Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | 0 | ||||||||
\(3\) | −0.217342 | −0.125483 | −0.0627413 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627413 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.76324 | 0.788546 | 0.394273 | − | 0.918993i | \(-0.370996\pi\) | ||||
0.394273 | + | 0.918993i | \(0.370996\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63306 | 0.617238 | 0.308619 | − | 0.951186i | \(-0.400133\pi\) | ||||
0.308619 | + | 0.951186i | \(0.400133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.95276 | −0.984254 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.73515 | −1.42770 | −0.713851 | − | 0.700298i | \(-0.753051\pi\) | ||||
−0.713851 | + | 0.700298i | \(0.753051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.29715 | 1.19181 | 0.595907 | − | 0.803053i | \(-0.296793\pi\) | ||||
0.595907 | + | 0.803053i | \(0.296793\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.383227 | −0.0989489 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.17157 | −1.49683 | −0.748413 | − | 0.663233i | \(-0.769184\pi\) | ||||
−0.748413 | + | 0.663233i | \(0.769184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.23590 | 0.742366 | 0.371183 | − | 0.928560i | \(-0.378952\pi\) | ||||
0.371183 | + | 0.928560i | \(0.378952\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.354933 | −0.0774527 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.20023 | −1.08432 | −0.542162 | − | 0.840274i | \(-0.682394\pi\) | ||||
−0.542162 | + | 0.840274i | \(0.682394\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.89097 | −0.378195 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.29379 | 0.248989 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.37319 | −0.997776 | −0.498888 | − | 0.866666i | \(-0.666258\pi\) | ||||
−0.498888 | + | 0.866666i | \(0.666258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.65068 | 0.655681 | 0.327840 | − | 0.944733i | \(-0.393679\pi\) | ||||
0.327840 | + | 0.944733i | \(0.393679\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.02915 | 0.179152 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.87948 | 0.486721 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2663 | 1.68777 | 0.843884 | − | 0.536525i | \(-0.180263\pi\) | ||||
0.843884 | + | 0.536525i | \(0.180263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.933952 | −0.149552 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.3293 | 1.92552 | 0.962760 | − | 0.270359i | \(-0.0871423\pi\) | ||||
0.962760 | + | 0.270359i | \(0.0871423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.50192 | −0.686536 | −0.343268 | − | 0.939238i | \(-0.611534\pi\) | ||||
−0.343268 | + | 0.939238i | \(0.611534\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.20644 | −0.776130 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0393 | 1.61024 | 0.805122 | − | 0.593109i | \(-0.202100\pi\) | ||||
0.805122 | + | 0.593109i | \(0.202100\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.33312 | −0.619017 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.34134 | 0.187826 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.84055 | −0.390179 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.34922 | −1.12581 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.703298 | −0.0931541 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.223774 | −0.0291329 | −0.0145665 | − | 0.999894i | \(-0.504637\pi\) | ||||
−0.0145665 | + | 0.999894i | \(0.504637\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2299 | 1.43784 | 0.718921 | − | 0.695092i | \(-0.244636\pi\) | ||||
0.718921 | + | 0.695092i | \(0.244636\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.82204 | −0.607519 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.57691 | 0.939800 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.71113 | 0.942064 | 0.471032 | − | 0.882116i | \(-0.343882\pi\) | ||||
0.471032 | + | 0.882116i | \(0.343882\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.13023 | 0.136064 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.66749 | −0.672607 | −0.336304 | − | 0.941754i | \(-0.609177\pi\) | ||||
−0.336304 | + | 0.941754i | \(0.609177\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.65373 | 0.778760 | 0.389380 | − | 0.921077i | \(-0.372689\pi\) | ||||
0.389380 | + | 0.921077i | \(0.372689\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.410989 | 0.0474569 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.73278 | −0.881232 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.73124 | 0.982341 | 0.491171 | − | 0.871063i | \(-0.336569\pi\) | ||||
0.491171 | + | 0.871063i | \(0.336569\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.57709 | 0.953010 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.13562 | −0.124650 | −0.0623252 | − | 0.998056i | \(-0.519852\pi\) | ||||
−0.0623252 | + | 0.998056i | \(0.519852\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8820 | −1.18032 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.16782 | 0.125204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.7119 | 1.87745 | 0.938727 | − | 0.344660i | \(-0.112006\pi\) | ||||
0.938727 | + | 0.344660i | \(0.112006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.01749 | 0.735633 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.793447 | −0.0822766 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.70568 | 0.585390 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.4828 | 1.47051 | 0.735254 | − | 0.677791i | \(-0.237063\pi\) | ||||
0.735254 | + | 0.677791i | \(0.237063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.9818 | 1.40522 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.51307 | −0.648075 | −0.324037 | − | 0.946044i | \(-0.605040\pi\) | ||||
−0.324037 | + | 0.946044i | \(0.605040\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7546 | 1.35529 | 0.677643 | − | 0.735391i | \(-0.263002\pi\) | ||||
0.677643 | + | 0.735391i | \(0.263002\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.625833 | −0.0610750 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.72856 | −0.553801 | −0.276901 | − | 0.960899i | \(-0.589307\pi\) | ||||
−0.276901 | + | 0.960899i | \(0.589307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8740 | 1.61624 | 0.808118 | − | 0.589021i | \(-0.200487\pi\) | ||||
0.808118 | + | 0.589021i | \(0.200487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.23130 | −0.211786 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9079 | 1.40241 | 0.701207 | − | 0.712957i | \(-0.252645\pi\) | ||||
0.701207 | + | 0.712957i | \(0.252645\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.16928 | −0.855040 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.6885 | −1.17305 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0785 | −0.923899 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.4217 | 1.03833 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.67969 | −0.241619 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1505 | −1.08677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6094 | −0.941435 | −0.470718 | − | 0.882284i | \(-0.656005\pi\) | ||||
−0.470718 | + | 0.882284i | \(0.656005\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.978457 | 0.0861483 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.3149 | −1.94966 | −0.974831 | − | 0.222943i | \(-0.928434\pi\) | ||||
−0.974831 | + | 0.222943i | \(0.928434\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.28442 | 0.458217 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.28126 | 0.196340 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0300 | 0.856919 | 0.428460 | − | 0.903561i | \(-0.359056\pi\) | ||||
0.428460 | + | 0.903561i | \(0.359056\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.27084 | 0.192611 | 0.0963053 | − | 0.995352i | \(-0.469298\pi\) | ||||
0.0963053 | + | 0.995352i | \(0.469298\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.39930 | −0.202058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.3476 | −1.70156 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.47424 | −0.786793 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.941770 | 0.0776759 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.92170 | −0.648971 | −0.324485 | − | 0.945891i | \(-0.605191\pi\) | ||||
−0.324485 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.29063 | −0.430546 | −0.215273 | − | 0.976554i | \(-0.569064\pi\) | ||||
−0.215273 | + | 0.976554i | \(0.569064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.2232 | 1.47326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.43703 | 0.517035 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.69056 | −0.613773 | −0.306887 | − | 0.951746i | \(-0.599287\pi\) | ||||
−0.306887 | + | 0.951746i | \(0.599287\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.617371 | 0.0489607 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.49229 | −0.669286 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.2163 | 1.11350 | 0.556752 | − | 0.830679i | \(-0.312047\pi\) | ||||
0.556752 | + | 0.830679i | \(0.312047\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.81464 | 0.141269 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.5366 | 1.97608 | 0.988040 | − | 0.154199i | \(-0.0492798\pi\) | ||||
0.988040 | + | 0.154199i | \(0.0492798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.46547 | 0.420421 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.55484 | −0.730677 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.30483 | −0.555376 | −0.277688 | − | 0.960671i | \(-0.589568\pi\) | ||||
−0.277688 | + | 0.960671i | \(0.589568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.08807 | −0.233436 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0486356 | 0.00365567 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.19399 | −0.462960 | −0.231480 | − | 0.972840i | \(-0.574357\pi\) | ||||
−0.231480 | + | 0.972840i | \(0.574357\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.51132 | 0.632641 | 0.316321 | − | 0.948652i | \(-0.397552\pi\) | ||||
0.316321 | + | 0.948652i | \(0.397552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.44073 | −0.180424 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.1020 | 1.33088 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.2233 | 2.13702 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.11283 | 0.153686 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.9988 | −0.795842 | −0.397921 | − | 0.917420i | \(-0.630268\pi\) | ||||
−0.397921 | + | 0.917420i | \(0.630268\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9670 | −0.933382 | −0.466691 | − | 0.884421i | \(-0.654554\pi\) | ||||
−0.466691 | + | 0.884421i | \(0.654554\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.64678 | −0.117929 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.60271 | 0.541671 | 0.270835 | − | 0.962626i | \(-0.412700\pi\) | ||||
0.270835 | + | 0.962626i | \(0.412700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.96777 | −0.564820 | −0.282410 | − | 0.959294i | \(-0.591134\pi\) | ||||
−0.282410 | + | 0.959294i | \(0.591134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.67595 | −0.118213 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.77474 | −0.615866 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.7396 | 1.51836 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.3551 | 1.06725 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.3225 | −1.05988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7030 | 0.874513 | 0.437256 | − | 0.899337i | \(-0.355950\pi\) | ||||
0.437256 | + | 0.899337i | \(0.355950\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.23178 | 0.0844005 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.93797 | −0.541365 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.96177 | 0.404711 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.44614 | −0.0977209 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.5202 | −1.78394 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7706 | −0.788219 | −0.394109 | − | 0.919064i | \(-0.628947\pi\) | ||||
−0.394109 | + | 0.919064i | \(0.628947\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.58360 | 0.372240 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.58907 | −0.304587 | −0.152294 | − | 0.988335i | \(-0.548666\pi\) | ||||
−0.152294 | + | 0.988335i | \(0.548666\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.76699 | 0.447175 | 0.223588 | − | 0.974684i | \(-0.428223\pi\) | ||||
0.223588 | + | 0.974684i | \(0.428223\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.68066 | 0.110579 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.23664 | 0.408576 | 0.204288 | − | 0.978911i | \(-0.434512\pi\) | ||||
0.204288 | + | 0.978911i | \(0.434512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.4649 | 1.26975 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.89767 | −0.123267 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.462154 | −0.0298943 | −0.0149471 | − | 0.999888i | \(-0.504758\pi\) | ||||
−0.0149471 | + | 0.999888i | \(0.504758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7355 | −0.949194 | −0.474597 | − | 0.880203i | \(-0.657406\pi\) | ||||
−0.474597 | + | 0.880203i | \(0.657406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.74553 | −0.368576 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.64034 | −0.488123 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.9051 | 0.884763 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.246818 | 0.0156415 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.5708 | 1.86649 | 0.933247 | − | 0.359235i | \(-0.116962\pi\) | ||||
0.933247 | + | 0.359235i | \(0.116962\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6239 | 1.54809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.36512 | 0.148109 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.5357 | −1.28098 | −0.640490 | − | 0.767967i | \(-0.721269\pi\) | ||||
−0.640490 | + | 0.767967i | \(0.721269\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.7655 | 1.04176 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.8658 | 0.982065 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.3586 | −1.25537 | −0.627683 | − | 0.778469i | \(-0.715997\pi\) | ||||
−0.627683 | + | 0.778469i | \(0.715997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.00858 | −0.307674 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.84954 | −0.235588 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.5190 | 0.885237 | 0.442619 | − | 0.896710i | \(-0.354050\pi\) | ||||
0.442619 | + | 0.896710i | \(0.354050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.2851 | −0.867759 | −0.433880 | − | 0.900971i | \(-0.642856\pi\) | ||||
−0.433880 | + | 0.900971i | \(0.642856\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.52520 | −0.0923092 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.95405 | 0.539949 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8056 | 1.06983 | 0.534916 | − | 0.844905i | \(-0.320343\pi\) | ||||
0.534916 | + | 0.844905i | \(0.320343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.7796 | −0.645357 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7804 | 1.12035 | 0.560173 | − | 0.828376i | \(-0.310735\pi\) | ||||
0.560173 | + | 0.828376i | \(0.310735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.5587 | −1.63819 | −0.819097 | − | 0.573655i | \(-0.805525\pi\) | ||||
−0.819097 | + | 0.573655i | \(0.805525\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.24009 | −0.0734563 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.1345 | 1.18850 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.0883 | 1.24049 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.14773 | −0.184523 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.80088 | −0.455733 | −0.227866 | − | 0.973692i | \(-0.573175\pi\) | ||||
−0.227866 | + | 0.973692i | \(0.573175\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.394568 | −0.0229726 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.12628 | −0.355483 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.3462 | −1.29231 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.35190 | −0.423756 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.41557 | 0.0813221 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.8011 | 1.13381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.75243 | −0.385382 | −0.192691 | − | 0.981260i | \(-0.561721\pi\) | ||||
−0.192691 | + | 0.981260i | \(0.561721\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.98947 | −0.170065 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.2693 | −1.82982 | −0.914912 | − | 0.403654i | \(-0.867740\pi\) | ||||
−0.914912 | + | 0.403654i | \(0.867740\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.0508 | 1.81162 | 0.905810 | − | 0.423685i | \(-0.139264\pi\) | ||||
0.905810 | + | 0.423685i | \(0.139264\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.50242 | −0.479057 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.4027 | −0.977431 | −0.488716 | − | 0.872443i | \(-0.662534\pi\) | ||||
−0.488716 | + | 0.872443i | \(0.662534\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.4429 | 1.42453 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.24506 | 0.0694924 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.9706 | −1.11119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.12579 | −0.450738 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.66743 | −0.202809 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.0278 | 0.993904 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5846 | 1.62612 | 0.813059 | − | 0.582182i | \(-0.197801\pi\) | ||||
0.813059 | + | 0.582182i | \(0.197801\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −30.3139 | −1.66119 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.5966 | 0.742861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.02154 | −0.328014 | −0.164007 | − | 0.986459i | \(-0.552442\pi\) | ||||
−0.164007 | + | 0.986459i | \(0.552442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.24011 | −0.175979 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2865 | −0.936117 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5077 | −0.999319 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.99287 | 0.107293 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.10663 | 0.0594068 | 0.0297034 | − | 0.999559i | \(-0.490544\pi\) | ||||
0.0297034 | + | 0.999559i | \(0.490544\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5033 | −0.990458 | −0.495229 | − | 0.868763i | \(-0.664916\pi\) | ||||
−0.495229 | + | 0.868763i | \(0.664916\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.55959 | 0.296749 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.31975 | −0.336366 | −0.168183 | − | 0.985756i | \(-0.553790\pi\) | ||||
−0.168183 | + | 0.985756i | \(0.553790\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.99316 | −0.530382 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.19049 | 0.115933 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.3704 | 1.44456 | 0.722278 | − | 0.691602i | \(-0.243095\pi\) | ||||
0.722278 | + | 0.691602i | \(0.243095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.52895 | −0.448892 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.48241 | −0.130293 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.7321 | 0.614088 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.6094 | −1.12800 | −0.564001 | − | 0.825774i | \(-0.690738\pi\) | ||||
−0.564001 | + | 0.825774i | \(0.690738\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.4056 | −1.89520 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.63878 | −0.240834 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6293 | −1.17170 | −0.585850 | − | 0.810419i | \(-0.699239\pi\) | ||||
−0.585850 | + | 0.810419i | \(0.699239\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.64081 | 0.136371 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.0894 | −1.18916 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.8768 | −1.17510 | −0.587550 | − | 0.809188i | \(-0.699908\pi\) | ||||
−0.587550 | + | 0.809188i | \(0.699908\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.30588 | 0.118134 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.6820 | −0.699119 | −0.349559 | − | 0.936914i | \(-0.613669\pi\) | ||||
−0.349559 | + | 0.936914i | \(0.613669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6348 | −0.694892 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.2931 | 0.675726 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.1384 | 0.615439 | 0.307719 | − | 0.951477i | \(-0.400434\pi\) | ||||
0.307719 | + | 0.951477i | \(0.400434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.0936 | 1.62304 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.84997 | 0.244649 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.3953 | 0.774621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.6967 | 1.54063 | 0.770313 | − | 0.637666i | \(-0.220100\pi\) | ||||
0.770313 | + | 0.637666i | \(0.220100\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.14853 | −0.0574983 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.65165 | 0.332167 | 0.166084 | − | 0.986112i | \(-0.446888\pi\) | ||||
0.166084 | + | 0.986112i | \(0.446888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6875 | 0.781450 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.1235 | 0.751493 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −48.6125 | −2.40963 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.2720 | 1.89243 | 0.946214 | − | 0.323541i | \(-0.104873\pi\) | ||||
0.946214 | + | 0.323541i | \(0.104873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.17994 | −0.107528 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.365436 | −0.0179819 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00237 | −0.0982927 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.493551 | −0.0241693 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.5974 | 1.54364 | 0.771818 | − | 0.635844i | \(-0.219348\pi\) | ||||
0.771818 | + | 0.635844i | \(0.219348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8718 | 1.16344 | 0.581720 | − | 0.813389i | \(-0.302380\pi\) | ||||
0.581720 | + | 0.813389i | \(0.302380\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32.5964 | −1.58489 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.6703 | 0.566092 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.3391 | 0.887491 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.42240 | 0.213516 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.75101 | 0.0843431 | 0.0421715 | − | 0.999110i | \(-0.486572\pi\) | ||||
0.0421715 | + | 0.999110i | \(0.486572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.36595 | −0.305928 | −0.152964 | − | 0.988232i | \(-0.548882\pi\) | ||||
−0.152964 | + | 0.988232i | \(0.548882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.05915 | 0.0987288 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.8274 | −0.804966 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6213 | 0.554655 | 0.277328 | − | 0.960775i | \(-0.410551\pi\) | ||||
0.277328 | + | 0.960775i | \(0.410551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.7947 | 0.609270 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8654 | 1.27641 | 0.638206 | − | 0.769865i | \(-0.279677\pi\) | ||||
0.638206 | + | 0.769865i | \(0.279677\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 31.2303 | 1.48046 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.72172 | 0.0814345 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.8136 | 0.699099 | 0.349549 | − | 0.936918i | \(-0.386335\pi\) | ||||
0.349549 | + | 0.936918i | \(0.386335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −58.3813 | −2.74907 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.14988 | 0.0540260 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.3735 | 0.580081 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.2920 | −0.528216 | −0.264108 | − | 0.964493i | \(-0.585078\pi\) | ||||
−0.264108 | + | 0.964493i | \(0.585078\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.98470 | −0.372694 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.1345 | 1.72953 | 0.864763 | − | 0.502180i | \(-0.167469\pi\) | ||||
0.864763 | + | 0.502180i | \(0.167469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.9567 | −0.880991 | −0.440495 | − | 0.897755i | \(-0.645197\pi\) | ||||
−0.440495 | + | 0.897755i | \(0.645197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.39904 | −0.0648789 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.79272 | 0.175506 | 0.0877531 | − | 0.996142i | \(-0.472031\pi\) | ||||
0.0877531 | + | 0.996142i | \(0.472031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.5927 | 0.581478 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.67148 | 0.0770179 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.3173 | 0.980169 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.11900 | −0.280759 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.38746 | 0.384036 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.5983 | 1.26100 | 0.630499 | − | 0.776190i | \(-0.282850\pi\) | ||||
0.630499 | + | 0.776190i | \(0.282850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.1158 | 2.01151 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.84573 | 0.0839838 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.5368 | 1.15956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.7583 | −1.48442 | −0.742210 | − | 0.670168i | \(-0.766222\pi\) | ||||
−0.742210 | + | 0.670168i | \(0.766222\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.08980 | −0.139725 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4034 | 1.73312 | 0.866561 | − | 0.499072i | \(-0.166326\pi\) | ||||
0.866561 | + | 0.499072i | \(0.166326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.1610 | 1.49350 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 24.6533 | 1.10808 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.25534 | −0.415159 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.5752 | −1.77163 | −0.885816 | − | 0.464037i | \(-0.846400\pi\) | ||||
−0.885816 | + | 0.464037i | \(0.846400\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.55018 | −0.247964 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.2094 | −0.722741 | −0.361371 | − | 0.932422i | \(-0.617691\pi\) | ||||
−0.361371 | + | 0.932422i | \(0.617691\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4841 | −0.511037 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.18788 | −0.0527555 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.90023 | 0.172875 | 0.0864374 | − | 0.996257i | \(-0.472452\pi\) | ||||
0.0864374 | + | 0.996257i | \(0.472452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8659 | 0.480681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.18657 | 0.184841 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.2528 | 1.06870 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −52.2726 | −2.29895 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.58765 | 0.0696900 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0831 | −0.485558 | −0.242779 | − | 0.970082i | \(-0.578059\pi\) | ||||
−0.242779 | + | 0.970082i | \(0.578059\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.54404 | 0.154970 | 0.0774850 | − | 0.996994i | \(-0.475311\pi\) | ||||
0.0774850 | + | 0.996994i | \(0.475311\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.671169 | 0.0292922 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.5304 | −0.981441 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.04244 | 0.175758 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.660752 | 0.0286742 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.9810 | 2.29486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.1008 | −0.436698 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.34621 | 0.0580935 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.5180 | 0.883772 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.6029 | −0.756808 | −0.378404 | − | 0.925640i | \(-0.623527\pi\) | ||||
−0.378404 | + | 0.925640i | \(0.623527\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.84987 | −0.0793855 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.7529 | 1.27448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.9882 | 0.512578 | 0.256289 | − | 0.966600i | \(-0.417500\pi\) | ||||
0.256289 | + | 0.966600i | \(0.417500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.1593 | −1.41520 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.3871 | −0.740716 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.2586 | 0.606339 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.93432 | −0.167003 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.7837 | 0.456921 | 0.228461 | − | 0.973553i | \(-0.426631\pi\) | ||||
0.228461 | + | 0.973553i | \(0.426631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.3454 | −0.818223 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.35147 | −0.268159 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6639 | −0.913025 | −0.456513 | − | 0.889717i | \(-0.650902\pi\) | ||||
−0.456513 | + | 0.889717i | \(0.650902\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.2862 | 1.10587 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.0069 | 0.588234 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.95093 | 0.165632 | 0.0828158 | − | 0.996565i | \(-0.473609\pi\) | ||||
0.0828158 | + | 0.996565i | \(0.473609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.3652 | −1.01965 | −0.509826 | − | 0.860278i | \(-0.670290\pi\) | ||||
−0.509826 | + | 0.860278i | \(0.670290\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.39050 | 0.0998644 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.83351 | 0.410086 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.6591 | 1.15146 | 0.575731 | − | 0.817639i | \(-0.304718\pi\) | ||||
0.575731 | + | 0.817639i | \(0.304718\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.81827 | 0.117123 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.85453 | −0.0769390 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.4504 | 0.557060 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.3728 | −0.925002 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.03413 | 0.207781 | 0.103890 | − | 0.994589i | \(-0.466871\pi\) | ||||
0.103890 | + | 0.994589i | \(0.466871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.8132 | 0.486755 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.65239 | −0.0679703 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.0095 | 0.985954 | 0.492977 | − | 0.870042i | \(-0.335909\pi\) | ||||
0.492977 | + | 0.870042i | \(0.335909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.7709 | −0.728537 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.73173 | 0.0708751 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.61773 | 0.147816 | 0.0739082 | − | 0.997265i | \(-0.476453\pi\) | ||||
0.0739082 | + | 0.997265i | \(0.476453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.3471 | −1.64579 | −0.822897 | − | 0.568190i | \(-0.807644\pi\) | ||||
−0.822897 | + | 0.568190i | \(0.807644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.7691 | −0.927231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.1392 | 0.818773 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.8461 | −0.805528 | −0.402764 | − | 0.915304i | \(-0.631950\pi\) | ||||
−0.402764 | + | 0.915304i | \(0.631950\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.90712 | 0.0772805 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 47.4374 | 1.91911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7510 | 0.757345 | 0.378672 | − | 0.925531i | \(-0.376381\pi\) | ||||
0.378672 | + | 0.925531i | \(0.376381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.72494 | −0.190528 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.7500 | −0.714590 | −0.357295 | − | 0.933992i | \(-0.616301\pi\) | ||||
−0.357295 | + | 0.933992i | \(0.616301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.69003 | −0.349282 | −0.174641 | − | 0.984632i | \(-0.555876\pi\) | ||||
−0.174641 | + | 0.984632i | \(0.555876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.72800 | −0.269985 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.9245 | 1.15884 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.9693 | −0.478774 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.33022 | 0.132996 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −63.3592 | −2.52630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3145 | 0.928136 | 0.464068 | − | 0.885800i | \(-0.346389\pi\) | ||||
0.464068 | + | 0.885800i | \(0.346389\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.76091 | −0.109736 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.7070 | −0.742365 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.6200 | −0.737753 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.7347 | 0.662016 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.3034 | 1.31540 | 0.657702 | − | 0.753279i | \(-0.271529\pi\) | ||||
0.657702 | + | 0.753279i | \(0.271529\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.5841 | 1.67935 | 0.839677 | − | 0.543087i | \(-0.182745\pi\) | ||||
0.839677 | + | 0.543087i | \(0.182745\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.72526 | 0.0679319 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.77584 | 0.227072 | 0.113536 | − | 0.993534i | \(-0.463782\pi\) | ||||
0.113536 | + | 0.993534i | \(0.463782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.05960 | 0.0415931 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.29575 | −0.0507843 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.6630 | 1.08254 | 0.541269 | − | 0.840850i | \(-0.317944\pi\) | ||||
0.541269 | + | 0.840850i | \(0.317944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.3466 | −1.53740 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.6469 | −0.766498 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.9222 | 0.892923 | 0.446462 | − | 0.894803i | \(-0.352684\pi\) | ||||
0.446462 | + | 0.894803i | \(0.352684\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.7645 | 1.35218 | 0.676091 | − | 0.736818i | \(-0.263673\pi\) | ||||
0.676091 | + | 0.736818i | \(0.263673\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.76395 | 0.223853 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.31771 | 0.361325 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.9418 | 1.08191 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.55825 | 0.0989078 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −53.1753 | −2.05281 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.57761 | 0.0608125 | 0.0304062 | − | 0.999538i | \(-0.490320\pi\) | ||||
0.0304062 | + | 0.999538i | \(0.490320\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.44652 | −0.0941665 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.7350 | 0.681612 | 0.340806 | − | 0.940134i | \(-0.389300\pi\) | ||||
0.340806 | + | 0.940134i | \(0.389300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.6513 | 0.907654 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.997399 | 0.0382204 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.3120 | −0.471106 | −0.235553 | − | 0.971862i | \(-0.575690\pi\) | ||||
−0.235553 | + | 0.971862i | \(0.575690\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.6853 | 0.675720 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.47075 | −0.0561127 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.2063 | −0.465021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.3776 | 0.623035 | 0.311518 | − | 0.950240i | \(-0.399163\pi\) | ||||
0.311518 | + | 0.950240i | \(0.399163\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.8331 | 0.867357 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00405 | 0.151882 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −76.0914 | −2.88217 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.35549 | −0.0512692 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1563 | 0.647984 | 0.323992 | − | 0.946060i | \(-0.394975\pi\) | ||||
0.323992 | + | 0.946060i | \(0.394975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.2207 | 1.25294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.23055 | −0.159332 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6362 | −0.400016 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.79811 | 0.217753 | 0.108876 | − | 0.994055i | \(-0.465275\pi\) | ||||
0.108876 | + | 0.994055i | \(0.465275\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.7813 | −0.966873 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.9844 | −0.710971 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.8778 | −1.34175 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.100446 | 0.00375121 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.0666 | 1.04671 | 0.523354 | − | 0.852115i | \(-0.324680\pi\) | ||||
0.523354 | + | 0.852115i | \(0.324680\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.4621 | 0.836534 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.20264 | 0.119107 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.1606 | 0.377354 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.7540 | −1.58566 | −0.792830 | − | 0.609443i | \(-0.791393\pi\) | ||||
−0.792830 | + | 0.609443i | \(0.791393\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.4825 | −0.906760 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.7839 | 1.02763 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.0366 | −0.370710 | −0.185355 | − | 0.982672i | \(-0.559343\pi\) | ||||
−0.185355 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.66057 | 0.0612510 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.5134 | −1.34499 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.4548 | 0.862798 | 0.431399 | − | 0.902161i | \(-0.358020\pi\) | ||||
0.431399 | + | 0.902161i | \(0.358020\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.02217 | −0.111022 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6455 | 0.830783 | 0.415392 | − | 0.909643i | \(-0.363645\pi\) | ||||
0.415392 | + | 0.909643i | \(0.363645\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.9679 | −0.511743 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.35322 | 0.122688 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.35508 | −0.341827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.42699 | −0.234213 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.32867 | −0.339505 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.1705 | −1.13291 | −0.566455 | − | 0.824093i | \(-0.691686\pi\) | ||||
−0.566455 | + | 0.824093i | \(0.691686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.35181 | −0.194259 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.3629 | −0.774403 | −0.387202 | − | 0.921995i | \(-0.626558\pi\) | ||||
−0.387202 | + | 0.921995i | \(0.626558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.5562 | 0.997602 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32.1319 | 1.16173 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.961590 | −0.0347210 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9756 | −1.04489 | −0.522444 | − | 0.852674i | \(-0.674980\pi\) | ||||
−0.522444 | + | 0.852674i | \(0.674980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.46327 | 0.160741 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.2980 | 0.622168 | 0.311084 | − | 0.950382i | \(-0.399308\pi\) | ||||
0.311084 | + | 0.950382i | \(0.399308\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.90334 | −0.247975 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.64385 | −0.130722 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.8965 | 1.42944 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.8364 | 0.960282 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.95176 | −0.248436 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.5603 | −0.483989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.8084 | −0.741740 | −0.370870 | − | 0.928685i | \(-0.620940\pi\) | ||||
−0.370870 | + | 0.928685i | \(0.620940\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.42479 | 0.157527 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.3454 | 0.865624 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.2566 | 1.71364 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.08858 | 0.0386078 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.2111 | 0.893025 | 0.446512 | − | 0.894778i | \(-0.352666\pi\) | ||||
0.446512 | + | 0.894778i | \(0.352666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68.1297 | −2.41026 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −52.2990 | −1.84789 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.5064 | −1.11184 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.9740 | −0.527763 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.15559 | −0.111082 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.1052 | −0.952968 | −0.476484 | − | 0.879183i | \(-0.658089\pi\) | ||||
−0.476484 | + | 0.879183i | \(0.658089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.8230 | −0.555619 | −0.277810 | − | 0.960636i | \(-0.589608\pi\) | ||||
−0.277810 | + | 0.960636i | \(0.589608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.10476 | 0.108889 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.0667 | 0.878050 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5678 | −0.509661 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.7210 | −0.724050 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.44493 | 0.0504285 | 0.0252143 | − | 0.999682i | \(-0.491973\pi\) | ||||
0.0252143 | + | 0.999682i | \(0.491973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.09322 | 0.316970 | 0.158485 | − | 0.987361i | \(-0.449339\pi\) | ||||
0.158485 | + | 0.987361i | \(0.449339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.94609 | −0.0677543 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.95363 | 0.137481 | 0.0687405 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687405 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.8653 | 0.828877 | 0.414438 | − | 0.910077i | \(-0.363978\pi\) | ||||
0.414438 | + | 0.910077i | \(0.363978\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.86990 | −0.134245 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.7422 | 0.926561 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.0272 | 1.55823 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.72320 | 0.163258 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.0805 | −0.382541 | −0.191270 | − | 0.981537i | \(-0.561261\pi\) | ||||
−0.191270 | + | 0.981537i | \(0.561261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.128833 | −0.00444250 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.08178 | −0.140584 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.63695 | 0.331521 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.6522 | 0.640899 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.98967 | 0.205565 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53.3872 | −1.83009 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.8275 | −0.952795 | −0.476398 | − | 0.879230i | \(-0.658058\pi\) | ||||
−0.476398 | + | 0.879230i | \(0.658058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.8475 | −0.576173 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.4486 | −1.04010 | −0.520052 | − | 0.854134i | \(-0.674088\pi\) | ||||
−0.520052 | + | 0.854134i | \(0.674088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.3728 | −0.660992 | −0.330496 | − | 0.943807i | \(-0.607216\pi\) | ||||
−0.330496 | + | 0.943807i | \(0.607216\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.37609 | −0.149137 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.7950 | 0.775951 | 0.387975 | − | 0.921670i | \(-0.373175\pi\) | ||||
0.387975 | + | 0.921670i | \(0.373175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.8802 | −0.437939 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.58338 | −0.155660 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.3437 | −1.40249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.1359 | 1.12277 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.7644 | −1.44735 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.8424 | −0.670796 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.50812 | −0.253531 | −0.126766 | − | 0.991933i | \(-0.540460\pi\) | ||||
−0.126766 | + | 0.991933i | \(0.540460\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.69546 | 0.0571865 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1458 | 0.476584 | 0.238292 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238292 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.6328 | −1.40106 | −0.700528 | − | 0.713625i | \(-0.747052\pi\) | ||||
−0.700528 | + | 0.713625i | \(0.747052\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0857564 | 0.00288267 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.6978 | 0.527082 | 0.263541 | − | 0.964648i | \(-0.415110\pi\) | ||||
0.263541 | + | 0.964648i | \(0.415110\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.3258 | −0.581090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.6138 | −1.36061 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.7220 | 1.19539 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.9215 | −0.365066 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.85677 | 0.162163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.6158 | −0.654223 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.5306 | 0.584031 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.59788 | 0.0531741 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.0075 | 0.498867 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3670 | 0.443844 | 0.221922 | − | 0.975064i | \(-0.428767\pi\) | ||||
0.221922 | + | 0.975064i | \(0.428767\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.2315 | 0.637870 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.3969 | −0.775174 | −0.387587 | − | 0.921833i | \(-0.626691\pi\) | ||||
−0.387587 | + | 0.921833i | \(0.626691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.37733 | 0.177964 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.30361 | −0.142273 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.4416 | −1.20341 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.7649 | 1.93847 | 0.969237 | − | 0.246129i | \(-0.0791588\pi\) | ||||
0.969237 | + | 0.246129i | \(0.0791588\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.46759 | 0.0483587 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.3540 | −0.801623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.4133 | −0.638305 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −40.6142 | −1.33394 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.9544 | −1.83580 | −0.917902 | − | 0.396807i | \(-0.870118\pi\) | ||||
−0.917902 | + | 0.396807i | \(0.870118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.0215 | −0.459537 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.01348 | 0.229611 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51.5278 | 1.68514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.14070 | 0.102602 | 0.0513011 | − | 0.998683i | \(-0.483663\pi\) | ||||
0.0513011 | + | 0.998683i | \(0.483663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.96600 | −0.227327 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.73923 | 0.317490 | 0.158745 | − | 0.987320i | \(-0.449255\pi\) | ||||
0.158745 | + | 0.987320i | \(0.449255\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −64.1155 | −2.08789 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.72543 | 0.121188 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.8318 | −1.45684 | −0.728419 | − | 0.685132i | \(-0.759745\pi\) | ||||
−0.728419 | + | 0.685132i | \(0.759745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.5921 | 0.928137 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.78234 | 0.122651 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.2386 | 1.01192 | 0.505958 | − | 0.862558i | \(-0.331139\pi\) | ||||
0.505958 | + | 0.862558i | \(0.331139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.3935 | −0.627558 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.52981 | −0.178753 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.3795 | 0.528923 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.6726 | −0.570082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9151 | 0.545081 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.8639 | −0.736015 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3706 | 0.751547 | 0.375774 | − | 0.926712i | \(-0.377377\pi\) | ||||
0.375774 | + | 0.926712i | \(0.377377\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.34045 | 0.139435 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0844 | 0.772904 | 0.386452 | − | 0.922310i | \(-0.373701\pi\) | ||||
0.386452 | + | 0.922310i | \(0.373701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.70842 | 0.118887 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.76608 | 0.0565598 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.5225 | 1.23244 | 0.616222 | − | 0.787573i | \(-0.288663\pi\) | ||||
0.616222 | + | 0.787573i | \(0.288663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −83.8684 | −2.68045 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −49.8249 | −1.59079 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.11774 | −0.0675453 | −0.0337726 | − | 0.999430i | \(-0.510752\pi\) | ||||
−0.0337726 | + | 0.999430i | \(0.510752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.4054 | 0.427133 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.91820 | −0.124718 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.4110 | 0.744427 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.7322 | −0.849175 | −0.424587 | − | 0.905387i | \(-0.639581\pi\) | ||||
−0.424587 | + | 0.905387i | \(0.639581\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.42999 | −0.204049 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0491 | −0.445387 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.1222 | 1.42903 | 0.714517 | − | 0.699618i | \(-0.246646\pi\) | ||||
0.714517 | + | 0.699618i | \(0.246646\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.2824 | 0.420237 |
(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 | 6008.2.a.e.1.23 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.23 | ✓ | 50 | 1.1 | even | 1 | trivial |