Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, 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("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(31.9800860095\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 128x^{6} + 14x^{5} - 358x^{4} - 59x^{3} + 344x^{2} + 71x - 21 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1335) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.167560\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.167560 | −0.118483 | −0.0592416 | − | 0.998244i | \(-0.518868\pi\) | ||||
−0.0592416 | + | 0.998244i | \(0.518868\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.97192 | −0.985962 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.76137 | −1.04370 | −0.521850 | − | 0.853037i | \(-0.674758\pi\) | ||||
−0.521850 | + | 0.853037i | \(0.674758\pi\) | |||||||
\(8\) | 0.665537 | 0.235303 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.167560 | −0.0529873 | ||||||||
\(11\) | −3.33531 | −1.00563 | −0.502817 | − | 0.864393i | \(-0.667703\pi\) | ||||
−0.502817 | + | 0.864393i | \(0.667703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.89095 | −1.35651 | −0.678253 | − | 0.734829i | \(-0.737263\pi\) | ||||
−0.678253 | + | 0.734829i | \(0.737263\pi\) | |||||||
\(14\) | 0.462697 | 0.123661 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.83233 | 0.958082 | ||||||||
\(17\) | −4.74870 | −1.15173 | −0.575865 | − | 0.817545i | \(-0.695335\pi\) | ||||
−0.575865 | + | 0.817545i | \(0.695335\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.12657 | −0.487870 | −0.243935 | − | 0.969792i | \(-0.578438\pi\) | ||||
−0.243935 | + | 0.969792i | \(0.578438\pi\) | |||||||
\(20\) | −1.97192 | −0.440935 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.558866 | 0.119151 | ||||||||
\(23\) | −6.48422 | −1.35205 | −0.676027 | − | 0.736877i | \(-0.736300\pi\) | ||||
−0.676027 | + | 0.736877i | \(0.736300\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.819530 | 0.160723 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.44521 | 1.02905 | ||||||||
\(29\) | 0.0885979 | 0.0164522 | 0.00822611 | − | 0.999966i | \(-0.497382\pi\) | ||||
0.00822611 | + | 0.999966i | \(0.497382\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02003 | −0.183203 | −0.0916013 | − | 0.995796i | \(-0.529199\pi\) | ||||
−0.0916013 | + | 0.995796i | \(0.529199\pi\) | |||||||
\(32\) | −1.97322 | −0.348820 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.795695 | 0.136461 | ||||||||
\(35\) | −2.76137 | −0.466757 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00644 | 1.15185 | 0.575925 | − | 0.817502i | \(-0.304642\pi\) | ||||
0.575925 | + | 0.817502i | \(0.304642\pi\) | |||||||
\(38\) | 0.356330 | 0.0578043 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.665537 | 0.105231 | ||||||||
\(41\) | −5.31495 | −0.830056 | −0.415028 | − | 0.909809i | \(-0.636228\pi\) | ||||
−0.415028 | + | 0.909809i | \(0.636228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4989 | 1.60107 | 0.800533 | − | 0.599288i | \(-0.204550\pi\) | ||||
0.800533 | + | 0.599288i | \(0.204550\pi\) | |||||||
\(44\) | 6.57698 | 0.991517 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.08650 | 0.160196 | ||||||||
\(47\) | 4.77531 | 0.696551 | 0.348275 | − | 0.937392i | \(-0.386767\pi\) | ||||
0.348275 | + | 0.937392i | \(0.386767\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.625170 | 0.0893101 | ||||||||
\(50\) | −0.167560 | −0.0236966 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.64458 | 1.33746 | ||||||||
\(53\) | −3.53639 | −0.485760 | −0.242880 | − | 0.970056i | \(-0.578092\pi\) | ||||
−0.242880 | + | 0.970056i | \(0.578092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.33531 | −0.449733 | ||||||||
\(56\) | −1.83780 | −0.245586 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0148455 | −0.00194931 | ||||||||
\(59\) | 1.10447 | 0.143789 | 0.0718946 | − | 0.997412i | \(-0.477095\pi\) | ||||
0.0718946 | + | 0.997412i | \(0.477095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.87568 | −0.240157 | −0.120078 | − | 0.992764i | \(-0.538315\pi\) | ||||
−0.120078 | + | 0.992764i | \(0.538315\pi\) | |||||||
\(62\) | 0.170917 | 0.0217064 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.33402 | −0.916753 | ||||||||
\(65\) | −4.89095 | −0.606648 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8567 | 1.57070 | 0.785350 | − | 0.619052i | \(-0.212483\pi\) | ||||
0.785350 | + | 0.619052i | \(0.212483\pi\) | |||||||
\(68\) | 9.36408 | 1.13556 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.462697 | 0.0553028 | ||||||||
\(71\) | −8.95798 | −1.06312 | −0.531558 | − | 0.847022i | \(-0.678393\pi\) | ||||
−0.531558 | + | 0.847022i | \(0.678393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.33743 | 0.507657 | 0.253829 | − | 0.967249i | \(-0.418310\pi\) | ||||
0.253829 | + | 0.967249i | \(0.418310\pi\) | |||||||
\(74\) | −1.17400 | −0.136475 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.19344 | 0.481021 | ||||||||
\(77\) | 9.21003 | 1.04958 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.560875 | −0.0631033 | −0.0315517 | − | 0.999502i | \(-0.510045\pi\) | ||||
−0.0315517 | + | 0.999502i | \(0.510045\pi\) | |||||||
\(80\) | 3.83233 | 0.428467 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.890575 | 0.0983476 | ||||||||
\(83\) | 2.04236 | 0.224179 | 0.112089 | − | 0.993698i | \(-0.464246\pi\) | ||||
0.112089 | + | 0.993698i | \(0.464246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.74870 | −0.515069 | ||||||||
\(86\) | −1.75920 | −0.189699 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.21977 | −0.236629 | ||||||||
\(89\) | 1.00000 | 0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5057 | 1.41579 | ||||||||
\(92\) | 12.7864 | 1.33307 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.800153 | −0.0825295 | ||||||||
\(95\) | −2.12657 | −0.218182 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5702 | 1.07324 | 0.536621 | − | 0.843824i | \(-0.319701\pi\) | ||||
0.536621 | + | 0.843824i | \(0.319701\pi\) | |||||||
\(98\) | −0.104754 | −0.0105817 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.97192 | −0.197192 | ||||||||
\(101\) | −6.50558 | −0.647329 | −0.323664 | − | 0.946172i | \(-0.604915\pi\) | ||||
−0.323664 | + | 0.946172i | \(0.604915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.3709 | −1.81014 | −0.905072 | − | 0.425259i | \(-0.860183\pi\) | ||||
−0.905072 | + | 0.425259i | \(0.860183\pi\) | |||||||
\(104\) | −3.25511 | −0.319190 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.592559 | 0.0575544 | ||||||||
\(107\) | −8.39617 | −0.811689 | −0.405844 | − | 0.913942i | \(-0.633022\pi\) | ||||
−0.405844 | + | 0.913942i | \(0.633022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1755 | −1.16620 | −0.583100 | − | 0.812401i | \(-0.698160\pi\) | ||||
−0.583100 | + | 0.812401i | \(0.698160\pi\) | |||||||
\(110\) | 0.558866 | 0.0532858 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.5825 | −0.999951 | ||||||||
\(113\) | −0.762011 | −0.0716840 | −0.0358420 | − | 0.999357i | \(-0.511411\pi\) | ||||
−0.0358420 | + | 0.999357i | \(0.511411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.48422 | −0.604657 | ||||||||
\(116\) | −0.174708 | −0.0162213 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.185065 | −0.0170366 | ||||||||
\(119\) | 13.1129 | 1.20206 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.124299 | 0.0112999 | ||||||||
\(122\) | 0.314290 | 0.0284545 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.01142 | 0.180631 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.5917 | 1.56101 | 0.780505 | − | 0.625150i | \(-0.214962\pi\) | ||||
0.780505 | + | 0.625150i | \(0.214962\pi\) | |||||||
\(128\) | 5.17533 | 0.457439 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.819530 | 0.0718775 | ||||||||
\(131\) | 16.4645 | 1.43851 | 0.719254 | − | 0.694747i | \(-0.244484\pi\) | ||||
0.719254 | + | 0.694747i | \(0.244484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.87226 | 0.509190 | ||||||||
\(134\) | −2.15428 | −0.186101 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.16044 | −0.271005 | ||||||||
\(137\) | 10.0200 | 0.856063 | 0.428031 | − | 0.903764i | \(-0.359207\pi\) | ||||
0.428031 | + | 0.903764i | \(0.359207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.15475 | 0.776496 | 0.388248 | − | 0.921555i | \(-0.373080\pi\) | ||||
0.388248 | + | 0.921555i | \(0.373080\pi\) | |||||||
\(140\) | 5.44521 | 0.460204 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.50100 | 0.125961 | ||||||||
\(143\) | 16.3128 | 1.36415 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0885979 | 0.00735766 | ||||||||
\(146\) | −0.726781 | −0.0601488 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.8162 | −1.13568 | ||||||||
\(149\) | 0.754909 | 0.0618446 | 0.0309223 | − | 0.999522i | \(-0.490156\pi\) | ||||
0.0309223 | + | 0.999522i | \(0.490156\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.3641 | 1.65720 | 0.828602 | − | 0.559839i | \(-0.189137\pi\) | ||||
0.828602 | + | 0.559839i | \(0.189137\pi\) | |||||||
\(152\) | −1.41531 | −0.114797 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.54324 | −0.124358 | ||||||||
\(155\) | −1.02003 | −0.0819307 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.7103 | −1.49324 | −0.746620 | − | 0.665250i | \(-0.768325\pi\) | ||||
−0.746620 | + | 0.665250i | \(0.768325\pi\) | |||||||
\(158\) | 0.0939804 | 0.00747668 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.97322 | −0.155997 | ||||||||
\(161\) | 17.9053 | 1.41114 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.39787 | −0.736098 | −0.368049 | − | 0.929806i | \(-0.619974\pi\) | ||||
−0.368049 | + | 0.929806i | \(0.619974\pi\) | |||||||
\(164\) | 10.4807 | 0.818403 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.342219 | −0.0265614 | ||||||||
\(167\) | 17.2812 | 1.33726 | 0.668629 | − | 0.743596i | \(-0.266881\pi\) | ||||
0.668629 | + | 0.743596i | \(0.266881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9214 | 0.840107 | ||||||||
\(170\) | 0.795695 | 0.0610270 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20.7030 | −1.57859 | ||||||||
\(173\) | −14.9919 | −1.13981 | −0.569905 | − | 0.821710i | \(-0.693020\pi\) | ||||
−0.569905 | + | 0.821710i | \(0.693020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.76137 | −0.208740 | ||||||||
\(176\) | −12.7820 | −0.963480 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.167560 | −0.0125592 | ||||||||
\(179\) | 11.1785 | 0.835522 | 0.417761 | − | 0.908557i | \(-0.362815\pi\) | ||||
0.417761 | + | 0.908557i | \(0.362815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.51645 | −0.335705 | −0.167852 | − | 0.985812i | \(-0.553683\pi\) | ||||
−0.167852 | + | 0.985812i | \(0.553683\pi\) | |||||||
\(182\) | −2.26303 | −0.167747 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.31549 | −0.318142 | ||||||||
\(185\) | 7.00644 | 0.515123 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8384 | 1.15822 | ||||||||
\(188\) | −9.41655 | −0.686772 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.356330 | 0.0258509 | ||||||||
\(191\) | −24.7702 | −1.79231 | −0.896153 | − | 0.443744i | \(-0.853650\pi\) | ||||
−0.896153 | + | 0.443744i | \(0.853650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.4522 | 1.97605 | 0.988026 | − | 0.154288i | \(-0.0493083\pi\) | ||||
0.988026 | + | 0.154288i | \(0.0493083\pi\) | |||||||
\(194\) | −1.77115 | −0.127161 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.23279 | −0.0880563 | ||||||||
\(197\) | −8.84300 | −0.630038 | −0.315019 | − | 0.949085i | \(-0.602011\pi\) | ||||
−0.315019 | + | 0.949085i | \(0.602011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1238 | −0.859430 | −0.429715 | − | 0.902964i | \(-0.641386\pi\) | ||||
−0.429715 | + | 0.902964i | \(0.641386\pi\) | |||||||
\(200\) | 0.665537 | 0.0470606 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.09008 | 0.0766976 | ||||||||
\(203\) | −0.244652 | −0.0171712 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.31495 | −0.371212 | ||||||||
\(206\) | 3.07824 | 0.214471 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.7437 | −1.29964 | ||||||||
\(209\) | 7.09279 | 0.490618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.68837 | −0.116232 | −0.0581161 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581161 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(212\) | 6.97349 | 0.478941 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.40687 | 0.0961714 | ||||||||
\(215\) | 10.4989 | 0.716019 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.81668 | 0.191209 | ||||||||
\(218\) | 2.04013 | 0.138175 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.57698 | 0.443420 | ||||||||
\(221\) | 23.2257 | 1.56233 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.5451 | 1.30884 | 0.654418 | − | 0.756133i | \(-0.272914\pi\) | ||||
0.654418 | + | 0.756133i | \(0.272914\pi\) | |||||||
\(224\) | 5.44880 | 0.364063 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.127683 | 0.00849334 | ||||||||
\(227\) | 7.16828 | 0.475776 | 0.237888 | − | 0.971293i | \(-0.423545\pi\) | ||||
0.237888 | + | 0.971293i | \(0.423545\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.47217 | 0.493775 | 0.246887 | − | 0.969044i | \(-0.420592\pi\) | ||||
0.246887 | + | 0.969044i | \(0.420592\pi\) | |||||||
\(230\) | 1.08650 | 0.0716416 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0589652 | 0.00387126 | ||||||||
\(233\) | −25.9048 | −1.69708 | −0.848540 | − | 0.529131i | \(-0.822518\pi\) | ||||
−0.848540 | + | 0.529131i | \(0.822518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.77531 | 0.311507 | ||||||||
\(236\) | −2.17792 | −0.141771 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.19721 | −0.142424 | ||||||||
\(239\) | 22.6981 | 1.46822 | 0.734110 | − | 0.679030i | \(-0.237599\pi\) | ||||
0.734110 | + | 0.679030i | \(0.237599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.37348 | 0.217305 | 0.108653 | − | 0.994080i | \(-0.465346\pi\) | ||||
0.108653 | + | 0.994080i | \(0.465346\pi\) | |||||||
\(242\) | −0.0208275 | −0.00133885 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.69871 | 0.236785 | ||||||||
\(245\) | 0.625170 | 0.0399407 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.4010 | 0.661798 | ||||||||
\(248\) | −0.678867 | −0.0431081 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.167560 | −0.0105975 | ||||||||
\(251\) | 0.179341 | 0.0113199 | 0.00565996 | − | 0.999984i | \(-0.498198\pi\) | ||||
0.00565996 | + | 0.999984i | \(0.498198\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.6269 | 1.35967 | ||||||||
\(254\) | −2.94767 | −0.184953 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.8009 | 0.862554 | ||||||||
\(257\) | 19.0232 | 1.18663 | 0.593316 | − | 0.804970i | \(-0.297818\pi\) | ||||
0.593316 | + | 0.804970i | \(0.297818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.3474 | −1.20219 | ||||||||
\(260\) | 9.64458 | 0.598131 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.75879 | −0.170439 | ||||||||
\(263\) | −9.99555 | −0.616352 | −0.308176 | − | 0.951329i | \(-0.599719\pi\) | ||||
−0.308176 | + | 0.951329i | \(0.599719\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.53639 | −0.217239 | ||||||||
\(266\) | −0.983959 | −0.0603304 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.3525 | −1.54865 | ||||||||
\(269\) | −21.4992 | −1.31083 | −0.655414 | − | 0.755269i | \(-0.727506\pi\) | ||||
−0.655414 | + | 0.755269i | \(0.727506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.04650 | −0.306553 | −0.153277 | − | 0.988183i | \(-0.548983\pi\) | ||||
−0.153277 | + | 0.988183i | \(0.548983\pi\) | |||||||
\(272\) | −18.1986 | −1.10345 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.67895 | −0.101429 | ||||||||
\(275\) | −3.33531 | −0.201127 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.35611 | −0.0814805 | −0.0407402 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407402 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(278\) | −1.53397 | −0.0920017 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.83780 | −0.109829 | ||||||||
\(281\) | 11.5826 | 0.690961 | 0.345481 | − | 0.938426i | \(-0.387716\pi\) | ||||
0.345481 | + | 0.938426i | \(0.387716\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0608 | 0.598053 | 0.299027 | − | 0.954245i | \(-0.403338\pi\) | ||||
0.299027 | + | 0.954245i | \(0.403338\pi\) | |||||||
\(284\) | 17.6644 | 1.04819 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.73339 | −0.161629 | ||||||||
\(287\) | 14.6765 | 0.866329 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.55019 | 0.326482 | ||||||||
\(290\) | −0.0148455 | −0.000871758 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.55307 | −0.500531 | ||||||||
\(293\) | 7.91473 | 0.462383 | 0.231192 | − | 0.972908i | \(-0.425738\pi\) | ||||
0.231192 | + | 0.972908i | \(0.425738\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.10447 | 0.0643045 | ||||||||
\(296\) | 4.66304 | 0.271034 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.126493 | −0.00732754 | ||||||||
\(299\) | 31.7140 | 1.83407 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.9913 | −1.67103 | ||||||||
\(302\) | −3.41221 | −0.196351 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.14973 | −0.467419 | ||||||||
\(305\) | −1.87568 | −0.107401 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.68306 | −0.324349 | −0.162175 | − | 0.986762i | \(-0.551851\pi\) | ||||
−0.162175 | + | 0.986762i | \(0.551851\pi\) | |||||||
\(308\) | −18.1615 | −1.03485 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.170917 | 0.00970741 | ||||||||
\(311\) | 32.8960 | 1.86536 | 0.932679 | − | 0.360706i | \(-0.117464\pi\) | ||||
0.932679 | + | 0.360706i | \(0.117464\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.66481 | 0.320194 | 0.160097 | − | 0.987101i | \(-0.448819\pi\) | ||||
0.160097 | + | 0.987101i | \(0.448819\pi\) | |||||||
\(314\) | 3.13510 | 0.176924 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.10600 | 0.0622175 | ||||||||
\(317\) | 19.8605 | 1.11548 | 0.557738 | − | 0.830017i | \(-0.311670\pi\) | ||||
0.557738 | + | 0.830017i | \(0.311670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.295502 | −0.0165449 | ||||||||
\(320\) | −7.33402 | −0.409984 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.00023 | −0.167196 | ||||||||
\(323\) | 10.0985 | 0.561894 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.89095 | −0.271301 | ||||||||
\(326\) | 1.57471 | 0.0872151 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.53730 | −0.195315 | ||||||||
\(329\) | −13.1864 | −0.726990 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2500 | −1.05807 | −0.529037 | − | 0.848599i | \(-0.677447\pi\) | ||||
−0.529037 | + | 0.848599i | \(0.677447\pi\) | |||||||
\(332\) | −4.02739 | −0.221032 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.89564 | −0.158443 | ||||||||
\(335\) | 12.8567 | 0.702439 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.1877 | 1.64443 | 0.822215 | − | 0.569177i | \(-0.192738\pi\) | ||||
0.822215 | + | 0.569177i | \(0.192738\pi\) | |||||||
\(338\) | −1.82999 | −0.0995385 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.36408 | 0.507839 | ||||||||
\(341\) | 3.40211 | 0.184235 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6033 | 0.950487 | ||||||||
\(344\) | 6.98741 | 0.376736 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.51204 | 0.135048 | ||||||||
\(347\) | −20.5587 | −1.10365 | −0.551824 | − | 0.833960i | \(-0.686068\pi\) | ||||
−0.551824 | + | 0.833960i | \(0.686068\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.1762 | 0.598249 | 0.299124 | − | 0.954214i | \(-0.403305\pi\) | ||||
0.299124 | + | 0.954214i | \(0.403305\pi\) | |||||||
\(350\) | 0.462697 | 0.0247322 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.58131 | 0.350785 | ||||||||
\(353\) | −25.6908 | −1.36738 | −0.683691 | − | 0.729772i | \(-0.739626\pi\) | ||||
−0.683691 | + | 0.729772i | \(0.739626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.95798 | −0.475440 | ||||||||
\(356\) | −1.97192 | −0.104512 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.87308 | −0.0989952 | ||||||||
\(359\) | −26.2724 | −1.38660 | −0.693301 | − | 0.720648i | \(-0.743844\pi\) | ||||
−0.693301 | + | 0.720648i | \(0.743844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4777 | −0.761983 | ||||||||
\(362\) | 0.756778 | 0.0397753 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −26.6323 | −1.39591 | ||||||||
\(365\) | 4.33743 | 0.227031 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.7123 | 1.91636 | 0.958182 | − | 0.286160i | \(-0.0923788\pi\) | ||||
0.958182 | + | 0.286160i | \(0.0923788\pi\) | |||||||
\(368\) | −24.8497 | −1.29538 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.17400 | −0.0610334 | ||||||||
\(371\) | 9.76528 | 0.506988 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5774 | −1.47968 | −0.739842 | − | 0.672781i | \(-0.765100\pi\) | ||||
−0.739842 | + | 0.672781i | \(0.765100\pi\) | |||||||
\(374\) | −2.65389 | −0.137229 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.17815 | 0.163900 | ||||||||
\(377\) | −0.433328 | −0.0223175 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7598 | −0.809529 | −0.404764 | − | 0.914421i | \(-0.632646\pi\) | ||||
−0.404764 | + | 0.914421i | \(0.632646\pi\) | |||||||
\(380\) | 4.19344 | 0.215119 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.15050 | 0.212358 | ||||||||
\(383\) | 29.3120 | 1.49777 | 0.748886 | − | 0.662699i | \(-0.230589\pi\) | ||||
0.748886 | + | 0.662699i | \(0.230589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.21003 | 0.469387 | ||||||||
\(386\) | −4.59990 | −0.234129 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −20.8436 | −1.05818 | ||||||||
\(389\) | 7.63643 | 0.387182 | 0.193591 | − | 0.981082i | \(-0.437987\pi\) | ||||
0.193591 | + | 0.981082i | \(0.437987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.7916 | 1.55720 | ||||||||
\(392\) | 0.416074 | 0.0210149 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.48174 | 0.0746488 | ||||||||
\(395\) | −0.560875 | −0.0282207 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.2875 | 0.867634 | 0.433817 | − | 0.901001i | \(-0.357166\pi\) | ||||
0.433817 | + | 0.901001i | \(0.357166\pi\) | |||||||
\(398\) | 2.03146 | 0.101828 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.83233 | 0.191616 | ||||||||
\(401\) | −27.7710 | −1.38682 | −0.693408 | − | 0.720545i | \(-0.743892\pi\) | ||||
−0.693408 | + | 0.720545i | \(0.743892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.98891 | 0.248515 | ||||||||
\(404\) | 12.8285 | 0.638242 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0409939 | 0.00203450 | ||||||||
\(407\) | −23.3686 | −1.15834 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.94849 | 0.294134 | 0.147067 | − | 0.989127i | \(-0.453017\pi\) | ||||
0.147067 | + | 0.989127i | \(0.453017\pi\) | |||||||
\(410\) | 0.890575 | 0.0439824 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 36.2261 | 1.78473 | ||||||||
\(413\) | −3.04984 | −0.150073 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.04236 | 0.100256 | ||||||||
\(416\) | 9.65093 | 0.473176 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.18847 | −0.0581300 | ||||||||
\(419\) | −22.5429 | −1.10129 | −0.550646 | − | 0.834739i | \(-0.685619\pi\) | ||||
−0.550646 | + | 0.834739i | \(0.685619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.87459 | −0.432521 | −0.216261 | − | 0.976336i | \(-0.569386\pi\) | ||||
−0.216261 | + | 0.976336i | \(0.569386\pi\) | |||||||
\(422\) | 0.282904 | 0.0137716 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.35360 | −0.114301 | ||||||||
\(425\) | −4.74870 | −0.230346 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.17946 | 0.250652 | ||||||||
\(428\) | 16.5566 | 0.800294 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.75920 | −0.0848361 | ||||||||
\(431\) | 28.2077 | 1.35872 | 0.679358 | − | 0.733807i | \(-0.262258\pi\) | ||||
0.679358 | + | 0.733807i | \(0.262258\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1190 | −0.918801 | −0.459400 | − | 0.888229i | \(-0.651936\pi\) | ||||
−0.459400 | + | 0.888229i | \(0.651936\pi\) | |||||||
\(434\) | −0.471964 | −0.0226550 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.0091 | 1.14983 | ||||||||
\(437\) | 13.7892 | 0.659626 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.00432 | 0.0479334 | 0.0239667 | − | 0.999713i | \(-0.492370\pi\) | ||||
0.0239667 | + | 0.999713i | \(0.492370\pi\) | |||||||
\(440\) | −2.21977 | −0.105824 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.89170 | −0.185110 | ||||||||
\(443\) | −12.4989 | −0.593841 | −0.296920 | − | 0.954902i | \(-0.595960\pi\) | ||||
−0.296920 | + | 0.954902i | \(0.595960\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | 0.0474045 | ||||||||
\(446\) | −3.27498 | −0.155075 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.2520 | 0.956815 | ||||||||
\(449\) | 16.2680 | 0.767735 | 0.383867 | − | 0.923388i | \(-0.374592\pi\) | ||||
0.383867 | + | 0.923388i | \(0.374592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.7270 | 0.834732 | ||||||||
\(452\) | 1.50263 | 0.0706777 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.20112 | −0.0563714 | ||||||||
\(455\) | 13.5057 | 0.633158 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.351528 | 0.0164438 | 0.00822189 | − | 0.999966i | \(-0.497383\pi\) | ||||
0.00822189 | + | 0.999966i | \(0.497383\pi\) | |||||||
\(458\) | −1.25204 | −0.0585040 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.7864 | 0.596168 | ||||||||
\(461\) | 12.5064 | 0.582482 | 0.291241 | − | 0.956650i | \(-0.405932\pi\) | ||||
0.291241 | + | 0.956650i | \(0.405932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.1522 | −0.890080 | −0.445040 | − | 0.895511i | \(-0.646811\pi\) | ||||
−0.445040 | + | 0.895511i | \(0.646811\pi\) | |||||||
\(464\) | 0.339536 | 0.0157626 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.34062 | 0.201075 | ||||||||
\(467\) | 32.9017 | 1.52251 | 0.761255 | − | 0.648452i | \(-0.224583\pi\) | ||||
0.761255 | + | 0.648452i | \(0.224583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.5022 | −1.63934 | ||||||||
\(470\) | −0.800153 | −0.0369083 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.735064 | 0.0338340 | ||||||||
\(473\) | −35.0171 | −1.61009 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.12657 | −0.0975739 | ||||||||
\(476\) | −25.8577 | −1.18519 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.80331 | −0.173959 | ||||||||
\(479\) | 16.9068 | 0.772494 | 0.386247 | − | 0.922395i | \(-0.373771\pi\) | ||||
0.386247 | + | 0.922395i | \(0.373771\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.2681 | −1.56249 | ||||||||
\(482\) | −0.565262 | −0.0257470 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.245108 | −0.0111413 | ||||||||
\(485\) | 10.5702 | 0.479968 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.5619 | −1.61147 | −0.805733 | − | 0.592279i | \(-0.798228\pi\) | ||||
−0.805733 | + | 0.592279i | \(0.798228\pi\) | |||||||
\(488\) | −1.24834 | −0.0565096 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.104754 | −0.00473230 | ||||||||
\(491\) | −20.4192 | −0.921505 | −0.460753 | − | 0.887529i | \(-0.652421\pi\) | ||||
−0.460753 | + | 0.887529i | \(0.652421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.420725 | −0.0189485 | ||||||||
\(494\) | −1.74279 | −0.0784119 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.90909 | −0.175523 | ||||||||
\(497\) | 24.7363 | 1.10957 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.6453 | −1.14804 | −0.574022 | − | 0.818840i | \(-0.694617\pi\) | ||||
−0.574022 | + | 0.818840i | \(0.694617\pi\) | |||||||
\(500\) | −1.97192 | −0.0881871 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.0300505 | −0.00134122 | ||||||||
\(503\) | 18.9559 | 0.845201 | 0.422601 | − | 0.906316i | \(-0.361117\pi\) | ||||
0.422601 | + | 0.906316i | \(0.361117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.50558 | −0.289494 | ||||||||
\(506\) | −3.62381 | −0.161098 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −34.6895 | −1.53910 | ||||||||
\(509\) | −32.3589 | −1.43428 | −0.717141 | − | 0.696929i | \(-0.754549\pi\) | ||||
−0.717141 | + | 0.696929i | \(0.754549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9772 | −0.529842 | ||||||||
\(512\) | −12.6631 | −0.559637 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.18753 | −0.140596 | ||||||||
\(515\) | −18.3709 | −0.809521 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.9271 | −0.700475 | ||||||||
\(518\) | 3.24185 | 0.142439 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.25511 | −0.142746 | ||||||||
\(521\) | 8.27462 | 0.362518 | 0.181259 | − | 0.983435i | \(-0.441983\pi\) | ||||
0.181259 | + | 0.983435i | \(0.441983\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9288 | 0.696519 | 0.348260 | − | 0.937398i | \(-0.386773\pi\) | ||||
0.348260 | + | 0.937398i | \(0.386773\pi\) | |||||||
\(524\) | −32.4667 | −1.41831 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.67486 | 0.0730273 | ||||||||
\(527\) | 4.84382 | 0.211000 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0451 | 0.828048 | ||||||||
\(530\) | 0.592559 | 0.0257391 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.5796 | −0.502041 | ||||||||
\(533\) | 25.9952 | 1.12598 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.39617 | −0.362998 | ||||||||
\(536\) | 8.55664 | 0.369590 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.60241 | 0.155311 | ||||||||
\(539\) | −2.08514 | −0.0898132 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.14871 | 0.0923804 | 0.0461902 | − | 0.998933i | \(-0.485292\pi\) | ||||
0.0461902 | + | 0.998933i | \(0.485292\pi\) | |||||||
\(542\) | 0.845594 | 0.0363214 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.37024 | 0.401746 | ||||||||
\(545\) | −12.1755 | −0.521540 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0513 | 0.814576 | 0.407288 | − | 0.913300i | \(-0.366475\pi\) | ||||
0.407288 | + | 0.913300i | \(0.366475\pi\) | |||||||
\(548\) | −19.7586 | −0.844045 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.558866 | 0.0238301 | ||||||||
\(551\) | −0.188410 | −0.00802654 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.54878 | 0.0658610 | ||||||||
\(554\) | 0.227230 | 0.00965406 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.0525 | −0.765595 | ||||||||
\(557\) | −6.15992 | −0.261004 | −0.130502 | − | 0.991448i | \(-0.541659\pi\) | ||||
−0.130502 | + | 0.991448i | \(0.541659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −51.3496 | −2.17186 | ||||||||
\(560\) | −10.5825 | −0.447192 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.94079 | −0.0818672 | ||||||||
\(563\) | −14.3245 | −0.603704 | −0.301852 | − | 0.953355i | \(-0.597605\pi\) | ||||
−0.301852 | + | 0.953355i | \(0.597605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.762011 | −0.0320580 | ||||||||
\(566\) | −1.68579 | −0.0708592 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.96187 | −0.250154 | ||||||||
\(569\) | −6.91851 | −0.290039 | −0.145020 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145020 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0087 | 0.795490 | 0.397745 | − | 0.917496i | \(-0.369793\pi\) | ||||
0.397745 | + | 0.917496i | \(0.369793\pi\) | |||||||
\(572\) | −32.1677 | −1.34500 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.45921 | −0.102645 | ||||||||
\(575\) | −6.48422 | −0.270411 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2198 | 0.425458 | 0.212729 | − | 0.977111i | \(-0.431765\pi\) | ||||
0.212729 | + | 0.977111i | \(0.431765\pi\) | |||||||
\(578\) | −0.929992 | −0.0386826 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.174708 | −0.00725437 | ||||||||
\(581\) | −5.63973 | −0.233975 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.7950 | 0.488497 | ||||||||
\(584\) | 2.88672 | 0.119453 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.32620 | −0.0547846 | ||||||||
\(587\) | 43.0236 | 1.77578 | 0.887888 | − | 0.460060i | \(-0.152172\pi\) | ||||
0.887888 | + | 0.460060i | \(0.152172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.16917 | 0.0893790 | ||||||||
\(590\) | −0.185065 | −0.00761900 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26.8510 | 1.10357 | ||||||||
\(593\) | −14.8859 | −0.611290 | −0.305645 | − | 0.952146i | \(-0.598872\pi\) | ||||
−0.305645 | + | 0.952146i | \(0.598872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1129 | 0.537578 | ||||||||
\(596\) | −1.48862 | −0.0609764 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.31401 | −0.217306 | ||||||||
\(599\) | −45.1669 | −1.84547 | −0.922735 | − | 0.385436i | \(-0.874051\pi\) | ||||
−0.922735 | + | 0.385436i | \(0.874051\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.4553 | 1.56862 | 0.784311 | − | 0.620368i | \(-0.213017\pi\) | ||||
0.784311 | + | 0.620368i | \(0.213017\pi\) | |||||||
\(602\) | 4.85780 | 0.197989 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −40.1564 | −1.63394 | ||||||||
\(605\) | 0.124299 | 0.00505346 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.5466 | 1.19926 | 0.599629 | − | 0.800278i | \(-0.295315\pi\) | ||||
0.599629 | + | 0.800278i | \(0.295315\pi\) | |||||||
\(608\) | 4.19620 | 0.170178 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.314290 | 0.0127252 | ||||||||
\(611\) | −23.3558 | −0.944875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.1853 | 1.62307 | 0.811534 | − | 0.584306i | \(-0.198633\pi\) | ||||
0.811534 | + | 0.584306i | \(0.198633\pi\) | |||||||
\(614\) | 0.952256 | 0.0384299 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.12962 | 0.246969 | ||||||||
\(617\) | −8.08517 | −0.325497 | −0.162748 | − | 0.986668i | \(-0.552036\pi\) | ||||
−0.162748 | + | 0.986668i | \(0.552036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4190 | −0.499161 | −0.249580 | − | 0.968354i | \(-0.580293\pi\) | ||||
−0.249580 | + | 0.968354i | \(0.580293\pi\) | |||||||
\(620\) | 2.01142 | 0.0807805 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.51206 | −0.221014 | ||||||||
\(623\) | −2.76137 | −0.110632 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.949197 | −0.0379376 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.8952 | 1.47228 | ||||||||
\(629\) | −33.2715 | −1.32662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.89333 | −0.354038 | −0.177019 | − | 0.984207i | \(-0.556645\pi\) | ||||
−0.177019 | + | 0.984207i | \(0.556645\pi\) | |||||||
\(632\) | −0.373283 | −0.0148484 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.32783 | −0.132165 | ||||||||
\(635\) | 17.5917 | 0.698105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.05768 | −0.121150 | ||||||||
\(638\) | 0.0495144 | 0.00196029 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.17533 | 0.204573 | ||||||||
\(641\) | −16.8770 | −0.666603 | −0.333302 | − | 0.942820i | \(-0.608163\pi\) | ||||
−0.333302 | + | 0.942820i | \(0.608163\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.09389 | 0.161447 | 0.0807235 | − | 0.996737i | \(-0.474277\pi\) | ||||
0.0807235 | + | 0.996737i | \(0.474277\pi\) | |||||||
\(644\) | −35.3080 | −1.39133 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.69210 | −0.0665750 | ||||||||
\(647\) | −15.1293 | −0.594795 | −0.297397 | − | 0.954754i | \(-0.596119\pi\) | ||||
−0.297397 | + | 0.954754i | \(0.596119\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.68374 | −0.144599 | ||||||||
\(650\) | 0.819530 | 0.0321446 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.5319 | 0.725764 | ||||||||
\(653\) | 7.52805 | 0.294595 | 0.147298 | − | 0.989092i | \(-0.452942\pi\) | ||||
0.147298 | + | 0.989092i | \(0.452942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.4645 | 0.643320 | ||||||||
\(656\) | −20.3686 | −0.795262 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.20952 | 0.0861361 | ||||||||
\(659\) | 2.57821 | 0.100433 | 0.0502164 | − | 0.998738i | \(-0.484009\pi\) | ||||
0.0502164 | + | 0.998738i | \(0.484009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1301 | −0.432910 | −0.216455 | − | 0.976293i | \(-0.569449\pi\) | ||||
−0.216455 | + | 0.976293i | \(0.569449\pi\) | |||||||
\(662\) | 3.22553 | 0.125364 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.35927 | 0.0527499 | ||||||||
\(665\) | 5.87226 | 0.227716 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.574488 | −0.0222443 | ||||||||
\(668\) | −34.0772 | −1.31849 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.15428 | −0.0832271 | ||||||||
\(671\) | 6.25599 | 0.241510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4043 | −0.516698 | −0.258349 | − | 0.966052i | \(-0.583178\pi\) | ||||
−0.258349 | + | 0.966052i | \(0.583178\pi\) | |||||||
\(674\) | −5.05827 | −0.194837 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.5362 | −0.828314 | ||||||||
\(677\) | −48.9734 | −1.88220 | −0.941101 | − | 0.338127i | \(-0.890207\pi\) | ||||
−0.941101 | + | 0.338127i | \(0.890207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1883 | −1.12014 | ||||||||
\(680\) | −3.16044 | −0.121197 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.570060 | −0.0218287 | ||||||||
\(683\) | −31.9190 | −1.22135 | −0.610673 | − | 0.791883i | \(-0.709101\pi\) | ||||
−0.610673 | + | 0.791883i | \(0.709101\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0200 | 0.382843 | ||||||||
\(686\) | −2.94961 | −0.112617 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 40.2352 | 1.53395 | ||||||||
\(689\) | 17.2963 | 0.658937 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3516 | −0.545960 | −0.272980 | − | 0.962020i | \(-0.588009\pi\) | ||||
−0.272980 | + | 0.962020i | \(0.588009\pi\) | |||||||
\(692\) | 29.5628 | 1.12381 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.44483 | 0.130764 | ||||||||
\(695\) | 9.15475 | 0.347260 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.2391 | 0.956000 | ||||||||
\(698\) | −1.87269 | −0.0708824 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.44521 | 0.205810 | ||||||||
\(701\) | 35.0461 | 1.32367 | 0.661836 | − | 0.749649i | \(-0.269778\pi\) | ||||
0.661836 | + | 0.749649i | \(0.269778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.8997 | −0.561953 | ||||||||
\(704\) | 24.4613 | 0.921918 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.30476 | 0.162012 | ||||||||
\(707\) | 17.9643 | 0.675617 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.0084 | 1.16455 | 0.582273 | − | 0.812993i | \(-0.302164\pi\) | ||||
0.582273 | + | 0.812993i | \(0.302164\pi\) | |||||||
\(710\) | 1.50100 | 0.0563316 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.665537 | 0.0249421 | ||||||||
\(713\) | 6.61409 | 0.247700 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.3128 | 0.610066 | ||||||||
\(716\) | −22.0432 | −0.823793 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.40221 | 0.164289 | ||||||||
\(719\) | −14.2269 | −0.530572 | −0.265286 | − | 0.964170i | \(-0.585466\pi\) | ||||
−0.265286 | + | 0.964170i | \(0.585466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.7290 | 1.88925 | ||||||||
\(722\) | 2.42589 | 0.0902822 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.90609 | 0.330992 | ||||||||
\(725\) | 0.0885979 | 0.00329044 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.1412 | 0.821172 | 0.410586 | − | 0.911822i | \(-0.365324\pi\) | ||||
0.410586 | + | 0.911822i | \(0.365324\pi\) | |||||||
\(728\) | 8.98857 | 0.333138 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.726781 | −0.0268994 | ||||||||
\(731\) | −49.8561 | −1.84400 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.7772 | −0.619679 | −0.309839 | − | 0.950789i | \(-0.600275\pi\) | ||||
−0.309839 | + | 0.950789i | \(0.600275\pi\) | |||||||
\(734\) | −6.15152 | −0.227057 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.7948 | 0.471623 | ||||||||
\(737\) | −42.8812 | −1.57955 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.2549 | −0.965802 | −0.482901 | − | 0.875675i | \(-0.660417\pi\) | ||||
−0.482901 | + | 0.875675i | \(0.660417\pi\) | |||||||
\(740\) | −13.8162 | −0.507892 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.63627 | −0.0600695 | ||||||||
\(743\) | 5.64662 | 0.207154 | 0.103577 | − | 0.994621i | \(-0.466971\pi\) | ||||
0.103577 | + | 0.994621i | \(0.466971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.754909 | 0.0276577 | ||||||||
\(746\) | 4.78845 | 0.175317 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −31.2321 | −1.14196 | ||||||||
\(749\) | 23.1849 | 0.847160 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.27816 | −0.0831314 | −0.0415657 | − | 0.999136i | \(-0.513235\pi\) | ||||
−0.0415657 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(752\) | 18.3006 | 0.667353 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.0726086 | 0.00264425 | ||||||||
\(755\) | 20.3641 | 0.741124 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.3296 | −1.75657 | −0.878284 | − | 0.478139i | \(-0.841311\pi\) | ||||
−0.878284 | + | 0.478139i | \(0.841311\pi\) | |||||||
\(758\) | 2.64073 | 0.0959155 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.41531 | −0.0513388 | ||||||||
\(761\) | 6.41780 | 0.232645 | 0.116323 | − | 0.993211i | \(-0.462889\pi\) | ||||
0.116323 | + | 0.993211i | \(0.462889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.6210 | 1.21716 | ||||||||
\(764\) | 48.8449 | 1.76715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.91152 | −0.177461 | ||||||||
\(767\) | −5.40189 | −0.195051 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.7999 | −1.00249 | −0.501246 | − | 0.865305i | \(-0.667125\pi\) | ||||
−0.501246 | + | 0.865305i | \(0.667125\pi\) | |||||||
\(770\) | −1.54324 | −0.0556144 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −54.1336 | −1.94831 | ||||||||
\(773\) | −6.26657 | −0.225393 | −0.112696 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112696 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.02003 | −0.0366405 | ||||||||
\(776\) | 7.03486 | 0.252537 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.27956 | −0.0458745 | ||||||||
\(779\) | 11.3026 | 0.404959 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.8776 | 1.06911 | ||||||||
\(782\) | −5.15946 | −0.184502 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.39586 | 0.0855664 | ||||||||
\(785\) | −18.7103 | −0.667798 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.3330 | 1.00996 | 0.504982 | − | 0.863130i | \(-0.331499\pi\) | ||||
0.504982 | + | 0.863130i | \(0.331499\pi\) | |||||||
\(788\) | 17.4377 | 0.621193 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.0939804 | 0.00334367 | ||||||||
\(791\) | 2.10420 | 0.0748166 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.17388 | 0.325774 | ||||||||
\(794\) | −2.89670 | −0.102800 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.9071 | 0.847365 | ||||||||
\(797\) | −22.2283 | −0.787366 | −0.393683 | − | 0.919246i | \(-0.628799\pi\) | ||||
−0.393683 | + | 0.919246i | \(0.628799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.6765 | −0.802238 | ||||||||
\(800\) | −1.97322 | −0.0697639 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.65332 | 0.164314 | ||||||||
\(803\) | −14.4667 | −0.510518 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.9053 | 0.631080 | ||||||||
\(806\) | −0.835944 | −0.0294449 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.32970 | −0.152318 | ||||||||
\(809\) | −21.9406 | −0.771389 | −0.385694 | − | 0.922627i | \(-0.626038\pi\) | ||||
−0.385694 | + | 0.922627i | \(0.626038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.38160 | 0.224088 | 0.112044 | − | 0.993703i | \(-0.464260\pi\) | ||||
0.112044 | + | 0.993703i | \(0.464260\pi\) | |||||||
\(812\) | 0.482434 | 0.0169301 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.91566 | 0.137244 | ||||||||
\(815\) | −9.39787 | −0.329193 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.3267 | −0.781112 | ||||||||
\(818\) | −0.996732 | −0.0348499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4807 | 0.366001 | ||||||||
\(821\) | −29.9161 | −1.04408 | −0.522040 | − | 0.852921i | \(-0.674829\pi\) | ||||
−0.522040 | + | 0.852921i | \(0.674829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.5172 | −1.44720 | −0.723600 | − | 0.690220i | \(-0.757514\pi\) | ||||
−0.723600 | + | 0.690220i | \(0.757514\pi\) | |||||||
\(824\) | −12.2265 | −0.425932 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.511033 | 0.0177811 | ||||||||
\(827\) | 23.8732 | 0.830153 | 0.415076 | − | 0.909787i | \(-0.363755\pi\) | ||||
0.415076 | + | 0.909787i | \(0.363755\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.3129 | 1.19174 | 0.595868 | − | 0.803083i | \(-0.296808\pi\) | ||||
0.595868 | + | 0.803083i | \(0.296808\pi\) | |||||||
\(830\) | −0.342219 | −0.0118786 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 35.8704 | 1.24358 | ||||||||
\(833\) | −2.96875 | −0.102861 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.2812 | 0.598040 | ||||||||
\(836\) | −13.9864 | −0.483731 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.77730 | 0.130485 | ||||||||
\(839\) | 20.4337 | 0.705451 | 0.352725 | − | 0.935727i | \(-0.385255\pi\) | ||||
0.352725 | + | 0.935727i | \(0.385255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9922 | −0.999729 | ||||||||
\(842\) | 1.48703 | 0.0512465 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.32934 | 0.114601 | ||||||||
\(845\) | 10.9214 | 0.375707 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.343235 | −0.0117937 | ||||||||
\(848\) | −13.5526 | −0.465398 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.795695 | 0.0272921 | ||||||||
\(851\) | −45.4313 | −1.55736 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.6032 | 0.568482 | 0.284241 | − | 0.958753i | \(-0.408258\pi\) | ||||
0.284241 | + | 0.958753i | \(0.408258\pi\) | |||||||
\(854\) | −0.867873 | −0.0296980 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.58797 | −0.190993 | ||||||||
\(857\) | −37.1328 | −1.26843 | −0.634217 | − | 0.773155i | \(-0.718677\pi\) | ||||
−0.634217 | + | 0.773155i | \(0.718677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.9169 | 1.25959 | 0.629795 | − | 0.776762i | \(-0.283139\pi\) | ||||
0.629795 | + | 0.776762i | \(0.283139\pi\) | |||||||
\(860\) | −20.7030 | −0.705967 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.72649 | −0.160985 | ||||||||
\(863\) | 19.2588 | 0.655577 | 0.327788 | − | 0.944751i | \(-0.393697\pi\) | ||||
0.327788 | + | 0.944751i | \(0.393697\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.9919 | −0.509739 | ||||||||
\(866\) | 3.20359 | 0.108862 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.55428 | −0.188524 | ||||||||
\(869\) | 1.87069 | 0.0634589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62.8817 | −2.13066 | ||||||||
\(872\) | −8.10323 | −0.274410 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.31052 | −0.0781545 | ||||||||
\(875\) | −2.76137 | −0.0933514 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.26192 | 0.177682 | 0.0888411 | − | 0.996046i | \(-0.471684\pi\) | ||||
0.0888411 | + | 0.996046i | \(0.471684\pi\) | |||||||
\(878\) | −0.168284 | −0.00567930 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.7820 | −0.430881 | ||||||||
\(881\) | −32.1477 | −1.08308 | −0.541541 | − | 0.840674i | \(-0.682159\pi\) | ||||
−0.541541 | + | 0.840674i | \(0.682159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.71530 | 0.192335 | 0.0961676 | − | 0.995365i | \(-0.469342\pi\) | ||||
0.0961676 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(884\) | −45.7993 | −1.54040 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.09432 | 0.0703601 | ||||||||
\(887\) | −0.829148 | −0.0278401 | −0.0139200 | − | 0.999903i | \(-0.504431\pi\) | ||||
−0.0139200 | + | 0.999903i | \(0.504431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.5772 | −1.62923 | ||||||||
\(890\) | −0.167560 | −0.00561664 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −38.5414 | −1.29046 | ||||||||
\(893\) | −10.1551 | −0.339826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1785 | 0.373657 | ||||||||
\(896\) | −14.2910 | −0.477429 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.72587 | −0.0909636 | ||||||||
\(899\) | −0.0903724 | −0.00301409 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7933 | 0.559465 | ||||||||
\(902\) | −2.97035 | −0.0989017 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.507147 | −0.0168675 | ||||||||
\(905\) | −4.51645 | −0.150132 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.5923 | −0.384916 | −0.192458 | − | 0.981305i | \(-0.561646\pi\) | ||||
−0.192458 | + | 0.981305i | \(0.561646\pi\) | |||||||
\(908\) | −14.1353 | −0.469096 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.26303 | −0.0750186 | ||||||||
\(911\) | 50.4744 | 1.67229 | 0.836146 | − | 0.548507i | \(-0.184804\pi\) | ||||
0.836146 | + | 0.548507i | \(0.184804\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.81192 | −0.225442 | ||||||||
\(914\) | −0.0589022 | −0.00194831 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.7346 | −0.486843 | ||||||||
\(917\) | −45.4645 | −1.50137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.86726 | 0.259517 | 0.129759 | − | 0.991546i | \(-0.458580\pi\) | ||||
0.129759 | + | 0.991546i | \(0.458580\pi\) | |||||||
\(920\) | −4.31549 | −0.142277 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.09558 | −0.0690143 | ||||||||
\(923\) | 43.8130 | 1.44212 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.00644 | 0.230370 | ||||||||
\(926\) | 3.20916 | 0.105459 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.174823 | −0.00573886 | ||||||||
\(929\) | −10.7076 | −0.351305 | −0.175652 | − | 0.984452i | \(-0.556203\pi\) | ||||
−0.175652 | + | 0.984452i | \(0.556203\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.32947 | −0.0435717 | ||||||||
\(932\) | 51.0823 | 1.67326 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.51303 | −0.180392 | ||||||||
\(935\) | 15.8384 | 0.517971 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0259 | 0.882896 | 0.441448 | − | 0.897287i | \(-0.354465\pi\) | ||||
0.441448 | + | 0.897287i | \(0.354465\pi\) | |||||||
\(938\) | 5.94877 | 0.194234 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.41655 | −0.307134 | ||||||||
\(941\) | 22.0874 | 0.720029 | 0.360015 | − | 0.932947i | \(-0.382772\pi\) | ||||
0.360015 | + | 0.932947i | \(0.382772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.4633 | 1.12228 | ||||||||
\(944\) | 4.23268 | 0.137762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.86748 | 0.190768 | ||||||||
\(947\) | 36.5249 | 1.18690 | 0.593449 | − | 0.804872i | \(-0.297766\pi\) | ||||
0.593449 | + | 0.804872i | \(0.297766\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.2141 | −0.688640 | ||||||||
\(950\) | 0.356330 | 0.0115609 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.72715 | 0.282848 | ||||||||
\(953\) | 44.9253 | 1.45527 | 0.727637 | − | 0.685962i | \(-0.240618\pi\) | ||||
0.727637 | + | 0.685962i | \(0.240618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.7702 | −0.801544 | ||||||||
\(956\) | −44.7590 | −1.44761 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.83292 | −0.0915274 | ||||||||
\(959\) | −27.6688 | −0.893473 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9595 | −0.966437 | ||||||||
\(962\) | 5.74198 | 0.185129 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.65225 | −0.214255 | ||||||||
\(965\) | 27.4522 | 0.883717 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.0562 | −1.19165 | −0.595823 | − | 0.803116i | \(-0.703174\pi\) | ||||
−0.595823 | + | 0.803116i | \(0.703174\pi\) | |||||||
\(968\) | 0.0827254 | 0.00265890 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.77115 | −0.0568681 | ||||||||
\(971\) | 31.3238 | 1.00523 | 0.502614 | − | 0.864511i | \(-0.332372\pi\) | ||||
0.502614 | + | 0.864511i | \(0.332372\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.2797 | −0.810429 | ||||||||
\(974\) | 5.95878 | 0.190931 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.18824 | −0.230090 | ||||||||
\(977\) | 17.7676 | 0.568437 | 0.284219 | − | 0.958759i | \(-0.408266\pi\) | ||||
0.284219 | + | 0.958759i | \(0.408266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.33531 | −0.106597 | ||||||||
\(980\) | −1.23279 | −0.0393800 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.42145 | 0.109183 | ||||||||
\(983\) | 20.7240 | 0.660993 | 0.330496 | − | 0.943807i | \(-0.392784\pi\) | ||||
0.330496 | + | 0.943807i | \(0.392784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.84300 | −0.281761 | ||||||||
\(986\) | 0.0704969 | 0.00224508 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.5099 | −0.652507 | ||||||||
\(989\) | −68.0772 | −2.16473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.3041 | 1.02618 | 0.513088 | − | 0.858336i | \(-0.328502\pi\) | ||||
0.513088 | + | 0.858336i | \(0.328502\pi\) | |||||||
\(992\) | 2.01274 | 0.0639047 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.14482 | −0.131466 | ||||||||
\(995\) | −12.1238 | −0.384349 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.7989 | 1.19710 | 0.598551 | − | 0.801085i | \(-0.295743\pi\) | ||||
0.598551 | + | 0.801085i | \(0.295743\pi\) | |||||||
\(998\) | 4.29714 | 0.136024 | ||||||||
\(999\) | 0 | 0 |
(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 | 4005.2.a.t.1.5 | 10 | ||
3.2 | odd | 2 | 1335.2.a.i.1.6 | ✓ | 10 | ||
15.14 | odd | 2 | 6675.2.a.ba.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1335.2.a.i.1.6 | ✓ | 10 | 3.2 | odd | 2 | ||
4005.2.a.t.1.5 | 10 | 1.1 | even | 1 | trivial | ||
6675.2.a.ba.1.5 | 10 | 15.14 | odd | 2 |