.6656 | 0.947138 | ||||||||
\(917\) | −18.6470 | −0.615779 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.97191 | 0.196995 | 0.0984975 | − | 0.995137i | \(-0.468596\pi\) | ||||
0.0984975 | + | 0.995137i | \(0.468596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.09266 | −0.200651 | ||||||||
\(923\) | 64.9718 | 2.13857 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.36370 | 0.110538 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.13854 | −0.299987 | ||||||||
\(929\) | −46.8756 | −1.53794 | −0.768970 | − | 0.639285i | \(-0.779230\pi\) | ||||
−0.768970 | + | 0.639285i | \(0.779230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.7003 | −0.743973 | ||||||||
\(932\) | 1.00636 | 0.0329644 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.33709 | 0.0764719 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.4335 | −0.634864 | −0.317432 | − | 0.948281i | \(-0.602821\pi\) | ||||
−0.317432 | + | 0.948281i | \(0.602821\pi\) | |||||||
\(938\) | −3.11458 | −0.101695 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.7097 | −0.707717 | −0.353858 | − | 0.935299i | \(-0.615130\pi\) | ||||
−0.353858 | + | 0.935299i | \(0.615130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.9610 | 0.454633 | ||||||||
\(944\) | 23.2593 | 0.757026 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.46085 | −0.0800091 | ||||||||
\(947\) | 6.31560 | 0.205229 | 0.102615 | − | 0.994721i | \(-0.467279\pi\) | ||||
0.102615 | + | 0.994721i | \(0.467279\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.2792 | 1.72952 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.07624 | 0.229342 | ||||||||
\(953\) | −21.8017 | −0.706227 | −0.353114 | − | 0.935580i | \(-0.614877\pi\) | ||||
−0.353114 | + | 0.935580i | \(0.614877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.9595 | 0.516167 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.34876 | −0.205119 | ||||||||
\(959\) | −13.0842 | −0.422510 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.5134 | 1.72624 | ||||||||
\(962\) | −1.47602 | −0.0475889 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.48435 | 0.0800154 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.01268 | −0.225513 | −0.112756 | − | 0.993623i | \(-0.535968\pi\) | ||||
−0.112756 | + | 0.993623i | \(0.535968\pi\) | |||||||
\(968\) | −4.27353 | −0.137356 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.41028 | −0.237807 | −0.118904 | − | 0.992906i | \(-0.537938\pi\) | ||||
−0.118904 | + | 0.992906i | \(0.537938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.5231 | −0.497647 | ||||||||
\(974\) | 7.00909 | 0.224586 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9237 | 0.445688 | ||||||||
\(977\) | −39.2585 | −1.25599 | −0.627995 | − | 0.778217i | \(-0.716124\pi\) | ||||
−0.627995 | + | 0.778217i | \(0.716124\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.54819 | −0.113401 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.50597 | −0.0480573 | ||||||||
\(983\) | 18.3827 | 0.586317 | 0.293159 | − | 0.956064i | \(-0.405294\pi\) | ||||
0.293159 | + | 0.956064i | \(0.405294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.63343 | 0.147558 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 37.8401 | 1.20385 | ||||||||
\(989\) | 6.23059 | 0.198121 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.4658 | 1.66663 | 0.833316 | − | 0.552797i | \(-0.186440\pi\) | ||||
0.833316 | + | 0.552797i | \(0.186440\pi\) | |||||||
\(992\) | 26.1252 | 0.829476 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.26989 | −0.135433 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.3720 | −1.15191 | −0.575956 | − | 0.817480i | \(-0.695370\pi\) | ||||
−0.575956 | + | 0.817480i | \(0.695370\pi\) | |||||||
\(998\) | 5.01322 | 0.158691 | ||||||||
\(999\) | 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 | 5625.2.a.p.1.3 | 6 | ||
3.2 | odd | 2 | 1875.2.a.j.1.4 | 6 | |||
5.4 | even | 2 | 5625.2.a.q.1.4 | 6 | |||
15.2 | even | 4 | 1875.2.b.f.1249.8 | 12 | |||
15.8 | even | 4 | 1875.2.b.f.1249.5 | 12 | |||
15.14 | odd | 2 | 1875.2.a.k.1.3 | 6 | |||
25.11 | even | 5 | 225.2.h.d.46.2 | 12 | |||
25.16 | even | 5 | 225.2.h.d.181.2 | 12 | |||
75.2 | even | 20 | 375.2.i.d.274.4 | 24 | |||
75.11 | odd | 10 | 75.2.g.c.46.2 | yes | 12 | ||
75.14 | odd | 10 | 375.2.g.c.226.2 | 12 | |||
75.23 | even | 20 | 375.2.i.d.274.3 | 24 | |||
75.38 | even | 20 | 375.2.i.d.349.4 | 24 | |||
75.41 | odd | 10 | 75.2.g.c.31.2 | ✓ | 12 | ||
75.59 | odd | 10 | 375.2.g.c.151.2 | 12 | |||
75.62 | even | 20 | 375.2.i.d.349.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.2 | ✓ | 12 | 75.41 | odd | 10 | ||
75.2.g.c.46.2 | yes | 12 | 75.11 | odd | 10 | ||
225.2.h.d.46.2 | 12 | 25.11 | even | 5 | |||
225.2.h.d.181.2 | 12 | 25.16 | even | 5 | |||
375.2.g.c.151.2 | 12 | 75.59 | odd | 10 | |||
375.2.g.c.226.2 | 12 | 75.14 | odd | 10 | |||
375.2.i.d.274.3 | 24 | 75.23 | even | 20 | |||
375.2.i.d.274.4 | 24 | 75.2 | even | 20 | |||
375.2.i.d.349.3 | 24 | 75.62 | even | 20 | |||
375.2.i.d.349.4 | 24 | 75.38 | even | 20 | |||
1875.2.a.j.1.4 | 6 | 3.2 | odd | 2 | |||
1875.2.a.k.1.3 | 6 | 15.14 | odd | 2 | |||
1875.2.b.f.1249.5 | 12 | 15.8 | even | 4 | |||
1875.2.b.f.1249.8 | 12 | 15.2 | even | 4 | |||
5625.2.a.p.1.3 | 6 | 1.1 | even | 1 | trivial | ||
5625.2.a.q.1.4 | 6 | 5.4 | even | 2 |