Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0480074613\) |
Analytic rank: | \(1\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38388 | −1.68565 | −0.842827 | − | 0.538184i | \(-0.819110\pi\) | ||||
−0.842827 | + | 0.538184i | \(0.819110\pi\) | |||||||
\(3\) | 0.0725376 | 0.0418796 | 0.0209398 | − | 0.999781i | \(-0.493334\pi\) | ||||
0.0209398 | + | 0.999781i | \(0.493334\pi\) | |||||||
\(4\) | 3.68286 | 1.84143 | ||||||||
\(5\) | −3.05924 | −1.36813 | −0.684067 | − | 0.729419i | \(-0.739790\pi\) | ||||
−0.684067 | + | 0.729419i | \(0.739790\pi\) | |||||||
\(6\) | −0.172921 | −0.0705945 | ||||||||
\(7\) | −4.27004 | −1.61392 | −0.806962 | − | 0.590603i | \(-0.798890\pi\) | ||||
−0.806962 | + | 0.590603i | \(0.798890\pi\) | |||||||
\(8\) | −4.01173 | −1.41836 | ||||||||
\(9\) | −2.99474 | −0.998246 | ||||||||
\(10\) | 7.29285 | 2.30620 | ||||||||
\(11\) | 2.46731 | 0.743921 | 0.371960 | − | 0.928249i | \(-0.378686\pi\) | ||||
0.371960 | + | 0.928249i | \(0.378686\pi\) | |||||||
\(12\) | 0.267146 | 0.0771183 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 10.1792 | 2.72052 | ||||||||
\(15\) | −0.221910 | −0.0572969 | ||||||||
\(16\) | 2.19774 | 0.549436 | ||||||||
\(17\) | −1.27222 | −0.308560 | −0.154280 | − | 0.988027i | \(-0.549306\pi\) | ||||
−0.154280 | + | 0.988027i | \(0.549306\pi\) | |||||||
\(18\) | 7.13908 | 1.68270 | ||||||||
\(19\) | 0.997990 | 0.228954 | 0.114477 | − | 0.993426i | \(-0.463481\pi\) | ||||
0.114477 | + | 0.993426i | \(0.463481\pi\) | |||||||
\(20\) | −11.2668 | −2.51932 | ||||||||
\(21\) | −0.309739 | −0.0675905 | ||||||||
\(22\) | −5.88175 | −1.25399 | ||||||||
\(23\) | −0.383553 | −0.0799764 | −0.0399882 | − | 0.999200i | \(-0.512732\pi\) | ||||
−0.0399882 | + | 0.999200i | \(0.512732\pi\) | |||||||
\(24\) | −0.291001 | −0.0594004 | ||||||||
\(25\) | 4.35895 | 0.871790 | ||||||||
\(26\) | −2.38388 | −0.467516 | ||||||||
\(27\) | −0.434844 | −0.0836857 | ||||||||
\(28\) | −15.7260 | −2.97193 | ||||||||
\(29\) | −4.72422 | −0.877265 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(30\) | 0.529005 | 0.0965827 | ||||||||
\(31\) | −3.53003 | −0.634013 | −0.317006 | − | 0.948423i | \(-0.602678\pi\) | ||||
−0.317006 | + | 0.948423i | \(0.602678\pi\) | |||||||
\(32\) | 2.78431 | 0.492202 | ||||||||
\(33\) | 0.178972 | 0.0311551 | ||||||||
\(34\) | 3.03282 | 0.520125 | ||||||||
\(35\) | 13.0631 | 2.20806 | ||||||||
\(36\) | −11.0292 | −1.83820 | ||||||||
\(37\) | 6.07208 | 0.998244 | 0.499122 | − | 0.866532i | \(-0.333656\pi\) | ||||
0.499122 | + | 0.866532i | \(0.333656\pi\) | |||||||
\(38\) | −2.37908 | −0.385938 | ||||||||
\(39\) | 0.0725376 | 0.0116153 | ||||||||
\(40\) | 12.2728 | 1.94051 | ||||||||
\(41\) | −1.30094 | −0.203173 | −0.101587 | − | 0.994827i | \(-0.532392\pi\) | ||||
−0.101587 | + | 0.994827i | \(0.532392\pi\) | |||||||
\(42\) | 0.738378 | 0.113934 | ||||||||
\(43\) | −9.71207 | −1.48108 | −0.740538 | − | 0.672014i | \(-0.765429\pi\) | ||||
−0.740538 | + | 0.672014i | \(0.765429\pi\) | |||||||
\(44\) | 9.08674 | 1.36988 | ||||||||
\(45\) | 9.16162 | 1.36573 | ||||||||
\(46\) | 0.914343 | 0.134813 | ||||||||
\(47\) | 9.52442 | 1.38928 | 0.694640 | − | 0.719357i | \(-0.255564\pi\) | ||||
0.694640 | + | 0.719357i | \(0.255564\pi\) | |||||||
\(48\) | 0.159419 | 0.0230102 | ||||||||
\(49\) | 11.2333 | 1.60475 | ||||||||
\(50\) | −10.3912 | −1.46954 | ||||||||
\(51\) | −0.0922840 | −0.0129223 | ||||||||
\(52\) | 3.68286 | 0.510721 | ||||||||
\(53\) | −11.0135 | −1.51283 | −0.756413 | − | 0.654095i | \(-0.773050\pi\) | ||||
−0.756413 | + | 0.654095i | \(0.773050\pi\) | |||||||
\(54\) | 1.03661 | 0.141065 | ||||||||
\(55\) | −7.54808 | −1.01778 | ||||||||
\(56\) | 17.1303 | 2.28913 | ||||||||
\(57\) | 0.0723917 | 0.00958852 | ||||||||
\(58\) | 11.2619 | 1.47877 | ||||||||
\(59\) | −1.91373 | −0.249147 | −0.124574 | − | 0.992210i | \(-0.539756\pi\) | ||||
−0.124574 | + | 0.992210i | \(0.539756\pi\) | |||||||
\(60\) | −0.817263 | −0.105508 | ||||||||
\(61\) | −6.27105 | −0.802925 | −0.401463 | − | 0.915875i | \(-0.631498\pi\) | ||||
−0.401463 | + | 0.915875i | \(0.631498\pi\) | |||||||
\(62\) | 8.41516 | 1.06873 | ||||||||
\(63\) | 12.7877 | 1.61109 | ||||||||
\(64\) | −11.0329 | −1.37912 | ||||||||
\(65\) | −3.05924 | −0.379452 | ||||||||
\(66\) | −0.426648 | −0.0525167 | ||||||||
\(67\) | −1.81943 | −0.222279 | −0.111139 | − | 0.993805i | \(-0.535450\pi\) | ||||
−0.111139 | + | 0.993805i | \(0.535450\pi\) | |||||||
\(68\) | −4.68542 | −0.568191 | ||||||||
\(69\) | −0.0278220 | −0.00334938 | ||||||||
\(70\) | −31.1408 | −3.72203 | ||||||||
\(71\) | −0.711972 | −0.0844955 | −0.0422478 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422478 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(72\) | 12.0141 | 1.41587 | ||||||||
\(73\) | 0.825468 | 0.0966137 | 0.0483069 | − | 0.998833i | \(-0.484617\pi\) | ||||
0.0483069 | + | 0.998833i | \(0.484617\pi\) | |||||||
\(74\) | −14.4751 | −1.68269 | ||||||||
\(75\) | 0.316188 | 0.0365102 | ||||||||
\(76\) | 3.67546 | 0.421604 | ||||||||
\(77\) | −10.5355 | −1.20063 | ||||||||
\(78\) | −0.172921 | −0.0195794 | ||||||||
\(79\) | 4.55458 | 0.512430 | 0.256215 | − | 0.966620i | \(-0.417524\pi\) | ||||
0.256215 | + | 0.966620i | \(0.417524\pi\) | |||||||
\(80\) | −6.72343 | −0.751702 | ||||||||
\(81\) | 8.95267 | 0.994741 | ||||||||
\(82\) | 3.10129 | 0.342480 | ||||||||
\(83\) | 10.8981 | 1.19622 | 0.598112 | − | 0.801413i | \(-0.295918\pi\) | ||||
0.598112 | + | 0.801413i | \(0.295918\pi\) | |||||||
\(84\) | −1.14072 | −0.124463 | ||||||||
\(85\) | 3.89204 | 0.422151 | ||||||||
\(86\) | 23.1524 | 2.49658 | ||||||||
\(87\) | −0.342683 | −0.0367395 | ||||||||
\(88\) | −9.89817 | −1.05515 | ||||||||
\(89\) | 0.955601 | 0.101294 | 0.0506468 | − | 0.998717i | \(-0.483872\pi\) | ||||
0.0506468 | + | 0.998717i | \(0.483872\pi\) | |||||||
\(90\) | −21.8402 | −2.30216 | ||||||||
\(91\) | −4.27004 | −0.447622 | ||||||||
\(92\) | −1.41257 | −0.147271 | ||||||||
\(93\) | −0.256060 | −0.0265522 | ||||||||
\(94\) | −22.7050 | −2.34185 | ||||||||
\(95\) | −3.05309 | −0.313240 | ||||||||
\(96\) | 0.201967 | 0.0206132 | ||||||||
\(97\) | −1.49314 | −0.151605 | −0.0758025 | − | 0.997123i | \(-0.524152\pi\) | ||||
−0.0758025 | + | 0.997123i | \(0.524152\pi\) | |||||||
\(98\) | −26.7787 | −2.70506 | ||||||||
\(99\) | −7.38893 | −0.742616 | ||||||||
\(100\) | 16.0534 | 1.60534 | ||||||||
\(101\) | 6.85917 | 0.682513 | 0.341256 | − | 0.939970i | \(-0.389148\pi\) | ||||
0.341256 | + | 0.939970i | \(0.389148\pi\) | |||||||
\(102\) | 0.219994 | 0.0217826 | ||||||||
\(103\) | 12.3642 | 1.21828 | 0.609138 | − | 0.793064i | \(-0.291515\pi\) | ||||
0.609138 | + | 0.793064i | \(0.291515\pi\) | |||||||
\(104\) | −4.01173 | −0.393383 | ||||||||
\(105\) | 0.947564 | 0.0924728 | ||||||||
\(106\) | 26.2549 | 2.55010 | ||||||||
\(107\) | 3.30425 | 0.319434 | 0.159717 | − | 0.987163i | \(-0.448942\pi\) | ||||
0.159717 | + | 0.987163i | \(0.448942\pi\) | |||||||
\(108\) | −1.60147 | −0.154101 | ||||||||
\(109\) | 1.91827 | 0.183737 | 0.0918684 | − | 0.995771i | \(-0.470716\pi\) | ||||
0.0918684 | + | 0.995771i | \(0.470716\pi\) | |||||||
\(110\) | 17.9937 | 1.71563 | ||||||||
\(111\) | 0.440454 | 0.0418060 | ||||||||
\(112\) | −9.38446 | −0.886748 | ||||||||
\(113\) | 12.0944 | 1.13775 | 0.568875 | − | 0.822424i | \(-0.307379\pi\) | ||||
0.568875 | + | 0.822424i | \(0.307379\pi\) | |||||||
\(114\) | −0.172573 | −0.0161629 | ||||||||
\(115\) | 1.17338 | 0.109418 | ||||||||
\(116\) | −17.3986 | −1.61542 | ||||||||
\(117\) | −2.99474 | −0.276864 | ||||||||
\(118\) | 4.56210 | 0.419976 | ||||||||
\(119\) | 5.43245 | 0.497992 | ||||||||
\(120\) | 0.890243 | 0.0812677 | ||||||||
\(121\) | −4.91240 | −0.446582 | ||||||||
\(122\) | 14.9494 | 1.35345 | ||||||||
\(123\) | −0.0943672 | −0.00850880 | ||||||||
\(124\) | −13.0006 | −1.16749 | ||||||||
\(125\) | 1.96113 | 0.175409 | ||||||||
\(126\) | −30.4842 | −2.71575 | ||||||||
\(127\) | 10.6555 | 0.945526 | 0.472763 | − | 0.881190i | \(-0.343257\pi\) | ||||
0.472763 | + | 0.881190i | \(0.343257\pi\) | |||||||
\(128\) | 20.7325 | 1.83251 | ||||||||
\(129\) | −0.704490 | −0.0620269 | ||||||||
\(130\) | 7.29285 | 0.639625 | ||||||||
\(131\) | 12.3178 | 1.07621 | 0.538107 | − | 0.842877i | \(-0.319140\pi\) | ||||
0.538107 | + | 0.842877i | \(0.319140\pi\) | |||||||
\(132\) | 0.659130 | 0.0573699 | ||||||||
\(133\) | −4.26146 | −0.369515 | ||||||||
\(134\) | 4.33729 | 0.374685 | ||||||||
\(135\) | 1.33029 | 0.114493 | ||||||||
\(136\) | 5.10382 | 0.437649 | ||||||||
\(137\) | 15.6891 | 1.34041 | 0.670204 | − | 0.742177i | \(-0.266206\pi\) | ||||
0.670204 | + | 0.742177i | \(0.266206\pi\) | |||||||
\(138\) | 0.0663242 | 0.00564589 | ||||||||
\(139\) | 7.26944 | 0.616586 | 0.308293 | − | 0.951291i | \(-0.400242\pi\) | ||||
0.308293 | + | 0.951291i | \(0.400242\pi\) | |||||||
\(140\) | 48.1095 | 4.06600 | ||||||||
\(141\) | 0.690879 | 0.0581825 | ||||||||
\(142\) | 1.69725 | 0.142430 | ||||||||
\(143\) | 2.46731 | 0.206326 | ||||||||
\(144\) | −6.58167 | −0.548472 | ||||||||
\(145\) | 14.4525 | 1.20022 | ||||||||
\(146\) | −1.96781 | −0.162857 | ||||||||
\(147\) | 0.814834 | 0.0672064 | ||||||||
\(148\) | 22.3626 | 1.83820 | ||||||||
\(149\) | −8.85272 | −0.725243 | −0.362621 | − | 0.931937i | \(-0.618118\pi\) | ||||
−0.362621 | + | 0.931937i | \(0.618118\pi\) | |||||||
\(150\) | −0.753752 | −0.0615436 | ||||||||
\(151\) | 17.7747 | 1.44648 | 0.723242 | − | 0.690595i | \(-0.242651\pi\) | ||||
0.723242 | + | 0.690595i | \(0.242651\pi\) | |||||||
\(152\) | −4.00367 | −0.324740 | ||||||||
\(153\) | 3.80998 | 0.308018 | ||||||||
\(154\) | 25.1153 | 2.02385 | ||||||||
\(155\) | 10.7992 | 0.867414 | ||||||||
\(156\) | 0.267146 | 0.0213888 | ||||||||
\(157\) | 18.0511 | 1.44063 | 0.720316 | − | 0.693646i | \(-0.243997\pi\) | ||||
0.720316 | + | 0.693646i | \(0.243997\pi\) | |||||||
\(158\) | −10.8575 | −0.863780 | ||||||||
\(159\) | −0.798895 | −0.0633565 | ||||||||
\(160\) | −8.51789 | −0.673398 | ||||||||
\(161\) | 1.63779 | 0.129076 | ||||||||
\(162\) | −21.3421 | −1.67679 | ||||||||
\(163\) | −8.17059 | −0.639970 | −0.319985 | − | 0.947423i | \(-0.603678\pi\) | ||||
−0.319985 | + | 0.947423i | \(0.603678\pi\) | |||||||
\(164\) | −4.79119 | −0.374129 | ||||||||
\(165\) | −0.547519 | −0.0426243 | ||||||||
\(166\) | −25.9798 | −2.01642 | ||||||||
\(167\) | 12.8700 | 0.995908 | 0.497954 | − | 0.867203i | \(-0.334085\pi\) | ||||
0.497954 | + | 0.867203i | \(0.334085\pi\) | |||||||
\(168\) | 1.24259 | 0.0958677 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −9.27813 | −0.711600 | ||||||||
\(171\) | −2.98872 | −0.228553 | ||||||||
\(172\) | −35.7682 | −2.72730 | ||||||||
\(173\) | 6.51353 | 0.495214 | 0.247607 | − | 0.968861i | \(-0.420356\pi\) | ||||
0.247607 | + | 0.968861i | \(0.420356\pi\) | |||||||
\(174\) | 0.816914 | 0.0619301 | ||||||||
\(175\) | −18.6129 | −1.40700 | ||||||||
\(176\) | 5.42251 | 0.408737 | ||||||||
\(177\) | −0.138818 | −0.0104342 | ||||||||
\(178\) | −2.27803 | −0.170746 | ||||||||
\(179\) | −2.87992 | −0.215255 | −0.107628 | − | 0.994191i | \(-0.534325\pi\) | ||||
−0.107628 | + | 0.994191i | \(0.534325\pi\) | |||||||
\(180\) | 33.7410 | 2.51490 | ||||||||
\(181\) | −8.19581 | −0.609190 | −0.304595 | − | 0.952482i | \(-0.598521\pi\) | ||||
−0.304595 | + | 0.952482i | \(0.598521\pi\) | |||||||
\(182\) | 10.1792 | 0.754536 | ||||||||
\(183\) | −0.454886 | −0.0336262 | ||||||||
\(184\) | 1.53871 | 0.113435 | ||||||||
\(185\) | −18.5760 | −1.36573 | ||||||||
\(186\) | 0.610415 | 0.0447578 | ||||||||
\(187\) | −3.13896 | −0.229544 | ||||||||
\(188\) | 35.0771 | 2.55826 | ||||||||
\(189\) | 1.85680 | 0.135062 | ||||||||
\(190\) | 7.27818 | 0.528015 | ||||||||
\(191\) | 8.70060 | 0.629554 | 0.314777 | − | 0.949166i | \(-0.398070\pi\) | ||||
0.314777 | + | 0.949166i | \(0.398070\pi\) | |||||||
\(192\) | −0.800303 | −0.0577569 | ||||||||
\(193\) | 5.83949 | 0.420336 | 0.210168 | − | 0.977665i | \(-0.432599\pi\) | ||||
0.210168 | + | 0.977665i | \(0.432599\pi\) | |||||||
\(194\) | 3.55945 | 0.255554 | ||||||||
\(195\) | −0.221910 | −0.0158913 | ||||||||
\(196\) | 41.3706 | 2.95504 | ||||||||
\(197\) | −3.31836 | −0.236423 | −0.118212 | − | 0.992988i | \(-0.537716\pi\) | ||||
−0.118212 | + | 0.992988i | \(0.537716\pi\) | |||||||
\(198\) | 17.6143 | 1.25179 | ||||||||
\(199\) | −27.2437 | −1.93125 | −0.965627 | − | 0.259931i | \(-0.916300\pi\) | ||||
−0.965627 | + | 0.259931i | \(0.916300\pi\) | |||||||
\(200\) | −17.4869 | −1.23651 | ||||||||
\(201\) | −0.131977 | −0.00930894 | ||||||||
\(202\) | −16.3514 | −1.15048 | ||||||||
\(203\) | 20.1726 | 1.41584 | ||||||||
\(204\) | −0.339869 | −0.0237956 | ||||||||
\(205\) | 3.97990 | 0.277968 | ||||||||
\(206\) | −29.4746 | −2.05359 | ||||||||
\(207\) | 1.14864 | 0.0798361 | ||||||||
\(208\) | 2.19774 | 0.152386 | ||||||||
\(209\) | 2.46234 | 0.170324 | ||||||||
\(210\) | −2.25888 | −0.155877 | ||||||||
\(211\) | −11.8659 | −0.816884 | −0.408442 | − | 0.912784i | \(-0.633928\pi\) | ||||
−0.408442 | + | 0.912784i | \(0.633928\pi\) | |||||||
\(212\) | −40.5613 | −2.78576 | ||||||||
\(213\) | −0.0516447 | −0.00353864 | ||||||||
\(214\) | −7.87692 | −0.538455 | ||||||||
\(215\) | 29.7116 | 2.02631 | ||||||||
\(216\) | 1.74448 | 0.118697 | ||||||||
\(217\) | 15.0734 | 1.02325 | ||||||||
\(218\) | −4.57291 | −0.309717 | ||||||||
\(219\) | 0.0598774 | 0.00404614 | ||||||||
\(220\) | −27.7985 | −1.87418 | ||||||||
\(221\) | −1.27222 | −0.0855790 | ||||||||
\(222\) | −1.04999 | −0.0704705 | ||||||||
\(223\) | 15.5717 | 1.04276 | 0.521378 | − | 0.853326i | \(-0.325418\pi\) | ||||
0.521378 | + | 0.853326i | \(0.325418\pi\) | |||||||
\(224\) | −11.8891 | −0.794377 | ||||||||
\(225\) | −13.0539 | −0.870261 | ||||||||
\(226\) | −28.8317 | −1.91785 | ||||||||
\(227\) | −17.2347 | −1.14391 | −0.571954 | − | 0.820286i | \(-0.693814\pi\) | ||||
−0.571954 | + | 0.820286i | \(0.693814\pi\) | |||||||
\(228\) | 0.266609 | 0.0176566 | ||||||||
\(229\) | 3.08595 | 0.203925 | 0.101963 | − | 0.994788i | \(-0.467488\pi\) | ||||
0.101963 | + | 0.994788i | \(0.467488\pi\) | |||||||
\(230\) | −2.79719 | −0.184442 | ||||||||
\(231\) | −0.764219 | −0.0502819 | ||||||||
\(232\) | 18.9523 | 1.24428 | ||||||||
\(233\) | 29.0422 | 1.90261 | 0.951307 | − | 0.308244i | \(-0.0997412\pi\) | ||||
0.951307 | + | 0.308244i | \(0.0997412\pi\) | |||||||
\(234\) | 7.13908 | 0.466696 | ||||||||
\(235\) | −29.1375 | −1.90072 | ||||||||
\(236\) | −7.04802 | −0.458787 | ||||||||
\(237\) | 0.330378 | 0.0214604 | ||||||||
\(238\) | −12.9503 | −0.839442 | ||||||||
\(239\) | 6.12984 | 0.396507 | 0.198253 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(240\) | −0.487701 | −0.0314810 | ||||||||
\(241\) | −12.0507 | −0.776253 | −0.388126 | − | 0.921606i | \(-0.626878\pi\) | ||||
−0.388126 | + | 0.921606i | \(0.626878\pi\) | |||||||
\(242\) | 11.7106 | 0.752783 | ||||||||
\(243\) | 1.95394 | 0.125345 | ||||||||
\(244\) | −23.0954 | −1.47853 | ||||||||
\(245\) | −34.3653 | −2.19552 | ||||||||
\(246\) | 0.224960 | 0.0143429 | ||||||||
\(247\) | 0.997990 | 0.0635006 | ||||||||
\(248\) | 14.1615 | 0.899259 | ||||||||
\(249\) | 0.790523 | 0.0500974 | ||||||||
\(250\) | −4.67508 | −0.295678 | ||||||||
\(251\) | −10.2379 | −0.646211 | −0.323105 | − | 0.946363i | \(-0.604727\pi\) | ||||
−0.323105 | + | 0.946363i | \(0.604727\pi\) | |||||||
\(252\) | 47.0952 | 2.96672 | ||||||||
\(253\) | −0.946343 | −0.0594961 | ||||||||
\(254\) | −25.4015 | −1.59383 | ||||||||
\(255\) | 0.282319 | 0.0176795 | ||||||||
\(256\) | −27.3579 | −1.70987 | ||||||||
\(257\) | −31.7414 | −1.97997 | −0.989986 | − | 0.141167i | \(-0.954915\pi\) | ||||
−0.989986 | + | 0.141167i | \(0.954915\pi\) | |||||||
\(258\) | 1.67942 | 0.104556 | ||||||||
\(259\) | −25.9280 | −1.61109 | ||||||||
\(260\) | −11.2668 | −0.698735 | ||||||||
\(261\) | 14.1478 | 0.875727 | ||||||||
\(262\) | −29.3642 | −1.81412 | ||||||||
\(263\) | 15.7889 | 0.973584 | 0.486792 | − | 0.873518i | \(-0.338167\pi\) | ||||
0.486792 | + | 0.873518i | \(0.338167\pi\) | |||||||
\(264\) | −0.717989 | −0.0441892 | ||||||||
\(265\) | 33.6930 | 2.06975 | ||||||||
\(266\) | 10.1588 | 0.622875 | ||||||||
\(267\) | 0.0693170 | 0.00424213 | ||||||||
\(268\) | −6.70071 | −0.409311 | ||||||||
\(269\) | 8.45013 | 0.515213 | 0.257607 | − | 0.966250i | \(-0.417066\pi\) | ||||
0.257607 | + | 0.966250i | \(0.417066\pi\) | |||||||
\(270\) | −3.17125 | −0.192996 | ||||||||
\(271\) | −5.72517 | −0.347779 | −0.173890 | − | 0.984765i | \(-0.555634\pi\) | ||||
−0.173890 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(272\) | −2.79602 | −0.169534 | ||||||||
\(273\) | −0.309739 | −0.0187462 | ||||||||
\(274\) | −37.4008 | −2.25947 | ||||||||
\(275\) | 10.7549 | 0.648542 | ||||||||
\(276\) | −0.102465 | −0.00616765 | ||||||||
\(277\) | −22.3451 | −1.34259 | −0.671293 | − | 0.741192i | \(-0.734261\pi\) | ||||
−0.671293 | + | 0.741192i | \(0.734261\pi\) | |||||||
\(278\) | −17.3294 | −1.03935 | ||||||||
\(279\) | 10.5715 | 0.632901 | ||||||||
\(280\) | −52.4056 | −3.13183 | ||||||||
\(281\) | 6.08074 | 0.362747 | 0.181373 | − | 0.983414i | \(-0.441946\pi\) | ||||
0.181373 | + | 0.983414i | \(0.441946\pi\) | |||||||
\(282\) | −1.64697 | −0.0980755 | ||||||||
\(283\) | −11.4280 | −0.679327 | −0.339663 | − | 0.940547i | \(-0.610313\pi\) | ||||
−0.339663 | + | 0.940547i | \(0.610313\pi\) | |||||||
\(284\) | −2.62209 | −0.155593 | ||||||||
\(285\) | −0.221464 | −0.0131184 | ||||||||
\(286\) | −5.88175 | −0.347795 | ||||||||
\(287\) | 5.55508 | 0.327906 | ||||||||
\(288\) | −8.33829 | −0.491339 | ||||||||
\(289\) | −15.3814 | −0.904791 | ||||||||
\(290\) | −34.4530 | −2.02315 | ||||||||
\(291\) | −0.108308 | −0.00634915 | ||||||||
\(292\) | 3.04008 | 0.177907 | ||||||||
\(293\) | 10.6980 | 0.624983 | 0.312491 | − | 0.949921i | \(-0.398836\pi\) | ||||
0.312491 | + | 0.949921i | \(0.398836\pi\) | |||||||
\(294\) | −1.94246 | −0.113287 | ||||||||
\(295\) | 5.85457 | 0.340866 | ||||||||
\(296\) | −24.3596 | −1.41587 | ||||||||
\(297\) | −1.07289 | −0.0622555 | ||||||||
\(298\) | 21.1038 | 1.22251 | ||||||||
\(299\) | −0.383553 | −0.0221815 | ||||||||
\(300\) | 1.16448 | 0.0672310 | ||||||||
\(301\) | 41.4710 | 2.39035 | ||||||||
\(302\) | −42.3726 | −2.43827 | ||||||||
\(303\) | 0.497547 | 0.0285834 | ||||||||
\(304\) | 2.19333 | 0.125796 | ||||||||
\(305\) | 19.1846 | 1.09851 | ||||||||
\(306\) | −9.08251 | −0.519213 | ||||||||
\(307\) | −28.0803 | −1.60263 | −0.801314 | − | 0.598243i | \(-0.795866\pi\) | ||||
−0.801314 | + | 0.598243i | \(0.795866\pi\) | |||||||
\(308\) | −38.8008 | −2.21088 | ||||||||
\(309\) | 0.896866 | 0.0510209 | ||||||||
\(310\) | −25.7440 | −1.46216 | ||||||||
\(311\) | −16.3006 | −0.924325 | −0.462162 | − | 0.886795i | \(-0.652926\pi\) | ||||
−0.462162 | + | 0.886795i | \(0.652926\pi\) | |||||||
\(312\) | −0.291001 | −0.0164747 | ||||||||
\(313\) | −24.1431 | −1.36465 | −0.682326 | − | 0.731048i | \(-0.739031\pi\) | ||||
−0.682326 | + | 0.731048i | \(0.739031\pi\) | |||||||
\(314\) | −43.0315 | −2.42841 | ||||||||
\(315\) | −39.1205 | −2.20419 | ||||||||
\(316\) | 16.7739 | 0.943605 | ||||||||
\(317\) | 9.14823 | 0.513816 | 0.256908 | − | 0.966436i | \(-0.417296\pi\) | ||||
0.256908 | + | 0.966436i | \(0.417296\pi\) | |||||||
\(318\) | 1.90447 | 0.106797 | ||||||||
\(319\) | −11.6561 | −0.652616 | ||||||||
\(320\) | 33.7524 | 1.88682 | ||||||||
\(321\) | 0.239682 | 0.0133778 | ||||||||
\(322\) | −3.90428 | −0.217577 | ||||||||
\(323\) | −1.26967 | −0.0706461 | ||||||||
\(324\) | 32.9715 | 1.83175 | ||||||||
\(325\) | 4.35895 | 0.241791 | ||||||||
\(326\) | 19.4777 | 1.07877 | ||||||||
\(327\) | 0.139147 | 0.00769482 | ||||||||
\(328\) | 5.21903 | 0.288173 | ||||||||
\(329\) | −40.6697 | −2.24219 | ||||||||
\(330\) | 1.30522 | 0.0718499 | ||||||||
\(331\) | 11.9367 | 0.656102 | 0.328051 | − | 0.944660i | \(-0.393608\pi\) | ||||
0.328051 | + | 0.944660i | \(0.393608\pi\) | |||||||
\(332\) | 40.1363 | 2.20276 | ||||||||
\(333\) | −18.1843 | −0.996493 | ||||||||
\(334\) | −30.6804 | −1.67876 | ||||||||
\(335\) | 5.56607 | 0.304107 | ||||||||
\(336\) | −0.680726 | −0.0371367 | ||||||||
\(337\) | −18.4406 | −1.00453 | −0.502263 | − | 0.864715i | \(-0.667499\pi\) | ||||
−0.502263 | + | 0.864715i | \(0.667499\pi\) | |||||||
\(338\) | −2.38388 | −0.129666 | ||||||||
\(339\) | 0.877302 | 0.0476485 | ||||||||
\(340\) | 14.3338 | 0.777361 | ||||||||
\(341\) | −8.70967 | −0.471655 | ||||||||
\(342\) | 7.12473 | 0.385261 | ||||||||
\(343\) | −18.0762 | −0.976025 | ||||||||
\(344\) | 38.9622 | 2.10070 | ||||||||
\(345\) | 0.0851142 | 0.00458240 | ||||||||
\(346\) | −15.5274 | −0.834760 | ||||||||
\(347\) | −17.0338 | −0.914425 | −0.457212 | − | 0.889358i | \(-0.651152\pi\) | ||||
−0.457212 | + | 0.889358i | \(0.651152\pi\) | |||||||
\(348\) | −1.26206 | −0.0676533 | ||||||||
\(349\) | 34.5070 | 1.84712 | 0.923559 | − | 0.383456i | \(-0.125266\pi\) | ||||
0.923559 | + | 0.383456i | \(0.125266\pi\) | |||||||
\(350\) | 44.3708 | 2.37172 | ||||||||
\(351\) | −0.434844 | −0.0232102 | ||||||||
\(352\) | 6.86975 | 0.366159 | ||||||||
\(353\) | −11.9159 | −0.634218 | −0.317109 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317109 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(354\) | 0.330924 | 0.0175884 | ||||||||
\(355\) | 2.17809 | 0.115601 | ||||||||
\(356\) | 3.51935 | 0.186525 | ||||||||
\(357\) | 0.394057 | 0.0208557 | ||||||||
\(358\) | 6.86537 | 0.362846 | ||||||||
\(359\) | 26.4579 | 1.39640 | 0.698198 | − | 0.715905i | \(-0.253985\pi\) | ||||
0.698198 | + | 0.715905i | \(0.253985\pi\) | |||||||
\(360\) | −36.7540 | −1.93710 | ||||||||
\(361\) | −18.0040 | −0.947580 | ||||||||
\(362\) | 19.5378 | 1.02688 | ||||||||
\(363\) | −0.356334 | −0.0187027 | ||||||||
\(364\) | −15.7260 | −0.824265 | ||||||||
\(365\) | −2.52531 | −0.132181 | ||||||||
\(366\) | 1.08439 | 0.0566821 | ||||||||
\(367\) | −12.1968 | −0.636668 | −0.318334 | − | 0.947979i | \(-0.603123\pi\) | ||||
−0.318334 | + | 0.947979i | \(0.603123\pi\) | |||||||
\(368\) | −0.842952 | −0.0439419 | ||||||||
\(369\) | 3.89598 | 0.202817 | ||||||||
\(370\) | 44.2828 | 2.30215 | ||||||||
\(371\) | 47.0283 | 2.44159 | ||||||||
\(372\) | −0.943034 | −0.0488940 | ||||||||
\(373\) | 13.3334 | 0.690379 | 0.345190 | − | 0.938533i | \(-0.387815\pi\) | ||||
0.345190 | + | 0.938533i | \(0.387815\pi\) | |||||||
\(374\) | 7.48290 | 0.386932 | ||||||||
\(375\) | 0.142255 | 0.00734603 | ||||||||
\(376\) | −38.2094 | −1.97050 | ||||||||
\(377\) | −4.72422 | −0.243310 | ||||||||
\(378\) | −4.42638 | −0.227669 | ||||||||
\(379\) | −12.2663 | −0.630079 | −0.315040 | − | 0.949079i | \(-0.602018\pi\) | ||||
−0.315040 | + | 0.949079i | \(0.602018\pi\) | |||||||
\(380\) | −11.2441 | −0.576810 | ||||||||
\(381\) | 0.772927 | 0.0395982 | ||||||||
\(382\) | −20.7412 | −1.06121 | ||||||||
\(383\) | 38.0672 | 1.94514 | 0.972571 | − | 0.232605i | \(-0.0747250\pi\) | ||||
0.972571 | + | 0.232605i | \(0.0747250\pi\) | |||||||
\(384\) | 1.50389 | 0.0767450 | ||||||||
\(385\) | 32.2306 | 1.64262 | ||||||||
\(386\) | −13.9206 | −0.708540 | ||||||||
\(387\) | 29.0851 | 1.47848 | ||||||||
\(388\) | −5.49901 | −0.279170 | ||||||||
\(389\) | −16.7141 | −0.847439 | −0.423719 | − | 0.905794i | \(-0.639276\pi\) | ||||
−0.423719 | + | 0.905794i | \(0.639276\pi\) | |||||||
\(390\) | 0.529005 | 0.0267872 | ||||||||
\(391\) | 0.487966 | 0.0246775 | ||||||||
\(392\) | −45.0648 | −2.27612 | ||||||||
\(393\) | 0.893505 | 0.0450714 | ||||||||
\(394\) | 7.91055 | 0.398528 | ||||||||
\(395\) | −13.9335 | −0.701073 | ||||||||
\(396\) | −27.2124 | −1.36748 | ||||||||
\(397\) | −15.3935 | −0.772579 | −0.386290 | − | 0.922378i | \(-0.626243\pi\) | ||||
−0.386290 | + | 0.922378i | \(0.626243\pi\) | |||||||
\(398\) | 64.9456 | 3.25543 | ||||||||
\(399\) | −0.309116 | −0.0154751 | ||||||||
\(400\) | 9.57986 | 0.478993 | ||||||||
\(401\) | 21.8936 | 1.09332 | 0.546658 | − | 0.837356i | \(-0.315900\pi\) | ||||
0.546658 | + | 0.837356i | \(0.315900\pi\) | |||||||
\(402\) | 0.314617 | 0.0156917 | ||||||||
\(403\) | −3.53003 | −0.175843 | ||||||||
\(404\) | 25.2614 | 1.25680 | ||||||||
\(405\) | −27.3884 | −1.36094 | ||||||||
\(406\) | −48.0890 | −2.38662 | ||||||||
\(407\) | 14.9817 | 0.742614 | ||||||||
\(408\) | 0.370219 | 0.0183286 | ||||||||
\(409\) | −25.2287 | −1.24748 | −0.623739 | − | 0.781633i | \(-0.714387\pi\) | ||||
−0.623739 | + | 0.781633i | \(0.714387\pi\) | |||||||
\(410\) | −9.48758 | −0.468558 | ||||||||
\(411\) | 1.13805 | 0.0561358 | ||||||||
\(412\) | 45.5355 | 2.24337 | ||||||||
\(413\) | 8.17173 | 0.402104 | ||||||||
\(414\) | −2.73822 | −0.134576 | ||||||||
\(415\) | −33.3400 | −1.63659 | ||||||||
\(416\) | 2.78431 | 0.136512 | ||||||||
\(417\) | 0.527307 | 0.0258224 | ||||||||
\(418\) | −5.86992 | −0.287107 | ||||||||
\(419\) | −18.4756 | −0.902594 | −0.451297 | − | 0.892374i | \(-0.649039\pi\) | ||||
−0.451297 | + | 0.892374i | \(0.649039\pi\) | |||||||
\(420\) | 3.48975 | 0.170282 | ||||||||
\(421\) | −2.85206 | −0.139001 | −0.0695004 | − | 0.997582i | \(-0.522141\pi\) | ||||
−0.0695004 | + | 0.997582i | \(0.522141\pi\) | |||||||
\(422\) | 28.2869 | 1.37698 | ||||||||
\(423\) | −28.5232 | −1.38684 | ||||||||
\(424\) | 44.1833 | 2.14573 | ||||||||
\(425\) | −5.54556 | −0.268999 | ||||||||
\(426\) | 0.123115 | 0.00596492 | ||||||||
\(427\) | 26.7776 | 1.29586 | ||||||||
\(428\) | 12.1691 | 0.588215 | ||||||||
\(429\) | 0.178972 | 0.00864086 | ||||||||
\(430\) | −70.8286 | −3.41566 | ||||||||
\(431\) | −33.4160 | −1.60959 | −0.804795 | − | 0.593552i | \(-0.797725\pi\) | ||||
−0.804795 | + | 0.593552i | \(0.797725\pi\) | |||||||
\(432\) | −0.955675 | −0.0459799 | ||||||||
\(433\) | 28.3945 | 1.36455 | 0.682276 | − | 0.731095i | \(-0.260990\pi\) | ||||
0.682276 | + | 0.731095i | \(0.260990\pi\) | |||||||
\(434\) | −35.9331 | −1.72484 | ||||||||
\(435\) | 1.04835 | 0.0502646 | ||||||||
\(436\) | 7.06472 | 0.338339 | ||||||||
\(437\) | −0.382782 | −0.0183110 | ||||||||
\(438\) | −0.142740 | −0.00682040 | ||||||||
\(439\) | −8.88657 | −0.424133 | −0.212066 | − | 0.977255i | \(-0.568019\pi\) | ||||
−0.212066 | + | 0.977255i | \(0.568019\pi\) | |||||||
\(440\) | 30.2809 | 1.44358 | ||||||||
\(441\) | −33.6407 | −1.60194 | ||||||||
\(442\) | 3.03282 | 0.144257 | ||||||||
\(443\) | 34.8510 | 1.65582 | 0.827911 | − | 0.560859i | \(-0.189529\pi\) | ||||
0.827911 | + | 0.560859i | \(0.189529\pi\) | |||||||
\(444\) | 1.62213 | 0.0769829 | ||||||||
\(445\) | −2.92341 | −0.138583 | ||||||||
\(446\) | −37.1209 | −1.75773 | ||||||||
\(447\) | −0.642154 | −0.0303729 | ||||||||
\(448\) | 47.1112 | 2.22579 | ||||||||
\(449\) | 6.71237 | 0.316776 | 0.158388 | − | 0.987377i | \(-0.449370\pi\) | ||||
0.158388 | + | 0.987377i | \(0.449370\pi\) | |||||||
\(450\) | 31.1189 | 1.46696 | ||||||||
\(451\) | −3.20982 | −0.151145 | ||||||||
\(452\) | 44.5422 | 2.09509 | ||||||||
\(453\) | 1.28933 | 0.0605781 | ||||||||
\(454\) | 41.0854 | 1.92823 | ||||||||
\(455\) | 13.0631 | 0.612407 | ||||||||
\(456\) | −0.290416 | −0.0136000 | ||||||||
\(457\) | −12.9944 | −0.607853 | −0.303926 | − | 0.952696i | \(-0.598298\pi\) | ||||
−0.303926 | + | 0.952696i | \(0.598298\pi\) | |||||||
\(458\) | −7.35653 | −0.343748 | ||||||||
\(459\) | 0.553219 | 0.0258220 | ||||||||
\(460\) | 4.32140 | 0.201486 | ||||||||
\(461\) | −28.0745 | −1.30756 | −0.653779 | − | 0.756686i | \(-0.726817\pi\) | ||||
−0.653779 | + | 0.756686i | \(0.726817\pi\) | |||||||
\(462\) | 1.82180 | 0.0847580 | ||||||||
\(463\) | 16.3439 | 0.759566 | 0.379783 | − | 0.925076i | \(-0.375999\pi\) | ||||
0.379783 | + | 0.925076i | \(0.375999\pi\) | |||||||
\(464\) | −10.3826 | −0.482001 | ||||||||
\(465\) | 0.783349 | 0.0363269 | ||||||||
\(466\) | −69.2329 | −3.20715 | ||||||||
\(467\) | 7.07365 | 0.327330 | 0.163665 | − | 0.986516i | \(-0.447668\pi\) | ||||
0.163665 | + | 0.986516i | \(0.447668\pi\) | |||||||
\(468\) | −11.0292 | −0.509825 | ||||||||
\(469\) | 7.76904 | 0.358741 | ||||||||
\(470\) | 69.4602 | 3.20396 | ||||||||
\(471\) | 1.30938 | 0.0603330 | ||||||||
\(472\) | 7.67739 | 0.353380 | ||||||||
\(473\) | −23.9626 | −1.10180 | ||||||||
\(474\) | −0.787580 | −0.0361747 | ||||||||
\(475\) | 4.35019 | 0.199600 | ||||||||
\(476\) | 20.0070 | 0.917018 | ||||||||
\(477\) | 32.9826 | 1.51017 | ||||||||
\(478\) | −14.6128 | −0.668373 | ||||||||
\(479\) | 30.3242 | 1.38555 | 0.692774 | − | 0.721154i | \(-0.256388\pi\) | ||||
0.692774 | + | 0.721154i | \(0.256388\pi\) | |||||||
\(480\) | −0.617867 | −0.0282016 | ||||||||
\(481\) | 6.07208 | 0.276863 | ||||||||
\(482\) | 28.7273 | 1.30849 | ||||||||
\(483\) | 0.118801 | 0.00540564 | ||||||||
\(484\) | −18.0917 | −0.822350 | ||||||||
\(485\) | 4.56786 | 0.207416 | ||||||||
\(486\) | −4.65794 | −0.211288 | ||||||||
\(487\) | −9.57286 | −0.433788 | −0.216894 | − | 0.976195i | \(-0.569593\pi\) | ||||
−0.216894 | + | 0.976195i | \(0.569593\pi\) | |||||||
\(488\) | 25.1578 | 1.13884 | ||||||||
\(489\) | −0.592675 | −0.0268017 | ||||||||
\(490\) | 81.9225 | 3.70088 | ||||||||
\(491\) | −21.2584 | −0.959378 | −0.479689 | − | 0.877439i | \(-0.659250\pi\) | ||||
−0.479689 | + | 0.877439i | \(0.659250\pi\) | |||||||
\(492\) | −0.347541 | −0.0156684 | ||||||||
\(493\) | 6.01026 | 0.270689 | ||||||||
\(494\) | −2.37908 | −0.107040 | ||||||||
\(495\) | 22.6045 | 1.01600 | ||||||||
\(496\) | −7.75811 | −0.348349 | ||||||||
\(497\) | 3.04015 | 0.136369 | ||||||||
\(498\) | −1.88451 | −0.0844468 | ||||||||
\(499\) | −0.956576 | −0.0428222 | −0.0214111 | − | 0.999771i | \(-0.506816\pi\) | ||||
−0.0214111 | + | 0.999771i | \(0.506816\pi\) | |||||||
\(500\) | 7.22256 | 0.323003 | ||||||||
\(501\) | 0.933556 | 0.0417082 | ||||||||
\(502\) | 24.4059 | 1.08929 | ||||||||
\(503\) | 8.33514 | 0.371645 | 0.185823 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185823 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(504\) | −51.3007 | −2.28511 | ||||||||
\(505\) | −20.9838 | −0.933769 | ||||||||
\(506\) | 2.25596 | 0.100290 | ||||||||
\(507\) | 0.0725376 | 0.00322151 | ||||||||
\(508\) | 39.2429 | 1.74112 | ||||||||
\(509\) | 28.7913 | 1.27615 | 0.638075 | − | 0.769974i | \(-0.279731\pi\) | ||||
0.638075 | + | 0.769974i | \(0.279731\pi\) | |||||||
\(510\) | −0.673013 | −0.0298015 | ||||||||
\(511\) | −3.52478 | −0.155927 | ||||||||
\(512\) | 23.7527 | 1.04973 | ||||||||
\(513\) | −0.433969 | −0.0191602 | ||||||||
\(514\) | 75.6674 | 3.33755 | ||||||||
\(515\) | −37.8249 | −1.66677 | ||||||||
\(516\) | −2.59454 | −0.114218 | ||||||||
\(517\) | 23.4997 | 1.03351 | ||||||||
\(518\) | 61.8092 | 2.71574 | ||||||||
\(519\) | 0.472475 | 0.0207394 | ||||||||
\(520\) | 12.2728 | 0.538200 | ||||||||
\(521\) | −20.7726 | −0.910066 | −0.455033 | − | 0.890475i | \(-0.650373\pi\) | ||||
−0.455033 | + | 0.890475i | \(0.650373\pi\) | |||||||
\(522\) | −33.7266 | −1.47617 | ||||||||
\(523\) | 2.94231 | 0.128658 | 0.0643292 | − | 0.997929i | \(-0.479509\pi\) | ||||
0.0643292 | + | 0.997929i | \(0.479509\pi\) | |||||||
\(524\) | 45.3649 | 1.98177 | ||||||||
\(525\) | −1.35013 | −0.0589247 | ||||||||
\(526\) | −37.6387 | −1.64113 | ||||||||
\(527\) | 4.49099 | 0.195631 | ||||||||
\(528\) | 0.393335 | 0.0171177 | ||||||||
\(529\) | −22.8529 | −0.993604 | ||||||||
\(530\) | −80.3200 | −3.48888 | ||||||||
\(531\) | 5.73113 | 0.248710 | ||||||||
\(532\) | −15.6944 | −0.680437 | ||||||||
\(533\) | −1.30094 | −0.0563501 | ||||||||
\(534\) | −0.165243 | −0.00715077 | ||||||||
\(535\) | −10.1085 | −0.437028 | ||||||||
\(536\) | 7.29906 | 0.315272 | ||||||||
\(537\) | −0.208902 | −0.00901480 | ||||||||
\(538\) | −20.1440 | −0.868472 | ||||||||
\(539\) | 27.7159 | 1.19381 | ||||||||
\(540\) | 4.89928 | 0.210831 | ||||||||
\(541\) | 2.54836 | 0.109562 | 0.0547812 | − | 0.998498i | \(-0.482554\pi\) | ||||
0.0547812 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(542\) | 13.6481 | 0.586236 | ||||||||
\(543\) | −0.594504 | −0.0255126 | ||||||||
\(544\) | −3.54227 | −0.151874 | ||||||||
\(545\) | −5.86845 | −0.251377 | ||||||||
\(546\) | 0.738378 | 0.0315997 | ||||||||
\(547\) | 29.7942 | 1.27391 | 0.636954 | − | 0.770902i | \(-0.280194\pi\) | ||||
0.636954 | + | 0.770902i | \(0.280194\pi\) | |||||||
\(548\) | 57.7807 | 2.46827 | ||||||||
\(549\) | 18.7801 | 0.801517 | ||||||||
\(550\) | −25.6382 | −1.09322 | ||||||||
\(551\) | −4.71472 | −0.200854 | ||||||||
\(552\) | 0.111614 | 0.00475063 | ||||||||
\(553\) | −19.4482 | −0.827024 | ||||||||
\(554\) | 53.2679 | 2.26314 | ||||||||
\(555\) | −1.34745 | −0.0571962 | ||||||||
\(556\) | 26.7723 | 1.13540 | ||||||||
\(557\) | 6.02751 | 0.255394 | 0.127697 | − | 0.991813i | \(-0.459242\pi\) | ||||
0.127697 | + | 0.991813i | \(0.459242\pi\) | |||||||
\(558\) | −25.2012 | −1.06685 | ||||||||
\(559\) | −9.71207 | −0.410777 | ||||||||
\(560\) | 28.7093 | 1.21319 | ||||||||
\(561\) | −0.227693 | −0.00961320 | ||||||||
\(562\) | −14.4957 | −0.611466 | ||||||||
\(563\) | −35.0784 | −1.47838 | −0.739188 | − | 0.673499i | \(-0.764791\pi\) | ||||
−0.739188 | + | 0.673499i | \(0.764791\pi\) | |||||||
\(564\) | 2.54441 | 0.107139 | ||||||||
\(565\) | −36.9998 | −1.55659 | ||||||||
\(566\) | 27.2430 | 1.14511 | ||||||||
\(567\) | −38.2283 | −1.60544 | ||||||||
\(568\) | 2.85624 | 0.119845 | ||||||||
\(569\) | 2.47185 | 0.103625 | 0.0518127 | − | 0.998657i | \(-0.483500\pi\) | ||||
0.0518127 | + | 0.998657i | \(0.483500\pi\) | |||||||
\(570\) | 0.527942 | 0.0221130 | ||||||||
\(571\) | −6.18518 | −0.258842 | −0.129421 | − | 0.991590i | \(-0.541312\pi\) | ||||
−0.129421 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(572\) | 9.08674 | 0.379936 | ||||||||
\(573\) | 0.631121 | 0.0263654 | ||||||||
\(574\) | −13.2426 | −0.552736 | ||||||||
\(575\) | −1.67189 | −0.0697226 | ||||||||
\(576\) | 33.0408 | 1.37670 | ||||||||
\(577\) | −22.5398 | −0.938345 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(578\) | 36.6674 | 1.52516 | ||||||||
\(579\) | 0.423582 | 0.0176035 | ||||||||
\(580\) | 53.2266 | 2.21012 | ||||||||
\(581\) | −46.5354 | −1.93061 | ||||||||
\(582\) | 0.258194 | 0.0107025 | ||||||||
\(583\) | −27.1737 | −1.12542 | ||||||||
\(584\) | −3.31156 | −0.137033 | ||||||||
\(585\) | 9.16162 | 0.378787 | ||||||||
\(586\) | −25.5027 | −1.05350 | ||||||||
\(587\) | −12.5970 | −0.519935 | −0.259968 | − | 0.965617i | \(-0.583712\pi\) | ||||
−0.259968 | + | 0.965617i | \(0.583712\pi\) | |||||||
\(588\) | 3.00092 | 0.123756 | ||||||||
\(589\) | −3.52294 | −0.145160 | ||||||||
\(590\) | −13.9566 | −0.574583 | ||||||||
\(591\) | −0.240706 | −0.00990130 | ||||||||
\(592\) | 13.3449 | 0.548471 | ||||||||
\(593\) | −37.3313 | −1.53301 | −0.766507 | − | 0.642236i | \(-0.778007\pi\) | ||||
−0.766507 | + | 0.642236i | \(0.778007\pi\) | |||||||
\(594\) | 2.55764 | 0.104941 | ||||||||
\(595\) | −16.6192 | −0.681320 | ||||||||
\(596\) | −32.6033 | −1.33548 | ||||||||
\(597\) | −1.97619 | −0.0808801 | ||||||||
\(598\) | 0.914343 | 0.0373903 | ||||||||
\(599\) | 9.83716 | 0.401935 | 0.200968 | − | 0.979598i | \(-0.435591\pi\) | ||||
0.200968 | + | 0.979598i | \(0.435591\pi\) | |||||||
\(600\) | −1.26846 | −0.0517846 | ||||||||
\(601\) | −20.3438 | −0.829842 | −0.414921 | − | 0.909857i | \(-0.636191\pi\) | ||||
−0.414921 | + | 0.909857i | \(0.636191\pi\) | |||||||
\(602\) | −98.8616 | −4.02930 | ||||||||
\(603\) | 5.44872 | 0.221889 | ||||||||
\(604\) | 65.4617 | 2.66360 | ||||||||
\(605\) | 15.0282 | 0.610984 | ||||||||
\(606\) | −1.18609 | −0.0481817 | ||||||||
\(607\) | −12.8597 | −0.521960 | −0.260980 | − | 0.965344i | \(-0.584046\pi\) | ||||
−0.260980 | + | 0.965344i | \(0.584046\pi\) | |||||||
\(608\) | 2.77872 | 0.112692 | ||||||||
\(609\) | 1.46327 | 0.0592948 | ||||||||
\(610\) | −45.7338 | −1.85171 | ||||||||
\(611\) | 9.52442 | 0.385317 | ||||||||
\(612\) | 14.0316 | 0.567195 | ||||||||
\(613\) | 31.9646 | 1.29104 | 0.645518 | − | 0.763745i | \(-0.276641\pi\) | ||||
0.645518 | + | 0.763745i | \(0.276641\pi\) | |||||||
\(614\) | 66.9400 | 2.70148 | ||||||||
\(615\) | 0.288692 | 0.0116412 | ||||||||
\(616\) | 42.2656 | 1.70293 | ||||||||
\(617\) | 1.00000 | 0.0402585 | ||||||||
\(618\) | −2.13802 | −0.0860036 | ||||||||
\(619\) | −13.9613 | −0.561153 | −0.280576 | − | 0.959832i | \(-0.590526\pi\) | ||||
−0.280576 | + | 0.959832i | \(0.590526\pi\) | |||||||
\(620\) | 39.7720 | 1.59728 | ||||||||
\(621\) | 0.166786 | 0.00669288 | ||||||||
\(622\) | 38.8587 | 1.55809 | ||||||||
\(623\) | −4.08046 | −0.163480 | ||||||||
\(624\) | 0.159419 | 0.00638187 | ||||||||
\(625\) | −27.7943 | −1.11177 | ||||||||
\(626\) | 57.5542 | 2.30033 | ||||||||
\(627\) | 0.178612 | 0.00713310 | ||||||||
\(628\) | 66.4795 | 2.65282 | ||||||||
\(629\) | −7.72505 | −0.308018 | ||||||||
\(630\) | 93.2585 | 3.71551 | ||||||||
\(631\) | −6.64143 | −0.264391 | −0.132196 | − | 0.991224i | \(-0.542203\pi\) | ||||
−0.132196 | + | 0.991224i | \(0.542203\pi\) | |||||||
\(632\) | −18.2717 | −0.726811 | ||||||||
\(633\) | −0.860725 | −0.0342107 | ||||||||
\(634\) | −21.8082 | −0.866116 | ||||||||
\(635\) | −32.5979 | −1.29361 | ||||||||
\(636\) | −2.94222 | −0.116667 | ||||||||
\(637\) | 11.2333 | 0.445078 | ||||||||
\(638\) | 27.7867 | 1.10008 | ||||||||
\(639\) | 2.13217 | 0.0843473 | ||||||||
\(640\) | −63.4258 | −2.50713 | ||||||||
\(641\) | 10.9178 | 0.431228 | 0.215614 | − | 0.976479i | \(-0.430825\pi\) | ||||
0.215614 | + | 0.976479i | \(0.430825\pi\) | |||||||
\(642\) | −0.571372 | −0.0225503 | ||||||||
\(643\) | −18.3957 | −0.725454 | −0.362727 | − | 0.931895i | \(-0.618154\pi\) | ||||
−0.362727 | + | 0.931895i | \(0.618154\pi\) | |||||||
\(644\) | 6.03175 | 0.237684 | ||||||||
\(645\) | 2.15520 | 0.0848611 | ||||||||
\(646\) | 3.02673 | 0.119085 | ||||||||
\(647\) | 9.93421 | 0.390554 | 0.195277 | − | 0.980748i | \(-0.437439\pi\) | ||||
0.195277 | + | 0.980748i | \(0.437439\pi\) | |||||||
\(648\) | −35.9157 | −1.41090 | ||||||||
\(649\) | −4.72177 | −0.185346 | ||||||||
\(650\) | −10.3912 | −0.407576 | ||||||||
\(651\) | 1.09339 | 0.0428532 | ||||||||
\(652\) | −30.0912 | −1.17846 | ||||||||
\(653\) | −19.6078 | −0.767312 | −0.383656 | − | 0.923476i | \(-0.625335\pi\) | ||||
−0.383656 | + | 0.923476i | \(0.625335\pi\) | |||||||
\(654\) | −0.331708 | −0.0129708 | ||||||||
\(655\) | −37.6832 | −1.47240 | ||||||||
\(656\) | −2.85914 | −0.111631 | ||||||||
\(657\) | −2.47206 | −0.0964443 | ||||||||
\(658\) | 96.9515 | 3.77956 | ||||||||
\(659\) | 20.1274 | 0.784052 | 0.392026 | − | 0.919954i | \(-0.371774\pi\) | ||||
0.392026 | + | 0.919954i | \(0.371774\pi\) | |||||||
\(660\) | −2.01644 | −0.0784897 | ||||||||
\(661\) | −4.93888 | −0.192100 | −0.0960502 | − | 0.995376i | \(-0.530621\pi\) | ||||
−0.0960502 | + | 0.995376i | \(0.530621\pi\) | |||||||
\(662\) | −28.4557 | −1.10596 | ||||||||
\(663\) | −0.0922840 | −0.00358401 | ||||||||
\(664\) | −43.7203 | −1.69668 | ||||||||
\(665\) | 13.0368 | 0.505546 | ||||||||
\(666\) | 43.3491 | 1.67974 | ||||||||
\(667\) | 1.81199 | 0.0701605 | ||||||||
\(668\) | 47.3983 | 1.83390 | ||||||||
\(669\) | 1.12953 | 0.0436702 | ||||||||
\(670\) | −13.2688 | −0.512619 | ||||||||
\(671\) | −15.4726 | −0.597313 | ||||||||
\(672\) | −0.862409 | −0.0332682 | ||||||||
\(673\) | 45.9981 | 1.77310 | 0.886548 | − | 0.462636i | \(-0.153096\pi\) | ||||
0.886548 | + | 0.462636i | \(0.153096\pi\) | |||||||
\(674\) | 43.9602 | 1.69328 | ||||||||
\(675\) | −1.89546 | −0.0729564 | ||||||||
\(676\) | 3.68286 | 0.141649 | ||||||||
\(677\) | 19.3094 | 0.742119 | 0.371060 | − | 0.928609i | \(-0.378995\pi\) | ||||
0.371060 | + | 0.928609i | \(0.378995\pi\) | |||||||
\(678\) | −2.09138 | −0.0803189 | ||||||||
\(679\) | 6.37575 | 0.244679 | ||||||||
\(680\) | −15.6138 | −0.598762 | ||||||||
\(681\) | −1.25016 | −0.0479064 | ||||||||
\(682\) | 20.7628 | 0.795047 | ||||||||
\(683\) | 37.1164 | 1.42022 | 0.710110 | − | 0.704091i | \(-0.248645\pi\) | ||||
0.710110 | + | 0.704091i | \(0.248645\pi\) | |||||||
\(684\) | −11.0070 | −0.420864 | ||||||||
\(685\) | −47.9967 | −1.83386 | ||||||||
\(686\) | 43.0915 | 1.64524 | ||||||||
\(687\) | 0.223847 | 0.00854031 | ||||||||
\(688\) | −21.3446 | −0.813757 | ||||||||
\(689\) | −11.0135 | −0.419582 | ||||||||
\(690\) | −0.202902 | −0.00772434 | ||||||||
\(691\) | 2.20217 | 0.0837745 | 0.0418872 | − | 0.999122i | \(-0.486663\pi\) | ||||
0.0418872 | + | 0.999122i | \(0.486663\pi\) | |||||||
\(692\) | 23.9884 | 0.911903 | ||||||||
\(693\) | 31.5511 | 1.19853 | ||||||||
\(694\) | 40.6066 | 1.54140 | ||||||||
\(695\) | −22.2390 | −0.843572 | ||||||||
\(696\) | 1.37475 | 0.0521099 | ||||||||
\(697\) | 1.65509 | 0.0626910 | ||||||||
\(698\) | −82.2604 | −3.11360 | ||||||||
\(699\) | 2.10665 | 0.0796807 | ||||||||
\(700\) | −68.5487 | −2.59090 | ||||||||
\(701\) | 3.88779 | 0.146840 | 0.0734199 | − | 0.997301i | \(-0.476609\pi\) | ||||
0.0734199 | + | 0.997301i | \(0.476609\pi\) | |||||||
\(702\) | 1.03661 | 0.0391244 | ||||||||
\(703\) | 6.05987 | 0.228552 | ||||||||
\(704\) | −27.2216 | −1.02595 | ||||||||
\(705\) | −2.11356 | −0.0796014 | ||||||||
\(706\) | 28.4060 | 1.06907 | ||||||||
\(707\) | −29.2889 | −1.10152 | ||||||||
\(708\) | −0.511246 | −0.0192138 | ||||||||
\(709\) | 13.5534 | 0.509009 | 0.254504 | − | 0.967072i | \(-0.418088\pi\) | ||||
0.254504 | + | 0.967072i | \(0.418088\pi\) | |||||||
\(710\) | −5.19230 | −0.194864 | ||||||||
\(711\) | −13.6398 | −0.511531 | ||||||||
\(712\) | −3.83362 | −0.143671 | ||||||||
\(713\) | 1.35396 | 0.0507060 | ||||||||
\(714\) | −0.939382 | −0.0351555 | ||||||||
\(715\) | −7.54808 | −0.282282 | ||||||||
\(716\) | −10.6063 | −0.396378 | ||||||||
\(717\) | 0.444644 | 0.0166055 | ||||||||
\(718\) | −63.0724 | −2.35384 | ||||||||
\(719\) | 48.4984 | 1.80869 | 0.904343 | − | 0.426807i | \(-0.140362\pi\) | ||||
0.904343 | + | 0.426807i | \(0.140362\pi\) | |||||||
\(720\) | 20.1349 | 0.750384 | ||||||||
\(721\) | −52.7955 | −1.96621 | ||||||||
\(722\) | 42.9193 | 1.59729 | ||||||||
\(723\) | −0.874127 | −0.0325091 | ||||||||
\(724\) | −30.1840 | −1.12178 | ||||||||
\(725\) | −20.5926 | −0.764791 | ||||||||
\(726\) | 0.849455 | 0.0315262 | ||||||||
\(727\) | 38.6817 | 1.43462 | 0.717312 | − | 0.696752i | \(-0.245372\pi\) | ||||
0.717312 | + | 0.696752i | \(0.245372\pi\) | |||||||
\(728\) | 17.1303 | 0.634890 | ||||||||
\(729\) | −26.7163 | −0.989492 | ||||||||
\(730\) | 6.02001 | 0.222811 | ||||||||
\(731\) | 12.3559 | 0.457000 | ||||||||
\(732\) | −1.67528 | −0.0619203 | ||||||||
\(733\) | −32.9949 | −1.21869 | −0.609347 | − | 0.792904i | \(-0.708568\pi\) | ||||
−0.609347 | + | 0.792904i | \(0.708568\pi\) | |||||||
\(734\) | 29.0757 | 1.07320 | ||||||||
\(735\) | −2.49277 | −0.0919473 | ||||||||
\(736\) | −1.06793 | −0.0393645 | ||||||||
\(737\) | −4.48909 | −0.165358 | ||||||||
\(738\) | −9.28754 | −0.341879 | ||||||||
\(739\) | 19.5545 | 0.719322 | 0.359661 | − | 0.933083i | \(-0.382892\pi\) | ||||
0.359661 | + | 0.933083i | \(0.382892\pi\) | |||||||
\(740\) | −68.4126 | −2.51490 | ||||||||
\(741\) | 0.0723917 | 0.00265938 | ||||||||
\(742\) | −112.110 | −4.11567 | ||||||||
\(743\) | −26.5914 | −0.975542 | −0.487771 | − | 0.872972i | \(-0.662190\pi\) | ||||
−0.487771 | + | 0.872972i | \(0.662190\pi\) | |||||||
\(744\) | 1.02724 | 0.0376606 | ||||||||
\(745\) | 27.0826 | 0.992229 | ||||||||
\(746\) | −31.7853 | −1.16374 | ||||||||
\(747\) | −32.6370 | −1.19413 | ||||||||
\(748\) | −11.5604 | −0.422689 | ||||||||
\(749\) | −14.1093 | −0.515542 | ||||||||
\(750\) | −0.339119 | −0.0123829 | ||||||||
\(751\) | −14.7040 | −0.536556 | −0.268278 | − | 0.963342i | \(-0.586455\pi\) | ||||
−0.268278 | + | 0.963342i | \(0.586455\pi\) | |||||||
\(752\) | 20.9323 | 0.763321 | ||||||||
\(753\) | −0.742632 | −0.0270630 | ||||||||
\(754\) | 11.2619 | 0.410136 | ||||||||
\(755\) | −54.3770 | −1.97898 | ||||||||
\(756\) | 6.83834 | 0.248708 | ||||||||
\(757\) | −12.1814 | −0.442740 | −0.221370 | − | 0.975190i | \(-0.571053\pi\) | ||||
−0.221370 | + | 0.975190i | \(0.571053\pi\) | |||||||
\(758\) | 29.2414 | 1.06210 | ||||||||
\(759\) | −0.0686454 | −0.00249167 | ||||||||
\(760\) | 12.2482 | 0.444288 | ||||||||
\(761\) | −19.8061 | −0.717970 | −0.358985 | − | 0.933343i | \(-0.616877\pi\) | ||||
−0.358985 | + | 0.933343i | \(0.616877\pi\) | |||||||
\(762\) | −1.84256 | −0.0667489 | ||||||||
\(763\) | −8.19109 | −0.296537 | ||||||||
\(764\) | 32.0431 | 1.15928 | ||||||||
\(765\) | −11.6556 | −0.421410 | ||||||||
\(766\) | −90.7474 | −3.27884 | ||||||||
\(767\) | −1.91373 | −0.0691009 | ||||||||
\(768\) | −1.98447 | −0.0716086 | ||||||||
\(769\) | 46.1661 | 1.66479 | 0.832397 | − | 0.554181i | \(-0.186968\pi\) | ||||
0.832397 | + | 0.554181i | \(0.186968\pi\) | |||||||
\(770\) | −76.8338 | −2.76890 | ||||||||
\(771\) | −2.30244 | −0.0829204 | ||||||||
\(772\) | 21.5060 | 0.774019 | ||||||||
\(773\) | −29.4075 | −1.05771 | −0.528857 | − | 0.848711i | \(-0.677379\pi\) | ||||
−0.528857 | + | 0.848711i | \(0.677379\pi\) | |||||||
\(774\) | −69.3353 | −2.49220 | ||||||||
\(775\) | −15.3872 | −0.552726 | ||||||||
\(776\) | 5.99006 | 0.215031 | ||||||||
\(777\) | −1.88076 | −0.0674718 | ||||||||
\(778\) | 39.8443 | 1.42849 | ||||||||
\(779\) | −1.29833 | −0.0465174 | ||||||||
\(780\) | −0.817263 | −0.0292627 | ||||||||
\(781\) | −1.75665 | −0.0628580 | ||||||||
\(782\) | −1.16325 | −0.0415977 | ||||||||
\(783\) | 2.05430 | 0.0734146 | ||||||||
\(784\) | 24.6878 | 0.881709 | ||||||||
\(785\) | −55.2225 | −1.97098 | ||||||||
\(786\) | −2.13001 | −0.0759748 | ||||||||
\(787\) | −15.1455 | −0.539880 | −0.269940 | − | 0.962877i | \(-0.587004\pi\) | ||||
−0.269940 | + | 0.962877i | \(0.587004\pi\) | |||||||
\(788\) | −12.2210 | −0.435357 | ||||||||
\(789\) | 1.14529 | 0.0407733 | ||||||||
\(790\) | 33.2158 | 1.18177 | ||||||||
\(791\) | −51.6438 | −1.83624 | ||||||||
\(792\) | 29.6424 | 1.05330 | ||||||||
\(793\) | −6.27105 | −0.222691 | ||||||||
\(794\) | 36.6963 | 1.30230 | ||||||||
\(795\) | 2.44401 | 0.0866801 | ||||||||
\(796\) | −100.335 | −3.55627 | ||||||||
\(797\) | 11.5353 | 0.408601 | 0.204301 | − | 0.978908i | \(-0.434508\pi\) | ||||
0.204301 | + | 0.978908i | \(0.434508\pi\) | |||||||
\(798\) | 0.736893 | 0.0260857 | ||||||||
\(799\) | −12.1172 | −0.428676 | ||||||||
\(800\) | 12.1367 | 0.429097 | ||||||||
\(801\) | −2.86178 | −0.101116 | ||||||||
\(802\) | −52.1917 | −1.84295 | ||||||||
\(803\) | 2.03668 | 0.0718729 | ||||||||
\(804\) | −0.486053 | −0.0171418 | ||||||||
\(805\) | −5.01039 | −0.176593 | ||||||||
\(806\) | 8.41516 | 0.296411 | ||||||||
\(807\) | 0.612952 | 0.0215769 | ||||||||
\(808\) | −27.5171 | −0.968050 | ||||||||
\(809\) | 13.6513 | 0.479954 | 0.239977 | − | 0.970779i | \(-0.422860\pi\) | ||||
0.239977 | + | 0.970779i | \(0.422860\pi\) | |||||||
\(810\) | 65.2905 | 2.29407 | ||||||||
\(811\) | 11.8884 | 0.417459 | 0.208730 | − | 0.977973i | \(-0.433067\pi\) | ||||
0.208730 | + | 0.977973i | \(0.433067\pi\) | |||||||
\(812\) | 74.2929 | 2.60717 | ||||||||
\(813\) | −0.415290 | −0.0145649 | ||||||||
\(814\) | −35.7144 | −1.25179 | ||||||||
\(815\) | 24.9958 | 0.875565 | ||||||||
\(816\) | −0.202817 | −0.00710000 | ||||||||
\(817\) | −9.69254 | −0.339099 | ||||||||
\(818\) | 60.1420 | 2.10282 | ||||||||
\(819\) | 12.7877 | 0.446837 | ||||||||
\(820\) | 14.6574 | 0.511859 | ||||||||
\(821\) | 47.8997 | 1.67171 | 0.835855 | − | 0.548950i | \(-0.184972\pi\) | ||||
0.835855 | + | 0.548950i | \(0.184972\pi\) | |||||||
\(822\) | −2.71296 | −0.0946255 | ||||||||
\(823\) | 3.92822 | 0.136929 | 0.0684646 | − | 0.997654i | \(-0.478190\pi\) | ||||
0.0684646 | + | 0.997654i | \(0.478190\pi\) | |||||||
\(824\) | −49.6017 | −1.72796 | ||||||||
\(825\) | 0.780131 | 0.0271607 | ||||||||
\(826\) | −19.4804 | −0.677809 | ||||||||
\(827\) | −7.76641 | −0.270065 | −0.135032 | − | 0.990841i | \(-0.543114\pi\) | ||||
−0.135032 | + | 0.990841i | \(0.543114\pi\) | |||||||
\(828\) | 4.23029 | 0.147013 | ||||||||
\(829\) | −9.22162 | −0.320280 | −0.160140 | − | 0.987094i | \(-0.551195\pi\) | ||||
−0.160140 | + | 0.987094i | \(0.551195\pi\) | |||||||
\(830\) | 79.4783 | 2.75873 | ||||||||
\(831\) | −1.62086 | −0.0562269 | ||||||||
\(832\) | −11.0329 | −0.382499 | ||||||||
\(833\) | −14.2912 | −0.495162 | ||||||||
\(834\) | −1.25703 | −0.0435276 | ||||||||
\(835\) | −39.3723 | −1.36254 | ||||||||
\(836\) | 9.06847 | 0.313640 | ||||||||
\(837\) | 1.53501 | 0.0530578 | ||||||||
\(838\) | 44.0436 | 1.52146 | ||||||||
\(839\) | 19.2824 | 0.665704 | 0.332852 | − | 0.942979i | \(-0.391989\pi\) | ||||
0.332852 | + | 0.942979i | \(0.391989\pi\) | |||||||
\(840\) | −3.80137 | −0.131160 | ||||||||
\(841\) | −6.68176 | −0.230405 | ||||||||
\(842\) | 6.79895 | 0.234307 | ||||||||
\(843\) | 0.441082 | 0.0151917 | ||||||||
\(844\) | −43.7005 | −1.50423 | ||||||||
\(845\) | −3.05924 | −0.105241 | ||||||||
\(846\) | 67.9957 | 2.33774 | ||||||||
\(847\) | 20.9762 | 0.720750 | ||||||||
\(848\) | −24.2049 | −0.831201 | ||||||||
\(849\) | −0.828963 | −0.0284499 | ||||||||
\(850\) | 13.2199 | 0.453440 | ||||||||
\(851\) | −2.32897 | −0.0798359 | ||||||||
\(852\) | −0.190200 | −0.00651616 | ||||||||
\(853\) | −36.6757 | −1.25575 | −0.627877 | − | 0.778313i | \(-0.716076\pi\) | ||||
−0.627877 | + | 0.778313i | \(0.716076\pi\) | |||||||
\(854\) | −63.8346 | −2.18437 | ||||||||
\(855\) | 9.14320 | 0.312691 | ||||||||
\(856\) | −13.2558 | −0.453072 | ||||||||
\(857\) | −9.77484 | −0.333902 | −0.166951 | − | 0.985965i | \(-0.553392\pi\) | ||||
−0.166951 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(858\) | −0.426648 | −0.0145655 | ||||||||
\(859\) | −27.9366 | −0.953183 | −0.476592 | − | 0.879125i | \(-0.658128\pi\) | ||||
−0.476592 | + | 0.879125i | \(0.658128\pi\) | |||||||
\(860\) | 109.424 | 3.73131 | ||||||||
\(861\) | 0.402952 | 0.0137326 | ||||||||
\(862\) | 79.6595 | 2.71321 | ||||||||
\(863\) | −16.3864 | −0.557801 | −0.278900 | − | 0.960320i | \(-0.589970\pi\) | ||||
−0.278900 | + | 0.960320i | \(0.589970\pi\) | |||||||
\(864\) | −1.21074 | −0.0411903 | ||||||||
\(865\) | −19.9264 | −0.677519 | ||||||||
\(866\) | −67.6889 | −2.30016 | ||||||||
\(867\) | −1.11573 | −0.0378923 | ||||||||
\(868\) | 55.5132 | 1.88424 | ||||||||
\(869\) | 11.2375 | 0.381207 | ||||||||
\(870\) | −2.49914 | −0.0847287 | ||||||||
\(871\) | −1.81943 | −0.0616490 | ||||||||
\(872\) | −7.69558 | −0.260605 | ||||||||
\(873\) | 4.47155 | 0.151339 | ||||||||
\(874\) | 0.912505 | 0.0308659 | ||||||||
\(875\) | −8.37410 | −0.283096 | ||||||||
\(876\) | 0.220520 | 0.00745069 | ||||||||
\(877\) | 47.1694 | 1.59280 | 0.796399 | − | 0.604772i | \(-0.206736\pi\) | ||||
0.796399 | + | 0.604772i | \(0.206736\pi\) | |||||||
\(878\) | 21.1845 | 0.714941 | ||||||||
\(879\) | 0.776006 | 0.0261740 | ||||||||
\(880\) | −16.5887 | −0.559207 | ||||||||
\(881\) | −36.2487 | −1.22125 | −0.610625 | − | 0.791920i | \(-0.709082\pi\) | ||||
−0.610625 | + | 0.791920i | \(0.709082\pi\) | |||||||
\(882\) | 80.1952 | 2.70031 | ||||||||
\(883\) | 57.9434 | 1.94995 | 0.974975 | − | 0.222315i | \(-0.0713612\pi\) | ||||
0.974975 | + | 0.222315i | \(0.0713612\pi\) | |||||||
\(884\) | −4.68542 | −0.157588 | ||||||||
\(885\) | 0.424676 | 0.0142753 | ||||||||
\(886\) | −83.0805 | −2.79114 | ||||||||
\(887\) | 53.9569 | 1.81170 | 0.905848 | − | 0.423603i | \(-0.139235\pi\) | ||||
0.905848 | + | 0.423603i | \(0.139235\pi\) | |||||||
\(888\) | −1.76698 | −0.0592961 | ||||||||
\(889\) | −45.4996 | −1.52601 | ||||||||
\(890\) | 6.96905 | 0.233603 | ||||||||
\(891\) | 22.0890 | 0.740009 | ||||||||
\(892\) | 57.3483 | 1.92016 | ||||||||
\(893\) | 9.50528 | 0.318082 | ||||||||
\(894\) | 1.53082 | 0.0511981 | ||||||||
\(895\) | 8.81037 | 0.294498 | ||||||||
\(896\) | −88.5288 | −2.95754 | ||||||||
\(897\) | −0.0278220 | −0.000928950 0 | ||||||||
\(898\) | −16.0015 | −0.533976 | ||||||||
\(899\) | 16.6767 | 0.556197 | ||||||||
\(900\) | −48.0758 | −1.60253 | ||||||||
\(901\) | 14.0117 | 0.466797 | ||||||||
\(902\) | 7.65182 | 0.254778 | ||||||||
\(903\) | 3.00820 | 0.100107 | ||||||||
\(904\) | −48.5197 | −1.61374 | ||||||||
\(905\) | 25.0730 | 0.833453 | ||||||||
\(906\) | −3.07361 | −0.102114 | ||||||||
\(907\) | 7.32727 | 0.243298 | 0.121649 | − | 0.992573i | \(-0.461182\pi\) | ||||
0.121649 | + | 0.992573i | \(0.461182\pi\) | |||||||
\(908\) | −63.4730 | −2.10643 | ||||||||
\(909\) | −20.5414 | −0.681316 | ||||||||
\(910\) | −31.1408 | −1.03231 | ||||||||
\(911\) | 5.48479 | 0.181719 | 0.0908596 | − | 0.995864i | \(-0.471039\pi\) | ||||
0.0908596 | + | 0.995864i | \(0.471039\pi\) | |||||||
\(912\) | 0.159099 | 0.00526828 | ||||||||
\(913\) | 26.8890 | 0.889895 | ||||||||
\(914\) | 30.9770 | 1.02463 | ||||||||
\(915\) | 1.39161 | 0.0460051 | ||||||||
\(916\) | 11.3651 | 0.375515 | ||||||||
\(917\) | −52.5977 | −1.73693 | ||||||||
\(918\) | −1.31880 | −0.0435270 | ||||||||
\(919\) | −42.3124 | −1.39576 | −0.697879 | − | 0.716215i | \(-0.745873\pi\) | ||||
−0.697879 | + | 0.716215i | \(0.745873\pi\) | |||||||
\(920\) | −4.70729 | −0.155195 | ||||||||
\(921\) | −2.03688 | −0.0671174 | ||||||||
\(922\) | 66.9260 | 2.20409 | ||||||||
\(923\) | −0.711972 | −0.0234348 | ||||||||
\(924\) | −2.81451 | −0.0925907 | ||||||||
\(925\) | 26.4679 | 0.870259 | ||||||||
\(926\) | −38.9618 | −1.28037 | ||||||||
\(927\) | −37.0274 | −1.21614 | ||||||||
\(928\) | −13.1537 | −0.431792 | ||||||||
\(929\) | −36.9977 | −1.21386 | −0.606928 | − | 0.794757i | \(-0.707598\pi\) | ||||
−0.606928 | + | 0.794757i | \(0.707598\pi\) | |||||||
\(930\) | −1.86741 | −0.0612347 | ||||||||
\(931\) | 11.2107 | 0.367415 | ||||||||
\(932\) | 106.958 | 3.50353 | ||||||||
\(933\) | −1.18241 | −0.0387103 | ||||||||
\(934\) | −16.8627 | −0.551765 | ||||||||
\(935\) | 9.60285 | 0.314047 | ||||||||
\(936\) | 12.0141 | 0.392693 | ||||||||
\(937\) | 8.92499 | 0.291567 | 0.145783 | − | 0.989317i | \(-0.453430\pi\) | ||||
0.145783 | + | 0.989317i | \(0.453430\pi\) | |||||||
\(938\) | −18.5204 | −0.604714 | ||||||||
\(939\) | −1.75128 | −0.0571510 | ||||||||
\(940\) | −107.309 | −3.50005 | ||||||||
\(941\) | −17.2917 | −0.563693 | −0.281846 | − | 0.959460i | \(-0.590947\pi\) | ||||
−0.281846 | + | 0.959460i | \(0.590947\pi\) | |||||||
\(942\) | −3.12140 | −0.101701 | ||||||||
\(943\) | 0.498981 | 0.0162490 | ||||||||
\(944\) | −4.20590 | −0.136890 | ||||||||
\(945\) | −5.68040 | −0.184783 | ||||||||
\(946\) | 57.1239 | 1.85726 | ||||||||
\(947\) | 13.5805 | 0.441308 | 0.220654 | − | 0.975352i | \(-0.429181\pi\) | ||||
0.220654 | + | 0.975352i | \(0.429181\pi\) | |||||||
\(948\) | 1.21674 | 0.0395178 | ||||||||
\(949\) | 0.825468 | 0.0267958 | ||||||||
\(950\) | −10.3703 | −0.336457 | ||||||||
\(951\) | 0.663591 | 0.0215184 | ||||||||
\(952\) | −21.7935 | −0.706332 | ||||||||
\(953\) | 3.84702 | 0.124617 | 0.0623086 | − | 0.998057i | \(-0.480154\pi\) | ||||
0.0623086 | + | 0.998057i | \(0.480154\pi\) | |||||||
\(954\) | −78.6265 | −2.54563 | ||||||||
\(955\) | −26.6172 | −0.861314 | ||||||||
\(956\) | 22.5754 | 0.730139 | ||||||||
\(957\) | −0.845504 | −0.0273313 | ||||||||
\(958\) | −72.2891 | −2.33556 | ||||||||
\(959\) | −66.9931 | −2.16332 | ||||||||
\(960\) | 2.44832 | 0.0790192 | ||||||||
\(961\) | −18.5389 | −0.598028 | ||||||||
\(962\) | −14.4751 | −0.466695 | ||||||||
\(963\) | −9.89536 | −0.318874 | ||||||||
\(964\) | −44.3810 | −1.42942 | ||||||||
\(965\) | −17.8644 | −0.575075 | ||||||||
\(966\) | −0.283207 | −0.00911204 | ||||||||
\(967\) | −37.8233 | −1.21632 | −0.608158 | − | 0.793816i | \(-0.708091\pi\) | ||||
−0.608158 | + | 0.793816i | \(0.708091\pi\) | |||||||
\(968\) | 19.7072 | 0.633415 | ||||||||
\(969\) | −0.0920985 | −0.00295863 | ||||||||
\(970\) | −10.8892 | −0.349632 | ||||||||
\(971\) | −59.3493 | −1.90461 | −0.952305 | − | 0.305148i | \(-0.901294\pi\) | ||||
−0.952305 | + | 0.305148i | \(0.901294\pi\) | |||||||
\(972\) | 7.19608 | 0.230814 | ||||||||
\(973\) | −31.0408 | −0.995123 | ||||||||
\(974\) | 22.8205 | 0.731216 | ||||||||
\(975\) | 0.316188 | 0.0101261 | ||||||||
\(976\) | −13.7822 | −0.441156 | ||||||||
\(977\) | 7.75157 | 0.247995 | 0.123997 | − | 0.992283i | \(-0.460429\pi\) | ||||
0.123997 | + | 0.992283i | \(0.460429\pi\) | |||||||
\(978\) | 1.41286 | 0.0451784 | ||||||||
\(979\) | 2.35776 | 0.0753544 | ||||||||
\(980\) | −126.562 | −4.04289 | ||||||||
\(981\) | −5.74471 | −0.183415 | ||||||||
\(982\) | 50.6774 | 1.61718 | ||||||||
\(983\) | 2.70192 | 0.0861779 | 0.0430889 | − | 0.999071i | \(-0.486280\pi\) | ||||
0.0430889 | + | 0.999071i | \(0.486280\pi\) | |||||||
\(984\) | 0.378576 | 0.0120686 | ||||||||
\(985\) | 10.1516 | 0.323458 | ||||||||
\(986\) | −14.3277 | −0.456288 | ||||||||
\(987\) | −2.95008 | −0.0939021 | ||||||||
\(988\) | 3.67546 | 0.116932 | ||||||||
\(989\) | 3.72510 | 0.118451 | ||||||||
\(990\) | −53.8864 | −1.71262 | ||||||||
\(991\) | −45.6185 | −1.44912 | −0.724560 | − | 0.689212i | \(-0.757957\pi\) | ||||
−0.724560 | + | 0.689212i | \(0.757957\pi\) | |||||||
\(992\) | −9.82872 | −0.312062 | ||||||||
\(993\) | 0.865862 | 0.0274773 | ||||||||
\(994\) | −7.24734 | −0.229872 | ||||||||
\(995\) | 83.3450 | 2.64221 | ||||||||
\(996\) | 2.91139 | 0.0922508 | ||||||||
\(997\) | 12.9654 | 0.410619 | 0.205310 | − | 0.978697i | \(-0.434180\pi\) | ||||
0.205310 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(998\) | 2.28036 | 0.0721835 | ||||||||
\(999\) | −2.64041 | −0.0835387 |
(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 | 8021.2.a.a.1.11 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.a.1.11 | ✓ | 134 | 1.1 | even | 1 | trivial |