Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(379,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.4 | ||
Root | \(-0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 945.379 |
Dual form | 945.2.d.c.379.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.456850i | − | 0.323042i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) | ||
0.986869 | − | 0.161521i | \(-0.0516399\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.79129 | 0.895644 | ||||||||
\(5\) | 0.456850 | − | 2.18890i | 0.204310 | − | 0.978906i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | − | 0.208712i | −0.316228 | − | 0.0660006i | ||||
\(11\) | −1.73205 | −0.522233 | −0.261116 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261116 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.208712i | − | 0.0578863i | −0.999581 | − | 0.0289432i | \(-0.990786\pi\) | ||
0.999581 | − | 0.0289432i | \(-0.00921418\pi\) | |||||||
\(14\) | −0.456850 | −0.122098 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | − | 3.00725i | − | 0.729366i | −0.931132 | − | 0.364683i | \(-0.881177\pi\) | ||
0.931132 | − | 0.364683i | \(-0.118823\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.20871 | 0.506713 | 0.253357 | − | 0.967373i | \(-0.418465\pi\) | ||||
0.253357 | + | 0.967373i | \(0.418465\pi\) | |||||||
\(20\) | 0.818350 | − | 3.92095i | 0.182989 | − | 0.876751i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.791288i | 0.168703i | ||||||||
\(23\) | − | 3.10260i | − | 0.646937i | −0.946239 | − | 0.323469i | \(-0.895151\pi\) | ||
0.946239 | − | 0.323469i | \(-0.104849\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58258 | − | 2.00000i | −0.916515 | − | 0.400000i | ||||
\(26\) | −0.0953502 | −0.0186997 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 1.79129i | − | 0.338522i | ||||||
\(29\) | −5.65300 | −1.04974 | −0.524868 | − | 0.851184i | \(-0.675885\pi\) | ||||
−0.524868 | + | 0.851184i | \(0.675885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.582576 | 0.104634 | 0.0523168 | − | 0.998631i | \(-0.483339\pi\) | ||||
0.0523168 | + | 0.998631i | \(0.483339\pi\) | |||||||
\(32\) | − | 4.73930i | − | 0.837798i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.37386 | −0.235616 | ||||||||
\(35\) | −2.18890 | − | 0.456850i | −0.369992 | − | 0.0772218i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.16515i | 1.34234i | 0.741302 | + | 0.671171i | \(0.234209\pi\) | ||||
−0.741302 | + | 0.671171i | \(0.765791\pi\) | |||||||
\(38\) | − | 1.00905i | − | 0.163690i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.79129 | − | 0.791288i | −0.599455 | − | 0.125114i | ||||
\(41\) | 6.47135 | 1.01066 | 0.505328 | − | 0.862927i | \(-0.331372\pi\) | ||||
0.505328 | + | 0.862927i | \(0.331372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000i | 0.152499i | 0.997089 | + | 0.0762493i | \(0.0242945\pi\) | ||||
−0.997089 | + | 0.0762493i | \(0.975706\pi\) | |||||||
\(44\) | −3.10260 | −0.467735 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.41742 | −0.208988 | ||||||||
\(47\) | 1.73205i | 0.252646i | 0.991989 | + | 0.126323i | \(0.0403175\pi\) | ||||
−0.991989 | + | 0.126323i | \(0.959682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.913701 | + | 2.09355i | −0.129217 | + | 0.296073i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 0.373864i | − | 0.0518455i | ||||||
\(53\) | 1.37055i | 0.188260i | 0.995560 | + | 0.0941298i | \(0.0300069\pi\) | ||||
−0.995560 | + | 0.0941298i | \(0.969993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.791288 | + | 3.79129i | −0.106697 | + | 0.511217i | ||||
\(56\) | −1.73205 | −0.231455 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.58258i | 0.339109i | ||||||||
\(59\) | 13.0381 | 1.69741 | 0.848705 | − | 0.528866i | \(-0.177383\pi\) | ||||
0.848705 | + | 0.528866i | \(0.177383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.208712 | 0.0267229 | 0.0133614 | − | 0.999911i | \(-0.495747\pi\) | ||||
0.0133614 | + | 0.999911i | \(0.495747\pi\) | |||||||
\(62\) | − | 0.266150i | − | 0.0338011i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.41742 | 0.427178 | ||||||||
\(65\) | −0.456850 | − | 0.0953502i | −0.0566653 | − | 0.0118267i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.3739i | − | 1.51171i | −0.654740 | − | 0.755854i | \(-0.727222\pi\) | ||
0.654740 | − | 0.755854i | \(-0.272778\pi\) | |||||||
\(68\) | − | 5.38685i | − | 0.653252i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.208712 | + | 1.00000i | −0.0249459 | + | 0.119523i | ||||
\(71\) | −14.4086 | −1.70999 | −0.854994 | − | 0.518639i | \(-0.826439\pi\) | ||||
−0.854994 | + | 0.518639i | \(0.826439\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.58258i | − | 0.536350i | −0.963370 | − | 0.268175i | \(-0.913579\pi\) | ||
0.963370 | − | 0.268175i | \(-0.0864205\pi\) | |||||||
\(74\) | 3.73025 | 0.433633 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.95644 | 0.453835 | ||||||||
\(77\) | 1.73205i | 0.197386i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3739 | 1.16715 | 0.583575 | − | 0.812059i | \(-0.301653\pi\) | ||||
0.583575 | + | 0.812059i | \(0.301653\pi\) | |||||||
\(80\) | 1.27520 | − | 6.10985i | 0.142572 | − | 0.683102i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 2.95644i | − | 0.326484i | ||||||
\(83\) | − | 6.83285i | − | 0.750003i | −0.927024 | − | 0.375002i | \(-0.877642\pi\) | ||
0.927024 | − | 0.375002i | \(-0.122358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.58258 | − | 1.37386i | −0.713981 | − | 0.149016i | ||||
\(86\) | 0.456850 | 0.0492634 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000i | 0.319801i | ||||||||
\(89\) | −8.66025 | −0.917985 | −0.458993 | − | 0.888440i | \(-0.651790\pi\) | ||||
−0.458993 | + | 0.888440i | \(0.651790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.208712 | −0.0218790 | ||||||||
\(92\) | − | 5.55765i | − | 0.579425i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.791288 | 0.0816151 | ||||||||
\(95\) | 1.00905 | − | 4.83465i | 0.103526 | − | 0.496025i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3739i | 1.25638i | 0.778062 | + | 0.628188i | \(0.216203\pi\) | ||||
−0.778062 | + | 0.628188i | \(0.783797\pi\) | |||||||
\(98\) | 0.456850i | 0.0461488i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.20871 | − | 3.58258i | −0.820871 | − | 0.358258i | ||||
\(101\) | 15.8745 | 1.57957 | 0.789786 | − | 0.613382i | \(-0.210191\pi\) | ||||
0.789786 | + | 0.613382i | \(0.210191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.37386i | 0.332437i | 0.986089 | + | 0.166218i | \(0.0531556\pi\) | ||||
−0.986089 | + | 0.166218i | \(0.946844\pi\) | |||||||
\(104\) | −0.361500 | −0.0354480 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.626136 | 0.0608157 | ||||||||
\(107\) | 7.02355i | 0.678993i | 0.940607 | + | 0.339496i | \(0.110257\pi\) | ||||
−0.940607 | + | 0.339496i | \(0.889743\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.79129 | 0.458922 | 0.229461 | − | 0.973318i | \(-0.426304\pi\) | ||||
0.229461 | + | 0.973318i | \(0.426304\pi\) | |||||||
\(110\) | 1.73205 | + | 0.361500i | 0.165145 | + | 0.0344677i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 2.79129i | − | 0.263752i | ||||||
\(113\) | 6.56670i | 0.617743i | 0.951104 | + | 0.308872i | \(0.0999514\pi\) | ||||
−0.951104 | + | 0.308872i | \(0.900049\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.79129 | − | 1.41742i | −0.633291 | − | 0.132175i | ||||
\(116\) | −10.1262 | −0.940190 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 5.95644i | − | 0.548335i | ||||||
\(119\) | −3.00725 | −0.275674 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | − | 0.0953502i | − | 0.00863260i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.04356 | 0.0937145 | ||||||||
\(125\) | −6.47135 | + | 9.11710i | −0.578815 | + | 0.815459i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.62614i | − | 0.144296i | −0.997394 | − | 0.0721481i | \(-0.977015\pi\) | ||
0.997394 | − | 0.0721481i | \(-0.0229854\pi\) | |||||||
\(128\) | − | 11.0399i | − | 0.975795i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0435608 | + | 0.208712i | −0.00382053 | + | 0.0183053i | ||||
\(131\) | 6.66205 | 0.582066 | 0.291033 | − | 0.956713i | \(-0.406001\pi\) | ||||
0.291033 | + | 0.956713i | \(0.406001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.20871i | − | 0.191520i | ||||||
\(134\) | −5.65300 | −0.488345 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.20871 | −0.446643 | ||||||||
\(137\) | 15.8745i | 1.35625i | 0.734946 | + | 0.678125i | \(0.237207\pi\) | ||||
−0.734946 | + | 0.678125i | \(0.762793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.5826 | 1.74579 | 0.872896 | − | 0.487907i | \(-0.162239\pi\) | ||||
0.872896 | + | 0.487907i | \(0.162239\pi\) | |||||||
\(140\) | −3.92095 | − | 0.818350i | −0.331381 | − | 0.0691632i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.58258i | 0.552397i | ||||||||
\(143\) | 0.361500i | 0.0302302i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.58258 | + | 12.3739i | −0.214471 | + | 1.02759i | ||||
\(146\) | −2.09355 | −0.173264 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.6261i | 1.20226i | ||||||||
\(149\) | 15.4177 | 1.26306 | 0.631532 | − | 0.775350i | \(-0.282426\pi\) | ||||
0.631532 | + | 0.775350i | \(0.282426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.83485 | −0.312076 | −0.156038 | − | 0.987751i | \(-0.549872\pi\) | ||||
−0.156038 | + | 0.987751i | \(0.549872\pi\) | |||||||
\(152\) | − | 3.82560i | − | 0.310297i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.791288 | 0.0637638 | ||||||||
\(155\) | 0.266150 | − | 1.27520i | 0.0213777 | − | 0.102427i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.7477i | − | 1.33661i | −0.743886 | − | 0.668307i | \(-0.767019\pi\) | ||
0.743886 | − | 0.668307i | \(-0.232981\pi\) | |||||||
\(158\) | − | 4.73930i | − | 0.377039i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.3739 | − | 2.16515i | −0.820126 | − | 0.171170i | ||||
\(161\) | −3.10260 | −0.244519 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.7477i | − | 1.15513i | −0.816344 | − | 0.577566i | \(-0.804003\pi\) | ||
0.816344 | − | 0.577566i | \(-0.195997\pi\) | |||||||
\(164\) | 11.5921 | 0.905187 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.12159 | −0.242282 | ||||||||
\(167\) | 11.4014i | 0.882263i | 0.897442 | + | 0.441132i | \(0.145423\pi\) | ||||
−0.897442 | + | 0.441132i | \(0.854577\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9564 | 0.996649 | ||||||||
\(170\) | −0.627650 | + | 3.00725i | −0.0481386 | + | 0.230646i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.79129i | 0.136584i | ||||||||
\(173\) | 21.0707i | 1.60197i | 0.598683 | + | 0.800986i | \(0.295691\pi\) | ||||
−0.598683 | + | 0.800986i | \(0.704309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 4.58258i | −0.151186 | + | 0.346410i | ||||
\(176\) | −4.83465 | −0.364426 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.95644i | 0.296548i | ||||||||
\(179\) | −16.6929 | −1.24768 | −0.623841 | − | 0.781551i | \(-0.714429\pi\) | ||||
−0.623841 | + | 0.781551i | \(0.714429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3303 | −1.13949 | −0.569746 | − | 0.821821i | \(-0.692959\pi\) | ||||
−0.569746 | + | 0.821821i | \(0.692959\pi\) | |||||||
\(182\) | 0.0953502i | 0.00706783i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.37386 | −0.396166 | ||||||||
\(185\) | 17.8727 | + | 3.73025i | 1.31403 | + | 0.274254i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.20871i | 0.380899i | ||||||||
\(188\) | 3.10260i | 0.226280i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.20871 | − | 0.460985i | −0.160237 | − | 0.0334434i | ||||
\(191\) | 13.4949 | 0.976457 | 0.488229 | − | 0.872716i | \(-0.337643\pi\) | ||||
0.488229 | + | 0.872716i | \(0.337643\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.9564i | 0.860643i | 0.902676 | + | 0.430322i | \(0.141600\pi\) | ||||
−0.902676 | + | 0.430322i | \(0.858400\pi\) | |||||||
\(194\) | 5.65300 | 0.405862 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.79129 | −0.127949 | ||||||||
\(197\) | 26.1715i | 1.86464i | 0.361635 | + | 0.932320i | \(0.382219\pi\) | ||||
−0.361635 | + | 0.932320i | \(0.617781\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7913 | 1.61563 | 0.807816 | − | 0.589435i | \(-0.200650\pi\) | ||||
0.807816 | + | 0.589435i | \(0.200650\pi\) | |||||||
\(200\) | −3.46410 | + | 7.93725i | −0.244949 | + | 0.561249i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 7.25227i | − | 0.510268i | ||||||
\(203\) | 5.65300i | 0.396763i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.95644 | − | 14.1652i | 0.206487 | − | 0.989337i | ||||
\(206\) | 1.54135 | 0.107391 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 0.582576i | − | 0.0403944i | ||||||
\(209\) | −3.82560 | −0.264622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.1652 | −1.31938 | −0.659692 | − | 0.751536i | \(-0.729313\pi\) | ||||
−0.659692 | + | 0.751536i | \(0.729313\pi\) | |||||||
\(212\) | 2.45505i | 0.168614i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.20871 | 0.219343 | ||||||||
\(215\) | 2.18890 | + | 0.456850i | 0.149282 | + | 0.0311569i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.582576i | − | 0.0395478i | ||||||
\(218\) | − | 2.18890i | − | 0.148251i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.41742 | + | 6.79129i | −0.0955627 | + | 0.457869i | ||||
\(221\) | −0.627650 | −0.0422203 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.00000i | − | 0.602685i | −0.953516 | − | 0.301342i | \(-0.902565\pi\) | ||
0.953516 | − | 0.301342i | \(-0.0974347\pi\) | |||||||
\(224\) | −4.73930 | −0.316658 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | 0.199557 | ||||||||
\(227\) | 6.47135i | 0.429519i | 0.976667 | + | 0.214759i | \(0.0688967\pi\) | ||||
−0.976667 | + | 0.214759i | \(0.931103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.0000 | 1.25556 | 0.627778 | − | 0.778393i | \(-0.283965\pi\) | ||||
0.627778 | + | 0.778393i | \(0.283965\pi\) | |||||||
\(230\) | −0.647551 | + | 3.10260i | −0.0426982 | + | 0.204579i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.79129i | 0.642830i | ||||||||
\(233\) | 20.6138i | 1.35046i | 0.737609 | + | 0.675228i | \(0.235955\pi\) | ||||
−0.737609 | + | 0.675228i | \(0.764045\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.79129 | + | 0.791288i | 0.247316 | + | 0.0516179i | ||||
\(236\) | 23.3549 | 1.52028 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.37386i | 0.0890543i | ||||||||
\(239\) | 1.73205 | 0.112037 | 0.0560185 | − | 0.998430i | \(-0.482159\pi\) | ||||
0.0560185 | + | 0.998430i | \(0.482159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3739 | −0.668239 | −0.334120 | − | 0.942531i | \(-0.608439\pi\) | ||||
−0.334120 | + | 0.942531i | \(0.608439\pi\) | |||||||
\(242\) | 3.65480i | 0.234940i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.373864 | 0.0239342 | ||||||||
\(245\) | −0.456850 | + | 2.18890i | −0.0291871 | + | 0.139844i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.460985i | − | 0.0293318i | ||||||
\(248\) | − | 1.00905i | − | 0.0640748i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.16515 | + | 2.95644i | 0.263427 | + | 0.186982i | ||||
\(251\) | −15.8745 | −1.00199 | −0.500995 | − | 0.865450i | \(-0.667033\pi\) | ||||
−0.500995 | + | 0.865450i | \(0.667033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.37386i | 0.337852i | ||||||||
\(254\) | −0.742901 | −0.0466137 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.79129 | 0.111955 | ||||||||
\(257\) | 1.82740i | 0.113990i | 0.998374 | + | 0.0569951i | \(0.0181519\pi\) | ||||
−0.998374 | + | 0.0569951i | \(0.981848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.16515 | 0.507358 | ||||||||
\(260\) | −0.818350 | − | 0.170800i | −0.0507519 | − | 0.0105925i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 3.04356i | − | 0.188032i | ||||||
\(263\) | 22.1552i | 1.36615i | 0.730350 | + | 0.683073i | \(0.239357\pi\) | ||||
−0.730350 | + | 0.683073i | \(0.760643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | + | 0.626136i | 0.184289 | + | 0.0384633i | ||||
\(266\) | −1.00905 | −0.0618689 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 22.1652i | − | 1.35395i | ||||||
\(269\) | 24.7255 | 1.50754 | 0.753769 | − | 0.657139i | \(-0.228234\pi\) | ||||
0.753769 | + | 0.657139i | \(0.228234\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.20871 | −0.437898 | −0.218949 | − | 0.975736i | \(-0.570263\pi\) | ||||
−0.218949 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(272\) | − | 8.39410i | − | 0.508967i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.25227 | 0.438126 | ||||||||
\(275\) | 7.93725 | + | 3.46410i | 0.478634 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.20871i | 0.0726245i | 0.999340 | + | 0.0363122i | \(0.0115611\pi\) | ||||
−0.999340 | + | 0.0363122i | \(0.988439\pi\) | |||||||
\(278\) | − | 9.40315i | − | 0.563964i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.791288 | + | 3.79129i | −0.0472885 | + | 0.226573i | ||||
\(281\) | −27.2560 | −1.62595 | −0.812977 | − | 0.582296i | \(-0.802155\pi\) | ||||
−0.812977 | + | 0.582296i | \(0.802155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3739i | 1.44888i | 0.689340 | + | 0.724438i | \(0.257901\pi\) | ||||
−0.689340 | + | 0.724438i | \(0.742099\pi\) | |||||||
\(284\) | −25.8100 | −1.53154 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.165151 | 0.00976561 | ||||||||
\(287\) | − | 6.47135i | − | 0.381992i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.95644 | 0.468026 | ||||||||
\(290\) | 5.65300 | + | 1.17985i | 0.331956 | + | 0.0692832i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 8.20871i | − | 0.480379i | ||||||
\(293\) | 17.3205i | 1.01187i | 0.862570 | + | 0.505937i | \(0.168853\pi\) | ||||
−0.862570 | + | 0.505937i | \(0.831147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.95644 | − | 28.5390i | 0.346797 | − | 1.66161i | ||||
\(296\) | 14.1425 | 0.822014 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 7.04356i | − | 0.408023i | ||||||
\(299\) | −0.647551 | −0.0374488 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | 0.0576390 | ||||||||
\(302\) | 1.75195i | 0.100813i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.16515 | 0.353596 | ||||||||
\(305\) | 0.0953502 | − | 0.456850i | 0.00545974 | − | 0.0261592i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5826i | 1.34593i | 0.739675 | + | 0.672964i | \(0.234979\pi\) | ||||
−0.739675 | + | 0.672964i | \(0.765021\pi\) | |||||||
\(308\) | 3.10260i | 0.176787i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.582576 | − | 0.121591i | −0.0330881 | − | 0.00690588i | ||||
\(311\) | 16.9590 | 0.961657 | 0.480829 | − | 0.876815i | \(-0.340336\pi\) | ||||
0.480829 | + | 0.876815i | \(0.340336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.41742i | − | 0.419258i | −0.977781 | − | 0.209629i | \(-0.932774\pi\) | ||
0.977781 | − | 0.209629i | \(-0.0672256\pi\) | |||||||
\(314\) | −7.65120 | −0.431782 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.5826 | 1.04535 | ||||||||
\(317\) | − | 25.2578i | − | 1.41862i | −0.704898 | − | 0.709309i | \(-0.749007\pi\) | ||
0.704898 | − | 0.709309i | \(-0.250993\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.79129 | 0.548207 | ||||||||
\(320\) | 1.56125 | − | 7.48040i | 0.0872766 | − | 0.418167i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.41742i | 0.0789900i | ||||||||
\(323\) | − | 6.64215i | − | 0.369579i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.417424 | + | 0.956439i | −0.0231545 | + | 0.0530537i | ||||
\(326\) | −6.73750 | −0.373156 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 11.2087i | − | 0.618898i | ||||||
\(329\) | 1.73205 | 0.0954911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3739 | −1.28474 | −0.642372 | − | 0.766393i | \(-0.722050\pi\) | ||||
−0.642372 | + | 0.766393i | \(0.722050\pi\) | |||||||
\(332\) | − | 12.2396i | − | 0.671736i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.20871 | 0.285008 | ||||||||
\(335\) | −27.0852 | − | 5.65300i | −1.47982 | − | 0.308857i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.7042i | − | 0.964407i | −0.876059 | − | 0.482204i | \(-0.839837\pi\) | ||
0.876059 | − | 0.482204i | \(-0.160163\pi\) | |||||||
\(338\) | − | 5.91915i | − | 0.321959i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.7913 | − | 2.46099i | −0.639472 | − | 0.133466i | ||||
\(341\) | −1.00905 | −0.0546432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 1.73205 | 0.0933859 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.62614 | 0.517504 | ||||||||
\(347\) | − | 22.0797i | − | 1.18530i | −0.805460 | − | 0.592650i | \(-0.798082\pi\) | ||
0.805460 | − | 0.592650i | \(-0.201918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.74773 | −0.307669 | −0.153834 | − | 0.988097i | \(-0.549162\pi\) | ||||
−0.153834 | + | 0.988097i | \(0.549162\pi\) | |||||||
\(350\) | 2.09355 | + | 0.913701i | 0.111905 | + | 0.0488393i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.20871i | 0.437526i | ||||||||
\(353\) | 1.46590i | 0.0780220i | 0.999239 | + | 0.0390110i | \(0.0124207\pi\) | ||||
−0.999239 | + | 0.0390110i | \(0.987579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.58258 | + | 31.5390i | −0.349367 | + | 1.67392i | ||||
\(356\) | −15.5130 | −0.822188 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.62614i | 0.403054i | ||||||||
\(359\) | 25.4485 | 1.34312 | 0.671559 | − | 0.740951i | \(-0.265625\pi\) | ||||
0.671559 | + | 0.740951i | \(0.265625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1216 | −0.743242 | ||||||||
\(362\) | 7.00365i | 0.368104i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.373864 | −0.0195958 | ||||||||
\(365\) | −10.0308 | − | 2.09355i | −0.525036 | − | 0.109581i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.95644i | − | 0.206524i | −0.994654 | − | 0.103262i | \(-0.967072\pi\) | ||
0.994654 | − | 0.103262i | \(-0.0329281\pi\) | |||||||
\(368\) | − | 8.66025i | − | 0.451447i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.70417 | − | 8.16515i | 0.0885954 | − | 0.424486i | ||||
\(371\) | 1.37055 | 0.0711554 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.9564i | − | 0.670859i | −0.942065 | − | 0.335429i | \(-0.891119\pi\) | ||
0.942065 | − | 0.335429i | \(-0.108881\pi\) | |||||||
\(374\) | 2.37960 | 0.123046 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 1.17985i | 0.0607654i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.58258 | −0.184025 | −0.0920123 | − | 0.995758i | \(-0.529330\pi\) | ||||
−0.0920123 | + | 0.995758i | \(0.529330\pi\) | |||||||
\(380\) | 1.80750 | − | 8.66025i | 0.0927228 | − | 0.444262i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 6.16515i | − | 0.315437i | ||||||
\(383\) | − | 15.3978i | − | 0.786789i | −0.919370 | − | 0.393394i | \(-0.871301\pi\) | ||
0.919370 | − | 0.393394i | \(-0.128699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.79129 | + | 0.791288i | 0.193222 | + | 0.0403278i | ||||
\(386\) | 5.46230 | 0.278024 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.1652i | 1.12527i | ||||||||
\(389\) | −24.3640 | −1.23530 | −0.617651 | − | 0.786452i | \(-0.711916\pi\) | ||||
−0.617651 | + | 0.786452i | \(0.711916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.33030 | −0.471854 | ||||||||
\(392\) | 1.73205i | 0.0874818i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.9564 | 0.602357 | ||||||||
\(395\) | 4.73930 | − | 22.7074i | 0.238460 | − | 1.14253i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.83485i | 0.343031i | 0.985181 | + | 0.171516i | \(0.0548664\pi\) | ||||
−0.985181 | + | 0.171516i | \(0.945134\pi\) | |||||||
\(398\) | − | 10.4122i | − | 0.521917i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.7913 | − | 5.58258i | −0.639564 | − | 0.279129i | ||||
\(401\) | 19.7001 | 0.983777 | 0.491888 | − | 0.870658i | \(-0.336307\pi\) | ||||
0.491888 | + | 0.870658i | \(0.336307\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.121591i | − | 0.00605686i | ||||||
\(404\) | 28.4358 | 1.41473 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.58258 | 0.128171 | ||||||||
\(407\) | − | 14.1425i | − | 0.701016i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.1652 | −0.848762 | −0.424381 | − | 0.905484i | \(-0.639508\pi\) | ||||
−0.424381 | + | 0.905484i | \(0.639508\pi\) | |||||||
\(410\) | −6.47135 | − | 1.35065i | −0.319597 | − | 0.0667038i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.04356i | 0.297745i | ||||||||
\(413\) | − | 13.0381i | − | 0.641561i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.9564 | − | 3.12159i | −0.734183 | − | 0.153233i | ||||
\(416\) | −0.989150 | −0.0484971 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.74773i | 0.0854841i | ||||||||
\(419\) | −22.5167 | −1.10001 | −0.550005 | − | 0.835161i | \(-0.685374\pi\) | ||||
−0.550005 | + | 0.835161i | \(0.685374\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2087 | −0.984912 | −0.492456 | − | 0.870337i | \(-0.663901\pi\) | ||||
−0.492456 | + | 0.870337i | \(0.663901\pi\) | |||||||
\(422\) | 8.75560i | 0.426216i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.37386 | 0.115285 | ||||||||
\(425\) | −6.01450 | + | 13.7810i | −0.291746 | + | 0.668475i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.208712i | − | 0.0101003i | ||||||
\(428\) | 12.5812i | 0.608136i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.208712 | − | 1.00000i | 0.0100650 | − | 0.0482243i | ||||
\(431\) | 1.17985 | 0.0568314 | 0.0284157 | − | 0.999596i | \(-0.490954\pi\) | ||||
0.0284157 | + | 0.999596i | \(0.490954\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.5390i | − | 0.650644i | −0.945603 | − | 0.325322i | \(-0.894527\pi\) | ||
0.945603 | − | 0.325322i | \(-0.105473\pi\) | |||||||
\(434\) | −0.266150 | −0.0127756 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.58258 | 0.411031 | ||||||||
\(437\) | − | 6.85275i | − | 0.327812i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.33030 | 0.158947 | 0.0794733 | − | 0.996837i | \(-0.474676\pi\) | ||||
0.0794733 | + | 0.996837i | \(0.474676\pi\) | |||||||
\(440\) | 6.56670 | + | 1.37055i | 0.313055 | + | 0.0653384i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.286742i | 0.0136389i | ||||||||
\(443\) | − | 40.6754i | − | 1.93255i | −0.257517 | − | 0.966274i | \(-0.582904\pi\) | ||
0.257517 | − | 0.966274i | \(-0.417096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.95644 | + | 18.9564i | −0.187553 | + | 0.898621i | ||||
\(446\) | −4.11165 | −0.194692 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.41742i | − | 0.161458i | ||||||
\(449\) | −3.27340 | −0.154481 | −0.0772407 | − | 0.997012i | \(-0.524611\pi\) | ||||
−0.0772407 | + | 0.997012i | \(0.524611\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.2087 | −0.527798 | ||||||||
\(452\) | 11.7629i | 0.553278i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.95644 | 0.138753 | ||||||||
\(455\) | −0.0953502 | + | 0.456850i | −0.00447009 | + | 0.0214175i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.8693i | 1.86501i | 0.361160 | + | 0.932504i | \(0.382381\pi\) | ||||
−0.361160 | + | 0.932504i | \(0.617619\pi\) | |||||||
\(458\) | − | 8.68015i | − | 0.405597i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.1652 | − | 2.53901i | −0.567203 | − | 0.118382i | ||||
\(461\) | −22.4412 | −1.04519 | −0.522596 | − | 0.852581i | \(-0.675036\pi\) | ||||
−0.522596 | + | 0.852581i | \(0.675036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.6261i | 1.14447i | 0.820088 | + | 0.572237i | \(0.193924\pi\) | ||||
−0.820088 | + | 0.572237i | \(0.806076\pi\) | |||||||
\(464\) | −15.7792 | −0.732529 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.41742 | 0.436254 | ||||||||
\(467\) | − | 32.4720i | − | 1.50263i | −0.659946 | − | 0.751313i | \(-0.729421\pi\) | ||
0.659946 | − | 0.751313i | \(-0.270579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.3739 | −0.571372 | ||||||||
\(470\) | 0.361500 | − | 1.73205i | 0.0166748 | − | 0.0798935i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 22.5826i | − | 1.03945i | ||||||
\(473\) | − | 1.73205i | − | 0.0796398i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.1216 | − | 4.41742i | −0.464410 | − | 0.202685i | ||||
\(476\) | −5.38685 | −0.246906 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 0.791288i | − | 0.0361927i | ||||||
\(479\) | 24.8963 | 1.13754 | 0.568770 | − | 0.822497i | \(-0.307420\pi\) | ||||
0.568770 | + | 0.822497i | \(0.307420\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.70417 | 0.0777033 | ||||||||
\(482\) | 4.73930i | 0.215869i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.3303 | −0.651377 | ||||||||
\(485\) | 27.0852 | + | 5.65300i | 1.22987 | + | 0.256690i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13.9129i | − | 0.630453i | −0.949017 | − | 0.315226i | \(-0.897920\pi\) | ||
0.949017 | − | 0.315226i | \(-0.102080\pi\) | |||||||
\(488\) | − | 0.361500i | − | 0.0163643i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | + | 0.208712i | 0.0451754 | + | 0.00942865i | ||||
\(491\) | −20.8999 | −0.943198 | −0.471599 | − | 0.881813i | \(-0.656323\pi\) | ||||
−0.471599 | + | 0.881813i | \(0.656323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.0000i | 0.765641i | ||||||||
\(494\) | −0.210601 | −0.00947539 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.62614 | 0.0730157 | ||||||||
\(497\) | 14.4086i | 0.646314i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.83485 | 0.0821391 | 0.0410696 | − | 0.999156i | \(-0.486923\pi\) | ||||
0.0410696 | + | 0.999156i | \(0.486923\pi\) | |||||||
\(500\) | −11.5921 | + | 16.3314i | −0.518413 | + | 0.730361i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.25227i | 0.323685i | ||||||||
\(503\) | 9.30780i | 0.415014i | 0.978233 | + | 0.207507i | \(0.0665351\pi\) | ||||
−0.978233 | + | 0.207507i | \(0.933465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.25227 | − | 34.7477i | 0.322722 | − | 1.54625i | ||||
\(506\) | 2.45505 | 0.109140 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 2.91288i | − | 0.129238i | ||||||
\(509\) | −6.49125 | −0.287720 | −0.143860 | − | 0.989598i | \(-0.545951\pi\) | ||||
−0.143860 | + | 0.989598i | \(0.545951\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.58258 | −0.202721 | ||||||||
\(512\) | − | 22.8981i | − | 1.01196i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.834849 | 0.0368236 | ||||||||
\(515\) | 7.38505 | + | 1.54135i | 0.325424 | + | 0.0679200i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.00000i | − | 0.131940i | ||||||
\(518\) | − | 3.73025i | − | 0.163898i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.165151 | + | 0.791288i | −0.00724237 | + | 0.0347003i | ||||
\(521\) | 19.9663 | 0.874738 | 0.437369 | − | 0.899282i | \(-0.355910\pi\) | ||||
0.437369 | + | 0.899282i | \(0.355910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 32.9564i | − | 1.44108i | −0.693411 | − | 0.720542i | \(-0.743893\pi\) | ||
0.693411 | − | 0.720542i | \(-0.256107\pi\) | |||||||
\(524\) | 11.9337 | 0.521324 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.1216 | 0.441322 | ||||||||
\(527\) | − | 1.75195i | − | 0.0763162i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.3739 | 0.581472 | ||||||||
\(530\) | 0.286051 | − | 1.37055i | 0.0124252 | − | 0.0595329i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 3.95644i | − | 0.171533i | ||||||
\(533\) | − | 1.35065i | − | 0.0585031i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.3739 | + | 3.20871i | 0.664670 | + | 0.138725i | ||||
\(536\) | −21.4322 | −0.925728 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 11.2958i | − | 0.486998i | ||||||
\(539\) | 1.73205 | 0.0746047 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7042 | 0.632181 | 0.316091 | − | 0.948729i | \(-0.397630\pi\) | ||||
0.316091 | + | 0.948729i | \(0.397630\pi\) | |||||||
\(542\) | 3.29330i | 0.141459i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.2523 | −0.611061 | ||||||||
\(545\) | 2.18890 | − | 10.4877i | 0.0937622 | − | 0.449242i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.582576i | 0.0249091i | 0.999922 | + | 0.0124546i | \(0.00396451\pi\) | ||||
−0.999922 | + | 0.0124546i | \(0.996035\pi\) | |||||||
\(548\) | 28.4358i | 1.21472i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.58258 | − | 3.62614i | 0.0674813 | − | 0.154619i | ||||
\(551\) | −12.4859 | −0.531915 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.3739i | − | 0.441142i | ||||||
\(554\) | 0.552200 | 0.0234607 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.8693 | 1.56361 | ||||||||
\(557\) | − | 10.4122i | − | 0.441179i | −0.975367 | − | 0.220590i | \(-0.929202\pi\) | ||
0.975367 | − | 0.220590i | \(-0.0707982\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.208712 | 0.00882758 | ||||||||
\(560\) | −6.10985 | − | 1.27520i | −0.258188 | − | 0.0538871i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.4519i | 0.525251i | ||||||||
\(563\) | − | 28.3604i | − | 1.19525i | −0.801777 | − | 0.597623i | \(-0.796112\pi\) | ||
0.801777 | − | 0.597623i | \(-0.203888\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.3739 | + | 3.00000i | 0.604713 | + | 0.126211i | ||||
\(566\) | 11.1352 | 0.468048 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24.9564i | 1.04715i | ||||||||
\(569\) | −21.0707 | −0.883328 | −0.441664 | − | 0.897181i | \(-0.645612\pi\) | ||||
−0.441664 | + | 0.897181i | \(0.645612\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.79129 | −0.284207 | −0.142103 | − | 0.989852i | \(-0.545387\pi\) | ||||
−0.142103 | + | 0.989852i | \(0.545387\pi\) | |||||||
\(572\) | 0.647551i | 0.0270755i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.95644 | −0.123399 | ||||||||
\(575\) | −6.20520 | + | 14.2179i | −0.258775 | + | 0.592928i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.3303i | − | 0.804731i | −0.915479 | − | 0.402366i | \(-0.868188\pi\) | ||
0.915479 | − | 0.402366i | \(-0.131812\pi\) | |||||||
\(578\) | − | 3.63490i | − | 0.151192i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.62614 | + | 22.1652i | −0.192090 | + | 0.920358i | ||||
\(581\) | −6.83285 | −0.283475 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.37386i | − | 0.0983154i | ||||||
\(584\) | −7.93725 | −0.328446 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.91288 | 0.326878 | ||||||||
\(587\) | − | 36.2976i | − | 1.49816i | −0.662478 | − | 0.749082i | \(-0.730495\pi\) | ||
0.662478 | − | 0.749082i | \(-0.269505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.28674 | 0.0530193 | ||||||||
\(590\) | −13.0381 | − | 2.72120i | −0.536768 | − | 0.112030i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.7913i | 0.936716i | ||||||||
\(593\) | − | 9.57395i | − | 0.393155i | −0.980488 | − | 0.196578i | \(-0.937017\pi\) | ||
0.980488 | − | 0.196578i | \(-0.0629828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37386 | + | 6.58258i | −0.0563229 | + | 0.269859i | ||||
\(596\) | 27.6175 | 1.13126 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.295834i | 0.0120975i | ||||||||
\(599\) | −13.5148 | −0.552200 | −0.276100 | − | 0.961129i | \(-0.589042\pi\) | ||||
−0.276100 | + | 0.961129i | \(0.589042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.6170 | 1.94234 | 0.971170 | − | 0.238388i | \(-0.0766191\pi\) | ||||
0.971170 | + | 0.238388i | \(0.0766191\pi\) | |||||||
\(602\) | − | 0.456850i | − | 0.0186198i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.86932 | −0.279509 | ||||||||
\(605\) | −3.65480 | + | 17.5112i | −0.148589 | + | 0.711932i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 48.1652i | − | 1.95496i | −0.211021 | − | 0.977482i | \(-0.567679\pi\) | ||
0.211021 | − | 0.977482i | \(-0.432321\pi\) | |||||||
\(608\) | − | 10.4678i | − | 0.424523i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.208712 | − | 0.0435608i | −0.00845051 | − | 0.00176372i | ||||
\(611\) | 0.361500 | 0.0146247 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.3303i | 0.942302i | 0.882053 | + | 0.471151i | \(0.156161\pi\) | ||||
−0.882053 | + | 0.471151i | \(0.843839\pi\) | |||||||
\(614\) | 10.7737 | 0.434791 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | − | 13.3996i | − | 0.539446i | −0.962938 | − | 0.269723i | \(-0.913068\pi\) | ||
0.962938 | − | 0.269723i | \(-0.0869321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4955 | −0.421848 | −0.210924 | − | 0.977502i | \(-0.567647\pi\) | ||||
−0.210924 | + | 0.977502i | \(0.567647\pi\) | |||||||
\(620\) | 0.476751 | − | 2.28425i | 0.0191468 | − | 0.0917377i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 7.74773i | − | 0.310656i | ||||||
\(623\) | 8.66025i | 0.346966i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0000 | + | 18.3303i | 0.680000 | + | 0.733212i | ||||
\(626\) | −3.38865 | −0.135438 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 30.0000i | − | 1.19713i | ||||||
\(629\) | 24.5547 | 0.979059 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0780 | 1.07796 | 0.538980 | − | 0.842319i | \(-0.318810\pi\) | ||||
0.538980 | + | 0.842319i | \(0.318810\pi\) | |||||||
\(632\) | − | 17.9681i | − | 0.714731i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.5390 | −0.458273 | ||||||||
\(635\) | −3.55945 | − | 0.742901i | −0.141253 | − | 0.0294811i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.208712i | 0.00826948i | ||||||||
\(638\) | − | 4.47315i | − | 0.177094i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.1652 | − | 5.04356i | −0.955211 | − | 0.199364i | ||||
\(641\) | 24.2686 | 0.958553 | 0.479276 | − | 0.877664i | \(-0.340899\pi\) | ||||
0.479276 | + | 0.877664i | \(0.340899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.208712i | − | 0.00823080i | −0.999992 | − | 0.00411540i | \(-0.998690\pi\) | ||
0.999992 | − | 0.00411540i | \(-0.00130998\pi\) | |||||||
\(644\) | −5.55765 | −0.219002 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.03447 | −0.119390 | ||||||||
\(647\) | − | 30.6446i | − | 1.20476i | −0.798208 | − | 0.602382i | \(-0.794218\pi\) | ||
0.798208 | − | 0.602382i | \(-0.205782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.5826 | −0.886444 | ||||||||
\(650\) | 0.436950 | + | 0.190700i | 0.0171386 | + | 0.00747989i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 26.4174i | − | 1.03459i | ||||||
\(653\) | 21.5275i | 0.842437i | 0.906959 | + | 0.421218i | \(0.138397\pi\) | ||||
−0.906959 | + | 0.421218i | \(0.861603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.04356 | − | 14.5826i | 0.118922 | − | 0.569788i | ||||
\(656\) | 18.0634 | 0.705258 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 0.791288i | − | 0.0308476i | ||||||
\(659\) | −19.3386 | −0.753325 | −0.376663 | − | 0.926351i | \(-0.622928\pi\) | ||||
−0.376663 | + | 0.926351i | \(0.622928\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.5390 | −0.565502 | −0.282751 | − | 0.959193i | \(-0.591247\pi\) | ||||
−0.282751 | + | 0.959193i | \(0.591247\pi\) | |||||||
\(662\) | 10.6784i | 0.415026i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.8348 | −0.459281 | ||||||||
\(665\) | −4.83465 | − | 1.00905i | −0.187480 | − | 0.0391293i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.5390i | 0.679113i | ||||||||
\(668\) | 20.4231i | 0.790194i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.58258 | + | 12.3739i | −0.0997736 | + | 0.478044i | ||||
\(671\) | −0.361500 | −0.0139556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.9129i | 1.46143i | 0.682680 | + | 0.730717i | \(0.260814\pi\) | ||||
−0.682680 | + | 0.730717i | \(0.739186\pi\) | |||||||
\(674\) | −8.08815 | −0.311544 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.2087 | 0.892643 | ||||||||
\(677\) | 25.4485i | 0.978064i | 0.872266 | + | 0.489032i | \(0.162650\pi\) | ||||
−0.872266 | + | 0.489032i | \(0.837350\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.3739 | 0.474865 | ||||||||
\(680\) | −2.37960 | + | 11.4014i | −0.0912536 | + | 0.437222i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.460985i | 0.0176520i | ||||||||
\(683\) | − | 39.5710i | − | 1.51414i | −0.653332 | − | 0.757071i | \(-0.726629\pi\) | ||
0.653332 | − | 0.757071i | \(-0.273371\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.7477 | + | 7.25227i | 1.32764 | + | 0.277095i | ||||
\(686\) | 0.456850 | 0.0174426 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.79129i | 0.106417i | ||||||||
\(689\) | 0.286051 | 0.0108977 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3303 | −1.11578 | −0.557889 | − | 0.829916i | \(-0.688388\pi\) | ||||
−0.557889 | + | 0.829916i | \(0.688388\pi\) | |||||||
\(692\) | 37.7436i | 1.43480i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.0871 | −0.382902 | ||||||||
\(695\) | 9.40315 | − | 45.0532i | 0.356682 | − | 1.70897i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.4610i | − | 0.737137i | ||||||
\(698\) | 2.62585i | 0.0993899i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.58258 | + | 8.20871i | −0.135409 | + | 0.310260i | ||||
\(701\) | 12.3151 | 0.465133 | 0.232567 | − | 0.972580i | \(-0.425288\pi\) | ||||
0.232567 | + | 0.972580i | \(0.425288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0345i | 0.680183i | ||||||||
\(704\) | −5.91915 | −0.223086 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.669697 | 0.0252044 | ||||||||
\(707\) | − | 15.8745i | − | 0.597022i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.4955 | −1.10773 | −0.553863 | − | 0.832608i | \(-0.686847\pi\) | ||||
−0.553863 | + | 0.832608i | \(0.686847\pi\) | |||||||
\(710\) | 14.4086 | + | 3.00725i | 0.540745 | + | 0.112860i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.0000i | 0.562149i | ||||||||
\(713\) | − | 1.80750i | − | 0.0676914i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.791288 | + | 0.165151i | 0.0295925 | + | 0.00617631i | ||||
\(716\) | −29.9017 | −1.11748 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 11.6261i | − | 0.433884i | ||||||
\(719\) | −33.1196 | −1.23515 | −0.617576 | − | 0.786511i | \(-0.711885\pi\) | ||||
−0.617576 | + | 0.786511i | \(0.711885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.37386 | 0.125649 | ||||||||
\(722\) | 6.45145i | 0.240098i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.4610 | −1.02058 | ||||||||
\(725\) | 25.9053 | + | 11.3060i | 0.962099 | + | 0.419894i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.4519i | 1.57445i | 0.616664 | + | 0.787227i | \(0.288484\pi\) | ||||
−0.616664 | + | 0.787227i | \(0.711516\pi\) | |||||||
\(728\) | 0.361500i | 0.0133981i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.956439 | + | 4.58258i | −0.0353994 | + | 0.169609i | ||||
\(731\) | 3.00725 | 0.111227 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 40.7913i | − | 1.50666i | −0.657642 | − | 0.753330i | \(-0.728446\pi\) | ||
0.657642 | − | 0.753330i | \(-0.271554\pi\) | |||||||
\(734\) | −1.80750 | −0.0667161 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.7042 | −0.542003 | ||||||||
\(737\) | 21.4322i | 0.789464i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.4955 | −1.15858 | −0.579290 | − | 0.815122i | \(-0.696670\pi\) | ||||
−0.579290 | + | 0.815122i | \(0.696670\pi\) | |||||||
\(740\) | 32.0152 | + | 6.68195i | 1.17690 | + | 0.245634i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 0.626136i | − | 0.0229862i | ||||||
\(743\) | 0.989150i | 0.0362884i | 0.999835 | + | 0.0181442i | \(0.00577579\pi\) | ||||
−0.999835 | + | 0.0181442i | \(0.994224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.04356 | − | 33.7477i | 0.258056 | − | 1.23642i | ||||
\(746\) | −5.91915 | −0.216716 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.33030i | 0.341150i | ||||||||
\(749\) | 7.02355 | 0.256635 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.6606 | 1.33776 | 0.668882 | − | 0.743368i | \(-0.266773\pi\) | ||||
0.668882 | + | 0.743368i | \(0.266773\pi\) | |||||||
\(752\) | 4.83465i | 0.176302i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.539015 | 0.0196298 | ||||||||
\(755\) | −1.75195 | + | 8.39410i | −0.0637600 | + | 0.305493i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.62614i | − | 0.0591029i | −0.999563 | − | 0.0295515i | \(-0.990592\pi\) | ||
0.999563 | − | 0.0295515i | \(-0.00940789\pi\) | |||||||
\(758\) | 1.63670i | 0.0594476i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.37386 | − | 1.74773i | −0.303752 | − | 0.0633967i | ||||
\(761\) | −30.6247 | −1.11015 | −0.555073 | − | 0.831802i | \(-0.687309\pi\) | ||||
−0.555073 | + | 0.831802i | \(0.687309\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.79129i | − | 0.173456i | ||||||
\(764\) | 24.1733 | 0.874558 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.03447 | −0.254166 | ||||||||
\(767\) | − | 2.72120i | − | 0.0982569i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.7477 | −0.712121 | −0.356061 | − | 0.934463i | \(-0.615880\pi\) | ||||
−0.356061 | + | 0.934463i | \(0.615880\pi\) | |||||||
\(770\) | 0.361500 | − | 1.73205i | 0.0130276 | − | 0.0624188i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.4174i | 0.770830i | ||||||||
\(773\) | − | 5.84370i | − | 0.210183i | −0.994463 | − | 0.105092i | \(-0.966486\pi\) | ||
0.994463 | − | 0.105092i | \(-0.0335136\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.66970 | − | 1.16515i | −0.0958984 | − | 0.0418535i | ||||
\(776\) | 21.4322 | 0.769370 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.1307i | 0.399054i | ||||||||
\(779\) | 14.2934 | 0.512113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9564 | 0.893012 | ||||||||
\(782\) | 4.26255i | 0.152429i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.79129 | −0.0996889 | ||||||||
\(785\) | −36.6591 | − | 7.65120i | −1.30842 | − | 0.273083i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.16515i | − | 0.255410i | −0.991812 | − | 0.127705i | \(-0.959239\pi\) | ||
0.991812 | − | 0.127705i | \(-0.0407611\pi\) | |||||||
\(788\) | 46.8806i | 1.67005i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.3739 | − | 2.16515i | −0.369086 | − | 0.0770326i | ||||
\(791\) | 6.56670 | 0.233485 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.0435608i | − | 0.00154689i | ||||||
\(794\) | 3.12250 | 0.110813 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 40.8258 | 1.44703 | ||||||||
\(797\) | − | 5.36695i | − | 0.190107i | −0.995472 | − | 0.0950536i | \(-0.969698\pi\) | ||
0.995472 | − | 0.0950536i | \(-0.0303022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.20871 | 0.184271 | ||||||||
\(800\) | −9.47860 | + | 21.7182i | −0.335119 | + | 0.767855i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 9.00000i | − | 0.317801i | ||||||
\(803\) | 7.93725i | 0.280100i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.41742 | + | 6.79129i | −0.0499576 | + | 0.239361i | ||||
\(806\) | −0.0555487 | −0.00195662 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 27.4955i | − | 0.967287i | ||||||
\(809\) | 31.4630 | 1.10618 | 0.553089 | − | 0.833122i | \(-0.313449\pi\) | ||||
0.553089 | + | 0.833122i | \(0.313449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.8693 | −1.22443 | −0.612214 | − | 0.790692i | \(-0.709721\pi\) | ||||
−0.612214 | + | 0.790692i | \(0.709721\pi\) | |||||||
\(812\) | 10.1262i | 0.355358i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.46099 | −0.226457 | ||||||||
\(815\) | −32.2813 | − | 6.73750i | −1.13077 | − | 0.236004i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.20871i | 0.0772731i | ||||||||
\(818\) | 7.84190i | 0.274186i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.29583 | − | 25.3739i | 0.184939 | − | 0.886094i | ||||
\(821\) | −37.8589 | −1.32128 | −0.660642 | − | 0.750701i | \(-0.729716\pi\) | ||||
−0.660642 | + | 0.750701i | \(0.729716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.0000i | 0.662298i | 0.943578 | + | 0.331149i | \(0.107436\pi\) | ||||
−0.943578 | + | 0.331149i | \(0.892564\pi\) | |||||||
\(824\) | 5.84370 | 0.203575 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.95644 | −0.207251 | ||||||||
\(827\) | 14.1425i | 0.491781i | 0.969298 | + | 0.245891i | \(0.0790804\pi\) | ||||
−0.969298 | + | 0.245891i | \(0.920920\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.9129 | 1.42096 | 0.710482 | − | 0.703716i | \(-0.248477\pi\) | ||||
0.710482 | + | 0.703716i | \(0.248477\pi\) | |||||||
\(830\) | −1.42610 | + | 6.83285i | −0.0495006 | + | 0.237172i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.713258i | − | 0.0247278i | ||||||
\(833\) | 3.00725i | 0.104195i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.9564 | + | 5.20871i | 0.863653 | + | 0.180255i | ||||
\(836\) | −6.85275 | −0.237007 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.2867i | 0.355350i | ||||||||
\(839\) | 11.7629 | 0.406099 | 0.203049 | − | 0.979168i | \(-0.434915\pi\) | ||||
0.203049 | + | 0.979168i | \(0.434915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.95644 | 0.101946 | ||||||||
\(842\) | 9.23236i | 0.318168i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −34.3303 | −1.18170 | ||||||||
\(845\) | 5.91915 | − | 28.3604i | 0.203625 | − | 0.975626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.00000i | 0.274883i | ||||||||
\(848\) | 3.82560i | 0.131372i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.29583 | + | 2.74773i | 0.215945 | + | 0.0942463i | ||||
\(851\) | 25.3332 | 0.868411 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 45.6606i | − | 1.56339i | −0.623661 | − | 0.781695i | \(-0.714356\pi\) | ||
0.623661 | − | 0.781695i | \(-0.285644\pi\) | |||||||
\(854\) | −0.0953502 | −0.00326282 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.1652 | 0.415796 | ||||||||
\(857\) | 58.4528i | 1.99671i | 0.0573449 | + | 0.998354i | \(0.481737\pi\) | ||||
−0.0573449 | + | 0.998354i | \(0.518263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5826 | −0.395192 | −0.197596 | − | 0.980284i | \(-0.563313\pi\) | ||||
−0.197596 | + | 0.980284i | \(0.563313\pi\) | |||||||
\(860\) | 3.92095 | + | 0.818350i | 0.133703 | + | 0.0279055i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 0.539015i | − | 0.0183589i | ||||||
\(863\) | 34.6410i | 1.17919i | 0.807698 | + | 0.589597i | \(0.200713\pi\) | ||||
−0.807698 | + | 0.589597i | \(0.799287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.1216 | + | 9.62614i | 1.56818 | + | 0.327298i | ||||
\(866\) | −6.18530 | −0.210185 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 1.04356i | − | 0.0354208i | ||||||
\(869\) | −17.9681 | −0.609525 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.58258 | −0.0875072 | ||||||||
\(872\) | − | 8.29875i | − | 0.281031i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.13068 | −0.105897 | ||||||||
\(875\) | 9.11710 | + | 6.47135i | 0.308214 | + | 0.218772i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 16.4955i | − | 0.557012i | −0.960435 | − | 0.278506i | \(-0.910161\pi\) | ||
0.960435 | − | 0.278506i | \(-0.0898392\pi\) | |||||||
\(878\) | − | 1.52145i | − | 0.0513464i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.20871 | + | 10.5826i | −0.0744557 | + | 0.356739i | ||||
\(881\) | 25.8854 | 0.872102 | 0.436051 | − | 0.899922i | \(-0.356377\pi\) | ||||
0.436051 | + | 0.899922i | \(0.356377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.6606i | 1.53660i | 0.640089 | + | 0.768301i | \(0.278898\pi\) | ||||
−0.640089 | + | 0.768301i | \(0.721102\pi\) | |||||||
\(884\) | −1.12430 | −0.0378144 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.5826 | −0.624294 | ||||||||
\(887\) | 31.9397i | 1.07243i | 0.844081 | + | 0.536215i | \(0.180147\pi\) | ||||
−0.844081 | + | 0.536215i | \(0.819853\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.62614 | −0.0545389 | ||||||||
\(890\) | 8.66025 | + | 1.80750i | 0.290292 | + | 0.0605875i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 16.1216i | − | 0.539791i | ||||||
\(893\) | 3.82560i | 0.128019i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.62614 | + | 36.5390i | −0.254914 | + | 1.22136i | ||||
\(896\) | −11.0399 | −0.368816 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.49545i | 0.0499040i | ||||||||
\(899\) | −3.29330 | −0.109838 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.12159 | 0.137310 | ||||||||
\(902\) | 5.12070i | 0.170501i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.3739 | 0.378289 | ||||||||
\(905\) | −7.00365 | + | 33.5565i | −0.232809 | + | 1.11546i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 13.3739i | − | 0.444072i | −0.975038 | − | 0.222036i | \(-0.928730\pi\) | ||
0.975038 | − | 0.222036i | \(-0.0712702\pi\) | |||||||
\(908\) | 11.5921i | 0.384696i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.208712 | + | 0.0435608i | 0.00691874 | + | 0.00144403i | ||||
\(911\) | 22.2306 | 0.736533 | 0.368266 | − | 0.929720i | \(-0.379951\pi\) | ||||
0.368266 | + | 0.929720i | \(0.379951\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.8348i | 0.391676i | ||||||||
\(914\) | 18.2143 | 0.602476 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 34.0345 | 1.12453 | ||||||||
\(917\) | − | 6.66205i | − | 0.220000i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.79129 | 0.289998 | 0.144999 | − | 0.989432i | \(-0.453682\pi\) | ||||
0.144999 | + | 0.989432i | \(0.453682\pi\) | |||||||
\(920\) | −2.45505 | + | 11.7629i | −0.0809406 | + | 0.387810i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.2523i | 0.337641i | ||||||||
\(923\) | 3.00725i | 0.0989849i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.3303 | − | 37.4174i | 0.536937 | − | 1.23028i | ||||
\(926\) | 11.2505 | 0.369713 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.7913i | 0.879467i | ||||||||
\(929\) | −40.5801 | −1.33139 | −0.665694 | − | 0.746224i | \(-0.731865\pi\) | ||||
−0.665694 | + | 0.746224i | \(0.731865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.20871 | −0.0723876 | ||||||||
\(932\) | 36.9253i | 1.20953i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.8348 | −0.485411 | ||||||||
\(935\) | 11.4014 | + | 2.37960i | 0.372864 | + | 0.0778213i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.33030i | 0.272139i | 0.990699 | + | 0.136070i | \(0.0434471\pi\) | ||||
−0.990699 | + | 0.136070i | \(0.956553\pi\) | |||||||
\(938\) | 5.65300i | 0.184577i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.79129 | + | 1.41742i | 0.221507 | + | 0.0462313i | ||||
\(941\) | 3.75015 | 0.122251 | 0.0611257 | − | 0.998130i | \(-0.480531\pi\) | ||||
0.0611257 | + | 0.998130i | \(0.480531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 20.0780i | − | 0.653831i | ||||||
\(944\) | 36.3930 | 1.18449 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.791288 | −0.0257270 | ||||||||
\(947\) | − | 33.8426i | − | 1.09974i | −0.835252 | − | 0.549868i | \(-0.814678\pi\) | ||
0.835252 | − | 0.549868i | \(-0.185322\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.956439 | −0.0310473 | ||||||||
\(950\) | −2.01810 | + | 4.62405i | −0.0654759 | + | 0.150024i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.20871i | 0.168815i | ||||||||
\(953\) | 52.2476i | 1.69246i | 0.532814 | + | 0.846232i | \(0.321135\pi\) | ||||
−0.532814 | + | 0.846232i | \(0.678865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.16515 | − | 29.5390i | 0.199500 | − | 0.955860i | ||||
\(956\) | 3.10260 | 0.100345 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 11.3739i | − | 0.367473i | ||||||
\(959\) | 15.8745 | 0.512615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6606 | −0.989052 | ||||||||
\(962\) | − | 0.778549i | − | 0.0251014i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.5826 | −0.598504 | ||||||||
\(965\) | 26.1715 | + | 5.46230i | 0.842489 | + | 0.175838i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25.8348i | − | 0.830793i | −0.909641 | − | 0.415396i | \(-0.863643\pi\) | ||
0.909641 | − | 0.415396i | \(-0.136357\pi\) | |||||||
\(968\) | 13.8564i | 0.445362i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.58258 | − | 12.3739i | 0.0829215 | − | 0.397301i | ||||
\(971\) | −30.6446 | −0.983432 | −0.491716 | − | 0.870755i | \(-0.663630\pi\) | ||||
−0.491716 | + | 0.870755i | \(0.663630\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 20.5826i | − | 0.659847i | ||||||
\(974\) | −6.35610 | −0.203663 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.582576 | 0.0186478 | ||||||||
\(977\) | 25.6947i | 0.822047i | 0.911625 | + | 0.411023i | \(0.134829\pi\) | ||||
−0.911625 | + | 0.411023i | \(0.865171\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.0000 | 0.479402 | ||||||||
\(980\) | −0.818350 | + | 3.92095i | −0.0261412 | + | 0.125250i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.54811i | 0.304692i | ||||||||
\(983\) | 45.9669i | 1.46612i | 0.680166 | + | 0.733059i | \(0.261908\pi\) | ||||
−0.680166 | + | 0.733059i | \(0.738092\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.2867 | + | 11.9564i | 1.82531 | + | 0.380964i | ||||
\(986\) | 7.76645 | 0.247334 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 0.825757i | − | 0.0262708i | ||||||
\(989\) | 3.10260 | 0.0986570 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0780 | −0.701332 | −0.350666 | − | 0.936501i | \(-0.614045\pi\) | ||||
−0.350666 | + | 0.936501i | \(0.614045\pi\) | |||||||
\(992\) | − | 2.76100i | − | 0.0876619i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.58258 | 0.208787 | ||||||||
\(995\) | 10.4122 | − | 49.8879i | 0.330089 | − | 1.58155i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.2432i | 1.55955i | 0.626062 | + | 0.779774i | \(0.284666\pi\) | ||||
−0.626062 | + | 0.779774i | \(0.715334\pi\) | |||||||
\(998\) | − | 0.838251i | − | 0.0265344i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.d.c.379.4 | yes | 8 | |
3.2 | odd | 2 | inner | 945.2.d.c.379.5 | yes | 8 | |
5.2 | odd | 4 | 4725.2.a.bs.1.3 | 4 | |||
5.3 | odd | 4 | 4725.2.a.br.1.2 | 4 | |||
5.4 | even | 2 | inner | 945.2.d.c.379.6 | yes | 8 | |
15.2 | even | 4 | 4725.2.a.bs.1.2 | 4 | |||
15.8 | even | 4 | 4725.2.a.br.1.3 | 4 | |||
15.14 | odd | 2 | inner | 945.2.d.c.379.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.d.c.379.3 | ✓ | 8 | 15.14 | odd | 2 | inner | |
945.2.d.c.379.4 | yes | 8 | 1.1 | even | 1 | trivial | |
945.2.d.c.379.5 | yes | 8 | 3.2 | odd | 2 | inner | |
945.2.d.c.379.6 | yes | 8 | 5.4 | even | 2 | inner | |
4725.2.a.br.1.2 | 4 | 5.3 | odd | 4 | |||
4725.2.a.br.1.3 | 4 | 15.8 | even | 4 | |||
4725.2.a.bs.1.2 | 4 | 15.2 | even | 4 | |||
4725.2.a.bs.1.3 | 4 | 5.2 | odd | 4 |