Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61907 | −1.14486 | −0.572428 | − | 0.819955i | \(-0.693998\pi\) | ||||
−0.572428 | + | 0.819955i | \(0.693998\pi\) | |||||||
\(3\) | −1.18857 | −0.686221 | −0.343111 | − | 0.939295i | \(-0.611481\pi\) | ||||
−0.343111 | + | 0.939295i | \(0.611481\pi\) | |||||||
\(4\) | 0.621387 | 0.310694 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.92438 | 0.785624 | ||||||||
\(7\) | −2.23190 | −0.843580 | −0.421790 | − | 0.906694i | \(-0.638598\pi\) | ||||
−0.421790 | + | 0.906694i | \(0.638598\pi\) | |||||||
\(8\) | 2.23207 | 0.789156 | ||||||||
\(9\) | −1.58730 | −0.529100 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.64478 | 1.70197 | 0.850983 | − | 0.525194i | \(-0.176007\pi\) | ||||
0.850983 | + | 0.525194i | \(0.176007\pi\) | |||||||
\(12\) | −0.738562 | −0.213204 | ||||||||
\(13\) | 4.70049 | 1.30368 | 0.651841 | − | 0.758355i | \(-0.273997\pi\) | ||||
0.651841 | + | 0.758355i | \(0.273997\pi\) | |||||||
\(14\) | 3.61361 | 0.965777 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85665 | −1.21416 | ||||||||
\(17\) | 0.785842 | 0.190595 | 0.0952973 | − | 0.995449i | \(-0.469620\pi\) | ||||
0.0952973 | + | 0.995449i | \(0.469620\pi\) | |||||||
\(18\) | 2.56995 | 0.605743 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.65277 | 0.578882 | ||||||||
\(22\) | −9.13929 | −1.94850 | ||||||||
\(23\) | 5.13041 | 1.06976 | 0.534882 | − | 0.844927i | \(-0.320356\pi\) | ||||
0.534882 | + | 0.844927i | \(0.320356\pi\) | |||||||
\(24\) | −2.65297 | −0.541536 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.61043 | −1.49253 | ||||||||
\(27\) | 5.45233 | 1.04930 | ||||||||
\(28\) | −1.38688 | −0.262095 | ||||||||
\(29\) | −3.03653 | −0.563869 | −0.281934 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281934 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.10416 | −1.45555 | −0.727775 | − | 0.685816i | \(-0.759445\pi\) | ||||
−0.727775 | + | 0.685816i | \(0.759445\pi\) | |||||||
\(32\) | 3.39912 | 0.600885 | ||||||||
\(33\) | −6.70922 | −1.16792 | ||||||||
\(34\) | −1.27233 | −0.218203 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.986329 | −0.164388 | ||||||||
\(37\) | −0.985141 | −0.161956 | −0.0809781 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809781 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.58687 | −0.894615 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41798 | −0.221451 | −0.110726 | − | 0.993851i | \(-0.535318\pi\) | ||||
−0.110726 | + | 0.993851i | \(0.535318\pi\) | |||||||
\(42\) | −4.29502 | −0.662737 | ||||||||
\(43\) | 1.52174 | 0.232063 | 0.116031 | − | 0.993246i | \(-0.462983\pi\) | ||||
0.116031 | + | 0.993246i | \(0.462983\pi\) | |||||||
\(44\) | 3.50759 | 0.528790 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.30649 | −1.22473 | ||||||||
\(47\) | −0.960695 | −0.140132 | −0.0700659 | − | 0.997542i | \(-0.522321\pi\) | ||||
−0.0700659 | + | 0.997542i | \(0.522321\pi\) | |||||||
\(48\) | 5.77247 | 0.833184 | ||||||||
\(49\) | −2.01861 | −0.288373 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.934028 | −0.130790 | ||||||||
\(52\) | 2.92083 | 0.405046 | ||||||||
\(53\) | 4.41123 | 0.605929 | 0.302964 | − | 0.953002i | \(-0.402024\pi\) | ||||
0.302964 | + | 0.953002i | \(0.402024\pi\) | |||||||
\(54\) | −8.82770 | −1.20130 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.98176 | −0.665716 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.91635 | 0.645548 | ||||||||
\(59\) | −9.87853 | −1.28608 | −0.643038 | − | 0.765835i | \(-0.722326\pi\) | ||||
−0.643038 | + | 0.765835i | \(0.722326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.09604 | 0.268370 | 0.134185 | − | 0.990956i | \(-0.457158\pi\) | ||||
0.134185 | + | 0.990956i | \(0.457158\pi\) | |||||||
\(62\) | 13.1212 | 1.66639 | ||||||||
\(63\) | 3.54270 | 0.446339 | ||||||||
\(64\) | 4.20990 | 0.526237 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.8627 | 1.33710 | ||||||||
\(67\) | −3.24811 | −0.396820 | −0.198410 | − | 0.980119i | \(-0.563578\pi\) | ||||
−0.198410 | + | 0.980119i | \(0.563578\pi\) | |||||||
\(68\) | 0.488312 | 0.0592165 | ||||||||
\(69\) | −6.09785 | −0.734095 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.17702 | −0.851755 | −0.425878 | − | 0.904781i | \(-0.640035\pi\) | ||||
−0.425878 | + | 0.904781i | \(0.640035\pi\) | |||||||
\(72\) | −3.54297 | −0.417543 | ||||||||
\(73\) | −15.1625 | −1.77463 | −0.887317 | − | 0.461160i | \(-0.847433\pi\) | ||||
−0.887317 | + | 0.461160i | \(0.847433\pi\) | |||||||
\(74\) | 1.59501 | 0.185416 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.5986 | −1.43574 | ||||||||
\(78\) | 9.04553 | 1.02420 | ||||||||
\(79\) | −1.33973 | −0.150731 | −0.0753655 | − | 0.997156i | \(-0.524012\pi\) | ||||
−0.0753655 | + | 0.997156i | \(0.524012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.71857 | −0.190952 | ||||||||
\(82\) | 2.29581 | 0.253530 | ||||||||
\(83\) | 7.52545 | 0.826026 | 0.413013 | − | 0.910725i | \(-0.364476\pi\) | ||||
0.413013 | + | 0.910725i | \(0.364476\pi\) | |||||||
\(84\) | 1.64840 | 0.179855 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.46380 | −0.265678 | ||||||||
\(87\) | 3.60912 | 0.386939 | ||||||||
\(88\) | 12.5995 | 1.34312 | ||||||||
\(89\) | −3.40299 | −0.360716 | −0.180358 | − | 0.983601i | \(-0.557726\pi\) | ||||
−0.180358 | + | 0.983601i | \(0.557726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.4910 | −1.09976 | ||||||||
\(92\) | 3.18797 | 0.332369 | ||||||||
\(93\) | 9.63236 | 0.998829 | ||||||||
\(94\) | 1.55543 | 0.160431 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.04009 | −0.412340 | ||||||||
\(97\) | −12.7601 | −1.29559 | −0.647793 | − | 0.761816i | \(-0.724308\pi\) | ||||
−0.647793 | + | 0.761816i | \(0.724308\pi\) | |||||||
\(98\) | 3.26827 | 0.330145 | ||||||||
\(99\) | −8.95997 | −0.900511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.57300 | 0.554534 | 0.277267 | − | 0.960793i | \(-0.410571\pi\) | ||||
0.277267 | + | 0.960793i | \(0.410571\pi\) | |||||||
\(102\) | 1.51226 | 0.149736 | ||||||||
\(103\) | −3.30768 | −0.325915 | −0.162958 | − | 0.986633i | \(-0.552103\pi\) | ||||
−0.162958 | + | 0.986633i | \(0.552103\pi\) | |||||||
\(104\) | 10.4918 | 1.02881 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.14209 | −0.693701 | ||||||||
\(107\) | 6.67267 | 0.645071 | 0.322536 | − | 0.946557i | \(-0.395465\pi\) | ||||
0.322536 | + | 0.946557i | \(0.395465\pi\) | |||||||
\(108\) | 3.38801 | 0.326011 | ||||||||
\(109\) | −15.6813 | −1.50199 | −0.750996 | − | 0.660307i | \(-0.770426\pi\) | ||||
−0.750996 | + | 0.660307i | \(0.770426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.17091 | 0.111138 | ||||||||
\(112\) | 10.8396 | 1.02424 | ||||||||
\(113\) | 6.58139 | 0.619125 | 0.309562 | − | 0.950879i | \(-0.399817\pi\) | ||||
0.309562 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.88686 | −0.175190 | ||||||||
\(117\) | −7.46110 | −0.689779 | ||||||||
\(118\) | 15.9940 | 1.47237 | ||||||||
\(119\) | −1.75392 | −0.160782 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8636 | 1.89669 | ||||||||
\(122\) | −3.39363 | −0.307245 | ||||||||
\(123\) | 1.68537 | 0.151965 | ||||||||
\(124\) | −5.03582 | −0.452230 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.73588 | −0.510993 | ||||||||
\(127\) | 1.33460 | 0.118427 | 0.0592135 | − | 0.998245i | \(-0.481141\pi\) | ||||
0.0592135 | + | 0.998245i | \(0.481141\pi\) | |||||||
\(128\) | −13.6144 | −1.20335 | ||||||||
\(129\) | −1.80869 | −0.159246 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7788 | 1.20386 | 0.601930 | − | 0.798549i | \(-0.294399\pi\) | ||||
0.601930 | + | 0.798549i | \(0.294399\pi\) | |||||||
\(132\) | −4.16902 | −0.362867 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.25892 | 0.454302 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.75405 | 0.150409 | ||||||||
\(137\) | 11.7423 | 1.00321 | 0.501605 | − | 0.865097i | \(-0.332743\pi\) | ||||
0.501605 | + | 0.865097i | \(0.332743\pi\) | |||||||
\(138\) | 9.87284 | 0.840432 | ||||||||
\(139\) | −9.34145 | −0.792331 | −0.396166 | − | 0.918179i | \(-0.629659\pi\) | ||||
−0.396166 | + | 0.918179i | \(0.629659\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.14185 | 0.0961614 | ||||||||
\(142\) | 11.6201 | 0.975136 | ||||||||
\(143\) | 26.5333 | 2.21882 | ||||||||
\(144\) | 7.70897 | 0.642414 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 24.5491 | 2.03170 | ||||||||
\(147\) | 2.39926 | 0.197887 | ||||||||
\(148\) | −0.612154 | −0.0503187 | ||||||||
\(149\) | 18.0234 | 1.47653 | 0.738265 | − | 0.674510i | \(-0.235645\pi\) | ||||
0.738265 | + | 0.674510i | \(0.235645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0159 | 1.05922 | 0.529611 | − | 0.848241i | \(-0.322338\pi\) | ||||
0.529611 | + | 0.848241i | \(0.322338\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.24737 | −0.100844 | ||||||||
\(154\) | 20.3980 | 1.64372 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.47161 | −0.277951 | ||||||||
\(157\) | 10.5071 | 0.838560 | 0.419280 | − | 0.907857i | \(-0.362283\pi\) | ||||
0.419280 | + | 0.907857i | \(0.362283\pi\) | |||||||
\(158\) | 2.16911 | 0.172565 | ||||||||
\(159\) | −5.24305 | −0.415801 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.4506 | −0.902432 | ||||||||
\(162\) | 2.78248 | 0.218613 | ||||||||
\(163\) | −3.62389 | −0.283845 | −0.141923 | − | 0.989878i | \(-0.545328\pi\) | ||||
−0.141923 | + | 0.989878i | \(0.545328\pi\) | |||||||
\(164\) | −0.881115 | −0.0688035 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.1842 | −0.945680 | ||||||||
\(167\) | 10.6399 | 0.823344 | 0.411672 | − | 0.911332i | \(-0.364945\pi\) | ||||
0.411672 | + | 0.911332i | \(0.364945\pi\) | |||||||
\(168\) | 5.92118 | 0.456829 | ||||||||
\(169\) | 9.09465 | 0.699588 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.945588 | 0.0721004 | ||||||||
\(173\) | −19.4108 | −1.47578 | −0.737888 | − | 0.674923i | \(-0.764177\pi\) | ||||
−0.737888 | + | 0.674923i | \(0.764177\pi\) | |||||||
\(174\) | −5.84342 | −0.442989 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −27.4147 | −2.06646 | ||||||||
\(177\) | 11.7413 | 0.882532 | ||||||||
\(178\) | 5.50967 | 0.412967 | ||||||||
\(179\) | −2.07052 | −0.154758 | −0.0773789 | − | 0.997002i | \(-0.524655\pi\) | ||||
−0.0773789 | + | 0.997002i | \(0.524655\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.6324 | −1.60793 | −0.803963 | − | 0.594679i | \(-0.797279\pi\) | ||||
−0.803963 | + | 0.594679i | \(0.797279\pi\) | |||||||
\(182\) | 16.9857 | 1.25907 | ||||||||
\(183\) | −2.49129 | −0.184161 | ||||||||
\(184\) | 11.4514 | 0.844211 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.5955 | −1.14351 | ||||||||
\(187\) | 4.43590 | 0.324385 | ||||||||
\(188\) | −0.596963 | −0.0435380 | ||||||||
\(189\) | −12.1691 | −0.885169 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.4061 | −1.62125 | −0.810626 | − | 0.585565i | \(-0.800873\pi\) | ||||
−0.810626 | + | 0.585565i | \(0.800873\pi\) | |||||||
\(192\) | −5.00376 | −0.361115 | ||||||||
\(193\) | −19.5987 | −1.41075 | −0.705374 | − | 0.708835i | \(-0.749221\pi\) | ||||
−0.705374 | + | 0.708835i | \(0.749221\pi\) | |||||||
\(194\) | 20.6594 | 1.48326 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.25434 | −0.0895955 | ||||||||
\(197\) | 15.4597 | 1.10146 | 0.550729 | − | 0.834684i | \(-0.314350\pi\) | ||||
0.550729 | + | 0.834684i | \(0.314350\pi\) | |||||||
\(198\) | 14.5068 | 1.03095 | ||||||||
\(199\) | −1.37296 | −0.0973268 | −0.0486634 | − | 0.998815i | \(-0.515496\pi\) | ||||
−0.0486634 | + | 0.998815i | \(0.515496\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.86061 | 0.272306 | ||||||||
\(202\) | −9.02307 | −0.634861 | ||||||||
\(203\) | 6.77723 | 0.475668 | ||||||||
\(204\) | −0.580393 | −0.0406356 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.35536 | 0.373126 | ||||||||
\(207\) | −8.14350 | −0.566013 | ||||||||
\(208\) | −22.8287 | −1.58288 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.57190 | −0.658957 | −0.329478 | − | 0.944163i | \(-0.606873\pi\) | ||||
−0.329478 | + | 0.944163i | \(0.606873\pi\) | |||||||
\(212\) | 2.74108 | 0.188258 | ||||||||
\(213\) | 8.53039 | 0.584492 | ||||||||
\(214\) | −10.8035 | −0.738513 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.1700 | 0.828062 | ||||||||
\(217\) | 18.0877 | 1.22787 | ||||||||
\(218\) | 25.3890 | 1.71956 | ||||||||
\(219\) | 18.0217 | 1.21779 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.69385 | 0.248475 | ||||||||
\(222\) | −1.89578 | −0.127237 | ||||||||
\(223\) | −6.53750 | −0.437783 | −0.218892 | − | 0.975749i | \(-0.570244\pi\) | ||||
−0.218892 | + | 0.975749i | \(0.570244\pi\) | |||||||
\(224\) | −7.58650 | −0.506894 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.6557 | −0.708808 | ||||||||
\(227\) | −8.88867 | −0.589962 | −0.294981 | − | 0.955503i | \(-0.595313\pi\) | ||||
−0.294981 | + | 0.955503i | \(0.595313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.22494 | −0.477438 | −0.238719 | − | 0.971089i | \(-0.576727\pi\) | ||||
−0.238719 | + | 0.971089i | \(0.576727\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.9743 | 0.985238 | ||||||||
\(232\) | −6.77774 | −0.444981 | ||||||||
\(233\) | 24.9780 | 1.63636 | 0.818181 | − | 0.574961i | \(-0.194983\pi\) | ||||
0.818181 | + | 0.574961i | \(0.194983\pi\) | |||||||
\(234\) | 12.0800 | 0.789697 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.13839 | −0.399575 | ||||||||
\(237\) | 1.59236 | 0.103435 | ||||||||
\(238\) | 2.83972 | 0.184072 | ||||||||
\(239\) | 16.8187 | 1.08791 | 0.543956 | − | 0.839114i | \(-0.316926\pi\) | ||||
0.543956 | + | 0.839114i | \(0.316926\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8463 | 0.698671 | 0.349335 | − | 0.936998i | \(-0.386407\pi\) | ||||
0.349335 | + | 0.936998i | \(0.386407\pi\) | |||||||
\(242\) | −33.7795 | −2.17143 | ||||||||
\(243\) | −14.3143 | −0.918266 | ||||||||
\(244\) | 1.30245 | 0.0833809 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.72873 | −0.173978 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −18.0891 | −1.14866 | ||||||||
\(249\) | −8.94453 | −0.566837 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.37067 | 0.402113 | 0.201056 | − | 0.979580i | \(-0.435563\pi\) | ||||
0.201056 | + | 0.979580i | \(0.435563\pi\) | |||||||
\(252\) | 2.20139 | 0.138675 | ||||||||
\(253\) | 28.9600 | 1.82070 | ||||||||
\(254\) | −2.16082 | −0.135582 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.6228 | 0.851425 | ||||||||
\(257\) | 13.6465 | 0.851245 | 0.425623 | − | 0.904901i | \(-0.360055\pi\) | ||||
0.425623 | + | 0.904901i | \(0.360055\pi\) | |||||||
\(258\) | 2.92840 | 0.182314 | ||||||||
\(259\) | 2.19874 | 0.136623 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.81988 | 0.298343 | ||||||||
\(262\) | −22.3088 | −1.37825 | ||||||||
\(263\) | −10.2215 | −0.630285 | −0.315143 | − | 0.949044i | \(-0.602052\pi\) | ||||
−0.315143 | + | 0.949044i | \(0.602052\pi\) | |||||||
\(264\) | −14.9754 | −0.921675 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.04469 | 0.247531 | ||||||||
\(268\) | −2.01834 | −0.123289 | ||||||||
\(269\) | 14.4499 | 0.881028 | 0.440514 | − | 0.897746i | \(-0.354796\pi\) | ||||
0.440514 | + | 0.897746i | \(0.354796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2054 | −0.984409 | −0.492204 | − | 0.870480i | \(-0.663809\pi\) | ||||
−0.492204 | + | 0.870480i | \(0.663809\pi\) | |||||||
\(272\) | −3.81656 | −0.231413 | ||||||||
\(273\) | 12.4693 | 0.754679 | ||||||||
\(274\) | −19.0116 | −1.14853 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.78912 | −0.228079 | ||||||||
\(277\) | −28.5943 | −1.71806 | −0.859032 | − | 0.511922i | \(-0.828934\pi\) | ||||
−0.859032 | + | 0.511922i | \(0.828934\pi\) | |||||||
\(278\) | 15.1245 | 0.907105 | ||||||||
\(279\) | 12.8637 | 0.770132 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.17770 | −0.428186 | −0.214093 | − | 0.976813i | \(-0.568680\pi\) | ||||
−0.214093 | + | 0.976813i | \(0.568680\pi\) | |||||||
\(282\) | −1.84874 | −0.110091 | ||||||||
\(283\) | 10.3656 | 0.616173 | 0.308086 | − | 0.951358i | \(-0.400311\pi\) | ||||
0.308086 | + | 0.951358i | \(0.400311\pi\) | |||||||
\(284\) | −4.45970 | −0.264635 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −42.9592 | −2.54023 | ||||||||
\(287\) | 3.16480 | 0.186812 | ||||||||
\(288\) | −5.39542 | −0.317928 | ||||||||
\(289\) | −16.3825 | −0.963674 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.1662 | 0.889059 | ||||||||
\(292\) | −9.42177 | −0.551367 | ||||||||
\(293\) | −9.09056 | −0.531076 | −0.265538 | − | 0.964100i | \(-0.585550\pi\) | ||||
−0.265538 | + | 0.964100i | \(0.585550\pi\) | |||||||
\(294\) | −3.88457 | −0.226553 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.19890 | −0.127809 | ||||||||
\(297\) | 30.7772 | 1.78587 | ||||||||
\(298\) | −29.1811 | −1.69041 | ||||||||
\(299\) | 24.1155 | 1.39463 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.39637 | −0.195764 | ||||||||
\(302\) | −21.0737 | −1.21266 | ||||||||
\(303\) | −6.62390 | −0.380533 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.01958 | 0.115451 | ||||||||
\(307\) | 14.6641 | 0.836923 | 0.418461 | − | 0.908235i | \(-0.362569\pi\) | ||||
0.418461 | + | 0.908235i | \(0.362569\pi\) | |||||||
\(308\) | −7.82861 | −0.446076 | ||||||||
\(309\) | 3.93141 | 0.223650 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.5811 | −1.79080 | −0.895400 | − | 0.445263i | \(-0.853110\pi\) | ||||
−0.895400 | + | 0.445263i | \(0.853110\pi\) | |||||||
\(312\) | −12.4703 | −0.705991 | ||||||||
\(313\) | −8.99070 | −0.508184 | −0.254092 | − | 0.967180i | \(-0.581777\pi\) | ||||
−0.254092 | + | 0.967180i | \(0.581777\pi\) | |||||||
\(314\) | −17.0118 | −0.960030 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.832489 | −0.0468312 | ||||||||
\(317\) | 10.4204 | 0.585269 | 0.292635 | − | 0.956224i | \(-0.405468\pi\) | ||||
0.292635 | + | 0.956224i | \(0.405468\pi\) | |||||||
\(318\) | 8.48887 | 0.476032 | ||||||||
\(319\) | −17.1405 | −0.959685 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.93093 | −0.442662 | ||||||||
\(322\) | 18.5393 | 1.03315 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.06790 | −0.0593276 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.86733 | 0.324962 | ||||||||
\(327\) | 18.6383 | 1.03070 | ||||||||
\(328\) | −3.16503 | −0.174760 | ||||||||
\(329\) | 2.14418 | 0.118212 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.03055 | 0.221539 | 0.110770 | − | 0.993846i | \(-0.464668\pi\) | ||||
0.110770 | + | 0.993846i | \(0.464668\pi\) | |||||||
\(332\) | 4.67622 | 0.256641 | ||||||||
\(333\) | 1.56372 | 0.0856911 | ||||||||
\(334\) | −17.2268 | −0.942609 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.8836 | −0.702858 | ||||||||
\(337\) | 24.7816 | 1.34994 | 0.674969 | − | 0.737846i | \(-0.264157\pi\) | ||||
0.674969 | + | 0.737846i | \(0.264157\pi\) | |||||||
\(338\) | −14.7249 | −0.800928 | ||||||||
\(339\) | −7.82244 | −0.424857 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.7462 | −2.47730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1287 | 1.08685 | ||||||||
\(344\) | 3.39663 | 0.183134 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.4275 | 1.68955 | ||||||||
\(347\) | −28.6239 | −1.53661 | −0.768306 | − | 0.640082i | \(-0.778900\pi\) | ||||
−0.768306 | + | 0.640082i | \(0.778900\pi\) | |||||||
\(348\) | 2.24266 | 0.120219 | ||||||||
\(349\) | 10.2217 | 0.547154 | 0.273577 | − | 0.961850i | \(-0.411793\pi\) | ||||
0.273577 | + | 0.961850i | \(0.411793\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.6286 | 1.36796 | ||||||||
\(352\) | 19.1873 | 1.02269 | ||||||||
\(353\) | −17.7919 | −0.946965 | −0.473483 | − | 0.880803i | \(-0.657003\pi\) | ||||
−0.473483 | + | 0.880803i | \(0.657003\pi\) | |||||||
\(354\) | −19.0100 | −1.01037 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.11457 | −0.112072 | ||||||||
\(357\) | 2.08466 | 0.110332 | ||||||||
\(358\) | 3.35231 | 0.177175 | ||||||||
\(359\) | −0.860591 | −0.0454202 | −0.0227101 | − | 0.999742i | \(-0.507229\pi\) | ||||
−0.0227101 | + | 0.999742i | \(0.507229\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 35.0244 | 1.84084 | ||||||||
\(363\) | −24.7978 | −1.30155 | ||||||||
\(364\) | −6.51900 | −0.341688 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.03357 | 0.210838 | ||||||||
\(367\) | 21.3109 | 1.11242 | 0.556209 | − | 0.831043i | \(-0.312256\pi\) | ||||
0.556209 | + | 0.831043i | \(0.312256\pi\) | |||||||
\(368\) | −24.9166 | −1.29887 | ||||||||
\(369\) | 2.25076 | 0.117170 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.84543 | −0.511150 | ||||||||
\(372\) | 5.98542 | 0.310330 | ||||||||
\(373\) | 14.1725 | 0.733822 | 0.366911 | − | 0.930256i | \(-0.380415\pi\) | ||||
0.366911 | + | 0.930256i | \(0.380415\pi\) | |||||||
\(374\) | −7.18204 | −0.371374 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.14434 | −0.110586 | ||||||||
\(377\) | −14.2732 | −0.735106 | ||||||||
\(378\) | 19.7026 | 1.01339 | ||||||||
\(379\) | 3.54496 | 0.182092 | 0.0910462 | − | 0.995847i | \(-0.470979\pi\) | ||||
0.0910462 | + | 0.995847i | \(0.470979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.58627 | −0.0812671 | ||||||||
\(382\) | 36.2771 | 1.85610 | ||||||||
\(383\) | −7.70846 | −0.393884 | −0.196942 | − | 0.980415i | \(-0.563101\pi\) | ||||
−0.196942 | + | 0.980415i | \(0.563101\pi\) | |||||||
\(384\) | 16.1816 | 0.825764 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.7317 | 1.61510 | ||||||||
\(387\) | −2.41546 | −0.122785 | ||||||||
\(388\) | −7.92893 | −0.402530 | ||||||||
\(389\) | 1.79987 | 0.0912571 | 0.0456285 | − | 0.998958i | \(-0.485471\pi\) | ||||
0.0456285 | + | 0.998958i | \(0.485471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.03169 | 0.203891 | ||||||||
\(392\) | −4.50568 | −0.227571 | ||||||||
\(393\) | −16.3771 | −0.826114 | ||||||||
\(394\) | −25.0303 | −1.26101 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.56761 | −0.279783 | ||||||||
\(397\) | 17.6756 | 0.887111 | 0.443556 | − | 0.896247i | \(-0.353717\pi\) | ||||
0.443556 | + | 0.896247i | \(0.353717\pi\) | |||||||
\(398\) | 2.22292 | 0.111425 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.1151 | 1.35406 | 0.677032 | − | 0.735954i | \(-0.263266\pi\) | ||||
0.677032 | + | 0.735954i | \(0.263266\pi\) | |||||||
\(402\) | −6.25060 | −0.311752 | ||||||||
\(403\) | −38.0936 | −1.89758 | ||||||||
\(404\) | 3.46299 | 0.172290 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.9728 | −0.544572 | ||||||||
\(407\) | −5.56090 | −0.275644 | ||||||||
\(408\) | −2.08482 | −0.103214 | ||||||||
\(409\) | −33.8712 | −1.67482 | −0.837411 | − | 0.546574i | \(-0.815932\pi\) | ||||
−0.837411 | + | 0.546574i | \(0.815932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.9565 | −0.688424 | ||||||||
\(412\) | −2.05535 | −0.101260 | ||||||||
\(413\) | 22.0479 | 1.08491 | ||||||||
\(414\) | 13.1849 | 0.648003 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.9775 | 0.783363 | ||||||||
\(417\) | 11.1030 | 0.543714 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.2338 | −1.13505 | −0.567524 | − | 0.823357i | \(-0.692099\pi\) | ||||
−0.567524 | + | 0.823357i | \(0.692099\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3476 | −0.942944 | −0.471472 | − | 0.881881i | \(-0.656277\pi\) | ||||
−0.471472 | + | 0.881881i | \(0.656277\pi\) | |||||||
\(422\) | 15.4976 | 0.754410 | ||||||||
\(423\) | 1.52491 | 0.0741438 | ||||||||
\(424\) | 9.84617 | 0.478173 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.8113 | −0.669159 | ||||||||
\(427\) | −4.67815 | −0.226392 | ||||||||
\(428\) | 4.14631 | 0.200419 | ||||||||
\(429\) | −31.5366 | −1.52260 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.0559 | 0.628881 | 0.314440 | − | 0.949277i | \(-0.398183\pi\) | ||||
0.314440 | + | 0.949277i | \(0.398183\pi\) | |||||||
\(432\) | −26.4801 | −1.27402 | ||||||||
\(433\) | −5.82886 | −0.280117 | −0.140059 | − | 0.990143i | \(-0.544729\pi\) | ||||
−0.140059 | + | 0.990143i | \(0.544729\pi\) | |||||||
\(434\) | −29.2852 | −1.40574 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.74413 | −0.466659 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −29.1783 | −1.39419 | ||||||||
\(439\) | 6.49004 | 0.309753 | 0.154876 | − | 0.987934i | \(-0.450502\pi\) | ||||
0.154876 | + | 0.987934i | \(0.450502\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.20414 | 0.152578 | ||||||||
\(442\) | −5.98059 | −0.284468 | ||||||||
\(443\) | −9.20328 | −0.437261 | −0.218631 | − | 0.975808i | \(-0.570159\pi\) | ||||
−0.218631 | + | 0.975808i | \(0.570159\pi\) | |||||||
\(444\) | 0.727588 | 0.0345298 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.5847 | 0.501198 | ||||||||
\(447\) | −21.4220 | −1.01323 | ||||||||
\(448\) | −9.39608 | −0.443923 | ||||||||
\(449\) | 17.4646 | 0.824206 | 0.412103 | − | 0.911137i | \(-0.364794\pi\) | ||||
0.412103 | + | 0.911137i | \(0.364794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.00419 | −0.376903 | ||||||||
\(452\) | 4.08959 | 0.192358 | ||||||||
\(453\) | −15.4703 | −0.726860 | ||||||||
\(454\) | 14.3914 | 0.675421 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.381827 | −0.0178611 | −0.00893055 | − | 0.999960i | \(-0.502843\pi\) | ||||
−0.00893055 | + | 0.999960i | \(0.502843\pi\) | |||||||
\(458\) | 11.6977 | 0.546597 | ||||||||
\(459\) | 4.28467 | 0.199991 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.51706 | 0.396679 | 0.198339 | − | 0.980133i | \(-0.436445\pi\) | ||||
0.198339 | + | 0.980133i | \(0.436445\pi\) | |||||||
\(462\) | −24.2445 | −1.12795 | ||||||||
\(463\) | 37.0178 | 1.72036 | 0.860181 | − | 0.509988i | \(-0.170350\pi\) | ||||
0.860181 | + | 0.509988i | \(0.170350\pi\) | |||||||
\(464\) | 14.7474 | 0.684629 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.4411 | −1.87340 | ||||||||
\(467\) | −25.9387 | −1.20030 | −0.600151 | − | 0.799887i | \(-0.704893\pi\) | ||||
−0.600151 | + | 0.799887i | \(0.704893\pi\) | |||||||
\(468\) | −4.63623 | −0.214310 | ||||||||
\(469\) | 7.24948 | 0.334750 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.4885 | −0.575438 | ||||||||
\(472\) | −22.0496 | −1.01491 | ||||||||
\(473\) | 8.58988 | 0.394963 | ||||||||
\(474\) | −2.57814 | −0.118418 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.08986 | −0.0499539 | ||||||||
\(477\) | −7.00195 | −0.320597 | ||||||||
\(478\) | −27.2307 | −1.24550 | ||||||||
\(479\) | 11.8388 | 0.540929 | 0.270464 | − | 0.962730i | \(-0.412823\pi\) | ||||
0.270464 | + | 0.962730i | \(0.412823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.63065 | −0.211139 | ||||||||
\(482\) | −17.5609 | −0.799877 | ||||||||
\(483\) | 13.6098 | 0.619268 | ||||||||
\(484\) | 12.9643 | 0.589288 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 23.1759 | 1.05128 | ||||||||
\(487\) | −29.3813 | −1.33139 | −0.665696 | − | 0.746223i | \(-0.731865\pi\) | ||||
−0.665696 | + | 0.746223i | \(0.731865\pi\) | |||||||
\(488\) | 4.67851 | 0.211786 | ||||||||
\(489\) | 4.30725 | 0.194781 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.81838 | −0.217451 | −0.108725 | − | 0.994072i | \(-0.534677\pi\) | ||||
−0.108725 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(492\) | 1.04727 | 0.0472145 | ||||||||
\(493\) | −2.38623 | −0.107470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 39.3591 | 1.76727 | ||||||||
\(497\) | 16.0184 | 0.718524 | ||||||||
\(498\) | 14.4818 | 0.648946 | ||||||||
\(499\) | 0.188226 | 0.00842614 | 0.00421307 | − | 0.999991i | \(-0.498659\pi\) | ||||
0.00421307 | + | 0.999991i | \(0.498659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.6463 | −0.564996 | ||||||||
\(502\) | −10.3146 | −0.460361 | ||||||||
\(503\) | 2.27585 | 0.101475 | 0.0507375 | − | 0.998712i | \(-0.483843\pi\) | ||||
0.0507375 | + | 0.998712i | \(0.483843\pi\) | |||||||
\(504\) | 7.90756 | 0.352231 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −46.8883 | −2.08444 | ||||||||
\(507\) | −10.8096 | −0.480072 | ||||||||
\(508\) | 0.829306 | 0.0367945 | ||||||||
\(509\) | 4.27456 | 0.189467 | 0.0947334 | − | 0.995503i | \(-0.469800\pi\) | ||||
0.0947334 | + | 0.995503i | \(0.469800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.8412 | 1.49705 | ||||||||
\(512\) | 5.17245 | 0.228592 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.0946 | −0.974552 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.12390 | −0.0494769 | ||||||||
\(517\) | −5.42291 | −0.238499 | ||||||||
\(518\) | −3.55991 | −0.156414 | ||||||||
\(519\) | 23.0711 | 1.01271 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.3273 | −1.41629 | −0.708143 | − | 0.706069i | \(-0.750467\pi\) | ||||
−0.708143 | + | 0.706069i | \(0.750467\pi\) | |||||||
\(522\) | −7.80373 | −0.341560 | ||||||||
\(523\) | −29.5161 | −1.29065 | −0.645325 | − | 0.763908i | \(-0.723278\pi\) | ||||
−0.645325 | + | 0.763908i | \(0.723278\pi\) | |||||||
\(524\) | 8.56197 | 0.374031 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.5493 | 0.721585 | ||||||||
\(527\) | −6.36859 | −0.277420 | ||||||||
\(528\) | 32.5843 | 1.41805 | ||||||||
\(529\) | 3.32109 | 0.144395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.6802 | 0.680463 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.66521 | −0.288702 | ||||||||
\(534\) | −6.54863 | −0.283387 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.25002 | −0.313153 | ||||||||
\(537\) | 2.46096 | 0.106198 | ||||||||
\(538\) | −23.3954 | −1.00865 | ||||||||
\(539\) | −11.3946 | −0.490800 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.8753 | 0.811515 | 0.405757 | − | 0.913981i | \(-0.367008\pi\) | ||||
0.405757 | + | 0.913981i | \(0.367008\pi\) | |||||||
\(542\) | 26.2377 | 1.12701 | ||||||||
\(543\) | 25.7117 | 1.10339 | ||||||||
\(544\) | 2.67117 | 0.114525 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −20.1887 | −0.863998 | ||||||||
\(547\) | 25.1190 | 1.07401 | 0.537006 | − | 0.843578i | \(-0.319555\pi\) | ||||
0.537006 | + | 0.843578i | \(0.319555\pi\) | |||||||
\(548\) | 7.29650 | 0.311691 | ||||||||
\(549\) | −3.32705 | −0.141995 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −13.6108 | −0.579315 | ||||||||
\(553\) | 2.99014 | 0.127154 | ||||||||
\(554\) | 46.2961 | 1.96693 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.80465 | −0.246172 | ||||||||
\(557\) | −28.1731 | −1.19373 | −0.596867 | − | 0.802340i | \(-0.703588\pi\) | ||||
−0.596867 | + | 0.802340i | \(0.703588\pi\) | |||||||
\(558\) | −20.8273 | −0.881690 | ||||||||
\(559\) | 7.15292 | 0.302536 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.27238 | −0.222600 | ||||||||
\(562\) | 11.6212 | 0.490211 | ||||||||
\(563\) | −20.4297 | −0.861010 | −0.430505 | − | 0.902588i | \(-0.641664\pi\) | ||||
−0.430505 | + | 0.902588i | \(0.641664\pi\) | |||||||
\(564\) | 0.709533 | 0.0298767 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.7827 | −0.705428 | ||||||||
\(567\) | 3.83568 | 0.161083 | ||||||||
\(568\) | −16.0196 | −0.672168 | ||||||||
\(569\) | 35.8386 | 1.50243 | 0.751217 | − | 0.660056i | \(-0.229467\pi\) | ||||
0.751217 | + | 0.660056i | \(0.229467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.82827 | −0.118359 | −0.0591797 | − | 0.998247i | \(-0.518848\pi\) | ||||
−0.0591797 | + | 0.998247i | \(0.518848\pi\) | |||||||
\(572\) | 16.4874 | 0.689374 | ||||||||
\(573\) | 26.6313 | 1.11254 | ||||||||
\(574\) | −5.12403 | −0.213873 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.68237 | −0.278432 | ||||||||
\(577\) | 43.3132 | 1.80315 | 0.901575 | − | 0.432622i | \(-0.142411\pi\) | ||||
0.901575 | + | 0.432622i | \(0.142411\pi\) | |||||||
\(578\) | 26.5243 | 1.10327 | ||||||||
\(579\) | 23.2945 | 0.968085 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.7961 | −0.696819 | ||||||||
\(582\) | −24.5552 | −1.01784 | ||||||||
\(583\) | 24.9004 | 1.03127 | ||||||||
\(584\) | −33.8437 | −1.40046 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7183 | 0.608006 | ||||||||
\(587\) | −24.5741 | −1.01428 | −0.507141 | − | 0.861863i | \(-0.669298\pi\) | ||||
−0.507141 | + | 0.861863i | \(0.669298\pi\) | |||||||
\(588\) | 1.49087 | 0.0614824 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.3749 | −0.755843 | ||||||||
\(592\) | 4.78449 | 0.196641 | ||||||||
\(593\) | −0.313720 | −0.0128829 | −0.00644147 | − | 0.999979i | \(-0.502050\pi\) | ||||
−0.00644147 | + | 0.999979i | \(0.502050\pi\) | |||||||
\(594\) | −49.8304 | −2.04457 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.1995 | 0.458748 | ||||||||
\(597\) | 1.63186 | 0.0667877 | ||||||||
\(598\) | −39.0446 | −1.59665 | ||||||||
\(599\) | −24.4964 | −1.00090 | −0.500448 | − | 0.865767i | \(-0.666831\pi\) | ||||
−0.500448 | + | 0.865767i | \(0.666831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.83045 | 0.319411 | 0.159705 | − | 0.987165i | \(-0.448946\pi\) | ||||
0.159705 | + | 0.987165i | \(0.448946\pi\) | |||||||
\(602\) | 5.49896 | 0.224121 | ||||||||
\(603\) | 5.15574 | 0.209958 | ||||||||
\(604\) | 8.08793 | 0.329093 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.7246 | 0.435655 | ||||||||
\(607\) | −12.4142 | −0.503876 | −0.251938 | − | 0.967743i | \(-0.581068\pi\) | ||||
−0.251938 | + | 0.967743i | \(0.581068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.05522 | −0.326414 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.51574 | −0.182687 | ||||||||
\(612\) | −0.775098 | −0.0313315 | ||||||||
\(613\) | −1.05853 | −0.0427534 | −0.0213767 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213767 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(614\) | −23.7422 | −0.958156 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28.1210 | −1.13303 | ||||||||
\(617\) | −28.5881 | −1.15091 | −0.575457 | − | 0.817832i | \(-0.695176\pi\) | ||||
−0.575457 | + | 0.817832i | \(0.695176\pi\) | |||||||
\(618\) | −6.36522 | −0.256047 | ||||||||
\(619\) | 9.41956 | 0.378604 | 0.189302 | − | 0.981919i | \(-0.439377\pi\) | ||||
0.189302 | + | 0.981919i | \(0.439377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.9727 | 1.12250 | ||||||||
\(622\) | 51.1320 | 2.05021 | ||||||||
\(623\) | 7.59514 | 0.304293 | ||||||||
\(624\) | 27.1335 | 1.08621 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.5566 | 0.581797 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.52899 | 0.260535 | ||||||||
\(629\) | −0.774165 | −0.0308680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.6280 | −1.57757 | −0.788784 | − | 0.614671i | \(-0.789289\pi\) | ||||
−0.788784 | + | 0.614671i | \(0.789289\pi\) | |||||||
\(632\) | −2.99037 | −0.118950 | ||||||||
\(633\) | 11.3769 | 0.452190 | ||||||||
\(634\) | −16.8714 | −0.670049 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.25797 | −0.129187 | ||||||||
\(637\) | −9.48846 | −0.375947 | ||||||||
\(638\) | 27.7517 | 1.09870 | ||||||||
\(639\) | 11.3921 | 0.450664 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.6559 | −0.776360 | −0.388180 | − | 0.921584i | \(-0.626896\pi\) | ||||
−0.388180 | + | 0.921584i | \(0.626896\pi\) | |||||||
\(642\) | 12.8407 | 0.506783 | ||||||||
\(643\) | 28.7116 | 1.13227 | 0.566137 | − | 0.824311i | \(-0.308437\pi\) | ||||
0.566137 | + | 0.824311i | \(0.308437\pi\) | |||||||
\(644\) | −7.11524 | −0.280380 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.4412 | −0.685686 | −0.342843 | − | 0.939393i | \(-0.611390\pi\) | ||||
−0.342843 | + | 0.939393i | \(0.611390\pi\) | |||||||
\(648\) | −3.83597 | −0.150691 | ||||||||
\(649\) | −55.7622 | −2.18886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.4985 | −0.842592 | ||||||||
\(652\) | −2.25184 | −0.0881889 | ||||||||
\(653\) | −30.3498 | −1.18768 | −0.593839 | − | 0.804584i | \(-0.702388\pi\) | ||||
−0.593839 | + | 0.804584i | \(0.702388\pi\) | |||||||
\(654\) | −30.1767 | −1.18000 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.88664 | 0.268878 | ||||||||
\(657\) | 24.0674 | 0.938959 | ||||||||
\(658\) | −3.47157 | −0.135336 | ||||||||
\(659\) | −6.53865 | −0.254709 | −0.127355 | − | 0.991857i | \(-0.540649\pi\) | ||||
−0.127355 | + | 0.991857i | \(0.540649\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.7996 | −0.925699 | −0.462849 | − | 0.886437i | \(-0.653173\pi\) | ||||
−0.462849 | + | 0.886437i | \(0.653173\pi\) | |||||||
\(662\) | −6.52575 | −0.253630 | ||||||||
\(663\) | −4.39039 | −0.170509 | ||||||||
\(664\) | 16.7973 | 0.651863 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.53176 | −0.0981039 | ||||||||
\(667\) | −15.5786 | −0.603207 | ||||||||
\(668\) | 6.61152 | 0.255808 | ||||||||
\(669\) | 7.77027 | 0.300416 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.8317 | 0.456757 | ||||||||
\(672\) | 9.01709 | 0.347842 | ||||||||
\(673\) | −49.9227 | −1.92438 | −0.962189 | − | 0.272381i | \(-0.912189\pi\) | ||||
−0.962189 | + | 0.272381i | \(0.912189\pi\) | |||||||
\(674\) | −40.1231 | −1.54548 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.65130 | 0.217358 | ||||||||
\(677\) | 34.5826 | 1.32912 | 0.664558 | − | 0.747237i | \(-0.268620\pi\) | ||||
0.664558 | + | 0.747237i | \(0.268620\pi\) | |||||||
\(678\) | 12.6651 | 0.486399 | ||||||||
\(679\) | 28.4792 | 1.09293 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5648 | 0.404844 | ||||||||
\(682\) | 74.0663 | 2.83614 | ||||||||
\(683\) | 21.1277 | 0.808429 | 0.404214 | − | 0.914664i | \(-0.367545\pi\) | ||||
0.404214 | + | 0.914664i | \(0.367545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −32.5897 | −1.24428 | ||||||||
\(687\) | 8.58735 | 0.327628 | ||||||||
\(688\) | −7.39055 | −0.281762 | ||||||||
\(689\) | 20.7350 | 0.789939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.8861 | 1.06084 | 0.530418 | − | 0.847736i | \(-0.322035\pi\) | ||||
0.530418 | + | 0.847736i | \(0.322035\pi\) | |||||||
\(692\) | −12.0616 | −0.458514 | ||||||||
\(693\) | 19.9978 | 0.759653 | ||||||||
\(694\) | 46.3441 | 1.75920 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.05582 | 0.305355 | ||||||||
\(697\) | −1.11431 | −0.0422075 | ||||||||
\(698\) | −16.5496 | −0.626412 | ||||||||
\(699\) | −29.6881 | −1.12291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.3344 | −1.48564 | −0.742821 | − | 0.669490i | \(-0.766513\pi\) | ||||
−0.742821 | + | 0.669490i | \(0.766513\pi\) | |||||||
\(702\) | −41.4946 | −1.56611 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 23.7639 | 0.895637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.8063 | 1.08414 | ||||||||
\(707\) | −12.4384 | −0.467794 | ||||||||
\(708\) | 7.29591 | 0.274197 | ||||||||
\(709\) | 4.28832 | 0.161051 | 0.0805256 | − | 0.996753i | \(-0.474340\pi\) | ||||
0.0805256 | + | 0.996753i | \(0.474340\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.12655 | 0.0797519 | ||||||||
\(712\) | −7.59571 | −0.284661 | ||||||||
\(713\) | −41.5776 | −1.55710 | ||||||||
\(714\) | −3.37521 | −0.126314 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.28659 | −0.0480822 | ||||||||
\(717\) | −19.9902 | −0.746549 | ||||||||
\(718\) | 1.39336 | 0.0519996 | ||||||||
\(719\) | −3.93252 | −0.146658 | −0.0733291 | − | 0.997308i | \(-0.523362\pi\) | ||||
−0.0733291 | + | 0.997308i | \(0.523362\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.38242 | 0.274936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.8916 | −0.479443 | ||||||||
\(724\) | −13.4421 | −0.499572 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 40.1494 | 1.49008 | ||||||||
\(727\) | −20.0574 | −0.743889 | −0.371944 | − | 0.928255i | \(-0.621309\pi\) | ||||
−0.371944 | + | 0.928255i | \(0.621309\pi\) | |||||||
\(728\) | −23.4168 | −0.867883 | ||||||||
\(729\) | 22.1693 | 0.821086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.19585 | 0.0442300 | ||||||||
\(732\) | −1.54805 | −0.0572177 | ||||||||
\(733\) | −0.205782 | −0.00760071 | −0.00380036 | − | 0.999993i | \(-0.501210\pi\) | ||||
−0.00380036 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(734\) | −34.5038 | −1.27356 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.4389 | 0.642805 | ||||||||
\(737\) | −18.3349 | −0.675374 | ||||||||
\(738\) | −3.64414 | −0.134143 | ||||||||
\(739\) | 32.6116 | 1.19964 | 0.599819 | − | 0.800136i | \(-0.295239\pi\) | ||||
0.599819 | + | 0.800136i | \(0.295239\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.9404 | 0.585192 | ||||||||
\(743\) | 29.5603 | 1.08446 | 0.542231 | − | 0.840230i | \(-0.317580\pi\) | ||||
0.542231 | + | 0.840230i | \(0.317580\pi\) | |||||||
\(744\) | 21.5001 | 0.788232 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.9462 | −0.840120 | ||||||||
\(747\) | −11.9452 | −0.437051 | ||||||||
\(748\) | 2.75641 | 0.100784 | ||||||||
\(749\) | −14.8927 | −0.544169 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0458 | 1.35182 | 0.675909 | − | 0.736985i | \(-0.263751\pi\) | ||||
0.675909 | + | 0.736985i | \(0.263751\pi\) | |||||||
\(752\) | 4.66576 | 0.170143 | ||||||||
\(753\) | −7.57198 | −0.275938 | ||||||||
\(754\) | 23.1093 | 0.841590 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.56170 | −0.275016 | ||||||||
\(757\) | 30.5480 | 1.11029 | 0.555143 | − | 0.831755i | \(-0.312664\pi\) | ||||
0.555143 | + | 0.831755i | \(0.312664\pi\) | |||||||
\(758\) | −5.73954 | −0.208470 | ||||||||
\(759\) | −34.4210 | −1.24940 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.0692 | −1.67001 | −0.835004 | − | 0.550244i | \(-0.814535\pi\) | ||||
−0.835004 | + | 0.550244i | \(0.814535\pi\) | |||||||
\(762\) | 2.56828 | 0.0930391 | ||||||||
\(763\) | 34.9990 | 1.26705 | ||||||||
\(764\) | −13.9229 | −0.503712 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.4805 | 0.450940 | ||||||||
\(767\) | −46.4340 | −1.67663 | ||||||||
\(768\) | −16.1916 | −0.584266 | ||||||||
\(769\) | 14.7199 | 0.530814 | 0.265407 | − | 0.964137i | \(-0.414494\pi\) | ||||
0.265407 | + | 0.964137i | \(0.414494\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.2198 | −0.584142 | ||||||||
\(772\) | −12.1784 | −0.438310 | ||||||||
\(773\) | −8.86483 | −0.318846 | −0.159423 | − | 0.987210i | \(-0.550963\pi\) | ||||
−0.159423 | + | 0.987210i | \(0.550963\pi\) | |||||||
\(774\) | 3.91079 | 0.140571 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −28.4813 | −1.02242 | ||||||||
\(777\) | −2.61336 | −0.0937536 | ||||||||
\(778\) | −2.91412 | −0.104476 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.5127 | −1.44966 | ||||||||
\(782\) | −6.52759 | −0.233426 | ||||||||
\(783\) | −16.5561 | −0.591668 | ||||||||
\(784\) | 9.80368 | 0.350132 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 26.5156 | 0.945781 | ||||||||
\(787\) | −13.1846 | −0.469979 | −0.234990 | − | 0.971998i | \(-0.575506\pi\) | ||||
−0.234990 | + | 0.971998i | \(0.575506\pi\) | |||||||
\(788\) | 9.60645 | 0.342216 | ||||||||
\(789\) | 12.1490 | 0.432515 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6890 | −0.522281 | ||||||||
\(792\) | −19.9993 | −0.710644 | ||||||||
\(793\) | 9.85242 | 0.349870 | ||||||||
\(794\) | −28.6180 | −1.01561 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.853141 | −0.0302388 | ||||||||
\(797\) | 38.1858 | 1.35261 | 0.676306 | − | 0.736621i | \(-0.263580\pi\) | ||||
0.676306 | + | 0.736621i | \(0.263580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.754954 | −0.0267084 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.40157 | 0.190855 | ||||||||
\(802\) | −43.9012 | −1.55021 | ||||||||
\(803\) | −85.5889 | −3.02037 | ||||||||
\(804\) | 2.39893 | 0.0846039 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 61.6761 | 2.17245 | ||||||||
\(807\) | −17.1747 | −0.604580 | ||||||||
\(808\) | 12.4393 | 0.437614 | ||||||||
\(809\) | 43.7667 | 1.53875 | 0.769377 | − | 0.638795i | \(-0.220567\pi\) | ||||
0.769377 | + | 0.638795i | \(0.220567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.95225 | 0.209012 | 0.104506 | − | 0.994524i | \(-0.466674\pi\) | ||||
0.104506 | + | 0.994524i | \(0.466674\pi\) | |||||||
\(812\) | 4.21128 | 0.147787 | ||||||||
\(813\) | 19.2613 | 0.675522 | ||||||||
\(814\) | 9.00349 | 0.315572 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.53625 | 0.158800 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 54.8398 | 1.91743 | ||||||||
\(819\) | 16.6525 | 0.581884 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.97019 | −0.278162 | −0.139081 | − | 0.990281i | \(-0.544415\pi\) | ||||
−0.139081 | + | 0.990281i | \(0.544415\pi\) | |||||||
\(822\) | 22.5966 | 0.788146 | ||||||||
\(823\) | −28.1907 | −0.982666 | −0.491333 | − | 0.870972i | \(-0.663490\pi\) | ||||
−0.491333 | + | 0.870972i | \(0.663490\pi\) | |||||||
\(824\) | −7.38297 | −0.257198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.6971 | −1.24206 | ||||||||
\(827\) | −54.5094 | −1.89548 | −0.947738 | − | 0.319048i | \(-0.896637\pi\) | ||||
−0.947738 | + | 0.319048i | \(0.896637\pi\) | |||||||
\(828\) | −5.06027 | −0.175856 | ||||||||
\(829\) | −8.40522 | −0.291925 | −0.145963 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145963 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.9863 | 1.17897 | ||||||||
\(832\) | 19.7886 | 0.686046 | ||||||||
\(833\) | −1.58631 | −0.0549623 | ||||||||
\(834\) | −17.9765 | −0.622474 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −44.1865 | −1.52731 | ||||||||
\(838\) | 37.6172 | 1.29947 | ||||||||
\(839\) | −37.7155 | −1.30208 | −0.651041 | − | 0.759042i | \(-0.725667\pi\) | ||||
−0.651041 | + | 0.759042i | \(0.725667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.7795 | −0.682052 | ||||||||
\(842\) | 31.3251 | 1.07953 | ||||||||
\(843\) | 8.53120 | 0.293830 | ||||||||
\(844\) | −5.94785 | −0.204734 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.46894 | −0.0848839 | ||||||||
\(847\) | −46.5654 | −1.60001 | ||||||||
\(848\) | −21.4238 | −0.735696 | ||||||||
\(849\) | −12.3203 | −0.422831 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.05418 | −0.173255 | ||||||||
\(852\) | 5.30067 | 0.181598 | ||||||||
\(853\) | −41.2975 | −1.41400 | −0.707000 | − | 0.707214i | \(-0.749952\pi\) | ||||
−0.707000 | + | 0.707214i | \(0.749952\pi\) | |||||||
\(854\) | 7.57426 | 0.259186 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.8939 | 0.509062 | ||||||||
\(857\) | −3.43473 | −0.117328 | −0.0586640 | − | 0.998278i | \(-0.518684\pi\) | ||||
−0.0586640 | + | 0.998278i | \(0.518684\pi\) | |||||||
\(858\) | 51.0600 | 1.74316 | ||||||||
\(859\) | −30.2921 | −1.03355 | −0.516777 | − | 0.856120i | \(-0.672868\pi\) | ||||
−0.516777 | + | 0.856120i | \(0.672868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.76158 | −0.128194 | ||||||||
\(862\) | −21.1384 | −0.719977 | ||||||||
\(863\) | 23.8589 | 0.812168 | 0.406084 | − | 0.913836i | \(-0.366894\pi\) | ||||
0.406084 | + | 0.913836i | \(0.366894\pi\) | |||||||
\(864\) | 18.5331 | 0.630509 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.43733 | 0.320694 | ||||||||
\(867\) | 19.4717 | 0.661293 | ||||||||
\(868\) | 11.2395 | 0.381492 | ||||||||
\(869\) | −7.56246 | −0.256539 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.2677 | −0.517328 | ||||||||
\(872\) | −35.0017 | −1.18531 | ||||||||
\(873\) | 20.2540 | 0.685496 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.1984 | 0.378360 | ||||||||
\(877\) | 13.2757 | 0.448288 | 0.224144 | − | 0.974556i | \(-0.428041\pi\) | ||||
0.224144 | + | 0.974556i | \(0.428041\pi\) | |||||||
\(878\) | −10.5078 | −0.354622 | ||||||||
\(879\) | 10.8048 | 0.364436 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.1998 | 0.680547 | 0.340274 | − | 0.940326i | \(-0.389480\pi\) | ||||
0.340274 | + | 0.940326i | \(0.389480\pi\) | |||||||
\(882\) | −5.18773 | −0.174680 | ||||||||
\(883\) | −58.2506 | −1.96029 | −0.980144 | − | 0.198289i | \(-0.936462\pi\) | ||||
−0.980144 | + | 0.198289i | \(0.936462\pi\) | |||||||
\(884\) | 2.29531 | 0.0771995 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.9008 | 0.500601 | ||||||||
\(887\) | −46.0826 | −1.54730 | −0.773651 | − | 0.633612i | \(-0.781571\pi\) | ||||
−0.773651 | + | 0.633612i | \(0.781571\pi\) | |||||||
\(888\) | 2.61355 | 0.0877050 | ||||||||
\(889\) | −2.97871 | −0.0999026 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.70095 | −0.324994 | ||||||||
\(892\) | −4.06232 | −0.136016 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 34.6837 | 1.16000 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 30.3859 | 1.01512 | ||||||||
\(897\) | −28.6629 | −0.957027 | ||||||||
\(898\) | −28.2764 | −0.943597 | ||||||||
\(899\) | 24.6085 | 0.820739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.46653 | 0.115487 | ||||||||
\(902\) | 12.9593 | 0.431499 | ||||||||
\(903\) | 4.03683 | 0.134337 | ||||||||
\(904\) | 14.6901 | 0.488586 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 25.0476 | 0.832150 | ||||||||
\(907\) | 43.6873 | 1.45061 | 0.725306 | − | 0.688426i | \(-0.241698\pi\) | ||||
0.725306 | + | 0.688426i | \(0.241698\pi\) | |||||||
\(908\) | −5.52331 | −0.183297 | ||||||||
\(909\) | −8.84603 | −0.293404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.7689 | 1.01942 | 0.509709 | − | 0.860347i | \(-0.329753\pi\) | ||||
0.509709 | + | 0.860347i | \(0.329753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.4795 | 1.40587 | ||||||||
\(914\) | 0.618204 | 0.0204484 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.48949 | −0.148337 | ||||||||
\(917\) | −30.7530 | −1.01555 | ||||||||
\(918\) | −6.93718 | −0.228961 | ||||||||
\(919\) | 12.0943 | 0.398953 | 0.199476 | − | 0.979903i | \(-0.436076\pi\) | ||||
0.199476 | + | 0.979903i | \(0.436076\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.4293 | −0.574314 | ||||||||
\(922\) | −13.7897 | −0.454140 | ||||||||
\(923\) | −33.7355 | −1.11042 | ||||||||
\(924\) | 9.30485 | 0.306107 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −59.9344 | −1.96957 | ||||||||
\(927\) | 5.25028 | 0.172442 | ||||||||
\(928\) | −10.3215 | −0.338820 | ||||||||
\(929\) | 15.9647 | 0.523785 | 0.261892 | − | 0.965097i | \(-0.415653\pi\) | ||||
0.261892 | + | 0.965097i | \(0.415653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.5210 | 0.508407 | ||||||||
\(933\) | 37.5363 | 1.22888 | ||||||||
\(934\) | 41.9966 | 1.37417 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.6537 | −0.544343 | ||||||||
\(937\) | 3.57961 | 0.116941 | 0.0584704 | − | 0.998289i | \(-0.481378\pi\) | ||||
0.0584704 | + | 0.998289i | \(0.481378\pi\) | |||||||
\(938\) | −11.7374 | −0.383240 | ||||||||
\(939\) | 10.6861 | 0.348727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.7060 | −1.13138 | −0.565691 | − | 0.824617i | \(-0.691391\pi\) | ||||
−0.565691 | + | 0.824617i | \(0.691391\pi\) | |||||||
\(942\) | 20.2197 | 0.658793 | ||||||||
\(943\) | −7.27482 | −0.236901 | ||||||||
\(944\) | 47.9766 | 1.56151 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.9076 | −0.452176 | ||||||||
\(947\) | −44.9696 | −1.46132 | −0.730658 | − | 0.682743i | \(-0.760787\pi\) | ||||
−0.730658 | + | 0.682743i | \(0.760787\pi\) | |||||||
\(948\) | 0.989471 | 0.0321365 | ||||||||
\(949\) | −71.2711 | −2.31356 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.3854 | −0.401624 | ||||||||
\(952\) | −3.91488 | −0.126882 | ||||||||
\(953\) | 1.67348 | 0.0542095 | 0.0271047 | − | 0.999633i | \(-0.491371\pi\) | ||||
0.0271047 | + | 0.999633i | \(0.491371\pi\) | |||||||
\(954\) | 11.3366 | 0.367037 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.4509 | 0.338007 | ||||||||
\(957\) | 20.3727 | 0.658556 | ||||||||
\(958\) | −19.1679 | −0.619285 | ||||||||
\(959\) | −26.2076 | −0.846288 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.6774 | 1.11863 | ||||||||
\(962\) | 7.49735 | 0.241724 | ||||||||
\(963\) | −10.5915 | −0.341307 | ||||||||
\(964\) | 6.73974 | 0.217072 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −22.0352 | −0.708972 | ||||||||
\(967\) | 18.1691 | 0.584279 | 0.292140 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292140 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(968\) | 46.5689 | 1.49678 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.64954 | −0.149211 | −0.0746054 | − | 0.997213i | \(-0.523770\pi\) | ||||
−0.0746054 | + | 0.997213i | \(0.523770\pi\) | |||||||
\(972\) | −8.89475 | −0.285299 | ||||||||
\(973\) | 20.8492 | 0.668395 | ||||||||
\(974\) | 47.5703 | 1.52425 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.1797 | −0.325845 | ||||||||
\(977\) | 13.7386 | 0.439535 | 0.219768 | − | 0.975552i | \(-0.429470\pi\) | ||||
0.219768 | + | 0.975552i | \(0.429470\pi\) | |||||||
\(978\) | −6.97374 | −0.222996 | ||||||||
\(979\) | −19.2091 | −0.613926 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.8909 | 0.794704 | ||||||||
\(982\) | 7.80130 | 0.248949 | ||||||||
\(983\) | 8.41202 | 0.268302 | 0.134151 | − | 0.990961i | \(-0.457169\pi\) | ||||
0.134151 | + | 0.990961i | \(0.457169\pi\) | |||||||
\(984\) | 3.76187 | 0.119924 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.86347 | 0.123038 | ||||||||
\(987\) | −2.54850 | −0.0811198 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.80714 | 0.248253 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5779 | −0.590145 | −0.295072 | − | 0.955475i | \(-0.595344\pi\) | ||||
−0.295072 | + | 0.955475i | \(0.595344\pi\) | |||||||
\(992\) | −27.5470 | −0.874618 | ||||||||
\(993\) | −4.79059 | −0.152025 | ||||||||
\(994\) | −25.9349 | −0.822605 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.55801 | −0.176112 | ||||||||
\(997\) | 38.4609 | 1.21807 | 0.609035 | − | 0.793143i | \(-0.291557\pi\) | ||||
0.609035 | + | 0.793143i | \(0.291557\pi\) | |||||||
\(998\) | −0.304751 | −0.00964671 | ||||||||
\(999\) | −5.37131 | −0.169941 |
(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 | 9025.2.a.ct.1.6 | 24 | ||
5.2 | odd | 4 | 1805.2.b.l.1084.6 | 24 | |||
5.3 | odd | 4 | 1805.2.b.l.1084.19 | 24 | |||
5.4 | even | 2 | inner | 9025.2.a.ct.1.19 | 24 | ||
19.14 | odd | 18 | 475.2.l.f.101.6 | 48 | |||
19.15 | odd | 18 | 475.2.l.f.301.6 | 48 | |||
19.18 | odd | 2 | 9025.2.a.cu.1.19 | 24 | |||
95.14 | odd | 18 | 475.2.l.f.101.3 | 48 | |||
95.18 | even | 4 | 1805.2.b.k.1084.6 | 24 | |||
95.33 | even | 36 | 95.2.p.a.44.3 | ✓ | 48 | ||
95.34 | odd | 18 | 475.2.l.f.301.3 | 48 | |||
95.37 | even | 4 | 1805.2.b.k.1084.19 | 24 | |||
95.52 | even | 36 | 95.2.p.a.44.6 | yes | 48 | ||
95.53 | even | 36 | 95.2.p.a.54.6 | yes | 48 | ||
95.72 | even | 36 | 95.2.p.a.54.3 | yes | 48 | ||
95.94 | odd | 2 | 9025.2.a.cu.1.6 | 24 | |||
285.53 | odd | 36 | 855.2.da.b.244.3 | 48 | |||
285.128 | odd | 36 | 855.2.da.b.424.6 | 48 | |||
285.167 | odd | 36 | 855.2.da.b.244.6 | 48 | |||
285.242 | odd | 36 | 855.2.da.b.424.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.44.3 | ✓ | 48 | 95.33 | even | 36 | ||
95.2.p.a.44.6 | yes | 48 | 95.52 | even | 36 | ||
95.2.p.a.54.3 | yes | 48 | 95.72 | even | 36 | ||
95.2.p.a.54.6 | yes | 48 | 95.53 | even | 36 | ||
475.2.l.f.101.3 | 48 | 95.14 | odd | 18 | |||
475.2.l.f.101.6 | 48 | 19.14 | odd | 18 | |||
475.2.l.f.301.3 | 48 | 95.34 | odd | 18 | |||
475.2.l.f.301.6 | 48 | 19.15 | odd | 18 | |||
855.2.da.b.244.3 | 48 | 285.53 | odd | 36 | |||
855.2.da.b.244.6 | 48 | 285.167 | odd | 36 | |||
855.2.da.b.424.3 | 48 | 285.242 | odd | 36 | |||
855.2.da.b.424.6 | 48 | 285.128 | odd | 36 | |||
1805.2.b.k.1084.6 | 24 | 95.18 | even | 4 | |||
1805.2.b.k.1084.19 | 24 | 95.37 | even | 4 | |||
1805.2.b.l.1084.6 | 24 | 5.2 | odd | 4 | |||
1805.2.b.l.1084.19 | 24 | 5.3 | odd | 4 | |||
9025.2.a.ct.1.6 | 24 | 1.1 | even | 1 | trivial | ||
9025.2.a.ct.1.19 | 24 | 5.4 | even | 2 | inner | ||
9025.2.a.cu.1.6 | 24 | 95.94 | odd | 2 | |||
9025.2.a.cu.1.19 | 24 | 19.18 | odd | 2 |