Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.13569\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13569 | −0.803055 | −0.401527 | − | 0.915847i | \(-0.631521\pi\) | ||||
−0.401527 | + | 0.915847i | \(0.631521\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.710206 | −0.355103 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.10132 | −1.55015 | −0.775077 | − | 0.631866i | \(-0.782289\pi\) | ||||
−0.775077 | + | 0.631866i | \(0.782289\pi\) | |||||||
\(8\) | 3.07796 | 1.08822 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.13569 | 0.359137 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.27388 | 0.630660 | 0.315330 | − | 0.948982i | \(-0.397885\pi\) | ||||
0.315330 | + | 0.948982i | \(0.397885\pi\) | |||||||
\(14\) | 4.65784 | 1.24486 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.07520 | −0.518799 | ||||||||
\(17\) | −5.01888 | −1.21726 | −0.608629 | − | 0.793455i | \(-0.708280\pi\) | ||||
−0.608629 | + | 0.793455i | \(0.708280\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.57794 | 1.73850 | 0.869249 | − | 0.494375i | \(-0.164603\pi\) | ||||
0.869249 | + | 0.494375i | \(0.164603\pi\) | |||||||
\(20\) | 0.710206 | 0.158807 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.97494 | 0.411803 | 0.205902 | − | 0.978573i | \(-0.433987\pi\) | ||||
0.205902 | + | 0.978573i | \(0.433987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.58242 | −0.506455 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.91278 | 0.550464 | ||||||||
\(29\) | 4.00136 | 0.743033 | 0.371517 | − | 0.928426i | \(-0.378838\pi\) | ||||
0.371517 | + | 0.928426i | \(0.378838\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.81490 | −0.685176 | −0.342588 | − | 0.939486i | \(-0.611304\pi\) | ||||
−0.342588 | + | 0.939486i | \(0.611304\pi\) | |||||||
\(32\) | −3.79913 | −0.671598 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.69990 | 0.977525 | ||||||||
\(35\) | 4.10132 | 0.693250 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.73089 | −1.10655 | −0.553276 | − | 0.832998i | \(-0.686623\pi\) | ||||
−0.553276 | + | 0.832998i | \(0.686623\pi\) | |||||||
\(38\) | −8.60619 | −1.39611 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.07796 | −0.486668 | ||||||||
\(41\) | 4.02336 | 0.628344 | 0.314172 | − | 0.949366i | \(-0.398273\pi\) | ||||
0.314172 | + | 0.949366i | \(0.398273\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.57903 | −1.46079 | −0.730394 | − | 0.683026i | \(-0.760664\pi\) | ||||
−0.730394 | + | 0.683026i | \(0.760664\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.24292 | −0.330701 | ||||||||
\(47\) | −3.18673 | −0.464832 | −0.232416 | − | 0.972616i | \(-0.574663\pi\) | ||||
−0.232416 | + | 0.972616i | \(0.574663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.82086 | 1.40298 | ||||||||
\(50\) | −1.13569 | −0.160611 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.61492 | −0.223949 | ||||||||
\(53\) | −11.2291 | −1.54244 | −0.771219 | − | 0.636570i | \(-0.780352\pi\) | ||||
−0.771219 | + | 0.636570i | \(0.780352\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.6237 | −1.68691 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.54431 | −0.596697 | ||||||||
\(59\) | 9.53769 | 1.24170 | 0.620851 | − | 0.783929i | \(-0.286787\pi\) | ||||
0.620851 | + | 0.783929i | \(0.286787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.61186 | −0.462452 | −0.231226 | − | 0.972900i | \(-0.574274\pi\) | ||||
−0.231226 | + | 0.972900i | \(0.574274\pi\) | |||||||
\(62\) | 4.33255 | 0.550234 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.46503 | 1.05813 | ||||||||
\(65\) | −2.27388 | −0.282040 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.31504 | −0.771505 | −0.385752 | − | 0.922602i | \(-0.626058\pi\) | ||||
−0.385752 | + | 0.922602i | \(0.626058\pi\) | |||||||
\(68\) | 3.56444 | 0.432252 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.65784 | −0.556718 | ||||||||
\(71\) | −12.2950 | −1.45915 | −0.729574 | − | 0.683901i | \(-0.760282\pi\) | ||||
−0.729574 | + | 0.683901i | \(0.760282\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.89030 | 0.455325 | 0.227663 | − | 0.973740i | \(-0.426892\pi\) | ||||
0.227663 | + | 0.973740i | \(0.426892\pi\) | |||||||
\(74\) | 7.64422 | 0.888622 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.38189 | −0.617345 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.5747 | −1.97731 | −0.988656 | − | 0.150196i | \(-0.952009\pi\) | ||||
−0.988656 | + | 0.150196i | \(0.952009\pi\) | |||||||
\(80\) | 2.07520 | 0.232014 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.56930 | −0.504594 | ||||||||
\(83\) | 13.8475 | 1.51996 | 0.759982 | − | 0.649944i | \(-0.225208\pi\) | ||||
0.759982 | + | 0.649944i | \(0.225208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.01888 | 0.544374 | ||||||||
\(86\) | 10.8788 | 1.17309 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.85399 | −0.832522 | −0.416261 | − | 0.909245i | \(-0.636660\pi\) | ||||
−0.416261 | + | 0.909245i | \(0.636660\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.32590 | −0.977620 | ||||||||
\(92\) | −1.40261 | −0.146232 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.61914 | 0.373286 | ||||||||
\(95\) | −7.57794 | −0.777480 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17866 | 0.525813 | 0.262907 | − | 0.964821i | \(-0.415319\pi\) | ||||
0.262907 | + | 0.964821i | \(0.415319\pi\) | |||||||
\(98\) | −11.1535 | −1.12667 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.710206 | −0.0710206 | ||||||||
\(101\) | −3.99265 | −0.397284 | −0.198642 | − | 0.980072i | \(-0.563653\pi\) | ||||
−0.198642 | + | 0.980072i | \(0.563653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.940967 | −0.0927162 | −0.0463581 | − | 0.998925i | \(-0.514762\pi\) | ||||
−0.0463581 | + | 0.998925i | \(0.514762\pi\) | |||||||
\(104\) | 6.99889 | 0.686298 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.7528 | 1.23866 | ||||||||
\(107\) | 14.5295 | 1.40462 | 0.702308 | − | 0.711873i | \(-0.252153\pi\) | ||||
0.702308 | + | 0.711873i | \(0.252153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.70193 | −0.737711 | −0.368855 | − | 0.929487i | \(-0.620250\pi\) | ||||
−0.368855 | + | 0.929487i | \(0.620250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.51105 | 0.804219 | ||||||||
\(113\) | 0.675502 | 0.0635459 | 0.0317729 | − | 0.999495i | \(-0.489885\pi\) | ||||
0.0317729 | + | 0.999495i | \(0.489885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.97494 | −0.184164 | ||||||||
\(116\) | −2.84179 | −0.263853 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.8319 | −0.997155 | ||||||||
\(119\) | 20.5841 | 1.88694 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.10196 | 0.371374 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.70936 | 0.243308 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.41105 | 0.391418 | 0.195709 | − | 0.980662i | \(-0.437299\pi\) | ||||
0.195709 | + | 0.980662i | \(0.437299\pi\) | |||||||
\(128\) | −2.01540 | −0.178138 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.58242 | 0.226493 | ||||||||
\(131\) | 21.4004 | 1.86976 | 0.934882 | − | 0.354959i | \(-0.115505\pi\) | ||||
0.934882 | + | 0.354959i | \(0.115505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.0796 | −2.69494 | ||||||||
\(134\) | 7.17193 | 0.619561 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.4479 | −1.32465 | ||||||||
\(137\) | 3.82130 | 0.326475 | 0.163238 | − | 0.986587i | \(-0.447806\pi\) | ||||
0.163238 | + | 0.986587i | \(0.447806\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.29721 | −0.534122 | −0.267061 | − | 0.963680i | \(-0.586053\pi\) | ||||
−0.267061 | + | 0.963680i | \(0.586053\pi\) | |||||||
\(140\) | −2.91278 | −0.246175 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.9633 | 1.17178 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00136 | −0.332295 | ||||||||
\(146\) | −4.41818 | −0.365651 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.78032 | 0.392940 | ||||||||
\(149\) | 22.4959 | 1.84293 | 0.921467 | − | 0.388457i | \(-0.126992\pi\) | ||||
0.921467 | + | 0.388457i | \(0.126992\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.99699 | 0.243892 | 0.121946 | − | 0.992537i | \(-0.461087\pi\) | ||||
0.121946 | + | 0.992537i | \(0.461087\pi\) | |||||||
\(152\) | 23.3246 | 1.89187 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.81490 | 0.306420 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1899 | −0.813244 | −0.406622 | − | 0.913597i | \(-0.633293\pi\) | ||||
−0.406622 | + | 0.913597i | \(0.633293\pi\) | |||||||
\(158\) | 19.9595 | 1.58789 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.79913 | 0.300348 | ||||||||
\(161\) | −8.09986 | −0.638359 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.8034 | −1.55112 | −0.775561 | − | 0.631273i | \(-0.782533\pi\) | ||||
−0.775561 | + | 0.631273i | \(0.782533\pi\) | |||||||
\(164\) | −2.85741 | −0.223127 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.7265 | −1.22061 | ||||||||
\(167\) | 4.96739 | 0.384388 | 0.192194 | − | 0.981357i | \(-0.438440\pi\) | ||||
0.192194 | + | 0.981357i | \(0.438440\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.82948 | −0.602268 | ||||||||
\(170\) | −5.69990 | −0.437162 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.80308 | 0.518730 | ||||||||
\(173\) | 16.2510 | 1.23554 | 0.617768 | − | 0.786360i | \(-0.288037\pi\) | ||||
0.617768 | + | 0.786360i | \(0.288037\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.10132 | −0.310031 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.91971 | 0.668561 | ||||||||
\(179\) | −3.18448 | −0.238019 | −0.119010 | − | 0.992893i | \(-0.537972\pi\) | ||||
−0.119010 | + | 0.992893i | \(0.537972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.50099 | 0.111568 | 0.0557838 | − | 0.998443i | \(-0.482234\pi\) | ||||
0.0557838 | + | 0.998443i | \(0.482234\pi\) | |||||||
\(182\) | 10.5913 | 0.785083 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.07877 | 0.448133 | ||||||||
\(185\) | 6.73089 | 0.494865 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.26323 | 0.165063 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.60619 | 0.624359 | ||||||||
\(191\) | −10.4428 | −0.755613 | −0.377807 | − | 0.925885i | \(-0.623322\pi\) | ||||
−0.377807 | + | 0.925885i | \(0.623322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.02750 | −0.433869 | −0.216935 | − | 0.976186i | \(-0.569606\pi\) | ||||
−0.216935 | + | 0.976186i | \(0.569606\pi\) | |||||||
\(194\) | −5.88136 | −0.422257 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.97483 | −0.498202 | ||||||||
\(197\) | −9.07040 | −0.646239 | −0.323120 | − | 0.946358i | \(-0.604732\pi\) | ||||
−0.323120 | + | 0.946358i | \(0.604732\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.3143 | 1.22738 | 0.613689 | − | 0.789548i | \(-0.289685\pi\) | ||||
0.613689 | + | 0.789548i | \(0.289685\pi\) | |||||||
\(200\) | 3.07796 | 0.217644 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.53442 | 0.319041 | ||||||||
\(203\) | −16.4109 | −1.15182 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.02336 | −0.281004 | ||||||||
\(206\) | 1.06865 | 0.0744562 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.71874 | −0.327186 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7153 | 1.08189 | 0.540945 | − | 0.841058i | \(-0.318067\pi\) | ||||
0.540945 | + | 0.841058i | \(0.318067\pi\) | |||||||
\(212\) | 7.97498 | 0.547724 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.5010 | −1.12798 | ||||||||
\(215\) | 9.57903 | 0.653285 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.6461 | 1.06213 | ||||||||
\(218\) | 8.74701 | 0.592422 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4123 | −0.767676 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.08382 | 0.0725778 | 0.0362889 | − | 0.999341i | \(-0.488446\pi\) | ||||
0.0362889 | + | 0.999341i | \(0.488446\pi\) | |||||||
\(224\) | 15.5815 | 1.04108 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.767162 | −0.0510308 | ||||||||
\(227\) | −1.99171 | −0.132195 | −0.0660974 | − | 0.997813i | \(-0.521055\pi\) | ||||
−0.0660974 | + | 0.997813i | \(0.521055\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.13974 | 0.537889 | 0.268945 | − | 0.963156i | \(-0.413325\pi\) | ||||
0.268945 | + | 0.963156i | \(0.413325\pi\) | |||||||
\(230\) | 2.24292 | 0.147894 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.3160 | 0.808585 | ||||||||
\(233\) | 24.4296 | 1.60043 | 0.800217 | − | 0.599710i | \(-0.204717\pi\) | ||||
0.800217 | + | 0.599710i | \(0.204717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.18673 | 0.207879 | ||||||||
\(236\) | −6.77372 | −0.440932 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −23.3771 | −1.51531 | ||||||||
\(239\) | −0.0709845 | −0.00459161 | −0.00229580 | − | 0.999997i | \(-0.500731\pi\) | ||||
−0.00229580 | + | 0.999997i | \(0.500731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6653 | 0.815842 | 0.407921 | − | 0.913017i | \(-0.366254\pi\) | ||||
0.407921 | + | 0.913017i | \(0.366254\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.56517 | 0.164218 | ||||||||
\(245\) | −9.82086 | −0.627431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.2313 | 1.09640 | ||||||||
\(248\) | −11.7421 | −0.745624 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.13569 | 0.0718274 | ||||||||
\(251\) | 7.65705 | 0.483309 | 0.241654 | − | 0.970362i | \(-0.422310\pi\) | ||||
0.241654 | + | 0.970362i | \(0.422310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.00959 | −0.314330 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.6412 | −0.915075 | ||||||||
\(257\) | 23.1101 | 1.44157 | 0.720784 | − | 0.693160i | \(-0.243782\pi\) | ||||
0.720784 | + | 0.693160i | \(0.243782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.6056 | 1.71533 | ||||||||
\(260\) | 1.61492 | 0.100153 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.3043 | −1.50152 | ||||||||
\(263\) | −9.67819 | −0.596783 | −0.298391 | − | 0.954444i | \(-0.596450\pi\) | ||||
−0.298391 | + | 0.954444i | \(0.596450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.2291 | 0.689799 | ||||||||
\(266\) | 35.2968 | 2.16418 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.48498 | 0.273964 | ||||||||
\(269\) | 1.82359 | 0.111186 | 0.0555931 | − | 0.998454i | \(-0.482295\pi\) | ||||
0.0555931 | + | 0.998454i | \(0.482295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7934 | 0.898635 | 0.449318 | − | 0.893372i | \(-0.351667\pi\) | ||||
0.449318 | + | 0.893372i | \(0.351667\pi\) | |||||||
\(272\) | 10.4152 | 0.631512 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.33981 | −0.262178 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9801 | −1.02024 | −0.510118 | − | 0.860104i | \(-0.670398\pi\) | ||||
−0.510118 | + | 0.860104i | \(0.670398\pi\) | |||||||
\(278\) | 7.15169 | 0.428930 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.6237 | 0.754410 | ||||||||
\(281\) | 4.60152 | 0.274504 | 0.137252 | − | 0.990536i | \(-0.456173\pi\) | ||||
0.137252 | + | 0.990536i | \(0.456173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7869 | −0.819545 | −0.409772 | − | 0.912188i | \(-0.634392\pi\) | ||||
−0.409772 | + | 0.912188i | \(0.634392\pi\) | |||||||
\(284\) | 8.73198 | 0.518148 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.5011 | −0.974030 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.18917 | 0.481716 | ||||||||
\(290\) | 4.54431 | 0.266851 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.76291 | −0.161687 | ||||||||
\(293\) | 31.4245 | 1.83584 | 0.917919 | − | 0.396769i | \(-0.129869\pi\) | ||||
0.917919 | + | 0.396769i | \(0.129869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.53769 | −0.555306 | ||||||||
\(296\) | −20.7174 | −1.20417 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −25.5484 | −1.47998 | ||||||||
\(299\) | 4.49077 | 0.259708 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.2867 | 2.26445 | ||||||||
\(302\) | −3.40366 | −0.195858 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.7257 | −0.901931 | ||||||||
\(305\) | 3.61186 | 0.206815 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.1733 | −1.15135 | −0.575676 | − | 0.817678i | \(-0.695261\pi\) | ||||
−0.575676 | + | 0.817678i | \(0.695261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.33255 | −0.246072 | ||||||||
\(311\) | 18.5810 | 1.05363 | 0.526816 | − | 0.849979i | \(-0.323386\pi\) | ||||
0.526816 | + | 0.849979i | \(0.323386\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4086 | 0.644854 | 0.322427 | − | 0.946594i | \(-0.395501\pi\) | ||||
0.322427 | + | 0.946594i | \(0.395501\pi\) | |||||||
\(314\) | 11.5726 | 0.653079 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.4817 | 0.702149 | ||||||||
\(317\) | −25.4611 | −1.43004 | −0.715018 | − | 0.699106i | \(-0.753581\pi\) | ||||
−0.715018 | + | 0.699106i | \(0.753581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.46503 | −0.473210 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.19894 | 0.512637 | ||||||||
\(323\) | −38.0328 | −2.11620 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.27388 | 0.126132 | ||||||||
\(326\) | 22.4905 | 1.24564 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.3837 | 0.683777 | ||||||||
\(329\) | 13.0698 | 0.720561 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.1055 | 1.70971 | 0.854857 | − | 0.518864i | \(-0.173645\pi\) | ||||
0.854857 | + | 0.518864i | \(0.173645\pi\) | |||||||
\(332\) | −9.83460 | −0.539744 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.64142 | −0.308684 | ||||||||
\(335\) | 6.31504 | 0.345027 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.6950 | 1.45417 | 0.727084 | − | 0.686548i | \(-0.240875\pi\) | ||||
0.727084 | + | 0.686548i | \(0.240875\pi\) | |||||||
\(338\) | 8.89188 | 0.483654 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.56444 | −0.193309 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.5692 | −0.624680 | ||||||||
\(344\) | −29.4838 | −1.58966 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.4561 | −0.992204 | ||||||||
\(347\) | 6.79251 | 0.364641 | 0.182321 | − | 0.983239i | \(-0.441639\pi\) | ||||
0.182321 | + | 0.983239i | \(0.441639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.84626 | 0.420001 | 0.210000 | − | 0.977701i | \(-0.432653\pi\) | ||||
0.210000 | + | 0.977701i | \(0.432653\pi\) | |||||||
\(350\) | 4.65784 | 0.248972 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.4136 | −0.980056 | −0.490028 | − | 0.871707i | \(-0.663014\pi\) | ||||
−0.490028 | + | 0.871707i | \(0.663014\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.2950 | 0.652551 | ||||||||
\(356\) | 5.57795 | 0.295631 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.61659 | 0.191142 | ||||||||
\(359\) | −25.4119 | −1.34119 | −0.670595 | − | 0.741823i | \(-0.733961\pi\) | ||||
−0.670595 | + | 0.741823i | \(0.733961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.4251 | 2.02237 | ||||||||
\(362\) | −1.70466 | −0.0895949 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.62331 | 0.347156 | ||||||||
\(365\) | −3.89030 | −0.203628 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.48293 | −0.181808 | −0.0909038 | − | 0.995860i | \(-0.528976\pi\) | ||||
−0.0909038 | + | 0.995860i | \(0.528976\pi\) | |||||||
\(368\) | −4.09839 | −0.213643 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.64422 | −0.397404 | ||||||||
\(371\) | 46.0542 | 2.39102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8348 | −0.664561 | −0.332281 | − | 0.943181i | \(-0.607818\pi\) | ||||
−0.332281 | + | 0.943181i | \(0.607818\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.80861 | −0.505840 | ||||||||
\(377\) | 9.09859 | 0.468601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0638 | −1.23607 | −0.618037 | − | 0.786149i | \(-0.712072\pi\) | ||||
−0.618037 | + | 0.786149i | \(0.712072\pi\) | |||||||
\(380\) | 5.38189 | 0.276085 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.8598 | 0.606799 | ||||||||
\(383\) | −3.17618 | −0.162295 | −0.0811477 | − | 0.996702i | \(-0.525859\pi\) | ||||
−0.0811477 | + | 0.996702i | \(0.525859\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.84538 | 0.348421 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.67791 | −0.186718 | ||||||||
\(389\) | −14.9001 | −0.755463 | −0.377731 | − | 0.925915i | \(-0.623296\pi\) | ||||
−0.377731 | + | 0.925915i | \(0.623296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.91198 | −0.501270 | ||||||||
\(392\) | 30.2282 | 1.52675 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.3012 | 0.518965 | ||||||||
\(395\) | 17.5747 | 0.884281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8837 | 0.546237 | 0.273119 | − | 0.961980i | \(-0.411945\pi\) | ||||
0.273119 | + | 0.961980i | \(0.411945\pi\) | |||||||
\(398\) | −19.6637 | −0.985651 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.07520 | −0.103760 | ||||||||
\(401\) | −33.2847 | −1.66216 | −0.831080 | − | 0.556153i | \(-0.812277\pi\) | ||||
−0.831080 | + | 0.556153i | \(0.812277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.67461 | −0.432113 | ||||||||
\(404\) | 2.83561 | 0.141077 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.6377 | 0.924972 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.77694 | −0.137311 | −0.0686554 | − | 0.997640i | \(-0.521871\pi\) | ||||
−0.0686554 | + | 0.997640i | \(0.521871\pi\) | |||||||
\(410\) | 4.56930 | 0.225661 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.668280 | 0.0329238 | ||||||||
\(413\) | −39.1172 | −1.92483 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8475 | −0.679749 | ||||||||
\(416\) | −8.63876 | −0.423550 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.5565 | 1.44393 | 0.721965 | − | 0.691930i | \(-0.243239\pi\) | ||||
0.721965 | + | 0.691930i | \(0.243239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.291904 | 0.0142265 | 0.00711326 | − | 0.999975i | \(-0.497736\pi\) | ||||
0.00711326 | + | 0.999975i | \(0.497736\pi\) | |||||||
\(422\) | −17.8478 | −0.868816 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −34.5627 | −1.67851 | ||||||||
\(425\) | −5.01888 | −0.243451 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.8134 | 0.716872 | ||||||||
\(428\) | −10.3189 | −0.498783 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.8788 | −0.524623 | ||||||||
\(431\) | −4.49580 | −0.216555 | −0.108277 | − | 0.994121i | \(-0.534534\pi\) | ||||
−0.108277 | + | 0.994121i | \(0.534534\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.56823 | −0.315649 | −0.157824 | − | 0.987467i | \(-0.550448\pi\) | ||||
−0.157824 | + | 0.987467i | \(0.550448\pi\) | |||||||
\(434\) | −17.7692 | −0.852948 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.46995 | 0.261963 | ||||||||
\(437\) | 14.9660 | 0.715919 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7142 | 1.27500 | 0.637500 | − | 0.770451i | \(-0.279969\pi\) | ||||
0.637500 | + | 0.770451i | \(0.279969\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.9609 | 0.616486 | ||||||||
\(443\) | 23.1670 | 1.10070 | 0.550349 | − | 0.834935i | \(-0.314495\pi\) | ||||
0.550349 | + | 0.834935i | \(0.314495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.85399 | 0.372315 | ||||||||
\(446\) | −1.23088 | −0.0582839 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −34.7178 | −1.64026 | ||||||||
\(449\) | 29.0593 | 1.37139 | 0.685696 | − | 0.727888i | \(-0.259498\pi\) | ||||
0.685696 | + | 0.727888i | \(0.259498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.479745 | −0.0225653 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.26197 | 0.106160 | ||||||||
\(455\) | 9.32590 | 0.437205 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.62741 | −0.356795 | −0.178398 | − | 0.983958i | \(-0.557091\pi\) | ||||
−0.178398 | + | 0.983958i | \(0.557091\pi\) | |||||||
\(458\) | −9.24423 | −0.431954 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.40261 | 0.0653971 | ||||||||
\(461\) | −34.0138 | −1.58418 | −0.792091 | − | 0.610404i | \(-0.791007\pi\) | ||||
−0.792091 | + | 0.610404i | \(0.791007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7564 | 0.732263 | 0.366131 | − | 0.930563i | \(-0.380682\pi\) | ||||
0.366131 | + | 0.930563i | \(0.380682\pi\) | |||||||
\(464\) | −8.30360 | −0.385485 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.7445 | −1.28524 | ||||||||
\(467\) | −10.1508 | −0.469724 | −0.234862 | − | 0.972029i | \(-0.575464\pi\) | ||||
−0.234862 | + | 0.972029i | \(0.575464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.9000 | 1.19595 | ||||||||
\(470\) | −3.61914 | −0.166938 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 29.3566 | 1.35125 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.57794 | 0.347700 | ||||||||
\(476\) | −14.6189 | −0.670057 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.0806165 | 0.00368731 | ||||||||
\(479\) | 4.04315 | 0.184736 | 0.0923681 | − | 0.995725i | \(-0.470556\pi\) | ||||
0.0923681 | + | 0.995725i | \(0.470556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.3052 | −0.697858 | ||||||||
\(482\) | −14.3838 | −0.655166 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.17866 | −0.235151 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.37591 | 0.334234 | 0.167117 | − | 0.985937i | \(-0.446554\pi\) | ||||
0.167117 | + | 0.985937i | \(0.446554\pi\) | |||||||
\(488\) | −11.1172 | −0.503250 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.1535 | 0.503862 | ||||||||
\(491\) | −2.19528 | −0.0990717 | −0.0495358 | − | 0.998772i | \(-0.515774\pi\) | ||||
−0.0495358 | + | 0.998772i | \(0.515774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0823 | −0.904463 | ||||||||
\(494\) | −19.5694 | −0.880470 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.91667 | 0.355469 | ||||||||
\(497\) | 50.4258 | 2.26191 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.06180 | 0.360896 | 0.180448 | − | 0.983585i | \(-0.442245\pi\) | ||||
0.180448 | + | 0.983585i | \(0.442245\pi\) | |||||||
\(500\) | 0.710206 | 0.0317614 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.69605 | −0.388124 | ||||||||
\(503\) | 33.3563 | 1.48728 | 0.743642 | − | 0.668579i | \(-0.233097\pi\) | ||||
0.743642 | + | 0.668579i | \(0.233097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.99265 | 0.177671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.13276 | −0.138994 | ||||||||
\(509\) | 16.7877 | 0.744100 | 0.372050 | − | 0.928213i | \(-0.378655\pi\) | ||||
0.372050 | + | 0.928213i | \(0.378655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.9554 | −0.705825 | ||||||||
\(512\) | 20.6587 | 0.912993 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.2459 | −1.15766 | ||||||||
\(515\) | 0.940967 | 0.0414639 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −31.3514 | −1.37750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.99889 | −0.306922 | ||||||||
\(521\) | 14.7904 | 0.647981 | 0.323991 | − | 0.946060i | \(-0.394975\pi\) | ||||
0.323991 | + | 0.946060i | \(0.394975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.41489 | 0.0618688 | 0.0309344 | − | 0.999521i | \(-0.490152\pi\) | ||||
0.0309344 | + | 0.999521i | \(0.490152\pi\) | |||||||
\(524\) | −15.1987 | −0.663958 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9914 | 0.479249 | ||||||||
\(527\) | 19.1465 | 0.834036 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0996 | −0.830418 | ||||||||
\(530\) | −12.7528 | −0.553946 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 22.0729 | 0.956981 | ||||||||
\(533\) | 9.14863 | 0.396271 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.5295 | −0.628163 | ||||||||
\(536\) | −19.4374 | −0.839568 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.07103 | −0.0892887 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.52676 | −0.108634 | −0.0543169 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543169 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(542\) | −16.8007 | −0.721653 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19.0674 | 0.817507 | ||||||||
\(545\) | 7.70193 | 0.329914 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.519111 | −0.0221956 | −0.0110978 | − | 0.999938i | \(-0.503533\pi\) | ||||
−0.0110978 | + | 0.999938i | \(0.503533\pi\) | |||||||
\(548\) | −2.71391 | −0.115932 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.3220 | 1.29176 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 72.0797 | 3.06514 | ||||||||
\(554\) | 19.2842 | 0.819306 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.47231 | 0.189668 | ||||||||
\(557\) | −11.8026 | −0.500091 | −0.250045 | − | 0.968234i | \(-0.580446\pi\) | ||||
−0.250045 | + | 0.968234i | \(0.580446\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.7815 | −0.921261 | ||||||||
\(560\) | −8.51105 | −0.359658 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.22591 | −0.220442 | ||||||||
\(563\) | −6.73272 | −0.283750 | −0.141875 | − | 0.989885i | \(-0.545313\pi\) | ||||
−0.141875 | + | 0.989885i | \(0.545313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.675502 | −0.0284186 | ||||||||
\(566\) | 15.6576 | 0.658140 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.8435 | −1.58788 | ||||||||
\(569\) | −31.4915 | −1.32019 | −0.660096 | − | 0.751181i | \(-0.729484\pi\) | ||||
−0.660096 | + | 0.751181i | \(0.729484\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.1049 | 1.00876 | 0.504380 | − | 0.863482i | \(-0.331721\pi\) | ||||
0.504380 | + | 0.863482i | \(0.331721\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.7402 | 0.782199 | ||||||||
\(575\) | 1.97494 | 0.0823606 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.2109 | −1.42422 | −0.712110 | − | 0.702068i | \(-0.752260\pi\) | ||||
−0.712110 | + | 0.702068i | \(0.752260\pi\) | |||||||
\(578\) | −9.30037 | −0.386844 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.84179 | 0.117999 | ||||||||
\(581\) | −56.7932 | −2.35618 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.9742 | 0.495495 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.6885 | −1.47428 | ||||||||
\(587\) | 17.6006 | 0.726457 | 0.363228 | − | 0.931700i | \(-0.381675\pi\) | ||||
0.363228 | + | 0.931700i | \(0.381675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.9091 | −1.19118 | ||||||||
\(590\) | 10.8319 | 0.445941 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.9679 | 0.574078 | ||||||||
\(593\) | 33.9143 | 1.39269 | 0.696347 | − | 0.717705i | \(-0.254807\pi\) | ||||
0.696347 | + | 0.717705i | \(0.254807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.5841 | −0.843864 | ||||||||
\(596\) | −15.9767 | −0.654431 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.10012 | −0.208560 | ||||||||
\(599\) | 30.1345 | 1.23126 | 0.615630 | − | 0.788035i | \(-0.288901\pi\) | ||||
0.615630 | + | 0.788035i | \(0.288901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.7612 | 1.13240 | 0.566202 | − | 0.824266i | \(-0.308412\pi\) | ||||
0.566202 | + | 0.824266i | \(0.308412\pi\) | |||||||
\(602\) | −44.6176 | −1.81848 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.12848 | −0.0866067 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.4949 | 1.03481 | 0.517404 | − | 0.855742i | \(-0.326899\pi\) | ||||
0.517404 | + | 0.855742i | \(0.326899\pi\) | |||||||
\(608\) | −28.7896 | −1.16757 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.10196 | −0.166084 | ||||||||
\(611\) | −7.24622 | −0.293151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.06728 | −0.0834967 | −0.0417484 | − | 0.999128i | \(-0.513293\pi\) | ||||
−0.0417484 | + | 0.999128i | \(0.513293\pi\) | |||||||
\(614\) | 22.9107 | 0.924599 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.7249 | −0.673321 | −0.336660 | − | 0.941626i | \(-0.609297\pi\) | ||||
−0.336660 | + | 0.941626i | \(0.609297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.2465 | −1.69803 | −0.849015 | − | 0.528369i | \(-0.822804\pi\) | ||||
−0.849015 | + | 0.528369i | \(0.822804\pi\) | |||||||
\(620\) | −2.70936 | −0.108811 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.1023 | −0.846125 | ||||||||
\(623\) | 32.2118 | 1.29054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.9567 | −0.517853 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.23693 | 0.288785 | ||||||||
\(629\) | 33.7816 | 1.34696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.8620 | 1.54707 | 0.773536 | − | 0.633753i | \(-0.218486\pi\) | ||||
0.773536 | + | 0.633753i | \(0.218486\pi\) | |||||||
\(632\) | −54.0943 | −2.15175 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.9159 | 1.14840 | ||||||||
\(635\) | −4.41105 | −0.175047 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3314 | 0.884803 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.01540 | 0.0796657 | ||||||||
\(641\) | 17.5446 | 0.692971 | 0.346486 | − | 0.938055i | \(-0.387375\pi\) | ||||
0.346486 | + | 0.938055i | \(0.387375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.6475 | 1.44524 | 0.722619 | − | 0.691246i | \(-0.242938\pi\) | ||||
0.722619 | + | 0.691246i | \(0.242938\pi\) | |||||||
\(644\) | 5.75257 | 0.226683 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 43.1935 | 1.69942 | ||||||||
\(647\) | 22.6182 | 0.889214 | 0.444607 | − | 0.895726i | \(-0.353343\pi\) | ||||
0.444607 | + | 0.895726i | \(0.353343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.58242 | −0.101291 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.0645 | 0.550808 | ||||||||
\(653\) | −6.34671 | −0.248366 | −0.124183 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124183 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.4004 | −0.836184 | ||||||||
\(656\) | −8.34927 | −0.325984 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.8433 | −0.578650 | ||||||||
\(659\) | 45.8649 | 1.78664 | 0.893321 | − | 0.449420i | \(-0.148369\pi\) | ||||
0.893321 | + | 0.449420i | \(0.148369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.4730 | 1.80759 | 0.903796 | − | 0.427964i | \(-0.140769\pi\) | ||||
0.903796 | + | 0.427964i | \(0.140769\pi\) | |||||||
\(662\) | −35.3263 | −1.37299 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 42.6221 | 1.65406 | ||||||||
\(665\) | 31.0796 | 1.20521 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.90243 | 0.305983 | ||||||||
\(668\) | −3.52787 | −0.136497 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.17193 | −0.277076 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.1001 | 0.427879 | 0.213939 | − | 0.976847i | \(-0.431371\pi\) | ||||
0.213939 | + | 0.976847i | \(0.431371\pi\) | |||||||
\(674\) | −30.3173 | −1.16778 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.56054 | 0.213867 | ||||||||
\(677\) | −15.9352 | −0.612441 | −0.306220 | − | 0.951961i | \(-0.599064\pi\) | ||||
−0.306220 | + | 0.951961i | \(0.599064\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.2394 | −0.815092 | ||||||||
\(680\) | 15.4479 | 0.592400 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.8344 | 0.835468 | 0.417734 | − | 0.908569i | \(-0.362824\pi\) | ||||
0.417734 | + | 0.908569i | \(0.362824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.82130 | −0.146004 | ||||||||
\(686\) | 13.1391 | 0.501653 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.8784 | 0.757856 | ||||||||
\(689\) | −25.5336 | −0.972753 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.9932 | −1.02687 | −0.513435 | − | 0.858128i | \(-0.671627\pi\) | ||||
−0.513435 | + | 0.858128i | \(0.671627\pi\) | |||||||
\(692\) | −11.5415 | −0.438743 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.71420 | −0.292827 | ||||||||
\(695\) | 6.29721 | 0.238867 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1928 | −0.764856 | ||||||||
\(698\) | −8.91093 | −0.337284 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.91278 | 0.110093 | ||||||||
\(701\) | −29.8366 | −1.12691 | −0.563455 | − | 0.826146i | \(-0.690528\pi\) | ||||
−0.563455 | + | 0.826146i | \(0.690528\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −51.0063 | −1.92374 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.9121 | 0.787039 | ||||||||
\(707\) | 16.3752 | 0.615851 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.4225 | 1.25521 | 0.627604 | − | 0.778533i | \(-0.284036\pi\) | ||||
0.627604 | + | 0.778533i | \(0.284036\pi\) | |||||||
\(710\) | −13.9633 | −0.524034 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −24.1743 | −0.905968 | ||||||||
\(713\) | −7.53419 | −0.282158 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.26164 | 0.0845213 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.8601 | 1.07705 | ||||||||
\(719\) | 11.2829 | 0.420782 | 0.210391 | − | 0.977617i | \(-0.432526\pi\) | ||||
0.210391 | + | 0.977617i | \(0.432526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.85921 | 0.143724 | ||||||||
\(722\) | −43.6391 | −1.62408 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.06601 | −0.0396180 | ||||||||
\(725\) | 4.00136 | 0.148607 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.3381 | 1.60732 | 0.803661 | − | 0.595087i | \(-0.202882\pi\) | ||||
0.803661 | + | 0.595087i | \(0.202882\pi\) | |||||||
\(728\) | −28.7047 | −1.06387 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.41818 | 0.163524 | ||||||||
\(731\) | 48.0760 | 1.77816 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −52.1642 | −1.92673 | −0.963365 | − | 0.268195i | \(-0.913573\pi\) | ||||
−0.963365 | + | 0.268195i | \(0.913573\pi\) | |||||||
\(734\) | 3.95554 | 0.146002 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.50305 | −0.276566 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.7098 | 0.541109 | 0.270555 | − | 0.962705i | \(-0.412793\pi\) | ||||
0.270555 | + | 0.962705i | \(0.412793\pi\) | |||||||
\(740\) | −4.78032 | −0.175728 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −52.3034 | −1.92012 | ||||||||
\(743\) | −2.72748 | −0.100062 | −0.0500308 | − | 0.998748i | \(-0.515932\pi\) | ||||
−0.0500308 | + | 0.998748i | \(0.515932\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.4959 | −0.824185 | ||||||||
\(746\) | 14.5764 | 0.533679 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −59.5900 | −2.17737 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7867 | 0.612555 | 0.306277 | − | 0.951942i | \(-0.400916\pi\) | ||||
0.306277 | + | 0.951942i | \(0.400916\pi\) | |||||||
\(752\) | 6.61309 | 0.241154 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.3332 | −0.376313 | ||||||||
\(755\) | −2.99699 | −0.109072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.9310 | −0.833442 | −0.416721 | − | 0.909034i | \(-0.636821\pi\) | ||||
−0.416721 | + | 0.909034i | \(0.636821\pi\) | |||||||
\(758\) | 27.3291 | 0.992636 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23.3246 | −0.846071 | ||||||||
\(761\) | −7.81520 | −0.283301 | −0.141650 | − | 0.989917i | \(-0.545241\pi\) | ||||
−0.141650 | + | 0.989917i | \(0.545241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.5881 | 1.14357 | ||||||||
\(764\) | 7.41652 | 0.268320 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.60716 | 0.130332 | ||||||||
\(767\) | 21.6875 | 0.783092 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.6765 | −1.39471 | −0.697355 | − | 0.716726i | \(-0.745640\pi\) | ||||
−0.697355 | + | 0.716726i | \(0.745640\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.28077 | 0.154068 | ||||||||
\(773\) | 16.8813 | 0.607178 | 0.303589 | − | 0.952803i | \(-0.401815\pi\) | ||||
0.303589 | + | 0.952803i | \(0.401815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.81490 | −0.137035 | ||||||||
\(776\) | 15.9397 | 0.572201 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.9219 | 0.606678 | ||||||||
\(779\) | 30.4888 | 1.09237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 11.2569 | 0.402548 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.3802 | −0.727864 | ||||||||
\(785\) | 10.1899 | 0.363694 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.1091 | −0.966335 | −0.483167 | − | 0.875528i | \(-0.660514\pi\) | ||||
−0.483167 | + | 0.875528i | \(0.660514\pi\) | |||||||
\(788\) | 6.44185 | 0.229481 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.9595 | −0.710126 | ||||||||
\(791\) | −2.77045 | −0.0985060 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.21293 | −0.291650 | ||||||||
\(794\) | −12.3605 | −0.438658 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.2967 | −0.435845 | ||||||||
\(797\) | 23.5525 | 0.834272 | 0.417136 | − | 0.908844i | \(-0.363034\pi\) | ||||
0.417136 | + | 0.908844i | \(0.363034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.9938 | 0.565820 | ||||||||
\(800\) | −3.79913 | −0.134320 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 37.8012 | 1.33481 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.09986 | 0.285483 | ||||||||
\(806\) | 9.85168 | 0.347011 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.2892 | −0.432333 | ||||||||
\(809\) | 18.0138 | 0.633330 | 0.316665 | − | 0.948537i | \(-0.397437\pi\) | ||||
0.316665 | + | 0.948537i | \(0.397437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.25684 | −0.219707 | −0.109854 | − | 0.993948i | \(-0.535038\pi\) | ||||
−0.109854 | + | 0.993948i | \(0.535038\pi\) | |||||||
\(812\) | 11.6551 | 0.409013 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.8034 | 0.693683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −72.5893 | −2.53958 | ||||||||
\(818\) | 3.15374 | 0.110268 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.85741 | 0.0997853 | ||||||||
\(821\) | 18.9344 | 0.660815 | 0.330408 | − | 0.943838i | \(-0.392814\pi\) | ||||
0.330408 | + | 0.943838i | \(0.392814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3683 | 0.814566 | 0.407283 | − | 0.913302i | \(-0.366476\pi\) | ||||
0.407283 | + | 0.913302i | \(0.366476\pi\) | |||||||
\(824\) | −2.89625 | −0.100896 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 44.4250 | 1.54574 | ||||||||
\(827\) | −5.01148 | −0.174266 | −0.0871330 | − | 0.996197i | \(-0.527771\pi\) | ||||
−0.0871330 | + | 0.996197i | \(0.527771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.9519 | 1.56124 | 0.780622 | − | 0.625003i | \(-0.214902\pi\) | ||||
0.780622 | + | 0.625003i | \(0.214902\pi\) | |||||||
\(830\) | 15.7265 | 0.545876 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.2484 | 0.667320 | ||||||||
\(833\) | −49.2897 | −1.70779 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.96739 | −0.171903 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −33.5670 | −1.15955 | ||||||||
\(839\) | 52.4551 | 1.81095 | 0.905475 | − | 0.424399i | \(-0.139514\pi\) | ||||
0.905475 | + | 0.424399i | \(0.139514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.9891 | −0.447901 | ||||||||
\(842\) | −0.331512 | −0.0114247 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.1611 | −0.384182 | ||||||||
\(845\) | 7.82948 | 0.269342 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 23.3026 | 0.800215 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.69990 | 0.195505 | ||||||||
\(851\) | −13.2931 | −0.455682 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.1056 | 1.71558 | 0.857791 | − | 0.513998i | \(-0.171836\pi\) | ||||
0.857791 | + | 0.513998i | \(0.171836\pi\) | |||||||
\(854\) | −16.8235 | −0.575687 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.7211 | 1.52853 | ||||||||
\(857\) | 13.2279 | 0.451856 | 0.225928 | − | 0.974144i | \(-0.427459\pi\) | ||||
0.225928 | + | 0.974144i | \(0.427459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.3765 | −1.71883 | −0.859413 | − | 0.511283i | \(-0.829171\pi\) | ||||
−0.859413 | + | 0.511283i | \(0.829171\pi\) | |||||||
\(860\) | −6.80308 | −0.231983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.10584 | 0.173906 | ||||||||
\(863\) | −13.6184 | −0.463576 | −0.231788 | − | 0.972766i | \(-0.574458\pi\) | ||||
−0.231788 | + | 0.972766i | \(0.574458\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.2510 | −0.552549 | ||||||||
\(866\) | 7.45948 | 0.253483 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.1120 | −0.377165 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.3596 | −0.486557 | ||||||||
\(872\) | −23.7062 | −0.802793 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.9967 | −0.574922 | ||||||||
\(875\) | 4.10132 | 0.138650 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0237 | 0.676152 | 0.338076 | − | 0.941119i | \(-0.390224\pi\) | ||||
0.338076 | + | 0.941119i | \(0.390224\pi\) | |||||||
\(878\) | −30.3391 | −1.02389 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0543 | 1.01256 | 0.506278 | − | 0.862371i | \(-0.331021\pi\) | ||||
0.506278 | + | 0.862371i | \(0.331021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0963 | 0.979168 | 0.489584 | − | 0.871956i | \(-0.337149\pi\) | ||||
0.489584 | + | 0.871956i | \(0.337149\pi\) | |||||||
\(884\) | 8.10509 | 0.272604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.3106 | −0.883921 | ||||||||
\(887\) | −18.7486 | −0.629515 | −0.314758 | − | 0.949172i | \(-0.601923\pi\) | ||||
−0.314758 | + | 0.949172i | \(0.601923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0912 | −0.606758 | ||||||||
\(890\) | −8.91971 | −0.298989 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.769733 | −0.0257726 | ||||||||
\(893\) | −24.1488 | −0.808109 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.18448 | 0.106445 | ||||||||
\(896\) | 8.26581 | 0.276141 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.0024 | −1.10130 | ||||||||
\(899\) | −15.2648 | −0.509109 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.3576 | 1.87754 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.07917 | 0.0691520 | ||||||||
\(905\) | −1.50099 | −0.0498945 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.7590 | 1.28697 | 0.643486 | − | 0.765458i | \(-0.277488\pi\) | ||||
0.643486 | + | 0.765458i | \(0.277488\pi\) | |||||||
\(908\) | 1.41453 | 0.0469427 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.5913 | −0.351100 | ||||||||
\(911\) | −34.8367 | −1.15419 | −0.577096 | − | 0.816677i | \(-0.695814\pi\) | ||||
−0.577096 | + | 0.816677i | \(0.695814\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 8.66238 | 0.286526 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.78089 | −0.191006 | ||||||||
\(917\) | −87.7701 | −2.89842 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.3492 | 0.902167 | 0.451083 | − | 0.892482i | \(-0.351038\pi\) | ||||
0.451083 | + | 0.892482i | \(0.351038\pi\) | |||||||
\(920\) | −6.07877 | −0.200411 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38.6292 | 1.27218 | ||||||||
\(923\) | −27.9573 | −0.920227 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.73089 | −0.221310 | ||||||||
\(926\) | −17.8944 | −0.588047 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.2017 | −0.499020 | ||||||||
\(929\) | 44.0757 | 1.44608 | 0.723039 | − | 0.690808i | \(-0.242745\pi\) | ||||
0.723039 | + | 0.690808i | \(0.242745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 74.4218 | 2.43908 | ||||||||
\(932\) | −17.3500 | −0.568319 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.5282 | 0.377214 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3465 | −0.664690 | −0.332345 | − | 0.943158i | \(-0.607840\pi\) | ||||
−0.332345 | + | 0.943158i | \(0.607840\pi\) | |||||||
\(938\) | −29.4144 | −0.960415 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.26323 | −0.0738185 | ||||||||
\(941\) | 3.86942 | 0.126140 | 0.0630698 | − | 0.998009i | \(-0.479911\pi\) | ||||
0.0630698 | + | 0.998009i | \(0.479911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.94589 | 0.258754 | ||||||||
\(944\) | −19.7926 | −0.644194 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.4898 | 1.77068 | 0.885340 | − | 0.464943i | \(-0.153925\pi\) | ||||
0.885340 | + | 0.464943i | \(0.153925\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.84607 | 0.287155 | ||||||||
\(950\) | −8.60619 | −0.279222 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 63.3568 | 2.05341 | ||||||||
\(953\) | −40.5032 | −1.31203 | −0.656014 | − | 0.754748i | \(-0.727759\pi\) | ||||
−0.656014 | + | 0.754748i | \(0.727759\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.4428 | 0.337921 | ||||||||
\(956\) | 0.0504136 | 0.00163049 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.59177 | −0.148353 | ||||||||
\(959\) | −15.6724 | −0.506087 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.4465 | −0.530533 | ||||||||
\(962\) | 17.3820 | 0.560418 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.99495 | −0.289708 | ||||||||
\(965\) | 6.02750 | 0.194032 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.9360 | −0.737572 | −0.368786 | − | 0.929514i | \(-0.620226\pi\) | ||||
−0.368786 | + | 0.929514i | \(0.620226\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.88136 | 0.188839 | ||||||||
\(971\) | −46.3553 | −1.48761 | −0.743806 | − | 0.668396i | \(-0.766981\pi\) | ||||
−0.743806 | + | 0.668396i | \(0.766981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.8269 | 0.827972 | ||||||||
\(974\) | −8.37675 | −0.268408 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.49533 | 0.239920 | ||||||||
\(977\) | −26.4057 | −0.844794 | −0.422397 | − | 0.906411i | \(-0.638811\pi\) | ||||
−0.422397 | + | 0.906411i | \(0.638811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.97483 | 0.222803 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.49316 | 0.0795600 | ||||||||
\(983\) | −15.7849 | −0.503461 | −0.251730 | − | 0.967797i | \(-0.581000\pi\) | ||||
−0.251730 | + | 0.967797i | \(0.581000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.07040 | 0.289007 | ||||||||
\(986\) | 22.8073 | 0.726333 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.2378 | −0.389335 | ||||||||
\(989\) | −18.9180 | −0.601557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.9885 | 0.889085 | 0.444542 | − | 0.895758i | \(-0.353366\pi\) | ||||
0.444542 | + | 0.895758i | \(0.353366\pi\) | |||||||
\(992\) | 14.4933 | 0.460163 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −57.2681 | −1.81644 | ||||||||
\(995\) | −17.3143 | −0.548900 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.5825 | −1.25359 | −0.626796 | − | 0.779184i | \(-0.715634\pi\) | ||||
−0.626796 | + | 0.779184i | \(0.715634\pi\) | |||||||
\(998\) | −9.15572 | −0.289819 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5445.2.a.cc.1.2 | 8 | ||
3.2 | odd | 2 | 5445.2.a.cb.1.7 | 8 | |||
11.2 | odd | 10 | 495.2.n.h.136.1 | yes | 16 | ||
11.6 | odd | 10 | 495.2.n.h.91.1 | yes | 16 | ||
11.10 | odd | 2 | 5445.2.a.ca.1.7 | 8 | |||
33.2 | even | 10 | 495.2.n.g.136.4 | yes | 16 | ||
33.17 | even | 10 | 495.2.n.g.91.4 | ✓ | 16 | ||
33.32 | even | 2 | 5445.2.a.cd.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.n.g.91.4 | ✓ | 16 | 33.17 | even | 10 | ||
495.2.n.g.136.4 | yes | 16 | 33.2 | even | 10 | ||
495.2.n.h.91.1 | yes | 16 | 11.6 | odd | 10 | ||
495.2.n.h.136.1 | yes | 16 | 11.2 | odd | 10 | ||
5445.2.a.ca.1.7 | 8 | 11.10 | odd | 2 | |||
5445.2.a.cb.1.7 | 8 | 3.2 | odd | 2 | |||
5445.2.a.cc.1.2 | 8 | 1.1 | even | 1 | trivial | ||
5445.2.a.cd.1.2 | 8 | 33.32 | even | 2 |