Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 26x^{16} + 281x^{14} - 1632x^{12} + 5482x^{10} - 10620x^{8} + 11052x^{6} - 5165x^{4} + 760x^{2} - 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 845) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.887876\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.887876 | −0.627823 | −0.313912 | − | 0.949452i | \(-0.601640\pi\) | ||||
−0.313912 | + | 0.949452i | \(0.601640\pi\) | |||||||
\(3\) | −1.26907 | −0.732697 | −0.366348 | − | 0.930478i | \(-0.619392\pi\) | ||||
−0.366348 | + | 0.930478i | \(0.619392\pi\) | |||||||
\(4\) | −1.21168 | −0.605838 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.12678 | 0.460004 | ||||||||
\(7\) | 2.28128 | 0.862242 | 0.431121 | − | 0.902294i | \(-0.358118\pi\) | ||||
0.431121 | + | 0.902294i | \(0.358118\pi\) | |||||||
\(8\) | 2.85157 | 1.00818 | ||||||||
\(9\) | −1.38947 | −0.463155 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.13829 | 0.946230 | 0.473115 | − | 0.881001i | \(-0.343130\pi\) | ||||
0.473115 | + | 0.881001i | \(0.343130\pi\) | |||||||
\(12\) | 1.53770 | 0.443896 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.02549 | −0.541335 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.108488 | −0.0271220 | ||||||||
\(17\) | −1.72423 | −0.418187 | −0.209094 | − | 0.977896i | \(-0.567051\pi\) | ||||
−0.209094 | + | 0.977896i | \(0.567051\pi\) | |||||||
\(18\) | 1.23367 | 0.290780 | ||||||||
\(19\) | 4.27007 | 0.979621 | 0.489810 | − | 0.871829i | \(-0.337066\pi\) | ||||
0.489810 | + | 0.871829i | \(0.337066\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.89510 | −0.631762 | ||||||||
\(22\) | −2.78641 | −0.594065 | ||||||||
\(23\) | −8.63424 | −1.80036 | −0.900182 | − | 0.435514i | \(-0.856567\pi\) | ||||
−0.900182 | + | 0.435514i | \(0.856567\pi\) | |||||||
\(24\) | −3.61884 | −0.738692 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.57053 | 1.07205 | ||||||||
\(28\) | −2.76417 | −0.522379 | ||||||||
\(29\) | −7.94250 | −1.47488 | −0.737442 | − | 0.675410i | \(-0.763967\pi\) | ||||
−0.737442 | + | 0.675410i | \(0.763967\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.17039 | −0.749024 | −0.374512 | − | 0.927222i | \(-0.622190\pi\) | ||||
−0.374512 | + | 0.927222i | \(0.622190\pi\) | |||||||
\(32\) | −5.60682 | −0.991154 | ||||||||
\(33\) | −3.98270 | −0.693300 | ||||||||
\(34\) | 1.53090 | 0.262548 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.68358 | 0.280597 | ||||||||
\(37\) | 8.80437 | 1.44743 | 0.723715 | − | 0.690099i | \(-0.242433\pi\) | ||||
0.723715 | + | 0.690099i | \(0.242433\pi\) | |||||||
\(38\) | −3.79129 | −0.615028 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.94700 | −0.460244 | −0.230122 | − | 0.973162i | \(-0.573912\pi\) | ||||
−0.230122 | + | 0.973162i | \(0.573912\pi\) | |||||||
\(42\) | 2.57049 | 0.396635 | ||||||||
\(43\) | 0.153762 | 0.0234486 | 0.0117243 | − | 0.999931i | \(-0.496268\pi\) | ||||
0.0117243 | + | 0.999931i | \(0.496268\pi\) | |||||||
\(44\) | −3.80259 | −0.573262 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.66614 | 1.13031 | ||||||||
\(47\) | 6.54786 | 0.955103 | 0.477552 | − | 0.878604i | \(-0.341524\pi\) | ||||
0.477552 | + | 0.878604i | \(0.341524\pi\) | |||||||
\(48\) | 0.137679 | 0.0198722 | ||||||||
\(49\) | −1.79577 | −0.256539 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.18817 | 0.306404 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.93126 | 0.265279 | 0.132640 | − | 0.991164i | \(-0.457655\pi\) | ||||
0.132640 | + | 0.991164i | \(0.457655\pi\) | |||||||
\(54\) | −4.94594 | −0.673057 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.50522 | 0.869297 | ||||||||
\(57\) | −5.41901 | −0.717765 | ||||||||
\(58\) | 7.05195 | 0.925967 | ||||||||
\(59\) | −5.51115 | −0.717490 | −0.358745 | − | 0.933436i | \(-0.616795\pi\) | ||||
−0.358745 | + | 0.933436i | \(0.616795\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.90052 | −1.26763 | −0.633816 | − | 0.773484i | \(-0.718512\pi\) | ||||
−0.633816 | + | 0.773484i | \(0.718512\pi\) | |||||||
\(62\) | 3.70279 | 0.470254 | ||||||||
\(63\) | −3.16976 | −0.399352 | ||||||||
\(64\) | 5.19513 | 0.649392 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.53615 | 0.435270 | ||||||||
\(67\) | −6.45526 | −0.788635 | −0.394318 | − | 0.918974i | \(-0.629019\pi\) | ||||
−0.394318 | + | 0.918974i | \(0.629019\pi\) | |||||||
\(68\) | 2.08921 | 0.253354 | ||||||||
\(69\) | 10.9574 | 1.31912 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.74432 | 0.563047 | 0.281524 | − | 0.959554i | \(-0.409160\pi\) | ||||
0.281524 | + | 0.959554i | \(0.409160\pi\) | |||||||
\(72\) | −3.96216 | −0.466945 | ||||||||
\(73\) | 13.1891 | 1.54367 | 0.771834 | − | 0.635824i | \(-0.219340\pi\) | ||||
0.771834 | + | 0.635824i | \(0.219340\pi\) | |||||||
\(74\) | −7.81719 | −0.908730 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.17394 | −0.593492 | ||||||||
\(77\) | 7.15931 | 0.815879 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4510 | 1.51335 | 0.756676 | − | 0.653791i | \(-0.226822\pi\) | ||||
0.756676 | + | 0.653791i | \(0.226822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.90099 | −0.322332 | ||||||||
\(82\) | 2.61657 | 0.288952 | ||||||||
\(83\) | 6.32511 | 0.694271 | 0.347136 | − | 0.937815i | \(-0.387154\pi\) | ||||
0.347136 | + | 0.937815i | \(0.387154\pi\) | |||||||
\(84\) | 3.50792 | 0.382745 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.136522 | −0.0147215 | ||||||||
\(87\) | 10.0796 | 1.08064 | ||||||||
\(88\) | 8.94905 | 0.953972 | ||||||||
\(89\) | −15.7373 | −1.66815 | −0.834077 | − | 0.551649i | \(-0.813999\pi\) | ||||
−0.834077 | + | 0.551649i | \(0.813999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.4619 | 1.09073 | ||||||||
\(93\) | 5.29250 | 0.548807 | ||||||||
\(94\) | −5.81368 | −0.599636 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.11543 | 0.726216 | ||||||||
\(97\) | 12.0815 | 1.22669 | 0.613345 | − | 0.789815i | \(-0.289823\pi\) | ||||
0.613345 | + | 0.789815i | \(0.289823\pi\) | |||||||
\(98\) | 1.59442 | 0.161061 | ||||||||
\(99\) | −4.36055 | −0.438251 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.79100 | 0.377218 | 0.188609 | − | 0.982052i | \(-0.439602\pi\) | ||||
0.188609 | + | 0.982052i | \(0.439602\pi\) | |||||||
\(102\) | −1.94282 | −0.192368 | ||||||||
\(103\) | 14.6259 | 1.44113 | 0.720564 | − | 0.693388i | \(-0.243883\pi\) | ||||
0.720564 | + | 0.693388i | \(0.243883\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.71472 | −0.166548 | ||||||||
\(107\) | −4.19100 | −0.405159 | −0.202580 | − | 0.979266i | \(-0.564933\pi\) | ||||
−0.202580 | + | 0.979266i | \(0.564933\pi\) | |||||||
\(108\) | −6.74968 | −0.649488 | ||||||||
\(109\) | −16.1460 | −1.54650 | −0.773252 | − | 0.634099i | \(-0.781371\pi\) | ||||
−0.773252 | + | 0.634099i | \(0.781371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.1733 | −1.06053 | ||||||||
\(112\) | −0.247491 | −0.0233857 | ||||||||
\(113\) | −3.51935 | −0.331072 | −0.165536 | − | 0.986204i | \(-0.552935\pi\) | ||||
−0.165536 | + | 0.986204i | \(0.552935\pi\) | |||||||
\(114\) | 4.81141 | 0.450629 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.62373 | 0.893541 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.89322 | 0.450457 | ||||||||
\(119\) | −3.93345 | −0.360579 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.15114 | −0.104649 | ||||||||
\(122\) | 8.79043 | 0.795848 | ||||||||
\(123\) | 3.73994 | 0.337219 | ||||||||
\(124\) | 5.05316 | 0.453787 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.81435 | 0.250722 | ||||||||
\(127\) | −2.42242 | −0.214955 | −0.107478 | − | 0.994208i | \(-0.534277\pi\) | ||||
−0.107478 | + | 0.994208i | \(0.534277\pi\) | |||||||
\(128\) | 6.60100 | 0.583451 | ||||||||
\(129\) | −0.195135 | −0.0171807 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.00647 | −0.437418 | −0.218709 | − | 0.975790i | \(-0.570184\pi\) | ||||
−0.218709 | + | 0.975790i | \(0.570184\pi\) | |||||||
\(132\) | 4.82575 | 0.420027 | ||||||||
\(133\) | 9.74121 | 0.844670 | ||||||||
\(134\) | 5.73147 | 0.495124 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.91676 | −0.421609 | ||||||||
\(137\) | −12.8154 | −1.09489 | −0.547447 | − | 0.836840i | \(-0.684400\pi\) | ||||
−0.547447 | + | 0.836840i | \(0.684400\pi\) | |||||||
\(138\) | −9.72885 | −0.828175 | ||||||||
\(139\) | −15.5289 | −1.31714 | −0.658571 | − | 0.752519i | \(-0.728839\pi\) | ||||
−0.658571 | + | 0.752519i | \(0.728839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.30968 | −0.699801 | ||||||||
\(142\) | −4.21237 | −0.353494 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.150740 | 0.0125617 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.7103 | −0.969151 | ||||||||
\(147\) | 2.27896 | 0.187965 | ||||||||
\(148\) | −10.6681 | −0.876908 | ||||||||
\(149\) | 0.0413812 | 0.00339008 | 0.00169504 | − | 0.999999i | \(-0.499460\pi\) | ||||
0.00169504 | + | 0.999999i | \(0.499460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.01321 | 0.489348 | 0.244674 | − | 0.969605i | \(-0.421319\pi\) | ||||
0.244674 | + | 0.969605i | \(0.421319\pi\) | |||||||
\(152\) | 12.1764 | 0.987636 | ||||||||
\(153\) | 2.39576 | 0.193686 | ||||||||
\(154\) | −6.35658 | −0.512228 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.7846 | −1.81841 | −0.909205 | − | 0.416348i | \(-0.863310\pi\) | ||||
−0.909205 | + | 0.416348i | \(0.863310\pi\) | |||||||
\(158\) | −11.9428 | −0.950117 | ||||||||
\(159\) | −2.45090 | −0.194369 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.6971 | −1.55235 | ||||||||
\(162\) | 2.57572 | 0.202367 | ||||||||
\(163\) | −1.52126 | −0.119154 | −0.0595772 | − | 0.998224i | \(-0.518975\pi\) | ||||
−0.0595772 | + | 0.998224i | \(0.518975\pi\) | |||||||
\(164\) | 3.57081 | 0.278833 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.61592 | −0.435880 | ||||||||
\(167\) | −0.0491982 | −0.00380707 | −0.00190353 | − | 0.999998i | \(-0.500606\pi\) | ||||
−0.00190353 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(168\) | −8.25557 | −0.636931 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.93311 | −0.453717 | ||||||||
\(172\) | −0.186310 | −0.0142060 | ||||||||
\(173\) | 9.00465 | 0.684611 | 0.342305 | − | 0.939589i | \(-0.388792\pi\) | ||||
0.342305 | + | 0.939589i | \(0.388792\pi\) | |||||||
\(174\) | −8.94941 | −0.678453 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.340467 | −0.0256637 | ||||||||
\(177\) | 6.99402 | 0.525703 | ||||||||
\(178\) | 13.9728 | 1.04731 | ||||||||
\(179\) | 22.8604 | 1.70866 | 0.854332 | − | 0.519727i | \(-0.173966\pi\) | ||||
0.854332 | + | 0.519727i | \(0.173966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.7138 | −1.31666 | −0.658328 | − | 0.752731i | \(-0.728736\pi\) | ||||
−0.658328 | + | 0.752731i | \(0.728736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5644 | 0.928789 | ||||||||
\(184\) | −24.6211 | −1.81509 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.69909 | −0.344554 | ||||||||
\(187\) | −5.41113 | −0.395701 | ||||||||
\(188\) | −7.93388 | −0.578638 | ||||||||
\(189\) | 12.7079 | 0.924366 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.73516 | 0.704411 | 0.352206 | − | 0.935923i | \(-0.385432\pi\) | ||||
0.352206 | + | 0.935923i | \(0.385432\pi\) | |||||||
\(192\) | −6.59298 | −0.475807 | ||||||||
\(193\) | 10.0009 | 0.719883 | 0.359942 | − | 0.932975i | \(-0.382797\pi\) | ||||
0.359942 | + | 0.932975i | \(0.382797\pi\) | |||||||
\(194\) | −10.7269 | −0.770145 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.17590 | 0.155421 | ||||||||
\(197\) | −5.99999 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 3.87162 | 0.275144 | ||||||||
\(199\) | 5.81284 | 0.412061 | 0.206031 | − | 0.978546i | \(-0.433945\pi\) | ||||
0.206031 | + | 0.978546i | \(0.433945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.19216 | 0.577831 | ||||||||
\(202\) | −3.36593 | −0.236826 | ||||||||
\(203\) | −18.1190 | −1.27171 | ||||||||
\(204\) | −2.65135 | −0.185632 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.9859 | −0.904774 | ||||||||
\(207\) | 11.9970 | 0.833848 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.4007 | 0.926946 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.71262 | 0.599801 | 0.299901 | − | 0.953970i | \(-0.403046\pi\) | ||||
0.299901 | + | 0.953970i | \(0.403046\pi\) | |||||||
\(212\) | −2.34006 | −0.160716 | ||||||||
\(213\) | −6.02087 | −0.412543 | ||||||||
\(214\) | 3.72109 | 0.254368 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.8848 | 1.08082 | ||||||||
\(217\) | −9.51381 | −0.645839 | ||||||||
\(218\) | 14.3356 | 0.970930 | ||||||||
\(219\) | −16.7379 | −1.13104 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.92055 | 0.665824 | ||||||||
\(223\) | 0.0454220 | 0.00304168 | 0.00152084 | − | 0.999999i | \(-0.499516\pi\) | ||||
0.00152084 | + | 0.999999i | \(0.499516\pi\) | |||||||
\(224\) | −12.7907 | −0.854615 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.12474 | 0.207855 | ||||||||
\(227\) | −6.42258 | −0.426281 | −0.213141 | − | 0.977022i | \(-0.568369\pi\) | ||||
−0.213141 | + | 0.977022i | \(0.568369\pi\) | |||||||
\(228\) | 6.56608 | 0.434849 | ||||||||
\(229\) | 7.27972 | 0.481057 | 0.240529 | − | 0.970642i | \(-0.422679\pi\) | ||||
0.240529 | + | 0.970642i | \(0.422679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.08565 | −0.597792 | ||||||||
\(232\) | −22.6486 | −1.48695 | ||||||||
\(233\) | −4.56107 | −0.298806 | −0.149403 | − | 0.988776i | \(-0.547735\pi\) | ||||
−0.149403 | + | 0.988776i | \(0.547735\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.67773 | 0.434683 | ||||||||
\(237\) | −17.0702 | −1.10883 | ||||||||
\(238\) | 3.49241 | 0.226380 | ||||||||
\(239\) | −16.9338 | −1.09536 | −0.547680 | − | 0.836688i | \(-0.684489\pi\) | ||||
−0.547680 | + | 0.836688i | \(0.684489\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.13059 | −0.394906 | −0.197453 | − | 0.980312i | \(-0.563267\pi\) | ||||
−0.197453 | + | 0.980312i | \(0.563267\pi\) | |||||||
\(242\) | 1.02207 | 0.0657010 | ||||||||
\(243\) | −13.0300 | −0.835878 | ||||||||
\(244\) | 11.9962 | 0.767979 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.32060 | −0.211714 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.8922 | −0.755152 | ||||||||
\(249\) | −8.02700 | −0.508690 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5843 | 0.731192 | 0.365596 | − | 0.930774i | \(-0.380865\pi\) | ||||
0.365596 | + | 0.930774i | \(0.380865\pi\) | |||||||
\(252\) | 3.84072 | 0.241943 | ||||||||
\(253\) | −27.0967 | −1.70356 | ||||||||
\(254\) | 2.15081 | 0.134954 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.2511 | −1.01570 | ||||||||
\(257\) | −12.4669 | −0.777665 | −0.388832 | − | 0.921309i | \(-0.627121\pi\) | ||||
−0.388832 | + | 0.921309i | \(0.627121\pi\) | |||||||
\(258\) | 0.173256 | 0.0107864 | ||||||||
\(259\) | 20.0852 | 1.24803 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.0358 | 0.683101 | ||||||||
\(262\) | 4.44513 | 0.274621 | ||||||||
\(263\) | −28.3288 | −1.74683 | −0.873416 | − | 0.486975i | \(-0.838100\pi\) | ||||
−0.873416 | + | 0.486975i | \(0.838100\pi\) | |||||||
\(264\) | −11.3570 | −0.698972 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.64898 | −0.530303 | ||||||||
\(267\) | 19.9717 | 1.22225 | ||||||||
\(268\) | 7.82168 | 0.477785 | ||||||||
\(269\) | −12.1886 | −0.743154 | −0.371577 | − | 0.928402i | \(-0.621183\pi\) | ||||
−0.371577 | + | 0.928402i | \(0.621183\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.6547 | −1.07245 | −0.536224 | − | 0.844076i | \(-0.680150\pi\) | ||||
−0.536224 | + | 0.844076i | \(0.680150\pi\) | |||||||
\(272\) | 0.187058 | 0.0113421 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.3785 | 0.687400 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.2769 | −0.799174 | ||||||||
\(277\) | −11.7250 | −0.704489 | −0.352245 | − | 0.935908i | \(-0.614581\pi\) | ||||
−0.352245 | + | 0.935908i | \(0.614581\pi\) | |||||||
\(278\) | 13.7877 | 0.826932 | ||||||||
\(279\) | 5.79461 | 0.346914 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.2642 | −1.20886 | −0.604430 | − | 0.796659i | \(-0.706599\pi\) | ||||
−0.604430 | + | 0.796659i | \(0.706599\pi\) | |||||||
\(282\) | 7.37796 | 0.439351 | ||||||||
\(283\) | −8.24330 | −0.490013 | −0.245007 | − | 0.969521i | \(-0.578790\pi\) | ||||
−0.245007 | + | 0.969521i | \(0.578790\pi\) | |||||||
\(284\) | −5.74858 | −0.341116 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.72292 | −0.396841 | ||||||||
\(288\) | 7.79048 | 0.459059 | ||||||||
\(289\) | −14.0270 | −0.825119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.3322 | −0.898792 | ||||||||
\(292\) | −15.9809 | −0.935213 | ||||||||
\(293\) | 21.3215 | 1.24562 | 0.622808 | − | 0.782375i | \(-0.285992\pi\) | ||||
0.622808 | + | 0.782375i | \(0.285992\pi\) | |||||||
\(294\) | −2.02343 | −0.118009 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 25.1063 | 1.45927 | ||||||||
\(297\) | 17.4819 | 1.01441 | ||||||||
\(298\) | −0.0367414 | −0.00212837 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.350775 | 0.0202183 | ||||||||
\(302\) | −5.33898 | −0.307224 | ||||||||
\(303\) | −4.81103 | −0.276387 | ||||||||
\(304\) | −0.463251 | −0.0265693 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.12714 | −0.121600 | ||||||||
\(307\) | −8.38560 | −0.478591 | −0.239296 | − | 0.970947i | \(-0.576917\pi\) | ||||
−0.239296 | + | 0.970947i | \(0.576917\pi\) | |||||||
\(308\) | −8.67476 | −0.494291 | ||||||||
\(309\) | −18.5612 | −1.05591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.82308 | −0.160082 | −0.0800412 | − | 0.996792i | \(-0.525505\pi\) | ||||
−0.0800412 | + | 0.996792i | \(0.525505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.1965 | −1.08505 | −0.542525 | − | 0.840040i | \(-0.682532\pi\) | ||||
−0.542525 | + | 0.840040i | \(0.682532\pi\) | |||||||
\(314\) | 20.2299 | 1.14164 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.2982 | −0.916846 | ||||||||
\(317\) | −5.76453 | −0.323768 | −0.161884 | − | 0.986810i | \(-0.551757\pi\) | ||||
−0.161884 | + | 0.986810i | \(0.551757\pi\) | |||||||
\(318\) | 2.17610 | 0.122029 | ||||||||
\(319\) | −24.9259 | −1.39558 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.31867 | 0.296859 | ||||||||
\(322\) | 17.4886 | 0.974600 | ||||||||
\(323\) | −7.36258 | −0.409665 | ||||||||
\(324\) | 3.51506 | 0.195281 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.35069 | 0.0748079 | ||||||||
\(327\) | 20.4903 | 1.13312 | ||||||||
\(328\) | −8.40357 | −0.464010 | ||||||||
\(329\) | 14.9375 | 0.823530 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.06009 | 0.223163 | 0.111581 | − | 0.993755i | \(-0.464408\pi\) | ||||
0.111581 | + | 0.993755i | \(0.464408\pi\) | |||||||
\(332\) | −7.66399 | −0.420616 | ||||||||
\(333\) | −12.2334 | −0.670385 | ||||||||
\(334\) | 0.0436819 | 0.00239017 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.314083 | 0.0171346 | ||||||||
\(337\) | −24.8339 | −1.35279 | −0.676395 | − | 0.736539i | \(-0.736459\pi\) | ||||
−0.676395 | + | 0.736539i | \(0.736459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.46629 | 0.242576 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.0879 | −0.708749 | ||||||||
\(342\) | 5.26787 | 0.284854 | ||||||||
\(343\) | −20.0656 | −1.08344 | ||||||||
\(344\) | 0.438465 | 0.0236404 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.99501 | −0.429815 | ||||||||
\(347\) | −29.1599 | −1.56538 | −0.782692 | − | 0.622409i | \(-0.786154\pi\) | ||||
−0.782692 | + | 0.622409i | \(0.786154\pi\) | |||||||
\(348\) | −12.2132 | −0.654695 | ||||||||
\(349\) | −7.29040 | −0.390246 | −0.195123 | − | 0.980779i | \(-0.562511\pi\) | ||||
−0.195123 | + | 0.980779i | \(0.562511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.5958 | −0.937860 | ||||||||
\(353\) | 13.9534 | 0.742665 | 0.371333 | − | 0.928500i | \(-0.378901\pi\) | ||||
0.371333 | + | 0.928500i | \(0.378901\pi\) | |||||||
\(354\) | −6.20982 | −0.330048 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 19.0685 | 1.01063 | ||||||||
\(357\) | 4.99181 | 0.264195 | ||||||||
\(358\) | −20.2972 | −1.07274 | ||||||||
\(359\) | −16.2637 | −0.858366 | −0.429183 | − | 0.903218i | \(-0.641198\pi\) | ||||
−0.429183 | + | 0.903218i | \(0.641198\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.766527 | −0.0403435 | ||||||||
\(362\) | 15.7276 | 0.826627 | ||||||||
\(363\) | 1.46087 | 0.0766759 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.1557 | −0.583115 | ||||||||
\(367\) | 34.4480 | 1.79817 | 0.899085 | − | 0.437774i | \(-0.144233\pi\) | ||||
0.899085 | + | 0.437774i | \(0.144233\pi\) | |||||||
\(368\) | 0.936712 | 0.0488295 | ||||||||
\(369\) | 4.09475 | 0.213164 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.40574 | 0.228735 | ||||||||
\(372\) | −6.41280 | −0.332488 | ||||||||
\(373\) | 23.2179 | 1.20218 | 0.601088 | − | 0.799183i | \(-0.294734\pi\) | ||||
0.601088 | + | 0.799183i | \(0.294734\pi\) | |||||||
\(374\) | 4.80442 | 0.248430 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.6717 | 0.962918 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −11.2831 | −0.580338 | ||||||||
\(379\) | −12.2666 | −0.630094 | −0.315047 | − | 0.949076i | \(-0.602020\pi\) | ||||
−0.315047 | + | 0.949076i | \(0.602020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.07422 | 0.157497 | ||||||||
\(382\) | −8.64361 | −0.442246 | ||||||||
\(383\) | 1.88332 | 0.0962329 | 0.0481165 | − | 0.998842i | \(-0.484678\pi\) | ||||
0.0481165 | + | 0.998842i | \(0.484678\pi\) | |||||||
\(384\) | −8.37712 | −0.427493 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.87959 | −0.451959 | ||||||||
\(387\) | −0.213648 | −0.0108603 | ||||||||
\(388\) | −14.6389 | −0.743176 | ||||||||
\(389\) | −20.0438 | −1.01626 | −0.508131 | − | 0.861280i | \(-0.669663\pi\) | ||||
−0.508131 | + | 0.861280i | \(0.669663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8874 | 0.752889 | ||||||||
\(392\) | −5.12078 | −0.258638 | ||||||||
\(393\) | 6.35356 | 0.320494 | ||||||||
\(394\) | 5.32725 | 0.268383 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.28357 | 0.265509 | ||||||||
\(397\) | 20.6134 | 1.03456 | 0.517279 | − | 0.855817i | \(-0.326945\pi\) | ||||
0.517279 | + | 0.855817i | \(0.326945\pi\) | |||||||
\(398\) | −5.16108 | −0.258702 | ||||||||
\(399\) | −12.3623 | −0.618887 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.8148 | 1.78851 | 0.894254 | − | 0.447560i | \(-0.147707\pi\) | ||||
0.894254 | + | 0.447560i | \(0.147707\pi\) | |||||||
\(402\) | −7.27362 | −0.362775 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.59346 | −0.228533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.0875 | 0.798407 | ||||||||
\(407\) | 27.6307 | 1.36960 | ||||||||
\(408\) | 6.23971 | 0.308912 | ||||||||
\(409\) | 0.221949 | 0.0109747 | 0.00548733 | − | 0.999985i | \(-0.498253\pi\) | ||||
0.00548733 | + | 0.999985i | \(0.498253\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.2636 | 0.802226 | ||||||||
\(412\) | −17.7218 | −0.873091 | ||||||||
\(413\) | −12.5725 | −0.618650 | ||||||||
\(414\) | −10.6518 | −0.523509 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.7072 | 0.965065 | ||||||||
\(418\) | −11.8982 | −0.581958 | ||||||||
\(419\) | 0.680369 | 0.0332382 | 0.0166191 | − | 0.999862i | \(-0.494710\pi\) | ||||
0.0166191 | + | 0.999862i | \(0.494710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.01932 | 0.0984155 | 0.0492078 | − | 0.998789i | \(-0.484330\pi\) | ||||
0.0492078 | + | 0.998789i | \(0.484330\pi\) | |||||||
\(422\) | −7.73572 | −0.376569 | ||||||||
\(423\) | −9.09803 | −0.442361 | ||||||||
\(424\) | 5.50712 | 0.267450 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.34578 | 0.259004 | ||||||||
\(427\) | −22.5858 | −1.09300 | ||||||||
\(428\) | 5.07814 | 0.245461 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.85397 | −0.330144 | −0.165072 | − | 0.986281i | \(-0.552786\pi\) | ||||
−0.165072 | + | 0.986281i | \(0.552786\pi\) | |||||||
\(432\) | −0.604336 | −0.0290761 | ||||||||
\(433\) | −0.520934 | −0.0250345 | −0.0125172 | − | 0.999922i | \(-0.503984\pi\) | ||||
−0.0125172 | + | 0.999922i | \(0.503984\pi\) | |||||||
\(434\) | 8.44708 | 0.405473 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.5637 | 0.936931 | ||||||||
\(437\) | −36.8688 | −1.76367 | ||||||||
\(438\) | 14.8612 | 0.710094 | ||||||||
\(439\) | −27.5889 | −1.31675 | −0.658374 | − | 0.752691i | \(-0.728756\pi\) | ||||
−0.658374 | + | 0.752691i | \(0.728756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.49517 | 0.118818 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.20684 | −0.342408 | −0.171204 | − | 0.985236i | \(-0.554766\pi\) | ||||
−0.171204 | + | 0.985236i | \(0.554766\pi\) | |||||||
\(444\) | 13.5385 | 0.642508 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.0403291 | −0.00190964 | ||||||||
\(447\) | −0.0525156 | −0.00248390 | ||||||||
\(448\) | 11.8515 | 0.559933 | ||||||||
\(449\) | −0.135634 | −0.00640098 | −0.00320049 | − | 0.999995i | \(-0.501019\pi\) | ||||
−0.00320049 | + | 0.999995i | \(0.501019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.24853 | −0.435496 | ||||||||
\(452\) | 4.26431 | 0.200576 | ||||||||
\(453\) | −7.63117 | −0.358544 | ||||||||
\(454\) | 5.70245 | 0.267629 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.4527 | −0.723638 | ||||||||
\(457\) | −0.308011 | −0.0144081 | −0.00720406 | − | 0.999974i | \(-0.502293\pi\) | ||||
−0.00720406 | + | 0.999974i | \(0.502293\pi\) | |||||||
\(458\) | −6.46349 | −0.302019 | ||||||||
\(459\) | −9.60488 | −0.448317 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.6721 | −1.33539 | −0.667696 | − | 0.744434i | \(-0.732719\pi\) | ||||
−0.667696 | + | 0.744434i | \(0.732719\pi\) | |||||||
\(462\) | 8.06693 | 0.375308 | ||||||||
\(463\) | 16.1023 | 0.748339 | 0.374169 | − | 0.927360i | \(-0.377928\pi\) | ||||
0.374169 | + | 0.927360i | \(0.377928\pi\) | |||||||
\(464\) | 0.861666 | 0.0400018 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.04967 | 0.187597 | ||||||||
\(467\) | 3.47589 | 0.160845 | 0.0804224 | − | 0.996761i | \(-0.474373\pi\) | ||||
0.0804224 | + | 0.996761i | \(0.474373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.7262 | −0.679994 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.9152 | 1.33234 | ||||||||
\(472\) | −15.7154 | −0.723361 | ||||||||
\(473\) | 0.482551 | 0.0221877 | ||||||||
\(474\) | 15.1562 | 0.696148 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.76606 | 0.218452 | ||||||||
\(477\) | −2.68342 | −0.122865 | ||||||||
\(478\) | 15.0352 | 0.687692 | ||||||||
\(479\) | 14.4576 | 0.660587 | 0.330293 | − | 0.943878i | \(-0.392852\pi\) | ||||
0.330293 | + | 0.943878i | \(0.392852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.44320 | 0.247931 | ||||||||
\(483\) | 24.9970 | 1.13740 | ||||||||
\(484\) | 1.39481 | 0.0634003 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 11.5691 | 0.524783 | ||||||||
\(487\) | −2.91278 | −0.131991 | −0.0659954 | − | 0.997820i | \(-0.521022\pi\) | ||||
−0.0659954 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(488\) | −28.2320 | −1.27800 | ||||||||
\(489\) | 1.93058 | 0.0873040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.60764 | −0.343328 | −0.171664 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171664 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(492\) | −4.53160 | −0.204300 | ||||||||
\(493\) | 13.6947 | 0.616778 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.452437 | 0.0203150 | ||||||||
\(497\) | 10.8231 | 0.485483 | ||||||||
\(498\) | 7.12698 | 0.319368 | ||||||||
\(499\) | 4.07246 | 0.182309 | 0.0911543 | − | 0.995837i | \(-0.470944\pi\) | ||||
0.0911543 | + | 0.995837i | \(0.470944\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0624358 | 0.00278943 | ||||||||
\(502\) | −10.2854 | −0.459059 | ||||||||
\(503\) | −34.0821 | −1.51965 | −0.759823 | − | 0.650130i | \(-0.774714\pi\) | ||||
−0.759823 | + | 0.650130i | \(0.774714\pi\) | |||||||
\(504\) | −9.03879 | −0.402620 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 24.0586 | 1.06953 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.93519 | 0.130228 | ||||||||
\(509\) | −1.30664 | −0.0579159 | −0.0289579 | − | 0.999581i | \(-0.509219\pi\) | ||||
−0.0289579 | + | 0.999581i | \(0.509219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0880 | 1.33102 | ||||||||
\(512\) | 1.22700 | 0.0542260 | ||||||||
\(513\) | 23.7865 | 1.05020 | ||||||||
\(514\) | 11.0691 | 0.488236 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.236441 | 0.0104087 | ||||||||
\(517\) | 20.5491 | 0.903747 | ||||||||
\(518\) | −17.8332 | −0.783545 | ||||||||
\(519\) | −11.4275 | −0.501612 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.550102 | −0.0241004 | −0.0120502 | − | 0.999927i | \(-0.503836\pi\) | ||||
−0.0120502 | + | 0.999927i | \(0.503836\pi\) | |||||||
\(522\) | −9.79845 | −0.428866 | ||||||||
\(523\) | 17.0531 | 0.745679 | 0.372840 | − | 0.927896i | \(-0.378384\pi\) | ||||
0.372840 | + | 0.927896i | \(0.378384\pi\) | |||||||
\(524\) | 6.06622 | 0.265004 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.1525 | 1.09670 | ||||||||
\(527\) | 7.19071 | 0.313232 | ||||||||
\(528\) | 0.432076 | 0.0188037 | ||||||||
\(529\) | 51.5501 | 2.24131 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.65755 | 0.332309 | ||||||||
\(532\) | −11.8032 | −0.511733 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −17.7324 | −0.767357 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −18.4076 | −0.795088 | ||||||||
\(537\) | −29.0114 | −1.25193 | ||||||||
\(538\) | 10.8220 | 0.466569 | ||||||||
\(539\) | −5.63566 | −0.242745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.1330 | −1.29552 | −0.647759 | − | 0.761845i | \(-0.724294\pi\) | ||||
−0.647759 | + | 0.761845i | \(0.724294\pi\) | |||||||
\(542\) | 15.6752 | 0.673307 | ||||||||
\(543\) | 22.4800 | 0.964709 | ||||||||
\(544\) | 9.66744 | 0.414488 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.36791 | −0.229515 | −0.114758 | − | 0.993394i | \(-0.536609\pi\) | ||||
−0.114758 | + | 0.993394i | \(0.536609\pi\) | |||||||
\(548\) | 15.5281 | 0.663329 | ||||||||
\(549\) | 13.7564 | 0.587110 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.9150 | −1.44483 | ||||||||
\(552\) | 31.2459 | 1.32991 | ||||||||
\(553\) | 30.6854 | 1.30487 | ||||||||
\(554\) | 10.4104 | 0.442294 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.8160 | 0.797974 | ||||||||
\(557\) | −7.05530 | −0.298943 | −0.149471 | − | 0.988766i | \(-0.547757\pi\) | ||||
−0.149471 | + | 0.988766i | \(0.547757\pi\) | |||||||
\(558\) | −5.14490 | −0.217801 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.86710 | 0.289929 | ||||||||
\(562\) | 17.9921 | 0.758950 | ||||||||
\(563\) | −31.6656 | −1.33455 | −0.667273 | − | 0.744814i | \(-0.732538\pi\) | ||||
−0.667273 | + | 0.744814i | \(0.732538\pi\) | |||||||
\(564\) | 10.0686 | 0.423966 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.31903 | 0.307642 | ||||||||
\(567\) | −6.61795 | −0.277928 | ||||||||
\(568\) | 13.5288 | 0.567655 | ||||||||
\(569\) | 13.5818 | 0.569380 | 0.284690 | − | 0.958620i | \(-0.408109\pi\) | ||||
0.284690 | + | 0.958620i | \(0.408109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.7338 | −1.45356 | −0.726782 | − | 0.686868i | \(-0.758985\pi\) | ||||
−0.726782 | + | 0.686868i | \(0.758985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.3546 | −0.516120 | ||||||||
\(574\) | 5.96912 | 0.249146 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.21846 | −0.300769 | ||||||||
\(577\) | 43.8511 | 1.82555 | 0.912773 | − | 0.408467i | \(-0.133937\pi\) | ||||
0.912773 | + | 0.408467i | \(0.133937\pi\) | |||||||
\(578\) | 12.4543 | 0.518029 | ||||||||
\(579\) | −12.6919 | −0.527456 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4293 | 0.598630 | ||||||||
\(582\) | 13.6131 | 0.564283 | ||||||||
\(583\) | 6.06085 | 0.251015 | ||||||||
\(584\) | 37.6097 | 1.55630 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.9308 | −0.782026 | ||||||||
\(587\) | −4.11991 | −0.170047 | −0.0850235 | − | 0.996379i | \(-0.527097\pi\) | ||||
−0.0850235 | + | 0.996379i | \(0.527097\pi\) | |||||||
\(588\) | −2.76136 | −0.113877 | ||||||||
\(589\) | −17.8078 | −0.733759 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.61440 | 0.313215 | ||||||||
\(592\) | −0.955169 | −0.0392572 | ||||||||
\(593\) | 2.16800 | 0.0890292 | 0.0445146 | − | 0.999009i | \(-0.485826\pi\) | ||||
0.0445146 | + | 0.999009i | \(0.485826\pi\) | |||||||
\(594\) | −15.5218 | −0.636867 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.0501407 | −0.00205384 | ||||||||
\(597\) | −7.37689 | −0.301916 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.1445 | −1.51768 | −0.758841 | − | 0.651276i | \(-0.774234\pi\) | ||||
−0.758841 | + | 0.651276i | \(0.774234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.11320 | −0.0454085 | −0.0227043 | − | 0.999742i | \(-0.507228\pi\) | ||||
−0.0227043 | + | 0.999742i | \(0.507228\pi\) | |||||||
\(602\) | −0.311445 | −0.0126935 | ||||||||
\(603\) | 8.96936 | 0.365261 | ||||||||
\(604\) | −7.28606 | −0.296466 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.27160 | 0.173522 | ||||||||
\(607\) | 8.21780 | 0.333550 | 0.166775 | − | 0.985995i | \(-0.446665\pi\) | ||||
0.166775 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(608\) | −23.9415 | −0.970955 | ||||||||
\(609\) | 22.9943 | 0.931776 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.90289 | −0.117342 | ||||||||
\(613\) | −28.6108 | −1.15558 | −0.577790 | − | 0.816185i | \(-0.696085\pi\) | ||||
−0.577790 | + | 0.816185i | \(0.696085\pi\) | |||||||
\(614\) | 7.44537 | 0.300471 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.4153 | 0.822555 | ||||||||
\(617\) | 0.844622 | 0.0340032 | 0.0170016 | − | 0.999855i | \(-0.494588\pi\) | ||||
0.0170016 | + | 0.999855i | \(0.494588\pi\) | |||||||
\(618\) | 16.4801 | 0.662925 | ||||||||
\(619\) | 9.06143 | 0.364210 | 0.182105 | − | 0.983279i | \(-0.441709\pi\) | ||||
0.182105 | + | 0.983279i | \(0.441709\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.0973 | −1.93008 | ||||||||
\(622\) | 2.50655 | 0.100503 | ||||||||
\(623\) | −35.9012 | −1.43835 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.0441 | 0.681219 | ||||||||
\(627\) | −17.0064 | −0.679171 | ||||||||
\(628\) | 27.6076 | 1.10166 | ||||||||
\(629\) | −15.1808 | −0.605297 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.1174 | −0.562003 | −0.281002 | − | 0.959707i | \(-0.590667\pi\) | ||||
−0.281002 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(632\) | 38.3564 | 1.52573 | ||||||||
\(633\) | −11.0569 | −0.439472 | ||||||||
\(634\) | 5.11819 | 0.203269 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.96970 | 0.117756 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.1311 | 0.876177 | ||||||||
\(639\) | −6.59208 | −0.260778 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.19011 | −0.362988 | −0.181494 | − | 0.983392i | \(-0.558093\pi\) | ||||
−0.181494 | + | 0.983392i | \(0.558093\pi\) | |||||||
\(642\) | −4.72232 | −0.186375 | ||||||||
\(643\) | −4.14150 | −0.163325 | −0.0816624 | − | 0.996660i | \(-0.526023\pi\) | ||||
−0.0816624 | + | 0.996660i | \(0.526023\pi\) | |||||||
\(644\) | 23.8665 | 0.940472 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.53706 | 0.257197 | ||||||||
\(647\) | 4.86077 | 0.191097 | 0.0955483 | − | 0.995425i | \(-0.469540\pi\) | ||||
0.0955483 | + | 0.995425i | \(0.469540\pi\) | |||||||
\(648\) | −8.27236 | −0.324969 | ||||||||
\(649\) | −17.2956 | −0.678911 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0737 | 0.473204 | ||||||||
\(652\) | 1.84328 | 0.0721883 | ||||||||
\(653\) | 42.8456 | 1.67668 | 0.838340 | − | 0.545148i | \(-0.183527\pi\) | ||||
0.838340 | + | 0.545148i | \(0.183527\pi\) | |||||||
\(654\) | −18.1929 | −0.711398 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.319714 | 0.0124827 | ||||||||
\(657\) | −18.3258 | −0.714958 | ||||||||
\(658\) | −13.2626 | −0.517031 | ||||||||
\(659\) | 0.355635 | 0.0138536 | 0.00692678 | − | 0.999976i | \(-0.497795\pi\) | ||||
0.00692678 | + | 0.999976i | \(0.497795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9399 | 0.503303 | 0.251651 | − | 0.967818i | \(-0.419026\pi\) | ||||
0.251651 | + | 0.967818i | \(0.419026\pi\) | |||||||
\(662\) | −3.60485 | −0.140107 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.0365 | 0.699952 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.8617 | 0.420883 | ||||||||
\(667\) | 68.5774 | 2.65533 | ||||||||
\(668\) | 0.0596123 | 0.00230647 | ||||||||
\(669\) | −0.0576436 | −0.00222863 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.0707 | −1.19947 | ||||||||
\(672\) | 16.2323 | 0.626174 | ||||||||
\(673\) | −27.5011 | −1.06009 | −0.530045 | − | 0.847970i | \(-0.677825\pi\) | ||||
−0.530045 | + | 0.847970i | \(0.677825\pi\) | |||||||
\(674\) | 22.0494 | 0.849312 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6270 | −0.485297 | −0.242648 | − | 0.970114i | \(-0.578016\pi\) | ||||
−0.242648 | + | 0.970114i | \(0.578016\pi\) | |||||||
\(678\) | −3.96551 | −0.152295 | ||||||||
\(679\) | 27.5613 | 1.05770 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.15069 | 0.312335 | ||||||||
\(682\) | 11.6204 | 0.444969 | ||||||||
\(683\) | −29.0442 | −1.11135 | −0.555673 | − | 0.831401i | \(-0.687539\pi\) | ||||
−0.555673 | + | 0.831401i | \(0.687539\pi\) | |||||||
\(684\) | 7.18901 | 0.274879 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.8158 | 0.680209 | ||||||||
\(687\) | −9.23846 | −0.352469 | ||||||||
\(688\) | −0.0166814 | −0.000635972 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.54360 | −0.210889 | −0.105444 | − | 0.994425i | \(-0.533626\pi\) | ||||
−0.105444 | + | 0.994425i | \(0.533626\pi\) | |||||||
\(692\) | −10.9107 | −0.414763 | ||||||||
\(693\) | −9.94762 | −0.377879 | ||||||||
\(694\) | 25.8904 | 0.982785 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 28.7426 | 1.08949 | ||||||||
\(697\) | 5.08130 | 0.192468 | ||||||||
\(698\) | 6.47297 | 0.245006 | ||||||||
\(699\) | 5.78831 | 0.218934 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.14386 | −0.269820 | −0.134910 | − | 0.990858i | \(-0.543075\pi\) | ||||
−0.134910 | + | 0.990858i | \(0.543075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.5953 | 1.41793 | ||||||||
\(704\) | 16.3038 | 0.614474 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.3889 | −0.466262 | ||||||||
\(707\) | 8.64831 | 0.325253 | ||||||||
\(708\) | −8.47449 | −0.318491 | ||||||||
\(709\) | 33.2696 | 1.24947 | 0.624733 | − | 0.780838i | \(-0.285208\pi\) | ||||
0.624733 | + | 0.780838i | \(0.285208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.6897 | −0.700917 | ||||||||
\(712\) | −44.8761 | −1.68180 | ||||||||
\(713\) | 36.0081 | 1.34851 | ||||||||
\(714\) | −4.43211 | −0.165868 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −27.6994 | −1.03517 | ||||||||
\(717\) | 21.4902 | 0.802567 | ||||||||
\(718\) | 14.4402 | 0.538902 | ||||||||
\(719\) | 2.93123 | 0.109317 | 0.0546583 | − | 0.998505i | \(-0.482593\pi\) | ||||
0.0546583 | + | 0.998505i | \(0.482593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.3656 | 1.24260 | ||||||||
\(722\) | 0.680581 | 0.0253286 | ||||||||
\(723\) | 7.78013 | 0.289346 | ||||||||
\(724\) | 21.4634 | 0.797680 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.29707 | −0.0481389 | ||||||||
\(727\) | 14.9385 | 0.554039 | 0.277019 | − | 0.960864i | \(-0.410653\pi\) | ||||
0.277019 | + | 0.960864i | \(0.410653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.2390 | 0.934777 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.265122 | −0.00980589 | ||||||||
\(732\) | −15.2240 | −0.562696 | ||||||||
\(733\) | −9.64485 | −0.356241 | −0.178120 | − | 0.984009i | \(-0.557002\pi\) | ||||
−0.178120 | + | 0.984009i | \(0.557002\pi\) | |||||||
\(734\) | −30.5855 | −1.12893 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 48.4106 | 1.78444 | ||||||||
\(737\) | −20.2585 | −0.746230 | ||||||||
\(738\) | −3.63563 | −0.133830 | ||||||||
\(739\) | 38.6006 | 1.41995 | 0.709973 | − | 0.704229i | \(-0.248707\pi\) | ||||
0.709973 | + | 0.704229i | \(0.248707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.91175 | −0.143605 | ||||||||
\(743\) | −43.3909 | −1.59186 | −0.795928 | − | 0.605391i | \(-0.793017\pi\) | ||||
−0.795928 | + | 0.605391i | \(0.793017\pi\) | |||||||
\(744\) | 15.0919 | 0.553298 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.6146 | −0.754754 | ||||||||
\(747\) | −8.78853 | −0.321555 | ||||||||
\(748\) | 6.55654 | 0.239731 | ||||||||
\(749\) | −9.56084 | −0.349345 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.8770 | −1.27268 | −0.636341 | − | 0.771408i | \(-0.719553\pi\) | ||||
−0.636341 | + | 0.771408i | \(0.719553\pi\) | |||||||
\(752\) | −0.710364 | −0.0259043 | ||||||||
\(753\) | −14.7012 | −0.535742 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −15.3979 | −0.560016 | ||||||||
\(757\) | −11.6518 | −0.423493 | −0.211746 | − | 0.977325i | \(-0.567915\pi\) | ||||
−0.211746 | + | 0.977325i | \(0.567915\pi\) | |||||||
\(758\) | 10.8912 | 0.395588 | ||||||||
\(759\) | 34.3876 | 1.24819 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.0684 | −1.77873 | −0.889364 | − | 0.457200i | \(-0.848852\pi\) | ||||
−0.889364 | + | 0.457200i | \(0.848852\pi\) | |||||||
\(762\) | −2.72952 | −0.0988803 | ||||||||
\(763\) | −36.8334 | −1.33346 | ||||||||
\(764\) | −11.7959 | −0.426759 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.67215 | −0.0604172 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 20.6238 | 0.744197 | ||||||||
\(769\) | 40.1202 | 1.44677 | 0.723386 | − | 0.690444i | \(-0.242585\pi\) | ||||
0.723386 | + | 0.690444i | \(0.242585\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.8214 | 0.569792 | ||||||||
\(772\) | −12.1179 | −0.436133 | ||||||||
\(773\) | −11.6461 | −0.418883 | −0.209441 | − | 0.977821i | \(-0.567165\pi\) | ||||
−0.209441 | + | 0.977821i | \(0.567165\pi\) | |||||||
\(774\) | 0.189693 | 0.00681836 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 34.4512 | 1.23673 | ||||||||
\(777\) | −25.4895 | −0.914431 | ||||||||
\(778\) | 17.7964 | 0.638032 | ||||||||
\(779\) | −12.5839 | −0.450864 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.8891 | 0.532772 | ||||||||
\(782\) | −13.2182 | −0.472681 | ||||||||
\(783\) | −44.2439 | −1.58115 | ||||||||
\(784\) | 0.194820 | 0.00695786 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.64117 | −0.201214 | ||||||||
\(787\) | −25.5641 | −0.911262 | −0.455631 | − | 0.890169i | \(-0.650586\pi\) | ||||
−0.455631 | + | 0.890169i | \(0.650586\pi\) | |||||||
\(788\) | 7.27005 | 0.258985 | ||||||||
\(789\) | 35.9512 | 1.27990 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.02860 | −0.285464 | ||||||||
\(792\) | −12.4344 | −0.441837 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −18.3022 | −0.649519 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.04328 | −0.249642 | ||||||||
\(797\) | −45.7347 | −1.62001 | −0.810003 | − | 0.586425i | \(-0.800535\pi\) | ||||
−0.810003 | + | 0.586425i | \(0.800535\pi\) | |||||||
\(798\) | 10.9761 | 0.388551 | ||||||||
\(799\) | −11.2900 | −0.399412 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.8665 | 0.772614 | ||||||||
\(802\) | −31.7991 | −1.12287 | ||||||||
\(803\) | 41.3912 | 1.46067 | ||||||||
\(804\) | −9.92625 | −0.350072 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.4682 | 0.544506 | ||||||||
\(808\) | 10.8103 | 0.380305 | ||||||||
\(809\) | 31.4562 | 1.10594 | 0.552970 | − | 0.833201i | \(-0.313494\pi\) | ||||
0.552970 | + | 0.833201i | \(0.313494\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.0128 | 1.33481 | 0.667406 | − | 0.744694i | \(-0.267405\pi\) | ||||
0.667406 | + | 0.744694i | \(0.267405\pi\) | |||||||
\(812\) | 21.9544 | 0.770449 | ||||||||
\(813\) | 22.4050 | 0.785779 | ||||||||
\(814\) | −24.5326 | −0.859868 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.237390 | −0.00831031 | ||||||||
\(817\) | 0.656576 | 0.0229707 | ||||||||
\(818\) | −0.197063 | −0.00689015 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 55.7593 | 1.94601 | 0.973006 | − | 0.230778i | \(-0.0741272\pi\) | ||||
0.973006 | + | 0.230778i | \(0.0741272\pi\) | |||||||
\(822\) | −14.4401 | −0.503656 | ||||||||
\(823\) | 30.7203 | 1.07084 | 0.535420 | − | 0.844586i | \(-0.320153\pi\) | ||||
0.535420 | + | 0.844586i | \(0.320153\pi\) | |||||||
\(824\) | 41.7067 | 1.45292 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.1628 | 0.388403 | ||||||||
\(827\) | 37.7024 | 1.31104 | 0.655520 | − | 0.755177i | \(-0.272449\pi\) | ||||
0.655520 | + | 0.755177i | \(0.272449\pi\) | |||||||
\(828\) | −14.5365 | −0.505177 | ||||||||
\(829\) | −13.8208 | −0.480015 | −0.240008 | − | 0.970771i | \(-0.577150\pi\) | ||||
−0.240008 | + | 0.970771i | \(0.577150\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.8799 | 0.516177 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.09633 | 0.107281 | ||||||||
\(834\) | −17.4975 | −0.605890 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16.2373 | −0.561579 | ||||||||
\(837\) | −23.2313 | −0.802990 | ||||||||
\(838\) | −0.604083 | −0.0208677 | ||||||||
\(839\) | −16.0902 | −0.555495 | −0.277747 | − | 0.960654i | \(-0.589588\pi\) | ||||
−0.277747 | + | 0.960654i | \(0.589588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.0833 | 1.17528 | ||||||||
\(842\) | −1.79290 | −0.0617875 | ||||||||
\(843\) | 25.7166 | 0.885727 | ||||||||
\(844\) | −10.5569 | −0.363382 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.07792 | 0.277725 | ||||||||
\(847\) | −2.62607 | −0.0902327 | ||||||||
\(848\) | −0.209519 | −0.00719490 | ||||||||
\(849\) | 10.4613 | 0.359031 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −76.0191 | −2.60590 | ||||||||
\(852\) | 7.29534 | 0.249934 | ||||||||
\(853\) | 48.9861 | 1.67725 | 0.838625 | − | 0.544709i | \(-0.183360\pi\) | ||||
0.838625 | + | 0.544709i | \(0.183360\pi\) | |||||||
\(854\) | 20.0534 | 0.686213 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.9509 | −0.408475 | ||||||||
\(857\) | 8.57696 | 0.292983 | 0.146492 | − | 0.989212i | \(-0.453202\pi\) | ||||
0.146492 | + | 0.989212i | \(0.453202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.9983 | −0.614095 | −0.307048 | − | 0.951694i | \(-0.599341\pi\) | ||||
−0.307048 | + | 0.951694i | \(0.599341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.53184 | 0.290764 | ||||||||
\(862\) | 6.08548 | 0.207272 | ||||||||
\(863\) | 2.18400 | 0.0743444 | 0.0371722 | − | 0.999309i | \(-0.488165\pi\) | ||||
0.0371722 | + | 0.999309i | \(0.488165\pi\) | |||||||
\(864\) | −31.2329 | −1.06257 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.462525 | 0.0157172 | ||||||||
\(867\) | 17.8013 | 0.604562 | ||||||||
\(868\) | 11.5277 | 0.391274 | ||||||||
\(869\) | 42.2130 | 1.43198 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −46.0414 | −1.55916 | ||||||||
\(873\) | −16.7868 | −0.568148 | ||||||||
\(874\) | 32.7349 | 1.10727 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.2809 | 0.685228 | ||||||||
\(877\) | −27.9605 | −0.944158 | −0.472079 | − | 0.881556i | \(-0.656496\pi\) | ||||
−0.472079 | + | 0.881556i | \(0.656496\pi\) | |||||||
\(878\) | 24.4956 | 0.826685 | ||||||||
\(879\) | −27.0584 | −0.912658 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.38544 | −0.114058 | −0.0570292 | − | 0.998373i | \(-0.518163\pi\) | ||||
−0.0570292 | + | 0.998373i | \(0.518163\pi\) | |||||||
\(882\) | −2.21540 | −0.0745964 | ||||||||
\(883\) | 9.67005 | 0.325423 | 0.162712 | − | 0.986674i | \(-0.447976\pi\) | ||||
0.162712 | + | 0.986674i | \(0.447976\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.39878 | 0.214971 | ||||||||
\(887\) | 10.1393 | 0.340445 | 0.170223 | − | 0.985406i | \(-0.445551\pi\) | ||||
0.170223 | + | 0.985406i | \(0.445551\pi\) | |||||||
\(888\) | −31.8616 | −1.06920 | ||||||||
\(889\) | −5.52622 | −0.185343 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.10413 | −0.305000 | ||||||||
\(892\) | −0.0550368 | −0.00184277 | ||||||||
\(893\) | 27.9598 | 0.935639 | ||||||||
\(894\) | 0.0466273 | 0.00155945 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.0587 | 0.503076 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.120427 | 0.00401869 | ||||||||
\(899\) | 33.1233 | 1.10472 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.32994 | −0.110936 | ||||||||
\(902\) | 8.21155 | 0.273415 | ||||||||
\(903\) | −0.445157 | −0.0148139 | ||||||||
\(904\) | −10.0357 | −0.333781 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.77553 | 0.225102 | ||||||||
\(907\) | −48.7631 | −1.61915 | −0.809577 | − | 0.587014i | \(-0.800303\pi\) | ||||
−0.809577 | + | 0.587014i | \(0.800303\pi\) | |||||||
\(908\) | 7.78208 | 0.258258 | ||||||||
\(909\) | −5.26746 | −0.174711 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.5943 | −1.77566 | −0.887829 | − | 0.460174i | \(-0.847787\pi\) | ||||
−0.887829 | + | 0.460174i | \(0.847787\pi\) | |||||||
\(912\) | 0.587897 | 0.0194672 | ||||||||
\(913\) | 19.8500 | 0.656940 | ||||||||
\(914\) | 0.273475 | 0.00904575 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.82066 | −0.291443 | ||||||||
\(917\) | −11.4212 | −0.377160 | ||||||||
\(918\) | 8.52794 | 0.281464 | ||||||||
\(919\) | −28.2142 | −0.930701 | −0.465350 | − | 0.885127i | \(-0.654072\pi\) | ||||
−0.465350 | + | 0.885127i | \(0.654072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.6419 | 0.350662 | ||||||||
\(922\) | 25.4572 | 0.838390 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 11.0089 | 0.362165 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.2969 | −0.469824 | ||||||||
\(927\) | −20.3221 | −0.667466 | ||||||||
\(928\) | 44.5321 | 1.46184 | ||||||||
\(929\) | 2.90575 | 0.0953346 | 0.0476673 | − | 0.998863i | \(-0.484821\pi\) | ||||
0.0476673 | + | 0.998863i | \(0.484821\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.66808 | −0.251311 | ||||||||
\(932\) | 5.52654 | 0.181028 | ||||||||
\(933\) | 3.58269 | 0.117292 | ||||||||
\(934\) | −3.08616 | −0.100982 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.6821 | 1.45970 | 0.729850 | − | 0.683607i | \(-0.239590\pi\) | ||||
0.729850 | + | 0.683607i | \(0.239590\pi\) | |||||||
\(938\) | 13.0751 | 0.426916 | ||||||||
\(939\) | 24.3616 | 0.795012 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.09938 | −0.166235 | −0.0831175 | − | 0.996540i | \(-0.526488\pi\) | ||||
−0.0831175 | + | 0.996540i | \(0.526488\pi\) | |||||||
\(942\) | −25.6731 | −0.836476 | ||||||||
\(943\) | 25.4451 | 0.828606 | ||||||||
\(944\) | 0.597894 | 0.0194598 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.428446 | −0.0139300 | ||||||||
\(947\) | −6.85210 | −0.222663 | −0.111332 | − | 0.993783i | \(-0.535512\pi\) | ||||
−0.111332 | + | 0.993783i | \(0.535512\pi\) | |||||||
\(948\) | 20.6835 | 0.671770 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.31558 | 0.237224 | ||||||||
\(952\) | −11.2165 | −0.363529 | ||||||||
\(953\) | −31.9155 | −1.03385 | −0.516923 | − | 0.856032i | \(-0.672923\pi\) | ||||
−0.516923 | + | 0.856032i | \(0.672923\pi\) | |||||||
\(954\) | 2.38254 | 0.0771377 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.5183 | 0.663611 | ||||||||
\(957\) | 31.6326 | 1.02254 | ||||||||
\(958\) | −12.8366 | −0.414732 | ||||||||
\(959\) | −29.2355 | −0.944064 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.6079 | −0.438964 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.82325 | 0.187652 | ||||||||
\(964\) | 7.42829 | 0.239249 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −22.1942 | −0.714087 | ||||||||
\(967\) | −15.8568 | −0.509920 | −0.254960 | − | 0.966952i | \(-0.582062\pi\) | ||||
−0.254960 | + | 0.966952i | \(0.582062\pi\) | |||||||
\(968\) | −3.28255 | −0.105505 | ||||||||
\(969\) | 9.34361 | 0.300160 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.3168 | 0.587813 | 0.293907 | − | 0.955834i | \(-0.405045\pi\) | ||||
0.293907 | + | 0.955834i | \(0.405045\pi\) | |||||||
\(972\) | 15.7882 | 0.506407 | ||||||||
\(973\) | −35.4256 | −1.13569 | ||||||||
\(974\) | 2.58619 | 0.0828669 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.07409 | 0.0343807 | ||||||||
\(977\) | 13.5382 | 0.433127 | 0.216563 | − | 0.976269i | \(-0.430515\pi\) | ||||
0.216563 | + | 0.976269i | \(0.430515\pi\) | |||||||
\(978\) | −1.71412 | −0.0548115 | ||||||||
\(979\) | −49.3883 | −1.57846 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.4343 | 0.716271 | ||||||||
\(982\) | 6.75464 | 0.215549 | ||||||||
\(983\) | −34.5313 | −1.10138 | −0.550688 | − | 0.834711i | \(-0.685635\pi\) | ||||
−0.550688 | + | 0.834711i | \(0.685635\pi\) | |||||||
\(984\) | 10.6647 | 0.339978 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.1592 | −0.387227 | ||||||||
\(987\) | −18.9567 | −0.603398 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.32762 | −0.0422159 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.5272 | 1.38269 | 0.691343 | − | 0.722526i | \(-0.257019\pi\) | ||||
0.691343 | + | 0.722526i | \(0.257019\pi\) | |||||||
\(992\) | 23.3826 | 0.742398 | ||||||||
\(993\) | −5.15253 | −0.163510 | ||||||||
\(994\) | −9.60958 | −0.304797 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.72612 | 0.308184 | ||||||||
\(997\) | 45.3802 | 1.43720 | 0.718602 | − | 0.695422i | \(-0.244782\pi\) | ||||
0.718602 | + | 0.695422i | \(0.244782\pi\) | |||||||
\(998\) | −3.61584 | −0.114457 | ||||||||
\(999\) | 49.0450 | 1.55172 |
(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 | 4225.2.a.ca.1.7 | 18 | ||
5.2 | odd | 4 | 845.2.b.g.339.7 | ✓ | 18 | ||
5.3 | odd | 4 | 845.2.b.g.339.12 | yes | 18 | ||
5.4 | even | 2 | inner | 4225.2.a.ca.1.12 | 18 | ||
13.12 | even | 2 | 4225.2.a.cb.1.12 | 18 | |||
65.2 | even | 12 | 845.2.l.g.654.23 | 72 | |||
65.3 | odd | 12 | 845.2.n.i.529.7 | 36 | |||
65.7 | even | 12 | 845.2.l.g.699.14 | 72 | |||
65.8 | even | 4 | 845.2.d.e.844.13 | 36 | |||
65.12 | odd | 4 | 845.2.b.h.339.12 | yes | 18 | ||
65.17 | odd | 12 | 845.2.n.h.484.12 | 36 | |||
65.18 | even | 4 | 845.2.d.e.844.23 | 36 | |||
65.22 | odd | 12 | 845.2.n.i.484.7 | 36 | |||
65.23 | odd | 12 | 845.2.n.h.529.12 | 36 | |||
65.28 | even | 12 | 845.2.l.g.654.14 | 72 | |||
65.32 | even | 12 | 845.2.l.g.699.24 | 72 | |||
65.33 | even | 12 | 845.2.l.g.699.23 | 72 | |||
65.37 | even | 12 | 845.2.l.g.654.13 | 72 | |||
65.38 | odd | 4 | 845.2.b.h.339.7 | yes | 18 | ||
65.42 | odd | 12 | 845.2.n.i.529.12 | 36 | |||
65.43 | odd | 12 | 845.2.n.h.484.7 | 36 | |||
65.47 | even | 4 | 845.2.d.e.844.24 | 36 | |||
65.48 | odd | 12 | 845.2.n.i.484.12 | 36 | |||
65.57 | even | 4 | 845.2.d.e.844.14 | 36 | |||
65.58 | even | 12 | 845.2.l.g.699.13 | 72 | |||
65.62 | odd | 12 | 845.2.n.h.529.7 | 36 | |||
65.63 | even | 12 | 845.2.l.g.654.24 | 72 | |||
65.64 | even | 2 | 4225.2.a.cb.1.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.b.g.339.7 | ✓ | 18 | 5.2 | odd | 4 | ||
845.2.b.g.339.12 | yes | 18 | 5.3 | odd | 4 | ||
845.2.b.h.339.7 | yes | 18 | 65.38 | odd | 4 | ||
845.2.b.h.339.12 | yes | 18 | 65.12 | odd | 4 | ||
845.2.d.e.844.13 | 36 | 65.8 | even | 4 | |||
845.2.d.e.844.14 | 36 | 65.57 | even | 4 | |||
845.2.d.e.844.23 | 36 | 65.18 | even | 4 | |||
845.2.d.e.844.24 | 36 | 65.47 | even | 4 | |||
845.2.l.g.654.13 | 72 | 65.37 | even | 12 | |||
845.2.l.g.654.14 | 72 | 65.28 | even | 12 | |||
845.2.l.g.654.23 | 72 | 65.2 | even | 12 | |||
845.2.l.g.654.24 | 72 | 65.63 | even | 12 | |||
845.2.l.g.699.13 | 72 | 65.58 | even | 12 | |||
845.2.l.g.699.14 | 72 | 65.7 | even | 12 | |||
845.2.l.g.699.23 | 72 | 65.33 | even | 12 | |||
845.2.l.g.699.24 | 72 | 65.32 | even | 12 | |||
845.2.n.h.484.7 | 36 | 65.43 | odd | 12 | |||
845.2.n.h.484.12 | 36 | 65.17 | odd | 12 | |||
845.2.n.h.529.7 | 36 | 65.62 | odd | 12 | |||
845.2.n.h.529.12 | 36 | 65.23 | odd | 12 | |||
845.2.n.i.484.7 | 36 | 65.22 | odd | 12 | |||
845.2.n.i.484.12 | 36 | 65.48 | odd | 12 | |||
845.2.n.i.529.7 | 36 | 65.3 | odd | 12 | |||
845.2.n.i.529.12 | 36 | 65.42 | odd | 12 | |||
4225.2.a.ca.1.7 | 18 | 1.1 | even | 1 | trivial | ||
4225.2.a.ca.1.12 | 18 | 5.4 | even | 2 | inner | ||
4225.2.a.cb.1.7 | 18 | 65.64 | even | 2 | |||
4225.2.a.cb.1.12 | 18 | 13.12 | even | 2 |