Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.962699 | −0.555815 | −0.277907 | − | 0.960608i | \(-0.589641\pi\) | ||||
−0.277907 | + | 0.960608i | \(0.589641\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73078 | 1.22124 | 0.610621 | − | 0.791923i | \(-0.290920\pi\) | ||||
0.610621 | + | 0.791923i | \(0.290920\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.42659 | −1.67309 | −0.836546 | − | 0.547896i | \(-0.815429\pi\) | ||||
−0.836546 | + | 0.547896i | \(0.815429\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.07321 | −0.691070 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59005 | −0.780931 | −0.390465 | − | 0.920618i | \(-0.627686\pi\) | ||||
−0.390465 | + | 0.920618i | \(0.627686\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44381 | 0.677791 | 0.338895 | − | 0.940824i | \(-0.389947\pi\) | ||||
0.338895 | + | 0.940824i | \(0.389947\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.62892 | −0.678784 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.359015 | 0.0870740 | 0.0435370 | − | 0.999052i | \(-0.486137\pi\) | ||||
0.0435370 | + | 0.999052i | \(0.486137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.11543 | 0.944145 | 0.472072 | − | 0.881560i | \(-0.343506\pi\) | ||||
0.472072 | + | 0.881560i | \(0.343506\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.26147 | 0.929930 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0487888 | 0.0101732 | 0.00508658 | − | 0.999987i | \(-0.498381\pi\) | ||||
0.00508658 | + | 0.999987i | \(0.498381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.45715 | 0.491431 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.88398 | 0.939922 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.62661 | 0.302054 | 0.151027 | − | 0.988530i | \(-0.451742\pi\) | ||||
0.151027 | + | 0.988530i | \(0.451742\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.82266 | −0.327360 | −0.163680 | − | 0.986513i | \(-0.552336\pi\) | ||||
−0.163680 | + | 0.986513i | \(0.552336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.49344 | 0.434053 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.0880 | −2.04325 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.04333 | 1.15792 | 0.578958 | − | 0.815357i | \(-0.303459\pi\) | ||||
0.578958 | + | 0.815357i | \(0.303459\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.35265 | −0.376726 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.33305 | −0.364361 | −0.182181 | − | 0.983265i | \(-0.558316\pi\) | ||||
−0.182181 | + | 0.983265i | \(0.558316\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.598973 | −0.0913425 | −0.0456712 | − | 0.998957i | \(-0.514543\pi\) | ||||
−0.0456712 | + | 0.998957i | \(0.514543\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.66148 | −0.843963 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.9710 | 1.89202 | 0.946010 | − | 0.324136i | \(-0.105074\pi\) | ||||
0.946010 | + | 0.324136i | \(0.105074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.5947 | 1.79924 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.345624 | −0.0483970 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.71721 | 0.510598 | 0.255299 | − | 0.966862i | \(-0.417826\pi\) | ||||
0.255299 | + | 0.966862i | \(0.417826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.07287 | −0.953705 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.96192 | −0.524770 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.779197 | 0.101443 | 0.0507214 | − | 0.998713i | \(-0.483848\pi\) | ||||
0.0507214 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.1921 | −1.56104 | −0.780522 | − | 0.625128i | \(-0.785047\pi\) | ||||
−0.780522 | + | 0.625128i | \(0.785047\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.17724 | 1.15622 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.67350 | 0.827746 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.58624 | −0.682468 | −0.341234 | − | 0.939978i | \(-0.610845\pi\) | ||||
−0.341234 | + | 0.939978i | \(0.610845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0469689 | −0.00565439 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.3849 | −1.70717 | −0.853585 | − | 0.520953i | \(-0.825577\pi\) | ||||
−0.853585 | + | 0.520953i | \(0.825577\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0286 | 1.17376 | 0.586881 | − | 0.809673i | \(-0.300356\pi\) | ||||
0.586881 | + | 0.809673i | \(0.300356\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.36550 | −0.273144 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.4651 | 1.30657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.23078 | −0.588509 | −0.294254 | − | 0.955727i | \(-0.595071\pi\) | ||||
−0.294254 | + | 0.955727i | \(0.595071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.51783 | 0.168647 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.6419 | −1.27786 | −0.638930 | − | 0.769265i | \(-0.720622\pi\) | ||||
−0.638930 | + | 0.769265i | \(0.720622\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.980391 | 0.106338 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.56594 | −0.167886 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4868 | 1.42959 | 0.714797 | − | 0.699332i | \(-0.246519\pi\) | ||||
0.714797 | + | 0.699332i | \(0.246519\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8177 | −1.13401 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.75468 | 0.181951 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.2383 | 1.15303 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.27432 | −0.637061 | −0.318530 | − | 0.947913i | \(-0.603189\pi\) | ||||
−0.318530 | + | 0.947913i | \(0.603189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.36973 | 0.539678 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.38530 | −0.535858 | −0.267929 | − | 0.963439i | \(-0.586339\pi\) | ||||
−0.267929 | + | 0.963439i | \(0.586339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.9396 | −1.37351 | −0.686754 | − | 0.726890i | \(-0.740965\pi\) | ||||
−0.686754 | + | 0.726890i | \(0.740965\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.6371 | 1.13567 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.61587 | −0.639581 | −0.319790 | − | 0.947488i | \(-0.603612\pi\) | ||||
−0.319790 | + | 0.947488i | \(0.603612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7060 | −1.12123 | −0.560614 | − | 0.828077i | \(-0.689435\pi\) | ||||
−0.560614 | + | 0.828077i | \(0.689435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.78061 | −0.643587 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.8266 | −1.58291 | −0.791455 | − | 0.611228i | \(-0.790676\pi\) | ||||
−0.791455 | + | 0.611228i | \(0.790676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.133231 | 0.0124239 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.06653 | −0.468401 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.58921 | −0.145683 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.29162 | −0.390147 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.24603 | 0.202517 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.94395 | −0.621086 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3619 | −0.919466 | −0.459733 | − | 0.888057i | \(-0.652055\pi\) | ||||
−0.459733 | + | 0.888057i | \(0.652055\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.576631 | 0.0507695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7168 | −0.936327 | −0.468163 | − | 0.883642i | \(-0.655084\pi\) | ||||
−0.468163 | + | 0.883642i | \(0.655084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.2173 | −1.57964 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.3371 | 1.14787 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.26324 | 0.705976 | 0.352988 | − | 0.935628i | \(-0.385166\pi\) | ||||
0.352988 | + | 0.935628i | \(0.385166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.86367 | −0.327712 | −0.163856 | − | 0.986484i | \(-0.552393\pi\) | ||||
−0.163856 | + | 0.986484i | \(0.552393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.4872 | −1.05161 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.32960 | −0.529308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.44192 | 0.368881 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1249 | −1.00004 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.5012 | 1.67952 | 0.839761 | − | 0.542957i | \(-0.182695\pi\) | ||||
0.839761 | + | 0.542957i | \(0.182695\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.70679 | 0.464412 | 0.232206 | − | 0.972667i | \(-0.425406\pi\) | ||||
0.232206 | + | 0.972667i | \(0.425406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.744314 | −0.0601742 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.97729 | −0.399785 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.28446 | 0.740980 | 0.370490 | − | 0.928836i | \(-0.379190\pi\) | ||||
0.370490 | + | 0.928836i | \(0.379190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.57856 | −0.283798 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.215968 | −0.0170206 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.709508 | −0.0555729 | −0.0277865 | − | 0.999614i | \(-0.508846\pi\) | ||||
−0.0277865 | + | 0.999614i | \(0.508846\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.80905 | 0.530083 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.30141 | 0.100706 | 0.0503531 | − | 0.998731i | \(-0.483965\pi\) | ||||
0.0503531 | + | 0.998731i | \(0.483965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.02780 | −0.540600 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.53215 | −0.652470 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.5407 | −1.10551 | −0.552753 | − | 0.833345i | \(-0.686423\pi\) | ||||
−0.552753 | + | 0.833345i | \(0.686423\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.8768 | −0.822209 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.750132 | −0.0563834 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.4508 | −1.90228 | −0.951139 | − | 0.308762i | \(-0.900085\pi\) | ||||
−0.951139 | + | 0.308762i | \(0.900085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.1748 | −1.35092 | −0.675461 | − | 0.737396i | \(-0.736055\pi\) | ||||
−0.675461 | + | 0.737396i | \(0.736055\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7374 | 0.867652 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.2338 | 1.41410 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.929869 | −0.0679988 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.6193 | −1.57258 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.9402 | −1.37047 | −0.685233 | − | 0.728324i | \(-0.740300\pi\) | ||||
−0.685233 | + | 0.728324i | \(0.740300\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.96192 | −0.285185 | −0.142592 | − | 0.989781i | \(-0.545544\pi\) | ||||
−0.142592 | + | 0.989781i | \(0.545544\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.42458 | −0.460073 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.44725 | −0.103112 | −0.0515562 | − | 0.998670i | \(-0.516418\pi\) | ||||
−0.0515562 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3615 | 0.805393 | 0.402696 | − | 0.915334i | \(-0.368073\pi\) | ||||
0.402696 | + | 0.915334i | \(0.368073\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.37787 | 0.379326 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.20034 | −0.505365 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.37104 | −0.444973 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.101149 | −0.00703036 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.6592 | −0.737312 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.52224 | −0.104796 | −0.0523978 | − | 0.998626i | \(-0.516686\pi\) | ||||
−0.0523978 | + | 0.998626i | \(0.516686\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.8483 | 0.948871 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.63566 | −0.111551 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.06817 | 0.547703 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.65455 | −0.652394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.877365 | 0.0590179 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.3186 | −1.56153 | −0.780763 | − | 0.624827i | \(-0.785169\pi\) | ||||
−0.780763 | + | 0.624827i | \(0.785169\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.09419 | −0.339613 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.70296 | −0.113030 | −0.0565148 | − | 0.998402i | \(-0.517999\pi\) | ||||
−0.0565148 | + | 0.998402i | \(0.517999\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.9024 | 1.31519 | 0.657593 | − | 0.753374i | \(-0.271575\pi\) | ||||
0.657593 | + | 0.753374i | \(0.271575\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.0374 | −0.726211 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.7608 | 1.16355 | 0.581774 | − | 0.813351i | \(-0.302359\pi\) | ||||
0.581774 | + | 0.813351i | \(0.302359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.4210 | 2.31061 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.03567 | 0.327102 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.89213 | 0.381130 | 0.190565 | − | 0.981675i | \(-0.438968\pi\) | ||||
0.190565 | + | 0.981675i | \(0.438968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.6483 | 1.84540 | 0.922698 | − | 0.385523i | \(-0.125979\pi\) | ||||
0.922698 | + | 0.385523i | \(0.125979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1131 | −1.03366 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 34.3932 | 2.19730 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0573 | 0.639932 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.2076 | 0.710253 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.9917 | 0.756908 | 0.378454 | − | 0.925620i | \(-0.376456\pi\) | ||||
0.378454 | + | 0.925620i | \(0.376456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.126366 | −0.00794454 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.943822 | −0.0591044 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.4754 | −1.21484 | −0.607422 | − | 0.794379i | \(-0.707796\pi\) | ||||
−0.607422 | + | 0.794379i | \(0.707796\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.1779 | −1.93730 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.37231 | −0.208741 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.5815 | 0.775811 | 0.387906 | − | 0.921699i | \(-0.373199\pi\) | ||||
0.387906 | + | 0.921699i | \(0.373199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.1509 | 0.623564 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9837 | −0.794590 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.5638 | −1.61962 | −0.809811 | − | 0.586691i | \(-0.800430\pi\) | ||||
−0.809811 | + | 0.586691i | \(0.800430\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9338 | 1.57537 | 0.787683 | − | 0.616081i | \(-0.211281\pi\) | ||||
0.787683 | + | 0.616081i | \(0.211281\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.4142 | 0.630297 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.36416 | −0.383773 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.12691 | −0.187878 | −0.0939388 | − | 0.995578i | \(-0.529946\pi\) | ||||
−0.0939388 | + | 0.995578i | \(0.529946\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.77876 | 0.226229 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.9313 | 0.890729 | 0.445364 | − | 0.895349i | \(-0.353074\pi\) | ||||
0.445364 | + | 0.895349i | \(0.353074\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.7259 | 1.17258 | 0.586291 | − | 0.810100i | \(-0.300587\pi\) | ||||
0.586291 | + | 0.810100i | \(0.300587\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.8191 | −0.640870 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3274 | 0.609610 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8711 | −0.992418 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.04028 | 0.354088 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.9695 | −0.816107 | −0.408053 | − | 0.912958i | \(-0.633792\pi\) | ||||
−0.408053 | + | 0.912958i | \(0.633792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.12781 | 0.123886 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.6498 | −0.734014 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.119230 | 0.00689527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.65140 | 0.152824 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.18443 | 0.297838 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.2941 | −1.90641 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7964 | 1.01569 | 0.507847 | − | 0.861447i | \(-0.330441\pi\) | ||||
0.507847 | + | 0.861447i | \(0.330441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4196 | 0.763416 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.9023 | 1.46878 | 0.734391 | − | 0.678727i | \(-0.237468\pi\) | ||||
0.734391 | + | 0.678727i | \(0.237468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6576 | 0.658925 | 0.329463 | − | 0.944169i | \(-0.393132\pi\) | ||||
0.329463 | + | 0.944169i | \(0.393132\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 25.0610 | 1.41203 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.5162 | −1.37697 | −0.688484 | − | 0.725251i | \(-0.741724\pi\) | ||||
−0.688484 | + | 0.725251i | \(0.741724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.21301 | −0.235883 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.36910 | 0.355488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.47750 | 0.0822104 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00481 | 0.333087 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2693 | 0.623195 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −57.4174 | −3.16553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.560641 | −0.0308156 | −0.0154078 | − | 0.999881i | \(-0.504905\pi\) | ||||
−0.0154078 | + | 0.999881i | \(0.504905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.6023 | −0.800201 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.2548 | −0.833458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.26878 | −0.0691147 | −0.0345573 | − | 0.999403i | \(-0.511002\pi\) | ||||
−0.0345573 | + | 0.999403i | \(0.511002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.1989 | 0.879805 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.72080 | 0.255645 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −24.7653 | −1.33720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.128262 | −0.00690538 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.4243 | −0.559607 | −0.279803 | − | 0.960057i | \(-0.590269\pi\) | ||||
−0.279803 | + | 0.960057i | \(0.590269\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2503 | 0.602216 | 0.301108 | − | 0.953590i | \(-0.402643\pi\) | ||||
0.301108 | + | 0.953590i | \(0.402643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9355 | 0.637070 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5508 | 0.827686 | 0.413843 | − | 0.910348i | \(-0.364186\pi\) | ||||
0.413843 | + | 0.910348i | \(0.364186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.2819 | −2.08487 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.52993 | 0.0809727 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.9534 | −1.58088 | −0.790440 | − | 0.612540i | \(-0.790148\pi\) | ||||
−0.790440 | + | 0.612540i | \(0.790148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.06323 | −0.108591 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.13154 | 0.216849 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.3860 | 1.43345 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.19537 | −0.271196 | −0.135598 | − | 0.990764i | \(-0.543296\pi\) | ||||
−0.135598 | + | 0.990764i | \(0.543296\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.83690 | 0.251799 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.4546 | −0.854278 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.3415 | −1.31213 | −0.656066 | − | 0.754704i | \(-0.727781\pi\) | ||||
−0.656066 | + | 0.754704i | \(0.727781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.68494 | 0.345209 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.97513 | 0.204729 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.82446 | 0.299182 | 0.149591 | − | 0.988748i | \(-0.452204\pi\) | ||||
0.149591 | + | 0.988748i | \(0.452204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.97535 | 0.511053 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.4681 | 1.30136 | 0.650678 | − | 0.759353i | \(-0.274485\pi\) | ||||
0.650678 | + | 0.759353i | \(0.274485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.3087 | 1.59564 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.24180 | 0.0631240 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.9788 | −1.57069 | −0.785343 | − | 0.619060i | \(-0.787514\pi\) | ||||
−0.785343 | + | 0.619060i | \(0.787514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0175159 | 0.000885818 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.3170 | 0.520424 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.2841 | −0.718711 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.2785 | −0.867186 | −0.433593 | − | 0.901109i | \(-0.642754\pi\) | ||||
−0.433593 | + | 0.901109i | \(0.642754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.5378 | 0.877988 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.6417 | −1.72992 | −0.864962 | − | 0.501837i | \(-0.832658\pi\) | ||||
−0.864962 | + | 0.501837i | \(0.832658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.45424 | −0.221881 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.14485 | 0.205959 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.2426 | −0.904253 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.92750 | −0.490883 | −0.245442 | − | 0.969411i | \(-0.578933\pi\) | ||||
−0.245442 | + | 0.969411i | \(0.578933\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.95501 | −0.392392 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.44918 | −0.169723 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.7913 | −1.56057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.71955 | 0.182147 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.4441 | 1.14532 | 0.572660 | − | 0.819793i | \(-0.305912\pi\) | ||||
0.572660 | + | 0.819793i | \(0.305912\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9664 | 0.924364 | 0.462182 | − | 0.886785i | \(-0.347067\pi\) | ||||
0.462182 | + | 0.886785i | \(0.347067\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.8917 | −1.30752 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.882156 | 0.0427908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 53.9696 | 2.61177 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.09350 | 0.294197 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.35894 | 0.450804 | 0.225402 | − | 0.974266i | \(-0.427630\pi\) | ||||
0.225402 | + | 0.974266i | \(0.427630\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.91181 | 0.428274 | 0.214137 | − | 0.976804i | \(-0.431306\pi\) | ||||
0.214137 | + | 0.976804i | \(0.431306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.27623 | −0.205030 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.200787 | 0.00960493 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.80387 | −0.133821 | −0.0669107 | − | 0.997759i | \(-0.521314\pi\) | ||||
−0.0669107 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.1114 | −1.24340 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.4842 | −1.49586 | −0.747931 | − | 0.663777i | \(-0.768952\pi\) | ||||
−0.747931 | + | 0.663777i | \(0.768952\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.8294 | 1.74588 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.7365 | −0.933503 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.79800 | 0.132046 | 0.0660230 | − | 0.997818i | \(-0.478969\pi\) | ||||
0.0660230 | + | 0.997818i | \(0.478969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.04273 | 0.284541 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.49392 | −0.258127 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.5408 | −1.38490 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.6301 | −1.38604 | −0.693020 | − | 0.720919i | \(-0.743720\pi\) | ||||
−0.693020 | + | 0.720919i | \(0.743720\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.75342 | 0.0818427 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.4306 | 1.32415 | 0.662074 | − | 0.749439i | \(-0.269677\pi\) | ||||
0.662074 | + | 0.749439i | \(0.269677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.60304 | −0.446291 | −0.223146 | − | 0.974785i | \(-0.571633\pi\) | ||||
−0.223146 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.79163 | 0.222207 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.5788 | −1.13737 | −0.568685 | − | 0.822555i | \(-0.692548\pi\) | ||||
−0.568685 | + | 0.822555i | \(0.692548\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.7280 | 1.14183 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.93814 | −0.411848 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.55137 | 0.0713322 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1122 | 0.463982 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.70656 | −0.352859 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.4632 | 1.02637 | 0.513186 | − | 0.858278i | \(-0.328465\pi\) | ||||
0.513186 | + | 0.858278i | \(0.328465\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2126 | 0.784825 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.207912 | 0.00946032 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.1338 | −0.778005 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.4568 | 1.06293 | 0.531465 | − | 0.847081i | \(-0.321642\pi\) | ||||
0.531465 | + | 0.847081i | \(0.321642\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.683043 | 0.0308883 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.3499 | 0.828119 | 0.414059 | − | 0.910250i | \(-0.364111\pi\) | ||||
0.414059 | + | 0.910250i | \(0.364111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.583978 | 0.0263011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.6635 | 0.659077 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 63.6759 | 2.85625 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.9004 | 1.29376 | 0.646880 | − | 0.762592i | \(-0.276074\pi\) | ||||
0.646880 | + | 0.762592i | \(0.276074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.25287 | −0.0559740 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.5369 | −1.09404 | −0.547022 | − | 0.837118i | \(-0.684239\pi\) | ||||
−0.547022 | + | 0.837118i | \(0.684239\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.7061 | −0.654412 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.76566 | 0.300473 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2975 | 1.25426 | 0.627132 | − | 0.778913i | \(-0.284228\pi\) | ||||
0.627132 | + | 0.778913i | \(0.284228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.3926 | −1.96381 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.0997 | 0.887422 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.0659 | −1.67739 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.5957 | −1.47754 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.9983 | 0.614457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.1186 | −1.49476 | −0.747381 | − | 0.664395i | \(-0.768689\pi\) | ||||
−0.747381 | + | 0.664395i | \(0.768689\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.0230 | 1.57518 | 0.787588 | − | 0.616202i | \(-0.211330\pi\) | ||||
0.787588 | + | 0.616202i | \(0.211330\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.4711 | 0.456996 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.654364 | −0.0285045 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9976 | −0.999897 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.61544 | −0.0701040 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.70153 | −0.246961 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0665 | −0.781082 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.5014 | 1.05731 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.6209 | −1.40508 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.10069 | −0.219296 | −0.109648 | − | 0.993970i | \(-0.534972\pi\) | ||||
−0.109648 | + | 0.993970i | \(0.534972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.4969 | 0.750863 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.9664 | −1.36929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3585 | −0.571169 | −0.285584 | − | 0.958354i | \(-0.592188\pi\) | ||||
−0.285584 | + | 0.958354i | \(0.592188\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.2769 | 1.07879 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.69421 | 0.285183 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.1545 | 0.984630 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.5164 | −0.785975 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.8853 | −1.52051 | −0.760255 | − | 0.649625i | \(-0.774926\pi\) | ||||
−0.760255 | + | 0.649625i | \(0.774926\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.46377 | −0.0619111 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.895185 | 0.0377947 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.3579 | −0.520822 | −0.260411 | − | 0.965498i | \(-0.583858\pi\) | ||||
−0.260411 | + | 0.965498i | \(0.583858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.9496 | −1.93311 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.71879 | −0.282163 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.4665 | −0.648389 | −0.324194 | − | 0.945990i | \(-0.605093\pi\) | ||||
−0.324194 | + | 0.945990i | \(0.605093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.4153 | 0.561412 | 0.280706 | − | 0.959794i | \(-0.409431\pi\) | ||||
0.280706 | + | 0.959794i | \(0.409431\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.2337 | 0.761725 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.119881 | 0.00499940 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.17308 | −0.381880 | −0.190940 | − | 0.981602i | \(-0.561154\pi\) | ||||
−0.190940 | + | 0.981602i | \(0.561154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.81413 | 0.158510 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 51.5337 | 2.13798 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.62778 | −0.398742 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.8356 | −0.572030 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.6720 | 1.47234 | 0.736170 | − | 0.676796i | \(-0.236632\pi\) | ||||
0.736170 | + | 0.676796i | \(0.236632\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.50104 | −0.309075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.39327 | 0.0573114 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7902 | 0.607361 | 0.303681 | − | 0.952774i | \(-0.401784\pi\) | ||||
0.303681 | + | 0.952774i | \(0.401784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.33979 | −0.177914 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.9377 | −0.447649 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.7824 | −0.481416 | −0.240708 | − | 0.970598i | \(-0.577380\pi\) | ||||
−0.240708 | + | 0.970598i | \(0.577380\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.8868 | 0.892783 | 0.446391 | − | 0.894838i | \(-0.352709\pi\) | ||||
0.446391 | + | 0.894838i | \(0.352709\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.5814 | 0.471633 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.7195 | −0.476464 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.8295 | −1.57604 | −0.788020 | − | 0.615650i | \(-0.788894\pi\) | ||||
−0.788020 | + | 0.615650i | \(0.788894\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.93176 | 0.280889 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.6987 | 1.28239 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.98728 | −0.362993 | −0.181496 | − | 0.983392i | \(-0.558094\pi\) | ||||
−0.181496 | + | 0.983392i | \(0.558094\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.13340 | 0.247323 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.9125 | −1.12371 | −0.561857 | − | 0.827234i | \(-0.689913\pi\) | ||||
−0.561857 | + | 0.827234i | \(0.689913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.7965 | −1.23782 | −0.618909 | − | 0.785463i | \(-0.712425\pi\) | ||||
−0.618909 | + | 0.785463i | \(0.712425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.238283 | 0.00956197 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −59.7003 | −2.39184 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2482 | −1.24993 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.2616 | 0.409809 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.52866 | 0.100824 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0024 | 0.796282 | 0.398141 | − | 0.917324i | \(-0.369655\pi\) | ||||
0.398141 | + | 0.917324i | \(0.369655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.46546 | 0.0582469 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.2959 | −1.12289 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.7790 | 1.21951 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.8229 | 1.17977 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.52474 | −0.0997212 | −0.0498606 | − | 0.998756i | \(-0.515878\pi\) | ||||
−0.0498606 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.6427 | −1.05069 | −0.525343 | − | 0.850890i | \(-0.676063\pi\) | ||||
−0.525343 | + | 0.850890i | \(0.676063\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.57465 | 0.0620018 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.1454 | 0.831312 | 0.415656 | − | 0.909522i | \(-0.363552\pi\) | ||||
0.415656 | + | 0.909522i | \(0.363552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.01816 | −0.0792198 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.76723 | −0.304422 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.1936 | −1.10330 | −0.551650 | − | 0.834076i | \(-0.686002\pi\) | ||||
−0.551650 | + | 0.834076i | \(0.686002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.2651 | −1.14348 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.7914 | −0.811151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.2653 | −0.438835 | −0.219418 | − | 0.975631i | \(-0.570416\pi\) | ||||
−0.219418 | + | 0.975631i | \(0.570416\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.65340 | −0.258787 | −0.129394 | − | 0.991593i | \(-0.541303\pi\) | ||||
−0.129394 | + | 0.991593i | \(0.541303\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.844639 | −0.0328030 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −49.7474 | −1.92912 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0793604 | 0.00307285 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.4488 | 0.867919 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.5783 | 1.21907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.0956 | −1.58412 | −0.792059 | − | 0.610444i | \(-0.790991\pi\) | ||||
−0.792059 | + | 0.610444i | \(0.790991\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.0007 | 0.461906 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.8256 | −1.64592 | −0.822960 | − | 0.568099i | \(-0.807679\pi\) | ||||
−0.822960 | + | 0.568099i | \(0.807679\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.7738 | 1.06586 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.63944 | 0.0628235 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.31978 | −0.165292 | −0.0826459 | − | 0.996579i | \(-0.526337\pi\) | ||||
−0.0826459 | + | 0.996579i | \(0.526337\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.5651 | 0.862167 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.1600 | −0.731000 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.08415 | 0.346079 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.9671 | 0.797626 | 0.398813 | − | 0.917032i | \(-0.369422\pi\) | ||||
0.398813 | + | 0.917032i | \(0.369422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.7696 | −0.902931 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.5508 | −0.400215 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.837600 | −0.0317264 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.0983 | −0.646717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.59617 | 0.286903 | 0.143452 | − | 0.989657i | \(-0.454180\pi\) | ||||
0.143452 | + | 0.989657i | \(0.454180\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.9863 | 1.09324 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.0998 | −1.28427 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.8385 | 0.896539 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0690 | −0.490816 | −0.245408 | − | 0.969420i | \(-0.578922\pi\) | ||||
−0.245408 | + | 0.969420i | \(0.578922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.8445 | 0.406701 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.0889255 | −0.00333028 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.2847 | −0.646412 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.67235 | −0.211838 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.7304 | −0.996876 | −0.498438 | − | 0.866925i | \(-0.666093\pi\) | ||||
−0.498438 | + | 0.866925i | \(0.666093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 61.7048 | 2.29801 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.5797 | −1.02570 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.99683 | 0.148439 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.7784 | −1.62365 | −0.811826 | − | 0.583899i | \(-0.801526\pi\) | ||||
−0.811826 | + | 0.583899i | \(0.801526\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.9586 | 0.405875 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.215040 | −0.00795356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.89844 | 0.217864 | 0.108932 | − | 0.994049i | \(-0.465257\pi\) | ||||
0.108932 | + | 0.994049i | \(0.465257\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −33.1104 | −1.22129 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.4687 | 0.532960 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2819 | 0.415010 | 0.207505 | − | 0.978234i | \(-0.433466\pi\) | ||||
0.207505 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.68218 | −0.355684 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.51753 | 0.0923591 | 0.0461796 | − | 0.998933i | \(-0.485295\pi\) | ||||
0.0461796 | + | 0.998933i | \(0.485295\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.9842 | 2.05110 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.1360 | 0.883090 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.2857 | 1.07008 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.5444 | −0.420701 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.5840 | 0.567159 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9539 | −0.652545 | −0.326272 | − | 0.945276i | \(-0.605793\pi\) | ||||
−0.326272 | + | 0.945276i | \(0.605793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.121652 | 0.00441569 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.3575 | 0.737957 | 0.368979 | − | 0.929438i | \(-0.379708\pi\) | ||||
0.368979 | + | 0.929438i | \(0.379708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.8174 | 1.87592 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.03256 | −0.0734873 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.90421 | 0.0687570 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.5643 | −0.849750 | −0.424875 | − | 0.905252i | \(-0.639682\pi\) | ||||
−0.424875 | + | 0.905252i | \(0.639682\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.7490 | 0.675228 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.7255 | 0.889315 | 0.444658 | − | 0.895701i | \(-0.353325\pi\) | ||||
0.444658 | + | 0.895701i | \(0.353325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.47856 | −0.160875 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 30.0150 | 1.07678 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.60150 | −0.344010 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.2576 | 1.33318 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.94433 | 0.283907 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.3538 | 0.904916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.8678 | −0.565627 | −0.282814 | − | 0.959175i | \(-0.591268\pi\) | ||||
−0.282814 | + | 0.959175i | \(0.591268\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.1122 | −0.431207 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 74.4842 | 2.64835 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.7953 | −1.05806 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.77225 | −0.346586 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.6301 | 0.943287 | 0.471643 | − | 0.881789i | \(-0.343661\pi\) | ||||
0.471643 | + | 0.881789i | \(0.343661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.65680 | 0.164746 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.9609 | −0.987950 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.9747 | −0.916627 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.589760 | −0.0207863 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.5729 | 0.900210 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.5436 | −0.651957 | −0.325978 | − | 0.945377i | \(-0.605694\pi\) | ||||
−0.325978 | + | 0.945377i | \(0.605694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6575 | −1.04142 | −0.520708 | − | 0.853735i | \(-0.674332\pi\) | ||||
−0.520708 | + | 0.853735i | \(0.674332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.9664 | −0.875611 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.93751 | −0.0678680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.46503 | −0.0862405 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.4274 | 0.783678 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.21087 | 0.0771599 | 0.0385799 | − | 0.999256i | \(-0.487717\pi\) | ||||
0.0385799 | + | 0.999256i | \(0.487717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.1404 | −1.15520 | −0.577601 | − | 0.816319i | \(-0.696011\pi\) | ||||
−0.577601 | + | 0.816319i | \(0.696011\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.12677 | 0.213307 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.0829 | −0.524485 | −0.262243 | − | 0.965002i | \(-0.584462\pi\) | ||||
−0.262243 | + | 0.965002i | \(0.584462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8670 | −0.759473 | −0.379736 | − | 0.925095i | \(-0.623985\pi\) | ||||
−0.379736 | + | 0.925095i | \(0.623985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.01027 | 0.104425 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.52168 | 0.156667 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.55387 | 0.122987 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.90184 | −0.307693 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.4485 | −1.63810 | −0.819052 | − | 0.573719i | \(-0.805500\pi\) | ||||
−0.819052 | + | 0.573719i | \(0.805500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3541 | −0.908763 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.3744 | −0.495080 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.1914 | −0.660203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9972 | 0.652752 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.9901 | −0.651739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.343635 | 0.0117797 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3940 | 0.766758 | 0.383379 | − | 0.923591i | \(-0.374760\pi\) | ||||
0.383379 | + | 0.923591i | \(0.374760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.2994 | −0.796823 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.4144 | 1.27805 | 0.639025 | − | 0.769186i | \(-0.279338\pi\) | ||||
0.639025 | + | 0.769186i | \(0.279338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.2153 | 1.67920 | 0.839601 | − | 0.543203i | \(-0.182789\pi\) | ||||
0.839601 | + | 0.543203i | \(0.182789\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.94223 | −0.338830 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.8303 | −0.538871 | −0.269435 | − | 0.963018i | \(-0.586837\pi\) | ||||
−0.269435 | + | 0.963018i | \(0.586837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.7073 | −1.35009 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.2418 | 0.551601 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.5480 | 0.459585 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.6517 | −0.462570 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.0080 | 0.440253 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.7380 | 1.03913 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.3618 | −0.417430 | −0.208715 | − | 0.977977i | \(-0.566928\pi\) | ||||
−0.208715 | + | 0.977977i | \(0.566928\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.4484 | 0.453604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.4019 | 0.788431 | 0.394215 | − | 0.919018i | \(-0.371016\pi\) | ||||
0.394215 | + | 0.919018i | \(0.371016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.79278 | 0.295901 | 0.147950 | − | 0.988995i | \(-0.452732\pi\) | ||||
0.147950 | + | 0.988995i | \(0.452732\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.04845 | −0.0688577 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.37404 | −0.180443 | −0.0902213 | − | 0.995922i | \(-0.528757\pi\) | ||||
−0.0902213 | + | 0.995922i | \(0.528757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.8676 | 1.53835 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.93126 | −0.131702 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53.3814 | 1.78634 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.5004 | −2.32314 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.114783 | −0.00383249 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.96476 | −0.0988804 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.33454 | 0.0444598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.55251 | −0.0849421 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49.6314 | −1.64980 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.7558 | −1.22046 | −0.610228 | − | 0.792226i | \(-0.708922\pi\) | ||||
−0.610228 | + | 0.792226i | \(0.708922\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.1649 | 0.370315 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.6696 | 1.57936 | 0.789682 | − | 0.613516i | \(-0.210246\pi\) | ||||
0.789682 | + | 0.613516i | \(0.210246\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.1530 | 0.997920 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.0522 | 1.05961 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.4386 | 1.56656 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.25440 | 0.0743657 | 0.0371828 | − | 0.999308i | \(-0.488162\pi\) | ||||
0.0371828 | + | 0.999308i | \(0.488162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.1326 | −0.564538 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.1539 | −1.15710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.3065 | 0.569036 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.8997 | 0.949190 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6970 | −0.350958 | −0.175479 | − | 0.984483i | \(-0.556147\pi\) | ||||
−0.175479 | + | 0.984483i | \(0.556147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.8325 | 1.69874 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.9361 | −0.816371 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.53927 | −0.0830429 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.0765 | 0.361853 | 0.180927 | − | 0.983497i | \(-0.442090\pi\) | ||||
0.180927 | + | 0.983497i | \(0.442090\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.2227 | −0.366240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.169037 | −0.00551045 | −0.00275523 | − | 0.999996i | \(-0.500877\pi\) | ||||
−0.00275523 | + | 0.999996i | \(0.500877\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.113827 | −0.00370670 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −59.0376 | −1.92049 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.8062 | 1.61848 | 0.809241 | − | 0.587476i | \(-0.199879\pi\) | ||||
0.809241 | + | 0.587476i | \(0.199879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5080 | 0.795565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.6018 | 0.765339 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.922640 | 0.0298873 | 0.0149436 | − | 0.999888i | \(-0.495243\pi\) | ||||
0.0149436 | + | 0.999888i | \(0.495243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −51.7216 | −1.67367 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.05587 | 0.131108 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.5779 | −1.18116 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6779 | −0.892836 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.7161 | 0.441995 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.8191 | −0.348280 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.89127 | −0.253766 | −0.126883 | − | 0.991918i | \(-0.540497\pi\) | ||||
−0.126883 | + | 0.991918i | \(0.540497\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.42239 | −0.0456938 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.6352 | −1.07940 | −0.539702 | − | 0.841856i | \(-0.681463\pi\) | ||||
−0.539702 | + | 0.841856i | \(0.681463\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.1028 | 0.548292 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.78083 | −0.185135 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.7841 | 0.600957 | 0.300479 | − | 0.953789i | \(-0.402854\pi\) | ||||
0.300479 | + | 0.953789i | \(0.402854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.9315 | −1.11641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.2689 | 0.774847 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.1163 | −0.354554 | −0.177277 | − | 0.984161i | \(-0.556729\pi\) | ||||
−0.177277 | + | 0.984161i | \(0.556729\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.95212 | −0.125925 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 55.2757 | 1.75945 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.0292231 | −0.000929242 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3653 | 0.361030 | 0.180515 | − | 0.983572i | \(-0.442224\pi\) | ||||
0.180515 | + | 0.983572i | \(0.442224\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.539729 | 0.0171278 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.0256 | 0.983579 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.96012 | −0.157088 | −0.0785442 | − | 0.996911i | \(-0.525027\pi\) | ||||
−0.0785442 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.3995 | 1.08835 |
(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 | 6008.2.a.b.1.19 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.19 | ✓ | 44 | 1.1 | even | 1 | trivial |