Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,4,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(78.0595269376\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 42x^{4} + 369x^{2} - 112 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.46131\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.46131 | 1.22376 | 0.611879 | − | 0.790951i | \(-0.290414\pi\) | ||||
0.611879 | + | 0.790951i | \(0.290414\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.98067 | 0.497583 | ||||||||
\(5\) | 6.55599 | 0.586386 | 0.293193 | − | 0.956053i | \(-0.405282\pi\) | ||||
0.293193 | + | 0.956053i | \(0.405282\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −13.9122 | −0.614837 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 22.6923 | 0.717594 | ||||||||
\(11\) | −2.29451 | −0.0628927 | −0.0314463 | − | 0.999505i | \(-0.510011\pi\) | ||||
−0.0314463 | + | 0.999505i | \(0.510011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28.6343 | 0.610902 | 0.305451 | − | 0.952208i | \(-0.401193\pi\) | ||||
0.305451 | + | 0.952208i | \(0.401193\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.9996 | −1.24999 | ||||||||
\(17\) | −46.6643 | −0.665750 | −0.332875 | − | 0.942971i | \(-0.608019\pi\) | ||||
−0.332875 | + | 0.942971i | \(0.608019\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −67.5183 | −0.815251 | −0.407625 | − | 0.913149i | \(-0.633643\pi\) | ||||
−0.407625 | + | 0.913149i | \(0.633643\pi\) | |||||||
\(20\) | 26.0972 | 0.291776 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.94200 | −0.0769654 | ||||||||
\(23\) | 30.1188 | 0.273053 | 0.136526 | − | 0.990636i | \(-0.456406\pi\) | ||||
0.136526 | + | 0.990636i | \(0.456406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −82.0190 | −0.656152 | ||||||||
\(26\) | 99.1122 | 0.747597 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −24.0840 | −0.154217 | −0.0771085 | − | 0.997023i | \(-0.524569\pi\) | ||||
−0.0771085 | + | 0.997023i | \(0.524569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −193.940 | −1.12363 | −0.561816 | − | 0.827262i | \(-0.689897\pi\) | ||||
−0.561816 | + | 0.827262i | \(0.689897\pi\) | |||||||
\(32\) | −165.606 | −0.914854 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −161.520 | −0.814717 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 208.767 | 0.927598 | 0.463799 | − | 0.885940i | \(-0.346486\pi\) | ||||
0.463799 | + | 0.885940i | \(0.346486\pi\) | |||||||
\(38\) | −233.702 | −0.997669 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −91.2080 | −0.360531 | ||||||||
\(41\) | −234.347 | −0.892656 | −0.446328 | − | 0.894869i | \(-0.647269\pi\) | ||||
−0.446328 | + | 0.894869i | \(0.647269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 46.0576 | 0.163342 | 0.0816712 | − | 0.996659i | \(-0.473974\pi\) | ||||
0.0816712 | + | 0.996659i | \(0.473974\pi\) | |||||||
\(44\) | −9.13366 | −0.0312943 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 104.251 | 0.334150 | ||||||||
\(47\) | 194.239 | 0.602823 | 0.301412 | − | 0.953494i | \(-0.402542\pi\) | ||||
0.301412 | + | 0.953494i | \(0.402542\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −283.893 | −0.802971 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 113.984 | 0.303975 | ||||||||
\(53\) | −221.635 | −0.574414 | −0.287207 | − | 0.957869i | \(-0.592727\pi\) | ||||
−0.287207 | + | 0.957869i | \(0.592727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.0428 | −0.0368794 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −83.3623 | −0.188724 | ||||||||
\(59\) | −710.748 | −1.56833 | −0.784165 | − | 0.620552i | \(-0.786908\pi\) | ||||
−0.784165 | + | 0.620552i | \(0.786908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −634.111 | −1.33098 | −0.665489 | − | 0.746408i | \(-0.731777\pi\) | ||||
−0.665489 | + | 0.746408i | \(0.731777\pi\) | |||||||
\(62\) | −671.285 | −1.37505 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 66.7827 | 0.130435 | ||||||||
\(65\) | 187.726 | 0.358224 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 269.671 | 0.491725 | 0.245862 | − | 0.969305i | \(-0.420929\pi\) | ||||
0.245862 | + | 0.969305i | \(0.420929\pi\) | |||||||
\(68\) | −185.755 | −0.331266 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 234.593 | 0.392127 | 0.196063 | − | 0.980591i | \(-0.437184\pi\) | ||||
0.196063 | + | 0.980591i | \(0.437184\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 213.368 | 0.342094 | 0.171047 | − | 0.985263i | \(-0.445285\pi\) | ||||
0.171047 | + | 0.985263i | \(0.445285\pi\) | |||||||
\(74\) | 722.608 | 1.13516 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −268.768 | −0.405655 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 242.405 | 0.345224 | 0.172612 | − | 0.984990i | \(-0.444779\pi\) | ||||
0.172612 | + | 0.984990i | \(0.444779\pi\) | |||||||
\(80\) | −524.477 | −0.732979 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −811.149 | −1.09240 | ||||||||
\(83\) | −1337.82 | −1.76922 | −0.884610 | − | 0.466332i | \(-0.845575\pi\) | ||||
−0.884610 | + | 0.466332i | \(0.845575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −305.931 | −0.390387 | ||||||||
\(86\) | 159.420 | 0.199892 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 31.9215 | 0.0386687 | ||||||||
\(89\) | 1105.39 | 1.31653 | 0.658263 | − | 0.752788i | \(-0.271292\pi\) | ||||
0.658263 | + | 0.752788i | \(0.271292\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 119.893 | 0.135866 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 672.322 | 0.737709 | ||||||||
\(95\) | −442.650 | −0.478051 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1139.50 | −1.19277 | −0.596387 | − | 0.802697i | \(-0.703398\pi\) | ||||
−0.596387 | + | 0.802697i | \(0.703398\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −326.490 | −0.326490 | ||||||||
\(101\) | −1351.19 | −1.33117 | −0.665586 | − | 0.746321i | \(-0.731818\pi\) | ||||
−0.665586 | + | 0.746321i | \(0.731818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −28.3780 | −0.0271472 | −0.0135736 | − | 0.999908i | \(-0.504321\pi\) | ||||
−0.0135736 | + | 0.999908i | \(0.504321\pi\) | |||||||
\(104\) | −398.365 | −0.375605 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −767.148 | −0.702943 | ||||||||
\(107\) | −1551.30 | −1.40159 | −0.700794 | − | 0.713364i | \(-0.747171\pi\) | ||||
−0.700794 | + | 0.713364i | \(0.747171\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1265.70 | −1.11222 | −0.556111 | − | 0.831108i | \(-0.687707\pi\) | ||||
−0.556111 | + | 0.831108i | \(0.687707\pi\) | |||||||
\(110\) | −52.0677 | −0.0451314 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 480.406 | 0.399937 | 0.199968 | − | 0.979802i | \(-0.435916\pi\) | ||||
0.199968 | + | 0.979802i | \(0.435916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 197.459 | 0.160114 | ||||||||
\(116\) | −95.8705 | −0.0767358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2460.12 | −1.91926 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1325.74 | −0.996045 | ||||||||
\(122\) | −2194.86 | −1.62879 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −772.009 | −0.559100 | ||||||||
\(125\) | −1357.21 | −0.971144 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1837.72 | 1.28403 | 0.642014 | − | 0.766693i | \(-0.278099\pi\) | ||||
0.642014 | + | 0.766693i | \(0.278099\pi\) | |||||||
\(128\) | 1556.01 | 1.07447 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 649.779 | 0.438380 | ||||||||
\(131\) | 1198.23 | 0.799157 | 0.399578 | − | 0.916699i | \(-0.369157\pi\) | ||||
0.399578 | + | 0.916699i | \(0.369157\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 933.415 | 0.601752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 649.201 | 0.409328 | ||||||||
\(137\) | 2019.83 | 1.25960 | 0.629802 | − | 0.776756i | \(-0.283136\pi\) | ||||
0.629802 | + | 0.776756i | \(0.283136\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2320.01 | −1.41569 | −0.707843 | − | 0.706370i | \(-0.750331\pi\) | ||||
−0.707843 | + | 0.706370i | \(0.750331\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 811.997 | 0.479868 | ||||||||
\(143\) | −65.7016 | −0.0384213 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −157.895 | −0.0904307 | ||||||||
\(146\) | 738.534 | 0.418640 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 831.033 | 0.461557 | ||||||||
\(149\) | −1230.57 | −0.676592 | −0.338296 | − | 0.941040i | \(-0.609851\pi\) | ||||
−0.338296 | + | 0.941040i | \(0.609851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.8369 | 0.0166190 | 0.00830952 | − | 0.999965i | \(-0.497355\pi\) | ||||
0.00830952 | + | 0.999965i | \(0.497355\pi\) | |||||||
\(152\) | 939.326 | 0.501246 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1271.47 | −0.658882 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2340.62 | 1.18982 | 0.594910 | − | 0.803792i | \(-0.297188\pi\) | ||||
0.594910 | + | 0.803792i | \(0.297188\pi\) | |||||||
\(158\) | 839.038 | 0.422470 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1085.71 | −0.536457 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2129.76 | 1.02341 | 0.511705 | − | 0.859161i | \(-0.329014\pi\) | ||||
0.511705 | + | 0.859161i | \(0.329014\pi\) | |||||||
\(164\) | −932.859 | −0.444171 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4630.62 | −2.16510 | ||||||||
\(167\) | −158.641 | −0.0735092 | −0.0367546 | − | 0.999324i | \(-0.511702\pi\) | ||||
−0.0367546 | + | 0.999324i | \(0.511702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1377.08 | −0.626798 | ||||||||
\(170\) | −1058.92 | −0.477739 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 183.340 | 0.0812764 | ||||||||
\(173\) | 1116.85 | 0.490823 | 0.245412 | − | 0.969419i | \(-0.421077\pi\) | ||||
0.245412 | + | 0.969419i | \(0.421077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 183.560 | 0.0786155 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3826.09 | 1.61111 | ||||||||
\(179\) | −3503.57 | −1.46295 | −0.731477 | − | 0.681866i | \(-0.761169\pi\) | ||||
−0.731477 | + | 0.681866i | \(0.761169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1591.32 | −0.653492 | −0.326746 | − | 0.945112i | \(-0.605952\pi\) | ||||
−0.326746 | + | 0.945112i | \(0.605952\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −419.018 | −0.167883 | ||||||||
\(185\) | 1368.68 | 0.543930 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 107.072 | 0.0418708 | ||||||||
\(188\) | 773.201 | 0.299955 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1532.15 | −0.585019 | ||||||||
\(191\) | 4924.24 | 1.86547 | 0.932737 | − | 0.360558i | \(-0.117414\pi\) | ||||
0.932737 | + | 0.360558i | \(0.117414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3314.07 | 1.23602 | 0.618011 | − | 0.786170i | \(-0.287939\pi\) | ||||
0.618011 | + | 0.786170i | \(0.287939\pi\) | |||||||
\(194\) | −3944.17 | −1.45967 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1024.59 | 0.370554 | 0.185277 | − | 0.982686i | \(-0.440682\pi\) | ||||
0.185277 | + | 0.982686i | \(0.440682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 795.124 | 0.283240 | 0.141620 | − | 0.989921i | \(-0.454769\pi\) | ||||
0.141620 | + | 0.989921i | \(0.454769\pi\) | |||||||
\(200\) | 1141.06 | 0.403426 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4676.89 | −1.62903 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1536.38 | −0.523441 | ||||||||
\(206\) | −98.2249 | −0.0332216 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2290.73 | −0.763624 | ||||||||
\(209\) | 154.921 | 0.0512733 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −850.964 | −0.277644 | −0.138822 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138822 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(212\) | −882.255 | −0.285819 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5369.53 | −1.71520 | ||||||||
\(215\) | 301.953 | 0.0957817 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4380.98 | −1.36109 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −59.8802 | −0.0183506 | ||||||||
\(221\) | −1336.20 | −0.406708 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4204.86 | −1.26268 | −0.631342 | − | 0.775505i | \(-0.717495\pi\) | ||||
−0.631342 | + | 0.775505i | \(0.717495\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1662.84 | 0.489426 | ||||||||
\(227\) | 5199.29 | 1.52022 | 0.760108 | − | 0.649796i | \(-0.225146\pi\) | ||||
0.760108 | + | 0.649796i | \(0.225146\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1357.28 | −0.391666 | −0.195833 | − | 0.980637i | \(-0.562741\pi\) | ||||
−0.195833 | + | 0.980637i | \(0.562741\pi\) | |||||||
\(230\) | 683.466 | 0.195941 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 335.061 | 0.0948183 | ||||||||
\(233\) | −6711.98 | −1.88720 | −0.943598 | − | 0.331093i | \(-0.892583\pi\) | ||||
−0.943598 | + | 0.331093i | \(0.892583\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1273.43 | 0.353487 | ||||||||
\(236\) | −2829.25 | −0.780375 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1850.76 | 0.500902 | 0.250451 | − | 0.968129i | \(-0.419421\pi\) | ||||
0.250451 | + | 0.968129i | \(0.419421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4864.74 | −1.30027 | −0.650136 | − | 0.759818i | \(-0.725288\pi\) | ||||
−0.650136 | + | 0.759818i | \(0.725288\pi\) | |||||||
\(242\) | −4588.78 | −1.21892 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2524.18 | −0.662272 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1933.34 | −0.498039 | ||||||||
\(248\) | 2698.12 | 0.690850 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4697.74 | −1.18844 | ||||||||
\(251\) | 1901.00 | 0.478049 | 0.239024 | − | 0.971014i | \(-0.423172\pi\) | ||||
0.239024 | + | 0.971014i | \(0.423172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −69.1078 | −0.0171730 | ||||||||
\(254\) | 6360.93 | 1.57134 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4851.55 | 1.18446 | ||||||||
\(257\) | 1670.33 | 0.405417 | 0.202709 | − | 0.979239i | \(-0.435026\pi\) | ||||
0.202709 | + | 0.979239i | \(0.435026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 747.276 | 0.178246 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4147.43 | 0.977974 | ||||||||
\(263\) | 3792.54 | 0.889195 | 0.444597 | − | 0.895731i | \(-0.353347\pi\) | ||||
0.444597 | + | 0.895731i | \(0.353347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1453.04 | −0.336828 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1073.47 | 0.244674 | ||||||||
\(269\) | 7923.59 | 1.79595 | 0.897973 | − | 0.440050i | \(-0.145039\pi\) | ||||
0.897973 | + | 0.440050i | \(0.145039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6340.76 | −1.42130 | −0.710652 | − | 0.703543i | \(-0.751600\pi\) | ||||
−0.710652 | + | 0.703543i | \(0.751600\pi\) | |||||||
\(272\) | 3733.13 | 0.832184 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6991.25 | 1.54145 | ||||||||
\(275\) | 188.193 | 0.0412671 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3169.14 | −0.687420 | −0.343710 | − | 0.939076i | \(-0.611684\pi\) | ||||
−0.343710 | + | 0.939076i | \(0.611684\pi\) | |||||||
\(278\) | −8030.26 | −1.73246 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3492.87 | −0.741520 | −0.370760 | − | 0.928729i | \(-0.620903\pi\) | ||||
−0.370760 | + | 0.928729i | \(0.620903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1904.23 | −0.399982 | −0.199991 | − | 0.979798i | \(-0.564091\pi\) | ||||
−0.199991 | + | 0.979798i | \(0.564091\pi\) | |||||||
\(284\) | 933.834 | 0.195116 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −227.414 | −0.0470184 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2735.44 | −0.556776 | ||||||||
\(290\) | −546.523 | −0.110665 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 849.348 | 0.170220 | ||||||||
\(293\) | 3988.81 | 0.795320 | 0.397660 | − | 0.917533i | \(-0.369822\pi\) | ||||
0.397660 | + | 0.917533i | \(0.369822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4659.66 | −0.919646 | ||||||||
\(296\) | −2904.40 | −0.570321 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4259.38 | −0.827985 | ||||||||
\(299\) | 862.432 | 0.166808 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 106.736 | 0.0203377 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5401.44 | 1.01906 | ||||||||
\(305\) | −4157.23 | −0.780466 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1415.59 | −0.263165 | −0.131583 | − | 0.991305i | \(-0.542006\pi\) | ||||
−0.131583 | + | 0.991305i | \(0.542006\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4400.94 | −0.806311 | ||||||||
\(311\) | 8808.57 | 1.60607 | 0.803036 | − | 0.595931i | \(-0.203217\pi\) | ||||
0.803036 | + | 0.595931i | \(0.203217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4338.32 | −0.783439 | −0.391719 | − | 0.920085i | \(-0.628120\pi\) | ||||
−0.391719 | + | 0.920085i | \(0.628120\pi\) | |||||||
\(314\) | 8101.61 | 1.45605 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 964.933 | 0.171778 | ||||||||
\(317\) | 8911.96 | 1.57901 | 0.789504 | − | 0.613745i | \(-0.210338\pi\) | ||||
0.789504 | + | 0.613745i | \(0.210338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 55.2610 | 0.00969913 | ||||||||
\(320\) | 437.827 | 0.0764852 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3150.69 | 0.542753 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2348.56 | −0.400845 | ||||||||
\(326\) | 7371.76 | 1.25240 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3260.28 | 0.548838 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8405.16 | 1.39574 | 0.697869 | − | 0.716226i | \(-0.254132\pi\) | ||||
0.697869 | + | 0.716226i | \(0.254132\pi\) | |||||||
\(332\) | −5325.43 | −0.880334 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −549.107 | −0.0899574 | ||||||||
\(335\) | 1767.96 | 0.288340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7481.10 | 1.20926 | 0.604631 | − | 0.796506i | \(-0.293321\pi\) | ||||
0.604631 | + | 0.796506i | \(0.293321\pi\) | |||||||
\(338\) | −4766.49 | −0.767049 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1217.81 | −0.194250 | ||||||||
\(341\) | 444.996 | 0.0706682 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −640.761 | −0.100429 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3865.76 | 0.600649 | ||||||||
\(347\) | −1603.13 | −0.248013 | −0.124006 | − | 0.992281i | \(-0.539574\pi\) | ||||
−0.124006 | + | 0.992281i | \(0.539574\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2238.34 | −0.343311 | −0.171656 | − | 0.985157i | \(-0.554912\pi\) | ||||
−0.171656 | + | 0.985157i | \(0.554912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 379.984 | 0.0575376 | ||||||||
\(353\) | 9507.71 | 1.43355 | 0.716777 | − | 0.697303i | \(-0.245617\pi\) | ||||
0.716777 | + | 0.697303i | \(0.245617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1537.99 | 0.229938 | ||||||||
\(356\) | 4400.17 | 0.655081 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12126.9 | −1.79030 | ||||||||
\(359\) | −7856.96 | −1.15508 | −0.577541 | − | 0.816361i | \(-0.695988\pi\) | ||||
−0.577541 | + | 0.816361i | \(0.695988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2300.28 | −0.335366 | ||||||||
\(362\) | −5508.06 | −0.799716 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1398.84 | 0.200599 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2258.91 | −0.321292 | −0.160646 | − | 0.987012i | \(-0.551358\pi\) | ||||
−0.160646 | + | 0.987012i | \(0.551358\pi\) | |||||||
\(368\) | −2409.50 | −0.341314 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4737.41 | 0.665639 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1789.23 | 0.248372 | 0.124186 | − | 0.992259i | \(-0.460368\pi\) | ||||
0.124186 | + | 0.992259i | \(0.460368\pi\) | |||||||
\(374\) | 370.608 | 0.0512398 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2702.29 | −0.370638 | ||||||||
\(377\) | −689.630 | −0.0942116 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7021.61 | −0.951651 | −0.475826 | − | 0.879540i | \(-0.657851\pi\) | ||||
−0.475826 | + | 0.879540i | \(0.657851\pi\) | |||||||
\(380\) | −1762.04 | −0.237870 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17044.3 | 2.28289 | ||||||||
\(383\) | 9614.42 | 1.28270 | 0.641350 | − | 0.767248i | \(-0.278375\pi\) | ||||
0.641350 | + | 0.767248i | \(0.278375\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11471.0 | 1.51259 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4535.98 | −0.593504 | ||||||||
\(389\) | 12211.5 | 1.59164 | 0.795822 | − | 0.605530i | \(-0.207039\pi\) | ||||
0.795822 | + | 0.605530i | \(0.207039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1405.47 | −0.181785 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3546.43 | 0.453468 | ||||||||
\(395\) | 1589.20 | 0.202434 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10404.7 | 1.31535 | 0.657677 | − | 0.753300i | \(-0.271539\pi\) | ||||
0.657677 | + | 0.753300i | \(0.271539\pi\) | |||||||
\(398\) | 2752.17 | 0.346618 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6561.49 | 0.820186 | ||||||||
\(401\) | 789.887 | 0.0983667 | 0.0491834 | − | 0.998790i | \(-0.484338\pi\) | ||||
0.0491834 | + | 0.998790i | \(0.484338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5553.33 | −0.686429 | ||||||||
\(404\) | −5378.63 | −0.662369 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −479.018 | −0.0583391 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8685.05 | −1.05000 | −0.524998 | − | 0.851104i | \(-0.675934\pi\) | ||||
−0.524998 | + | 0.851104i | \(0.675934\pi\) | |||||||
\(410\) | −5317.89 | −0.640565 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −112.963 | −0.0135080 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8770.76 | −1.03745 | ||||||||
\(416\) | −4742.02 | −0.558886 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 536.230 | 0.0627461 | ||||||||
\(419\) | −1296.36 | −0.151148 | −0.0755741 | − | 0.997140i | \(-0.524079\pi\) | ||||
−0.0755741 | + | 0.997140i | \(0.524079\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1303.36 | 0.150884 | 0.0754418 | − | 0.997150i | \(-0.475963\pi\) | ||||
0.0754418 | + | 0.997150i | \(0.475963\pi\) | |||||||
\(422\) | −2945.45 | −0.339768 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3083.42 | 0.353170 | ||||||||
\(425\) | 3827.36 | 0.436833 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6175.21 | −0.697407 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1045.15 | 0.117214 | ||||||||
\(431\) | 70.6768 | 0.00789880 | 0.00394940 | − | 0.999992i | \(-0.498743\pi\) | ||||
0.00394940 | + | 0.999992i | \(0.498743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6842.92 | −0.759468 | −0.379734 | − | 0.925096i | \(-0.623984\pi\) | ||||
−0.379734 | + | 0.925096i | \(0.623984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5038.33 | −0.553423 | ||||||||
\(437\) | −2033.57 | −0.222606 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18342.5 | 1.99417 | 0.997084 | − | 0.0763102i | \(-0.0243139\pi\) | ||||
0.997084 | + | 0.0763102i | \(0.0243139\pi\) | |||||||
\(440\) | 209.277 | 0.0226748 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4625.00 | −0.497713 | ||||||||
\(443\) | 10938.1 | 1.17310 | 0.586552 | − | 0.809911i | \(-0.300485\pi\) | ||||
0.586552 | + | 0.809911i | \(0.300485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7246.91 | 0.771992 | ||||||||
\(446\) | −14554.3 | −1.54522 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10816.8 | −1.13692 | −0.568461 | − | 0.822710i | \(-0.692461\pi\) | ||||
−0.568461 | + | 0.822710i | \(0.692461\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 537.712 | 0.0561416 | ||||||||
\(452\) | 1912.34 | 0.199002 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17996.4 | 1.86038 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4525.45 | 0.463220 | 0.231610 | − | 0.972809i | \(-0.425601\pi\) | ||||
0.231610 | + | 0.972809i | \(0.425601\pi\) | |||||||
\(458\) | −4697.96 | −0.479304 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 786.018 | 0.0796701 | ||||||||
\(461\) | −11088.4 | −1.12025 | −0.560126 | − | 0.828407i | \(-0.689247\pi\) | ||||
−0.560126 | + | 0.828407i | \(0.689247\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17567.2 | 1.76332 | 0.881660 | − | 0.471884i | \(-0.156426\pi\) | ||||
0.881660 | + | 0.471884i | \(0.156426\pi\) | |||||||
\(464\) | 1926.71 | 0.192770 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23232.3 | −2.30947 | ||||||||
\(467\) | 6326.26 | 0.626862 | 0.313431 | − | 0.949611i | \(-0.398522\pi\) | ||||
0.313431 | + | 0.949611i | \(0.398522\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4407.74 | 0.432582 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9888.04 | 0.964266 | ||||||||
\(473\) | −105.680 | −0.0102730 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5537.78 | 0.534928 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6406.05 | 0.612983 | ||||||||
\(479\) | 375.365 | 0.0358055 | 0.0179028 | − | 0.999840i | \(-0.494301\pi\) | ||||
0.0179028 | + | 0.999840i | \(0.494301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5977.91 | 0.566672 | ||||||||
\(482\) | −16838.4 | −1.59122 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5277.31 | −0.495615 | ||||||||
\(485\) | −7470.57 | −0.699425 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.9467 | 0.00241429 | 0.00120714 | − | 0.999999i | \(-0.499616\pi\) | ||||
0.00120714 | + | 0.999999i | \(0.499616\pi\) | |||||||
\(488\) | 8821.86 | 0.818333 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6282.99 | 0.577490 | 0.288745 | − | 0.957406i | \(-0.406762\pi\) | ||||
0.288745 | + | 0.957406i | \(0.406762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1123.87 | 0.102670 | ||||||||
\(494\) | −6691.89 | −0.609479 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15515.1 | 1.40453 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2371.78 | −0.212776 | −0.106388 | − | 0.994325i | \(-0.533929\pi\) | ||||
−0.106388 | + | 0.994325i | \(0.533929\pi\) | |||||||
\(500\) | −5402.62 | −0.483225 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6579.96 | 0.585016 | ||||||||
\(503\) | −11080.3 | −0.982201 | −0.491100 | − | 0.871103i | \(-0.663405\pi\) | ||||
−0.491100 | + | 0.871103i | \(0.663405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8858.39 | −0.780580 | ||||||||
\(506\) | −239.204 | −0.0210156 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7315.36 | 0.638910 | ||||||||
\(509\) | 10063.7 | 0.876355 | 0.438178 | − | 0.898888i | \(-0.355624\pi\) | ||||
0.438178 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4344.69 | 0.375020 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5781.52 | 0.496132 | ||||||||
\(515\) | −186.046 | −0.0159187 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −445.683 | −0.0379132 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2611.68 | −0.220249 | ||||||||
\(521\) | −9181.24 | −0.772048 | −0.386024 | − | 0.922489i | \(-0.626152\pi\) | ||||
−0.386024 | + | 0.922489i | \(0.626152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9392.06 | 0.785250 | 0.392625 | − | 0.919699i | \(-0.371567\pi\) | ||||
0.392625 | + | 0.919699i | \(0.371567\pi\) | |||||||
\(524\) | 4769.74 | 0.397647 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13127.2 | 1.08816 | ||||||||
\(527\) | 9050.06 | 0.748058 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11259.9 | −0.925442 | ||||||||
\(530\) | −5029.42 | −0.412196 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6710.38 | −0.545326 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10170.3 | −0.821871 | ||||||||
\(536\) | −3751.71 | −0.302330 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27426.0 | 2.19780 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4114.52 | 0.326982 | 0.163491 | − | 0.986545i | \(-0.447725\pi\) | ||||
0.163491 | + | 0.986545i | \(0.447725\pi\) | |||||||
\(542\) | −21947.3 | −1.73933 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7727.90 | 0.609064 | ||||||||
\(545\) | −8297.92 | −0.652191 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9796.38 | −0.765746 | −0.382873 | − | 0.923801i | \(-0.625065\pi\) | ||||
−0.382873 | + | 0.923801i | \(0.625065\pi\) | |||||||
\(548\) | 8040.26 | 0.626757 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 651.394 | 0.0505010 | ||||||||
\(551\) | 1626.11 | 0.125726 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10969.4 | −0.841236 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9235.16 | −0.704421 | ||||||||
\(557\) | 4197.53 | 0.319309 | 0.159655 | − | 0.987173i | \(-0.448962\pi\) | ||||
0.159655 | + | 0.987173i | \(0.448962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1318.83 | 0.0997863 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12089.9 | −0.907441 | ||||||||
\(563\) | −10742.4 | −0.804151 | −0.402075 | − | 0.915607i | \(-0.631711\pi\) | ||||
−0.402075 | + | 0.915607i | \(0.631711\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3149.54 | 0.234517 | ||||||||
\(566\) | −6591.15 | −0.489482 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3263.69 | −0.241094 | ||||||||
\(569\) | −7915.86 | −0.583216 | −0.291608 | − | 0.956538i | \(-0.594190\pi\) | ||||
−0.291608 | + | 0.956538i | \(0.594190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16923.1 | 1.24030 | 0.620149 | − | 0.784484i | \(-0.287072\pi\) | ||||
0.620149 | + | 0.784484i | \(0.287072\pi\) | |||||||
\(572\) | −261.536 | −0.0191178 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2470.32 | −0.179164 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24108.2 | −1.73941 | −0.869704 | − | 0.493573i | \(-0.835690\pi\) | ||||
−0.869704 | + | 0.493573i | \(0.835690\pi\) | |||||||
\(578\) | −9468.21 | −0.681360 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −628.526 | −0.0449968 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 508.543 | 0.0361264 | ||||||||
\(584\) | −2968.41 | −0.210332 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13806.5 | 0.973279 | ||||||||
\(587\) | −13259.2 | −0.932308 | −0.466154 | − | 0.884704i | \(-0.654361\pi\) | ||||
−0.466154 | + | 0.884704i | \(0.654361\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13094.5 | 0.916041 | ||||||||
\(590\) | −16128.5 | −1.12542 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16701.3 | −1.15949 | ||||||||
\(593\) | 18789.8 | 1.30119 | 0.650596 | − | 0.759424i | \(-0.274519\pi\) | ||||
0.650596 | + | 0.759424i | \(0.274519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4898.49 | −0.336661 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2985.14 | 0.204133 | ||||||||
\(599\) | −7105.41 | −0.484673 | −0.242337 | − | 0.970192i | \(-0.577914\pi\) | ||||
−0.242337 | + | 0.970192i | \(0.577914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 800.460 | 0.0543286 | 0.0271643 | − | 0.999631i | \(-0.491352\pi\) | ||||
0.0271643 | + | 0.999631i | \(0.491352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 122.752 | 0.00826935 | ||||||||
\(605\) | −8691.51 | −0.584066 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8771.51 | 0.586532 | 0.293266 | − | 0.956031i | \(-0.405258\pi\) | ||||
0.293266 | + | 0.956031i | \(0.405258\pi\) | |||||||
\(608\) | 11181.5 | 0.745835 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14389.5 | −0.955102 | ||||||||
\(611\) | 5561.90 | 0.368266 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2533.30 | −0.166915 | −0.0834577 | − | 0.996511i | \(-0.526596\pi\) | ||||
−0.0834577 | + | 0.996511i | \(0.526596\pi\) | |||||||
\(614\) | −4899.78 | −0.322050 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1464.17 | 0.0955350 | 0.0477675 | − | 0.998858i | \(-0.484789\pi\) | ||||
0.0477675 | + | 0.998858i | \(0.484789\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18519.8 | −1.20254 | −0.601271 | − | 0.799045i | \(-0.705339\pi\) | ||||
−0.601271 | + | 0.799045i | \(0.705339\pi\) | |||||||
\(620\) | −5061.28 | −0.327848 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30489.2 | 1.96544 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1354.48 | 0.0866867 | ||||||||
\(626\) | −15016.3 | −0.958739 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9317.23 | 0.592035 | ||||||||
\(629\) | −9741.98 | −0.617549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5128.62 | 0.323562 | 0.161781 | − | 0.986827i | \(-0.448276\pi\) | ||||
0.161781 | + | 0.986827i | \(0.448276\pi\) | |||||||
\(632\) | −3372.38 | −0.212256 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30847.1 | 1.93232 | ||||||||
\(635\) | 12048.1 | 0.752935 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 191.275 | 0.0118694 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10201.2 | 0.630057 | ||||||||
\(641\) | −20864.3 | −1.28563 | −0.642817 | − | 0.766020i | \(-0.722234\pi\) | ||||
−0.642817 | + | 0.766020i | \(0.722234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9799.87 | −0.601040 | −0.300520 | − | 0.953775i | \(-0.597160\pi\) | ||||
−0.300520 | + | 0.953775i | \(0.597160\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10905.5 | 0.664199 | ||||||||
\(647\) | −8180.42 | −0.497072 | −0.248536 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248536 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1630.81 | 0.0986365 | ||||||||
\(650\) | −8129.08 | −0.490537 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8477.86 | 0.509231 | ||||||||
\(653\) | 13509.9 | 0.809619 | 0.404810 | − | 0.914401i | \(-0.367338\pi\) | ||||
0.404810 | + | 0.914401i | \(0.367338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7855.56 | 0.468614 | ||||||||
\(656\) | 18747.7 | 1.11582 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18426.1 | 1.08919 | 0.544597 | − | 0.838698i | \(-0.316683\pi\) | ||||
0.544597 | + | 0.838698i | \(0.316683\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12328.0 | −0.725424 | −0.362712 | − | 0.931901i | \(-0.618149\pi\) | ||||
−0.362712 | + | 0.931901i | \(0.618149\pi\) | |||||||
\(662\) | 29092.8 | 1.70804 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18612.0 | 1.08778 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −725.383 | −0.0421094 | ||||||||
\(668\) | −631.498 | −0.0365769 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6119.46 | 0.352859 | ||||||||
\(671\) | 1454.97 | 0.0837087 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20866.3 | −1.19515 | −0.597575 | − | 0.801813i | \(-0.703869\pi\) | ||||
−0.597575 | + | 0.801813i | \(0.703869\pi\) | |||||||
\(674\) | 25894.4 | 1.47984 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5481.68 | −0.311884 | ||||||||
\(677\) | 638.005 | 0.0362194 | 0.0181097 | − | 0.999836i | \(-0.494235\pi\) | ||||
0.0181097 | + | 0.999836i | \(0.494235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4256.16 | 0.240024 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1540.27 | 0.0864808 | ||||||||
\(683\) | 25045.2 | 1.40312 | 0.701558 | − | 0.712612i | \(-0.252488\pi\) | ||||
0.701558 | + | 0.712612i | \(0.252488\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13242.0 | 0.738613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3684.59 | −0.204177 | ||||||||
\(689\) | −6346.37 | −0.350911 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3371.26 | 0.185599 | 0.0927994 | − | 0.995685i | \(-0.470418\pi\) | ||||
0.0927994 | + | 0.995685i | \(0.470418\pi\) | |||||||
\(692\) | 4445.80 | 0.244225 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5548.93 | −0.303508 | ||||||||
\(695\) | −15209.9 | −0.830138 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10935.7 | 0.594286 | ||||||||
\(698\) | −7747.59 | −0.420130 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24430.3 | −1.31629 | −0.658146 | − | 0.752890i | \(-0.728659\pi\) | ||||
−0.658146 | + | 0.752890i | \(0.728659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14095.6 | −0.756225 | ||||||||
\(704\) | −153.233 | −0.00820340 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32909.1 | 1.75432 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24270.6 | 1.28562 | 0.642809 | − | 0.766026i | \(-0.277769\pi\) | ||||
0.642809 | + | 0.766026i | \(0.277769\pi\) | |||||||
\(710\) | 5323.45 | 0.281388 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15378.3 | −0.809448 | ||||||||
\(713\) | −5841.23 | −0.306811 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −430.739 | −0.0225297 | ||||||||
\(716\) | −13946.5 | −0.727941 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −27195.4 | −1.41354 | ||||||||
\(719\) | −6891.17 | −0.357437 | −0.178718 | − | 0.983900i | \(-0.557195\pi\) | ||||
−0.178718 | + | 0.983900i | \(0.557195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7961.97 | −0.410407 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6334.53 | −0.325167 | ||||||||
\(725\) | 1975.35 | 0.101190 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4904.38 | −0.250197 | −0.125099 | − | 0.992144i | \(-0.539925\pi\) | ||||
−0.125099 | + | 0.992144i | \(0.539925\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4841.82 | 0.245485 | ||||||||
\(731\) | −2149.25 | −0.108745 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6610.71 | −0.333114 | −0.166557 | − | 0.986032i | \(-0.553265\pi\) | ||||
−0.166557 | + | 0.986032i | \(0.553265\pi\) | |||||||
\(734\) | −7818.78 | −0.393183 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4987.86 | −0.249803 | ||||||||
\(737\) | −618.762 | −0.0309259 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27941.3 | −1.39085 | −0.695425 | − | 0.718599i | \(-0.744784\pi\) | ||||
−0.695425 | + | 0.718599i | \(0.744784\pi\) | |||||||
\(740\) | 5448.24 | 0.270651 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29535.5 | 1.45835 | 0.729174 | − | 0.684328i | \(-0.239905\pi\) | ||||
0.729174 | + | 0.684328i | \(0.239905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8067.61 | −0.396744 | ||||||||
\(746\) | 6193.07 | 0.303947 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 426.216 | 0.0208342 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35047.9 | −1.70295 | −0.851475 | − | 0.524395i | \(-0.824291\pi\) | ||||
−0.851475 | + | 0.524395i | \(0.824291\pi\) | |||||||
\(752\) | −15539.1 | −0.753525 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2387.02 | −0.115292 | ||||||||
\(755\) | 202.167 | 0.00974517 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19501.6 | 0.936326 | 0.468163 | − | 0.883642i | \(-0.344916\pi\) | ||||
0.468163 | + | 0.883642i | \(0.344916\pi\) | |||||||
\(758\) | −24304.0 | −1.16459 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6158.21 | 0.293923 | ||||||||
\(761\) | −22813.5 | −1.08672 | −0.543358 | − | 0.839501i | \(-0.682847\pi\) | ||||
−0.543358 | + | 0.839501i | \(0.682847\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19601.7 | 0.928228 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33278.5 | 1.56971 | ||||||||
\(767\) | −20351.8 | −0.958096 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23272.0 | 1.09130 | 0.545650 | − | 0.838013i | \(-0.316283\pi\) | ||||
0.545650 | + | 0.838013i | \(0.316283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13192.2 | 0.615023 | ||||||||
\(773\) | 29648.9 | 1.37956 | 0.689778 | − | 0.724021i | \(-0.257708\pi\) | ||||
0.689778 | + | 0.724021i | \(0.257708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15906.7 | 0.737273 | ||||||||
\(776\) | 15853.0 | 0.733361 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 42267.9 | 1.94779 | ||||||||
\(779\) | 15822.7 | 0.727739 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −538.274 | −0.0246619 | ||||||||
\(782\) | −4864.78 | −0.222461 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15345.1 | 0.697694 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19003.2 | −0.860726 | −0.430363 | − | 0.902656i | \(-0.641614\pi\) | ||||
−0.430363 | + | 0.902656i | \(0.641614\pi\) | |||||||
\(788\) | 4078.56 | 0.184381 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5500.73 | 0.247731 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18157.3 | −0.813097 | ||||||||
\(794\) | 36013.8 | 1.60968 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3165.12 | 0.140936 | ||||||||
\(797\) | 19286.8 | 0.857182 | 0.428591 | − | 0.903499i | \(-0.359010\pi\) | ||||
0.428591 | + | 0.903499i | \(0.359010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9064.03 | −0.401330 | ||||||||
\(800\) | 13582.8 | 0.600283 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2734.04 | 0.120377 | ||||||||
\(803\) | −489.575 | −0.0215152 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19221.8 | −0.840023 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18798.0 | 0.818453 | ||||||||
\(809\) | 26463.5 | 1.15007 | 0.575034 | − | 0.818129i | \(-0.304989\pi\) | ||||
0.575034 | + | 0.818129i | \(0.304989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28814.1 | −1.24759 | −0.623797 | − | 0.781586i | \(-0.714411\pi\) | ||||
−0.623797 | + | 0.781586i | \(0.714411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1658.03 | −0.0713930 | ||||||||
\(815\) | 13962.7 | 0.600113 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3109.73 | −0.133165 | ||||||||
\(818\) | −30061.6 | −1.28494 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6115.81 | −0.260455 | ||||||||
\(821\) | −34564.5 | −1.46932 | −0.734658 | − | 0.678437i | \(-0.762658\pi\) | ||||
−0.734658 | + | 0.678437i | \(0.762658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10429.7 | 0.441746 | 0.220873 | − | 0.975303i | \(-0.429109\pi\) | ||||
0.220873 | + | 0.975303i | \(0.429109\pi\) | |||||||
\(824\) | 394.799 | 0.0166911 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33622.9 | −1.41376 | −0.706881 | − | 0.707332i | \(-0.749899\pi\) | ||||
−0.706881 | + | 0.707332i | \(0.749899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37426.6 | −1.56801 | −0.784004 | − | 0.620756i | \(-0.786826\pi\) | ||||
−0.784004 | + | 0.620756i | \(0.786826\pi\) | |||||||
\(830\) | −30358.3 | −1.26958 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1912.28 | 0.0796830 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1040.05 | −0.0431047 | ||||||||
\(836\) | 616.689 | 0.0255127 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4487.09 | −0.184969 | ||||||||
\(839\) | 20073.3 | 0.825993 | 0.412996 | − | 0.910733i | \(-0.364482\pi\) | ||||
0.412996 | + | 0.910733i | \(0.364482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23809.0 | −0.976217 | ||||||||
\(842\) | 4511.34 | 0.184645 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3387.40 | −0.138151 | ||||||||
\(845\) | −9028.10 | −0.367546 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17730.7 | 0.718014 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13247.7 | 0.534578 | ||||||||
\(851\) | 6287.82 | 0.253283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31621.1 | −1.26927 | −0.634635 | − | 0.772812i | \(-0.718849\pi\) | ||||
−0.634635 | + | 0.772812i | \(0.718849\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21581.9 | 0.861747 | ||||||||
\(857\) | −5655.26 | −0.225414 | −0.112707 | − | 0.993628i | \(-0.535952\pi\) | ||||
−0.112707 | + | 0.993628i | \(0.535952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25859.7 | 1.02715 | 0.513574 | − | 0.858045i | \(-0.328321\pi\) | ||||
0.513574 | + | 0.858045i | \(0.328321\pi\) | |||||||
\(860\) | 1201.98 | 0.0476593 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 244.634 | 0.00966621 | ||||||||
\(863\) | 12328.5 | 0.486288 | 0.243144 | − | 0.969990i | \(-0.421821\pi\) | ||||
0.243144 | + | 0.969990i | \(0.421821\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7322.05 | 0.287812 | ||||||||
\(866\) | −23685.5 | −0.929405 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −556.200 | −0.0217121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7721.84 | 0.300396 | ||||||||
\(872\) | 17608.6 | 0.683834 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7038.82 | −0.272416 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18980.7 | −0.730825 | −0.365412 | − | 0.930846i | \(-0.619072\pi\) | ||||
−0.365412 | + | 0.930846i | \(0.619072\pi\) | |||||||
\(878\) | 63489.1 | 2.44038 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1203.42 | 0.0460990 | ||||||||
\(881\) | 38081.2 | 1.45629 | 0.728144 | − | 0.685424i | \(-0.240383\pi\) | ||||
0.728144 | + | 0.685424i | \(0.240383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6338.38 | 0.241567 | 0.120783 | − | 0.992679i | \(-0.461459\pi\) | ||||
0.120783 | + | 0.992679i | \(0.461459\pi\) | |||||||
\(884\) | −5318.97 | −0.202371 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 37860.2 | 1.43560 | ||||||||
\(887\) | −22874.3 | −0.865889 | −0.432944 | − | 0.901421i | \(-0.642525\pi\) | ||||
−0.432944 | + | 0.901421i | \(0.642525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 25083.8 | 0.944731 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16738.1 | −0.628290 | ||||||||
\(893\) | −13114.7 | −0.491452 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22969.4 | −0.857856 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37440.4 | −1.39132 | ||||||||
\(899\) | 4670.85 | 0.173283 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10342.4 | 0.382416 | ||||||||
\(902\) | 1861.19 | 0.0687037 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6683.49 | −0.245896 | ||||||||
\(905\) | −10432.7 | −0.383199 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33888.9 | −1.24064 | −0.620320 | − | 0.784349i | \(-0.712997\pi\) | ||||
−0.620320 | + | 0.784349i | \(0.712997\pi\) | |||||||
\(908\) | 20696.6 | 0.756434 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10145.9 | 0.368990 | 0.184495 | − | 0.982833i | \(-0.440935\pi\) | ||||
0.184495 | + | 0.982833i | \(0.440935\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3069.65 | 0.111271 | ||||||||
\(914\) | 15664.0 | 0.566870 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5402.87 | −0.194886 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30423.3 | 1.09203 | 0.546013 | − | 0.837777i | \(-0.316145\pi\) | ||||
0.546013 | + | 0.837777i | \(0.316145\pi\) | |||||||
\(920\) | −2747.08 | −0.0984440 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −38380.3 | −1.37092 | ||||||||
\(923\) | 6717.40 | 0.239551 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17122.9 | −0.608645 | ||||||||
\(926\) | 60805.6 | 2.15788 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3988.47 | 0.141086 | ||||||||
\(929\) | −18206.1 | −0.642976 | −0.321488 | − | 0.946914i | \(-0.604183\pi\) | ||||
−0.321488 | + | 0.946914i | \(0.604183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −26718.2 | −0.939037 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21897.2 | 0.767127 | ||||||||
\(935\) | 701.960 | 0.0245525 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15511.4 | −0.540806 | −0.270403 | − | 0.962747i | \(-0.587157\pi\) | ||||
−0.270403 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5069.10 | 0.175889 | ||||||||
\(941\) | 90.6984 | 0.00314206 | 0.00157103 | − | 0.999999i | \(-0.499500\pi\) | ||||
0.00157103 | + | 0.999999i | \(0.499500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7058.27 | −0.243742 | ||||||||
\(944\) | 56859.5 | 1.96040 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −365.790 | −0.0125717 | ||||||||
\(947\) | −35516.0 | −1.21871 | −0.609354 | − | 0.792899i | \(-0.708571\pi\) | ||||
−0.609354 | + | 0.792899i | \(0.708571\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6109.66 | 0.208986 | ||||||||
\(950\) | 19168.0 | 0.654622 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22433.4 | −0.762526 | −0.381263 | − | 0.924467i | \(-0.624511\pi\) | ||||
−0.381263 | + | 0.924467i | \(0.624511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32283.3 | 1.09389 | ||||||||
\(956\) | 7367.25 | 0.249241 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1299.25 | 0.0438173 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7821.56 | 0.262548 | ||||||||
\(962\) | 20691.4 | 0.693469 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19364.9 | −0.646994 | ||||||||
\(965\) | 21727.0 | 0.724785 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2753.37 | 0.0915639 | 0.0457820 | − | 0.998951i | \(-0.485422\pi\) | ||||
0.0457820 | + | 0.998951i | \(0.485422\pi\) | |||||||
\(968\) | 18443.8 | 0.612405 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25858.0 | −0.855927 | ||||||||
\(971\) | −46754.1 | −1.54522 | −0.772611 | − | 0.634880i | \(-0.781050\pi\) | ||||
−0.772611 | + | 0.634880i | \(0.781050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 89.8096 | 0.00295450 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 50728.7 | 1.66371 | ||||||||
\(977\) | −34781.1 | −1.13894 | −0.569471 | − | 0.822011i | \(-0.692852\pi\) | ||||
−0.569471 | + | 0.822011i | \(0.692852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2536.32 | −0.0827998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21747.4 | 0.706708 | ||||||||
\(983\) | 29661.0 | 0.962401 | 0.481200 | − | 0.876611i | \(-0.340201\pi\) | ||||
0.481200 | + | 0.876611i | \(0.340201\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6717.22 | 0.217288 | ||||||||
\(986\) | 3890.05 | 0.125643 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7695.98 | −0.247816 | ||||||||
\(989\) | 1387.20 | 0.0446011 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13621.6 | −0.436636 | −0.218318 | − | 0.975878i | \(-0.570057\pi\) | ||||
−0.218318 | + | 0.975878i | \(0.570057\pi\) | |||||||
\(992\) | 32117.6 | 1.02796 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5212.83 | 0.166088 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9439.71 | −0.299858 | −0.149929 | − | 0.988697i | \(-0.547905\pi\) | ||||
−0.149929 | + | 0.988697i | \(0.547905\pi\) | |||||||
\(998\) | −8209.46 | −0.260387 | ||||||||
\(999\) | 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 | 1323.4.a.bf.1.5 | yes | 6 | |
3.2 | odd | 2 | inner | 1323.4.a.bf.1.2 | ✓ | 6 | |
7.6 | odd | 2 | 1323.4.a.bg.1.5 | yes | 6 | ||
21.20 | even | 2 | 1323.4.a.bg.1.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.4.a.bf.1.2 | ✓ | 6 | 3.2 | odd | 2 | inner | |
1323.4.a.bf.1.5 | yes | 6 | 1.1 | even | 1 | trivial | |
1323.4.a.bg.1.2 | yes | 6 | 21.20 | even | 2 | ||
1323.4.a.bg.1.5 | yes | 6 | 7.6 | odd | 2 |