Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 9x^{7} + 45x^{6} + 7x^{5} - 123x^{4} + 37x^{3} + 87x^{2} - 54x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.20969\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.20969 | −1.43542 | −0.717709 | − | 0.696344i | \(-0.754809\pi\) | ||||
−0.717709 | + | 0.696344i | \(0.754809\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.02210 | −0.764284 | −0.382142 | − | 0.924104i | \(-0.624813\pi\) | ||||
−0.382142 | + | 0.924104i | \(0.624813\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.20969 | −1.01499 | ||||||||
\(11\) | −1.72557 | −0.520279 | −0.260139 | − | 0.965571i | \(-0.583769\pi\) | ||||
−0.260139 | + | 0.965571i | \(0.583769\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.02210 | −0.540430 | ||||||||
\(15\) | 3.20969 | 0.828739 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.669533 | −0.162386 | −0.0811928 | − | 0.996698i | \(-0.525873\pi\) | ||||
−0.0811928 | + | 0.996698i | \(0.525873\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.70293 | 1.53776 | 0.768879 | − | 0.639395i | \(-0.220815\pi\) | ||||
0.768879 | + | 0.639395i | \(0.220815\pi\) | |||||||
\(20\) | −3.20969 | −0.717709 | ||||||||
\(21\) | 2.02210 | 0.441259 | ||||||||
\(22\) | −1.72557 | −0.367893 | ||||||||
\(23\) | 2.38462 | 0.497227 | 0.248613 | − | 0.968603i | \(-0.420025\pi\) | ||||
0.248613 | + | 0.968603i | \(0.420025\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 5.30211 | 1.06042 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.02210 | −0.382142 | ||||||||
\(29\) | −2.29980 | −0.427063 | −0.213531 | − | 0.976936i | \(-0.568497\pi\) | ||||
−0.213531 | + | 0.976936i | \(0.568497\pi\) | |||||||
\(30\) | 3.20969 | 0.586007 | ||||||||
\(31\) | −4.65872 | −0.836731 | −0.418365 | − | 0.908279i | \(-0.637397\pi\) | ||||
−0.418365 | + | 0.908279i | \(0.637397\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.72557 | 0.300383 | ||||||||
\(34\) | −0.669533 | −0.114824 | ||||||||
\(35\) | 6.49033 | 1.09707 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.89073 | −0.475233 | −0.237617 | − | 0.971359i | \(-0.576366\pi\) | ||||
−0.237617 | + | 0.971359i | \(0.576366\pi\) | |||||||
\(38\) | 6.70293 | 1.08736 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −3.20969 | −0.507497 | ||||||||
\(41\) | −1.52823 | −0.238670 | −0.119335 | − | 0.992854i | \(-0.538076\pi\) | ||||
−0.119335 | + | 0.992854i | \(0.538076\pi\) | |||||||
\(42\) | 2.02210 | 0.312018 | ||||||||
\(43\) | 3.74925 | 0.571755 | 0.285878 | − | 0.958266i | \(-0.407715\pi\) | ||||
0.285878 | + | 0.958266i | \(0.407715\pi\) | |||||||
\(44\) | −1.72557 | −0.260139 | ||||||||
\(45\) | −3.20969 | −0.478472 | ||||||||
\(46\) | 2.38462 | 0.351593 | ||||||||
\(47\) | 8.51407 | 1.24190 | 0.620952 | − | 0.783848i | \(-0.286746\pi\) | ||||
0.620952 | + | 0.783848i | \(0.286746\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −2.91109 | −0.415870 | ||||||||
\(50\) | 5.30211 | 0.749832 | ||||||||
\(51\) | 0.669533 | 0.0937534 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 11.6372 | 1.59849 | 0.799247 | − | 0.601003i | \(-0.205232\pi\) | ||||
0.799247 | + | 0.601003i | \(0.205232\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 5.53854 | 0.746817 | ||||||||
\(56\) | −2.02210 | −0.270215 | ||||||||
\(57\) | −6.70293 | −0.887825 | ||||||||
\(58\) | −2.29980 | −0.301979 | ||||||||
\(59\) | −3.76784 | −0.490530 | −0.245265 | − | 0.969456i | \(-0.578875\pi\) | ||||
−0.245265 | + | 0.969456i | \(0.578875\pi\) | |||||||
\(60\) | 3.20969 | 0.414369 | ||||||||
\(61\) | −3.46636 | −0.443822 | −0.221911 | − | 0.975067i | \(-0.571229\pi\) | ||||
−0.221911 | + | 0.975067i | \(0.571229\pi\) | |||||||
\(62\) | −4.65872 | −0.591658 | ||||||||
\(63\) | −2.02210 | −0.254761 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.20969 | −0.398113 | ||||||||
\(66\) | 1.72557 | 0.212403 | ||||||||
\(67\) | −13.5209 | −1.65184 | −0.825919 | − | 0.563789i | \(-0.809343\pi\) | ||||
−0.825919 | + | 0.563789i | \(0.809343\pi\) | |||||||
\(68\) | −0.669533 | −0.0811928 | ||||||||
\(69\) | −2.38462 | −0.287074 | ||||||||
\(70\) | 6.49033 | 0.775743 | ||||||||
\(71\) | 6.69404 | 0.794436 | 0.397218 | − | 0.917724i | \(-0.369976\pi\) | ||||
0.397218 | + | 0.917724i | \(0.369976\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.7410 | 1.37418 | 0.687091 | − | 0.726571i | \(-0.258887\pi\) | ||||
0.687091 | + | 0.726571i | \(0.258887\pi\) | |||||||
\(74\) | −2.89073 | −0.336041 | ||||||||
\(75\) | −5.30211 | −0.612235 | ||||||||
\(76\) | 6.70293 | 0.768879 | ||||||||
\(77\) | 3.48928 | 0.397641 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 0.941600 | 0.105938 | 0.0529692 | − | 0.998596i | \(-0.483132\pi\) | ||||
0.0529692 | + | 0.998596i | \(0.483132\pi\) | |||||||
\(80\) | −3.20969 | −0.358854 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.52823 | −0.168765 | ||||||||
\(83\) | 0.0679630 | 0.00745991 | 0.00372996 | − | 0.999993i | \(-0.498813\pi\) | ||||
0.00372996 | + | 0.999993i | \(0.498813\pi\) | |||||||
\(84\) | 2.02210 | 0.220630 | ||||||||
\(85\) | 2.14899 | 0.233091 | ||||||||
\(86\) | 3.74925 | 0.404292 | ||||||||
\(87\) | 2.29980 | 0.246565 | ||||||||
\(88\) | −1.72557 | −0.183946 | ||||||||
\(89\) | 15.8437 | 1.67943 | 0.839716 | − | 0.543026i | \(-0.182721\pi\) | ||||
0.839716 | + | 0.543026i | \(0.182721\pi\) | |||||||
\(90\) | −3.20969 | −0.338331 | ||||||||
\(91\) | −2.02210 | −0.211974 | ||||||||
\(92\) | 2.38462 | 0.248613 | ||||||||
\(93\) | 4.65872 | 0.483087 | ||||||||
\(94\) | 8.51407 | 0.878159 | ||||||||
\(95\) | −21.5143 | −2.20732 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −14.9124 | −1.51413 | −0.757064 | − | 0.653341i | \(-0.773367\pi\) | ||||
−0.757064 | + | 0.653341i | \(0.773367\pi\) | |||||||
\(98\) | −2.91109 | −0.294065 | ||||||||
\(99\) | −1.72557 | −0.173426 | ||||||||
\(100\) | 5.30211 | 0.530211 | ||||||||
\(101\) | 18.7134 | 1.86205 | 0.931027 | − | 0.364950i | \(-0.118914\pi\) | ||||
0.931027 | + | 0.364950i | \(0.118914\pi\) | |||||||
\(102\) | 0.669533 | 0.0662937 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −6.49033 | −0.633391 | ||||||||
\(106\) | 11.6372 | 1.13031 | ||||||||
\(107\) | 3.67967 | 0.355727 | 0.177863 | − | 0.984055i | \(-0.443081\pi\) | ||||
0.177863 | + | 0.984055i | \(0.443081\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.643981 | −0.0616822 | −0.0308411 | − | 0.999524i | \(-0.509819\pi\) | ||||
−0.0308411 | + | 0.999524i | \(0.509819\pi\) | |||||||
\(110\) | 5.53854 | 0.528079 | ||||||||
\(111\) | 2.89073 | 0.274376 | ||||||||
\(112\) | −2.02210 | −0.191071 | ||||||||
\(113\) | −2.61607 | −0.246099 | −0.123049 | − | 0.992401i | \(-0.539267\pi\) | ||||
−0.123049 | + | 0.992401i | \(0.539267\pi\) | |||||||
\(114\) | −6.70293 | −0.627787 | ||||||||
\(115\) | −7.65388 | −0.713728 | ||||||||
\(116\) | −2.29980 | −0.213531 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −3.76784 | −0.346857 | ||||||||
\(119\) | 1.35387 | 0.124109 | ||||||||
\(120\) | 3.20969 | 0.293003 | ||||||||
\(121\) | −8.02241 | −0.729310 | ||||||||
\(122\) | −3.46636 | −0.313829 | ||||||||
\(123\) | 1.52823 | 0.137796 | ||||||||
\(124\) | −4.65872 | −0.418365 | ||||||||
\(125\) | −0.969688 | −0.0867315 | ||||||||
\(126\) | −2.02210 | −0.180143 | ||||||||
\(127\) | −17.1214 | −1.51928 | −0.759639 | − | 0.650345i | \(-0.774624\pi\) | ||||
−0.759639 | + | 0.650345i | \(0.774624\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.74925 | −0.330103 | ||||||||
\(130\) | −3.20969 | −0.281508 | ||||||||
\(131\) | −11.9320 | −1.04251 | −0.521253 | − | 0.853402i | \(-0.674535\pi\) | ||||
−0.521253 | + | 0.853402i | \(0.674535\pi\) | |||||||
\(132\) | 1.72557 | 0.150192 | ||||||||
\(133\) | −13.5540 | −1.17528 | ||||||||
\(134\) | −13.5209 | −1.16803 | ||||||||
\(135\) | 3.20969 | 0.276246 | ||||||||
\(136\) | −0.669533 | −0.0574120 | ||||||||
\(137\) | −6.86144 | −0.586212 | −0.293106 | − | 0.956080i | \(-0.594689\pi\) | ||||
−0.293106 | + | 0.956080i | \(0.594689\pi\) | |||||||
\(138\) | −2.38462 | −0.202992 | ||||||||
\(139\) | −13.0202 | −1.10436 | −0.552181 | − | 0.833724i | \(-0.686204\pi\) | ||||
−0.552181 | + | 0.833724i | \(0.686204\pi\) | |||||||
\(140\) | 6.49033 | 0.548533 | ||||||||
\(141\) | −8.51407 | −0.717014 | ||||||||
\(142\) | 6.69404 | 0.561751 | ||||||||
\(143\) | −1.72557 | −0.144299 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.38166 | 0.613013 | ||||||||
\(146\) | 11.7410 | 0.971694 | ||||||||
\(147\) | 2.91109 | 0.240103 | ||||||||
\(148\) | −2.89073 | −0.237617 | ||||||||
\(149\) | 11.3872 | 0.932873 | 0.466437 | − | 0.884555i | \(-0.345538\pi\) | ||||
0.466437 | + | 0.884555i | \(0.345538\pi\) | |||||||
\(150\) | −5.30211 | −0.432916 | ||||||||
\(151\) | 6.07828 | 0.494643 | 0.247322 | − | 0.968933i | \(-0.420450\pi\) | ||||
0.247322 | + | 0.968933i | \(0.420450\pi\) | |||||||
\(152\) | 6.70293 | 0.543679 | ||||||||
\(153\) | −0.669533 | −0.0541285 | ||||||||
\(154\) | 3.48928 | 0.281174 | ||||||||
\(155\) | 14.9530 | 1.20106 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −10.3162 | −0.823326 | −0.411663 | − | 0.911336i | \(-0.635052\pi\) | ||||
−0.411663 | + | 0.911336i | \(0.635052\pi\) | |||||||
\(158\) | 0.941600 | 0.0749097 | ||||||||
\(159\) | −11.6372 | −0.922891 | ||||||||
\(160\) | −3.20969 | −0.253748 | ||||||||
\(161\) | −4.82194 | −0.380022 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −15.6784 | −1.22803 | −0.614013 | − | 0.789296i | \(-0.710446\pi\) | ||||
−0.614013 | + | 0.789296i | \(0.710446\pi\) | |||||||
\(164\) | −1.52823 | −0.119335 | ||||||||
\(165\) | −5.53854 | −0.431175 | ||||||||
\(166\) | 0.0679630 | 0.00527495 | ||||||||
\(167\) | 1.59761 | 0.123627 | 0.0618134 | − | 0.998088i | \(-0.480312\pi\) | ||||
0.0618134 | + | 0.998088i | \(0.480312\pi\) | |||||||
\(168\) | 2.02210 | 0.156009 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.14899 | 0.164820 | ||||||||
\(171\) | 6.70293 | 0.512586 | ||||||||
\(172\) | 3.74925 | 0.285878 | ||||||||
\(173\) | −1.82588 | −0.138819 | −0.0694096 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694096 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(174\) | 2.29980 | 0.174348 | ||||||||
\(175\) | −10.7214 | −0.810464 | ||||||||
\(176\) | −1.72557 | −0.130070 | ||||||||
\(177\) | 3.76784 | 0.283208 | ||||||||
\(178\) | 15.8437 | 1.18754 | ||||||||
\(179\) | −6.67663 | −0.499035 | −0.249517 | − | 0.968370i | \(-0.580272\pi\) | ||||
−0.249517 | + | 0.968370i | \(0.580272\pi\) | |||||||
\(180\) | −3.20969 | −0.239236 | ||||||||
\(181\) | −21.0273 | −1.56295 | −0.781475 | − | 0.623936i | \(-0.785532\pi\) | ||||
−0.781475 | + | 0.623936i | \(0.785532\pi\) | |||||||
\(182\) | −2.02210 | −0.149888 | ||||||||
\(183\) | 3.46636 | 0.256241 | ||||||||
\(184\) | 2.38462 | 0.175796 | ||||||||
\(185\) | 9.27836 | 0.682158 | ||||||||
\(186\) | 4.65872 | 0.341594 | ||||||||
\(187\) | 1.15533 | 0.0844858 | ||||||||
\(188\) | 8.51407 | 0.620952 | ||||||||
\(189\) | 2.02210 | 0.147086 | ||||||||
\(190\) | −21.5143 | −1.56081 | ||||||||
\(191\) | −20.1793 | −1.46013 | −0.730063 | − | 0.683380i | \(-0.760509\pi\) | ||||
−0.730063 | + | 0.683380i | \(0.760509\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −6.28353 | −0.452298 | −0.226149 | − | 0.974093i | \(-0.572614\pi\) | ||||
−0.226149 | + | 0.974093i | \(0.572614\pi\) | |||||||
\(194\) | −14.9124 | −1.07065 | ||||||||
\(195\) | 3.20969 | 0.229851 | ||||||||
\(196\) | −2.91109 | −0.207935 | ||||||||
\(197\) | −17.1542 | −1.22219 | −0.611094 | − | 0.791558i | \(-0.709270\pi\) | ||||
−0.611094 | + | 0.791558i | \(0.709270\pi\) | |||||||
\(198\) | −1.72557 | −0.122631 | ||||||||
\(199\) | −25.3168 | −1.79466 | −0.897330 | − | 0.441360i | \(-0.854496\pi\) | ||||
−0.897330 | + | 0.441360i | \(0.854496\pi\) | |||||||
\(200\) | 5.30211 | 0.374916 | ||||||||
\(201\) | 13.5209 | 0.953689 | ||||||||
\(202\) | 18.7134 | 1.31667 | ||||||||
\(203\) | 4.65044 | 0.326397 | ||||||||
\(204\) | 0.669533 | 0.0468767 | ||||||||
\(205\) | 4.90515 | 0.342591 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 2.38462 | 0.165742 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −11.5664 | −0.800063 | ||||||||
\(210\) | −6.49033 | −0.447875 | ||||||||
\(211\) | 2.77247 | 0.190865 | 0.0954323 | − | 0.995436i | \(-0.469577\pi\) | ||||
0.0954323 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(212\) | 11.6372 | 0.799247 | ||||||||
\(213\) | −6.69404 | −0.458668 | ||||||||
\(214\) | 3.67967 | 0.251537 | ||||||||
\(215\) | −12.0339 | −0.820708 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 9.42042 | 0.639500 | ||||||||
\(218\) | −0.643981 | −0.0436159 | ||||||||
\(219\) | −11.7410 | −0.793385 | ||||||||
\(220\) | 5.53854 | 0.373409 | ||||||||
\(221\) | −0.669533 | −0.0450377 | ||||||||
\(222\) | 2.89073 | 0.194013 | ||||||||
\(223\) | 29.2727 | 1.96025 | 0.980123 | − | 0.198392i | \(-0.0635718\pi\) | ||||
0.980123 | + | 0.198392i | \(0.0635718\pi\) | |||||||
\(224\) | −2.02210 | −0.135108 | ||||||||
\(225\) | 5.30211 | 0.353474 | ||||||||
\(226\) | −2.61607 | −0.174018 | ||||||||
\(227\) | 17.6781 | 1.17334 | 0.586669 | − | 0.809827i | \(-0.300439\pi\) | ||||
0.586669 | + | 0.809827i | \(0.300439\pi\) | |||||||
\(228\) | −6.70293 | −0.443912 | ||||||||
\(229\) | −22.4144 | −1.48119 | −0.740593 | − | 0.671953i | \(-0.765455\pi\) | ||||
−0.740593 | + | 0.671953i | \(0.765455\pi\) | |||||||
\(230\) | −7.65388 | −0.504682 | ||||||||
\(231\) | −3.48928 | −0.229578 | ||||||||
\(232\) | −2.29980 | −0.150989 | ||||||||
\(233\) | −20.3329 | −1.33205 | −0.666026 | − | 0.745929i | \(-0.732006\pi\) | ||||
−0.666026 | + | 0.745929i | \(0.732006\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −27.3275 | −1.78265 | ||||||||
\(236\) | −3.76784 | −0.245265 | ||||||||
\(237\) | −0.941600 | −0.0611635 | ||||||||
\(238\) | 1.35387 | 0.0877581 | ||||||||
\(239\) | −18.4706 | −1.19477 | −0.597383 | − | 0.801956i | \(-0.703793\pi\) | ||||
−0.597383 | + | 0.801956i | \(0.703793\pi\) | |||||||
\(240\) | 3.20969 | 0.207185 | ||||||||
\(241\) | 15.6356 | 1.00718 | 0.503588 | − | 0.863944i | \(-0.332013\pi\) | ||||
0.503588 | + | 0.863944i | \(0.332013\pi\) | |||||||
\(242\) | −8.02241 | −0.515700 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.46636 | −0.221911 | ||||||||
\(245\) | 9.34370 | 0.596947 | ||||||||
\(246\) | 1.52823 | 0.0974365 | ||||||||
\(247\) | 6.70293 | 0.426497 | ||||||||
\(248\) | −4.65872 | −0.295829 | ||||||||
\(249\) | −0.0679630 | −0.00430698 | ||||||||
\(250\) | −0.969688 | −0.0613284 | ||||||||
\(251\) | −12.3105 | −0.777033 | −0.388517 | − | 0.921442i | \(-0.627012\pi\) | ||||
−0.388517 | + | 0.921442i | \(0.627012\pi\) | |||||||
\(252\) | −2.02210 | −0.127381 | ||||||||
\(253\) | −4.11482 | −0.258697 | ||||||||
\(254\) | −17.1214 | −1.07429 | ||||||||
\(255\) | −2.14899 | −0.134575 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.6930 | −1.60269 | −0.801344 | − | 0.598204i | \(-0.795881\pi\) | ||||
−0.801344 | + | 0.598204i | \(0.795881\pi\) | |||||||
\(258\) | −3.74925 | −0.233418 | ||||||||
\(259\) | 5.84536 | 0.363213 | ||||||||
\(260\) | −3.20969 | −0.199057 | ||||||||
\(261\) | −2.29980 | −0.142354 | ||||||||
\(262\) | −11.9320 | −0.737163 | ||||||||
\(263\) | −12.2397 | −0.754734 | −0.377367 | − | 0.926064i | \(-0.623171\pi\) | ||||
−0.377367 | + | 0.926064i | \(0.623171\pi\) | |||||||
\(264\) | 1.72557 | 0.106201 | ||||||||
\(265\) | −37.3518 | −2.29451 | ||||||||
\(266\) | −13.5540 | −0.831051 | ||||||||
\(267\) | −15.8437 | −0.969620 | ||||||||
\(268\) | −13.5209 | −0.825919 | ||||||||
\(269\) | −18.2413 | −1.11219 | −0.556097 | − | 0.831117i | \(-0.687702\pi\) | ||||
−0.556097 | + | 0.831117i | \(0.687702\pi\) | |||||||
\(270\) | 3.20969 | 0.195336 | ||||||||
\(271\) | 3.96166 | 0.240654 | 0.120327 | − | 0.992734i | \(-0.461606\pi\) | ||||
0.120327 | + | 0.992734i | \(0.461606\pi\) | |||||||
\(272\) | −0.669533 | −0.0405964 | ||||||||
\(273\) | 2.02210 | 0.122383 | ||||||||
\(274\) | −6.86144 | −0.414515 | ||||||||
\(275\) | −9.14916 | −0.551715 | ||||||||
\(276\) | −2.38462 | −0.143537 | ||||||||
\(277\) | −18.5109 | −1.11221 | −0.556106 | − | 0.831112i | \(-0.687705\pi\) | ||||
−0.556106 | + | 0.831112i | \(0.687705\pi\) | |||||||
\(278\) | −13.0202 | −0.780903 | ||||||||
\(279\) | −4.65872 | −0.278910 | ||||||||
\(280\) | 6.49033 | 0.387871 | ||||||||
\(281\) | 18.6586 | 1.11308 | 0.556541 | − | 0.830820i | \(-0.312128\pi\) | ||||
0.556541 | + | 0.830820i | \(0.312128\pi\) | |||||||
\(282\) | −8.51407 | −0.507005 | ||||||||
\(283\) | 26.3081 | 1.56386 | 0.781928 | − | 0.623368i | \(-0.214236\pi\) | ||||
0.781928 | + | 0.623368i | \(0.214236\pi\) | |||||||
\(284\) | 6.69404 | 0.397218 | ||||||||
\(285\) | 21.5143 | 1.27440 | ||||||||
\(286\) | −1.72557 | −0.102035 | ||||||||
\(287\) | 3.09025 | 0.182411 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.5517 | −0.973631 | ||||||||
\(290\) | 7.38166 | 0.433466 | ||||||||
\(291\) | 14.9124 | 0.874182 | ||||||||
\(292\) | 11.7410 | 0.687091 | ||||||||
\(293\) | −8.53157 | −0.498420 | −0.249210 | − | 0.968450i | \(-0.580171\pi\) | ||||
−0.249210 | + | 0.968450i | \(0.580171\pi\) | |||||||
\(294\) | 2.91109 | 0.169778 | ||||||||
\(295\) | 12.0936 | 0.704116 | ||||||||
\(296\) | −2.89073 | −0.168020 | ||||||||
\(297\) | 1.72557 | 0.100128 | ||||||||
\(298\) | 11.3872 | 0.659641 | ||||||||
\(299\) | 2.38462 | 0.137906 | ||||||||
\(300\) | −5.30211 | −0.306118 | ||||||||
\(301\) | −7.58138 | −0.436983 | ||||||||
\(302\) | 6.07828 | 0.349766 | ||||||||
\(303\) | −18.7134 | −1.07506 | ||||||||
\(304\) | 6.70293 | 0.384439 | ||||||||
\(305\) | 11.1259 | 0.637069 | ||||||||
\(306\) | −0.669533 | −0.0382747 | ||||||||
\(307\) | −17.3226 | −0.988651 | −0.494325 | − | 0.869277i | \(-0.664585\pi\) | ||||
−0.494325 | + | 0.869277i | \(0.664585\pi\) | |||||||
\(308\) | 3.48928 | 0.198820 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 14.9530 | 0.849276 | ||||||||
\(311\) | −1.53808 | −0.0872165 | −0.0436083 | − | 0.999049i | \(-0.513885\pi\) | ||||
−0.0436083 | + | 0.999049i | \(0.513885\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −19.6423 | −1.11025 | −0.555125 | − | 0.831767i | \(-0.687330\pi\) | ||||
−0.555125 | + | 0.831767i | \(0.687330\pi\) | |||||||
\(314\) | −10.3162 | −0.582179 | ||||||||
\(315\) | 6.49033 | 0.365689 | ||||||||
\(316\) | 0.941600 | 0.0529692 | ||||||||
\(317\) | 11.6707 | 0.655489 | 0.327745 | − | 0.944766i | \(-0.393711\pi\) | ||||
0.327745 | + | 0.944766i | \(0.393711\pi\) | |||||||
\(318\) | −11.6372 | −0.652582 | ||||||||
\(319\) | 3.96847 | 0.222192 | ||||||||
\(320\) | −3.20969 | −0.179427 | ||||||||
\(321\) | −3.67967 | −0.205379 | ||||||||
\(322\) | −4.82194 | −0.268716 | ||||||||
\(323\) | −4.48783 | −0.249710 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.30211 | 0.294108 | ||||||||
\(326\) | −15.6784 | −0.868345 | ||||||||
\(327\) | 0.643981 | 0.0356122 | ||||||||
\(328\) | −1.52823 | −0.0843825 | ||||||||
\(329\) | −17.2163 | −0.949168 | ||||||||
\(330\) | −5.53854 | −0.304887 | ||||||||
\(331\) | 28.6487 | 1.57467 | 0.787337 | − | 0.616522i | \(-0.211459\pi\) | ||||
0.787337 | + | 0.616522i | \(0.211459\pi\) | |||||||
\(332\) | 0.0679630 | 0.00372996 | ||||||||
\(333\) | −2.89073 | −0.158411 | ||||||||
\(334\) | 1.59761 | 0.0874173 | ||||||||
\(335\) | 43.3978 | 2.37108 | ||||||||
\(336\) | 2.02210 | 0.110315 | ||||||||
\(337\) | −4.12431 | −0.224666 | −0.112333 | − | 0.993671i | \(-0.535832\pi\) | ||||
−0.112333 | + | 0.993671i | \(0.535832\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 2.61607 | 0.142085 | ||||||||
\(340\) | 2.14899 | 0.116546 | ||||||||
\(341\) | 8.03894 | 0.435333 | ||||||||
\(342\) | 6.70293 | 0.362453 | ||||||||
\(343\) | 20.0413 | 1.08213 | ||||||||
\(344\) | 3.74925 | 0.202146 | ||||||||
\(345\) | 7.65388 | 0.412071 | ||||||||
\(346\) | −1.82588 | −0.0981600 | ||||||||
\(347\) | −0.273562 | −0.0146856 | −0.00734278 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734278 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(348\) | 2.29980 | 0.123282 | ||||||||
\(349\) | −12.3688 | −0.662086 | −0.331043 | − | 0.943616i | \(-0.607400\pi\) | ||||
−0.331043 | + | 0.943616i | \(0.607400\pi\) | |||||||
\(350\) | −10.7214 | −0.573084 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.72557 | −0.0919732 | ||||||||
\(353\) | 18.6874 | 0.994631 | 0.497315 | − | 0.867570i | \(-0.334319\pi\) | ||||
0.497315 | + | 0.867570i | \(0.334319\pi\) | |||||||
\(354\) | 3.76784 | 0.200258 | ||||||||
\(355\) | −21.4858 | −1.14035 | ||||||||
\(356\) | 15.8437 | 0.839716 | ||||||||
\(357\) | −1.35387 | −0.0716542 | ||||||||
\(358\) | −6.67663 | −0.352871 | ||||||||
\(359\) | −10.1397 | −0.535151 | −0.267576 | − | 0.963537i | \(-0.586223\pi\) | ||||
−0.267576 | + | 0.963537i | \(0.586223\pi\) | |||||||
\(360\) | −3.20969 | −0.169166 | ||||||||
\(361\) | 25.9293 | 1.36470 | ||||||||
\(362\) | −21.0273 | −1.10517 | ||||||||
\(363\) | 8.02241 | 0.421067 | ||||||||
\(364\) | −2.02210 | −0.105987 | ||||||||
\(365\) | −37.6850 | −1.97253 | ||||||||
\(366\) | 3.46636 | 0.181189 | ||||||||
\(367\) | −16.8044 | −0.877185 | −0.438592 | − | 0.898686i | \(-0.644523\pi\) | ||||
−0.438592 | + | 0.898686i | \(0.644523\pi\) | |||||||
\(368\) | 2.38462 | 0.124307 | ||||||||
\(369\) | −1.52823 | −0.0795566 | ||||||||
\(370\) | 9.27836 | 0.482359 | ||||||||
\(371\) | −23.5317 | −1.22170 | ||||||||
\(372\) | 4.65872 | 0.241543 | ||||||||
\(373\) | 1.24141 | 0.0642777 | 0.0321389 | − | 0.999483i | \(-0.489768\pi\) | ||||
0.0321389 | + | 0.999483i | \(0.489768\pi\) | |||||||
\(374\) | 1.15533 | 0.0597405 | ||||||||
\(375\) | 0.969688 | 0.0500745 | ||||||||
\(376\) | 8.51407 | 0.439080 | ||||||||
\(377\) | −2.29980 | −0.118446 | ||||||||
\(378\) | 2.02210 | 0.104006 | ||||||||
\(379\) | 2.51633 | 0.129255 | 0.0646277 | − | 0.997909i | \(-0.479414\pi\) | ||||
0.0646277 | + | 0.997909i | \(0.479414\pi\) | |||||||
\(380\) | −21.5143 | −1.10366 | ||||||||
\(381\) | 17.1214 | 0.877155 | ||||||||
\(382\) | −20.1793 | −1.03246 | ||||||||
\(383\) | 16.4674 | 0.841447 | 0.420724 | − | 0.907189i | \(-0.361776\pi\) | ||||
0.420724 | + | 0.907189i | \(0.361776\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −11.1995 | −0.570780 | ||||||||
\(386\) | −6.28353 | −0.319823 | ||||||||
\(387\) | 3.74925 | 0.190585 | ||||||||
\(388\) | −14.9124 | −0.757064 | ||||||||
\(389\) | 4.75752 | 0.241216 | 0.120608 | − | 0.992700i | \(-0.461516\pi\) | ||||
0.120608 | + | 0.992700i | \(0.461516\pi\) | |||||||
\(390\) | 3.20969 | 0.162529 | ||||||||
\(391\) | −1.59658 | −0.0807425 | ||||||||
\(392\) | −2.91109 | −0.147032 | ||||||||
\(393\) | 11.9320 | 0.601891 | ||||||||
\(394\) | −17.1542 | −0.864217 | ||||||||
\(395\) | −3.02225 | −0.152066 | ||||||||
\(396\) | −1.72557 | −0.0867131 | ||||||||
\(397\) | −28.4890 | −1.42982 | −0.714912 | − | 0.699215i | \(-0.753533\pi\) | ||||
−0.714912 | + | 0.699215i | \(0.753533\pi\) | |||||||
\(398\) | −25.3168 | −1.26902 | ||||||||
\(399\) | 13.5540 | 0.678550 | ||||||||
\(400\) | 5.30211 | 0.265106 | ||||||||
\(401\) | −33.9746 | −1.69661 | −0.848306 | − | 0.529507i | \(-0.822377\pi\) | ||||
−0.848306 | + | 0.529507i | \(0.822377\pi\) | |||||||
\(402\) | 13.5209 | 0.674360 | ||||||||
\(403\) | −4.65872 | −0.232067 | ||||||||
\(404\) | 18.7134 | 0.931027 | ||||||||
\(405\) | −3.20969 | −0.159491 | ||||||||
\(406\) | 4.65044 | 0.230798 | ||||||||
\(407\) | 4.98816 | 0.247254 | ||||||||
\(408\) | 0.669533 | 0.0331468 | ||||||||
\(409\) | 27.7269 | 1.37101 | 0.685504 | − | 0.728069i | \(-0.259582\pi\) | ||||
0.685504 | + | 0.728069i | \(0.259582\pi\) | |||||||
\(410\) | 4.90515 | 0.242248 | ||||||||
\(411\) | 6.86144 | 0.338450 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 7.61896 | 0.374904 | ||||||||
\(414\) | 2.38462 | 0.117198 | ||||||||
\(415\) | −0.218140 | −0.0107081 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 13.0202 | 0.637604 | ||||||||
\(418\) | −11.5664 | −0.565730 | ||||||||
\(419\) | 14.6390 | 0.715161 | 0.357581 | − | 0.933882i | \(-0.383602\pi\) | ||||
0.357581 | + | 0.933882i | \(0.383602\pi\) | |||||||
\(420\) | −6.49033 | −0.316696 | ||||||||
\(421\) | 7.33989 | 0.357724 | 0.178862 | − | 0.983874i | \(-0.442758\pi\) | ||||
0.178862 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(422\) | 2.77247 | 0.134962 | ||||||||
\(423\) | 8.51407 | 0.413968 | ||||||||
\(424\) | 11.6372 | 0.565153 | ||||||||
\(425\) | −3.54994 | −0.172197 | ||||||||
\(426\) | −6.69404 | −0.324327 | ||||||||
\(427\) | 7.00934 | 0.339206 | ||||||||
\(428\) | 3.67967 | 0.177863 | ||||||||
\(429\) | 1.72557 | 0.0833113 | ||||||||
\(430\) | −12.0339 | −0.580328 | ||||||||
\(431\) | 25.2104 | 1.21434 | 0.607171 | − | 0.794571i | \(-0.292304\pi\) | ||||
0.607171 | + | 0.794571i | \(0.292304\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 15.4861 | 0.744213 | 0.372107 | − | 0.928190i | \(-0.378636\pi\) | ||||
0.372107 | + | 0.928190i | \(0.378636\pi\) | |||||||
\(434\) | 9.42042 | 0.452195 | ||||||||
\(435\) | −7.38166 | −0.353923 | ||||||||
\(436\) | −0.643981 | −0.0308411 | ||||||||
\(437\) | 15.9839 | 0.764614 | ||||||||
\(438\) | −11.7410 | −0.561008 | ||||||||
\(439\) | 31.5746 | 1.50697 | 0.753486 | − | 0.657464i | \(-0.228371\pi\) | ||||
0.753486 | + | 0.657464i | \(0.228371\pi\) | |||||||
\(440\) | 5.53854 | 0.264040 | ||||||||
\(441\) | −2.91109 | −0.138623 | ||||||||
\(442\) | −0.669533 | −0.0318464 | ||||||||
\(443\) | −6.71458 | −0.319019 | −0.159510 | − | 0.987196i | \(-0.550991\pi\) | ||||
−0.159510 | + | 0.987196i | \(0.550991\pi\) | |||||||
\(444\) | 2.89073 | 0.137188 | ||||||||
\(445\) | −50.8535 | −2.41069 | ||||||||
\(446\) | 29.2727 | 1.38610 | ||||||||
\(447\) | −11.3872 | −0.538595 | ||||||||
\(448\) | −2.02210 | −0.0955355 | ||||||||
\(449\) | 16.4048 | 0.774190 | 0.387095 | − | 0.922040i | \(-0.373479\pi\) | ||||
0.387095 | + | 0.922040i | \(0.373479\pi\) | |||||||
\(450\) | 5.30211 | 0.249944 | ||||||||
\(451\) | 2.63707 | 0.124175 | ||||||||
\(452\) | −2.61607 | −0.123049 | ||||||||
\(453\) | −6.07828 | −0.285582 | ||||||||
\(454\) | 17.6781 | 0.829675 | ||||||||
\(455\) | 6.49033 | 0.304271 | ||||||||
\(456\) | −6.70293 | −0.313893 | ||||||||
\(457\) | −22.4703 | −1.05112 | −0.525559 | − | 0.850757i | \(-0.676144\pi\) | ||||
−0.525559 | + | 0.850757i | \(0.676144\pi\) | |||||||
\(458\) | −22.4144 | −1.04736 | ||||||||
\(459\) | 0.669533 | 0.0312511 | ||||||||
\(460\) | −7.65388 | −0.356864 | ||||||||
\(461\) | −18.0083 | −0.838729 | −0.419365 | − | 0.907818i | \(-0.637747\pi\) | ||||
−0.419365 | + | 0.907818i | \(0.637747\pi\) | |||||||
\(462\) | −3.48928 | −0.162336 | ||||||||
\(463\) | −5.02690 | −0.233620 | −0.116810 | − | 0.993154i | \(-0.537267\pi\) | ||||
−0.116810 | + | 0.993154i | \(0.537267\pi\) | |||||||
\(464\) | −2.29980 | −0.106766 | ||||||||
\(465\) | −14.9530 | −0.693431 | ||||||||
\(466\) | −20.3329 | −0.941903 | ||||||||
\(467\) | −8.50870 | −0.393736 | −0.196868 | − | 0.980430i | \(-0.563077\pi\) | ||||
−0.196868 | + | 0.980430i | \(0.563077\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 27.3406 | 1.26247 | ||||||||
\(470\) | −27.3275 | −1.26052 | ||||||||
\(471\) | 10.3162 | 0.475347 | ||||||||
\(472\) | −3.76784 | −0.173429 | ||||||||
\(473\) | −6.46959 | −0.297472 | ||||||||
\(474\) | −0.941600 | −0.0432491 | ||||||||
\(475\) | 35.5397 | 1.63067 | ||||||||
\(476\) | 1.35387 | 0.0620544 | ||||||||
\(477\) | 11.6372 | 0.532831 | ||||||||
\(478\) | −18.4706 | −0.844827 | ||||||||
\(479\) | 6.33157 | 0.289297 | 0.144648 | − | 0.989483i | \(-0.453795\pi\) | ||||
0.144648 | + | 0.989483i | \(0.453795\pi\) | |||||||
\(480\) | 3.20969 | 0.146502 | ||||||||
\(481\) | −2.89073 | −0.131806 | ||||||||
\(482\) | 15.6356 | 0.712182 | ||||||||
\(483\) | 4.82194 | 0.219406 | ||||||||
\(484\) | −8.02241 | −0.364655 | ||||||||
\(485\) | 47.8643 | 2.17340 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 28.0705 | 1.27199 | 0.635997 | − | 0.771692i | \(-0.280589\pi\) | ||||
0.635997 | + | 0.771692i | \(0.280589\pi\) | |||||||
\(488\) | −3.46636 | −0.156915 | ||||||||
\(489\) | 15.6784 | 0.709001 | ||||||||
\(490\) | 9.34370 | 0.422105 | ||||||||
\(491\) | −25.3670 | −1.14480 | −0.572399 | − | 0.819975i | \(-0.693987\pi\) | ||||
−0.572399 | + | 0.819975i | \(0.693987\pi\) | |||||||
\(492\) | 1.52823 | 0.0688980 | ||||||||
\(493\) | 1.53979 | 0.0693489 | ||||||||
\(494\) | 6.70293 | 0.301579 | ||||||||
\(495\) | 5.53854 | 0.248939 | ||||||||
\(496\) | −4.65872 | −0.209183 | ||||||||
\(497\) | −13.5360 | −0.607175 | ||||||||
\(498\) | −0.0679630 | −0.00304550 | ||||||||
\(499\) | −9.91564 | −0.443885 | −0.221942 | − | 0.975060i | \(-0.571240\pi\) | ||||
−0.221942 | + | 0.975060i | \(0.571240\pi\) | |||||||
\(500\) | −0.969688 | −0.0433658 | ||||||||
\(501\) | −1.59761 | −0.0713759 | ||||||||
\(502\) | −12.3105 | −0.549445 | ||||||||
\(503\) | 33.6282 | 1.49941 | 0.749704 | − | 0.661773i | \(-0.230196\pi\) | ||||
0.749704 | + | 0.661773i | \(0.230196\pi\) | |||||||
\(504\) | −2.02210 | −0.0900717 | ||||||||
\(505\) | −60.0643 | −2.67283 | ||||||||
\(506\) | −4.11482 | −0.182926 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −17.1214 | −0.759639 | ||||||||
\(509\) | 5.30327 | 0.235063 | 0.117532 | − | 0.993069i | \(-0.462502\pi\) | ||||
0.117532 | + | 0.993069i | \(0.462502\pi\) | |||||||
\(510\) | −2.14899 | −0.0951591 | ||||||||
\(511\) | −23.7416 | −1.05027 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.70293 | −0.295942 | ||||||||
\(514\) | −25.6930 | −1.13327 | ||||||||
\(515\) | 3.20969 | 0.141436 | ||||||||
\(516\) | −3.74925 | −0.165052 | ||||||||
\(517\) | −14.6916 | −0.646136 | ||||||||
\(518\) | 5.84536 | 0.256831 | ||||||||
\(519\) | 1.82588 | 0.0801473 | ||||||||
\(520\) | −3.20969 | −0.140754 | ||||||||
\(521\) | 12.0147 | 0.526376 | 0.263188 | − | 0.964745i | \(-0.415226\pi\) | ||||
0.263188 | + | 0.964745i | \(0.415226\pi\) | |||||||
\(522\) | −2.29980 | −0.100660 | ||||||||
\(523\) | −17.9439 | −0.784631 | −0.392316 | − | 0.919831i | \(-0.628326\pi\) | ||||
−0.392316 | + | 0.919831i | \(0.628326\pi\) | |||||||
\(524\) | −11.9320 | −0.521253 | ||||||||
\(525\) | 10.7214 | 0.467921 | ||||||||
\(526\) | −12.2397 | −0.533678 | ||||||||
\(527\) | 3.11917 | 0.135873 | ||||||||
\(528\) | 1.72557 | 0.0750958 | ||||||||
\(529\) | −17.3136 | −0.752765 | ||||||||
\(530\) | −37.3518 | −1.62246 | ||||||||
\(531\) | −3.76784 | −0.163510 | ||||||||
\(532\) | −13.5540 | −0.587642 | ||||||||
\(533\) | −1.52823 | −0.0661951 | ||||||||
\(534\) | −15.8437 | −0.685625 | ||||||||
\(535\) | −11.8106 | −0.510616 | ||||||||
\(536\) | −13.5209 | −0.584013 | ||||||||
\(537\) | 6.67663 | 0.288118 | ||||||||
\(538\) | −18.2413 | −0.786440 | ||||||||
\(539\) | 5.02329 | 0.216368 | ||||||||
\(540\) | 3.20969 | 0.138123 | ||||||||
\(541\) | 32.7794 | 1.40930 | 0.704649 | − | 0.709556i | \(-0.251104\pi\) | ||||
0.704649 | + | 0.709556i | \(0.251104\pi\) | |||||||
\(542\) | 3.96166 | 0.170168 | ||||||||
\(543\) | 21.0273 | 0.902370 | ||||||||
\(544\) | −0.669533 | −0.0287060 | ||||||||
\(545\) | 2.06698 | 0.0885396 | ||||||||
\(546\) | 2.02210 | 0.0865381 | ||||||||
\(547\) | 8.57173 | 0.366501 | 0.183250 | − | 0.983066i | \(-0.441338\pi\) | ||||
0.183250 | + | 0.983066i | \(0.441338\pi\) | |||||||
\(548\) | −6.86144 | −0.293106 | ||||||||
\(549\) | −3.46636 | −0.147941 | ||||||||
\(550\) | −9.14916 | −0.390122 | ||||||||
\(551\) | −15.4154 | −0.656719 | ||||||||
\(552\) | −2.38462 | −0.101496 | ||||||||
\(553\) | −1.90401 | −0.0809669 | ||||||||
\(554\) | −18.5109 | −0.786452 | ||||||||
\(555\) | −9.27836 | −0.393844 | ||||||||
\(556\) | −13.0202 | −0.552181 | ||||||||
\(557\) | 0.0836573 | 0.00354467 | 0.00177234 | − | 0.999998i | \(-0.499436\pi\) | ||||
0.00177234 | + | 0.999998i | \(0.499436\pi\) | |||||||
\(558\) | −4.65872 | −0.197219 | ||||||||
\(559\) | 3.74925 | 0.158576 | ||||||||
\(560\) | 6.49033 | 0.274267 | ||||||||
\(561\) | −1.15533 | −0.0487779 | ||||||||
\(562\) | 18.6586 | 0.787067 | ||||||||
\(563\) | 4.82841 | 0.203493 | 0.101747 | − | 0.994810i | \(-0.467557\pi\) | ||||
0.101747 | + | 0.994810i | \(0.467557\pi\) | |||||||
\(564\) | −8.51407 | −0.358507 | ||||||||
\(565\) | 8.39677 | 0.353255 | ||||||||
\(566\) | 26.3081 | 1.10581 | ||||||||
\(567\) | −2.02210 | −0.0849204 | ||||||||
\(568\) | 6.69404 | 0.280876 | ||||||||
\(569\) | 41.6502 | 1.74607 | 0.873033 | − | 0.487661i | \(-0.162150\pi\) | ||||
0.873033 | + | 0.487661i | \(0.162150\pi\) | |||||||
\(570\) | 21.5143 | 0.901136 | ||||||||
\(571\) | 30.5388 | 1.27801 | 0.639004 | − | 0.769203i | \(-0.279347\pi\) | ||||
0.639004 | + | 0.769203i | \(0.279347\pi\) | |||||||
\(572\) | −1.72557 | −0.0721497 | ||||||||
\(573\) | 20.1793 | 0.843004 | ||||||||
\(574\) | 3.09025 | 0.128984 | ||||||||
\(575\) | 12.6435 | 0.527271 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −25.1388 | −1.04654 | −0.523272 | − | 0.852166i | \(-0.675289\pi\) | ||||
−0.523272 | + | 0.852166i | \(0.675289\pi\) | |||||||
\(578\) | −16.5517 | −0.688461 | ||||||||
\(579\) | 6.28353 | 0.261134 | ||||||||
\(580\) | 7.38166 | 0.306507 | ||||||||
\(581\) | −0.137428 | −0.00570149 | ||||||||
\(582\) | 14.9124 | 0.618140 | ||||||||
\(583\) | −20.0808 | −0.831662 | ||||||||
\(584\) | 11.7410 | 0.485847 | ||||||||
\(585\) | −3.20969 | −0.132704 | ||||||||
\(586\) | −8.53157 | −0.352436 | ||||||||
\(587\) | −21.8038 | −0.899938 | −0.449969 | − | 0.893044i | \(-0.648565\pi\) | ||||
−0.449969 | + | 0.893044i | \(0.648565\pi\) | |||||||
\(588\) | 2.91109 | 0.120051 | ||||||||
\(589\) | −31.2271 | −1.28669 | ||||||||
\(590\) | 12.0936 | 0.497885 | ||||||||
\(591\) | 17.1542 | 0.705630 | ||||||||
\(592\) | −2.89073 | −0.118808 | ||||||||
\(593\) | 24.1980 | 0.993691 | 0.496846 | − | 0.867839i | \(-0.334492\pi\) | ||||
0.496846 | + | 0.867839i | \(0.334492\pi\) | |||||||
\(594\) | 1.72557 | 0.0708010 | ||||||||
\(595\) | −4.34549 | −0.178148 | ||||||||
\(596\) | 11.3872 | 0.466437 | ||||||||
\(597\) | 25.3168 | 1.03615 | ||||||||
\(598\) | 2.38462 | 0.0975142 | ||||||||
\(599\) | −7.97659 | −0.325915 | −0.162957 | − | 0.986633i | \(-0.552103\pi\) | ||||
−0.162957 | + | 0.986633i | \(0.552103\pi\) | |||||||
\(600\) | −5.30211 | −0.216458 | ||||||||
\(601\) | 45.4210 | 1.85276 | 0.926381 | − | 0.376588i | \(-0.122903\pi\) | ||||
0.926381 | + | 0.376588i | \(0.122903\pi\) | |||||||
\(602\) | −7.58138 | −0.308994 | ||||||||
\(603\) | −13.5209 | −0.550612 | ||||||||
\(604\) | 6.07828 | 0.247322 | ||||||||
\(605\) | 25.7495 | 1.04686 | ||||||||
\(606\) | −18.7134 | −0.760181 | ||||||||
\(607\) | −2.64554 | −0.107379 | −0.0536897 | − | 0.998558i | \(-0.517098\pi\) | ||||
−0.0536897 | + | 0.998558i | \(0.517098\pi\) | |||||||
\(608\) | 6.70293 | 0.271840 | ||||||||
\(609\) | −4.65044 | −0.188445 | ||||||||
\(610\) | 11.1259 | 0.450476 | ||||||||
\(611\) | 8.51407 | 0.344442 | ||||||||
\(612\) | −0.669533 | −0.0270643 | ||||||||
\(613\) | −33.0710 | −1.33573 | −0.667863 | − | 0.744284i | \(-0.732791\pi\) | ||||
−0.667863 | + | 0.744284i | \(0.732791\pi\) | |||||||
\(614\) | −17.3226 | −0.699082 | ||||||||
\(615\) | −4.90515 | −0.197795 | ||||||||
\(616\) | 3.48928 | 0.140587 | ||||||||
\(617\) | −23.4625 | −0.944564 | −0.472282 | − | 0.881447i | \(-0.656570\pi\) | ||||
−0.472282 | + | 0.881447i | \(0.656570\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −24.7794 | −0.995968 | −0.497984 | − | 0.867186i | \(-0.665926\pi\) | ||||
−0.497984 | + | 0.867186i | \(0.665926\pi\) | |||||||
\(620\) | 14.9530 | 0.600529 | ||||||||
\(621\) | −2.38462 | −0.0956914 | ||||||||
\(622\) | −1.53808 | −0.0616714 | ||||||||
\(623\) | −32.0377 | −1.28356 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −23.3982 | −0.935927 | ||||||||
\(626\) | −19.6423 | −0.785065 | ||||||||
\(627\) | 11.5664 | 0.461916 | ||||||||
\(628\) | −10.3162 | −0.411663 | ||||||||
\(629\) | 1.93544 | 0.0771711 | ||||||||
\(630\) | 6.49033 | 0.258581 | ||||||||
\(631\) | 9.08319 | 0.361596 | 0.180798 | − | 0.983520i | \(-0.442132\pi\) | ||||
0.180798 | + | 0.983520i | \(0.442132\pi\) | |||||||
\(632\) | 0.941600 | 0.0374548 | ||||||||
\(633\) | −2.77247 | −0.110196 | ||||||||
\(634\) | 11.6707 | 0.463501 | ||||||||
\(635\) | 54.9544 | 2.18080 | ||||||||
\(636\) | −11.6372 | −0.461445 | ||||||||
\(637\) | −2.91109 | −0.115342 | ||||||||
\(638\) | 3.96847 | 0.157113 | ||||||||
\(639\) | 6.69404 | 0.264812 | ||||||||
\(640\) | −3.20969 | −0.126874 | ||||||||
\(641\) | −44.2213 | −1.74664 | −0.873318 | − | 0.487150i | \(-0.838036\pi\) | ||||
−0.873318 | + | 0.487150i | \(0.838036\pi\) | |||||||
\(642\) | −3.67967 | −0.145225 | ||||||||
\(643\) | −24.8201 | −0.978810 | −0.489405 | − | 0.872057i | \(-0.662786\pi\) | ||||
−0.489405 | + | 0.872057i | \(0.662786\pi\) | |||||||
\(644\) | −4.82194 | −0.190011 | ||||||||
\(645\) | 12.0339 | 0.473836 | ||||||||
\(646\) | −4.48783 | −0.176571 | ||||||||
\(647\) | 21.8686 | 0.859744 | 0.429872 | − | 0.902890i | \(-0.358559\pi\) | ||||
0.429872 | + | 0.902890i | \(0.358559\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 6.50166 | 0.255213 | ||||||||
\(650\) | 5.30211 | 0.207966 | ||||||||
\(651\) | −9.42042 | −0.369215 | ||||||||
\(652\) | −15.6784 | −0.614013 | ||||||||
\(653\) | 33.3162 | 1.30376 | 0.651882 | − | 0.758320i | \(-0.273980\pi\) | ||||
0.651882 | + | 0.758320i | \(0.273980\pi\) | |||||||
\(654\) | 0.643981 | 0.0251816 | ||||||||
\(655\) | 38.2981 | 1.49643 | ||||||||
\(656\) | −1.52823 | −0.0596675 | ||||||||
\(657\) | 11.7410 | 0.458061 | ||||||||
\(658\) | −17.2163 | −0.671163 | ||||||||
\(659\) | −25.0845 | −0.977153 | −0.488577 | − | 0.872521i | \(-0.662484\pi\) | ||||
−0.488577 | + | 0.872521i | \(0.662484\pi\) | |||||||
\(660\) | −5.53854 | −0.215588 | ||||||||
\(661\) | 33.1111 | 1.28787 | 0.643936 | − | 0.765079i | \(-0.277300\pi\) | ||||
0.643936 | + | 0.765079i | \(0.277300\pi\) | |||||||
\(662\) | 28.6487 | 1.11346 | ||||||||
\(663\) | 0.669533 | 0.0260025 | ||||||||
\(664\) | 0.0679630 | 0.00263748 | ||||||||
\(665\) | 43.5042 | 1.68702 | ||||||||
\(666\) | −2.89073 | −0.112014 | ||||||||
\(667\) | −5.48415 | −0.212347 | ||||||||
\(668\) | 1.59761 | 0.0618134 | ||||||||
\(669\) | −29.2727 | −1.13175 | ||||||||
\(670\) | 43.3978 | 1.67660 | ||||||||
\(671\) | 5.98144 | 0.230911 | ||||||||
\(672\) | 2.02210 | 0.0780044 | ||||||||
\(673\) | −19.3297 | −0.745105 | −0.372553 | − | 0.928011i | \(-0.621517\pi\) | ||||
−0.372553 | + | 0.928011i | \(0.621517\pi\) | |||||||
\(674\) | −4.12431 | −0.158863 | ||||||||
\(675\) | −5.30211 | −0.204078 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 42.8994 | 1.64876 | 0.824380 | − | 0.566037i | \(-0.191524\pi\) | ||||
0.824380 | + | 0.566037i | \(0.191524\pi\) | |||||||
\(678\) | 2.61607 | 0.100469 | ||||||||
\(679\) | 30.1545 | 1.15722 | ||||||||
\(680\) | 2.14899 | 0.0824102 | ||||||||
\(681\) | −17.6781 | −0.677427 | ||||||||
\(682\) | 8.03894 | 0.307827 | ||||||||
\(683\) | −26.5193 | −1.01473 | −0.507365 | − | 0.861731i | \(-0.669381\pi\) | ||||
−0.507365 | + | 0.861731i | \(0.669381\pi\) | |||||||
\(684\) | 6.70293 | 0.256293 | ||||||||
\(685\) | 22.0231 | 0.841459 | ||||||||
\(686\) | 20.0413 | 0.765179 | ||||||||
\(687\) | 22.4144 | 0.855164 | ||||||||
\(688\) | 3.74925 | 0.142939 | ||||||||
\(689\) | 11.6372 | 0.443342 | ||||||||
\(690\) | 7.65388 | 0.291378 | ||||||||
\(691\) | −30.4249 | −1.15742 | −0.578709 | − | 0.815534i | \(-0.696443\pi\) | ||||
−0.578709 | + | 0.815534i | \(0.696443\pi\) | |||||||
\(692\) | −1.82588 | −0.0694096 | ||||||||
\(693\) | 3.48928 | 0.132547 | ||||||||
\(694\) | −0.273562 | −0.0103843 | ||||||||
\(695\) | 41.7910 | 1.58522 | ||||||||
\(696\) | 2.29980 | 0.0871738 | ||||||||
\(697\) | 1.02320 | 0.0387566 | ||||||||
\(698\) | −12.3688 | −0.468165 | ||||||||
\(699\) | 20.3329 | 0.769060 | ||||||||
\(700\) | −10.7214 | −0.405232 | ||||||||
\(701\) | −6.24257 | −0.235778 | −0.117889 | − | 0.993027i | \(-0.537613\pi\) | ||||
−0.117889 | + | 0.993027i | \(0.537613\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −19.3764 | −0.730794 | ||||||||
\(704\) | −1.72557 | −0.0650348 | ||||||||
\(705\) | 27.3275 | 1.02921 | ||||||||
\(706\) | 18.6874 | 0.703310 | ||||||||
\(707\) | −37.8405 | −1.42314 | ||||||||
\(708\) | 3.76784 | 0.141604 | ||||||||
\(709\) | 1.68983 | 0.0634627 | 0.0317314 | − | 0.999496i | \(-0.489898\pi\) | ||||
0.0317314 | + | 0.999496i | \(0.489898\pi\) | |||||||
\(710\) | −21.4858 | −0.806347 | ||||||||
\(711\) | 0.941600 | 0.0353128 | ||||||||
\(712\) | 15.8437 | 0.593769 | ||||||||
\(713\) | −11.1093 | −0.416045 | ||||||||
\(714\) | −1.35387 | −0.0506672 | ||||||||
\(715\) | 5.53854 | 0.207130 | ||||||||
\(716\) | −6.67663 | −0.249517 | ||||||||
\(717\) | 18.4706 | 0.689798 | ||||||||
\(718\) | −10.1397 | −0.378409 | ||||||||
\(719\) | −46.1759 | −1.72207 | −0.861034 | − | 0.508547i | \(-0.830183\pi\) | ||||
−0.861034 | + | 0.508547i | \(0.830183\pi\) | |||||||
\(720\) | −3.20969 | −0.119618 | ||||||||
\(721\) | 2.02210 | 0.0753071 | ||||||||
\(722\) | 25.9293 | 0.964988 | ||||||||
\(723\) | −15.6356 | −0.581494 | ||||||||
\(724\) | −21.0273 | −0.781475 | ||||||||
\(725\) | −12.1938 | −0.452867 | ||||||||
\(726\) | 8.02241 | 0.297740 | ||||||||
\(727\) | 8.06916 | 0.299268 | 0.149634 | − | 0.988741i | \(-0.452190\pi\) | ||||
0.149634 | + | 0.988741i | \(0.452190\pi\) | |||||||
\(728\) | −2.02210 | −0.0749442 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −37.6850 | −1.39479 | ||||||||
\(731\) | −2.51025 | −0.0928449 | ||||||||
\(732\) | 3.46636 | 0.128120 | ||||||||
\(733\) | 7.59474 | 0.280518 | 0.140259 | − | 0.990115i | \(-0.455206\pi\) | ||||
0.140259 | + | 0.990115i | \(0.455206\pi\) | |||||||
\(734\) | −16.8044 | −0.620263 | ||||||||
\(735\) | −9.34370 | −0.344648 | ||||||||
\(736\) | 2.38462 | 0.0878981 | ||||||||
\(737\) | 23.3312 | 0.859416 | ||||||||
\(738\) | −1.52823 | −0.0562550 | ||||||||
\(739\) | −18.5847 | −0.683648 | −0.341824 | − | 0.939764i | \(-0.611045\pi\) | ||||
−0.341824 | + | 0.939764i | \(0.611045\pi\) | |||||||
\(740\) | 9.27836 | 0.341079 | ||||||||
\(741\) | −6.70293 | −0.246238 | ||||||||
\(742\) | −23.5317 | −0.863874 | ||||||||
\(743\) | −16.2897 | −0.597613 | −0.298806 | − | 0.954314i | \(-0.596588\pi\) | ||||
−0.298806 | + | 0.954314i | \(0.596588\pi\) | |||||||
\(744\) | 4.65872 | 0.170797 | ||||||||
\(745\) | −36.5493 | −1.33906 | ||||||||
\(746\) | 1.24141 | 0.0454512 | ||||||||
\(747\) | 0.0679630 | 0.00248664 | ||||||||
\(748\) | 1.15533 | 0.0422429 | ||||||||
\(749\) | −7.44067 | −0.271876 | ||||||||
\(750\) | 0.969688 | 0.0354080 | ||||||||
\(751\) | −40.2701 | −1.46948 | −0.734739 | − | 0.678350i | \(-0.762695\pi\) | ||||
−0.734739 | + | 0.678350i | \(0.762695\pi\) | |||||||
\(752\) | 8.51407 | 0.310476 | ||||||||
\(753\) | 12.3105 | 0.448620 | ||||||||
\(754\) | −2.29980 | −0.0837539 | ||||||||
\(755\) | −19.5094 | −0.710020 | ||||||||
\(756\) | 2.02210 | 0.0735432 | ||||||||
\(757\) | −36.6762 | −1.33302 | −0.666510 | − | 0.745496i | \(-0.732213\pi\) | ||||
−0.666510 | + | 0.745496i | \(0.732213\pi\) | |||||||
\(758\) | 2.51633 | 0.0913973 | ||||||||
\(759\) | 4.11482 | 0.149359 | ||||||||
\(760\) | −21.5143 | −0.780407 | ||||||||
\(761\) | −0.506560 | −0.0183628 | −0.00918140 | − | 0.999958i | \(-0.502923\pi\) | ||||
−0.00918140 | + | 0.999958i | \(0.502923\pi\) | |||||||
\(762\) | 17.1214 | 0.620243 | ||||||||
\(763\) | 1.30220 | 0.0471427 | ||||||||
\(764\) | −20.1793 | −0.730063 | ||||||||
\(765\) | 2.14899 | 0.0776970 | ||||||||
\(766\) | 16.4674 | 0.594993 | ||||||||
\(767\) | −3.76784 | −0.136049 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −19.2648 | −0.694705 | −0.347353 | − | 0.937735i | \(-0.612919\pi\) | ||||
−0.347353 | + | 0.937735i | \(0.612919\pi\) | |||||||
\(770\) | −11.1995 | −0.403603 | ||||||||
\(771\) | 25.6930 | 0.925312 | ||||||||
\(772\) | −6.28353 | −0.226149 | ||||||||
\(773\) | −19.7072 | −0.708818 | −0.354409 | − | 0.935091i | \(-0.615318\pi\) | ||||
−0.354409 | + | 0.935091i | \(0.615318\pi\) | |||||||
\(774\) | 3.74925 | 0.134764 | ||||||||
\(775\) | −24.7011 | −0.887288 | ||||||||
\(776\) | −14.9124 | −0.535325 | ||||||||
\(777\) | −5.84536 | −0.209701 | ||||||||
\(778\) | 4.75752 | 0.170565 | ||||||||
\(779\) | −10.2436 | −0.367016 | ||||||||
\(780\) | 3.20969 | 0.114925 | ||||||||
\(781\) | −11.5510 | −0.413328 | ||||||||
\(782\) | −1.59658 | −0.0570936 | ||||||||
\(783\) | 2.29980 | 0.0821883 | ||||||||
\(784\) | −2.91109 | −0.103968 | ||||||||
\(785\) | 33.1120 | 1.18182 | ||||||||
\(786\) | 11.9320 | 0.425601 | ||||||||
\(787\) | 41.3177 | 1.47282 | 0.736409 | − | 0.676536i | \(-0.236520\pi\) | ||||
0.736409 | + | 0.676536i | \(0.236520\pi\) | |||||||
\(788\) | −17.1542 | −0.611094 | ||||||||
\(789\) | 12.2397 | 0.435746 | ||||||||
\(790\) | −3.02225 | −0.107527 | ||||||||
\(791\) | 5.28996 | 0.188089 | ||||||||
\(792\) | −1.72557 | −0.0613154 | ||||||||
\(793\) | −3.46636 | −0.123094 | ||||||||
\(794\) | −28.4890 | −1.01104 | ||||||||
\(795\) | 37.3518 | 1.32473 | ||||||||
\(796\) | −25.3168 | −0.897330 | ||||||||
\(797\) | 43.7552 | 1.54989 | 0.774944 | − | 0.632030i | \(-0.217778\pi\) | ||||
0.774944 | + | 0.632030i | \(0.217778\pi\) | |||||||
\(798\) | 13.5540 | 0.479807 | ||||||||
\(799\) | −5.70045 | −0.201667 | ||||||||
\(800\) | 5.30211 | 0.187458 | ||||||||
\(801\) | 15.8437 | 0.559811 | ||||||||
\(802\) | −33.9746 | −1.19969 | ||||||||
\(803\) | −20.2599 | −0.714958 | ||||||||
\(804\) | 13.5209 | 0.476844 | ||||||||
\(805\) | 15.4770 | 0.545491 | ||||||||
\(806\) | −4.65872 | −0.164096 | ||||||||
\(807\) | 18.2413 | 0.642126 | ||||||||
\(808\) | 18.7134 | 0.658336 | ||||||||
\(809\) | −32.3788 | −1.13838 | −0.569189 | − | 0.822207i | \(-0.692743\pi\) | ||||
−0.569189 | + | 0.822207i | \(0.692743\pi\) | |||||||
\(810\) | −3.20969 | −0.112777 | ||||||||
\(811\) | −7.11397 | −0.249805 | −0.124903 | − | 0.992169i | \(-0.539862\pi\) | ||||
−0.124903 | + | 0.992169i | \(0.539862\pi\) | |||||||
\(812\) | 4.65044 | 0.163199 | ||||||||
\(813\) | −3.96166 | −0.138942 | ||||||||
\(814\) | 4.98816 | 0.174835 | ||||||||
\(815\) | 50.3227 | 1.76273 | ||||||||
\(816\) | 0.669533 | 0.0234383 | ||||||||
\(817\) | 25.1310 | 0.879221 | ||||||||
\(818\) | 27.7269 | 0.969450 | ||||||||
\(819\) | −2.02210 | −0.0706581 | ||||||||
\(820\) | 4.90515 | 0.171295 | ||||||||
\(821\) | −40.6722 | −1.41947 | −0.709735 | − | 0.704469i | \(-0.751185\pi\) | ||||
−0.709735 | + | 0.704469i | \(0.751185\pi\) | |||||||
\(822\) | 6.86144 | 0.239320 | ||||||||
\(823\) | 23.9583 | 0.835132 | 0.417566 | − | 0.908647i | \(-0.362883\pi\) | ||||
0.417566 | + | 0.908647i | \(0.362883\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 9.14916 | 0.318533 | ||||||||
\(826\) | 7.61896 | 0.265097 | ||||||||
\(827\) | −8.40864 | −0.292397 | −0.146198 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146198 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(828\) | 2.38462 | 0.0828712 | ||||||||
\(829\) | 44.9658 | 1.56173 | 0.780864 | − | 0.624701i | \(-0.214779\pi\) | ||||
0.780864 | + | 0.624701i | \(0.214779\pi\) | |||||||
\(830\) | −0.218140 | −0.00757176 | ||||||||
\(831\) | 18.5109 | 0.642136 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 1.94907 | 0.0675314 | ||||||||
\(834\) | 13.0202 | 0.450854 | ||||||||
\(835\) | −5.12783 | −0.177456 | ||||||||
\(836\) | −11.5664 | −0.400031 | ||||||||
\(837\) | 4.65872 | 0.161029 | ||||||||
\(838\) | 14.6390 | 0.505695 | ||||||||
\(839\) | 7.81663 | 0.269860 | 0.134930 | − | 0.990855i | \(-0.456919\pi\) | ||||
0.134930 | + | 0.990855i | \(0.456919\pi\) | |||||||
\(840\) | −6.49033 | −0.223938 | ||||||||
\(841\) | −23.7109 | −0.817617 | ||||||||
\(842\) | 7.33989 | 0.252949 | ||||||||
\(843\) | −18.6586 | −0.642638 | ||||||||
\(844\) | 2.77247 | 0.0954323 | ||||||||
\(845\) | −3.20969 | −0.110417 | ||||||||
\(846\) | 8.51407 | 0.292720 | ||||||||
\(847\) | 16.2222 | 0.557400 | ||||||||
\(848\) | 11.6372 | 0.399623 | ||||||||
\(849\) | −26.3081 | −0.902893 | ||||||||
\(850\) | −3.54994 | −0.121762 | ||||||||
\(851\) | −6.89329 | −0.236299 | ||||||||
\(852\) | −6.69404 | −0.229334 | ||||||||
\(853\) | 24.0738 | 0.824270 | 0.412135 | − | 0.911123i | \(-0.364783\pi\) | ||||
0.412135 | + | 0.911123i | \(0.364783\pi\) | |||||||
\(854\) | 7.00934 | 0.239855 | ||||||||
\(855\) | −21.5143 | −0.735775 | ||||||||
\(856\) | 3.67967 | 0.125768 | ||||||||
\(857\) | −25.2461 | −0.862389 | −0.431194 | − | 0.902259i | \(-0.641908\pi\) | ||||
−0.431194 | + | 0.902259i | \(0.641908\pi\) | |||||||
\(858\) | 1.72557 | 0.0589100 | ||||||||
\(859\) | −30.8226 | −1.05165 | −0.525826 | − | 0.850592i | \(-0.676244\pi\) | ||||
−0.525826 | + | 0.850592i | \(0.676244\pi\) | |||||||
\(860\) | −12.0339 | −0.410354 | ||||||||
\(861\) | −3.09025 | −0.105315 | ||||||||
\(862\) | 25.2104 | 0.858670 | ||||||||
\(863\) | 47.8889 | 1.63016 | 0.815079 | − | 0.579350i | \(-0.196694\pi\) | ||||
0.815079 | + | 0.579350i | \(0.196694\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 5.86051 | 0.199263 | ||||||||
\(866\) | 15.4861 | 0.526238 | ||||||||
\(867\) | 16.5517 | 0.562126 | ||||||||
\(868\) | 9.42042 | 0.319750 | ||||||||
\(869\) | −1.62480 | −0.0551174 | ||||||||
\(870\) | −7.38166 | −0.250262 | ||||||||
\(871\) | −13.5209 | −0.458137 | ||||||||
\(872\) | −0.643981 | −0.0218079 | ||||||||
\(873\) | −14.9124 | −0.504709 | ||||||||
\(874\) | 15.9839 | 0.540664 | ||||||||
\(875\) | 1.96081 | 0.0662875 | ||||||||
\(876\) | −11.7410 | −0.396692 | ||||||||
\(877\) | −38.3110 | −1.29367 | −0.646835 | − | 0.762630i | \(-0.723908\pi\) | ||||
−0.646835 | + | 0.762630i | \(0.723908\pi\) | |||||||
\(878\) | 31.5746 | 1.06559 | ||||||||
\(879\) | 8.53157 | 0.287763 | ||||||||
\(880\) | 5.53854 | 0.186704 | ||||||||
\(881\) | −26.6819 | −0.898936 | −0.449468 | − | 0.893296i | \(-0.648386\pi\) | ||||
−0.449468 | + | 0.893296i | \(0.648386\pi\) | |||||||
\(882\) | −2.91109 | −0.0980215 | ||||||||
\(883\) | 28.2227 | 0.949769 | 0.474884 | − | 0.880048i | \(-0.342490\pi\) | ||||
0.474884 | + | 0.880048i | \(0.342490\pi\) | |||||||
\(884\) | −0.669533 | −0.0225188 | ||||||||
\(885\) | −12.0936 | −0.406521 | ||||||||
\(886\) | −6.71458 | −0.225581 | ||||||||
\(887\) | 40.3094 | 1.35346 | 0.676729 | − | 0.736232i | \(-0.263397\pi\) | ||||
0.676729 | + | 0.736232i | \(0.263397\pi\) | |||||||
\(888\) | 2.89073 | 0.0970066 | ||||||||
\(889\) | 34.6212 | 1.16116 | ||||||||
\(890\) | −50.8535 | −1.70461 | ||||||||
\(891\) | −1.72557 | −0.0578087 | ||||||||
\(892\) | 29.2727 | 0.980123 | ||||||||
\(893\) | 57.0692 | 1.90975 | ||||||||
\(894\) | −11.3872 | −0.380844 | ||||||||
\(895\) | 21.4299 | 0.716323 | ||||||||
\(896\) | −2.02210 | −0.0675538 | ||||||||
\(897\) | −2.38462 | −0.0796200 | ||||||||
\(898\) | 16.4048 | 0.547435 | ||||||||
\(899\) | 10.7141 | 0.357337 | ||||||||
\(900\) | 5.30211 | 0.176737 | ||||||||
\(901\) | −7.79150 | −0.259572 | ||||||||
\(902\) | 2.63707 | 0.0878049 | ||||||||
\(903\) | 7.58138 | 0.252293 | ||||||||
\(904\) | −2.61607 | −0.0870091 | ||||||||
\(905\) | 67.4913 | 2.24349 | ||||||||
\(906\) | −6.07828 | −0.201937 | ||||||||
\(907\) | 38.1235 | 1.26587 | 0.632935 | − | 0.774205i | \(-0.281850\pi\) | ||||
0.632935 | + | 0.774205i | \(0.281850\pi\) | |||||||
\(908\) | 17.6781 | 0.586669 | ||||||||
\(909\) | 18.7134 | 0.620685 | ||||||||
\(910\) | 6.49033 | 0.215152 | ||||||||
\(911\) | 26.6119 | 0.881691 | 0.440845 | − | 0.897583i | \(-0.354679\pi\) | ||||
0.440845 | + | 0.897583i | \(0.354679\pi\) | |||||||
\(912\) | −6.70293 | −0.221956 | ||||||||
\(913\) | −0.117275 | −0.00388123 | ||||||||
\(914\) | −22.4703 | −0.743253 | ||||||||
\(915\) | −11.1259 | −0.367812 | ||||||||
\(916\) | −22.4144 | −0.740593 | ||||||||
\(917\) | 24.1278 | 0.796770 | ||||||||
\(918\) | 0.669533 | 0.0220979 | ||||||||
\(919\) | 8.12414 | 0.267991 | 0.133995 | − | 0.990982i | \(-0.457219\pi\) | ||||
0.133995 | + | 0.990982i | \(0.457219\pi\) | |||||||
\(920\) | −7.65388 | −0.252341 | ||||||||
\(921\) | 17.3226 | 0.570798 | ||||||||
\(922\) | −18.0083 | −0.593071 | ||||||||
\(923\) | 6.69404 | 0.220337 | ||||||||
\(924\) | −3.48928 | −0.114789 | ||||||||
\(925\) | −15.3270 | −0.503948 | ||||||||
\(926\) | −5.02690 | −0.165194 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −2.29980 | −0.0754947 | ||||||||
\(929\) | 1.09825 | 0.0360323 | 0.0180162 | − | 0.999838i | \(-0.494265\pi\) | ||||
0.0180162 | + | 0.999838i | \(0.494265\pi\) | |||||||
\(930\) | −14.9530 | −0.490330 | ||||||||
\(931\) | −19.5128 | −0.639508 | ||||||||
\(932\) | −20.3329 | −0.666026 | ||||||||
\(933\) | 1.53808 | 0.0503545 | ||||||||
\(934\) | −8.50870 | −0.278413 | ||||||||
\(935\) | −3.70824 | −0.121272 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 15.9949 | 0.522530 | 0.261265 | − | 0.965267i | \(-0.415860\pi\) | ||||
0.261265 | + | 0.965267i | \(0.415860\pi\) | |||||||
\(938\) | 27.3406 | 0.892703 | ||||||||
\(939\) | 19.6423 | 0.641003 | ||||||||
\(940\) | −27.3275 | −0.891326 | ||||||||
\(941\) | 13.6922 | 0.446354 | 0.223177 | − | 0.974778i | \(-0.428357\pi\) | ||||
0.223177 | + | 0.974778i | \(0.428357\pi\) | |||||||
\(942\) | 10.3162 | 0.336121 | ||||||||
\(943\) | −3.64425 | −0.118673 | ||||||||
\(944\) | −3.76784 | −0.122633 | ||||||||
\(945\) | −6.49033 | −0.211130 | ||||||||
\(946\) | −6.46959 | −0.210345 | ||||||||
\(947\) | −6.82474 | −0.221774 | −0.110887 | − | 0.993833i | \(-0.535369\pi\) | ||||
−0.110887 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(948\) | −0.941600 | −0.0305818 | ||||||||
\(949\) | 11.7410 | 0.381130 | ||||||||
\(950\) | 35.5397 | 1.15306 | ||||||||
\(951\) | −11.6707 | −0.378447 | ||||||||
\(952\) | 1.35387 | 0.0438791 | ||||||||
\(953\) | −54.0833 | −1.75193 | −0.875965 | − | 0.482374i | \(-0.839775\pi\) | ||||
−0.875965 | + | 0.482374i | \(0.839775\pi\) | |||||||
\(954\) | 11.6372 | 0.376769 | ||||||||
\(955\) | 64.7694 | 2.09589 | ||||||||
\(956\) | −18.4706 | −0.597383 | ||||||||
\(957\) | −3.96847 | −0.128282 | ||||||||
\(958\) | 6.33157 | 0.204564 | ||||||||
\(959\) | 13.8746 | 0.448033 | ||||||||
\(960\) | 3.20969 | 0.103592 | ||||||||
\(961\) | −9.29633 | −0.299882 | ||||||||
\(962\) | −2.89073 | −0.0932010 | ||||||||
\(963\) | 3.67967 | 0.118576 | ||||||||
\(964\) | 15.6356 | 0.503588 | ||||||||
\(965\) | 20.1682 | 0.649237 | ||||||||
\(966\) | 4.82194 | 0.155144 | ||||||||
\(967\) | −27.6290 | −0.888489 | −0.444244 | − | 0.895906i | \(-0.646528\pi\) | ||||
−0.444244 | + | 0.895906i | \(0.646528\pi\) | |||||||
\(968\) | −8.02241 | −0.257850 | ||||||||
\(969\) | 4.48783 | 0.144170 | ||||||||
\(970\) | 47.8643 | 1.53683 | ||||||||
\(971\) | −53.1314 | −1.70507 | −0.852535 | − | 0.522671i | \(-0.824936\pi\) | ||||
−0.852535 | + | 0.522671i | \(0.824936\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 26.3283 | 0.844047 | ||||||||
\(974\) | 28.0705 | 0.899435 | ||||||||
\(975\) | −5.30211 | −0.169804 | ||||||||
\(976\) | −3.46636 | −0.110955 | ||||||||
\(977\) | −6.80034 | −0.217562 | −0.108781 | − | 0.994066i | \(-0.534695\pi\) | ||||
−0.108781 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(978\) | 15.6784 | 0.501339 | ||||||||
\(979\) | −27.3395 | −0.873773 | ||||||||
\(980\) | 9.34370 | 0.298474 | ||||||||
\(981\) | −0.643981 | −0.0205607 | ||||||||
\(982\) | −25.3670 | −0.809494 | ||||||||
\(983\) | 9.75903 | 0.311265 | 0.155632 | − | 0.987815i | \(-0.450258\pi\) | ||||
0.155632 | + | 0.987815i | \(0.450258\pi\) | |||||||
\(984\) | 1.52823 | 0.0487183 | ||||||||
\(985\) | 55.0597 | 1.75435 | ||||||||
\(986\) | 1.53979 | 0.0490371 | ||||||||
\(987\) | 17.2163 | 0.548002 | ||||||||
\(988\) | 6.70293 | 0.213249 | ||||||||
\(989\) | 8.94053 | 0.284292 | ||||||||
\(990\) | 5.53854 | 0.176026 | ||||||||
\(991\) | 25.2699 | 0.802724 | 0.401362 | − | 0.915919i | \(-0.368537\pi\) | ||||
0.401362 | + | 0.915919i | \(0.368537\pi\) | |||||||
\(992\) | −4.65872 | −0.147915 | ||||||||
\(993\) | −28.6487 | −0.909139 | ||||||||
\(994\) | −13.5360 | −0.429337 | ||||||||
\(995\) | 81.2591 | 2.57609 | ||||||||
\(996\) | −0.0679630 | −0.00215349 | ||||||||
\(997\) | −19.5110 | −0.617920 | −0.308960 | − | 0.951075i | \(-0.599981\pi\) | ||||
−0.308960 | + | 0.951075i | \(0.599981\pi\) | |||||||
\(998\) | −9.91564 | −0.313874 | ||||||||
\(999\) | 2.89073 | 0.0914587 |
(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 | 8034.2.a.r.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.r.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |