Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65266 | −1.87571 | −0.937857 | − | 0.347021i | \(-0.887193\pi\) | ||||
−0.937857 | + | 0.347021i | \(0.887193\pi\) | |||||||
\(3\) | 3.05290 | 1.76259 | 0.881295 | − | 0.472566i | \(-0.156672\pi\) | ||||
0.881295 | + | 0.472566i | \(0.156672\pi\) | |||||||
\(4\) | 5.03661 | 2.51831 | ||||||||
\(5\) | −1.94746 | −0.870932 | −0.435466 | − | 0.900205i | \(-0.643416\pi\) | ||||
−0.435466 | + | 0.900205i | \(0.643416\pi\) | |||||||
\(6\) | −8.09830 | −3.30612 | ||||||||
\(7\) | 2.48037 | 0.937490 | 0.468745 | − | 0.883333i | \(-0.344706\pi\) | ||||
0.468745 | + | 0.883333i | \(0.344706\pi\) | |||||||
\(8\) | −8.05510 | −2.84791 | ||||||||
\(9\) | 6.32018 | 2.10673 | ||||||||
\(10\) | 5.16596 | 1.63362 | ||||||||
\(11\) | −2.94497 | −0.887942 | −0.443971 | − | 0.896041i | \(-0.646431\pi\) | ||||
−0.443971 | + | 0.896041i | \(0.646431\pi\) | |||||||
\(12\) | 15.3763 | 4.43874 | ||||||||
\(13\) | 0.192789 | 0.0534702 | 0.0267351 | − | 0.999643i | \(-0.491489\pi\) | ||||
0.0267351 | + | 0.999643i | \(0.491489\pi\) | |||||||
\(14\) | −6.57957 | −1.75846 | ||||||||
\(15\) | −5.94540 | −1.53510 | ||||||||
\(16\) | 11.2942 | 2.82356 | ||||||||
\(17\) | 4.76794 | 1.15640 | 0.578198 | − | 0.815897i | \(-0.303756\pi\) | ||||
0.578198 | + | 0.815897i | \(0.303756\pi\) | |||||||
\(18\) | −16.7653 | −3.95162 | ||||||||
\(19\) | −2.90135 | −0.665616 | −0.332808 | − | 0.942995i | \(-0.607996\pi\) | ||||
−0.332808 | + | 0.942995i | \(0.607996\pi\) | |||||||
\(20\) | −9.80861 | −2.19327 | ||||||||
\(21\) | 7.57230 | 1.65241 | ||||||||
\(22\) | 7.81201 | 1.66553 | ||||||||
\(23\) | −3.08821 | −0.643937 | −0.321969 | − | 0.946750i | \(-0.604345\pi\) | ||||
−0.321969 | + | 0.946750i | \(0.604345\pi\) | |||||||
\(24\) | −24.5914 | −5.01970 | ||||||||
\(25\) | −1.20739 | −0.241478 | ||||||||
\(26\) | −0.511405 | −0.100295 | ||||||||
\(27\) | 10.1362 | 1.95070 | ||||||||
\(28\) | 12.4926 | 2.36089 | ||||||||
\(29\) | 2.23235 | 0.414537 | 0.207268 | − | 0.978284i | \(-0.433543\pi\) | ||||
0.207268 | + | 0.978284i | \(0.433543\pi\) | |||||||
\(30\) | 15.7711 | 2.87940 | ||||||||
\(31\) | −3.07974 | −0.553138 | −0.276569 | − | 0.960994i | \(-0.589197\pi\) | ||||
−0.276569 | + | 0.960994i | \(0.589197\pi\) | |||||||
\(32\) | −13.8496 | −2.44828 | ||||||||
\(33\) | −8.99069 | −1.56508 | ||||||||
\(34\) | −12.6477 | −2.16907 | ||||||||
\(35\) | −4.83042 | −0.816490 | ||||||||
\(36\) | 31.8323 | 5.30538 | ||||||||
\(37\) | 8.80848 | 1.44810 | 0.724052 | − | 0.689745i | \(-0.242277\pi\) | ||||
0.724052 | + | 0.689745i | \(0.242277\pi\) | |||||||
\(38\) | 7.69631 | 1.24851 | ||||||||
\(39\) | 0.588566 | 0.0942460 | ||||||||
\(40\) | 15.6870 | 2.48033 | ||||||||
\(41\) | −2.72877 | −0.426162 | −0.213081 | − | 0.977035i | \(-0.568350\pi\) | ||||
−0.213081 | + | 0.977035i | \(0.568350\pi\) | |||||||
\(42\) | −20.0867 | −3.09945 | ||||||||
\(43\) | 11.9799 | 1.82692 | 0.913460 | − | 0.406929i | \(-0.133400\pi\) | ||||
0.913460 | + | 0.406929i | \(0.133400\pi\) | |||||||
\(44\) | −14.8327 | −2.23611 | ||||||||
\(45\) | −12.3083 | −1.83481 | ||||||||
\(46\) | 8.19199 | 1.20784 | ||||||||
\(47\) | −4.38663 | −0.639856 | −0.319928 | − | 0.947442i | \(-0.603659\pi\) | ||||
−0.319928 | + | 0.947442i | \(0.603659\pi\) | |||||||
\(48\) | 34.4801 | 4.97678 | ||||||||
\(49\) | −0.847785 | −0.121112 | ||||||||
\(50\) | 3.20280 | 0.452944 | ||||||||
\(51\) | 14.5560 | 2.03825 | ||||||||
\(52\) | 0.971006 | 0.134654 | ||||||||
\(53\) | 14.3594 | 1.97242 | 0.986209 | − | 0.165504i | \(-0.0529250\pi\) | ||||
0.986209 | + | 0.165504i | \(0.0529250\pi\) | |||||||
\(54\) | −26.8878 | −3.65896 | ||||||||
\(55\) | 5.73522 | 0.773337 | ||||||||
\(56\) | −19.9796 | −2.66989 | ||||||||
\(57\) | −8.85753 | −1.17321 | ||||||||
\(58\) | −5.92167 | −0.777553 | ||||||||
\(59\) | −3.28792 | −0.428050 | −0.214025 | − | 0.976828i | \(-0.568657\pi\) | ||||
−0.214025 | + | 0.976828i | \(0.568657\pi\) | |||||||
\(60\) | −29.9447 | −3.86584 | ||||||||
\(61\) | 12.6102 | 1.61458 | 0.807288 | − | 0.590158i | \(-0.200935\pi\) | ||||
0.807288 | + | 0.590158i | \(0.200935\pi\) | |||||||
\(62\) | 8.16952 | 1.03753 | ||||||||
\(63\) | 15.6764 | 1.97503 | ||||||||
\(64\) | 14.1497 | 1.76872 | ||||||||
\(65\) | −0.375450 | −0.0465689 | ||||||||
\(66\) | 23.8493 | 2.93564 | ||||||||
\(67\) | 4.80775 | 0.587360 | 0.293680 | − | 0.955904i | \(-0.405120\pi\) | ||||
0.293680 | + | 0.955904i | \(0.405120\pi\) | |||||||
\(68\) | 24.0143 | 2.91216 | ||||||||
\(69\) | −9.42800 | −1.13500 | ||||||||
\(70\) | 12.8135 | 1.53150 | ||||||||
\(71\) | 0.546449 | 0.0648516 | 0.0324258 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324258 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(72\) | −50.9097 | −5.99976 | ||||||||
\(73\) | 4.67236 | 0.546858 | 0.273429 | − | 0.961892i | \(-0.411842\pi\) | ||||
0.273429 | + | 0.961892i | \(0.411842\pi\) | |||||||
\(74\) | −23.3659 | −2.71623 | ||||||||
\(75\) | −3.68604 | −0.425627 | ||||||||
\(76\) | −14.6130 | −1.67622 | ||||||||
\(77\) | −7.30461 | −0.832437 | ||||||||
\(78\) | −1.56127 | −0.176779 | ||||||||
\(79\) | −4.07327 | −0.458279 | −0.229140 | − | 0.973394i | \(-0.573591\pi\) | ||||
−0.229140 | + | 0.973394i | \(0.573591\pi\) | |||||||
\(80\) | −21.9951 | −2.45913 | ||||||||
\(81\) | 11.9841 | 1.33157 | ||||||||
\(82\) | 7.23849 | 0.799357 | ||||||||
\(83\) | −0.610918 | −0.0670570 | −0.0335285 | − | 0.999438i | \(-0.510674\pi\) | ||||
−0.0335285 | + | 0.999438i | \(0.510674\pi\) | |||||||
\(84\) | 38.1387 | 4.16128 | ||||||||
\(85\) | −9.28538 | −1.00714 | ||||||||
\(86\) | −31.7787 | −3.42678 | ||||||||
\(87\) | 6.81513 | 0.730659 | ||||||||
\(88\) | 23.7220 | 2.52878 | ||||||||
\(89\) | 4.34903 | 0.460996 | 0.230498 | − | 0.973073i | \(-0.425965\pi\) | ||||
0.230498 | + | 0.973073i | \(0.425965\pi\) | |||||||
\(90\) | 32.6498 | 3.44159 | ||||||||
\(91\) | 0.478188 | 0.0501278 | ||||||||
\(92\) | −15.5541 | −1.62163 | ||||||||
\(93\) | −9.40214 | −0.974956 | ||||||||
\(94\) | 11.6363 | 1.20019 | ||||||||
\(95\) | 5.65028 | 0.579706 | ||||||||
\(96\) | −42.2813 | −4.31532 | ||||||||
\(97\) | 6.32560 | 0.642267 | 0.321134 | − | 0.947034i | \(-0.395936\pi\) | ||||
0.321134 | + | 0.947034i | \(0.395936\pi\) | |||||||
\(98\) | 2.24889 | 0.227172 | ||||||||
\(99\) | −18.6127 | −1.87065 | ||||||||
\(100\) | −6.08115 | −0.608115 | ||||||||
\(101\) | −4.28037 | −0.425912 | −0.212956 | − | 0.977062i | \(-0.568309\pi\) | ||||
−0.212956 | + | 0.977062i | \(0.568309\pi\) | |||||||
\(102\) | −38.6122 | −3.82318 | ||||||||
\(103\) | −2.94064 | −0.289750 | −0.144875 | − | 0.989450i | \(-0.546278\pi\) | ||||
−0.144875 | + | 0.989450i | \(0.546278\pi\) | |||||||
\(104\) | −1.55294 | −0.152278 | ||||||||
\(105\) | −14.7468 | −1.43914 | ||||||||
\(106\) | −38.0907 | −3.69969 | ||||||||
\(107\) | 2.21393 | 0.214028 | 0.107014 | − | 0.994257i | \(-0.465871\pi\) | ||||
0.107014 | + | 0.994257i | \(0.465871\pi\) | |||||||
\(108\) | 51.0519 | 4.91247 | ||||||||
\(109\) | 8.23984 | 0.789234 | 0.394617 | − | 0.918846i | \(-0.370877\pi\) | ||||
0.394617 | + | 0.918846i | \(0.370877\pi\) | |||||||
\(110\) | −15.2136 | −1.45056 | ||||||||
\(111\) | 26.8914 | 2.55242 | ||||||||
\(112\) | 28.0138 | 2.64706 | ||||||||
\(113\) | 7.94211 | 0.747131 | 0.373566 | − | 0.927604i | \(-0.378135\pi\) | ||||
0.373566 | + | 0.927604i | \(0.378135\pi\) | |||||||
\(114\) | 23.4960 | 2.20060 | ||||||||
\(115\) | 6.01418 | 0.560825 | ||||||||
\(116\) | 11.2435 | 1.04393 | ||||||||
\(117\) | 1.21846 | 0.112647 | ||||||||
\(118\) | 8.72173 | 0.802900 | ||||||||
\(119\) | 11.8262 | 1.08411 | ||||||||
\(120\) | 47.8908 | 4.37181 | ||||||||
\(121\) | −2.32714 | −0.211558 | ||||||||
\(122\) | −33.4507 | −3.02848 | ||||||||
\(123\) | −8.33064 | −0.751148 | ||||||||
\(124\) | −15.5115 | −1.39297 | ||||||||
\(125\) | 12.0887 | 1.08124 | ||||||||
\(126\) | −41.5840 | −3.70460 | ||||||||
\(127\) | 0.723073 | 0.0641623 | 0.0320812 | − | 0.999485i | \(-0.489786\pi\) | ||||
0.0320812 | + | 0.999485i | \(0.489786\pi\) | |||||||
\(128\) | −9.83535 | −0.869330 | ||||||||
\(129\) | 36.5734 | 3.22011 | ||||||||
\(130\) | 0.995942 | 0.0873499 | ||||||||
\(131\) | −4.71928 | −0.412325 | −0.206163 | − | 0.978518i | \(-0.566098\pi\) | ||||
−0.206163 | + | 0.978518i | \(0.566098\pi\) | |||||||
\(132\) | −45.2826 | −3.94135 | ||||||||
\(133\) | −7.19642 | −0.624008 | ||||||||
\(134\) | −12.7533 | −1.10172 | ||||||||
\(135\) | −19.7398 | −1.69893 | ||||||||
\(136\) | −38.4062 | −3.29331 | ||||||||
\(137\) | 8.90380 | 0.760703 | 0.380351 | − | 0.924842i | \(-0.375803\pi\) | ||||
0.380351 | + | 0.924842i | \(0.375803\pi\) | |||||||
\(138\) | 25.0093 | 2.12893 | ||||||||
\(139\) | 14.5272 | 1.23219 | 0.616093 | − | 0.787674i | \(-0.288715\pi\) | ||||
0.616093 | + | 0.787674i | \(0.288715\pi\) | |||||||
\(140\) | −24.3289 | −2.05617 | ||||||||
\(141\) | −13.3919 | −1.12780 | ||||||||
\(142\) | −1.44954 | −0.121643 | ||||||||
\(143\) | −0.567760 | −0.0474784 | ||||||||
\(144\) | 71.3815 | 5.94846 | ||||||||
\(145\) | −4.34742 | −0.361033 | ||||||||
\(146\) | −12.3942 | −1.02575 | ||||||||
\(147\) | −2.58820 | −0.213471 | ||||||||
\(148\) | 44.3649 | 3.64677 | ||||||||
\(149\) | −8.73860 | −0.715894 | −0.357947 | − | 0.933742i | \(-0.616523\pi\) | ||||
−0.357947 | + | 0.933742i | \(0.616523\pi\) | |||||||
\(150\) | 9.77780 | 0.798354 | ||||||||
\(151\) | 17.6680 | 1.43781 | 0.718903 | − | 0.695111i | \(-0.244645\pi\) | ||||
0.718903 | + | 0.695111i | \(0.244645\pi\) | |||||||
\(152\) | 23.3707 | 1.89561 | ||||||||
\(153\) | 30.1342 | 2.43621 | ||||||||
\(154\) | 19.3767 | 1.56142 | ||||||||
\(155\) | 5.99769 | 0.481746 | ||||||||
\(156\) | 2.96438 | 0.237340 | ||||||||
\(157\) | 10.0397 | 0.801253 | 0.400627 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400627 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(158\) | 10.8050 | 0.859601 | ||||||||
\(159\) | 43.8378 | 3.47657 | ||||||||
\(160\) | 26.9715 | 2.13229 | ||||||||
\(161\) | −7.65990 | −0.603685 | ||||||||
\(162\) | −31.7898 | −2.49764 | ||||||||
\(163\) | 13.5668 | 1.06263 | 0.531316 | − | 0.847174i | \(-0.321698\pi\) | ||||
0.531316 | + | 0.847174i | \(0.321698\pi\) | |||||||
\(164\) | −13.7437 | −1.07321 | ||||||||
\(165\) | 17.5090 | 1.36308 | ||||||||
\(166\) | 1.62056 | 0.125780 | ||||||||
\(167\) | −10.5826 | −0.818910 | −0.409455 | − | 0.912330i | \(-0.634281\pi\) | ||||
−0.409455 | + | 0.912330i | \(0.634281\pi\) | |||||||
\(168\) | −60.9956 | −4.70592 | ||||||||
\(169\) | −12.9628 | −0.997141 | ||||||||
\(170\) | 24.6310 | 1.88911 | ||||||||
\(171\) | −18.3371 | −1.40227 | ||||||||
\(172\) | 60.3382 | 4.60074 | ||||||||
\(173\) | −18.4685 | −1.40414 | −0.702068 | − | 0.712110i | \(-0.747740\pi\) | ||||
−0.702068 | + | 0.712110i | \(0.747740\pi\) | |||||||
\(174\) | −18.0782 | −1.37051 | ||||||||
\(175\) | −2.99477 | −0.226383 | ||||||||
\(176\) | −33.2612 | −2.50716 | ||||||||
\(177\) | −10.0377 | −0.754477 | ||||||||
\(178\) | −11.5365 | −0.864697 | ||||||||
\(179\) | 22.2879 | 1.66588 | 0.832938 | − | 0.553366i | \(-0.186657\pi\) | ||||
0.832938 | + | 0.553366i | \(0.186657\pi\) | |||||||
\(180\) | −61.9922 | −4.62062 | ||||||||
\(181\) | −7.48911 | −0.556661 | −0.278331 | − | 0.960485i | \(-0.589781\pi\) | ||||
−0.278331 | + | 0.960485i | \(0.589781\pi\) | |||||||
\(182\) | −1.26847 | −0.0940254 | ||||||||
\(183\) | 38.4977 | 2.84584 | ||||||||
\(184\) | 24.8759 | 1.83387 | ||||||||
\(185\) | −17.1542 | −1.26120 | ||||||||
\(186\) | 24.9407 | 1.82874 | ||||||||
\(187\) | −14.0414 | −1.02681 | ||||||||
\(188\) | −22.0938 | −1.61135 | ||||||||
\(189\) | 25.1414 | 1.82877 | ||||||||
\(190\) | −14.9883 | −1.08736 | ||||||||
\(191\) | 22.8566 | 1.65385 | 0.826923 | − | 0.562315i | \(-0.190089\pi\) | ||||
0.826923 | + | 0.562315i | \(0.190089\pi\) | |||||||
\(192\) | 43.1977 | 3.11753 | ||||||||
\(193\) | 20.0189 | 1.44099 | 0.720496 | − | 0.693459i | \(-0.243914\pi\) | ||||
0.720496 | + | 0.693459i | \(0.243914\pi\) | |||||||
\(194\) | −16.7797 | −1.20471 | ||||||||
\(195\) | −1.14621 | −0.0820819 | ||||||||
\(196\) | −4.26996 | −0.304997 | ||||||||
\(197\) | −13.5736 | −0.967079 | −0.483540 | − | 0.875322i | \(-0.660649\pi\) | ||||
−0.483540 | + | 0.875322i | \(0.660649\pi\) | |||||||
\(198\) | 49.3733 | 3.50881 | ||||||||
\(199\) | 13.6861 | 0.970183 | 0.485091 | − | 0.874464i | \(-0.338786\pi\) | ||||
0.485091 | + | 0.874464i | \(0.338786\pi\) | |||||||
\(200\) | 9.72565 | 0.687707 | ||||||||
\(201\) | 14.6776 | 1.03528 | ||||||||
\(202\) | 11.3544 | 0.798890 | ||||||||
\(203\) | 5.53704 | 0.388624 | ||||||||
\(204\) | 73.3130 | 5.13294 | ||||||||
\(205\) | 5.31417 | 0.371158 | ||||||||
\(206\) | 7.80053 | 0.543489 | ||||||||
\(207\) | −19.5181 | −1.35660 | ||||||||
\(208\) | 2.17741 | 0.150976 | ||||||||
\(209\) | 8.54440 | 0.591029 | ||||||||
\(210\) | 39.1182 | 2.69941 | ||||||||
\(211\) | −24.1510 | −1.66262 | −0.831312 | − | 0.555805i | \(-0.812410\pi\) | ||||
−0.831312 | + | 0.555805i | \(0.812410\pi\) | |||||||
\(212\) | 72.3228 | 4.96715 | ||||||||
\(213\) | 1.66825 | 0.114307 | ||||||||
\(214\) | −5.87280 | −0.401456 | ||||||||
\(215\) | −23.3304 | −1.59112 | ||||||||
\(216\) | −81.6477 | −5.55543 | ||||||||
\(217\) | −7.63889 | −0.518562 | ||||||||
\(218\) | −21.8575 | −1.48038 | ||||||||
\(219\) | 14.2642 | 0.963887 | ||||||||
\(220\) | 28.8861 | 1.94750 | ||||||||
\(221\) | 0.919209 | 0.0618327 | ||||||||
\(222\) | −71.3337 | −4.78760 | ||||||||
\(223\) | 19.6211 | 1.31393 | 0.656964 | − | 0.753922i | \(-0.271840\pi\) | ||||
0.656964 | + | 0.753922i | \(0.271840\pi\) | |||||||
\(224\) | −34.3520 | −2.29524 | ||||||||
\(225\) | −7.63092 | −0.508728 | ||||||||
\(226\) | −21.0677 | −1.40141 | ||||||||
\(227\) | 17.1133 | 1.13585 | 0.567926 | − | 0.823080i | \(-0.307746\pi\) | ||||
0.567926 | + | 0.823080i | \(0.307746\pi\) | |||||||
\(228\) | −44.6119 | −2.95450 | ||||||||
\(229\) | −19.4868 | −1.28773 | −0.643863 | − | 0.765141i | \(-0.722669\pi\) | ||||
−0.643863 | + | 0.765141i | \(0.722669\pi\) | |||||||
\(230\) | −15.9536 | −1.05195 | ||||||||
\(231\) | −22.3002 | −1.46725 | ||||||||
\(232\) | −17.9818 | −1.18056 | ||||||||
\(233\) | −25.1005 | −1.64439 | −0.822196 | − | 0.569205i | \(-0.807251\pi\) | ||||
−0.822196 | + | 0.569205i | \(0.807251\pi\) | |||||||
\(234\) | −3.23217 | −0.211294 | ||||||||
\(235\) | 8.54281 | 0.557271 | ||||||||
\(236\) | −16.5600 | −1.07796 | ||||||||
\(237\) | −12.4353 | −0.807758 | ||||||||
\(238\) | −31.3710 | −2.03348 | ||||||||
\(239\) | 3.75871 | 0.243130 | 0.121565 | − | 0.992583i | \(-0.461209\pi\) | ||||
0.121565 | + | 0.992583i | \(0.461209\pi\) | |||||||
\(240\) | −67.1487 | −4.33443 | ||||||||
\(241\) | −21.4799 | −1.38364 | −0.691820 | − | 0.722070i | \(-0.743191\pi\) | ||||
−0.691820 | + | 0.722070i | \(0.743191\pi\) | |||||||
\(242\) | 6.17311 | 0.396823 | ||||||||
\(243\) | 6.17775 | 0.396303 | ||||||||
\(244\) | 63.5129 | 4.06599 | ||||||||
\(245\) | 1.65103 | 0.105480 | ||||||||
\(246\) | 22.0984 | 1.40894 | ||||||||
\(247\) | −0.559350 | −0.0355906 | ||||||||
\(248\) | 24.8076 | 1.57529 | ||||||||
\(249\) | −1.86507 | −0.118194 | ||||||||
\(250\) | −32.0671 | −2.02810 | ||||||||
\(251\) | 13.8248 | 0.872617 | 0.436308 | − | 0.899797i | \(-0.356286\pi\) | ||||
0.436308 | + | 0.899797i | \(0.356286\pi\) | |||||||
\(252\) | 78.9557 | 4.97374 | ||||||||
\(253\) | 9.09470 | 0.571779 | ||||||||
\(254\) | −1.91807 | −0.120350 | ||||||||
\(255\) | −28.3473 | −1.77518 | ||||||||
\(256\) | −2.20965 | −0.138103 | ||||||||
\(257\) | −25.7785 | −1.60802 | −0.804010 | − | 0.594615i | \(-0.797304\pi\) | ||||
−0.804010 | + | 0.594615i | \(0.797304\pi\) | |||||||
\(258\) | −97.0169 | −6.04001 | ||||||||
\(259\) | 21.8482 | 1.35758 | ||||||||
\(260\) | −1.89100 | −0.117275 | ||||||||
\(261\) | 14.1088 | 0.873315 | ||||||||
\(262\) | 12.5187 | 0.773405 | ||||||||
\(263\) | −9.63979 | −0.594415 | −0.297208 | − | 0.954813i | \(-0.596055\pi\) | ||||
−0.297208 | + | 0.954813i | \(0.596055\pi\) | |||||||
\(264\) | 72.4210 | 4.45720 | ||||||||
\(265\) | −27.9644 | −1.71784 | ||||||||
\(266\) | 19.0897 | 1.17046 | ||||||||
\(267\) | 13.2771 | 0.812547 | ||||||||
\(268\) | 24.2148 | 1.47915 | ||||||||
\(269\) | 3.78475 | 0.230760 | 0.115380 | − | 0.993321i | \(-0.463191\pi\) | ||||
0.115380 | + | 0.993321i | \(0.463191\pi\) | |||||||
\(270\) | 52.3630 | 3.18671 | ||||||||
\(271\) | 7.70490 | 0.468040 | 0.234020 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234020 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(272\) | 53.8502 | 3.26515 | ||||||||
\(273\) | 1.45986 | 0.0883547 | ||||||||
\(274\) | −23.6188 | −1.42686 | ||||||||
\(275\) | 3.55573 | 0.214419 | ||||||||
\(276\) | −47.4852 | −2.85827 | ||||||||
\(277\) | −20.1388 | −1.21003 | −0.605013 | − | 0.796216i | \(-0.706832\pi\) | ||||
−0.605013 | + | 0.796216i | \(0.706832\pi\) | |||||||
\(278\) | −38.5359 | −2.31123 | ||||||||
\(279\) | −19.4645 | −1.16531 | ||||||||
\(280\) | 38.9095 | 2.32529 | ||||||||
\(281\) | −22.7383 | −1.35645 | −0.678225 | − | 0.734854i | \(-0.737251\pi\) | ||||
−0.678225 | + | 0.734854i | \(0.737251\pi\) | |||||||
\(282\) | 35.5243 | 2.11544 | ||||||||
\(283\) | 3.82502 | 0.227374 | 0.113687 | − | 0.993517i | \(-0.463734\pi\) | ||||
0.113687 | + | 0.993517i | \(0.463734\pi\) | |||||||
\(284\) | 2.75225 | 0.163316 | ||||||||
\(285\) | 17.2497 | 1.02178 | ||||||||
\(286\) | 1.50607 | 0.0890560 | ||||||||
\(287\) | −6.76834 | −0.399522 | ||||||||
\(288\) | −87.5317 | −5.15786 | ||||||||
\(289\) | 5.73325 | 0.337250 | ||||||||
\(290\) | 11.5322 | 0.677195 | ||||||||
\(291\) | 19.3114 | 1.13205 | ||||||||
\(292\) | 23.5329 | 1.37716 | ||||||||
\(293\) | −8.91049 | −0.520556 | −0.260278 | − | 0.965534i | \(-0.583814\pi\) | ||||
−0.260278 | + | 0.965534i | \(0.583814\pi\) | |||||||
\(294\) | 6.86562 | 0.400411 | ||||||||
\(295\) | 6.40309 | 0.372803 | ||||||||
\(296\) | −70.9532 | −4.12407 | ||||||||
\(297\) | −29.8507 | −1.73211 | ||||||||
\(298\) | 23.1805 | 1.34281 | ||||||||
\(299\) | −0.595375 | −0.0344314 | ||||||||
\(300\) | −18.5651 | −1.07186 | ||||||||
\(301\) | 29.7146 | 1.71272 | ||||||||
\(302\) | −46.8673 | −2.69691 | ||||||||
\(303\) | −13.0675 | −0.750709 | ||||||||
\(304\) | −32.7686 | −1.87941 | ||||||||
\(305\) | −24.5580 | −1.40618 | ||||||||
\(306\) | −79.9359 | −4.56963 | ||||||||
\(307\) | −22.9425 | −1.30940 | −0.654698 | − | 0.755891i | \(-0.727204\pi\) | ||||
−0.654698 | + | 0.755891i | \(0.727204\pi\) | |||||||
\(308\) | −36.7905 | −2.09633 | ||||||||
\(309\) | −8.97748 | −0.510711 | ||||||||
\(310\) | −15.9098 | −0.903618 | ||||||||
\(311\) | 13.8497 | 0.785346 | 0.392673 | − | 0.919678i | \(-0.371550\pi\) | ||||
0.392673 | + | 0.919678i | \(0.371550\pi\) | |||||||
\(312\) | −4.74096 | −0.268404 | ||||||||
\(313\) | 18.9952 | 1.07367 | 0.536837 | − | 0.843686i | \(-0.319619\pi\) | ||||
0.536837 | + | 0.843686i | \(0.319619\pi\) | |||||||
\(314\) | −26.6319 | −1.50292 | ||||||||
\(315\) | −30.5291 | −1.72012 | ||||||||
\(316\) | −20.5155 | −1.15409 | ||||||||
\(317\) | −8.11643 | −0.455864 | −0.227932 | − | 0.973677i | \(-0.573196\pi\) | ||||
−0.227932 | + | 0.973677i | \(0.573196\pi\) | |||||||
\(318\) | −116.287 | −6.52105 | ||||||||
\(319\) | −6.57421 | −0.368085 | ||||||||
\(320\) | −27.5561 | −1.54043 | ||||||||
\(321\) | 6.75889 | 0.377244 | ||||||||
\(322\) | 20.3191 | 1.13234 | ||||||||
\(323\) | −13.8335 | −0.769715 | ||||||||
\(324\) | 60.3593 | 3.35329 | ||||||||
\(325\) | −0.232772 | −0.0129119 | ||||||||
\(326\) | −35.9881 | −1.99319 | ||||||||
\(327\) | 25.1554 | 1.39110 | ||||||||
\(328\) | 21.9805 | 1.21367 | ||||||||
\(329\) | −10.8805 | −0.599859 | ||||||||
\(330\) | −46.4456 | −2.55674 | ||||||||
\(331\) | −16.8979 | −0.928792 | −0.464396 | − | 0.885628i | \(-0.653729\pi\) | ||||
−0.464396 | + | 0.885628i | \(0.653729\pi\) | |||||||
\(332\) | −3.07696 | −0.168870 | ||||||||
\(333\) | 55.6711 | 3.05076 | ||||||||
\(334\) | 28.0722 | 1.53604 | ||||||||
\(335\) | −9.36292 | −0.511551 | ||||||||
\(336\) | 85.5233 | 4.66568 | ||||||||
\(337\) | −13.9713 | −0.761068 | −0.380534 | − | 0.924767i | \(-0.624260\pi\) | ||||
−0.380534 | + | 0.924767i | \(0.624260\pi\) | |||||||
\(338\) | 34.3860 | 1.87035 | ||||||||
\(339\) | 24.2465 | 1.31689 | ||||||||
\(340\) | −46.7669 | −2.53629 | ||||||||
\(341\) | 9.06976 | 0.491155 | ||||||||
\(342\) | 48.6420 | 2.63026 | ||||||||
\(343\) | −19.4654 | −1.05103 | ||||||||
\(344\) | −96.4994 | −5.20290 | ||||||||
\(345\) | 18.3607 | 0.988505 | ||||||||
\(346\) | 48.9907 | 2.63376 | ||||||||
\(347\) | 7.97316 | 0.428022 | 0.214011 | − | 0.976831i | \(-0.431347\pi\) | ||||
0.214011 | + | 0.976831i | \(0.431347\pi\) | |||||||
\(348\) | 34.3252 | 1.84002 | ||||||||
\(349\) | −17.7457 | −0.949908 | −0.474954 | − | 0.880011i | \(-0.657535\pi\) | ||||
−0.474954 | + | 0.880011i | \(0.657535\pi\) | |||||||
\(350\) | 7.94411 | 0.424630 | ||||||||
\(351\) | 1.95414 | 0.104304 | ||||||||
\(352\) | 40.7866 | 2.17393 | ||||||||
\(353\) | −8.17292 | −0.435001 | −0.217500 | − | 0.976060i | \(-0.569790\pi\) | ||||
−0.217500 | + | 0.976060i | \(0.569790\pi\) | |||||||
\(354\) | 26.6265 | 1.41518 | ||||||||
\(355\) | −1.06419 | −0.0564813 | ||||||||
\(356\) | 21.9044 | 1.16093 | ||||||||
\(357\) | 36.1043 | 1.91084 | ||||||||
\(358\) | −59.1223 | −3.12471 | ||||||||
\(359\) | 11.1681 | 0.589427 | 0.294714 | − | 0.955586i | \(-0.404776\pi\) | ||||
0.294714 | + | 0.955586i | \(0.404776\pi\) | |||||||
\(360\) | 99.1447 | 5.22538 | ||||||||
\(361\) | −10.5822 | −0.556955 | ||||||||
\(362\) | 19.8661 | 1.04414 | ||||||||
\(363\) | −7.10452 | −0.372890 | ||||||||
\(364\) | 2.40845 | 0.126237 | ||||||||
\(365\) | −9.09925 | −0.476276 | ||||||||
\(366\) | −102.121 | −5.33798 | ||||||||
\(367\) | 31.1719 | 1.62716 | 0.813580 | − | 0.581453i | \(-0.197516\pi\) | ||||
0.813580 | + | 0.581453i | \(0.197516\pi\) | |||||||
\(368\) | −34.8790 | −1.81819 | ||||||||
\(369\) | −17.2463 | −0.897805 | ||||||||
\(370\) | 45.5042 | 2.36565 | ||||||||
\(371\) | 35.6166 | 1.84912 | ||||||||
\(372\) | −47.3549 | −2.45524 | ||||||||
\(373\) | 20.2679 | 1.04943 | 0.524716 | − | 0.851277i | \(-0.324172\pi\) | ||||
0.524716 | + | 0.851277i | \(0.324172\pi\) | |||||||
\(374\) | 37.2472 | 1.92601 | ||||||||
\(375\) | 36.9054 | 1.90579 | ||||||||
\(376\) | 35.3348 | 1.82225 | ||||||||
\(377\) | 0.430373 | 0.0221654 | ||||||||
\(378\) | −66.6915 | −3.43024 | ||||||||
\(379\) | −25.1834 | −1.29358 | −0.646792 | − | 0.762667i | \(-0.723890\pi\) | ||||
−0.646792 | + | 0.762667i | \(0.723890\pi\) | |||||||
\(380\) | 28.4582 | 1.45988 | ||||||||
\(381\) | 2.20747 | 0.113092 | ||||||||
\(382\) | −60.6309 | −3.10214 | ||||||||
\(383\) | 12.7415 | 0.651059 | 0.325530 | − | 0.945532i | \(-0.394457\pi\) | ||||
0.325530 | + | 0.945532i | \(0.394457\pi\) | |||||||
\(384\) | −30.0263 | −1.53227 | ||||||||
\(385\) | 14.2255 | 0.724996 | ||||||||
\(386\) | −53.1034 | −2.70289 | ||||||||
\(387\) | 75.7152 | 3.84882 | ||||||||
\(388\) | 31.8596 | 1.61743 | ||||||||
\(389\) | 15.4663 | 0.784172 | 0.392086 | − | 0.919929i | \(-0.371754\pi\) | ||||
0.392086 | + | 0.919929i | \(0.371754\pi\) | |||||||
\(390\) | 3.04051 | 0.153962 | ||||||||
\(391\) | −14.7244 | −0.744646 | ||||||||
\(392\) | 6.82899 | 0.344916 | ||||||||
\(393\) | −14.4075 | −0.726761 | ||||||||
\(394\) | 36.0062 | 1.81396 | ||||||||
\(395\) | 7.93255 | 0.399130 | ||||||||
\(396\) | −93.7452 | −4.71087 | ||||||||
\(397\) | −3.06504 | −0.153830 | −0.0769150 | − | 0.997038i | \(-0.524507\pi\) | ||||
−0.0769150 | + | 0.997038i | \(0.524507\pi\) | |||||||
\(398\) | −36.3046 | −1.81979 | ||||||||
\(399\) | −21.9699 | −1.09987 | ||||||||
\(400\) | −13.6365 | −0.681827 | ||||||||
\(401\) | 0.0629464 | 0.00314339 | 0.00157170 | − | 0.999999i | \(-0.499500\pi\) | ||||
0.00157170 | + | 0.999999i | \(0.499500\pi\) | |||||||
\(402\) | −38.9346 | −1.94188 | ||||||||
\(403\) | −0.593742 | −0.0295764 | ||||||||
\(404\) | −21.5585 | −1.07258 | ||||||||
\(405\) | −23.3386 | −1.15970 | ||||||||
\(406\) | −14.6879 | −0.728948 | ||||||||
\(407\) | −25.9407 | −1.28583 | ||||||||
\(408\) | −117.250 | −5.80475 | ||||||||
\(409\) | 2.35100 | 0.116250 | 0.0581248 | − | 0.998309i | \(-0.481488\pi\) | ||||
0.0581248 | + | 0.998309i | \(0.481488\pi\) | |||||||
\(410\) | −14.0967 | −0.696186 | ||||||||
\(411\) | 27.1824 | 1.34081 | ||||||||
\(412\) | −14.8109 | −0.729680 | ||||||||
\(413\) | −8.15524 | −0.401293 | ||||||||
\(414\) | 51.7748 | 2.54459 | ||||||||
\(415\) | 1.18974 | 0.0584021 | ||||||||
\(416\) | −2.67005 | −0.130910 | ||||||||
\(417\) | 44.3502 | 2.17184 | ||||||||
\(418\) | −22.6654 | −1.10860 | ||||||||
\(419\) | 8.56477 | 0.418417 | 0.209208 | − | 0.977871i | \(-0.432911\pi\) | ||||
0.209208 | + | 0.977871i | \(0.432911\pi\) | |||||||
\(420\) | −74.2738 | −3.62419 | ||||||||
\(421\) | 23.3286 | 1.13696 | 0.568482 | − | 0.822695i | \(-0.307531\pi\) | ||||
0.568482 | + | 0.822695i | \(0.307531\pi\) | |||||||
\(422\) | 64.0645 | 3.11861 | ||||||||
\(423\) | −27.7243 | −1.34800 | ||||||||
\(424\) | −115.667 | −5.61727 | ||||||||
\(425\) | −5.75676 | −0.279244 | ||||||||
\(426\) | −4.42531 | −0.214407 | ||||||||
\(427\) | 31.2780 | 1.51365 | ||||||||
\(428\) | 11.1507 | 0.538989 | ||||||||
\(429\) | −1.73331 | −0.0836851 | ||||||||
\(430\) | 61.8877 | 2.98449 | ||||||||
\(431\) | 16.4071 | 0.790300 | 0.395150 | − | 0.918617i | \(-0.370693\pi\) | ||||
0.395150 | + | 0.918617i | \(0.370693\pi\) | |||||||
\(432\) | 114.480 | 5.50793 | ||||||||
\(433\) | 15.6613 | 0.752632 | 0.376316 | − | 0.926491i | \(-0.377191\pi\) | ||||
0.376316 | + | 0.926491i | \(0.377191\pi\) | |||||||
\(434\) | 20.2634 | 0.972674 | ||||||||
\(435\) | −13.2722 | −0.636354 | ||||||||
\(436\) | 41.5009 | 1.98753 | ||||||||
\(437\) | 8.96000 | 0.428615 | ||||||||
\(438\) | −37.8382 | −1.80798 | ||||||||
\(439\) | −33.3839 | −1.59333 | −0.796663 | − | 0.604424i | \(-0.793404\pi\) | ||||
−0.796663 | + | 0.604424i | \(0.793404\pi\) | |||||||
\(440\) | −46.1978 | −2.20239 | ||||||||
\(441\) | −5.35815 | −0.255150 | ||||||||
\(442\) | −2.43835 | −0.115980 | ||||||||
\(443\) | 28.2026 | 1.33995 | 0.669973 | − | 0.742385i | \(-0.266306\pi\) | ||||
0.669973 | + | 0.742385i | \(0.266306\pi\) | |||||||
\(444\) | 135.441 | 6.42776 | ||||||||
\(445\) | −8.46957 | −0.401496 | ||||||||
\(446\) | −52.0482 | −2.46455 | ||||||||
\(447\) | −26.6780 | −1.26183 | ||||||||
\(448\) | 35.0965 | 1.65816 | ||||||||
\(449\) | 31.4341 | 1.48347 | 0.741734 | − | 0.670694i | \(-0.234004\pi\) | ||||
0.741734 | + | 0.670694i | \(0.234004\pi\) | |||||||
\(450\) | 20.2422 | 0.954228 | ||||||||
\(451\) | 8.03614 | 0.378407 | ||||||||
\(452\) | 40.0013 | 1.88150 | ||||||||
\(453\) | 53.9387 | 2.53426 | ||||||||
\(454\) | −45.3958 | −2.13053 | ||||||||
\(455\) | −0.931254 | −0.0436579 | ||||||||
\(456\) | 71.3483 | 3.34119 | ||||||||
\(457\) | 14.4247 | 0.674760 | 0.337380 | − | 0.941369i | \(-0.390459\pi\) | ||||
0.337380 | + | 0.941369i | \(0.390459\pi\) | |||||||
\(458\) | 51.6919 | 2.41541 | ||||||||
\(459\) | 48.3286 | 2.25578 | ||||||||
\(460\) | 30.2911 | 1.41233 | ||||||||
\(461\) | 23.2219 | 1.08155 | 0.540775 | − | 0.841167i | \(-0.318131\pi\) | ||||
0.540775 | + | 0.841167i | \(0.318131\pi\) | |||||||
\(462\) | 59.1549 | 2.75214 | ||||||||
\(463\) | −26.5874 | −1.23562 | −0.617811 | − | 0.786327i | \(-0.711980\pi\) | ||||
−0.617811 | + | 0.786327i | \(0.711980\pi\) | |||||||
\(464\) | 25.2127 | 1.17047 | ||||||||
\(465\) | 18.3103 | 0.849120 | ||||||||
\(466\) | 66.5832 | 3.08441 | ||||||||
\(467\) | 5.02961 | 0.232743 | 0.116371 | − | 0.993206i | \(-0.462874\pi\) | ||||
0.116371 | + | 0.993206i | \(0.462874\pi\) | |||||||
\(468\) | 6.13693 | 0.283680 | ||||||||
\(469\) | 11.9250 | 0.550645 | ||||||||
\(470\) | −22.6612 | −1.04528 | ||||||||
\(471\) | 30.6501 | 1.41228 | ||||||||
\(472\) | 26.4845 | 1.21905 | ||||||||
\(473\) | −35.2805 | −1.62220 | ||||||||
\(474\) | 32.9866 | 1.51512 | ||||||||
\(475\) | 3.50306 | 0.160732 | ||||||||
\(476\) | 59.5642 | 2.73012 | ||||||||
\(477\) | 90.7541 | 4.15534 | ||||||||
\(478\) | −9.97057 | −0.456043 | ||||||||
\(479\) | 19.0655 | 0.871126 | 0.435563 | − | 0.900158i | \(-0.356549\pi\) | ||||
0.435563 | + | 0.900158i | \(0.356549\pi\) | |||||||
\(480\) | 82.3412 | 3.75835 | ||||||||
\(481\) | 1.69818 | 0.0774304 | ||||||||
\(482\) | 56.9788 | 2.59532 | ||||||||
\(483\) | −23.3849 | −1.06405 | ||||||||
\(484\) | −11.7209 | −0.532768 | ||||||||
\(485\) | −12.3189 | −0.559371 | ||||||||
\(486\) | −16.3875 | −0.743351 | ||||||||
\(487\) | 10.5597 | 0.478504 | 0.239252 | − | 0.970957i | \(-0.423098\pi\) | ||||
0.239252 | + | 0.970957i | \(0.423098\pi\) | |||||||
\(488\) | −101.577 | −4.59816 | ||||||||
\(489\) | 41.4180 | 1.87299 | ||||||||
\(490\) | −4.37962 | −0.197851 | ||||||||
\(491\) | −19.7303 | −0.890416 | −0.445208 | − | 0.895427i | \(-0.646870\pi\) | ||||
−0.445208 | + | 0.895427i | \(0.646870\pi\) | |||||||
\(492\) | −41.9582 | −1.89162 | ||||||||
\(493\) | 10.6437 | 0.479368 | ||||||||
\(494\) | 1.48377 | 0.0667578 | ||||||||
\(495\) | 36.2476 | 1.62921 | ||||||||
\(496\) | −34.7833 | −1.56182 | ||||||||
\(497\) | 1.35539 | 0.0607977 | ||||||||
\(498\) | 4.94740 | 0.221698 | ||||||||
\(499\) | −36.7245 | −1.64401 | −0.822007 | − | 0.569477i | \(-0.807146\pi\) | ||||
−0.822007 | + | 0.569477i | \(0.807146\pi\) | |||||||
\(500\) | 60.8859 | 2.72290 | ||||||||
\(501\) | −32.3077 | −1.44340 | ||||||||
\(502\) | −36.6726 | −1.63678 | ||||||||
\(503\) | 17.0151 | 0.758664 | 0.379332 | − | 0.925261i | \(-0.376154\pi\) | ||||
0.379332 | + | 0.925261i | \(0.376154\pi\) | |||||||
\(504\) | −126.275 | −5.62472 | ||||||||
\(505\) | 8.33585 | 0.370941 | ||||||||
\(506\) | −24.1252 | −1.07249 | ||||||||
\(507\) | −39.5742 | −1.75755 | ||||||||
\(508\) | 3.64184 | 0.161580 | ||||||||
\(509\) | 23.0865 | 1.02329 | 0.511647 | − | 0.859196i | \(-0.329036\pi\) | ||||
0.511647 | + | 0.859196i | \(0.329036\pi\) | |||||||
\(510\) | 75.1958 | 3.32973 | ||||||||
\(511\) | 11.5892 | 0.512674 | ||||||||
\(512\) | 25.5321 | 1.12837 | ||||||||
\(513\) | −29.4086 | −1.29842 | ||||||||
\(514\) | 68.3817 | 3.01619 | ||||||||
\(515\) | 5.72679 | 0.252353 | ||||||||
\(516\) | 184.206 | 8.10922 | ||||||||
\(517\) | 12.9185 | 0.568156 | ||||||||
\(518\) | −57.9560 | −2.54644 | ||||||||
\(519\) | −56.3825 | −2.47492 | ||||||||
\(520\) | 3.02429 | 0.132624 | ||||||||
\(521\) | 10.9621 | 0.480260 | 0.240130 | − | 0.970741i | \(-0.422810\pi\) | ||||
0.240130 | + | 0.970741i | \(0.422810\pi\) | |||||||
\(522\) | −37.4260 | −1.63809 | ||||||||
\(523\) | 9.53969 | 0.417141 | 0.208571 | − | 0.978007i | \(-0.433119\pi\) | ||||
0.208571 | + | 0.978007i | \(0.433119\pi\) | |||||||
\(524\) | −23.7692 | −1.03836 | ||||||||
\(525\) | −9.14272 | −0.399021 | ||||||||
\(526\) | 25.5711 | 1.11495 | ||||||||
\(527\) | −14.6840 | −0.639647 | ||||||||
\(528\) | −101.543 | −4.41909 | ||||||||
\(529\) | −13.4629 | −0.585345 | ||||||||
\(530\) | 74.1802 | 3.22218 | ||||||||
\(531\) | −20.7802 | −0.901784 | ||||||||
\(532\) | −36.2456 | −1.57144 | ||||||||
\(533\) | −0.526077 | −0.0227869 | ||||||||
\(534\) | −35.2197 | −1.52411 | ||||||||
\(535\) | −4.31154 | −0.186404 | ||||||||
\(536\) | −38.7269 | −1.67275 | ||||||||
\(537\) | 68.0427 | 2.93626 | ||||||||
\(538\) | −10.0397 | −0.432841 | ||||||||
\(539\) | 2.49670 | 0.107541 | ||||||||
\(540\) | −99.4216 | −4.27842 | ||||||||
\(541\) | −42.0727 | −1.80885 | −0.904423 | − | 0.426637i | \(-0.859698\pi\) | ||||
−0.904423 | + | 0.426637i | \(0.859698\pi\) | |||||||
\(542\) | −20.4385 | −0.877909 | ||||||||
\(543\) | −22.8635 | −0.981166 | ||||||||
\(544\) | −66.0339 | −2.83118 | ||||||||
\(545\) | −16.0468 | −0.687369 | ||||||||
\(546\) | −3.87251 | −0.165728 | ||||||||
\(547\) | −14.8311 | −0.634132 | −0.317066 | − | 0.948403i | \(-0.602698\pi\) | ||||
−0.317066 | + | 0.948403i | \(0.602698\pi\) | |||||||
\(548\) | 44.8450 | 1.91568 | ||||||||
\(549\) | 79.6989 | 3.40147 | ||||||||
\(550\) | −9.43214 | −0.402188 | ||||||||
\(551\) | −6.47683 | −0.275922 | ||||||||
\(552\) | 75.9435 | 3.23237 | ||||||||
\(553\) | −10.1032 | −0.429632 | ||||||||
\(554\) | 53.4215 | 2.26966 | ||||||||
\(555\) | −52.3699 | −2.22298 | ||||||||
\(556\) | 73.1681 | 3.10302 | ||||||||
\(557\) | 1.04920 | 0.0444562 | 0.0222281 | − | 0.999753i | \(-0.492924\pi\) | ||||
0.0222281 | + | 0.999753i | \(0.492924\pi\) | |||||||
\(558\) | 51.6328 | 2.18579 | ||||||||
\(559\) | 2.30960 | 0.0976857 | ||||||||
\(560\) | −54.5559 | −2.30541 | ||||||||
\(561\) | −42.8671 | −1.80985 | ||||||||
\(562\) | 60.3169 | 2.54431 | ||||||||
\(563\) | −30.8680 | −1.30093 | −0.650465 | − | 0.759536i | \(-0.725426\pi\) | ||||
−0.650465 | + | 0.759536i | \(0.725426\pi\) | |||||||
\(564\) | −67.4500 | −2.84016 | ||||||||
\(565\) | −15.4670 | −0.650700 | ||||||||
\(566\) | −10.1465 | −0.426488 | ||||||||
\(567\) | 29.7250 | 1.24833 | ||||||||
\(568\) | −4.40170 | −0.184691 | ||||||||
\(569\) | −40.4706 | −1.69662 | −0.848308 | − | 0.529502i | \(-0.822379\pi\) | ||||
−0.848308 | + | 0.529502i | \(0.822379\pi\) | |||||||
\(570\) | −45.7576 | −1.91658 | ||||||||
\(571\) | 0.232265 | 0.00971999 | 0.00485999 | − | 0.999988i | \(-0.498453\pi\) | ||||
0.00485999 | + | 0.999988i | \(0.498453\pi\) | |||||||
\(572\) | −2.85958 | −0.119565 | ||||||||
\(573\) | 69.7789 | 2.91505 | ||||||||
\(574\) | 17.9541 | 0.749390 | ||||||||
\(575\) | 3.72868 | 0.155497 | ||||||||
\(576\) | 89.4289 | 3.72620 | ||||||||
\(577\) | −6.15819 | −0.256369 | −0.128184 | − | 0.991750i | \(-0.540915\pi\) | ||||
−0.128184 | + | 0.991750i | \(0.540915\pi\) | |||||||
\(578\) | −15.2084 | −0.632585 | ||||||||
\(579\) | 61.1156 | 2.53988 | ||||||||
\(580\) | −21.8962 | −0.909192 | ||||||||
\(581\) | −1.51530 | −0.0628653 | ||||||||
\(582\) | −51.2266 | −2.12341 | ||||||||
\(583\) | −42.2881 | −1.75139 | ||||||||
\(584\) | −37.6363 | −1.55740 | ||||||||
\(585\) | −2.37291 | −0.0981078 | ||||||||
\(586\) | 23.6365 | 0.976415 | ||||||||
\(587\) | 36.2164 | 1.49481 | 0.747405 | − | 0.664368i | \(-0.231299\pi\) | ||||
0.747405 | + | 0.664368i | \(0.231299\pi\) | |||||||
\(588\) | −13.0358 | −0.537585 | ||||||||
\(589\) | 8.93542 | 0.368178 | ||||||||
\(590\) | −16.9852 | −0.699271 | ||||||||
\(591\) | −41.4388 | −1.70456 | ||||||||
\(592\) | 99.4850 | 4.08881 | ||||||||
\(593\) | −46.6241 | −1.91462 | −0.957312 | − | 0.289058i | \(-0.906658\pi\) | ||||
−0.957312 | + | 0.289058i | \(0.906658\pi\) | |||||||
\(594\) | 79.1838 | 3.24895 | ||||||||
\(595\) | −23.0312 | −0.944185 | ||||||||
\(596\) | −44.0129 | −1.80284 | ||||||||
\(597\) | 41.7823 | 1.71003 | ||||||||
\(598\) | 1.57933 | 0.0645836 | ||||||||
\(599\) | 16.5338 | 0.675551 | 0.337776 | − | 0.941227i | \(-0.390326\pi\) | ||||
0.337776 | + | 0.941227i | \(0.390326\pi\) | |||||||
\(600\) | 29.6914 | 1.21215 | ||||||||
\(601\) | 22.3970 | 0.913593 | 0.456797 | − | 0.889571i | \(-0.348997\pi\) | ||||
0.456797 | + | 0.889571i | \(0.348997\pi\) | |||||||
\(602\) | −78.8227 | −3.21257 | ||||||||
\(603\) | 30.3858 | 1.23741 | ||||||||
\(604\) | 88.9871 | 3.62083 | ||||||||
\(605\) | 4.53202 | 0.184253 | ||||||||
\(606\) | 34.6637 | 1.40812 | ||||||||
\(607\) | 2.43468 | 0.0988205 | 0.0494103 | − | 0.998779i | \(-0.484266\pi\) | ||||
0.0494103 | + | 0.998779i | \(0.484266\pi\) | |||||||
\(608\) | 40.1825 | 1.62961 | ||||||||
\(609\) | 16.9040 | 0.684985 | ||||||||
\(610\) | 65.1440 | 2.63760 | ||||||||
\(611\) | −0.845697 | −0.0342132 | ||||||||
\(612\) | 151.774 | 6.13511 | ||||||||
\(613\) | −12.1857 | −0.492177 | −0.246089 | − | 0.969247i | \(-0.579145\pi\) | ||||
−0.246089 | + | 0.969247i | \(0.579145\pi\) | |||||||
\(614\) | 60.8586 | 2.45605 | ||||||||
\(615\) | 16.2236 | 0.654199 | ||||||||
\(616\) | 58.8394 | 2.37071 | ||||||||
\(617\) | 5.63392 | 0.226813 | 0.113407 | − | 0.993549i | \(-0.463824\pi\) | ||||
0.113407 | + | 0.993549i | \(0.463824\pi\) | |||||||
\(618\) | 23.8142 | 0.957948 | ||||||||
\(619\) | −17.8395 | −0.717028 | −0.358514 | − | 0.933524i | \(-0.616716\pi\) | ||||
−0.358514 | + | 0.933524i | \(0.616716\pi\) | |||||||
\(620\) | 30.2080 | 1.21318 | ||||||||
\(621\) | −31.3026 | −1.25613 | ||||||||
\(622\) | −36.7387 | −1.47309 | ||||||||
\(623\) | 10.7872 | 0.432179 | ||||||||
\(624\) | 6.64740 | 0.266109 | ||||||||
\(625\) | −17.5053 | −0.700210 | ||||||||
\(626\) | −50.3879 | −2.01391 | ||||||||
\(627\) | 26.0852 | 1.04174 | ||||||||
\(628\) | 50.5659 | 2.01780 | ||||||||
\(629\) | 41.9983 | 1.67458 | ||||||||
\(630\) | 80.9834 | 3.22645 | ||||||||
\(631\) | −13.0005 | −0.517544 | −0.258772 | − | 0.965938i | \(-0.583318\pi\) | ||||
−0.258772 | + | 0.965938i | \(0.583318\pi\) | |||||||
\(632\) | 32.8106 | 1.30514 | ||||||||
\(633\) | −73.7306 | −2.93053 | ||||||||
\(634\) | 21.5301 | 0.855071 | ||||||||
\(635\) | −1.40816 | −0.0558810 | ||||||||
\(636\) | 220.794 | 8.75506 | ||||||||
\(637\) | −0.163444 | −0.00647589 | ||||||||
\(638\) | 17.4391 | 0.690422 | ||||||||
\(639\) | 3.45366 | 0.136625 | ||||||||
\(640\) | 19.1540 | 0.757127 | ||||||||
\(641\) | 29.2012 | 1.15338 | 0.576690 | − | 0.816963i | \(-0.304344\pi\) | ||||
0.576690 | + | 0.816963i | \(0.304344\pi\) | |||||||
\(642\) | −17.9290 | −0.707603 | ||||||||
\(643\) | 25.6030 | 1.00968 | 0.504841 | − | 0.863212i | \(-0.331551\pi\) | ||||
0.504841 | + | 0.863212i | \(0.331551\pi\) | |||||||
\(644\) | −38.5799 | −1.52026 | ||||||||
\(645\) | −71.2254 | −2.80450 | ||||||||
\(646\) | 36.6955 | 1.44377 | ||||||||
\(647\) | 31.7663 | 1.24886 | 0.624432 | − | 0.781080i | \(-0.285331\pi\) | ||||
0.624432 | + | 0.781080i | \(0.285331\pi\) | |||||||
\(648\) | −96.5331 | −3.79218 | ||||||||
\(649\) | 9.68282 | 0.380084 | ||||||||
\(650\) | 0.617465 | 0.0242190 | ||||||||
\(651\) | −23.3207 | −0.914012 | ||||||||
\(652\) | 68.3306 | 2.67603 | ||||||||
\(653\) | 0.771188 | 0.0301789 | 0.0150895 | − | 0.999886i | \(-0.495197\pi\) | ||||
0.0150895 | + | 0.999886i | \(0.495197\pi\) | |||||||
\(654\) | −66.7287 | −2.60930 | ||||||||
\(655\) | 9.19062 | 0.359107 | ||||||||
\(656\) | −30.8193 | −1.20329 | ||||||||
\(657\) | 29.5301 | 1.15208 | ||||||||
\(658\) | 28.8622 | 1.12516 | ||||||||
\(659\) | −35.1877 | −1.37072 | −0.685359 | − | 0.728205i | \(-0.740355\pi\) | ||||
−0.685359 | + | 0.728205i | \(0.740355\pi\) | |||||||
\(660\) | 88.1862 | 3.43264 | ||||||||
\(661\) | −11.3851 | −0.442829 | −0.221415 | − | 0.975180i | \(-0.571067\pi\) | ||||
−0.221415 | + | 0.975180i | \(0.571067\pi\) | |||||||
\(662\) | 44.8244 | 1.74215 | ||||||||
\(663\) | 2.80625 | 0.108986 | ||||||||
\(664\) | 4.92101 | 0.190972 | ||||||||
\(665\) | 14.0148 | 0.543469 | ||||||||
\(666\) | −147.677 | −5.72235 | ||||||||
\(667\) | −6.89397 | −0.266936 | ||||||||
\(668\) | −53.3007 | −2.06227 | ||||||||
\(669\) | 59.9013 | 2.31592 | ||||||||
\(670\) | 24.8366 | 0.959523 | ||||||||
\(671\) | −37.1368 | −1.43365 | ||||||||
\(672\) | −104.873 | −4.04557 | ||||||||
\(673\) | −33.2938 | −1.28338 | −0.641690 | − | 0.766964i | \(-0.721766\pi\) | ||||
−0.641690 | + | 0.766964i | \(0.721766\pi\) | |||||||
\(674\) | 37.0613 | 1.42755 | ||||||||
\(675\) | −12.2383 | −0.471052 | ||||||||
\(676\) | −65.2887 | −2.51111 | ||||||||
\(677\) | 47.7487 | 1.83513 | 0.917566 | − | 0.397583i | \(-0.130151\pi\) | ||||
0.917566 | + | 0.397583i | \(0.130151\pi\) | |||||||
\(678\) | −64.3176 | −2.47010 | ||||||||
\(679\) | 15.6898 | 0.602119 | ||||||||
\(680\) | 74.7947 | 2.86825 | ||||||||
\(681\) | 52.2452 | 2.00204 | ||||||||
\(682\) | −24.0590 | −0.921267 | ||||||||
\(683\) | −18.2576 | −0.698608 | −0.349304 | − | 0.937010i | \(-0.613582\pi\) | ||||
−0.349304 | + | 0.937010i | \(0.613582\pi\) | |||||||
\(684\) | −92.3567 | −3.53134 | ||||||||
\(685\) | −17.3398 | −0.662520 | ||||||||
\(686\) | 51.6351 | 1.97144 | ||||||||
\(687\) | −59.4912 | −2.26973 | ||||||||
\(688\) | 135.304 | 5.15841 | ||||||||
\(689\) | 2.76835 | 0.105466 | ||||||||
\(690\) | −48.7046 | −1.85415 | ||||||||
\(691\) | 26.2426 | 0.998317 | 0.499159 | − | 0.866511i | \(-0.333643\pi\) | ||||
0.499159 | + | 0.866511i | \(0.333643\pi\) | |||||||
\(692\) | −93.0188 | −3.53604 | ||||||||
\(693\) | −46.1664 | −1.75372 | ||||||||
\(694\) | −21.1501 | −0.802846 | ||||||||
\(695\) | −28.2913 | −1.07315 | ||||||||
\(696\) | −54.8966 | −2.08085 | ||||||||
\(697\) | −13.0106 | −0.492811 | ||||||||
\(698\) | 47.0734 | 1.78176 | ||||||||
\(699\) | −76.6293 | −2.89839 | ||||||||
\(700\) | −15.0835 | −0.570102 | ||||||||
\(701\) | 25.3670 | 0.958100 | 0.479050 | − | 0.877788i | \(-0.340981\pi\) | ||||
0.479050 | + | 0.877788i | \(0.340981\pi\) | |||||||
\(702\) | −5.18368 | −0.195645 | ||||||||
\(703\) | −25.5565 | −0.963881 | ||||||||
\(704\) | −41.6706 | −1.57052 | ||||||||
\(705\) | 26.0803 | 0.982241 | ||||||||
\(706\) | 21.6800 | 0.815937 | ||||||||
\(707\) | −10.6169 | −0.399289 | ||||||||
\(708\) | −50.5558 | −1.90000 | ||||||||
\(709\) | −10.6978 | −0.401764 | −0.200882 | − | 0.979615i | \(-0.564381\pi\) | ||||
−0.200882 | + | 0.979615i | \(0.564381\pi\) | |||||||
\(710\) | 2.82293 | 0.105943 | ||||||||
\(711\) | −25.7438 | −0.965468 | ||||||||
\(712\) | −35.0318 | −1.31287 | ||||||||
\(713\) | 9.51091 | 0.356186 | ||||||||
\(714\) | −95.7724 | −3.58419 | ||||||||
\(715\) | 1.10569 | 0.0413505 | ||||||||
\(716\) | 112.256 | 4.19519 | ||||||||
\(717\) | 11.4749 | 0.428539 | ||||||||
\(718\) | −29.6251 | −1.10560 | ||||||||
\(719\) | 15.7594 | 0.587726 | 0.293863 | − | 0.955848i | \(-0.405059\pi\) | ||||
0.293863 | + | 0.955848i | \(0.405059\pi\) | |||||||
\(720\) | −139.013 | −5.18070 | ||||||||
\(721\) | −7.29387 | −0.271638 | ||||||||
\(722\) | 28.0709 | 1.04469 | ||||||||
\(723\) | −65.5759 | −2.43879 | ||||||||
\(724\) | −37.7197 | −1.40184 | ||||||||
\(725\) | −2.69532 | −0.100101 | ||||||||
\(726\) | 18.8459 | 0.699436 | ||||||||
\(727\) | −28.4397 | −1.05477 | −0.527386 | − | 0.849626i | \(-0.676828\pi\) | ||||
−0.527386 | + | 0.849626i | \(0.676828\pi\) | |||||||
\(728\) | −3.85186 | −0.142759 | ||||||||
\(729\) | −17.0923 | −0.633047 | ||||||||
\(730\) | 24.1372 | 0.893359 | ||||||||
\(731\) | 57.1195 | 2.11264 | ||||||||
\(732\) | 193.898 | 7.16668 | ||||||||
\(733\) | 12.5454 | 0.463377 | 0.231688 | − | 0.972790i | \(-0.425575\pi\) | ||||
0.231688 | + | 0.972790i | \(0.425575\pi\) | |||||||
\(734\) | −82.6885 | −3.05209 | ||||||||
\(735\) | 5.04042 | 0.185919 | ||||||||
\(736\) | 42.7704 | 1.57654 | ||||||||
\(737\) | −14.1587 | −0.521542 | ||||||||
\(738\) | 45.7485 | 1.68403 | ||||||||
\(739\) | 27.6264 | 1.01625 | 0.508126 | − | 0.861282i | \(-0.330338\pi\) | ||||
0.508126 | + | 0.861282i | \(0.330338\pi\) | |||||||
\(740\) | −86.3989 | −3.17609 | ||||||||
\(741\) | −1.70764 | −0.0627317 | ||||||||
\(742\) | −94.4788 | −3.46843 | ||||||||
\(743\) | 36.1684 | 1.32689 | 0.663444 | − | 0.748226i | \(-0.269094\pi\) | ||||
0.663444 | + | 0.748226i | \(0.269094\pi\) | |||||||
\(744\) | 75.7352 | 2.77659 | ||||||||
\(745\) | 17.0181 | 0.623495 | ||||||||
\(746\) | −53.7639 | −1.96843 | ||||||||
\(747\) | −3.86111 | −0.141271 | ||||||||
\(748\) | −70.7213 | −2.58583 | ||||||||
\(749\) | 5.49135 | 0.200649 | ||||||||
\(750\) | −97.8976 | −3.57471 | ||||||||
\(751\) | −35.1141 | −1.28133 | −0.640667 | − | 0.767819i | \(-0.721342\pi\) | ||||
−0.640667 | + | 0.767819i | \(0.721342\pi\) | |||||||
\(752\) | −49.5437 | −1.80667 | ||||||||
\(753\) | 42.2058 | 1.53807 | ||||||||
\(754\) | −1.14163 | −0.0415759 | ||||||||
\(755\) | −34.4079 | −1.25223 | ||||||||
\(756\) | 126.627 | 4.60539 | ||||||||
\(757\) | −33.3690 | −1.21282 | −0.606409 | − | 0.795153i | \(-0.707391\pi\) | ||||
−0.606409 | + | 0.795153i | \(0.707391\pi\) | |||||||
\(758\) | 66.8030 | 2.42639 | ||||||||
\(759\) | 27.7652 | 1.00781 | ||||||||
\(760\) | −45.5135 | −1.65095 | ||||||||
\(761\) | 8.83761 | 0.320363 | 0.160182 | − | 0.987088i | \(-0.448792\pi\) | ||||
0.160182 | + | 0.987088i | \(0.448792\pi\) | |||||||
\(762\) | −5.85566 | −0.212128 | ||||||||
\(763\) | 20.4378 | 0.739899 | ||||||||
\(764\) | 115.120 | 4.16489 | ||||||||
\(765\) | −58.6853 | −2.12177 | ||||||||
\(766\) | −33.7988 | −1.22120 | ||||||||
\(767\) | −0.633876 | −0.0228879 | ||||||||
\(768\) | −6.74582 | −0.243419 | ||||||||
\(769\) | −6.33489 | −0.228442 | −0.114221 | − | 0.993455i | \(-0.536437\pi\) | ||||
−0.114221 | + | 0.993455i | \(0.536437\pi\) | |||||||
\(770\) | −37.7353 | −1.35989 | ||||||||
\(771\) | −78.6992 | −2.83428 | ||||||||
\(772\) | 100.827 | 3.62886 | ||||||||
\(773\) | −36.3218 | −1.30641 | −0.653203 | − | 0.757183i | \(-0.726575\pi\) | ||||
−0.653203 | + | 0.757183i | \(0.726575\pi\) | |||||||
\(774\) | −200.847 | −7.21928 | ||||||||
\(775\) | 3.71845 | 0.133571 | ||||||||
\(776\) | −50.9533 | −1.82912 | ||||||||
\(777\) | 66.7004 | 2.39286 | ||||||||
\(778\) | −41.0268 | −1.47088 | ||||||||
\(779\) | 7.91711 | 0.283660 | ||||||||
\(780\) | −5.77302 | −0.206707 | ||||||||
\(781\) | −1.60928 | −0.0575845 | ||||||||
\(782\) | 39.0589 | 1.39674 | ||||||||
\(783\) | 22.6274 | 0.808639 | ||||||||
\(784\) | −9.57508 | −0.341967 | ||||||||
\(785\) | −19.5519 | −0.697837 | ||||||||
\(786\) | 38.2182 | 1.36320 | ||||||||
\(787\) | −12.2804 | −0.437750 | −0.218875 | − | 0.975753i | \(-0.570239\pi\) | ||||
−0.218875 | + | 0.975753i | \(0.570239\pi\) | |||||||
\(788\) | −68.3650 | −2.43540 | ||||||||
\(789\) | −29.4293 | −1.04771 | ||||||||
\(790\) | −21.0424 | −0.748654 | ||||||||
\(791\) | 19.6993 | 0.700428 | ||||||||
\(792\) | 149.928 | 5.32744 | ||||||||
\(793\) | 2.43112 | 0.0863316 | ||||||||
\(794\) | 8.13052 | 0.288541 | ||||||||
\(795\) | −85.3725 | −3.02785 | ||||||||
\(796\) | 68.9316 | 2.44322 | ||||||||
\(797\) | 7.89371 | 0.279610 | 0.139805 | − | 0.990179i | \(-0.455352\pi\) | ||||
0.139805 | + | 0.990179i | \(0.455352\pi\) | |||||||
\(798\) | 58.2787 | 2.06305 | ||||||||
\(799\) | −20.9152 | −0.739927 | ||||||||
\(800\) | 16.7218 | 0.591206 | ||||||||
\(801\) | 27.4866 | 0.971192 | ||||||||
\(802\) | −0.166975 | −0.00589611 | ||||||||
\(803\) | −13.7600 | −0.485579 | ||||||||
\(804\) | 73.9252 | 2.60714 | ||||||||
\(805\) | 14.9174 | 0.525768 | ||||||||
\(806\) | 1.57500 | 0.0554769 | ||||||||
\(807\) | 11.5545 | 0.406736 | ||||||||
\(808\) | 34.4788 | 1.21296 | ||||||||
\(809\) | 36.9078 | 1.29761 | 0.648804 | − | 0.760956i | \(-0.275269\pi\) | ||||
0.648804 | + | 0.760956i | \(0.275269\pi\) | |||||||
\(810\) | 61.9094 | 2.17527 | ||||||||
\(811\) | 0.639212 | 0.0224458 | 0.0112229 | − | 0.999937i | \(-0.496428\pi\) | ||||
0.0112229 | + | 0.999937i | \(0.496428\pi\) | |||||||
\(812\) | 27.8879 | 0.978674 | ||||||||
\(813\) | 23.5223 | 0.824962 | ||||||||
\(814\) | 68.8119 | 2.41186 | ||||||||
\(815\) | −26.4208 | −0.925480 | ||||||||
\(816\) | 164.399 | 5.75512 | ||||||||
\(817\) | −34.7580 | −1.21603 | ||||||||
\(818\) | −6.23642 | −0.218051 | ||||||||
\(819\) | 3.02224 | 0.105605 | ||||||||
\(820\) | 26.7654 | 0.934688 | ||||||||
\(821\) | 11.7143 | 0.408833 | 0.204416 | − | 0.978884i | \(-0.434470\pi\) | ||||
0.204416 | + | 0.978884i | \(0.434470\pi\) | |||||||
\(822\) | −72.1056 | −2.51497 | ||||||||
\(823\) | −27.2835 | −0.951044 | −0.475522 | − | 0.879704i | \(-0.657741\pi\) | ||||
−0.475522 | + | 0.879704i | \(0.657741\pi\) | |||||||
\(824\) | 23.6872 | 0.825182 | ||||||||
\(825\) | 10.8553 | 0.377932 | ||||||||
\(826\) | 21.6331 | 0.752711 | ||||||||
\(827\) | −44.5108 | −1.54779 | −0.773895 | − | 0.633314i | \(-0.781694\pi\) | ||||
−0.773895 | + | 0.633314i | \(0.781694\pi\) | |||||||
\(828\) | −98.3049 | −3.41633 | ||||||||
\(829\) | −35.5248 | −1.23383 | −0.616913 | − | 0.787031i | \(-0.711617\pi\) | ||||
−0.616913 | + | 0.787031i | \(0.711617\pi\) | |||||||
\(830\) | −3.15598 | −0.109546 | ||||||||
\(831\) | −61.4818 | −2.13278 | ||||||||
\(832\) | 2.72792 | 0.0945737 | ||||||||
\(833\) | −4.04219 | −0.140053 | ||||||||
\(834\) | −117.646 | −4.07375 | ||||||||
\(835\) | 20.6093 | 0.713215 | ||||||||
\(836\) | 43.0348 | 1.48839 | ||||||||
\(837\) | −31.2168 | −1.07901 | ||||||||
\(838\) | −22.7194 | −0.784830 | ||||||||
\(839\) | 27.0186 | 0.932784 | 0.466392 | − | 0.884578i | \(-0.345554\pi\) | ||||
0.466392 | + | 0.884578i | \(0.345554\pi\) | |||||||
\(840\) | 118.787 | 4.09853 | ||||||||
\(841\) | −24.0166 | −0.828159 | ||||||||
\(842\) | −61.8828 | −2.13262 | ||||||||
\(843\) | −69.4175 | −2.39087 | ||||||||
\(844\) | −121.639 | −4.18700 | ||||||||
\(845\) | 25.2446 | 0.868442 | ||||||||
\(846\) | 73.5432 | 2.52847 | ||||||||
\(847\) | −5.77216 | −0.198334 | ||||||||
\(848\) | 162.179 | 5.56924 | ||||||||
\(849\) | 11.6774 | 0.400766 | ||||||||
\(850\) | 15.2707 | 0.523782 | ||||||||
\(851\) | −27.2025 | −0.932488 | ||||||||
\(852\) | 8.40234 | 0.287860 | ||||||||
\(853\) | 37.9312 | 1.29874 | 0.649369 | − | 0.760474i | \(-0.275033\pi\) | ||||
0.649369 | + | 0.760474i | \(0.275033\pi\) | |||||||
\(854\) | −82.9699 | −2.83917 | ||||||||
\(855\) | 35.7107 | 1.22128 | ||||||||
\(856\) | −17.8334 | −0.609533 | ||||||||
\(857\) | −31.0229 | −1.05972 | −0.529862 | − | 0.848084i | \(-0.677756\pi\) | ||||
−0.529862 | + | 0.848084i | \(0.677756\pi\) | |||||||
\(858\) | 4.59789 | 0.156969 | ||||||||
\(859\) | 25.8123 | 0.880703 | 0.440351 | − | 0.897826i | \(-0.354854\pi\) | ||||
0.440351 | + | 0.897826i | \(0.354854\pi\) | |||||||
\(860\) | −117.506 | −4.00693 | ||||||||
\(861\) | −20.6630 | −0.704194 | ||||||||
\(862\) | −43.5224 | −1.48238 | ||||||||
\(863\) | −7.14893 | −0.243352 | −0.121676 | − | 0.992570i | \(-0.538827\pi\) | ||||
−0.121676 | + | 0.992570i | \(0.538827\pi\) | |||||||
\(864\) | −140.381 | −4.77587 | ||||||||
\(865\) | 35.9668 | 1.22291 | ||||||||
\(866\) | −41.5440 | −1.41172 | ||||||||
\(867\) | 17.5030 | 0.594434 | ||||||||
\(868\) | −38.4741 | −1.30590 | ||||||||
\(869\) | 11.9957 | 0.406925 | ||||||||
\(870\) | 35.2067 | 1.19362 | ||||||||
\(871\) | 0.926884 | 0.0314063 | ||||||||
\(872\) | −66.3728 | −2.24767 | ||||||||
\(873\) | 39.9789 | 1.35308 | ||||||||
\(874\) | −23.7678 | −0.803959 | ||||||||
\(875\) | 29.9843 | 1.01365 | ||||||||
\(876\) | 71.8434 | 2.42736 | ||||||||
\(877\) | −12.0065 | −0.405431 | −0.202716 | − | 0.979238i | \(-0.564977\pi\) | ||||
−0.202716 | + | 0.979238i | \(0.564977\pi\) | |||||||
\(878\) | 88.5562 | 2.98863 | ||||||||
\(879\) | −27.2028 | −0.917528 | ||||||||
\(880\) | 64.7749 | 2.18356 | ||||||||
\(881\) | −32.1303 | −1.08250 | −0.541249 | − | 0.840862i | \(-0.682049\pi\) | ||||
−0.541249 | + | 0.840862i | \(0.682049\pi\) | |||||||
\(882\) | 14.2134 | 0.478589 | ||||||||
\(883\) | −19.6821 | −0.662356 | −0.331178 | − | 0.943568i | \(-0.607446\pi\) | ||||
−0.331178 | + | 0.943568i | \(0.607446\pi\) | |||||||
\(884\) | 4.62970 | 0.155714 | ||||||||
\(885\) | 19.5480 | 0.657098 | ||||||||
\(886\) | −74.8120 | −2.51336 | ||||||||
\(887\) | −1.13995 | −0.0382759 | −0.0191379 | − | 0.999817i | \(-0.506092\pi\) | ||||
−0.0191379 | + | 0.999817i | \(0.506092\pi\) | |||||||
\(888\) | −216.613 | −7.26904 | ||||||||
\(889\) | 1.79349 | 0.0601516 | ||||||||
\(890\) | 22.4669 | 0.753092 | ||||||||
\(891\) | −35.2928 | −1.18235 | ||||||||
\(892\) | 98.8240 | 3.30887 | ||||||||
\(893\) | 12.7272 | 0.425899 | ||||||||
\(894\) | 70.7678 | 2.36683 | ||||||||
\(895\) | −43.4049 | −1.45086 | ||||||||
\(896\) | −24.3953 | −0.814988 | ||||||||
\(897\) | −1.81762 | −0.0606885 | ||||||||
\(898\) | −83.3841 | −2.78256 | ||||||||
\(899\) | −6.87506 | −0.229296 | ||||||||
\(900\) | −38.4340 | −1.28113 | ||||||||
\(901\) | 68.4649 | 2.28090 | ||||||||
\(902\) | −21.3172 | −0.709783 | ||||||||
\(903\) | 90.7155 | 3.01882 | ||||||||
\(904\) | −63.9745 | −2.12776 | ||||||||
\(905\) | 14.5848 | 0.484814 | ||||||||
\(906\) | −143.081 | −4.75355 | ||||||||
\(907\) | −36.9999 | −1.22856 | −0.614281 | − | 0.789088i | \(-0.710554\pi\) | ||||
−0.614281 | + | 0.789088i | \(0.710554\pi\) | |||||||
\(908\) | 86.1932 | 2.86042 | ||||||||
\(909\) | −27.0527 | −0.897280 | ||||||||
\(910\) | 2.47030 | 0.0818897 | ||||||||
\(911\) | 49.1117 | 1.62714 | 0.813572 | − | 0.581465i | \(-0.197520\pi\) | ||||
0.813572 | + | 0.581465i | \(0.197520\pi\) | |||||||
\(912\) | −100.039 | −3.31262 | ||||||||
\(913\) | 1.79914 | 0.0595428 | ||||||||
\(914\) | −38.2639 | −1.26566 | ||||||||
\(915\) | −74.9729 | −2.47853 | ||||||||
\(916\) | −98.1475 | −3.24289 | ||||||||
\(917\) | −11.7055 | −0.386551 | ||||||||
\(918\) | −128.199 | −4.23121 | ||||||||
\(919\) | 36.1027 | 1.19092 | 0.595459 | − | 0.803386i | \(-0.296970\pi\) | ||||
0.595459 | + | 0.803386i | \(0.296970\pi\) | |||||||
\(920\) | −48.4448 | −1.59718 | ||||||||
\(921\) | −70.0410 | −2.30793 | ||||||||
\(922\) | −61.5997 | −2.02868 | ||||||||
\(923\) | 0.105350 | 0.00346763 | ||||||||
\(924\) | −112.318 | −3.69497 | ||||||||
\(925\) | −10.6353 | −0.349685 | ||||||||
\(926\) | 70.5274 | 2.31767 | ||||||||
\(927\) | −18.5854 | −0.610424 | ||||||||
\(928\) | −30.9171 | −1.01490 | ||||||||
\(929\) | 35.9924 | 1.18087 | 0.590436 | − | 0.807084i | \(-0.298956\pi\) | ||||
0.590436 | + | 0.807084i | \(0.298956\pi\) | |||||||
\(930\) | −48.5711 | −1.59271 | ||||||||
\(931\) | 2.45972 | 0.0806142 | ||||||||
\(932\) | −126.422 | −4.14108 | ||||||||
\(933\) | 42.2818 | 1.38424 | ||||||||
\(934\) | −13.3419 | −0.436559 | ||||||||
\(935\) | 27.3452 | 0.894284 | ||||||||
\(936\) | −9.81485 | −0.320808 | ||||||||
\(937\) | 0.368168 | 0.0120275 | 0.00601377 | − | 0.999982i | \(-0.498086\pi\) | ||||
0.00601377 | + | 0.999982i | \(0.498086\pi\) | |||||||
\(938\) | −31.6329 | −1.03285 | ||||||||
\(939\) | 57.9904 | 1.89245 | ||||||||
\(940\) | 43.0268 | 1.40338 | ||||||||
\(941\) | 10.1487 | 0.330837 | 0.165418 | − | 0.986223i | \(-0.447103\pi\) | ||||
0.165418 | + | 0.986223i | \(0.447103\pi\) | |||||||
\(942\) | −81.3043 | −2.64904 | ||||||||
\(943\) | 8.42701 | 0.274421 | ||||||||
\(944\) | −37.1345 | −1.20862 | ||||||||
\(945\) | −48.9619 | −1.59273 | ||||||||
\(946\) | 93.5872 | 3.04278 | ||||||||
\(947\) | 5.78211 | 0.187893 | 0.0939467 | − | 0.995577i | \(-0.470052\pi\) | ||||
0.0939467 | + | 0.995577i | \(0.470052\pi\) | |||||||
\(948\) | −62.6317 | −2.03418 | ||||||||
\(949\) | 0.900782 | 0.0292406 | ||||||||
\(950\) | −9.29244 | −0.301487 | ||||||||
\(951\) | −24.7786 | −0.803502 | ||||||||
\(952\) | −95.2615 | −3.08744 | ||||||||
\(953\) | 35.5792 | 1.15252 | 0.576262 | − | 0.817265i | \(-0.304511\pi\) | ||||
0.576262 | + | 0.817265i | \(0.304511\pi\) | |||||||
\(954\) | −240.740 | −7.79424 | ||||||||
\(955\) | −44.5124 | −1.44039 | ||||||||
\(956\) | 18.9311 | 0.612277 | ||||||||
\(957\) | −20.0704 | −0.648783 | ||||||||
\(958\) | −50.5744 | −1.63398 | ||||||||
\(959\) | 22.0847 | 0.713151 | ||||||||
\(960\) | −84.1259 | −2.71515 | ||||||||
\(961\) | −21.5152 | −0.694038 | ||||||||
\(962\) | −4.50470 | −0.145237 | ||||||||
\(963\) | 13.9924 | 0.450899 | ||||||||
\(964\) | −108.186 | −3.48443 | ||||||||
\(965\) | −38.9861 | −1.25501 | ||||||||
\(966\) | 62.0322 | 1.99585 | ||||||||
\(967\) | 54.9249 | 1.76626 | 0.883132 | − | 0.469124i | \(-0.155430\pi\) | ||||
0.883132 | + | 0.469124i | \(0.155430\pi\) | |||||||
\(968\) | 18.7453 | 0.602498 | ||||||||
\(969\) | −42.2322 | −1.35669 | ||||||||
\(970\) | 32.6778 | 1.04922 | ||||||||
\(971\) | −24.6072 | −0.789682 | −0.394841 | − | 0.918749i | \(-0.629200\pi\) | ||||
−0.394841 | + | 0.918749i | \(0.629200\pi\) | |||||||
\(972\) | 31.1149 | 0.998012 | ||||||||
\(973\) | 36.0329 | 1.15516 | ||||||||
\(974\) | −28.0112 | −0.897537 | ||||||||
\(975\) | −0.710629 | −0.0227583 | ||||||||
\(976\) | 142.423 | 4.55885 | ||||||||
\(977\) | 39.1338 | 1.25200 | 0.626001 | − | 0.779822i | \(-0.284691\pi\) | ||||
0.626001 | + | 0.779822i | \(0.284691\pi\) | |||||||
\(978\) | −109.868 | −3.51319 | ||||||||
\(979\) | −12.8078 | −0.409338 | ||||||||
\(980\) | 8.31559 | 0.265632 | ||||||||
\(981\) | 52.0773 | 1.66270 | ||||||||
\(982\) | 52.3378 | 1.67017 | ||||||||
\(983\) | −5.02643 | −0.160318 | −0.0801591 | − | 0.996782i | \(-0.525543\pi\) | ||||
−0.0801591 | + | 0.996782i | \(0.525543\pi\) | |||||||
\(984\) | 67.1041 | 2.13920 | ||||||||
\(985\) | 26.4341 | 0.842260 | ||||||||
\(986\) | −28.2341 | −0.899158 | ||||||||
\(987\) | −33.2169 | −1.05731 | ||||||||
\(988\) | −2.81723 | −0.0896280 | ||||||||
\(989\) | −36.9965 | −1.17642 | ||||||||
\(990\) | −96.1527 | −3.05593 | ||||||||
\(991\) | 12.3304 | 0.391688 | 0.195844 | − | 0.980635i | \(-0.437255\pi\) | ||||
0.195844 | + | 0.980635i | \(0.437255\pi\) | |||||||
\(992\) | 42.6531 | 1.35424 | ||||||||
\(993\) | −51.5875 | −1.63708 | ||||||||
\(994\) | −3.59540 | −0.114039 | ||||||||
\(995\) | −26.6532 | −0.844963 | ||||||||
\(996\) | −9.39364 | −0.297649 | ||||||||
\(997\) | −51.5304 | −1.63198 | −0.815991 | − | 0.578064i | \(-0.803808\pi\) | ||||
−0.815991 | + | 0.578064i | \(0.803808\pi\) | |||||||
\(998\) | 97.4176 | 3.08370 | ||||||||
\(999\) | 89.2841 | 2.82482 |
(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 | 4001.2.a.b.1.10 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.10 | ✓ | 184 | 1.1 | even | 1 | trivial |