Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.823573\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.823573 | −0.582354 | −0.291177 | − | 0.956669i | \(-0.594047\pi\) | ||||
−0.291177 | + | 0.956669i | \(0.594047\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.32173 | −0.660863 | ||||||||
\(5\) | 2.87784 | 1.28701 | 0.643504 | − | 0.765443i | \(-0.277480\pi\) | ||||
0.643504 | + | 0.765443i | \(0.277480\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.73569 | 0.967211 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.37011 | −0.749495 | ||||||||
\(11\) | 2.49735 | 0.752980 | 0.376490 | − | 0.926421i | \(-0.377131\pi\) | ||||
0.376490 | + | 0.926421i | \(0.377131\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.14350 | −0.871850 | −0.435925 | − | 0.899983i | \(-0.643579\pi\) | ||||
−0.435925 | + | 0.899983i | \(0.643579\pi\) | |||||||
\(14\) | −0.823573 | −0.220109 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.390415 | 0.0976038 | ||||||||
\(17\) | 2.04099 | 0.495012 | 0.247506 | − | 0.968886i | \(-0.420389\pi\) | ||||
0.247506 | + | 0.968886i | \(0.420389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.80024 | 0.871836 | 0.435918 | − | 0.899987i | \(-0.356424\pi\) | ||||
0.435918 | + | 0.899987i | \(0.356424\pi\) | |||||||
\(20\) | −3.80372 | −0.850537 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.05675 | −0.438501 | ||||||||
\(23\) | 0.178746 | 0.0372711 | 0.0186355 | − | 0.999826i | \(-0.494068\pi\) | ||||
0.0186355 | + | 0.999826i | \(0.494068\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.28195 | 0.656391 | ||||||||
\(26\) | 2.58890 | 0.507726 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.32173 | −0.249783 | ||||||||
\(29\) | −7.77822 | −1.44438 | −0.722189 | − | 0.691695i | \(-0.756864\pi\) | ||||
−0.722189 | + | 0.691695i | \(0.756864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.24454 | 1.48076 | 0.740382 | − | 0.672187i | \(-0.234645\pi\) | ||||
0.740382 | + | 0.672187i | \(0.234645\pi\) | |||||||
\(32\) | −5.79291 | −1.02405 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.68090 | −0.288273 | ||||||||
\(35\) | 2.87784 | 0.486444 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0498363 | 0.00819303 | 0.00409652 | − | 0.999992i | \(-0.498696\pi\) | ||||
0.00409652 | + | 0.999992i | \(0.498696\pi\) | |||||||
\(38\) | −3.12978 | −0.507717 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.87286 | 1.24481 | ||||||||
\(41\) | 2.14558 | 0.335084 | 0.167542 | − | 0.985865i | \(-0.446417\pi\) | ||||
0.167542 | + | 0.985865i | \(0.446417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.51117 | 0.687946 | 0.343973 | − | 0.938979i | \(-0.388227\pi\) | ||||
0.343973 | + | 0.938979i | \(0.388227\pi\) | |||||||
\(44\) | −3.30082 | −0.497617 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.147210 | −0.0217050 | ||||||||
\(47\) | 0.391553 | 0.0571138 | 0.0285569 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285569 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.70293 | −0.382252 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.15485 | 0.576174 | ||||||||
\(53\) | 8.31101 | 1.14160 | 0.570802 | − | 0.821088i | \(-0.306632\pi\) | ||||
0.570802 | + | 0.821088i | \(0.306632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.18698 | 0.969092 | ||||||||
\(56\) | 2.73569 | 0.365571 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.40593 | 0.841140 | ||||||||
\(59\) | −14.3285 | −1.86542 | −0.932709 | − | 0.360630i | \(-0.882562\pi\) | ||||
−0.932709 | + | 0.360630i | \(0.882562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.25276 | 1.05666 | 0.528329 | − | 0.849040i | \(-0.322819\pi\) | ||||
0.528329 | + | 0.849040i | \(0.322819\pi\) | |||||||
\(62\) | −6.78999 | −0.862329 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.99005 | 0.498757 | ||||||||
\(65\) | −9.04648 | −1.12208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.83463 | −0.712814 | −0.356407 | − | 0.934331i | \(-0.615998\pi\) | ||||
−0.356407 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(68\) | −2.69763 | −0.327136 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.37011 | −0.283283 | ||||||||
\(71\) | −8.03307 | −0.953349 | −0.476675 | − | 0.879080i | \(-0.658158\pi\) | ||||
−0.476675 | + | 0.879080i | \(0.658158\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0099 | 1.63973 | 0.819866 | − | 0.572556i | \(-0.194048\pi\) | ||||
0.819866 | + | 0.572556i | \(0.194048\pi\) | |||||||
\(74\) | −0.0410438 | −0.00477125 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.02288 | −0.576164 | ||||||||
\(77\) | 2.49735 | 0.284600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.72861 | −0.644520 | −0.322260 | − | 0.946651i | \(-0.604442\pi\) | ||||
−0.322260 | + | 0.946651i | \(0.604442\pi\) | |||||||
\(80\) | 1.12355 | 0.125617 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.76704 | −0.195137 | ||||||||
\(83\) | 8.13150 | 0.892548 | 0.446274 | − | 0.894896i | \(-0.352751\pi\) | ||||
0.446274 | + | 0.894896i | \(0.352751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.87364 | 0.637085 | ||||||||
\(86\) | −3.71528 | −0.400629 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.83197 | 0.728291 | ||||||||
\(89\) | 15.4810 | 1.64098 | 0.820490 | − | 0.571660i | \(-0.193701\pi\) | ||||
0.820490 | + | 0.571660i | \(0.193701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.14350 | −0.329528 | ||||||||
\(92\) | −0.236253 | −0.0246311 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.322472 | −0.0332605 | ||||||||
\(95\) | 10.9365 | 1.12206 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.62954 | −0.165455 | −0.0827275 | − | 0.996572i | \(-0.526363\pi\) | ||||
−0.0827275 | + | 0.996572i | \(0.526363\pi\) | |||||||
\(98\) | −0.823573 | −0.0831935 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.33785 | −0.433785 | ||||||||
\(101\) | 18.5531 | 1.84611 | 0.923054 | − | 0.384672i | \(-0.125685\pi\) | ||||
0.923054 | + | 0.384672i | \(0.125685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8022 | 1.35997 | 0.679984 | − | 0.733227i | \(-0.261987\pi\) | ||||
0.679984 | + | 0.733227i | \(0.261987\pi\) | |||||||
\(104\) | −8.59963 | −0.843263 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.84472 | −0.664818 | ||||||||
\(107\) | −11.5898 | −1.12043 | −0.560216 | − | 0.828347i | \(-0.689282\pi\) | ||||
−0.560216 | + | 0.828347i | \(0.689282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.90568 | 0.469879 | 0.234939 | − | 0.972010i | \(-0.424511\pi\) | ||||
0.234939 | + | 0.972010i | \(0.424511\pi\) | |||||||
\(110\) | −5.91900 | −0.564355 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.390415 | 0.0368908 | ||||||||
\(113\) | −11.4900 | −1.08089 | −0.540446 | − | 0.841379i | \(-0.681744\pi\) | ||||
−0.540446 | + | 0.841379i | \(0.681744\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.514401 | 0.0479682 | ||||||||
\(116\) | 10.2807 | 0.954537 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.8006 | 1.08633 | ||||||||
\(119\) | 2.04099 | 0.187097 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.76323 | −0.433021 | ||||||||
\(122\) | −6.79675 | −0.615349 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.8970 | −0.978582 | ||||||||
\(125\) | −4.94426 | −0.442228 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 8.29971 | 0.733598 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.45044 | 0.653447 | ||||||||
\(131\) | −4.61325 | −0.403062 | −0.201531 | − | 0.979482i | \(-0.564592\pi\) | ||||
−0.201531 | + | 0.979482i | \(0.564592\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.80024 | 0.329523 | ||||||||
\(134\) | 4.80525 | 0.415110 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.58350 | 0.478781 | ||||||||
\(137\) | 7.76252 | 0.663197 | 0.331599 | − | 0.943421i | \(-0.392412\pi\) | ||||
0.331599 | + | 0.943421i | \(0.392412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1628 | 1.11646 | 0.558228 | − | 0.829688i | \(-0.311481\pi\) | ||||
0.558228 | + | 0.829688i | \(0.311481\pi\) | |||||||
\(140\) | −3.80372 | −0.321473 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.61582 | 0.555187 | ||||||||
\(143\) | −7.85043 | −0.656486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.3845 | −1.85893 | ||||||||
\(146\) | −11.5382 | −0.954905 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.0658699 | −0.00541447 | ||||||||
\(149\) | −14.6464 | −1.19988 | −0.599940 | − | 0.800045i | \(-0.704809\pi\) | ||||
−0.599940 | + | 0.800045i | \(0.704809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.84407 | −0.475584 | −0.237792 | − | 0.971316i | \(-0.576424\pi\) | ||||
−0.237792 | + | 0.971316i | \(0.576424\pi\) | |||||||
\(152\) | 10.3963 | 0.843249 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.05675 | −0.165738 | ||||||||
\(155\) | 23.7265 | 1.90576 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.25235 | 0.179757 | 0.0898786 | − | 0.995953i | \(-0.471352\pi\) | ||||
0.0898786 | + | 0.995953i | \(0.471352\pi\) | |||||||
\(158\) | 4.71794 | 0.375339 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.6711 | −1.31796 | ||||||||
\(161\) | 0.178746 | 0.0140871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.9604 | 1.40677 | 0.703385 | − | 0.710809i | \(-0.251671\pi\) | ||||
0.703385 | + | 0.710809i | \(0.251671\pi\) | |||||||
\(164\) | −2.83587 | −0.221445 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.69689 | −0.519779 | ||||||||
\(167\) | −6.74574 | −0.522001 | −0.261000 | − | 0.965339i | \(-0.584052\pi\) | ||||
−0.261000 | + | 0.965339i | \(0.584052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.11841 | −0.239878 | ||||||||
\(170\) | −4.83737 | −0.371009 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.96253 | −0.454639 | ||||||||
\(173\) | −13.0095 | −0.989096 | −0.494548 | − | 0.869150i | \(-0.664666\pi\) | ||||
−0.494548 | + | 0.869150i | \(0.664666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.28195 | 0.248092 | ||||||||
\(176\) | 0.975004 | 0.0734937 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.7497 | −0.955632 | ||||||||
\(179\) | 13.0566 | 0.975894 | 0.487947 | − | 0.872873i | \(-0.337746\pi\) | ||||
0.487947 | + | 0.872873i | \(0.337746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.28417 | −0.615758 | −0.307879 | − | 0.951426i | \(-0.599619\pi\) | ||||
−0.307879 | + | 0.951426i | \(0.599619\pi\) | |||||||
\(182\) | 2.58890 | 0.191902 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.488992 | 0.0360490 | ||||||||
\(185\) | 0.143421 | 0.0105445 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.09707 | 0.372734 | ||||||||
\(188\) | −0.517526 | −0.0377444 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.00700 | −0.653436 | ||||||||
\(191\) | −1.47363 | −0.106628 | −0.0533140 | − | 0.998578i | \(-0.516978\pi\) | ||||
−0.0533140 | + | 0.998578i | \(0.516978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.64272 | −0.262209 | −0.131104 | − | 0.991369i | \(-0.541852\pi\) | ||||
−0.131104 | + | 0.991369i | \(0.541852\pi\) | |||||||
\(194\) | 1.34205 | 0.0963534 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.32173 | −0.0944091 | ||||||||
\(197\) | −1.55636 | −0.110886 | −0.0554429 | − | 0.998462i | \(-0.517657\pi\) | ||||
−0.0554429 | + | 0.998462i | \(0.517657\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.82683 | −0.342165 | −0.171083 | − | 0.985257i | \(-0.554726\pi\) | ||||
−0.171083 | + | 0.985257i | \(0.554726\pi\) | |||||||
\(200\) | 8.97840 | 0.634869 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.2799 | −1.07509 | ||||||||
\(203\) | −7.77822 | −0.545924 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.17464 | 0.431256 | ||||||||
\(206\) | −11.3671 | −0.791984 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.22727 | −0.0850959 | ||||||||
\(209\) | 9.49055 | 0.656475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2751 | 0.913893 | 0.456947 | − | 0.889494i | \(-0.348943\pi\) | ||||
0.456947 | + | 0.889494i | \(0.348943\pi\) | |||||||
\(212\) | −10.9849 | −0.754445 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.54508 | 0.652488 | ||||||||
\(215\) | 12.9824 | 0.885393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.24454 | 0.559676 | ||||||||
\(218\) | −4.04019 | −0.273636 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.49922 | −0.640437 | ||||||||
\(221\) | −6.41585 | −0.431577 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5530 | 1.17544 | 0.587718 | − | 0.809066i | \(-0.300027\pi\) | ||||
0.587718 | + | 0.809066i | \(0.300027\pi\) | |||||||
\(224\) | −5.79291 | −0.387055 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.46288 | 0.629462 | ||||||||
\(227\) | −18.5774 | −1.23303 | −0.616514 | − | 0.787344i | \(-0.711455\pi\) | ||||
−0.616514 | + | 0.787344i | \(0.711455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.9178 | 1.51445 | 0.757226 | − | 0.653153i | \(-0.226554\pi\) | ||||
0.757226 | + | 0.653153i | \(0.226554\pi\) | |||||||
\(230\) | −0.423647 | −0.0279345 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.2788 | −1.39702 | ||||||||
\(233\) | 4.19204 | 0.274630 | 0.137315 | − | 0.990527i | \(-0.456153\pi\) | ||||
0.137315 | + | 0.990527i | \(0.456153\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.12683 | 0.0735060 | ||||||||
\(236\) | 18.9384 | 1.23279 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.68090 | −0.108957 | ||||||||
\(239\) | 16.4112 | 1.06155 | 0.530776 | − | 0.847512i | \(-0.321901\pi\) | ||||
0.530776 | + | 0.847512i | \(0.321901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.4130 | −1.25050 | −0.625252 | − | 0.780423i | \(-0.715004\pi\) | ||||
−0.625252 | + | 0.780423i | \(0.715004\pi\) | |||||||
\(242\) | 3.92287 | 0.252172 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.9079 | −0.698306 | ||||||||
\(245\) | 2.87784 | 0.183858 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.9461 | −0.760110 | ||||||||
\(248\) | 22.5545 | 1.43221 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.07196 | 0.257533 | ||||||||
\(251\) | −2.54869 | −0.160872 | −0.0804359 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804359 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.446391 | 0.0280644 | ||||||||
\(254\) | −0.823573 | −0.0516756 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.8155 | −0.925971 | ||||||||
\(257\) | −9.24122 | −0.576451 | −0.288226 | − | 0.957563i | \(-0.593065\pi\) | ||||
−0.288226 | + | 0.957563i | \(0.593065\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0498363 | 0.00309668 | ||||||||
\(260\) | 11.9570 | 0.741540 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.79935 | 0.234725 | ||||||||
\(263\) | −9.94843 | −0.613447 | −0.306723 | − | 0.951799i | \(-0.599233\pi\) | ||||
−0.306723 | + | 0.951799i | \(0.599233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.9177 | 1.46925 | ||||||||
\(266\) | −3.12978 | −0.191899 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.71179 | 0.471072 | ||||||||
\(269\) | −3.68337 | −0.224579 | −0.112290 | − | 0.993676i | \(-0.535818\pi\) | ||||
−0.112290 | + | 0.993676i | \(0.535818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.76862 | 0.532656 | 0.266328 | − | 0.963883i | \(-0.414190\pi\) | ||||
0.266328 | + | 0.963883i | \(0.414190\pi\) | |||||||
\(272\) | 0.796833 | 0.0483151 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.39301 | −0.386216 | ||||||||
\(275\) | 8.19620 | 0.494249 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.04083 | 0.362958 | 0.181479 | − | 0.983395i | \(-0.441912\pi\) | ||||
0.181479 | + | 0.983395i | \(0.441912\pi\) | |||||||
\(278\) | −10.8406 | −0.650173 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.87286 | 0.470494 | ||||||||
\(281\) | 29.8481 | 1.78059 | 0.890293 | − | 0.455388i | \(-0.150499\pi\) | ||||
0.890293 | + | 0.455388i | \(0.150499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.479453 | −0.0285005 | −0.0142502 | − | 0.999898i | \(-0.504536\pi\) | ||||
−0.0142502 | + | 0.999898i | \(0.504536\pi\) | |||||||
\(284\) | 10.6175 | 0.630034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.46540 | 0.382307 | ||||||||
\(287\) | 2.14558 | 0.126650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8344 | −0.754963 | ||||||||
\(290\) | 18.4352 | 1.08255 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18.5172 | −1.08364 | ||||||||
\(293\) | 20.9011 | 1.22106 | 0.610528 | − | 0.791994i | \(-0.290957\pi\) | ||||
0.610528 | + | 0.791994i | \(0.290957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.2352 | −2.40081 | ||||||||
\(296\) | 0.136336 | 0.00792439 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.0624 | 0.698755 | ||||||||
\(299\) | −0.561887 | −0.0324948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.51117 | 0.260019 | ||||||||
\(302\) | 4.81302 | 0.276958 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.48367 | 0.0850944 | ||||||||
\(305\) | 23.7501 | 1.35993 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.1940 | −1.32375 | −0.661876 | − | 0.749613i | \(-0.730240\pi\) | ||||
−0.661876 | + | 0.749613i | \(0.730240\pi\) | |||||||
\(308\) | −3.30082 | −0.188082 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.5405 | −1.10982 | ||||||||
\(311\) | −25.8909 | −1.46814 | −0.734069 | − | 0.679075i | \(-0.762381\pi\) | ||||
−0.734069 | + | 0.679075i | \(0.762381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.2780 | 1.03313 | 0.516566 | − | 0.856247i | \(-0.327210\pi\) | ||||
0.516566 | + | 0.856247i | \(0.327210\pi\) | |||||||
\(314\) | −1.85498 | −0.104682 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.57166 | 0.425939 | ||||||||
\(317\) | −25.2643 | −1.41898 | −0.709491 | − | 0.704714i | \(-0.751075\pi\) | ||||
−0.709491 | + | 0.704714i | \(0.751075\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.4249 | −1.08759 | ||||||||
\(320\) | 11.4827 | 0.641904 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.147210 | −0.00820370 | ||||||||
\(323\) | 7.75625 | 0.431569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.3168 | −0.572274 | ||||||||
\(326\) | −14.7917 | −0.819239 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.86964 | 0.324097 | ||||||||
\(329\) | 0.391553 | 0.0215870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.71108 | −0.533769 | −0.266885 | − | 0.963728i | \(-0.585994\pi\) | ||||
−0.266885 | + | 0.963728i | \(0.585994\pi\) | |||||||
\(332\) | −10.7476 | −0.589852 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.55561 | 0.303989 | ||||||||
\(335\) | −16.7911 | −0.917397 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.338072 | −0.0184159 | −0.00920797 | − | 0.999958i | \(-0.502931\pi\) | ||||
−0.00920797 | + | 0.999958i | \(0.502931\pi\) | |||||||
\(338\) | 2.56824 | 0.139694 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.76334 | −0.421026 | ||||||||
\(341\) | 20.5895 | 1.11499 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 12.3411 | 0.665389 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.7143 | 0.576005 | ||||||||
\(347\) | −10.8081 | −0.580211 | −0.290106 | − | 0.956995i | \(-0.593690\pi\) | ||||
−0.290106 | + | 0.956995i | \(0.593690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.2039 | −1.61678 | −0.808388 | − | 0.588650i | \(-0.799660\pi\) | ||||
−0.808388 | + | 0.588650i | \(0.799660\pi\) | |||||||
\(350\) | −2.70293 | −0.144478 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.4669 | −0.771090 | ||||||||
\(353\) | 24.0686 | 1.28104 | 0.640521 | − | 0.767941i | \(-0.278719\pi\) | ||||
0.640521 | + | 0.767941i | \(0.278719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.1179 | −1.22697 | ||||||||
\(356\) | −20.4616 | −1.08446 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.7530 | −0.568316 | ||||||||
\(359\) | −6.18593 | −0.326481 | −0.163240 | − | 0.986586i | \(-0.552195\pi\) | ||||
−0.163240 | + | 0.986586i | \(0.552195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.55815 | −0.239903 | ||||||||
\(362\) | 6.82262 | 0.358589 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.15485 | 0.217773 | ||||||||
\(365\) | 40.3182 | 2.11035 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.5359 | −0.602170 | −0.301085 | − | 0.953597i | \(-0.597349\pi\) | ||||
−0.301085 | + | 0.953597i | \(0.597349\pi\) | |||||||
\(368\) | 0.0697850 | 0.00363780 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.118118 | −0.00614064 | ||||||||
\(371\) | 8.31101 | 0.431486 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8284 | −1.02668 | −0.513338 | − | 0.858186i | \(-0.671591\pi\) | ||||
−0.513338 | + | 0.858186i | \(0.671591\pi\) | |||||||
\(374\) | −4.19781 | −0.217064 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.07116 | 0.0552411 | ||||||||
\(377\) | 24.4508 | 1.25928 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.80003 | −0.503394 | −0.251697 | − | 0.967806i | \(-0.580989\pi\) | ||||
−0.251697 | + | 0.967806i | \(0.580989\pi\) | |||||||
\(380\) | −14.4550 | −0.741528 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.21364 | 0.0620953 | ||||||||
\(383\) | −8.47434 | −0.433018 | −0.216509 | − | 0.976281i | \(-0.569467\pi\) | ||||
−0.216509 | + | 0.976281i | \(0.569467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.18698 | 0.366282 | ||||||||
\(386\) | 3.00005 | 0.152698 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.15381 | 0.109343 | ||||||||
\(389\) | 38.7291 | 1.96365 | 0.981823 | − | 0.189800i | \(-0.0607840\pi\) | ||||
0.981823 | + | 0.189800i | \(0.0607840\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.364818 | 0.0184496 | ||||||||
\(392\) | 2.73569 | 0.138173 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.28177 | 0.0645749 | ||||||||
\(395\) | −16.4860 | −0.829502 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0600 | 0.755838 | 0.377919 | − | 0.925839i | \(-0.376640\pi\) | ||||
0.377919 | + | 0.925839i | \(0.376640\pi\) | |||||||
\(398\) | 3.97525 | 0.199261 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.28132 | 0.0640662 | ||||||||
\(401\) | −7.21253 | −0.360177 | −0.180088 | − | 0.983650i | \(-0.557638\pi\) | ||||
−0.180088 | + | 0.983650i | \(0.557638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.9167 | −1.29100 | ||||||||
\(404\) | −24.5222 | −1.22002 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.40593 | 0.317921 | ||||||||
\(407\) | 0.124459 | 0.00616919 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.4241 | 1.10880 | 0.554400 | − | 0.832250i | \(-0.312948\pi\) | ||||
0.554400 | + | 0.832250i | \(0.312948\pi\) | |||||||
\(410\) | −5.08527 | −0.251144 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.2427 | −0.898753 | ||||||||
\(413\) | −14.3285 | −0.705062 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.4011 | 1.14872 | ||||||||
\(416\) | 18.2100 | 0.892819 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.81616 | −0.382301 | ||||||||
\(419\) | 35.0231 | 1.71099 | 0.855496 | − | 0.517809i | \(-0.173252\pi\) | ||||
0.855496 | + | 0.517809i | \(0.173252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.53382 | 0.220965 | 0.110483 | − | 0.993878i | \(-0.464760\pi\) | ||||
0.110483 | + | 0.993878i | \(0.464760\pi\) | |||||||
\(422\) | −10.9330 | −0.532210 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.7363 | 1.10417 | ||||||||
\(425\) | 6.69843 | 0.324922 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.25276 | 0.399379 | ||||||||
\(428\) | 15.3186 | 0.740452 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.6920 | −0.515612 | ||||||||
\(431\) | 7.51951 | 0.362202 | 0.181101 | − | 0.983464i | \(-0.442034\pi\) | ||||
0.181101 | + | 0.983464i | \(0.442034\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4018 | 1.36490 | 0.682452 | − | 0.730930i | \(-0.260914\pi\) | ||||
0.682452 | + | 0.730930i | \(0.260914\pi\) | |||||||
\(434\) | −6.78999 | −0.325930 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.48397 | −0.310526 | ||||||||
\(437\) | 0.679277 | 0.0324942 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3607 | 1.01949 | 0.509745 | − | 0.860325i | \(-0.329740\pi\) | ||||
0.509745 | + | 0.860325i | \(0.329740\pi\) | |||||||
\(440\) | 19.6613 | 0.937316 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.28392 | 0.251330 | ||||||||
\(443\) | −14.5312 | −0.690400 | −0.345200 | − | 0.938529i | \(-0.612189\pi\) | ||||
−0.345200 | + | 0.938529i | \(0.612189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.5518 | 2.11196 | ||||||||
\(446\) | −14.4562 | −0.684520 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.99005 | 0.188512 | ||||||||
\(449\) | 1.55717 | 0.0734876 | 0.0367438 | − | 0.999325i | \(-0.488301\pi\) | ||||
0.0367438 | + | 0.999325i | \(0.488301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.35827 | 0.252311 | ||||||||
\(452\) | 15.1867 | 0.714321 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.2999 | 0.718059 | ||||||||
\(455\) | −9.04648 | −0.424106 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.20252 | −0.0562515 | −0.0281258 | − | 0.999604i | \(-0.508954\pi\) | ||||
−0.0281258 | + | 0.999604i | \(0.508954\pi\) | |||||||
\(458\) | −18.8745 | −0.881948 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.679898 | −0.0317004 | ||||||||
\(461\) | −32.4395 | −1.51086 | −0.755429 | − | 0.655231i | \(-0.772571\pi\) | ||||
−0.755429 | + | 0.655231i | \(0.772571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1154 | 1.12074 | 0.560368 | − | 0.828244i | \(-0.310660\pi\) | ||||
0.560368 | + | 0.828244i | \(0.310660\pi\) | |||||||
\(464\) | −3.03673 | −0.140977 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.45245 | −0.159932 | ||||||||
\(467\) | −27.5828 | −1.27638 | −0.638191 | − | 0.769878i | \(-0.720317\pi\) | ||||
−0.638191 | + | 0.769878i | \(0.720317\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.83463 | −0.269418 | ||||||||
\(470\) | −0.928023 | −0.0428065 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −39.1984 | −1.80425 | ||||||||
\(473\) | 11.2660 | 0.518010 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.4722 | 0.572265 | ||||||||
\(476\) | −2.69763 | −0.123646 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.5158 | −0.618199 | ||||||||
\(479\) | 26.6971 | 1.21982 | 0.609910 | − | 0.792471i | \(-0.291206\pi\) | ||||
0.609910 | + | 0.792471i | \(0.291206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.156660 | −0.00714309 | ||||||||
\(482\) | 15.9881 | 0.728237 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.29569 | 0.286168 | ||||||||
\(485\) | −4.68956 | −0.212942 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3423 | 0.921798 | 0.460899 | − | 0.887453i | \(-0.347527\pi\) | ||||
0.460899 | + | 0.887453i | \(0.347527\pi\) | |||||||
\(488\) | 22.5770 | 1.02201 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.37011 | −0.107071 | ||||||||
\(491\) | 10.3444 | 0.466838 | 0.233419 | − | 0.972376i | \(-0.425009\pi\) | ||||
0.233419 | + | 0.972376i | \(0.425009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.8753 | −0.714985 | ||||||||
\(494\) | 9.83846 | 0.442653 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.21879 | 0.144528 | ||||||||
\(497\) | −8.03307 | −0.360332 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.63127 | 0.386389 | 0.193194 | − | 0.981161i | \(-0.438115\pi\) | ||||
0.193194 | + | 0.981161i | \(0.438115\pi\) | |||||||
\(500\) | 6.53496 | 0.292252 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.09903 | 0.0936844 | ||||||||
\(503\) | −3.53121 | −0.157449 | −0.0787245 | − | 0.996896i | \(-0.525085\pi\) | ||||
−0.0787245 | + | 0.996896i | \(0.525085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.3930 | 2.37596 | ||||||||
\(506\) | −0.367636 | −0.0163434 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.32173 | −0.0586421 | ||||||||
\(509\) | 14.8864 | 0.659830 | 0.329915 | − | 0.944011i | \(-0.392980\pi\) | ||||
0.329915 | + | 0.944011i | \(0.392980\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0099 | 0.619760 | ||||||||
\(512\) | −4.39775 | −0.194355 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.61082 | 0.335699 | ||||||||
\(515\) | 39.7204 | 1.75029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.977845 | 0.0430056 | ||||||||
\(518\) | −0.0410438 | −0.00180336 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.7483 | −1.08529 | ||||||||
\(521\) | 35.0975 | 1.53765 | 0.768826 | − | 0.639458i | \(-0.220841\pi\) | ||||
0.768826 | + | 0.639458i | \(0.220841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.8044 | 1.39071 | 0.695355 | − | 0.718667i | \(-0.255247\pi\) | ||||
0.695355 | + | 0.718667i | \(0.255247\pi\) | |||||||
\(524\) | 6.09746 | 0.266369 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.19326 | 0.357243 | ||||||||
\(527\) | 16.8270 | 0.732996 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9680 | −0.998611 | ||||||||
\(530\) | −19.6980 | −0.855627 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.02288 | −0.217770 | ||||||||
\(533\) | −6.74464 | −0.292143 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.3537 | −1.44201 | ||||||||
\(536\) | −15.9617 | −0.689441 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.03353 | 0.130785 | ||||||||
\(539\) | 2.49735 | 0.107569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.82729 | 0.121555 | 0.0607774 | − | 0.998151i | \(-0.480642\pi\) | ||||
0.0607774 | + | 0.998151i | \(0.480642\pi\) | |||||||
\(542\) | −7.22160 | −0.310194 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.8233 | −0.506918 | ||||||||
\(545\) | 14.1178 | 0.604738 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1788 | 1.29035 | 0.645176 | − | 0.764034i | \(-0.276784\pi\) | ||||
0.645176 | + | 0.764034i | \(0.276784\pi\) | |||||||
\(548\) | −10.2599 | −0.438283 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.75017 | −0.287828 | ||||||||
\(551\) | −29.5591 | −1.25926 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.72861 | −0.243605 | ||||||||
\(554\) | −4.97507 | −0.211370 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.3977 | −0.737825 | ||||||||
\(557\) | 31.9667 | 1.35447 | 0.677236 | − | 0.735766i | \(-0.263178\pi\) | ||||
0.677236 | + | 0.735766i | \(0.263178\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.1809 | −0.599786 | ||||||||
\(560\) | 1.12355 | 0.0474787 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.5821 | −1.03693 | ||||||||
\(563\) | −45.6546 | −1.92411 | −0.962057 | − | 0.272849i | \(-0.912034\pi\) | ||||
−0.962057 | + | 0.272849i | \(0.912034\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.0665 | −1.39112 | ||||||||
\(566\) | 0.394864 | 0.0165974 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.9759 | −0.922090 | ||||||||
\(569\) | 18.7255 | 0.785012 | 0.392506 | − | 0.919749i | \(-0.371608\pi\) | ||||
0.392506 | + | 0.919749i | \(0.371608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.52907 | −0.189536 | −0.0947678 | − | 0.995499i | \(-0.530211\pi\) | ||||
−0.0947678 | + | 0.995499i | \(0.530211\pi\) | |||||||
\(572\) | 10.3761 | 0.433847 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.76704 | −0.0737550 | ||||||||
\(575\) | 0.586635 | 0.0244644 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.47904 | −0.352987 | −0.176494 | − | 0.984302i | \(-0.556475\pi\) | ||||
−0.176494 | + | 0.984302i | \(0.556475\pi\) | |||||||
\(578\) | 10.5700 | 0.439656 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 29.5861 | 1.22850 | ||||||||
\(581\) | 8.13150 | 0.337352 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7555 | 0.859605 | ||||||||
\(584\) | 38.3266 | 1.58597 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.2136 | −0.711088 | ||||||||
\(587\) | 0.755169 | 0.0311691 | 0.0155846 | − | 0.999879i | \(-0.495039\pi\) | ||||
0.0155846 | + | 0.999879i | \(0.495039\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3313 | 1.29098 | ||||||||
\(590\) | 33.9603 | 1.39812 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0194568 | 0.000799671 0 | ||||||||
\(593\) | −29.2749 | −1.20218 | −0.601088 | − | 0.799183i | \(-0.705266\pi\) | ||||
−0.601088 | + | 0.799183i | \(0.705266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.87364 | 0.240796 | ||||||||
\(596\) | 19.3585 | 0.792957 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.462755 | 0.0189235 | ||||||||
\(599\) | 1.60224 | 0.0654658 | 0.0327329 | − | 0.999464i | \(-0.489579\pi\) | ||||
0.0327329 | + | 0.999464i | \(0.489579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8736 | 1.17778 | 0.588889 | − | 0.808214i | \(-0.299566\pi\) | ||||
0.588889 | + | 0.808214i | \(0.299566\pi\) | |||||||
\(602\) | −3.71528 | −0.151423 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.72427 | 0.314296 | ||||||||
\(605\) | −13.7078 | −0.557302 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.4619 | 1.84524 | 0.922621 | − | 0.385707i | \(-0.126043\pi\) | ||||
0.922621 | + | 0.385707i | \(0.126043\pi\) | |||||||
\(608\) | −22.0145 | −0.892804 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.5600 | −0.791959 | ||||||||
\(611\) | −1.23085 | −0.0497947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.01541 | −0.0814015 | −0.0407008 | − | 0.999171i | \(-0.512959\pi\) | ||||
−0.0407008 | + | 0.999171i | \(0.512959\pi\) | |||||||
\(614\) | 19.1020 | 0.770893 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.83197 | 0.275268 | ||||||||
\(617\) | 17.0285 | 0.685541 | 0.342771 | − | 0.939419i | \(-0.388635\pi\) | ||||
0.342771 | + | 0.939419i | \(0.388635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6985 | 1.39465 | 0.697325 | − | 0.716755i | \(-0.254374\pi\) | ||||
0.697325 | + | 0.716755i | \(0.254374\pi\) | |||||||
\(620\) | −31.3599 | −1.25944 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.3230 | 0.854976 | ||||||||
\(623\) | 15.4810 | 0.620232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6385 | −1.22554 | ||||||||
\(626\) | −15.0533 | −0.601649 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.97699 | −0.118795 | ||||||||
\(629\) | 0.101715 | 0.00405565 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.6586 | 1.81764 | 0.908820 | − | 0.417187i | \(-0.136984\pi\) | ||||
0.908820 | + | 0.417187i | \(0.136984\pi\) | |||||||
\(632\) | −15.6717 | −0.623386 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20.8070 | 0.826350 | ||||||||
\(635\) | 2.87784 | 0.114204 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.14350 | −0.124550 | ||||||||
\(638\) | 15.9979 | 0.633362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23.8852 | 0.944147 | ||||||||
\(641\) | −29.6589 | −1.17146 | −0.585728 | − | 0.810508i | \(-0.699191\pi\) | ||||
−0.585728 | + | 0.810508i | \(0.699191\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.6046 | 1.52242 | 0.761209 | − | 0.648507i | \(-0.224606\pi\) | ||||
0.761209 | + | 0.648507i | \(0.224606\pi\) | |||||||
\(644\) | −0.236253 | −0.00930967 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.38784 | −0.251326 | ||||||||
\(647\) | 43.7708 | 1.72081 | 0.860404 | − | 0.509613i | \(-0.170211\pi\) | ||||
0.860404 | + | 0.509613i | \(0.170211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.7834 | −1.40462 | ||||||||
\(650\) | 8.49666 | 0.333267 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.7388 | −0.929683 | ||||||||
\(653\) | −29.4964 | −1.15428 | −0.577142 | − | 0.816644i | \(-0.695832\pi\) | ||||
−0.577142 | + | 0.816644i | \(0.695832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2762 | −0.518744 | ||||||||
\(656\) | 0.837668 | 0.0327054 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.322472 | −0.0125713 | ||||||||
\(659\) | 19.0408 | 0.741724 | 0.370862 | − | 0.928688i | \(-0.379062\pi\) | ||||
0.370862 | + | 0.928688i | \(0.379062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.6329 | 0.919213 | 0.459607 | − | 0.888123i | \(-0.347990\pi\) | ||||
0.459607 | + | 0.888123i | \(0.347990\pi\) | |||||||
\(662\) | 7.99779 | 0.310843 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.2452 | 0.863282 | ||||||||
\(665\) | 10.9365 | 0.424099 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.39032 | −0.0538335 | ||||||||
\(668\) | 8.91602 | 0.344971 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.8287 | 0.534250 | ||||||||
\(671\) | 20.6100 | 0.795642 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.4509 | −0.402853 | −0.201426 | − | 0.979504i | \(-0.564558\pi\) | ||||
−0.201426 | + | 0.979504i | \(0.564558\pi\) | |||||||
\(674\) | 0.278427 | 0.0107246 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.12169 | 0.158526 | ||||||||
\(677\) | −26.1735 | −1.00593 | −0.502965 | − | 0.864307i | \(-0.667758\pi\) | ||||
−0.502965 | + | 0.864307i | \(0.667758\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.62954 | −0.0625361 | ||||||||
\(680\) | 16.0684 | 0.616196 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.9570 | −0.649317 | ||||||||
\(683\) | −40.9830 | −1.56817 | −0.784085 | − | 0.620653i | \(-0.786867\pi\) | ||||
−0.784085 | + | 0.620653i | \(0.786867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.3393 | 0.853540 | ||||||||
\(686\) | −0.823573 | −0.0314442 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.76123 | 0.0671462 | ||||||||
\(689\) | −26.1256 | −0.995308 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.1490 | −0.994754 | −0.497377 | − | 0.867534i | \(-0.665703\pi\) | ||||
−0.497377 | + | 0.867534i | \(0.665703\pi\) | |||||||
\(692\) | 17.1950 | 0.653658 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.90130 | 0.337889 | ||||||||
\(695\) | 37.8805 | 1.43689 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.37911 | 0.165871 | ||||||||
\(698\) | 24.8751 | 0.941537 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.33785 | −0.163955 | ||||||||
\(701\) | −4.34759 | −0.164206 | −0.0821030 | − | 0.996624i | \(-0.526164\pi\) | ||||
−0.0821030 | + | 0.996624i | \(0.526164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.189390 | 0.00714298 | ||||||||
\(704\) | 9.96457 | 0.375554 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.8222 | −0.746020 | ||||||||
\(707\) | 18.5531 | 0.697763 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.4246 | 1.21773 | 0.608865 | − | 0.793274i | \(-0.291625\pi\) | ||||
0.608865 | + | 0.793274i | \(0.291625\pi\) | |||||||
\(710\) | 19.0393 | 0.714531 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 42.3511 | 1.58717 | ||||||||
\(713\) | 1.47368 | 0.0551896 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.5923 | −0.844903 | ||||||||
\(716\) | −17.2572 | −0.644933 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.09457 | 0.190128 | ||||||||
\(719\) | 8.83585 | 0.329522 | 0.164761 | − | 0.986334i | \(-0.447315\pi\) | ||||
0.164761 | + | 0.986334i | \(0.447315\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8022 | 0.514020 | ||||||||
\(722\) | 3.75397 | 0.139708 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.9494 | 0.406932 | ||||||||
\(725\) | −25.5278 | −0.948077 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5666 | 0.836950 | 0.418475 | − | 0.908228i | \(-0.362565\pi\) | ||||
0.418475 | + | 0.908228i | \(0.362565\pi\) | |||||||
\(728\) | −8.59963 | −0.318723 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −33.2050 | −1.22897 | ||||||||
\(731\) | 9.20724 | 0.340542 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.1667 | 0.671001 | 0.335501 | − | 0.942040i | \(-0.391095\pi\) | ||||
0.335501 | + | 0.942040i | \(0.391095\pi\) | |||||||
\(734\) | 9.50068 | 0.350677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.03546 | −0.0381675 | ||||||||
\(737\) | −14.5711 | −0.536734 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3064 | 0.563055 | 0.281527 | − | 0.959553i | \(-0.409159\pi\) | ||||
0.281527 | + | 0.959553i | \(0.409159\pi\) | |||||||
\(740\) | −0.189563 | −0.00696848 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.84472 | −0.251278 | ||||||||
\(743\) | 12.1332 | 0.445125 | 0.222562 | − | 0.974918i | \(-0.428558\pi\) | ||||
0.222562 | + | 0.974918i | \(0.428558\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42.1500 | −1.54426 | ||||||||
\(746\) | 16.3302 | 0.597889 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.73693 | −0.246327 | ||||||||
\(749\) | −11.5898 | −0.423483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.2242 | −1.50429 | −0.752147 | − | 0.658996i | \(-0.770981\pi\) | ||||
−0.752147 | + | 0.658996i | \(0.770981\pi\) | |||||||
\(752\) | 0.152868 | 0.00557452 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.1371 | −0.733348 | ||||||||
\(755\) | −16.8183 | −0.612081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.3673 | −1.50352 | −0.751759 | − | 0.659437i | \(-0.770795\pi\) | ||||
−0.751759 | + | 0.659437i | \(0.770795\pi\) | |||||||
\(758\) | 8.07105 | 0.293154 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 29.9188 | 1.08527 | ||||||||
\(761\) | 1.38604 | 0.0502440 | 0.0251220 | − | 0.999684i | \(-0.492003\pi\) | ||||
0.0251220 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.90568 | 0.177598 | ||||||||
\(764\) | 1.94773 | 0.0704666 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.97924 | 0.252170 | ||||||||
\(767\) | 45.0418 | 1.62636 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.4676 | −1.09869 | −0.549344 | − | 0.835596i | \(-0.685122\pi\) | ||||
−0.549344 | + | 0.835596i | \(0.685122\pi\) | |||||||
\(770\) | −5.91900 | −0.213306 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.81468 | 0.173284 | ||||||||
\(773\) | 40.1159 | 1.44287 | 0.721435 | − | 0.692482i | \(-0.243483\pi\) | ||||
0.721435 | + | 0.692482i | \(0.243483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.0582 | 0.971960 | ||||||||
\(776\) | −4.45792 | −0.160030 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.8963 | −1.14354 | ||||||||
\(779\) | 8.15373 | 0.292138 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0614 | −0.717853 | ||||||||
\(782\) | −0.300454 | −0.0107442 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.390415 | 0.0139434 | ||||||||
\(785\) | 6.48190 | 0.231349 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.5702 | −1.12536 | −0.562678 | − | 0.826676i | \(-0.690229\pi\) | ||||
−0.562678 | + | 0.826676i | \(0.690229\pi\) | |||||||
\(788\) | 2.05708 | 0.0732804 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.5775 | 0.483064 | ||||||||
\(791\) | −11.4900 | −0.408538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.9425 | −0.921247 | ||||||||
\(794\) | −12.4030 | −0.440166 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.37976 | 0.226124 | ||||||||
\(797\) | −46.5952 | −1.65049 | −0.825244 | − | 0.564777i | \(-0.808962\pi\) | ||||
−0.825244 | + | 0.564777i | \(0.808962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.799154 | 0.0282720 | ||||||||
\(800\) | −19.0121 | −0.672178 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.94005 | 0.209750 | ||||||||
\(803\) | 34.9876 | 1.23469 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.514401 | 0.0181303 | ||||||||
\(806\) | 21.3443 | 0.751822 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 50.7556 | 1.78558 | ||||||||
\(809\) | 1.54408 | 0.0542868 | 0.0271434 | − | 0.999632i | \(-0.491359\pi\) | ||||
0.0271434 | + | 0.999632i | \(0.491359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5329 | 0.721009 | 0.360505 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360505 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(812\) | 10.2807 | 0.360781 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.102501 | −0.00359265 | ||||||||
\(815\) | 51.6873 | 1.81053 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.1435 | 0.599776 | ||||||||
\(818\) | −18.4679 | −0.645715 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.16119 | −0.285001 | ||||||||
\(821\) | −15.0246 | −0.524362 | −0.262181 | − | 0.965019i | \(-0.584442\pi\) | ||||
−0.262181 | + | 0.965019i | \(0.584442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.6086 | −0.683513 | −0.341756 | − | 0.939789i | \(-0.611022\pi\) | ||||
−0.341756 | + | 0.939789i | \(0.611022\pi\) | |||||||
\(824\) | 37.7584 | 1.31538 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.8006 | 0.410596 | ||||||||
\(827\) | 21.4027 | 0.744246 | 0.372123 | − | 0.928183i | \(-0.378630\pi\) | ||||
0.372123 | + | 0.928183i | \(0.378630\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.52819 | −0.261465 | −0.130732 | − | 0.991418i | \(-0.541733\pi\) | ||||
−0.130732 | + | 0.991418i | \(0.541733\pi\) | |||||||
\(830\) | −19.2726 | −0.668960 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.5427 | −0.434841 | ||||||||
\(833\) | 2.04099 | 0.0707161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.4131 | −0.671819 | ||||||||
\(836\) | −12.5439 | −0.433840 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.8441 | −0.996404 | ||||||||
\(839\) | −1.62392 | −0.0560640 | −0.0280320 | − | 0.999607i | \(-0.508924\pi\) | ||||
−0.0280320 | + | 0.999607i | \(0.508924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.5007 | 1.08623 | ||||||||
\(842\) | −3.73394 | −0.128680 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.5460 | −0.603959 | ||||||||
\(845\) | −8.97428 | −0.308725 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.76323 | −0.163667 | ||||||||
\(848\) | 3.24474 | 0.111425 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.51665 | −0.189220 | ||||||||
\(851\) | 0.00890802 | 0.000305363 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.2026 | 1.71891 | 0.859453 | − | 0.511215i | \(-0.170804\pi\) | ||||
0.859453 | + | 0.511215i | \(0.170804\pi\) | |||||||
\(854\) | −6.79675 | −0.232580 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.7062 | −1.08369 | ||||||||
\(857\) | 14.6499 | 0.500430 | 0.250215 | − | 0.968190i | \(-0.419499\pi\) | ||||
0.250215 | + | 0.968190i | \(0.419499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5012 | 0.528893 | 0.264447 | − | 0.964400i | \(-0.414811\pi\) | ||||
0.264447 | + | 0.964400i | \(0.414811\pi\) | |||||||
\(860\) | −17.1592 | −0.585124 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.19287 | −0.210930 | ||||||||
\(863\) | 4.15587 | 0.141468 | 0.0707338 | − | 0.997495i | \(-0.477466\pi\) | ||||
0.0707338 | + | 0.997495i | \(0.477466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.4393 | −1.27298 | ||||||||
\(866\) | −23.3910 | −0.794858 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.8970 | −0.369869 | ||||||||
\(869\) | −14.3064 | −0.485310 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3412 | 0.621466 | ||||||||
\(872\) | 13.4204 | 0.454472 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.559435 | −0.0189232 | ||||||||
\(875\) | −4.94426 | −0.167146 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.3465 | −0.990963 | −0.495481 | − | 0.868619i | \(-0.665008\pi\) | ||||
−0.495481 | + | 0.868619i | \(0.665008\pi\) | |||||||
\(878\) | −17.5921 | −0.593705 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.80590 | 0.0945870 | ||||||||
\(881\) | 43.6729 | 1.47138 | 0.735688 | − | 0.677320i | \(-0.236859\pi\) | ||||
0.735688 | + | 0.677320i | \(0.236859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.3693 | −1.52680 | −0.763399 | − | 0.645927i | \(-0.776471\pi\) | ||||
−0.763399 | + | 0.645927i | \(0.776471\pi\) | |||||||
\(884\) | 8.48000 | 0.285213 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.9675 | 0.402057 | ||||||||
\(887\) | 29.4945 | 0.990330 | 0.495165 | − | 0.868799i | \(-0.335108\pi\) | ||||
0.495165 | + | 0.868799i | \(0.335108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −36.6916 | −1.22991 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.2003 | −0.776802 | ||||||||
\(893\) | 1.48799 | 0.0497939 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.5747 | 1.25598 | ||||||||
\(896\) | 8.29971 | 0.277274 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.28245 | −0.0427958 | ||||||||
\(899\) | −64.1278 | −2.13878 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.9627 | 0.565108 | ||||||||
\(902\) | −4.41293 | −0.146935 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −31.4331 | −1.04545 | ||||||||
\(905\) | −23.8405 | −0.792485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.5099 | −1.31190 | −0.655952 | − | 0.754802i | \(-0.727733\pi\) | ||||
−0.655952 | + | 0.754802i | \(0.727733\pi\) | |||||||
\(908\) | 24.5543 | 0.814863 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.45044 | 0.246980 | ||||||||
\(911\) | −14.6770 | −0.486271 | −0.243135 | − | 0.969992i | \(-0.578176\pi\) | ||||
−0.243135 | + | 0.969992i | \(0.578176\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.3072 | 0.672071 | ||||||||
\(914\) | 0.990364 | 0.0327583 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.2911 | −1.00085 | ||||||||
\(917\) | −4.61325 | −0.152343 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.1107 | 0.498457 | 0.249229 | − | 0.968445i | \(-0.419823\pi\) | ||||
0.249229 | + | 0.968445i | \(0.419823\pi\) | |||||||
\(920\) | 1.40724 | 0.0463953 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.7163 | 0.879854 | ||||||||
\(923\) | 25.2519 | 0.831178 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.163560 | 0.00537783 | ||||||||
\(926\) | −19.8608 | −0.652665 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 45.0585 | 1.47912 | ||||||||
\(929\) | 27.4154 | 0.899469 | 0.449735 | − | 0.893162i | \(-0.351519\pi\) | ||||
0.449735 | + | 0.893162i | \(0.351519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.80024 | 0.124548 | ||||||||
\(932\) | −5.54073 | −0.181493 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.7165 | 0.743306 | ||||||||
\(935\) | 14.6685 | 0.479712 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.63753 | 0.0861644 | 0.0430822 | − | 0.999072i | \(-0.486282\pi\) | ||||
0.0430822 | + | 0.999072i | \(0.486282\pi\) | |||||||
\(938\) | 4.80525 | 0.156897 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.48935 | −0.0485774 | ||||||||
\(941\) | −47.8351 | −1.55938 | −0.779690 | − | 0.626166i | \(-0.784623\pi\) | ||||
−0.779690 | + | 0.626166i | \(0.784623\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.383514 | 0.0124889 | ||||||||
\(944\) | −5.59408 | −0.182072 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.27836 | −0.301665 | ||||||||
\(947\) | 59.9898 | 1.94941 | 0.974704 | − | 0.223500i | \(-0.0717483\pi\) | ||||
0.974704 | + | 0.223500i | \(0.0717483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.0400 | −1.42960 | ||||||||
\(950\) | −10.2718 | −0.333261 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.58350 | 0.180962 | ||||||||
\(953\) | 10.9525 | 0.354785 | 0.177393 | − | 0.984140i | \(-0.443234\pi\) | ||||
0.177393 | + | 0.984140i | \(0.443234\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.24087 | −0.137231 | ||||||||
\(956\) | −21.6911 | −0.701541 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.9870 | −0.710367 | ||||||||
\(959\) | 7.76252 | 0.250665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.9725 | 1.19266 | ||||||||
\(962\) | 0.129021 | 0.00415981 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.6587 | 0.826412 | ||||||||
\(965\) | −10.4832 | −0.337465 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.81937 | 0.187138 | 0.0935692 | − | 0.995613i | \(-0.470172\pi\) | ||||
0.0935692 | + | 0.995613i | \(0.470172\pi\) | |||||||
\(968\) | −13.0307 | −0.418823 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.86220 | 0.124008 | ||||||||
\(971\) | −27.0322 | −0.867505 | −0.433752 | − | 0.901032i | \(-0.642811\pi\) | ||||
−0.433752 | + | 0.901032i | \(0.642811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.1628 | 0.421981 | ||||||||
\(974\) | −16.7534 | −0.536813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.22200 | 0.103134 | ||||||||
\(977\) | −18.5562 | −0.593666 | −0.296833 | − | 0.954929i | \(-0.595930\pi\) | ||||
−0.296833 | + | 0.954929i | \(0.595930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.6615 | 1.23563 | ||||||||
\(980\) | −3.80372 | −0.121505 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.51941 | −0.271865 | ||||||||
\(983\) | −0.886444 | −0.0282732 | −0.0141366 | − | 0.999900i | \(-0.504500\pi\) | ||||
−0.0141366 | + | 0.999900i | \(0.504500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.47895 | −0.142711 | ||||||||
\(986\) | 13.0744 | 0.416375 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.7894 | 0.502329 | ||||||||
\(989\) | 0.806352 | 0.0256405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.64119 | 0.115666 | 0.0578331 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578331 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(992\) | −47.7599 | −1.51638 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.61582 | 0.209841 | ||||||||
\(995\) | −13.8908 | −0.440370 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.8191 | −1.10273 | −0.551367 | − | 0.834263i | \(-0.685893\pi\) | ||||
−0.551367 | + | 0.834263i | \(0.685893\pi\) | |||||||
\(998\) | −7.10848 | −0.225015 | ||||||||
\(999\) | 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 | 8001.2.a.v.1.9 | 19 | ||
3.2 | odd | 2 | 2667.2.a.q.1.11 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.q.1.11 | ✓ | 19 | 3.2 | odd | 2 | ||
8001.2.a.v.1.9 | 19 | 1.1 | even | 1 | trivial |