Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6006,2,Mod(1,6006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6006.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: | \(47.9581514540\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.72306708.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - x^{3} + 10x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.916622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6006.1 |
$q$-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 | ||||||||
\(5\) | −2.18192 | −0.975786 | −0.487893 | − | 0.872903i | \(-0.662234\pi\) | ||||
−0.487893 | + | 0.872903i | \(0.662234\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.18192 | −0.689985 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.18192 | 0.563371 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.83324 | −0.444627 | −0.222313 | − | 0.974975i | \(-0.571361\pi\) | ||||
−0.222313 | + | 0.974975i | \(0.571361\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.82525 | −1.10699 | −0.553494 | − | 0.832853i | \(-0.686706\pi\) | ||||
−0.553494 | + | 0.832853i | \(0.686706\pi\) | |||||||
\(20\) | −2.18192 | −0.487893 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.733562 | −0.152958 | −0.0764791 | − | 0.997071i | \(-0.524368\pi\) | ||||
−0.0764791 | + | 0.997071i | \(0.524368\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −0.239205 | −0.0478409 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 9.89770 | 1.83796 | 0.918978 | − | 0.394308i | \(-0.129016\pi\) | ||||
0.918978 | + | 0.394308i | \(0.129016\pi\) | |||||||
\(30\) | 2.18192 | 0.398363 | ||||||||
\(31\) | 1.24900 | 0.224327 | 0.112163 | − | 0.993690i | \(-0.464222\pi\) | ||||
0.112163 | + | 0.993690i | \(0.464222\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.83324 | −0.314399 | ||||||||
\(35\) | −2.18192 | −0.368813 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.65132 | 0.271475 | 0.135738 | − | 0.990745i | \(-0.456660\pi\) | ||||
0.135738 | + | 0.990745i | \(0.456660\pi\) | |||||||
\(38\) | −4.82525 | −0.782759 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.18192 | −0.344993 | ||||||||
\(41\) | −2.09169 | −0.326667 | −0.163333 | − | 0.986571i | \(-0.552225\pi\) | ||||
−0.163333 | + | 0.986571i | \(0.552225\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 2.45161 | 0.373867 | 0.186933 | − | 0.982373i | \(-0.440145\pi\) | ||||
0.186933 | + | 0.982373i | \(0.440145\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.18192 | −0.325262 | ||||||||
\(46\) | −0.733562 | −0.108158 | ||||||||
\(47\) | 6.31961 | 0.921810 | 0.460905 | − | 0.887450i | \(-0.347525\pi\) | ||||
0.460905 | + | 0.887450i | \(0.347525\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.239205 | −0.0338286 | ||||||||
\(51\) | 1.83324 | 0.256705 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −11.6233 | −1.59658 | −0.798289 | − | 0.602274i | \(-0.794261\pi\) | ||||
−0.798289 | + | 0.602274i | \(0.794261\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.18192 | −0.294211 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 4.82525 | 0.639120 | ||||||||
\(58\) | 9.89770 | 1.29963 | ||||||||
\(59\) | 4.38488 | 0.570863 | 0.285431 | − | 0.958399i | \(-0.407863\pi\) | ||||
0.285431 | + | 0.958399i | \(0.407863\pi\) | |||||||
\(60\) | 2.18192 | 0.281685 | ||||||||
\(61\) | 14.1289 | 1.80902 | 0.904511 | − | 0.426451i | \(-0.140236\pi\) | ||||
0.904511 | + | 0.426451i | \(0.140236\pi\) | |||||||
\(62\) | 1.24900 | 0.158623 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.18192 | 0.270634 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −1.21488 | −0.148421 | −0.0742106 | − | 0.997243i | \(-0.523644\pi\) | ||||
−0.0742106 | + | 0.997243i | \(0.523644\pi\) | |||||||
\(68\) | −1.83324 | −0.222313 | ||||||||
\(69\) | 0.733562 | 0.0883105 | ||||||||
\(70\) | −2.18192 | −0.260790 | ||||||||
\(71\) | 8.74873 | 1.03828 | 0.519142 | − | 0.854688i | \(-0.326252\pi\) | ||||
0.519142 | + | 0.854688i | \(0.326252\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −11.5316 | −1.34967 | −0.674835 | − | 0.737969i | \(-0.735785\pi\) | ||||
−0.674835 | + | 0.737969i | \(0.735785\pi\) | |||||||
\(74\) | 1.65132 | 0.191962 | ||||||||
\(75\) | 0.239205 | 0.0276210 | ||||||||
\(76\) | −4.82525 | −0.553494 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 7.21993 | 0.812305 | 0.406153 | − | 0.913805i | \(-0.366870\pi\) | ||||
0.406153 | + | 0.913805i | \(0.366870\pi\) | |||||||
\(80\) | −2.18192 | −0.243947 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.09169 | −0.230988 | ||||||||
\(83\) | −10.9625 | −1.20329 | −0.601646 | − | 0.798763i | \(-0.705488\pi\) | ||||
−0.601646 | + | 0.798763i | \(0.705488\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 2.45161 | 0.264364 | ||||||||
\(87\) | −9.89770 | −1.06114 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 12.7595 | 1.35251 | 0.676255 | − | 0.736668i | \(-0.263602\pi\) | ||||
0.676255 | + | 0.736668i | \(0.263602\pi\) | |||||||
\(90\) | −2.18192 | −0.229995 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | −0.733562 | −0.0764791 | ||||||||
\(93\) | −1.24900 | −0.129515 | ||||||||
\(94\) | 6.31961 | 0.651818 | ||||||||
\(95\) | 10.5283 | 1.08018 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.28161 | 0.130127 | 0.0650637 | − | 0.997881i | \(-0.479275\pi\) | ||||
0.0650637 | + | 0.997881i | \(0.479275\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −0.239205 | −0.0239205 | ||||||||
\(101\) | −6.21018 | −0.617936 | −0.308968 | − | 0.951072i | \(-0.599984\pi\) | ||||
−0.308968 | + | 0.951072i | \(0.599984\pi\) | |||||||
\(102\) | 1.83324 | 0.181518 | ||||||||
\(103\) | −6.31961 | −0.622690 | −0.311345 | − | 0.950297i | \(-0.600779\pi\) | ||||
−0.311345 | + | 0.950297i | \(0.600779\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.18192 | 0.212934 | ||||||||
\(106\) | −11.6233 | −1.12895 | ||||||||
\(107\) | −6.69799 | −0.647519 | −0.323759 | − | 0.946139i | \(-0.604947\pi\) | ||||
−0.323759 | + | 0.946139i | \(0.604947\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.49800 | 0.430830 | 0.215415 | − | 0.976523i | \(-0.430890\pi\) | ||||
0.215415 | + | 0.976523i | \(0.430890\pi\) | |||||||
\(110\) | −2.18192 | −0.208038 | ||||||||
\(111\) | −1.65132 | −0.156736 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −8.75378 | −0.823486 | −0.411743 | − | 0.911300i | \(-0.635080\pi\) | ||||
−0.411743 | + | 0.911300i | \(0.635080\pi\) | |||||||
\(114\) | 4.82525 | 0.451926 | ||||||||
\(115\) | 1.60058 | 0.149255 | ||||||||
\(116\) | 9.89770 | 0.918978 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 4.38488 | 0.403661 | ||||||||
\(119\) | −1.83324 | −0.168053 | ||||||||
\(120\) | 2.18192 | 0.199182 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 14.1289 | 1.27917 | ||||||||
\(123\) | 2.09169 | 0.188601 | ||||||||
\(124\) | 1.24900 | 0.112163 | ||||||||
\(125\) | 11.4315 | 1.02247 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 22.0622 | 1.95770 | 0.978851 | − | 0.204574i | \(-0.0655808\pi\) | ||||
0.978851 | + | 0.204574i | \(0.0655808\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.45161 | −0.215852 | ||||||||
\(130\) | 2.18192 | 0.191367 | ||||||||
\(131\) | 0.503804 | 0.0440176 | 0.0220088 | − | 0.999758i | \(-0.492994\pi\) | ||||
0.0220088 | + | 0.999758i | \(0.492994\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −4.82525 | −0.418402 | ||||||||
\(134\) | −1.21488 | −0.104950 | ||||||||
\(135\) | 2.18192 | 0.187790 | ||||||||
\(136\) | −1.83324 | −0.157199 | ||||||||
\(137\) | 17.8767 | 1.52731 | 0.763653 | − | 0.645626i | \(-0.223404\pi\) | ||||
0.763653 | + | 0.645626i | \(0.223404\pi\) | |||||||
\(138\) | 0.733562 | 0.0624449 | ||||||||
\(139\) | −7.74258 | −0.656717 | −0.328358 | − | 0.944553i | \(-0.606495\pi\) | ||||
−0.328358 | + | 0.944553i | \(0.606495\pi\) | |||||||
\(140\) | −2.18192 | −0.184406 | ||||||||
\(141\) | −6.31961 | −0.532207 | ||||||||
\(142\) | 8.74873 | 0.734177 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −21.5960 | −1.79345 | ||||||||
\(146\) | −11.5316 | −0.954360 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 1.65132 | 0.135738 | ||||||||
\(149\) | 18.3308 | 1.50171 | 0.750857 | − | 0.660465i | \(-0.229641\pi\) | ||||
0.750857 | + | 0.660465i | \(0.229641\pi\) | |||||||
\(150\) | 0.239205 | 0.0195310 | ||||||||
\(151\) | 7.62264 | 0.620322 | 0.310161 | − | 0.950684i | \(-0.399617\pi\) | ||||
0.310161 | + | 0.950684i | \(0.399617\pi\) | |||||||
\(152\) | −4.82525 | −0.391380 | ||||||||
\(153\) | −1.83324 | −0.148209 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −2.72522 | −0.218895 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 8.68346 | 0.693015 | 0.346508 | − | 0.938047i | \(-0.387367\pi\) | ||||
0.346508 | + | 0.938047i | \(0.387367\pi\) | |||||||
\(158\) | 7.21993 | 0.574387 | ||||||||
\(159\) | 11.6233 | 0.921785 | ||||||||
\(160\) | −2.18192 | −0.172496 | ||||||||
\(161\) | −0.733562 | −0.0578128 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −2.83505 | −0.222058 | −0.111029 | − | 0.993817i | \(-0.535415\pi\) | ||||
−0.111029 | + | 0.993817i | \(0.535415\pi\) | |||||||
\(164\) | −2.09169 | −0.163333 | ||||||||
\(165\) | 2.18192 | 0.169863 | ||||||||
\(166\) | −10.9625 | −0.850855 | ||||||||
\(167\) | −5.40369 | −0.418150 | −0.209075 | − | 0.977900i | \(-0.567045\pi\) | ||||
−0.209075 | + | 0.977900i | \(0.567045\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | −4.82525 | −0.368996 | ||||||||
\(172\) | 2.45161 | 0.186933 | ||||||||
\(173\) | 16.9444 | 1.28826 | 0.644128 | − | 0.764918i | \(-0.277220\pi\) | ||||
0.644128 | + | 0.764918i | \(0.277220\pi\) | |||||||
\(174\) | −9.89770 | −0.750343 | ||||||||
\(175\) | −0.239205 | −0.0180822 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −4.38488 | −0.329588 | ||||||||
\(178\) | 12.7595 | 0.956368 | ||||||||
\(179\) | 19.7320 | 1.47484 | 0.737418 | − | 0.675436i | \(-0.236045\pi\) | ||||
0.737418 | + | 0.675436i | \(0.236045\pi\) | |||||||
\(180\) | −2.18192 | −0.162631 | ||||||||
\(181\) | 2.27216 | 0.168888 | 0.0844442 | − | 0.996428i | \(-0.473089\pi\) | ||||
0.0844442 | + | 0.996428i | \(0.473089\pi\) | |||||||
\(182\) | −1.00000 | −0.0741249 | ||||||||
\(183\) | −14.1289 | −1.04444 | ||||||||
\(184\) | −0.733562 | −0.0540789 | ||||||||
\(185\) | −3.60305 | −0.264902 | ||||||||
\(186\) | −1.24900 | −0.0915810 | ||||||||
\(187\) | −1.83324 | −0.134060 | ||||||||
\(188\) | 6.31961 | 0.460905 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 10.5283 | 0.763806 | ||||||||
\(191\) | 23.0618 | 1.66870 | 0.834348 | − | 0.551238i | \(-0.185844\pi\) | ||||
0.834348 | + | 0.551238i | \(0.185844\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 1.75715 | 0.126483 | 0.0632414 | − | 0.997998i | \(-0.479856\pi\) | ||||
0.0632414 | + | 0.997998i | \(0.479856\pi\) | |||||||
\(194\) | 1.28161 | 0.0920140 | ||||||||
\(195\) | −2.18192 | −0.156251 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −20.3872 | −1.45253 | −0.726263 | − | 0.687417i | \(-0.758744\pi\) | ||||
−0.726263 | + | 0.687417i | \(0.758744\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −22.0426 | −1.56256 | −0.781280 | − | 0.624181i | \(-0.785433\pi\) | ||||
−0.781280 | + | 0.624181i | \(0.785433\pi\) | |||||||
\(200\) | −0.239205 | −0.0169143 | ||||||||
\(201\) | 1.21488 | 0.0856910 | ||||||||
\(202\) | −6.21018 | −0.436947 | ||||||||
\(203\) | 9.89770 | 0.694682 | ||||||||
\(204\) | 1.83324 | 0.128353 | ||||||||
\(205\) | 4.56391 | 0.318757 | ||||||||
\(206\) | −6.31961 | −0.440308 | ||||||||
\(207\) | −0.733562 | −0.0509861 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −4.82525 | −0.333770 | ||||||||
\(210\) | 2.18192 | 0.150567 | ||||||||
\(211\) | −12.4660 | −0.858192 | −0.429096 | − | 0.903259i | \(-0.641168\pi\) | ||||
−0.429096 | + | 0.903259i | \(0.641168\pi\) | |||||||
\(212\) | −11.6233 | −0.798289 | ||||||||
\(213\) | −8.74873 | −0.599453 | ||||||||
\(214\) | −6.69799 | −0.457865 | ||||||||
\(215\) | −5.34922 | −0.364814 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 1.24900 | 0.0847876 | ||||||||
\(218\) | 4.49800 | 0.304643 | ||||||||
\(219\) | 11.5316 | 0.779232 | ||||||||
\(220\) | −2.18192 | −0.147105 | ||||||||
\(221\) | 1.83324 | 0.123317 | ||||||||
\(222\) | −1.65132 | −0.110829 | ||||||||
\(223\) | −0.272592 | −0.0182541 | −0.00912705 | − | 0.999958i | \(-0.502905\pi\) | ||||
−0.00912705 | + | 0.999958i | \(0.502905\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −0.239205 | −0.0159470 | ||||||||
\(226\) | −8.75378 | −0.582293 | ||||||||
\(227\) | 23.1263 | 1.53495 | 0.767473 | − | 0.641081i | \(-0.221514\pi\) | ||||
0.767473 | + | 0.641081i | \(0.221514\pi\) | |||||||
\(228\) | 4.82525 | 0.319560 | ||||||||
\(229\) | −4.19860 | −0.277452 | −0.138726 | − | 0.990331i | \(-0.544301\pi\) | ||||
−0.138726 | + | 0.990331i | \(0.544301\pi\) | |||||||
\(230\) | 1.60058 | 0.105539 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 9.89770 | 0.649816 | ||||||||
\(233\) | 6.44644 | 0.422320 | 0.211160 | − | 0.977451i | \(-0.432276\pi\) | ||||
0.211160 | + | 0.977451i | \(0.432276\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −13.7889 | −0.899489 | ||||||||
\(236\) | 4.38488 | 0.285431 | ||||||||
\(237\) | −7.21993 | −0.468985 | ||||||||
\(238\) | −1.83324 | −0.118832 | ||||||||
\(239\) | 14.7039 | 0.951113 | 0.475557 | − | 0.879685i | \(-0.342247\pi\) | ||||
0.475557 | + | 0.879685i | \(0.342247\pi\) | |||||||
\(240\) | 2.18192 | 0.140843 | ||||||||
\(241\) | 19.3315 | 1.24525 | 0.622626 | − | 0.782519i | \(-0.286066\pi\) | ||||
0.622626 | + | 0.782519i | \(0.286066\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 14.1289 | 0.904511 | ||||||||
\(245\) | −2.18192 | −0.139398 | ||||||||
\(246\) | 2.09169 | 0.133361 | ||||||||
\(247\) | 4.82525 | 0.307023 | ||||||||
\(248\) | 1.24900 | 0.0793115 | ||||||||
\(249\) | 10.9625 | 0.694720 | ||||||||
\(250\) | 11.4315 | 0.722995 | ||||||||
\(251\) | 17.0067 | 1.07346 | 0.536728 | − | 0.843755i | \(-0.319660\pi\) | ||||
0.536728 | + | 0.843755i | \(0.319660\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −0.733562 | −0.0461186 | ||||||||
\(254\) | 22.0622 | 1.38430 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.25108 | −0.577066 | −0.288533 | − | 0.957470i | \(-0.593168\pi\) | ||||
−0.288533 | + | 0.957470i | \(0.593168\pi\) | |||||||
\(258\) | −2.45161 | −0.152630 | ||||||||
\(259\) | 1.65132 | 0.102608 | ||||||||
\(260\) | 2.18192 | 0.135317 | ||||||||
\(261\) | 9.89770 | 0.612652 | ||||||||
\(262\) | 0.503804 | 0.0311251 | ||||||||
\(263\) | 11.0663 | 0.682375 | 0.341187 | − | 0.939995i | \(-0.389171\pi\) | ||||
0.341187 | + | 0.939995i | \(0.389171\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 25.3611 | 1.55792 | ||||||||
\(266\) | −4.82525 | −0.295855 | ||||||||
\(267\) | −12.7595 | −0.780872 | ||||||||
\(268\) | −1.21488 | −0.0742106 | ||||||||
\(269\) | −10.6537 | −0.649570 | −0.324785 | − | 0.945788i | \(-0.605292\pi\) | ||||
−0.324785 | + | 0.945788i | \(0.605292\pi\) | |||||||
\(270\) | 2.18192 | 0.132788 | ||||||||
\(271\) | 28.4158 | 1.72614 | 0.863069 | − | 0.505086i | \(-0.168539\pi\) | ||||
0.863069 | + | 0.505086i | \(0.168539\pi\) | |||||||
\(272\) | −1.83324 | −0.111157 | ||||||||
\(273\) | 1.00000 | 0.0605228 | ||||||||
\(274\) | 17.8767 | 1.07997 | ||||||||
\(275\) | −0.239205 | −0.0144246 | ||||||||
\(276\) | 0.733562 | 0.0441552 | ||||||||
\(277\) | −15.7796 | −0.948105 | −0.474052 | − | 0.880497i | \(-0.657209\pi\) | ||||
−0.474052 | + | 0.880497i | \(0.657209\pi\) | |||||||
\(278\) | −7.74258 | −0.464369 | ||||||||
\(279\) | 1.24900 | 0.0747756 | ||||||||
\(280\) | −2.18192 | −0.130395 | ||||||||
\(281\) | 29.6619 | 1.76948 | 0.884742 | − | 0.466082i | \(-0.154335\pi\) | ||||
0.884742 | + | 0.466082i | \(0.154335\pi\) | |||||||
\(282\) | −6.31961 | −0.376327 | ||||||||
\(283\) | −9.02923 | −0.536732 | −0.268366 | − | 0.963317i | \(-0.586484\pi\) | ||||
−0.268366 | + | 0.963317i | \(0.586484\pi\) | |||||||
\(284\) | 8.74873 | 0.519142 | ||||||||
\(285\) | −10.5283 | −0.623645 | ||||||||
\(286\) | −1.00000 | −0.0591312 | ||||||||
\(287\) | −2.09169 | −0.123469 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.6392 | −0.802307 | ||||||||
\(290\) | −21.5960 | −1.26816 | ||||||||
\(291\) | −1.28161 | −0.0751291 | ||||||||
\(292\) | −11.5316 | −0.674835 | ||||||||
\(293\) | 21.0756 | 1.23125 | 0.615624 | − | 0.788040i | \(-0.288904\pi\) | ||||
0.615624 | + | 0.788040i | \(0.288904\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −9.56748 | −0.557040 | ||||||||
\(296\) | 1.65132 | 0.0959810 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 18.3308 | 1.06187 | ||||||||
\(299\) | 0.733562 | 0.0424230 | ||||||||
\(300\) | 0.239205 | 0.0138105 | ||||||||
\(301\) | 2.45161 | 0.141308 | ||||||||
\(302\) | 7.62264 | 0.438634 | ||||||||
\(303\) | 6.21018 | 0.356766 | ||||||||
\(304\) | −4.82525 | −0.276747 | ||||||||
\(305\) | −30.8282 | −1.76522 | ||||||||
\(306\) | −1.83324 | −0.104800 | ||||||||
\(307\) | −7.65854 | −0.437096 | −0.218548 | − | 0.975826i | \(-0.570132\pi\) | ||||
−0.218548 | + | 0.975826i | \(0.570132\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 6.31961 | 0.359510 | ||||||||
\(310\) | −2.72522 | −0.154782 | ||||||||
\(311\) | 24.4586 | 1.38692 | 0.693461 | − | 0.720494i | \(-0.256085\pi\) | ||||
0.693461 | + | 0.720494i | \(0.256085\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 26.9065 | 1.52085 | 0.760424 | − | 0.649427i | \(-0.224991\pi\) | ||||
0.760424 | + | 0.649427i | \(0.224991\pi\) | |||||||
\(314\) | 8.68346 | 0.490036 | ||||||||
\(315\) | −2.18192 | −0.122938 | ||||||||
\(316\) | 7.21993 | 0.406153 | ||||||||
\(317\) | 26.1731 | 1.47003 | 0.735013 | − | 0.678053i | \(-0.237176\pi\) | ||||
0.735013 | + | 0.678053i | \(0.237176\pi\) | |||||||
\(318\) | 11.6233 | 0.651801 | ||||||||
\(319\) | 9.89770 | 0.554165 | ||||||||
\(320\) | −2.18192 | −0.121973 | ||||||||
\(321\) | 6.69799 | 0.373845 | ||||||||
\(322\) | −0.733562 | −0.0408798 | ||||||||
\(323\) | 8.84586 | 0.492197 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.239205 | 0.0132687 | ||||||||
\(326\) | −2.83505 | −0.157019 | ||||||||
\(327\) | −4.49800 | −0.248740 | ||||||||
\(328\) | −2.09169 | −0.115494 | ||||||||
\(329\) | 6.31961 | 0.348411 | ||||||||
\(330\) | 2.18192 | 0.120111 | ||||||||
\(331\) | 9.76211 | 0.536574 | 0.268287 | − | 0.963339i | \(-0.413542\pi\) | ||||
0.268287 | + | 0.963339i | \(0.413542\pi\) | |||||||
\(332\) | −10.9625 | −0.601646 | ||||||||
\(333\) | 1.65132 | 0.0904917 | ||||||||
\(334\) | −5.40369 | −0.295677 | ||||||||
\(335\) | 2.65078 | 0.144827 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 18.7182 | 1.01965 | 0.509823 | − | 0.860279i | \(-0.329711\pi\) | ||||
0.509823 | + | 0.860279i | \(0.329711\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 8.75378 | 0.475440 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 1.24900 | 0.0676371 | ||||||||
\(342\) | −4.82525 | −0.260920 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.45161 | 0.132182 | ||||||||
\(345\) | −1.60058 | −0.0861722 | ||||||||
\(346\) | 16.9444 | 0.910935 | ||||||||
\(347\) | 15.5758 | 0.836154 | 0.418077 | − | 0.908412i | \(-0.362704\pi\) | ||||
0.418077 | + | 0.908412i | \(0.362704\pi\) | |||||||
\(348\) | −9.89770 | −0.530572 | ||||||||
\(349\) | 14.2771 | 0.764238 | 0.382119 | − | 0.924113i | \(-0.375194\pi\) | ||||
0.382119 | + | 0.924113i | \(0.375194\pi\) | |||||||
\(350\) | −0.239205 | −0.0127860 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 2.45665 | 0.130754 | 0.0653772 | − | 0.997861i | \(-0.479175\pi\) | ||||
0.0653772 | + | 0.997861i | \(0.479175\pi\) | |||||||
\(354\) | −4.38488 | −0.233054 | ||||||||
\(355\) | −19.0891 | −1.01314 | ||||||||
\(356\) | 12.7595 | 0.676255 | ||||||||
\(357\) | 1.83324 | 0.0970256 | ||||||||
\(358\) | 19.7320 | 1.04287 | ||||||||
\(359\) | −25.5915 | −1.35067 | −0.675334 | − | 0.737512i | \(-0.736000\pi\) | ||||
−0.675334 | + | 0.737512i | \(0.736000\pi\) | |||||||
\(360\) | −2.18192 | −0.114998 | ||||||||
\(361\) | 4.28305 | 0.225424 | ||||||||
\(362\) | 2.27216 | 0.119422 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −1.00000 | −0.0524142 | ||||||||
\(365\) | 25.1610 | 1.31699 | ||||||||
\(366\) | −14.1289 | −0.738530 | ||||||||
\(367\) | −13.4271 | −0.700891 | −0.350446 | − | 0.936583i | \(-0.613970\pi\) | ||||
−0.350446 | + | 0.936583i | \(0.613970\pi\) | |||||||
\(368\) | −0.733562 | −0.0382396 | ||||||||
\(369\) | −2.09169 | −0.108889 | ||||||||
\(370\) | −3.60305 | −0.187314 | ||||||||
\(371\) | −11.6233 | −0.603450 | ||||||||
\(372\) | −1.24900 | −0.0647576 | ||||||||
\(373\) | −2.15944 | −0.111812 | −0.0559058 | − | 0.998436i | \(-0.517805\pi\) | ||||
−0.0559058 | + | 0.998436i | \(0.517805\pi\) | |||||||
\(374\) | −1.83324 | −0.0947948 | ||||||||
\(375\) | −11.4315 | −0.590323 | ||||||||
\(376\) | 6.31961 | 0.325909 | ||||||||
\(377\) | −9.89770 | −0.509757 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −37.4146 | −1.92186 | −0.960928 | − | 0.276797i | \(-0.910727\pi\) | ||||
−0.960928 | + | 0.276797i | \(0.910727\pi\) | |||||||
\(380\) | 10.5283 | 0.540092 | ||||||||
\(381\) | −22.0622 | −1.13028 | ||||||||
\(382\) | 23.0618 | 1.17995 | ||||||||
\(383\) | 20.5340 | 1.04924 | 0.524620 | − | 0.851337i | \(-0.324208\pi\) | ||||
0.524620 | + | 0.851337i | \(0.324208\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.18192 | −0.111201 | ||||||||
\(386\) | 1.75715 | 0.0894368 | ||||||||
\(387\) | 2.45161 | 0.124622 | ||||||||
\(388\) | 1.28161 | 0.0650637 | ||||||||
\(389\) | −19.4714 | −0.987237 | −0.493618 | − | 0.869679i | \(-0.664326\pi\) | ||||
−0.493618 | + | 0.869679i | \(0.664326\pi\) | |||||||
\(390\) | −2.18192 | −0.110486 | ||||||||
\(391\) | 1.34480 | 0.0680093 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −0.503804 | −0.0254135 | ||||||||
\(394\) | −20.3872 | −1.02709 | ||||||||
\(395\) | −15.7533 | −0.792636 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 4.14996 | 0.208280 | 0.104140 | − | 0.994563i | \(-0.466791\pi\) | ||||
0.104140 | + | 0.994563i | \(0.466791\pi\) | |||||||
\(398\) | −22.0426 | −1.10490 | ||||||||
\(399\) | 4.82525 | 0.241565 | ||||||||
\(400\) | −0.239205 | −0.0119602 | ||||||||
\(401\) | −4.94437 | −0.246910 | −0.123455 | − | 0.992350i | \(-0.539397\pi\) | ||||
−0.123455 | + | 0.992350i | \(0.539397\pi\) | |||||||
\(402\) | 1.21488 | 0.0605927 | ||||||||
\(403\) | −1.24900 | −0.0622171 | ||||||||
\(404\) | −6.21018 | −0.308968 | ||||||||
\(405\) | −2.18192 | −0.108421 | ||||||||
\(406\) | 9.89770 | 0.491215 | ||||||||
\(407\) | 1.65132 | 0.0818529 | ||||||||
\(408\) | 1.83324 | 0.0907591 | ||||||||
\(409\) | −27.7874 | −1.37400 | −0.686998 | − | 0.726659i | \(-0.741072\pi\) | ||||
−0.686998 | + | 0.726659i | \(0.741072\pi\) | |||||||
\(410\) | 4.56391 | 0.225395 | ||||||||
\(411\) | −17.8767 | −0.881791 | ||||||||
\(412\) | −6.31961 | −0.311345 | ||||||||
\(413\) | 4.38488 | 0.215766 | ||||||||
\(414\) | −0.733562 | −0.0360526 | ||||||||
\(415\) | 23.9194 | 1.17416 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 7.74258 | 0.379156 | ||||||||
\(418\) | −4.82525 | −0.236011 | ||||||||
\(419\) | 27.7533 | 1.35584 | 0.677920 | − | 0.735136i | \(-0.262882\pi\) | ||||
0.677920 | + | 0.735136i | \(0.262882\pi\) | |||||||
\(420\) | 2.18192 | 0.106467 | ||||||||
\(421\) | −22.3811 | −1.09079 | −0.545393 | − | 0.838180i | \(-0.683620\pi\) | ||||
−0.545393 | + | 0.838180i | \(0.683620\pi\) | |||||||
\(422\) | −12.4660 | −0.606833 | ||||||||
\(423\) | 6.31961 | 0.307270 | ||||||||
\(424\) | −11.6233 | −0.564476 | ||||||||
\(425\) | 0.438520 | 0.0212714 | ||||||||
\(426\) | −8.74873 | −0.423877 | ||||||||
\(427\) | 14.1289 | 0.683746 | ||||||||
\(428\) | −6.69799 | −0.323759 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | −5.34922 | −0.257962 | ||||||||
\(431\) | −25.3366 | −1.22042 | −0.610210 | − | 0.792240i | \(-0.708915\pi\) | ||||
−0.610210 | + | 0.792240i | \(0.708915\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −34.2673 | −1.64678 | −0.823391 | − | 0.567474i | \(-0.807921\pi\) | ||||
−0.823391 | + | 0.567474i | \(0.807921\pi\) | |||||||
\(434\) | 1.24900 | 0.0599539 | ||||||||
\(435\) | 21.5960 | 1.03545 | ||||||||
\(436\) | 4.49800 | 0.215415 | ||||||||
\(437\) | 3.53962 | 0.169323 | ||||||||
\(438\) | 11.5316 | 0.551000 | ||||||||
\(439\) | 2.09725 | 0.100096 | 0.0500482 | − | 0.998747i | \(-0.484062\pi\) | ||||
0.0500482 | + | 0.998747i | \(0.484062\pi\) | |||||||
\(440\) | −2.18192 | −0.104019 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 1.83324 | 0.0871985 | ||||||||
\(443\) | −15.1828 | −0.721359 | −0.360679 | − | 0.932690i | \(-0.617455\pi\) | ||||
−0.360679 | + | 0.932690i | \(0.617455\pi\) | |||||||
\(444\) | −1.65132 | −0.0783681 | ||||||||
\(445\) | −27.8404 | −1.31976 | ||||||||
\(446\) | −0.272592 | −0.0129076 | ||||||||
\(447\) | −18.3308 | −0.867015 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 34.3812 | 1.62255 | 0.811274 | − | 0.584667i | \(-0.198775\pi\) | ||||
0.811274 | + | 0.584667i | \(0.198775\pi\) | |||||||
\(450\) | −0.239205 | −0.0112762 | ||||||||
\(451\) | −2.09169 | −0.0984938 | ||||||||
\(452\) | −8.75378 | −0.411743 | ||||||||
\(453\) | −7.62264 | −0.358143 | ||||||||
\(454\) | 23.1263 | 1.08537 | ||||||||
\(455\) | 2.18192 | 0.102290 | ||||||||
\(456\) | 4.82525 | 0.225963 | ||||||||
\(457\) | 23.0258 | 1.07710 | 0.538550 | − | 0.842594i | \(-0.318972\pi\) | ||||
0.538550 | + | 0.842594i | \(0.318972\pi\) | |||||||
\(458\) | −4.19860 | −0.196188 | ||||||||
\(459\) | 1.83324 | 0.0855685 | ||||||||
\(460\) | 1.60058 | 0.0746273 | ||||||||
\(461\) | −5.79994 | −0.270130 | −0.135065 | − | 0.990837i | \(-0.543124\pi\) | ||||
−0.135065 | + | 0.990837i | \(0.543124\pi\) | |||||||
\(462\) | −1.00000 | −0.0465242 | ||||||||
\(463\) | −20.9602 | −0.974105 | −0.487052 | − | 0.873373i | \(-0.661928\pi\) | ||||
−0.487052 | + | 0.873373i | \(0.661928\pi\) | |||||||
\(464\) | 9.89770 | 0.459489 | ||||||||
\(465\) | 2.72522 | 0.126379 | ||||||||
\(466\) | 6.44644 | 0.298626 | ||||||||
\(467\) | 27.1046 | 1.25425 | 0.627126 | − | 0.778918i | \(-0.284231\pi\) | ||||
0.627126 | + | 0.778918i | \(0.284231\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −1.21488 | −0.0560980 | ||||||||
\(470\) | −13.7889 | −0.636035 | ||||||||
\(471\) | −8.68346 | −0.400113 | ||||||||
\(472\) | 4.38488 | 0.201831 | ||||||||
\(473\) | 2.45161 | 0.112725 | ||||||||
\(474\) | −7.21993 | −0.331622 | ||||||||
\(475\) | 1.15422 | 0.0529593 | ||||||||
\(476\) | −1.83324 | −0.0840266 | ||||||||
\(477\) | −11.6233 | −0.532193 | ||||||||
\(478\) | 14.7039 | 0.672538 | ||||||||
\(479\) | −13.2625 | −0.605980 | −0.302990 | − | 0.952994i | \(-0.597985\pi\) | ||||
−0.302990 | + | 0.952994i | \(0.597985\pi\) | |||||||
\(480\) | 2.18192 | 0.0995908 | ||||||||
\(481\) | −1.65132 | −0.0752937 | ||||||||
\(482\) | 19.3315 | 0.880527 | ||||||||
\(483\) | 0.733562 | 0.0333782 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −2.79637 | −0.126977 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 14.4688 | 0.655645 | 0.327822 | − | 0.944739i | \(-0.393685\pi\) | ||||
0.327822 | + | 0.944739i | \(0.393685\pi\) | |||||||
\(488\) | 14.1289 | 0.639586 | ||||||||
\(489\) | 2.83505 | 0.128205 | ||||||||
\(490\) | −2.18192 | −0.0985693 | ||||||||
\(491\) | −13.6098 | −0.614200 | −0.307100 | − | 0.951677i | \(-0.599359\pi\) | ||||
−0.307100 | + | 0.951677i | \(0.599359\pi\) | |||||||
\(492\) | 2.09169 | 0.0943006 | ||||||||
\(493\) | −18.1449 | −0.817205 | ||||||||
\(494\) | 4.82525 | 0.217098 | ||||||||
\(495\) | −2.18192 | −0.0980702 | ||||||||
\(496\) | 1.24900 | 0.0560817 | ||||||||
\(497\) | 8.74873 | 0.392434 | ||||||||
\(498\) | 10.9625 | 0.491242 | ||||||||
\(499\) | −41.2145 | −1.84501 | −0.922507 | − | 0.385980i | \(-0.873863\pi\) | ||||
−0.922507 | + | 0.385980i | \(0.873863\pi\) | |||||||
\(500\) | 11.4315 | 0.511234 | ||||||||
\(501\) | 5.40369 | 0.241419 | ||||||||
\(502\) | 17.0067 | 0.759048 | ||||||||
\(503\) | 10.3949 | 0.463485 | 0.231742 | − | 0.972777i | \(-0.425557\pi\) | ||||
0.231742 | + | 0.972777i | \(0.425557\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 13.5501 | 0.602974 | ||||||||
\(506\) | −0.733562 | −0.0326108 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 22.0622 | 0.978851 | ||||||||
\(509\) | 22.8036 | 1.01075 | 0.505376 | − | 0.862899i | \(-0.331354\pi\) | ||||
0.505376 | + | 0.862899i | \(0.331354\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | −11.5316 | −0.510127 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.82525 | 0.213040 | ||||||||
\(514\) | −9.25108 | −0.408048 | ||||||||
\(515\) | 13.7889 | 0.607612 | ||||||||
\(516\) | −2.45161 | −0.107926 | ||||||||
\(517\) | 6.31961 | 0.277936 | ||||||||
\(518\) | 1.65132 | 0.0725548 | ||||||||
\(519\) | −16.9444 | −0.743775 | ||||||||
\(520\) | 2.18192 | 0.0956837 | ||||||||
\(521\) | −5.95503 | −0.260895 | −0.130447 | − | 0.991455i | \(-0.541641\pi\) | ||||
−0.130447 | + | 0.991455i | \(0.541641\pi\) | |||||||
\(522\) | 9.89770 | 0.433211 | ||||||||
\(523\) | −6.73788 | −0.294627 | −0.147313 | − | 0.989090i | \(-0.547063\pi\) | ||||
−0.147313 | + | 0.989090i | \(0.547063\pi\) | |||||||
\(524\) | 0.503804 | 0.0220088 | ||||||||
\(525\) | 0.239205 | 0.0104397 | ||||||||
\(526\) | 11.0663 | 0.482512 | ||||||||
\(527\) | −2.28972 | −0.0997418 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −22.4619 | −0.976604 | ||||||||
\(530\) | 25.3611 | 1.10162 | ||||||||
\(531\) | 4.38488 | 0.190288 | ||||||||
\(532\) | −4.82525 | −0.209201 | ||||||||
\(533\) | 2.09169 | 0.0906011 | ||||||||
\(534\) | −12.7595 | −0.552160 | ||||||||
\(535\) | 14.6145 | 0.631840 | ||||||||
\(536\) | −1.21488 | −0.0524748 | ||||||||
\(537\) | −19.7320 | −0.851497 | ||||||||
\(538\) | −10.6537 | −0.459316 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 2.18192 | 0.0938951 | ||||||||
\(541\) | −26.8197 | −1.15307 | −0.576534 | − | 0.817073i | \(-0.695595\pi\) | ||||
−0.576534 | + | 0.817073i | \(0.695595\pi\) | |||||||
\(542\) | 28.4158 | 1.22056 | ||||||||
\(543\) | −2.27216 | −0.0975077 | ||||||||
\(544\) | −1.83324 | −0.0785997 | ||||||||
\(545\) | −9.81429 | −0.420398 | ||||||||
\(546\) | 1.00000 | 0.0427960 | ||||||||
\(547\) | −7.24096 | −0.309601 | −0.154801 | − | 0.987946i | \(-0.549473\pi\) | ||||
−0.154801 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(548\) | 17.8767 | 0.763653 | ||||||||
\(549\) | 14.1289 | 0.603007 | ||||||||
\(550\) | −0.239205 | −0.0101997 | ||||||||
\(551\) | −47.7589 | −2.03460 | ||||||||
\(552\) | 0.733562 | 0.0312225 | ||||||||
\(553\) | 7.21993 | 0.307023 | ||||||||
\(554\) | −15.7796 | −0.670411 | ||||||||
\(555\) | 3.60305 | 0.152941 | ||||||||
\(556\) | −7.74258 | −0.328358 | ||||||||
\(557\) | 13.5118 | 0.572514 | 0.286257 | − | 0.958153i | \(-0.407589\pi\) | ||||
0.286257 | + | 0.958153i | \(0.407589\pi\) | |||||||
\(558\) | 1.24900 | 0.0528743 | ||||||||
\(559\) | −2.45161 | −0.103692 | ||||||||
\(560\) | −2.18192 | −0.0922031 | ||||||||
\(561\) | 1.83324 | 0.0773996 | ||||||||
\(562\) | 29.6619 | 1.25121 | ||||||||
\(563\) | −31.8630 | −1.34286 | −0.671432 | − | 0.741066i | \(-0.734320\pi\) | ||||
−0.671432 | + | 0.741066i | \(0.734320\pi\) | |||||||
\(564\) | −6.31961 | −0.266104 | ||||||||
\(565\) | 19.1001 | 0.803546 | ||||||||
\(566\) | −9.02923 | −0.379527 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 8.74873 | 0.367089 | ||||||||
\(569\) | 24.8849 | 1.04323 | 0.521615 | − | 0.853181i | \(-0.325330\pi\) | ||||
0.521615 | + | 0.853181i | \(0.325330\pi\) | |||||||
\(570\) | −10.5283 | −0.440983 | ||||||||
\(571\) | −14.1701 | −0.592999 | −0.296499 | − | 0.955033i | \(-0.595819\pi\) | ||||
−0.296499 | + | 0.955033i | \(0.595819\pi\) | |||||||
\(572\) | −1.00000 | −0.0418121 | ||||||||
\(573\) | −23.0618 | −0.963422 | ||||||||
\(574\) | −2.09169 | −0.0873054 | ||||||||
\(575\) | 0.175471 | 0.00731766 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −19.1126 | −0.795667 | −0.397834 | − | 0.917458i | \(-0.630238\pi\) | ||||
−0.397834 | + | 0.917458i | \(0.630238\pi\) | |||||||
\(578\) | −13.6392 | −0.567317 | ||||||||
\(579\) | −1.75715 | −0.0730249 | ||||||||
\(580\) | −21.5960 | −0.896727 | ||||||||
\(581\) | −10.9625 | −0.454801 | ||||||||
\(582\) | −1.28161 | −0.0531243 | ||||||||
\(583\) | −11.6233 | −0.481387 | ||||||||
\(584\) | −11.5316 | −0.477180 | ||||||||
\(585\) | 2.18192 | 0.0902115 | ||||||||
\(586\) | 21.0756 | 0.870623 | ||||||||
\(587\) | 2.27032 | 0.0937062 | 0.0468531 | − | 0.998902i | \(-0.485081\pi\) | ||||
0.0468531 | + | 0.998902i | \(0.485081\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −6.02673 | −0.248327 | ||||||||
\(590\) | −9.56748 | −0.393887 | ||||||||
\(591\) | 20.3872 | 0.838616 | ||||||||
\(592\) | 1.65132 | 0.0678688 | ||||||||
\(593\) | 1.62636 | 0.0667864 | 0.0333932 | − | 0.999442i | \(-0.489369\pi\) | ||||
0.0333932 | + | 0.999442i | \(0.489369\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 4.00000 | 0.163984 | ||||||||
\(596\) | 18.3308 | 0.750857 | ||||||||
\(597\) | 22.0426 | 0.902144 | ||||||||
\(598\) | 0.733562 | 0.0299976 | ||||||||
\(599\) | −14.3907 | −0.587986 | −0.293993 | − | 0.955808i | \(-0.594984\pi\) | ||||
−0.293993 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(600\) | 0.239205 | 0.00976549 | ||||||||
\(601\) | −13.6310 | −0.556019 | −0.278009 | − | 0.960578i | \(-0.589675\pi\) | ||||
−0.278009 | + | 0.960578i | \(0.589675\pi\) | |||||||
\(602\) | 2.45161 | 0.0999201 | ||||||||
\(603\) | −1.21488 | −0.0494737 | ||||||||
\(604\) | 7.62264 | 0.310161 | ||||||||
\(605\) | −2.18192 | −0.0887079 | ||||||||
\(606\) | 6.21018 | 0.252271 | ||||||||
\(607\) | −10.5698 | −0.429014 | −0.214507 | − | 0.976722i | \(-0.568814\pi\) | ||||
−0.214507 | + | 0.976722i | \(0.568814\pi\) | |||||||
\(608\) | −4.82525 | −0.195690 | ||||||||
\(609\) | −9.89770 | −0.401075 | ||||||||
\(610\) | −30.8282 | −1.24820 | ||||||||
\(611\) | −6.31961 | −0.255664 | ||||||||
\(612\) | −1.83324 | −0.0741045 | ||||||||
\(613\) | −11.4717 | −0.463336 | −0.231668 | − | 0.972795i | \(-0.574418\pi\) | ||||
−0.231668 | + | 0.972795i | \(0.574418\pi\) | |||||||
\(614\) | −7.65854 | −0.309074 | ||||||||
\(615\) | −4.56391 | −0.184035 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −45.5174 | −1.83246 | −0.916231 | − | 0.400651i | \(-0.868784\pi\) | ||||
−0.916231 | + | 0.400651i | \(0.868784\pi\) | |||||||
\(618\) | 6.31961 | 0.254212 | ||||||||
\(619\) | 24.4404 | 0.982342 | 0.491171 | − | 0.871063i | \(-0.336569\pi\) | ||||
0.491171 | + | 0.871063i | \(0.336569\pi\) | |||||||
\(620\) | −2.72522 | −0.109448 | ||||||||
\(621\) | 0.733562 | 0.0294368 | ||||||||
\(622\) | 24.4586 | 0.980702 | ||||||||
\(623\) | 12.7595 | 0.511200 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −23.7468 | −0.949870 | ||||||||
\(626\) | 26.9065 | 1.07540 | ||||||||
\(627\) | 4.82525 | 0.192702 | ||||||||
\(628\) | 8.68346 | 0.346508 | ||||||||
\(629\) | −3.02727 | −0.120705 | ||||||||
\(630\) | −2.18192 | −0.0869300 | ||||||||
\(631\) | 8.54937 | 0.340345 | 0.170172 | − | 0.985414i | \(-0.445568\pi\) | ||||
0.170172 | + | 0.985414i | \(0.445568\pi\) | |||||||
\(632\) | 7.21993 | 0.287193 | ||||||||
\(633\) | 12.4660 | 0.495477 | ||||||||
\(634\) | 26.1731 | 1.03947 | ||||||||
\(635\) | −48.1380 | −1.91030 | ||||||||
\(636\) | 11.6233 | 0.460893 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 9.89770 | 0.391854 | ||||||||
\(639\) | 8.74873 | 0.346094 | ||||||||
\(640\) | −2.18192 | −0.0862481 | ||||||||
\(641\) | −11.9856 | −0.473405 | −0.236702 | − | 0.971582i | \(-0.576067\pi\) | ||||
−0.236702 | + | 0.971582i | \(0.576067\pi\) | |||||||
\(642\) | 6.69799 | 0.264349 | ||||||||
\(643\) | 23.3792 | 0.921985 | 0.460992 | − | 0.887404i | \(-0.347494\pi\) | ||||
0.460992 | + | 0.887404i | \(0.347494\pi\) | |||||||
\(644\) | −0.733562 | −0.0289064 | ||||||||
\(645\) | 5.34922 | 0.210625 | ||||||||
\(646\) | 8.84586 | 0.348036 | ||||||||
\(647\) | −8.04119 | −0.316132 | −0.158066 | − | 0.987429i | \(-0.550526\pi\) | ||||
−0.158066 | + | 0.987429i | \(0.550526\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 4.38488 | 0.172122 | ||||||||
\(650\) | 0.239205 | 0.00938238 | ||||||||
\(651\) | −1.24900 | −0.0489521 | ||||||||
\(652\) | −2.83505 | −0.111029 | ||||||||
\(653\) | 1.36918 | 0.0535800 | 0.0267900 | − | 0.999641i | \(-0.491471\pi\) | ||||
0.0267900 | + | 0.999641i | \(0.491471\pi\) | |||||||
\(654\) | −4.49800 | −0.175886 | ||||||||
\(655\) | −1.09926 | −0.0429517 | ||||||||
\(656\) | −2.09169 | −0.0816667 | ||||||||
\(657\) | −11.5316 | −0.449890 | ||||||||
\(658\) | 6.31961 | 0.246364 | ||||||||
\(659\) | 2.32339 | 0.0905064 | 0.0452532 | − | 0.998976i | \(-0.485591\pi\) | ||||
0.0452532 | + | 0.998976i | \(0.485591\pi\) | |||||||
\(660\) | 2.18192 | 0.0849313 | ||||||||
\(661\) | −6.65249 | −0.258752 | −0.129376 | − | 0.991596i | \(-0.541297\pi\) | ||||
−0.129376 | + | 0.991596i | \(0.541297\pi\) | |||||||
\(662\) | 9.76211 | 0.379415 | ||||||||
\(663\) | −1.83324 | −0.0711973 | ||||||||
\(664\) | −10.9625 | −0.425428 | ||||||||
\(665\) | 10.5283 | 0.408271 | ||||||||
\(666\) | 1.65132 | 0.0639873 | ||||||||
\(667\) | −7.26058 | −0.281131 | ||||||||
\(668\) | −5.40369 | −0.209075 | ||||||||
\(669\) | 0.272592 | 0.0105390 | ||||||||
\(670\) | 2.65078 | 0.102408 | ||||||||
\(671\) | 14.1289 | 0.545441 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 29.6793 | 1.14405 | 0.572026 | − | 0.820235i | \(-0.306158\pi\) | ||||
0.572026 | + | 0.820235i | \(0.306158\pi\) | |||||||
\(674\) | 18.7182 | 0.720998 | ||||||||
\(675\) | 0.239205 | 0.00920699 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −26.2614 | −1.00931 | −0.504653 | − | 0.863322i | \(-0.668380\pi\) | ||||
−0.504653 | + | 0.863322i | \(0.668380\pi\) | |||||||
\(678\) | 8.75378 | 0.336187 | ||||||||
\(679\) | 1.28161 | 0.0491835 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | −23.1263 | −0.886201 | ||||||||
\(682\) | 1.24900 | 0.0478266 | ||||||||
\(683\) | 19.6923 | 0.753504 | 0.376752 | − | 0.926314i | \(-0.377041\pi\) | ||||
0.376752 | + | 0.926314i | \(0.377041\pi\) | |||||||
\(684\) | −4.82525 | −0.184498 | ||||||||
\(685\) | −39.0055 | −1.49033 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 4.19860 | 0.160187 | ||||||||
\(688\) | 2.45161 | 0.0934667 | ||||||||
\(689\) | 11.6233 | 0.442811 | ||||||||
\(690\) | −1.60058 | −0.0609329 | ||||||||
\(691\) | 30.9151 | 1.17607 | 0.588033 | − | 0.808837i | \(-0.299902\pi\) | ||||
0.588033 | + | 0.808837i | \(0.299902\pi\) | |||||||
\(692\) | 16.9444 | 0.644128 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 15.5758 | 0.591250 | ||||||||
\(695\) | 16.8937 | 0.640815 | ||||||||
\(696\) | −9.89770 | −0.375171 | ||||||||
\(697\) | 3.83458 | 0.145245 | ||||||||
\(698\) | 14.2771 | 0.540398 | ||||||||
\(699\) | −6.44644 | −0.243827 | ||||||||
\(700\) | −0.239205 | −0.00904108 | ||||||||
\(701\) | −16.1855 | −0.611320 | −0.305660 | − | 0.952141i | \(-0.598877\pi\) | ||||
−0.305660 | + | 0.952141i | \(0.598877\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −7.96803 | −0.300520 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 13.7889 | 0.519320 | ||||||||
\(706\) | 2.45665 | 0.0924574 | ||||||||
\(707\) | −6.21018 | −0.233558 | ||||||||
\(708\) | −4.38488 | −0.164794 | ||||||||
\(709\) | 17.4467 | 0.655225 | 0.327613 | − | 0.944812i | \(-0.393756\pi\) | ||||
0.327613 | + | 0.944812i | \(0.393756\pi\) | |||||||
\(710\) | −19.0891 | −0.716400 | ||||||||
\(711\) | 7.21993 | 0.270768 | ||||||||
\(712\) | 12.7595 | 0.478184 | ||||||||
\(713\) | −0.916218 | −0.0343126 | ||||||||
\(714\) | 1.83324 | 0.0686074 | ||||||||
\(715\) | 2.18192 | 0.0815994 | ||||||||
\(716\) | 19.7320 | 0.737418 | ||||||||
\(717\) | −14.7039 | −0.549125 | ||||||||
\(718\) | −25.5915 | −0.955066 | ||||||||
\(719\) | −18.0170 | −0.671921 | −0.335960 | − | 0.941876i | \(-0.609061\pi\) | ||||
−0.335960 | + | 0.941876i | \(0.609061\pi\) | |||||||
\(720\) | −2.18192 | −0.0813155 | ||||||||
\(721\) | −6.31961 | −0.235355 | ||||||||
\(722\) | 4.28305 | 0.159399 | ||||||||
\(723\) | −19.3315 | −0.718947 | ||||||||
\(724\) | 2.27216 | 0.0844442 | ||||||||
\(725\) | −2.36758 | −0.0879295 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 21.5257 | 0.798345 | 0.399172 | − | 0.916876i | \(-0.369298\pi\) | ||||
0.399172 | + | 0.916876i | \(0.369298\pi\) | |||||||
\(728\) | −1.00000 | −0.0370625 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 25.1610 | 0.931252 | ||||||||
\(731\) | −4.49439 | −0.166231 | ||||||||
\(732\) | −14.1289 | −0.522220 | ||||||||
\(733\) | −12.8172 | −0.473414 | −0.236707 | − | 0.971581i | \(-0.576068\pi\) | ||||
−0.236707 | + | 0.971581i | \(0.576068\pi\) | |||||||
\(734\) | −13.4271 | −0.495605 | ||||||||
\(735\) | 2.18192 | 0.0804815 | ||||||||
\(736\) | −0.733562 | −0.0270394 | ||||||||
\(737\) | −1.21488 | −0.0447507 | ||||||||
\(738\) | −2.09169 | −0.0769961 | ||||||||
\(739\) | −0.757692 | −0.0278721 | −0.0139361 | − | 0.999903i | \(-0.504436\pi\) | ||||
−0.0139361 | + | 0.999903i | \(0.504436\pi\) | |||||||
\(740\) | −3.60305 | −0.132451 | ||||||||
\(741\) | −4.82525 | −0.177260 | ||||||||
\(742\) | −11.6233 | −0.426704 | ||||||||
\(743\) | 34.8980 | 1.28028 | 0.640141 | − | 0.768257i | \(-0.278876\pi\) | ||||
0.640141 | + | 0.768257i | \(0.278876\pi\) | |||||||
\(744\) | −1.24900 | −0.0457905 | ||||||||
\(745\) | −39.9963 | −1.46535 | ||||||||
\(746\) | −2.15944 | −0.0790627 | ||||||||
\(747\) | −10.9625 | −0.401097 | ||||||||
\(748\) | −1.83324 | −0.0670300 | ||||||||
\(749\) | −6.69799 | −0.244739 | ||||||||
\(750\) | −11.4315 | −0.417421 | ||||||||
\(751\) | 10.2778 | 0.375044 | 0.187522 | − | 0.982260i | \(-0.439954\pi\) | ||||
0.187522 | + | 0.982260i | \(0.439954\pi\) | |||||||
\(752\) | 6.31961 | 0.230452 | ||||||||
\(753\) | −17.0067 | −0.619760 | ||||||||
\(754\) | −9.89770 | −0.360453 | ||||||||
\(755\) | −16.6320 | −0.605302 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 25.7302 | 0.935179 | 0.467590 | − | 0.883946i | \(-0.345122\pi\) | ||||
0.467590 | + | 0.883946i | \(0.345122\pi\) | |||||||
\(758\) | −37.4146 | −1.35896 | ||||||||
\(759\) | 0.733562 | 0.0266266 | ||||||||
\(760\) | 10.5283 | 0.381903 | ||||||||
\(761\) | −49.2245 | −1.78439 | −0.892193 | − | 0.451654i | \(-0.850834\pi\) | ||||
−0.892193 | + | 0.451654i | \(0.850834\pi\) | |||||||
\(762\) | −22.0622 | −0.799229 | ||||||||
\(763\) | 4.49800 | 0.162838 | ||||||||
\(764\) | 23.0618 | 0.834348 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | 20.5340 | 0.741924 | ||||||||
\(767\) | −4.38488 | −0.158329 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −35.1595 | −1.26788 | −0.633942 | − | 0.773380i | \(-0.718564\pi\) | ||||
−0.633942 | + | 0.773380i | \(0.718564\pi\) | |||||||
\(770\) | −2.18192 | −0.0786311 | ||||||||
\(771\) | 9.25108 | 0.333169 | ||||||||
\(772\) | 1.75715 | 0.0632414 | ||||||||
\(773\) | −18.5154 | −0.665954 | −0.332977 | − | 0.942935i | \(-0.608053\pi\) | ||||
−0.332977 | + | 0.942935i | \(0.608053\pi\) | |||||||
\(774\) | 2.45161 | 0.0881212 | ||||||||
\(775\) | −0.298766 | −0.0107320 | ||||||||
\(776\) | 1.28161 | 0.0460070 | ||||||||
\(777\) | −1.65132 | −0.0592407 | ||||||||
\(778\) | −19.4714 | −0.698082 | ||||||||
\(779\) | 10.0929 | 0.361617 | ||||||||
\(780\) | −2.18192 | −0.0781254 | ||||||||
\(781\) | 8.74873 | 0.313054 | ||||||||
\(782\) | 1.34480 | 0.0480899 | ||||||||
\(783\) | −9.89770 | −0.353715 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −18.9467 | −0.676235 | ||||||||
\(786\) | −0.503804 | −0.0179701 | ||||||||
\(787\) | −22.9820 | −0.819221 | −0.409610 | − | 0.912261i | \(-0.634335\pi\) | ||||
−0.409610 | + | 0.912261i | \(0.634335\pi\) | |||||||
\(788\) | −20.3872 | −0.726263 | ||||||||
\(789\) | −11.0663 | −0.393969 | ||||||||
\(790\) | −15.7533 | −0.560479 | ||||||||
\(791\) | −8.75378 | −0.311248 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −14.1289 | −0.501732 | ||||||||
\(794\) | 4.14996 | 0.147276 | ||||||||
\(795\) | −25.3611 | −0.899465 | ||||||||
\(796\) | −22.0426 | −0.781280 | ||||||||
\(797\) | −43.6908 | −1.54761 | −0.773804 | − | 0.633425i | \(-0.781649\pi\) | ||||
−0.773804 | + | 0.633425i | \(0.781649\pi\) | |||||||
\(798\) | 4.82525 | 0.170812 | ||||||||
\(799\) | −11.5854 | −0.409861 | ||||||||
\(800\) | −0.239205 | −0.00845716 | ||||||||
\(801\) | 12.7595 | 0.450836 | ||||||||
\(802\) | −4.94437 | −0.174592 | ||||||||
\(803\) | −11.5316 | −0.406941 | ||||||||
\(804\) | 1.21488 | 0.0428455 | ||||||||
\(805\) | 1.60058 | 0.0564129 | ||||||||
\(806\) | −1.24900 | −0.0439941 | ||||||||
\(807\) | 10.6537 | 0.375030 | ||||||||
\(808\) | −6.21018 | −0.218473 | ||||||||
\(809\) | 33.1790 | 1.16651 | 0.583256 | − | 0.812289i | \(-0.301779\pi\) | ||||
0.583256 | + | 0.812289i | \(0.301779\pi\) | |||||||
\(810\) | −2.18192 | −0.0766650 | ||||||||
\(811\) | −14.0825 | −0.494503 | −0.247251 | − | 0.968951i | \(-0.579527\pi\) | ||||
−0.247251 | + | 0.968951i | \(0.579527\pi\) | |||||||
\(812\) | 9.89770 | 0.347341 | ||||||||
\(813\) | −28.4158 | −0.996586 | ||||||||
\(814\) | 1.65132 | 0.0578787 | ||||||||
\(815\) | 6.18586 | 0.216681 | ||||||||
\(816\) | 1.83324 | 0.0641764 | ||||||||
\(817\) | −11.8296 | −0.413866 | ||||||||
\(818\) | −27.7874 | −0.971562 | ||||||||
\(819\) | −1.00000 | −0.0349428 | ||||||||
\(820\) | 4.56391 | 0.159379 | ||||||||
\(821\) | −42.8899 | −1.49687 | −0.748433 | − | 0.663210i | \(-0.769194\pi\) | ||||
−0.748433 | + | 0.663210i | \(0.769194\pi\) | |||||||
\(822\) | −17.8767 | −0.623520 | ||||||||
\(823\) | −8.74892 | −0.304968 | −0.152484 | − | 0.988306i | \(-0.548727\pi\) | ||||
−0.152484 | + | 0.988306i | \(0.548727\pi\) | |||||||
\(824\) | −6.31961 | −0.220154 | ||||||||
\(825\) | 0.239205 | 0.00832803 | ||||||||
\(826\) | 4.38488 | 0.152570 | ||||||||
\(827\) | −29.4594 | −1.02440 | −0.512202 | − | 0.858865i | \(-0.671170\pi\) | ||||
−0.512202 | + | 0.858865i | \(0.671170\pi\) | |||||||
\(828\) | −0.733562 | −0.0254930 | ||||||||
\(829\) | −10.2105 | −0.354626 | −0.177313 | − | 0.984155i | \(-0.556740\pi\) | ||||
−0.177313 | + | 0.984155i | \(0.556740\pi\) | |||||||
\(830\) | 23.9194 | 0.830253 | ||||||||
\(831\) | 15.7796 | 0.547388 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −1.83324 | −0.0635181 | ||||||||
\(834\) | 7.74258 | 0.268104 | ||||||||
\(835\) | 11.7904 | 0.408025 | ||||||||
\(836\) | −4.82525 | −0.166885 | ||||||||
\(837\) | −1.24900 | −0.0431717 | ||||||||
\(838\) | 27.7533 | 0.958723 | ||||||||
\(839\) | 1.59559 | 0.0550858 | 0.0275429 | − | 0.999621i | \(-0.491232\pi\) | ||||
0.0275429 | + | 0.999621i | \(0.491232\pi\) | |||||||
\(840\) | 2.18192 | 0.0752836 | ||||||||
\(841\) | 68.9645 | 2.37808 | ||||||||
\(842\) | −22.3811 | −0.771302 | ||||||||
\(843\) | −29.6619 | −1.02161 | ||||||||
\(844\) | −12.4660 | −0.429096 | ||||||||
\(845\) | −2.18192 | −0.0750605 | ||||||||
\(846\) | 6.31961 | 0.217273 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −11.6233 | −0.399145 | ||||||||
\(849\) | 9.02923 | 0.309882 | ||||||||
\(850\) | 0.438520 | 0.0150411 | ||||||||
\(851\) | −1.21134 | −0.0415244 | ||||||||
\(852\) | −8.74873 | −0.299727 | ||||||||
\(853\) | −11.5068 | −0.393986 | −0.196993 | − | 0.980405i | \(-0.563118\pi\) | ||||
−0.196993 | + | 0.980405i | \(0.563118\pi\) | |||||||
\(854\) | 14.1289 | 0.483481 | ||||||||
\(855\) | 10.5283 | 0.360061 | ||||||||
\(856\) | −6.69799 | −0.228933 | ||||||||
\(857\) | −35.5980 | −1.21601 | −0.608003 | − | 0.793935i | \(-0.708029\pi\) | ||||
−0.608003 | + | 0.793935i | \(0.708029\pi\) | |||||||
\(858\) | 1.00000 | 0.0341394 | ||||||||
\(859\) | 10.4220 | 0.355596 | 0.177798 | − | 0.984067i | \(-0.443103\pi\) | ||||
0.177798 | + | 0.984067i | \(0.443103\pi\) | |||||||
\(860\) | −5.34922 | −0.182407 | ||||||||
\(861\) | 2.09169 | 0.0712846 | ||||||||
\(862\) | −25.3366 | −0.862967 | ||||||||
\(863\) | 49.1051 | 1.67156 | 0.835779 | − | 0.549066i | \(-0.185016\pi\) | ||||
0.835779 | + | 0.549066i | \(0.185016\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −36.9713 | −1.25706 | ||||||||
\(866\) | −34.2673 | −1.16445 | ||||||||
\(867\) | 13.6392 | 0.463212 | ||||||||
\(868\) | 1.24900 | 0.0423938 | ||||||||
\(869\) | 7.21993 | 0.244919 | ||||||||
\(870\) | 21.5960 | 0.732174 | ||||||||
\(871\) | 1.21488 | 0.0411646 | ||||||||
\(872\) | 4.49800 | 0.152321 | ||||||||
\(873\) | 1.28161 | 0.0433758 | ||||||||
\(874\) | 3.53962 | 0.119729 | ||||||||
\(875\) | 11.4315 | 0.386457 | ||||||||
\(876\) | 11.5316 | 0.389616 | ||||||||
\(877\) | −9.22238 | −0.311417 | −0.155709 | − | 0.987803i | \(-0.549766\pi\) | ||||
−0.155709 | + | 0.987803i | \(0.549766\pi\) | |||||||
\(878\) | 2.09725 | 0.0707789 | ||||||||
\(879\) | −21.0756 | −0.710861 | ||||||||
\(880\) | −2.18192 | −0.0735527 | ||||||||
\(881\) | 7.33367 | 0.247078 | 0.123539 | − | 0.992340i | \(-0.460576\pi\) | ||||
0.123539 | + | 0.992340i | \(0.460576\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 9.08080 | 0.305593 | 0.152797 | − | 0.988258i | \(-0.451172\pi\) | ||||
0.152797 | + | 0.988258i | \(0.451172\pi\) | |||||||
\(884\) | 1.83324 | 0.0616587 | ||||||||
\(885\) | 9.56748 | 0.321607 | ||||||||
\(886\) | −15.1828 | −0.510078 | ||||||||
\(887\) | 48.2562 | 1.62028 | 0.810142 | − | 0.586233i | \(-0.199390\pi\) | ||||
0.810142 | + | 0.586233i | \(0.199390\pi\) | |||||||
\(888\) | −1.65132 | −0.0554146 | ||||||||
\(889\) | 22.0622 | 0.739942 | ||||||||
\(890\) | −27.8404 | −0.933211 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −0.272592 | −0.00912705 | ||||||||
\(893\) | −30.4937 | −1.02043 | ||||||||
\(894\) | −18.3308 | −0.613072 | ||||||||
\(895\) | −43.0537 | −1.43913 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −0.733562 | −0.0244929 | ||||||||
\(898\) | 34.3812 | 1.14731 | ||||||||
\(899\) | 12.3622 | 0.412303 | ||||||||
\(900\) | −0.239205 | −0.00797349 | ||||||||
\(901\) | 21.3083 | 0.709882 | ||||||||
\(902\) | −2.09169 | −0.0696456 | ||||||||
\(903\) | −2.45161 | −0.0815844 | ||||||||
\(904\) | −8.75378 | −0.291146 | ||||||||
\(905\) | −4.95768 | −0.164799 | ||||||||
\(906\) | −7.62264 | −0.253245 | ||||||||
\(907\) | 18.2513 | 0.606026 | 0.303013 | − | 0.952986i | \(-0.402008\pi\) | ||||
0.303013 | + | 0.952986i | \(0.402008\pi\) | |||||||
\(908\) | 23.1263 | 0.767473 | ||||||||
\(909\) | −6.21018 | −0.205979 | ||||||||
\(910\) | 2.18192 | 0.0723301 | ||||||||
\(911\) | 13.1556 | 0.435863 | 0.217932 | − | 0.975964i | \(-0.430069\pi\) | ||||
0.217932 | + | 0.975964i | \(0.430069\pi\) | |||||||
\(912\) | 4.82525 | 0.159780 | ||||||||
\(913\) | −10.9625 | −0.362806 | ||||||||
\(914\) | 23.0258 | 0.761624 | ||||||||
\(915\) | 30.8282 | 1.01915 | ||||||||
\(916\) | −4.19860 | −0.138726 | ||||||||
\(917\) | 0.503804 | 0.0166371 | ||||||||
\(918\) | 1.83324 | 0.0605061 | ||||||||
\(919\) | −10.4863 | −0.345911 | −0.172955 | − | 0.984930i | \(-0.555332\pi\) | ||||
−0.172955 | + | 0.984930i | \(0.555332\pi\) | |||||||
\(920\) | 1.60058 | 0.0527695 | ||||||||
\(921\) | 7.65854 | 0.252358 | ||||||||
\(922\) | −5.79994 | −0.191011 | ||||||||
\(923\) | −8.74873 | −0.287968 | ||||||||
\(924\) | −1.00000 | −0.0328976 | ||||||||
\(925\) | −0.395003 | −0.0129876 | ||||||||
\(926\) | −20.9602 | −0.688796 | ||||||||
\(927\) | −6.31961 | −0.207563 | ||||||||
\(928\) | 9.89770 | 0.324908 | ||||||||
\(929\) | −35.9632 | −1.17992 | −0.589958 | − | 0.807434i | \(-0.700856\pi\) | ||||
−0.589958 | + | 0.807434i | \(0.700856\pi\) | |||||||
\(930\) | 2.72522 | 0.0893635 | ||||||||
\(931\) | −4.82525 | −0.158141 | ||||||||
\(932\) | 6.44644 | 0.211160 | ||||||||
\(933\) | −24.4586 | −0.800740 | ||||||||
\(934\) | 27.1046 | 0.886890 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −40.1360 | −1.31119 | −0.655594 | − | 0.755114i | \(-0.727582\pi\) | ||||
−0.655594 | + | 0.755114i | \(0.727582\pi\) | |||||||
\(938\) | −1.21488 | −0.0396672 | ||||||||
\(939\) | −26.9065 | −0.878062 | ||||||||
\(940\) | −13.7889 | −0.449745 | ||||||||
\(941\) | −9.89193 | −0.322468 | −0.161234 | − | 0.986916i | \(-0.551547\pi\) | ||||
−0.161234 | + | 0.986916i | \(0.551547\pi\) | |||||||
\(942\) | −8.68346 | −0.282922 | ||||||||
\(943\) | 1.53438 | 0.0499664 | ||||||||
\(944\) | 4.38488 | 0.142716 | ||||||||
\(945\) | 2.18192 | 0.0709780 | ||||||||
\(946\) | 2.45161 | 0.0797086 | ||||||||
\(947\) | −2.93793 | −0.0954697 | −0.0477349 | − | 0.998860i | \(-0.515200\pi\) | ||||
−0.0477349 | + | 0.998860i | \(0.515200\pi\) | |||||||
\(948\) | −7.21993 | −0.234492 | ||||||||
\(949\) | 11.5316 | 0.374331 | ||||||||
\(950\) | 1.15422 | 0.0374479 | ||||||||
\(951\) | −26.1731 | −0.848720 | ||||||||
\(952\) | −1.83324 | −0.0594158 | ||||||||
\(953\) | −56.7108 | −1.83704 | −0.918521 | − | 0.395373i | \(-0.870615\pi\) | ||||
−0.918521 | + | 0.395373i | \(0.870615\pi\) | |||||||
\(954\) | −11.6233 | −0.376317 | ||||||||
\(955\) | −50.3192 | −1.62829 | ||||||||
\(956\) | 14.7039 | 0.475557 | ||||||||
\(957\) | −9.89770 | −0.319947 | ||||||||
\(958\) | −13.2625 | −0.428493 | ||||||||
\(959\) | 17.8767 | 0.577268 | ||||||||
\(960\) | 2.18192 | 0.0704213 | ||||||||
\(961\) | −29.4400 | −0.949677 | ||||||||
\(962\) | −1.65132 | −0.0532407 | ||||||||
\(963\) | −6.69799 | −0.215840 | ||||||||
\(964\) | 19.3315 | 0.622626 | ||||||||
\(965\) | −3.83398 | −0.123420 | ||||||||
\(966\) | 0.733562 | 0.0236020 | ||||||||
\(967\) | 41.0517 | 1.32013 | 0.660067 | − | 0.751207i | \(-0.270528\pi\) | ||||
0.660067 | + | 0.751207i | \(0.270528\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −8.84586 | −0.284170 | ||||||||
\(970\) | −2.79637 | −0.0897860 | ||||||||
\(971\) | 41.9125 | 1.34504 | 0.672518 | − | 0.740081i | \(-0.265213\pi\) | ||||
0.672518 | + | 0.740081i | \(0.265213\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −7.74258 | −0.248216 | ||||||||
\(974\) | 14.4688 | 0.463611 | ||||||||
\(975\) | −0.239205 | −0.00766068 | ||||||||
\(976\) | 14.1289 | 0.452255 | ||||||||
\(977\) | 36.8188 | 1.17794 | 0.588969 | − | 0.808156i | \(-0.299534\pi\) | ||||
0.588969 | + | 0.808156i | \(0.299534\pi\) | |||||||
\(978\) | 2.83505 | 0.0906548 | ||||||||
\(979\) | 12.7595 | 0.407797 | ||||||||
\(980\) | −2.18192 | −0.0696990 | ||||||||
\(981\) | 4.49800 | 0.143610 | ||||||||
\(982\) | −13.6098 | −0.434305 | ||||||||
\(983\) | 8.15638 | 0.260148 | 0.130074 | − | 0.991504i | \(-0.458479\pi\) | ||||
0.130074 | + | 0.991504i | \(0.458479\pi\) | |||||||
\(984\) | 2.09169 | 0.0666806 | ||||||||
\(985\) | 44.4833 | 1.41735 | ||||||||
\(986\) | −18.1449 | −0.577851 | ||||||||
\(987\) | −6.31961 | −0.201155 | ||||||||
\(988\) | 4.82525 | 0.153512 | ||||||||
\(989\) | −1.79841 | −0.0571860 | ||||||||
\(990\) | −2.18192 | −0.0693461 | ||||||||
\(991\) | 38.3123 | 1.21703 | 0.608516 | − | 0.793542i | \(-0.291765\pi\) | ||||
0.608516 | + | 0.793542i | \(0.291765\pi\) | |||||||
\(992\) | 1.24900 | 0.0396558 | ||||||||
\(993\) | −9.76211 | −0.309791 | ||||||||
\(994\) | 8.74873 | 0.277493 | ||||||||
\(995\) | 48.0953 | 1.52472 | ||||||||
\(996\) | 10.9625 | 0.347360 | ||||||||
\(997\) | −32.1201 | −1.01725 | −0.508627 | − | 0.860987i | \(-0.669847\pi\) | ||||
−0.508627 | + | 0.860987i | \(0.669847\pi\) | |||||||
\(998\) | −41.2145 | −1.30462 | ||||||||
\(999\) | −1.65132 | −0.0522454 |
(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 | 6006.2.a.cf.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6006.2.a.cf.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |