Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,3,Mod(4049,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.4049");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(112.806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.13 | ||
Character | \(\chi\) | \(=\) | 4140.4049 |
Dual form | 4140.3.c.a.4049.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.49878 | − | 2.18197i | −0.899756 | − | 0.436394i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 10.0913i | − | 1.44161i | −0.693136 | − | 0.720807i | \(-0.743772\pi\) | ||
0.693136 | − | 0.720807i | \(-0.256228\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.456013i | 0.0414557i | 0.999785 | + | 0.0207279i | \(0.00659836\pi\) | ||||
−0.999785 | + | 0.0207279i | \(0.993402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.213952i | 0.0164578i | 0.999966 | + | 0.00822892i | \(0.00261938\pi\) | ||||
−0.999966 | + | 0.00822892i | \(0.997381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.67892 | 0.334054 | 0.167027 | − | 0.985952i | \(-0.446583\pi\) | ||||
0.167027 | + | 0.985952i | \(0.446583\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.0820 | 1.32011 | 0.660053 | − | 0.751219i | \(-0.270534\pi\) | ||||
0.660053 | + | 0.751219i | \(0.270534\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79583 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.4780 | + | 19.6324i | 0.619120 | + | 0.785296i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 50.8783i | − | 1.75443i | −0.480102 | − | 0.877213i | \(-0.659400\pi\) | ||
0.480102 | − | 0.877213i | \(-0.340600\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.3745 | 0.463695 | 0.231847 | − | 0.972752i | \(-0.425523\pi\) | ||||
0.231847 | + | 0.972752i | \(0.425523\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −22.0189 | + | 45.3985i | −0.629112 | + | 1.29710i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 64.5468i | 1.74451i | 0.489052 | + | 0.872255i | \(0.337343\pi\) | ||||
−0.489052 | + | 0.872255i | \(0.662657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 47.9986i | − | 1.17070i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) | ||
0.810782 | − | 0.585348i | \(-0.199042\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.886502i | − | 0.0206163i | −0.999947 | − | 0.0103082i | \(-0.996719\pi\) | ||
0.999947 | − | 0.0103082i | \(-0.00328125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 61.7325 | 1.31346 | 0.656729 | − | 0.754127i | \(-0.271940\pi\) | ||||
0.656729 | + | 0.754127i | \(0.271940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −52.8342 | −1.07825 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 74.2027 | 1.40005 | 0.700025 | − | 0.714118i | \(-0.253172\pi\) | ||||
0.700025 | + | 0.714118i | \(0.253172\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.995007 | − | 2.05150i | 0.0180910 | − | 0.0373000i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 20.8696i | 0.353722i | 0.984236 | + | 0.176861i | \(0.0565944\pi\) | ||||
−0.984236 | + | 0.176861i | \(0.943406\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.4855 | 1.18829 | 0.594144 | − | 0.804359i | \(-0.297491\pi\) | ||||
0.594144 | + | 0.804359i | \(0.297491\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.466837 | − | 0.962522i | 0.00718211 | − | 0.0148080i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47.2709i | 0.705536i | 0.935711 | + | 0.352768i | \(0.114759\pi\) | ||||
−0.935711 | + | 0.352768i | \(0.885241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 77.6702i | 1.09395i | 0.837150 | + | 0.546973i | \(0.184220\pi\) | ||||
−0.837150 | + | 0.546973i | \(0.815780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 76.1012i | 1.04248i | 0.853410 | + | 0.521241i | \(0.174531\pi\) | ||||
−0.853410 | + | 0.521241i | \(0.825469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.60176 | 0.0597631 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 123.462 | 1.56280 | 0.781402 | − | 0.624028i | \(-0.214505\pi\) | ||||
0.781402 | + | 0.624028i | \(0.214505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −116.582 | −1.40460 | −0.702302 | − | 0.711879i | \(-0.747844\pi\) | ||||
−0.702302 | + | 0.711879i | \(0.747844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.5482 | − | 12.3912i | −0.300567 | − | 0.145779i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 52.0421i | 0.584743i | 0.956305 | + | 0.292371i | \(0.0944443\pi\) | ||||
−0.956305 | + | 0.292371i | \(0.905556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.15905 | 0.0237258 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −112.838 | − | 54.7282i | −1.18777 | − | 0.576086i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.7460i | − | 0.162330i | −0.996701 | − | 0.0811650i | \(-0.974136\pi\) | ||
0.996701 | − | 0.0811650i | \(-0.0258641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 46.8637i | − | 0.463997i | −0.972716 | − | 0.231999i | \(-0.925474\pi\) | ||
0.972716 | − | 0.231999i | \(-0.0745265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 89.5615i | 0.869529i | 0.900544 | + | 0.434764i | \(0.143168\pi\) | ||||
−0.900544 | + | 0.434764i | \(0.856832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 28.6251 | 0.267525 | 0.133762 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133762 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 188.237 | 1.72695 | 0.863474 | − | 0.504393i | \(-0.168284\pi\) | ||||
0.863474 | + | 0.504393i | \(0.168284\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −63.0780 | −0.558212 | −0.279106 | − | 0.960260i | \(-0.590038\pi\) | ||||
−0.279106 | + | 0.960260i | \(0.590038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.5754 | − | 10.4644i | −0.187612 | − | 0.0909945i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 57.3077i | − | 0.481577i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.792 | 0.998281 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −26.7948 | − | 122.094i | −0.214358 | − | 0.976755i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 209.870i | − | 1.65252i | −0.563289 | − | 0.826260i | \(-0.690464\pi\) | ||
0.563289 | − | 0.826260i | \(-0.309536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 117.183i | − | 0.894527i | −0.894402 | − | 0.447264i | \(-0.852399\pi\) | ||
0.894402 | − | 0.447264i | \(-0.147601\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 253.110i | − | 1.90308i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 63.8768 | 0.466254 | 0.233127 | − | 0.972446i | \(-0.425104\pi\) | ||||
0.233127 | + | 0.972446i | \(0.425104\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 92.0960 | 0.662561 | 0.331281 | − | 0.943532i | \(-0.392519\pi\) | ||||
0.331281 | + | 0.943532i | \(0.392519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0975649 | −0.000682272 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −111.015 | + | 228.890i | −0.765621 | + | 1.57855i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 127.096i | 0.852990i | 0.904490 | + | 0.426495i | \(0.140252\pi\) | ||||
−0.904490 | + | 0.426495i | \(0.859748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −251.780 | −1.66741 | −0.833707 | − | 0.552207i | \(-0.813786\pi\) | ||||
−0.833707 | + | 0.552207i | \(0.813786\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −64.6679 | − | 31.3648i | −0.417212 | − | 0.202354i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 195.073i | − | 1.24251i | −0.783610 | − | 0.621253i | \(-0.786624\pi\) | ||
0.783610 | − | 0.621253i | \(-0.213376\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 48.3961i | − | 0.300597i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 128.920i | 0.790922i | 0.918483 | + | 0.395461i | \(0.129415\pi\) | ||||
−0.918483 | + | 0.395461i | \(0.870585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −37.5842 | −0.225055 | −0.112528 | − | 0.993649i | \(-0.535895\pi\) | ||||
−0.112528 | + | 0.993649i | \(0.535895\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.954 | 0.999729 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −90.9797 | −0.525894 | −0.262947 | − | 0.964810i | \(-0.584694\pi\) | ||||
−0.262947 | + | 0.964810i | \(0.584694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 198.116 | − | 156.193i | 1.13209 | − | 0.892532i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.5078i | 0.108982i | 0.998514 | + | 0.0544911i | \(0.0173537\pi\) | ||||
−0.998514 | + | 0.0544911i | \(0.982646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −174.603 | −0.964656 | −0.482328 | − | 0.875991i | \(-0.660209\pi\) | ||||
−0.482328 | + | 0.875991i | \(0.660209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 140.839 | − | 290.382i | 0.761294 | − | 1.56963i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.58966i | 0.0138485i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 98.4380i | − | 0.515382i | −0.966227 | − | 0.257691i | \(-0.917038\pi\) | ||
0.966227 | − | 0.257691i | \(-0.0829617\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 330.925i | − | 1.71464i | −0.514785 | − | 0.857319i | \(-0.672128\pi\) | ||
0.514785 | − | 0.857319i | \(-0.327872\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −309.042 | −1.56874 | −0.784371 | − | 0.620292i | \(-0.787014\pi\) | ||||
−0.784371 | + | 0.620292i | \(0.787014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.2565 | −0.0615906 | −0.0307953 | − | 0.999526i | \(-0.509804\pi\) | ||||
−0.0307953 | + | 0.999526i | \(0.509804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −513.428 | −2.52920 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −104.731 | + | 215.935i | −0.510885 | + | 1.05334i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.4377i | 0.0547259i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −30.4591 | −0.144356 | −0.0721780 | − | 0.997392i | \(-0.522995\pi\) | ||||
−0.0721780 | + | 0.997392i | \(0.522995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.93432 | + | 3.98817i | −0.00899684 | + | 0.0185496i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 145.058i | − | 0.668469i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.21502i | 0.00549781i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 34.0476i | − | 0.152680i | −0.997082 | − | 0.0763400i | \(-0.975677\pi\) | ||
0.997082 | − | 0.0763400i | \(-0.0243234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −390.716 | −1.72121 | −0.860607 | − | 0.509270i | \(-0.829916\pi\) | ||||
−0.860607 | + | 0.509270i | \(0.829916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 60.7427 | 0.265252 | 0.132626 | − | 0.991166i | \(-0.457659\pi\) | ||||
0.132626 | + | 0.991166i | \(0.457659\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 170.929 | 0.733603 | 0.366801 | − | 0.930299i | \(-0.380453\pi\) | ||||
0.366801 | + | 0.930299i | \(0.380453\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −277.721 | − | 134.699i | −1.18179 | − | 0.573185i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.1922i | − | 0.0468293i | −0.999726 | − | 0.0234147i | \(-0.992546\pi\) | ||
0.999726 | − | 0.0234147i | \(-0.00745380\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 83.6136 | 0.346944 | 0.173472 | − | 0.984839i | \(-0.444501\pi\) | ||||
0.173472 | + | 0.984839i | \(0.444501\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 237.689 | + | 115.283i | 0.970161 | + | 0.470542i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.36634i | 0.0217261i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 420.150i | − | 1.67391i | −0.547275 | − | 0.836953i | \(-0.684335\pi\) | ||
0.547275 | − | 0.836953i | \(-0.315665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.18696i | 0.00864412i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 179.388 | 0.698009 | 0.349004 | − | 0.937121i | \(-0.386520\pi\) | ||||
0.349004 | + | 0.937121i | \(0.386520\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 651.361 | 2.51491 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 441.954 | 1.68043 | 0.840217 | − | 0.542251i | \(-0.182428\pi\) | ||||
0.840217 | + | 0.542251i | \(0.182428\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −333.821 | − | 161.908i | −1.25970 | − | 0.610974i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.3172i | 0.101551i | 0.998710 | + | 0.0507754i | \(0.0161693\pi\) | ||||
−0.998710 | + | 0.0507754i | \(0.983831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 291.313 | 1.07496 | 0.537478 | − | 0.843278i | \(-0.319377\pi\) | ||||
0.537478 | + | 0.843278i | \(0.319377\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.95263 | + | 7.05817i | −0.0325550 | + | 0.0256661i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 188.753i | 0.681417i | 0.940169 | + | 0.340709i | \(0.110667\pi\) | ||||
−0.940169 | + | 0.340709i | \(0.889333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 472.884i | − | 1.68286i | −0.540364 | − | 0.841431i | \(-0.681713\pi\) | ||
0.540364 | − | 0.841431i | \(-0.318287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 281.426i | − | 0.994438i | −0.867625 | − | 0.497219i | \(-0.834355\pi\) | ||
0.867625 | − | 0.497219i | \(-0.165645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −484.368 | −1.68769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −256.750 | −0.888408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 388.192 | 1.32489 | 0.662443 | − | 0.749112i | \(-0.269520\pi\) | ||||
0.662443 | + | 0.749112i | \(0.269520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.5369 | − | 93.8878i | 0.154362 | − | 0.318264i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.02608i | 0.00343170i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.94595 | −0.0297208 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −326.096 | − | 158.161i | −1.06917 | − | 0.518562i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 213.835i | − | 0.696531i | −0.937396 | − | 0.348265i | \(-0.886771\pi\) | ||
0.937396 | − | 0.348265i | \(-0.113229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 331.277i | 1.06520i | 0.846368 | + | 0.532599i | \(0.178785\pi\) | ||||
−0.846368 | + | 0.532599i | \(0.821215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 392.652i | − | 1.25448i | −0.778826 | − | 0.627239i | \(-0.784185\pi\) | ||
0.778826 | − | 0.627239i | \(-0.215815\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 83.6598 | 0.263911 | 0.131956 | − | 0.991256i | \(-0.457874\pi\) | ||||
0.131956 | + | 0.991256i | \(0.457874\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.2012 | 0.0727310 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 142.439 | 0.440987 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.20039 | + | 3.31155i | −0.0129243 | + | 0.0101894i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 622.961i | − | 1.89350i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −113.701 | −0.343507 | −0.171753 | − | 0.985140i | \(-0.554943\pi\) | ||||
−0.171753 | + | 0.985140i | \(0.554943\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 103.144 | − | 212.661i | 0.307892 | − | 0.634810i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 278.872i | 0.827513i | 0.910387 | + | 0.413757i | \(0.135784\pi\) | ||||
−0.910387 | + | 0.413757i | \(0.864216\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.55498i | 0.0192228i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 38.6922i | 0.112805i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −252.355 | −0.727247 | −0.363623 | − | 0.931546i | \(-0.618460\pi\) | ||||
−0.363623 | + | 0.931546i | \(0.618460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 333.461 | 0.955477 | 0.477738 | − | 0.878502i | \(-0.341457\pi\) | ||||
0.477738 | + | 0.878502i | \(0.341457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −221.720 | −0.628102 | −0.314051 | − | 0.949406i | \(-0.601686\pi\) | ||||
−0.314051 | + | 0.949406i | \(0.601686\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 169.474 | − | 349.421i | 0.477392 | − | 0.984284i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 66.9184i | 0.186402i | 0.995647 | + | 0.0932011i | \(0.0297099\pi\) | ||||
−0.995647 | + | 0.0932011i | \(0.970290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 268.107 | 0.742678 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 166.051 | − | 342.362i | 0.454933 | − | 0.937979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 459.145i | 1.25108i | 0.780194 | + | 0.625538i | \(0.215120\pi\) | ||||
−0.780194 | + | 0.625538i | \(0.784880\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 748.801i | − | 2.01833i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 280.330i | 0.751556i | 0.926710 | + | 0.375778i | \(0.122624\pi\) | ||||
−0.926710 | + | 0.375778i | \(0.877376\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8855 | 0.0288741 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 441.415 | 1.16468 | 0.582341 | − | 0.812944i | \(-0.302137\pi\) | ||||
0.582341 | + | 0.812944i | \(0.302137\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.3805 | −0.0688786 | −0.0344393 | − | 0.999407i | \(-0.510965\pi\) | ||||
−0.0344393 | + | 0.999407i | \(0.510965\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.7023 | − | 10.0409i | −0.0537722 | − | 0.0260803i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 525.157i | − | 1.35002i | −0.737810 | − | 0.675008i | \(-0.764140\pi\) | ||
0.737810 | − | 0.675008i | \(-0.235860\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.2352 | 0.0696551 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −555.426 | − | 269.389i | −1.40614 | − | 0.681999i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 520.403i | 1.31084i | 0.755265 | + | 0.655419i | \(0.227508\pi\) | ||||
−0.755265 | + | 0.655419i | \(0.772492\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 182.030i | 0.453939i | 0.973902 | + | 0.226970i | \(0.0728818\pi\) | ||||
−0.973902 | + | 0.226970i | \(0.927118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.07546i | 0.00763142i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.4342 | −0.0723199 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −563.216 | −1.37706 | −0.688529 | − | 0.725209i | \(-0.741743\pi\) | ||||
−0.688529 | + | 0.725209i | \(0.741743\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 210.602 | 0.509931 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 524.477 | + | 254.379i | 1.26380 | + | 0.612961i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 125.092i | 0.298549i | 0.988796 | + | 0.149274i | \(0.0476937\pi\) | ||||
−0.988796 | + | 0.149274i | \(0.952306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −83.9028 | −0.199294 | −0.0996470 | − | 0.995023i | \(-0.531771\pi\) | ||||
−0.0996470 | + | 0.995023i | \(0.531771\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 87.8984 | + | 111.491i | 0.206820 | + | 0.262332i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 731.473i | − | 1.71305i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 796.050i | − | 1.84698i | −0.383619 | − | 0.923491i | \(-0.625323\pi\) | ||
0.383619 | − | 0.923491i | \(-0.374677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 146.392i | 0.338087i | 0.985609 | + | 0.169044i | \(0.0540678\pi\) | ||||
−0.985609 | + | 0.169044i | \(0.945932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 120.289 | 0.275261 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 248.094 | 0.565135 | 0.282568 | − | 0.959247i | \(-0.408814\pi\) | ||||
0.282568 | + | 0.959247i | \(0.408814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 247.807 | 0.559383 | 0.279691 | − | 0.960090i | \(-0.409768\pi\) | ||||
0.279691 | + | 0.960090i | \(0.409768\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 113.554 | − | 234.126i | 0.255178 | − | 0.526126i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 814.811i | − | 1.81472i | −0.420351 | − | 0.907362i | \(-0.638093\pi\) | ||
0.420351 | − | 0.907362i | \(-0.361907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.8880 | 0.0485321 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.71309 | − | 4.71099i | −0.0213475 | − | 0.0103538i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 225.952i | − | 0.494425i | −0.968961 | − | 0.247213i | \(-0.920485\pi\) | ||
0.968961 | − | 0.247213i | \(-0.0795146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 249.107i | 0.540362i | 0.962810 | + | 0.270181i | \(0.0870836\pi\) | ||||
−0.962810 | + | 0.270181i | \(0.912916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 78.6025i | − | 0.169768i | −0.996391 | − | 0.0848839i | \(-0.972948\pi\) | ||
0.996391 | − | 0.0848839i | \(-0.0270519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 506.114 | 1.08376 | 0.541878 | − | 0.840457i | \(-0.317714\pi\) | ||||
0.541878 | + | 0.840457i | \(0.317714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 477.025 | 1.01711 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.404256 | 0.000854665 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 388.219 | + | 492.420i | 0.817304 | + | 1.03667i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 394.563i | 0.823723i | 0.911247 | + | 0.411861i | \(0.135121\pi\) | ||||
−0.911247 | + | 0.411861i | \(0.864879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.8099 | −0.0287109 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.3574 | + | 70.8378i | −0.0708399 | + | 0.146057i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 606.423i | 1.24522i | 0.782532 | + | 0.622610i | \(0.213928\pi\) | ||||
−0.782532 | + | 0.622610i | \(0.786072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 329.600i | 0.671283i | 0.941990 | + | 0.335641i | \(0.108953\pi\) | ||||
−0.941990 | + | 0.335641i | \(0.891047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 288.934i | − | 0.586074i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 783.793 | 1.57705 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 385.046 | 0.771635 | 0.385817 | − | 0.922575i | \(-0.373920\pi\) | ||||
0.385817 | + | 0.922575i | \(0.373920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −464.735 | −0.923926 | −0.461963 | − | 0.886899i | \(-0.652855\pi\) | ||||
−0.461963 | + | 0.886899i | \(0.652855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −102.255 | + | 210.829i | −0.202486 | + | 0.417484i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 944.209i | 1.85503i | 0.373788 | + | 0.927514i | \(0.378059\pi\) | ||||
−0.373788 | + | 0.927514i | \(0.621941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 767.959 | 1.50286 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 195.421 | − | 402.917i | 0.379457 | − | 0.782363i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.1508i | 0.0544504i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 702.408i | 1.34819i | 0.738644 | + | 0.674096i | \(0.235467\pi\) | ||||
−0.738644 | + | 0.674096i | \(0.764533\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 487.025i | − | 0.931214i | −0.884992 | − | 0.465607i | \(-0.845836\pi\) | ||
0.884992 | − | 0.465607i | \(-0.154164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 81.6319 | 0.154899 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.2694 | 0.0192671 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −128.778 | − | 62.4592i | −0.240707 | − | 0.116746i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 24.0931i | − | 0.0446996i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 142.175 | 0.262800 | 0.131400 | − | 0.991329i | \(-0.458053\pi\) | ||||
0.131400 | + | 0.991329i | \(0.458053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −846.838 | − | 410.728i | −1.55383 | − | 0.753630i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1011.54i | 1.84924i | 0.380888 | + | 0.924621i | \(0.375618\pi\) | ||||
−0.380888 | + | 0.924621i | \(0.624382\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1276.13i | − | 2.31603i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1245.89i | − | 2.25296i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −804.458 | −1.44427 | −0.722134 | − | 0.691753i | \(-0.756839\pi\) | ||||
−0.722134 | + | 0.691753i | \(0.756839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.189669 | 0.000339300 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −692.845 | −1.23063 | −0.615316 | − | 0.788281i | \(-0.710971\pi\) | ||||
−0.615316 | + | 0.788281i | \(0.710971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 283.774 | + | 137.634i | 0.502254 | + | 0.243600i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 299.787i | 0.526866i | 0.964678 | + | 0.263433i | \(0.0848548\pi\) | ||||
−0.964678 | + | 0.263433i | \(0.915145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 522.141 | 0.914432 | 0.457216 | − | 0.889356i | \(-0.348847\pi\) | ||||
0.457216 | + | 0.889356i | \(0.348847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 74.2299 | + | 94.1537i | 0.129096 | + | 0.163746i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 72.0944i | − | 0.124947i | −0.998047 | − | 0.0624735i | \(-0.980101\pi\) | ||
0.998047 | − | 0.0624735i | \(-0.0198989\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1176.46i | 2.02490i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.8374i | 0.0580401i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −579.228 | −0.986760 | −0.493380 | − | 0.869814i | \(-0.664239\pi\) | ||||
−0.493380 | + | 0.869814i | \(0.664239\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 360.542 | 0.612126 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.3152 | 0.0258266 | 0.0129133 | − | 0.999917i | \(-0.495889\pi\) | ||||
0.0129133 | + | 0.999917i | \(0.495889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −125.044 | + | 257.815i | −0.210157 | + | 0.433302i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 656.299i | − | 1.09566i | −0.836591 | − | 0.547829i | \(-0.815455\pi\) | ||
0.836591 | − | 0.547829i | \(-0.184545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 589.765 | 0.981307 | 0.490653 | − | 0.871355i | \(-0.336758\pi\) | ||||
0.490653 | + | 0.871355i | \(0.336758\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −543.417 | − | 263.565i | −0.898209 | − | 0.435644i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 430.985i | − | 0.710025i | −0.934862 | − | 0.355012i | \(-0.884477\pi\) | ||
0.934862 | − | 0.355012i | \(-0.115523\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.2078i | 0.0216167i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 231.974i | 0.378423i | 0.981936 | + | 0.189212i | \(0.0605933\pi\) | ||||
−0.981936 | + | 0.189212i | \(0.939407\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −268.727 | −0.435538 | −0.217769 | − | 0.976000i | \(-0.569878\pi\) | ||||
−0.217769 | + | 0.976000i | \(0.569878\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1156.45 | −1.86826 | −0.934129 | − | 0.356937i | \(-0.883821\pi\) | ||||
−0.934129 | + | 0.356937i | \(0.883821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 525.172 | 0.842973 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −145.863 | + | 607.741i | −0.233380 | + | 0.972386i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 366.557i | 0.582761i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −872.840 | −1.38326 | −0.691632 | − | 0.722250i | \(-0.743108\pi\) | ||||
−0.691632 | + | 0.722250i | \(0.743108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −457.930 | + | 944.158i | −0.721150 | + | 1.48686i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 11.3040i | − | 0.0177457i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1077.19i | − | 1.68049i | −0.542207 | − | 0.840245i | \(-0.682411\pi\) | ||
0.542207 | − | 0.840245i | \(-0.317589\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 567.675i | − | 0.882854i | −0.897297 | − | 0.441427i | \(-0.854472\pi\) | ||
0.897297 | − | 0.441427i | \(-0.145528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 455.891 | 0.704623 | 0.352311 | − | 0.935883i | \(-0.385396\pi\) | ||||
0.352311 | + | 0.935883i | \(0.385396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.51682 | −0.0146638 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −818.894 | −1.25405 | −0.627025 | − | 0.778999i | \(-0.715728\pi\) | ||||
−0.627025 | + | 0.778999i | \(0.715728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −255.690 | + | 527.180i | −0.390366 | + | 0.804856i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.6188i | 0.0661893i | 0.999452 | + | 0.0330947i | \(0.0105363\pi\) | ||||
−0.999452 | + | 0.0330947i | \(0.989464\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −699.302 | −1.05795 | −0.528973 | − | 0.848639i | \(-0.677423\pi\) | ||||
−0.528973 | + | 0.848639i | \(0.677423\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −552.278 | + | 1138.69i | −0.830494 | + | 1.71231i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 244.004i | − | 0.365823i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.0544i | 0.0492613i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 982.321i | − | 1.45962i | −0.683652 | − | 0.729808i | \(-0.739610\pi\) | ||
0.683652 | − | 0.729808i | \(-0.260390\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −611.511 | −0.903266 | −0.451633 | − | 0.892204i | \(-0.649158\pi\) | ||||
−0.451633 | + | 0.892204i | \(0.649158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −158.898 | −0.234017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.0480 | 0.0439942 | 0.0219971 | − | 0.999758i | \(-0.492998\pi\) | ||||
0.0219971 | + | 0.999758i | \(0.492998\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −287.368 | − | 139.377i | −0.419515 | − | 0.203471i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.8758i | 0.0230418i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −740.707 | −1.07194 | −0.535968 | − | 0.844239i | \(-0.680053\pi\) | ||||
−0.535968 | + | 0.844239i | \(0.680053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −414.320 | − | 200.951i | −0.596143 | − | 0.289138i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 272.580i | − | 0.391076i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1033.99i | − | 1.47502i | −0.675336 | − | 0.737511i | \(-0.736001\pi\) | ||
0.675336 | − | 0.737511i | \(-0.263999\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1618.96i | 2.30294i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −472.915 | −0.668904 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 365.755 | 0.515874 | 0.257937 | − | 0.966162i | \(-0.416957\pi\) | ||||
0.257937 | + | 0.966162i | \(0.416957\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 68.9379 | 0.0966871 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.438923 | + | 0.212884i | 0.000613878 | + | 0.000297739i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 0.979382i | − | 0.00136214i | −1.00000 | 0.000681072i | \(-0.999783\pi\) | |||
1.00000 | 0.000681072i | \(-0.000216792\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 903.791 | 1.25352 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 998.864 | − | 787.495i | 1.37774 | − | 1.08620i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 193.163i | − | 0.265699i | −0.991136 | − | 0.132850i | \(-0.957587\pi\) | ||
0.991136 | − | 0.132850i | \(-0.0424127\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.03438i | − | 0.00688697i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 609.311i | 0.831257i | 0.909534 | + | 0.415628i | \(0.136438\pi\) | ||||
−0.909534 | + | 0.415628i | \(0.863562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.5561 | −0.0292485 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1143.30 | 1.54709 | 0.773547 | − | 0.633739i | \(-0.218481\pi\) | ||||
0.773547 | + | 0.633739i | \(0.218481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.3555 | 0.0556602 | 0.0278301 | − | 0.999613i | \(-0.491140\pi\) | ||||
0.0278301 | + | 0.999613i | \(0.491140\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 277.319 | − | 571.775i | 0.372240 | − | 0.767483i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 288.865i | − | 0.385667i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1414.17 | 1.88305 | 0.941525 | − | 0.336943i | \(-0.109393\pi\) | ||||
0.941525 | + | 0.336943i | \(0.109393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1132.70 | + | 549.376i | 1.50027 | + | 0.727650i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 145.741i | 0.192524i | 0.995356 | + | 0.0962621i | \(0.0306887\pi\) | ||||
−0.995356 | + | 0.0962621i | \(0.969311\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 450.235i | 0.591636i | 0.955244 | + | 0.295818i | \(0.0955923\pi\) | ||||
−0.955244 | + | 0.295818i | \(0.904408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1899.56i | − | 2.48959i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.46510 | −0.00582151 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −204.046 | −0.265339 | −0.132669 | − | 0.991160i | \(-0.542355\pi\) | ||||
−0.132669 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1474.26 | 1.90720 | 0.953599 | − | 0.301080i | \(-0.0973472\pi\) | ||||
0.953599 | + | 0.301080i | \(0.0973472\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 222.489 | + | 282.207i | 0.287083 | + | 0.364138i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1203.90i | − | 1.54544i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.4186 | −0.0453503 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −425.645 | + | 877.592i | −0.542222 | + | 1.11795i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 786.144i | − | 0.998912i | −0.866339 | − | 0.499456i | \(-0.833533\pi\) | ||
0.866339 | − | 0.499456i | \(-0.166467\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 636.538i | 0.804726i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5084i | 0.0195566i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1050.07 | −1.31753 | −0.658765 | − | 0.752349i | \(-0.728921\pi\) | ||||
−0.658765 | + | 0.752349i | \(0.728921\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 350.574 | 0.438766 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.7031 | −0.0432168 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −105.599 | + | 217.724i | −0.131179 | + | 0.270464i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1251.93i | 1.54750i | 0.633490 | + | 0.773751i | \(0.281622\pi\) | ||||
−0.633490 | + | 0.773751i | \(0.718378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1068.89 | 1.31799 | 0.658997 | − | 0.752146i | \(-0.270981\pi\) | ||||
0.658997 | + | 0.752146i | \(0.270981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 281.300 | − | 579.984i | 0.345154 | − | 0.711636i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 22.2352i | − | 0.0272157i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1013.06i | 1.23394i | 0.786988 | + | 0.616968i | \(0.211639\pi\) | ||||
−0.786988 | + | 0.616968i | \(0.788361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.2166i | 0.0512960i | 0.999671 | + | 0.0256480i | \(0.00816490\pi\) | ||||
−0.999671 | + | 0.0256480i | \(0.991835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −992.092 | −1.19963 | −0.599814 | − | 0.800140i | \(-0.704759\pi\) | ||||
−0.599814 | + | 0.800140i | \(0.704759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1062.71 | −1.28192 | −0.640959 | − | 0.767575i | \(-0.721463\pi\) | ||||
−0.640959 | + | 0.767575i | \(0.721463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −300.041 | −0.360194 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 169.083 | + | 82.0077i | 0.202495 | + | 0.0982128i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1630.82i | − | 1.94376i | −0.235469 | − | 0.971882i | \(-0.575663\pi\) | ||
0.235469 | − | 0.971882i | \(-0.424337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1747.61 | −2.07801 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −760.088 | − | 368.653i | −0.899512 | − | 0.436276i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1218.95i | − | 1.43914i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 309.556i | 0.363755i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 713.109i | 0.836001i | 0.908447 | + | 0.418000i | \(0.137269\pi\) | ||||
−0.908447 | + | 0.418000i | \(0.862731\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 680.264 | 0.793774 | 0.396887 | − | 0.917868i | \(-0.370091\pi\) | ||||
0.396887 | + | 0.917868i | \(0.370091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −170.477 | −0.198459 | −0.0992297 | − | 0.995065i | \(-0.531638\pi\) | ||||
−0.0992297 | + | 0.995065i | \(0.531638\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1090.72 | 1.26387 | 0.631933 | − | 0.775023i | \(-0.282262\pi\) | ||||
0.631933 | + | 0.775023i | \(0.282262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 409.298 | + | 198.515i | 0.473176 | + | 0.229497i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 56.3001i | 0.0647872i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1137 | −0.0116116 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1232.09 | + | 270.394i | −1.40810 | + | 0.309022i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1080.87i | − | 1.23247i | −0.787564 | − | 0.616233i | \(-0.788658\pi\) | ||
0.787564 | − | 0.616233i | \(-0.211342\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1632.76i | 1.85330i | 0.375923 | + | 0.926651i | \(0.377326\pi\) | ||||
−0.375923 | + | 0.926651i | \(0.622674\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 429.629i | − | 0.486557i | −0.969957 | − | 0.243278i | \(-0.921777\pi\) | ||
0.969957 | − | 0.243278i | \(-0.0782228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1537.25 | 1.73308 | 0.866542 | − | 0.499104i | \(-0.166338\pi\) | ||||
0.866542 | + | 0.499104i | \(0.166338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2117.86 | −2.38229 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1548.38 | 1.73390 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.5655 | − | 87.7613i | 0.0475592 | − | 0.0980573i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 731.353i | − | 0.813518i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 421.391 | 0.467693 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 785.499 | + | 380.978i | 0.867955 | + | 0.420970i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 491.466i | 0.541859i | 0.962599 | + | 0.270930i | \(0.0873311\pi\) | ||||
−0.962599 | + | 0.270930i | \(0.912669\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 276.630i | 0.303655i | 0.988407 | + | 0.151827i | \(0.0485158\pi\) | ||||
−0.988407 | + | 0.151827i | \(0.951484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 53.1630i | − | 0.0582289i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1182.53 | −1.28956 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1723.53 | −1.87544 | −0.937722 | − | 0.347387i | \(-0.887069\pi\) | ||||
−0.937722 | + | 0.347387i | \(0.887069\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.6177 | −0.0180040 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1267.21 | + | 999.056i | −1.36996 | + | 1.08006i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 435.765i | − | 0.469069i | −0.972108 | − | 0.234534i | \(-0.924643\pi\) | ||
0.972108 | − | 0.234534i | \(-0.0753566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1325.19 | −1.42340 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.65057 | − | 11.6503i | 0.00604339 | − | 0.0124602i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1439.57i | 1.53636i | 0.640237 | + | 0.768178i | \(0.278836\pi\) | ||||
−0.640237 | + | 0.768178i | \(0.721164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 349.601i | 0.371521i | 0.982595 | + | 0.185761i | \(0.0594749\pi\) | ||||
−0.982595 | + | 0.185761i | \(0.940525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 230.193i | − | 0.244107i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1204.96 | 1.27240 | 0.636198 | − | 0.771526i | \(-0.280506\pi\) | ||||
0.636198 | + | 0.771526i | \(0.280506\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.2820 | −0.0171570 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −169.630 | −0.177995 | −0.0889977 | − | 0.996032i | \(-0.528366\pi\) | ||||
−0.0889977 | + | 0.996032i | \(0.528366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −214.789 | + | 442.851i | −0.224910 | + | 0.463718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 644.600i | − | 0.672158i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −754.373 | −0.784987 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −722.069 | + | 1488.76i | −0.748258 | + | 1.54276i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 62.3819i | 0.0645108i | 0.999480 | + | 0.0322554i | \(0.0102690\pi\) | ||||
−0.999480 | + | 0.0322554i | \(0.989731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 934.246i | − | 0.962148i | −0.876680 | − | 0.481074i | \(-0.840247\pi\) | ||
0.876680 | − | 0.481074i | \(-0.159753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 929.368i | − | 0.955157i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −611.285 | −0.625676 | −0.312838 | − | 0.949807i | \(-0.601280\pi\) | ||||
−0.312838 | + | 0.949807i | \(0.601280\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.7319 | −0.0242409 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −553.953 | −0.563533 | −0.281767 | − | 0.959483i | \(-0.590920\pi\) | ||||
−0.281767 | + | 0.959483i | \(0.590920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1390.31 | + | 674.321i | 1.41148 | + | 0.684590i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.25151i | − | 0.00429880i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1609.14 | −1.62375 | −0.811874 | − | 0.583832i | \(-0.801553\pi\) | ||||
−0.811874 | + | 0.583832i | \(0.801553\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 55.1394 | + | 26.7434i | 0.0554165 | + | 0.0268778i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.1069i | 0.0261855i | 0.999914 | + | 0.0130927i | \(0.00416767\pi\) | ||||
−0.999914 | + | 0.0130927i | \(0.995832\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4140.3.c.a.4049.13 | ✓ | 88 | |
3.2 | odd | 2 | inner | 4140.3.c.a.4049.76 | yes | 88 | |
5.4 | even | 2 | inner | 4140.3.c.a.4049.75 | yes | 88 | |
15.14 | odd | 2 | inner | 4140.3.c.a.4049.14 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.3.c.a.4049.13 | ✓ | 88 | 1.1 | even | 1 | trivial | |
4140.3.c.a.4049.14 | yes | 88 | 15.14 | odd | 2 | inner | |
4140.3.c.a.4049.75 | yes | 88 | 5.4 | even | 2 | inner | |
4140.3.c.a.4049.76 | yes | 88 | 3.2 | odd | 2 | inner |