Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 23x^{6} - 3x^{5} + 163x^{4} + 13x^{3} - 418x^{2} + 4x + 269 \) |
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 | 1.1 | ||
Root | \(-3.24252\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.24252 | −1.45010 | −0.725049 | − | 0.688697i | \(-0.758183\pi\) | ||||
−0.725049 | + | 0.688697i | \(0.758183\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.21024 | −1.21335 | −0.606677 | − | 0.794948i | \(-0.707498\pi\) | ||||
−0.606677 | + | 0.794948i | \(0.707498\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82128 | 0.850649 | 0.425324 | − | 0.905041i | \(-0.360160\pi\) | ||||
0.425324 | + | 0.905041i | \(0.360160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.85040 | −1.62261 | −0.811304 | − | 0.584625i | \(-0.801242\pi\) | ||||
−0.811304 | + | 0.584625i | \(0.801242\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.24252 | 0.837215 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.86063 | 0.451269 | 0.225635 | − | 0.974212i | \(-0.427554\pi\) | ||||
0.225635 | + | 0.974212i | \(0.427554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.37894 | 1.23401 | 0.617007 | − | 0.786958i | \(-0.288345\pi\) | ||||
0.617007 | + | 0.786958i | \(0.288345\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.21024 | 0.700531 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.21024 | 0.877895 | 0.438947 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438947 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.51393 | 1.10279 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.33063 | 0.618483 | 0.309241 | − | 0.950984i | \(-0.399925\pi\) | ||||
0.309241 | + | 0.950984i | \(0.399925\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.27146 | 0.228361 | 0.114180 | − | 0.993460i | \(-0.463576\pi\) | ||||
0.114180 | + | 0.993460i | \(0.463576\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82128 | −0.491122 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.4092 | 1.75948 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.06358 | −0.339251 | −0.169625 | − | 0.985509i | \(-0.554256\pi\) | ||||
−0.169625 | + | 0.985509i | \(0.554256\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.85040 | 0.936813 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.10689 | 0.329041 | 0.164521 | − | 0.986374i | \(-0.447392\pi\) | ||||
0.164521 | + | 0.986374i | \(0.447392\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.96695 | 1.06245 | 0.531225 | − | 0.847231i | \(-0.321732\pi\) | ||||
0.531225 | + | 0.847231i | \(0.321732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.24252 | −0.483366 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.68686 | −0.975380 | −0.487690 | − | 0.873017i | \(-0.662160\pi\) | ||||
−0.487690 | + | 0.873017i | \(0.662160\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.30561 | 0.472230 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.86063 | −0.260540 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.34827 | 1.28408 | 0.642042 | − | 0.766670i | \(-0.278088\pi\) | ||||
0.642042 | + | 0.766670i | \(0.278088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.14806 | −1.23352 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.37894 | −0.712458 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.2378 | −1.46304 | −0.731518 | − | 0.681822i | \(-0.761188\pi\) | ||||
−0.731518 | + | 0.681822i | \(0.761188\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.78735 | 0.997068 | 0.498534 | − | 0.866870i | \(-0.333872\pi\) | ||||
0.498534 | + | 0.866870i | \(0.333872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.21024 | −0.404452 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.9700 | 2.35294 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.51420 | 0.429327 | 0.214664 | − | 0.976688i | \(-0.431134\pi\) | ||||
0.214664 | + | 0.976688i | \(0.431134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.21024 | −0.506853 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6222 | −1.37930 | −0.689651 | − | 0.724142i | \(-0.742236\pi\) | ||||
−0.689651 | + | 0.724142i | \(0.742236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.43704 | −0.636357 | −0.318179 | − | 0.948031i | \(-0.603071\pi\) | ||||
−0.318179 | + | 0.948031i | \(0.603071\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.51393 | −0.636694 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.05698 | −1.03214 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.16325 | −0.468402 | −0.234201 | − | 0.972188i | \(-0.575247\pi\) | ||||
−0.234201 | + | 0.972188i | \(0.575247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.27361 | −0.139797 | −0.0698987 | − | 0.997554i | \(-0.522268\pi\) | ||||
−0.0698987 | + | 0.997554i | \(0.522268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.03313 | −0.654385 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.33063 | −0.357081 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.91690 | −0.627190 | −0.313595 | − | 0.949557i | \(-0.601533\pi\) | ||||
−0.313595 | + | 0.949557i | \(0.601533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.7811 | 1.96880 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.27146 | −0.131844 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.4413 | −1.78944 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.01613 | 0.407776 | 0.203888 | − | 0.978994i | \(-0.434642\pi\) | ||||
0.203888 | + | 0.978994i | \(0.434642\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82128 | 0.283550 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.09153 | 0.904641 | 0.452321 | − | 0.891855i | \(-0.350596\pi\) | ||||
0.452321 | + | 0.891855i | \(0.350596\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.5592 | −1.53309 | −0.766545 | − | 0.642190i | \(-0.778026\pi\) | ||||
−0.766545 | + | 0.642190i | \(0.778026\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.4092 | −1.01584 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.95284 | 0.478809 | 0.239404 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239404 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.59455 | 0.918991 | 0.459495 | − | 0.888180i | \(-0.348030\pi\) | ||||
0.459495 | + | 0.888180i | \(0.348030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.06358 | 0.195866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.1378 | −1.32998 | −0.664988 | − | 0.746854i | \(-0.731563\pi\) | ||||
−0.664988 | + | 0.746854i | \(0.731563\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.6518 | −1.27303 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.85040 | −0.540869 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.97306 | −0.547550 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.04036 | −0.276397 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.10689 | −0.189972 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.66643 | −0.149050 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.06152 | 0.182930 | 0.0914651 | − | 0.995808i | \(-0.470845\pi\) | ||||
0.0914651 | + | 0.995808i | \(0.470845\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.96695 | −0.613406 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.0106 | −1.22411 | −0.612055 | − | 0.790815i | \(-0.709657\pi\) | ||||
−0.612055 | + | 0.790815i | \(0.709657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.2677 | −1.49730 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.24252 | 0.279072 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.83399 | 0.840174 | 0.420087 | − | 0.907484i | \(-0.362000\pi\) | ||||
0.420087 | + | 0.907484i | \(0.362000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.61893 | 0.391773 | 0.195886 | − | 0.980627i | \(-0.437242\pi\) | ||||
0.195886 | + | 0.980627i | \(0.437242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.68686 | 0.563136 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.5056 | −1.38027 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7996 | −0.896861 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.30561 | −0.272642 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6341 | 0.953105 | 0.476553 | − | 0.879146i | \(-0.341886\pi\) | ||||
0.476553 | + | 0.879146i | \(0.341886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1949 | 1.07379 | 0.536893 | − | 0.843651i | \(-0.319598\pi\) | ||||
0.536893 | + | 0.843651i | \(0.319598\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.86063 | 0.150423 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.12273 | −0.331146 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.22817 | −0.417254 | −0.208627 | − | 0.977995i | \(-0.566899\pi\) | ||||
−0.208627 | + | 0.977995i | \(0.566899\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.34827 | −0.741366 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.5158 | −1.06520 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.261930 | 0.0205160 | 0.0102580 | − | 0.999947i | \(-0.496735\pi\) | ||||
0.0102580 | + | 0.999947i | \(0.496735\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.14806 | 0.712176 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.2271 | 1.63286 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.37894 | 0.411338 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.5287 | −1.48474 | −0.742370 | − | 0.669990i | \(-0.766298\pi\) | ||||
−0.742370 | + | 0.669990i | \(0.766298\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.7010 | −1.33807 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.2378 | 0.844685 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.0968 | −1.42737 | −0.713683 | − | 0.700469i | \(-0.752974\pi\) | ||||
−0.713683 | + | 0.700469i | \(0.752974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.26626 | −0.614427 | −0.307213 | − | 0.951641i | \(-0.599396\pi\) | ||||
−0.307213 | + | 0.951641i | \(0.599396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.78735 | −0.575658 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.69120 | 0.491947 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.24936 | 0.383872 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.21024 | 0.233510 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.0760 | −1.52501 | −0.762504 | − | 0.646984i | \(-0.776030\pi\) | ||||
−0.762504 | + | 0.646984i | \(0.776030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.3043 | 1.60550 | 0.802749 | − | 0.596318i | \(-0.203370\pi\) | ||||
0.802749 | + | 0.596318i | \(0.203370\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.9700 | −1.35847 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7503 | −0.765925 | −0.382962 | − | 0.923764i | \(-0.625096\pi\) | ||||
−0.382962 | + | 0.923764i | \(0.625096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7649 | −0.904877 | −0.452439 | − | 0.891796i | \(-0.649446\pi\) | ||||
−0.452439 | + | 0.891796i | \(0.649446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.51420 | −0.247872 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.6921 | −0.750439 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.83164 | −0.477143 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.21024 | 0.292632 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.1755 | 1.04971 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9680 | 1.16812 | 0.584061 | − | 0.811710i | \(-0.301463\pi\) | ||||
0.584061 | + | 0.811710i | \(0.301463\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.6222 | 0.796340 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.5905 | −1.54066 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.08168 | −0.277083 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.43704 | 0.367401 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8854 | −0.732233 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7467 | −0.987514 | −0.493757 | − | 0.869600i | \(-0.664377\pi\) | ||||
−0.493757 | + | 0.869600i | \(0.664377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.51393 | 0.367595 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.120587 | 0.00800367 | 0.00400183 | − | 0.999992i | \(-0.498726\pi\) | ||||
0.00400183 | + | 0.999992i | \(0.498726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.33643 | 0.0883139 | 0.0441570 | − | 0.999025i | \(-0.485940\pi\) | ||||
0.0441570 | + | 0.999025i | \(0.485940\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.05698 | 0.595906 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.77423 | −0.574819 | −0.287409 | − | 0.957808i | \(-0.592794\pi\) | ||||
−0.287409 | + | 0.957808i | \(0.592794\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.6823 | 1.41440 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.16325 | 0.270432 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.99261 | −0.387630 | −0.193815 | − | 0.981038i | \(-0.562086\pi\) | ||||
−0.193815 | + | 0.981038i | \(0.562086\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6690 | 1.33141 | 0.665704 | − | 0.746216i | \(-0.268132\pi\) | ||||
0.665704 | + | 0.746216i | \(0.268132\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.7185 | −0.684780 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.4689 | −2.00232 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.27361 | 0.0807121 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.72679 | 0.613950 | 0.306975 | − | 0.951718i | \(-0.400683\pi\) | ||||
0.306975 | + | 0.951718i | \(0.400683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.8783 | 0.746780 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.03313 | 0.377809 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.72200 | −0.419307 | −0.209654 | − | 0.977776i | \(-0.567234\pi\) | ||||
−0.209654 | + | 0.977776i | \(0.567234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.62458 | 0.411631 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.33063 | 0.206161 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.9835 | −1.29390 | −0.646948 | − | 0.762534i | \(-0.723955\pi\) | ||||
−0.646948 | + | 0.762534i | \(0.723955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.3119 | −1.86205 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.91690 | 0.362109 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.08333 | −0.127023 | −0.0635115 | − | 0.997981i | \(-0.520230\pi\) | ||||
−0.0635115 | + | 0.997981i | \(0.520230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9907 | 0.667639 | 0.333819 | − | 0.942637i | \(-0.391662\pi\) | ||||
0.333819 | + | 0.942637i | \(0.391662\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.7811 | −1.13669 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.5564 | 0.938084 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.5833 | −1.53715 | −0.768577 | − | 0.639758i | \(-0.779035\pi\) | ||||
−0.768577 | + | 0.639758i | \(0.779035\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.27146 | 0.0761203 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.2733 | −0.672507 | −0.336253 | − | 0.941772i | \(-0.609160\pi\) | ||||
−0.336253 | + | 0.941772i | \(0.609160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.5911 | 1.40235 | 0.701174 | − | 0.712991i | \(-0.252660\pi\) | ||||
0.701174 | + | 0.712991i | \(0.252660\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.4413 | 1.03313 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.76362 | −0.399244 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5381 | −0.796356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.01613 | −0.235430 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.21613 | −0.538412 | −0.269206 | − | 0.963083i | \(-0.586761\pi\) | ||||
−0.269206 | + | 0.963083i | \(0.586761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.4388 | 2.12155 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.82128 | −0.163707 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.6315 | −1.42448 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.3656 | −1.28913 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.09153 | −0.522295 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −25.2506 | −1.44585 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.3545 | −0.762183 | −0.381091 | − | 0.924537i | \(-0.624452\pi\) | ||||
−0.381091 | + | 0.924537i | \(0.624452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5592 | 0.885130 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.9770 | −1.07609 | −0.538043 | − | 0.842918i | \(-0.680836\pi\) | ||||
−0.538043 | + | 0.842918i | \(0.680836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.865518 | 0.0489220 | 0.0244610 | − | 0.999701i | \(-0.492213\pi\) | ||||
0.0244610 | + | 0.999701i | \(0.492213\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.4092 | 0.586495 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.57367 | 0.369214 | 0.184607 | − | 0.982812i | \(-0.440899\pi\) | ||||
0.184607 | + | 0.982812i | \(0.440899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.39666 | 0.526112 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.95284 | −0.276440 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0082 | 0.556872 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.2587 | −1.78939 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.59455 | −0.530580 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.4664 | 1.18348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.69256 | 0.312892 | 0.156446 | − | 0.987687i | \(-0.449996\pi\) | ||||
0.156446 | + | 0.987687i | \(0.449996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.06358 | −0.113084 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3948 | −0.622567 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1210 | −0.551323 | −0.275662 | − | 0.961255i | \(-0.588897\pi\) | ||||
−0.275662 | + | 0.961255i | \(0.588897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.1378 | 0.767862 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.58715 | 0.194255 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.8599 | 0.640372 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.6518 | 0.734987 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.4498 | −1.90304 | −0.951521 | − | 0.307583i | \(-0.900480\pi\) | ||||
−0.951521 | + | 0.307583i | \(0.900480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6545 | 1.42678 | 0.713392 | − | 0.700765i | \(-0.247158\pi\) | ||||
0.713392 | + | 0.700765i | \(0.247158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.85040 | 0.312271 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.94068 | 0.422640 | 0.211320 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211320 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.6852 | 2.00012 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.97306 | 0.316128 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.7685 | 0.832228 | 0.416114 | − | 0.909312i | \(-0.363392\pi\) | ||||
0.416114 | + | 0.909312i | \(0.363392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.93298 | 0.522789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.04036 | 0.159578 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.6297 | 0.922781 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.32595 | 0.121414 | 0.0607068 | − | 0.998156i | \(-0.480665\pi\) | ||||
0.0607068 | + | 0.998156i | \(0.480665\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.10689 | 0.109680 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.0101 | −1.55805 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.77773 | 0.247382 | 0.123691 | − | 0.992321i | \(-0.460527\pi\) | ||||
0.123691 | + | 0.992321i | \(0.460527\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.66643 | 0.0860539 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.4855 | −1.00356 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7452 | −0.757410 | −0.378705 | − | 0.925517i | \(-0.623631\pi\) | ||||
−0.378705 | + | 0.925517i | \(0.623631\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.06152 | −0.105615 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.62816 | 0.389781 | 0.194890 | − | 0.980825i | \(-0.437565\pi\) | ||||
0.194890 | + | 0.980825i | \(0.437565\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.3674 | 1.49670 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.96695 | 0.354150 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.0716 | 1.47399 | 0.736993 | − | 0.675900i | \(-0.236245\pi\) | ||||
0.736993 | + | 0.675900i | \(0.236245\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.83369 | 0.396167 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.0106 | 0.706740 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4994 | 0.679229 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.2476 | −0.564499 | −0.282249 | − | 0.959341i | \(-0.591081\pi\) | ||||
−0.282249 | + | 0.959341i | \(0.591081\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.2677 | 0.864464 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.80206 | 0.439554 | 0.219777 | − | 0.975550i | \(-0.429467\pi\) | ||||
0.219777 | + | 0.975550i | \(0.429467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.43854 | −0.370540 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.24252 | −0.161122 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.82195 | −0.288583 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.7694 | 1.76868 | 0.884340 | − | 0.466843i | \(-0.154609\pi\) | ||||
0.884340 | + | 0.466843i | \(0.154609\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.83399 | −0.485075 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.0760 | 1.77518 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.12972 | 0.202720 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.61893 | −0.226190 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.5130 | −1.19754 | −0.598770 | − | 0.800921i | \(-0.704344\pi\) | ||||
−0.598770 | + | 0.800921i | \(0.704344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.85223 | 0.236483 | 0.118242 | − | 0.992985i | \(-0.462274\pi\) | ||||
0.118242 | + | 0.992985i | \(0.462274\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.68686 | −0.325127 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.2594 | 0.497653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.9992 | −1.20980 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.5056 | 0.796899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5070 | 0.795116 | 0.397558 | − | 0.917577i | \(-0.369858\pi\) | ||||
0.397558 | + | 0.917577i | \(0.369858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.5559 | −0.987851 | −0.493926 | − | 0.869504i | \(-0.664439\pi\) | ||||
−0.493926 | + | 0.869504i | \(0.664439\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.7996 | 0.517803 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.6466 | 1.08333 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.71337 | 0.177229 | 0.0886147 | − | 0.996066i | \(-0.471756\pi\) | ||||
0.0886147 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.30561 | 0.157410 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.80205 | −0.228153 | −0.114076 | − | 0.993472i | \(-0.536391\pi\) | ||||
−0.114076 | + | 0.993472i | \(0.536391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.1857 | 0.909488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.6341 | −0.550276 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.6862 | 0.551507 | 0.275753 | − | 0.961228i | \(-0.411073\pi\) | ||||
0.275753 | + | 0.961228i | \(0.411073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.94414 | 0.279899 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.1949 | −0.619950 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −60.8982 | −2.85495 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.66756 | 0.311895 | 0.155948 | − | 0.987765i | \(-0.450157\pi\) | ||||
0.155948 | + | 0.987765i | \(0.450157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.86063 | −0.0868468 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.11682 | −0.238314 | −0.119157 | − | 0.992875i | \(-0.538019\pi\) | ||||
−0.119157 | + | 0.992875i | \(0.538019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.7320 | −1.19587 | −0.597934 | − | 0.801546i | \(-0.704011\pi\) | ||||
−0.597934 | + | 0.801546i | \(0.704011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.12273 | 0.191187 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.1888 | −0.471482 | −0.235741 | − | 0.971816i | \(-0.575752\pi\) | ||||
−0.235741 | + | 0.971816i | \(0.575752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.2814 | −0.520927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.22817 | 0.240901 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.6557 | 0.903772 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.6591 | 1.36085 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.34827 | 0.428028 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.1075 | 1.01012 | 0.505059 | − | 0.863085i | \(-0.331471\pi\) | ||||
0.505059 | + | 0.863085i | \(0.331471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0728 | 0.550471 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.5158 | 0.614992 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0224 | −0.591316 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.9470 | −1.44766 | −0.723829 | − | 0.689980i | \(-0.757619\pi\) | ||||
−0.723829 | + | 0.689980i | \(0.757619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.261930 | −0.0118449 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.9820 | 1.57871 | 0.789357 | − | 0.613934i | \(-0.210414\pi\) | ||||
0.789357 | + | 0.613934i | \(0.210414\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.19708 | 0.279102 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.14806 | −0.411175 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 37.3100 | 1.67358 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.2314 | −1.17428 | −0.587140 | − | 0.809486i | \(-0.699746\pi\) | ||||
−0.587140 | + | 0.809486i | \(0.699746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.3106 | −1.08396 | −0.541979 | − | 0.840392i | \(-0.682325\pi\) | ||||
−0.541979 | + | 0.840392i | \(0.682325\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.4795 | −1.31182 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.2271 | −0.942730 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.5371 | −1.44218 | −0.721090 | − | 0.692841i | \(-0.756359\pi\) | ||||
−0.721090 | + | 0.692841i | \(0.756359\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.4542 | 0.772127 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.37894 | −0.237486 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 50.4509 | 2.22313 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.8655 | −0.829705 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.5287 | 0.857215 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.9927 | 1.44543 | 0.722717 | − | 0.691144i | \(-0.242893\pi\) | ||||
0.722717 | + | 0.691144i | \(0.242893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.4021 | −0.848393 | −0.424197 | − | 0.905570i | \(-0.639443\pi\) | ||||
−0.424197 | + | 0.905570i | \(0.639443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.7010 | 0.772536 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.36572 | 0.103052 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.27392 | −0.229301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.2378 | −0.487679 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.3262 | −0.533905 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.0597 | −0.694320 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.0968 | 0.824090 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.32606 | 0.401702 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4863 | 0.880773 | 0.440386 | − | 0.897808i | \(-0.354841\pi\) | ||||
0.440386 | + | 0.897808i | \(0.354841\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.26626 | 0.354739 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.1105 | −1.33263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.16456 | −0.0925498 | −0.0462749 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462749 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.78735 | 0.332356 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.9153 | 0.763216 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3650 | 0.568338 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.69120 | −0.284026 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.20589 | −0.0510952 | −0.0255476 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255476 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.7594 | −1.72394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.24936 | −0.221628 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.05092 | −0.0442909 | −0.0221455 | − | 0.999755i | \(-0.507050\pi\) | ||||
−0.0221455 | + | 0.999755i | \(0.507050\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 45.8422 | 1.92860 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.21024 | −0.134817 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.65108 | 0.194983 | 0.0974917 | − | 0.995236i | \(-0.468918\pi\) | ||||
0.0974917 | + | 0.995236i | \(0.468918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.8655 | −0.998739 | −0.499370 | − | 0.866389i | \(-0.666435\pi\) | ||||
−0.499370 | + | 0.866389i | \(0.666435\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.0760 | 0.880463 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.2149 | 0.968130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.4676 | −1.85121 | −0.925605 | − | 0.378490i | \(-0.876443\pi\) | ||||
−0.925605 | + | 0.378490i | \(0.876443\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.3043 | −0.926934 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.08860 | 0.169624 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.3741 | 1.09230 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.9700 | 0.784314 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −48.2366 | −1.99094 | −0.995469 | − | 0.0950882i | \(-0.969687\pi\) | ||||
−0.995469 | + | 0.0950882i | \(0.969687\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.83910 | 0.281800 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.7503 | 0.442207 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.81080 | 0.197556 | 0.0987779 | − | 0.995110i | \(-0.468507\pi\) | ||||
0.0987779 | + | 0.995110i | \(0.468507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.3678 | 0.794001 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.7649 | 0.522431 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.7293 | −0.969552 | −0.484776 | − | 0.874638i | \(-0.661099\pi\) | ||||
−0.484776 | + | 0.874638i | \(0.661099\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1161 | −0.616597 | −0.308299 | − | 0.951290i | \(-0.599760\pi\) | ||||
−0.308299 | + | 0.951290i | \(0.599760\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.51420 | 0.143109 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.85843 | 0.400802 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.6031 | −1.52626 | −0.763132 | − | 0.646242i | \(-0.776340\pi\) | ||||
−0.763132 | + | 0.646242i | \(0.776340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.6921 | 0.433266 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.1208 | 1.58266 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0653 | −0.527701 | −0.263850 | − | 0.964564i | \(-0.584992\pi\) | ||||
−0.263850 | + | 0.964564i | \(0.584992\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.83164 | 0.275478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.4263 | −1.22492 | −0.612459 | − | 0.790502i | \(-0.709820\pi\) | ||||
−0.612459 | + | 0.790502i | \(0.709820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9971 | 0.924332 | 0.462166 | − | 0.886793i | \(-0.347072\pi\) | ||||
0.462166 | + | 0.886793i | \(0.347072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.21024 | −0.168951 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.9947 | 0.761005 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.1662 | −0.886649 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.1755 | −0.606051 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.83956 | −0.153093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.3341 | −1.80472 | −0.902360 | − | 0.430982i | \(-0.858167\pi\) | ||||
−0.902360 | + | 0.430982i | \(0.858167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.9680 | −0.674416 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.68452 | −0.265267 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.3391 | −0.766244 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.6222 | −0.459767 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.60629 | −0.181937 | −0.0909687 | − | 0.995854i | \(-0.528996\pi\) | ||||
−0.0909687 | + | 0.995854i | \(0.528996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7066 | 0.422227 | 0.211114 | − | 0.977462i | \(-0.432291\pi\) | ||||
0.211114 | + | 0.977462i | \(0.432291\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.5905 | 0.889499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.1350 | −0.988158 | −0.494079 | − | 0.869417i | \(-0.664495\pi\) | ||||
−0.494079 | + | 0.869417i | \(0.664495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.7050 | −1.24453 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.08168 | 0.159974 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.5769 | −1.15743 | −0.578717 | − | 0.815528i | \(-0.696447\pi\) | ||||
−0.578717 | + | 0.815528i | \(0.696447\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.4296 | 1.77508 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.43704 | −0.212119 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.7918 | −1.04366 | −0.521831 | − | 0.853049i | \(-0.674751\pi\) | ||||
−0.521831 | + | 0.853049i | \(0.674751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.89353 | 0.229232 | 0.114616 | − | 0.993410i | \(-0.463436\pi\) | ||||
0.114616 | + | 0.993410i | \(0.463436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.8854 | 0.422755 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.9907 | 2.17123 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0227 | 0.542963 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.7467 | 0.570141 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.9703 | 0.848155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.26057 | −0.125686 | −0.0628428 | − | 0.998023i | \(-0.520017\pi\) | ||||
−0.0628428 | + | 0.998023i | \(0.520017\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.51393 | −0.212231 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.15513 | 0.159695 | 0.0798474 | − | 0.996807i | \(-0.474557\pi\) | ||||
0.0798474 | + | 0.996807i | \(0.474557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.8927 | −0.494777 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.120587 | −0.00462092 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 51.4838 | 1.96997 | 0.984987 | − | 0.172629i | \(-0.0552261\pi\) | ||||
0.984987 | + | 0.172629i | \(0.0552261\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.8869 | −1.21834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.33643 | −0.0509881 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.6911 | −2.08356 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.5334 | 1.38980 | 0.694899 | − | 0.719108i | \(-0.255449\pi\) | ||||
0.694899 | + | 0.719108i | \(0.255449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.05698 | −0.344046 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.9770 | −0.568109 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.92015 | 0.148486 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.77423 | 0.331872 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.6445 | −0.779731 | −0.389866 | − | 0.920872i | \(-0.627479\pi\) | ||||
−0.389866 | + | 0.920872i | \(0.627479\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.0999 | −0.418640 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.6823 | −0.816602 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.1860 | −1.09765 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.5779 | 1.26105 | 0.630523 | − | 0.776171i | \(-0.282840\pi\) | ||||
0.630523 | + | 0.776171i | \(0.282840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.16325 | −0.156134 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.35314 | 0.200477 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 53.5198 | 2.00153 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.99261 | 0.223798 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.2353 | 0.829236 | 0.414618 | − | 0.909996i | \(-0.363915\pi\) | ||||
0.414618 | + | 0.909996i | \(0.363915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.9486 | 1.86018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.6690 | −0.768688 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.3649 | 0.682054 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.90158 | 0.255966 | 0.127983 | − | 0.991776i | \(-0.459150\pi\) | ||||
0.127983 | + | 0.991776i | \(0.459150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.9629 | 0.479451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.0601 | 1.73821 | 0.869103 | − | 0.494632i | \(-0.164697\pi\) | ||||
0.869103 | + | 0.494632i | \(0.164697\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.7185 | 0.395358 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.91454 | 0.365207 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.09124 | 0.113713 | 0.0568565 | − | 0.998382i | \(-0.481892\pi\) | ||||
0.0568565 | + | 0.998382i | \(0.481892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.4689 | 1.15604 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7232 | −0.980380 | −0.490190 | − | 0.871616i | \(-0.663073\pi\) | ||||
−0.490190 | + | 0.871616i | \(0.663073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.7239 | −1.38210 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.27361 | −0.0465991 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.8998 | −0.580965 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6355 | 0.497566 | 0.248783 | − | 0.968559i | \(-0.419969\pi\) | ||||
0.248783 | + | 0.968559i | \(0.419969\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.72679 | −0.354464 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −42.7847 | −1.55709 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.5231 | 1.65456 | 0.827282 | − | 0.561787i | \(-0.189886\pi\) | ||||
0.827282 | + | 0.561787i | \(0.189886\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.8783 | −0.431154 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −54.7160 | −1.98345 | −0.991727 | − | 0.128367i | \(-0.959026\pi\) | ||||
−0.991727 | + | 0.128367i | \(0.959026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.8007 | −1.11506 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.03313 | −0.218128 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 65.7456 | 2.37393 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8454 | 0.391097 | 0.195548 | − | 0.980694i | \(-0.437351\pi\) | ||||
0.195548 | + | 0.980694i | \(0.437351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.72200 | 0.242087 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.57334 | −0.308362 | −0.154181 | − | 0.988043i | \(-0.549274\pi\) | ||||
−0.154181 | + | 0.988043i | \(0.549274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.01074 | 0.251833 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.62458 | −0.237655 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.3329 | 0.406042 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.7895 | −1.17330 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.33063 | −0.119027 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.9524 | 0.605059 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.0373 | 1.92622 | 0.963111 | − | 0.269104i | \(-0.0867277\pi\) | ||||
0.963111 | + | 0.269104i | \(0.0867277\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.9835 | 0.747031 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.3858 | 1.61373 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.5591 | −1.61785 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 30.3119 | 1.07505 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.5826 | 0.799917 | 0.399958 | − | 0.916533i | \(-0.369025\pi\) | ||||
0.399958 | + | 0.916533i | \(0.369025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4418 | −0.440159 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.91690 | −0.209063 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.3394 | −0.541316 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.8254 | 1.54464 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.08333 | 0.0733368 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.2340 | −1.41455 | −0.707277 | − | 0.706937i | \(-0.750076\pi\) | ||||
−0.707277 | + | 0.706937i | \(0.750076\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.9998 | −1.75573 | −0.877865 | − | 0.478909i | \(-0.841032\pi\) | ||||
−0.877865 | + | 0.478909i | \(0.841032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.9907 | −0.385462 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.849314 | −0.0297502 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.4748 | 1.31108 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.7811 | 0.656266 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.4031 | 1.37518 | 0.687589 | − | 0.726100i | \(-0.258669\pi\) | ||||
0.687589 | + | 0.726100i | \(0.258669\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.3232 | −1.51015 | −0.755077 | − | 0.655636i | \(-0.772400\pi\) | ||||
−0.755077 | + | 0.655636i | \(0.772400\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.5564 | −0.541603 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.1930 | 1.46719 | 0.733597 | − | 0.679585i | \(-0.237840\pi\) | ||||
0.733597 | + | 0.679585i | \(0.237840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.1711 | 0.943693 | 0.471846 | − | 0.881681i | \(-0.343588\pi\) | ||||
0.471846 | + | 0.881681i | \(0.343588\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.5833 | 0.887476 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.15052 | 0.213103 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.24252 | −0.112212 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.27146 | −0.0439481 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.5522 | −1.22740 | −0.613698 | − | 0.789541i | \(-0.710319\pi\) | ||||
−0.613698 | + | 0.789541i | \(0.710319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.9069 | −0.617479 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.2733 | 0.388272 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −68.8294 | −2.36780 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.76028 | 0.335367 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.5911 | −0.809646 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.68816 | −0.297826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.9119 | 1.94863 | 0.974313 | − | 0.225200i | \(-0.0723034\pi\) | ||||
0.974313 | + | 0.225200i | \(0.0723034\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.4413 | −0.596480 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.1803 | −1.16758 | −0.583788 | − | 0.811906i | \(-0.698430\pi\) | ||||
−0.583788 | + | 0.811906i | \(0.698430\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9625 | −0.578754 | −0.289377 | − | 0.957215i | \(-0.593448\pi\) | ||||
−0.289377 | + | 0.957215i | \(0.593448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.76362 | 0.230504 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.6654 | 1.52043 | 0.760214 | − | 0.649672i | \(-0.225094\pi\) | ||||
0.760214 | + | 0.649672i | \(0.225094\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 63.3222 | 2.15302 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.5381 | 0.459776 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7457 | −0.398446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.5594 | −0.696630 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.01613 | 0.135925 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.34962 | 0.180850 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.65783 | 0.0559808 | 0.0279904 | − | 0.999608i | \(-0.491089\pi\) | ||||
0.0279904 | + | 0.999608i | \(0.491089\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.21613 | 0.310852 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.0757 | −0.373150 | −0.186575 | − | 0.982441i | \(-0.559739\pi\) | ||||
−0.186575 | + | 0.982441i | \(0.559739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.29928 | 0.211988 | 0.105994 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105994 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.4388 | −1.22488 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.7138 | −0.460463 | −0.230231 | − | 0.973136i | \(-0.573948\pi\) | ||||
−0.230231 | + | 0.973136i | \(0.573948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.61796 | −0.221959 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.82128 | 0.0945165 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.9682 | −1.20363 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 61.9219 | 2.06982 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.6315 | 0.822423 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.23476 | 0.141237 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.3937 | 0.579467 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.3656 | 0.744279 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.8035 | 0.890979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.5148 | −1.17925 | −0.589625 | − | 0.807677i | \(-0.700725\pi\) | ||||
−0.589625 | + | 0.807677i | \(0.700725\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.09153 | 0.301547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.4589 | 1.27420 | 0.637100 | − | 0.770781i | \(-0.280134\pi\) | ||||
0.637100 | + | 0.770781i | \(0.280134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.59323 | −0.118918 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.2506 | 0.834760 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.9773 | 1.48528 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.7347 | 1.34371 | 0.671856 | − | 0.740682i | \(-0.265497\pi\) | ||||
0.671856 | + | 0.740682i | \(0.265497\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.3545 | 0.440046 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.9945 | 2.23807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.3784 | −0.374121 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.5592 | −0.511030 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.9417 | 1.73696 | 0.868481 | − | 0.495723i | \(-0.165097\pi\) | ||||
0.868481 | + | 0.495723i | \(0.165097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.7807 | 0.582738 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9770 | 0.621278 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.0212 | −0.556652 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6766 | 0.740811 | 0.370406 | − | 0.928870i | \(-0.379219\pi\) | ||||
0.370406 | + | 0.928870i | \(0.379219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.865518 | −0.0282451 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.9912 | −1.62967 | −0.814834 | − | 0.579694i | \(-0.803172\pi\) | ||||
−0.814834 | + | 0.579694i | \(0.803172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.87052 | 0.288864 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.4092 | −0.338613 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.4522 | −0.697103 | −0.348552 | − | 0.937290i | \(-0.613326\pi\) | ||||
−0.348552 | + | 0.937290i | \(0.613326\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.8088 | 1.03256 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.57367 | −0.213166 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.3902 | −1.14640 | −0.573201 | − | 0.819415i | \(-0.694298\pi\) | ||||
−0.573201 | + | 0.819415i | \(0.694298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 68.3394 | 2.21141 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.39666 | −0.303751 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.5694 | −1.01943 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3834 | −0.947851 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.95284 | 0.159603 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −72.3221 | −2.32813 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.2924 | 1.32787 | 0.663937 | − | 0.747789i | \(-0.268884\pi\) | ||||
0.663937 | + | 0.747789i | \(0.268884\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.0082 | −0.321510 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.6855 | 0.535464 | 0.267732 | − | 0.963493i | \(-0.413726\pi\) | ||||
0.267732 | + | 0.963493i | \(0.413726\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.8279 | −0.475359 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.2587 | 1.03310 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.3143 | 0.553932 | 0.276966 | − | 0.960880i | \(-0.410671\pi\) | ||||
0.276966 | + | 0.960880i | \(0.410671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.6933 | −0.533519 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.59455 | 0.306330 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.8464 | 1.04764 | 0.523819 | − | 0.851830i | \(-0.324507\pi\) | ||||
0.523819 | + | 0.851830i | \(0.324507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.8579 | 1.11067 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.4664 | −0.683283 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.3325 | 0.932719 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.3128 | 0.804087 | 0.402044 | − | 0.915621i | \(-0.368300\pi\) | ||||
0.402044 | + | 0.915621i | \(0.368300\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.69256 | −0.180648 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.3903 | 1.31216 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56.1380 | −1.77791 | −0.888954 | − | 0.457996i | \(-0.848567\pi\) | ||||
−0.888954 | + | 0.457996i | \(0.848567\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.06358 | 0.0652888 |
(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 | 4008.2.a.h.1.1 | ✓ | 8 | |
4.3 | odd | 2 | 8016.2.a.y.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.h.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
8016.2.a.y.1.1 | 8 | 4.3 | odd | 2 |