Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58646 | −1.82890 | −0.914451 | − | 0.404696i | \(-0.867377\pi\) | ||||
−0.914451 | + | 0.404696i | \(0.867377\pi\) | |||||||
\(3\) | −1.10071 | −0.635495 | −0.317748 | − | 0.948175i | \(-0.602926\pi\) | ||||
−0.317748 | + | 0.948175i | \(0.602926\pi\) | |||||||
\(4\) | 4.68977 | 2.34488 | ||||||||
\(5\) | −0.828720 | −0.370615 | −0.185307 | − | 0.982681i | \(-0.559328\pi\) | ||||
−0.185307 | + | 0.982681i | \(0.559328\pi\) | |||||||
\(6\) | 2.84694 | 1.16226 | ||||||||
\(7\) | −1.43853 | −0.543714 | −0.271857 | − | 0.962338i | \(-0.587638\pi\) | ||||
−0.271857 | + | 0.962338i | \(0.587638\pi\) | |||||||
\(8\) | −6.95698 | −2.45966 | ||||||||
\(9\) | −1.78844 | −0.596146 | ||||||||
\(10\) | 2.14345 | 0.677818 | ||||||||
\(11\) | 4.30556 | 1.29818 | 0.649088 | − | 0.760713i | \(-0.275151\pi\) | ||||
0.649088 | + | 0.760713i | \(0.275151\pi\) | |||||||
\(12\) | −5.16208 | −1.49016 | ||||||||
\(13\) | 5.68051 | 1.57549 | 0.787744 | − | 0.616002i | \(-0.211249\pi\) | ||||
0.787744 | + | 0.616002i | \(0.211249\pi\) | |||||||
\(14\) | 3.72070 | 0.994400 | ||||||||
\(15\) | 0.912180 | 0.235524 | ||||||||
\(16\) | 8.61440 | 2.15360 | ||||||||
\(17\) | 0.204728 | 0.0496538 | 0.0248269 | − | 0.999692i | \(-0.492097\pi\) | ||||
0.0248269 | + | 0.999692i | \(0.492097\pi\) | |||||||
\(18\) | 4.62572 | 1.09029 | ||||||||
\(19\) | −1.11011 | −0.254677 | −0.127338 | − | 0.991859i | \(-0.540643\pi\) | ||||
−0.127338 | + | 0.991859i | \(0.540643\pi\) | |||||||
\(20\) | −3.88651 | −0.869049 | ||||||||
\(21\) | 1.58341 | 0.345527 | ||||||||
\(22\) | −11.1362 | −2.37424 | ||||||||
\(23\) | −1.09978 | −0.229320 | −0.114660 | − | 0.993405i | \(-0.536578\pi\) | ||||
−0.114660 | + | 0.993405i | \(0.536578\pi\) | |||||||
\(24\) | 7.65761 | 1.56310 | ||||||||
\(25\) | −4.31322 | −0.862645 | ||||||||
\(26\) | −14.6924 | −2.88142 | ||||||||
\(27\) | 5.27068 | 1.01434 | ||||||||
\(28\) | −6.74638 | −1.27495 | ||||||||
\(29\) | 0.550487 | 0.102223 | 0.0511114 | − | 0.998693i | \(-0.483724\pi\) | ||||
0.0511114 | + | 0.998693i | \(0.483724\pi\) | |||||||
\(30\) | −2.35932 | −0.430750 | ||||||||
\(31\) | −5.70327 | −1.02434 | −0.512169 | − | 0.858885i | \(-0.671158\pi\) | ||||
−0.512169 | + | 0.858885i | \(0.671158\pi\) | |||||||
\(32\) | −8.36683 | −1.47906 | ||||||||
\(33\) | −4.73917 | −0.824984 | ||||||||
\(34\) | −0.529520 | −0.0908120 | ||||||||
\(35\) | 1.19214 | 0.201508 | ||||||||
\(36\) | −8.38736 | −1.39789 | ||||||||
\(37\) | −10.8782 | −1.78837 | −0.894183 | − | 0.447701i | \(-0.852243\pi\) | ||||
−0.894183 | + | 0.447701i | \(0.852243\pi\) | |||||||
\(38\) | 2.87126 | 0.465779 | ||||||||
\(39\) | −6.25259 | −1.00122 | ||||||||
\(40\) | 5.76539 | 0.911588 | ||||||||
\(41\) | −9.68391 | −1.51237 | −0.756186 | − | 0.654357i | \(-0.772939\pi\) | ||||
−0.756186 | + | 0.654357i | \(0.772939\pi\) | |||||||
\(42\) | −4.09541 | −0.631936 | ||||||||
\(43\) | 7.33515 | 1.11860 | 0.559300 | − | 0.828966i | \(-0.311070\pi\) | ||||
0.559300 | + | 0.828966i | \(0.311070\pi\) | |||||||
\(44\) | 20.1921 | 3.04407 | ||||||||
\(45\) | 1.48211 | 0.220941 | ||||||||
\(46\) | 2.84454 | 0.419405 | ||||||||
\(47\) | 12.3431 | 1.80042 | 0.900212 | − | 0.435452i | \(-0.143411\pi\) | ||||
0.900212 | + | 0.435452i | \(0.143411\pi\) | |||||||
\(48\) | −9.48195 | −1.36860 | ||||||||
\(49\) | −4.93063 | −0.704375 | ||||||||
\(50\) | 11.1560 | 1.57769 | ||||||||
\(51\) | −0.225346 | −0.0315547 | ||||||||
\(52\) | 26.6403 | 3.69434 | ||||||||
\(53\) | 3.70866 | 0.509424 | 0.254712 | − | 0.967017i | \(-0.418019\pi\) | ||||
0.254712 | + | 0.967017i | \(0.418019\pi\) | |||||||
\(54\) | −13.6324 | −1.85513 | ||||||||
\(55\) | −3.56810 | −0.481123 | ||||||||
\(56\) | 10.0078 | 1.33735 | ||||||||
\(57\) | 1.22191 | 0.161846 | ||||||||
\(58\) | −1.42381 | −0.186956 | ||||||||
\(59\) | 13.3936 | 1.74370 | 0.871851 | − | 0.489771i | \(-0.162919\pi\) | ||||
0.871851 | + | 0.489771i | \(0.162919\pi\) | |||||||
\(60\) | 4.27791 | 0.552276 | ||||||||
\(61\) | 2.02183 | 0.258868 | 0.129434 | − | 0.991588i | \(-0.458684\pi\) | ||||
0.129434 | + | 0.991588i | \(0.458684\pi\) | |||||||
\(62\) | 14.7513 | 1.87341 | ||||||||
\(63\) | 2.57272 | 0.324133 | ||||||||
\(64\) | 4.41167 | 0.551459 | ||||||||
\(65\) | −4.70755 | −0.583899 | ||||||||
\(66\) | 12.2577 | 1.50882 | ||||||||
\(67\) | −16.1756 | −1.97616 | −0.988080 | − | 0.153942i | \(-0.950803\pi\) | ||||
−0.988080 | + | 0.153942i | \(0.950803\pi\) | |||||||
\(68\) | 0.960127 | 0.116432 | ||||||||
\(69\) | 1.21054 | 0.145732 | ||||||||
\(70\) | −3.08342 | −0.368539 | ||||||||
\(71\) | −2.30638 | −0.273717 | −0.136859 | − | 0.990591i | \(-0.543701\pi\) | ||||
−0.136859 | + | 0.990591i | \(0.543701\pi\) | |||||||
\(72\) | 12.4421 | 1.46632 | ||||||||
\(73\) | −0.0880236 | −0.0103024 | −0.00515119 | − | 0.999987i | \(-0.501640\pi\) | ||||
−0.00515119 | + | 0.999987i | \(0.501640\pi\) | |||||||
\(74\) | 28.1360 | 3.27075 | ||||||||
\(75\) | 4.74761 | 0.548206 | ||||||||
\(76\) | −5.20616 | −0.597188 | ||||||||
\(77\) | −6.19369 | −0.705836 | ||||||||
\(78\) | 16.1721 | 1.83113 | ||||||||
\(79\) | −2.05059 | −0.230709 | −0.115355 | − | 0.993324i | \(-0.536800\pi\) | ||||
−0.115355 | + | 0.993324i | \(0.536800\pi\) | |||||||
\(80\) | −7.13892 | −0.798156 | ||||||||
\(81\) | −0.436175 | −0.0484639 | ||||||||
\(82\) | 25.0470 | 2.76598 | ||||||||
\(83\) | 9.20626 | 1.01052 | 0.505259 | − | 0.862968i | \(-0.331397\pi\) | ||||
0.505259 | + | 0.862968i | \(0.331397\pi\) | |||||||
\(84\) | 7.42581 | 0.810222 | ||||||||
\(85\) | −0.169662 | −0.0184024 | ||||||||
\(86\) | −18.9721 | −2.04581 | ||||||||
\(87\) | −0.605927 | −0.0649621 | ||||||||
\(88\) | −29.9537 | −3.19307 | ||||||||
\(89\) | −3.27083 | −0.346708 | −0.173354 | − | 0.984860i | \(-0.555460\pi\) | ||||
−0.173354 | + | 0.984860i | \(0.555460\pi\) | |||||||
\(90\) | −3.83343 | −0.404079 | ||||||||
\(91\) | −8.17159 | −0.856615 | ||||||||
\(92\) | −5.15773 | −0.537730 | ||||||||
\(93\) | 6.27764 | 0.650961 | ||||||||
\(94\) | −31.9249 | −3.29280 | ||||||||
\(95\) | 0.919971 | 0.0943870 | ||||||||
\(96\) | 9.20945 | 0.939936 | ||||||||
\(97\) | 9.21504 | 0.935646 | 0.467823 | − | 0.883822i | \(-0.345039\pi\) | ||||
0.467823 | + | 0.883822i | \(0.345039\pi\) | |||||||
\(98\) | 12.7529 | 1.28823 | ||||||||
\(99\) | −7.70023 | −0.773902 | ||||||||
\(100\) | −20.2280 | −2.02280 | ||||||||
\(101\) | −8.92869 | −0.888438 | −0.444219 | − | 0.895918i | \(-0.646519\pi\) | ||||
−0.444219 | + | 0.895918i | \(0.646519\pi\) | |||||||
\(102\) | 0.582848 | 0.0577106 | ||||||||
\(103\) | 13.3121 | 1.31168 | 0.655842 | − | 0.754898i | \(-0.272314\pi\) | ||||
0.655842 | + | 0.754898i | \(0.272314\pi\) | |||||||
\(104\) | −39.5192 | −3.87517 | ||||||||
\(105\) | −1.31220 | −0.128058 | ||||||||
\(106\) | −9.59231 | −0.931687 | ||||||||
\(107\) | −11.3041 | −1.09281 | −0.546407 | − | 0.837520i | \(-0.684005\pi\) | ||||
−0.546407 | + | 0.837520i | \(0.684005\pi\) | |||||||
\(108\) | 24.7183 | 2.37852 | ||||||||
\(109\) | −3.74546 | −0.358750 | −0.179375 | − | 0.983781i | \(-0.557408\pi\) | ||||
−0.179375 | + | 0.983781i | \(0.557408\pi\) | |||||||
\(110\) | 9.22876 | 0.879927 | ||||||||
\(111\) | 11.9738 | 1.13650 | ||||||||
\(112\) | −12.3921 | −1.17094 | ||||||||
\(113\) | 16.0777 | 1.51246 | 0.756231 | − | 0.654305i | \(-0.227039\pi\) | ||||
0.756231 | + | 0.654305i | \(0.227039\pi\) | |||||||
\(114\) | −3.16042 | −0.296000 | ||||||||
\(115\) | 0.911412 | 0.0849896 | ||||||||
\(116\) | 2.58166 | 0.239701 | ||||||||
\(117\) | −10.1592 | −0.939221 | ||||||||
\(118\) | −34.6421 | −3.18906 | ||||||||
\(119\) | −0.294507 | −0.0269975 | ||||||||
\(120\) | −6.34602 | −0.579309 | ||||||||
\(121\) | 7.53786 | 0.685260 | ||||||||
\(122\) | −5.22937 | −0.473445 | ||||||||
\(123\) | 10.6592 | 0.961105 | ||||||||
\(124\) | −26.7470 | −2.40195 | ||||||||
\(125\) | 7.71805 | 0.690324 | ||||||||
\(126\) | −6.65425 | −0.592807 | ||||||||
\(127\) | −7.00536 | −0.621625 | −0.310812 | − | 0.950471i | \(-0.600601\pi\) | ||||
−0.310812 | + | 0.950471i | \(0.600601\pi\) | |||||||
\(128\) | 5.32306 | 0.470497 | ||||||||
\(129\) | −8.07387 | −0.710864 | ||||||||
\(130\) | 12.1759 | 1.06790 | ||||||||
\(131\) | −5.71902 | −0.499673 | −0.249836 | − | 0.968288i | \(-0.580377\pi\) | ||||
−0.249836 | + | 0.968288i | \(0.580377\pi\) | |||||||
\(132\) | −22.2256 | −1.93449 | ||||||||
\(133\) | 1.59693 | 0.138471 | ||||||||
\(134\) | 41.8374 | 3.61420 | ||||||||
\(135\) | −4.36792 | −0.375930 | ||||||||
\(136\) | −1.42429 | −0.122132 | ||||||||
\(137\) | 10.4831 | 0.895629 | 0.447814 | − | 0.894127i | \(-0.352203\pi\) | ||||
0.447814 | + | 0.894127i | \(0.352203\pi\) | |||||||
\(138\) | −3.13102 | −0.266530 | ||||||||
\(139\) | −15.8050 | −1.34056 | −0.670282 | − | 0.742107i | \(-0.733827\pi\) | ||||
−0.670282 | + | 0.742107i | \(0.733827\pi\) | |||||||
\(140\) | 5.59086 | 0.472514 | ||||||||
\(141\) | −13.5862 | −1.14416 | ||||||||
\(142\) | 5.96536 | 0.500602 | ||||||||
\(143\) | 24.4578 | 2.04526 | ||||||||
\(144\) | −15.4063 | −1.28386 | ||||||||
\(145\) | −0.456200 | −0.0378853 | ||||||||
\(146\) | 0.227669 | 0.0188421 | ||||||||
\(147\) | 5.42719 | 0.447627 | ||||||||
\(148\) | −51.0163 | −4.19351 | ||||||||
\(149\) | 4.04694 | 0.331538 | 0.165769 | − | 0.986165i | \(-0.446989\pi\) | ||||
0.165769 | + | 0.986165i | \(0.446989\pi\) | |||||||
\(150\) | −12.2795 | −1.00262 | ||||||||
\(151\) | 14.4336 | 1.17459 | 0.587293 | − | 0.809374i | \(-0.300194\pi\) | ||||
0.587293 | + | 0.809374i | \(0.300194\pi\) | |||||||
\(152\) | 7.72301 | 0.626419 | ||||||||
\(153\) | −0.366143 | −0.0296009 | ||||||||
\(154\) | 16.0197 | 1.29091 | ||||||||
\(155\) | 4.72641 | 0.379635 | ||||||||
\(156\) | −29.3232 | −2.34773 | ||||||||
\(157\) | −9.68420 | −0.772883 | −0.386442 | − | 0.922314i | \(-0.626296\pi\) | ||||
−0.386442 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(158\) | 5.30377 | 0.421945 | ||||||||
\(159\) | −4.08216 | −0.323737 | ||||||||
\(160\) | 6.93376 | 0.548162 | ||||||||
\(161\) | 1.58207 | 0.124685 | ||||||||
\(162\) | 1.12815 | 0.0886357 | ||||||||
\(163\) | 7.28419 | 0.570542 | 0.285271 | − | 0.958447i | \(-0.407916\pi\) | ||||
0.285271 | + | 0.958447i | \(0.407916\pi\) | |||||||
\(164\) | −45.4153 | −3.54634 | ||||||||
\(165\) | 3.92745 | 0.305751 | ||||||||
\(166\) | −23.8116 | −1.84814 | ||||||||
\(167\) | −12.1871 | −0.943069 | −0.471534 | − | 0.881848i | \(-0.656300\pi\) | ||||
−0.471534 | + | 0.881848i | \(0.656300\pi\) | |||||||
\(168\) | −11.0157 | −0.849881 | ||||||||
\(169\) | 19.2681 | 1.48217 | ||||||||
\(170\) | 0.438824 | 0.0336563 | ||||||||
\(171\) | 1.98536 | 0.151825 | ||||||||
\(172\) | 34.4001 | 2.62299 | ||||||||
\(173\) | −0.170098 | −0.0129323 | −0.00646616 | − | 0.999979i | \(-0.502058\pi\) | ||||
−0.00646616 | + | 0.999979i | \(0.502058\pi\) | |||||||
\(174\) | 1.56720 | 0.118809 | ||||||||
\(175\) | 6.20471 | 0.469032 | ||||||||
\(176\) | 37.0898 | 2.79575 | ||||||||
\(177\) | −14.7425 | −1.10811 | ||||||||
\(178\) | 8.45987 | 0.634094 | ||||||||
\(179\) | 3.47482 | 0.259720 | 0.129860 | − | 0.991532i | \(-0.458547\pi\) | ||||
0.129860 | + | 0.991532i | \(0.458547\pi\) | |||||||
\(180\) | 6.95077 | 0.518080 | ||||||||
\(181\) | 0.324027 | 0.0240847 | 0.0120424 | − | 0.999927i | \(-0.496167\pi\) | ||||
0.0120424 | + | 0.999927i | \(0.496167\pi\) | |||||||
\(182\) | 21.1355 | 1.56667 | ||||||||
\(183\) | −2.22544 | −0.164510 | ||||||||
\(184\) | 7.65116 | 0.564051 | ||||||||
\(185\) | 9.01499 | 0.662795 | ||||||||
\(186\) | −16.2369 | −1.19054 | ||||||||
\(187\) | 0.881468 | 0.0644594 | ||||||||
\(188\) | 57.8862 | 4.22179 | ||||||||
\(189\) | −7.58204 | −0.551512 | ||||||||
\(190\) | −2.37947 | −0.172625 | ||||||||
\(191\) | −15.4486 | −1.11782 | −0.558910 | − | 0.829228i | \(-0.688780\pi\) | ||||
−0.558910 | + | 0.829228i | \(0.688780\pi\) | |||||||
\(192\) | −4.85597 | −0.350449 | ||||||||
\(193\) | 12.2829 | 0.884141 | 0.442070 | − | 0.896980i | \(-0.354244\pi\) | ||||
0.442070 | + | 0.896980i | \(0.354244\pi\) | |||||||
\(194\) | −23.8343 | −1.71120 | ||||||||
\(195\) | 5.18164 | 0.371065 | ||||||||
\(196\) | −23.1235 | −1.65168 | ||||||||
\(197\) | 7.37020 | 0.525105 | 0.262552 | − | 0.964918i | \(-0.415436\pi\) | ||||
0.262552 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(198\) | 19.9163 | 1.41539 | ||||||||
\(199\) | 17.4053 | 1.23383 | 0.616916 | − | 0.787029i | \(-0.288382\pi\) | ||||
0.616916 | + | 0.787029i | \(0.288382\pi\) | |||||||
\(200\) | 30.0070 | 2.12182 | ||||||||
\(201\) | 17.8046 | 1.25584 | ||||||||
\(202\) | 23.0937 | 1.62487 | ||||||||
\(203\) | −0.791893 | −0.0555800 | ||||||||
\(204\) | −1.05682 | −0.0739922 | ||||||||
\(205\) | 8.02525 | 0.560507 | ||||||||
\(206\) | −34.4313 | −2.39894 | ||||||||
\(207\) | 1.96689 | 0.136709 | ||||||||
\(208\) | 48.9341 | 3.39297 | ||||||||
\(209\) | −4.77965 | −0.330615 | ||||||||
\(210\) | 3.39395 | 0.234205 | ||||||||
\(211\) | −19.8550 | −1.36687 | −0.683437 | − | 0.730010i | \(-0.739515\pi\) | ||||
−0.683437 | + | 0.730010i | \(0.739515\pi\) | |||||||
\(212\) | 17.3928 | 1.19454 | ||||||||
\(213\) | 2.53866 | 0.173946 | ||||||||
\(214\) | 29.2377 | 1.99865 | ||||||||
\(215\) | −6.07878 | −0.414569 | ||||||||
\(216\) | −36.6680 | −2.49494 | ||||||||
\(217\) | 8.20433 | 0.556946 | ||||||||
\(218\) | 9.68748 | 0.656119 | ||||||||
\(219\) | 0.0968884 | 0.00654711 | ||||||||
\(220\) | −16.7336 | −1.12818 | ||||||||
\(221\) | 1.16296 | 0.0782290 | ||||||||
\(222\) | −30.9696 | −2.07854 | ||||||||
\(223\) | −19.5533 | −1.30939 | −0.654693 | − | 0.755894i | \(-0.727202\pi\) | ||||
−0.654693 | + | 0.755894i | \(0.727202\pi\) | |||||||
\(224\) | 12.0360 | 0.804186 | ||||||||
\(225\) | 7.71393 | 0.514262 | ||||||||
\(226\) | −41.5843 | −2.76614 | ||||||||
\(227\) | −10.2233 | −0.678547 | −0.339273 | − | 0.940688i | \(-0.610181\pi\) | ||||
−0.339273 | + | 0.940688i | \(0.610181\pi\) | |||||||
\(228\) | 5.73047 | 0.379510 | ||||||||
\(229\) | 12.8232 | 0.847384 | 0.423692 | − | 0.905806i | \(-0.360734\pi\) | ||||
0.423692 | + | 0.905806i | \(0.360734\pi\) | |||||||
\(230\) | −2.35733 | −0.155438 | ||||||||
\(231\) | 6.81745 | 0.448555 | ||||||||
\(232\) | −3.82973 | −0.251434 | ||||||||
\(233\) | −14.9323 | −0.978248 | −0.489124 | − | 0.872214i | \(-0.662683\pi\) | ||||
−0.489124 | + | 0.872214i | \(0.662683\pi\) | |||||||
\(234\) | 26.2764 | 1.71774 | ||||||||
\(235\) | −10.2290 | −0.667264 | ||||||||
\(236\) | 62.8131 | 4.08878 | ||||||||
\(237\) | 2.25710 | 0.146615 | ||||||||
\(238\) | 0.761731 | 0.0493757 | ||||||||
\(239\) | −4.65723 | −0.301251 | −0.150626 | − | 0.988591i | \(-0.548129\pi\) | ||||
−0.150626 | + | 0.988591i | \(0.548129\pi\) | |||||||
\(240\) | 7.85788 | 0.507224 | ||||||||
\(241\) | 9.73791 | 0.627274 | 0.313637 | − | 0.949543i | \(-0.398452\pi\) | ||||
0.313637 | + | 0.949543i | \(0.398452\pi\) | |||||||
\(242\) | −19.4964 | −1.25327 | ||||||||
\(243\) | −15.3319 | −0.983544 | ||||||||
\(244\) | 9.48190 | 0.607017 | ||||||||
\(245\) | 4.08611 | 0.261052 | ||||||||
\(246\) | −27.5695 | −1.75777 | ||||||||
\(247\) | −6.30599 | −0.401241 | ||||||||
\(248\) | 39.6775 | 2.51952 | ||||||||
\(249\) | −10.1334 | −0.642179 | ||||||||
\(250\) | −19.9624 | −1.26253 | ||||||||
\(251\) | 6.50042 | 0.410303 | 0.205152 | − | 0.978730i | \(-0.434231\pi\) | ||||
0.205152 | + | 0.978730i | \(0.434231\pi\) | |||||||
\(252\) | 12.0655 | 0.760054 | ||||||||
\(253\) | −4.73518 | −0.297698 | ||||||||
\(254\) | 18.1191 | 1.13689 | ||||||||
\(255\) | 0.186749 | 0.0116947 | ||||||||
\(256\) | −22.5912 | −1.41195 | ||||||||
\(257\) | 29.5625 | 1.84406 | 0.922030 | − | 0.387118i | \(-0.126529\pi\) | ||||
0.922030 | + | 0.387118i | \(0.126529\pi\) | |||||||
\(258\) | 20.8827 | 1.30010 | ||||||||
\(259\) | 15.6487 | 0.972360 | ||||||||
\(260\) | −22.0773 | −1.36918 | ||||||||
\(261\) | −0.984512 | −0.0609398 | ||||||||
\(262\) | 14.7920 | 0.913853 | ||||||||
\(263\) | 16.2205 | 1.00020 | 0.500100 | − | 0.865968i | \(-0.333297\pi\) | ||||
0.500100 | + | 0.865968i | \(0.333297\pi\) | |||||||
\(264\) | 32.9703 | 2.02918 | ||||||||
\(265\) | −3.07344 | −0.188800 | ||||||||
\(266\) | −4.13039 | −0.253251 | ||||||||
\(267\) | 3.60024 | 0.220331 | ||||||||
\(268\) | −75.8597 | −4.63387 | ||||||||
\(269\) | −23.4511 | −1.42984 | −0.714920 | − | 0.699206i | \(-0.753537\pi\) | ||||
−0.714920 | + | 0.699206i | \(0.753537\pi\) | |||||||
\(270\) | 11.2974 | 0.687540 | ||||||||
\(271\) | −14.5396 | −0.883218 | −0.441609 | − | 0.897208i | \(-0.645592\pi\) | ||||
−0.441609 | + | 0.897208i | \(0.645592\pi\) | |||||||
\(272\) | 1.76361 | 0.106934 | ||||||||
\(273\) | 8.99455 | 0.544375 | ||||||||
\(274\) | −27.1140 | −1.63802 | ||||||||
\(275\) | −18.5708 | −1.11986 | ||||||||
\(276\) | 5.67716 | 0.341725 | ||||||||
\(277\) | 17.6860 | 1.06265 | 0.531324 | − | 0.847169i | \(-0.321695\pi\) | ||||
0.531324 | + | 0.847169i | \(0.321695\pi\) | |||||||
\(278\) | 40.8790 | 2.45176 | ||||||||
\(279\) | 10.1999 | 0.610655 | ||||||||
\(280\) | −8.29369 | −0.495643 | ||||||||
\(281\) | −15.6611 | −0.934260 | −0.467130 | − | 0.884189i | \(-0.654712\pi\) | ||||
−0.467130 | + | 0.884189i | \(0.654712\pi\) | |||||||
\(282\) | 35.1400 | 2.09256 | ||||||||
\(283\) | −25.9833 | −1.54455 | −0.772275 | − | 0.635289i | \(-0.780881\pi\) | ||||
−0.772275 | + | 0.635289i | \(0.780881\pi\) | |||||||
\(284\) | −10.8164 | −0.641835 | ||||||||
\(285\) | −1.01262 | −0.0599825 | ||||||||
\(286\) | −63.2590 | −3.74058 | ||||||||
\(287\) | 13.9306 | 0.822298 | ||||||||
\(288\) | 14.9636 | 0.881736 | ||||||||
\(289\) | −16.9581 | −0.997535 | ||||||||
\(290\) | 1.17994 | 0.0692886 | ||||||||
\(291\) | −10.1431 | −0.594598 | ||||||||
\(292\) | −0.412810 | −0.0241579 | ||||||||
\(293\) | −11.8971 | −0.695035 | −0.347517 | − | 0.937674i | \(-0.612975\pi\) | ||||
−0.347517 | + | 0.937674i | \(0.612975\pi\) | |||||||
\(294\) | −14.0372 | −0.818666 | ||||||||
\(295\) | −11.0996 | −0.646242 | ||||||||
\(296\) | 75.6795 | 4.39878 | ||||||||
\(297\) | 22.6932 | 1.31680 | ||||||||
\(298\) | −10.4672 | −0.606351 | ||||||||
\(299\) | −6.24732 | −0.361292 | ||||||||
\(300\) | 22.2652 | 1.28548 | ||||||||
\(301\) | −10.5518 | −0.608198 | ||||||||
\(302\) | −37.3318 | −2.14820 | ||||||||
\(303\) | 9.82789 | 0.564598 | ||||||||
\(304\) | −9.56294 | −0.548472 | ||||||||
\(305\) | −1.67553 | −0.0959405 | ||||||||
\(306\) | 0.947014 | 0.0541372 | ||||||||
\(307\) | 6.79767 | 0.387964 | 0.193982 | − | 0.981005i | \(-0.437860\pi\) | ||||
0.193982 | + | 0.981005i | \(0.437860\pi\) | |||||||
\(308\) | −29.0470 | −1.65510 | ||||||||
\(309\) | −14.6528 | −0.833569 | ||||||||
\(310\) | −12.2247 | −0.694315 | ||||||||
\(311\) | 30.3767 | 1.72251 | 0.861254 | − | 0.508175i | \(-0.169680\pi\) | ||||
0.861254 | + | 0.508175i | \(0.169680\pi\) | |||||||
\(312\) | 43.4991 | 2.46265 | ||||||||
\(313\) | 16.5336 | 0.934532 | 0.467266 | − | 0.884117i | \(-0.345239\pi\) | ||||
0.467266 | + | 0.884117i | \(0.345239\pi\) | |||||||
\(314\) | 25.0478 | 1.41353 | ||||||||
\(315\) | −2.13207 | −0.120128 | ||||||||
\(316\) | −9.61679 | −0.540987 | ||||||||
\(317\) | −7.18606 | −0.403609 | −0.201805 | − | 0.979426i | \(-0.564681\pi\) | ||||
−0.201805 | + | 0.979426i | \(0.564681\pi\) | |||||||
\(318\) | 10.5583 | 0.592083 | ||||||||
\(319\) | 2.37016 | 0.132703 | ||||||||
\(320\) | −3.65604 | −0.204379 | ||||||||
\(321\) | 12.4426 | 0.694477 | ||||||||
\(322\) | −4.09196 | −0.228036 | ||||||||
\(323\) | −0.227271 | −0.0126457 | ||||||||
\(324\) | −2.04556 | −0.113642 | ||||||||
\(325\) | −24.5013 | −1.35909 | ||||||||
\(326\) | −18.8403 | −1.04346 | ||||||||
\(327\) | 4.12266 | 0.227984 | ||||||||
\(328\) | 67.3707 | 3.71993 | ||||||||
\(329\) | −17.7559 | −0.978915 | ||||||||
\(330\) | −10.1582 | −0.559189 | ||||||||
\(331\) | −20.5435 | −1.12917 | −0.564586 | − | 0.825374i | \(-0.690964\pi\) | ||||
−0.564586 | + | 0.825374i | \(0.690964\pi\) | |||||||
\(332\) | 43.1752 | 2.36955 | ||||||||
\(333\) | 19.4550 | 1.06613 | ||||||||
\(334\) | 31.5215 | 1.72478 | ||||||||
\(335\) | 13.4050 | 0.732394 | ||||||||
\(336\) | 13.6401 | 0.744128 | ||||||||
\(337\) | −20.1185 | −1.09592 | −0.547962 | − | 0.836503i | \(-0.684596\pi\) | ||||
−0.547962 | + | 0.836503i | \(0.684596\pi\) | |||||||
\(338\) | −49.8363 | −2.71074 | ||||||||
\(339\) | −17.6969 | −0.961162 | ||||||||
\(340\) | −0.795676 | −0.0431516 | ||||||||
\(341\) | −24.5558 | −1.32977 | ||||||||
\(342\) | −5.13506 | −0.277672 | ||||||||
\(343\) | 17.1626 | 0.926692 | ||||||||
\(344\) | −51.0305 | −2.75138 | ||||||||
\(345\) | −1.00320 | −0.0540105 | ||||||||
\(346\) | 0.439952 | 0.0236520 | ||||||||
\(347\) | 11.9334 | 0.640618 | 0.320309 | − | 0.947313i | \(-0.396213\pi\) | ||||
0.320309 | + | 0.947313i | \(0.396213\pi\) | |||||||
\(348\) | −2.84166 | −0.152329 | ||||||||
\(349\) | 18.3110 | 0.980167 | 0.490083 | − | 0.871676i | \(-0.336966\pi\) | ||||
0.490083 | + | 0.871676i | \(0.336966\pi\) | |||||||
\(350\) | −16.0482 | −0.857814 | ||||||||
\(351\) | 29.9401 | 1.59809 | ||||||||
\(352\) | −36.0239 | −1.92008 | ||||||||
\(353\) | −14.6976 | −0.782273 | −0.391137 | − | 0.920333i | \(-0.627918\pi\) | ||||
−0.391137 | + | 0.920333i | \(0.627918\pi\) | |||||||
\(354\) | 38.1309 | 2.02663 | ||||||||
\(355\) | 1.91134 | 0.101444 | ||||||||
\(356\) | −15.3394 | −0.812989 | ||||||||
\(357\) | 0.324167 | 0.0171568 | ||||||||
\(358\) | −8.98748 | −0.475003 | ||||||||
\(359\) | −32.3422 | −1.70695 | −0.853477 | − | 0.521131i | \(-0.825510\pi\) | ||||
−0.853477 | + | 0.521131i | \(0.825510\pi\) | |||||||
\(360\) | −10.3110 | −0.543439 | ||||||||
\(361\) | −17.7677 | −0.935140 | ||||||||
\(362\) | −0.838081 | −0.0440486 | ||||||||
\(363\) | −8.29700 | −0.435479 | ||||||||
\(364\) | −38.3229 | −2.00866 | ||||||||
\(365\) | 0.0729469 | 0.00381822 | ||||||||
\(366\) | 5.75602 | 0.300872 | ||||||||
\(367\) | −17.0680 | −0.890944 | −0.445472 | − | 0.895296i | \(-0.646964\pi\) | ||||
−0.445472 | + | 0.895296i | \(0.646964\pi\) | |||||||
\(368\) | −9.47397 | −0.493865 | ||||||||
\(369\) | 17.3191 | 0.901595 | ||||||||
\(370\) | −23.3169 | −1.21219 | ||||||||
\(371\) | −5.33503 | −0.276981 | ||||||||
\(372\) | 29.4407 | 1.52643 | ||||||||
\(373\) | −9.49606 | −0.491687 | −0.245844 | − | 0.969309i | \(-0.579065\pi\) | ||||
−0.245844 | + | 0.969309i | \(0.579065\pi\) | |||||||
\(374\) | −2.27988 | −0.117890 | ||||||||
\(375\) | −8.49534 | −0.438697 | ||||||||
\(376\) | −85.8706 | −4.42844 | ||||||||
\(377\) | 3.12705 | 0.161051 | ||||||||
\(378\) | 19.6106 | 1.00866 | ||||||||
\(379\) | −24.4920 | −1.25807 | −0.629034 | − | 0.777378i | \(-0.716550\pi\) | ||||
−0.629034 | + | 0.777378i | \(0.716550\pi\) | |||||||
\(380\) | 4.31445 | 0.221327 | ||||||||
\(381\) | 7.71087 | 0.395040 | ||||||||
\(382\) | 39.9571 | 2.04438 | ||||||||
\(383\) | −32.8566 | −1.67890 | −0.839448 | − | 0.543440i | \(-0.817121\pi\) | ||||
−0.839448 | + | 0.543440i | \(0.817121\pi\) | |||||||
\(384\) | −5.85915 | −0.298998 | ||||||||
\(385\) | 5.13283 | 0.261593 | ||||||||
\(386\) | −31.7691 | −1.61701 | ||||||||
\(387\) | −13.1185 | −0.666849 | ||||||||
\(388\) | 43.2164 | 2.19398 | ||||||||
\(389\) | 2.75465 | 0.139666 | 0.0698330 | − | 0.997559i | \(-0.477753\pi\) | ||||
0.0698330 | + | 0.997559i | \(0.477753\pi\) | |||||||
\(390\) | −13.4021 | −0.678642 | ||||||||
\(391\) | −0.225156 | −0.0113866 | ||||||||
\(392\) | 34.3023 | 1.73253 | ||||||||
\(393\) | 6.29498 | 0.317540 | ||||||||
\(394\) | −19.0627 | −0.960366 | ||||||||
\(395\) | 1.69936 | 0.0855043 | ||||||||
\(396\) | −36.1123 | −1.81471 | ||||||||
\(397\) | 9.21044 | 0.462259 | 0.231129 | − | 0.972923i | \(-0.425758\pi\) | ||||
0.231129 | + | 0.972923i | \(0.425758\pi\) | |||||||
\(398\) | −45.0182 | −2.25656 | ||||||||
\(399\) | −1.75776 | −0.0879978 | ||||||||
\(400\) | −37.1558 | −1.85779 | ||||||||
\(401\) | 17.7197 | 0.884879 | 0.442440 | − | 0.896798i | \(-0.354113\pi\) | ||||
0.442440 | + | 0.896798i | \(0.354113\pi\) | |||||||
\(402\) | −46.0509 | −2.29681 | ||||||||
\(403\) | −32.3974 | −1.61383 | ||||||||
\(404\) | −41.8735 | −2.08328 | ||||||||
\(405\) | 0.361467 | 0.0179614 | ||||||||
\(406\) | 2.04820 | 0.101650 | ||||||||
\(407\) | −46.8368 | −2.32161 | ||||||||
\(408\) | 1.56773 | 0.0776140 | ||||||||
\(409\) | 15.3811 | 0.760549 | 0.380274 | − | 0.924874i | \(-0.375830\pi\) | ||||
0.380274 | + | 0.924874i | \(0.375830\pi\) | |||||||
\(410\) | −20.7570 | −1.02511 | ||||||||
\(411\) | −11.5388 | −0.569168 | ||||||||
\(412\) | 62.4309 | 3.07575 | ||||||||
\(413\) | −19.2672 | −0.948075 | ||||||||
\(414\) | −5.08729 | −0.250027 | ||||||||
\(415\) | −7.62941 | −0.374513 | ||||||||
\(416\) | −47.5278 | −2.33024 | ||||||||
\(417\) | 17.3967 | 0.851922 | ||||||||
\(418\) | 12.3624 | 0.604663 | ||||||||
\(419\) | −30.6074 | −1.49527 | −0.747634 | − | 0.664111i | \(-0.768810\pi\) | ||||
−0.747634 | + | 0.664111i | \(0.768810\pi\) | |||||||
\(420\) | −6.15391 | −0.300280 | ||||||||
\(421\) | −7.35995 | −0.358702 | −0.179351 | − | 0.983785i | \(-0.557400\pi\) | ||||
−0.179351 | + | 0.983785i | \(0.557400\pi\) | |||||||
\(422\) | 51.3541 | 2.49988 | ||||||||
\(423\) | −22.0748 | −1.07332 | ||||||||
\(424\) | −25.8011 | −1.25301 | ||||||||
\(425\) | −0.883037 | −0.0428336 | ||||||||
\(426\) | −6.56613 | −0.318130 | ||||||||
\(427\) | −2.90846 | −0.140750 | ||||||||
\(428\) | −53.0138 | −2.56252 | ||||||||
\(429\) | −26.9209 | −1.29975 | ||||||||
\(430\) | 15.7225 | 0.758207 | ||||||||
\(431\) | 13.3903 | 0.644987 | 0.322494 | − | 0.946572i | \(-0.395479\pi\) | ||||
0.322494 | + | 0.946572i | \(0.395479\pi\) | |||||||
\(432\) | 45.4037 | 2.18449 | ||||||||
\(433\) | 2.29984 | 0.110523 | 0.0552616 | − | 0.998472i | \(-0.482401\pi\) | ||||
0.0552616 | + | 0.998472i | \(0.482401\pi\) | |||||||
\(434\) | −21.2202 | −1.01860 | ||||||||
\(435\) | 0.502143 | 0.0240759 | ||||||||
\(436\) | −17.5653 | −0.841227 | ||||||||
\(437\) | 1.22088 | 0.0584026 | ||||||||
\(438\) | −0.250598 | −0.0119740 | ||||||||
\(439\) | −34.6791 | −1.65514 | −0.827571 | − | 0.561361i | \(-0.810278\pi\) | ||||
−0.827571 | + | 0.561361i | \(0.810278\pi\) | |||||||
\(440\) | 24.8232 | 1.18340 | ||||||||
\(441\) | 8.81812 | 0.419911 | ||||||||
\(442\) | −3.00794 | −0.143073 | ||||||||
\(443\) | −23.9884 | −1.13972 | −0.569861 | − | 0.821741i | \(-0.693003\pi\) | ||||
−0.569861 | + | 0.821741i | \(0.693003\pi\) | |||||||
\(444\) | 56.1541 | 2.66496 | ||||||||
\(445\) | 2.71060 | 0.128495 | ||||||||
\(446\) | 50.5738 | 2.39474 | ||||||||
\(447\) | −4.45451 | −0.210691 | ||||||||
\(448\) | −6.34633 | −0.299836 | ||||||||
\(449\) | −3.33285 | −0.157287 | −0.0786435 | − | 0.996903i | \(-0.525059\pi\) | ||||
−0.0786435 | + | 0.996903i | \(0.525059\pi\) | |||||||
\(450\) | −19.9518 | −0.940535 | ||||||||
\(451\) | −41.6947 | −1.96332 | ||||||||
\(452\) | 75.4006 | 3.54655 | ||||||||
\(453\) | −15.8872 | −0.746444 | ||||||||
\(454\) | 26.4422 | 1.24100 | ||||||||
\(455\) | 6.77196 | 0.317474 | ||||||||
\(456\) | −8.50080 | −0.398086 | ||||||||
\(457\) | −17.6869 | −0.827360 | −0.413680 | − | 0.910422i | \(-0.635757\pi\) | ||||
−0.413680 | + | 0.910422i | \(0.635757\pi\) | |||||||
\(458\) | −33.1668 | −1.54978 | ||||||||
\(459\) | 1.07906 | 0.0503660 | ||||||||
\(460\) | 4.27431 | 0.199291 | ||||||||
\(461\) | −16.0136 | −0.745826 | −0.372913 | − | 0.927866i | \(-0.621641\pi\) | ||||
−0.372913 | + | 0.927866i | \(0.621641\pi\) | |||||||
\(462\) | −17.6331 | −0.820364 | ||||||||
\(463\) | −24.9357 | −1.15886 | −0.579431 | − | 0.815021i | \(-0.696725\pi\) | ||||
−0.579431 | + | 0.815021i | \(0.696725\pi\) | |||||||
\(464\) | 4.74212 | 0.220147 | ||||||||
\(465\) | −5.20241 | −0.241256 | ||||||||
\(466\) | 38.6218 | 1.78912 | ||||||||
\(467\) | −0.946708 | −0.0438084 | −0.0219042 | − | 0.999760i | \(-0.506973\pi\) | ||||
−0.0219042 | + | 0.999760i | \(0.506973\pi\) | |||||||
\(468\) | −47.6445 | −2.20237 | ||||||||
\(469\) | 23.2691 | 1.07447 | ||||||||
\(470\) | 26.4568 | 1.22036 | ||||||||
\(471\) | 10.6595 | 0.491163 | ||||||||
\(472\) | −93.1792 | −4.28892 | ||||||||
\(473\) | 31.5819 | 1.45214 | ||||||||
\(474\) | −5.83791 | −0.268144 | ||||||||
\(475\) | 4.78815 | 0.219696 | ||||||||
\(476\) | −1.38117 | −0.0633059 | ||||||||
\(477\) | −6.63272 | −0.303691 | ||||||||
\(478\) | 12.0457 | 0.550960 | ||||||||
\(479\) | 19.5675 | 0.894063 | 0.447032 | − | 0.894518i | \(-0.352481\pi\) | ||||
0.447032 | + | 0.894518i | \(0.352481\pi\) | |||||||
\(480\) | −7.63206 | −0.348354 | ||||||||
\(481\) | −61.7937 | −2.81755 | ||||||||
\(482\) | −25.1867 | −1.14722 | ||||||||
\(483\) | −1.74140 | −0.0792365 | ||||||||
\(484\) | 35.3508 | 1.60686 | ||||||||
\(485\) | −7.63669 | −0.346764 | ||||||||
\(486\) | 39.6554 | 1.79881 | ||||||||
\(487\) | −5.92462 | −0.268470 | −0.134235 | − | 0.990950i | \(-0.542858\pi\) | ||||
−0.134235 | + | 0.990950i | \(0.542858\pi\) | |||||||
\(488\) | −14.0658 | −0.636729 | ||||||||
\(489\) | −8.01778 | −0.362576 | ||||||||
\(490\) | −10.5686 | −0.477439 | ||||||||
\(491\) | −14.8770 | −0.671391 | −0.335695 | − | 0.941971i | \(-0.608971\pi\) | ||||
−0.335695 | + | 0.941971i | \(0.608971\pi\) | |||||||
\(492\) | 49.9890 | 2.25368 | ||||||||
\(493\) | 0.112700 | 0.00507576 | ||||||||
\(494\) | 16.3102 | 0.733830 | ||||||||
\(495\) | 6.38133 | 0.286820 | ||||||||
\(496\) | −49.1302 | −2.20601 | ||||||||
\(497\) | 3.31780 | 0.148824 | ||||||||
\(498\) | 26.2097 | 1.17448 | ||||||||
\(499\) | −21.0463 | −0.942162 | −0.471081 | − | 0.882090i | \(-0.656136\pi\) | ||||
−0.471081 | + | 0.882090i | \(0.656136\pi\) | |||||||
\(500\) | 36.1959 | 1.61873 | ||||||||
\(501\) | 13.4145 | 0.599315 | ||||||||
\(502\) | −16.8131 | −0.750404 | ||||||||
\(503\) | −12.9687 | −0.578244 | −0.289122 | − | 0.957292i | \(-0.593363\pi\) | ||||
−0.289122 | + | 0.957292i | \(0.593363\pi\) | |||||||
\(504\) | −17.8984 | −0.797258 | ||||||||
\(505\) | 7.39938 | 0.329268 | ||||||||
\(506\) | 12.2474 | 0.544461 | ||||||||
\(507\) | −21.2086 | −0.941909 | ||||||||
\(508\) | −32.8535 | −1.45764 | ||||||||
\(509\) | 9.53843 | 0.422784 | 0.211392 | − | 0.977401i | \(-0.432200\pi\) | ||||
0.211392 | + | 0.977401i | \(0.432200\pi\) | |||||||
\(510\) | −0.483018 | −0.0213884 | ||||||||
\(511\) | 0.126625 | 0.00560155 | ||||||||
\(512\) | 47.7851 | 2.11182 | ||||||||
\(513\) | −5.85104 | −0.258330 | ||||||||
\(514\) | −76.4623 | −3.37261 | ||||||||
\(515\) | −11.0320 | −0.486130 | ||||||||
\(516\) | −37.8646 | −1.66690 | ||||||||
\(517\) | 53.1439 | 2.33727 | ||||||||
\(518\) | −40.4746 | −1.77835 | ||||||||
\(519\) | 0.187229 | 0.00821843 | ||||||||
\(520\) | 32.7503 | 1.43620 | ||||||||
\(521\) | 9.19325 | 0.402764 | 0.201382 | − | 0.979513i | \(-0.435457\pi\) | ||||
0.201382 | + | 0.979513i | \(0.435457\pi\) | |||||||
\(522\) | 2.54640 | 0.111453 | ||||||||
\(523\) | 32.7411 | 1.43167 | 0.715834 | − | 0.698270i | \(-0.246047\pi\) | ||||
0.715834 | + | 0.698270i | \(0.246047\pi\) | |||||||
\(524\) | −26.8209 | −1.17168 | ||||||||
\(525\) | −6.82958 | −0.298067 | ||||||||
\(526\) | −41.9537 | −1.82927 | ||||||||
\(527\) | −1.16762 | −0.0508622 | ||||||||
\(528\) | −40.8251 | −1.77669 | ||||||||
\(529\) | −21.7905 | −0.947412 | ||||||||
\(530\) | 7.94934 | 0.345297 | ||||||||
\(531\) | −23.9537 | −1.03950 | ||||||||
\(532\) | 7.48923 | 0.324699 | ||||||||
\(533\) | −55.0095 | −2.38273 | ||||||||
\(534\) | −9.31186 | −0.402964 | ||||||||
\(535\) | 9.36797 | 0.405013 | ||||||||
\(536\) | 112.533 | 4.86069 | ||||||||
\(537\) | −3.82477 | −0.165051 | ||||||||
\(538\) | 60.6553 | 2.61504 | ||||||||
\(539\) | −21.2291 | −0.914403 | ||||||||
\(540\) | −20.4845 | −0.881514 | ||||||||
\(541\) | −38.7962 | −1.66798 | −0.833989 | − | 0.551781i | \(-0.813948\pi\) | ||||
−0.833989 | + | 0.551781i | \(0.813948\pi\) | |||||||
\(542\) | 37.6061 | 1.61532 | ||||||||
\(543\) | −0.356659 | −0.0153057 | ||||||||
\(544\) | −1.71292 | −0.0734410 | ||||||||
\(545\) | 3.10394 | 0.132958 | ||||||||
\(546\) | −23.2640 | −0.995608 | ||||||||
\(547\) | 7.41686 | 0.317122 | 0.158561 | − | 0.987349i | \(-0.449315\pi\) | ||||
0.158561 | + | 0.987349i | \(0.449315\pi\) | |||||||
\(548\) | 49.1632 | 2.10015 | ||||||||
\(549\) | −3.61591 | −0.154323 | ||||||||
\(550\) | 48.0327 | 2.04812 | ||||||||
\(551\) | −0.611102 | −0.0260338 | ||||||||
\(552\) | −8.42171 | −0.358452 | ||||||||
\(553\) | 2.94984 | 0.125440 | ||||||||
\(554\) | −45.7441 | −1.94348 | ||||||||
\(555\) | −9.92289 | −0.421203 | ||||||||
\(556\) | −74.1219 | −3.14347 | ||||||||
\(557\) | −21.8107 | −0.924150 | −0.462075 | − | 0.886841i | \(-0.652895\pi\) | ||||
−0.462075 | + | 0.886841i | \(0.652895\pi\) | |||||||
\(558\) | −26.3817 | −1.11683 | ||||||||
\(559\) | 41.6673 | 1.76234 | ||||||||
\(560\) | 10.2696 | 0.433968 | ||||||||
\(561\) | −0.970241 | −0.0409636 | ||||||||
\(562\) | 40.5067 | 1.70867 | ||||||||
\(563\) | −10.1224 | −0.426608 | −0.213304 | − | 0.976986i | \(-0.568423\pi\) | ||||
−0.213304 | + | 0.976986i | \(0.568423\pi\) | |||||||
\(564\) | −63.7159 | −2.68292 | ||||||||
\(565\) | −13.3239 | −0.560541 | ||||||||
\(566\) | 67.2048 | 2.82483 | ||||||||
\(567\) | 0.627452 | 0.0263505 | ||||||||
\(568\) | 16.0454 | 0.673252 | ||||||||
\(569\) | 30.7376 | 1.28859 | 0.644293 | − | 0.764778i | \(-0.277152\pi\) | ||||
0.644293 | + | 0.764778i | \(0.277152\pi\) | |||||||
\(570\) | 2.61910 | 0.109702 | ||||||||
\(571\) | 25.5805 | 1.07051 | 0.535256 | − | 0.844690i | \(-0.320215\pi\) | ||||
0.535256 | + | 0.844690i | \(0.320215\pi\) | |||||||
\(572\) | 114.701 | 4.79590 | ||||||||
\(573\) | 17.0044 | 0.710369 | ||||||||
\(574\) | −36.0309 | −1.50390 | ||||||||
\(575\) | 4.74361 | 0.197822 | ||||||||
\(576\) | −7.89000 | −0.328750 | ||||||||
\(577\) | 32.1704 | 1.33927 | 0.669636 | − | 0.742690i | \(-0.266450\pi\) | ||||
0.669636 | + | 0.742690i | \(0.266450\pi\) | |||||||
\(578\) | 43.8614 | 1.82439 | ||||||||
\(579\) | −13.5199 | −0.561867 | ||||||||
\(580\) | −2.13947 | −0.0888367 | ||||||||
\(581\) | −13.2435 | −0.549433 | ||||||||
\(582\) | 26.2347 | 1.08746 | ||||||||
\(583\) | 15.9679 | 0.661322 | ||||||||
\(584\) | 0.612378 | 0.0253404 | ||||||||
\(585\) | 8.41916 | 0.348089 | ||||||||
\(586\) | 30.7713 | 1.27115 | ||||||||
\(587\) | 40.9828 | 1.69154 | 0.845771 | − | 0.533546i | \(-0.179141\pi\) | ||||
0.845771 | + | 0.533546i | \(0.179141\pi\) | |||||||
\(588\) | 25.4523 | 1.04963 | ||||||||
\(589\) | 6.33126 | 0.260875 | ||||||||
\(590\) | 28.7086 | 1.18191 | ||||||||
\(591\) | −8.11245 | −0.333702 | ||||||||
\(592\) | −93.7093 | −3.85143 | ||||||||
\(593\) | −11.7325 | −0.481797 | −0.240898 | − | 0.970550i | \(-0.577442\pi\) | ||||
−0.240898 | + | 0.970550i | \(0.577442\pi\) | |||||||
\(594\) | −58.6951 | −2.40829 | ||||||||
\(595\) | 0.244064 | 0.0100057 | ||||||||
\(596\) | 18.9792 | 0.777419 | ||||||||
\(597\) | −19.1582 | −0.784094 | ||||||||
\(598\) | 16.1584 | 0.660768 | ||||||||
\(599\) | 36.1695 | 1.47785 | 0.738923 | − | 0.673790i | \(-0.235335\pi\) | ||||
0.738923 | + | 0.673790i | \(0.235335\pi\) | |||||||
\(600\) | −33.0290 | −1.34840 | ||||||||
\(601\) | −31.9739 | −1.30424 | −0.652120 | − | 0.758115i | \(-0.726120\pi\) | ||||
−0.652120 | + | 0.758115i | \(0.726120\pi\) | |||||||
\(602\) | 27.2919 | 1.11233 | ||||||||
\(603\) | 28.9290 | 1.17808 | ||||||||
\(604\) | 67.6901 | 2.75427 | ||||||||
\(605\) | −6.24677 | −0.253967 | ||||||||
\(606\) | −25.4194 | −1.03259 | ||||||||
\(607\) | 16.2795 | 0.660764 | 0.330382 | − | 0.943847i | \(-0.392822\pi\) | ||||
0.330382 | + | 0.943847i | \(0.392822\pi\) | |||||||
\(608\) | 9.28811 | 0.376683 | ||||||||
\(609\) | 0.871644 | 0.0353208 | ||||||||
\(610\) | 4.33368 | 0.175466 | ||||||||
\(611\) | 70.1150 | 2.83655 | ||||||||
\(612\) | −1.71713 | −0.0694107 | ||||||||
\(613\) | −33.9852 | −1.37265 | −0.686325 | − | 0.727295i | \(-0.740777\pi\) | ||||
−0.686325 | + | 0.727295i | \(0.740777\pi\) | |||||||
\(614\) | −17.5819 | −0.709547 | ||||||||
\(615\) | −8.83347 | −0.356200 | ||||||||
\(616\) | 43.0893 | 1.73612 | ||||||||
\(617\) | −36.4428 | −1.46713 | −0.733566 | − | 0.679618i | \(-0.762146\pi\) | ||||
−0.733566 | + | 0.679618i | \(0.762146\pi\) | |||||||
\(618\) | 37.8989 | 1.52452 | ||||||||
\(619\) | 19.6736 | 0.790750 | 0.395375 | − | 0.918520i | \(-0.370615\pi\) | ||||
0.395375 | + | 0.918520i | \(0.370615\pi\) | |||||||
\(620\) | 22.1658 | 0.890199 | ||||||||
\(621\) | −5.79660 | −0.232610 | ||||||||
\(622\) | −78.5682 | −3.15030 | ||||||||
\(623\) | 4.70519 | 0.188510 | ||||||||
\(624\) | −53.8623 | −2.15622 | ||||||||
\(625\) | 15.1700 | 0.606801 | ||||||||
\(626\) | −42.7634 | −1.70917 | ||||||||
\(627\) | 5.26101 | 0.210104 | ||||||||
\(628\) | −45.4167 | −1.81232 | ||||||||
\(629\) | −2.22707 | −0.0887992 | ||||||||
\(630\) | 5.51451 | 0.219703 | ||||||||
\(631\) | 1.06728 | 0.0424877 | 0.0212439 | − | 0.999774i | \(-0.493237\pi\) | ||||
0.0212439 | + | 0.999774i | \(0.493237\pi\) | |||||||
\(632\) | 14.2659 | 0.567467 | ||||||||
\(633\) | 21.8546 | 0.868641 | ||||||||
\(634\) | 18.5864 | 0.738162 | ||||||||
\(635\) | 5.80548 | 0.230383 | ||||||||
\(636\) | −19.1444 | −0.759125 | ||||||||
\(637\) | −28.0085 | −1.10974 | ||||||||
\(638\) | −6.13031 | −0.242701 | ||||||||
\(639\) | 4.12482 | 0.163175 | ||||||||
\(640\) | −4.41133 | −0.174373 | ||||||||
\(641\) | −3.67957 | −0.145334 | −0.0726672 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726672 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(642\) | −32.1822 | −1.27013 | ||||||||
\(643\) | 12.7689 | 0.503557 | 0.251778 | − | 0.967785i | \(-0.418985\pi\) | ||||
0.251778 | + | 0.967785i | \(0.418985\pi\) | |||||||
\(644\) | 7.41955 | 0.292371 | ||||||||
\(645\) | 6.69097 | 0.263457 | ||||||||
\(646\) | 0.587826 | 0.0231277 | ||||||||
\(647\) | 2.14580 | 0.0843601 | 0.0421801 | − | 0.999110i | \(-0.486570\pi\) | ||||
0.0421801 | + | 0.999110i | \(0.486570\pi\) | |||||||
\(648\) | 3.03446 | 0.119205 | ||||||||
\(649\) | 57.6671 | 2.26363 | ||||||||
\(650\) | 63.3716 | 2.48564 | ||||||||
\(651\) | −9.03059 | −0.353937 | ||||||||
\(652\) | 34.1612 | 1.33785 | ||||||||
\(653\) | 9.45981 | 0.370191 | 0.185096 | − | 0.982721i | \(-0.440741\pi\) | ||||
0.185096 | + | 0.982721i | \(0.440741\pi\) | |||||||
\(654\) | −10.6631 | −0.416960 | ||||||||
\(655\) | 4.73946 | 0.185186 | ||||||||
\(656\) | −83.4210 | −3.25704 | ||||||||
\(657\) | 0.157425 | 0.00614173 | ||||||||
\(658\) | 45.9250 | 1.79034 | ||||||||
\(659\) | −36.6516 | −1.42774 | −0.713872 | − | 0.700276i | \(-0.753060\pi\) | ||||
−0.713872 | + | 0.700276i | \(0.753060\pi\) | |||||||
\(660\) | 18.4188 | 0.716952 | ||||||||
\(661\) | 19.9342 | 0.775350 | 0.387675 | − | 0.921796i | \(-0.373278\pi\) | ||||
0.387675 | + | 0.921796i | \(0.373278\pi\) | |||||||
\(662\) | 53.1349 | 2.06515 | ||||||||
\(663\) | −1.28008 | −0.0497142 | ||||||||
\(664\) | −64.0477 | −2.48553 | ||||||||
\(665\) | −1.32341 | −0.0513195 | ||||||||
\(666\) | −50.3196 | −1.94984 | ||||||||
\(667\) | −0.605416 | −0.0234418 | ||||||||
\(668\) | −57.1548 | −2.21139 | ||||||||
\(669\) | 21.5225 | 0.832109 | ||||||||
\(670\) | −34.6715 | −1.33948 | ||||||||
\(671\) | 8.70510 | 0.336057 | ||||||||
\(672\) | −13.2481 | −0.511056 | ||||||||
\(673\) | −25.7282 | −0.991751 | −0.495875 | − | 0.868394i | \(-0.665153\pi\) | ||||
−0.495875 | + | 0.868394i | \(0.665153\pi\) | |||||||
\(674\) | 52.0357 | 2.00434 | ||||||||
\(675\) | −22.7336 | −0.875018 | ||||||||
\(676\) | 90.3632 | 3.47551 | ||||||||
\(677\) | −31.4474 | −1.20862 | −0.604310 | − | 0.796749i | \(-0.706551\pi\) | ||||
−0.604310 | + | 0.796749i | \(0.706551\pi\) | |||||||
\(678\) | 45.7722 | 1.75787 | ||||||||
\(679\) | −13.2561 | −0.508723 | ||||||||
\(680\) | 1.18034 | 0.0452638 | ||||||||
\(681\) | 11.2529 | 0.431213 | ||||||||
\(682\) | 63.5125 | 2.43202 | ||||||||
\(683\) | 8.39234 | 0.321124 | 0.160562 | − | 0.987026i | \(-0.448669\pi\) | ||||
0.160562 | + | 0.987026i | \(0.448669\pi\) | |||||||
\(684\) | 9.31090 | 0.356011 | ||||||||
\(685\) | −8.68753 | −0.331933 | ||||||||
\(686\) | −44.3903 | −1.69483 | ||||||||
\(687\) | −14.1147 | −0.538508 | ||||||||
\(688\) | 63.1879 | 2.40902 | ||||||||
\(689\) | 21.0671 | 0.802592 | ||||||||
\(690\) | 2.59473 | 0.0987799 | ||||||||
\(691\) | −50.5503 | −1.92302 | −0.961512 | − | 0.274764i | \(-0.911400\pi\) | ||||
−0.961512 | + | 0.274764i | \(0.911400\pi\) | |||||||
\(692\) | −0.797721 | −0.0303248 | ||||||||
\(693\) | 11.0770 | 0.420781 | ||||||||
\(694\) | −30.8652 | −1.17163 | ||||||||
\(695\) | 13.0979 | 0.496833 | ||||||||
\(696\) | 4.21542 | 0.159785 | ||||||||
\(697\) | −1.98257 | −0.0750950 | ||||||||
\(698\) | −47.3607 | −1.79263 | ||||||||
\(699\) | 16.4361 | 0.621672 | ||||||||
\(700\) | 29.0986 | 1.09983 | ||||||||
\(701\) | 22.1506 | 0.836618 | 0.418309 | − | 0.908305i | \(-0.362623\pi\) | ||||
0.418309 | + | 0.908305i | \(0.362623\pi\) | |||||||
\(702\) | −77.4389 | −2.92274 | ||||||||
\(703\) | 12.0760 | 0.455456 | ||||||||
\(704\) | 18.9947 | 0.715890 | ||||||||
\(705\) | 11.2591 | 0.424043 | ||||||||
\(706\) | 38.0147 | 1.43070 | ||||||||
\(707\) | 12.8442 | 0.483056 | ||||||||
\(708\) | −69.1389 | −2.59840 | ||||||||
\(709\) | −42.2098 | −1.58522 | −0.792610 | − | 0.609728i | \(-0.791279\pi\) | ||||
−0.792610 | + | 0.609728i | \(0.791279\pi\) | |||||||
\(710\) | −4.94361 | −0.185530 | ||||||||
\(711\) | 3.66735 | 0.137536 | ||||||||
\(712\) | 22.7551 | 0.852784 | ||||||||
\(713\) | 6.27235 | 0.234902 | ||||||||
\(714\) | −0.838445 | −0.0313780 | ||||||||
\(715\) | −20.2686 | −0.758004 | ||||||||
\(716\) | 16.2961 | 0.609014 | ||||||||
\(717\) | 5.12626 | 0.191444 | ||||||||
\(718\) | 83.6517 | 3.12185 | ||||||||
\(719\) | −26.0383 | −0.971063 | −0.485532 | − | 0.874219i | \(-0.661374\pi\) | ||||
−0.485532 | + | 0.874219i | \(0.661374\pi\) | |||||||
\(720\) | 12.7675 | 0.475817 | ||||||||
\(721\) | −19.1499 | −0.713181 | ||||||||
\(722\) | 45.9553 | 1.71028 | ||||||||
\(723\) | −10.7186 | −0.398630 | ||||||||
\(724\) | 1.51961 | 0.0564759 | ||||||||
\(725\) | −2.37437 | −0.0881820 | ||||||||
\(726\) | 21.4598 | 0.796449 | ||||||||
\(727\) | −47.7304 | −1.77022 | −0.885111 | − | 0.465381i | \(-0.845917\pi\) | ||||
−0.885111 | + | 0.465381i | \(0.845917\pi\) | |||||||
\(728\) | 56.8496 | 2.10698 | ||||||||
\(729\) | 18.1845 | 0.673501 | ||||||||
\(730\) | −0.188674 | −0.00698315 | ||||||||
\(731\) | 1.50171 | 0.0555427 | ||||||||
\(732\) | −10.4368 | −0.385756 | ||||||||
\(733\) | −1.42247 | −0.0525400 | −0.0262700 | − | 0.999655i | \(-0.508363\pi\) | ||||
−0.0262700 | + | 0.999655i | \(0.508363\pi\) | |||||||
\(734\) | 44.1458 | 1.62945 | ||||||||
\(735\) | −4.49762 | −0.165897 | ||||||||
\(736\) | 9.20170 | 0.339179 | ||||||||
\(737\) | −69.6449 | −2.56540 | ||||||||
\(738\) | −44.7951 | −1.64893 | ||||||||
\(739\) | 27.9718 | 1.02896 | 0.514479 | − | 0.857503i | \(-0.327985\pi\) | ||||
0.514479 | + | 0.857503i | \(0.327985\pi\) | |||||||
\(740\) | 42.2782 | 1.55418 | ||||||||
\(741\) | 6.94106 | 0.254986 | ||||||||
\(742\) | 13.7988 | 0.506571 | ||||||||
\(743\) | −8.19505 | −0.300647 | −0.150324 | − | 0.988637i | \(-0.548032\pi\) | ||||
−0.150324 | + | 0.988637i | \(0.548032\pi\) | |||||||
\(744\) | −43.6734 | −1.60115 | ||||||||
\(745\) | −3.35378 | −0.122873 | ||||||||
\(746\) | 24.5612 | 0.899249 | ||||||||
\(747\) | −16.4648 | −0.602416 | ||||||||
\(748\) | 4.13388 | 0.151150 | ||||||||
\(749\) | 16.2614 | 0.594178 | ||||||||
\(750\) | 21.9728 | 0.802335 | ||||||||
\(751\) | −49.2692 | −1.79786 | −0.898929 | − | 0.438093i | \(-0.855654\pi\) | ||||
−0.898929 | + | 0.438093i | \(0.855654\pi\) | |||||||
\(752\) | 106.328 | 3.87739 | ||||||||
\(753\) | −7.15508 | −0.260746 | ||||||||
\(754\) | −8.08797 | −0.294547 | ||||||||
\(755\) | −11.9614 | −0.435319 | ||||||||
\(756\) | −35.5580 | −1.29323 | ||||||||
\(757\) | −10.2093 | −0.371064 | −0.185532 | − | 0.982638i | \(-0.559401\pi\) | ||||
−0.185532 | + | 0.982638i | \(0.559401\pi\) | |||||||
\(758\) | 63.3475 | 2.30088 | ||||||||
\(759\) | 5.21206 | 0.189186 | ||||||||
\(760\) | −6.40022 | −0.232160 | ||||||||
\(761\) | 15.8815 | 0.575702 | 0.287851 | − | 0.957675i | \(-0.407059\pi\) | ||||
0.287851 | + | 0.957675i | \(0.407059\pi\) | |||||||
\(762\) | −19.9438 | −0.722489 | ||||||||
\(763\) | 5.38796 | 0.195057 | ||||||||
\(764\) | −72.4503 | −2.62116 | ||||||||
\(765\) | 0.303430 | 0.0109705 | ||||||||
\(766\) | 84.9823 | 3.07054 | ||||||||
\(767\) | 76.0826 | 2.74718 | ||||||||
\(768\) | 24.8664 | 0.897288 | ||||||||
\(769\) | 6.70360 | 0.241738 | 0.120869 | − | 0.992668i | \(-0.461432\pi\) | ||||
0.120869 | + | 0.992668i | \(0.461432\pi\) | |||||||
\(770\) | −13.2759 | −0.478429 | ||||||||
\(771\) | −32.5398 | −1.17189 | ||||||||
\(772\) | 57.6038 | 2.07321 | ||||||||
\(773\) | 14.7305 | 0.529818 | 0.264909 | − | 0.964273i | \(-0.414658\pi\) | ||||
0.264909 | + | 0.964273i | \(0.414658\pi\) | |||||||
\(774\) | 33.9303 | 1.21960 | ||||||||
\(775\) | 24.5995 | 0.883639 | ||||||||
\(776\) | −64.1088 | −2.30137 | ||||||||
\(777\) | −17.2246 | −0.617930 | ||||||||
\(778\) | −7.12478 | −0.255436 | ||||||||
\(779\) | 10.7502 | 0.385166 | ||||||||
\(780\) | 24.3007 | 0.870105 | ||||||||
\(781\) | −9.93026 | −0.355333 | ||||||||
\(782\) | 0.582357 | 0.0208250 | ||||||||
\(783\) | 2.90144 | 0.103689 | ||||||||
\(784\) | −42.4744 | −1.51694 | ||||||||
\(785\) | 8.02549 | 0.286442 | ||||||||
\(786\) | −16.2817 | −0.580749 | ||||||||
\(787\) | −40.9702 | −1.46043 | −0.730214 | − | 0.683218i | \(-0.760580\pi\) | ||||
−0.730214 | + | 0.683218i | \(0.760580\pi\) | |||||||
\(788\) | 34.5645 | 1.23131 | ||||||||
\(789\) | −17.8541 | −0.635622 | ||||||||
\(790\) | −4.39534 | −0.156379 | ||||||||
\(791\) | −23.1283 | −0.822346 | ||||||||
\(792\) | 53.5703 | 1.90354 | ||||||||
\(793\) | 11.4850 | 0.407844 | ||||||||
\(794\) | −23.8224 | −0.845426 | ||||||||
\(795\) | 3.38297 | 0.119982 | ||||||||
\(796\) | 81.6270 | 2.89319 | ||||||||
\(797\) | −3.13785 | −0.111148 | −0.0555742 | − | 0.998455i | \(-0.517699\pi\) | ||||
−0.0555742 | + | 0.998455i | \(0.517699\pi\) | |||||||
\(798\) | 4.54636 | 0.160939 | ||||||||
\(799\) | 2.52697 | 0.0893979 | ||||||||
\(800\) | 36.0880 | 1.27590 | ||||||||
\(801\) | 5.84968 | 0.206688 | ||||||||
\(802\) | −45.8312 | −1.61836 | ||||||||
\(803\) | −0.378991 | −0.0133743 | ||||||||
\(804\) | 83.4995 | 2.94480 | ||||||||
\(805\) | −1.31109 | −0.0462100 | ||||||||
\(806\) | 83.7947 | 2.95154 | ||||||||
\(807\) | 25.8129 | 0.908656 | ||||||||
\(808\) | 62.1167 | 2.18526 | ||||||||
\(809\) | −6.64458 | −0.233611 | −0.116805 | − | 0.993155i | \(-0.537265\pi\) | ||||
−0.116805 | + | 0.993155i | \(0.537265\pi\) | |||||||
\(810\) | −0.934919 | −0.0328497 | ||||||||
\(811\) | −17.1886 | −0.603572 | −0.301786 | − | 0.953376i | \(-0.597583\pi\) | ||||
−0.301786 | + | 0.953376i | \(0.597583\pi\) | |||||||
\(812\) | −3.71380 | −0.130329 | ||||||||
\(813\) | 16.0039 | 0.561281 | ||||||||
\(814\) | 121.141 | 4.24601 | ||||||||
\(815\) | −6.03655 | −0.211451 | ||||||||
\(816\) | −1.94122 | −0.0679563 | ||||||||
\(817\) | −8.14282 | −0.284881 | ||||||||
\(818\) | −39.7827 | −1.39097 | ||||||||
\(819\) | 14.6144 | 0.510668 | ||||||||
\(820\) | 37.6366 | 1.31433 | ||||||||
\(821\) | 23.1309 | 0.807273 | 0.403637 | − | 0.914919i | \(-0.367746\pi\) | ||||
0.403637 | + | 0.914919i | \(0.367746\pi\) | |||||||
\(822\) | 29.8447 | 1.04095 | ||||||||
\(823\) | −16.1841 | −0.564143 | −0.282072 | − | 0.959393i | \(-0.591022\pi\) | ||||
−0.282072 | + | 0.959393i | \(0.591022\pi\) | |||||||
\(824\) | −92.6123 | −3.22630 | ||||||||
\(825\) | 20.4411 | 0.711668 | ||||||||
\(826\) | 49.8337 | 1.73394 | ||||||||
\(827\) | −7.31883 | −0.254501 | −0.127250 | − | 0.991871i | \(-0.540615\pi\) | ||||
−0.127250 | + | 0.991871i | \(0.540615\pi\) | |||||||
\(828\) | 9.22427 | 0.320566 | ||||||||
\(829\) | −13.5660 | −0.471168 | −0.235584 | − | 0.971854i | \(-0.575700\pi\) | ||||
−0.235584 | + | 0.971854i | \(0.575700\pi\) | |||||||
\(830\) | 19.7332 | 0.684948 | ||||||||
\(831\) | −19.4671 | −0.675307 | ||||||||
\(832\) | 25.0605 | 0.868817 | ||||||||
\(833\) | −1.00944 | −0.0349749 | ||||||||
\(834\) | −44.9959 | −1.55808 | ||||||||
\(835\) | 10.0997 | 0.349515 | ||||||||
\(836\) | −22.4155 | −0.775255 | ||||||||
\(837\) | −30.0601 | −1.03903 | ||||||||
\(838\) | 79.1647 | 2.73470 | ||||||||
\(839\) | 33.2951 | 1.14947 | 0.574737 | − | 0.818338i | \(-0.305104\pi\) | ||||
0.574737 | + | 0.818338i | \(0.305104\pi\) | |||||||
\(840\) | 9.12894 | 0.314979 | ||||||||
\(841\) | −28.6970 | −0.989550 | ||||||||
\(842\) | 19.0362 | 0.656031 | ||||||||
\(843\) | 17.2383 | 0.593718 | ||||||||
\(844\) | −93.1153 | −3.20516 | ||||||||
\(845\) | −15.9679 | −0.549312 | ||||||||
\(846\) | 57.0957 | 1.96299 | ||||||||
\(847\) | −10.8434 | −0.372585 | ||||||||
\(848\) | 31.9479 | 1.09710 | ||||||||
\(849\) | 28.6001 | 0.981553 | ||||||||
\(850\) | 2.28394 | 0.0783385 | ||||||||
\(851\) | 11.9637 | 0.410109 | ||||||||
\(852\) | 11.9057 | 0.407883 | ||||||||
\(853\) | −21.7475 | −0.744619 | −0.372310 | − | 0.928109i | \(-0.621434\pi\) | ||||
−0.372310 | + | 0.928109i | \(0.621434\pi\) | |||||||
\(854\) | 7.52262 | 0.257419 | ||||||||
\(855\) | −1.64531 | −0.0562684 | ||||||||
\(856\) | 78.6427 | 2.68795 | ||||||||
\(857\) | −10.2882 | −0.351439 | −0.175719 | − | 0.984440i | \(-0.556225\pi\) | ||||
−0.175719 | + | 0.984440i | \(0.556225\pi\) | |||||||
\(858\) | 69.6298 | 2.37712 | ||||||||
\(859\) | 37.1281 | 1.26679 | 0.633397 | − | 0.773827i | \(-0.281660\pi\) | ||||
0.633397 | + | 0.773827i | \(0.281660\pi\) | |||||||
\(860\) | −28.5081 | −0.972118 | ||||||||
\(861\) | −15.3336 | −0.522566 | ||||||||
\(862\) | −34.6334 | −1.17962 | ||||||||
\(863\) | −51.1954 | −1.74271 | −0.871355 | − | 0.490653i | \(-0.836758\pi\) | ||||
−0.871355 | + | 0.490653i | \(0.836758\pi\) | |||||||
\(864\) | −44.0989 | −1.50028 | ||||||||
\(865\) | 0.140964 | 0.00479291 | ||||||||
\(866\) | −5.94844 | −0.202136 | ||||||||
\(867\) | 18.6659 | 0.633928 | ||||||||
\(868\) | 38.4764 | 1.30597 | ||||||||
\(869\) | −8.82894 | −0.299501 | ||||||||
\(870\) | −1.29877 | −0.0440325 | ||||||||
\(871\) | −91.8854 | −3.11342 | ||||||||
\(872\) | 26.0571 | 0.882404 | ||||||||
\(873\) | −16.4805 | −0.557781 | ||||||||
\(874\) | −3.15776 | −0.106813 | ||||||||
\(875\) | −11.1027 | −0.375339 | ||||||||
\(876\) | 0.454384 | 0.0153522 | ||||||||
\(877\) | 33.9883 | 1.14770 | 0.573852 | − | 0.818959i | \(-0.305448\pi\) | ||||
0.573852 | + | 0.818959i | \(0.305448\pi\) | |||||||
\(878\) | 89.6960 | 3.02709 | ||||||||
\(879\) | 13.0952 | 0.441691 | ||||||||
\(880\) | −30.7371 | −1.03615 | ||||||||
\(881\) | −10.0506 | −0.338614 | −0.169307 | − | 0.985563i | \(-0.554153\pi\) | ||||
−0.169307 | + | 0.985563i | \(0.554153\pi\) | |||||||
\(882\) | −22.8077 | −0.767975 | ||||||||
\(883\) | −34.7134 | −1.16820 | −0.584100 | − | 0.811682i | \(-0.698552\pi\) | ||||
−0.584100 | + | 0.811682i | \(0.698552\pi\) | |||||||
\(884\) | 5.45400 | 0.183438 | ||||||||
\(885\) | 12.2174 | 0.410684 | ||||||||
\(886\) | 62.0449 | 2.08444 | ||||||||
\(887\) | 25.7238 | 0.863722 | 0.431861 | − | 0.901940i | \(-0.357857\pi\) | ||||
0.431861 | + | 0.901940i | \(0.357857\pi\) | |||||||
\(888\) | −83.3011 | −2.79540 | ||||||||
\(889\) | 10.0774 | 0.337986 | ||||||||
\(890\) | −7.01086 | −0.235005 | ||||||||
\(891\) | −1.87798 | −0.0629146 | ||||||||
\(892\) | −91.7005 | −3.07036 | ||||||||
\(893\) | −13.7022 | −0.458526 | ||||||||
\(894\) | 11.5214 | 0.385333 | ||||||||
\(895\) | −2.87965 | −0.0962562 | ||||||||
\(896\) | −7.65739 | −0.255815 | ||||||||
\(897\) | 6.87649 | 0.229599 | ||||||||
\(898\) | 8.62029 | 0.287663 | ||||||||
\(899\) | −3.13958 | −0.104711 | ||||||||
\(900\) | 36.1766 | 1.20589 | ||||||||
\(901\) | 0.759267 | 0.0252948 | ||||||||
\(902\) | 107.842 | 3.59073 | ||||||||
\(903\) | 11.6145 | 0.386507 | ||||||||
\(904\) | −111.852 | −3.72015 | ||||||||
\(905\) | −0.268527 | −0.00892615 | ||||||||
\(906\) | 41.0915 | 1.36517 | ||||||||
\(907\) | 10.4991 | 0.348617 | 0.174309 | − | 0.984691i | \(-0.444231\pi\) | ||||
0.174309 | + | 0.984691i | \(0.444231\pi\) | |||||||
\(908\) | −47.9451 | −1.59111 | ||||||||
\(909\) | 15.9684 | 0.529639 | ||||||||
\(910\) | −17.5154 | −0.580629 | ||||||||
\(911\) | 6.79969 | 0.225284 | 0.112642 | − | 0.993636i | \(-0.464069\pi\) | ||||
0.112642 | + | 0.993636i | \(0.464069\pi\) | |||||||
\(912\) | 10.5260 | 0.348551 | ||||||||
\(913\) | 39.6381 | 1.31183 | ||||||||
\(914\) | 45.7465 | 1.51316 | ||||||||
\(915\) | 1.84427 | 0.0609697 | ||||||||
\(916\) | 60.1380 | 1.98702 | ||||||||
\(917\) | 8.22699 | 0.271679 | ||||||||
\(918\) | −2.79093 | −0.0921145 | ||||||||
\(919\) | −22.1483 | −0.730604 | −0.365302 | − | 0.930889i | \(-0.619034\pi\) | ||||
−0.365302 | + | 0.930889i | \(0.619034\pi\) | |||||||
\(920\) | −6.34067 | −0.209046 | ||||||||
\(921\) | −7.48226 | −0.246549 | ||||||||
\(922\) | 41.4184 | 1.36404 | ||||||||
\(923\) | −13.1014 | −0.431238 | ||||||||
\(924\) | 31.9723 | 1.05181 | ||||||||
\(925\) | 46.9202 | 1.54273 | ||||||||
\(926\) | 64.4953 | 2.11945 | ||||||||
\(927\) | −23.8079 | −0.781955 | ||||||||
\(928\) | −4.60583 | −0.151194 | ||||||||
\(929\) | −55.9373 | −1.83524 | −0.917621 | − | 0.397456i | \(-0.869893\pi\) | ||||
−0.917621 | + | 0.397456i | \(0.869893\pi\) | |||||||
\(930\) | 13.4558 | 0.441233 | ||||||||
\(931\) | 5.47354 | 0.179388 | ||||||||
\(932\) | −70.0291 | −2.29388 | ||||||||
\(933\) | −33.4360 | −1.09464 | ||||||||
\(934\) | 2.44862 | 0.0801213 | ||||||||
\(935\) | −0.730490 | −0.0238896 | ||||||||
\(936\) | 70.6776 | 2.31017 | ||||||||
\(937\) | 52.0302 | 1.69975 | 0.849876 | − | 0.526983i | \(-0.176677\pi\) | ||||
0.849876 | + | 0.526983i | \(0.176677\pi\) | |||||||
\(938\) | −60.1845 | −1.96509 | ||||||||
\(939\) | −18.1986 | −0.593890 | ||||||||
\(940\) | −47.9715 | −1.56466 | ||||||||
\(941\) | −37.2946 | −1.21577 | −0.607885 | − | 0.794025i | \(-0.707982\pi\) | ||||
−0.607885 | + | 0.794025i | \(0.707982\pi\) | |||||||
\(942\) | −27.5703 | −0.898290 | ||||||||
\(943\) | 10.6502 | 0.346818 | ||||||||
\(944\) | 115.378 | 3.75524 | ||||||||
\(945\) | 6.28339 | 0.204399 | ||||||||
\(946\) | −81.6853 | −2.65582 | ||||||||
\(947\) | −50.8260 | −1.65162 | −0.825812 | − | 0.563946i | \(-0.809283\pi\) | ||||
−0.825812 | + | 0.563946i | \(0.809283\pi\) | |||||||
\(948\) | 10.5853 | 0.343794 | ||||||||
\(949\) | −0.500019 | −0.0162313 | ||||||||
\(950\) | −12.3844 | −0.401802 | ||||||||
\(951\) | 7.90976 | 0.256492 | ||||||||
\(952\) | 2.04888 | 0.0664047 | ||||||||
\(953\) | 40.7835 | 1.32111 | 0.660553 | − | 0.750779i | \(-0.270322\pi\) | ||||
0.660553 | + | 0.750779i | \(0.270322\pi\) | |||||||
\(954\) | 17.1552 | 0.555422 | ||||||||
\(955\) | 12.8025 | 0.414281 | ||||||||
\(956\) | −21.8414 | −0.706400 | ||||||||
\(957\) | −2.60885 | −0.0843323 | ||||||||
\(958\) | −50.6106 | −1.63515 | ||||||||
\(959\) | −15.0802 | −0.486966 | ||||||||
\(960\) | 4.02424 | 0.129882 | ||||||||
\(961\) | 1.52727 | 0.0492667 | ||||||||
\(962\) | 159.827 | 5.15303 | ||||||||
\(963\) | 20.2168 | 0.651476 | ||||||||
\(964\) | 45.6686 | 1.47089 | ||||||||
\(965\) | −10.1791 | −0.327676 | ||||||||
\(966\) | 4.50406 | 0.144916 | ||||||||
\(967\) | 49.4076 | 1.58884 | 0.794420 | − | 0.607369i | \(-0.207775\pi\) | ||||
0.794420 | + | 0.607369i | \(0.207775\pi\) | |||||||
\(968\) | −52.4407 | −1.68551 | ||||||||
\(969\) | 0.250159 | 0.00803626 | ||||||||
\(970\) | 19.7520 | 0.634198 | ||||||||
\(971\) | 21.4751 | 0.689167 | 0.344584 | − | 0.938756i | \(-0.388020\pi\) | ||||
0.344584 | + | 0.938756i | \(0.388020\pi\) | |||||||
\(972\) | −71.9033 | −2.30630 | ||||||||
\(973\) | 22.7360 | 0.728883 | ||||||||
\(974\) | 15.3238 | 0.491006 | ||||||||
\(975\) | 26.9688 | 0.863693 | ||||||||
\(976\) | 17.4168 | 0.557499 | ||||||||
\(977\) | −15.2844 | −0.488992 | −0.244496 | − | 0.969650i | \(-0.578622\pi\) | ||||
−0.244496 | + | 0.969650i | \(0.578622\pi\) | |||||||
\(978\) | 20.7376 | 0.663117 | ||||||||
\(979\) | −14.0828 | −0.450087 | ||||||||
\(980\) | 19.1629 | 0.612137 | ||||||||
\(981\) | 6.69852 | 0.213867 | ||||||||
\(982\) | 38.4788 | 1.22791 | ||||||||
\(983\) | 44.4677 | 1.41830 | 0.709150 | − | 0.705058i | \(-0.249079\pi\) | ||||
0.709150 | + | 0.705058i | \(0.249079\pi\) | |||||||
\(984\) | −74.1556 | −2.36399 | ||||||||
\(985\) | −6.10783 | −0.194612 | ||||||||
\(986\) | −0.291494 | −0.00928306 | ||||||||
\(987\) | 19.5441 | 0.622096 | ||||||||
\(988\) | −29.5736 | −0.940863 | ||||||||
\(989\) | −8.06707 | −0.256518 | ||||||||
\(990\) | −16.5051 | −0.524565 | ||||||||
\(991\) | −40.4447 | −1.28477 | −0.642384 | − | 0.766383i | \(-0.722054\pi\) | ||||
−0.642384 | + | 0.766383i | \(0.722054\pi\) | |||||||
\(992\) | 47.7183 | 1.51506 | ||||||||
\(993\) | 22.6124 | 0.717584 | ||||||||
\(994\) | −8.58136 | −0.272184 | ||||||||
\(995\) | −14.4242 | −0.457276 | ||||||||
\(996\) | −47.5234 | −1.50584 | ||||||||
\(997\) | 31.6645 | 1.00282 | 0.501412 | − | 0.865209i | \(-0.332814\pi\) | ||||
0.501412 | + | 0.865209i | \(0.332814\pi\) | |||||||
\(998\) | 54.4354 | 1.72312 | ||||||||
\(999\) | −57.3356 | −1.81402 |
(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 | 4001.2.a.a.1.8 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.a.1.8 | ✓ | 149 | 1.1 | even | 1 | trivial |