Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80025 | −1.27297 | −0.636485 | − | 0.771289i | \(-0.719612\pi\) | ||||
−0.636485 | + | 0.771289i | \(0.719612\pi\) | |||||||
\(3\) | 1.41167 | 0.815028 | 0.407514 | − | 0.913199i | \(-0.366396\pi\) | ||||
0.407514 | + | 0.913199i | \(0.366396\pi\) | |||||||
\(4\) | 1.24090 | 0.620451 | ||||||||
\(5\) | 0.213559 | 0.0955063 | 0.0477532 | − | 0.998859i | \(-0.484794\pi\) | ||||
0.0477532 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(6\) | −2.54136 | −1.03751 | ||||||||
\(7\) | −2.54704 | −0.962690 | −0.481345 | − | 0.876531i | \(-0.659852\pi\) | ||||
−0.481345 | + | 0.876531i | \(0.659852\pi\) | |||||||
\(8\) | 1.36657 | 0.483154 | ||||||||
\(9\) | −1.00719 | −0.335730 | ||||||||
\(10\) | −0.384459 | −0.121577 | ||||||||
\(11\) | 1.24725 | 0.376061 | 0.188030 | − | 0.982163i | \(-0.439790\pi\) | ||||
0.188030 | + | 0.982163i | \(0.439790\pi\) | |||||||
\(12\) | 1.75174 | 0.505685 | ||||||||
\(13\) | 1.90462 | 0.528247 | 0.264124 | − | 0.964489i | \(-0.414917\pi\) | ||||
0.264124 | + | 0.964489i | \(0.414917\pi\) | |||||||
\(14\) | 4.58531 | 1.22547 | ||||||||
\(15\) | 0.301474 | 0.0778403 | ||||||||
\(16\) | −4.94197 | −1.23549 | ||||||||
\(17\) | −3.92660 | −0.952339 | −0.476170 | − | 0.879353i | \(-0.657975\pi\) | ||||
−0.476170 | + | 0.879353i | \(0.657975\pi\) | |||||||
\(18\) | 1.81319 | 0.427374 | ||||||||
\(19\) | 5.27048 | 1.20913 | 0.604566 | − | 0.796555i | \(-0.293347\pi\) | ||||
0.604566 | + | 0.796555i | \(0.293347\pi\) | |||||||
\(20\) | 0.265005 | 0.0592570 | ||||||||
\(21\) | −3.59558 | −0.784619 | ||||||||
\(22\) | −2.24537 | −0.478714 | ||||||||
\(23\) | 2.59275 | 0.540625 | 0.270313 | − | 0.962773i | \(-0.412873\pi\) | ||||
0.270313 | + | 0.962773i | \(0.412873\pi\) | |||||||
\(24\) | 1.92914 | 0.393784 | ||||||||
\(25\) | −4.95439 | −0.990879 | ||||||||
\(26\) | −3.42880 | −0.672443 | ||||||||
\(27\) | −5.65683 | −1.08866 | ||||||||
\(28\) | −3.16063 | −0.597302 | ||||||||
\(29\) | 4.85757 | 0.902027 | 0.451014 | − | 0.892517i | \(-0.351063\pi\) | ||||
0.451014 | + | 0.892517i | \(0.351063\pi\) | |||||||
\(30\) | −0.542729 | −0.0990883 | ||||||||
\(31\) | 1.57742 | 0.283313 | 0.141656 | − | 0.989916i | \(-0.454757\pi\) | ||||
0.141656 | + | 0.989916i | \(0.454757\pi\) | |||||||
\(32\) | 6.16365 | 1.08959 | ||||||||
\(33\) | 1.76071 | 0.306500 | ||||||||
\(34\) | 7.06886 | 1.21230 | ||||||||
\(35\) | −0.543942 | −0.0919430 | ||||||||
\(36\) | −1.24983 | −0.208304 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −9.48819 | −1.53919 | ||||||||
\(39\) | 2.68870 | 0.430536 | ||||||||
\(40\) | 0.291842 | 0.0461442 | ||||||||
\(41\) | −7.59622 | −1.18633 | −0.593165 | − | 0.805081i | \(-0.702122\pi\) | ||||
−0.593165 | + | 0.805081i | \(0.702122\pi\) | |||||||
\(42\) | 6.47294 | 0.998796 | ||||||||
\(43\) | −3.23107 | −0.492733 | −0.246366 | − | 0.969177i | \(-0.579237\pi\) | ||||
−0.246366 | + | 0.969177i | \(0.579237\pi\) | |||||||
\(44\) | 1.54772 | 0.233328 | ||||||||
\(45\) | −0.215094 | −0.0320643 | ||||||||
\(46\) | −4.66760 | −0.688199 | ||||||||
\(47\) | −1.14828 | −0.167494 | −0.0837469 | − | 0.996487i | \(-0.526689\pi\) | ||||
−0.0837469 | + | 0.996487i | \(0.526689\pi\) | |||||||
\(48\) | −6.97642 | −1.00696 | ||||||||
\(49\) | −0.512597 | −0.0732282 | ||||||||
\(50\) | 8.91915 | 1.26136 | ||||||||
\(51\) | −5.54305 | −0.776183 | ||||||||
\(52\) | 2.36345 | 0.327752 | ||||||||
\(53\) | 11.3924 | 1.56486 | 0.782430 | − | 0.622738i | \(-0.213980\pi\) | ||||
0.782430 | + | 0.622738i | \(0.213980\pi\) | |||||||
\(54\) | 10.1837 | 1.38583 | ||||||||
\(55\) | 0.266362 | 0.0359162 | ||||||||
\(56\) | −3.48069 | −0.465127 | ||||||||
\(57\) | 7.44018 | 0.985476 | ||||||||
\(58\) | −8.74484 | −1.14825 | ||||||||
\(59\) | 4.17419 | 0.543434 | 0.271717 | − | 0.962377i | \(-0.412409\pi\) | ||||
0.271717 | + | 0.962377i | \(0.412409\pi\) | |||||||
\(60\) | 0.374100 | 0.0482961 | ||||||||
\(61\) | 4.10910 | 0.526117 | 0.263058 | − | 0.964780i | \(-0.415269\pi\) | ||||
0.263058 | + | 0.964780i | \(0.415269\pi\) | |||||||
\(62\) | −2.83975 | −0.360649 | ||||||||
\(63\) | 2.56535 | 0.323204 | ||||||||
\(64\) | −1.21218 | −0.151522 | ||||||||
\(65\) | 0.406749 | 0.0504510 | ||||||||
\(66\) | −3.16972 | −0.390165 | ||||||||
\(67\) | −5.17598 | −0.632346 | −0.316173 | − | 0.948701i | \(-0.602398\pi\) | ||||
−0.316173 | + | 0.948701i | \(0.602398\pi\) | |||||||
\(68\) | −4.87252 | −0.590880 | ||||||||
\(69\) | 3.66010 | 0.440624 | ||||||||
\(70\) | 0.979232 | 0.117041 | ||||||||
\(71\) | −16.1412 | −1.91560 | −0.957802 | − | 0.287429i | \(-0.907199\pi\) | ||||
−0.957802 | + | 0.287429i | \(0.907199\pi\) | |||||||
\(72\) | −1.37639 | −0.162209 | ||||||||
\(73\) | −4.41986 | −0.517305 | −0.258653 | − | 0.965970i | \(-0.583279\pi\) | ||||
−0.258653 | + | 0.965970i | \(0.583279\pi\) | |||||||
\(74\) | 1.80025 | 0.209275 | ||||||||
\(75\) | −6.99396 | −0.807593 | ||||||||
\(76\) | 6.54016 | 0.750207 | ||||||||
\(77\) | −3.17680 | −0.362030 | ||||||||
\(78\) | −4.84033 | −0.548059 | ||||||||
\(79\) | −2.92425 | −0.329004 | −0.164502 | − | 0.986377i | \(-0.552602\pi\) | ||||
−0.164502 | + | 0.986377i | \(0.552602\pi\) | |||||||
\(80\) | −1.05540 | −0.117997 | ||||||||
\(81\) | −4.96400 | −0.551555 | ||||||||
\(82\) | 13.6751 | 1.51016 | ||||||||
\(83\) | 7.83025 | 0.859482 | 0.429741 | − | 0.902952i | \(-0.358605\pi\) | ||||
0.429741 | + | 0.902952i | \(0.358605\pi\) | |||||||
\(84\) | −4.46176 | −0.486818 | ||||||||
\(85\) | −0.838558 | −0.0909544 | ||||||||
\(86\) | 5.81673 | 0.627234 | ||||||||
\(87\) | 6.85727 | 0.735177 | ||||||||
\(88\) | 1.70445 | 0.181695 | ||||||||
\(89\) | 4.91950 | 0.521466 | 0.260733 | − | 0.965411i | \(-0.416036\pi\) | ||||
0.260733 | + | 0.965411i | \(0.416036\pi\) | |||||||
\(90\) | 0.387223 | 0.0408169 | ||||||||
\(91\) | −4.85115 | −0.508538 | ||||||||
\(92\) | 3.21735 | 0.335432 | ||||||||
\(93\) | 2.22679 | 0.230908 | ||||||||
\(94\) | 2.06719 | 0.213214 | ||||||||
\(95\) | 1.12556 | 0.115480 | ||||||||
\(96\) | 8.70103 | 0.888045 | ||||||||
\(97\) | 11.2210 | 1.13932 | 0.569662 | − | 0.821879i | \(-0.307074\pi\) | ||||
0.569662 | + | 0.821879i | \(0.307074\pi\) | |||||||
\(98\) | 0.922803 | 0.0932172 | ||||||||
\(99\) | −1.25622 | −0.126255 | ||||||||
\(100\) | −6.14792 | −0.614792 | ||||||||
\(101\) | 6.77092 | 0.673732 | 0.336866 | − | 0.941553i | \(-0.390633\pi\) | ||||
0.336866 | + | 0.941553i | \(0.390633\pi\) | |||||||
\(102\) | 9.97889 | 0.988057 | ||||||||
\(103\) | 2.91963 | 0.287679 | 0.143840 | − | 0.989601i | \(-0.454055\pi\) | ||||
0.143840 | + | 0.989601i | \(0.454055\pi\) | |||||||
\(104\) | 2.60279 | 0.255225 | ||||||||
\(105\) | −0.767866 | −0.0749360 | ||||||||
\(106\) | −20.5091 | −1.99202 | ||||||||
\(107\) | −8.02324 | −0.775636 | −0.387818 | − | 0.921736i | \(-0.626771\pi\) | ||||
−0.387818 | + | 0.921736i | \(0.626771\pi\) | |||||||
\(108\) | −7.01957 | −0.675459 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −0.479518 | −0.0457202 | ||||||||
\(111\) | −1.41167 | −0.133990 | ||||||||
\(112\) | 12.5874 | 1.18940 | ||||||||
\(113\) | −11.1729 | −1.05106 | −0.525530 | − | 0.850775i | \(-0.676133\pi\) | ||||
−0.525530 | + | 0.850775i | \(0.676133\pi\) | |||||||
\(114\) | −13.3942 | −1.25448 | ||||||||
\(115\) | 0.553703 | 0.0516331 | ||||||||
\(116\) | 6.02777 | 0.559664 | ||||||||
\(117\) | −1.91832 | −0.177349 | ||||||||
\(118\) | −7.51460 | −0.691775 | ||||||||
\(119\) | 10.0012 | 0.916807 | ||||||||
\(120\) | 0.411984 | 0.0376088 | ||||||||
\(121\) | −9.44436 | −0.858578 | ||||||||
\(122\) | −7.39742 | −0.669731 | ||||||||
\(123\) | −10.7234 | −0.966892 | ||||||||
\(124\) | 1.95742 | 0.175782 | ||||||||
\(125\) | −2.12585 | −0.190141 | ||||||||
\(126\) | −4.61828 | −0.411429 | ||||||||
\(127\) | −20.4583 | −1.81538 | −0.907690 | − | 0.419641i | \(-0.862156\pi\) | ||||
−0.907690 | + | 0.419641i | \(0.862156\pi\) | |||||||
\(128\) | −10.1451 | −0.896706 | ||||||||
\(129\) | −4.56120 | −0.401591 | ||||||||
\(130\) | −0.732250 | −0.0642225 | ||||||||
\(131\) | −15.9608 | −1.39450 | −0.697250 | − | 0.716828i | \(-0.745593\pi\) | ||||
−0.697250 | + | 0.716828i | \(0.745593\pi\) | |||||||
\(132\) | 2.18487 | 0.190168 | ||||||||
\(133\) | −13.4241 | −1.16402 | ||||||||
\(134\) | 9.31806 | 0.804958 | ||||||||
\(135\) | −1.20806 | −0.103974 | ||||||||
\(136\) | −5.36595 | −0.460126 | ||||||||
\(137\) | −13.2797 | −1.13456 | −0.567282 | − | 0.823524i | \(-0.692005\pi\) | ||||
−0.567282 | + | 0.823524i | \(0.692005\pi\) | |||||||
\(138\) | −6.58910 | −0.560901 | ||||||||
\(139\) | 21.2954 | 1.80625 | 0.903124 | − | 0.429380i | \(-0.141268\pi\) | ||||
0.903124 | + | 0.429380i | \(0.141268\pi\) | |||||||
\(140\) | −0.674979 | −0.0570461 | ||||||||
\(141\) | −1.62099 | −0.136512 | ||||||||
\(142\) | 29.0581 | 2.43851 | ||||||||
\(143\) | 2.37555 | 0.198653 | ||||||||
\(144\) | 4.97750 | 0.414792 | ||||||||
\(145\) | 1.03737 | 0.0861493 | ||||||||
\(146\) | 7.95686 | 0.658514 | ||||||||
\(147\) | −0.723618 | −0.0596830 | ||||||||
\(148\) | −1.24090 | −0.102002 | ||||||||
\(149\) | −18.6716 | −1.52963 | −0.764817 | − | 0.644247i | \(-0.777171\pi\) | ||||
−0.764817 | + | 0.644247i | \(0.777171\pi\) | |||||||
\(150\) | 12.5909 | 1.02804 | ||||||||
\(151\) | −1.68125 | −0.136818 | −0.0684090 | − | 0.997657i | \(-0.521792\pi\) | ||||
−0.0684090 | + | 0.997657i | \(0.521792\pi\) | |||||||
\(152\) | 7.20246 | 0.584196 | ||||||||
\(153\) | 3.95483 | 0.319729 | ||||||||
\(154\) | 5.71904 | 0.460853 | ||||||||
\(155\) | 0.336871 | 0.0270582 | ||||||||
\(156\) | 3.33641 | 0.267127 | ||||||||
\(157\) | −20.7802 | −1.65844 | −0.829221 | − | 0.558921i | \(-0.811216\pi\) | ||||
−0.829221 | + | 0.558921i | \(0.811216\pi\) | |||||||
\(158\) | 5.26439 | 0.418812 | ||||||||
\(159\) | 16.0822 | 1.27540 | ||||||||
\(160\) | 1.31630 | 0.104063 | ||||||||
\(161\) | −6.60383 | −0.520454 | ||||||||
\(162\) | 8.93644 | 0.702113 | ||||||||
\(163\) | −1.41071 | −0.110495 | −0.0552475 | − | 0.998473i | \(-0.517595\pi\) | ||||
−0.0552475 | + | 0.998473i | \(0.517595\pi\) | |||||||
\(164\) | −9.42618 | −0.736061 | ||||||||
\(165\) | 0.376014 | 0.0292727 | ||||||||
\(166\) | −14.0964 | −1.09409 | ||||||||
\(167\) | 17.5776 | 1.36020 | 0.680100 | − | 0.733120i | \(-0.261937\pi\) | ||||
0.680100 | + | 0.733120i | \(0.261937\pi\) | |||||||
\(168\) | −4.91359 | −0.379092 | ||||||||
\(169\) | −9.37241 | −0.720955 | ||||||||
\(170\) | 1.50961 | 0.115782 | ||||||||
\(171\) | −5.30838 | −0.405942 | ||||||||
\(172\) | −4.00944 | −0.305717 | ||||||||
\(173\) | −14.5096 | −1.10314 | −0.551572 | − | 0.834127i | \(-0.685972\pi\) | ||||
−0.551572 | + | 0.834127i | \(0.685972\pi\) | |||||||
\(174\) | −12.3448 | −0.935858 | ||||||||
\(175\) | 12.6190 | 0.953909 | ||||||||
\(176\) | −6.16388 | −0.464620 | ||||||||
\(177\) | 5.89258 | 0.442914 | ||||||||
\(178\) | −8.85634 | −0.663810 | ||||||||
\(179\) | 12.3478 | 0.922918 | 0.461459 | − | 0.887161i | \(-0.347326\pi\) | ||||
0.461459 | + | 0.887161i | \(0.347326\pi\) | |||||||
\(180\) | −0.266911 | −0.0198944 | ||||||||
\(181\) | 22.1524 | 1.64657 | 0.823287 | − | 0.567626i | \(-0.192138\pi\) | ||||
0.823287 | + | 0.567626i | \(0.192138\pi\) | |||||||
\(182\) | 8.73328 | 0.647354 | ||||||||
\(183\) | 5.80069 | 0.428800 | ||||||||
\(184\) | 3.54316 | 0.261205 | ||||||||
\(185\) | −0.213559 | −0.0157011 | ||||||||
\(186\) | −4.00879 | −0.293938 | ||||||||
\(187\) | −4.89746 | −0.358138 | ||||||||
\(188\) | −1.42490 | −0.103922 | ||||||||
\(189\) | 14.4082 | 1.04804 | ||||||||
\(190\) | −2.02628 | −0.147002 | ||||||||
\(191\) | 15.1479 | 1.09607 | 0.548033 | − | 0.836456i | \(-0.315377\pi\) | ||||
0.548033 | + | 0.836456i | \(0.315377\pi\) | |||||||
\(192\) | −1.71120 | −0.123495 | ||||||||
\(193\) | −23.5997 | −1.69874 | −0.849372 | − | 0.527794i | \(-0.823019\pi\) | ||||
−0.849372 | + | 0.527794i | \(0.823019\pi\) | |||||||
\(194\) | −20.2007 | −1.45032 | ||||||||
\(195\) | 0.574195 | 0.0411189 | ||||||||
\(196\) | −0.636083 | −0.0454345 | ||||||||
\(197\) | −18.6758 | −1.33060 | −0.665298 | − | 0.746578i | \(-0.731696\pi\) | ||||
−0.665298 | + | 0.746578i | \(0.731696\pi\) | |||||||
\(198\) | 2.26151 | 0.160719 | ||||||||
\(199\) | 6.98773 | 0.495347 | 0.247674 | − | 0.968844i | \(-0.420334\pi\) | ||||
0.247674 | + | 0.968844i | \(0.420334\pi\) | |||||||
\(200\) | −6.77050 | −0.478747 | ||||||||
\(201\) | −7.30677 | −0.515380 | ||||||||
\(202\) | −12.1894 | −0.857640 | ||||||||
\(203\) | −12.3724 | −0.868372 | ||||||||
\(204\) | −6.87839 | −0.481584 | ||||||||
\(205\) | −1.62224 | −0.113302 | ||||||||
\(206\) | −5.25606 | −0.366207 | ||||||||
\(207\) | −2.61139 | −0.181504 | ||||||||
\(208\) | −9.41258 | −0.652645 | ||||||||
\(209\) | 6.57363 | 0.454707 | ||||||||
\(210\) | 1.38235 | 0.0953913 | ||||||||
\(211\) | −12.7140 | −0.875266 | −0.437633 | − | 0.899154i | \(-0.644183\pi\) | ||||
−0.437633 | + | 0.899154i | \(0.644183\pi\) | |||||||
\(212\) | 14.1368 | 0.970920 | ||||||||
\(213\) | −22.7860 | −1.56127 | ||||||||
\(214\) | 14.4438 | 0.987361 | ||||||||
\(215\) | −0.690022 | −0.0470591 | ||||||||
\(216\) | −7.73042 | −0.525989 | ||||||||
\(217\) | −4.01775 | −0.272742 | ||||||||
\(218\) | 1.80025 | 0.121928 | ||||||||
\(219\) | −6.23938 | −0.421618 | ||||||||
\(220\) | 0.330529 | 0.0222843 | ||||||||
\(221\) | −7.47868 | −0.503071 | ||||||||
\(222\) | 2.54136 | 0.170565 | ||||||||
\(223\) | 16.6781 | 1.11685 | 0.558425 | − | 0.829555i | \(-0.311406\pi\) | ||||
0.558425 | + | 0.829555i | \(0.311406\pi\) | |||||||
\(224\) | −15.6990 | −1.04894 | ||||||||
\(225\) | 4.99002 | 0.332668 | ||||||||
\(226\) | 20.1140 | 1.33797 | ||||||||
\(227\) | −13.6199 | −0.903982 | −0.451991 | − | 0.892023i | \(-0.649286\pi\) | ||||
−0.451991 | + | 0.892023i | \(0.649286\pi\) | |||||||
\(228\) | 9.23254 | 0.611440 | ||||||||
\(229\) | −15.5217 | −1.02571 | −0.512853 | − | 0.858477i | \(-0.671411\pi\) | ||||
−0.512853 | + | 0.858477i | \(0.671411\pi\) | |||||||
\(230\) | −0.996805 | −0.0657274 | ||||||||
\(231\) | −4.48459 | −0.295065 | ||||||||
\(232\) | 6.63818 | 0.435818 | ||||||||
\(233\) | −0.525509 | −0.0344273 | −0.0172136 | − | 0.999852i | \(-0.505480\pi\) | ||||
−0.0172136 | + | 0.999852i | \(0.505480\pi\) | |||||||
\(234\) | 3.45345 | 0.225759 | ||||||||
\(235\) | −0.245225 | −0.0159967 | ||||||||
\(236\) | 5.17977 | 0.337174 | ||||||||
\(237\) | −4.12808 | −0.268148 | ||||||||
\(238\) | −18.0046 | −1.16707 | ||||||||
\(239\) | −25.9358 | −1.67765 | −0.838824 | − | 0.544403i | \(-0.816756\pi\) | ||||
−0.838824 | + | 0.544403i | \(0.816756\pi\) | |||||||
\(240\) | −1.48987 | −0.0961710 | ||||||||
\(241\) | −1.29649 | −0.0835143 | −0.0417572 | − | 0.999128i | \(-0.513296\pi\) | ||||
−0.0417572 | + | 0.999128i | \(0.513296\pi\) | |||||||
\(242\) | 17.0022 | 1.09294 | ||||||||
\(243\) | 9.96296 | 0.639124 | ||||||||
\(244\) | 5.09900 | 0.326430 | ||||||||
\(245\) | −0.109470 | −0.00699375 | ||||||||
\(246\) | 19.3047 | 1.23082 | ||||||||
\(247\) | 10.0383 | 0.638721 | ||||||||
\(248\) | 2.15565 | 0.136884 | ||||||||
\(249\) | 11.0537 | 0.700501 | ||||||||
\(250\) | 3.82706 | 0.242044 | ||||||||
\(251\) | 22.6741 | 1.43117 | 0.715587 | − | 0.698524i | \(-0.246159\pi\) | ||||
0.715587 | + | 0.698524i | \(0.246159\pi\) | |||||||
\(252\) | 3.18335 | 0.200532 | ||||||||
\(253\) | 3.23381 | 0.203308 | ||||||||
\(254\) | 36.8301 | 2.31092 | ||||||||
\(255\) | −1.18377 | −0.0741303 | ||||||||
\(256\) | 20.6880 | 1.29300 | ||||||||
\(257\) | 5.53155 | 0.345049 | 0.172524 | − | 0.985005i | \(-0.444808\pi\) | ||||
0.172524 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(258\) | 8.21130 | 0.511213 | ||||||||
\(259\) | 2.54704 | 0.158265 | ||||||||
\(260\) | 0.504736 | 0.0313024 | ||||||||
\(261\) | −4.89249 | −0.302838 | ||||||||
\(262\) | 28.7334 | 1.77516 | ||||||||
\(263\) | −24.3064 | −1.49880 | −0.749398 | − | 0.662119i | \(-0.769657\pi\) | ||||
−0.749398 | + | 0.662119i | \(0.769657\pi\) | |||||||
\(264\) | 2.40612 | 0.148087 | ||||||||
\(265\) | 2.43293 | 0.149454 | ||||||||
\(266\) | 24.1668 | 1.48176 | ||||||||
\(267\) | 6.94471 | 0.425009 | ||||||||
\(268\) | −6.42289 | −0.392340 | ||||||||
\(269\) | 2.16670 | 0.132106 | 0.0660531 | − | 0.997816i | \(-0.478959\pi\) | ||||
0.0660531 | + | 0.997816i | \(0.478959\pi\) | |||||||
\(270\) | 2.17482 | 0.132355 | ||||||||
\(271\) | −5.39620 | −0.327796 | −0.163898 | − | 0.986477i | \(-0.552407\pi\) | ||||
−0.163898 | + | 0.986477i | \(0.552407\pi\) | |||||||
\(272\) | 19.4051 | 1.17661 | ||||||||
\(273\) | −6.84822 | −0.414473 | ||||||||
\(274\) | 23.9068 | 1.44426 | ||||||||
\(275\) | −6.17938 | −0.372631 | ||||||||
\(276\) | 4.54183 | 0.273386 | ||||||||
\(277\) | 3.88107 | 0.233191 | 0.116595 | − | 0.993179i | \(-0.462802\pi\) | ||||
0.116595 | + | 0.993179i | \(0.462802\pi\) | |||||||
\(278\) | −38.3370 | −2.29930 | ||||||||
\(279\) | −1.58876 | −0.0951166 | ||||||||
\(280\) | −0.743332 | −0.0444226 | ||||||||
\(281\) | −10.8055 | −0.644603 | −0.322302 | − | 0.946637i | \(-0.604457\pi\) | ||||
−0.322302 | + | 0.946637i | \(0.604457\pi\) | |||||||
\(282\) | 2.91819 | 0.173776 | ||||||||
\(283\) | 5.45346 | 0.324175 | 0.162087 | − | 0.986776i | \(-0.448177\pi\) | ||||
0.162087 | + | 0.986776i | \(0.448177\pi\) | |||||||
\(284\) | −20.0296 | −1.18854 | ||||||||
\(285\) | 1.58891 | 0.0941191 | ||||||||
\(286\) | −4.27658 | −0.252880 | ||||||||
\(287\) | 19.3479 | 1.14207 | ||||||||
\(288\) | −6.20797 | −0.365808 | ||||||||
\(289\) | −1.58185 | −0.0930500 | ||||||||
\(290\) | −1.86753 | −0.109665 | ||||||||
\(291\) | 15.8404 | 0.928580 | ||||||||
\(292\) | −5.48462 | −0.320963 | ||||||||
\(293\) | 6.74315 | 0.393939 | 0.196970 | − | 0.980410i | \(-0.436890\pi\) | ||||
0.196970 | + | 0.980410i | \(0.436890\pi\) | |||||||
\(294\) | 1.30269 | 0.0759746 | ||||||||
\(295\) | 0.891435 | 0.0519014 | ||||||||
\(296\) | −1.36657 | −0.0794300 | ||||||||
\(297\) | −7.05550 | −0.409401 | ||||||||
\(298\) | 33.6135 | 1.94718 | ||||||||
\(299\) | 4.93821 | 0.285584 | ||||||||
\(300\) | −8.67883 | −0.501072 | ||||||||
\(301\) | 8.22965 | 0.474349 | ||||||||
\(302\) | 3.02667 | 0.174165 | ||||||||
\(303\) | 9.55830 | 0.549110 | ||||||||
\(304\) | −26.0465 | −1.49387 | ||||||||
\(305\) | 0.877534 | 0.0502475 | ||||||||
\(306\) | −7.11968 | −0.407005 | ||||||||
\(307\) | −7.00194 | −0.399622 | −0.199811 | − | 0.979834i | \(-0.564033\pi\) | ||||
−0.199811 | + | 0.979834i | \(0.564033\pi\) | |||||||
\(308\) | −3.94210 | −0.224622 | ||||||||
\(309\) | 4.12155 | 0.234467 | ||||||||
\(310\) | −0.606453 | −0.0344442 | ||||||||
\(311\) | 6.95327 | 0.394284 | 0.197142 | − | 0.980375i | \(-0.436834\pi\) | ||||
0.197142 | + | 0.980375i | \(0.436834\pi\) | |||||||
\(312\) | 3.67428 | 0.208015 | ||||||||
\(313\) | 23.7959 | 1.34502 | 0.672512 | − | 0.740086i | \(-0.265215\pi\) | ||||
0.672512 | + | 0.740086i | \(0.265215\pi\) | |||||||
\(314\) | 37.4096 | 2.11115 | ||||||||
\(315\) | 0.547853 | 0.0308680 | ||||||||
\(316\) | −3.62872 | −0.204131 | ||||||||
\(317\) | 0.222151 | 0.0124773 | 0.00623863 | − | 0.999981i | \(-0.498014\pi\) | ||||
0.00623863 | + | 0.999981i | \(0.498014\pi\) | |||||||
\(318\) | −28.9521 | −1.62355 | ||||||||
\(319\) | 6.05861 | 0.339217 | ||||||||
\(320\) | −0.258871 | −0.0144713 | ||||||||
\(321\) | −11.3262 | −0.632165 | ||||||||
\(322\) | 11.8885 | 0.662523 | ||||||||
\(323\) | −20.6950 | −1.15150 | ||||||||
\(324\) | −6.15984 | −0.342213 | ||||||||
\(325\) | −9.43625 | −0.523429 | ||||||||
\(326\) | 2.53962 | 0.140657 | ||||||||
\(327\) | −1.41167 | −0.0780655 | ||||||||
\(328\) | −10.3807 | −0.573180 | ||||||||
\(329\) | 2.92471 | 0.161245 | ||||||||
\(330\) | −0.676920 | −0.0372632 | ||||||||
\(331\) | −28.7581 | −1.58069 | −0.790343 | − | 0.612665i | \(-0.790098\pi\) | ||||
−0.790343 | + | 0.612665i | \(0.790098\pi\) | |||||||
\(332\) | 9.71658 | 0.533267 | ||||||||
\(333\) | 1.00719 | 0.0551937 | ||||||||
\(334\) | −31.6442 | −1.73149 | ||||||||
\(335\) | −1.10537 | −0.0603931 | ||||||||
\(336\) | 17.7692 | 0.969390 | ||||||||
\(337\) | 1.70024 | 0.0926181 | 0.0463090 | − | 0.998927i | \(-0.485254\pi\) | ||||
0.0463090 | + | 0.998927i | \(0.485254\pi\) | |||||||
\(338\) | 16.8727 | 0.917753 | ||||||||
\(339\) | −15.7725 | −0.856642 | ||||||||
\(340\) | −1.04057 | −0.0564328 | ||||||||
\(341\) | 1.96744 | 0.106543 | ||||||||
\(342\) | 9.55641 | 0.516752 | ||||||||
\(343\) | 19.1349 | 1.03319 | ||||||||
\(344\) | −4.41546 | −0.238066 | ||||||||
\(345\) | 0.781646 | 0.0420824 | ||||||||
\(346\) | 26.1209 | 1.40427 | ||||||||
\(347\) | −28.8999 | −1.55143 | −0.775714 | − | 0.631085i | \(-0.782610\pi\) | ||||
−0.775714 | + | 0.631085i | \(0.782610\pi\) | |||||||
\(348\) | 8.50921 | 0.456142 | ||||||||
\(349\) | 14.5565 | 0.779194 | 0.389597 | − | 0.920985i | \(-0.372614\pi\) | ||||
0.389597 | + | 0.920985i | \(0.372614\pi\) | |||||||
\(350\) | −22.7174 | −1.21430 | ||||||||
\(351\) | −10.7741 | −0.575080 | ||||||||
\(352\) | 7.68763 | 0.409752 | ||||||||
\(353\) | 0.608885 | 0.0324077 | 0.0162038 | − | 0.999869i | \(-0.494842\pi\) | ||||
0.0162038 | + | 0.999869i | \(0.494842\pi\) | |||||||
\(354\) | −10.6081 | −0.563815 | ||||||||
\(355\) | −3.44708 | −0.182952 | ||||||||
\(356\) | 6.10462 | 0.323544 | ||||||||
\(357\) | 14.1184 | 0.747223 | ||||||||
\(358\) | −22.2291 | −1.17485 | ||||||||
\(359\) | 4.48611 | 0.236768 | 0.118384 | − | 0.992968i | \(-0.462229\pi\) | ||||
0.118384 | + | 0.992968i | \(0.462229\pi\) | |||||||
\(360\) | −0.293940 | −0.0154920 | ||||||||
\(361\) | 8.77798 | 0.461999 | ||||||||
\(362\) | −39.8798 | −2.09604 | ||||||||
\(363\) | −13.3323 | −0.699765 | ||||||||
\(364\) | −6.01980 | −0.315523 | ||||||||
\(365\) | −0.943899 | −0.0494059 | ||||||||
\(366\) | −10.4427 | −0.545849 | ||||||||
\(367\) | −11.0145 | −0.574952 | −0.287476 | − | 0.957788i | \(-0.592816\pi\) | ||||
−0.287476 | + | 0.957788i | \(0.592816\pi\) | |||||||
\(368\) | −12.8133 | −0.667938 | ||||||||
\(369\) | 7.65084 | 0.398287 | ||||||||
\(370\) | 0.384459 | 0.0199871 | ||||||||
\(371\) | −29.0168 | −1.50648 | ||||||||
\(372\) | 2.76323 | 0.143267 | ||||||||
\(373\) | 7.38632 | 0.382449 | 0.191225 | − | 0.981546i | \(-0.438754\pi\) | ||||
0.191225 | + | 0.981546i | \(0.438754\pi\) | |||||||
\(374\) | 8.81665 | 0.455898 | ||||||||
\(375\) | −3.00099 | −0.154971 | ||||||||
\(376\) | −1.56920 | −0.0809252 | ||||||||
\(377\) | 9.25183 | 0.476494 | ||||||||
\(378\) | −25.9383 | −1.33412 | ||||||||
\(379\) | 22.1161 | 1.13603 | 0.568013 | − | 0.823019i | \(-0.307712\pi\) | ||||
0.568013 | + | 0.823019i | \(0.307712\pi\) | |||||||
\(380\) | 1.39671 | 0.0716495 | ||||||||
\(381\) | −28.8803 | −1.47959 | ||||||||
\(382\) | −27.2701 | −1.39526 | ||||||||
\(383\) | −17.9409 | −0.916735 | −0.458367 | − | 0.888763i | \(-0.651566\pi\) | ||||
−0.458367 | + | 0.888763i | \(0.651566\pi\) | |||||||
\(384\) | −14.3215 | −0.730840 | ||||||||
\(385\) | −0.678433 | −0.0345762 | ||||||||
\(386\) | 42.4854 | 2.16245 | ||||||||
\(387\) | 3.25430 | 0.165425 | ||||||||
\(388\) | 13.9242 | 0.706895 | ||||||||
\(389\) | −2.56891 | −0.130249 | −0.0651244 | − | 0.997877i | \(-0.520744\pi\) | ||||
−0.0651244 | + | 0.997877i | \(0.520744\pi\) | |||||||
\(390\) | −1.03369 | −0.0523431 | ||||||||
\(391\) | −10.1807 | −0.514859 | ||||||||
\(392\) | −0.700497 | −0.0353805 | ||||||||
\(393\) | −22.5313 | −1.13656 | ||||||||
\(394\) | 33.6211 | 1.69381 | ||||||||
\(395\) | −0.624500 | −0.0314220 | ||||||||
\(396\) | −1.55885 | −0.0783351 | ||||||||
\(397\) | −5.25847 | −0.263915 | −0.131958 | − | 0.991255i | \(-0.542126\pi\) | ||||
−0.131958 | + | 0.991255i | \(0.542126\pi\) | |||||||
\(398\) | −12.5797 | −0.630562 | ||||||||
\(399\) | −18.9504 | −0.948707 | ||||||||
\(400\) | 24.4844 | 1.22422 | ||||||||
\(401\) | −26.7064 | −1.33366 | −0.666828 | − | 0.745212i | \(-0.732348\pi\) | ||||
−0.666828 | + | 0.745212i | \(0.732348\pi\) | |||||||
\(402\) | 13.1540 | 0.656063 | ||||||||
\(403\) | 3.00439 | 0.149659 | ||||||||
\(404\) | 8.40205 | 0.418018 | ||||||||
\(405\) | −1.06010 | −0.0526770 | ||||||||
\(406\) | 22.2734 | 1.10541 | ||||||||
\(407\) | −1.24725 | −0.0618240 | ||||||||
\(408\) | −7.57494 | −0.375016 | ||||||||
\(409\) | 7.22754 | 0.357379 | 0.178689 | − | 0.983906i | \(-0.442814\pi\) | ||||
0.178689 | + | 0.983906i | \(0.442814\pi\) | |||||||
\(410\) | 2.92044 | 0.144230 | ||||||||
\(411\) | −18.7466 | −0.924701 | ||||||||
\(412\) | 3.62297 | 0.178491 | ||||||||
\(413\) | −10.6318 | −0.523158 | ||||||||
\(414\) | 4.70116 | 0.231049 | ||||||||
\(415\) | 1.67222 | 0.0820859 | ||||||||
\(416\) | 11.7394 | 0.575573 | ||||||||
\(417\) | 30.0620 | 1.47214 | ||||||||
\(418\) | −11.8342 | −0.578828 | ||||||||
\(419\) | −30.1586 | −1.47335 | −0.736673 | − | 0.676249i | \(-0.763604\pi\) | ||||
−0.736673 | + | 0.676249i | \(0.763604\pi\) | |||||||
\(420\) | −0.952847 | −0.0464942 | ||||||||
\(421\) | −38.2342 | −1.86342 | −0.931711 | − | 0.363201i | \(-0.881684\pi\) | ||||
−0.931711 | + | 0.363201i | \(0.881684\pi\) | |||||||
\(422\) | 22.8883 | 1.11419 | ||||||||
\(423\) | 1.15654 | 0.0562327 | ||||||||
\(424\) | 15.5684 | 0.756068 | ||||||||
\(425\) | 19.4539 | 0.943652 | ||||||||
\(426\) | 41.0205 | 1.98745 | ||||||||
\(427\) | −10.4660 | −0.506487 | ||||||||
\(428\) | −9.95606 | −0.481244 | ||||||||
\(429\) | 3.35349 | 0.161908 | ||||||||
\(430\) | 1.24221 | 0.0599048 | ||||||||
\(431\) | 29.8305 | 1.43688 | 0.718441 | − | 0.695588i | \(-0.244856\pi\) | ||||
0.718441 | + | 0.695588i | \(0.244856\pi\) | |||||||
\(432\) | 27.9558 | 1.34503 | ||||||||
\(433\) | −39.4970 | −1.89810 | −0.949052 | − | 0.315120i | \(-0.897955\pi\) | ||||
−0.949052 | + | 0.315120i | \(0.897955\pi\) | |||||||
\(434\) | 7.23295 | 0.347193 | ||||||||
\(435\) | 1.46443 | 0.0702140 | ||||||||
\(436\) | −1.24090 | −0.0594285 | ||||||||
\(437\) | 13.6650 | 0.653687 | ||||||||
\(438\) | 11.2324 | 0.536707 | ||||||||
\(439\) | −6.49411 | −0.309947 | −0.154974 | − | 0.987919i | \(-0.549529\pi\) | ||||
−0.154974 | + | 0.987919i | \(0.549529\pi\) | |||||||
\(440\) | 0.364001 | 0.0173530 | ||||||||
\(441\) | 0.516283 | 0.0245849 | ||||||||
\(442\) | 13.4635 | 0.640394 | ||||||||
\(443\) | −30.9260 | −1.46934 | −0.734669 | − | 0.678426i | \(-0.762663\pi\) | ||||
−0.734669 | + | 0.678426i | \(0.762663\pi\) | |||||||
\(444\) | −1.75174 | −0.0831341 | ||||||||
\(445\) | 1.05060 | 0.0498033 | ||||||||
\(446\) | −30.0248 | −1.42172 | ||||||||
\(447\) | −26.3581 | −1.24669 | ||||||||
\(448\) | 3.08747 | 0.145869 | ||||||||
\(449\) | −25.2817 | −1.19312 | −0.596559 | − | 0.802570i | \(-0.703466\pi\) | ||||
−0.596559 | + | 0.802570i | \(0.703466\pi\) | |||||||
\(450\) | −8.98328 | −0.423476 | ||||||||
\(451\) | −9.47441 | −0.446133 | ||||||||
\(452\) | −13.8645 | −0.652131 | ||||||||
\(453\) | −2.37336 | −0.111510 | ||||||||
\(454\) | 24.5192 | 1.15074 | ||||||||
\(455\) | −1.03600 | −0.0485686 | ||||||||
\(456\) | 10.1675 | 0.476136 | ||||||||
\(457\) | 38.5460 | 1.80310 | 0.901552 | − | 0.432671i | \(-0.142429\pi\) | ||||
0.901552 | + | 0.432671i | \(0.142429\pi\) | |||||||
\(458\) | 27.9430 | 1.30569 | ||||||||
\(459\) | 22.2121 | 1.03677 | ||||||||
\(460\) | 0.687092 | 0.0320358 | ||||||||
\(461\) | −37.5321 | −1.74805 | −0.874023 | − | 0.485884i | \(-0.838498\pi\) | ||||
−0.874023 | + | 0.485884i | \(0.838498\pi\) | |||||||
\(462\) | 8.07339 | 0.375608 | ||||||||
\(463\) | 40.8846 | 1.90007 | 0.950033 | − | 0.312149i | \(-0.101049\pi\) | ||||
0.950033 | + | 0.312149i | \(0.101049\pi\) | |||||||
\(464\) | −24.0059 | −1.11445 | ||||||||
\(465\) | 0.475551 | 0.0220531 | ||||||||
\(466\) | 0.946049 | 0.0438249 | ||||||||
\(467\) | 23.3733 | 1.08159 | 0.540794 | − | 0.841155i | \(-0.318124\pi\) | ||||
0.540794 | + | 0.841155i | \(0.318124\pi\) | |||||||
\(468\) | −2.38045 | −0.110036 | ||||||||
\(469\) | 13.1834 | 0.608753 | ||||||||
\(470\) | 0.441466 | 0.0203633 | ||||||||
\(471\) | −29.3348 | −1.35168 | ||||||||
\(472\) | 5.70431 | 0.262562 | ||||||||
\(473\) | −4.02996 | −0.185298 | ||||||||
\(474\) | 7.43158 | 0.341344 | ||||||||
\(475\) | −26.1120 | −1.19810 | ||||||||
\(476\) | 12.4105 | 0.568834 | ||||||||
\(477\) | −11.4743 | −0.525371 | ||||||||
\(478\) | 46.6909 | 2.13559 | ||||||||
\(479\) | −38.0047 | −1.73648 | −0.868240 | − | 0.496144i | \(-0.834749\pi\) | ||||
−0.868240 | + | 0.496144i | \(0.834749\pi\) | |||||||
\(480\) | 1.85818 | 0.0848139 | ||||||||
\(481\) | −1.90462 | −0.0868433 | ||||||||
\(482\) | 2.33401 | 0.106311 | ||||||||
\(483\) | −9.32242 | −0.424185 | ||||||||
\(484\) | −11.7195 | −0.532706 | ||||||||
\(485\) | 2.39635 | 0.108813 | ||||||||
\(486\) | −17.9358 | −0.813586 | ||||||||
\(487\) | −13.8591 | −0.628015 | −0.314007 | − | 0.949421i | \(-0.601672\pi\) | ||||
−0.314007 | + | 0.949421i | \(0.601672\pi\) | |||||||
\(488\) | 5.61536 | 0.254195 | ||||||||
\(489\) | −1.99145 | −0.0900565 | ||||||||
\(490\) | 0.197073 | 0.00890283 | ||||||||
\(491\) | 29.9389 | 1.35112 | 0.675562 | − | 0.737303i | \(-0.263901\pi\) | ||||
0.675562 | + | 0.737303i | \(0.263901\pi\) | |||||||
\(492\) | −13.3066 | −0.599910 | ||||||||
\(493\) | −19.0737 | −0.859036 | ||||||||
\(494\) | −18.0714 | −0.813072 | ||||||||
\(495\) | −0.268277 | −0.0120581 | ||||||||
\(496\) | −7.79555 | −0.350030 | ||||||||
\(497\) | 41.1122 | 1.84413 | ||||||||
\(498\) | −19.8995 | −0.891717 | ||||||||
\(499\) | −16.9268 | −0.757745 | −0.378873 | − | 0.925449i | \(-0.623688\pi\) | ||||
−0.378873 | + | 0.925449i | \(0.623688\pi\) | |||||||
\(500\) | −2.63797 | −0.117974 | ||||||||
\(501\) | 24.8138 | 1.10860 | ||||||||
\(502\) | −40.8190 | −1.82184 | ||||||||
\(503\) | −38.7637 | −1.72839 | −0.864193 | − | 0.503161i | \(-0.832170\pi\) | ||||
−0.864193 | + | 0.503161i | \(0.832170\pi\) | |||||||
\(504\) | 3.50572 | 0.156157 | ||||||||
\(505\) | 1.44599 | 0.0643456 | ||||||||
\(506\) | −5.82167 | −0.258805 | ||||||||
\(507\) | −13.2307 | −0.587598 | ||||||||
\(508\) | −25.3868 | −1.12636 | ||||||||
\(509\) | −17.6837 | −0.783816 | −0.391908 | − | 0.920004i | \(-0.628185\pi\) | ||||
−0.391908 | + | 0.920004i | \(0.628185\pi\) | |||||||
\(510\) | 2.13108 | 0.0943657 | ||||||||
\(511\) | 11.2575 | 0.498005 | ||||||||
\(512\) | −16.9535 | −0.749246 | ||||||||
\(513\) | −29.8142 | −1.31633 | ||||||||
\(514\) | −9.95818 | −0.439237 | ||||||||
\(515\) | 0.623511 | 0.0274752 | ||||||||
\(516\) | −5.66000 | −0.249168 | ||||||||
\(517\) | −1.43220 | −0.0629879 | ||||||||
\(518\) | −4.58531 | −0.201467 | ||||||||
\(519\) | −20.4827 | −0.899092 | ||||||||
\(520\) | 0.555849 | 0.0243756 | ||||||||
\(521\) | 5.32183 | 0.233154 | 0.116577 | − | 0.993182i | \(-0.462808\pi\) | ||||
0.116577 | + | 0.993182i | \(0.462808\pi\) | |||||||
\(522\) | 8.80771 | 0.385503 | ||||||||
\(523\) | 8.01136 | 0.350312 | 0.175156 | − | 0.984541i | \(-0.443957\pi\) | ||||
0.175156 | + | 0.984541i | \(0.443957\pi\) | |||||||
\(524\) | −19.8058 | −0.865219 | ||||||||
\(525\) | 17.8139 | 0.777462 | ||||||||
\(526\) | 43.7576 | 1.90792 | ||||||||
\(527\) | −6.19388 | −0.269810 | ||||||||
\(528\) | −8.70136 | −0.378678 | ||||||||
\(529\) | −16.2777 | −0.707724 | ||||||||
\(530\) | −4.37989 | −0.190250 | ||||||||
\(531\) | −4.20421 | −0.182447 | ||||||||
\(532\) | −16.6580 | −0.722217 | ||||||||
\(533\) | −14.4679 | −0.626676 | ||||||||
\(534\) | −12.5022 | −0.541024 | ||||||||
\(535\) | −1.71343 | −0.0740781 | ||||||||
\(536\) | −7.07331 | −0.305521 | ||||||||
\(537\) | 17.4310 | 0.752204 | ||||||||
\(538\) | −3.90061 | −0.168167 | ||||||||
\(539\) | −0.639338 | −0.0275383 | ||||||||
\(540\) | −1.49909 | −0.0645106 | ||||||||
\(541\) | 41.5949 | 1.78831 | 0.894153 | − | 0.447762i | \(-0.147779\pi\) | ||||
0.894153 | + | 0.447762i | \(0.147779\pi\) | |||||||
\(542\) | 9.71451 | 0.417274 | ||||||||
\(543\) | 31.2718 | 1.34200 | ||||||||
\(544\) | −24.2021 | −1.03766 | ||||||||
\(545\) | −0.213559 | −0.00914784 | ||||||||
\(546\) | 12.3285 | 0.527611 | ||||||||
\(547\) | −2.56527 | −0.109683 | −0.0548416 | − | 0.998495i | \(-0.517465\pi\) | ||||
−0.0548416 | + | 0.998495i | \(0.517465\pi\) | |||||||
\(548\) | −16.4789 | −0.703942 | ||||||||
\(549\) | −4.13865 | −0.176633 | ||||||||
\(550\) | 11.1244 | 0.474348 | ||||||||
\(551\) | 25.6017 | 1.09067 | ||||||||
\(552\) | 5.00177 | 0.212889 | ||||||||
\(553\) | 7.44819 | 0.316729 | ||||||||
\(554\) | −6.98690 | −0.296845 | ||||||||
\(555\) | −0.301474 | −0.0127969 | ||||||||
\(556\) | 26.4255 | 1.12069 | ||||||||
\(557\) | 4.01493 | 0.170118 | 0.0850590 | − | 0.996376i | \(-0.472892\pi\) | ||||
0.0850590 | + | 0.996376i | \(0.472892\pi\) | |||||||
\(558\) | 2.86017 | 0.121081 | ||||||||
\(559\) | −6.15396 | −0.260285 | ||||||||
\(560\) | 2.68814 | 0.113595 | ||||||||
\(561\) | −6.91359 | −0.291892 | ||||||||
\(562\) | 19.4526 | 0.820560 | ||||||||
\(563\) | 5.53414 | 0.233236 | 0.116618 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116618 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(564\) | −2.01149 | −0.0846991 | ||||||||
\(565\) | −2.38607 | −0.100383 | ||||||||
\(566\) | −9.81760 | −0.412665 | ||||||||
\(567\) | 12.6435 | 0.530977 | ||||||||
\(568\) | −22.0580 | −0.925531 | ||||||||
\(569\) | −4.96786 | −0.208263 | −0.104132 | − | 0.994564i | \(-0.533206\pi\) | ||||
−0.104132 | + | 0.994564i | \(0.533206\pi\) | |||||||
\(570\) | −2.86044 | −0.119811 | ||||||||
\(571\) | 0.262219 | 0.0109735 | 0.00548676 | − | 0.999985i | \(-0.498253\pi\) | ||||
0.00548676 | + | 0.999985i | \(0.498253\pi\) | |||||||
\(572\) | 2.94782 | 0.123255 | ||||||||
\(573\) | 21.3839 | 0.893325 | ||||||||
\(574\) | −34.8310 | −1.45382 | ||||||||
\(575\) | −12.8455 | −0.535694 | ||||||||
\(576\) | 1.22090 | 0.0508706 | ||||||||
\(577\) | −27.1979 | −1.13226 | −0.566131 | − | 0.824315i | \(-0.691560\pi\) | ||||
−0.566131 | + | 0.824315i | \(0.691560\pi\) | |||||||
\(578\) | 2.84773 | 0.118450 | ||||||||
\(579\) | −33.3150 | −1.38452 | ||||||||
\(580\) | 1.28728 | 0.0534514 | ||||||||
\(581\) | −19.9439 | −0.827414 | ||||||||
\(582\) | −28.5167 | −1.18205 | ||||||||
\(583\) | 14.2091 | 0.588483 | ||||||||
\(584\) | −6.04003 | −0.249938 | ||||||||
\(585\) | −0.409673 | −0.0169379 | ||||||||
\(586\) | −12.1394 | −0.501472 | ||||||||
\(587\) | −39.4103 | −1.62664 | −0.813319 | − | 0.581818i | \(-0.802341\pi\) | ||||
−0.813319 | + | 0.581818i | \(0.802341\pi\) | |||||||
\(588\) | −0.897939 | −0.0370304 | ||||||||
\(589\) | 8.31376 | 0.342562 | ||||||||
\(590\) | −1.60481 | −0.0660688 | ||||||||
\(591\) | −26.3641 | −1.08447 | ||||||||
\(592\) | 4.94197 | 0.203114 | ||||||||
\(593\) | 41.0366 | 1.68517 | 0.842586 | − | 0.538562i | \(-0.181032\pi\) | ||||
0.842586 | + | 0.538562i | \(0.181032\pi\) | |||||||
\(594\) | 12.7017 | 0.521155 | ||||||||
\(595\) | 2.13584 | 0.0875609 | ||||||||
\(596\) | −23.1696 | −0.949064 | ||||||||
\(597\) | 9.86437 | 0.403722 | ||||||||
\(598\) | −8.89001 | −0.363540 | ||||||||
\(599\) | −30.6206 | −1.25112 | −0.625562 | − | 0.780175i | \(-0.715130\pi\) | ||||
−0.625562 | + | 0.780175i | \(0.715130\pi\) | |||||||
\(600\) | −9.55771 | −0.390192 | ||||||||
\(601\) | 19.2508 | 0.785257 | 0.392629 | − | 0.919697i | \(-0.371566\pi\) | ||||
0.392629 | + | 0.919697i | \(0.371566\pi\) | |||||||
\(602\) | −14.8154 | −0.603832 | ||||||||
\(603\) | 5.21319 | 0.212298 | ||||||||
\(604\) | −2.08626 | −0.0848889 | ||||||||
\(605\) | −2.01692 | −0.0819996 | ||||||||
\(606\) | −17.2073 | −0.699000 | ||||||||
\(607\) | −15.0844 | −0.612257 | −0.306128 | − | 0.951990i | \(-0.599034\pi\) | ||||
−0.306128 | + | 0.951990i | \(0.599034\pi\) | |||||||
\(608\) | 32.4854 | 1.31746 | ||||||||
\(609\) | −17.4657 | −0.707747 | ||||||||
\(610\) | −1.57978 | −0.0639635 | ||||||||
\(611\) | −2.18704 | −0.0884782 | ||||||||
\(612\) | 4.90756 | 0.198376 | ||||||||
\(613\) | −11.2684 | −0.455128 | −0.227564 | − | 0.973763i | \(-0.573076\pi\) | ||||
−0.227564 | + | 0.973763i | \(0.573076\pi\) | |||||||
\(614\) | 12.6053 | 0.508707 | ||||||||
\(615\) | −2.29006 | −0.0923443 | ||||||||
\(616\) | −4.34131 | −0.174916 | ||||||||
\(617\) | −46.9949 | −1.89194 | −0.945972 | − | 0.324247i | \(-0.894889\pi\) | ||||
−0.945972 | + | 0.324247i | \(0.894889\pi\) | |||||||
\(618\) | −7.41982 | −0.298469 | ||||||||
\(619\) | −41.6769 | −1.67514 | −0.837569 | − | 0.546332i | \(-0.816024\pi\) | ||||
−0.837569 | + | 0.546332i | \(0.816024\pi\) | |||||||
\(620\) | 0.418025 | 0.0167883 | ||||||||
\(621\) | −14.6667 | −0.588555 | ||||||||
\(622\) | −12.5176 | −0.501911 | ||||||||
\(623\) | −12.5302 | −0.502010 | ||||||||
\(624\) | −13.2875 | −0.531924 | ||||||||
\(625\) | 24.3180 | 0.972719 | ||||||||
\(626\) | −42.8386 | −1.71217 | ||||||||
\(627\) | 9.27978 | 0.370599 | ||||||||
\(628\) | −25.7862 | −1.02898 | ||||||||
\(629\) | 3.92660 | 0.156564 | ||||||||
\(630\) | −0.986273 | −0.0392940 | ||||||||
\(631\) | 45.7407 | 1.82091 | 0.910454 | − | 0.413610i | \(-0.135732\pi\) | ||||
0.910454 | + | 0.413610i | \(0.135732\pi\) | |||||||
\(632\) | −3.99618 | −0.158960 | ||||||||
\(633\) | −17.9479 | −0.713366 | ||||||||
\(634\) | −0.399928 | −0.0158832 | ||||||||
\(635\) | −4.36904 | −0.173380 | ||||||||
\(636\) | 19.9565 | 0.791326 | ||||||||
\(637\) | −0.976305 | −0.0386826 | ||||||||
\(638\) | −10.9070 | −0.431813 | ||||||||
\(639\) | 16.2572 | 0.643126 | ||||||||
\(640\) | −2.16657 | −0.0856411 | ||||||||
\(641\) | −21.0365 | −0.830893 | −0.415447 | − | 0.909618i | \(-0.636375\pi\) | ||||
−0.415447 | + | 0.909618i | \(0.636375\pi\) | |||||||
\(642\) | 20.3899 | 0.804726 | ||||||||
\(643\) | 46.3141 | 1.82645 | 0.913224 | − | 0.407458i | \(-0.133585\pi\) | ||||
0.913224 | + | 0.407458i | \(0.133585\pi\) | |||||||
\(644\) | −8.19471 | −0.322917 | ||||||||
\(645\) | −0.974083 | −0.0383545 | ||||||||
\(646\) | 37.2563 | 1.46583 | ||||||||
\(647\) | 40.7174 | 1.60077 | 0.800383 | − | 0.599489i | \(-0.204630\pi\) | ||||
0.800383 | + | 0.599489i | \(0.204630\pi\) | |||||||
\(648\) | −6.78363 | −0.266486 | ||||||||
\(649\) | 5.20628 | 0.204364 | ||||||||
\(650\) | 16.9876 | 0.666309 | ||||||||
\(651\) | −5.67173 | −0.222293 | ||||||||
\(652\) | −1.75055 | −0.0685568 | ||||||||
\(653\) | −46.9420 | −1.83698 | −0.918491 | − | 0.395442i | \(-0.870591\pi\) | ||||
−0.918491 | + | 0.395442i | \(0.870591\pi\) | |||||||
\(654\) | 2.54136 | 0.0993750 | ||||||||
\(655\) | −3.40856 | −0.133184 | ||||||||
\(656\) | 37.5403 | 1.46570 | ||||||||
\(657\) | 4.45164 | 0.173675 | ||||||||
\(658\) | −5.26521 | −0.205259 | ||||||||
\(659\) | 15.0726 | 0.587147 | 0.293573 | − | 0.955937i | \(-0.405156\pi\) | ||||
0.293573 | + | 0.955937i | \(0.405156\pi\) | |||||||
\(660\) | 0.466597 | 0.0181623 | ||||||||
\(661\) | 14.8072 | 0.575933 | 0.287967 | − | 0.957640i | \(-0.407021\pi\) | ||||
0.287967 | + | 0.957640i | \(0.407021\pi\) | |||||||
\(662\) | 51.7717 | 2.01216 | ||||||||
\(663\) | −10.5574 | −0.410017 | ||||||||
\(664\) | 10.7005 | 0.415262 | ||||||||
\(665\) | −2.86684 | −0.111171 | ||||||||
\(666\) | −1.81319 | −0.0702599 | ||||||||
\(667\) | 12.5944 | 0.487659 | ||||||||
\(668\) | 21.8122 | 0.843938 | ||||||||
\(669\) | 23.5440 | 0.910263 | ||||||||
\(670\) | 1.98995 | 0.0768785 | ||||||||
\(671\) | 5.12509 | 0.197852 | ||||||||
\(672\) | −22.1619 | −0.854912 | ||||||||
\(673\) | 46.0429 | 1.77482 | 0.887412 | − | 0.460978i | \(-0.152501\pi\) | ||||
0.887412 | + | 0.460978i | \(0.152501\pi\) | |||||||
\(674\) | −3.06086 | −0.117900 | ||||||||
\(675\) | 28.0261 | 1.07873 | ||||||||
\(676\) | −11.6303 | −0.447317 | ||||||||
\(677\) | 20.6941 | 0.795339 | 0.397669 | − | 0.917529i | \(-0.369819\pi\) | ||||
0.397669 | + | 0.917529i | \(0.369819\pi\) | |||||||
\(678\) | 28.3944 | 1.09048 | ||||||||
\(679\) | −28.5804 | −1.09682 | ||||||||
\(680\) | −1.14594 | −0.0439450 | ||||||||
\(681\) | −19.2267 | −0.736770 | ||||||||
\(682\) | −3.54189 | −0.135626 | ||||||||
\(683\) | −20.2855 | −0.776202 | −0.388101 | − | 0.921617i | \(-0.626869\pi\) | ||||
−0.388101 | + | 0.921617i | \(0.626869\pi\) | |||||||
\(684\) | −6.58718 | −0.251867 | ||||||||
\(685\) | −2.83600 | −0.108358 | ||||||||
\(686\) | −34.4476 | −1.31521 | ||||||||
\(687\) | −21.9116 | −0.835978 | ||||||||
\(688\) | 15.9678 | 0.608767 | ||||||||
\(689\) | 21.6981 | 0.826633 | ||||||||
\(690\) | −1.40716 | −0.0535696 | ||||||||
\(691\) | 3.13865 | 0.119400 | 0.0596999 | − | 0.998216i | \(-0.480986\pi\) | ||||
0.0596999 | + | 0.998216i | \(0.480986\pi\) | |||||||
\(692\) | −18.0050 | −0.684447 | ||||||||
\(693\) | 3.19964 | 0.121544 | ||||||||
\(694\) | 52.0271 | 1.97492 | ||||||||
\(695\) | 4.54781 | 0.172508 | ||||||||
\(696\) | 9.37091 | 0.355204 | ||||||||
\(697\) | 29.8273 | 1.12979 | ||||||||
\(698\) | −26.2054 | −0.991890 | ||||||||
\(699\) | −0.741845 | −0.0280592 | ||||||||
\(700\) | 15.6590 | 0.591854 | ||||||||
\(701\) | −2.61768 | −0.0988684 | −0.0494342 | − | 0.998777i | \(-0.515742\pi\) | ||||
−0.0494342 | + | 0.998777i | \(0.515742\pi\) | |||||||
\(702\) | 19.3961 | 0.732060 | ||||||||
\(703\) | −5.27048 | −0.198780 | ||||||||
\(704\) | −1.51189 | −0.0569817 | ||||||||
\(705\) | −0.346176 | −0.0130378 | ||||||||
\(706\) | −1.09615 | −0.0412540 | ||||||||
\(707\) | −17.2458 | −0.648595 | ||||||||
\(708\) | 7.31212 | 0.274806 | ||||||||
\(709\) | 3.07494 | 0.115482 | 0.0577408 | − | 0.998332i | \(-0.481610\pi\) | ||||
0.0577408 | + | 0.998332i | \(0.481610\pi\) | |||||||
\(710\) | 6.20562 | 0.232893 | ||||||||
\(711\) | 2.94528 | 0.110457 | ||||||||
\(712\) | 6.72282 | 0.251948 | ||||||||
\(713\) | 4.08985 | 0.153166 | ||||||||
\(714\) | −25.4166 | −0.951192 | ||||||||
\(715\) | 0.507319 | 0.0189726 | ||||||||
\(716\) | 15.3224 | 0.572626 | ||||||||
\(717\) | −36.6128 | −1.36733 | ||||||||
\(718\) | −8.07612 | −0.301398 | ||||||||
\(719\) | −46.9200 | −1.74982 | −0.874910 | − | 0.484285i | \(-0.839080\pi\) | ||||
−0.874910 | + | 0.484285i | \(0.839080\pi\) | |||||||
\(720\) | 1.06299 | 0.0396152 | ||||||||
\(721\) | −7.43640 | −0.276946 | ||||||||
\(722\) | −15.8026 | −0.588111 | ||||||||
\(723\) | −1.83022 | −0.0680665 | ||||||||
\(724\) | 27.4889 | 1.02162 | ||||||||
\(725\) | −24.0663 | −0.893799 | ||||||||
\(726\) | 24.0015 | 0.890779 | ||||||||
\(727\) | 23.0194 | 0.853743 | 0.426871 | − | 0.904312i | \(-0.359616\pi\) | ||||
0.426871 | + | 0.904312i | \(0.359616\pi\) | |||||||
\(728\) | −6.62941 | −0.245702 | ||||||||
\(729\) | 28.9564 | 1.07246 | ||||||||
\(730\) | 1.69925 | 0.0628922 | ||||||||
\(731\) | 12.6871 | 0.469249 | ||||||||
\(732\) | 7.19810 | 0.266049 | ||||||||
\(733\) | −14.8495 | −0.548478 | −0.274239 | − | 0.961662i | \(-0.588426\pi\) | ||||
−0.274239 | + | 0.961662i | \(0.588426\pi\) | |||||||
\(734\) | 19.8288 | 0.731896 | ||||||||
\(735\) | −0.154535 | −0.00570010 | ||||||||
\(736\) | 15.9808 | 0.589059 | ||||||||
\(737\) | −6.45576 | −0.237801 | ||||||||
\(738\) | −13.7734 | −0.507007 | ||||||||
\(739\) | 18.8250 | 0.692488 | 0.346244 | − | 0.938145i | \(-0.387457\pi\) | ||||
0.346244 | + | 0.938145i | \(0.387457\pi\) | |||||||
\(740\) | −0.265005 | −0.00974179 | ||||||||
\(741\) | 14.1707 | 0.520575 | ||||||||
\(742\) | 52.2374 | 1.91770 | ||||||||
\(743\) | 13.5052 | 0.495458 | 0.247729 | − | 0.968829i | \(-0.420316\pi\) | ||||
0.247729 | + | 0.968829i | \(0.420316\pi\) | |||||||
\(744\) | 3.04306 | 0.111564 | ||||||||
\(745\) | −3.98747 | −0.146090 | ||||||||
\(746\) | −13.2972 | −0.486846 | ||||||||
\(747\) | −7.88655 | −0.288554 | ||||||||
\(748\) | −6.07727 | −0.222207 | ||||||||
\(749\) | 20.4355 | 0.746697 | ||||||||
\(750\) | 5.40254 | 0.197273 | ||||||||
\(751\) | −24.1608 | −0.881640 | −0.440820 | − | 0.897596i | \(-0.645312\pi\) | ||||
−0.440820 | + | 0.897596i | \(0.645312\pi\) | |||||||
\(752\) | 5.67476 | 0.206937 | ||||||||
\(753\) | 32.0083 | 1.16645 | ||||||||
\(754\) | −16.6556 | −0.606562 | ||||||||
\(755\) | −0.359045 | −0.0130670 | ||||||||
\(756\) | 17.8791 | 0.650257 | ||||||||
\(757\) | 17.1605 | 0.623710 | 0.311855 | − | 0.950130i | \(-0.399050\pi\) | ||||
0.311855 | + | 0.950130i | \(0.399050\pi\) | |||||||
\(758\) | −39.8145 | −1.44613 | ||||||||
\(759\) | 4.56507 | 0.165702 | ||||||||
\(760\) | 1.53815 | 0.0557944 | ||||||||
\(761\) | −8.22391 | −0.298117 | −0.149058 | − | 0.988828i | \(-0.547624\pi\) | ||||
−0.149058 | + | 0.988828i | \(0.547624\pi\) | |||||||
\(762\) | 51.9919 | 1.88347 | ||||||||
\(763\) | 2.54704 | 0.0922090 | ||||||||
\(764\) | 18.7971 | 0.680056 | ||||||||
\(765\) | 0.844588 | 0.0305361 | ||||||||
\(766\) | 32.2980 | 1.16698 | ||||||||
\(767\) | 7.95027 | 0.287068 | ||||||||
\(768\) | 29.2046 | 1.05383 | ||||||||
\(769\) | 31.8215 | 1.14751 | 0.573757 | − | 0.819026i | \(-0.305485\pi\) | ||||
0.573757 | + | 0.819026i | \(0.305485\pi\) | |||||||
\(770\) | 1.22135 | 0.0440144 | ||||||||
\(771\) | 7.80872 | 0.281224 | ||||||||
\(772\) | −29.2849 | −1.05399 | ||||||||
\(773\) | 36.9921 | 1.33051 | 0.665257 | − | 0.746614i | \(-0.268322\pi\) | ||||
0.665257 | + | 0.746614i | \(0.268322\pi\) | |||||||
\(774\) | −5.85855 | −0.210581 | ||||||||
\(775\) | −7.81515 | −0.280729 | ||||||||
\(776\) | 15.3343 | 0.550468 | ||||||||
\(777\) | 3.59558 | 0.128991 | ||||||||
\(778\) | 4.62468 | 0.165803 | ||||||||
\(779\) | −40.0358 | −1.43443 | ||||||||
\(780\) | 0.712520 | 0.0255123 | ||||||||
\(781\) | −20.1321 | −0.720384 | ||||||||
\(782\) | 18.3278 | 0.655399 | ||||||||
\(783\) | −27.4784 | −0.981998 | ||||||||
\(784\) | 2.53324 | 0.0904728 | ||||||||
\(785\) | −4.43779 | −0.158392 | ||||||||
\(786\) | 40.5621 | 1.44680 | ||||||||
\(787\) | 39.0593 | 1.39231 | 0.696156 | − | 0.717890i | \(-0.254892\pi\) | ||||
0.696156 | + | 0.717890i | \(0.254892\pi\) | |||||||
\(788\) | −23.1749 | −0.825570 | ||||||||
\(789\) | −34.3126 | −1.22156 | ||||||||
\(790\) | 1.12426 | 0.0399992 | ||||||||
\(791\) | 28.4578 | 1.01184 | ||||||||
\(792\) | −1.71671 | −0.0610006 | ||||||||
\(793\) | 7.82629 | 0.277920 | ||||||||
\(794\) | 9.46657 | 0.335956 | ||||||||
\(795\) | 3.43450 | 0.121809 | ||||||||
\(796\) | 8.67110 | 0.307339 | ||||||||
\(797\) | −33.8021 | −1.19733 | −0.598666 | − | 0.800999i | \(-0.704302\pi\) | ||||
−0.598666 | + | 0.800999i | \(0.704302\pi\) | |||||||
\(798\) | 34.1155 | 1.20768 | ||||||||
\(799\) | 4.50883 | 0.159511 | ||||||||
\(800\) | −30.5371 | −1.07965 | ||||||||
\(801\) | −4.95487 | −0.175072 | ||||||||
\(802\) | 48.0783 | 1.69770 | ||||||||
\(803\) | −5.51268 | −0.194538 | ||||||||
\(804\) | −9.06699 | −0.319768 | ||||||||
\(805\) | −1.41030 | −0.0497067 | ||||||||
\(806\) | −5.40865 | −0.190512 | ||||||||
\(807\) | 3.05867 | 0.107670 | ||||||||
\(808\) | 9.25290 | 0.325516 | ||||||||
\(809\) | 16.1064 | 0.566272 | 0.283136 | − | 0.959080i | \(-0.408625\pi\) | ||||
0.283136 | + | 0.959080i | \(0.408625\pi\) | |||||||
\(810\) | 1.90845 | 0.0670562 | ||||||||
\(811\) | −19.2934 | −0.677482 | −0.338741 | − | 0.940880i | \(-0.610001\pi\) | ||||
−0.338741 | + | 0.940880i | \(0.610001\pi\) | |||||||
\(812\) | −15.3530 | −0.538783 | ||||||||
\(813\) | −7.61765 | −0.267163 | ||||||||
\(814\) | 2.24537 | 0.0787001 | ||||||||
\(815\) | −0.301268 | −0.0105530 | ||||||||
\(816\) | 27.3936 | 0.958967 | ||||||||
\(817\) | −17.0293 | −0.595779 | ||||||||
\(818\) | −13.0114 | −0.454932 | ||||||||
\(819\) | 4.88603 | 0.170732 | ||||||||
\(820\) | −2.01304 | −0.0702984 | ||||||||
\(821\) | 17.1033 | 0.596908 | 0.298454 | − | 0.954424i | \(-0.403529\pi\) | ||||
0.298454 | + | 0.954424i | \(0.403529\pi\) | |||||||
\(822\) | 33.7485 | 1.17712 | ||||||||
\(823\) | 19.2070 | 0.669516 | 0.334758 | − | 0.942304i | \(-0.391345\pi\) | ||||
0.334758 | + | 0.942304i | \(0.391345\pi\) | |||||||
\(824\) | 3.98986 | 0.138993 | ||||||||
\(825\) | −8.72324 | −0.303704 | ||||||||
\(826\) | 19.1400 | 0.665964 | ||||||||
\(827\) | 8.31783 | 0.289239 | 0.144620 | − | 0.989487i | \(-0.453804\pi\) | ||||
0.144620 | + | 0.989487i | \(0.453804\pi\) | |||||||
\(828\) | −3.24048 | −0.112614 | ||||||||
\(829\) | 35.2352 | 1.22377 | 0.611884 | − | 0.790947i | \(-0.290412\pi\) | ||||
0.611884 | + | 0.790947i | \(0.290412\pi\) | |||||||
\(830\) | −3.01041 | −0.104493 | ||||||||
\(831\) | 5.47879 | 0.190057 | ||||||||
\(832\) | −2.30875 | −0.0800413 | ||||||||
\(833\) | 2.01276 | 0.0697381 | ||||||||
\(834\) | −54.1191 | −1.87399 | ||||||||
\(835\) | 3.75386 | 0.129908 | ||||||||
\(836\) | 8.15723 | 0.282124 | ||||||||
\(837\) | −8.92318 | −0.308430 | ||||||||
\(838\) | 54.2931 | 1.87552 | ||||||||
\(839\) | 52.8401 | 1.82424 | 0.912122 | − | 0.409919i | \(-0.134443\pi\) | ||||
0.912122 | + | 0.409919i | \(0.134443\pi\) | |||||||
\(840\) | −1.04934 | −0.0362056 | ||||||||
\(841\) | −5.40406 | −0.186347 | ||||||||
\(842\) | 68.8312 | 2.37208 | ||||||||
\(843\) | −15.2538 | −0.525369 | ||||||||
\(844\) | −15.7768 | −0.543060 | ||||||||
\(845\) | −2.00156 | −0.0688557 | ||||||||
\(846\) | −2.08205 | −0.0715825 | ||||||||
\(847\) | 24.0551 | 0.826545 | ||||||||
\(848\) | −56.3006 | −1.93337 | ||||||||
\(849\) | 7.69849 | 0.264211 | ||||||||
\(850\) | −35.0219 | −1.20124 | ||||||||
\(851\) | −2.59275 | −0.0888782 | ||||||||
\(852\) | −28.2752 | −0.968692 | ||||||||
\(853\) | 36.0002 | 1.23262 | 0.616311 | − | 0.787503i | \(-0.288626\pi\) | ||||
0.616311 | + | 0.787503i | \(0.288626\pi\) | |||||||
\(854\) | 18.8415 | 0.644743 | ||||||||
\(855\) | −1.13365 | −0.0387700 | ||||||||
\(856\) | −10.9643 | −0.374751 | ||||||||
\(857\) | 14.7071 | 0.502386 | 0.251193 | − | 0.967937i | \(-0.419177\pi\) | ||||
0.251193 | + | 0.967937i | \(0.419177\pi\) | |||||||
\(858\) | −6.03712 | −0.206104 | ||||||||
\(859\) | −1.52695 | −0.0520990 | −0.0260495 | − | 0.999661i | \(-0.508293\pi\) | ||||
−0.0260495 | + | 0.999661i | \(0.508293\pi\) | |||||||
\(860\) | −0.856250 | −0.0291979 | ||||||||
\(861\) | 27.3128 | 0.930818 | ||||||||
\(862\) | −53.7023 | −1.82911 | ||||||||
\(863\) | −33.0974 | −1.12665 | −0.563324 | − | 0.826236i | \(-0.690478\pi\) | ||||
−0.563324 | + | 0.826236i | \(0.690478\pi\) | |||||||
\(864\) | −34.8667 | −1.18619 | ||||||||
\(865\) | −3.09865 | −0.105357 | ||||||||
\(866\) | 71.1045 | 2.41623 | ||||||||
\(867\) | −2.23305 | −0.0758384 | ||||||||
\(868\) | −4.98563 | −0.169223 | ||||||||
\(869\) | −3.64729 | −0.123726 | ||||||||
\(870\) | −2.63634 | −0.0893803 | ||||||||
\(871\) | −9.85829 | −0.334035 | ||||||||
\(872\) | −1.36657 | −0.0462777 | ||||||||
\(873\) | −11.3017 | −0.382505 | ||||||||
\(874\) | −24.6005 | −0.832124 | ||||||||
\(875\) | 5.41461 | 0.183047 | ||||||||
\(876\) | −7.74246 | −0.261594 | ||||||||
\(877\) | 41.9607 | 1.41691 | 0.708457 | − | 0.705754i | \(-0.249392\pi\) | ||||
0.708457 | + | 0.705754i | \(0.249392\pi\) | |||||||
\(878\) | 11.6910 | 0.394553 | ||||||||
\(879\) | 9.51910 | 0.321071 | ||||||||
\(880\) | −1.31635 | −0.0443741 | ||||||||
\(881\) | 12.1140 | 0.408130 | 0.204065 | − | 0.978957i | \(-0.434585\pi\) | ||||
0.204065 | + | 0.978957i | \(0.434585\pi\) | |||||||
\(882\) | −0.929439 | −0.0312958 | ||||||||
\(883\) | 6.11719 | 0.205860 | 0.102930 | − | 0.994689i | \(-0.467178\pi\) | ||||
0.102930 | + | 0.994689i | \(0.467178\pi\) | |||||||
\(884\) | −9.28032 | −0.312131 | ||||||||
\(885\) | 1.25841 | 0.0423010 | ||||||||
\(886\) | 55.6745 | 1.87042 | ||||||||
\(887\) | −42.9961 | −1.44367 | −0.721834 | − | 0.692066i | \(-0.756701\pi\) | ||||
−0.721834 | + | 0.692066i | \(0.756701\pi\) | |||||||
\(888\) | −1.92914 | −0.0647376 | ||||||||
\(889\) | 52.1081 | 1.74765 | ||||||||
\(890\) | −1.89135 | −0.0633981 | ||||||||
\(891\) | −6.19136 | −0.207418 | ||||||||
\(892\) | 20.6959 | 0.692951 | ||||||||
\(893\) | −6.05199 | −0.202522 | ||||||||
\(894\) | 47.4511 | 1.58700 | ||||||||
\(895\) | 2.63698 | 0.0881445 | ||||||||
\(896\) | 25.8399 | 0.863250 | ||||||||
\(897\) | 6.97111 | 0.232759 | ||||||||
\(898\) | 45.5134 | 1.51880 | ||||||||
\(899\) | 7.66241 | 0.255556 | ||||||||
\(900\) | 6.19213 | 0.206404 | ||||||||
\(901\) | −44.7332 | −1.49028 | ||||||||
\(902\) | 17.0563 | 0.567913 | ||||||||
\(903\) | 11.6175 | 0.386608 | ||||||||
\(904\) | −15.2685 | −0.507823 | ||||||||
\(905\) | 4.73083 | 0.157258 | ||||||||
\(906\) | 4.27265 | 0.141949 | ||||||||
\(907\) | −46.6362 | −1.54853 | −0.774265 | − | 0.632861i | \(-0.781880\pi\) | ||||
−0.774265 | + | 0.632861i | \(0.781880\pi\) | |||||||
\(908\) | −16.9009 | −0.560877 | ||||||||
\(909\) | −6.81961 | −0.226192 | ||||||||
\(910\) | 1.86507 | 0.0618264 | ||||||||
\(911\) | −4.25752 | −0.141058 | −0.0705289 | − | 0.997510i | \(-0.522469\pi\) | ||||
−0.0705289 | + | 0.997510i | \(0.522469\pi\) | |||||||
\(912\) | −36.7691 | −1.21755 | ||||||||
\(913\) | 9.76630 | 0.323217 | ||||||||
\(914\) | −69.3924 | −2.29530 | ||||||||
\(915\) | 1.23879 | 0.0409531 | ||||||||
\(916\) | −19.2610 | −0.636400 | ||||||||
\(917\) | 40.6527 | 1.34247 | ||||||||
\(918\) | −39.9873 | −1.31978 | ||||||||
\(919\) | −53.8262 | −1.77556 | −0.887782 | − | 0.460264i | \(-0.847755\pi\) | ||||
−0.887782 | + | 0.460264i | \(0.847755\pi\) | |||||||
\(920\) | 0.756672 | 0.0249467 | ||||||||
\(921\) | −9.88443 | −0.325703 | ||||||||
\(922\) | 67.5673 | 2.22521 | ||||||||
\(923\) | −30.7428 | −1.01191 | ||||||||
\(924\) | −5.56494 | −0.183073 | ||||||||
\(925\) | 4.95439 | 0.162899 | ||||||||
\(926\) | −73.6025 | −2.41873 | ||||||||
\(927\) | −2.94062 | −0.0965826 | ||||||||
\(928\) | 29.9403 | 0.982839 | ||||||||
\(929\) | 4.32903 | 0.142031 | 0.0710154 | − | 0.997475i | \(-0.477376\pi\) | ||||
0.0710154 | + | 0.997475i | \(0.477376\pi\) | |||||||
\(930\) | −0.856111 | −0.0280730 | ||||||||
\(931\) | −2.70163 | −0.0885425 | ||||||||
\(932\) | −0.652106 | −0.0213604 | ||||||||
\(933\) | 9.81571 | 0.321352 | ||||||||
\(934\) | −42.0778 | −1.37683 | ||||||||
\(935\) | −1.04589 | −0.0342044 | ||||||||
\(936\) | −2.62151 | −0.0856866 | ||||||||
\(937\) | 9.44016 | 0.308397 | 0.154198 | − | 0.988040i | \(-0.450721\pi\) | ||||
0.154198 | + | 0.988040i | \(0.450721\pi\) | |||||||
\(938\) | −23.7335 | −0.774925 | ||||||||
\(939\) | 33.5919 | 1.09623 | ||||||||
\(940\) | −0.304300 | −0.00992518 | ||||||||
\(941\) | 54.0288 | 1.76129 | 0.880644 | − | 0.473779i | \(-0.157110\pi\) | ||||
0.880644 | + | 0.473779i | \(0.157110\pi\) | |||||||
\(942\) | 52.8100 | 1.72064 | ||||||||
\(943\) | −19.6951 | −0.641360 | ||||||||
\(944\) | −20.6287 | −0.671408 | ||||||||
\(945\) | 3.07698 | 0.100094 | ||||||||
\(946\) | 7.25493 | 0.235878 | ||||||||
\(947\) | −13.1895 | −0.428602 | −0.214301 | − | 0.976768i | \(-0.568747\pi\) | ||||
−0.214301 | + | 0.976768i | \(0.568747\pi\) | |||||||
\(948\) | −5.12255 | −0.166373 | ||||||||
\(949\) | −8.41817 | −0.273265 | ||||||||
\(950\) | 47.0082 | 1.52515 | ||||||||
\(951\) | 0.313604 | 0.0101693 | ||||||||
\(952\) | 13.6673 | 0.442959 | ||||||||
\(953\) | 40.4313 | 1.30970 | 0.654850 | − | 0.755759i | \(-0.272732\pi\) | ||||
0.654850 | + | 0.755759i | \(0.272732\pi\) | |||||||
\(954\) | 20.6566 | 0.668781 | ||||||||
\(955\) | 3.23497 | 0.104681 | ||||||||
\(956\) | −32.1838 | −1.04090 | ||||||||
\(957\) | 8.55276 | 0.276471 | ||||||||
\(958\) | 68.4180 | 2.21049 | ||||||||
\(959\) | 33.8240 | 1.09223 | ||||||||
\(960\) | −0.365441 | −0.0117945 | ||||||||
\(961\) | −28.5118 | −0.919734 | ||||||||
\(962\) | 3.42880 | 0.110549 | ||||||||
\(963\) | 8.08093 | 0.260404 | ||||||||
\(964\) | −1.60882 | −0.0518166 | ||||||||
\(965\) | −5.03992 | −0.162241 | ||||||||
\(966\) | 16.7827 | 0.539974 | ||||||||
\(967\) | −16.8395 | −0.541522 | −0.270761 | − | 0.962647i | \(-0.587275\pi\) | ||||
−0.270761 | + | 0.962647i | \(0.587275\pi\) | |||||||
\(968\) | −12.9063 | −0.414825 | ||||||||
\(969\) | −29.2146 | −0.938507 | ||||||||
\(970\) | −4.31403 | −0.138515 | ||||||||
\(971\) | 13.1838 | 0.423087 | 0.211544 | − | 0.977369i | \(-0.432151\pi\) | ||||
0.211544 | + | 0.977369i | \(0.432151\pi\) | |||||||
\(972\) | 12.3631 | 0.396545 | ||||||||
\(973\) | −54.2401 | −1.73886 | ||||||||
\(974\) | 24.9498 | 0.799444 | ||||||||
\(975\) | −13.3209 | −0.426609 | ||||||||
\(976\) | −20.3070 | −0.650013 | ||||||||
\(977\) | −47.5642 | −1.52171 | −0.760856 | − | 0.648921i | \(-0.775221\pi\) | ||||
−0.760856 | + | 0.648921i | \(0.775221\pi\) | |||||||
\(978\) | 3.58511 | 0.114639 | ||||||||
\(979\) | 6.13586 | 0.196103 | ||||||||
\(980\) | −0.135841 | −0.00433928 | ||||||||
\(981\) | 1.00719 | 0.0321571 | ||||||||
\(982\) | −53.8976 | −1.71994 | ||||||||
\(983\) | −47.5978 | −1.51813 | −0.759067 | − | 0.651013i | \(-0.774344\pi\) | ||||
−0.759067 | + | 0.651013i | \(0.774344\pi\) | |||||||
\(984\) | −14.6542 | −0.467158 | ||||||||
\(985\) | −3.98838 | −0.127080 | ||||||||
\(986\) | 34.3374 | 1.09353 | ||||||||
\(987\) | 4.12872 | 0.131419 | ||||||||
\(988\) | 12.4565 | 0.396295 | ||||||||
\(989\) | −8.37734 | −0.266384 | ||||||||
\(990\) | 0.482966 | 0.0153497 | ||||||||
\(991\) | 12.2593 | 0.389429 | 0.194715 | − | 0.980860i | \(-0.437622\pi\) | ||||
0.194715 | + | 0.980860i | \(0.437622\pi\) | |||||||
\(992\) | 9.72265 | 0.308695 | ||||||||
\(993\) | −40.5969 | −1.28830 | ||||||||
\(994\) | −74.0122 | −2.34752 | ||||||||
\(995\) | 1.49229 | 0.0473088 | ||||||||
\(996\) | 13.7166 | 0.434627 | ||||||||
\(997\) | 21.3222 | 0.675281 | 0.337641 | − | 0.941275i | \(-0.390371\pi\) | ||||
0.337641 | + | 0.941275i | \(0.390371\pi\) | |||||||
\(998\) | 30.4724 | 0.964587 | ||||||||
\(999\) | 5.65683 | 0.178974 |
(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 | 4033.2.a.d.1.18 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.18 | ✓ | 79 | 1.1 | even | 1 | trivial |