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: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.75223\) 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 | ||||||||
\(5\) | −3.75223 | −1.67805 | −0.839024 | − | 0.544095i | \(-0.816873\pi\) | ||||
−0.839024 | + | 0.544095i | \(0.816873\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.91373 | 0.723321 | 0.361660 | − | 0.932310i | \(-0.382210\pi\) | ||||
0.361660 | + | 0.932310i | \(0.382210\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.75223 | 1.18656 | ||||||||
\(11\) | −4.14756 | −1.25054 | −0.625268 | − | 0.780410i | \(-0.715010\pi\) | ||||
−0.625268 | + | 0.780410i | \(0.715010\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.91373 | −0.511465 | ||||||||
\(15\) | −3.75223 | −0.968821 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.83878 | −1.17358 | −0.586789 | − | 0.809740i | \(-0.699608\pi\) | ||||
−0.586789 | + | 0.809740i | \(0.699608\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.13299 | 0.489342 | 0.244671 | − | 0.969606i | \(-0.421320\pi\) | ||||
0.244671 | + | 0.969606i | \(0.421320\pi\) | |||||||
\(20\) | −3.75223 | −0.839024 | ||||||||
\(21\) | 1.91373 | 0.417610 | ||||||||
\(22\) | 4.14756 | 0.884262 | ||||||||
\(23\) | 2.08206 | 0.434140 | 0.217070 | − | 0.976156i | \(-0.430350\pi\) | ||||
0.217070 | + | 0.976156i | \(0.430350\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 9.07922 | 1.81584 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.91373 | 0.361660 | ||||||||
\(29\) | −2.19238 | −0.407114 | −0.203557 | − | 0.979063i | \(-0.565250\pi\) | ||||
−0.203557 | + | 0.979063i | \(0.565250\pi\) | |||||||
\(30\) | 3.75223 | 0.685060 | ||||||||
\(31\) | 5.15289 | 0.925487 | 0.462743 | − | 0.886492i | \(-0.346865\pi\) | ||||
0.462743 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.14756 | −0.721997 | ||||||||
\(34\) | 4.83878 | 0.829845 | ||||||||
\(35\) | −7.18074 | −1.21377 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.63112 | 1.58335 | 0.791674 | − | 0.610944i | \(-0.209210\pi\) | ||||
0.791674 | + | 0.610944i | \(0.209210\pi\) | |||||||
\(38\) | −2.13299 | −0.346017 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 3.75223 | 0.593279 | ||||||||
\(41\) | 7.88650 | 1.23166 | 0.615832 | − | 0.787878i | \(-0.288820\pi\) | ||||
0.615832 | + | 0.787878i | \(0.288820\pi\) | |||||||
\(42\) | −1.91373 | −0.295295 | ||||||||
\(43\) | 1.60304 | 0.244461 | 0.122230 | − | 0.992502i | \(-0.460995\pi\) | ||||
0.122230 | + | 0.992502i | \(0.460995\pi\) | |||||||
\(44\) | −4.14756 | −0.625268 | ||||||||
\(45\) | −3.75223 | −0.559349 | ||||||||
\(46\) | −2.08206 | −0.306983 | ||||||||
\(47\) | −9.35222 | −1.36416 | −0.682081 | − | 0.731277i | \(-0.738925\pi\) | ||||
−0.682081 | + | 0.731277i | \(0.738925\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.33765 | −0.476807 | ||||||||
\(50\) | −9.07922 | −1.28400 | ||||||||
\(51\) | −4.83878 | −0.677565 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 12.8161 | 1.76042 | 0.880212 | − | 0.474580i | \(-0.157400\pi\) | ||||
0.880212 | + | 0.474580i | \(0.157400\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 15.5626 | 2.09846 | ||||||||
\(56\) | −1.91373 | −0.255733 | ||||||||
\(57\) | 2.13299 | 0.282522 | ||||||||
\(58\) | 2.19238 | 0.287873 | ||||||||
\(59\) | −7.21379 | −0.939156 | −0.469578 | − | 0.882891i | \(-0.655594\pi\) | ||||
−0.469578 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(60\) | −3.75223 | −0.484411 | ||||||||
\(61\) | 10.2293 | 1.30973 | 0.654864 | − | 0.755747i | \(-0.272726\pi\) | ||||
0.654864 | + | 0.755747i | \(0.272726\pi\) | |||||||
\(62\) | −5.15289 | −0.654418 | ||||||||
\(63\) | 1.91373 | 0.241107 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.75223 | 0.465407 | ||||||||
\(66\) | 4.14756 | 0.510529 | ||||||||
\(67\) | −8.07141 | −0.986079 | −0.493040 | − | 0.870007i | \(-0.664114\pi\) | ||||
−0.493040 | + | 0.870007i | \(0.664114\pi\) | |||||||
\(68\) | −4.83878 | −0.586789 | ||||||||
\(69\) | 2.08206 | 0.250651 | ||||||||
\(70\) | 7.18074 | 0.858263 | ||||||||
\(71\) | 9.46244 | 1.12298 | 0.561492 | − | 0.827482i | \(-0.310227\pi\) | ||||
0.561492 | + | 0.827482i | \(0.310227\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 4.11647 | 0.481797 | 0.240898 | − | 0.970550i | \(-0.422558\pi\) | ||||
0.240898 | + | 0.970550i | \(0.422558\pi\) | |||||||
\(74\) | −9.63112 | −1.11960 | ||||||||
\(75\) | 9.07922 | 1.04838 | ||||||||
\(76\) | 2.13299 | 0.244671 | ||||||||
\(77\) | −7.93729 | −0.904538 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −8.08441 | −0.909567 | −0.454783 | − | 0.890602i | \(-0.650283\pi\) | ||||
−0.454783 | + | 0.890602i | \(0.650283\pi\) | |||||||
\(80\) | −3.75223 | −0.419512 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.88650 | −0.870918 | ||||||||
\(83\) | 0.397774 | 0.0436614 | 0.0218307 | − | 0.999762i | \(-0.493051\pi\) | ||||
0.0218307 | + | 0.999762i | \(0.493051\pi\) | |||||||
\(84\) | 1.91373 | 0.208805 | ||||||||
\(85\) | 18.1562 | 1.96932 | ||||||||
\(86\) | −1.60304 | −0.172860 | ||||||||
\(87\) | −2.19238 | −0.235048 | ||||||||
\(88\) | 4.14756 | 0.442131 | ||||||||
\(89\) | −12.6791 | −1.34399 | −0.671993 | − | 0.740557i | \(-0.734562\pi\) | ||||
−0.671993 | + | 0.740557i | \(0.734562\pi\) | |||||||
\(90\) | 3.75223 | 0.395520 | ||||||||
\(91\) | −1.91373 | −0.200613 | ||||||||
\(92\) | 2.08206 | 0.217070 | ||||||||
\(93\) | 5.15289 | 0.534330 | ||||||||
\(94\) | 9.35222 | 0.964608 | ||||||||
\(95\) | −8.00347 | −0.821139 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −14.9290 | −1.51581 | −0.757905 | − | 0.652365i | \(-0.773777\pi\) | ||||
−0.757905 | + | 0.652365i | \(0.773777\pi\) | |||||||
\(98\) | 3.33765 | 0.337153 | ||||||||
\(99\) | −4.14756 | −0.416845 | ||||||||
\(100\) | 9.07922 | 0.907922 | ||||||||
\(101\) | 16.7182 | 1.66353 | 0.831763 | − | 0.555130i | \(-0.187332\pi\) | ||||
0.831763 | + | 0.555130i | \(0.187332\pi\) | |||||||
\(102\) | 4.83878 | 0.479111 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −7.18074 | −0.700769 | ||||||||
\(106\) | −12.8161 | −1.24481 | ||||||||
\(107\) | 15.6347 | 1.51146 | 0.755729 | − | 0.654884i | \(-0.227283\pi\) | ||||
0.755729 | + | 0.654884i | \(0.227283\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −20.5955 | −1.97269 | −0.986346 | − | 0.164686i | \(-0.947339\pi\) | ||||
−0.986346 | + | 0.164686i | \(0.947339\pi\) | |||||||
\(110\) | −15.5626 | −1.48383 | ||||||||
\(111\) | 9.63112 | 0.914146 | ||||||||
\(112\) | 1.91373 | 0.180830 | ||||||||
\(113\) | −0.0306698 | −0.00288518 | −0.00144259 | − | 0.999999i | \(-0.500459\pi\) | ||||
−0.00144259 | + | 0.999999i | \(0.500459\pi\) | |||||||
\(114\) | −2.13299 | −0.199773 | ||||||||
\(115\) | −7.81237 | −0.728507 | ||||||||
\(116\) | −2.19238 | −0.203557 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 7.21379 | 0.664083 | ||||||||
\(119\) | −9.26011 | −0.848873 | ||||||||
\(120\) | 3.75223 | 0.342530 | ||||||||
\(121\) | 6.20223 | 0.563839 | ||||||||
\(122\) | −10.2293 | −0.926117 | ||||||||
\(123\) | 7.88650 | 0.711101 | ||||||||
\(124\) | 5.15289 | 0.462743 | ||||||||
\(125\) | −15.3062 | −1.36903 | ||||||||
\(126\) | −1.91373 | −0.170488 | ||||||||
\(127\) | −4.17744 | −0.370688 | −0.185344 | − | 0.982674i | \(-0.559340\pi\) | ||||
−0.185344 | + | 0.982674i | \(0.559340\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.60304 | 0.141139 | ||||||||
\(130\) | −3.75223 | −0.329092 | ||||||||
\(131\) | 0.693576 | 0.0605981 | 0.0302990 | − | 0.999541i | \(-0.490354\pi\) | ||||
0.0302990 | + | 0.999541i | \(0.490354\pi\) | |||||||
\(132\) | −4.14756 | −0.360998 | ||||||||
\(133\) | 4.08196 | 0.353951 | ||||||||
\(134\) | 8.07141 | 0.697263 | ||||||||
\(135\) | −3.75223 | −0.322940 | ||||||||
\(136\) | 4.83878 | 0.414922 | ||||||||
\(137\) | −15.5620 | −1.32955 | −0.664775 | − | 0.747044i | \(-0.731473\pi\) | ||||
−0.664775 | + | 0.747044i | \(0.731473\pi\) | |||||||
\(138\) | −2.08206 | −0.177237 | ||||||||
\(139\) | −14.8728 | −1.26149 | −0.630747 | − | 0.775988i | \(-0.717252\pi\) | ||||
−0.630747 | + | 0.775988i | \(0.717252\pi\) | |||||||
\(140\) | −7.18074 | −0.606884 | ||||||||
\(141\) | −9.35222 | −0.787599 | ||||||||
\(142\) | −9.46244 | −0.794070 | ||||||||
\(143\) | 4.14756 | 0.346836 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.22631 | 0.683158 | ||||||||
\(146\) | −4.11647 | −0.340682 | ||||||||
\(147\) | −3.33765 | −0.275285 | ||||||||
\(148\) | 9.63112 | 0.791674 | ||||||||
\(149\) | 6.78344 | 0.555721 | 0.277861 | − | 0.960621i | \(-0.410375\pi\) | ||||
0.277861 | + | 0.960621i | \(0.410375\pi\) | |||||||
\(150\) | −9.07922 | −0.741315 | ||||||||
\(151\) | −19.0254 | −1.54826 | −0.774132 | − | 0.633024i | \(-0.781813\pi\) | ||||
−0.774132 | + | 0.633024i | \(0.781813\pi\) | |||||||
\(152\) | −2.13299 | −0.173008 | ||||||||
\(153\) | −4.83878 | −0.391193 | ||||||||
\(154\) | 7.93729 | 0.639605 | ||||||||
\(155\) | −19.3348 | −1.55301 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −24.8181 | −1.98070 | −0.990352 | − | 0.138577i | \(-0.955747\pi\) | ||||
−0.990352 | + | 0.138577i | \(0.955747\pi\) | |||||||
\(158\) | 8.08441 | 0.643161 | ||||||||
\(159\) | 12.8161 | 1.01638 | ||||||||
\(160\) | 3.75223 | 0.296640 | ||||||||
\(161\) | 3.98450 | 0.314022 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.4078 | −0.893525 | −0.446762 | − | 0.894653i | \(-0.647423\pi\) | ||||
−0.446762 | + | 0.894653i | \(0.647423\pi\) | |||||||
\(164\) | 7.88650 | 0.615832 | ||||||||
\(165\) | 15.5626 | 1.21155 | ||||||||
\(166\) | −0.397774 | −0.0308733 | ||||||||
\(167\) | −8.21066 | −0.635360 | −0.317680 | − | 0.948198i | \(-0.602904\pi\) | ||||
−0.317680 | + | 0.948198i | \(0.602904\pi\) | |||||||
\(168\) | −1.91373 | −0.147647 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −18.1562 | −1.39252 | ||||||||
\(171\) | 2.13299 | 0.163114 | ||||||||
\(172\) | 1.60304 | 0.122230 | ||||||||
\(173\) | 9.58909 | 0.729045 | 0.364523 | − | 0.931195i | \(-0.381232\pi\) | ||||
0.364523 | + | 0.931195i | \(0.381232\pi\) | |||||||
\(174\) | 2.19238 | 0.166204 | ||||||||
\(175\) | 17.3752 | 1.31344 | ||||||||
\(176\) | −4.14756 | −0.312634 | ||||||||
\(177\) | −7.21379 | −0.542222 | ||||||||
\(178\) | 12.6791 | 0.950342 | ||||||||
\(179\) | 8.14337 | 0.608664 | 0.304332 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304332 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(180\) | −3.75223 | −0.279675 | ||||||||
\(181\) | 1.68358 | 0.125139 | 0.0625697 | − | 0.998041i | \(-0.480070\pi\) | ||||
0.0625697 | + | 0.998041i | \(0.480070\pi\) | |||||||
\(182\) | 1.91373 | 0.141855 | ||||||||
\(183\) | 10.2293 | 0.756171 | ||||||||
\(184\) | −2.08206 | −0.153492 | ||||||||
\(185\) | −36.1382 | −2.65693 | ||||||||
\(186\) | −5.15289 | −0.377828 | ||||||||
\(187\) | 20.0691 | 1.46760 | ||||||||
\(188\) | −9.35222 | −0.682081 | ||||||||
\(189\) | 1.91373 | 0.139203 | ||||||||
\(190\) | 8.00347 | 0.580633 | ||||||||
\(191\) | −21.2826 | −1.53995 | −0.769976 | − | 0.638072i | \(-0.779732\pi\) | ||||
−0.769976 | + | 0.638072i | \(0.779732\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 19.4142 | 1.39747 | 0.698733 | − | 0.715382i | \(-0.253747\pi\) | ||||
0.698733 | + | 0.715382i | \(0.253747\pi\) | |||||||
\(194\) | 14.9290 | 1.07184 | ||||||||
\(195\) | 3.75223 | 0.268703 | ||||||||
\(196\) | −3.33765 | −0.238403 | ||||||||
\(197\) | −11.6487 | −0.829933 | −0.414966 | − | 0.909837i | \(-0.636207\pi\) | ||||
−0.414966 | + | 0.909837i | \(0.636207\pi\) | |||||||
\(198\) | 4.14756 | 0.294754 | ||||||||
\(199\) | 15.3303 | 1.08674 | 0.543370 | − | 0.839494i | \(-0.317148\pi\) | ||||
0.543370 | + | 0.839494i | \(0.317148\pi\) | |||||||
\(200\) | −9.07922 | −0.641998 | ||||||||
\(201\) | −8.07141 | −0.569313 | ||||||||
\(202\) | −16.7182 | −1.17629 | ||||||||
\(203\) | −4.19561 | −0.294474 | ||||||||
\(204\) | −4.83878 | −0.338783 | ||||||||
\(205\) | −29.5919 | −2.06679 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 2.08206 | 0.144713 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −8.84670 | −0.611939 | ||||||||
\(210\) | 7.18074 | 0.495518 | ||||||||
\(211\) | −11.7754 | −0.810654 | −0.405327 | − | 0.914172i | \(-0.632842\pi\) | ||||
−0.405327 | + | 0.914172i | \(0.632842\pi\) | |||||||
\(212\) | 12.8161 | 0.880212 | ||||||||
\(213\) | 9.46244 | 0.648356 | ||||||||
\(214\) | −15.6347 | −1.06876 | ||||||||
\(215\) | −6.01496 | −0.410217 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 9.86123 | 0.669424 | ||||||||
\(218\) | 20.5955 | 1.39490 | ||||||||
\(219\) | 4.11647 | 0.278165 | ||||||||
\(220\) | 15.5626 | 1.04923 | ||||||||
\(221\) | 4.83878 | 0.325492 | ||||||||
\(222\) | −9.63112 | −0.646399 | ||||||||
\(223\) | −20.7006 | −1.38621 | −0.693107 | − | 0.720835i | \(-0.743759\pi\) | ||||
−0.693107 | + | 0.720835i | \(0.743759\pi\) | |||||||
\(224\) | −1.91373 | −0.127866 | ||||||||
\(225\) | 9.07922 | 0.605282 | ||||||||
\(226\) | 0.0306698 | 0.00204013 | ||||||||
\(227\) | 16.2577 | 1.07906 | 0.539530 | − | 0.841967i | \(-0.318602\pi\) | ||||
0.539530 | + | 0.841967i | \(0.318602\pi\) | |||||||
\(228\) | 2.13299 | 0.141261 | ||||||||
\(229\) | −13.6150 | −0.899703 | −0.449851 | − | 0.893103i | \(-0.648523\pi\) | ||||
−0.449851 | + | 0.893103i | \(0.648523\pi\) | |||||||
\(230\) | 7.81237 | 0.515133 | ||||||||
\(231\) | −7.93729 | −0.522236 | ||||||||
\(232\) | 2.19238 | 0.143937 | ||||||||
\(233\) | −19.0339 | −1.24695 | −0.623477 | − | 0.781842i | \(-0.714280\pi\) | ||||
−0.623477 | + | 0.781842i | \(0.714280\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 35.0917 | 2.28913 | ||||||||
\(236\) | −7.21379 | −0.469578 | ||||||||
\(237\) | −8.08441 | −0.525139 | ||||||||
\(238\) | 9.26011 | 0.600244 | ||||||||
\(239\) | 7.92027 | 0.512320 | 0.256160 | − | 0.966634i | \(-0.417543\pi\) | ||||
0.256160 | + | 0.966634i | \(0.417543\pi\) | |||||||
\(240\) | −3.75223 | −0.242205 | ||||||||
\(241\) | 17.3089 | 1.11496 | 0.557482 | − | 0.830189i | \(-0.311767\pi\) | ||||
0.557482 | + | 0.830189i | \(0.311767\pi\) | |||||||
\(242\) | −6.20223 | −0.398694 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.2293 | 0.654864 | ||||||||
\(245\) | 12.5236 | 0.800105 | ||||||||
\(246\) | −7.88650 | −0.502825 | ||||||||
\(247\) | −2.13299 | −0.135719 | ||||||||
\(248\) | −5.15289 | −0.327209 | ||||||||
\(249\) | 0.397774 | 0.0252079 | ||||||||
\(250\) | 15.3062 | 0.968048 | ||||||||
\(251\) | 6.93300 | 0.437607 | 0.218804 | − | 0.975769i | \(-0.429785\pi\) | ||||
0.218804 | + | 0.975769i | \(0.429785\pi\) | |||||||
\(252\) | 1.91373 | 0.120553 | ||||||||
\(253\) | −8.63547 | −0.542907 | ||||||||
\(254\) | 4.17744 | 0.262116 | ||||||||
\(255\) | 18.1562 | 1.13699 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.6390 | 1.16267 | 0.581335 | − | 0.813664i | \(-0.302531\pi\) | ||||
0.581335 | + | 0.813664i | \(0.302531\pi\) | |||||||
\(258\) | −1.60304 | −0.0998006 | ||||||||
\(259\) | 18.4313 | 1.14527 | ||||||||
\(260\) | 3.75223 | 0.232703 | ||||||||
\(261\) | −2.19238 | −0.135705 | ||||||||
\(262\) | −0.693576 | −0.0428493 | ||||||||
\(263\) | −19.2932 | −1.18967 | −0.594835 | − | 0.803847i | \(-0.702783\pi\) | ||||
−0.594835 | + | 0.803847i | \(0.702783\pi\) | |||||||
\(264\) | 4.14756 | 0.255264 | ||||||||
\(265\) | −48.0889 | −2.95408 | ||||||||
\(266\) | −4.08196 | −0.250281 | ||||||||
\(267\) | −12.6791 | −0.775951 | ||||||||
\(268\) | −8.07141 | −0.493040 | ||||||||
\(269\) | −25.0184 | −1.52540 | −0.762698 | − | 0.646755i | \(-0.776126\pi\) | ||||
−0.762698 | + | 0.646755i | \(0.776126\pi\) | |||||||
\(270\) | 3.75223 | 0.228353 | ||||||||
\(271\) | 8.50393 | 0.516577 | 0.258289 | − | 0.966068i | \(-0.416841\pi\) | ||||
0.258289 | + | 0.966068i | \(0.416841\pi\) | |||||||
\(272\) | −4.83878 | −0.293394 | ||||||||
\(273\) | −1.91373 | −0.115824 | ||||||||
\(274\) | 15.5620 | 0.940134 | ||||||||
\(275\) | −37.6566 | −2.27078 | ||||||||
\(276\) | 2.08206 | 0.125325 | ||||||||
\(277\) | 16.2159 | 0.974321 | 0.487160 | − | 0.873313i | \(-0.338033\pi\) | ||||
0.487160 | + | 0.873313i | \(0.338033\pi\) | |||||||
\(278\) | 14.8728 | 0.892011 | ||||||||
\(279\) | 5.15289 | 0.308496 | ||||||||
\(280\) | 7.18074 | 0.429131 | ||||||||
\(281\) | 18.6296 | 1.11135 | 0.555673 | − | 0.831401i | \(-0.312461\pi\) | ||||
0.555673 | + | 0.831401i | \(0.312461\pi\) | |||||||
\(282\) | 9.35222 | 0.556917 | ||||||||
\(283\) | 2.72112 | 0.161754 | 0.0808769 | − | 0.996724i | \(-0.474228\pi\) | ||||
0.0808769 | + | 0.996724i | \(0.474228\pi\) | |||||||
\(284\) | 9.46244 | 0.561492 | ||||||||
\(285\) | −8.00347 | −0.474085 | ||||||||
\(286\) | −4.14756 | −0.245250 | ||||||||
\(287\) | 15.0926 | 0.890888 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 6.41383 | 0.377284 | ||||||||
\(290\) | −8.22631 | −0.483065 | ||||||||
\(291\) | −14.9290 | −0.875153 | ||||||||
\(292\) | 4.11647 | 0.240898 | ||||||||
\(293\) | 29.3839 | 1.71662 | 0.858312 | − | 0.513128i | \(-0.171513\pi\) | ||||
0.858312 | + | 0.513128i | \(0.171513\pi\) | |||||||
\(294\) | 3.33765 | 0.194656 | ||||||||
\(295\) | 27.0678 | 1.57595 | ||||||||
\(296\) | −9.63112 | −0.559798 | ||||||||
\(297\) | −4.14756 | −0.240666 | ||||||||
\(298\) | −6.78344 | −0.392954 | ||||||||
\(299\) | −2.08206 | −0.120409 | ||||||||
\(300\) | 9.07922 | 0.524189 | ||||||||
\(301\) | 3.06777 | 0.176823 | ||||||||
\(302\) | 19.0254 | 1.09479 | ||||||||
\(303\) | 16.7182 | 0.960438 | ||||||||
\(304\) | 2.13299 | 0.122335 | ||||||||
\(305\) | −38.3827 | −2.19778 | ||||||||
\(306\) | 4.83878 | 0.276615 | ||||||||
\(307\) | −7.72568 | −0.440928 | −0.220464 | − | 0.975395i | \(-0.570757\pi\) | ||||
−0.220464 | + | 0.975395i | \(0.570757\pi\) | |||||||
\(308\) | −7.93729 | −0.452269 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 19.3348 | 1.09814 | ||||||||
\(311\) | 23.8089 | 1.35008 | 0.675040 | − | 0.737781i | \(-0.264126\pi\) | ||||
0.675040 | + | 0.737781i | \(0.264126\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −7.23019 | −0.408675 | −0.204337 | − | 0.978901i | \(-0.565504\pi\) | ||||
−0.204337 | + | 0.978901i | \(0.565504\pi\) | |||||||
\(314\) | 24.8181 | 1.40057 | ||||||||
\(315\) | −7.18074 | −0.404589 | ||||||||
\(316\) | −8.08441 | −0.454783 | ||||||||
\(317\) | 15.4352 | 0.866929 | 0.433464 | − | 0.901171i | \(-0.357291\pi\) | ||||
0.433464 | + | 0.901171i | \(0.357291\pi\) | |||||||
\(318\) | −12.8161 | −0.718690 | ||||||||
\(319\) | 9.09301 | 0.509111 | ||||||||
\(320\) | −3.75223 | −0.209756 | ||||||||
\(321\) | 15.6347 | 0.872641 | ||||||||
\(322\) | −3.98450 | −0.222047 | ||||||||
\(323\) | −10.3211 | −0.574281 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −9.07922 | −0.503625 | ||||||||
\(326\) | 11.4078 | 0.631818 | ||||||||
\(327\) | −20.5955 | −1.13893 | ||||||||
\(328\) | −7.88650 | −0.435459 | ||||||||
\(329\) | −17.8976 | −0.986727 | ||||||||
\(330\) | −15.5626 | −0.856692 | ||||||||
\(331\) | −31.3126 | −1.72110 | −0.860548 | − | 0.509370i | \(-0.829879\pi\) | ||||
−0.860548 | + | 0.509370i | \(0.829879\pi\) | |||||||
\(332\) | 0.397774 | 0.0218307 | ||||||||
\(333\) | 9.63112 | 0.527782 | ||||||||
\(334\) | 8.21066 | 0.449267 | ||||||||
\(335\) | 30.2858 | 1.65469 | ||||||||
\(336\) | 1.91373 | 0.104402 | ||||||||
\(337\) | 21.7554 | 1.18509 | 0.592547 | − | 0.805536i | \(-0.298122\pi\) | ||||
0.592547 | + | 0.805536i | \(0.298122\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −0.0306698 | −0.00166576 | ||||||||
\(340\) | 18.1562 | 0.984660 | ||||||||
\(341\) | −21.3719 | −1.15735 | ||||||||
\(342\) | −2.13299 | −0.115339 | ||||||||
\(343\) | −19.7834 | −1.06821 | ||||||||
\(344\) | −1.60304 | −0.0864299 | ||||||||
\(345\) | −7.81237 | −0.420604 | ||||||||
\(346\) | −9.58909 | −0.515513 | ||||||||
\(347\) | −5.69161 | −0.305542 | −0.152771 | − | 0.988262i | \(-0.548820\pi\) | ||||
−0.152771 | + | 0.988262i | \(0.548820\pi\) | |||||||
\(348\) | −2.19238 | −0.117524 | ||||||||
\(349\) | −9.10237 | −0.487238 | −0.243619 | − | 0.969871i | \(-0.578335\pi\) | ||||
−0.243619 | + | 0.969871i | \(0.578335\pi\) | |||||||
\(350\) | −17.3752 | −0.928741 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 4.14756 | 0.221066 | ||||||||
\(353\) | −20.7573 | −1.10480 | −0.552400 | − | 0.833579i | \(-0.686288\pi\) | ||||
−0.552400 | + | 0.833579i | \(0.686288\pi\) | |||||||
\(354\) | 7.21379 | 0.383409 | ||||||||
\(355\) | −35.5052 | −1.88442 | ||||||||
\(356\) | −12.6791 | −0.671993 | ||||||||
\(357\) | −9.26011 | −0.490097 | ||||||||
\(358\) | −8.14337 | −0.430390 | ||||||||
\(359\) | −33.7756 | −1.78261 | −0.891304 | − | 0.453406i | \(-0.850209\pi\) | ||||
−0.891304 | + | 0.453406i | \(0.850209\pi\) | |||||||
\(360\) | 3.75223 | 0.197760 | ||||||||
\(361\) | −14.4503 | −0.760545 | ||||||||
\(362\) | −1.68358 | −0.0884869 | ||||||||
\(363\) | 6.20223 | 0.325533 | ||||||||
\(364\) | −1.91373 | −0.100307 | ||||||||
\(365\) | −15.4459 | −0.808478 | ||||||||
\(366\) | −10.2293 | −0.534694 | ||||||||
\(367\) | −7.16383 | −0.373949 | −0.186975 | − | 0.982365i | \(-0.559868\pi\) | ||||
−0.186975 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(368\) | 2.08206 | 0.108535 | ||||||||
\(369\) | 7.88650 | 0.410555 | ||||||||
\(370\) | 36.1382 | 1.87873 | ||||||||
\(371\) | 24.5265 | 1.27335 | ||||||||
\(372\) | 5.15289 | 0.267165 | ||||||||
\(373\) | −31.8515 | −1.64921 | −0.824604 | − | 0.565710i | \(-0.808602\pi\) | ||||
−0.824604 | + | 0.565710i | \(0.808602\pi\) | |||||||
\(374\) | −20.0691 | −1.03775 | ||||||||
\(375\) | −15.3062 | −0.790408 | ||||||||
\(376\) | 9.35222 | 0.482304 | ||||||||
\(377\) | 2.19238 | 0.112913 | ||||||||
\(378\) | −1.91373 | −0.0984315 | ||||||||
\(379\) | 0.748216 | 0.0384333 | 0.0192166 | − | 0.999815i | \(-0.493883\pi\) | ||||
0.0192166 | + | 0.999815i | \(0.493883\pi\) | |||||||
\(380\) | −8.00347 | −0.410569 | ||||||||
\(381\) | −4.17744 | −0.214017 | ||||||||
\(382\) | 21.2826 | 1.08891 | ||||||||
\(383\) | 15.9351 | 0.814247 | 0.407124 | − | 0.913373i | \(-0.366532\pi\) | ||||
0.407124 | + | 0.913373i | \(0.366532\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 29.7825 | 1.51786 | ||||||||
\(386\) | −19.4142 | −0.988158 | ||||||||
\(387\) | 1.60304 | 0.0814869 | ||||||||
\(388\) | −14.9290 | −0.757905 | ||||||||
\(389\) | −5.36783 | −0.272160 | −0.136080 | − | 0.990698i | \(-0.543450\pi\) | ||||
−0.136080 | + | 0.990698i | \(0.543450\pi\) | |||||||
\(390\) | −3.75223 | −0.190002 | ||||||||
\(391\) | −10.0746 | −0.509497 | ||||||||
\(392\) | 3.33765 | 0.168577 | ||||||||
\(393\) | 0.693576 | 0.0349863 | ||||||||
\(394\) | 11.6487 | 0.586851 | ||||||||
\(395\) | 30.3345 | 1.52630 | ||||||||
\(396\) | −4.14756 | −0.208423 | ||||||||
\(397\) | −5.30293 | −0.266147 | −0.133073 | − | 0.991106i | \(-0.542485\pi\) | ||||
−0.133073 | + | 0.991106i | \(0.542485\pi\) | |||||||
\(398\) | −15.3303 | −0.768441 | ||||||||
\(399\) | 4.08196 | 0.204354 | ||||||||
\(400\) | 9.07922 | 0.453961 | ||||||||
\(401\) | −30.6283 | −1.52951 | −0.764753 | − | 0.644323i | \(-0.777139\pi\) | ||||
−0.764753 | + | 0.644323i | \(0.777139\pi\) | |||||||
\(402\) | 8.07141 | 0.402565 | ||||||||
\(403\) | −5.15289 | −0.256684 | ||||||||
\(404\) | 16.7182 | 0.831763 | ||||||||
\(405\) | −3.75223 | −0.186450 | ||||||||
\(406\) | 4.19561 | 0.208225 | ||||||||
\(407\) | −39.9456 | −1.98003 | ||||||||
\(408\) | 4.83878 | 0.239556 | ||||||||
\(409\) | −25.3342 | −1.25270 | −0.626348 | − | 0.779543i | \(-0.715451\pi\) | ||||
−0.626348 | + | 0.779543i | \(0.715451\pi\) | |||||||
\(410\) | 29.5919 | 1.46144 | ||||||||
\(411\) | −15.5620 | −0.767616 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −13.8052 | −0.679311 | ||||||||
\(414\) | −2.08206 | −0.102328 | ||||||||
\(415\) | −1.49254 | −0.0732659 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −14.8728 | −0.728324 | ||||||||
\(418\) | 8.84670 | 0.432706 | ||||||||
\(419\) | 29.4907 | 1.44071 | 0.720356 | − | 0.693604i | \(-0.243978\pi\) | ||||
0.720356 | + | 0.693604i | \(0.243978\pi\) | |||||||
\(420\) | −7.18074 | −0.350384 | ||||||||
\(421\) | 27.7454 | 1.35223 | 0.676114 | − | 0.736797i | \(-0.263663\pi\) | ||||
0.676114 | + | 0.736797i | \(0.263663\pi\) | |||||||
\(422\) | 11.7754 | 0.573219 | ||||||||
\(423\) | −9.35222 | −0.454721 | ||||||||
\(424\) | −12.8161 | −0.622404 | ||||||||
\(425\) | −43.9324 | −2.13103 | ||||||||
\(426\) | −9.46244 | −0.458457 | ||||||||
\(427\) | 19.5761 | 0.947353 | ||||||||
\(428\) | 15.6347 | 0.755729 | ||||||||
\(429\) | 4.14756 | 0.200246 | ||||||||
\(430\) | 6.01496 | 0.290067 | ||||||||
\(431\) | −2.87789 | −0.138623 | −0.0693115 | − | 0.997595i | \(-0.522080\pi\) | ||||
−0.0693115 | + | 0.997595i | \(0.522080\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −16.0609 | −0.771838 | −0.385919 | − | 0.922533i | \(-0.626116\pi\) | ||||
−0.385919 | + | 0.922533i | \(0.626116\pi\) | |||||||
\(434\) | −9.86123 | −0.473354 | ||||||||
\(435\) | 8.22631 | 0.394421 | ||||||||
\(436\) | −20.5955 | −0.986346 | ||||||||
\(437\) | 4.44102 | 0.212443 | ||||||||
\(438\) | −4.11647 | −0.196693 | ||||||||
\(439\) | 26.0727 | 1.24438 | 0.622190 | − | 0.782866i | \(-0.286243\pi\) | ||||
0.622190 | + | 0.782866i | \(0.286243\pi\) | |||||||
\(440\) | −15.5626 | −0.741917 | ||||||||
\(441\) | −3.33765 | −0.158936 | ||||||||
\(442\) | −4.83878 | −0.230157 | ||||||||
\(443\) | −17.8236 | −0.846827 | −0.423413 | − | 0.905937i | \(-0.639168\pi\) | ||||
−0.423413 | + | 0.905937i | \(0.639168\pi\) | |||||||
\(444\) | 9.63112 | 0.457073 | ||||||||
\(445\) | 47.5751 | 2.25527 | ||||||||
\(446\) | 20.7006 | 0.980202 | ||||||||
\(447\) | 6.78344 | 0.320846 | ||||||||
\(448\) | 1.91373 | 0.0904151 | ||||||||
\(449\) | −31.6248 | −1.49247 | −0.746234 | − | 0.665684i | \(-0.768140\pi\) | ||||
−0.746234 | + | 0.665684i | \(0.768140\pi\) | |||||||
\(450\) | −9.07922 | −0.427999 | ||||||||
\(451\) | −32.7097 | −1.54024 | ||||||||
\(452\) | −0.0306698 | −0.00144259 | ||||||||
\(453\) | −19.0254 | −0.893890 | ||||||||
\(454\) | −16.2577 | −0.763010 | ||||||||
\(455\) | 7.18074 | 0.336638 | ||||||||
\(456\) | −2.13299 | −0.0998865 | ||||||||
\(457\) | −30.9954 | −1.44990 | −0.724951 | − | 0.688800i | \(-0.758138\pi\) | ||||
−0.724951 | + | 0.688800i | \(0.758138\pi\) | |||||||
\(458\) | 13.6150 | 0.636186 | ||||||||
\(459\) | −4.83878 | −0.225855 | ||||||||
\(460\) | −7.81237 | −0.364254 | ||||||||
\(461\) | −36.7779 | −1.71292 | −0.856459 | − | 0.516215i | \(-0.827341\pi\) | ||||
−0.856459 | + | 0.516215i | \(0.827341\pi\) | |||||||
\(462\) | 7.93729 | 0.369276 | ||||||||
\(463\) | −10.4965 | −0.487813 | −0.243907 | − | 0.969799i | \(-0.578429\pi\) | ||||
−0.243907 | + | 0.969799i | \(0.578429\pi\) | |||||||
\(464\) | −2.19238 | −0.101779 | ||||||||
\(465\) | −19.3348 | −0.896631 | ||||||||
\(466\) | 19.0339 | 0.881729 | ||||||||
\(467\) | 16.3515 | 0.756656 | 0.378328 | − | 0.925672i | \(-0.376499\pi\) | ||||
0.378328 | + | 0.925672i | \(0.376499\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −15.4465 | −0.713252 | ||||||||
\(470\) | −35.0917 | −1.61866 | ||||||||
\(471\) | −24.8181 | −1.14356 | ||||||||
\(472\) | 7.21379 | 0.332042 | ||||||||
\(473\) | −6.64868 | −0.305707 | ||||||||
\(474\) | 8.08441 | 0.371329 | ||||||||
\(475\) | 19.3659 | 0.888569 | ||||||||
\(476\) | −9.26011 | −0.424437 | ||||||||
\(477\) | 12.8161 | 0.586808 | ||||||||
\(478\) | −7.92027 | −0.362265 | ||||||||
\(479\) | −35.5629 | −1.62491 | −0.812456 | − | 0.583022i | \(-0.801870\pi\) | ||||
−0.812456 | + | 0.583022i | \(0.801870\pi\) | |||||||
\(480\) | 3.75223 | 0.171265 | ||||||||
\(481\) | −9.63112 | −0.439141 | ||||||||
\(482\) | −17.3089 | −0.788399 | ||||||||
\(483\) | 3.98450 | 0.181301 | ||||||||
\(484\) | 6.20223 | 0.281919 | ||||||||
\(485\) | 56.0170 | 2.54360 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 1.39658 | 0.0632850 | 0.0316425 | − | 0.999499i | \(-0.489926\pi\) | ||||
0.0316425 | + | 0.999499i | \(0.489926\pi\) | |||||||
\(488\) | −10.2293 | −0.463059 | ||||||||
\(489\) | −11.4078 | −0.515877 | ||||||||
\(490\) | −12.5236 | −0.565759 | ||||||||
\(491\) | 2.49644 | 0.112663 | 0.0563315 | − | 0.998412i | \(-0.482060\pi\) | ||||
0.0563315 | + | 0.998412i | \(0.482060\pi\) | |||||||
\(492\) | 7.88650 | 0.355551 | ||||||||
\(493\) | 10.6084 | 0.477780 | ||||||||
\(494\) | 2.13299 | 0.0959678 | ||||||||
\(495\) | 15.5626 | 0.699486 | ||||||||
\(496\) | 5.15289 | 0.231372 | ||||||||
\(497\) | 18.1085 | 0.812279 | ||||||||
\(498\) | −0.397774 | −0.0178247 | ||||||||
\(499\) | 18.8673 | 0.844616 | 0.422308 | − | 0.906452i | \(-0.361220\pi\) | ||||
0.422308 | + | 0.906452i | \(0.361220\pi\) | |||||||
\(500\) | −15.3062 | −0.684513 | ||||||||
\(501\) | −8.21066 | −0.366825 | ||||||||
\(502\) | −6.93300 | −0.309435 | ||||||||
\(503\) | −11.0795 | −0.494010 | −0.247005 | − | 0.969014i | \(-0.579446\pi\) | ||||
−0.247005 | + | 0.969014i | \(0.579446\pi\) | |||||||
\(504\) | −1.91373 | −0.0852442 | ||||||||
\(505\) | −62.7307 | −2.79148 | ||||||||
\(506\) | 8.63547 | 0.383893 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −4.17744 | −0.185344 | ||||||||
\(509\) | −0.550164 | −0.0243856 | −0.0121928 | − | 0.999926i | \(-0.503881\pi\) | ||||
−0.0121928 | + | 0.999926i | \(0.503881\pi\) | |||||||
\(510\) | −18.1562 | −0.803971 | ||||||||
\(511\) | 7.87780 | 0.348493 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.13299 | 0.0941739 | ||||||||
\(514\) | −18.6390 | −0.822132 | ||||||||
\(515\) | −3.75223 | −0.165343 | ||||||||
\(516\) | 1.60304 | 0.0705697 | ||||||||
\(517\) | 38.7889 | 1.70593 | ||||||||
\(518\) | −18.4313 | −0.809827 | ||||||||
\(519\) | 9.58909 | 0.420915 | ||||||||
\(520\) | −3.75223 | −0.164546 | ||||||||
\(521\) | 25.6635 | 1.12434 | 0.562169 | − | 0.827022i | \(-0.309967\pi\) | ||||
0.562169 | + | 0.827022i | \(0.309967\pi\) | |||||||
\(522\) | 2.19238 | 0.0959578 | ||||||||
\(523\) | 37.4839 | 1.63906 | 0.819528 | − | 0.573039i | \(-0.194236\pi\) | ||||
0.819528 | + | 0.573039i | \(0.194236\pi\) | |||||||
\(524\) | 0.693576 | 0.0302990 | ||||||||
\(525\) | 17.3752 | 0.758314 | ||||||||
\(526\) | 19.2932 | 0.841224 | ||||||||
\(527\) | −24.9337 | −1.08613 | ||||||||
\(528\) | −4.14756 | −0.180499 | ||||||||
\(529\) | −18.6650 | −0.811523 | ||||||||
\(530\) | 48.0889 | 2.08885 | ||||||||
\(531\) | −7.21379 | −0.313052 | ||||||||
\(532\) | 4.08196 | 0.176976 | ||||||||
\(533\) | −7.88650 | −0.341602 | ||||||||
\(534\) | 12.6791 | 0.548680 | ||||||||
\(535\) | −58.6648 | −2.53630 | ||||||||
\(536\) | 8.07141 | 0.348632 | ||||||||
\(537\) | 8.14337 | 0.351412 | ||||||||
\(538\) | 25.0184 | 1.07862 | ||||||||
\(539\) | 13.8431 | 0.596264 | ||||||||
\(540\) | −3.75223 | −0.161470 | ||||||||
\(541\) | 26.1597 | 1.12469 | 0.562346 | − | 0.826902i | \(-0.309899\pi\) | ||||
0.562346 | + | 0.826902i | \(0.309899\pi\) | |||||||
\(542\) | −8.50393 | −0.365275 | ||||||||
\(543\) | 1.68358 | 0.0722492 | ||||||||
\(544\) | 4.83878 | 0.207461 | ||||||||
\(545\) | 77.2791 | 3.31027 | ||||||||
\(546\) | 1.91373 | 0.0819000 | ||||||||
\(547\) | 7.54438 | 0.322574 | 0.161287 | − | 0.986908i | \(-0.448435\pi\) | ||||
0.161287 | + | 0.986908i | \(0.448435\pi\) | |||||||
\(548\) | −15.5620 | −0.664775 | ||||||||
\(549\) | 10.2293 | 0.436576 | ||||||||
\(550\) | 37.6566 | 1.60568 | ||||||||
\(551\) | −4.67632 | −0.199218 | ||||||||
\(552\) | −2.08206 | −0.0886184 | ||||||||
\(553\) | −15.4713 | −0.657909 | ||||||||
\(554\) | −16.2159 | −0.688949 | ||||||||
\(555\) | −36.1382 | −1.53398 | ||||||||
\(556\) | −14.8728 | −0.630747 | ||||||||
\(557\) | −36.7923 | −1.55894 | −0.779471 | − | 0.626438i | \(-0.784512\pi\) | ||||
−0.779471 | + | 0.626438i | \(0.784512\pi\) | |||||||
\(558\) | −5.15289 | −0.218139 | ||||||||
\(559\) | −1.60304 | −0.0678012 | ||||||||
\(560\) | −7.18074 | −0.303442 | ||||||||
\(561\) | 20.0691 | 0.847319 | ||||||||
\(562\) | −18.6296 | −0.785841 | ||||||||
\(563\) | −5.96214 | −0.251274 | −0.125637 | − | 0.992076i | \(-0.540097\pi\) | ||||
−0.125637 | + | 0.992076i | \(0.540097\pi\) | |||||||
\(564\) | −9.35222 | −0.393800 | ||||||||
\(565\) | 0.115080 | 0.00484146 | ||||||||
\(566\) | −2.72112 | −0.114377 | ||||||||
\(567\) | 1.91373 | 0.0803690 | ||||||||
\(568\) | −9.46244 | −0.397035 | ||||||||
\(569\) | 5.23201 | 0.219337 | 0.109669 | − | 0.993968i | \(-0.465021\pi\) | ||||
0.109669 | + | 0.993968i | \(0.465021\pi\) | |||||||
\(570\) | 8.00347 | 0.335229 | ||||||||
\(571\) | 9.05233 | 0.378828 | 0.189414 | − | 0.981897i | \(-0.439341\pi\) | ||||
0.189414 | + | 0.981897i | \(0.439341\pi\) | |||||||
\(572\) | 4.14756 | 0.173418 | ||||||||
\(573\) | −21.2826 | −0.889092 | ||||||||
\(574\) | −15.0926 | −0.629953 | ||||||||
\(575\) | 18.9035 | 0.788330 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 28.5282 | 1.18764 | 0.593822 | − | 0.804596i | \(-0.297618\pi\) | ||||
0.593822 | + | 0.804596i | \(0.297618\pi\) | |||||||
\(578\) | −6.41383 | −0.266780 | ||||||||
\(579\) | 19.4142 | 0.806828 | ||||||||
\(580\) | 8.22631 | 0.341579 | ||||||||
\(581\) | 0.761232 | 0.0315812 | ||||||||
\(582\) | 14.9290 | 0.618827 | ||||||||
\(583\) | −53.1554 | −2.20147 | ||||||||
\(584\) | −4.11647 | −0.170341 | ||||||||
\(585\) | 3.75223 | 0.155136 | ||||||||
\(586\) | −29.3839 | −1.21384 | ||||||||
\(587\) | 1.97365 | 0.0814612 | 0.0407306 | − | 0.999170i | \(-0.487031\pi\) | ||||
0.0407306 | + | 0.999170i | \(0.487031\pi\) | |||||||
\(588\) | −3.33765 | −0.137642 | ||||||||
\(589\) | 10.9911 | 0.452879 | ||||||||
\(590\) | −27.0678 | −1.11436 | ||||||||
\(591\) | −11.6487 | −0.479162 | ||||||||
\(592\) | 9.63112 | 0.395837 | ||||||||
\(593\) | −6.79289 | −0.278951 | −0.139475 | − | 0.990226i | \(-0.544542\pi\) | ||||
−0.139475 | + | 0.990226i | \(0.544542\pi\) | |||||||
\(594\) | 4.14756 | 0.170176 | ||||||||
\(595\) | 34.7461 | 1.42445 | ||||||||
\(596\) | 6.78344 | 0.277861 | ||||||||
\(597\) | 15.3303 | 0.627429 | ||||||||
\(598\) | 2.08206 | 0.0851418 | ||||||||
\(599\) | −1.22559 | −0.0500763 | −0.0250382 | − | 0.999686i | \(-0.507971\pi\) | ||||
−0.0250382 | + | 0.999686i | \(0.507971\pi\) | |||||||
\(600\) | −9.07922 | −0.370658 | ||||||||
\(601\) | −13.5109 | −0.551121 | −0.275560 | − | 0.961284i | \(-0.588863\pi\) | ||||
−0.275560 | + | 0.961284i | \(0.588863\pi\) | |||||||
\(602\) | −3.06777 | −0.125033 | ||||||||
\(603\) | −8.07141 | −0.328693 | ||||||||
\(604\) | −19.0254 | −0.774132 | ||||||||
\(605\) | −23.2722 | −0.946149 | ||||||||
\(606\) | −16.7182 | −0.679132 | ||||||||
\(607\) | −27.2985 | −1.10801 | −0.554005 | − | 0.832513i | \(-0.686901\pi\) | ||||
−0.554005 | + | 0.832513i | \(0.686901\pi\) | |||||||
\(608\) | −2.13299 | −0.0865042 | ||||||||
\(609\) | −4.19561 | −0.170015 | ||||||||
\(610\) | 38.3827 | 1.55407 | ||||||||
\(611\) | 9.35222 | 0.378350 | ||||||||
\(612\) | −4.83878 | −0.195596 | ||||||||
\(613\) | 5.48355 | 0.221479 | 0.110739 | − | 0.993849i | \(-0.464678\pi\) | ||||
0.110739 | + | 0.993849i | \(0.464678\pi\) | |||||||
\(614\) | 7.72568 | 0.311783 | ||||||||
\(615\) | −29.5919 | −1.19326 | ||||||||
\(616\) | 7.93729 | 0.319803 | ||||||||
\(617\) | 26.7890 | 1.07848 | 0.539241 | − | 0.842151i | \(-0.318711\pi\) | ||||
0.539241 | + | 0.842151i | \(0.318711\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −7.65296 | −0.307598 | −0.153799 | − | 0.988102i | \(-0.549151\pi\) | ||||
−0.153799 | + | 0.988102i | \(0.549151\pi\) | |||||||
\(620\) | −19.3348 | −0.776505 | ||||||||
\(621\) | 2.08206 | 0.0835503 | ||||||||
\(622\) | −23.8089 | −0.954651 | ||||||||
\(623\) | −24.2644 | −0.972134 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 12.0362 | 0.481447 | ||||||||
\(626\) | 7.23019 | 0.288977 | ||||||||
\(627\) | −8.84670 | −0.353303 | ||||||||
\(628\) | −24.8181 | −0.990352 | ||||||||
\(629\) | −46.6029 | −1.85818 | ||||||||
\(630\) | 7.18074 | 0.286088 | ||||||||
\(631\) | 29.8512 | 1.18836 | 0.594178 | − | 0.804334i | \(-0.297477\pi\) | ||||
0.594178 | + | 0.804334i | \(0.297477\pi\) | |||||||
\(632\) | 8.08441 | 0.321580 | ||||||||
\(633\) | −11.7754 | −0.468031 | ||||||||
\(634\) | −15.4352 | −0.613011 | ||||||||
\(635\) | 15.6747 | 0.622032 | ||||||||
\(636\) | 12.8161 | 0.508191 | ||||||||
\(637\) | 3.33765 | 0.132242 | ||||||||
\(638\) | −9.09301 | −0.359996 | ||||||||
\(639\) | 9.46244 | 0.374328 | ||||||||
\(640\) | 3.75223 | 0.148320 | ||||||||
\(641\) | 33.8726 | 1.33789 | 0.668943 | − | 0.743314i | \(-0.266747\pi\) | ||||
0.668943 | + | 0.743314i | \(0.266747\pi\) | |||||||
\(642\) | −15.6347 | −0.617050 | ||||||||
\(643\) | 43.0406 | 1.69736 | 0.848678 | − | 0.528910i | \(-0.177399\pi\) | ||||
0.848678 | + | 0.528910i | \(0.177399\pi\) | |||||||
\(644\) | 3.98450 | 0.157011 | ||||||||
\(645\) | −6.01496 | −0.236839 | ||||||||
\(646\) | 10.3211 | 0.406078 | ||||||||
\(647\) | 18.4015 | 0.723439 | 0.361720 | − | 0.932287i | \(-0.382190\pi\) | ||||
0.361720 | + | 0.932287i | \(0.382190\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 29.9196 | 1.17445 | ||||||||
\(650\) | 9.07922 | 0.356116 | ||||||||
\(651\) | 9.86123 | 0.386492 | ||||||||
\(652\) | −11.4078 | −0.446762 | ||||||||
\(653\) | −12.1955 | −0.477246 | −0.238623 | − | 0.971112i | \(-0.576696\pi\) | ||||
−0.238623 | + | 0.971112i | \(0.576696\pi\) | |||||||
\(654\) | 20.5955 | 0.805348 | ||||||||
\(655\) | −2.60246 | −0.101686 | ||||||||
\(656\) | 7.88650 | 0.307916 | ||||||||
\(657\) | 4.11647 | 0.160599 | ||||||||
\(658\) | 17.8976 | 0.697721 | ||||||||
\(659\) | −27.2559 | −1.06174 | −0.530869 | − | 0.847454i | \(-0.678134\pi\) | ||||
−0.530869 | + | 0.847454i | \(0.678134\pi\) | |||||||
\(660\) | 15.5626 | 0.605773 | ||||||||
\(661\) | −48.4571 | −1.88476 | −0.942381 | − | 0.334541i | \(-0.891419\pi\) | ||||
−0.942381 | + | 0.334541i | \(0.891419\pi\) | |||||||
\(662\) | 31.3126 | 1.21700 | ||||||||
\(663\) | 4.83878 | 0.187923 | ||||||||
\(664\) | −0.397774 | −0.0154366 | ||||||||
\(665\) | −15.3165 | −0.593947 | ||||||||
\(666\) | −9.63112 | −0.373199 | ||||||||
\(667\) | −4.56467 | −0.176745 | ||||||||
\(668\) | −8.21066 | −0.317680 | ||||||||
\(669\) | −20.7006 | −0.800331 | ||||||||
\(670\) | −30.2858 | −1.17004 | ||||||||
\(671\) | −42.4266 | −1.63786 | ||||||||
\(672\) | −1.91373 | −0.0738236 | ||||||||
\(673\) | 3.73117 | 0.143826 | 0.0719130 | − | 0.997411i | \(-0.477090\pi\) | ||||
0.0719130 | + | 0.997411i | \(0.477090\pi\) | |||||||
\(674\) | −21.7554 | −0.837989 | ||||||||
\(675\) | 9.07922 | 0.349459 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 38.5407 | 1.48124 | 0.740620 | − | 0.671924i | \(-0.234532\pi\) | ||||
0.740620 | + | 0.671924i | \(0.234532\pi\) | |||||||
\(678\) | 0.0306698 | 0.00117787 | ||||||||
\(679\) | −28.5700 | −1.09642 | ||||||||
\(680\) | −18.1562 | −0.696260 | ||||||||
\(681\) | 16.2577 | 0.622995 | ||||||||
\(682\) | 21.3719 | 0.818373 | ||||||||
\(683\) | −41.1026 | −1.57275 | −0.786373 | − | 0.617752i | \(-0.788043\pi\) | ||||
−0.786373 | + | 0.617752i | \(0.788043\pi\) | |||||||
\(684\) | 2.13299 | 0.0815570 | ||||||||
\(685\) | 58.3921 | 2.23105 | ||||||||
\(686\) | 19.7834 | 0.755335 | ||||||||
\(687\) | −13.6150 | −0.519444 | ||||||||
\(688\) | 1.60304 | 0.0611151 | ||||||||
\(689\) | −12.8161 | −0.488254 | ||||||||
\(690\) | 7.81237 | 0.297412 | ||||||||
\(691\) | 35.5935 | 1.35404 | 0.677020 | − | 0.735965i | \(-0.263271\pi\) | ||||
0.677020 | + | 0.735965i | \(0.263271\pi\) | |||||||
\(692\) | 9.58909 | 0.364523 | ||||||||
\(693\) | −7.93729 | −0.301513 | ||||||||
\(694\) | 5.69161 | 0.216051 | ||||||||
\(695\) | 55.8062 | 2.11685 | ||||||||
\(696\) | 2.19238 | 0.0831019 | ||||||||
\(697\) | −38.1611 | −1.44545 | ||||||||
\(698\) | 9.10237 | 0.344530 | ||||||||
\(699\) | −19.0339 | −0.719929 | ||||||||
\(700\) | 17.3752 | 0.656719 | ||||||||
\(701\) | −4.01572 | −0.151672 | −0.0758358 | − | 0.997120i | \(-0.524162\pi\) | ||||
−0.0758358 | + | 0.997120i | \(0.524162\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 20.5431 | 0.774798 | ||||||||
\(704\) | −4.14756 | −0.156317 | ||||||||
\(705\) | 35.0917 | 1.32163 | ||||||||
\(706\) | 20.7573 | 0.781211 | ||||||||
\(707\) | 31.9941 | 1.20326 | ||||||||
\(708\) | −7.21379 | −0.271111 | ||||||||
\(709\) | −37.7839 | −1.41900 | −0.709501 | − | 0.704704i | \(-0.751080\pi\) | ||||
−0.709501 | + | 0.704704i | \(0.751080\pi\) | |||||||
\(710\) | 35.5052 | 1.33249 | ||||||||
\(711\) | −8.08441 | −0.303189 | ||||||||
\(712\) | 12.6791 | 0.475171 | ||||||||
\(713\) | 10.7286 | 0.401791 | ||||||||
\(714\) | 9.26011 | 0.346551 | ||||||||
\(715\) | −15.5626 | −0.582008 | ||||||||
\(716\) | 8.14337 | 0.304332 | ||||||||
\(717\) | 7.92027 | 0.295788 | ||||||||
\(718\) | 33.7756 | 1.26049 | ||||||||
\(719\) | −28.2566 | −1.05379 | −0.526897 | − | 0.849929i | \(-0.676645\pi\) | ||||
−0.526897 | + | 0.849929i | \(0.676645\pi\) | |||||||
\(720\) | −3.75223 | −0.139837 | ||||||||
\(721\) | 1.91373 | 0.0712709 | ||||||||
\(722\) | 14.4503 | 0.537786 | ||||||||
\(723\) | 17.3089 | 0.643725 | ||||||||
\(724\) | 1.68358 | 0.0625697 | ||||||||
\(725\) | −19.9051 | −0.739257 | ||||||||
\(726\) | −6.20223 | −0.230186 | ||||||||
\(727\) | −41.8677 | −1.55279 | −0.776394 | − | 0.630248i | \(-0.782953\pi\) | ||||
−0.776394 | + | 0.630248i | \(0.782953\pi\) | |||||||
\(728\) | 1.91373 | 0.0709275 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.4459 | 0.571680 | ||||||||
\(731\) | −7.75674 | −0.286893 | ||||||||
\(732\) | 10.2293 | 0.378086 | ||||||||
\(733\) | −45.1539 | −1.66780 | −0.833900 | − | 0.551916i | \(-0.813897\pi\) | ||||
−0.833900 | + | 0.551916i | \(0.813897\pi\) | |||||||
\(734\) | 7.16383 | 0.264422 | ||||||||
\(735\) | 12.5236 | 0.461941 | ||||||||
\(736\) | −2.08206 | −0.0767458 | ||||||||
\(737\) | 33.4766 | 1.23313 | ||||||||
\(738\) | −7.88650 | −0.290306 | ||||||||
\(739\) | 31.9727 | 1.17614 | 0.588068 | − | 0.808812i | \(-0.299889\pi\) | ||||
0.588068 | + | 0.808812i | \(0.299889\pi\) | |||||||
\(740\) | −36.1382 | −1.32847 | ||||||||
\(741\) | −2.13299 | −0.0783574 | ||||||||
\(742\) | −24.5265 | −0.900396 | ||||||||
\(743\) | −27.6910 | −1.01589 | −0.507943 | − | 0.861391i | \(-0.669594\pi\) | ||||
−0.507943 | + | 0.861391i | \(0.669594\pi\) | |||||||
\(744\) | −5.15289 | −0.188914 | ||||||||
\(745\) | −25.4530 | −0.932527 | ||||||||
\(746\) | 31.8515 | 1.16617 | ||||||||
\(747\) | 0.397774 | 0.0145538 | ||||||||
\(748\) | 20.0691 | 0.733800 | ||||||||
\(749\) | 29.9205 | 1.09327 | ||||||||
\(750\) | 15.3062 | 0.558903 | ||||||||
\(751\) | 34.4297 | 1.25636 | 0.628179 | − | 0.778069i | \(-0.283801\pi\) | ||||
0.628179 | + | 0.778069i | \(0.283801\pi\) | |||||||
\(752\) | −9.35222 | −0.341040 | ||||||||
\(753\) | 6.93300 | 0.252653 | ||||||||
\(754\) | −2.19238 | −0.0798417 | ||||||||
\(755\) | 71.3876 | 2.59806 | ||||||||
\(756\) | 1.91373 | 0.0696016 | ||||||||
\(757\) | −11.4723 | −0.416969 | −0.208485 | − | 0.978026i | \(-0.566853\pi\) | ||||
−0.208485 | + | 0.978026i | \(0.566853\pi\) | |||||||
\(758\) | −0.748216 | −0.0271764 | ||||||||
\(759\) | −8.63547 | −0.313448 | ||||||||
\(760\) | 8.00347 | 0.290316 | ||||||||
\(761\) | 34.5110 | 1.25102 | 0.625512 | − | 0.780215i | \(-0.284890\pi\) | ||||
0.625512 | + | 0.780215i | \(0.284890\pi\) | |||||||
\(762\) | 4.17744 | 0.151333 | ||||||||
\(763\) | −39.4142 | −1.42689 | ||||||||
\(764\) | −21.2826 | −0.769976 | ||||||||
\(765\) | 18.1562 | 0.656440 | ||||||||
\(766\) | −15.9351 | −0.575760 | ||||||||
\(767\) | 7.21379 | 0.260475 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −0.332765 | −0.0119998 | −0.00599991 | − | 0.999982i | \(-0.501910\pi\) | ||||
−0.00599991 | + | 0.999982i | \(0.501910\pi\) | |||||||
\(770\) | −29.7825 | −1.07329 | ||||||||
\(771\) | 18.6390 | 0.671268 | ||||||||
\(772\) | 19.4142 | 0.698733 | ||||||||
\(773\) | 9.97635 | 0.358824 | 0.179412 | − | 0.983774i | \(-0.442580\pi\) | ||||
0.179412 | + | 0.983774i | \(0.442580\pi\) | |||||||
\(774\) | −1.60304 | −0.0576199 | ||||||||
\(775\) | 46.7842 | 1.68054 | ||||||||
\(776\) | 14.9290 | 0.535920 | ||||||||
\(777\) | 18.4313 | 0.661221 | ||||||||
\(778\) | 5.36783 | 0.192446 | ||||||||
\(779\) | 16.8218 | 0.602705 | ||||||||
\(780\) | 3.75223 | 0.134351 | ||||||||
\(781\) | −39.2460 | −1.40433 | ||||||||
\(782\) | 10.0746 | 0.360269 | ||||||||
\(783\) | −2.19238 | −0.0783492 | ||||||||
\(784\) | −3.33765 | −0.119202 | ||||||||
\(785\) | 93.1233 | 3.32371 | ||||||||
\(786\) | −0.693576 | −0.0247391 | ||||||||
\(787\) | 21.4623 | 0.765049 | 0.382525 | − | 0.923945i | \(-0.375055\pi\) | ||||
0.382525 | + | 0.923945i | \(0.375055\pi\) | |||||||
\(788\) | −11.6487 | −0.414966 | ||||||||
\(789\) | −19.2932 | −0.686857 | ||||||||
\(790\) | −30.3345 | −1.07925 | ||||||||
\(791\) | −0.0586937 | −0.00208691 | ||||||||
\(792\) | 4.14756 | 0.147377 | ||||||||
\(793\) | −10.2293 | −0.363253 | ||||||||
\(794\) | 5.30293 | 0.188194 | ||||||||
\(795\) | −48.0889 | −1.70554 | ||||||||
\(796\) | 15.3303 | 0.543370 | ||||||||
\(797\) | 0.719890 | 0.0254998 | 0.0127499 | − | 0.999919i | \(-0.495941\pi\) | ||||
0.0127499 | + | 0.999919i | \(0.495941\pi\) | |||||||
\(798\) | −4.08196 | −0.144500 | ||||||||
\(799\) | 45.2534 | 1.60095 | ||||||||
\(800\) | −9.07922 | −0.320999 | ||||||||
\(801\) | −12.6791 | −0.447996 | ||||||||
\(802\) | 30.6283 | 1.08152 | ||||||||
\(803\) | −17.0733 | −0.602504 | ||||||||
\(804\) | −8.07141 | −0.284657 | ||||||||
\(805\) | −14.9507 | −0.526945 | ||||||||
\(806\) | 5.15289 | 0.181503 | ||||||||
\(807\) | −25.0184 | −0.880688 | ||||||||
\(808\) | −16.7182 | −0.588146 | ||||||||
\(809\) | 7.41244 | 0.260608 | 0.130304 | − | 0.991474i | \(-0.458405\pi\) | ||||
0.130304 | + | 0.991474i | \(0.458405\pi\) | |||||||
\(810\) | 3.75223 | 0.131840 | ||||||||
\(811\) | −49.5990 | −1.74165 | −0.870827 | − | 0.491589i | \(-0.836416\pi\) | ||||
−0.870827 | + | 0.491589i | \(0.836416\pi\) | |||||||
\(812\) | −4.19561 | −0.147237 | ||||||||
\(813\) | 8.50393 | 0.298246 | ||||||||
\(814\) | 39.9456 | 1.40009 | ||||||||
\(815\) | 42.8045 | 1.49938 | ||||||||
\(816\) | −4.83878 | −0.169391 | ||||||||
\(817\) | 3.41926 | 0.119625 | ||||||||
\(818\) | 25.3342 | 0.885790 | ||||||||
\(819\) | −1.91373 | −0.0668710 | ||||||||
\(820\) | −29.5919 | −1.03340 | ||||||||
\(821\) | −16.0854 | −0.561385 | −0.280692 | − | 0.959798i | \(-0.590564\pi\) | ||||
−0.280692 | + | 0.959798i | \(0.590564\pi\) | |||||||
\(822\) | 15.5620 | 0.542787 | ||||||||
\(823\) | 40.7960 | 1.42206 | 0.711029 | − | 0.703163i | \(-0.248230\pi\) | ||||
0.711029 | + | 0.703163i | \(0.248230\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −37.6566 | −1.31103 | ||||||||
\(826\) | 13.8052 | 0.480345 | ||||||||
\(827\) | −1.22302 | −0.0425286 | −0.0212643 | − | 0.999774i | \(-0.506769\pi\) | ||||
−0.0212643 | + | 0.999774i | \(0.506769\pi\) | |||||||
\(828\) | 2.08206 | 0.0723566 | ||||||||
\(829\) | 20.6281 | 0.716442 | 0.358221 | − | 0.933637i | \(-0.383383\pi\) | ||||
0.358221 | + | 0.933637i | \(0.383383\pi\) | |||||||
\(830\) | 1.49254 | 0.0518068 | ||||||||
\(831\) | 16.2159 | 0.562524 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 16.1502 | 0.559570 | ||||||||
\(834\) | 14.8728 | 0.515003 | ||||||||
\(835\) | 30.8083 | 1.06616 | ||||||||
\(836\) | −8.84670 | −0.305970 | ||||||||
\(837\) | 5.15289 | 0.178110 | ||||||||
\(838\) | −29.4907 | −1.01874 | ||||||||
\(839\) | 3.31359 | 0.114398 | 0.0571989 | − | 0.998363i | \(-0.481783\pi\) | ||||
0.0571989 | + | 0.998363i | \(0.481783\pi\) | |||||||
\(840\) | 7.18074 | 0.247759 | ||||||||
\(841\) | −24.1935 | −0.834258 | ||||||||
\(842\) | −27.7454 | −0.956169 | ||||||||
\(843\) | 18.6296 | 0.641636 | ||||||||
\(844\) | −11.7754 | −0.405327 | ||||||||
\(845\) | −3.75223 | −0.129081 | ||||||||
\(846\) | 9.35222 | 0.321536 | ||||||||
\(847\) | 11.8694 | 0.407836 | ||||||||
\(848\) | 12.8161 | 0.440106 | ||||||||
\(849\) | 2.72112 | 0.0933886 | ||||||||
\(850\) | 43.9324 | 1.50687 | ||||||||
\(851\) | 20.0526 | 0.687394 | ||||||||
\(852\) | 9.46244 | 0.324178 | ||||||||
\(853\) | 4.81021 | 0.164698 | 0.0823492 | − | 0.996604i | \(-0.473758\pi\) | ||||
0.0823492 | + | 0.996604i | \(0.473758\pi\) | |||||||
\(854\) | −19.5761 | −0.669880 | ||||||||
\(855\) | −8.00347 | −0.273713 | ||||||||
\(856\) | −15.6347 | −0.534381 | ||||||||
\(857\) | −29.0740 | −0.993150 | −0.496575 | − | 0.867994i | \(-0.665409\pi\) | ||||
−0.496575 | + | 0.867994i | \(0.665409\pi\) | |||||||
\(858\) | −4.14756 | −0.141595 | ||||||||
\(859\) | 23.2416 | 0.792992 | 0.396496 | − | 0.918036i | \(-0.370226\pi\) | ||||
0.396496 | + | 0.918036i | \(0.370226\pi\) | |||||||
\(860\) | −6.01496 | −0.205108 | ||||||||
\(861\) | 15.0926 | 0.514355 | ||||||||
\(862\) | 2.87789 | 0.0980213 | ||||||||
\(863\) | −18.9313 | −0.644428 | −0.322214 | − | 0.946667i | \(-0.604427\pi\) | ||||
−0.322214 | + | 0.946667i | \(0.604427\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −35.9805 | −1.22337 | ||||||||
\(866\) | 16.0609 | 0.545772 | ||||||||
\(867\) | 6.41383 | 0.217825 | ||||||||
\(868\) | 9.86123 | 0.334712 | ||||||||
\(869\) | 33.5305 | 1.13745 | ||||||||
\(870\) | −8.22631 | −0.278898 | ||||||||
\(871\) | 8.07141 | 0.273489 | ||||||||
\(872\) | 20.5955 | 0.697452 | ||||||||
\(873\) | −14.9290 | −0.505270 | ||||||||
\(874\) | −4.44102 | −0.150220 | ||||||||
\(875\) | −29.2918 | −0.990245 | ||||||||
\(876\) | 4.11647 | 0.139083 | ||||||||
\(877\) | −7.28841 | −0.246112 | −0.123056 | − | 0.992400i | \(-0.539270\pi\) | ||||
−0.123056 | + | 0.992400i | \(0.539270\pi\) | |||||||
\(878\) | −26.0727 | −0.879910 | ||||||||
\(879\) | 29.3839 | 0.991093 | ||||||||
\(880\) | 15.5626 | 0.524615 | ||||||||
\(881\) | 14.5805 | 0.491230 | 0.245615 | − | 0.969367i | \(-0.421010\pi\) | ||||
0.245615 | + | 0.969367i | \(0.421010\pi\) | |||||||
\(882\) | 3.33765 | 0.112384 | ||||||||
\(883\) | 14.8464 | 0.499621 | 0.249810 | − | 0.968295i | \(-0.419632\pi\) | ||||
0.249810 | + | 0.968295i | \(0.419632\pi\) | |||||||
\(884\) | 4.83878 | 0.162746 | ||||||||
\(885\) | 27.0678 | 0.909874 | ||||||||
\(886\) | 17.8236 | 0.598797 | ||||||||
\(887\) | −1.25625 | −0.0421808 | −0.0210904 | − | 0.999778i | \(-0.506714\pi\) | ||||
−0.0210904 | + | 0.999778i | \(0.506714\pi\) | |||||||
\(888\) | −9.63112 | −0.323199 | ||||||||
\(889\) | −7.99448 | −0.268126 | ||||||||
\(890\) | −47.5751 | −1.59472 | ||||||||
\(891\) | −4.14756 | −0.138948 | ||||||||
\(892\) | −20.7006 | −0.693107 | ||||||||
\(893\) | −19.9482 | −0.667541 | ||||||||
\(894\) | −6.78344 | −0.226872 | ||||||||
\(895\) | −30.5558 | −1.02137 | ||||||||
\(896\) | −1.91373 | −0.0639331 | ||||||||
\(897\) | −2.08206 | −0.0695180 | ||||||||
\(898\) | 31.6248 | 1.05533 | ||||||||
\(899\) | −11.2971 | −0.376779 | ||||||||
\(900\) | 9.07922 | 0.302641 | ||||||||
\(901\) | −62.0143 | −2.06599 | ||||||||
\(902\) | 32.7097 | 1.08911 | ||||||||
\(903\) | 3.06777 | 0.102089 | ||||||||
\(904\) | 0.0306698 | 0.00102006 | ||||||||
\(905\) | −6.31717 | −0.209990 | ||||||||
\(906\) | 19.0254 | 0.632076 | ||||||||
\(907\) | −45.0966 | −1.49741 | −0.748705 | − | 0.662904i | \(-0.769324\pi\) | ||||
−0.748705 | + | 0.662904i | \(0.769324\pi\) | |||||||
\(908\) | 16.2577 | 0.539530 | ||||||||
\(909\) | 16.7182 | 0.554509 | ||||||||
\(910\) | −7.18074 | −0.238039 | ||||||||
\(911\) | −33.9383 | −1.12442 | −0.562212 | − | 0.826993i | \(-0.690050\pi\) | ||||
−0.562212 | + | 0.826993i | \(0.690050\pi\) | |||||||
\(912\) | 2.13299 | 0.0706304 | ||||||||
\(913\) | −1.64979 | −0.0546001 | ||||||||
\(914\) | 30.9954 | 1.02524 | ||||||||
\(915\) | −38.3827 | −1.26889 | ||||||||
\(916\) | −13.6150 | −0.449851 | ||||||||
\(917\) | 1.32732 | 0.0438318 | ||||||||
\(918\) | 4.83878 | 0.159704 | ||||||||
\(919\) | 2.80843 | 0.0926415 | 0.0463207 | − | 0.998927i | \(-0.485250\pi\) | ||||
0.0463207 | + | 0.998927i | \(0.485250\pi\) | |||||||
\(920\) | 7.81237 | 0.257566 | ||||||||
\(921\) | −7.72568 | −0.254570 | ||||||||
\(922\) | 36.7779 | 1.21122 | ||||||||
\(923\) | −9.46244 | −0.311460 | ||||||||
\(924\) | −7.93729 | −0.261118 | ||||||||
\(925\) | 87.4431 | 2.87511 | ||||||||
\(926\) | 10.4965 | 0.344936 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 2.19238 | 0.0719683 | ||||||||
\(929\) | −6.37691 | −0.209220 | −0.104610 | − | 0.994513i | \(-0.533359\pi\) | ||||
−0.104610 | + | 0.994513i | \(0.533359\pi\) | |||||||
\(930\) | 19.3348 | 0.634014 | ||||||||
\(931\) | −7.11917 | −0.233322 | ||||||||
\(932\) | −19.0339 | −0.623477 | ||||||||
\(933\) | 23.8089 | 0.779469 | ||||||||
\(934\) | −16.3515 | −0.535036 | ||||||||
\(935\) | −75.3040 | −2.46270 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 2.86601 | 0.0936283 | 0.0468142 | − | 0.998904i | \(-0.485093\pi\) | ||||
0.0468142 | + | 0.998904i | \(0.485093\pi\) | |||||||
\(938\) | 15.4465 | 0.504345 | ||||||||
\(939\) | −7.23019 | −0.235948 | ||||||||
\(940\) | 35.0917 | 1.14456 | ||||||||
\(941\) | −9.15333 | −0.298390 | −0.149195 | − | 0.988808i | \(-0.547668\pi\) | ||||
−0.149195 | + | 0.988808i | \(0.547668\pi\) | |||||||
\(942\) | 24.8181 | 0.808619 | ||||||||
\(943\) | 16.4202 | 0.534714 | ||||||||
\(944\) | −7.21379 | −0.234789 | ||||||||
\(945\) | −7.18074 | −0.233590 | ||||||||
\(946\) | 6.64868 | 0.216167 | ||||||||
\(947\) | −35.7862 | −1.16290 | −0.581448 | − | 0.813583i | \(-0.697514\pi\) | ||||
−0.581448 | + | 0.813583i | \(0.697514\pi\) | |||||||
\(948\) | −8.08441 | −0.262569 | ||||||||
\(949\) | −4.11647 | −0.133626 | ||||||||
\(950\) | −19.3659 | −0.628313 | ||||||||
\(951\) | 15.4352 | 0.500521 | ||||||||
\(952\) | 9.26011 | 0.300122 | ||||||||
\(953\) | −44.3315 | −1.43604 | −0.718019 | − | 0.696024i | \(-0.754951\pi\) | ||||
−0.718019 | + | 0.696024i | \(0.754951\pi\) | |||||||
\(954\) | −12.8161 | −0.414936 | ||||||||
\(955\) | 79.8571 | 2.58411 | ||||||||
\(956\) | 7.92027 | 0.256160 | ||||||||
\(957\) | 9.09301 | 0.293935 | ||||||||
\(958\) | 35.5629 | 1.14899 | ||||||||
\(959\) | −29.7814 | −0.961691 | ||||||||
\(960\) | −3.75223 | −0.121103 | ||||||||
\(961\) | −4.44772 | −0.143475 | ||||||||
\(962\) | 9.63112 | 0.310520 | ||||||||
\(963\) | 15.6347 | 0.503820 | ||||||||
\(964\) | 17.3089 | 0.557482 | ||||||||
\(965\) | −72.8466 | −2.34502 | ||||||||
\(966\) | −3.98450 | −0.128199 | ||||||||
\(967\) | −53.2003 | −1.71081 | −0.855404 | − | 0.517962i | \(-0.826691\pi\) | ||||
−0.855404 | + | 0.517962i | \(0.826691\pi\) | |||||||
\(968\) | −6.20223 | −0.199347 | ||||||||
\(969\) | −10.3211 | −0.331561 | ||||||||
\(970\) | −56.0170 | −1.79860 | ||||||||
\(971\) | 27.6174 | 0.886284 | 0.443142 | − | 0.896451i | \(-0.353864\pi\) | ||||
0.443142 | + | 0.896451i | \(0.353864\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −28.4625 | −0.912465 | ||||||||
\(974\) | −1.39658 | −0.0447493 | ||||||||
\(975\) | −9.07922 | −0.290768 | ||||||||
\(976\) | 10.2293 | 0.327432 | ||||||||
\(977\) | −30.5303 | −0.976750 | −0.488375 | − | 0.872634i | \(-0.662410\pi\) | ||||
−0.488375 | + | 0.872634i | \(0.662410\pi\) | |||||||
\(978\) | 11.4078 | 0.364780 | ||||||||
\(979\) | 52.5875 | 1.68070 | ||||||||
\(980\) | 12.5236 | 0.400052 | ||||||||
\(981\) | −20.5955 | −0.657564 | ||||||||
\(982\) | −2.49644 | −0.0796647 | ||||||||
\(983\) | 15.9005 | 0.507147 | 0.253573 | − | 0.967316i | \(-0.418394\pi\) | ||||
0.253573 | + | 0.967316i | \(0.418394\pi\) | |||||||
\(984\) | −7.88650 | −0.251412 | ||||||||
\(985\) | 43.7084 | 1.39267 | ||||||||
\(986\) | −10.6084 | −0.337842 | ||||||||
\(987\) | −17.8976 | −0.569687 | ||||||||
\(988\) | −2.13299 | −0.0678595 | ||||||||
\(989\) | 3.33762 | 0.106130 | ||||||||
\(990\) | −15.5626 | −0.494611 | ||||||||
\(991\) | −49.8508 | −1.58356 | −0.791781 | − | 0.610805i | \(-0.790846\pi\) | ||||
−0.791781 | + | 0.610805i | \(0.790846\pi\) | |||||||
\(992\) | −5.15289 | −0.163604 | ||||||||
\(993\) | −31.3126 | −0.993675 | ||||||||
\(994\) | −18.1085 | −0.574368 | ||||||||
\(995\) | −57.5230 | −1.82360 | ||||||||
\(996\) | 0.397774 | 0.0126040 | ||||||||
\(997\) | −31.7453 | −1.00538 | −0.502691 | − | 0.864466i | \(-0.667657\pi\) | ||||
−0.502691 | + | 0.864466i | \(0.667657\pi\) | |||||||
\(998\) | −18.8673 | −0.597233 | ||||||||
\(999\) | 9.63112 | 0.304715 |
(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.bb.1.3 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.3 | ✓ | 14 | 1.1 | even | 1 | trivial |