Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(1,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.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: | \(6.90322347067\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{14}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 14 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.74166\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74166 | 0.969322 | 0.484661 | − | 0.874702i | \(-0.338943\pi\) | ||||
0.484661 | + | 0.874702i | \(0.338943\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.483315 | −0.0604143 | ||||||||
\(5\) | −19.4833 | −1.74264 | −0.871320 | − | 0.490715i | \(-0.836736\pi\) | ||||
−0.871320 | + | 0.490715i | \(0.836736\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.48331 | 0.404061 | 0.202031 | − | 0.979379i | \(-0.435246\pi\) | ||||
0.202031 | + | 0.979379i | \(0.435246\pi\) | |||||||
\(8\) | −23.2583 | −1.02788 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −53.4166 | −1.68918 | ||||||||
\(11\) | −22.8999 | −0.627689 | −0.313844 | − | 0.949474i | \(-0.601617\pi\) | ||||
−0.313844 | + | 0.949474i | \(0.601617\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 20.5167 | 0.391665 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −59.8999 | −0.935936 | ||||||||
\(17\) | −67.0334 | −0.956352 | −0.478176 | − | 0.878264i | \(-0.658702\pi\) | ||||
−0.478176 | + | 0.878264i | \(0.658702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.5167 | 0.199431 | 0.0997155 | − | 0.995016i | \(-0.468207\pi\) | ||||
0.0997155 | + | 0.995016i | \(0.468207\pi\) | |||||||
\(20\) | 9.41657 | 0.105280 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −62.7836 | −0.608433 | ||||||||
\(23\) | 175.600 | 1.59196 | 0.795979 | − | 0.605324i | \(-0.206956\pi\) | ||||
0.795979 | + | 0.605324i | \(0.206956\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 254.600 | 2.03680 | ||||||||
\(26\) | −35.6415 | −0.268842 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.61680 | −0.0244111 | ||||||||
\(29\) | −291.800 | −1.86848 | −0.934239 | − | 0.356648i | \(-0.883920\pi\) | ||||
−0.934239 | + | 0.356648i | \(0.883920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 117.283 | 0.679505 | 0.339753 | − | 0.940515i | \(-0.389657\pi\) | ||||
0.339753 | + | 0.940515i | \(0.389657\pi\) | |||||||
\(32\) | 21.8418 | 0.120660 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −183.783 | −0.927013 | ||||||||
\(35\) | −145.800 | −0.704133 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −154.766 | −0.687661 | −0.343830 | − | 0.939032i | \(-0.611724\pi\) | ||||
−0.343830 | + | 0.939032i | \(0.611724\pi\) | |||||||
\(38\) | 45.2831 | 0.193313 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 453.150 | 1.79123 | ||||||||
\(41\) | 251.716 | 0.958815 | 0.479407 | − | 0.877592i | \(-0.340852\pi\) | ||||
0.479407 | + | 0.877592i | \(0.340852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −502.566 | −1.78234 | −0.891170 | − | 0.453669i | \(-0.850115\pi\) | ||||
−0.891170 | + | 0.453669i | \(0.850115\pi\) | |||||||
\(44\) | 11.0679 | 0.0379214 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 481.434 | 1.54312 | ||||||||
\(47\) | 281.733 | 0.874361 | 0.437181 | − | 0.899374i | \(-0.355977\pi\) | ||||
0.437181 | + | 0.899374i | \(0.355977\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −287.000 | −0.836735 | ||||||||
\(50\) | 698.025 | 1.97431 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.28309 | 0.0167559 | ||||||||
\(53\) | −366.999 | −0.951154 | −0.475577 | − | 0.879674i | \(-0.657761\pi\) | ||||
−0.475577 | + | 0.879674i | \(0.657761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 446.166 | 1.09384 | ||||||||
\(56\) | −174.049 | −0.415328 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −800.015 | −1.81116 | ||||||||
\(59\) | 79.6663 | 0.175791 | 0.0878955 | − | 0.996130i | \(-0.471986\pi\) | ||||
0.0878955 | + | 0.996130i | \(0.471986\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −194.865 | −0.409016 | −0.204508 | − | 0.978865i | \(-0.565559\pi\) | ||||
−0.204508 | + | 0.978865i | \(0.565559\pi\) | |||||||
\(62\) | 321.550 | 0.658660 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 539.082 | 1.05289 | ||||||||
\(65\) | 253.283 | 0.483322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 400.082 | 0.729519 | 0.364759 | − | 0.931102i | \(-0.381151\pi\) | ||||
0.364759 | + | 0.931102i | \(0.381151\pi\) | |||||||
\(68\) | 32.3982 | 0.0577774 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −399.733 | −0.682532 | ||||||||
\(71\) | −528.299 | −0.883065 | −0.441532 | − | 0.897245i | \(-0.645565\pi\) | ||||
−0.441532 | + | 0.897245i | \(0.645565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −734.366 | −1.17741 | −0.588706 | − | 0.808347i | \(-0.700362\pi\) | ||||
−0.588706 | + | 0.808347i | \(0.700362\pi\) | |||||||
\(74\) | −424.316 | −0.666565 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.98276 | −0.0120485 | ||||||||
\(77\) | −171.367 | −0.253625 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 113.266 | 0.161309 | 0.0806545 | − | 0.996742i | \(-0.474299\pi\) | ||||
0.0806545 | + | 0.996742i | \(0.474299\pi\) | |||||||
\(80\) | 1167.05 | 1.63100 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 690.118 | 0.929400 | ||||||||
\(83\) | 933.466 | 1.23447 | 0.617236 | − | 0.786778i | \(-0.288252\pi\) | ||||
0.617236 | + | 0.786778i | \(0.288252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1306.03 | 1.66658 | ||||||||
\(86\) | −1377.86 | −1.72766 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 532.613 | 0.645191 | ||||||||
\(89\) | −1190.91 | −1.41839 | −0.709195 | − | 0.705012i | \(-0.750941\pi\) | ||||
−0.709195 | + | 0.705012i | \(0.750941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −97.2831 | −0.112066 | ||||||||
\(92\) | −84.8699 | −0.0961771 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 772.415 | 0.847538 | ||||||||
\(95\) | −321.800 | −0.347536 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 557.165 | 0.583211 | 0.291606 | − | 0.956539i | \(-0.405811\pi\) | ||||
0.291606 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(98\) | −786.856 | −0.811066 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −123.052 | −0.123052 | ||||||||
\(101\) | 286.766 | 0.282518 | 0.141259 | − | 0.989973i | \(-0.454885\pi\) | ||||
0.141259 | + | 0.989973i | \(0.454885\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1911.36 | −1.82847 | −0.914234 | − | 0.405187i | \(-0.867206\pi\) | ||||
−0.914234 | + | 0.405187i | \(0.867206\pi\) | |||||||
\(104\) | 302.358 | 0.285084 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1006.19 | −0.921975 | ||||||||
\(107\) | −834.334 | −0.753814 | −0.376907 | − | 0.926251i | \(-0.623012\pi\) | ||||
−0.376907 | + | 0.926251i | \(0.623012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1077.66 | −0.946986 | −0.473493 | − | 0.880798i | \(-0.657007\pi\) | ||||
−0.473493 | + | 0.880798i | \(0.657007\pi\) | |||||||
\(110\) | 1223.23 | 1.06028 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −448.250 | −0.378175 | ||||||||
\(113\) | 166.065 | 0.138248 | 0.0691241 | − | 0.997608i | \(-0.477980\pi\) | ||||
0.0691241 | + | 0.997608i | \(0.477980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3421.26 | −2.77421 | ||||||||
\(116\) | 141.031 | 0.112883 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 218.418 | 0.170398 | ||||||||
\(119\) | −501.632 | −0.386424 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −806.595 | −0.606007 | ||||||||
\(122\) | −534.254 | −0.396468 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −56.6847 | −0.0410519 | ||||||||
\(125\) | −2525.03 | −1.80676 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1296.16 | 0.905637 | 0.452819 | − | 0.891603i | \(-0.350419\pi\) | ||||
0.452819 | + | 0.891603i | \(0.350419\pi\) | |||||||
\(128\) | 1303.24 | 0.899934 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 694.415 | 0.468494 | ||||||||
\(131\) | 197.201 | 0.131523 | 0.0657617 | − | 0.997835i | \(-0.479052\pi\) | ||||
0.0657617 | + | 0.997835i | \(0.479052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 123.600 | 0.0805823 | ||||||||
\(134\) | 1096.89 | 0.707139 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1559.09 | 0.983018 | ||||||||
\(137\) | 546.915 | 0.341066 | 0.170533 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170533 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 609.666 | 0.372023 | 0.186012 | − | 0.982548i | \(-0.440444\pi\) | ||||
0.186012 | + | 0.982548i | \(0.440444\pi\) | |||||||
\(140\) | 70.4672 | 0.0425397 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1448.42 | −0.855974 | ||||||||
\(143\) | 297.699 | 0.174090 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5685.23 | 3.25609 | ||||||||
\(146\) | −2013.38 | −1.14129 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 74.8009 | 0.0415446 | ||||||||
\(149\) | 2165.08 | 1.19040 | 0.595202 | − | 0.803576i | \(-0.297072\pi\) | ||||
0.595202 | + | 0.803576i | \(0.297072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −846.549 | −0.456233 | −0.228116 | − | 0.973634i | \(-0.573257\pi\) | ||||
−0.228116 | + | 0.973634i | \(0.573257\pi\) | |||||||
\(152\) | −384.151 | −0.204992 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −469.830 | −0.245844 | ||||||||
\(155\) | −2285.06 | −1.18413 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1653.60 | 0.840581 | 0.420291 | − | 0.907390i | \(-0.361928\pi\) | ||||
0.420291 | + | 0.907390i | \(0.361928\pi\) | |||||||
\(158\) | 310.536 | 0.156360 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −425.550 | −0.210267 | ||||||||
\(161\) | 1314.07 | 0.643248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2866.51 | −1.37744 | −0.688720 | − | 0.725027i | \(-0.741827\pi\) | ||||
−0.688720 | + | 0.725027i | \(0.741827\pi\) | |||||||
\(164\) | −121.658 | −0.0579262 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2559.24 | 1.19660 | ||||||||
\(167\) | −729.066 | −0.337825 | −0.168913 | − | 0.985631i | \(-0.554026\pi\) | ||||
−0.168913 | + | 0.985631i | \(0.554026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 3580.69 | 1.61545 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 242.898 | 0.107679 | ||||||||
\(173\) | 3834.83 | 1.68530 | 0.842650 | − | 0.538462i | \(-0.180995\pi\) | ||||
0.842650 | + | 0.538462i | \(0.180995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1905.25 | 0.822990 | ||||||||
\(176\) | 1371.70 | 0.587476 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3265.08 | −1.37488 | ||||||||
\(179\) | 283.862 | 0.118530 | 0.0592649 | − | 0.998242i | \(-0.481124\pi\) | ||||
0.0592649 | + | 0.998242i | \(0.481124\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2363.60 | 0.970634 | 0.485317 | − | 0.874338i | \(-0.338704\pi\) | ||||
0.485317 | + | 0.874338i | \(0.338704\pi\) | |||||||
\(182\) | −266.717 | −0.108628 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4084.15 | −1.63635 | ||||||||
\(185\) | 3015.36 | 1.19835 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1535.06 | 0.600291 | ||||||||
\(188\) | −136.166 | −0.0528240 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −882.265 | −0.336875 | ||||||||
\(191\) | −2514.26 | −0.952491 | −0.476246 | − | 0.879312i | \(-0.658003\pi\) | ||||
−0.476246 | + | 0.879312i | \(0.658003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2420.73 | 0.902839 | 0.451420 | − | 0.892312i | \(-0.350918\pi\) | ||||
0.451420 | + | 0.892312i | \(0.350918\pi\) | |||||||
\(194\) | 1527.55 | 0.565320 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 138.711 | 0.0505508 | ||||||||
\(197\) | 4633.65 | 1.67581 | 0.837903 | − | 0.545819i | \(-0.183781\pi\) | ||||
0.837903 | + | 0.545819i | \(0.183781\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3054.17 | 1.08796 | 0.543980 | − | 0.839098i | \(-0.316917\pi\) | ||||
0.543980 | + | 0.839098i | \(0.316917\pi\) | |||||||
\(200\) | −5921.56 | −2.09359 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 786.215 | 0.273851 | ||||||||
\(203\) | −2183.63 | −0.754979 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4904.26 | −1.67087 | ||||||||
\(206\) | −5240.30 | −1.77237 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 778.699 | 0.259582 | ||||||||
\(209\) | −378.230 | −0.125181 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4031.60 | −1.31539 | −0.657694 | − | 0.753285i | \(-0.728468\pi\) | ||||
−0.657694 | + | 0.753285i | \(0.728468\pi\) | |||||||
\(212\) | 177.376 | 0.0574634 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2287.46 | −0.730689 | ||||||||
\(215\) | 9791.66 | 3.10598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 877.666 | 0.274562 | ||||||||
\(218\) | −2954.59 | −0.917935 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −215.638 | −0.0660834 | ||||||||
\(221\) | 871.434 | 0.265244 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3784.95 | 1.13659 | 0.568294 | − | 0.822826i | \(-0.307604\pi\) | ||||
0.568294 | + | 0.822826i | \(0.307604\pi\) | |||||||
\(224\) | 163.449 | 0.0487539 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 455.292 | 0.134007 | ||||||||
\(227\) | −2013.83 | −0.588821 | −0.294411 | − | 0.955679i | \(-0.595123\pi\) | ||||
−0.294411 | + | 0.955679i | \(0.595123\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3050.73 | −0.880340 | −0.440170 | − | 0.897915i | \(-0.645082\pi\) | ||||
−0.440170 | + | 0.897915i | \(0.645082\pi\) | |||||||
\(230\) | −9379.93 | −2.68910 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6786.78 | 1.92058 | ||||||||
\(233\) | −5587.49 | −1.57103 | −0.785513 | − | 0.618846i | \(-0.787601\pi\) | ||||
−0.785513 | + | 0.618846i | \(0.787601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5489.09 | −1.52370 | ||||||||
\(236\) | −38.5039 | −0.0106203 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1375.30 | −0.374570 | ||||||||
\(239\) | 1335.69 | 0.361501 | 0.180750 | − | 0.983529i | \(-0.442147\pi\) | ||||
0.180750 | + | 0.983529i | \(0.442147\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −571.558 | −0.152769 | −0.0763845 | − | 0.997078i | \(-0.524338\pi\) | ||||
−0.0763845 | + | 0.997078i | \(0.524338\pi\) | |||||||
\(242\) | −2211.41 | −0.587416 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 94.1813 | 0.0247104 | ||||||||
\(245\) | 5591.71 | 1.45813 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −214.717 | −0.0553122 | ||||||||
\(248\) | −2727.81 | −0.698452 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6922.76 | −1.75134 | ||||||||
\(251\) | −4088.60 | −1.02817 | −0.514084 | − | 0.857740i | \(-0.671868\pi\) | ||||
−0.514084 | + | 0.857740i | \(0.671868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4021.21 | −0.999254 | ||||||||
\(254\) | 3553.64 | 0.877854 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −739.607 | −0.180568 | ||||||||
\(257\) | −3050.23 | −0.740342 | −0.370171 | − | 0.928964i | \(-0.620701\pi\) | ||||
−0.370171 | + | 0.928964i | \(0.620701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1158.17 | −0.277857 | ||||||||
\(260\) | −122.415 | −0.0291996 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 540.659 | 0.127489 | ||||||||
\(263\) | −5770.99 | −1.35306 | −0.676530 | − | 0.736415i | \(-0.736517\pi\) | ||||
−0.676530 | + | 0.736415i | \(0.736517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7150.35 | 1.65752 | ||||||||
\(266\) | 338.868 | 0.0781102 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −193.365 | −0.0440734 | ||||||||
\(269\) | 2079.40 | 0.471314 | 0.235657 | − | 0.971836i | \(-0.424276\pi\) | ||||
0.235657 | + | 0.971836i | \(0.424276\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6012.00 | 1.34761 | 0.673807 | − | 0.738908i | \(-0.264658\pi\) | ||||
0.673807 | + | 0.738908i | \(0.264658\pi\) | |||||||
\(272\) | 4015.29 | 0.895084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1499.45 | 0.330603 | ||||||||
\(275\) | −5830.30 | −1.27847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −735.201 | −0.159473 | −0.0797364 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797364 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(278\) | 1671.50 | 0.360610 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3391.06 | 0.723767 | ||||||||
\(281\) | 1902.92 | 0.403981 | 0.201990 | − | 0.979387i | \(-0.435259\pi\) | ||||
0.201990 | + | 0.979387i | \(0.435259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2125.71 | 0.446502 | 0.223251 | − | 0.974761i | \(-0.428333\pi\) | ||||
0.223251 | + | 0.974761i | \(0.428333\pi\) | |||||||
\(284\) | 255.335 | 0.0533498 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 816.187 | 0.168749 | ||||||||
\(287\) | 1883.67 | 0.387420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −419.527 | −0.0853913 | ||||||||
\(290\) | 15586.9 | 3.15620 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 354.930 | 0.0711325 | ||||||||
\(293\) | 1641.03 | 0.327200 | 0.163600 | − | 0.986527i | \(-0.447689\pi\) | ||||
0.163600 | + | 0.986527i | \(0.447689\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1552.16 | −0.306341 | ||||||||
\(296\) | 3599.61 | 0.706835 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5935.91 | 1.15389 | ||||||||
\(299\) | −2282.79 | −0.441530 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3760.86 | −0.720174 | ||||||||
\(302\) | −2320.95 | −0.442237 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −989.348 | −0.186655 | ||||||||
\(305\) | 3796.62 | 0.712767 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3373.27 | −0.627111 | −0.313555 | − | 0.949570i | \(-0.601520\pi\) | ||||
−0.313555 | + | 0.949570i | \(0.601520\pi\) | |||||||
\(308\) | 82.8242 | 0.0153226 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6264.86 | −1.14781 | ||||||||
\(311\) | 868.525 | 0.158359 | 0.0791793 | − | 0.996860i | \(-0.474770\pi\) | ||||
0.0791793 | + | 0.996860i | \(0.474770\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4343.19 | −0.784319 | −0.392159 | − | 0.919897i | \(-0.628272\pi\) | ||||
−0.392159 | + | 0.919897i | \(0.628272\pi\) | |||||||
\(314\) | 4533.59 | 0.814794 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −54.7431 | −0.00974537 | ||||||||
\(317\) | 3277.65 | 0.580730 | 0.290365 | − | 0.956916i | \(-0.406223\pi\) | ||||
0.290365 | + | 0.956916i | \(0.406223\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6682.18 | 1.17282 | ||||||||
\(320\) | −10503.1 | −1.83482 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3602.72 | 0.623515 | ||||||||
\(323\) | −1107.17 | −0.190726 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3309.79 | −0.564906 | ||||||||
\(326\) | −7859.00 | −1.33518 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5854.49 | −0.985550 | ||||||||
\(329\) | 2108.30 | 0.353295 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5589.62 | 0.928197 | 0.464099 | − | 0.885784i | \(-0.346378\pi\) | ||||
0.464099 | + | 0.885784i | \(0.346378\pi\) | |||||||
\(332\) | −451.158 | −0.0745798 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1998.85 | −0.327461 | ||||||||
\(335\) | −7794.92 | −1.27129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 901.544 | 0.145728 | 0.0728638 | − | 0.997342i | \(-0.476786\pi\) | ||||
0.0728638 | + | 0.997342i | \(0.476786\pi\) | |||||||
\(338\) | 463.340 | 0.0745633 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −631.225 | −0.100685 | ||||||||
\(341\) | −2685.77 | −0.426518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4714.49 | −0.742153 | ||||||||
\(344\) | 11688.9 | 1.83204 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10513.8 | 1.63360 | ||||||||
\(347\) | 812.318 | 0.125670 | 0.0628350 | − | 0.998024i | \(-0.479986\pi\) | ||||
0.0628350 | + | 0.998024i | \(0.479986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4437.96 | 0.680683 | 0.340342 | − | 0.940302i | \(-0.389457\pi\) | ||||
0.340342 | + | 0.940302i | \(0.389457\pi\) | |||||||
\(350\) | 5223.54 | 0.797743 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −500.174 | −0.0757368 | ||||||||
\(353\) | −7115.35 | −1.07284 | −0.536419 | − | 0.843952i | \(-0.680223\pi\) | ||||
−0.536419 | + | 0.843952i | \(0.680223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10293.0 | 1.53886 | ||||||||
\(356\) | 575.587 | 0.0856911 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 778.253 | 0.114894 | ||||||||
\(359\) | −4693.98 | −0.690081 | −0.345040 | − | 0.938588i | \(-0.612135\pi\) | ||||
−0.345040 | + | 0.938588i | \(0.612135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6586.20 | −0.960227 | ||||||||
\(362\) | 6480.17 | 0.940857 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 47.0184 | 0.00677042 | ||||||||
\(365\) | 14307.9 | 2.05181 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9243.98 | 1.31480 | 0.657400 | − | 0.753542i | \(-0.271656\pi\) | ||||
0.657400 | + | 0.753542i | \(0.271656\pi\) | |||||||
\(368\) | −10518.4 | −1.48997 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8267.09 | 1.16158 | ||||||||
\(371\) | −2746.37 | −0.384324 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4311.99 | −0.598569 | −0.299285 | − | 0.954164i | \(-0.596748\pi\) | ||||
−0.299285 | + | 0.954164i | \(0.596748\pi\) | |||||||
\(374\) | 4208.60 | 0.581876 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6552.64 | −0.898741 | ||||||||
\(377\) | 3793.40 | 0.518223 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2382.73 | −0.322936 | −0.161468 | − | 0.986878i | \(-0.551623\pi\) | ||||
−0.161468 | + | 0.986878i | \(0.551623\pi\) | |||||||
\(380\) | 155.531 | 0.0209962 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6893.25 | −0.923271 | ||||||||
\(383\) | −4845.81 | −0.646499 | −0.323250 | − | 0.946314i | \(-0.604775\pi\) | ||||
−0.323250 | + | 0.946314i | \(0.604775\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3338.80 | 0.441976 | ||||||||
\(386\) | 6636.81 | 0.875142 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −269.286 | −0.0352343 | ||||||||
\(389\) | −9561.50 | −1.24624 | −0.623120 | − | 0.782127i | \(-0.714135\pi\) | ||||
−0.623120 | + | 0.782127i | \(0.714135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11771.0 | −1.52247 | ||||||||
\(392\) | 6675.14 | 0.860066 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12703.9 | 1.62440 | ||||||||
\(395\) | −2206.79 | −0.281103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7440.11 | −0.940575 | −0.470287 | − | 0.882513i | \(-0.655850\pi\) | ||||
−0.470287 | + | 0.882513i | \(0.655850\pi\) | |||||||
\(398\) | 8373.48 | 1.05458 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15250.5 | −1.90631 | ||||||||
\(401\) | 8687.80 | 1.08192 | 0.540958 | − | 0.841050i | \(-0.318062\pi\) | ||||
0.540958 | + | 0.841050i | \(0.318062\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1524.68 | −0.188461 | ||||||||
\(404\) | −138.598 | −0.0170681 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5986.76 | −0.731818 | ||||||||
\(407\) | 3544.13 | 0.431637 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2556.10 | 0.309024 | 0.154512 | − | 0.987991i | \(-0.450619\pi\) | ||||
0.154512 | + | 0.987991i | \(0.450619\pi\) | |||||||
\(410\) | −13445.8 | −1.61961 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 923.790 | 0.110466 | ||||||||
\(413\) | 596.168 | 0.0710303 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18187.0 | −2.15124 | ||||||||
\(416\) | −283.943 | −0.0334650 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1036.98 | −0.121340 | ||||||||
\(419\) | 3347.46 | 0.390296 | 0.195148 | − | 0.980774i | \(-0.437481\pi\) | ||||
0.195148 | + | 0.980774i | \(0.437481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1854.48 | −0.214684 | −0.107342 | − | 0.994222i | \(-0.534234\pi\) | ||||
−0.107342 | + | 0.994222i | \(0.534234\pi\) | |||||||
\(422\) | −11053.3 | −1.27503 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8535.79 | 0.977675 | ||||||||
\(425\) | −17066.7 | −1.94789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1458.24 | −0.165267 | ||||||||
\(428\) | 403.246 | 0.0455412 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26845.4 | 3.01069 | ||||||||
\(431\) | 14043.1 | 1.56945 | 0.784725 | − | 0.619844i | \(-0.212804\pi\) | ||||
0.784725 | + | 0.619844i | \(0.212804\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3086.47 | 0.342555 | 0.171278 | − | 0.985223i | \(-0.445210\pi\) | ||||
0.171278 | + | 0.985223i | \(0.445210\pi\) | |||||||
\(434\) | 2406.26 | 0.266139 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 520.851 | 0.0572116 | ||||||||
\(437\) | 2900.32 | 0.317486 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2837.68 | 0.308508 | 0.154254 | − | 0.988031i | \(-0.450703\pi\) | ||||
0.154254 | + | 0.988031i | \(0.450703\pi\) | |||||||
\(440\) | −10377.1 | −1.12434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2389.17 | 0.257107 | ||||||||
\(443\) | −18309.4 | −1.96367 | −0.981834 | − | 0.189744i | \(-0.939234\pi\) | ||||
−0.981834 | + | 0.189744i | \(0.939234\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23203.0 | 2.47174 | ||||||||
\(446\) | 10377.0 | 1.10172 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4034.12 | 0.425433 | ||||||||
\(449\) | −13861.2 | −1.45690 | −0.728451 | − | 0.685098i | \(-0.759759\pi\) | ||||
−0.728451 | + | 0.685098i | \(0.759759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5764.26 | −0.601837 | ||||||||
\(452\) | −80.2614 | −0.00835217 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5521.23 | −0.570758 | ||||||||
\(455\) | 1895.40 | 0.195291 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8990.36 | −0.920243 | −0.460122 | − | 0.887856i | \(-0.652194\pi\) | ||||
−0.460122 | + | 0.887856i | \(0.652194\pi\) | |||||||
\(458\) | −8364.05 | −0.853333 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1653.55 | 0.167602 | ||||||||
\(461\) | 3406.90 | 0.344198 | 0.172099 | − | 0.985080i | \(-0.444945\pi\) | ||||
0.172099 | + | 0.985080i | \(0.444945\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7498.45 | −0.752662 | −0.376331 | − | 0.926485i | \(-0.622814\pi\) | ||||
−0.376331 | + | 0.926485i | \(0.622814\pi\) | |||||||
\(464\) | 17478.8 | 1.74878 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15319.0 | −1.52283 | ||||||||
\(467\) | −7711.38 | −0.764112 | −0.382056 | − | 0.924139i | \(-0.624784\pi\) | ||||
−0.382056 | + | 0.924139i | \(0.624784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2993.94 | 0.294770 | ||||||||
\(470\) | −15049.2 | −1.47695 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1852.91 | −0.180693 | ||||||||
\(473\) | 11508.7 | 1.11875 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4205.14 | 0.406200 | ||||||||
\(476\) | 242.446 | 0.0233456 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3662.01 | 0.350411 | ||||||||
\(479\) | 9439.82 | 0.900451 | 0.450226 | − | 0.892915i | \(-0.351344\pi\) | ||||
0.450226 | + | 0.892915i | \(0.351344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2011.96 | 0.190723 | ||||||||
\(482\) | −1567.02 | −0.148082 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 389.839 | 0.0366115 | ||||||||
\(485\) | −10855.4 | −1.01633 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6156.20 | −0.572821 | −0.286411 | − | 0.958107i | \(-0.592462\pi\) | ||||
−0.286411 | + | 0.958107i | \(0.592462\pi\) | |||||||
\(488\) | 4532.25 | 0.420420 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15330.6 | 1.41340 | ||||||||
\(491\) | −3842.74 | −0.353198 | −0.176599 | − | 0.984283i | \(-0.556510\pi\) | ||||
−0.176599 | + | 0.984283i | \(0.556510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19560.3 | 1.78692 | ||||||||
\(494\) | −588.680 | −0.0536153 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7025.24 | −0.635973 | ||||||||
\(497\) | −3953.43 | −0.356812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12842.4 | −1.15211 | −0.576056 | − | 0.817410i | \(-0.695409\pi\) | ||||
−0.576056 | + | 0.817410i | \(0.695409\pi\) | |||||||
\(500\) | 1220.38 | 0.109154 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11209.5 | −0.996627 | ||||||||
\(503\) | −8580.11 | −0.760573 | −0.380287 | − | 0.924869i | \(-0.624175\pi\) | ||||
−0.380287 | + | 0.924869i | \(0.624175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5587.16 | −0.492327 | ||||||||
\(506\) | −11024.8 | −0.968599 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −626.455 | −0.0547135 | ||||||||
\(509\) | 43.5957 | 0.00379635 | 0.00189818 | − | 0.999998i | \(-0.499396\pi\) | ||||
0.00189818 | + | 0.999998i | \(0.499396\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5495.49 | −0.475746 | ||||||||
\(512\) | −12453.7 | −1.07496 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8362.68 | −0.717630 | ||||||||
\(515\) | 37239.7 | 3.18636 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6451.66 | −0.548827 | ||||||||
\(518\) | −3175.29 | −0.269333 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5890.94 | −0.496798 | ||||||||
\(521\) | −11368.1 | −0.955939 | −0.477969 | − | 0.878377i | \(-0.658627\pi\) | ||||
−0.477969 | + | 0.878377i | \(0.658627\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5229.53 | −0.437230 | −0.218615 | − | 0.975811i | \(-0.570154\pi\) | ||||
−0.218615 | + | 0.975811i | \(0.570154\pi\) | |||||||
\(524\) | −95.3103 | −0.00794590 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15822.1 | −1.31155 | ||||||||
\(527\) | −7861.88 | −0.649846 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18668.2 | 1.53433 | ||||||||
\(530\) | 19603.8 | 1.60667 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −59.7375 | −0.00486832 | ||||||||
\(533\) | −3272.31 | −0.265927 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16255.6 | 1.31363 | ||||||||
\(536\) | −9305.24 | −0.749860 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5701.01 | 0.456855 | ||||||||
\(539\) | 6572.27 | 0.525209 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6567.99 | −0.521959 | −0.260980 | − | 0.965344i | \(-0.584046\pi\) | ||||
−0.260980 | + | 0.965344i | \(0.584046\pi\) | |||||||
\(542\) | 16482.9 | 1.30627 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1464.13 | −0.115393 | ||||||||
\(545\) | 20996.5 | 1.65026 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13675.7 | −1.06897 | −0.534487 | − | 0.845177i | \(-0.679495\pi\) | ||||
−0.534487 | + | 0.845177i | \(0.679495\pi\) | |||||||
\(548\) | −264.332 | −0.0206053 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15984.7 | −1.23925 | ||||||||
\(551\) | −4819.57 | −0.372632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 847.604 | 0.0651786 | ||||||||
\(554\) | −2015.67 | −0.154581 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −294.661 | −0.0224755 | ||||||||
\(557\) | −4527.96 | −0.344445 | −0.172222 | − | 0.985058i | \(-0.555095\pi\) | ||||
−0.172222 | + | 0.985058i | \(0.555095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6533.36 | 0.494332 | ||||||||
\(560\) | 8733.39 | 0.659023 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5217.15 | 0.391588 | ||||||||
\(563\) | −18441.8 | −1.38051 | −0.690256 | − | 0.723566i | \(-0.742502\pi\) | ||||
−0.690256 | + | 0.723566i | \(0.742502\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3235.49 | −0.240917 | ||||||||
\(566\) | 5827.96 | 0.432804 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12287.4 | 0.907687 | ||||||||
\(569\) | 13553.5 | 0.998578 | 0.499289 | − | 0.866436i | \(-0.333595\pi\) | ||||
0.499289 | + | 0.866436i | \(0.333595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14815.5 | 1.08583 | 0.542915 | − | 0.839788i | \(-0.317321\pi\) | ||||
0.542915 | + | 0.839788i | \(0.317321\pi\) | |||||||
\(572\) | −143.882 | −0.0105175 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5164.37 | 0.375534 | ||||||||
\(575\) | 44707.6 | 3.24249 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21596.2 | 1.55816 | 0.779081 | − | 0.626923i | \(-0.215686\pi\) | ||||
0.779081 | + | 0.626923i | \(0.215686\pi\) | |||||||
\(578\) | −1150.20 | −0.0827716 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2747.75 | −0.196714 | ||||||||
\(581\) | 6985.42 | 0.498802 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8404.23 | 0.597029 | ||||||||
\(584\) | 17080.1 | 1.21024 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4499.13 | 0.317163 | ||||||||
\(587\) | 918.801 | 0.0646047 | 0.0323024 | − | 0.999478i | \(-0.489716\pi\) | ||||
0.0323024 | + | 0.999478i | \(0.489716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1937.13 | 0.135514 | ||||||||
\(590\) | −4255.50 | −0.296943 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9270.49 | 0.643606 | ||||||||
\(593\) | −19816.0 | −1.37226 | −0.686128 | − | 0.727481i | \(-0.740691\pi\) | ||||
−0.686128 | + | 0.727481i | \(0.740691\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9773.45 | 0.673399 | ||||||||
\(596\) | −1046.42 | −0.0719175 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6258.64 | −0.427985 | ||||||||
\(599\) | 5141.86 | 0.350736 | 0.175368 | − | 0.984503i | \(-0.443889\pi\) | ||||
0.175368 | + | 0.984503i | \(0.443889\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12380.9 | 0.840312 | 0.420156 | − | 0.907452i | \(-0.361975\pi\) | ||||
0.420156 | + | 0.907452i | \(0.361975\pi\) | |||||||
\(602\) | −10311.0 | −0.698081 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 409.150 | 0.0275630 | ||||||||
\(605\) | 15715.1 | 1.05605 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23717.0 | −1.58590 | −0.792951 | − | 0.609286i | \(-0.791456\pi\) | ||||
−0.792951 | + | 0.609286i | \(0.791456\pi\) | |||||||
\(608\) | 360.754 | 0.0240633 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10409.0 | 0.690901 | ||||||||
\(611\) | −3662.53 | −0.242504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26157.1 | −1.72345 | −0.861726 | − | 0.507373i | \(-0.830617\pi\) | ||||
−0.861726 | + | 0.507373i | \(0.830617\pi\) | |||||||
\(614\) | −9248.36 | −0.607872 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3985.71 | 0.260696 | ||||||||
\(617\) | −23613.9 | −1.54077 | −0.770387 | − | 0.637576i | \(-0.779937\pi\) | ||||
−0.770387 | + | 0.637576i | \(0.779937\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23345.4 | 1.51588 | 0.757940 | − | 0.652324i | \(-0.226206\pi\) | ||||
0.757940 | + | 0.652324i | \(0.226206\pi\) | |||||||
\(620\) | 1104.40 | 0.0715387 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2381.20 | 0.153501 | ||||||||
\(623\) | −8911.99 | −0.573116 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17371.0 | 1.11174 | ||||||||
\(626\) | −11907.5 | −0.760258 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −799.207 | −0.0507832 | ||||||||
\(629\) | 10374.5 | 0.657645 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15245.7 | 0.961841 | 0.480921 | − | 0.876764i | \(-0.340302\pi\) | ||||
0.480921 | + | 0.876764i | \(0.340302\pi\) | |||||||
\(632\) | −2634.38 | −0.165807 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8986.20 | 0.562914 | ||||||||
\(635\) | −25253.6 | −1.57820 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3731.00 | 0.232068 | ||||||||
\(638\) | 18320.3 | 1.13684 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −25391.5 | −1.56826 | ||||||||
\(641\) | −10192.7 | −0.628063 | −0.314032 | − | 0.949413i | \(-0.601680\pi\) | ||||
−0.314032 | + | 0.949413i | \(0.601680\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5506.31 | −0.337710 | −0.168855 | − | 0.985641i | \(-0.554007\pi\) | ||||
−0.168855 | + | 0.985641i | \(0.554007\pi\) | |||||||
\(644\) | −635.108 | −0.0388614 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3035.48 | −0.184875 | ||||||||
\(647\) | 13297.5 | 0.808005 | 0.404003 | − | 0.914758i | \(-0.367619\pi\) | ||||
0.404003 | + | 0.914758i | \(0.367619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1824.35 | −0.110342 | ||||||||
\(650\) | −9074.32 | −0.547576 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1385.43 | 0.0832171 | ||||||||
\(653\) | 12440.2 | 0.745519 | 0.372760 | − | 0.927928i | \(-0.378412\pi\) | ||||
0.372760 | + | 0.927928i | \(0.378412\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3842.14 | −0.229198 | ||||||||
\(656\) | −15077.7 | −0.897389 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5780.23 | 0.342457 | ||||||||
\(659\) | 9562.87 | 0.565276 | 0.282638 | − | 0.959227i | \(-0.408791\pi\) | ||||
0.282638 | + | 0.959227i | \(0.408791\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2409.69 | 0.141795 | 0.0708973 | − | 0.997484i | \(-0.477414\pi\) | ||||
0.0708973 | + | 0.997484i | \(0.477414\pi\) | |||||||
\(662\) | 15324.8 | 0.899722 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21710.9 | −1.26889 | ||||||||
\(665\) | −2408.13 | −0.140426 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51239.9 | −2.97454 | ||||||||
\(668\) | 352.368 | 0.0204095 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21371.0 | −1.23229 | ||||||||
\(671\) | 4462.40 | 0.256735 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7929.02 | 0.454147 | 0.227074 | − | 0.973878i | \(-0.427084\pi\) | ||||
0.227074 | + | 0.973878i | \(0.427084\pi\) | |||||||
\(674\) | 2471.72 | 0.141257 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −81.6802 | −0.00464726 | ||||||||
\(677\) | 2628.26 | 0.149206 | 0.0746030 | − | 0.997213i | \(-0.476231\pi\) | ||||
0.0746030 | + | 0.997213i | \(0.476231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4169.44 | 0.235653 | ||||||||
\(680\) | −30376.1 | −1.71305 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7363.46 | −0.413433 | ||||||||
\(683\) | −10021.5 | −0.561437 | −0.280719 | − | 0.959790i | \(-0.590573\pi\) | ||||
−0.280719 | + | 0.959790i | \(0.590573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10655.7 | −0.594356 | ||||||||
\(686\) | −12925.5 | −0.719385 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30103.7 | 1.66816 | ||||||||
\(689\) | 4770.99 | 0.263803 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23987.2 | 1.32057 | 0.660286 | − | 0.751014i | \(-0.270435\pi\) | ||||
0.660286 | + | 0.751014i | \(0.270435\pi\) | |||||||
\(692\) | −1853.43 | −0.101816 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2227.10 | 0.121815 | ||||||||
\(695\) | −11878.3 | −0.648303 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16873.4 | −0.916964 | ||||||||
\(698\) | 12167.4 | 0.659801 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −920.835 | −0.0497204 | ||||||||
\(701\) | 3763.71 | 0.202787 | 0.101393 | − | 0.994846i | \(-0.467670\pi\) | ||||
0.101393 | + | 0.994846i | \(0.467670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2556.23 | −0.137141 | ||||||||
\(704\) | −12344.9 | −0.660890 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19507.8 | −1.03993 | ||||||||
\(707\) | 2145.96 | 0.114155 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36047.8 | −1.90946 | −0.954728 | − | 0.297479i | \(-0.903854\pi\) | ||||
−0.954728 | + | 0.297479i | \(0.903854\pi\) | |||||||
\(710\) | 28219.9 | 1.49166 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27698.7 | 1.45794 | ||||||||
\(713\) | 20594.9 | 1.08174 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5800.15 | −0.303376 | ||||||||
\(716\) | −137.195 | −0.00716090 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12869.3 | −0.668910 | ||||||||
\(719\) | 3944.18 | 0.204580 | 0.102290 | − | 0.994755i | \(-0.467383\pi\) | ||||
0.102290 | + | 0.994755i | \(0.467383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14303.3 | −0.738812 | ||||||||
\(722\) | −18057.1 | −0.930770 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1142.36 | −0.0586402 | ||||||||
\(725\) | −74292.1 | −3.80571 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20447.8 | −1.04315 | −0.521573 | − | 0.853206i | \(-0.674655\pi\) | ||||
−0.521573 | + | 0.853206i | \(0.674655\pi\) | |||||||
\(728\) | 2262.64 | 0.115191 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 39227.3 | 1.98886 | ||||||||
\(731\) | 33688.7 | 1.70454 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13536.2 | −0.682089 | −0.341045 | − | 0.940047i | \(-0.610781\pi\) | ||||
−0.341045 | + | 0.940047i | \(0.610781\pi\) | |||||||
\(734\) | 25343.8 | 1.27447 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3835.40 | 0.192085 | ||||||||
\(737\) | −9161.83 | −0.457911 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15839.1 | 0.788433 | 0.394217 | − | 0.919018i | \(-0.371016\pi\) | ||||
0.394217 | + | 0.919018i | \(0.371016\pi\) | |||||||
\(740\) | −1457.37 | −0.0723972 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7529.60 | −0.372534 | ||||||||
\(743\) | 1664.92 | 0.0822075 | 0.0411037 | − | 0.999155i | \(-0.486913\pi\) | ||||
0.0411037 | + | 0.999155i | \(0.486913\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42182.9 | −2.07445 | ||||||||
\(746\) | −11822.0 | −0.580206 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −741.916 | −0.0362662 | ||||||||
\(749\) | −6243.58 | −0.304587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22399.1 | 1.08835 | 0.544177 | − | 0.838970i | \(-0.316842\pi\) | ||||
0.544177 | + | 0.838970i | \(0.316842\pi\) | |||||||
\(752\) | −16875.8 | −0.818346 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10400.2 | 0.502325 | ||||||||
\(755\) | 16493.6 | 0.795050 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23798.9 | 1.14265 | 0.571326 | − | 0.820723i | \(-0.306429\pi\) | ||||
0.571326 | + | 0.820723i | \(0.306429\pi\) | |||||||
\(758\) | −6532.64 | −0.313029 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7484.53 | 0.357227 | ||||||||
\(761\) | −13693.5 | −0.652285 | −0.326142 | − | 0.945321i | \(-0.605749\pi\) | ||||
−0.326142 | + | 0.945321i | \(0.605749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8064.50 | −0.382640 | ||||||||
\(764\) | 1215.18 | 0.0575441 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13285.5 | −0.626666 | ||||||||
\(767\) | −1035.66 | −0.0487556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16299.9 | 0.764358 | 0.382179 | − | 0.924088i | \(-0.375174\pi\) | ||||
0.382179 | + | 0.924088i | \(0.375174\pi\) | |||||||
\(770\) | 9153.84 | 0.428418 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1169.97 | −0.0545444 | ||||||||
\(773\) | −33532.2 | −1.56024 | −0.780122 | − | 0.625628i | \(-0.784843\pi\) | ||||
−0.780122 | + | 0.625628i | \(0.784843\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29860.2 | 1.38401 | ||||||||
\(776\) | −12958.7 | −0.599473 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26214.3 | −1.20801 | ||||||||
\(779\) | 4157.51 | 0.191217 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12098.0 | 0.554290 | ||||||||
\(782\) | −32272.1 | −1.47577 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17191.3 | 0.783130 | ||||||||
\(785\) | −32217.5 | −1.46483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16163.3 | 0.732097 | 0.366049 | − | 0.930596i | \(-0.380710\pi\) | ||||
0.366049 | + | 0.930596i | \(0.380710\pi\) | |||||||
\(788\) | −2239.51 | −0.101243 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6050.27 | −0.272480 | ||||||||
\(791\) | 1242.71 | 0.0558607 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2533.25 | 0.113441 | ||||||||
\(794\) | −20398.2 | −0.911720 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1476.12 | −0.0657284 | ||||||||
\(797\) | 39636.4 | 1.76160 | 0.880798 | − | 0.473492i | \(-0.157007\pi\) | ||||
0.880798 | + | 0.473492i | \(0.157007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18885.5 | −0.836197 | ||||||||
\(800\) | 5560.90 | 0.245760 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23819.0 | 1.04872 | ||||||||
\(803\) | 16816.9 | 0.739048 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25602.4 | −1.12095 | ||||||||
\(806\) | −4180.15 | −0.182679 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6669.71 | −0.290396 | ||||||||
\(809\) | 23811.2 | 1.03481 | 0.517403 | − | 0.855742i | \(-0.326899\pi\) | ||||
0.517403 | + | 0.855742i | \(0.326899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27218.6 | 1.17851 | 0.589256 | − | 0.807946i | \(-0.299421\pi\) | ||||
0.589256 | + | 0.807946i | \(0.299421\pi\) | |||||||
\(812\) | 1055.38 | 0.0456116 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9716.80 | 0.418395 | ||||||||
\(815\) | 55849.2 | 2.40038 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8300.73 | −0.355454 | ||||||||
\(818\) | 7007.94 | 0.299544 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2370.30 | 0.100944 | ||||||||
\(821\) | 43094.8 | 1.83193 | 0.915967 | − | 0.401253i | \(-0.131425\pi\) | ||||
0.915967 | + | 0.401253i | \(0.131425\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26541.1 | 1.12414 | 0.562068 | − | 0.827091i | \(-0.310006\pi\) | ||||
0.562068 | + | 0.827091i | \(0.310006\pi\) | |||||||
\(824\) | 44455.1 | 1.87945 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1634.49 | 0.0688512 | ||||||||
\(827\) | 44898.7 | 1.88788 | 0.943942 | − | 0.330112i | \(-0.107087\pi\) | ||||
0.943942 | + | 0.330112i | \(0.107087\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7137.48 | −0.299029 | −0.149514 | − | 0.988760i | \(-0.547771\pi\) | ||||
−0.149514 | + | 0.988760i | \(0.547771\pi\) | |||||||
\(830\) | −49862.6 | −2.08525 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7008.06 | −0.292020 | ||||||||
\(833\) | 19238.6 | 0.800213 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14204.6 | 0.588708 | ||||||||
\(836\) | 182.804 | 0.00756270 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9177.59 | 0.378323 | ||||||||
\(839\) | 4387.17 | 0.180527 | 0.0902634 | − | 0.995918i | \(-0.471229\pi\) | ||||
0.0902634 | + | 0.995918i | \(0.471229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 60758.1 | 2.49121 | ||||||||
\(842\) | −5084.36 | −0.208098 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1948.53 | 0.0794683 | ||||||||
\(845\) | −3292.68 | −0.134049 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6036.01 | −0.244864 | ||||||||
\(848\) | 21983.2 | 0.890219 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −46791.0 | −1.88814 | ||||||||
\(851\) | −27176.9 | −1.09473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9328.85 | −0.374459 | −0.187230 | − | 0.982316i | \(-0.559951\pi\) | ||||
−0.187230 | + | 0.982316i | \(0.559951\pi\) | |||||||
\(854\) | −3997.99 | −0.160197 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19405.2 | 0.774833 | ||||||||
\(857\) | 5010.39 | 0.199710 | 0.0998552 | − | 0.995002i | \(-0.468162\pi\) | ||||
0.0998552 | + | 0.995002i | \(0.468162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30233.4 | 1.20088 | 0.600438 | − | 0.799672i | \(-0.294993\pi\) | ||||
0.600438 | + | 0.799672i | \(0.294993\pi\) | |||||||
\(860\) | −4732.45 | −0.187646 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38501.4 | 1.52130 | ||||||||
\(863\) | −4334.93 | −0.170988 | −0.0854940 | − | 0.996339i | \(-0.527247\pi\) | ||||
−0.0854940 | + | 0.996339i | \(0.527247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −74715.2 | −2.93687 | ||||||||
\(866\) | 8462.05 | 0.332047 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −424.189 | −0.0165875 | ||||||||
\(869\) | −2593.78 | −0.101252 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5201.06 | −0.202332 | ||||||||
\(872\) | 25064.7 | 0.973391 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7951.69 | 0.307746 | ||||||||
\(875\) | −18895.6 | −0.730043 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34683.3 | 1.33543 | 0.667716 | − | 0.744416i | \(-0.267272\pi\) | ||||
0.667716 | + | 0.744416i | \(0.267272\pi\) | |||||||
\(878\) | 7779.95 | 0.299044 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −26725.3 | −1.02376 | ||||||||
\(881\) | 18269.2 | 0.698642 | 0.349321 | − | 0.937003i | \(-0.386412\pi\) | ||||
0.349321 | + | 0.937003i | \(0.386412\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14592.0 | −0.556128 | −0.278064 | − | 0.960563i | \(-0.589693\pi\) | ||||
−0.278064 | + | 0.960563i | \(0.589693\pi\) | |||||||
\(884\) | −421.177 | −0.0160246 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50198.0 | −1.90343 | ||||||||
\(887\) | −30459.3 | −1.15301 | −0.576507 | − | 0.817092i | \(-0.695585\pi\) | ||||
−0.576507 | + | 0.817092i | \(0.695585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9699.60 | 0.365933 | ||||||||
\(890\) | 63614.6 | 2.39592 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1829.32 | −0.0686662 | ||||||||
\(893\) | 4653.30 | 0.174375 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5530.57 | −0.206555 | ||||||||
\(896\) | 9752.58 | 0.363628 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −38002.6 | −1.41221 | ||||||||
\(899\) | −34223.2 | −1.26964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24601.2 | 0.909638 | ||||||||
\(902\) | −15803.6 | −0.583374 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3862.39 | −0.142103 | ||||||||
\(905\) | −46050.7 | −1.69147 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9364.89 | −0.342840 | −0.171420 | − | 0.985198i | \(-0.554836\pi\) | ||||
−0.171420 | + | 0.985198i | \(0.554836\pi\) | |||||||
\(908\) | 973.313 | 0.0355733 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5196.53 | 0.189300 | ||||||||
\(911\) | −32479.8 | −1.18123 | −0.590616 | − | 0.806952i | \(-0.701115\pi\) | ||||
−0.590616 | + | 0.806952i | \(0.701115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21376.3 | −0.774864 | ||||||||
\(914\) | −24648.5 | −0.892012 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1474.46 | 0.0531851 | ||||||||
\(917\) | 1475.72 | 0.0531435 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 295.958 | 0.0106232 | 0.00531161 | − | 0.999986i | \(-0.498309\pi\) | ||||
0.00531161 | + | 0.999986i | \(0.498309\pi\) | |||||||
\(920\) | 79572.9 | 2.85157 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9340.56 | 0.333639 | ||||||||
\(923\) | 6867.89 | 0.244918 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39403.5 | −1.40062 | ||||||||
\(926\) | −20558.2 | −0.729572 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6373.42 | −0.225450 | ||||||||
\(929\) | 5620.38 | 0.198492 | 0.0992458 | − | 0.995063i | \(-0.468357\pi\) | ||||
0.0992458 | + | 0.995063i | \(0.468357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4740.29 | −0.166871 | ||||||||
\(932\) | 2700.52 | 0.0949125 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21142.0 | −0.740670 | ||||||||
\(935\) | −29908.0 | −1.04609 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32583.1 | −1.13601 | −0.568006 | − | 0.823024i | \(-0.692285\pi\) | ||||
−0.568006 | + | 0.823024i | \(0.692285\pi\) | |||||||
\(938\) | 8208.35 | 0.285727 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2652.96 | 0.0920532 | ||||||||
\(941\) | −8812.99 | −0.305308 | −0.152654 | − | 0.988280i | \(-0.548782\pi\) | ||||
−0.152654 | + | 0.988280i | \(0.548782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44201.2 | 1.52639 | ||||||||
\(944\) | −4772.00 | −0.164529 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31552.9 | 1.08443 | ||||||||
\(947\) | −13426.8 | −0.460732 | −0.230366 | − | 0.973104i | \(-0.573992\pi\) | ||||
−0.230366 | + | 0.973104i | \(0.573992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9546.76 | 0.326555 | ||||||||
\(950\) | 11529.1 | 0.393739 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11667.1 | 0.397199 | ||||||||
\(953\) | 13394.6 | 0.455293 | 0.227647 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227647 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48986.2 | 1.65985 | ||||||||
\(956\) | −645.560 | −0.0218398 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25880.7 | 0.872828 | ||||||||
\(959\) | 4092.74 | 0.137812 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16035.7 | −0.538273 | ||||||||
\(962\) | 5516.11 | 0.184872 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 276.243 | 0.00922944 | ||||||||
\(965\) | −47163.8 | −1.57332 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45590.8 | 1.51613 | 0.758066 | − | 0.652178i | \(-0.226144\pi\) | ||||
0.758066 | + | 0.652178i | \(0.226144\pi\) | |||||||
\(968\) | 18760.1 | 0.622904 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29761.8 | −0.985149 | ||||||||
\(971\) | −264.763 | −0.00875041 | −0.00437521 | − | 0.999990i | \(-0.501393\pi\) | ||||
−0.00437521 | + | 0.999990i | \(0.501393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4562.32 | 0.150320 | ||||||||
\(974\) | −16878.2 | −0.555248 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11672.4 | 0.382812 | ||||||||
\(977\) | −610.521 | −0.0199921 | −0.00999606 | − | 0.999950i | \(-0.503182\pi\) | ||||
−0.00999606 | + | 0.999950i | \(0.503182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27271.8 | 0.890308 | ||||||||
\(980\) | −2702.56 | −0.0880918 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10535.5 | −0.342363 | ||||||||
\(983\) | 57829.7 | 1.87638 | 0.938190 | − | 0.346121i | \(-0.112501\pi\) | ||||
0.938190 | + | 0.346121i | \(0.112501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −90278.8 | −2.92033 | ||||||||
\(986\) | 53627.7 | 1.73210 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 103.776 | 0.00334165 | ||||||||
\(989\) | −88250.4 | −2.83741 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56780.7 | −1.82008 | −0.910039 | − | 0.414522i | \(-0.863949\pi\) | ||||
−0.910039 | + | 0.414522i | \(0.863949\pi\) | |||||||
\(992\) | 2561.67 | 0.0819890 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10838.9 | −0.345866 | ||||||||
\(995\) | −59505.3 | −1.89592 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18616.6 | 0.591369 | 0.295684 | − | 0.955286i | \(-0.404452\pi\) | ||||
0.295684 | + | 0.955286i | \(0.404452\pi\) | |||||||
\(998\) | −35209.4 | −1.11677 | ||||||||
\(999\) | 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 | 117.4.a.c.1.2 | 2 | ||
3.2 | odd | 2 | 39.4.a.b.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 1872.4.a.t.1.1 | 2 | |||
12.11 | even | 2 | 624.4.a.r.1.2 | 2 | |||
13.12 | even | 2 | 1521.4.a.s.1.1 | 2 | |||
15.14 | odd | 2 | 975.4.a.j.1.2 | 2 | |||
21.20 | even | 2 | 1911.4.a.h.1.1 | 2 | |||
24.5 | odd | 2 | 2496.4.a.bc.1.1 | 2 | |||
24.11 | even | 2 | 2496.4.a.s.1.1 | 2 | |||
39.5 | even | 4 | 507.4.b.f.337.3 | 4 | |||
39.8 | even | 4 | 507.4.b.f.337.2 | 4 | |||
39.38 | odd | 2 | 507.4.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.b.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
117.4.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
507.4.a.f.1.2 | 2 | 39.38 | odd | 2 | |||
507.4.b.f.337.2 | 4 | 39.8 | even | 4 | |||
507.4.b.f.337.3 | 4 | 39.5 | even | 4 | |||
624.4.a.r.1.2 | 2 | 12.11 | even | 2 | |||
975.4.a.j.1.2 | 2 | 15.14 | odd | 2 | |||
1521.4.a.s.1.1 | 2 | 13.12 | even | 2 | |||
1872.4.a.t.1.1 | 2 | 4.3 | odd | 2 | |||
1911.4.a.h.1.1 | 2 | 21.20 | even | 2 | |||
2496.4.a.s.1.1 | 2 | 24.11 | even | 2 | |||
2496.4.a.bc.1.1 | 2 | 24.5 | odd | 2 |