Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.305611 | 0.216100 | 0.108050 | − | 0.994145i | \(-0.465539\pi\) | ||||
0.108050 | + | 0.994145i | \(0.465539\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.90660 | −0.953301 | ||||||||
\(5\) | −1.63568 | −0.731500 | −0.365750 | − | 0.930713i | \(-0.619188\pi\) | ||||
−0.365750 | + | 0.930713i | \(0.619188\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.53407 | −1.33575 | −0.667876 | − | 0.744273i | \(-0.732796\pi\) | ||||
−0.667876 | + | 0.744273i | \(0.732796\pi\) | |||||||
\(8\) | −1.19390 | −0.422108 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.499884 | −0.158077 | ||||||||
\(11\) | −3.40800 | −1.02755 | −0.513775 | − | 0.857925i | \(-0.671754\pi\) | ||||
−0.513775 | + | 0.857925i | \(0.671754\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.61987 | −0.449272 | −0.224636 | − | 0.974443i | \(-0.572119\pi\) | ||||
−0.224636 | + | 0.974443i | \(0.572119\pi\) | |||||||
\(14\) | −1.08005 | −0.288656 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.44833 | 0.862083 | ||||||||
\(17\) | −2.63124 | −0.638169 | −0.319085 | − | 0.947726i | \(-0.603375\pi\) | ||||
−0.319085 | + | 0.947726i | \(0.603375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.77340 | −0.636262 | −0.318131 | − | 0.948047i | \(-0.603055\pi\) | ||||
−0.318131 | + | 0.948047i | \(0.603055\pi\) | |||||||
\(20\) | 3.11860 | 0.697340 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.04152 | −0.222054 | ||||||||
\(23\) | −4.69302 | −0.978563 | −0.489281 | − | 0.872126i | \(-0.662741\pi\) | ||||
−0.489281 | + | 0.872126i | \(0.662741\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.32454 | −0.464907 | ||||||||
\(26\) | −0.495052 | −0.0970877 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.73806 | 1.27337 | ||||||||
\(29\) | 5.63940 | 1.04721 | 0.523605 | − | 0.851961i | \(-0.324587\pi\) | ||||
0.523605 | + | 0.851961i | \(0.324587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.83543 | −1.22768 | −0.613840 | − | 0.789431i | \(-0.710376\pi\) | ||||
−0.613840 | + | 0.789431i | \(0.710376\pi\) | |||||||
\(32\) | 3.44165 | 0.608404 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.804137 | −0.137908 | ||||||||
\(35\) | 5.78062 | 0.977103 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.59407 | −0.755261 | −0.377630 | − | 0.925956i | \(-0.623261\pi\) | ||||
−0.377630 | + | 0.925956i | \(0.623261\pi\) | |||||||
\(38\) | −0.847583 | −0.137496 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.95285 | 0.308772 | ||||||||
\(41\) | −9.48524 | −1.48135 | −0.740673 | − | 0.671866i | \(-0.765493\pi\) | ||||
−0.740673 | + | 0.671866i | \(0.765493\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.3879 | −1.88913 | −0.944565 | − | 0.328324i | \(-0.893516\pi\) | ||||
−0.944565 | + | 0.328324i | \(0.893516\pi\) | |||||||
\(44\) | 6.49770 | 0.979565 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.43424 | −0.211467 | ||||||||
\(47\) | −12.4560 | −1.81689 | −0.908445 | − | 0.418005i | \(-0.862729\pi\) | ||||
−0.908445 | + | 0.418005i | \(0.862729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.48963 | 0.784233 | ||||||||
\(50\) | −0.710404 | −0.100466 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.08846 | 0.428292 | ||||||||
\(53\) | −2.81468 | −0.386626 | −0.193313 | − | 0.981137i | \(-0.561923\pi\) | ||||
−0.193313 | + | 0.981137i | \(0.561923\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.57441 | 0.751654 | ||||||||
\(56\) | 4.21933 | 0.563832 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.72347 | 0.226302 | ||||||||
\(59\) | −11.9950 | −1.56162 | −0.780809 | − | 0.624769i | \(-0.785193\pi\) | ||||
−0.780809 | + | 0.624769i | \(0.785193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.73342 | 1.11820 | 0.559100 | − | 0.829100i | \(-0.311147\pi\) | ||||
0.559100 | + | 0.829100i | \(0.311147\pi\) | |||||||
\(62\) | −2.08898 | −0.265301 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.84486 | −0.730607 | ||||||||
\(65\) | 2.64960 | 0.328643 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9026 | 1.33196 | 0.665981 | − | 0.745969i | \(-0.268013\pi\) | ||||
0.665981 | + | 0.745969i | \(0.268013\pi\) | |||||||
\(68\) | 5.01672 | 0.608367 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.76662 | 0.211152 | ||||||||
\(71\) | 5.04883 | 0.599186 | 0.299593 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299593 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.96534 | 1.16636 | 0.583178 | − | 0.812345i | \(-0.301809\pi\) | ||||
0.583178 | + | 0.812345i | \(0.301809\pi\) | |||||||
\(74\) | −1.40400 | −0.163212 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.28777 | 0.606549 | ||||||||
\(77\) | 12.0441 | 1.37255 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.47523 | 0.503503 | 0.251752 | − | 0.967792i | \(-0.418993\pi\) | ||||
0.251752 | + | 0.967792i | \(0.418993\pi\) | |||||||
\(80\) | −5.64039 | −0.630614 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.89880 | −0.320119 | ||||||||
\(83\) | 16.4364 | 1.80413 | 0.902065 | − | 0.431601i | \(-0.142051\pi\) | ||||
0.902065 | + | 0.431601i | \(0.142051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.30388 | 0.466821 | ||||||||
\(86\) | −3.78587 | −0.408241 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.06882 | 0.433737 | ||||||||
\(89\) | 13.3055 | 1.41038 | 0.705189 | − | 0.709019i | \(-0.250862\pi\) | ||||
0.705189 | + | 0.709019i | \(0.250862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.72475 | 0.600117 | ||||||||
\(92\) | 8.94772 | 0.932865 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.80668 | −0.392629 | ||||||||
\(95\) | 4.53641 | 0.465426 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6727 | −1.59132 | −0.795661 | − | 0.605742i | \(-0.792876\pi\) | ||||
−0.795661 | + | 0.605742i | \(0.792876\pi\) | |||||||
\(98\) | 1.67769 | 0.169473 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.43196 | 0.443196 | ||||||||
\(101\) | 6.81158 | 0.677777 | 0.338889 | − | 0.940826i | \(-0.389949\pi\) | ||||
0.338889 | + | 0.940826i | \(0.389949\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.64803 | −0.556517 | −0.278258 | − | 0.960506i | \(-0.589757\pi\) | ||||
−0.278258 | + | 0.960506i | \(0.589757\pi\) | |||||||
\(104\) | 1.93397 | 0.189642 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.860198 | −0.0835498 | ||||||||
\(107\) | −0.952294 | −0.0920617 | −0.0460309 | − | 0.998940i | \(-0.514657\pi\) | ||||
−0.0460309 | + | 0.998940i | \(0.514657\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1665 | −1.16534 | −0.582669 | − | 0.812709i | \(-0.697992\pi\) | ||||
−0.582669 | + | 0.812709i | \(0.697992\pi\) | |||||||
\(110\) | 1.70360 | 0.162432 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.1866 | −1.15153 | ||||||||
\(113\) | 14.4131 | 1.35587 | 0.677936 | − | 0.735121i | \(-0.262875\pi\) | ||||
0.677936 | + | 0.735121i | \(0.262875\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.67630 | 0.715819 | ||||||||
\(116\) | −10.7521 | −0.998307 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.66582 | −0.337466 | ||||||||
\(119\) | 9.29898 | 0.852436 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.614468 | 0.0558607 | ||||||||
\(122\) | 2.66903 | 0.241643 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.0324 | 1.17035 | ||||||||
\(125\) | 11.9806 | 1.07158 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.60930 | 0.763952 | 0.381976 | − | 0.924172i | \(-0.375244\pi\) | ||||
0.381976 | + | 0.924172i | \(0.375244\pi\) | |||||||
\(128\) | −8.66956 | −0.766288 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.809749 | 0.0710197 | ||||||||
\(131\) | −12.4781 | −1.09021 | −0.545107 | − | 0.838366i | \(-0.683511\pi\) | ||||
−0.545107 | + | 0.838366i | \(0.683511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.80139 | 0.849888 | ||||||||
\(134\) | 3.33195 | 0.287837 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.14144 | 0.269376 | ||||||||
\(137\) | 16.9230 | 1.44583 | 0.722914 | − | 0.690938i | \(-0.242802\pi\) | ||||
0.722914 | + | 0.690938i | \(0.242802\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.0137 | −1.95200 | −0.976000 | − | 0.217771i | \(-0.930121\pi\) | ||||
−0.976000 | + | 0.217771i | \(0.930121\pi\) | |||||||
\(140\) | −11.0213 | −0.931473 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.54298 | 0.129484 | ||||||||
\(143\) | 5.52053 | 0.461650 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.22428 | −0.766035 | ||||||||
\(146\) | 3.04552 | 0.252049 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.75907 | 0.719991 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.110557 | 0.00899702 | 0.00449851 | − | 0.999990i | \(-0.498568\pi\) | ||||
0.00449851 | + | 0.999990i | \(0.498568\pi\) | |||||||
\(152\) | 3.31117 | 0.268571 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.68081 | 0.296609 | ||||||||
\(155\) | 11.1806 | 0.898048 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.55212 | −0.443107 | −0.221554 | − | 0.975148i | \(-0.571113\pi\) | ||||
−0.221554 | + | 0.975148i | \(0.571113\pi\) | |||||||
\(158\) | 1.36768 | 0.108807 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.62946 | −0.445048 | ||||||||
\(161\) | 16.5855 | 1.30712 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.01697 | 0.392960 | 0.196480 | − | 0.980508i | \(-0.437049\pi\) | ||||
0.196480 | + | 0.980508i | \(0.437049\pi\) | |||||||
\(164\) | 18.0846 | 1.41217 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.02315 | 0.389872 | ||||||||
\(167\) | 1.51685 | 0.117378 | 0.0586888 | − | 0.998276i | \(-0.481308\pi\) | ||||
0.0586888 | + | 0.998276i | \(0.481308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3760 | −0.798154 | ||||||||
\(170\) | 1.31531 | 0.100880 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 23.6187 | 1.80091 | ||||||||
\(173\) | 4.97703 | 0.378397 | 0.189198 | − | 0.981939i | \(-0.439411\pi\) | ||||
0.189198 | + | 0.981939i | \(0.439411\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.21507 | 0.621001 | ||||||||
\(176\) | −11.7519 | −0.885834 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.06631 | 0.304782 | ||||||||
\(179\) | −11.3993 | −0.852020 | −0.426010 | − | 0.904718i | \(-0.640081\pi\) | ||||
−0.426010 | + | 0.904718i | \(0.640081\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.56349 | −0.487860 | −0.243930 | − | 0.969793i | \(-0.578437\pi\) | ||||
−0.243930 | + | 0.969793i | \(0.578437\pi\) | |||||||
\(182\) | 1.74955 | 0.129685 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.60301 | 0.413059 | ||||||||
\(185\) | 7.51445 | 0.552474 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.96726 | 0.655751 | ||||||||
\(188\) | 23.7486 | 1.73204 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.38638 | 0.100579 | ||||||||
\(191\) | 8.52455 | 0.616815 | 0.308407 | − | 0.951254i | \(-0.400204\pi\) | ||||
0.308407 | + | 0.951254i | \(0.400204\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.44184 | 0.607657 | 0.303829 | − | 0.952727i | \(-0.401735\pi\) | ||||
0.303829 | + | 0.952727i | \(0.401735\pi\) | |||||||
\(194\) | −4.78976 | −0.343884 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.4665 | −0.747610 | ||||||||
\(197\) | −15.7509 | −1.12220 | −0.561101 | − | 0.827747i | \(-0.689622\pi\) | ||||
−0.561101 | + | 0.827747i | \(0.689622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7755 | −0.905629 | −0.452814 | − | 0.891605i | \(-0.649580\pi\) | ||||
−0.452814 | + | 0.891605i | \(0.649580\pi\) | |||||||
\(200\) | 2.77527 | 0.196241 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.08170 | 0.146468 | ||||||||
\(203\) | −19.9300 | −1.39881 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.5149 | 1.08361 | ||||||||
\(206\) | −1.72610 | −0.120263 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.58587 | −0.387310 | ||||||||
\(209\) | 9.45176 | 0.653792 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6958 | −1.01170 | −0.505850 | − | 0.862622i | \(-0.668821\pi\) | ||||
−0.505850 | + | 0.862622i | \(0.668821\pi\) | |||||||
\(212\) | 5.36647 | 0.368571 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.291032 | −0.0198945 | ||||||||
\(215\) | 20.2626 | 1.38190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.1569 | 1.63988 | ||||||||
\(218\) | −3.71822 | −0.251829 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.6282 | −0.716552 | ||||||||
\(221\) | 4.26228 | 0.286712 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.2278 | −1.95724 | −0.978618 | − | 0.205685i | \(-0.934058\pi\) | ||||
−0.978618 | + | 0.205685i | \(0.934058\pi\) | |||||||
\(224\) | −12.1630 | −0.812677 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.40481 | 0.293004 | ||||||||
\(227\) | 24.8935 | 1.65224 | 0.826120 | − | 0.563494i | \(-0.190543\pi\) | ||||
0.826120 | + | 0.563494i | \(0.190543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.102112 | 0.00674772 | 0.00337386 | − | 0.999994i | \(-0.498926\pi\) | ||||
0.00337386 | + | 0.999994i | \(0.498926\pi\) | |||||||
\(230\) | 2.34597 | 0.154688 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.73289 | −0.442036 | ||||||||
\(233\) | 28.2129 | 1.84829 | 0.924143 | − | 0.382046i | \(-0.124780\pi\) | ||||
0.924143 | + | 0.382046i | \(0.124780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.3740 | 1.32906 | ||||||||
\(236\) | 22.8697 | 1.48869 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.84187 | 0.184211 | ||||||||
\(239\) | −7.85767 | −0.508271 | −0.254135 | − | 0.967169i | \(-0.581791\pi\) | ||||
−0.254135 | + | 0.967169i | \(0.581791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2146 | −1.36656 | −0.683278 | − | 0.730158i | \(-0.739446\pi\) | ||||
−0.683278 | + | 0.730158i | \(0.739446\pi\) | |||||||
\(242\) | 0.187788 | 0.0120715 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.6512 | −1.06598 | ||||||||
\(245\) | −8.97931 | −0.573667 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.49256 | 0.285855 | ||||||||
\(248\) | 8.16083 | 0.518213 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.66142 | 0.231568 | ||||||||
\(251\) | 7.56275 | 0.477356 | 0.238678 | − | 0.971099i | \(-0.423286\pi\) | ||||
0.238678 | + | 0.971099i | \(0.423286\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.9938 | 1.00552 | ||||||||
\(254\) | 2.63110 | 0.165090 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.04020 | 0.565013 | ||||||||
\(257\) | −29.0286 | −1.81075 | −0.905377 | − | 0.424609i | \(-0.860412\pi\) | ||||
−0.905377 | + | 0.424609i | \(0.860412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.2358 | 1.00884 | ||||||||
\(260\) | −5.05174 | −0.313296 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.81344 | −0.235595 | ||||||||
\(263\) | −28.5695 | −1.76167 | −0.880835 | − | 0.473423i | \(-0.843018\pi\) | ||||
−0.880835 | + | 0.473423i | \(0.843018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.60393 | 0.282817 | ||||||||
\(266\) | 2.99542 | 0.183661 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −20.7869 | −1.26976 | ||||||||
\(269\) | 14.1136 | 0.860523 | 0.430262 | − | 0.902704i | \(-0.358421\pi\) | ||||
0.430262 | + | 0.902704i | \(0.358421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.60205 | −0.0973179 | −0.0486589 | − | 0.998815i | \(-0.515495\pi\) | ||||
−0.0486589 | + | 0.998815i | \(0.515495\pi\) | |||||||
\(272\) | −9.07339 | −0.550155 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.17186 | 0.312443 | ||||||||
\(275\) | 7.92202 | 0.477716 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.2828 | −1.87960 | −0.939801 | − | 0.341722i | \(-0.888990\pi\) | ||||
−0.939801 | + | 0.341722i | \(0.888990\pi\) | |||||||
\(278\) | −7.03326 | −0.421827 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.90149 | −0.412443 | ||||||||
\(281\) | −26.1541 | −1.56022 | −0.780111 | − | 0.625641i | \(-0.784838\pi\) | ||||
−0.780111 | + | 0.625641i | \(0.784838\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.0406 | −1.13185 | −0.565924 | − | 0.824457i | \(-0.691481\pi\) | ||||
−0.565924 | + | 0.824457i | \(0.691481\pi\) | |||||||
\(284\) | −9.62611 | −0.571205 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.68714 | 0.0997626 | ||||||||
\(287\) | 33.5215 | 1.97871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0766 | −0.592740 | ||||||||
\(290\) | −2.81905 | −0.165540 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18.9999 | −1.11189 | ||||||||
\(293\) | −9.64954 | −0.563732 | −0.281866 | − | 0.959454i | \(-0.590953\pi\) | ||||
−0.281866 | + | 0.959454i | \(0.590953\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.6201 | 1.14232 | ||||||||
\(296\) | 5.48487 | 0.318802 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.305611 | 0.0177036 | ||||||||
\(299\) | 7.60211 | 0.439641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 43.7795 | 2.52341 | ||||||||
\(302\) | 0.0337875 | 0.00194425 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.56362 | −0.548511 | ||||||||
\(305\) | −14.2851 | −0.817964 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8112 | 1.01654 | 0.508270 | − | 0.861198i | \(-0.330285\pi\) | ||||
0.508270 | + | 0.861198i | \(0.330285\pi\) | |||||||
\(308\) | −22.9633 | −1.30846 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.41692 | 0.194068 | ||||||||
\(311\) | −24.1349 | −1.36857 | −0.684283 | − | 0.729216i | \(-0.739885\pi\) | ||||
−0.684283 | + | 0.729216i | \(0.739885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.1597 | −0.913399 | −0.456699 | − | 0.889621i | \(-0.650969\pi\) | ||||
−0.456699 | + | 0.889621i | \(0.650969\pi\) | |||||||
\(314\) | −1.69679 | −0.0957554 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.53249 | −0.479990 | ||||||||
\(317\) | 4.30766 | 0.241942 | 0.120971 | − | 0.992656i | \(-0.461399\pi\) | ||||
0.120971 | + | 0.992656i | \(0.461399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.2191 | −1.07606 | ||||||||
\(320\) | 9.56035 | 0.534440 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.06870 | 0.282468 | ||||||||
\(323\) | 7.29748 | 0.406043 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.76546 | 0.208870 | ||||||||
\(326\) | 1.53324 | 0.0849185 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.3244 | 0.625288 | ||||||||
\(329\) | 44.0202 | 2.42691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.16566 | 0.448825 | 0.224413 | − | 0.974494i | \(-0.427954\pi\) | ||||
0.224413 | + | 0.974494i | \(0.427954\pi\) | |||||||
\(332\) | −31.3377 | −1.71988 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.463567 | 0.0253653 | ||||||||
\(335\) | −17.8332 | −0.974331 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.74800 | 0.0952198 | 0.0476099 | − | 0.998866i | \(-0.484840\pi\) | ||||
0.0476099 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(338\) | −3.17103 | −0.172481 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.20578 | −0.445021 | ||||||||
\(341\) | 23.2951 | 1.26150 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.33774 | 0.288211 | ||||||||
\(344\) | 14.7899 | 0.797417 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.52104 | 0.0817714 | ||||||||
\(347\) | 13.7440 | 0.737815 | 0.368908 | − | 0.929466i | \(-0.379732\pi\) | ||||
0.368908 | + | 0.929466i | \(0.379732\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.5051 | 1.47231 | 0.736157 | − | 0.676811i | \(-0.236638\pi\) | ||||
0.736157 | + | 0.676811i | \(0.236638\pi\) | |||||||
\(350\) | 2.51062 | 0.134198 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.7292 | −0.625166 | ||||||||
\(353\) | 28.3401 | 1.50839 | 0.754195 | − | 0.656650i | \(-0.228027\pi\) | ||||
0.754195 | + | 0.656650i | \(0.228027\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.25830 | −0.438305 | ||||||||
\(356\) | −25.3683 | −1.34451 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.48374 | −0.184121 | ||||||||
\(359\) | 12.6727 | 0.668841 | 0.334420 | − | 0.942424i | \(-0.391459\pi\) | ||||
0.334420 | + | 0.942424i | \(0.391459\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3082 | −0.595170 | ||||||||
\(362\) | −2.00588 | −0.105427 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.9148 | −0.572092 | ||||||||
\(365\) | −16.3002 | −0.853189 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.224210 | −0.0117037 | −0.00585183 | − | 0.999983i | \(-0.501863\pi\) | ||||
−0.00585183 | + | 0.999983i | \(0.501863\pi\) | |||||||
\(368\) | −16.1831 | −0.843603 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.29650 | 0.119389 | ||||||||
\(371\) | 9.94726 | 0.516436 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4341 | 1.05804 | 0.529018 | − | 0.848610i | \(-0.322560\pi\) | ||||
0.529018 | + | 0.848610i | \(0.322560\pi\) | |||||||
\(374\) | 2.74050 | 0.141708 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.8712 | 0.766924 | ||||||||
\(377\) | −9.13513 | −0.470483 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.7493 | 0.654886 | 0.327443 | − | 0.944871i | \(-0.393813\pi\) | ||||
0.327443 | + | 0.944871i | \(0.393813\pi\) | |||||||
\(380\) | −8.64913 | −0.443691 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.60520 | 0.133294 | ||||||||
\(383\) | 18.9807 | 0.969867 | 0.484933 | − | 0.874551i | \(-0.338844\pi\) | ||||
0.484933 | + | 0.874551i | \(0.338844\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.7004 | −1.00402 | ||||||||
\(386\) | 2.57992 | 0.131315 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 29.8816 | 1.51701 | ||||||||
\(389\) | 5.72304 | 0.290170 | 0.145085 | − | 0.989419i | \(-0.453655\pi\) | ||||
0.145085 | + | 0.989419i | \(0.453655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3485 | 0.624489 | ||||||||
\(392\) | −6.55408 | −0.331031 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.81364 | −0.242508 | ||||||||
\(395\) | −7.32007 | −0.368313 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.01956 | −0.101359 | −0.0506795 | − | 0.998715i | \(-0.516139\pi\) | ||||
−0.0506795 | + | 0.998715i | \(0.516139\pi\) | |||||||
\(398\) | −3.90433 | −0.195706 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.01577 | −0.400789 | ||||||||
\(401\) | −31.8242 | −1.58923 | −0.794613 | − | 0.607116i | \(-0.792326\pi\) | ||||
−0.794613 | + | 0.607116i | \(0.792326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0725 | 0.551563 | ||||||||
\(404\) | −12.9870 | −0.646126 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.09084 | −0.302283 | ||||||||
\(407\) | 15.6566 | 0.776069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.7115 | −1.56803 | −0.784017 | − | 0.620739i | \(-0.786833\pi\) | ||||
−0.784017 | + | 0.620739i | \(0.786833\pi\) | |||||||
\(410\) | 4.74152 | 0.234167 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.7685 | 0.530528 | ||||||||
\(413\) | 42.3912 | 2.08594 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.8848 | −1.31972 | ||||||||
\(416\) | −5.57505 | −0.273339 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.88856 | 0.141284 | ||||||||
\(419\) | 11.2750 | 0.550819 | 0.275410 | − | 0.961327i | \(-0.411186\pi\) | ||||
0.275410 | + | 0.961327i | \(0.411186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4940 | −0.560184 | −0.280092 | − | 0.959973i | \(-0.590365\pi\) | ||||
−0.280092 | + | 0.959973i | \(0.590365\pi\) | |||||||
\(422\) | −4.49120 | −0.218628 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.36045 | 0.163198 | ||||||||
\(425\) | 6.11641 | 0.296689 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.8645 | −1.49364 | ||||||||
\(428\) | 1.81565 | 0.0877625 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.19249 | 0.298628 | ||||||||
\(431\) | −9.26265 | −0.446166 | −0.223083 | − | 0.974799i | \(-0.571612\pi\) | ||||
−0.223083 | + | 0.974799i | \(0.571612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.5177 | −1.46659 | −0.733293 | − | 0.679913i | \(-0.762018\pi\) | ||||
−0.733293 | + | 0.679913i | \(0.762018\pi\) | |||||||
\(434\) | 7.38261 | 0.354377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.1966 | 1.11092 | ||||||||
\(437\) | 13.0156 | 0.622622 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.692973 | 0.0330738 | 0.0165369 | − | 0.999863i | \(-0.494736\pi\) | ||||
0.0165369 | + | 0.999863i | \(0.494736\pi\) | |||||||
\(440\) | −6.65530 | −0.317279 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.30260 | 0.0619584 | ||||||||
\(443\) | 8.80697 | 0.418432 | 0.209216 | − | 0.977870i | \(-0.432909\pi\) | ||||
0.209216 | + | 0.977870i | \(0.432909\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.7636 | −1.03169 | ||||||||
\(446\) | −8.93234 | −0.422959 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.6561 | 0.975910 | ||||||||
\(449\) | 15.2076 | 0.717693 | 0.358846 | − | 0.933397i | \(-0.383170\pi\) | ||||
0.358846 | + | 0.933397i | \(0.383170\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.3257 | 1.52216 | ||||||||
\(452\) | −27.4801 | −1.29255 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.60774 | 0.357049 | ||||||||
\(455\) | −9.36388 | −0.438986 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.2345 | 0.759418 | 0.379709 | − | 0.925106i | \(-0.376024\pi\) | ||||
0.379709 | + | 0.925106i | \(0.376024\pi\) | |||||||
\(458\) | 0.0312065 | 0.00145818 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.6357 | −0.682391 | ||||||||
\(461\) | −34.7376 | −1.61789 | −0.808945 | − | 0.587884i | \(-0.799961\pi\) | ||||
−0.808945 | + | 0.587884i | \(0.799961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.4505 | −1.46163 | −0.730814 | − | 0.682577i | \(-0.760859\pi\) | ||||
−0.730814 | + | 0.682577i | \(0.760859\pi\) | |||||||
\(464\) | 19.4465 | 0.902783 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.62217 | 0.399415 | ||||||||
\(467\) | −16.9108 | −0.782540 | −0.391270 | − | 0.920276i | \(-0.627964\pi\) | ||||
−0.391270 | + | 0.920276i | \(0.627964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −38.5305 | −1.77917 | ||||||||
\(470\) | 6.22653 | 0.287209 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.3209 | 0.659172 | ||||||||
\(473\) | 42.2178 | 1.94118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.44687 | 0.295803 | ||||||||
\(476\) | −17.7294 | −0.812628 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.40139 | −0.109837 | ||||||||
\(479\) | −15.0101 | −0.685827 | −0.342914 | − | 0.939367i | \(-0.611414\pi\) | ||||
−0.342914 | + | 0.939367i | \(0.611414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.44182 | 0.339318 | ||||||||
\(482\) | −6.48344 | −0.295313 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.17154 | −0.0532520 | ||||||||
\(485\) | 25.6356 | 1.16405 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.5594 | −0.795692 | −0.397846 | − | 0.917452i | \(-0.630242\pi\) | ||||
−0.397846 | + | 0.917452i | \(0.630242\pi\) | |||||||
\(488\) | −10.4268 | −0.472001 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.74418 | −0.123969 | ||||||||
\(491\) | −42.0390 | −1.89719 | −0.948597 | − | 0.316488i | \(-0.897496\pi\) | ||||
−0.948597 | + | 0.316488i | \(0.897496\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.8386 | −0.668298 | ||||||||
\(494\) | 1.37298 | 0.0617732 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.5708 | −1.05836 | ||||||||
\(497\) | −17.8429 | −0.800364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.7477 | 0.973563 | 0.486781 | − | 0.873524i | \(-0.338171\pi\) | ||||
0.486781 | + | 0.873524i | \(0.338171\pi\) | |||||||
\(500\) | −22.8423 | −1.02154 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.31126 | 0.103157 | ||||||||
\(503\) | −12.1713 | −0.542693 | −0.271347 | − | 0.962482i | \(-0.587469\pi\) | ||||
−0.271347 | + | 0.962482i | \(0.587469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1416 | −0.495794 | ||||||||
\(506\) | 4.88789 | 0.217293 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.4145 | −0.728276 | ||||||||
\(509\) | −22.2123 | −0.984543 | −0.492271 | − | 0.870442i | \(-0.663833\pi\) | ||||
−0.492271 | + | 0.870442i | \(0.663833\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.2182 | −1.55796 | ||||||||
\(512\) | 20.1019 | 0.888387 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.87147 | −0.391304 | ||||||||
\(515\) | 9.23840 | 0.407092 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.4499 | 1.86695 | ||||||||
\(518\) | 4.96183 | 0.218010 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.16337 | −0.138723 | ||||||||
\(521\) | −21.6867 | −0.950110 | −0.475055 | − | 0.879956i | \(-0.657572\pi\) | ||||
−0.475055 | + | 0.879956i | \(0.657572\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.9180 | −1.61431 | −0.807156 | − | 0.590339i | \(-0.798994\pi\) | ||||
−0.807156 | + | 0.590339i | \(0.798994\pi\) | |||||||
\(524\) | 23.7907 | 1.03930 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.73116 | −0.380697 | ||||||||
\(527\) | 17.9856 | 0.783467 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.975551 | −0.0424152 | ||||||||
\(530\) | 1.40701 | 0.0611167 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.6873 | −0.810199 | ||||||||
\(533\) | 15.3649 | 0.665528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.55765 | 0.0673432 | ||||||||
\(536\) | −13.0166 | −0.562232 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.31329 | 0.185959 | ||||||||
\(539\) | −18.7087 | −0.805840 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5914 | 0.971281 | 0.485641 | − | 0.874159i | \(-0.338586\pi\) | ||||
0.485641 | + | 0.874159i | \(0.338586\pi\) | |||||||
\(542\) | −0.489606 | −0.0210304 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.05581 | −0.388265 | ||||||||
\(545\) | 19.9005 | 0.852445 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.27839 | −0.0974169 | −0.0487084 | − | 0.998813i | \(-0.515511\pi\) | ||||
−0.0487084 | + | 0.998813i | \(0.515511\pi\) | |||||||
\(548\) | −32.2654 | −1.37831 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.42106 | 0.103234 | ||||||||
\(551\) | −15.6403 | −0.666301 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.8158 | −0.672555 | ||||||||
\(554\) | −9.56038 | −0.406182 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 43.8780 | 1.86084 | ||||||||
\(557\) | 14.7170 | 0.623578 | 0.311789 | − | 0.950151i | \(-0.399072\pi\) | ||||
0.311789 | + | 0.950151i | \(0.399072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.0668 | 0.848734 | ||||||||
\(560\) | 19.9335 | 0.842344 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.99299 | −0.337164 | ||||||||
\(563\) | −31.0953 | −1.31051 | −0.655256 | − | 0.755407i | \(-0.727439\pi\) | ||||
−0.655256 | + | 0.755407i | \(0.727439\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.5753 | −0.991821 | ||||||||
\(566\) | −5.81904 | −0.244592 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.02781 | −0.252921 | ||||||||
\(569\) | 1.46472 | 0.0614043 | 0.0307021 | − | 0.999529i | \(-0.490226\pi\) | ||||
0.0307021 | + | 0.999529i | \(0.490226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.0412 | 1.13164 | 0.565821 | − | 0.824528i | \(-0.308560\pi\) | ||||
0.565821 | + | 0.824528i | \(0.308560\pi\) | |||||||
\(572\) | −10.5255 | −0.440092 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.2445 | 0.427599 | ||||||||
\(575\) | 10.9091 | 0.454941 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.9350 | 0.996426 | 0.498213 | − | 0.867055i | \(-0.333990\pi\) | ||||
0.498213 | + | 0.867055i | \(0.333990\pi\) | |||||||
\(578\) | −3.07952 | −0.128091 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.5870 | 0.730262 | ||||||||
\(581\) | −58.0874 | −2.40987 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.59243 | 0.397278 | ||||||||
\(584\) | −11.8976 | −0.492328 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.94901 | −0.121822 | ||||||||
\(587\) | 39.8918 | 1.64651 | 0.823256 | − | 0.567670i | \(-0.192155\pi\) | ||||
0.823256 | + | 0.567670i | \(0.192155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9574 | 0.781126 | ||||||||
\(590\) | 5.99612 | 0.246856 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.8419 | −0.651098 | ||||||||
\(593\) | 34.8118 | 1.42955 | 0.714774 | − | 0.699356i | \(-0.246530\pi\) | ||||
0.714774 | + | 0.699356i | \(0.246530\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.2102 | −0.623557 | ||||||||
\(596\) | −1.90660 | −0.0780974 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.32329 | 0.0950064 | ||||||||
\(599\) | −10.1936 | −0.416498 | −0.208249 | − | 0.978076i | \(-0.566776\pi\) | ||||
−0.208249 | + | 0.978076i | \(0.566776\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8285 | −0.441702 | −0.220851 | − | 0.975308i | \(-0.570883\pi\) | ||||
−0.220851 | + | 0.975308i | \(0.570883\pi\) | |||||||
\(602\) | 13.3795 | 0.545308 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.210789 | −0.00857687 | ||||||||
\(605\) | −1.00508 | −0.0408621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9228 | 0.808642 | 0.404321 | − | 0.914617i | \(-0.367508\pi\) | ||||
0.404321 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(608\) | −9.54509 | −0.387105 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.36570 | −0.176762 | ||||||||
\(611\) | 20.1771 | 0.816278 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.2848 | 0.455787 | 0.227893 | − | 0.973686i | \(-0.426816\pi\) | ||||
0.227893 | + | 0.973686i | \(0.426816\pi\) | |||||||
\(614\) | 5.44331 | 0.219674 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.3795 | −0.579366 | ||||||||
\(617\) | 38.0300 | 1.53103 | 0.765515 | − | 0.643418i | \(-0.222484\pi\) | ||||
0.765515 | + | 0.643418i | \(0.222484\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0309 | 1.12666 | 0.563328 | − | 0.826233i | \(-0.309521\pi\) | ||||
0.563328 | + | 0.826233i | \(0.309521\pi\) | |||||||
\(620\) | −21.3170 | −0.856110 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.37591 | −0.295747 | ||||||||
\(623\) | −47.0225 | −1.88392 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.97386 | −0.318954 | ||||||||
\(626\) | −4.93858 | −0.197385 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.5857 | 0.422414 | ||||||||
\(629\) | 12.0881 | 0.481984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.58906 | −0.142878 | −0.0714390 | − | 0.997445i | \(-0.522759\pi\) | ||||
−0.0714390 | + | 0.997445i | \(0.522759\pi\) | |||||||
\(632\) | −5.34299 | −0.212533 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.31647 | 0.0522836 | ||||||||
\(635\) | −14.0821 | −0.558831 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.89252 | −0.352334 | ||||||||
\(638\) | −5.87357 | −0.232537 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.1807 | 0.560540 | ||||||||
\(641\) | 17.6313 | 0.696393 | 0.348197 | − | 0.937422i | \(-0.386794\pi\) | ||||
0.348197 | + | 0.937422i | \(0.386794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.61672 | 0.379246 | 0.189623 | − | 0.981857i | \(-0.439273\pi\) | ||||
0.189623 | + | 0.981857i | \(0.439273\pi\) | |||||||
\(644\) | −31.6219 | −1.24608 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.23019 | 0.0877458 | ||||||||
\(647\) | −43.9383 | −1.72739 | −0.863697 | − | 0.504012i | \(-0.831857\pi\) | ||||
−0.863697 | + | 0.504012i | \(0.831857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.8790 | 1.60464 | ||||||||
\(650\) | 1.15077 | 0.0451368 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.56537 | −0.374609 | ||||||||
\(653\) | −7.96035 | −0.311513 | −0.155756 | − | 0.987796i | \(-0.549781\pi\) | ||||
−0.155756 | + | 0.987796i | \(0.549781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.4102 | 0.797492 | ||||||||
\(656\) | −32.7083 | −1.27704 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.4531 | 0.524456 | ||||||||
\(659\) | −8.96854 | −0.349365 | −0.174682 | − | 0.984625i | \(-0.555890\pi\) | ||||
−0.174682 | + | 0.984625i | \(0.555890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.2703 | −1.44965 | −0.724824 | − | 0.688934i | \(-0.758079\pi\) | ||||
−0.724824 | + | 0.688934i | \(0.758079\pi\) | |||||||
\(662\) | 2.49552 | 0.0969910 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.6234 | −0.761538 | ||||||||
\(665\) | −16.0320 | −0.621694 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.4658 | −1.02476 | ||||||||
\(668\) | −2.89203 | −0.111896 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.45002 | −0.210553 | ||||||||
\(671\) | −29.7635 | −1.14901 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.24605 | 0.279315 | 0.139657 | − | 0.990200i | \(-0.455400\pi\) | ||||
0.139657 | + | 0.990200i | \(0.455400\pi\) | |||||||
\(674\) | 0.534210 | 0.0205770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.7829 | 0.760881 | ||||||||
\(677\) | 21.9263 | 0.842695 | 0.421347 | − | 0.906899i | \(-0.361557\pi\) | ||||
0.421347 | + | 0.906899i | \(0.361557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 55.3884 | 2.12561 | ||||||||
\(680\) | −5.13841 | −0.197049 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.11926 | 0.272611 | ||||||||
\(683\) | 13.2757 | 0.507982 | 0.253991 | − | 0.967207i | \(-0.418257\pi\) | ||||
0.253991 | + | 0.967207i | \(0.418257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.6807 | −1.05762 | ||||||||
\(686\) | 1.63127 | 0.0622823 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −42.7175 | −1.62859 | ||||||||
\(689\) | 4.55943 | 0.173700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.1778 | −1.41431 | −0.707156 | − | 0.707058i | \(-0.750022\pi\) | ||||
−0.707156 | + | 0.707058i | \(0.750022\pi\) | |||||||
\(692\) | −9.48921 | −0.360726 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.20032 | 0.159442 | ||||||||
\(695\) | 37.6432 | 1.42789 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.9579 | 0.945349 | ||||||||
\(698\) | 8.40587 | 0.318167 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.6629 | −0.592000 | ||||||||
\(701\) | −21.0544 | −0.795212 | −0.397606 | − | 0.917556i | \(-0.630159\pi\) | ||||
−0.397606 | + | 0.917556i | \(0.630159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.7412 | 0.480544 | ||||||||
\(704\) | 19.9193 | 0.750736 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.66105 | 0.325963 | ||||||||
\(707\) | −24.0726 | −0.905342 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.4549 | 1.18131 | 0.590656 | − | 0.806924i | \(-0.298869\pi\) | ||||
0.590656 | + | 0.806924i | \(0.298869\pi\) | |||||||
\(710\) | −2.52383 | −0.0947176 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.8854 | −0.595332 | ||||||||
\(713\) | 32.0788 | 1.20136 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.02985 | −0.337697 | ||||||||
\(716\) | 21.7338 | 0.812232 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.87293 | 0.144536 | ||||||||
\(719\) | 30.6402 | 1.14269 | 0.571344 | − | 0.820711i | \(-0.306422\pi\) | ||||
0.571344 | + | 0.820711i | \(0.306422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.9605 | 0.743368 | ||||||||
\(722\) | −3.45593 | −0.128616 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.5140 | 0.465078 | ||||||||
\(725\) | −13.1090 | −0.486856 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.27198 | 0.0842631 | 0.0421315 | − | 0.999112i | \(-0.486585\pi\) | ||||
0.0421315 | + | 0.999112i | \(0.486585\pi\) | |||||||
\(728\) | −6.83479 | −0.253314 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.98151 | −0.184374 | ||||||||
\(731\) | 32.5954 | 1.20558 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.6681 | 0.985007 | 0.492504 | − | 0.870310i | \(-0.336082\pi\) | ||||
0.492504 | + | 0.870310i | \(0.336082\pi\) | |||||||
\(734\) | −0.0685211 | −0.00252916 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.1518 | −0.595362 | ||||||||
\(737\) | −37.1560 | −1.36866 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.14116 | −0.152335 | −0.0761675 | − | 0.997095i | \(-0.524268\pi\) | ||||
−0.0761675 | + | 0.997095i | \(0.524268\pi\) | |||||||
\(740\) | −14.3271 | −0.526674 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.04000 | 0.111602 | ||||||||
\(743\) | −26.3954 | −0.968354 | −0.484177 | − | 0.874970i | \(-0.660881\pi\) | ||||
−0.484177 | + | 0.874970i | \(0.660881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.63568 | −0.0599269 | ||||||||
\(746\) | 6.24489 | 0.228642 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.0970 | −0.625128 | ||||||||
\(749\) | 3.36547 | 0.122972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.9987 | −1.78799 | −0.893994 | − | 0.448080i | \(-0.852108\pi\) | ||||
−0.893994 | + | 0.448080i | \(0.852108\pi\) | |||||||
\(752\) | −42.9523 | −1.56631 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.79180 | −0.101671 | ||||||||
\(755\) | −0.180837 | −0.00658132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.0094 | −1.41782 | −0.708911 | − | 0.705298i | \(-0.750813\pi\) | ||||
−0.708911 | + | 0.705298i | \(0.750813\pi\) | |||||||
\(758\) | 3.89632 | 0.141521 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.41603 | −0.196460 | ||||||||
\(761\) | 20.3545 | 0.737851 | 0.368926 | − | 0.929459i | \(-0.379726\pi\) | ||||
0.368926 | + | 0.929459i | \(0.379726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.9972 | 1.55660 | ||||||||
\(764\) | −16.2529 | −0.588010 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.80071 | 0.209588 | ||||||||
\(767\) | 19.4304 | 0.701592 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.3911 | 0.446834 | 0.223417 | − | 0.974723i | \(-0.428279\pi\) | ||||
0.223417 | + | 0.974723i | \(0.428279\pi\) | |||||||
\(770\) | −6.02065 | −0.216969 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.0952 | −0.579280 | ||||||||
\(773\) | −24.4773 | −0.880387 | −0.440193 | − | 0.897903i | \(-0.645090\pi\) | ||||
−0.440193 | + | 0.897903i | \(0.645090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.8892 | 0.570757 | ||||||||
\(776\) | 18.7117 | 0.671710 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.74903 | 0.0627056 | ||||||||
\(779\) | 26.3064 | 0.942524 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.2064 | −0.615694 | ||||||||
\(782\) | 3.77383 | 0.134952 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.9301 | 0.676074 | ||||||||
\(785\) | 9.08151 | 0.324133 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.5061 | 0.837904 | 0.418952 | − | 0.908008i | \(-0.362398\pi\) | ||||
0.418952 | + | 0.908008i | \(0.362398\pi\) | |||||||
\(788\) | 30.0306 | 1.06980 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.23710 | −0.0795923 | ||||||||
\(791\) | −50.9369 | −1.81111 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.1471 | −0.502376 | ||||||||
\(794\) | −0.617201 | −0.0219037 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.3577 | 0.863337 | ||||||||
\(797\) | 25.5059 | 0.903465 | 0.451732 | − | 0.892153i | \(-0.350806\pi\) | ||||
0.451732 | + | 0.892153i | \(0.350806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.7746 | 1.15948 | ||||||||
\(800\) | −8.00025 | −0.282851 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.72585 | −0.343432 | ||||||||
\(803\) | −33.9619 | −1.19849 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.1286 | −0.956157 | ||||||||
\(806\) | 3.38389 | 0.119193 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.13235 | −0.286095 | ||||||||
\(809\) | 12.4633 | 0.438187 | 0.219093 | − | 0.975704i | \(-0.429690\pi\) | ||||
0.219093 | + | 0.975704i | \(0.429690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1894 | 0.428026 | 0.214013 | − | 0.976831i | \(-0.431346\pi\) | ||||
0.214013 | + | 0.976831i | \(0.431346\pi\) | |||||||
\(812\) | 37.9986 | 1.33349 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.78484 | 0.167708 | ||||||||
\(815\) | −8.20618 | −0.287450 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.3565 | 1.20198 | ||||||||
\(818\) | −9.69141 | −0.338852 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.5807 | −1.03300 | ||||||||
\(821\) | −2.08885 | −0.0729013 | −0.0364507 | − | 0.999335i | \(-0.511605\pi\) | ||||
−0.0364507 | + | 0.999335i | \(0.511605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.9137 | 1.04272 | 0.521362 | − | 0.853335i | \(-0.325424\pi\) | ||||
0.521362 | + | 0.853335i | \(0.325424\pi\) | |||||||
\(824\) | 6.74319 | 0.234910 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9552 | 0.450770 | ||||||||
\(827\) | −38.5243 | −1.33962 | −0.669810 | − | 0.742532i | \(-0.733625\pi\) | ||||
−0.669810 | + | 0.742532i | \(0.733625\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.01966 | −0.174340 | −0.0871699 | − | 0.996193i | \(-0.527782\pi\) | ||||
−0.0871699 | + | 0.996193i | \(0.527782\pi\) | |||||||
\(830\) | −8.21629 | −0.285192 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.46794 | 0.328242 | ||||||||
\(833\) | −14.4445 | −0.500474 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.48109 | −0.0858617 | ||||||||
\(836\) | −18.0207 | −0.623260 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.44577 | 0.119032 | ||||||||
\(839\) | 20.2606 | 0.699474 | 0.349737 | − | 0.936848i | \(-0.386271\pi\) | ||||
0.349737 | + | 0.936848i | \(0.386271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.80286 | 0.0966502 | ||||||||
\(842\) | −3.51270 | −0.121056 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.0190 | 0.964454 | ||||||||
\(845\) | 16.9719 | 0.583850 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.17157 | −0.0746160 | ||||||||
\(848\) | −9.70595 | −0.333304 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.86924 | 0.0641145 | ||||||||
\(851\) | 21.5601 | 0.739070 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.8874 | −1.33148 | −0.665740 | − | 0.746184i | \(-0.731884\pi\) | ||||
−0.665740 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(854\) | −9.43254 | −0.322775 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.13695 | 0.0388600 | ||||||||
\(857\) | 10.8572 | 0.370874 | 0.185437 | − | 0.982656i | \(-0.440630\pi\) | ||||
0.185437 | + | 0.982656i | \(0.440630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.9307 | −0.714145 | −0.357073 | − | 0.934077i | \(-0.616225\pi\) | ||||
−0.357073 | + | 0.934077i | \(0.616225\pi\) | |||||||
\(860\) | −38.6328 | −1.31737 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.83077 | −0.0964165 | ||||||||
\(863\) | −30.8139 | −1.04892 | −0.524459 | − | 0.851435i | \(-0.675733\pi\) | ||||
−0.524459 | + | 0.851435i | \(0.675733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.14085 | −0.276797 | ||||||||
\(866\) | −9.32655 | −0.316929 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −46.0575 | −1.56329 | ||||||||
\(869\) | −15.2516 | −0.517375 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.6608 | −0.598414 | ||||||||
\(872\) | 14.5256 | 0.491899 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.97773 | 0.134549 | ||||||||
\(875\) | −42.3404 | −1.43137 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.4847 | 1.43461 | 0.717303 | − | 0.696762i | \(-0.245376\pi\) | ||||
0.717303 | + | 0.696762i | \(0.245376\pi\) | |||||||
\(878\) | 0.211781 | 0.00714725 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.2224 | 0.647988 | ||||||||
\(881\) | −43.4583 | −1.46415 | −0.732073 | − | 0.681226i | \(-0.761447\pi\) | ||||
−0.732073 | + | 0.681226i | \(0.761447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0935 | −0.440632 | −0.220316 | − | 0.975429i | \(-0.570709\pi\) | ||||
−0.220316 | + | 0.975429i | \(0.570709\pi\) | |||||||
\(884\) | −8.12647 | −0.273323 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.69151 | 0.0904230 | ||||||||
\(887\) | 45.3324 | 1.52211 | 0.761057 | − | 0.648685i | \(-0.224681\pi\) | ||||
0.761057 | + | 0.648685i | \(0.224681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.4258 | −1.02045 | ||||||||
\(890\) | −6.65119 | −0.222949 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 55.7257 | 1.86584 | ||||||||
\(893\) | 34.5454 | 1.15602 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.6456 | 0.623253 | ||||||||
\(896\) | 30.6388 | 1.02357 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.64763 | 0.155093 | ||||||||
\(899\) | −38.5477 | −1.28564 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.40609 | 0.246733 | ||||||||
\(902\) | 9.87910 | 0.328938 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.2078 | −0.572324 | ||||||||
\(905\) | 10.7358 | 0.356870 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.1130 | −1.03309 | −0.516545 | − | 0.856260i | \(-0.672782\pi\) | ||||
−0.516545 | + | 0.856260i | \(0.672782\pi\) | |||||||
\(908\) | −47.4620 | −1.57508 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.86171 | −0.0948647 | ||||||||
\(911\) | −47.7208 | −1.58106 | −0.790530 | − | 0.612424i | \(-0.790195\pi\) | ||||
−0.790530 | + | 0.612424i | \(0.790195\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.0153 | −1.85383 | ||||||||
\(914\) | 4.96145 | 0.164110 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.194686 | −0.00643261 | ||||||||
\(917\) | 44.0983 | 1.45626 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.9434 | 1.48255 | 0.741273 | − | 0.671203i | \(-0.234222\pi\) | ||||
0.741273 | + | 0.671203i | \(0.234222\pi\) | |||||||
\(920\) | −9.16475 | −0.302153 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.6162 | −0.349626 | ||||||||
\(923\) | −8.17848 | −0.269198 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6791 | 0.351126 | ||||||||
\(926\) | −9.61162 | −0.315858 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 19.4089 | 0.637127 | ||||||||
\(929\) | 32.6595 | 1.07152 | 0.535761 | − | 0.844370i | \(-0.320025\pi\) | ||||
0.535761 | + | 0.844370i | \(0.320025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.2250 | −0.498978 | ||||||||
\(932\) | −53.7907 | −1.76197 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.16815 | −0.169107 | ||||||||
\(935\) | −14.6676 | −0.479682 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.5359 | 0.572873 | 0.286437 | − | 0.958099i | \(-0.407529\pi\) | ||||
0.286437 | + | 0.958099i | \(0.407529\pi\) | |||||||
\(938\) | −11.7753 | −0.384479 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −38.8452 | −1.26699 | ||||||||
\(941\) | −14.9992 | −0.488961 | −0.244480 | − | 0.969654i | \(-0.578617\pi\) | ||||
−0.244480 | + | 0.969654i | \(0.578617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.5144 | 1.44959 | ||||||||
\(944\) | −41.3628 | −1.34625 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.9022 | 0.419488 | ||||||||
\(947\) | −4.99323 | −0.162258 | −0.0811292 | − | 0.996704i | \(-0.525853\pi\) | ||||
−0.0811292 | + | 0.996704i | \(0.525853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.1426 | −0.524011 | ||||||||
\(950\) | 1.97024 | 0.0639229 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.1021 | −0.359820 | ||||||||
\(953\) | −24.5163 | −0.794161 | −0.397081 | − | 0.917784i | \(-0.629977\pi\) | ||||
−0.397081 | + | 0.917784i | \(0.629977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.9435 | −0.451200 | ||||||||
\(956\) | 14.9815 | 0.484535 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.58724 | −0.148207 | ||||||||
\(959\) | −59.8070 | −1.93127 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.7231 | 0.507197 | ||||||||
\(962\) | 2.27431 | 0.0733266 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 40.4479 | 1.30274 | ||||||||
\(965\) | −13.8082 | −0.444502 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.3735 | 0.783800 | 0.391900 | − | 0.920008i | \(-0.371818\pi\) | ||||
0.391900 | + | 0.920008i | \(0.371818\pi\) | |||||||
\(968\) | −0.733614 | −0.0235792 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.83453 | 0.251552 | ||||||||
\(971\) | 6.16139 | 0.197728 | 0.0988642 | − | 0.995101i | \(-0.468479\pi\) | ||||
0.0988642 | + | 0.995101i | \(0.468479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 81.3321 | 2.60739 | ||||||||
\(974\) | −5.36635 | −0.171949 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.1157 | 0.963982 | ||||||||
\(977\) | −20.1046 | −0.643203 | −0.321601 | − | 0.946875i | \(-0.604221\pi\) | ||||
−0.321601 | + | 0.946875i | \(0.604221\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45.3451 | −1.44924 | ||||||||
\(980\) | 17.1200 | 0.546877 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.8476 | −0.409983 | ||||||||
\(983\) | −42.4939 | −1.35534 | −0.677672 | − | 0.735364i | \(-0.737011\pi\) | ||||
−0.677672 | + | 0.735364i | \(0.737011\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.7634 | 0.820891 | ||||||||
\(986\) | −4.53485 | −0.144419 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.56553 | −0.272506 | ||||||||
\(989\) | 58.1365 | 1.84863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.68049 | −0.0533824 | −0.0266912 | − | 0.999644i | \(-0.508497\pi\) | ||||
−0.0266912 | + | 0.999644i | \(0.508497\pi\) | |||||||
\(992\) | −23.5252 | −0.746925 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.45300 | −0.172959 | ||||||||
\(995\) | 20.8966 | 0.662468 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.88157 | 0.0595898 | 0.0297949 | − | 0.999556i | \(-0.490515\pi\) | ||||
0.0297949 | + | 0.999556i | \(0.490515\pi\) | |||||||
\(998\) | 6.64636 | 0.210387 | ||||||||
\(999\) | 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 | 4023.2.a.f.1.13 | yes | 25 | |
3.2 | odd | 2 | 4023.2.a.e.1.13 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.13 | ✓ | 25 | 3.2 | odd | 2 | ||
4023.2.a.f.1.13 | yes | 25 | 1.1 | even | 1 | trivial |