Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8025,2,Mod(1,8025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8025, 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("8025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8025 = 3 \cdot 5^{2} \cdot 107 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8025.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: | \(64.0799476221\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 15 x^{10} + 49 x^{9} + 71 x^{8} - 278 x^{7} - 92 x^{6} + 649 x^{5} - 127 x^{4} - 529 x^{3} + 267 x^{2} + 15 x - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1605) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.155707\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.155707 | 0.110101 | 0.0550507 | − | 0.998484i | \(-0.482468\pi\) | ||||
0.0550507 | + | 0.998484i | \(0.482468\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.97576 | −0.987878 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.155707 | −0.0635671 | ||||||||
\(7\) | −3.91791 | −1.48083 | −0.740415 | − | 0.672150i | \(-0.765371\pi\) | ||||
−0.740415 | + | 0.672150i | \(0.765371\pi\) | |||||||
\(8\) | −0.619053 | −0.218868 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.20576 | −1.26809 | −0.634043 | − | 0.773298i | \(-0.718606\pi\) | ||||
−0.634043 | + | 0.773298i | \(0.718606\pi\) | |||||||
\(12\) | 1.97576 | 0.570351 | ||||||||
\(13\) | −6.15258 | −1.70642 | −0.853209 | − | 0.521568i | \(-0.825347\pi\) | ||||
−0.853209 | + | 0.521568i | \(0.825347\pi\) | |||||||
\(14\) | −0.610045 | −0.163041 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.85512 | 0.963780 | ||||||||
\(17\) | 4.53299 | 1.09941 | 0.549705 | − | 0.835359i | \(-0.314740\pi\) | ||||
0.549705 | + | 0.835359i | \(0.314740\pi\) | |||||||
\(18\) | 0.155707 | 0.0367005 | ||||||||
\(19\) | 6.39031 | 1.46604 | 0.733018 | − | 0.680209i | \(-0.238111\pi\) | ||||
0.733018 | + | 0.680209i | \(0.238111\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.91791 | 0.854958 | ||||||||
\(22\) | −0.654866 | −0.139618 | ||||||||
\(23\) | 1.55096 | 0.323397 | 0.161699 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161699 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(24\) | 0.619053 | 0.126364 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.957999 | −0.187879 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.74083 | 1.46288 | ||||||||
\(29\) | −3.34760 | −0.621634 | −0.310817 | − | 0.950470i | \(-0.600603\pi\) | ||||
−0.310817 | + | 0.950470i | \(0.600603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.12813 | −0.741434 | −0.370717 | − | 0.928746i | \(-0.620888\pi\) | ||||
−0.370717 | + | 0.928746i | \(0.620888\pi\) | |||||||
\(32\) | 1.83837 | 0.324982 | ||||||||
\(33\) | 4.20576 | 0.732129 | ||||||||
\(34\) | 0.705817 | 0.121047 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.97576 | −0.329293 | ||||||||
\(37\) | −7.16219 | −1.17746 | −0.588728 | − | 0.808331i | \(-0.700371\pi\) | ||||
−0.588728 | + | 0.808331i | \(0.700371\pi\) | |||||||
\(38\) | 0.995015 | 0.161413 | ||||||||
\(39\) | 6.15258 | 0.985201 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.18328 | 1.12184 | 0.560920 | − | 0.827870i | \(-0.310448\pi\) | ||||
0.560920 | + | 0.827870i | \(0.310448\pi\) | |||||||
\(42\) | 0.610045 | 0.0941320 | ||||||||
\(43\) | 9.32016 | 1.42131 | 0.710656 | − | 0.703540i | \(-0.248398\pi\) | ||||
0.710656 | + | 0.703540i | \(0.248398\pi\) | |||||||
\(44\) | 8.30956 | 1.25271 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.241495 | 0.0356065 | ||||||||
\(47\) | −11.9785 | −1.74725 | −0.873623 | − | 0.486603i | \(-0.838236\pi\) | ||||
−0.873623 | + | 0.486603i | \(0.838236\pi\) | |||||||
\(48\) | −3.85512 | −0.556439 | ||||||||
\(49\) | 8.35000 | 1.19286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.53299 | −0.634745 | ||||||||
\(52\) | 12.1560 | 1.68573 | ||||||||
\(53\) | 12.4671 | 1.71249 | 0.856247 | − | 0.516567i | \(-0.172790\pi\) | ||||
0.856247 | + | 0.516567i | \(0.172790\pi\) | |||||||
\(54\) | −0.155707 | −0.0211890 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.42539 | 0.324107 | ||||||||
\(57\) | −6.39031 | −0.846417 | ||||||||
\(58\) | −0.521244 | −0.0684428 | ||||||||
\(59\) | 6.02997 | 0.785035 | 0.392518 | − | 0.919744i | \(-0.371604\pi\) | ||||
0.392518 | + | 0.919744i | \(0.371604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.14686 | 1.17113 | 0.585567 | − | 0.810624i | \(-0.300872\pi\) | ||||
0.585567 | + | 0.810624i | \(0.300872\pi\) | |||||||
\(62\) | −0.642779 | −0.0816330 | ||||||||
\(63\) | −3.91791 | −0.493610 | ||||||||
\(64\) | −7.42399 | −0.927999 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.654866 | 0.0806085 | ||||||||
\(67\) | −5.70713 | −0.697237 | −0.348619 | − | 0.937265i | \(-0.613349\pi\) | ||||
−0.348619 | + | 0.937265i | \(0.613349\pi\) | |||||||
\(68\) | −8.95607 | −1.08608 | ||||||||
\(69\) | −1.55096 | −0.186714 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.85627 | 0.932368 | 0.466184 | − | 0.884688i | \(-0.345628\pi\) | ||||
0.466184 | + | 0.884688i | \(0.345628\pi\) | |||||||
\(72\) | −0.619053 | −0.0729561 | ||||||||
\(73\) | 9.15535 | 1.07155 | 0.535776 | − | 0.844360i | \(-0.320019\pi\) | ||||
0.535776 | + | 0.844360i | \(0.320019\pi\) | |||||||
\(74\) | −1.11520 | −0.129640 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.6257 | −1.44827 | ||||||||
\(77\) | 16.4778 | 1.87782 | ||||||||
\(78\) | 0.957999 | 0.108472 | ||||||||
\(79\) | 3.30344 | 0.371666 | 0.185833 | − | 0.982581i | \(-0.440502\pi\) | ||||
0.185833 | + | 0.982581i | \(0.440502\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.11849 | 0.123516 | ||||||||
\(83\) | −3.87613 | −0.425460 | −0.212730 | − | 0.977111i | \(-0.568236\pi\) | ||||
−0.212730 | + | 0.977111i | \(0.568236\pi\) | |||||||
\(84\) | −7.74083 | −0.844594 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.45121 | 0.156488 | ||||||||
\(87\) | 3.34760 | 0.358900 | ||||||||
\(88\) | 2.60359 | 0.277543 | ||||||||
\(89\) | −6.68613 | −0.708728 | −0.354364 | − | 0.935107i | \(-0.615303\pi\) | ||||
−0.354364 | + | 0.935107i | \(0.615303\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.1052 | 2.52692 | ||||||||
\(92\) | −3.06432 | −0.319477 | ||||||||
\(93\) | 4.12813 | 0.428067 | ||||||||
\(94\) | −1.86514 | −0.192374 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.83837 | −0.187628 | ||||||||
\(97\) | 6.56241 | 0.666312 | 0.333156 | − | 0.942872i | \(-0.391886\pi\) | ||||
0.333156 | + | 0.942872i | \(0.391886\pi\) | |||||||
\(98\) | 1.30015 | 0.131335 | ||||||||
\(99\) | −4.20576 | −0.422695 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.61730 | 0.160927 | 0.0804637 | − | 0.996758i | \(-0.474360\pi\) | ||||
0.0804637 | + | 0.996758i | \(0.474360\pi\) | |||||||
\(102\) | −0.705817 | −0.0698863 | ||||||||
\(103\) | 2.47404 | 0.243775 | 0.121887 | − | 0.992544i | \(-0.461105\pi\) | ||||
0.121887 | + | 0.992544i | \(0.461105\pi\) | |||||||
\(104\) | 3.80877 | 0.373481 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.94122 | 0.188548 | ||||||||
\(107\) | −1.00000 | −0.0966736 | ||||||||
\(108\) | 1.97576 | 0.190117 | ||||||||
\(109\) | 16.1850 | 1.55024 | 0.775121 | − | 0.631812i | \(-0.217689\pi\) | ||||
0.775121 | + | 0.631812i | \(0.217689\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.16219 | 0.679805 | ||||||||
\(112\) | −15.1040 | −1.42719 | ||||||||
\(113\) | −16.5476 | −1.55667 | −0.778334 | − | 0.627851i | \(-0.783935\pi\) | ||||
−0.778334 | + | 0.627851i | \(0.783935\pi\) | |||||||
\(114\) | −0.995015 | −0.0931917 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.61404 | 0.614098 | ||||||||
\(117\) | −6.15258 | −0.568806 | ||||||||
\(118\) | 0.938908 | 0.0864335 | ||||||||
\(119\) | −17.7598 | −1.62804 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.68844 | 0.608040 | ||||||||
\(122\) | 1.42423 | 0.128944 | ||||||||
\(123\) | −7.18328 | −0.647694 | ||||||||
\(124\) | 8.15618 | 0.732447 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.610045 | −0.0543472 | ||||||||
\(127\) | −21.3131 | −1.89123 | −0.945615 | − | 0.325288i | \(-0.894539\pi\) | ||||
−0.945615 | + | 0.325288i | \(0.894539\pi\) | |||||||
\(128\) | −4.83272 | −0.427156 | ||||||||
\(129\) | −9.32016 | −0.820595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.55127 | 0.659758 | 0.329879 | − | 0.944023i | \(-0.392992\pi\) | ||||
0.329879 | + | 0.944023i | \(0.392992\pi\) | |||||||
\(132\) | −8.30956 | −0.723254 | ||||||||
\(133\) | −25.0366 | −2.17095 | ||||||||
\(134\) | −0.888640 | −0.0767668 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.80616 | −0.240626 | ||||||||
\(137\) | 13.2009 | 1.12783 | 0.563915 | − | 0.825833i | \(-0.309294\pi\) | ||||
0.563915 | + | 0.825833i | \(0.309294\pi\) | |||||||
\(138\) | −0.241495 | −0.0205574 | ||||||||
\(139\) | −13.2352 | −1.12260 | −0.561298 | − | 0.827614i | \(-0.689698\pi\) | ||||
−0.561298 | + | 0.827614i | \(0.689698\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.9785 | 1.00877 | ||||||||
\(142\) | 1.22328 | 0.102655 | ||||||||
\(143\) | 25.8763 | 2.16388 | ||||||||
\(144\) | 3.85512 | 0.321260 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.42555 | 0.117979 | ||||||||
\(147\) | −8.35000 | −0.688697 | ||||||||
\(148\) | 14.1507 | 1.16318 | ||||||||
\(149\) | −0.813693 | −0.0666603 | −0.0333302 | − | 0.999444i | \(-0.510611\pi\) | ||||
−0.0333302 | + | 0.999444i | \(0.510611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.50264 | −0.447799 | −0.223899 | − | 0.974612i | \(-0.571879\pi\) | ||||
−0.223899 | + | 0.974612i | \(0.571879\pi\) | |||||||
\(152\) | −3.95594 | −0.320869 | ||||||||
\(153\) | 4.53299 | 0.366470 | ||||||||
\(154\) | 2.56571 | 0.206750 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.1560 | −0.973258 | ||||||||
\(157\) | 0.601189 | 0.0479801 | 0.0239900 | − | 0.999712i | \(-0.492363\pi\) | ||||
0.0239900 | + | 0.999712i | \(0.492363\pi\) | |||||||
\(158\) | 0.514369 | 0.0409210 | ||||||||
\(159\) | −12.4671 | −0.988709 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.07652 | −0.478897 | ||||||||
\(162\) | 0.155707 | 0.0122335 | ||||||||
\(163\) | 21.6686 | 1.69721 | 0.848607 | − | 0.529025i | \(-0.177442\pi\) | ||||
0.848607 | + | 0.529025i | \(0.177442\pi\) | |||||||
\(164\) | −14.1924 | −1.10824 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.603540 | −0.0468438 | ||||||||
\(167\) | −6.89307 | −0.533402 | −0.266701 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266701 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(168\) | −2.42539 | −0.187123 | ||||||||
\(169\) | 24.8543 | 1.91187 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.39031 | 0.488679 | ||||||||
\(172\) | −18.4144 | −1.40408 | ||||||||
\(173\) | −13.4977 | −1.02621 | −0.513107 | − | 0.858325i | \(-0.671506\pi\) | ||||
−0.513107 | + | 0.858325i | \(0.671506\pi\) | |||||||
\(174\) | 0.521244 | 0.0395154 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.2137 | −1.22216 | ||||||||
\(177\) | −6.02997 | −0.453240 | ||||||||
\(178\) | −1.04108 | −0.0780320 | ||||||||
\(179\) | −23.0759 | −1.72478 | −0.862389 | − | 0.506247i | \(-0.831032\pi\) | ||||
−0.862389 | + | 0.506247i | \(0.831032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.23219 | 0.240247 | 0.120123 | − | 0.992759i | \(-0.461671\pi\) | ||||
0.120123 | + | 0.992759i | \(0.461671\pi\) | |||||||
\(182\) | 3.75335 | 0.278217 | ||||||||
\(183\) | −9.14686 | −0.676155 | ||||||||
\(184\) | −0.960125 | −0.0707814 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.642779 | 0.0471308 | ||||||||
\(187\) | −19.0647 | −1.39415 | ||||||||
\(188\) | 23.6666 | 1.72607 | ||||||||
\(189\) | 3.91791 | 0.284986 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.48523 | 0.541612 | 0.270806 | − | 0.962634i | \(-0.412710\pi\) | ||||
0.270806 | + | 0.962634i | \(0.412710\pi\) | |||||||
\(192\) | 7.42399 | 0.535780 | ||||||||
\(193\) | 23.6594 | 1.70304 | 0.851519 | − | 0.524324i | \(-0.175682\pi\) | ||||
0.851519 | + | 0.524324i | \(0.175682\pi\) | |||||||
\(194\) | 1.02181 | 0.0733619 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.4976 | −1.17840 | ||||||||
\(197\) | 0.502435 | 0.0357970 | 0.0178985 | − | 0.999840i | \(-0.494302\pi\) | ||||
0.0178985 | + | 0.999840i | \(0.494302\pi\) | |||||||
\(198\) | −0.654866 | −0.0465393 | ||||||||
\(199\) | 12.0176 | 0.851906 | 0.425953 | − | 0.904745i | \(-0.359939\pi\) | ||||
0.425953 | + | 0.904745i | \(0.359939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.70713 | 0.402550 | ||||||||
\(202\) | 0.251825 | 0.0177183 | ||||||||
\(203\) | 13.1156 | 0.920534 | ||||||||
\(204\) | 8.95607 | 0.627051 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.385226 | 0.0268399 | ||||||||
\(207\) | 1.55096 | 0.107799 | ||||||||
\(208\) | −23.7189 | −1.64461 | ||||||||
\(209\) | −26.8761 | −1.85906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.5450 | −1.55206 | −0.776032 | − | 0.630694i | \(-0.782770\pi\) | ||||
−0.776032 | + | 0.630694i | \(0.782770\pi\) | |||||||
\(212\) | −24.6320 | −1.69173 | ||||||||
\(213\) | −7.85627 | −0.538303 | ||||||||
\(214\) | −0.155707 | −0.0106439 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.619053 | 0.0421212 | ||||||||
\(217\) | 16.1736 | 1.09794 | ||||||||
\(218\) | 2.52012 | 0.170684 | ||||||||
\(219\) | −9.15535 | −0.618661 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.8896 | −1.87606 | ||||||||
\(222\) | 1.11520 | 0.0748475 | ||||||||
\(223\) | 11.2208 | 0.751399 | 0.375700 | − | 0.926741i | \(-0.377402\pi\) | ||||
0.375700 | + | 0.926741i | \(0.377402\pi\) | |||||||
\(224\) | −7.20258 | −0.481243 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.57658 | −0.171391 | ||||||||
\(227\) | −3.79410 | −0.251823 | −0.125912 | − | 0.992041i | \(-0.540186\pi\) | ||||
−0.125912 | + | 0.992041i | \(0.540186\pi\) | |||||||
\(228\) | 12.6257 | 0.836156 | ||||||||
\(229\) | −21.8196 | −1.44188 | −0.720941 | − | 0.692996i | \(-0.756290\pi\) | ||||
−0.720941 | + | 0.692996i | \(0.756290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.4778 | −1.08416 | ||||||||
\(232\) | 2.07234 | 0.136056 | ||||||||
\(233\) | −2.52926 | −0.165698 | −0.0828488 | − | 0.996562i | \(-0.526402\pi\) | ||||
−0.0828488 | + | 0.996562i | \(0.526402\pi\) | |||||||
\(234\) | −0.957999 | −0.0626264 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.9137 | −0.775519 | ||||||||
\(237\) | −3.30344 | −0.214582 | ||||||||
\(238\) | −2.76533 | −0.179250 | ||||||||
\(239\) | −0.0952535 | −0.00616144 | −0.00308072 | − | 0.999995i | \(-0.500981\pi\) | ||||
−0.00308072 | + | 0.999995i | \(0.500981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.8084 | −1.27597 | −0.637984 | − | 0.770050i | \(-0.720231\pi\) | ||||
−0.637984 | + | 0.770050i | \(0.720231\pi\) | |||||||
\(242\) | 1.04144 | 0.0669461 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −18.0719 | −1.15694 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.11849 | −0.0713121 | ||||||||
\(247\) | −39.3169 | −2.50167 | ||||||||
\(248\) | 2.55553 | 0.162276 | ||||||||
\(249\) | 3.87613 | 0.245640 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.15527 | −0.388517 | −0.194259 | − | 0.980950i | \(-0.562230\pi\) | ||||
−0.194259 | + | 0.980950i | \(0.562230\pi\) | |||||||
\(252\) | 7.74083 | 0.487626 | ||||||||
\(253\) | −6.52297 | −0.410095 | ||||||||
\(254\) | −3.31859 | −0.208227 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.0955 | 0.880969 | ||||||||
\(257\) | −11.0517 | −0.689384 | −0.344692 | − | 0.938716i | \(-0.612017\pi\) | ||||
−0.344692 | + | 0.938716i | \(0.612017\pi\) | |||||||
\(258\) | −1.45121 | −0.0903486 | ||||||||
\(259\) | 28.0608 | 1.74361 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.34760 | −0.207211 | ||||||||
\(262\) | 1.17579 | 0.0726403 | ||||||||
\(263\) | −17.1372 | −1.05672 | −0.528361 | − | 0.849020i | \(-0.677193\pi\) | ||||
−0.528361 | + | 0.849020i | \(0.677193\pi\) | |||||||
\(264\) | −2.60359 | −0.160240 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.89838 | −0.239025 | ||||||||
\(267\) | 6.68613 | 0.409185 | ||||||||
\(268\) | 11.2759 | 0.688785 | ||||||||
\(269\) | −2.71376 | −0.165461 | −0.0827303 | − | 0.996572i | \(-0.526364\pi\) | ||||
−0.0827303 | + | 0.996572i | \(0.526364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.31668 | −0.505202 | −0.252601 | − | 0.967571i | \(-0.581286\pi\) | ||||
−0.252601 | + | 0.967571i | \(0.581286\pi\) | |||||||
\(272\) | 17.4752 | 1.05959 | ||||||||
\(273\) | −24.1052 | −1.45892 | ||||||||
\(274\) | 2.05547 | 0.124176 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.06432 | 0.184450 | ||||||||
\(277\) | −0.169617 | −0.0101913 | −0.00509565 | − | 0.999987i | \(-0.501622\pi\) | ||||
−0.00509565 | + | 0.999987i | \(0.501622\pi\) | |||||||
\(278\) | −2.06081 | −0.123599 | ||||||||
\(279\) | −4.12813 | −0.247145 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.6929 | −1.77133 | −0.885665 | − | 0.464324i | \(-0.846297\pi\) | ||||
−0.885665 | + | 0.464324i | \(0.846297\pi\) | |||||||
\(282\) | 1.86514 | 0.111067 | ||||||||
\(283\) | 11.3215 | 0.672995 | 0.336497 | − | 0.941684i | \(-0.390758\pi\) | ||||
0.336497 | + | 0.941684i | \(0.390758\pi\) | |||||||
\(284\) | −15.5221 | −0.921066 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.02912 | 0.238247 | ||||||||
\(287\) | −28.1434 | −1.66125 | ||||||||
\(288\) | 1.83837 | 0.108327 | ||||||||
\(289\) | 3.54797 | 0.208704 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.56241 | −0.384695 | ||||||||
\(292\) | −18.0887 | −1.05856 | ||||||||
\(293\) | 32.0481 | 1.87227 | 0.936134 | − | 0.351642i | \(-0.114377\pi\) | ||||
0.936134 | + | 0.351642i | \(0.114377\pi\) | |||||||
\(294\) | −1.30015 | −0.0758265 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.43377 | 0.257708 | ||||||||
\(297\) | 4.20576 | 0.244043 | ||||||||
\(298\) | −0.126698 | −0.00733940 | ||||||||
\(299\) | −9.54240 | −0.551851 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.5155 | −2.10472 | ||||||||
\(302\) | −0.856799 | −0.0493033 | ||||||||
\(303\) | −1.61730 | −0.0929115 | ||||||||
\(304\) | 24.6354 | 1.41294 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.705817 | 0.0403489 | ||||||||
\(307\) | 3.07724 | 0.175627 | 0.0878135 | − | 0.996137i | \(-0.472012\pi\) | ||||
0.0878135 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(308\) | −32.5561 | −1.85505 | ||||||||
\(309\) | −2.47404 | −0.140743 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.6191 | 0.715562 | 0.357781 | − | 0.933806i | \(-0.383533\pi\) | ||||
0.357781 | + | 0.933806i | \(0.383533\pi\) | |||||||
\(312\) | −3.80877 | −0.215629 | ||||||||
\(313\) | 24.2861 | 1.37273 | 0.686364 | − | 0.727258i | \(-0.259206\pi\) | ||||
0.686364 | + | 0.727258i | \(0.259206\pi\) | |||||||
\(314\) | 0.0936093 | 0.00528268 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.52679 | −0.367161 | ||||||||
\(317\) | −9.52720 | −0.535101 | −0.267550 | − | 0.963544i | \(-0.586214\pi\) | ||||
−0.267550 | + | 0.963544i | \(0.586214\pi\) | |||||||
\(318\) | −1.94122 | −0.108858 | ||||||||
\(319\) | 14.0792 | 0.788284 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.00000 | 0.0558146 | ||||||||
\(322\) | −0.946156 | −0.0527272 | ||||||||
\(323\) | 28.9672 | 1.61178 | ||||||||
\(324\) | −1.97576 | −0.109764 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.37395 | 0.186866 | ||||||||
\(327\) | −16.1850 | −0.895033 | ||||||||
\(328\) | −4.44683 | −0.245535 | ||||||||
\(329\) | 46.9307 | 2.58737 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.655437 | −0.0360261 | −0.0180130 | − | 0.999838i | \(-0.505734\pi\) | ||||
−0.0180130 | + | 0.999838i | \(0.505734\pi\) | |||||||
\(332\) | 7.65828 | 0.420303 | ||||||||
\(333\) | −7.16219 | −0.392485 | ||||||||
\(334\) | −1.07330 | −0.0587283 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.1040 | 0.823991 | ||||||||
\(337\) | 17.5012 | 0.953352 | 0.476676 | − | 0.879079i | \(-0.341841\pi\) | ||||
0.476676 | + | 0.879079i | \(0.341841\pi\) | |||||||
\(338\) | 3.86998 | 0.210499 | ||||||||
\(339\) | 16.5476 | 0.898742 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.3619 | 0.940202 | ||||||||
\(342\) | 0.995015 | 0.0538042 | ||||||||
\(343\) | −5.28919 | −0.285589 | ||||||||
\(344\) | −5.76967 | −0.311080 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.10169 | −0.112988 | ||||||||
\(347\) | 9.99897 | 0.536773 | 0.268386 | − | 0.963311i | \(-0.413510\pi\) | ||||
0.268386 | + | 0.963311i | \(0.413510\pi\) | |||||||
\(348\) | −6.61404 | −0.354550 | ||||||||
\(349\) | 3.77143 | 0.201880 | 0.100940 | − | 0.994893i | \(-0.467815\pi\) | ||||
0.100940 | + | 0.994893i | \(0.467815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.15258 | 0.328400 | ||||||||
\(352\) | −7.73177 | −0.412104 | ||||||||
\(353\) | −17.2527 | −0.918267 | −0.459133 | − | 0.888367i | \(-0.651840\pi\) | ||||
−0.459133 | + | 0.888367i | \(0.651840\pi\) | |||||||
\(354\) | −0.938908 | −0.0499024 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.2102 | 0.700137 | ||||||||
\(357\) | 17.7598 | 0.939950 | ||||||||
\(358\) | −3.59308 | −0.189900 | ||||||||
\(359\) | 20.3780 | 1.07551 | 0.537755 | − | 0.843101i | \(-0.319272\pi\) | ||||
0.537755 | + | 0.843101i | \(0.319272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.8360 | 1.14926 | ||||||||
\(362\) | 0.503275 | 0.0264515 | ||||||||
\(363\) | −6.68844 | −0.351052 | ||||||||
\(364\) | −47.6261 | −2.49628 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.42423 | −0.0744456 | ||||||||
\(367\) | −17.4162 | −0.909119 | −0.454560 | − | 0.890716i | \(-0.650203\pi\) | ||||
−0.454560 | + | 0.890716i | \(0.650203\pi\) | |||||||
\(368\) | 5.97913 | 0.311684 | ||||||||
\(369\) | 7.18328 | 0.373947 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −48.8451 | −2.53591 | ||||||||
\(372\) | −8.15618 | −0.422878 | ||||||||
\(373\) | 0.0544363 | 0.00281861 | 0.00140930 | − | 0.999999i | \(-0.499551\pi\) | ||||
0.00140930 | + | 0.999999i | \(0.499551\pi\) | |||||||
\(374\) | −2.96850 | −0.153498 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.41533 | 0.382417 | ||||||||
\(377\) | 20.5964 | 1.06077 | ||||||||
\(378\) | 0.610045 | 0.0313773 | ||||||||
\(379\) | 5.64875 | 0.290157 | 0.145079 | − | 0.989420i | \(-0.453657\pi\) | ||||
0.145079 | + | 0.989420i | \(0.453657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.3131 | 1.09190 | ||||||||
\(382\) | 1.16550 | 0.0596323 | ||||||||
\(383\) | 33.3118 | 1.70216 | 0.851078 | − | 0.525040i | \(-0.175950\pi\) | ||||
0.851078 | + | 0.525040i | \(0.175950\pi\) | |||||||
\(384\) | 4.83272 | 0.246618 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.68393 | 0.187507 | ||||||||
\(387\) | 9.32016 | 0.473771 | ||||||||
\(388\) | −12.9657 | −0.658235 | ||||||||
\(389\) | −8.32421 | −0.422054 | −0.211027 | − | 0.977480i | \(-0.567681\pi\) | ||||
−0.211027 | + | 0.977480i | \(0.567681\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.03048 | 0.355547 | ||||||||
\(392\) | −5.16909 | −0.261079 | ||||||||
\(393\) | −7.55127 | −0.380911 | ||||||||
\(394\) | 0.0782325 | 0.00394130 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.30956 | 0.417571 | ||||||||
\(397\) | −7.56190 | −0.379521 | −0.189760 | − | 0.981830i | \(-0.560771\pi\) | ||||
−0.189760 | + | 0.981830i | \(0.560771\pi\) | |||||||
\(398\) | 1.87123 | 0.0937961 | ||||||||
\(399\) | 25.0366 | 1.25340 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.2500 | −0.661676 | −0.330838 | − | 0.943688i | \(-0.607331\pi\) | ||||
−0.330838 | + | 0.943688i | \(0.607331\pi\) | |||||||
\(402\) | 0.888640 | 0.0443213 | ||||||||
\(403\) | 25.3987 | 1.26520 | ||||||||
\(404\) | −3.19539 | −0.158977 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.04219 | 0.101352 | ||||||||
\(407\) | 30.1225 | 1.49311 | ||||||||
\(408\) | 2.80616 | 0.138925 | ||||||||
\(409\) | −26.6915 | −1.31981 | −0.659906 | − | 0.751348i | \(-0.729404\pi\) | ||||
−0.659906 | + | 0.751348i | \(0.729404\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.2009 | −0.651153 | ||||||||
\(412\) | −4.88810 | −0.240820 | ||||||||
\(413\) | −23.6249 | −1.16250 | ||||||||
\(414\) | 0.241495 | 0.0118688 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.3107 | −0.554555 | ||||||||
\(417\) | 13.2352 | 0.648131 | ||||||||
\(418\) | −4.18480 | −0.204685 | ||||||||
\(419\) | −26.2407 | −1.28194 | −0.640971 | − | 0.767565i | \(-0.721468\pi\) | ||||
−0.640971 | + | 0.767565i | \(0.721468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0876 | 1.12522 | 0.562609 | − | 0.826723i | \(-0.309798\pi\) | ||||
0.562609 | + | 0.826723i | \(0.309798\pi\) | |||||||
\(422\) | −3.51042 | −0.170884 | ||||||||
\(423\) | −11.9785 | −0.582415 | ||||||||
\(424\) | −7.71782 | −0.374810 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.22328 | −0.0592679 | ||||||||
\(427\) | −35.8365 | −1.73425 | ||||||||
\(428\) | 1.97576 | 0.0955017 | ||||||||
\(429\) | −25.8763 | −1.24932 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.4525 | −1.08150 | −0.540748 | − | 0.841184i | \(-0.681859\pi\) | ||||
−0.540748 | + | 0.841184i | \(0.681859\pi\) | |||||||
\(432\) | −3.85512 | −0.185480 | ||||||||
\(433\) | 10.3947 | 0.499538 | 0.249769 | − | 0.968305i | \(-0.419645\pi\) | ||||
0.249769 | + | 0.968305i | \(0.419645\pi\) | |||||||
\(434\) | 2.51835 | 0.120885 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.9776 | −1.53145 | ||||||||
\(437\) | 9.91111 | 0.474112 | ||||||||
\(438\) | −1.42555 | −0.0681155 | ||||||||
\(439\) | −31.2659 | −1.49224 | −0.746120 | − | 0.665812i | \(-0.768085\pi\) | ||||
−0.746120 | + | 0.665812i | \(0.768085\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.35000 | 0.397619 | ||||||||
\(442\) | −4.34260 | −0.206556 | ||||||||
\(443\) | 3.36078 | 0.159676 | 0.0798378 | − | 0.996808i | \(-0.474560\pi\) | ||||
0.0798378 | + | 0.996808i | \(0.474560\pi\) | |||||||
\(444\) | −14.1507 | −0.671564 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.74715 | 0.0827301 | ||||||||
\(447\) | 0.813693 | 0.0384864 | ||||||||
\(448\) | 29.0865 | 1.37421 | ||||||||
\(449\) | 5.41796 | 0.255689 | 0.127845 | − | 0.991794i | \(-0.459194\pi\) | ||||
0.127845 | + | 0.991794i | \(0.459194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.2112 | −1.42259 | ||||||||
\(452\) | 32.6940 | 1.53780 | ||||||||
\(453\) | 5.50264 | 0.258537 | ||||||||
\(454\) | −0.590768 | −0.0277261 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.95594 | 0.185254 | ||||||||
\(457\) | −14.4160 | −0.674354 | −0.337177 | − | 0.941441i | \(-0.609472\pi\) | ||||
−0.337177 | + | 0.941441i | \(0.609472\pi\) | |||||||
\(458\) | −3.39747 | −0.158753 | ||||||||
\(459\) | −4.53299 | −0.211582 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.3177 | 1.31889 | 0.659444 | − | 0.751754i | \(-0.270792\pi\) | ||||
0.659444 | + | 0.751754i | \(0.270792\pi\) | |||||||
\(462\) | −2.56571 | −0.119367 | ||||||||
\(463\) | −17.7568 | −0.825227 | −0.412614 | − | 0.910906i | \(-0.635384\pi\) | ||||
−0.412614 | + | 0.910906i | \(0.635384\pi\) | |||||||
\(464\) | −12.9054 | −0.599118 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.393824 | −0.0182435 | ||||||||
\(467\) | 32.4812 | 1.50305 | 0.751525 | − | 0.659705i | \(-0.229319\pi\) | ||||
0.751525 | + | 0.659705i | \(0.229319\pi\) | |||||||
\(468\) | 12.1560 | 0.561911 | ||||||||
\(469\) | 22.3600 | 1.03249 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.601189 | −0.0277013 | ||||||||
\(472\) | −3.73287 | −0.171819 | ||||||||
\(473\) | −39.1984 | −1.80234 | ||||||||
\(474\) | −0.514369 | −0.0236257 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 35.0891 | 1.60830 | ||||||||
\(477\) | 12.4671 | 0.570831 | ||||||||
\(478\) | −0.0148316 | −0.000678383 0 | ||||||||
\(479\) | 32.5182 | 1.48579 | 0.742897 | − | 0.669405i | \(-0.233451\pi\) | ||||
0.742897 | + | 0.669405i | \(0.233451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.0659 | 2.00923 | ||||||||
\(482\) | −3.08430 | −0.140486 | ||||||||
\(483\) | 6.07652 | 0.276491 | ||||||||
\(484\) | −13.2147 | −0.600669 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.155707 | −0.00706301 | ||||||||
\(487\) | 34.8343 | 1.57849 | 0.789245 | − | 0.614078i | \(-0.210472\pi\) | ||||
0.789245 | + | 0.614078i | \(0.210472\pi\) | |||||||
\(488\) | −5.66238 | −0.256324 | ||||||||
\(489\) | −21.6686 | −0.979886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.42858 | −0.425506 | −0.212753 | − | 0.977106i | \(-0.568243\pi\) | ||||
−0.212753 | + | 0.977106i | \(0.568243\pi\) | |||||||
\(492\) | 14.1924 | 0.639843 | ||||||||
\(493\) | −15.1746 | −0.683431 | ||||||||
\(494\) | −6.12191 | −0.275438 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.9144 | −0.714580 | ||||||||
\(497\) | −30.7802 | −1.38068 | ||||||||
\(498\) | 0.603540 | 0.0270453 | ||||||||
\(499\) | 11.1288 | 0.498192 | 0.249096 | − | 0.968479i | \(-0.419866\pi\) | ||||
0.249096 | + | 0.968479i | \(0.419866\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.89307 | 0.307960 | ||||||||
\(502\) | −0.958418 | −0.0427763 | ||||||||
\(503\) | 5.12488 | 0.228507 | 0.114253 | − | 0.993452i | \(-0.463552\pi\) | ||||
0.114253 | + | 0.993452i | \(0.463552\pi\) | |||||||
\(504\) | 2.42539 | 0.108036 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.01567 | −0.0451521 | ||||||||
\(507\) | −24.8543 | −1.10382 | ||||||||
\(508\) | 42.1094 | 1.86830 | ||||||||
\(509\) | −32.5419 | −1.44240 | −0.721198 | − | 0.692729i | \(-0.756408\pi\) | ||||
−0.721198 | + | 0.692729i | \(0.756408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.8698 | −1.58679 | ||||||||
\(512\) | 11.8602 | 0.524152 | ||||||||
\(513\) | −6.39031 | −0.282139 | ||||||||
\(514\) | −1.72082 | −0.0759021 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 18.4144 | 0.810647 | ||||||||
\(517\) | 50.3788 | 2.21566 | ||||||||
\(518\) | 4.36926 | 0.191974 | ||||||||
\(519\) | 13.4977 | 0.592485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.6282 | −1.29803 | −0.649017 | − | 0.760774i | \(-0.724820\pi\) | ||||
−0.649017 | + | 0.760774i | \(0.724820\pi\) | |||||||
\(522\) | −0.521244 | −0.0228143 | ||||||||
\(523\) | −18.7648 | −0.820528 | −0.410264 | − | 0.911967i | \(-0.634563\pi\) | ||||
−0.410264 | + | 0.911967i | \(0.634563\pi\) | |||||||
\(524\) | −14.9195 | −0.651760 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.66837 | −0.116347 | ||||||||
\(527\) | −18.7128 | −0.815141 | ||||||||
\(528\) | 16.2137 | 0.705612 | ||||||||
\(529\) | −20.5945 | −0.895414 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.02997 | 0.261678 | ||||||||
\(532\) | 49.4663 | 2.14463 | ||||||||
\(533\) | −44.1957 | −1.91433 | ||||||||
\(534\) | 1.04108 | 0.0450518 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.53302 | 0.152603 | ||||||||
\(537\) | 23.0759 | 0.995801 | ||||||||
\(538\) | −0.422551 | −0.0182175 | ||||||||
\(539\) | −35.1181 | −1.51264 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.0478 | −1.42084 | −0.710419 | − | 0.703779i | \(-0.751494\pi\) | ||||
−0.710419 | + | 0.703779i | \(0.751494\pi\) | |||||||
\(542\) | −1.29496 | −0.0556235 | ||||||||
\(543\) | −3.23219 | −0.138707 | ||||||||
\(544\) | 8.33333 | 0.357288 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.75335 | −0.160629 | ||||||||
\(547\) | −20.6974 | −0.884958 | −0.442479 | − | 0.896779i | \(-0.645901\pi\) | ||||
−0.442479 | + | 0.896779i | \(0.645901\pi\) | |||||||
\(548\) | −26.0818 | −1.11416 | ||||||||
\(549\) | 9.14686 | 0.390378 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.3922 | −0.911338 | ||||||||
\(552\) | 0.960125 | 0.0408657 | ||||||||
\(553\) | −12.9426 | −0.550375 | ||||||||
\(554\) | −0.0264105 | −0.00112208 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.1495 | 1.10899 | ||||||||
\(557\) | −14.0895 | −0.596991 | −0.298496 | − | 0.954411i | \(-0.596485\pi\) | ||||
−0.298496 | + | 0.954411i | \(0.596485\pi\) | |||||||
\(558\) | −0.642779 | −0.0272110 | ||||||||
\(559\) | −57.3431 | −2.42535 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.0647 | 0.804911 | ||||||||
\(562\) | −4.62339 | −0.195026 | ||||||||
\(563\) | −39.1610 | −1.65044 | −0.825221 | − | 0.564811i | \(-0.808949\pi\) | ||||
−0.825221 | + | 0.564811i | \(0.808949\pi\) | |||||||
\(564\) | −23.6666 | −0.996544 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.76284 | 0.0740977 | ||||||||
\(567\) | −3.91791 | −0.164537 | ||||||||
\(568\) | −4.86345 | −0.204066 | ||||||||
\(569\) | 16.7962 | 0.704134 | 0.352067 | − | 0.935975i | \(-0.385479\pi\) | ||||
0.352067 | + | 0.935975i | \(0.385479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.40957 | −0.310081 | −0.155040 | − | 0.987908i | \(-0.549551\pi\) | ||||
−0.155040 | + | 0.987908i | \(0.549551\pi\) | |||||||
\(572\) | −51.1252 | −2.13765 | ||||||||
\(573\) | −7.48523 | −0.312700 | ||||||||
\(574\) | −4.38213 | −0.182906 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.42399 | −0.309333 | ||||||||
\(577\) | 4.43326 | 0.184559 | 0.0922795 | − | 0.995733i | \(-0.470585\pi\) | ||||
0.0922795 | + | 0.995733i | \(0.470585\pi\) | |||||||
\(578\) | 0.552444 | 0.0229786 | ||||||||
\(579\) | −23.6594 | −0.983250 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.1863 | 0.630034 | ||||||||
\(582\) | −1.02181 | −0.0423555 | ||||||||
\(583\) | −52.4338 | −2.17159 | ||||||||
\(584\) | −5.66764 | −0.234529 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.99011 | 0.206139 | ||||||||
\(587\) | 33.3266 | 1.37554 | 0.687769 | − | 0.725930i | \(-0.258590\pi\) | ||||
0.687769 | + | 0.725930i | \(0.258590\pi\) | |||||||
\(588\) | 16.4976 | 0.680348 | ||||||||
\(589\) | −26.3800 | −1.08697 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.502435 | −0.0206674 | ||||||||
\(592\) | −27.6111 | −1.13481 | ||||||||
\(593\) | 23.9282 | 0.982612 | 0.491306 | − | 0.870987i | \(-0.336520\pi\) | ||||
0.491306 | + | 0.870987i | \(0.336520\pi\) | |||||||
\(594\) | 0.654866 | 0.0268695 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.60766 | 0.0658522 | ||||||||
\(597\) | −12.0176 | −0.491848 | ||||||||
\(598\) | −1.48582 | −0.0607596 | ||||||||
\(599\) | 11.5448 | 0.471707 | 0.235854 | − | 0.971789i | \(-0.424211\pi\) | ||||
0.235854 | + | 0.971789i | \(0.424211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.2357 | 0.662268 | 0.331134 | − | 0.943584i | \(-0.392569\pi\) | ||||
0.331134 | + | 0.943584i | \(0.392569\pi\) | |||||||
\(602\) | −5.68572 | −0.231733 | ||||||||
\(603\) | −5.70713 | −0.232412 | ||||||||
\(604\) | 10.8719 | 0.442370 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.251825 | −0.0102297 | ||||||||
\(607\) | 10.3573 | 0.420391 | 0.210196 | − | 0.977659i | \(-0.432590\pi\) | ||||
0.210196 | + | 0.977659i | \(0.432590\pi\) | |||||||
\(608\) | 11.7478 | 0.476435 | ||||||||
\(609\) | −13.1156 | −0.531470 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 73.6988 | 2.98153 | ||||||||
\(612\) | −8.95607 | −0.362028 | ||||||||
\(613\) | −5.74382 | −0.231991 | −0.115995 | − | 0.993250i | \(-0.537006\pi\) | ||||
−0.115995 | + | 0.993250i | \(0.537006\pi\) | |||||||
\(614\) | 0.479147 | 0.0193368 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.2006 | −0.410995 | ||||||||
\(617\) | −11.0518 | −0.444929 | −0.222465 | − | 0.974941i | \(-0.571410\pi\) | ||||
−0.222465 | + | 0.974941i | \(0.571410\pi\) | |||||||
\(618\) | −0.385226 | −0.0154960 | ||||||||
\(619\) | 11.5390 | 0.463792 | 0.231896 | − | 0.972741i | \(-0.425507\pi\) | ||||
0.231896 | + | 0.972741i | \(0.425507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.55096 | −0.0622379 | ||||||||
\(622\) | 1.96488 | 0.0787844 | ||||||||
\(623\) | 26.1956 | 1.04951 | ||||||||
\(624\) | 23.7189 | 0.949517 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.78151 | 0.151139 | ||||||||
\(627\) | 26.8761 | 1.07333 | ||||||||
\(628\) | −1.18780 | −0.0473985 | ||||||||
\(629\) | −32.4661 | −1.29451 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.9927 | 0.716278 | 0.358139 | − | 0.933668i | \(-0.383411\pi\) | ||||
0.358139 | + | 0.933668i | \(0.383411\pi\) | |||||||
\(632\) | −2.04500 | −0.0813459 | ||||||||
\(633\) | 22.5450 | 0.896084 | ||||||||
\(634\) | −1.48345 | −0.0589154 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 24.6320 | 0.976723 | ||||||||
\(637\) | −51.3741 | −2.03551 | ||||||||
\(638\) | 2.19223 | 0.0867912 | ||||||||
\(639\) | 7.85627 | 0.310789 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.1989 | 0.481826 | 0.240913 | − | 0.970547i | \(-0.422553\pi\) | ||||
0.240913 | + | 0.970547i | \(0.422553\pi\) | |||||||
\(642\) | 0.155707 | 0.00614526 | ||||||||
\(643\) | −32.4279 | −1.27883 | −0.639416 | − | 0.768861i | \(-0.720824\pi\) | ||||
−0.639416 | + | 0.768861i | \(0.720824\pi\) | |||||||
\(644\) | 12.0057 | 0.473091 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.51039 | 0.177459 | ||||||||
\(647\) | −24.5804 | −0.966354 | −0.483177 | − | 0.875523i | \(-0.660517\pi\) | ||||
−0.483177 | + | 0.875523i | \(0.660517\pi\) | |||||||
\(648\) | −0.619053 | −0.0243187 | ||||||||
\(649\) | −25.3606 | −0.995492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.1736 | −0.633895 | ||||||||
\(652\) | −42.8118 | −1.67664 | ||||||||
\(653\) | 48.6767 | 1.90487 | 0.952433 | − | 0.304749i | \(-0.0985727\pi\) | ||||
0.952433 | + | 0.304749i | \(0.0985727\pi\) | |||||||
\(654\) | −2.52012 | −0.0985444 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 27.6924 | 1.08121 | ||||||||
\(657\) | 9.15535 | 0.357184 | ||||||||
\(658\) | 7.30744 | 0.284874 | ||||||||
\(659\) | 41.9601 | 1.63453 | 0.817267 | − | 0.576259i | \(-0.195488\pi\) | ||||
0.817267 | + | 0.576259i | \(0.195488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.9051 | −1.55213 | −0.776064 | − | 0.630654i | \(-0.782787\pi\) | ||||
−0.776064 | + | 0.630654i | \(0.782787\pi\) | |||||||
\(662\) | −0.102056 | −0.00396652 | ||||||||
\(663\) | 27.8896 | 1.08314 | ||||||||
\(664\) | 2.39953 | 0.0931197 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.11520 | −0.0432132 | ||||||||
\(667\) | −5.19199 | −0.201035 | ||||||||
\(668\) | 13.6190 | 0.526936 | ||||||||
\(669\) | −11.2208 | −0.433821 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.4695 | −1.48510 | ||||||||
\(672\) | 7.20258 | 0.277846 | ||||||||
\(673\) | −29.9856 | −1.15586 | −0.577930 | − | 0.816086i | \(-0.696139\pi\) | ||||
−0.577930 | + | 0.816086i | \(0.696139\pi\) | |||||||
\(674\) | 2.72506 | 0.104965 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −49.1059 | −1.88869 | ||||||||
\(677\) | −27.3960 | −1.05291 | −0.526456 | − | 0.850202i | \(-0.676480\pi\) | ||||
−0.526456 | + | 0.850202i | \(0.676480\pi\) | |||||||
\(678\) | 2.57658 | 0.0989528 | ||||||||
\(679\) | −25.7109 | −0.986695 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.79410 | 0.145390 | ||||||||
\(682\) | 2.70338 | 0.103518 | ||||||||
\(683\) | −3.71237 | −0.142050 | −0.0710249 | − | 0.997475i | \(-0.522627\pi\) | ||||
−0.0710249 | + | 0.997475i | \(0.522627\pi\) | |||||||
\(684\) | −12.6257 | −0.482755 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.823563 | −0.0314438 | ||||||||
\(687\) | 21.8196 | 0.832471 | ||||||||
\(688\) | 35.9303 | 1.36983 | ||||||||
\(689\) | −76.7051 | −2.92223 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.2686 | −1.11343 | −0.556714 | − | 0.830704i | \(-0.687938\pi\) | ||||
−0.556714 | + | 0.830704i | \(0.687938\pi\) | |||||||
\(692\) | 26.6682 | 1.01377 | ||||||||
\(693\) | 16.4778 | 0.625939 | ||||||||
\(694\) | 1.55691 | 0.0590994 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.07234 | −0.0785519 | ||||||||
\(697\) | 32.5617 | 1.23336 | ||||||||
\(698\) | 0.587237 | 0.0222273 | ||||||||
\(699\) | 2.52926 | 0.0956655 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.3801 | 1.48736 | 0.743682 | − | 0.668534i | \(-0.233078\pi\) | ||||
0.743682 | + | 0.668534i | \(0.233078\pi\) | |||||||
\(702\) | 0.957999 | 0.0361574 | ||||||||
\(703\) | −45.7686 | −1.72619 | ||||||||
\(704\) | 31.2235 | 1.17678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.68636 | −0.101102 | ||||||||
\(707\) | −6.33644 | −0.238306 | ||||||||
\(708\) | 11.9137 | 0.447746 | ||||||||
\(709\) | 24.6721 | 0.926582 | 0.463291 | − | 0.886206i | \(-0.346669\pi\) | ||||
0.463291 | + | 0.886206i | \(0.346669\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.30344 | 0.123889 | ||||||||
\(712\) | 4.13907 | 0.155118 | ||||||||
\(713\) | −6.40257 | −0.239778 | ||||||||
\(714\) | 2.76533 | 0.103490 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 45.5924 | 1.70387 | ||||||||
\(717\) | 0.0952535 | 0.00355731 | ||||||||
\(718\) | 3.17300 | 0.118415 | ||||||||
\(719\) | −23.8360 | −0.888933 | −0.444467 | − | 0.895795i | \(-0.646607\pi\) | ||||
−0.444467 | + | 0.895795i | \(0.646607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.69307 | −0.360989 | ||||||||
\(722\) | 3.40002 | 0.126536 | ||||||||
\(723\) | 19.8084 | 0.736681 | ||||||||
\(724\) | −6.38602 | −0.237335 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.04144 | −0.0386513 | ||||||||
\(727\) | −47.3237 | −1.75514 | −0.877570 | − | 0.479449i | \(-0.840837\pi\) | ||||
−0.877570 | + | 0.479449i | \(0.840837\pi\) | |||||||
\(728\) | −14.9224 | −0.553062 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.2482 | 1.56261 | ||||||||
\(732\) | 18.0719 | 0.667958 | ||||||||
\(733\) | −39.1381 | −1.44560 | −0.722799 | − | 0.691058i | \(-0.757145\pi\) | ||||
−0.722799 | + | 0.691058i | \(0.757145\pi\) | |||||||
\(734\) | −2.71183 | −0.100095 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.85124 | 0.105098 | ||||||||
\(737\) | 24.0028 | 0.884156 | ||||||||
\(738\) | 1.11849 | 0.0411720 | ||||||||
\(739\) | 20.0503 | 0.737564 | 0.368782 | − | 0.929516i | \(-0.379775\pi\) | ||||
0.368782 | + | 0.929516i | \(0.379775\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 39.3169 | 1.44434 | ||||||||
\(742\) | −7.60552 | −0.279208 | ||||||||
\(743\) | −52.0682 | −1.91020 | −0.955099 | − | 0.296287i | \(-0.904251\pi\) | ||||
−0.955099 | + | 0.296287i | \(0.904251\pi\) | |||||||
\(744\) | −2.55553 | −0.0936903 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.00847611 | 0.000310332 0 | ||||||||
\(747\) | −3.87613 | −0.141820 | ||||||||
\(748\) | 37.6671 | 1.37725 | ||||||||
\(749\) | 3.91791 | 0.143157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5212 | −0.675848 | −0.337924 | − | 0.941173i | \(-0.609725\pi\) | ||||
−0.337924 | + | 0.941173i | \(0.609725\pi\) | |||||||
\(752\) | −46.1786 | −1.68396 | ||||||||
\(753\) | 6.15527 | 0.224310 | ||||||||
\(754\) | 3.20700 | 0.116792 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.74083 | −0.281531 | ||||||||
\(757\) | 12.1790 | 0.442655 | 0.221327 | − | 0.975200i | \(-0.428961\pi\) | ||||
0.221327 | + | 0.975200i | \(0.428961\pi\) | |||||||
\(758\) | 0.879550 | 0.0319467 | ||||||||
\(759\) | 6.52297 | 0.236769 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.4420 | −1.39352 | −0.696760 | − | 0.717304i | \(-0.745376\pi\) | ||||
−0.696760 | + | 0.717304i | \(0.745376\pi\) | |||||||
\(762\) | 3.31859 | 0.120220 | ||||||||
\(763\) | −63.4114 | −2.29565 | ||||||||
\(764\) | −14.7890 | −0.535047 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.18688 | 0.187410 | ||||||||
\(767\) | −37.0999 | −1.33960 | ||||||||
\(768\) | −14.0955 | −0.508627 | ||||||||
\(769\) | 16.9516 | 0.611290 | 0.305645 | − | 0.952145i | \(-0.401128\pi\) | ||||
0.305645 | + | 0.952145i | \(0.401128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0517 | 0.398016 | ||||||||
\(772\) | −46.7451 | −1.68239 | ||||||||
\(773\) | 43.7652 | 1.57412 | 0.787062 | − | 0.616874i | \(-0.211601\pi\) | ||||
0.787062 | + | 0.616874i | \(0.211601\pi\) | |||||||
\(774\) | 1.45121 | 0.0521628 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.06248 | −0.145835 | ||||||||
\(777\) | −28.0608 | −1.00668 | ||||||||
\(778\) | −1.29614 | −0.0464688 | ||||||||
\(779\) | 45.9033 | 1.64466 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.0416 | −1.18232 | ||||||||
\(782\) | 1.09469 | 0.0391462 | ||||||||
\(783\) | 3.34760 | 0.119633 | ||||||||
\(784\) | 32.1903 | 1.14965 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.17579 | −0.0419389 | ||||||||
\(787\) | 37.0068 | 1.31915 | 0.659574 | − | 0.751639i | \(-0.270737\pi\) | ||||
0.659574 | + | 0.751639i | \(0.270737\pi\) | |||||||
\(788\) | −0.992688 | −0.0353630 | ||||||||
\(789\) | 17.1372 | 0.610099 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 64.8320 | 2.30516 | ||||||||
\(792\) | 2.60359 | 0.0925145 | ||||||||
\(793\) | −56.2768 | −1.99845 | ||||||||
\(794\) | −1.17744 | −0.0417858 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.7439 | −0.841579 | ||||||||
\(797\) | −1.30055 | −0.0460680 | −0.0230340 | − | 0.999735i | \(-0.507333\pi\) | ||||
−0.0230340 | + | 0.999735i | \(0.507333\pi\) | |||||||
\(798\) | 3.89838 | 0.138001 | ||||||||
\(799\) | −54.2985 | −1.92094 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.68613 | −0.236243 | ||||||||
\(802\) | −2.06312 | −0.0728515 | ||||||||
\(803\) | −38.5052 | −1.35882 | ||||||||
\(804\) | −11.2759 | −0.397670 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.95475 | 0.139300 | ||||||||
\(807\) | 2.71376 | 0.0955287 | ||||||||
\(808\) | −1.00119 | −0.0352219 | ||||||||
\(809\) | 18.8423 | 0.662459 | 0.331230 | − | 0.943550i | \(-0.392537\pi\) | ||||
0.331230 | + | 0.943550i | \(0.392537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.6066 | −0.372448 | −0.186224 | − | 0.982507i | \(-0.559625\pi\) | ||||
−0.186224 | + | 0.982507i | \(0.559625\pi\) | |||||||
\(812\) | −25.9132 | −0.909375 | ||||||||
\(813\) | 8.31668 | 0.291679 | ||||||||
\(814\) | 4.69027 | 0.164394 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −17.4752 | −0.611755 | ||||||||
\(817\) | 59.5587 | 2.08370 | ||||||||
\(818\) | −4.15606 | −0.145313 | ||||||||
\(819\) | 24.1052 | 0.842305 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.1312 | 0.458281 | 0.229141 | − | 0.973393i | \(-0.426408\pi\) | ||||
0.229141 | + | 0.973393i | \(0.426408\pi\) | |||||||
\(822\) | −2.05547 | −0.0716929 | ||||||||
\(823\) | 27.6426 | 0.963561 | 0.481781 | − | 0.876292i | \(-0.339990\pi\) | ||||
0.481781 | + | 0.876292i | \(0.339990\pi\) | |||||||
\(824\) | −1.53156 | −0.0533545 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.67856 | −0.127993 | ||||||||
\(827\) | −33.2253 | −1.15536 | −0.577679 | − | 0.816264i | \(-0.696041\pi\) | ||||
−0.577679 | + | 0.816264i | \(0.696041\pi\) | |||||||
\(828\) | −3.06432 | −0.106492 | ||||||||
\(829\) | 23.1934 | 0.805540 | 0.402770 | − | 0.915301i | \(-0.368047\pi\) | ||||
0.402770 | + | 0.915301i | \(0.368047\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.169617 | 0.00588395 | ||||||||
\(832\) | 45.6767 | 1.58356 | ||||||||
\(833\) | 37.8505 | 1.31144 | ||||||||
\(834\) | 2.06081 | 0.0713601 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 53.1006 | 1.83652 | ||||||||
\(837\) | 4.12813 | 0.142689 | ||||||||
\(838\) | −4.08586 | −0.141144 | ||||||||
\(839\) | 22.1976 | 0.766347 | 0.383174 | − | 0.923676i | \(-0.374831\pi\) | ||||
0.383174 | + | 0.923676i | \(0.374831\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.7936 | −0.613572 | ||||||||
\(842\) | 3.59489 | 0.123888 | ||||||||
\(843\) | 29.6929 | 1.02268 | ||||||||
\(844\) | 44.5434 | 1.53325 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.86514 | −0.0641248 | ||||||||
\(847\) | −26.2047 | −0.900404 | ||||||||
\(848\) | 48.0623 | 1.65047 | ||||||||
\(849\) | −11.3215 | −0.388554 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1083 | −0.380786 | ||||||||
\(852\) | 15.5221 | 0.531778 | ||||||||
\(853\) | 33.7654 | 1.15611 | 0.578053 | − | 0.815999i | \(-0.303813\pi\) | ||||
0.578053 | + | 0.815999i | \(0.303813\pi\) | |||||||
\(854\) | −5.58000 | −0.190944 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.619053 | 0.0211588 | ||||||||
\(857\) | 8.43718 | 0.288209 | 0.144104 | − | 0.989562i | \(-0.453970\pi\) | ||||
0.144104 | + | 0.989562i | \(0.453970\pi\) | |||||||
\(858\) | −4.02912 | −0.137552 | ||||||||
\(859\) | 10.2973 | 0.351338 | 0.175669 | − | 0.984449i | \(-0.443791\pi\) | ||||
0.175669 | + | 0.984449i | \(0.443791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.1434 | 0.959125 | ||||||||
\(862\) | −3.49600 | −0.119074 | ||||||||
\(863\) | 42.9481 | 1.46197 | 0.730985 | − | 0.682394i | \(-0.239061\pi\) | ||||
0.730985 | + | 0.682394i | \(0.239061\pi\) | |||||||
\(864\) | −1.83837 | −0.0625428 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.61853 | 0.0549999 | ||||||||
\(867\) | −3.54797 | −0.120495 | ||||||||
\(868\) | −31.9552 | −1.08463 | ||||||||
\(869\) | −13.8935 | −0.471304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.1136 | 1.18978 | ||||||||
\(872\) | −10.0194 | −0.339299 | ||||||||
\(873\) | 6.56241 | 0.222104 | ||||||||
\(874\) | 1.54323 | 0.0522005 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.0887 | 0.611162 | ||||||||
\(877\) | −39.5482 | −1.33545 | −0.667724 | − | 0.744409i | \(-0.732731\pi\) | ||||
−0.667724 | + | 0.744409i | \(0.732731\pi\) | |||||||
\(878\) | −4.86832 | −0.164298 | ||||||||
\(879\) | −32.0481 | −1.08095 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.331700 | 0.0111752 | 0.00558762 | − | 0.999984i | \(-0.498221\pi\) | ||||
0.00558762 | + | 0.999984i | \(0.498221\pi\) | |||||||
\(882\) | 1.30015 | 0.0437784 | ||||||||
\(883\) | 3.97236 | 0.133680 | 0.0668402 | − | 0.997764i | \(-0.478708\pi\) | ||||
0.0668402 | + | 0.997764i | \(0.478708\pi\) | |||||||
\(884\) | 55.1030 | 1.85331 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.523297 | 0.0175805 | ||||||||
\(887\) | −41.9397 | −1.40820 | −0.704099 | − | 0.710102i | \(-0.748649\pi\) | ||||
−0.704099 | + | 0.710102i | \(0.748649\pi\) | |||||||
\(888\) | −4.43377 | −0.148788 | ||||||||
\(889\) | 83.5027 | 2.80059 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.20576 | −0.140898 | ||||||||
\(892\) | −22.1695 | −0.742291 | ||||||||
\(893\) | −76.5464 | −2.56153 | ||||||||
\(894\) | 0.126698 | 0.00423740 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 18.9341 | 0.632545 | ||||||||
\(897\) | 9.54240 | 0.318612 | ||||||||
\(898\) | 0.843613 | 0.0281517 | ||||||||
\(899\) | 13.8193 | 0.460901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.5134 | 1.88273 | ||||||||
\(902\) | −4.70409 | −0.156629 | ||||||||
\(903\) | 36.5155 | 1.21516 | ||||||||
\(904\) | 10.2438 | 0.340705 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.856799 | 0.0284653 | ||||||||
\(907\) | −19.3926 | −0.643922 | −0.321961 | − | 0.946753i | \(-0.604342\pi\) | ||||
−0.321961 | + | 0.946753i | \(0.604342\pi\) | |||||||
\(908\) | 7.49622 | 0.248771 | ||||||||
\(909\) | 1.61730 | 0.0536425 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.3443 | −0.475248 | −0.237624 | − | 0.971357i | \(-0.576369\pi\) | ||||
−0.237624 | + | 0.971357i | \(0.576369\pi\) | |||||||
\(912\) | −24.6354 | −0.815760 | ||||||||
\(913\) | 16.3021 | 0.539520 | ||||||||
\(914\) | −2.24468 | −0.0742473 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.1103 | 1.42440 | ||||||||
\(917\) | −29.5852 | −0.976989 | ||||||||
\(918\) | −0.705817 | −0.0232954 | ||||||||
\(919\) | −44.0493 | −1.45305 | −0.726526 | − | 0.687138i | \(-0.758867\pi\) | ||||
−0.726526 | + | 0.687138i | \(0.758867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.07724 | −0.101398 | ||||||||
\(922\) | 4.40926 | 0.145211 | ||||||||
\(923\) | −48.3364 | −1.59101 | ||||||||
\(924\) | 32.5561 | 1.07102 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.76485 | −0.0908587 | ||||||||
\(927\) | 2.47404 | 0.0812582 | ||||||||
\(928\) | −6.15414 | −0.202020 | ||||||||
\(929\) | −11.7163 | −0.384400 | −0.192200 | − | 0.981356i | \(-0.561562\pi\) | ||||
−0.192200 | + | 0.981356i | \(0.561562\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53.3591 | 1.74877 | ||||||||
\(932\) | 4.99721 | 0.163689 | ||||||||
\(933\) | −12.6191 | −0.413130 | ||||||||
\(934\) | 5.05755 | 0.165488 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.80877 | 0.124494 | ||||||||
\(937\) | 14.2892 | 0.466808 | 0.233404 | − | 0.972380i | \(-0.425013\pi\) | ||||
0.233404 | + | 0.972380i | \(0.425013\pi\) | |||||||
\(938\) | 3.48161 | 0.113679 | ||||||||
\(939\) | −24.2861 | −0.792545 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.1338 | −0.362950 | −0.181475 | − | 0.983396i | \(-0.558087\pi\) | ||||
−0.181475 | + | 0.983396i | \(0.558087\pi\) | |||||||
\(942\) | −0.0936093 | −0.00304995 | ||||||||
\(943\) | 11.1410 | 0.362800 | ||||||||
\(944\) | 23.2463 | 0.756601 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.10346 | −0.198441 | ||||||||
\(947\) | 41.4663 | 1.34747 | 0.673737 | − | 0.738971i | \(-0.264688\pi\) | ||||
0.673737 | + | 0.738971i | \(0.264688\pi\) | |||||||
\(948\) | 6.52679 | 0.211980 | ||||||||
\(949\) | −56.3290 | −1.82852 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.52720 | 0.308941 | ||||||||
\(952\) | 10.9943 | 0.356326 | ||||||||
\(953\) | 33.3251 | 1.07951 | 0.539753 | − | 0.841824i | \(-0.318518\pi\) | ||||
0.539753 | + | 0.841824i | \(0.318518\pi\) | |||||||
\(954\) | 1.94122 | 0.0628493 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.188198 | 0.00608674 | ||||||||
\(957\) | −14.0792 | −0.455116 | ||||||||
\(958\) | 5.06331 | 0.163588 | ||||||||
\(959\) | −51.7200 | −1.67013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9585 | −0.450275 | ||||||||
\(962\) | 6.86137 | 0.221219 | ||||||||
\(963\) | −1.00000 | −0.0322245 | ||||||||
\(964\) | 39.1365 | 1.26050 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.946156 | 0.0304421 | ||||||||
\(967\) | −50.1545 | −1.61286 | −0.806431 | − | 0.591329i | \(-0.798604\pi\) | ||||
−0.806431 | + | 0.591329i | \(0.798604\pi\) | |||||||
\(968\) | −4.14050 | −0.133081 | ||||||||
\(969\) | −28.9672 | −0.930560 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.04282 | 0.0334657 | 0.0167329 | − | 0.999860i | \(-0.494674\pi\) | ||||
0.0167329 | + | 0.999860i | \(0.494674\pi\) | |||||||
\(972\) | 1.97576 | 0.0633724 | ||||||||
\(973\) | 51.8543 | 1.66237 | ||||||||
\(974\) | 5.42393 | 0.173794 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35.2622 | 1.12872 | ||||||||
\(977\) | 59.7517 | 1.91163 | 0.955813 | − | 0.293976i | \(-0.0949785\pi\) | ||||
0.955813 | + | 0.293976i | \(0.0949785\pi\) | |||||||
\(978\) | −3.37395 | −0.107887 | ||||||||
\(979\) | 28.1203 | 0.898728 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1850 | 0.516748 | ||||||||
\(982\) | −1.46809 | −0.0468488 | ||||||||
\(983\) | −19.2009 | −0.612413 | −0.306207 | − | 0.951965i | \(-0.599060\pi\) | ||||
−0.306207 | + | 0.951965i | \(0.599060\pi\) | |||||||
\(984\) | 4.44683 | 0.141760 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.36279 | −0.0752467 | ||||||||
\(987\) | −46.9307 | −1.49382 | ||||||||
\(988\) | 77.6805 | 2.47135 | ||||||||
\(989\) | 14.4552 | 0.459648 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.6856 | −0.847695 | −0.423848 | − | 0.905734i | \(-0.639321\pi\) | ||||
−0.423848 | + | 0.905734i | \(0.639321\pi\) | |||||||
\(992\) | −7.58905 | −0.240953 | ||||||||
\(993\) | 0.655437 | 0.0207997 | ||||||||
\(994\) | −4.79268 | −0.152015 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.65828 | −0.242662 | ||||||||
\(997\) | −10.7703 | −0.341099 | −0.170550 | − | 0.985349i | \(-0.554554\pi\) | ||||
−0.170550 | + | 0.985349i | \(0.554554\pi\) | |||||||
\(998\) | 1.73283 | 0.0548517 | ||||||||
\(999\) | 7.16219 | 0.226602 |
(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 | 8025.2.a.bf.1.8 | 12 | ||
5.4 | even | 2 | 1605.2.a.n.1.5 | ✓ | 12 | ||
15.14 | odd | 2 | 4815.2.a.u.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1605.2.a.n.1.5 | ✓ | 12 | 5.4 | even | 2 | ||
4815.2.a.u.1.8 | 12 | 15.14 | odd | 2 | |||
8025.2.a.bf.1.8 | 12 | 1.1 | even | 1 | trivial |