Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(109.684550701\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.641292 | −0.226731 | −0.113366 | − | 0.993553i | \(-0.536163\pi\) | ||||
−0.113366 | + | 0.993553i | \(0.536163\pi\) | |||||||
\(3\) | −1.91302 | −0.368161 | −0.184081 | − | 0.982911i | \(-0.558931\pi\) | ||||
−0.184081 | + | 0.982911i | \(0.558931\pi\) | |||||||
\(4\) | −7.58874 | −0.948593 | ||||||||
\(5\) | −0.642358 | −0.0574542 | −0.0287271 | − | 0.999587i | \(-0.509145\pi\) | ||||
−0.0287271 | + | 0.999587i | \(0.509145\pi\) | |||||||
\(6\) | 1.22681 | 0.0834735 | ||||||||
\(7\) | −23.2338 | −1.25451 | −0.627253 | − | 0.778815i | \(-0.715821\pi\) | ||||
−0.627253 | + | 0.778815i | \(0.715821\pi\) | |||||||
\(8\) | 9.99694 | 0.441807 | ||||||||
\(9\) | −23.3404 | −0.864457 | ||||||||
\(10\) | 0.411939 | 0.0130267 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 14.5174 | 0.349235 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 14.8997 | 0.284436 | ||||||||
\(15\) | 1.22884 | 0.0211524 | ||||||||
\(16\) | 54.2990 | 0.848422 | ||||||||
\(17\) | −35.1893 | −0.502038 | −0.251019 | − | 0.967982i | \(-0.580766\pi\) | ||||
−0.251019 | + | 0.967982i | \(0.580766\pi\) | |||||||
\(18\) | 14.9680 | 0.195999 | ||||||||
\(19\) | −37.3835 | −0.451388 | −0.225694 | − | 0.974198i | \(-0.572465\pi\) | ||||
−0.225694 | + | 0.974198i | \(0.572465\pi\) | |||||||
\(20\) | 4.87469 | 0.0545007 | ||||||||
\(21\) | 44.4467 | 0.461861 | ||||||||
\(22\) | −7.05421 | −0.0683620 | ||||||||
\(23\) | 121.805 | 1.10427 | 0.552135 | − | 0.833755i | \(-0.313813\pi\) | ||||
0.552135 | + | 0.833755i | \(0.313813\pi\) | |||||||
\(24\) | −19.1244 | −0.162656 | ||||||||
\(25\) | −124.587 | −0.996699 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 96.3021 | 0.686421 | ||||||||
\(28\) | 176.315 | 1.19002 | ||||||||
\(29\) | −19.7597 | −0.126527 | −0.0632637 | − | 0.997997i | \(-0.520151\pi\) | ||||
−0.0632637 | + | 0.997997i | \(0.520151\pi\) | |||||||
\(30\) | −0.788048 | −0.00479591 | ||||||||
\(31\) | −30.1301 | −0.174566 | −0.0872828 | − | 0.996184i | \(-0.527818\pi\) | ||||
−0.0872828 | + | 0.996184i | \(0.527818\pi\) | |||||||
\(32\) | −114.797 | −0.634170 | ||||||||
\(33\) | −21.0432 | −0.111005 | ||||||||
\(34\) | 22.5666 | 0.113828 | ||||||||
\(35\) | 14.9244 | 0.0720767 | ||||||||
\(36\) | 177.124 | 0.820018 | ||||||||
\(37\) | 193.485 | 0.859697 | 0.429849 | − | 0.902901i | \(-0.358567\pi\) | ||||
0.429849 | + | 0.902901i | \(0.358567\pi\) | |||||||
\(38\) | 23.9738 | 0.102344 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.42161 | −0.0253836 | ||||||||
\(41\) | 80.8749 | 0.308062 | 0.154031 | − | 0.988066i | \(-0.450774\pi\) | ||||
0.154031 | + | 0.988066i | \(0.450774\pi\) | |||||||
\(42\) | −28.5033 | −0.104718 | ||||||||
\(43\) | 196.760 | 0.697805 | 0.348903 | − | 0.937159i | \(-0.386554\pi\) | ||||
0.348903 | + | 0.937159i | \(0.386554\pi\) | |||||||
\(44\) | −83.4762 | −0.286012 | ||||||||
\(45\) | 14.9929 | 0.0496667 | ||||||||
\(46\) | −78.1129 | −0.250372 | ||||||||
\(47\) | 182.123 | 0.565220 | 0.282610 | − | 0.959235i | \(-0.408800\pi\) | ||||
0.282610 | + | 0.959235i | \(0.408800\pi\) | |||||||
\(48\) | −103.875 | −0.312356 | ||||||||
\(49\) | 196.809 | 0.573788 | ||||||||
\(50\) | 79.8969 | 0.225983 | ||||||||
\(51\) | 67.3178 | 0.184831 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 451.627 | 1.17049 | 0.585243 | − | 0.810858i | \(-0.300999\pi\) | ||||
0.585243 | + | 0.810858i | \(0.300999\pi\) | |||||||
\(54\) | −61.7578 | −0.155633 | ||||||||
\(55\) | −7.06593 | −0.0173231 | ||||||||
\(56\) | −232.267 | −0.554249 | ||||||||
\(57\) | 71.5155 | 0.166183 | ||||||||
\(58\) | 12.6718 | 0.0286877 | ||||||||
\(59\) | −270.352 | −0.596557 | −0.298279 | − | 0.954479i | \(-0.596412\pi\) | ||||
−0.298279 | + | 0.954479i | \(0.596412\pi\) | |||||||
\(60\) | −9.32538 | −0.0200650 | ||||||||
\(61\) | 694.071 | 1.45683 | 0.728415 | − | 0.685136i | \(-0.240257\pi\) | ||||
0.728415 | + | 0.685136i | \(0.240257\pi\) | |||||||
\(62\) | 19.3222 | 0.0395794 | ||||||||
\(63\) | 542.285 | 1.08447 | ||||||||
\(64\) | −360.774 | −0.704636 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.4949 | 0.0251682 | ||||||||
\(67\) | −364.013 | −0.663749 | −0.331875 | − | 0.943323i | \(-0.607681\pi\) | ||||
−0.331875 | + | 0.943323i | \(0.607681\pi\) | |||||||
\(68\) | 267.042 | 0.476230 | ||||||||
\(69\) | −233.016 | −0.406549 | ||||||||
\(70\) | −9.57091 | −0.0163420 | ||||||||
\(71\) | 772.939 | 1.29199 | 0.645993 | − | 0.763344i | \(-0.276444\pi\) | ||||
0.645993 | + | 0.763344i | \(0.276444\pi\) | |||||||
\(72\) | −233.332 | −0.381923 | ||||||||
\(73\) | −160.608 | −0.257504 | −0.128752 | − | 0.991677i | \(-0.541097\pi\) | ||||
−0.128752 | + | 0.991677i | \(0.541097\pi\) | |||||||
\(74\) | −124.081 | −0.194920 | ||||||||
\(75\) | 238.338 | 0.366946 | ||||||||
\(76\) | 283.694 | 0.428184 | ||||||||
\(77\) | −255.572 | −0.378248 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46.4472 | 0.0661483 | 0.0330741 | − | 0.999453i | \(-0.489470\pi\) | ||||
0.0330741 | + | 0.999453i | \(0.489470\pi\) | |||||||
\(80\) | −34.8794 | −0.0487454 | ||||||||
\(81\) | 445.961 | 0.611744 | ||||||||
\(82\) | −51.8645 | −0.0698472 | ||||||||
\(83\) | 520.415 | 0.688228 | 0.344114 | − | 0.938928i | \(-0.388179\pi\) | ||||
0.344114 | + | 0.938928i | \(0.388179\pi\) | |||||||
\(84\) | −337.295 | −0.438118 | ||||||||
\(85\) | 22.6041 | 0.0288442 | ||||||||
\(86\) | −126.181 | −0.158214 | ||||||||
\(87\) | 37.8008 | 0.0465824 | ||||||||
\(88\) | 109.966 | 0.133210 | ||||||||
\(89\) | −394.789 | −0.470197 | −0.235099 | − | 0.971971i | \(-0.575541\pi\) | ||||
−0.235099 | + | 0.971971i | \(0.575541\pi\) | |||||||
\(90\) | −9.61480 | −0.0112610 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −924.351 | −1.04750 | ||||||||
\(93\) | 57.6396 | 0.0642683 | ||||||||
\(94\) | −116.794 | −0.128153 | ||||||||
\(95\) | 24.0136 | 0.0259341 | ||||||||
\(96\) | 219.609 | 0.233477 | ||||||||
\(97\) | 17.2969 | 0.0181055 | 0.00905276 | − | 0.999959i | \(-0.497118\pi\) | ||||
0.00905276 | + | 0.999959i | \(0.497118\pi\) | |||||||
\(98\) | −126.212 | −0.130095 | ||||||||
\(99\) | −256.744 | −0.260644 | ||||||||
\(100\) | 945.462 | 0.945462 | ||||||||
\(101\) | −310.625 | −0.306023 | −0.153012 | − | 0.988224i | \(-0.548897\pi\) | ||||
−0.153012 | + | 0.988224i | \(0.548897\pi\) | |||||||
\(102\) | −43.1704 | −0.0419069 | ||||||||
\(103\) | −1176.13 | −1.12512 | −0.562561 | − | 0.826756i | \(-0.690184\pi\) | ||||
−0.562561 | + | 0.826756i | \(0.690184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −28.5507 | −0.0265358 | ||||||||
\(106\) | −289.625 | −0.265385 | ||||||||
\(107\) | −312.926 | −0.282727 | −0.141363 | − | 0.989958i | \(-0.545149\pi\) | ||||
−0.141363 | + | 0.989958i | \(0.545149\pi\) | |||||||
\(108\) | −730.812 | −0.651134 | ||||||||
\(109\) | 1339.09 | 1.17671 | 0.588355 | − | 0.808603i | \(-0.299776\pi\) | ||||
0.588355 | + | 0.808603i | \(0.299776\pi\) | |||||||
\(110\) | 4.53133 | 0.00392768 | ||||||||
\(111\) | −370.142 | −0.316507 | ||||||||
\(112\) | −1261.57 | −1.06435 | ||||||||
\(113\) | 1217.74 | 1.01377 | 0.506883 | − | 0.862015i | \(-0.330798\pi\) | ||||
0.506883 | + | 0.862015i | \(0.330798\pi\) | |||||||
\(114\) | −45.8623 | −0.0376790 | ||||||||
\(115\) | −78.2427 | −0.0634449 | ||||||||
\(116\) | 149.952 | 0.120023 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 173.375 | 0.135258 | ||||||||
\(119\) | 817.580 | 0.629811 | ||||||||
\(120\) | 12.2847 | 0.00934527 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −445.102 | −0.330309 | ||||||||
\(123\) | −154.715 | −0.113416 | ||||||||
\(124\) | 228.650 | 0.165592 | ||||||||
\(125\) | 160.324 | 0.114719 | ||||||||
\(126\) | −347.763 | −0.245883 | ||||||||
\(127\) | −1594.23 | −1.11390 | −0.556950 | − | 0.830546i | \(-0.688028\pi\) | ||||
−0.556950 | + | 0.830546i | \(0.688028\pi\) | |||||||
\(128\) | 1149.74 | 0.793933 | ||||||||
\(129\) | −376.406 | −0.256905 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2627.82 | −1.75262 | −0.876311 | − | 0.481745i | \(-0.840003\pi\) | ||||
−0.876311 | + | 0.481745i | \(0.840003\pi\) | |||||||
\(132\) | 159.692 | 0.105298 | ||||||||
\(133\) | 868.562 | 0.566269 | ||||||||
\(134\) | 233.438 | 0.150493 | ||||||||
\(135\) | −61.8604 | −0.0394378 | ||||||||
\(136\) | −351.785 | −0.221804 | ||||||||
\(137\) | −3032.80 | −1.89131 | −0.945655 | − | 0.325173i | \(-0.894577\pi\) | ||||
−0.945655 | + | 0.325173i | \(0.894577\pi\) | |||||||
\(138\) | 149.432 | 0.0921773 | ||||||||
\(139\) | 1685.94 | 1.02878 | 0.514388 | − | 0.857558i | \(-0.328019\pi\) | ||||
0.514388 | + | 0.857558i | \(0.328019\pi\) | |||||||
\(140\) | −113.258 | −0.0683715 | ||||||||
\(141\) | −348.404 | −0.208092 | ||||||||
\(142\) | −495.680 | −0.292933 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1267.36 | −0.733425 | ||||||||
\(145\) | 12.6928 | 0.00726953 | ||||||||
\(146\) | 102.997 | 0.0583841 | ||||||||
\(147\) | −376.500 | −0.211246 | ||||||||
\(148\) | −1468.31 | −0.815503 | ||||||||
\(149\) | 1612.83 | 0.886764 | 0.443382 | − | 0.896333i | \(-0.353778\pi\) | ||||
0.443382 | + | 0.896333i | \(0.353778\pi\) | |||||||
\(150\) | −152.844 | −0.0831980 | ||||||||
\(151\) | 2699.78 | 1.45500 | 0.727501 | − | 0.686106i | \(-0.240682\pi\) | ||||
0.727501 | + | 0.686106i | \(0.240682\pi\) | |||||||
\(152\) | −373.721 | −0.199426 | ||||||||
\(153\) | 821.330 | 0.433991 | ||||||||
\(154\) | 163.896 | 0.0857606 | ||||||||
\(155\) | 19.3543 | 0.0100295 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −761.773 | −0.387236 | −0.193618 | − | 0.981077i | \(-0.562022\pi\) | ||||
−0.193618 | + | 0.981077i | \(0.562022\pi\) | |||||||
\(158\) | −29.7862 | −0.0149979 | ||||||||
\(159\) | −863.972 | −0.430927 | ||||||||
\(160\) | 73.7408 | 0.0364357 | ||||||||
\(161\) | −2830.00 | −1.38531 | ||||||||
\(162\) | −285.992 | −0.138701 | ||||||||
\(163\) | −565.770 | −0.271868 | −0.135934 | − | 0.990718i | \(-0.543404\pi\) | ||||
−0.135934 | + | 0.990718i | \(0.543404\pi\) | |||||||
\(164\) | −613.739 | −0.292226 | ||||||||
\(165\) | 13.5173 | 0.00637769 | ||||||||
\(166\) | −333.738 | −0.156043 | ||||||||
\(167\) | −1746.16 | −0.809114 | −0.404557 | − | 0.914513i | \(-0.632574\pi\) | ||||
−0.404557 | + | 0.914513i | \(0.632574\pi\) | |||||||
\(168\) | 444.331 | 0.204053 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −14.4958 | −0.00653988 | ||||||||
\(171\) | 872.545 | 0.390206 | ||||||||
\(172\) | −1493.16 | −0.661933 | ||||||||
\(173\) | −58.9246 | −0.0258957 | −0.0129478 | − | 0.999916i | \(-0.504122\pi\) | ||||
−0.0129478 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(174\) | −24.2414 | −0.0105617 | ||||||||
\(175\) | 2894.64 | 1.25037 | ||||||||
\(176\) | 597.289 | 0.255809 | ||||||||
\(177\) | 517.190 | 0.219629 | ||||||||
\(178\) | 253.175 | 0.106608 | ||||||||
\(179\) | 436.558 | 0.182290 | 0.0911448 | − | 0.995838i | \(-0.470947\pi\) | ||||
0.0911448 | + | 0.995838i | \(0.470947\pi\) | |||||||
\(180\) | −113.777 | −0.0471135 | ||||||||
\(181\) | 453.369 | 0.186181 | 0.0930903 | − | 0.995658i | \(-0.470325\pi\) | ||||
0.0930903 | + | 0.995658i | \(0.470325\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1327.77 | −0.536348 | ||||||||
\(184\) | 1217.68 | 0.487873 | ||||||||
\(185\) | −124.287 | −0.0493932 | ||||||||
\(186\) | −36.9638 | −0.0145716 | ||||||||
\(187\) | −387.082 | −0.151370 | ||||||||
\(188\) | −1382.08 | −0.536163 | ||||||||
\(189\) | −2237.46 | −0.861119 | ||||||||
\(190\) | −15.3997 | −0.00588008 | ||||||||
\(191\) | −1937.48 | −0.733986 | −0.366993 | − | 0.930224i | \(-0.619613\pi\) | ||||
−0.366993 | + | 0.930224i | \(0.619613\pi\) | |||||||
\(192\) | 690.167 | 0.259419 | ||||||||
\(193\) | 1622.95 | 0.605300 | 0.302650 | − | 0.953102i | \(-0.402129\pi\) | ||||
0.302650 | + | 0.953102i | \(0.402129\pi\) | |||||||
\(194\) | −11.0924 | −0.00410508 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1493.53 | −0.544291 | ||||||||
\(197\) | 2742.17 | 0.991732 | 0.495866 | − | 0.868399i | \(-0.334851\pi\) | ||||
0.495866 | + | 0.868399i | \(0.334851\pi\) | |||||||
\(198\) | 164.648 | 0.0590960 | ||||||||
\(199\) | −4261.14 | −1.51791 | −0.758956 | − | 0.651142i | \(-0.774290\pi\) | ||||
−0.758956 | + | 0.651142i | \(0.774290\pi\) | |||||||
\(200\) | −1245.49 | −0.440348 | ||||||||
\(201\) | 696.364 | 0.244367 | ||||||||
\(202\) | 199.201 | 0.0693850 | ||||||||
\(203\) | 459.094 | 0.158729 | ||||||||
\(204\) | −510.858 | −0.175329 | ||||||||
\(205\) | −51.9506 | −0.0176995 | ||||||||
\(206\) | 754.244 | 0.255100 | ||||||||
\(207\) | −2842.98 | −0.954594 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −411.219 | −0.136099 | ||||||||
\(210\) | 18.3093 | 0.00601650 | ||||||||
\(211\) | −13.6015 | −0.00443776 | −0.00221888 | − | 0.999998i | \(-0.500706\pi\) | ||||
−0.00221888 | + | 0.999998i | \(0.500706\pi\) | |||||||
\(212\) | −3427.28 | −1.11031 | ||||||||
\(213\) | −1478.65 | −0.475659 | ||||||||
\(214\) | 200.677 | 0.0641029 | ||||||||
\(215\) | −126.390 | −0.0400918 | ||||||||
\(216\) | 962.727 | 0.303265 | ||||||||
\(217\) | 700.038 | 0.218994 | ||||||||
\(218\) | −858.746 | −0.266797 | ||||||||
\(219\) | 307.247 | 0.0948029 | ||||||||
\(220\) | 53.6216 | 0.0164326 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 237.369 | 0.0717620 | ||||||||
\(223\) | 4944.64 | 1.48483 | 0.742417 | − | 0.669938i | \(-0.233679\pi\) | ||||
0.742417 | + | 0.669938i | \(0.233679\pi\) | |||||||
\(224\) | 2667.17 | 0.795571 | ||||||||
\(225\) | 2907.91 | 0.861604 | ||||||||
\(226\) | −780.928 | −0.229852 | ||||||||
\(227\) | −978.487 | −0.286099 | −0.143049 | − | 0.989716i | \(-0.545691\pi\) | ||||
−0.143049 | + | 0.989716i | \(0.545691\pi\) | |||||||
\(228\) | −542.713 | −0.157641 | ||||||||
\(229\) | 4614.01 | 1.33145 | 0.665725 | − | 0.746197i | \(-0.268122\pi\) | ||||
0.665725 | + | 0.746197i | \(0.268122\pi\) | |||||||
\(230\) | 50.1764 | 0.0143849 | ||||||||
\(231\) | 488.914 | 0.139256 | ||||||||
\(232\) | −197.537 | −0.0559006 | ||||||||
\(233\) | −3289.10 | −0.924789 | −0.462395 | − | 0.886674i | \(-0.653010\pi\) | ||||
−0.462395 | + | 0.886674i | \(0.653010\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −116.988 | −0.0324742 | ||||||||
\(236\) | 2051.64 | 0.565890 | ||||||||
\(237\) | −88.8544 | −0.0243532 | ||||||||
\(238\) | −524.308 | −0.142798 | ||||||||
\(239\) | −1517.69 | −0.410757 | −0.205379 | − | 0.978683i | \(-0.565843\pi\) | ||||
−0.205379 | + | 0.978683i | \(0.565843\pi\) | |||||||
\(240\) | 66.7250 | 0.0179462 | ||||||||
\(241\) | −2219.80 | −0.593320 | −0.296660 | − | 0.954983i | \(-0.595873\pi\) | ||||
−0.296660 | + | 0.954983i | \(0.595873\pi\) | |||||||
\(242\) | −77.5964 | −0.0206119 | ||||||||
\(243\) | −3453.29 | −0.911641 | ||||||||
\(244\) | −5267.12 | −1.38194 | ||||||||
\(245\) | −126.422 | −0.0329665 | ||||||||
\(246\) | 99.2178 | 0.0257150 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −301.209 | −0.0771242 | ||||||||
\(249\) | −995.564 | −0.253379 | ||||||||
\(250\) | −102.815 | −0.0260103 | ||||||||
\(251\) | −3805.91 | −0.957080 | −0.478540 | − | 0.878066i | \(-0.658834\pi\) | ||||
−0.478540 | + | 0.878066i | \(0.658834\pi\) | |||||||
\(252\) | −4115.26 | −1.02872 | ||||||||
\(253\) | 1339.86 | 0.332950 | ||||||||
\(254\) | 1022.37 | 0.252556 | ||||||||
\(255\) | −43.2421 | −0.0106193 | ||||||||
\(256\) | 2148.87 | 0.524627 | ||||||||
\(257\) | −4987.53 | −1.21056 | −0.605279 | − | 0.796013i | \(-0.706939\pi\) | ||||
−0.605279 | + | 0.796013i | \(0.706939\pi\) | |||||||
\(258\) | 241.386 | 0.0582483 | ||||||||
\(259\) | −4495.40 | −1.07850 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 461.199 | 0.109377 | ||||||||
\(262\) | 1685.20 | 0.397374 | ||||||||
\(263\) | −1099.76 | −0.257847 | −0.128924 | − | 0.991655i | \(-0.541152\pi\) | ||||
−0.128924 | + | 0.991655i | \(0.541152\pi\) | |||||||
\(264\) | −210.368 | −0.0490426 | ||||||||
\(265\) | −290.106 | −0.0672494 | ||||||||
\(266\) | −557.002 | −0.128391 | ||||||||
\(267\) | 755.240 | 0.173108 | ||||||||
\(268\) | 2762.40 | 0.629628 | ||||||||
\(269\) | 4740.51 | 1.07448 | 0.537238 | − | 0.843431i | \(-0.319468\pi\) | ||||
0.537238 | + | 0.843431i | \(0.319468\pi\) | |||||||
\(270\) | 39.6706 | 0.00894176 | ||||||||
\(271\) | 7507.72 | 1.68288 | 0.841441 | − | 0.540348i | \(-0.181708\pi\) | ||||
0.841441 | + | 0.540348i | \(0.181708\pi\) | |||||||
\(272\) | −1910.74 | −0.425940 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1944.91 | 0.428818 | ||||||||
\(275\) | −1370.46 | −0.300516 | ||||||||
\(276\) | 1768.30 | 0.385650 | ||||||||
\(277\) | −8224.58 | −1.78400 | −0.891999 | − | 0.452038i | \(-0.850697\pi\) | ||||
−0.891999 | + | 0.452038i | \(0.850697\pi\) | |||||||
\(278\) | −1081.18 | −0.233255 | ||||||||
\(279\) | 703.248 | 0.150905 | ||||||||
\(280\) | 149.198 | 0.0318440 | ||||||||
\(281\) | 374.647 | 0.0795358 | 0.0397679 | − | 0.999209i | \(-0.487338\pi\) | ||||
0.0397679 | + | 0.999209i | \(0.487338\pi\) | |||||||
\(282\) | 223.429 | 0.0471809 | ||||||||
\(283\) | −6545.41 | −1.37486 | −0.687428 | − | 0.726253i | \(-0.741260\pi\) | ||||
−0.687428 | + | 0.726253i | \(0.741260\pi\) | |||||||
\(284\) | −5865.63 | −1.22557 | ||||||||
\(285\) | −45.9385 | −0.00954794 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1879.03 | −0.386466 | ||||||||
\(288\) | 2679.40 | 0.548213 | ||||||||
\(289\) | −3674.72 | −0.747957 | ||||||||
\(290\) | −8.13981 | −0.00164823 | ||||||||
\(291\) | −33.0894 | −0.00666575 | ||||||||
\(292\) | 1218.82 | 0.244266 | ||||||||
\(293\) | −9231.30 | −1.84061 | −0.920304 | − | 0.391203i | \(-0.872059\pi\) | ||||
−0.920304 | + | 0.391203i | \(0.872059\pi\) | |||||||
\(294\) | 241.447 | 0.0478961 | ||||||||
\(295\) | 173.663 | 0.0342747 | ||||||||
\(296\) | 1934.26 | 0.379820 | ||||||||
\(297\) | 1059.32 | 0.206964 | ||||||||
\(298\) | −1034.29 | −0.201057 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1808.69 | −0.348082 | ||||||||
\(301\) | −4571.48 | −0.875401 | ||||||||
\(302\) | −1731.35 | −0.329894 | ||||||||
\(303\) | 594.232 | 0.112666 | ||||||||
\(304\) | −2029.89 | −0.382967 | ||||||||
\(305\) | −445.842 | −0.0837010 | ||||||||
\(306\) | −526.712 | −0.0983992 | ||||||||
\(307\) | 3679.11 | 0.683968 | 0.341984 | − | 0.939706i | \(-0.388901\pi\) | ||||
0.341984 | + | 0.939706i | \(0.388901\pi\) | |||||||
\(308\) | 1939.47 | 0.358803 | ||||||||
\(309\) | 2249.96 | 0.414226 | ||||||||
\(310\) | −12.4118 | −0.00227401 | ||||||||
\(311\) | −8590.95 | −1.56639 | −0.783196 | − | 0.621775i | \(-0.786412\pi\) | ||||
−0.783196 | + | 0.621775i | \(0.786412\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8092.74 | −1.46143 | −0.730717 | − | 0.682681i | \(-0.760814\pi\) | ||||
−0.730717 | + | 0.682681i | \(0.760814\pi\) | |||||||
\(314\) | 488.519 | 0.0877985 | ||||||||
\(315\) | −348.341 | −0.0623073 | ||||||||
\(316\) | −352.476 | −0.0627478 | ||||||||
\(317\) | 6112.44 | 1.08299 | 0.541496 | − | 0.840703i | \(-0.317858\pi\) | ||||
0.541496 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(318\) | 554.059 | 0.0977046 | ||||||||
\(319\) | −217.357 | −0.0381494 | ||||||||
\(320\) | 231.746 | 0.0404843 | ||||||||
\(321\) | 598.635 | 0.104089 | ||||||||
\(322\) | 1814.86 | 0.314094 | ||||||||
\(323\) | 1315.50 | 0.226614 | ||||||||
\(324\) | −3384.29 | −0.580296 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 362.824 | 0.0616409 | ||||||||
\(327\) | −2561.70 | −0.433219 | ||||||||
\(328\) | 808.502 | 0.136104 | ||||||||
\(329\) | −4231.40 | −0.709072 | ||||||||
\(330\) | −8.66853 | −0.00144602 | ||||||||
\(331\) | −200.492 | −0.0332931 | −0.0166466 | − | 0.999861i | \(-0.505299\pi\) | ||||
−0.0166466 | + | 0.999861i | \(0.505299\pi\) | |||||||
\(332\) | −3949.30 | −0.652849 | ||||||||
\(333\) | −4516.02 | −0.743172 | ||||||||
\(334\) | 1119.80 | 0.183451 | ||||||||
\(335\) | 233.826 | 0.0381352 | ||||||||
\(336\) | 2413.41 | 0.391853 | ||||||||
\(337\) | 7750.18 | 1.25276 | 0.626379 | − | 0.779519i | \(-0.284536\pi\) | ||||
0.626379 | + | 0.779519i | \(0.284536\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2329.57 | −0.373229 | ||||||||
\(340\) | −171.537 | −0.0273614 | ||||||||
\(341\) | −331.432 | −0.0526335 | ||||||||
\(342\) | −559.556 | −0.0884718 | ||||||||
\(343\) | 3396.57 | 0.534686 | ||||||||
\(344\) | 1967.00 | 0.308295 | ||||||||
\(345\) | 149.680 | 0.0233580 | ||||||||
\(346\) | 37.7879 | 0.00587135 | ||||||||
\(347\) | −2636.26 | −0.407844 | −0.203922 | − | 0.978987i | \(-0.565369\pi\) | ||||
−0.203922 | + | 0.978987i | \(0.565369\pi\) | |||||||
\(348\) | −286.861 | −0.0441878 | ||||||||
\(349\) | −1218.52 | −0.186893 | −0.0934466 | − | 0.995624i | \(-0.529788\pi\) | ||||
−0.0934466 | + | 0.995624i | \(0.529788\pi\) | |||||||
\(350\) | −1856.31 | −0.283497 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1262.77 | −0.191209 | ||||||||
\(353\) | 7942.50 | 1.19755 | 0.598777 | − | 0.800916i | \(-0.295654\pi\) | ||||
0.598777 | + | 0.800916i | \(0.295654\pi\) | |||||||
\(354\) | −331.670 | −0.0497968 | ||||||||
\(355\) | −496.503 | −0.0742300 | ||||||||
\(356\) | 2995.95 | 0.446026 | ||||||||
\(357\) | −1564.05 | −0.231872 | ||||||||
\(358\) | −279.961 | −0.0413307 | ||||||||
\(359\) | −8507.63 | −1.25074 | −0.625370 | − | 0.780328i | \(-0.715052\pi\) | ||||
−0.625370 | + | 0.780328i | \(0.715052\pi\) | |||||||
\(360\) | 149.883 | 0.0219431 | ||||||||
\(361\) | −5461.47 | −0.796249 | ||||||||
\(362\) | −290.742 | −0.0422129 | ||||||||
\(363\) | −231.476 | −0.0334692 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 103.168 | 0.0147947 | ||||||||
\(366\) | 851.490 | 0.121607 | ||||||||
\(367\) | 9323.72 | 1.32614 | 0.663071 | − | 0.748557i | \(-0.269253\pi\) | ||||
0.663071 | + | 0.748557i | \(0.269253\pi\) | |||||||
\(368\) | 6613.91 | 0.936886 | ||||||||
\(369\) | −1887.65 | −0.266307 | ||||||||
\(370\) | 79.7042 | 0.0111990 | ||||||||
\(371\) | −10493.0 | −1.46838 | ||||||||
\(372\) | −437.412 | −0.0609644 | ||||||||
\(373\) | 10712.5 | 1.48705 | 0.743526 | − | 0.668707i | \(-0.233152\pi\) | ||||
0.743526 | + | 0.668707i | \(0.233152\pi\) | |||||||
\(374\) | 248.233 | 0.0343203 | ||||||||
\(375\) | −306.704 | −0.0422350 | ||||||||
\(376\) | 1820.67 | 0.249718 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1434.87 | 0.195242 | ||||||||
\(379\) | −7598.29 | −1.02981 | −0.514905 | − | 0.857247i | \(-0.672173\pi\) | ||||
−0.514905 | + | 0.857247i | \(0.672173\pi\) | |||||||
\(380\) | −182.233 | −0.0246010 | ||||||||
\(381\) | 3049.80 | 0.410094 | ||||||||
\(382\) | 1242.49 | 0.166417 | ||||||||
\(383\) | −6189.02 | −0.825703 | −0.412851 | − | 0.910798i | \(-0.635467\pi\) | ||||
−0.412851 | + | 0.910798i | \(0.635467\pi\) | |||||||
\(384\) | −2199.47 | −0.292295 | ||||||||
\(385\) | 164.168 | 0.0217319 | ||||||||
\(386\) | −1040.79 | −0.137240 | ||||||||
\(387\) | −4592.45 | −0.603223 | ||||||||
\(388\) | −131.262 | −0.0171748 | ||||||||
\(389\) | −6579.48 | −0.857566 | −0.428783 | − | 0.903408i | \(-0.641057\pi\) | ||||
−0.428783 | + | 0.903408i | \(0.641057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4286.25 | −0.554386 | ||||||||
\(392\) | 1967.49 | 0.253503 | ||||||||
\(393\) | 5027.07 | 0.645247 | ||||||||
\(394\) | −1758.53 | −0.224857 | ||||||||
\(395\) | −29.8357 | −0.00380050 | ||||||||
\(396\) | 1948.36 | 0.247245 | ||||||||
\(397\) | −1423.19 | −0.179920 | −0.0899598 | − | 0.995945i | \(-0.528674\pi\) | ||||
−0.0899598 | + | 0.995945i | \(0.528674\pi\) | |||||||
\(398\) | 2732.64 | 0.344158 | ||||||||
\(399\) | −1661.58 | −0.208478 | ||||||||
\(400\) | −6764.97 | −0.845621 | ||||||||
\(401\) | 12569.6 | 1.56532 | 0.782661 | − | 0.622448i | \(-0.213862\pi\) | ||||
0.782661 | + | 0.622448i | \(0.213862\pi\) | |||||||
\(402\) | −446.573 | −0.0554055 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2357.25 | 0.290292 | ||||||||
\(405\) | −286.467 | −0.0351473 | ||||||||
\(406\) | −294.413 | −0.0359889 | ||||||||
\(407\) | 2128.34 | 0.259209 | ||||||||
\(408\) | 672.972 | 0.0816595 | ||||||||
\(409\) | −13436.8 | −1.62447 | −0.812236 | − | 0.583329i | \(-0.801750\pi\) | ||||
−0.812236 | + | 0.583329i | \(0.801750\pi\) | |||||||
\(410\) | 33.3155 | 0.00401302 | ||||||||
\(411\) | 5801.80 | 0.696306 | ||||||||
\(412\) | 8925.36 | 1.06728 | ||||||||
\(413\) | 6281.31 | 0.748385 | ||||||||
\(414\) | 1823.18 | 0.216436 | ||||||||
\(415\) | −334.292 | −0.0395416 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3225.24 | −0.378755 | ||||||||
\(418\) | 263.712 | 0.0308578 | ||||||||
\(419\) | 13701.6 | 1.59754 | 0.798769 | − | 0.601638i | \(-0.205485\pi\) | ||||
0.798769 | + | 0.601638i | \(0.205485\pi\) | |||||||
\(420\) | 216.664 | 0.0251717 | ||||||||
\(421\) | 6376.59 | 0.738186 | 0.369093 | − | 0.929393i | \(-0.379668\pi\) | ||||
0.369093 | + | 0.929393i | \(0.379668\pi\) | |||||||
\(422\) | 8.72255 | 0.00100618 | ||||||||
\(423\) | −4250.81 | −0.488608 | ||||||||
\(424\) | 4514.89 | 0.517128 | ||||||||
\(425\) | 4384.14 | 0.500381 | ||||||||
\(426\) | 948.245 | 0.107847 | ||||||||
\(427\) | −16125.9 | −1.82760 | ||||||||
\(428\) | 2374.72 | 0.268192 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 81.0531 | 0.00909007 | ||||||||
\(431\) | −7396.12 | −0.826586 | −0.413293 | − | 0.910598i | \(-0.635621\pi\) | ||||
−0.413293 | + | 0.910598i | \(0.635621\pi\) | |||||||
\(432\) | 5229.11 | 0.582374 | ||||||||
\(433\) | −8609.35 | −0.955518 | −0.477759 | − | 0.878491i | \(-0.658551\pi\) | ||||
−0.477759 | + | 0.878491i | \(0.658551\pi\) | |||||||
\(434\) | −448.929 | −0.0496527 | ||||||||
\(435\) | −24.2816 | −0.00267636 | ||||||||
\(436\) | −10162.0 | −1.11622 | ||||||||
\(437\) | −4553.52 | −0.498454 | ||||||||
\(438\) | −197.035 | −0.0214948 | ||||||||
\(439\) | 13835.1 | 1.50413 | 0.752067 | − | 0.659086i | \(-0.229057\pi\) | ||||
0.752067 | + | 0.659086i | \(0.229057\pi\) | |||||||
\(440\) | −70.6377 | −0.00765346 | ||||||||
\(441\) | −4593.60 | −0.496015 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1210.42 | −0.129816 | −0.0649082 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649082 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(444\) | 2808.91 | 0.300236 | ||||||||
\(445\) | 253.596 | 0.0270148 | ||||||||
\(446\) | −3170.96 | −0.336658 | ||||||||
\(447\) | −3085.37 | −0.326472 | ||||||||
\(448\) | 8382.14 | 0.883970 | ||||||||
\(449\) | −8956.87 | −0.941427 | −0.470713 | − | 0.882286i | \(-0.656003\pi\) | ||||
−0.470713 | + | 0.882286i | \(0.656003\pi\) | |||||||
\(450\) | −1864.82 | −0.195352 | ||||||||
\(451\) | 889.624 | 0.0928842 | ||||||||
\(452\) | −9241.13 | −0.961651 | ||||||||
\(453\) | −5164.74 | −0.535675 | ||||||||
\(454\) | 627.496 | 0.0648675 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 714.936 | 0.0734209 | ||||||||
\(457\) | −5215.31 | −0.533834 | −0.266917 | − | 0.963720i | \(-0.586005\pi\) | ||||
−0.266917 | + | 0.963720i | \(0.586005\pi\) | |||||||
\(458\) | −2958.93 | −0.301881 | ||||||||
\(459\) | −3388.80 | −0.344609 | ||||||||
\(460\) | 593.764 | 0.0601834 | ||||||||
\(461\) | 307.230 | 0.0310393 | 0.0155197 | − | 0.999880i | \(-0.495060\pi\) | ||||
0.0155197 | + | 0.999880i | \(0.495060\pi\) | |||||||
\(462\) | −313.537 | −0.0315737 | ||||||||
\(463\) | 12781.2 | 1.28292 | 0.641461 | − | 0.767156i | \(-0.278329\pi\) | ||||
0.641461 | + | 0.767156i | \(0.278329\pi\) | |||||||
\(464\) | −1072.93 | −0.107349 | ||||||||
\(465\) | −37.0252 | −0.00369248 | ||||||||
\(466\) | 2109.27 | 0.209678 | ||||||||
\(467\) | 3416.13 | 0.338500 | 0.169250 | − | 0.985573i | \(-0.445865\pi\) | ||||
0.169250 | + | 0.985573i | \(0.445865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8457.39 | 0.832678 | ||||||||
\(470\) | 75.0234 | 0.00736292 | ||||||||
\(471\) | 1457.29 | 0.142565 | ||||||||
\(472\) | −2702.70 | −0.263563 | ||||||||
\(473\) | 2164.36 | 0.210396 | ||||||||
\(474\) | 56.9816 | 0.00552163 | ||||||||
\(475\) | 4657.52 | 0.449898 | ||||||||
\(476\) | −6204.41 | −0.597434 | ||||||||
\(477\) | −10541.1 | −1.01184 | ||||||||
\(478\) | 973.280 | 0.0931314 | ||||||||
\(479\) | 10912.7 | 1.04094 | 0.520472 | − | 0.853879i | \(-0.325756\pi\) | ||||
0.520472 | + | 0.853879i | \(0.325756\pi\) | |||||||
\(480\) | −141.068 | −0.0134142 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1423.54 | 0.134524 | ||||||||
\(483\) | 5413.86 | 0.510019 | ||||||||
\(484\) | −918.238 | −0.0862357 | ||||||||
\(485\) | −11.1108 | −0.00104024 | ||||||||
\(486\) | 2214.57 | 0.206697 | ||||||||
\(487\) | 11010.1 | 1.02447 | 0.512234 | − | 0.858846i | \(-0.328818\pi\) | ||||
0.512234 | + | 0.858846i | \(0.328818\pi\) | |||||||
\(488\) | 6938.58 | 0.643637 | ||||||||
\(489\) | 1082.33 | 0.100091 | ||||||||
\(490\) | 81.0734 | 0.00747453 | ||||||||
\(491\) | 11064.5 | 1.01698 | 0.508488 | − | 0.861069i | \(-0.330205\pi\) | ||||
0.508488 | + | 0.861069i | \(0.330205\pi\) | |||||||
\(492\) | 1174.10 | 0.107586 | ||||||||
\(493\) | 695.331 | 0.0635216 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 164.921 | 0.0149751 | ||||||||
\(496\) | −1636.04 | −0.148105 | ||||||||
\(497\) | −17958.3 | −1.62080 | ||||||||
\(498\) | 638.448 | 0.0574488 | ||||||||
\(499\) | −3107.21 | −0.278754 | −0.139377 | − | 0.990239i | \(-0.544510\pi\) | ||||
−0.139377 | + | 0.990239i | \(0.544510\pi\) | |||||||
\(500\) | −1216.66 | −0.108821 | ||||||||
\(501\) | 3340.45 | 0.297884 | ||||||||
\(502\) | 2440.70 | 0.217000 | ||||||||
\(503\) | −10479.9 | −0.928973 | −0.464487 | − | 0.885580i | \(-0.653761\pi\) | ||||
−0.464487 | + | 0.885580i | \(0.653761\pi\) | |||||||
\(504\) | 5421.19 | 0.479125 | ||||||||
\(505\) | 199.532 | 0.0175823 | ||||||||
\(506\) | −859.242 | −0.0754900 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12098.2 | 1.05664 | ||||||||
\(509\) | −3034.10 | −0.264213 | −0.132106 | − | 0.991236i | \(-0.542174\pi\) | ||||
−0.132106 | + | 0.991236i | \(0.542174\pi\) | |||||||
\(510\) | 27.7308 | 0.00240773 | ||||||||
\(511\) | 3731.54 | 0.323040 | ||||||||
\(512\) | −10576.0 | −0.912882 | ||||||||
\(513\) | −3600.12 | −0.309842 | ||||||||
\(514\) | 3198.46 | 0.274471 | ||||||||
\(515\) | 755.497 | 0.0646431 | ||||||||
\(516\) | 2856.45 | 0.243698 | ||||||||
\(517\) | 2003.35 | 0.170420 | ||||||||
\(518\) | 2882.87 | 0.244529 | ||||||||
\(519\) | 112.724 | 0.00953378 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11635.9 | −0.978462 | −0.489231 | − | 0.872154i | \(-0.662723\pi\) | ||||
−0.489231 | + | 0.872154i | \(0.662723\pi\) | |||||||
\(522\) | −295.764 | −0.0247993 | ||||||||
\(523\) | 23580.2 | 1.97149 | 0.985744 | − | 0.168253i | \(-0.0538125\pi\) | ||||
0.985744 | + | 0.168253i | \(0.0538125\pi\) | |||||||
\(524\) | 19941.8 | 1.66253 | ||||||||
\(525\) | −5537.50 | −0.460336 | ||||||||
\(526\) | 705.265 | 0.0584620 | ||||||||
\(527\) | 1060.26 | 0.0876386 | ||||||||
\(528\) | −1142.63 | −0.0941788 | ||||||||
\(529\) | 2669.57 | 0.219411 | ||||||||
\(530\) | 186.043 | 0.0152475 | ||||||||
\(531\) | 6310.12 | 0.515699 | ||||||||
\(532\) | −6591.29 | −0.537159 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −484.330 | −0.0392490 | ||||||||
\(535\) | 201.011 | 0.0162438 | ||||||||
\(536\) | −3639.01 | −0.293249 | ||||||||
\(537\) | −835.144 | −0.0671120 | ||||||||
\(538\) | −3040.05 | −0.243617 | ||||||||
\(539\) | 2164.90 | 0.173003 | ||||||||
\(540\) | 469.443 | 0.0374104 | ||||||||
\(541\) | −3474.82 | −0.276145 | −0.138072 | − | 0.990422i | \(-0.544091\pi\) | ||||
−0.138072 | + | 0.990422i | \(0.544091\pi\) | |||||||
\(542\) | −4814.64 | −0.381562 | ||||||||
\(543\) | −867.305 | −0.0685444 | ||||||||
\(544\) | 4039.62 | 0.318378 | ||||||||
\(545\) | −860.173 | −0.0676069 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 614.529 | 0.0480354 | 0.0240177 | − | 0.999712i | \(-0.492354\pi\) | ||||
0.0240177 | + | 0.999712i | \(0.492354\pi\) | |||||||
\(548\) | 23015.1 | 1.79408 | ||||||||
\(549\) | −16199.9 | −1.25937 | ||||||||
\(550\) | 878.866 | 0.0681363 | ||||||||
\(551\) | 738.689 | 0.0571129 | ||||||||
\(552\) | −2329.45 | −0.179616 | ||||||||
\(553\) | −1079.14 | −0.0829835 | ||||||||
\(554\) | 5274.36 | 0.404488 | ||||||||
\(555\) | 237.763 | 0.0181847 | ||||||||
\(556\) | −12794.2 | −0.975889 | ||||||||
\(557\) | 14685.3 | 1.11712 | 0.558561 | − | 0.829463i | \(-0.311354\pi\) | ||||
0.558561 | + | 0.829463i | \(0.311354\pi\) | |||||||
\(558\) | −450.988 | −0.0342147 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 810.380 | 0.0611515 | ||||||||
\(561\) | 740.496 | 0.0557286 | ||||||||
\(562\) | −240.258 | −0.0180332 | ||||||||
\(563\) | −13189.3 | −0.987326 | −0.493663 | − | 0.869653i | \(-0.664342\pi\) | ||||
−0.493663 | + | 0.869653i | \(0.664342\pi\) | |||||||
\(564\) | 2643.95 | 0.197394 | ||||||||
\(565\) | −782.226 | −0.0582451 | ||||||||
\(566\) | 4197.52 | 0.311722 | ||||||||
\(567\) | −10361.4 | −0.767437 | ||||||||
\(568\) | 7727.02 | 0.570807 | ||||||||
\(569\) | −2606.91 | −0.192069 | −0.0960346 | − | 0.995378i | \(-0.530616\pi\) | ||||
−0.0960346 | + | 0.995378i | \(0.530616\pi\) | |||||||
\(570\) | 29.4600 | 0.00216481 | ||||||||
\(571\) | 12777.9 | 0.936496 | 0.468248 | − | 0.883597i | \(-0.344885\pi\) | ||||
0.468248 | + | 0.883597i | \(0.344885\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3706.44 | 0.270225 | ||||||||
\(574\) | 1205.01 | 0.0876238 | ||||||||
\(575\) | −15175.4 | −1.10062 | ||||||||
\(576\) | 8420.58 | 0.609128 | ||||||||
\(577\) | −19155.7 | −1.38208 | −0.691040 | − | 0.722816i | \(-0.742847\pi\) | ||||
−0.691040 | + | 0.722816i | \(0.742847\pi\) | |||||||
\(578\) | 2356.57 | 0.169585 | ||||||||
\(579\) | −3104.75 | −0.222848 | ||||||||
\(580\) | −96.3226 | −0.00689582 | ||||||||
\(581\) | −12091.2 | −0.863387 | ||||||||
\(582\) | 21.2199 | 0.00151133 | ||||||||
\(583\) | 4967.90 | 0.352915 | ||||||||
\(584\) | −1605.59 | −0.113767 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5919.96 | 0.417323 | ||||||||
\(587\) | −15737.9 | −1.10660 | −0.553300 | − | 0.832982i | \(-0.686632\pi\) | ||||
−0.553300 | + | 0.832982i | \(0.686632\pi\) | |||||||
\(588\) | 2857.16 | 0.200387 | ||||||||
\(589\) | 1126.37 | 0.0787968 | ||||||||
\(590\) | −111.369 | −0.00777115 | ||||||||
\(591\) | −5245.82 | −0.365117 | ||||||||
\(592\) | 10506.1 | 0.729386 | ||||||||
\(593\) | −20361.6 | −1.41004 | −0.705018 | − | 0.709189i | \(-0.749061\pi\) | ||||
−0.705018 | + | 0.709189i | \(0.749061\pi\) | |||||||
\(594\) | −679.336 | −0.0469251 | ||||||||
\(595\) | −525.179 | −0.0361853 | ||||||||
\(596\) | −12239.3 | −0.841178 | ||||||||
\(597\) | 8151.66 | 0.558836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10727.2 | 0.731723 | 0.365862 | − | 0.930669i | \(-0.380774\pi\) | ||||
0.365862 | + | 0.930669i | \(0.380774\pi\) | |||||||
\(600\) | 2382.65 | 0.162119 | ||||||||
\(601\) | −24952.4 | −1.69356 | −0.846780 | − | 0.531943i | \(-0.821462\pi\) | ||||
−0.846780 | + | 0.531943i | \(0.821462\pi\) | |||||||
\(602\) | 2931.66 | 0.198481 | ||||||||
\(603\) | 8496.18 | 0.573783 | ||||||||
\(604\) | −20488.0 | −1.38021 | ||||||||
\(605\) | −77.7253 | −0.00522311 | ||||||||
\(606\) | −381.076 | −0.0255448 | ||||||||
\(607\) | 6389.25 | 0.427235 | 0.213617 | − | 0.976917i | \(-0.431475\pi\) | ||||
0.213617 | + | 0.976917i | \(0.431475\pi\) | |||||||
\(608\) | 4291.52 | 0.286257 | ||||||||
\(609\) | −878.256 | −0.0584380 | ||||||||
\(610\) | 285.915 | 0.0189776 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6232.86 | −0.411681 | ||||||||
\(613\) | 2053.42 | 0.135297 | 0.0676483 | − | 0.997709i | \(-0.478450\pi\) | ||||
0.0676483 | + | 0.997709i | \(0.478450\pi\) | |||||||
\(614\) | −2359.39 | −0.155077 | ||||||||
\(615\) | 99.3827 | 0.00651625 | ||||||||
\(616\) | −2554.94 | −0.167112 | ||||||||
\(617\) | 10442.3 | 0.681350 | 0.340675 | − | 0.940181i | \(-0.389344\pi\) | ||||
0.340675 | + | 0.940181i | \(0.389344\pi\) | |||||||
\(618\) | −1442.88 | −0.0939180 | ||||||||
\(619\) | 9436.66 | 0.612749 | 0.306374 | − | 0.951911i | \(-0.400884\pi\) | ||||
0.306374 | + | 0.951911i | \(0.400884\pi\) | |||||||
\(620\) | −146.875 | −0.00951394 | ||||||||
\(621\) | 11730.1 | 0.757993 | ||||||||
\(622\) | 5509.31 | 0.355150 | ||||||||
\(623\) | 9172.45 | 0.589866 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15470.4 | 0.990108 | ||||||||
\(626\) | 5189.81 | 0.331352 | ||||||||
\(627\) | 786.670 | 0.0501062 | ||||||||
\(628\) | 5780.90 | 0.367330 | ||||||||
\(629\) | −6808.61 | −0.431601 | ||||||||
\(630\) | 223.388 | 0.0141270 | ||||||||
\(631\) | 14355.2 | 0.905663 | 0.452831 | − | 0.891596i | \(-0.350414\pi\) | ||||
0.452831 | + | 0.891596i | \(0.350414\pi\) | |||||||
\(632\) | 464.330 | 0.0292247 | ||||||||
\(633\) | 26.0200 | 0.00163381 | ||||||||
\(634\) | −3919.86 | −0.245548 | ||||||||
\(635\) | 1024.07 | 0.0639982 | ||||||||
\(636\) | 6556.46 | 0.408775 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 139.389 | 0.00864966 | ||||||||
\(639\) | −18040.7 | −1.11687 | ||||||||
\(640\) | −738.543 | −0.0456148 | ||||||||
\(641\) | −4003.79 | −0.246709 | −0.123354 | − | 0.992363i | \(-0.539365\pi\) | ||||
−0.123354 | + | 0.992363i | \(0.539365\pi\) | |||||||
\(642\) | −383.900 | −0.0236002 | ||||||||
\(643\) | 21342.9 | 1.30899 | 0.654497 | − | 0.756064i | \(-0.272880\pi\) | ||||
0.654497 | + | 0.756064i | \(0.272880\pi\) | |||||||
\(644\) | 21476.2 | 1.31410 | ||||||||
\(645\) | 241.787 | 0.0147603 | ||||||||
\(646\) | −843.620 | −0.0513805 | ||||||||
\(647\) | −11010.9 | −0.669063 | −0.334531 | − | 0.942385i | \(-0.608578\pi\) | ||||
−0.334531 | + | 0.942385i | \(0.608578\pi\) | |||||||
\(648\) | 4458.25 | 0.270273 | ||||||||
\(649\) | −2973.88 | −0.179869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1339.19 | −0.0806250 | ||||||||
\(652\) | 4293.48 | 0.257892 | ||||||||
\(653\) | −3056.38 | −0.183163 | −0.0915815 | − | 0.995798i | \(-0.529192\pi\) | ||||
−0.0915815 | + | 0.995798i | \(0.529192\pi\) | |||||||
\(654\) | 1642.80 | 0.0982241 | ||||||||
\(655\) | 1688.00 | 0.100696 | ||||||||
\(656\) | 4391.43 | 0.261367 | ||||||||
\(657\) | 3748.65 | 0.222601 | ||||||||
\(658\) | 2713.56 | 0.160769 | ||||||||
\(659\) | −3838.61 | −0.226906 | −0.113453 | − | 0.993543i | \(-0.536191\pi\) | ||||
−0.113453 | + | 0.993543i | \(0.536191\pi\) | |||||||
\(660\) | −102.579 | −0.00604983 | ||||||||
\(661\) | −18941.5 | −1.11458 | −0.557290 | − | 0.830318i | \(-0.688159\pi\) | ||||
−0.557290 | + | 0.830318i | \(0.688159\pi\) | |||||||
\(662\) | 128.574 | 0.00754858 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5202.56 | 0.304064 | ||||||||
\(665\) | −557.927 | −0.0325346 | ||||||||
\(666\) | 2896.09 | 0.168500 | ||||||||
\(667\) | −2406.84 | −0.139720 | ||||||||
\(668\) | 13251.2 | 0.767520 | ||||||||
\(669\) | −9459.21 | −0.546658 | ||||||||
\(670\) | −149.951 | −0.00864643 | ||||||||
\(671\) | 7634.78 | 0.439251 | ||||||||
\(672\) | −5102.35 | −0.292898 | ||||||||
\(673\) | 5208.05 | 0.298300 | 0.149150 | − | 0.988815i | \(-0.452346\pi\) | ||||
0.149150 | + | 0.988815i | \(0.452346\pi\) | |||||||
\(674\) | −4970.13 | −0.284039 | ||||||||
\(675\) | −11998.0 | −0.684155 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15939.9 | −0.904905 | −0.452453 | − | 0.891788i | \(-0.649451\pi\) | ||||
−0.452453 | + | 0.891788i | \(0.649451\pi\) | |||||||
\(678\) | 1493.93 | 0.0846226 | ||||||||
\(679\) | −401.873 | −0.0227135 | ||||||||
\(680\) | 225.972 | 0.0127436 | ||||||||
\(681\) | 1871.87 | 0.105330 | ||||||||
\(682\) | 212.545 | 0.0119337 | ||||||||
\(683\) | 28757.2 | 1.61107 | 0.805537 | − | 0.592546i | \(-0.201877\pi\) | ||||
0.805537 | + | 0.592546i | \(0.201877\pi\) | |||||||
\(684\) | −6621.52 | −0.370146 | ||||||||
\(685\) | 1948.14 | 0.108664 | ||||||||
\(686\) | −2178.19 | −0.121230 | ||||||||
\(687\) | −8826.69 | −0.490188 | ||||||||
\(688\) | 10683.9 | 0.592033 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −95.9885 | −0.00529597 | ||||||||
\(691\) | −4884.96 | −0.268933 | −0.134466 | − | 0.990918i | \(-0.542932\pi\) | ||||
−0.134466 | + | 0.990918i | \(0.542932\pi\) | |||||||
\(692\) | 447.163 | 0.0245645 | ||||||||
\(693\) | 5965.13 | 0.326979 | ||||||||
\(694\) | 1690.61 | 0.0924709 | ||||||||
\(695\) | −1082.98 | −0.0591075 | ||||||||
\(696\) | 377.892 | 0.0205804 | ||||||||
\(697\) | −2845.93 | −0.154659 | ||||||||
\(698\) | 781.425 | 0.0423745 | ||||||||
\(699\) | 6292.11 | 0.340471 | ||||||||
\(700\) | −21966.7 | −1.18609 | ||||||||
\(701\) | 35673.0 | 1.92204 | 0.961019 | − | 0.276481i | \(-0.0891682\pi\) | ||||
0.961019 | + | 0.276481i | \(0.0891682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7233.17 | −0.388057 | ||||||||
\(704\) | −3968.51 | −0.212456 | ||||||||
\(705\) | 223.800 | 0.0119558 | ||||||||
\(706\) | −5093.46 | −0.271523 | ||||||||
\(707\) | 7217.00 | 0.383908 | ||||||||
\(708\) | −3924.82 | −0.208339 | ||||||||
\(709\) | 7058.41 | 0.373885 | 0.186942 | − | 0.982371i | \(-0.440142\pi\) | ||||
0.186942 | + | 0.982371i | \(0.440142\pi\) | |||||||
\(710\) | 318.404 | 0.0168302 | ||||||||
\(711\) | −1084.09 | −0.0571824 | ||||||||
\(712\) | −3946.68 | −0.207736 | ||||||||
\(713\) | −3670.02 | −0.192767 | ||||||||
\(714\) | 1003.01 | 0.0525725 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3312.92 | −0.172919 | ||||||||
\(717\) | 2903.37 | 0.151225 | ||||||||
\(718\) | 5455.88 | 0.283582 | ||||||||
\(719\) | 20783.4 | 1.07801 | 0.539005 | − | 0.842302i | \(-0.318800\pi\) | ||||
0.539005 | + | 0.842302i | \(0.318800\pi\) | |||||||
\(720\) | 814.097 | 0.0421383 | ||||||||
\(721\) | 27326.0 | 1.41147 | ||||||||
\(722\) | 3502.40 | 0.180534 | ||||||||
\(723\) | 4246.53 | 0.218437 | ||||||||
\(724\) | −3440.50 | −0.176610 | ||||||||
\(725\) | 2461.81 | 0.126110 | ||||||||
\(726\) | 148.443 | 0.00758850 | ||||||||
\(727\) | 7296.24 | 0.372218 | 0.186109 | − | 0.982529i | \(-0.440412\pi\) | ||||
0.186109 | + | 0.982529i | \(0.440412\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5434.74 | −0.276113 | ||||||||
\(730\) | −66.1608 | −0.00335441 | ||||||||
\(731\) | −6923.84 | −0.350325 | ||||||||
\(732\) | 10076.1 | 0.508776 | ||||||||
\(733\) | 24021.0 | 1.21041 | 0.605207 | − | 0.796068i | \(-0.293090\pi\) | ||||
0.605207 | + | 0.796068i | \(0.293090\pi\) | |||||||
\(734\) | −5979.23 | −0.300677 | ||||||||
\(735\) | 241.848 | 0.0121370 | ||||||||
\(736\) | −13982.9 | −0.700295 | ||||||||
\(737\) | −4004.14 | −0.200128 | ||||||||
\(738\) | 1210.53 | 0.0603800 | ||||||||
\(739\) | −34721.3 | −1.72834 | −0.864171 | − | 0.503198i | \(-0.832157\pi\) | ||||
−0.864171 | + | 0.503198i | \(0.832157\pi\) | |||||||
\(740\) | 943.181 | 0.0468541 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6729.09 | 0.332928 | ||||||||
\(743\) | −25702.4 | −1.26909 | −0.634543 | − | 0.772887i | \(-0.718812\pi\) | ||||
−0.634543 | + | 0.772887i | \(0.718812\pi\) | |||||||
\(744\) | 576.220 | 0.0283941 | ||||||||
\(745\) | −1036.01 | −0.0509483 | ||||||||
\(746\) | −6869.82 | −0.337161 | ||||||||
\(747\) | −12146.7 | −0.594944 | ||||||||
\(748\) | 2937.47 | 0.143589 | ||||||||
\(749\) | 7270.47 | 0.354682 | ||||||||
\(750\) | 196.687 | 0.00957598 | ||||||||
\(751\) | −14220.7 | −0.690973 | −0.345486 | − | 0.938424i | \(-0.612286\pi\) | ||||
−0.345486 | + | 0.938424i | \(0.612286\pi\) | |||||||
\(752\) | 9889.08 | 0.479545 | ||||||||
\(753\) | 7280.79 | 0.352360 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1734.23 | −0.0835960 | ||||||||
\(756\) | 16979.5 | 0.816852 | ||||||||
\(757\) | −21078.6 | −1.01204 | −0.506020 | − | 0.862522i | \(-0.668884\pi\) | ||||
−0.506020 | + | 0.862522i | \(0.668884\pi\) | |||||||
\(758\) | 4872.72 | 0.233490 | ||||||||
\(759\) | −2563.18 | −0.122579 | ||||||||
\(760\) | 240.063 | 0.0114579 | ||||||||
\(761\) | −16736.1 | −0.797217 | −0.398608 | − | 0.917121i | \(-0.630507\pi\) | ||||
−0.398608 | + | 0.917121i | \(0.630507\pi\) | |||||||
\(762\) | −1955.81 | −0.0929811 | ||||||||
\(763\) | −31112.1 | −1.47619 | ||||||||
\(764\) | 14703.1 | 0.696254 | ||||||||
\(765\) | −527.588 | −0.0249346 | ||||||||
\(766\) | 3968.97 | 0.187212 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4110.83 | −0.193147 | ||||||||
\(769\) | −33100.3 | −1.55218 | −0.776092 | − | 0.630620i | \(-0.782801\pi\) | ||||
−0.776092 | + | 0.630620i | \(0.782801\pi\) | |||||||
\(770\) | −105.280 | −0.00492731 | ||||||||
\(771\) | 9541.25 | 0.445681 | ||||||||
\(772\) | −12316.2 | −0.574183 | ||||||||
\(773\) | −11960.8 | −0.556532 | −0.278266 | − | 0.960504i | \(-0.589760\pi\) | ||||
−0.278266 | + | 0.960504i | \(0.589760\pi\) | |||||||
\(774\) | 2945.10 | 0.136769 | ||||||||
\(775\) | 3753.84 | 0.173989 | ||||||||
\(776\) | 172.916 | 0.00799914 | ||||||||
\(777\) | 8599.79 | 0.397060 | ||||||||
\(778\) | 4219.37 | 0.194437 | ||||||||
\(779\) | −3023.39 | −0.139056 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8502.33 | 0.389548 | ||||||||
\(782\) | 2748.74 | 0.125696 | ||||||||
\(783\) | −1902.91 | −0.0868510 | ||||||||
\(784\) | 10686.5 | 0.486814 | ||||||||
\(785\) | 489.331 | 0.0222484 | ||||||||
\(786\) | −3223.82 | −0.146298 | ||||||||
\(787\) | 23486.2 | 1.06378 | 0.531888 | − | 0.846815i | \(-0.321483\pi\) | ||||
0.531888 | + | 0.846815i | \(0.321483\pi\) | |||||||
\(788\) | −20809.6 | −0.940750 | ||||||||
\(789\) | 2103.86 | 0.0949293 | ||||||||
\(790\) | 19.1334 | 0.000861691 0 | ||||||||
\(791\) | −28292.8 | −1.27178 | ||||||||
\(792\) | −2566.65 | −0.115154 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 912.683 | 0.0407934 | ||||||||
\(795\) | 554.979 | 0.0247586 | ||||||||
\(796\) | 32336.7 | 1.43988 | ||||||||
\(797\) | 15997.4 | 0.710987 | 0.355493 | − | 0.934679i | \(-0.384313\pi\) | ||||
0.355493 | + | 0.934679i | \(0.384313\pi\) | |||||||
\(798\) | 1065.56 | 0.0472685 | ||||||||
\(799\) | −6408.76 | −0.283762 | ||||||||
\(800\) | 14302.3 | 0.632077 | ||||||||
\(801\) | 9214.52 | 0.406466 | ||||||||
\(802\) | −8060.76 | −0.354907 | ||||||||
\(803\) | −1766.69 | −0.0776403 | ||||||||
\(804\) | −5284.53 | −0.231805 | ||||||||
\(805\) | 1817.87 | 0.0795921 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9068.70 | −0.395580 | ||||||||
\(808\) | −3105.30 | −0.135203 | ||||||||
\(809\) | 10407.2 | 0.452282 | 0.226141 | − | 0.974095i | \(-0.427389\pi\) | ||||
0.226141 | + | 0.974095i | \(0.427389\pi\) | |||||||
\(810\) | 183.709 | 0.00796898 | ||||||||
\(811\) | 34198.0 | 1.48071 | 0.740355 | − | 0.672216i | \(-0.234657\pi\) | ||||
0.740355 | + | 0.672216i | \(0.234657\pi\) | |||||||
\(812\) | −3483.95 | −0.150570 | ||||||||
\(813\) | −14362.4 | −0.619572 | ||||||||
\(814\) | −1364.89 | −0.0587706 | ||||||||
\(815\) | 363.427 | 0.0156200 | ||||||||
\(816\) | 3655.29 | 0.156815 | ||||||||
\(817\) | −7355.59 | −0.314981 | ||||||||
\(818\) | 8616.94 | 0.368318 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 394.240 | 0.0167896 | ||||||||
\(821\) | 13645.8 | 0.580075 | 0.290038 | − | 0.957015i | \(-0.406332\pi\) | ||||
0.290038 | + | 0.957015i | \(0.406332\pi\) | |||||||
\(822\) | −3720.65 | −0.157874 | ||||||||
\(823\) | 3660.62 | 0.155044 | 0.0775220 | − | 0.996991i | \(-0.475299\pi\) | ||||
0.0775220 | + | 0.996991i | \(0.475299\pi\) | |||||||
\(824\) | −11757.7 | −0.497087 | ||||||||
\(825\) | 2621.72 | 0.110638 | ||||||||
\(826\) | −4028.16 | −0.169682 | ||||||||
\(827\) | −13815.9 | −0.580927 | −0.290463 | − | 0.956886i | \(-0.593809\pi\) | ||||
−0.290463 | + | 0.956886i | \(0.593809\pi\) | |||||||
\(828\) | 21574.7 | 0.905521 | ||||||||
\(829\) | 21839.6 | 0.914985 | 0.457492 | − | 0.889214i | \(-0.348748\pi\) | ||||
0.457492 | + | 0.889214i | \(0.348748\pi\) | |||||||
\(830\) | 214.379 | 0.00896531 | ||||||||
\(831\) | 15733.8 | 0.656798 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6925.57 | −0.288063 | ||||||||
\(834\) | 2068.32 | 0.0858755 | ||||||||
\(835\) | 1121.66 | 0.0464870 | ||||||||
\(836\) | 3120.64 | 0.129102 | ||||||||
\(837\) | −2901.60 | −0.119825 | ||||||||
\(838\) | −8786.75 | −0.362211 | ||||||||
\(839\) | 3940.06 | 0.162129 | 0.0810643 | − | 0.996709i | \(-0.474168\pi\) | ||||
0.0810643 | + | 0.996709i | \(0.474168\pi\) | |||||||
\(840\) | −285.420 | −0.0117237 | ||||||||
\(841\) | −23998.6 | −0.983991 | ||||||||
\(842\) | −4089.26 | −0.167370 | ||||||||
\(843\) | −716.707 | −0.0292820 | ||||||||
\(844\) | 103.218 | 0.00420963 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2726.01 | 0.110783 | ||||||||
\(847\) | −2811.29 | −0.114046 | ||||||||
\(848\) | 24522.9 | 0.993066 | ||||||||
\(849\) | 12521.5 | 0.506168 | ||||||||
\(850\) | −2811.51 | −0.113452 | ||||||||
\(851\) | 23567.6 | 0.949338 | ||||||||
\(852\) | 11221.1 | 0.451206 | ||||||||
\(853\) | −8929.29 | −0.358421 | −0.179211 | − | 0.983811i | \(-0.557354\pi\) | ||||
−0.179211 | + | 0.983811i | \(0.557354\pi\) | |||||||
\(854\) | 10341.4 | 0.414374 | ||||||||
\(855\) | −560.486 | −0.0224190 | ||||||||
\(856\) | −3128.31 | −0.124910 | ||||||||
\(857\) | 6873.94 | 0.273990 | 0.136995 | − | 0.990572i | \(-0.456256\pi\) | ||||
0.136995 | + | 0.990572i | \(0.456256\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11987.7 | 0.476153 | 0.238077 | − | 0.971246i | \(-0.423483\pi\) | ||||
0.238077 | + | 0.971246i | \(0.423483\pi\) | |||||||
\(860\) | 959.144 | 0.0380308 | ||||||||
\(861\) | 3594.63 | 0.142282 | ||||||||
\(862\) | 4743.08 | 0.187413 | ||||||||
\(863\) | −440.273 | −0.0173662 | −0.00868312 | − | 0.999962i | \(-0.502764\pi\) | ||||
−0.00868312 | + | 0.999962i | \(0.502764\pi\) | |||||||
\(864\) | −11055.2 | −0.435307 | ||||||||
\(865\) | 37.8506 | 0.00148782 | ||||||||
\(866\) | 5521.11 | 0.216645 | ||||||||
\(867\) | 7029.81 | 0.275369 | ||||||||
\(868\) | −5312.41 | −0.207736 | ||||||||
\(869\) | 510.919 | 0.0199445 | ||||||||
\(870\) | 15.5716 | 0.000606813 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 13386.8 | 0.519878 | ||||||||
\(873\) | −403.716 | −0.0156515 | ||||||||
\(874\) | 2920.14 | 0.113015 | ||||||||
\(875\) | −3724.94 | −0.143916 | ||||||||
\(876\) | −2331.62 | −0.0899293 | ||||||||
\(877\) | 46606.1 | 1.79450 | 0.897251 | − | 0.441521i | \(-0.145561\pi\) | ||||
0.897251 | + | 0.441521i | \(0.145561\pi\) | |||||||
\(878\) | −8872.37 | −0.341034 | ||||||||
\(879\) | 17659.7 | 0.677640 | ||||||||
\(880\) | −383.673 | −0.0146973 | ||||||||
\(881\) | 16735.5 | 0.639991 | 0.319996 | − | 0.947419i | \(-0.396319\pi\) | ||||
0.319996 | + | 0.947419i | \(0.396319\pi\) | |||||||
\(882\) | 2945.84 | 0.112462 | ||||||||
\(883\) | 31789.3 | 1.21155 | 0.605773 | − | 0.795637i | \(-0.292864\pi\) | ||||
0.605773 | + | 0.795637i | \(0.292864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −332.221 | −0.0126186 | ||||||||
\(886\) | 776.231 | 0.0294334 | ||||||||
\(887\) | −757.412 | −0.0286713 | −0.0143356 | − | 0.999897i | \(-0.504563\pi\) | ||||
−0.0143356 | + | 0.999897i | \(0.504563\pi\) | |||||||
\(888\) | −3700.28 | −0.139835 | ||||||||
\(889\) | 37040.1 | 1.39739 | ||||||||
\(890\) | −162.629 | −0.00612510 | ||||||||
\(891\) | 4905.58 | 0.184448 | ||||||||
\(892\) | −37523.6 | −1.40850 | ||||||||
\(893\) | −6808.39 | −0.255133 | ||||||||
\(894\) | 1978.62 | 0.0740213 | ||||||||
\(895\) | −280.426 | −0.0104733 | ||||||||
\(896\) | −26712.8 | −0.995994 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5743.97 | 0.213451 | ||||||||
\(899\) | 595.364 | 0.0220873 | ||||||||
\(900\) | −22067.4 | −0.817311 | ||||||||
\(901\) | −15892.4 | −0.587629 | ||||||||
\(902\) | −570.509 | −0.0210597 | ||||||||
\(903\) | 8745.34 | 0.322289 | ||||||||
\(904\) | 12173.7 | 0.447888 | ||||||||
\(905\) | −291.225 | −0.0106969 | ||||||||
\(906\) | 3312.11 | 0.121454 | ||||||||
\(907\) | −8676.53 | −0.317640 | −0.158820 | − | 0.987308i | \(-0.550769\pi\) | ||||
−0.158820 | + | 0.987308i | \(0.550769\pi\) | |||||||
\(908\) | 7425.49 | 0.271391 | ||||||||
\(909\) | 7250.10 | 0.264544 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34427.4 | 1.25206 | 0.626032 | − | 0.779797i | \(-0.284678\pi\) | ||||
0.626032 | + | 0.779797i | \(0.284678\pi\) | |||||||
\(912\) | 3883.22 | 0.140994 | ||||||||
\(913\) | 5724.56 | 0.207509 | ||||||||
\(914\) | 3344.54 | 0.121037 | ||||||||
\(915\) | 852.904 | 0.0308155 | ||||||||
\(916\) | −35014.5 | −1.26300 | ||||||||
\(917\) | 61054.2 | 2.19868 | ||||||||
\(918\) | 2173.21 | 0.0781337 | ||||||||
\(919\) | −28622.6 | −1.02739 | −0.513696 | − | 0.857972i | \(-0.671724\pi\) | ||||
−0.513696 | + | 0.857972i | \(0.671724\pi\) | |||||||
\(920\) | −782.187 | −0.0280304 | ||||||||
\(921\) | −7038.22 | −0.251810 | ||||||||
\(922\) | −197.024 | −0.00703757 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3710.24 | −0.132097 | ||||||||
\(925\) | −24105.8 | −0.856860 | ||||||||
\(926\) | −8196.48 | −0.290878 | ||||||||
\(927\) | 27451.3 | 0.972621 | ||||||||
\(928\) | 2268.36 | 0.0802398 | ||||||||
\(929\) | −24018.3 | −0.848240 | −0.424120 | − | 0.905606i | \(-0.639416\pi\) | ||||
−0.424120 | + | 0.905606i | \(0.639416\pi\) | |||||||
\(930\) | 23.7440 | 0.000837200 0 | ||||||||
\(931\) | −7357.42 | −0.259001 | ||||||||
\(932\) | 24960.1 | 0.877249 | ||||||||
\(933\) | 16434.7 | 0.576684 | ||||||||
\(934\) | −2190.74 | −0.0767485 | ||||||||
\(935\) | 248.645 | 0.00869686 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38501.7 | 1.34236 | 0.671182 | − | 0.741292i | \(-0.265787\pi\) | ||||
0.671182 | + | 0.741292i | \(0.265787\pi\) | |||||||
\(938\) | −5423.66 | −0.188794 | ||||||||
\(939\) | 15481.6 | 0.538043 | ||||||||
\(940\) | 887.791 | 0.0308048 | ||||||||
\(941\) | 54231.7 | 1.87875 | 0.939375 | − | 0.342890i | \(-0.111406\pi\) | ||||
0.939375 | + | 0.342890i | \(0.111406\pi\) | |||||||
\(942\) | −934.547 | −0.0323240 | ||||||||
\(943\) | 9851.01 | 0.340184 | ||||||||
\(944\) | −14679.9 | −0.506132 | ||||||||
\(945\) | 1437.25 | 0.0494749 | ||||||||
\(946\) | −1387.99 | −0.0477033 | ||||||||
\(947\) | 42375.7 | 1.45409 | 0.727046 | − | 0.686589i | \(-0.240893\pi\) | ||||
0.727046 | + | 0.686589i | \(0.240893\pi\) | |||||||
\(948\) | 674.293 | 0.0231013 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2986.83 | −0.102006 | ||||||||
\(951\) | −11693.2 | −0.398716 | ||||||||
\(952\) | 8173.30 | 0.278254 | ||||||||
\(953\) | −41712.9 | −1.41785 | −0.708927 | − | 0.705282i | \(-0.750820\pi\) | ||||
−0.708927 | + | 0.705282i | \(0.750820\pi\) | |||||||
\(954\) | 6759.95 | 0.229414 | ||||||||
\(955\) | 1244.56 | 0.0421706 | ||||||||
\(956\) | 11517.3 | 0.389641 | ||||||||
\(957\) | 415.809 | 0.0140451 | ||||||||
\(958\) | −6998.21 | −0.236014 | ||||||||
\(959\) | 70463.4 | 2.37266 | ||||||||
\(960\) | −443.334 | −0.0149047 | ||||||||
\(961\) | −28883.2 | −0.969527 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7303.81 | 0.244405 | ||||||||
\(964\) | 16845.5 | 0.562819 | ||||||||
\(965\) | −1042.52 | −0.0347770 | ||||||||
\(966\) | −3471.86 | −0.115637 | ||||||||
\(967\) | 865.994 | 0.0287988 | 0.0143994 | − | 0.999896i | \(-0.495416\pi\) | ||||
0.0143994 | + | 0.999896i | \(0.495416\pi\) | |||||||
\(968\) | 1209.63 | 0.0401642 | ||||||||
\(969\) | −2516.58 | −0.0834305 | ||||||||
\(970\) | 7.12527 | 0.000235854 0 | ||||||||
\(971\) | −55107.5 | −1.82130 | −0.910651 | − | 0.413175i | \(-0.864420\pi\) | ||||
−0.910651 | + | 0.413175i | \(0.864420\pi\) | |||||||
\(972\) | 26206.1 | 0.864776 | ||||||||
\(973\) | −39170.8 | −1.29061 | ||||||||
\(974\) | −7060.71 | −0.232279 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 37687.3 | 1.23601 | ||||||||
\(977\) | −22585.3 | −0.739579 | −0.369789 | − | 0.929116i | \(-0.620570\pi\) | ||||
−0.369789 | + | 0.929116i | \(0.620570\pi\) | |||||||
\(978\) | −694.089 | −0.0226938 | ||||||||
\(979\) | −4342.68 | −0.141770 | ||||||||
\(980\) | 959.383 | 0.0312718 | ||||||||
\(981\) | −31254.8 | −1.01722 | ||||||||
\(982\) | −7095.60 | −0.230580 | ||||||||
\(983\) | 10571.6 | 0.343013 | 0.171506 | − | 0.985183i | \(-0.445137\pi\) | ||||
0.171506 | + | 0.985183i | \(0.445137\pi\) | |||||||
\(984\) | −1546.68 | −0.0501081 | ||||||||
\(985\) | −1761.45 | −0.0569792 | ||||||||
\(986\) | −445.910 | −0.0144023 | ||||||||
\(987\) | 8094.76 | 0.261053 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23966.4 | 0.770565 | ||||||||
\(990\) | −105.763 | −0.00339532 | ||||||||
\(991\) | −13212.6 | −0.423523 | −0.211762 | − | 0.977321i | \(-0.567920\pi\) | ||||
−0.211762 | + | 0.977321i | \(0.567920\pi\) | |||||||
\(992\) | 3458.85 | 0.110704 | ||||||||
\(993\) | 383.545 | 0.0122572 | ||||||||
\(994\) | 11516.5 | 0.367487 | ||||||||
\(995\) | 2737.18 | 0.0872104 | ||||||||
\(996\) | 7555.08 | 0.240353 | ||||||||
\(997\) | −33543.8 | −1.06554 | −0.532770 | − | 0.846260i | \(-0.678849\pi\) | ||||
−0.532770 | + | 0.846260i | \(0.678849\pi\) | |||||||
\(998\) | 1992.63 | 0.0632021 | ||||||||
\(999\) | 18633.1 | 0.590114 |
(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 | 1859.4.a.n.1.18 | ✓ | 39 | |
13.12 | even | 2 | 1859.4.a.o.1.22 | yes | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.4.a.n.1.18 | ✓ | 39 | 1.1 | even | 1 | trivial | |
1859.4.a.o.1.22 | yes | 39 | 13.12 | even | 2 |