Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, 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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 13 x^{10} + 60 x^{9} + 48 x^{8} - 289 x^{7} - 89 x^{6} + 602 x^{5} + 161 x^{4} + \cdots + 82 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.70453\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 1.70453 | 0.984110 | 0.492055 | − | 0.870564i | \(-0.336246\pi\) | ||||
0.492055 | + | 0.870564i | \(0.336246\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.637713 | −0.285194 | −0.142597 | − | 0.989781i | \(-0.545545\pi\) | ||||
−0.142597 | + | 0.989781i | \(0.545545\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14740 | 0.433678 | 0.216839 | − | 0.976207i | \(-0.430425\pi\) | ||||
0.216839 | + | 0.976207i | \(0.430425\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0945840 | −0.0315280 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.485761 | 0.146462 | 0.0732312 | − | 0.997315i | \(-0.476669\pi\) | ||||
0.0732312 | + | 0.997315i | \(0.476669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.68138 | −1.29838 | −0.649191 | − | 0.760625i | \(-0.724892\pi\) | ||||
−0.649191 | + | 0.760625i | \(0.724892\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.08700 | −0.280662 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.90066 | 0.436042 | 0.218021 | − | 0.975944i | \(-0.430040\pi\) | ||||
0.218021 | + | 0.975944i | \(0.430040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.95578 | 0.426787 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.312411 | −0.0651422 | −0.0325711 | − | 0.999469i | \(-0.510370\pi\) | ||||
−0.0325711 | + | 0.999469i | \(0.510370\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.59332 | −0.918664 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.27481 | −1.01514 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.80295 | −0.706190 | −0.353095 | − | 0.935587i | \(-0.614871\pi\) | ||||
−0.353095 | + | 0.935587i | \(0.614871\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.49914 | −0.269254 | −0.134627 | − | 0.990896i | \(-0.542984\pi\) | ||||
−0.134627 | + | 0.990896i | \(0.542984\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.827993 | 0.144135 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.731715 | −0.123682 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.52029 | 0.578732 | 0.289366 | − | 0.957218i | \(-0.406555\pi\) | ||||
0.289366 | + | 0.957218i | \(0.406555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.97955 | −1.27775 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.10566 | −0.797371 | −0.398685 | − | 0.917088i | \(-0.630533\pi\) | ||||
−0.398685 | + | 0.917088i | \(0.630533\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.74040 | −0.417908 | −0.208954 | − | 0.977926i | \(-0.567006\pi\) | ||||
−0.208954 | + | 0.977926i | \(0.567006\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0603175 | 0.00899159 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.63321 | 0.821689 | 0.410844 | − | 0.911706i | \(-0.365234\pi\) | ||||
0.410844 | + | 0.911706i | \(0.365234\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.68346 | −0.811923 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.70453 | −0.238682 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.67494 | −0.779513 | −0.389756 | − | 0.920918i | \(-0.627441\pi\) | ||||
−0.389756 | + | 0.920918i | \(0.627441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.309776 | −0.0417702 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.23974 | 0.429113 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.8658 | −1.51926 | −0.759628 | − | 0.650358i | \(-0.774619\pi\) | ||||
−0.759628 | + | 0.650358i | \(0.774619\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.108526 | −0.0136730 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.98538 | 0.370291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.64584 | 0.934088 | 0.467044 | − | 0.884234i | \(-0.345319\pi\) | ||||
0.467044 | + | 0.884234i | \(0.345319\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.532514 | −0.0641071 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.03706 | 0.123077 | 0.0615385 | − | 0.998105i | \(-0.480399\pi\) | ||||
0.0615385 | + | 0.998105i | \(0.480399\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9506 | 1.28167 | 0.640833 | − | 0.767680i | \(-0.278589\pi\) | ||||
0.640833 | + | 0.767680i | \(0.278589\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.82945 | −0.904067 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.557364 | 0.0635175 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.162183 | −0.0182471 | −0.00912353 | − | 0.999958i | \(-0.502904\pi\) | ||||
−0.00912353 | + | 0.999958i | \(0.502904\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.70730 | −0.967478 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.63200 | −0.179135 | −0.0895676 | − | 0.995981i | \(-0.528548\pi\) | ||||
−0.0895676 | + | 0.995981i | \(0.528548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.637713 | 0.0691697 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.48224 | −0.694969 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.8243 | −1.99537 | −0.997686 | − | 0.0679960i | \(-0.978339\pi\) | ||||
−0.997686 | + | 0.0679960i | \(0.978339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.37144 | −0.563080 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.55533 | −0.264976 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.21208 | −0.124357 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.5538 | −1.47771 | −0.738857 | − | 0.673862i | \(-0.764634\pi\) | ||||
−0.738857 | + | 0.673862i | \(0.764634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0459452 | −0.00461766 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.44284 | −0.939598 | −0.469799 | − | 0.882774i | \(-0.655674\pi\) | ||||
−0.469799 | + | 0.882774i | \(0.655674\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.38169 | 0.333208 | 0.166604 | − | 0.986024i | \(-0.446720\pi\) | ||||
0.166604 | + | 0.986024i | \(0.446720\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.24723 | −0.121717 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0081 | 1.54756 | 0.773782 | − | 0.633452i | \(-0.218363\pi\) | ||||
0.773782 | + | 0.633452i | \(0.218363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.29824 | 0.411697 | 0.205849 | − | 0.978584i | \(-0.434005\pi\) | ||||
0.205849 | + | 0.978584i | \(0.434005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00044 | 0.569536 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.77885 | −0.167340 | −0.0836699 | − | 0.996494i | \(-0.526664\pi\) | ||||
−0.0836699 | + | 0.996494i | \(0.526664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.199229 | 0.0185782 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.442784 | 0.0409354 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.14740 | −0.105182 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7640 | −0.978549 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.70275 | −0.784700 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.11779 | 0.547192 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0428 | 1.24609 | 0.623047 | − | 0.782185i | \(-0.285895\pi\) | ||||
0.623047 | + | 0.782185i | \(0.285895\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.67109 | −0.411267 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.95537 | −0.782435 | −0.391217 | − | 0.920298i | \(-0.627946\pi\) | ||||
−0.391217 | + | 0.920298i | \(0.627946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.18083 | 0.189102 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.36381 | 0.289511 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.70810 | 0.316804 | 0.158402 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158402 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.6235 | −1.24035 | −0.620173 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620173 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.60197 | 0.808632 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.27403 | −0.190164 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.42519 | 0.201401 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.68762 | −0.799022 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.1980 | 1.49084 | 0.745419 | − | 0.666596i | \(-0.232250\pi\) | ||||
0.745419 | + | 0.666596i | \(0.232250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.68115 | 0.462325 | 0.231163 | − | 0.972915i | \(-0.425747\pi\) | ||||
0.231163 | + | 0.972915i | \(0.425747\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0945840 | 0.00764666 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.956025 | 0.0767897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.0170 | −1.67734 | −0.838670 | − | 0.544639i | \(-0.816667\pi\) | ||||
−0.838670 | + | 0.544639i | \(0.816667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.67309 | −0.767126 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.358462 | −0.0282507 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1591 | 0.952372 | 0.476186 | − | 0.879345i | \(-0.342019\pi\) | ||||
0.476186 | + | 0.879345i | \(0.342019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.528022 | −0.0411065 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.38644 | −0.571580 | −0.285790 | − | 0.958292i | \(-0.592256\pi\) | ||||
−0.285790 | + | 0.958292i | \(0.592256\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.91535 | 0.685796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.179772 | −0.0137475 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.6279 | −0.808022 | −0.404011 | − | 0.914754i | \(-0.632384\pi\) | ||||
−0.404011 | + | 0.914754i | \(0.632384\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.27040 | −0.398404 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.70453 | 0.128120 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.34917 | −0.698790 | −0.349395 | − | 0.936976i | \(-0.613613\pi\) | ||||
−0.349395 | + | 0.936976i | \(0.613613\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.31537 | 0.692406 | 0.346203 | − | 0.938160i | \(-0.387471\pi\) | ||||
0.346203 | + | 0.938160i | \(0.387471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.2255 | −1.49512 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.24494 | −0.165051 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.485761 | −0.0355223 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.05233 | −0.440242 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.95791 | 0.286384 | 0.143192 | − | 0.989695i | \(-0.454263\pi\) | ||||
0.143192 | + | 0.989695i | \(0.454263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.55163 | −0.687541 | −0.343771 | − | 0.939054i | \(-0.611704\pi\) | ||||
−0.343771 | + | 0.939054i | \(0.611704\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.08866 | 0.364407 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.701314 | −0.0499666 | −0.0249833 | − | 0.999688i | \(-0.507953\pi\) | ||||
−0.0249833 | + | 0.999688i | \(0.507953\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9001 | 1.55246 | 0.776229 | − | 0.630451i | \(-0.217130\pi\) | ||||
0.776229 | + | 0.630451i | \(0.217130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.0326 | 0.919245 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.36352 | −0.306259 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.25595 | 0.227405 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0295491 | 0.00205380 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.923268 | 0.0638638 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.40422 | −0.0966703 | −0.0483351 | − | 0.998831i | \(-0.515392\pi\) | ||||
−0.0483351 | + | 0.998831i | \(0.515392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.76771 | 0.121121 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.74759 | 0.119185 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.72012 | −0.116770 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.6655 | 1.26130 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.68138 | 0.314904 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.04980 | 0.472090 | 0.236045 | − | 0.971742i | \(-0.424149\pi\) | ||||
0.236045 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.434455 | 0.0289636 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.36642 | 0.157065 | 0.0785324 | − | 0.996912i | \(-0.474977\pi\) | ||||
0.0785324 | + | 0.996912i | \(0.474977\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.83183 | −0.121051 | −0.0605255 | − | 0.998167i | \(-0.519278\pi\) | ||||
−0.0605255 | + | 0.998167i | \(0.519278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.950042 | 0.0625082 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.2098 | −1.38950 | −0.694750 | − | 0.719251i | \(-0.744485\pi\) | ||||
−0.694750 | + | 0.719251i | \(0.744485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.59238 | −0.234341 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.276446 | −0.0179571 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1137 | 0.718882 | 0.359441 | − | 0.933168i | \(-0.382967\pi\) | ||||
0.359441 | + | 0.933168i | \(0.382967\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.29182 | 0.405292 | 0.202646 | − | 0.979252i | \(-0.435046\pi\) | ||||
0.202646 | + | 0.979252i | \(0.435046\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.982575 | 0.0630322 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.62442 | 0.231556 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.89774 | −0.566150 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.78179 | −0.176289 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.30846 | 0.145708 | 0.0728542 | − | 0.997343i | \(-0.476789\pi\) | ||||
0.0728542 | + | 0.997343i | \(0.476789\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.151757 | −0.00954089 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.08700 | 0.0680706 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.6249 | 1.22417 | 0.612084 | − | 0.790793i | \(-0.290331\pi\) | ||||
0.612084 | + | 0.790793i | \(0.290331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.03920 | 0.250983 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.359698 | 0.0222648 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.1353 | −1.67323 | −0.836617 | − | 0.547789i | \(-0.815470\pi\) | ||||
−0.836617 | + | 0.547789i | \(0.815470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.61898 | 0.222312 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.0865 | −1.96366 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.18261 | −0.255018 | −0.127509 | − | 0.991837i | \(-0.540698\pi\) | ||||
−0.127509 | + | 0.991837i | \(0.540698\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.8254 | −1.14356 | −0.571781 | − | 0.820406i | \(-0.693747\pi\) | ||||
−0.571781 | + | 0.820406i | \(0.693747\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.15577 | −0.554132 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.23126 | −0.134550 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.20874 | −0.0726263 | −0.0363132 | − | 0.999340i | \(-0.511561\pi\) | ||||
−0.0363132 | + | 0.999340i | \(0.511561\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.141795 | 0.00848905 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.8339 | −0.884915 | −0.442458 | − | 0.896789i | \(-0.645893\pi\) | ||||
−0.442458 | + | 0.896789i | \(0.645893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0173913 | −0.00103381 | −0.000516903 | − | 1.00000i | \(-0.500165\pi\) | ||||
−0.000516903 | 1.00000i | \(0.500165\pi\) | ||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.06602 | −0.122381 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.85826 | −0.345802 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.8073 | −1.45423 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.862325 | −0.0503775 | −0.0251888 | − | 0.999683i | \(-0.508019\pi\) | ||||
−0.0251888 | + | 0.999683i | \(0.508019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.637713 | −0.0371291 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.56229 | −0.148679 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.46252 | 0.0845795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.14435 | −0.181237 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.0956 | −0.924667 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.56696 | 0.433283 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4961 | 1.22685 | 0.613424 | − | 0.789754i | \(-0.289792\pi\) | ||||
0.613424 | + | 0.789754i | \(0.289792\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.76419 | 0.327913 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.09850 | −0.459224 | −0.229612 | − | 0.973282i | \(-0.573746\pi\) | ||||
−0.229612 | + | 0.973282i | \(0.573746\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6870 | 1.39539 | 0.697696 | − | 0.716394i | \(-0.254209\pi\) | ||||
0.697696 | + | 0.716394i | \(0.254209\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0692085 | 0.00389946 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.51323 | −0.421985 | −0.210993 | − | 0.977488i | \(-0.567670\pi\) | ||||
−0.210993 | + | 0.977488i | \(0.567670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.84732 | −0.103430 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.2863 | 1.52297 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.90066 | −0.105756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.5031 | 1.19278 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.32648 | 0.405155 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.46357 | 0.356348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.10110 | −0.0605218 | −0.0302609 | − | 0.999542i | \(-0.509634\pi\) | ||||
−0.0302609 | + | 0.999542i | \(0.509634\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.332963 | −0.0182463 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.87585 | −0.266396 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.1140 | −1.25910 | −0.629549 | − | 0.776961i | \(-0.716760\pi\) | ||||
−0.629549 | + | 0.776961i | \(0.716760\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.03209 | −0.164681 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.728226 | −0.0394356 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.5531 | −0.785791 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.339591 | 0.0182830 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3881 | −0.772392 | −0.386196 | − | 0.922417i | \(-0.626211\pi\) | ||||
−0.386196 | + | 0.922417i | \(0.626211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.3754 | 0.930083 | 0.465041 | − | 0.885289i | \(-0.346039\pi\) | ||||
0.465041 | + | 0.885289i | \(0.346039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.6934 | 1.31804 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.2975 | −0.867428 | −0.433714 | − | 0.901051i | \(-0.642797\pi\) | ||||
−0.433714 | + | 0.901051i | \(0.642797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.661350 | −0.0351008 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.95578 | −0.103511 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.0062 | 1.53089 | 0.765444 | − | 0.643502i | \(-0.222519\pi\) | ||||
0.765444 | + | 0.643502i | \(0.222519\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3875 | −0.809867 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.3476 | −0.962999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.98332 | −0.365524 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.6968 | −0.923768 | −0.461884 | − | 0.886940i | \(-0.652826\pi\) | ||||
−0.461884 | + | 0.886940i | \(0.652826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.482914 | 0.0251395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.51145 | −0.338058 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.8060 | 0.663068 | 0.331534 | − | 0.943443i | \(-0.392434\pi\) | ||||
0.331534 | + | 0.943443i | \(0.392434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.4279 | 0.538497 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.8031 | 0.916905 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0149 | −0.514431 | −0.257215 | − | 0.966354i | \(-0.582805\pi\) | ||||
−0.257215 | + | 0.966354i | \(0.582805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.9363 | 1.22629 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0024 | 1.22646 | 0.613232 | − | 0.789903i | \(-0.289869\pi\) | ||||
0.613232 | + | 0.789903i | \(0.289869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.355438 | −0.0181148 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.259198 | 0.0131758 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.31841 | −0.320356 | −0.160178 | − | 0.987088i | \(-0.551207\pi\) | ||||
−0.160178 | + | 0.987088i | \(0.551207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.312411 | 0.0157993 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.2647 | −0.770002 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.103427 | 0.00520395 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.1736 | −0.861917 | −0.430958 | − | 0.902372i | \(-0.641824\pi\) | ||||
−0.430958 | + | 0.902372i | \(0.641824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.71729 | 0.186097 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1027 | −0.554441 | −0.277220 | − | 0.960806i | \(-0.589413\pi\) | ||||
−0.277220 | + | 0.960806i | \(0.589413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.01807 | 0.349595 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.55276 | 0.275919 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.71002 | 0.0847625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.4879 | 1.45808 | 0.729040 | − | 0.684471i | \(-0.239967\pi\) | ||||
0.729040 | + | 0.684471i | \(0.239967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.32055 | 0.311770 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.14740 | 0.0564601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.04075 | 0.0510883 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.9261 | −1.22064 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.42964 | −0.167549 | −0.0837746 | − | 0.996485i | \(-0.526698\pi\) | ||||
−0.0837746 | + | 0.996485i | \(0.526698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5576 | 1.00191 | 0.500957 | − | 0.865472i | \(-0.332981\pi\) | ||||
0.500957 | + | 0.865472i | \(0.332981\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.532812 | −0.0259062 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.59332 | 0.222809 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.6148 | −0.658868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.87615 | −0.187142 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.27470 | 0.157737 | 0.0788684 | − | 0.996885i | \(-0.474869\pi\) | ||||
0.0788684 | + | 0.996885i | \(0.474869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.38688 | −0.0666490 | −0.0333245 | − | 0.999445i | \(-0.510609\pi\) | ||||
−0.0333245 | + | 0.999445i | \(0.510609\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.13381 | 0.198201 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.593789 | −0.0284048 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2628 | 0.585271 | 0.292636 | − | 0.956224i | \(-0.405468\pi\) | ||||
0.292636 | + | 0.956224i | \(0.405468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.537565 | 0.0255983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.6510 | 1.88388 | 0.941938 | − | 0.335786i | \(-0.109002\pi\) | ||||
0.941938 | + | 0.335786i | \(0.109002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0045 | 0.569068 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.0190 | 1.46715 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3128 | −1.28897 | −0.644486 | − | 0.764616i | \(-0.722929\pi\) | ||||
−0.644486 | + | 0.764616i | \(0.722929\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.48013 | −0.116785 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.68367 | 0.454979 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.42544 | 0.160587 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.2849 | 1.27633 | 0.638167 | − | 0.769898i | \(-0.279693\pi\) | ||||
0.638167 | + | 0.769898i | \(0.279693\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.27481 | 0.246207 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5523 | 0.724341 | 0.362170 | − | 0.932112i | \(-0.382036\pi\) | ||||
0.362170 | + | 0.932112i | \(0.382036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.5039 | 1.46411 | 0.732055 | − | 0.681245i | \(-0.238561\pi\) | ||||
0.732055 | + | 0.681245i | \(0.238561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.62957 | 0.0755695 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.5065 | 0.578732 | 0.289366 | − | 0.957218i | \(-0.406555\pi\) | ||||
0.289366 | + | 0.957218i | \(0.406555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.77287 | 0.405093 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.8241 | −1.65069 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.33118 | −0.0612078 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.73036 | −0.400577 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.536758 | 0.0245765 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.596960 | −0.0272758 | −0.0136379 | − | 0.999907i | \(-0.504341\pi\) | ||||
−0.0136379 | + | 0.999907i | \(0.504341\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4798 | −0.751416 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.611008 | −0.0278018 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.28115 | 0.421435 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.3507 | 0.650292 | 0.325146 | − | 0.945664i | \(-0.394587\pi\) | ||||
0.325146 | + | 0.945664i | \(0.394587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.7255 | 0.937239 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.1501 | 0.593457 | 0.296729 | − | 0.954962i | \(-0.404104\pi\) | ||||
0.296729 | + | 0.954962i | \(0.404104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.80295 | 0.171276 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0292999 | 0.00131693 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.18993 | 0.0533758 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.2142 | 0.636316 | 0.318158 | − | 0.948038i | \(-0.396936\pi\) | ||||
0.318158 | + | 0.948038i | \(0.396936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.5904 | −0.562497 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.0178 | −0.937138 | −0.468569 | − | 0.883427i | \(-0.655230\pi\) | ||||
−0.468569 | + | 0.883427i | \(0.655230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.02182 | 0.267968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.1965 | 0.674899 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.9540 | 1.01742 | 0.508709 | − | 0.860938i | \(-0.330123\pi\) | ||||
0.508709 | + | 0.860938i | \(0.330123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.5647 | 0.555831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.0256 | −0.442643 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.15655 | −0.0950290 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.73639 | 0.120346 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.1155 | −0.795182 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.4341 | −1.72764 | −0.863819 | − | 0.503802i | \(-0.831934\pi\) | ||||
−0.863819 | + | 0.503802i | \(0.831934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2025 | −0.839665 | −0.419832 | − | 0.907602i | \(-0.637911\pi\) | ||||
−0.419832 | + | 0.907602i | \(0.637911\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.98354 | −0.392074 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.49914 | 0.0653038 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9024 | −0.995756 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0945840 | −0.00410459 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.9016 | 1.03529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2086 | −0.441356 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.9359 | −0.687686 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.76080 | −0.118916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.1214 | 1.55298 | 0.776489 | − | 0.630130i | \(-0.216999\pi\) | ||||
0.776489 | + | 0.630130i | \(0.216999\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.8783 | 0.681403 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.74105 | −0.117414 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.7174 | −1.05684 | −0.528420 | − | 0.848983i | \(-0.677215\pi\) | ||||
−0.528420 | + | 0.848983i | \(0.677215\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.12231 | 0.0478991 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.22813 | −0.307929 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.186090 | −0.00791335 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.82656 | −0.162428 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.46580 | −0.358707 | −0.179354 | − | 0.983785i | \(-0.557401\pi\) | ||||
−0.179354 | + | 0.983785i | \(0.557401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8289 | 0.542604 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.827993 | −0.0349579 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.9654 | −1.68434 | −0.842171 | − | 0.539210i | \(-0.818723\pi\) | ||||
−0.842171 | + | 0.539210i | \(0.818723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.13439 | 0.0477243 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.99079 | −0.419574 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.3309 | −1.02001 | −0.510003 | − | 0.860173i | \(-0.670356\pi\) | ||||
−0.510003 | + | 0.860173i | \(0.670356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.2309 | 1.55807 | 0.779033 | − | 0.626983i | \(-0.215711\pi\) | ||||
0.779033 | + | 0.626983i | \(0.215711\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.74636 | 0.281833 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.43500 | 0.0598438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.8250 | 0.950217 | 0.475108 | − | 0.879927i | \(-0.342409\pi\) | ||||
0.475108 | + | 0.879927i | \(0.342409\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.2810 | −0.676616 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.87256 | −0.0776870 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.75666 | −0.114169 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.282369 | −0.0116745 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.2429 | −1.53718 | −0.768590 | − | 0.639742i | \(-0.779041\pi\) | ||||
−0.768590 | + | 0.639742i | \(0.779041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.84937 | −0.117406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.19541 | −0.0491726 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.8471 | 0.815023 | 0.407512 | − | 0.913200i | \(-0.366397\pi\) | ||||
0.407512 | + | 0.913200i | \(0.366397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.731715 | 0.0299974 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.3293 | 1.52779 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.2999 | −1.52403 | −0.762016 | − | 0.647559i | \(-0.775790\pi\) | ||||
−0.762016 | + | 0.647559i | \(0.775790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.86276 | 0.239147 | 0.119574 | − | 0.992825i | \(-0.461847\pi\) | ||||
0.119574 | + | 0.992825i | \(0.461847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.723174 | −0.0294499 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.86437 | 0.279076 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.20210 | −0.0487918 | −0.0243959 | − | 0.999702i | \(-0.507766\pi\) | ||||
−0.0243959 | + | 0.999702i | \(0.507766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.43774 | −0.301393 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.3712 | −1.06687 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.18529 | −0.290211 | −0.145106 | − | 0.989416i | \(-0.546352\pi\) | ||||
−0.145106 | + | 0.989416i | \(0.546352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.54986 | 0.223792 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.9495 | −0.521327 | −0.260664 | − | 0.965430i | \(-0.583941\pi\) | ||||
−0.260664 | + | 0.965430i | \(0.583941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.3802 | −1.62302 | −0.811509 | − | 0.584340i | \(-0.801353\pi\) | ||||
−0.811509 | + | 0.584340i | \(0.801353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.64791 | 0.0661283 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.5991 | −0.865348 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.0652 | 0.762609 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.57374 | 0.0628490 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.52029 | −0.140363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.09133 | 0.123064 | 0.0615320 | − | 0.998105i | \(-0.480401\pi\) | ||||
0.0615320 | + | 0.998105i | \(0.480401\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.39353 | −0.0951342 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.95526 | −0.355378 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.6065 | 1.05419 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0980897 | −0.00388037 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0742 | −0.674390 | −0.337195 | − | 0.941435i | \(-0.609478\pi\) | ||||
−0.337195 | + | 0.941435i | \(0.609478\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.5473 | 0.652562 | 0.326281 | − | 0.945273i | \(-0.394204\pi\) | ||||
0.326281 | + | 0.945273i | \(0.394204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.97882 | 0.117291 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.2654 | −1.54368 | −0.771841 | − | 0.635816i | \(-0.780664\pi\) | ||||
−0.771841 | + | 0.635816i | \(0.780664\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.485761 | 0.0190678 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.93200 | −0.114914 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.1985 | −0.516497 | −0.258249 | − | 0.966078i | \(-0.583145\pi\) | ||||
−0.258249 | + | 0.966078i | \(0.583145\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.71096 | 0.223146 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.03575 | −0.0404084 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.0782 | −0.626318 | −0.313159 | − | 0.949701i | \(-0.601387\pi\) | ||||
−0.313159 | + | 0.949701i | \(0.601387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.55488 | 0.293851 | 0.146925 | − | 0.989148i | \(-0.453062\pi\) | ||||
0.146925 | + | 0.989148i | \(0.453062\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.97955 | 0.309900 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.39074 | −0.0539307 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.18808 | 0.0460028 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0166 | 0.464588 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.76393 | −0.222514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0573 | −0.965887 | −0.482943 | − | 0.875652i | \(-0.660432\pi\) | ||||
−0.482943 | + | 0.875652i | \(0.660432\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.2289 | 0.932570 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.42370 | −0.323749 | −0.161875 | − | 0.986811i | \(-0.551754\pi\) | ||||
−0.161875 | + | 0.986811i | \(0.551754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.6991 | −0.640852 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.03363 | 0.154569 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.6844 | 1.78633 | 0.893165 | − | 0.449729i | \(-0.148480\pi\) | ||||
0.893165 | + | 0.449729i | \(0.148480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.36470 | −0.0903506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.12241 | −0.119127 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.5666 | 1.01211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7165 | −0.635926 | −0.317963 | − | 0.948103i | \(-0.602999\pi\) | ||||
−0.317963 | + | 0.948103i | \(0.602999\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0527177 | −0.00200258 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.32557 | 0.353739 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.10566 | 0.193391 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.1527 | −1.36742 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.32012 | 0.352016 | 0.176008 | − | 0.984389i | \(-0.443682\pi\) | ||||
0.176008 | + | 0.984389i | \(0.443682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.69089 | 0.252352 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.12330 | −0.230617 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.8348 | −0.407483 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.6498 | 1.48908 | 0.744540 | − | 0.667578i | \(-0.232669\pi\) | ||||
0.744540 | + | 0.667578i | \(0.232669\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0153400 | 0.000575293 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.468350 | 0.0175398 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.45018 | 0.0542337 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.9435 | 0.707459 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.6919 | 1.66673 | 0.833363 | − | 0.552726i | \(-0.186412\pi\) | ||||
0.833363 | + | 0.552726i | \(0.186412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.88017 | 0.144505 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.7246 | 0.398852 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.4682 | 0.648752 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.6270 | −0.987539 | −0.493770 | − | 0.869593i | \(-0.664381\pi\) | ||||
−0.493770 | + | 0.869593i | \(0.664381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.7967 | 1.02951 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.74040 | 0.101357 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.6174 | −1.09394 | −0.546971 | − | 0.837152i | \(-0.684219\pi\) | ||||
−0.546971 | + | 0.837152i | \(0.684219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.17793 | 0.227876 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.71405 | 0.136809 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.08773 | 0.0400126 | 0.0200063 | − | 0.999800i | \(-0.493631\pi\) | ||||
0.0200063 | + | 0.999800i | \(0.493631\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.1664 | −0.557153 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.9563 | 1.50254 | 0.751271 | − | 0.659994i | \(-0.229441\pi\) | ||||
0.751271 | + | 0.659994i | \(0.229441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.6051 | −0.425178 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.154361 | 0.00564777 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.3678 | 0.671144 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.1748 | −0.590228 | −0.295114 | − | 0.955462i | \(-0.595358\pi\) | ||||
−0.295114 | + | 0.955462i | \(0.595358\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.93483 | 0.143393 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.62294 | −0.131852 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.3359 | 1.46603 | 0.733016 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733016 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.258674 | −0.00938928 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.9761 | −1.19538 | −0.597692 | − | 0.801726i | \(-0.703915\pi\) | ||||
−0.597692 | + | 0.801726i | \(0.703915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.93182 | 0.178544 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0603175 | −0.00218078 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.68138 | −0.169035 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.18564 | 0.331243 | 0.165621 | − | 0.986189i | \(-0.447037\pi\) | ||||
0.165621 | + | 0.986189i | \(0.447037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.4512 | 1.20472 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.0972 | −1.62203 | −0.811017 | − | 0.585023i | \(-0.801085\pi\) | ||||
−0.811017 | + | 0.585023i | \(0.801085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.88605 | 0.247354 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.88492 | 0.246995 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.70415 | −0.347687 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.503765 | 0.0180261 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.0598 | 0.716880 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.4028 | 0.478368 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.7593 | 0.989513 | 0.494756 | − | 0.869032i | \(-0.335257\pi\) | ||||
0.494756 | + | 0.869032i | \(0.335257\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −46.2528 | −1.64665 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.04106 | −0.0725716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.5482 | 1.97258 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.16866 | 0.218780 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.96118 | −0.175734 | −0.0878670 | − | 0.996132i | \(-0.528005\pi\) | ||||
−0.0878670 | + | 0.996132i | \(0.528005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.63321 | −0.199289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.78048 | 0.0629100 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.31935 | 0.187716 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.228596 | 0.00805694 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.12937 | −0.250966 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.3202 | 0.784737 | 0.392369 | − | 0.919808i | \(-0.371656\pi\) | ||||
0.392369 | + | 0.919808i | \(0.371656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0718 | 0.950618 | 0.475309 | − | 0.879819i | \(-0.342336\pi\) | ||||
0.475309 | + | 0.879819i | \(0.342336\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.0884 | −1.12539 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.75400 | −0.271611 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.20859 | −0.182225 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.508052 | 0.0177528 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.5750 | 0.543571 | 0.271785 | − | 0.962358i | \(-0.412386\pi\) | ||||
0.271785 | + | 0.962358i | \(0.412386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.6838 | −1.03471 | −0.517357 | − | 0.855770i | \(-0.673084\pi\) | ||||
−0.517357 | + | 0.855770i | \(0.673084\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.80324 | −0.132412 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.9658 | −1.63316 | −0.816581 | − | 0.577231i | \(-0.804133\pi\) | ||||
−0.816581 | + | 0.577231i | \(0.804133\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.63810 | 0.195819 | 0.0979097 | − | 0.995195i | \(-0.468784\pi\) | ||||
0.0979097 | + | 0.995195i | \(0.468784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.06034 | −0.0714723 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.68346 | 0.196920 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.71043 | 0.163011 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.90770 | 0.273330 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.4978 | 0.914807 | 0.457403 | − | 0.889259i | \(-0.348780\pi\) | ||||
0.457403 | + | 0.889259i | \(0.348780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5376 | −0.501295 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.2848 | −0.870854 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.68544 | −0.195585 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3507 | −0.424375 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.0296440 | −0.00101738 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.09978 | −0.0376999 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.77672 | −0.266270 | −0.133135 | − | 0.991098i | \(-0.542504\pi\) | ||||
−0.133135 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.114643 | 0.00392072 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.93663 | 0.339429 | 0.169714 | − | 0.985493i | \(-0.445715\pi\) | ||||
0.169714 | + | 0.985493i | \(0.445715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.9040 | 1.02031 | 0.510156 | − | 0.860082i | \(-0.329588\pi\) | ||||
0.510156 | + | 0.860082i | \(0.329588\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.98557 | −0.340307 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0132 | −1.22590 | −0.612952 | − | 0.790120i | \(-0.710018\pi\) | ||||
−0.612952 | + | 0.790120i | \(0.710018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.77753 | 0.230443 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.70453 | 0.0578888 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.0787824 | −0.00267251 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.7931 | −1.21280 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.37656 | 0.0465893 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.01958 | 0.237305 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.4356 | 1.53425 | 0.767125 | − | 0.641498i | \(-0.221687\pi\) | ||||
0.767125 | + | 0.641498i | \(0.221687\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.46986 | −0.0495770 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.6125 | 0.896599 | 0.448299 | − | 0.893883i | \(-0.352030\pi\) | ||||
0.448299 | + | 0.893883i | \(0.352030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5010 | 0.723567 | 0.361784 | − | 0.932262i | \(-0.382168\pi\) | ||||
0.361784 | + | 0.932262i | \(0.382168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.08700 | −0.0365391 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.25498 | 0.210022 | 0.105011 | − | 0.994471i | \(-0.466512\pi\) | ||||
0.105011 | + | 0.994471i | \(0.466512\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.1127 | 0.540403 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.22967 | −0.141699 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.7068 | 0.358291 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.96209 | 0.199291 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.49290 | 0.0832355 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.70117 | 0.190145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.67494 | 0.189060 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.35963 | −0.178357 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.94053 | −0.197470 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.7009 | −0.753770 | −0.376885 | − | 0.926260i | \(-0.623005\pi\) | ||||
−0.376885 | + | 0.926260i | \(0.623005\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.893141 | 0.0296236 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.5418 | −0.978765 | −0.489382 | − | 0.872069i | \(-0.662778\pi\) | ||||
−0.489382 | + | 0.872069i | \(0.662778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.792761 | −0.0262366 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.8981 | 0.426398 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2754 | −0.339325 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0345 | 0.331006 | 0.165503 | − | 0.986209i | \(-0.447075\pi\) | ||||
0.165503 | + | 0.986209i | \(0.447075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.6407 | 1.20735 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.85490 | −0.159801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.1698 | −0.531661 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.319854 | −0.0105054 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.13078 | −0.233953 | −0.116977 | − | 0.993135i | \(-0.537320\pi\) | ||||
−0.116977 | + | 0.993135i | \(0.537320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.8024 | −0.354033 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.8041 | −0.451927 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.309776 | 0.0101308 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.648603 | 0.0211889 | 0.0105945 | − | 0.999944i | \(-0.496628\pi\) | ||||
0.0105945 | + | 0.999944i | \(0.496628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.0797 | 1.37322 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.7146 | 1.09907 | 0.549533 | − | 0.835472i | \(-0.314806\pi\) | ||||
0.549533 | + | 0.835472i | \(0.314806\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.59507 | 0.0519425 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.85965 | 0.125555 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.2779 | −1.27636 | −0.638181 | − | 0.769887i | \(-0.720313\pi\) | ||||
−0.638181 | + | 0.769887i | \(0.720313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51.2638 | −1.66409 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.8065 | −0.415280 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6513 | 1.44640 | 0.723199 | − | 0.690640i | \(-0.242671\pi\) | ||||
0.723199 | + | 0.690640i | \(0.242671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.52401 | −0.0816750 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.14882 | −0.101787 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.25468 | 0.137391 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7526 | −0.927502 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.51411 | −0.0487916 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.09120 | 0.196083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.9750 | 1.83219 | 0.916096 | − | 0.400959i | \(-0.131323\pi\) | ||||
0.916096 | + | 0.400959i | \(0.131323\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.23974 | −0.104075 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.1333 | −1.03121 | −0.515604 | − | 0.856827i | \(-0.672432\pi\) | ||||
−0.515604 | + | 0.856827i | \(0.672432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.7790 | −0.537911 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 36.6526 | 1.17382 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.2357 | 1.70316 | 0.851580 | − | 0.524224i | \(-0.175645\pi\) | ||||
0.851580 | + | 0.524224i | \(0.175645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.14410 | −0.292247 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.406545 | −0.0129800 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.1645 | 1.18536 | 0.592681 | − | 0.805437i | \(-0.298069\pi\) | ||||
0.592681 | + | 0.805437i | \(0.298069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.447237 | 0.0142502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.0173 | 0.350686 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.856132 | 0.0272234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.1445 | 1.59289 | 0.796446 | − | 0.604710i | \(-0.206711\pi\) | ||||
0.796446 | + | 0.604710i | \(0.206711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.87685 | −0.0595601 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.9660 | −0.442752 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.4874 | 0.743852 | 0.371926 | − | 0.928262i | \(-0.378697\pi\) | ||||
0.371926 | + | 0.928262i | \(0.378697\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.5689 | −0.587493 |
(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 | 4012.2.a.g.1.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.g.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial |