Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809520 | −0.572417 | −0.286208 | − | 0.958167i | \(-0.592395\pi\) | ||||
−0.286208 | + | 0.958167i | \(0.592395\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.34468 | −0.672339 | ||||||||
\(5\) | −2.87436 | −1.28545 | −0.642726 | − | 0.766096i | \(-0.722196\pi\) | ||||
−0.642726 | + | 0.766096i | \(0.722196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.883619 | 0.333977 | 0.166988 | − | 0.985959i | \(-0.446596\pi\) | ||||
0.166988 | + | 0.985959i | \(0.446596\pi\) | |||||||
\(8\) | 2.70758 | 0.957275 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.32685 | 0.735814 | ||||||||
\(11\) | −3.13012 | −0.943768 | −0.471884 | − | 0.881661i | \(-0.656426\pi\) | ||||
−0.471884 | + | 0.881661i | \(0.656426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.71846 | −1.03132 | −0.515658 | − | 0.856794i | \(-0.672453\pi\) | ||||
−0.515658 | + | 0.856794i | \(0.672453\pi\) | |||||||
\(14\) | −0.715307 | −0.191174 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.497513 | 0.124378 | ||||||||
\(17\) | 7.58717 | 1.84016 | 0.920079 | − | 0.391733i | \(-0.128124\pi\) | ||||
0.920079 | + | 0.391733i | \(0.128124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.80564 | 0.643658 | 0.321829 | − | 0.946798i | \(-0.395702\pi\) | ||||
0.321829 | + | 0.946798i | \(0.395702\pi\) | |||||||
\(20\) | 3.86508 | 0.864259 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.53390 | 0.540229 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.26192 | 0.652385 | ||||||||
\(26\) | 3.01017 | 0.590343 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.18818 | −0.224545 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.437909 | 0.0786508 | 0.0393254 | − | 0.999226i | \(-0.487479\pi\) | ||||
0.0393254 | + | 0.999226i | \(0.487479\pi\) | |||||||
\(32\) | −5.81791 | −1.02847 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.14196 | −1.05334 | ||||||||
\(35\) | −2.53984 | −0.429311 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.43453 | 1.22223 | 0.611115 | − | 0.791542i | \(-0.290721\pi\) | ||||
0.611115 | + | 0.791542i | \(0.290721\pi\) | |||||||
\(38\) | −2.27122 | −0.368441 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.78256 | −1.23053 | ||||||||
\(41\) | −6.99969 | −1.09317 | −0.546584 | − | 0.837404i | \(-0.684072\pi\) | ||||
−0.546584 | + | 0.837404i | \(0.684072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.35447 | −0.206555 | −0.103277 | − | 0.994653i | \(-0.532933\pi\) | ||||
−0.103277 | + | 0.994653i | \(0.532933\pi\) | |||||||
\(44\) | 4.20901 | 0.634532 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.809520 | −0.119357 | ||||||||
\(47\) | −8.71212 | −1.27079 | −0.635396 | − | 0.772186i | \(-0.719163\pi\) | ||||
−0.635396 | + | 0.772186i | \(0.719163\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.21922 | −0.888460 | ||||||||
\(50\) | −2.64059 | −0.373436 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.00013 | 0.693394 | ||||||||
\(53\) | −13.0730 | −1.79572 | −0.897860 | − | 0.440280i | \(-0.854879\pi\) | ||||
−0.897860 | + | 0.440280i | \(0.854879\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.99709 | 1.21317 | ||||||||
\(56\) | 2.39247 | 0.319708 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.809520 | 0.106295 | ||||||||
\(59\) | 1.55333 | 0.202227 | 0.101113 | − | 0.994875i | \(-0.467760\pi\) | ||||
0.101113 | + | 0.994875i | \(0.467760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.35753 | 0.557925 | 0.278962 | − | 0.960302i | \(-0.410010\pi\) | ||||
0.278962 | + | 0.960302i | \(0.410010\pi\) | |||||||
\(62\) | −0.354496 | −0.0450210 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.71469 | 0.464336 | ||||||||
\(65\) | 10.6882 | 1.32571 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.46860 | 0.790266 | 0.395133 | − | 0.918624i | \(-0.370699\pi\) | ||||
0.395133 | + | 0.918624i | \(0.370699\pi\) | |||||||
\(68\) | −10.2023 | −1.23721 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.05605 | 0.245745 | ||||||||
\(71\) | −13.8126 | −1.63925 | −0.819627 | − | 0.572897i | \(-0.805819\pi\) | ||||
−0.819627 | + | 0.572897i | \(0.805819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4979 | −1.22868 | −0.614342 | − | 0.789040i | \(-0.710578\pi\) | ||||
−0.614342 | + | 0.789040i | \(0.710578\pi\) | |||||||
\(74\) | −6.01840 | −0.699625 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.77268 | −0.432756 | ||||||||
\(77\) | −2.76584 | −0.315196 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.47449 | 0.503420 | 0.251710 | − | 0.967803i | \(-0.419007\pi\) | ||||
0.251710 | + | 0.967803i | \(0.419007\pi\) | |||||||
\(80\) | −1.43003 | −0.159882 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.66639 | 0.625748 | ||||||||
\(83\) | −4.00053 | −0.439115 | −0.219558 | − | 0.975600i | \(-0.570461\pi\) | ||||
−0.219558 | + | 0.975600i | \(0.570461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.8082 | −2.36543 | ||||||||
\(86\) | 1.09647 | 0.118235 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.47507 | −0.903445 | ||||||||
\(89\) | −9.36855 | −0.993064 | −0.496532 | − | 0.868018i | \(-0.665393\pi\) | ||||
−0.496532 | + | 0.868018i | \(0.665393\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.28571 | −0.344436 | ||||||||
\(92\) | −1.34468 | −0.140192 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.05263 | 0.727423 | ||||||||
\(95\) | −8.06441 | −0.827391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.35023 | 0.441699 | 0.220849 | − | 0.975308i | \(-0.429117\pi\) | ||||
0.220849 | + | 0.975308i | \(0.429117\pi\) | |||||||
\(98\) | 5.03458 | 0.508569 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.38624 | −0.438624 | ||||||||
\(101\) | 17.3662 | 1.72800 | 0.864001 | − | 0.503490i | \(-0.167951\pi\) | ||||
0.864001 | + | 0.503490i | \(0.167951\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.02647 | 0.495273 | 0.247636 | − | 0.968853i | \(-0.420346\pi\) | ||||
0.247636 | + | 0.968853i | \(0.420346\pi\) | |||||||
\(104\) | −10.0680 | −0.987253 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.5829 | 1.02790 | ||||||||
\(107\) | 4.57065 | 0.441862 | 0.220931 | − | 0.975289i | \(-0.429090\pi\) | ||||
0.220931 | + | 0.975289i | \(0.429090\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.72662 | 0.165380 | 0.0826902 | − | 0.996575i | \(-0.473649\pi\) | ||||
0.0826902 | + | 0.996575i | \(0.473649\pi\) | |||||||
\(110\) | −7.28332 | −0.694437 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.439612 | 0.0415394 | ||||||||
\(113\) | −7.22055 | −0.679252 | −0.339626 | − | 0.940561i | \(-0.610301\pi\) | ||||
−0.339626 | + | 0.940561i | \(0.610301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.87436 | −0.268035 | ||||||||
\(116\) | 1.34468 | 0.124850 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.25745 | −0.115758 | ||||||||
\(119\) | 6.70417 | 0.614570 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.20233 | −0.109303 | ||||||||
\(122\) | −3.52751 | −0.319366 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.588846 | −0.0528800 | ||||||||
\(125\) | 4.99585 | 0.446842 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0287 | 1.24484 | 0.622422 | − | 0.782682i | \(-0.286149\pi\) | ||||
0.622422 | + | 0.782682i | \(0.286149\pi\) | |||||||
\(128\) | 8.62871 | 0.762677 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.65230 | −0.758857 | ||||||||
\(131\) | −5.02385 | −0.438936 | −0.219468 | − | 0.975620i | \(-0.570432\pi\) | ||||
−0.219468 | + | 0.975620i | \(0.570432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.47912 | 0.214967 | ||||||||
\(134\) | −5.23646 | −0.452361 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.5429 | 1.76154 | ||||||||
\(137\) | 11.5563 | 0.987325 | 0.493662 | − | 0.869654i | \(-0.335658\pi\) | ||||
0.493662 | + | 0.869654i | \(0.335658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0949 | 1.11070 | 0.555349 | − | 0.831618i | \(-0.312585\pi\) | ||||
0.555349 | + | 0.831618i | \(0.312585\pi\) | |||||||
\(140\) | 3.41526 | 0.288642 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.1816 | 0.938337 | ||||||||
\(143\) | 11.6392 | 0.973323 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.87436 | 0.238702 | ||||||||
\(146\) | 8.49824 | 0.703320 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.99705 | −0.821752 | ||||||||
\(149\) | 0.0991848 | 0.00812553 | 0.00406277 | − | 0.999992i | \(-0.498707\pi\) | ||||
0.00406277 | + | 0.999992i | \(0.498707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.619231 | −0.0503923 | −0.0251962 | − | 0.999683i | \(-0.508021\pi\) | ||||
−0.0251962 | + | 0.999683i | \(0.508021\pi\) | |||||||
\(152\) | 7.59650 | 0.616158 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.23900 | 0.180424 | ||||||||
\(155\) | −1.25871 | −0.101102 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.83176 | 0.625043 | 0.312521 | − | 0.949911i | \(-0.398826\pi\) | ||||
0.312521 | + | 0.949911i | \(0.398826\pi\) | |||||||
\(158\) | −3.62219 | −0.288166 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.7228 | 1.32205 | ||||||||
\(161\) | 0.883619 | 0.0696390 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.29528 | −0.336432 | −0.168216 | − | 0.985750i | \(-0.553801\pi\) | ||||
−0.168216 | + | 0.985750i | \(0.553801\pi\) | |||||||
\(164\) | 9.41233 | 0.734980 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.23851 | 0.251357 | ||||||||
\(167\) | −12.4381 | −0.962489 | −0.481244 | − | 0.876586i | \(-0.659815\pi\) | ||||
−0.481244 | + | 0.876586i | \(0.659815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.826970 | 0.0636131 | ||||||||
\(170\) | 17.6542 | 1.35401 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.82132 | 0.138875 | ||||||||
\(173\) | 3.20942 | 0.244008 | 0.122004 | − | 0.992530i | \(-0.461068\pi\) | ||||
0.122004 | + | 0.992530i | \(0.461068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.88230 | 0.217881 | ||||||||
\(176\) | −1.55728 | −0.117384 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.58402 | 0.568447 | ||||||||
\(179\) | −11.2810 | −0.843180 | −0.421590 | − | 0.906787i | \(-0.638528\pi\) | ||||
−0.421590 | + | 0.906787i | \(0.638528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.10430 | 0.453729 | 0.226864 | − | 0.973926i | \(-0.427153\pi\) | ||||
0.226864 | + | 0.973926i | \(0.427153\pi\) | |||||||
\(182\) | 2.65984 | 0.197161 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.70758 | 0.199606 | ||||||||
\(185\) | −21.3695 | −1.57112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.7488 | −1.73668 | ||||||||
\(188\) | 11.7150 | 0.854403 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.52830 | 0.473612 | ||||||||
\(191\) | 11.7280 | 0.848606 | 0.424303 | − | 0.905520i | \(-0.360519\pi\) | ||||
0.424303 | + | 0.905520i | \(0.360519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.83076 | −0.203762 | −0.101881 | − | 0.994797i | \(-0.532486\pi\) | ||||
−0.101881 | + | 0.994797i | \(0.532486\pi\) | |||||||
\(194\) | −3.52160 | −0.252836 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.36284 | 0.597346 | ||||||||
\(197\) | 4.42451 | 0.315233 | 0.157617 | − | 0.987500i | \(-0.449619\pi\) | ||||
0.157617 | + | 0.987500i | \(0.449619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.4160 | −1.58903 | −0.794513 | − | 0.607248i | \(-0.792274\pi\) | ||||
−0.794513 | + | 0.607248i | \(0.792274\pi\) | |||||||
\(200\) | 8.83193 | 0.624512 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.0583 | −0.989137 | ||||||||
\(203\) | −0.883619 | −0.0620179 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.1196 | 1.40521 | ||||||||
\(206\) | −4.06903 | −0.283502 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.84998 | −0.128273 | ||||||||
\(209\) | −8.78199 | −0.607463 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.31524 | 0.572445 | 0.286222 | − | 0.958163i | \(-0.407600\pi\) | ||||
0.286222 | + | 0.958163i | \(0.407600\pi\) | |||||||
\(212\) | 17.5790 | 1.20733 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.70004 | −0.252929 | ||||||||
\(215\) | 3.89323 | 0.265516 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.386945 | 0.0262675 | ||||||||
\(218\) | −1.39773 | −0.0946665 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.0982 | −0.815659 | ||||||||
\(221\) | −28.2126 | −1.89778 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.6285 | −1.51532 | −0.757659 | − | 0.652651i | \(-0.773657\pi\) | ||||
−0.757659 | + | 0.652651i | \(0.773657\pi\) | |||||||
\(224\) | −5.14082 | −0.343485 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.84518 | 0.388815 | ||||||||
\(227\) | −9.82855 | −0.652344 | −0.326172 | − | 0.945311i | \(-0.605759\pi\) | ||||
−0.326172 | + | 0.945311i | \(0.605759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.91799 | 0.192826 | 0.0964130 | − | 0.995341i | \(-0.469263\pi\) | ||||
0.0964130 | + | 0.995341i | \(0.469263\pi\) | |||||||
\(230\) | 2.32685 | 0.153428 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.70758 | −0.177762 | ||||||||
\(233\) | −2.31506 | −0.151664 | −0.0758322 | − | 0.997121i | \(-0.524161\pi\) | ||||
−0.0758322 | + | 0.997121i | \(0.524161\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.0417 | 1.63354 | ||||||||
\(236\) | −2.08873 | −0.135965 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.42716 | −0.351790 | ||||||||
\(239\) | 2.08815 | 0.135071 | 0.0675355 | − | 0.997717i | \(-0.478486\pi\) | ||||
0.0675355 | + | 0.997717i | \(0.478486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.15468 | 0.460874 | 0.230437 | − | 0.973087i | \(-0.425985\pi\) | ||||
0.230437 | + | 0.973087i | \(0.425985\pi\) | |||||||
\(242\) | 0.973311 | 0.0625668 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.85948 | −0.375114 | ||||||||
\(245\) | 17.8762 | 1.14207 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4327 | −0.663815 | ||||||||
\(248\) | 1.18567 | 0.0752904 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.04424 | −0.255780 | ||||||||
\(251\) | −4.78209 | −0.301843 | −0.150921 | − | 0.988546i | \(-0.548224\pi\) | ||||
−0.150921 | + | 0.988546i | \(0.548224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.13012 | −0.196789 | ||||||||
\(254\) | −11.3565 | −0.712570 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.4145 | −0.900906 | ||||||||
\(257\) | −31.2725 | −1.95072 | −0.975362 | − | 0.220612i | \(-0.929195\pi\) | ||||
−0.975362 | + | 0.220612i | \(0.929195\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.56930 | 0.408196 | ||||||||
\(260\) | −14.3722 | −0.891324 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.06691 | 0.251254 | ||||||||
\(263\) | 6.91848 | 0.426612 | 0.213306 | − | 0.976985i | \(-0.431577\pi\) | ||||
0.213306 | + | 0.976985i | \(0.431577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.5766 | 2.30831 | ||||||||
\(266\) | −2.00689 | −0.123051 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.69819 | −0.531326 | ||||||||
\(269\) | 13.7129 | 0.836091 | 0.418046 | − | 0.908426i | \(-0.362715\pi\) | ||||
0.418046 | + | 0.908426i | \(0.362715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.14468 | 0.191026 | 0.0955128 | − | 0.995428i | \(-0.469551\pi\) | ||||
0.0955128 | + | 0.995428i | \(0.469551\pi\) | |||||||
\(272\) | 3.77471 | 0.228876 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.35509 | −0.565162 | ||||||||
\(275\) | −10.2102 | −0.615700 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6186 | 1.29894 | 0.649468 | − | 0.760389i | \(-0.274992\pi\) | ||||
0.649468 | + | 0.760389i | \(0.274992\pi\) | |||||||
\(278\) | −10.6006 | −0.635782 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.87682 | −0.410968 | ||||||||
\(281\) | 16.8548 | 1.00548 | 0.502738 | − | 0.864439i | \(-0.332326\pi\) | ||||
0.502738 | + | 0.864439i | \(0.332326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.7015 | 1.29002 | 0.645011 | − | 0.764174i | \(-0.276853\pi\) | ||||
0.645011 | + | 0.764174i | \(0.276853\pi\) | |||||||
\(284\) | 18.5735 | 1.10213 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.42220 | −0.557146 | ||||||||
\(287\) | −6.18507 | −0.365093 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.5651 | 2.38618 | ||||||||
\(290\) | −2.32685 | −0.136637 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.1163 | 0.826092 | ||||||||
\(293\) | 3.09119 | 0.180589 | 0.0902947 | − | 0.995915i | \(-0.471219\pi\) | ||||
0.0902947 | + | 0.995915i | \(0.471219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.46483 | −0.259952 | ||||||||
\(296\) | 20.1296 | 1.17001 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.0802920 | −0.00465119 | ||||||||
\(299\) | −3.71846 | −0.215044 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.19683 | −0.0689844 | ||||||||
\(302\) | 0.501280 | 0.0288454 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.39584 | 0.0800570 | ||||||||
\(305\) | −12.5251 | −0.717185 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.2889 | 1.67161 | 0.835803 | − | 0.549030i | \(-0.185003\pi\) | ||||
0.835803 | + | 0.549030i | \(0.185003\pi\) | |||||||
\(308\) | 3.71916 | 0.211919 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.01895 | 0.0578723 | ||||||||
\(311\) | 25.0994 | 1.42326 | 0.711629 | − | 0.702556i | \(-0.247958\pi\) | ||||
0.711629 | + | 0.702556i | \(0.247958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.9053 | 1.80340 | 0.901698 | − | 0.432367i | \(-0.142322\pi\) | ||||
0.901698 | + | 0.432367i | \(0.142322\pi\) | |||||||
\(314\) | −6.33997 | −0.357785 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.01675 | −0.338469 | ||||||||
\(317\) | 2.41067 | 0.135397 | 0.0676985 | − | 0.997706i | \(-0.478434\pi\) | ||||
0.0676985 | + | 0.997706i | \(0.478434\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.13012 | 0.175253 | ||||||||
\(320\) | −10.6773 | −0.596881 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.715307 | −0.0398625 | ||||||||
\(323\) | 21.2868 | 1.18443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1293 | −0.672815 | ||||||||
\(326\) | 3.47711 | 0.192580 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.9523 | −1.04646 | ||||||||
\(329\) | −7.69819 | −0.424415 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.27304 | −0.289833 | −0.144916 | − | 0.989444i | \(-0.546291\pi\) | ||||
−0.144916 | + | 0.989444i | \(0.546291\pi\) | |||||||
\(332\) | 5.37942 | 0.295234 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.0689 | 0.550945 | ||||||||
\(335\) | −18.5931 | −1.01585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.9350 | −1.19488 | −0.597438 | − | 0.801915i | \(-0.703815\pi\) | ||||
−0.597438 | + | 0.801915i | \(0.703815\pi\) | |||||||
\(338\) | −0.669448 | −0.0364132 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 29.3250 | 1.59037 | ||||||||
\(341\) | −1.37071 | −0.0742281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.6808 | −0.630701 | ||||||||
\(344\) | −3.66734 | −0.197730 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.59809 | −0.139674 | ||||||||
\(347\) | −10.3430 | −0.555244 | −0.277622 | − | 0.960690i | \(-0.589546\pi\) | ||||
−0.277622 | + | 0.960690i | \(0.589546\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0168 | −0.643247 | −0.321624 | − | 0.946868i | \(-0.604229\pi\) | ||||
−0.321624 | + | 0.946868i | \(0.604229\pi\) | |||||||
\(350\) | −2.33328 | −0.124719 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18.2108 | 0.970638 | ||||||||
\(353\) | −17.3683 | −0.924421 | −0.462210 | − | 0.886770i | \(-0.652944\pi\) | ||||
−0.462210 | + | 0.886770i | \(0.652944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.7024 | 2.10718 | ||||||||
\(356\) | 12.5977 | 0.667675 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.13217 | 0.482650 | ||||||||
\(359\) | 9.90317 | 0.522669 | 0.261335 | − | 0.965248i | \(-0.415837\pi\) | ||||
0.261335 | + | 0.965248i | \(0.415837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.1284 | −0.585705 | ||||||||
\(362\) | −4.94155 | −0.259722 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.41822 | 0.231577 | ||||||||
\(365\) | 30.1746 | 1.57941 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0885 | 0.526614 | 0.263307 | − | 0.964712i | \(-0.415187\pi\) | ||||
0.263307 | + | 0.964712i | \(0.415187\pi\) | |||||||
\(368\) | 0.497513 | 0.0259347 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.2990 | 0.899334 | ||||||||
\(371\) | −11.5516 | −0.599729 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.12698 | −0.369021 | −0.184511 | − | 0.982831i | \(-0.559070\pi\) | ||||
−0.184511 | + | 0.982831i | \(0.559070\pi\) | |||||||
\(374\) | 19.2251 | 0.994106 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.5888 | −1.21650 | ||||||||
\(377\) | 3.71846 | 0.191511 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.9649 | 1.48783 | 0.743914 | − | 0.668276i | \(-0.232967\pi\) | ||||
0.743914 | + | 0.668276i | \(0.232967\pi\) | |||||||
\(380\) | 10.8440 | 0.556287 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.49403 | −0.485757 | ||||||||
\(383\) | −32.2072 | −1.64571 | −0.822857 | − | 0.568249i | \(-0.807621\pi\) | ||||
−0.822857 | + | 0.568249i | \(0.807621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.95000 | 0.405170 | ||||||||
\(386\) | 2.29156 | 0.116637 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.84965 | −0.296971 | ||||||||
\(389\) | 18.8698 | 0.956738 | 0.478369 | − | 0.878159i | \(-0.341228\pi\) | ||||
0.478369 | + | 0.878159i | \(0.341228\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.58717 | 0.383699 | ||||||||
\(392\) | −16.8390 | −0.850500 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.58173 | −0.180445 | ||||||||
\(395\) | −12.8613 | −0.647122 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.26705 | −0.113780 | −0.0568900 | − | 0.998380i | \(-0.518118\pi\) | ||||
−0.0568900 | + | 0.998380i | \(0.518118\pi\) | |||||||
\(398\) | 18.1462 | 0.909585 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.62285 | 0.0811425 | ||||||||
\(401\) | 19.4241 | 0.969992 | 0.484996 | − | 0.874517i | \(-0.338821\pi\) | ||||
0.484996 | + | 0.874517i | \(0.338821\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.62835 | −0.0811138 | ||||||||
\(404\) | −23.3519 | −1.16180 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.715307 | 0.0355001 | ||||||||
\(407\) | −23.2710 | −1.15350 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.96080 | 0.245296 | 0.122648 | − | 0.992450i | \(-0.460861\pi\) | ||||
0.122648 | + | 0.992450i | \(0.460861\pi\) | |||||||
\(410\) | −16.2872 | −0.804369 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.75898 | −0.332991 | ||||||||
\(413\) | 1.37255 | 0.0675390 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.4989 | 0.564461 | ||||||||
\(416\) | 21.6337 | 1.06068 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.10920 | 0.347722 | ||||||||
\(419\) | 34.2462 | 1.67304 | 0.836518 | − | 0.547939i | \(-0.184588\pi\) | ||||
0.836518 | + | 0.547939i | \(0.184588\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.614100 | −0.0299294 | −0.0149647 | − | 0.999888i | \(-0.504764\pi\) | ||||
−0.0149647 | + | 0.999888i | \(0.504764\pi\) | |||||||
\(422\) | −6.73135 | −0.327677 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −35.3963 | −1.71900 | ||||||||
\(425\) | 24.7488 | 1.20049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.85040 | 0.186334 | ||||||||
\(428\) | −6.14606 | −0.297081 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.15164 | −0.151986 | ||||||||
\(431\) | 24.4445 | 1.17745 | 0.588726 | − | 0.808333i | \(-0.299630\pi\) | ||||
0.588726 | + | 0.808333i | \(0.299630\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.8240 | 1.57742 | 0.788710 | − | 0.614766i | \(-0.210749\pi\) | ||||
0.788710 | + | 0.614766i | \(0.210749\pi\) | |||||||
\(434\) | −0.313240 | −0.0150360 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.32175 | −0.111192 | ||||||||
\(437\) | 2.80564 | 0.134212 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.8312 | 1.47149 | 0.735746 | − | 0.677257i | \(-0.236832\pi\) | ||||
0.735746 | + | 0.677257i | \(0.236832\pi\) | |||||||
\(440\) | 24.3604 | 1.16133 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.8387 | 1.08632 | ||||||||
\(443\) | 3.00139 | 0.142601 | 0.0713003 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0713003 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.9285 | 1.27654 | ||||||||
\(446\) | 18.3182 | 0.867394 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.28237 | 0.155077 | ||||||||
\(449\) | 19.2743 | 0.909609 | 0.454805 | − | 0.890591i | \(-0.349709\pi\) | ||||
0.454805 | + | 0.890591i | \(0.349709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.9099 | 1.03170 | ||||||||
\(452\) | 9.70931 | 0.456688 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.95640 | 0.373413 | ||||||||
\(455\) | 9.44429 | 0.442755 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.01229 | −0.281243 | −0.140622 | − | 0.990063i | \(-0.544910\pi\) | ||||
−0.140622 | + | 0.990063i | \(0.544910\pi\) | |||||||
\(458\) | −2.36217 | −0.110377 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.86508 | 0.180210 | ||||||||
\(461\) | 8.56537 | 0.398929 | 0.199465 | − | 0.979905i | \(-0.436080\pi\) | ||||
0.199465 | + | 0.979905i | \(0.436080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.85107 | 0.271922 | 0.135961 | − | 0.990714i | \(-0.456588\pi\) | ||||
0.135961 | + | 0.990714i | \(0.456588\pi\) | |||||||
\(464\) | −0.497513 | −0.0230965 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.87409 | 0.0868153 | ||||||||
\(467\) | 1.80231 | 0.0834008 | 0.0417004 | − | 0.999130i | \(-0.486722\pi\) | ||||
0.0417004 | + | 0.999130i | \(0.486722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.71578 | 0.263930 | ||||||||
\(470\) | −20.2718 | −0.935067 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.20577 | 0.193586 | ||||||||
\(473\) | 4.23965 | 0.194939 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.15178 | 0.419912 | ||||||||
\(476\) | −9.01494 | −0.413199 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.69040 | −0.0773170 | ||||||||
\(479\) | 24.1615 | 1.10397 | 0.551984 | − | 0.833854i | \(-0.313871\pi\) | ||||
0.551984 | + | 0.833854i | \(0.313871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.6450 | −1.26051 | ||||||||
\(482\) | −5.79186 | −0.263812 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.61675 | 0.0734885 | ||||||||
\(485\) | −12.5041 | −0.567782 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.3798 | 0.968810 | 0.484405 | − | 0.874844i | \(-0.339036\pi\) | ||||
0.484405 | + | 0.874844i | \(0.339036\pi\) | |||||||
\(488\) | 11.7984 | 0.534088 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.4712 | −0.653741 | ||||||||
\(491\) | −7.76902 | −0.350611 | −0.175305 | − | 0.984514i | \(-0.556091\pi\) | ||||
−0.175305 | + | 0.984514i | \(0.556091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.58717 | −0.341709 | ||||||||
\(494\) | 8.44545 | 0.379979 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.217865 | 0.00978245 | ||||||||
\(497\) | −12.2051 | −0.547473 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.2323 | −0.771425 | −0.385712 | − | 0.922619i | \(-0.626044\pi\) | ||||
−0.385712 | + | 0.922619i | \(0.626044\pi\) | |||||||
\(500\) | −6.71781 | −0.300430 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.87120 | 0.172780 | ||||||||
\(503\) | 31.7244 | 1.41452 | 0.707261 | − | 0.706953i | \(-0.249931\pi\) | ||||
0.707261 | + | 0.706953i | \(0.249931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −49.9166 | −2.22126 | ||||||||
\(506\) | 2.53390 | 0.112645 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.8640 | −0.836957 | ||||||||
\(509\) | 18.1047 | 0.802477 | 0.401238 | − | 0.915974i | \(-0.368580\pi\) | ||||
0.401238 | + | 0.915974i | \(0.368580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.27613 | −0.410352 | ||||||||
\(512\) | −5.58860 | −0.246984 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.3157 | 1.11663 | ||||||||
\(515\) | −14.4479 | −0.636649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.2700 | 1.19933 | ||||||||
\(518\) | −5.31798 | −0.233658 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 28.9392 | 1.26907 | ||||||||
\(521\) | −13.9997 | −0.613339 | −0.306670 | − | 0.951816i | \(-0.599215\pi\) | ||||
−0.306670 | + | 0.951816i | \(0.599215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.2533 | 1.10425 | 0.552125 | − | 0.833761i | \(-0.313817\pi\) | ||||
0.552125 | + | 0.833761i | \(0.313817\pi\) | |||||||
\(524\) | 6.75546 | 0.295114 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.60065 | −0.244200 | ||||||||
\(527\) | 3.32249 | 0.144730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −30.4190 | −1.32132 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.33361 | −0.144530 | ||||||||
\(533\) | 26.0281 | 1.12740 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1377 | −0.567992 | ||||||||
\(536\) | 17.5143 | 0.756502 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.1009 | −0.478593 | ||||||||
\(539\) | 19.4669 | 0.838499 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.1425 | 0.994973 | 0.497486 | − | 0.867472i | \(-0.334256\pi\) | ||||
0.497486 | + | 0.867472i | \(0.334256\pi\) | |||||||
\(542\) | −2.54568 | −0.109346 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −44.1415 | −1.89255 | ||||||||
\(545\) | −4.96293 | −0.212588 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9010 | −1.57777 | −0.788887 | − | 0.614538i | \(-0.789342\pi\) | ||||
−0.788887 | + | 0.614538i | \(0.789342\pi\) | |||||||
\(548\) | −15.5396 | −0.663817 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.26538 | 0.352437 | ||||||||
\(551\) | −2.80564 | −0.119524 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.95375 | 0.168130 | ||||||||
\(554\) | −17.5007 | −0.743533 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.6085 | −0.746765 | ||||||||
\(557\) | 36.7219 | 1.55596 | 0.777978 | − | 0.628291i | \(-0.216245\pi\) | ||||
0.777978 | + | 0.628291i | \(0.216245\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.03654 | 0.213023 | ||||||||
\(560\) | −1.26360 | −0.0533969 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.6443 | −0.575551 | ||||||||
\(563\) | 17.3866 | 0.732759 | 0.366379 | − | 0.930466i | \(-0.380597\pi\) | ||||
0.366379 | + | 0.930466i | \(0.380597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.7544 | 0.873145 | ||||||||
\(566\) | −17.5678 | −0.738430 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.3988 | −1.56922 | ||||||||
\(569\) | −22.6275 | −0.948594 | −0.474297 | − | 0.880365i | \(-0.657298\pi\) | ||||
−0.474297 | + | 0.880365i | \(0.657298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.1499 | −1.63837 | −0.819186 | − | 0.573529i | \(-0.805574\pi\) | ||||
−0.819186 | + | 0.573529i | \(0.805574\pi\) | |||||||
\(572\) | −15.6510 | −0.654403 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.00693 | 0.208985 | ||||||||
\(575\) | 3.26192 | 0.136032 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.97090 | −0.206941 | −0.103471 | − | 0.994633i | \(-0.532995\pi\) | ||||
−0.103471 | + | 0.994633i | \(0.532995\pi\) | |||||||
\(578\) | −32.8382 | −1.36589 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.86508 | −0.160489 | ||||||||
\(581\) | −3.53494 | −0.146654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.9202 | 1.69474 | ||||||||
\(584\) | −28.4239 | −1.17619 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.50238 | −0.103372 | ||||||||
\(587\) | −9.44544 | −0.389855 | −0.194927 | − | 0.980818i | \(-0.562447\pi\) | ||||
−0.194927 | + | 0.980818i | \(0.562447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.22861 | 0.0506242 | ||||||||
\(590\) | 3.61437 | 0.148801 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.69878 | 0.152019 | ||||||||
\(593\) | −43.5097 | −1.78673 | −0.893364 | − | 0.449334i | \(-0.851661\pi\) | ||||
−0.893364 | + | 0.449334i | \(0.851661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.2702 | −0.790000 | ||||||||
\(596\) | −0.133372 | −0.00546311 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.01017 | 0.123095 | ||||||||
\(599\) | 37.1909 | 1.51958 | 0.759790 | − | 0.650169i | \(-0.225302\pi\) | ||||
0.759790 | + | 0.650169i | \(0.225302\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6491 | 0.923877 | 0.461938 | − | 0.886912i | \(-0.347154\pi\) | ||||
0.461938 | + | 0.886912i | \(0.347154\pi\) | |||||||
\(602\) | 0.968861 | 0.0394878 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.832666 | 0.0338807 | ||||||||
\(605\) | 3.45593 | 0.140503 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.7230 | 1.24701 | 0.623504 | − | 0.781821i | \(-0.285709\pi\) | ||||
0.623504 | + | 0.781821i | \(0.285709\pi\) | |||||||
\(608\) | −16.3230 | −0.661984 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.1393 | 0.410529 | ||||||||
\(611\) | 32.3957 | 1.31059 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.20728 | 0.0487616 | 0.0243808 | − | 0.999703i | \(-0.492239\pi\) | ||||
0.0243808 | + | 0.999703i | \(0.492239\pi\) | |||||||
\(614\) | −23.7099 | −0.956856 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.48873 | −0.301730 | ||||||||
\(617\) | −20.6889 | −0.832906 | −0.416453 | − | 0.909157i | \(-0.636727\pi\) | ||||
−0.416453 | + | 0.909157i | \(0.636727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.6432 | −0.990496 | −0.495248 | − | 0.868752i | \(-0.664923\pi\) | ||||
−0.495248 | + | 0.868752i | \(0.664923\pi\) | |||||||
\(620\) | 1.69255 | 0.0679746 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.3185 | −0.814697 | ||||||||
\(623\) | −8.27823 | −0.331660 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6695 | −1.22678 | ||||||||
\(626\) | −25.8280 | −1.03229 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.5312 | −0.420241 | ||||||||
\(629\) | 56.4070 | 2.24910 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.58591 | 0.142753 | 0.0713764 | − | 0.997449i | \(-0.477261\pi\) | ||||
0.0713764 | + | 0.997449i | \(0.477261\pi\) | |||||||
\(632\) | 12.1151 | 0.481911 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.95149 | −0.0775035 | ||||||||
\(635\) | −40.3234 | −1.60019 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.1259 | 0.916283 | ||||||||
\(638\) | −2.53390 | −0.100318 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.8020 | −0.980385 | ||||||||
\(641\) | −22.5787 | −0.891805 | −0.445902 | − | 0.895082i | \(-0.647117\pi\) | ||||
−0.445902 | + | 0.895082i | \(0.647117\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.5402 | −0.731153 | −0.365577 | − | 0.930781i | \(-0.619128\pi\) | ||||
−0.365577 | + | 0.930781i | \(0.619128\pi\) | |||||||
\(644\) | −1.18818 | −0.0468210 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.2321 | −0.677989 | ||||||||
\(647\) | −16.6734 | −0.655501 | −0.327750 | − | 0.944764i | \(-0.606290\pi\) | ||||
−0.327750 | + | 0.944764i | \(0.606290\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.86212 | −0.190855 | ||||||||
\(650\) | 9.81894 | 0.385131 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.77577 | 0.226196 | ||||||||
\(653\) | −12.4616 | −0.487662 | −0.243831 | − | 0.969818i | \(-0.578404\pi\) | ||||
−0.243831 | + | 0.969818i | \(0.578404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.4403 | 0.564231 | ||||||||
\(656\) | −3.48244 | −0.135966 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.23184 | 0.242942 | ||||||||
\(659\) | 16.5058 | 0.642973 | 0.321487 | − | 0.946914i | \(-0.395817\pi\) | ||||
0.321487 | + | 0.946914i | \(0.395817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0840 | −1.28682 | −0.643408 | − | 0.765523i | \(-0.722480\pi\) | ||||
−0.643408 | + | 0.765523i | \(0.722480\pi\) | |||||||
\(662\) | 4.26863 | 0.165905 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.8318 | −0.420354 | ||||||||
\(665\) | −7.12586 | −0.276329 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 16.7252 | 0.647119 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.0515 | 0.581489 | ||||||||
\(671\) | −13.6396 | −0.526551 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.1514 | −1.20080 | −0.600399 | − | 0.799700i | \(-0.704992\pi\) | ||||
−0.600399 | + | 0.799700i | \(0.704992\pi\) | |||||||
\(674\) | 17.7568 | 0.683968 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.11201 | −0.0427695 | ||||||||
\(677\) | 9.31505 | 0.358006 | 0.179003 | − | 0.983848i | \(-0.442713\pi\) | ||||
0.179003 | + | 0.983848i | \(0.442713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.84394 | 0.147517 | ||||||||
\(680\) | −59.0476 | −2.26437 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.10962 | 0.0424894 | ||||||||
\(683\) | 3.54564 | 0.135670 | 0.0678350 | − | 0.997697i | \(-0.478391\pi\) | ||||
0.0678350 | + | 0.997697i | \(0.478391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.2170 | −1.26916 | ||||||||
\(686\) | 9.45580 | 0.361024 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.673866 | −0.0256909 | ||||||||
\(689\) | 48.6116 | 1.85196 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.1377 | 1.07041 | 0.535204 | − | 0.844723i | \(-0.320235\pi\) | ||||
0.535204 | + | 0.844723i | \(0.320235\pi\) | |||||||
\(692\) | −4.31563 | −0.164056 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.37290 | 0.317831 | ||||||||
\(695\) | −37.6395 | −1.42775 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53.1078 | −2.01160 | ||||||||
\(698\) | 9.72788 | 0.368206 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.87576 | −0.146490 | ||||||||
\(701\) | 8.36492 | 0.315939 | 0.157969 | − | 0.987444i | \(-0.449505\pi\) | ||||
0.157969 | + | 0.987444i | \(0.449505\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.8586 | 0.786697 | ||||||||
\(704\) | −11.6274 | −0.438225 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.0600 | 0.529154 | ||||||||
\(707\) | 15.3451 | 0.577112 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.2293 | −1.28551 | −0.642754 | − | 0.766073i | \(-0.722208\pi\) | ||||
−0.642754 | + | 0.766073i | \(0.722208\pi\) | |||||||
\(710\) | −32.1398 | −1.20619 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.3661 | −0.950635 | ||||||||
\(713\) | 0.437909 | 0.0163998 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.4553 | −1.25116 | ||||||||
\(716\) | 15.1693 | 0.566902 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.01681 | −0.299185 | ||||||||
\(719\) | −22.2665 | −0.830399 | −0.415199 | − | 0.909730i | \(-0.636288\pi\) | ||||
−0.415199 | + | 0.909730i | \(0.636288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.44148 | 0.165410 | ||||||||
\(722\) | 9.00865 | 0.335267 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.20831 | −0.305060 | ||||||||
\(725\) | −3.26192 | −0.121145 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.3621 | 0.903541 | 0.451770 | − | 0.892134i | \(-0.350793\pi\) | ||||
0.451770 | + | 0.892134i | \(0.350793\pi\) | |||||||
\(728\) | −8.89632 | −0.329720 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.4270 | −0.904083 | ||||||||
\(731\) | −10.2766 | −0.380093 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.6426 | −1.02100 | −0.510502 | − | 0.859876i | \(-0.670540\pi\) | ||||
−0.510502 | + | 0.859876i | \(0.670540\pi\) | |||||||
\(734\) | −8.16682 | −0.301443 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.81791 | −0.214451 | ||||||||
\(737\) | −20.2475 | −0.745827 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.2693 | −1.22383 | −0.611916 | − | 0.790922i | \(-0.709601\pi\) | ||||
−0.611916 | + | 0.790922i | \(0.709601\pi\) | |||||||
\(740\) | 28.7351 | 1.05632 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.35124 | 0.343295 | ||||||||
\(743\) | 33.1298 | 1.21541 | 0.607707 | − | 0.794162i | \(-0.292090\pi\) | ||||
0.607707 | + | 0.794162i | \(0.292090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.285092 | −0.0104450 | ||||||||
\(746\) | 5.76943 | 0.211234 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 31.9344 | 1.16764 | ||||||||
\(749\) | 4.03872 | 0.147572 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.19627 | 0.0801429 | 0.0400714 | − | 0.999197i | \(-0.487241\pi\) | ||||
0.0400714 | + | 0.999197i | \(0.487241\pi\) | |||||||
\(752\) | −4.33439 | −0.158059 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.01017 | −0.109624 | ||||||||
\(755\) | 1.77989 | 0.0647769 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.4768 | 1.87096 | 0.935478 | − | 0.353386i | \(-0.114970\pi\) | ||||
0.935478 | + | 0.353386i | \(0.114970\pi\) | |||||||
\(758\) | −23.4477 | −0.851658 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.8350 | −0.792040 | ||||||||
\(761\) | −0.0490802 | −0.00177916 | −0.000889578 | − | 1.00000i | \(-0.500283\pi\) | ||||
−0.000889578 | 1.00000i | \(0.500283\pi\) | ||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.52568 | 0.0552332 | ||||||||
\(764\) | −15.7703 | −0.570551 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.0724 | 0.942034 | ||||||||
\(767\) | −5.77601 | −0.208560 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.0182 | 1.01036 | 0.505181 | − | 0.863013i | \(-0.331426\pi\) | ||||
0.505181 | + | 0.863013i | \(0.331426\pi\) | |||||||
\(770\) | −6.43568 | −0.231926 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.80646 | 0.136997 | ||||||||
\(773\) | 2.48136 | 0.0892484 | 0.0446242 | − | 0.999004i | \(-0.485791\pi\) | ||||
0.0446242 | + | 0.999004i | \(0.485791\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.42843 | 0.0513106 | ||||||||
\(776\) | 11.7786 | 0.422827 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.2755 | −0.547653 | ||||||||
\(779\) | −19.6386 | −0.703626 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.2352 | 1.54708 | ||||||||
\(782\) | −6.14196 | −0.219636 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.09414 | −0.110505 | ||||||||
\(785\) | −22.5113 | −0.803462 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8187 | −0.492583 | −0.246292 | − | 0.969196i | \(-0.579212\pi\) | ||||
−0.246292 | + | 0.969196i | \(0.579212\pi\) | |||||||
\(788\) | −5.94954 | −0.211943 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.4115 | 0.370423 | ||||||||
\(791\) | −6.38022 | −0.226854 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.2033 | −0.575397 | ||||||||
\(794\) | 1.83522 | 0.0651296 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30.1422 | 1.06836 | ||||||||
\(797\) | −53.7952 | −1.90552 | −0.952761 | − | 0.303721i | \(-0.901771\pi\) | ||||
−0.952761 | + | 0.303721i | \(0.901771\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66.1003 | −2.33846 | ||||||||
\(800\) | −18.9776 | −0.670959 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.7242 | −0.555240 | ||||||||
\(803\) | 32.8597 | 1.15959 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.53984 | −0.0895175 | ||||||||
\(806\) | 1.31818 | 0.0464309 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 47.0204 | 1.65417 | ||||||||
\(809\) | 31.2565 | 1.09892 | 0.549460 | − | 0.835520i | \(-0.314833\pi\) | ||||
0.549460 | + | 0.835520i | \(0.314833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.48433 | 0.333040 | 0.166520 | − | 0.986038i | \(-0.446747\pi\) | ||||
0.166520 | + | 0.986038i | \(0.446747\pi\) | |||||||
\(812\) | 1.18818 | 0.0416971 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.8383 | 0.660283 | ||||||||
\(815\) | 12.3462 | 0.432467 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.80015 | −0.132950 | ||||||||
\(818\) | −4.01586 | −0.140411 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.0544 | −0.944781 | ||||||||
\(821\) | 14.1716 | 0.494594 | 0.247297 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247297 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.50100 | 0.122037 | 0.0610186 | − | 0.998137i | \(-0.480565\pi\) | ||||
0.0610186 | + | 0.998137i | \(0.480565\pi\) | |||||||
\(824\) | 13.6096 | 0.474112 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.11111 | −0.0386604 | ||||||||
\(827\) | 47.8189 | 1.66283 | 0.831413 | − | 0.555655i | \(-0.187532\pi\) | ||||
0.831413 | + | 0.555655i | \(0.187532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.6429 | 0.786421 | 0.393211 | − | 0.919448i | \(-0.371364\pi\) | ||||
0.393211 | + | 0.919448i | \(0.371364\pi\) | |||||||
\(830\) | −9.30862 | −0.323107 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13.8129 | −0.478877 | ||||||||
\(833\) | −47.1862 | −1.63491 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.7515 | 1.23723 | ||||||||
\(836\) | 11.8090 | 0.408421 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.7230 | −0.957674 | ||||||||
\(839\) | 17.4978 | 0.604091 | 0.302046 | − | 0.953294i | \(-0.402331\pi\) | ||||
0.302046 | + | 0.953294i | \(0.402331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0.497126 | 0.0171321 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.1813 | −0.384877 | ||||||||
\(845\) | −2.37701 | −0.0817715 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.06240 | −0.0365046 | ||||||||
\(848\) | −6.50401 | −0.223349 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −20.0346 | −0.687181 | ||||||||
\(851\) | 7.43453 | 0.254852 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.4760 | −0.598368 | −0.299184 | − | 0.954195i | \(-0.596715\pi\) | ||||
−0.299184 | + | 0.954195i | \(0.596715\pi\) | |||||||
\(854\) | −3.11697 | −0.106661 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.3754 | 0.422983 | ||||||||
\(857\) | −3.15401 | −0.107739 | −0.0538695 | − | 0.998548i | \(-0.517155\pi\) | ||||
−0.0538695 | + | 0.998548i | \(0.517155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3857 | 0.354355 | 0.177177 | − | 0.984179i | \(-0.443303\pi\) | ||||
0.177177 | + | 0.984179i | \(0.443303\pi\) | |||||||
\(860\) | −5.23513 | −0.178517 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.7883 | −0.673993 | ||||||||
\(863\) | −39.1616 | −1.33308 | −0.666538 | − | 0.745471i | \(-0.732225\pi\) | ||||
−0.666538 | + | 0.745471i | \(0.732225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.22502 | −0.313660 | ||||||||
\(866\) | −26.5717 | −0.902942 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.520316 | −0.0176607 | ||||||||
\(869\) | −14.0057 | −0.475111 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0533 | −0.815014 | ||||||||
\(872\) | 4.67497 | 0.158314 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.27122 | −0.0768252 | ||||||||
\(875\) | 4.41443 | 0.149235 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.0623 | 1.15020 | 0.575102 | − | 0.818082i | \(-0.304962\pi\) | ||||
0.575102 | + | 0.818082i | \(0.304962\pi\) | |||||||
\(878\) | −24.9585 | −0.842307 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.47617 | 0.150892 | ||||||||
\(881\) | −22.4562 | −0.756568 | −0.378284 | − | 0.925690i | \(-0.623486\pi\) | ||||
−0.378284 | + | 0.925690i | \(0.623486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.5167 | 0.791401 | 0.395701 | − | 0.918380i | \(-0.370502\pi\) | ||||
0.395701 | + | 0.918380i | \(0.370502\pi\) | |||||||
\(884\) | 37.9368 | 1.27595 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.42969 | −0.0816270 | ||||||||
\(887\) | −28.7714 | −0.966048 | −0.483024 | − | 0.875607i | \(-0.660462\pi\) | ||||
−0.483024 | + | 0.875607i | \(0.660462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.3960 | 0.415749 | ||||||||
\(890\) | −21.7992 | −0.730710 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30.4281 | 1.01881 | ||||||||
\(893\) | −24.4431 | −0.817956 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.4255 | 1.08387 | ||||||||
\(896\) | 7.62449 | 0.254716 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.6029 | −0.520676 | ||||||||
\(899\) | −0.437909 | −0.0146051 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −99.1873 | −3.30441 | ||||||||
\(902\) | −17.7365 | −0.590561 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.5502 | −0.650231 | ||||||||
\(905\) | −17.5459 | −0.583246 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.9992 | −1.46097 | −0.730484 | − | 0.682929i | \(-0.760706\pi\) | ||||
−0.730484 | + | 0.682929i | \(0.760706\pi\) | |||||||
\(908\) | 13.2162 | 0.438596 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.64534 | −0.253441 | ||||||||
\(911\) | −1.66879 | −0.0552894 | −0.0276447 | − | 0.999618i | \(-0.508801\pi\) | ||||
−0.0276447 | + | 0.999618i | \(0.508801\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.5221 | 0.414423 | ||||||||
\(914\) | 4.86707 | 0.160988 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.92375 | −0.129644 | ||||||||
\(917\) | −4.43917 | −0.146594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.9710 | −1.18657 | −0.593287 | − | 0.804991i | \(-0.702170\pi\) | ||||
−0.593287 | + | 0.804991i | \(0.702170\pi\) | |||||||
\(920\) | −7.78256 | −0.256583 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.93384 | −0.228354 | ||||||||
\(923\) | 51.3617 | 1.69059 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.2509 | 0.797364 | ||||||||
\(926\) | −4.73655 | −0.155653 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.81791 | 0.190982 | ||||||||
\(929\) | −2.08561 | −0.0684265 | −0.0342133 | − | 0.999415i | \(-0.510893\pi\) | ||||
−0.0342133 | + | 0.999415i | \(0.510893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.4489 | −0.571864 | ||||||||
\(932\) | 3.11301 | 0.101970 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.45900 | −0.0477401 | ||||||||
\(935\) | 68.2624 | 2.23242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7301 | 0.938572 | 0.469286 | − | 0.883046i | \(-0.344511\pi\) | ||||
0.469286 | + | 0.883046i | \(0.344511\pi\) | |||||||
\(938\) | −4.62704 | −0.151078 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −33.6730 | −1.09829 | ||||||||
\(941\) | 11.0462 | 0.360096 | 0.180048 | − | 0.983658i | \(-0.442375\pi\) | ||||
0.180048 | + | 0.983658i | \(0.442375\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.99969 | −0.227941 | ||||||||
\(944\) | 0.772803 | 0.0251526 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.43208 | −0.111587 | ||||||||
\(947\) | −7.63217 | −0.248012 | −0.124006 | − | 0.992281i | \(-0.539574\pi\) | ||||
−0.124006 | + | 0.992281i | \(0.539574\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.0360 | 1.26716 | ||||||||
\(950\) | −7.40855 | −0.240365 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.1521 | 0.588312 | ||||||||
\(953\) | 44.0031 | 1.42540 | 0.712700 | − | 0.701469i | \(-0.247472\pi\) | ||||
0.712700 | + | 0.701469i | \(0.247472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.7104 | −1.09084 | ||||||||
\(956\) | −2.80789 | −0.0908135 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19.5592 | −0.631931 | ||||||||
\(959\) | 10.2114 | 0.329744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8082 | −0.993814 | ||||||||
\(962\) | 22.3792 | 0.721535 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.62074 | −0.309863 | ||||||||
\(965\) | 8.13661 | 0.261927 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.2064 | 0.456846 | 0.228423 | − | 0.973562i | \(-0.426643\pi\) | ||||
0.228423 | + | 0.973562i | \(0.426643\pi\) | |||||||
\(968\) | −3.25541 | −0.104633 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.1223 | 0.325008 | ||||||||
\(971\) | 49.4161 | 1.58584 | 0.792919 | − | 0.609327i | \(-0.208560\pi\) | ||||
0.792919 | + | 0.609327i | \(0.208560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.5709 | 0.370947 | ||||||||
\(974\) | −17.3074 | −0.554564 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.16793 | 0.0693937 | ||||||||
\(977\) | 40.2639 | 1.28816 | 0.644078 | − | 0.764959i | \(-0.277241\pi\) | ||||
0.644078 | + | 0.764959i | \(0.277241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.3247 | 0.937221 | ||||||||
\(980\) | −24.0378 | −0.767859 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.28917 | 0.200696 | ||||||||
\(983\) | 6.79464 | 0.216715 | 0.108358 | − | 0.994112i | \(-0.465441\pi\) | ||||
0.108358 | + | 0.994112i | \(0.465441\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.7176 | −0.405217 | ||||||||
\(986\) | 6.14196 | 0.195600 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.0286 | 0.446308 | ||||||||
\(989\) | −1.35447 | −0.0430696 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.70480 | −0.244751 | −0.122375 | − | 0.992484i | \(-0.539051\pi\) | ||||
−0.122375 | + | 0.992484i | \(0.539051\pi\) | |||||||
\(992\) | −2.54772 | −0.0808901 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.88026 | 0.313383 | ||||||||
\(995\) | 64.4315 | 2.04261 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.70589 | −0.244048 | −0.122024 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122024 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(998\) | 13.9499 | 0.441577 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.v.1.12 | ✓ | 30 | |
3.2 | odd | 2 | 6003.2.a.w.1.19 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.v.1.12 | ✓ | 30 | 1.1 | even | 1 | trivial | |
6003.2.a.w.1.19 | yes | 30 | 3.2 | odd | 2 |