Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.6 | ||
Root | \(-1.52087 + 2.63422i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.d.151.6 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52087 | + | 2.63422i | 0.537709 | + | 0.931339i | 0.999027 | + | 0.0441043i | \(0.0140434\pi\) |
−0.461318 | + | 0.887235i | \(0.652623\pi\) | |||||||
\(3\) | −4.01867 | + | 3.29398i | −0.773393 | + | 0.633927i | ||||
\(4\) | −0.626094 | + | 1.08443i | −0.0782617 | + | 0.135553i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.7890 | − | 5.57636i | −1.00626 | − | 0.379423i | ||||
\(7\) | −6.85611 | − | 11.8751i | −0.370195 | − | 0.641197i | 0.619400 | − | 0.785075i | \(-0.287376\pi\) |
−0.989595 | + | 0.143879i | \(0.954043\pi\) | |||||||
\(8\) | 20.5251 | 0.907090 | ||||||||
\(9\) | 5.29939 | − | 26.4748i | 0.196274 | − | 0.980549i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.9034 | − | 27.5455i | −0.435914 | − | 0.755026i | 0.561455 | − | 0.827507i | \(-0.310242\pi\) |
−0.997370 | + | 0.0724812i | \(0.976908\pi\) | |||||||
\(12\) | −1.05602 | − | 6.42029i | −0.0254038 | − | 0.154448i | ||||
\(13\) | 29.1216 | − | 50.4401i | 0.621298 | − | 1.07612i | −0.367946 | − | 0.929847i | \(-0.619939\pi\) |
0.989244 | − | 0.146272i | \(-0.0467276\pi\) | |||||||
\(14\) | 20.8545 | − | 36.1211i | 0.398115 | − | 0.689555i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 36.2248 | + | 62.7431i | 0.566012 | + | 0.980361i | ||||
\(17\) | −109.055 | −1.55586 | −0.777932 | − | 0.628348i | \(-0.783731\pi\) | ||||
−0.777932 | + | 0.628348i | \(0.783731\pi\) | |||||||
\(18\) | 77.8003 | − | 26.3050i | 1.01876 | − | 0.344453i | ||||
\(19\) | 129.695 | 1.56601 | 0.783004 | − | 0.622017i | \(-0.213687\pi\) | ||||
0.783004 | + | 0.622017i | \(0.213687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 66.6689 | + | 25.1383i | 0.692778 | + | 0.261221i | ||||
\(22\) | 48.3740 | − | 83.7863i | 0.468790 | − | 0.811968i | ||||
\(23\) | 39.8342 | − | 68.9949i | 0.361131 | − | 0.625497i | −0.627017 | − | 0.779006i | \(-0.715724\pi\) |
0.988147 | + | 0.153509i | \(0.0490575\pi\) | |||||||
\(24\) | −82.4836 | + | 67.6093i | −0.701537 | + | 0.575028i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 177.161 | 1.33631 | ||||||||
\(27\) | 65.9111 | + | 123.850i | 0.469800 | + | 0.882773i | ||||
\(28\) | 17.1703 | 0.115888 | ||||||||
\(29\) | −4.51769 | − | 7.82486i | −0.0289280 | − | 0.0501048i | 0.851199 | − | 0.524843i | \(-0.175876\pi\) |
−0.880127 | + | 0.474738i | \(0.842543\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.6904 | − | 28.9087i | 0.0966998 | − | 0.167489i | −0.813617 | − | 0.581401i | \(-0.802505\pi\) |
0.910317 | + | 0.413912i | \(0.135838\pi\) | |||||||
\(32\) | −28.0860 | + | 48.6463i | −0.155154 | + | 0.268735i | ||||
\(33\) | 154.645 | + | 58.3108i | 0.815764 | + | 0.307594i | ||||
\(34\) | −165.858 | − | 287.275i | −0.836602 | − | 1.44904i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25.3921 | + | 22.3225i | 0.117556 | + | 0.103345i | ||||
\(37\) | 22.1645 | 0.0984817 | 0.0492408 | − | 0.998787i | \(-0.484320\pi\) | ||||
0.0492408 | + | 0.998787i | \(0.484320\pi\) | |||||||
\(38\) | 197.250 | + | 341.647i | 0.842056 | + | 1.45848i | ||||
\(39\) | 49.1186 | + | 298.628i | 0.201673 | + | 1.22612i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −60.8698 | + | 105.430i | −0.231860 | + | 0.401593i | −0.958356 | − | 0.285578i | \(-0.907814\pi\) |
0.726495 | + | 0.687171i | \(0.241148\pi\) | |||||||
\(42\) | 35.1747 | + | 213.853i | 0.129228 | + | 0.785672i | ||||
\(43\) | 5.07086 | + | 8.78298i | 0.0179837 | + | 0.0311487i | 0.874877 | − | 0.484345i | \(-0.160942\pi\) |
−0.856894 | + | 0.515493i | \(0.827609\pi\) | |||||||
\(44\) | 39.8281 | 0.136462 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 242.331 | 0.776733 | ||||||||
\(47\) | −220.746 | − | 382.343i | −0.685088 | − | 1.18661i | −0.973409 | − | 0.229073i | \(-0.926430\pi\) |
0.288321 | − | 0.957534i | \(-0.406903\pi\) | |||||||
\(48\) | −352.250 | − | 132.820i | −1.05923 | − | 0.399395i | ||||
\(49\) | 77.4875 | − | 134.212i | 0.225911 | − | 0.391289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 438.255 | − | 359.225i | 1.20329 | − | 0.986304i | ||||
\(52\) | 36.4657 | + | 63.1604i | 0.0972477 | + | 0.168438i | ||||
\(53\) | 593.610 | 1.53846 | 0.769232 | − | 0.638969i | \(-0.220639\pi\) | ||||
0.769232 | + | 0.638969i | \(0.220639\pi\) | |||||||
\(54\) | −226.006 | + | 361.984i | −0.569546 | + | 0.912218i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −140.722 | − | 243.738i | −0.335800 | − | 0.581623i | ||||
\(57\) | −521.202 | + | 427.214i | −1.21114 | + | 0.992734i | ||||
\(58\) | 13.7416 | − | 23.8012i | 0.0311097 | − | 0.0538836i | ||||
\(59\) | −221.230 | + | 383.182i | −0.488164 | + | 0.845525i | −0.999907 | − | 0.0136133i | \(-0.995667\pi\) |
0.511743 | + | 0.859139i | \(0.329000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.2881 | − | 125.207i | −0.151730 | − | 0.262804i | 0.780133 | − | 0.625613i | \(-0.215151\pi\) |
−0.931864 | + | 0.362809i | \(0.881818\pi\) | |||||||
\(62\) | 101.536 | 0.207985 | ||||||||
\(63\) | −350.725 | + | 118.583i | −0.701385 | + | 0.237145i | ||||
\(64\) | 408.736 | 0.798312 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 81.5912 | + | 496.052i | 0.152169 | + | 0.925149i | ||||
\(67\) | 431.360 | − | 747.138i | 0.786553 | − | 1.36235i | −0.141514 | − | 0.989936i | \(-0.545197\pi\) |
0.928067 | − | 0.372414i | \(-0.121470\pi\) | |||||||
\(68\) | 68.2786 | − | 118.262i | 0.121765 | − | 0.210902i | ||||
\(69\) | 67.1873 | + | 408.481i | 0.117223 | + | 0.712685i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −818.541 | −1.36821 | −0.684105 | − | 0.729384i | \(-0.739807\pi\) | ||||
−0.684105 | + | 0.729384i | \(0.739807\pi\) | |||||||
\(72\) | 108.771 | − | 543.398i | 0.178038 | − | 0.889446i | ||||
\(73\) | −495.052 | −0.793719 | −0.396859 | − | 0.917879i | \(-0.629900\pi\) | ||||
−0.396859 | + | 0.917879i | \(0.629900\pi\) | |||||||
\(74\) | 33.7093 | + | 58.3863i | 0.0529545 | + | 0.0917198i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −81.2014 | + | 140.645i | −0.122558 | + | 0.212277i | ||||
\(77\) | −218.071 | + | 377.710i | −0.322747 | + | 0.559014i | ||||
\(78\) | −711.950 | + | 583.563i | −1.03349 | + | 0.847122i | ||||
\(79\) | −585.263 | − | 1013.71i | −0.833510 | − | 1.44368i | −0.895238 | − | 0.445588i | \(-0.852995\pi\) |
0.0617284 | − | 0.998093i | \(-0.480339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −672.833 | − | 280.601i | −0.922953 | − | 0.384912i | ||||
\(82\) | −370.300 | −0.498693 | ||||||||
\(83\) | −212.022 | − | 367.232i | −0.280390 | − | 0.485651i | 0.691090 | − | 0.722768i | \(-0.257131\pi\) |
−0.971481 | + | 0.237118i | \(0.923797\pi\) | |||||||
\(84\) | −69.0017 | + | 56.5586i | −0.0896273 | + | 0.0734648i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.4242 | + | 26.7156i | −0.0193400 | + | 0.0334978i | ||||
\(87\) | 43.9300 | + | 16.5644i | 0.0541355 | + | 0.0204125i | ||||
\(88\) | −326.419 | − | 565.374i | −0.395413 | − | 0.684876i | ||||
\(89\) | 1031.37 | 1.22837 | 0.614183 | − | 0.789163i | \(-0.289486\pi\) | ||||
0.614183 | + | 0.789163i | \(0.289486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −798.643 | −0.920006 | ||||||||
\(92\) | 49.8799 | + | 86.3945i | 0.0565254 | + | 0.0979049i | ||||
\(93\) | 28.1513 | + | 171.152i | 0.0313888 | + | 0.190835i | ||||
\(94\) | 671.452 | − | 1162.99i | 0.736756 | − | 1.27610i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −47.3718 | − | 288.008i | −0.0503632 | − | 0.306195i | ||||
\(97\) | 799.356 | + | 1384.53i | 0.836725 | + | 1.44925i | 0.892618 | + | 0.450814i | \(0.148866\pi\) |
−0.0558930 | + | 0.998437i | \(0.517801\pi\) | |||||||
\(98\) | 471.394 | 0.485897 | ||||||||
\(99\) | −813.541 | + | 275.066i | −0.825898 | + | 0.279244i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107.000 | + | 185.330i | 0.105415 | + | 0.182584i | 0.913908 | − | 0.405922i | \(-0.133050\pi\) |
−0.808493 | + | 0.588506i | \(0.799716\pi\) | |||||||
\(102\) | 1612.81 | + | 608.129i | 1.56561 | + | 0.590331i | ||||
\(103\) | 836.160 | − | 1448.27i | 0.799897 | − | 1.38546i | −0.119786 | − | 0.992800i | \(-0.538221\pi\) |
0.919683 | − | 0.392662i | \(-0.128446\pi\) | |||||||
\(104\) | 597.723 | − | 1035.29i | 0.563573 | − | 0.976137i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 902.804 | + | 1563.70i | 0.827246 | + | 1.43283i | ||||
\(107\) | 600.699 | 0.542727 | 0.271363 | − | 0.962477i | \(-0.412525\pi\) | ||||
0.271363 | + | 0.962477i | \(0.412525\pi\) | |||||||
\(108\) | −175.572 | − | 6.06581i | −0.156430 | − | 0.00540447i | ||||
\(109\) | −771.570 | −0.678009 | −0.339005 | − | 0.940785i | \(-0.610090\pi\) | ||||
−0.339005 | + | 0.940785i | \(0.610090\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −89.0718 | + | 73.0094i | −0.0761650 | + | 0.0624302i | ||||
\(112\) | 496.722 | − | 860.348i | 0.419070 | − | 0.725850i | ||||
\(113\) | −583.338 | + | 1010.37i | −0.485627 | + | 0.841131i | −0.999864 | − | 0.0165177i | \(-0.994742\pi\) |
0.514237 | + | 0.857648i | \(0.328075\pi\) | |||||||
\(114\) | −1918.06 | − | 723.228i | −1.57581 | − | 0.594180i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11.3140 | 0.00905583 | ||||||||
\(117\) | −1181.06 | − | 1038.29i | −0.933244 | − | 0.820427i | ||||
\(118\) | −1345.85 | −1.04996 | ||||||||
\(119\) | 747.692 | + | 1295.04i | 0.575973 | + | 0.997615i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 159.663 | − | 276.545i | 0.119957 | − | 0.207772i | ||||
\(122\) | 219.882 | − | 380.846i | 0.163173 | − | 0.282624i | ||||
\(123\) | −102.667 | − | 624.190i | −0.0752618 | − | 0.457572i | ||||
\(124\) | 20.8996 | + | 36.1991i | 0.0151358 | + | 0.0262159i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −845.783 | − | 743.539i | −0.598003 | − | 0.525712i | ||||
\(127\) | −1630.10 | −1.13896 | −0.569479 | − | 0.822006i | \(-0.692855\pi\) | ||||
−0.569479 | + | 0.822006i | \(0.692855\pi\) | |||||||
\(128\) | 846.322 | + | 1465.87i | 0.584414 | + | 1.01223i | ||||
\(129\) | −49.3091 | − | 18.5926i | −0.0336544 | − | 0.0126898i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −129.412 | + | 224.149i | −0.0863115 | + | 0.149496i | −0.905949 | − | 0.423386i | \(-0.860841\pi\) |
0.819638 | + | 0.572882i | \(0.194175\pi\) | |||||||
\(132\) | −160.056 | + | 131.193i | −0.105538 | + | 0.0865067i | ||||
\(133\) | −889.206 | − | 1540.15i | −0.579729 | − | 1.00412i | ||||
\(134\) | 2624.17 | 1.69175 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2238.36 | −1.41131 | ||||||||
\(137\) | 526.385 | + | 911.726i | 0.328264 | + | 0.568569i | 0.982167 | − | 0.188009i | \(-0.0602033\pi\) |
−0.653904 | + | 0.756578i | \(0.726870\pi\) | |||||||
\(138\) | −973.847 | + | 798.232i | −0.600720 | + | 0.492392i | ||||
\(139\) | −1192.25 | + | 2065.03i | −0.727519 | + | 1.26010i | 0.230410 | + | 0.973094i | \(0.425993\pi\) |
−0.957929 | + | 0.287006i | \(0.907340\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2146.54 | + | 809.378i | 1.28206 | + | 0.483418i | ||||
\(142\) | −1244.89 | − | 2156.22i | −0.735699 | − | 1.27427i | ||||
\(143\) | −1852.53 | −1.08333 | ||||||||
\(144\) | 1853.08 | − | 626.544i | 1.07239 | − | 0.362583i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −752.910 | − | 1304.08i | −0.426790 | − | 0.739221i | ||||
\(147\) | 130.696 | + | 794.597i | 0.0733308 | + | 0.445831i | ||||
\(148\) | −13.8771 | + | 24.0358i | −0.00770735 | + | 0.0133495i | ||||
\(149\) | −573.144 | + | 992.715i | −0.315126 | + | 0.545815i | −0.979464 | − | 0.201617i | \(-0.935380\pi\) |
0.664338 | + | 0.747432i | \(0.268714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 583.058 | + | 1009.89i | 0.314229 | + | 0.544261i | 0.979273 | − | 0.202543i | \(-0.0649207\pi\) |
−0.665044 | + | 0.746804i | \(0.731587\pi\) | |||||||
\(152\) | 2662.01 | 1.42051 | ||||||||
\(153\) | −577.924 | + | 2887.21i | −0.305375 | + | 1.52560i | ||||
\(154\) | −1326.63 | −0.694175 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −354.593 | − | 133.704i | −0.181988 | − | 0.0686208i | ||||
\(157\) | −1737.81 | + | 3009.97i | −0.883390 | + | 1.53008i | −0.0358423 | + | 0.999357i | \(0.511411\pi\) |
−0.847548 | + | 0.530719i | \(0.821922\pi\) | |||||||
\(158\) | 1780.22 | − | 3083.43i | 0.896371 | − | 1.55256i | ||||
\(159\) | −2385.52 | + | 1955.34i | −1.18984 | + | 0.975274i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1092.43 | −0.534755 | ||||||||
\(162\) | −284.126 | − | 2199.15i | −0.137796 | − | 1.06655i | ||||
\(163\) | 2223.32 | 1.06837 | 0.534183 | − | 0.845369i | \(-0.320619\pi\) | ||||
0.534183 | + | 0.845369i | \(0.320619\pi\) | |||||||
\(164\) | −76.2204 | − | 132.018i | −0.0362915 | − | 0.0628588i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 644.915 | − | 1117.03i | 0.301537 | − | 0.522277i | ||||
\(167\) | −793.991 | + | 1375.23i | −0.367909 | + | 0.637238i | −0.989239 | − | 0.146312i | \(-0.953260\pi\) |
0.621329 | + | 0.783550i | \(0.286593\pi\) | |||||||
\(168\) | 1368.39 | + | 515.967i | 0.628412 | + | 0.236951i | ||||
\(169\) | −597.632 | − | 1035.13i | −0.272022 | − | 0.471156i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 687.306 | − | 3433.66i | 0.307366 | − | 1.53555i | ||||
\(172\) | −12.6993 | −0.00562974 | ||||||||
\(173\) | 753.898 | + | 1305.79i | 0.331317 | + | 0.573857i | 0.982770 | − | 0.184831i | \(-0.0591738\pi\) |
−0.651454 | + | 0.758689i | \(0.725840\pi\) | |||||||
\(174\) | 23.1776 | + | 140.914i | 0.0100982 | + | 0.0613945i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1152.19 | − | 1995.66i | 0.493465 | − | 0.854707i | ||||
\(177\) | −373.143 | − | 2268.61i | −0.158458 | − | 0.963384i | ||||
\(178\) | 1568.58 | + | 2716.85i | 0.660504 | + | 1.14403i | ||||
\(179\) | 1572.66 | 0.656683 | 0.328341 | − | 0.944559i | \(-0.393510\pi\) | ||||
0.328341 | + | 0.944559i | \(0.393510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1984.41 | 0.814918 | 0.407459 | − | 0.913223i | \(-0.366415\pi\) | ||||
0.407459 | + | 0.913223i | \(0.366415\pi\) | |||||||
\(182\) | −1214.63 | − | 2103.81i | −0.494695 | − | 0.856838i | ||||
\(183\) | 702.930 | + | 265.048i | 0.283946 | + | 0.107065i | ||||
\(184\) | 817.601 | − | 1416.13i | 0.327578 | − | 0.567382i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −408.040 | + | 334.458i | −0.160854 | + | 0.131847i | ||||
\(187\) | 1734.34 | + | 3003.97i | 0.678223 | + | 1.17472i | ||||
\(188\) | 552.831 | 0.214465 | ||||||||
\(189\) | 1018.84 | − | 1631.83i | 0.392114 | − | 0.628032i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1174.18 | + | 2033.73i | 0.444819 | + | 0.770450i | 0.998040 | − | 0.0625853i | \(-0.0199345\pi\) |
−0.553220 | + | 0.833035i | \(0.686601\pi\) | |||||||
\(192\) | −1642.57 | + | 1346.37i | −0.617409 | + | 0.506071i | ||||
\(193\) | −117.085 | + | 202.797i | −0.0436681 | + | 0.0756354i | −0.887033 | − | 0.461705i | \(-0.847238\pi\) |
0.843365 | + | 0.537341i | \(0.180571\pi\) | |||||||
\(194\) | −2431.43 | + | 4211.37i | −0.899829 | + | 1.55855i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 97.0288 | + | 168.059i | 0.0353604 | + | 0.0612460i | ||||
\(197\) | 717.846 | 0.259616 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(198\) | −1961.87 | − | 1724.71i | −0.704163 | − | 0.619040i | ||||
\(199\) | 1701.45 | 0.606094 | 0.303047 | − | 0.952976i | \(-0.401996\pi\) | ||||
0.303047 | + | 0.952976i | \(0.401996\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 727.564 | + | 4423.39i | 0.255315 | + | 1.55225i | ||||
\(202\) | −325.467 | + | 563.725i | −0.113365 | + | 0.196354i | ||||
\(203\) | −61.9475 | + | 107.296i | −0.0214180 | + | 0.0370971i | ||||
\(204\) | 115.164 | + | 700.164i | 0.0395248 | + | 0.240300i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5086.77 | 1.72045 | ||||||||
\(207\) | −1615.53 | − | 1420.23i | −0.542450 | − | 0.476875i | ||||
\(208\) | 4219.69 | 1.40665 | ||||||||
\(209\) | −2062.60 | − | 3572.52i | −0.682645 | − | 1.18238i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2469.33 | − | 4277.01i | 0.805667 | − | 1.39546i | −0.110172 | − | 0.993912i | \(-0.535140\pi\) |
0.915840 | − | 0.401544i | \(-0.131526\pi\) | |||||||
\(212\) | −371.656 | + | 643.727i | −0.120403 | + | 0.208544i | ||||
\(213\) | 3289.44 | − | 2696.26i | 1.05816 | − | 0.867345i | ||||
\(214\) | 913.585 | + | 1582.38i | 0.291829 | + | 0.505463i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1352.83 | + | 2542.03i | 0.426150 | + | 0.800754i | ||||
\(217\) | −457.726 | −0.143191 | ||||||||
\(218\) | −1173.46 | − | 2032.49i | −0.364572 | − | 0.631456i | ||||
\(219\) | 1989.45 | − | 1630.69i | 0.613857 | − | 0.503160i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3175.85 | + | 5500.73i | −0.966655 | + | 1.67430i | ||||
\(222\) | −327.790 | − | 123.597i | −0.0990983 | − | 0.0373662i | ||||
\(223\) | −1526.57 | − | 2644.10i | −0.458416 | − | 0.794001i | 0.540461 | − | 0.841369i | \(-0.318250\pi\) |
−0.998877 | + | 0.0473684i | \(0.984917\pi\) | |||||||
\(224\) | 770.242 | 0.229750 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3548.73 | −1.04450 | ||||||||
\(227\) | −419.976 | − | 727.420i | −0.122797 | − | 0.212690i | 0.798073 | − | 0.602561i | \(-0.205853\pi\) |
−0.920869 | + | 0.389871i | \(0.872520\pi\) | |||||||
\(228\) | −136.960 | − | 832.682i | −0.0397825 | − | 0.241867i | ||||
\(229\) | −700.753 | + | 1213.74i | −0.202214 | + | 0.350245i | −0.949242 | − | 0.314548i | \(-0.898147\pi\) |
0.747027 | + | 0.664793i | \(0.231480\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −367.814 | − | 2236.21i | −0.104764 | − | 0.636935i | ||||
\(232\) | −92.7259 | − | 160.606i | −0.0262403 | − | 0.0454496i | ||||
\(233\) | 2856.99 | 0.803295 | 0.401647 | − | 0.915794i | \(-0.368438\pi\) | ||||
0.401647 | + | 0.915794i | \(0.368438\pi\) | |||||||
\(234\) | 938.843 | − | 4690.30i | 0.262282 | − | 1.31032i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −277.021 | − | 479.815i | −0.0764092 | − | 0.132345i | ||||
\(237\) | 5691.11 | + | 2145.90i | 1.55982 | + | 0.588149i | ||||
\(238\) | −2274.29 | + | 3939.18i | −0.619412 | + | 1.07285i | ||||
\(239\) | 854.917 | − | 1480.76i | 0.231381 | − | 0.400763i | −0.726834 | − | 0.686813i | \(-0.759009\pi\) |
0.958215 | + | 0.286050i | \(0.0923424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2166.23 | + | 3752.02i | 0.579000 | + | 1.00286i | 0.995594 | + | 0.0937648i | \(0.0298902\pi\) |
−0.416594 | + | 0.909092i | \(0.636776\pi\) | |||||||
\(242\) | 971.309 | 0.258009 | ||||||||
\(243\) | 3628.19 | − | 1088.66i | 0.957812 | − | 0.287396i | ||||
\(244\) | 181.036 | 0.0474987 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1488.11 | − | 1219.76i | 0.385686 | − | 0.316135i | ||||
\(247\) | 3776.93 | − | 6541.84i | 0.972957 | − | 1.68521i | ||||
\(248\) | 342.573 | − | 593.354i | 0.0877154 | − | 0.151927i | ||||
\(249\) | 2061.70 | + | 777.390i | 0.524719 | + | 0.197852i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1724.73 | −0.433722 | −0.216861 | − | 0.976202i | \(-0.569582\pi\) | ||||
−0.216861 | + | 0.976202i | \(0.569582\pi\) | |||||||
\(252\) | 90.9920 | − | 454.580i | 0.0227459 | − | 0.113634i | ||||
\(253\) | −2534.00 | −0.629688 | ||||||||
\(254\) | −2479.16 | − | 4294.04i | −0.612428 | − | 1.06076i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −939.349 | + | 1627.00i | −0.229333 | + | 0.397217i | ||||
\(257\) | −2926.63 | + | 5069.07i | −0.710342 | + | 1.23035i | 0.254386 | + | 0.967103i | \(0.418127\pi\) |
−0.964729 | + | 0.263246i | \(0.915207\pi\) | |||||||
\(258\) | −26.0156 | − | 158.168i | −0.00627776 | − | 0.0381671i | ||||
\(259\) | −151.962 | − | 263.206i | −0.0364574 | − | 0.0631462i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −231.103 | + | 78.1380i | −0.0548081 | + | 0.0185311i | ||||
\(262\) | −787.277 | −0.185642 | ||||||||
\(263\) | 196.180 | + | 339.794i | 0.0459962 | + | 0.0796677i | 0.888107 | − | 0.459637i | \(-0.152020\pi\) |
−0.842111 | + | 0.539305i | \(0.818687\pi\) | |||||||
\(264\) | 3174.10 | + | 1196.83i | 0.739971 | + | 0.279015i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2704.73 | − | 4684.73i | 0.623450 | − | 1.07985i | ||||
\(267\) | −4144.72 | + | 3397.30i | −0.950010 | + | 0.778695i | ||||
\(268\) | 540.144 | + | 935.557i | 0.123114 | + | 0.213240i | ||||
\(269\) | −4610.33 | −1.04497 | −0.522485 | − | 0.852648i | \(-0.674995\pi\) | ||||
−0.522485 | + | 0.852648i | \(0.674995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1155.72 | −0.259058 | −0.129529 | − | 0.991576i | \(-0.541347\pi\) | ||||
−0.129529 | + | 0.991576i | \(0.541347\pi\) | |||||||
\(272\) | −3950.49 | − | 6842.44i | −0.880638 | − | 1.52531i | ||||
\(273\) | 3209.48 | − | 2630.71i | 0.711526 | − | 0.583216i | ||||
\(274\) | −1601.13 | + | 2773.23i | −0.353020 | + | 0.611449i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −485.033 | − | 182.888i | −0.105781 | − | 0.0398860i | ||||
\(277\) | −304.205 | − | 526.898i | −0.0659852 | − | 0.114290i | 0.831145 | − | 0.556055i | \(-0.187686\pi\) |
−0.897131 | + | 0.441765i | \(0.854352\pi\) | |||||||
\(278\) | −7253.02 | −1.56477 | ||||||||
\(279\) | −676.904 | − | 595.075i | −0.145251 | − | 0.127693i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1374.62 | − | 2380.91i | −0.291825 | − | 0.505456i | 0.682416 | − | 0.730964i | \(-0.260929\pi\) |
−0.974241 | + | 0.225508i | \(0.927596\pi\) | |||||||
\(282\) | 1132.52 | + | 6885.42i | 0.239151 | + | 1.45397i | ||||
\(283\) | 510.780 | − | 884.697i | 0.107289 | − | 0.185830i | −0.807382 | − | 0.590029i | \(-0.799116\pi\) |
0.914671 | + | 0.404199i | \(0.132450\pi\) | |||||||
\(284\) | 512.483 | − | 887.647i | 0.107078 | − | 0.185465i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2817.46 | − | 4879.98i | −0.582516 | − | 1.00895i | ||||
\(287\) | 1669.32 | 0.343334 | ||||||||
\(288\) | 1139.06 | + | 1001.37i | 0.233056 | + | 0.204882i | ||||
\(289\) | 6979.96 | 1.42071 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7772.95 | − | 2930.89i | −1.56584 | − | 0.590418i | ||||
\(292\) | 309.949 | − | 536.848i | 0.0621178 | − | 0.107591i | ||||
\(293\) | −2616.25 | + | 4531.47i | −0.521648 | + | 0.903521i | 0.478035 | + | 0.878341i | \(0.341349\pi\) |
−0.999683 | + | 0.0251800i | \(0.991984\pi\) | |||||||
\(294\) | −1894.37 | + | 1552.76i | −0.375790 | + | 0.308023i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 454.929 | 0.0893317 | ||||||||
\(297\) | 2363.29 | − | 3785.18i | 0.461724 | − | 0.739524i | ||||
\(298\) | −3486.71 | −0.677785 | ||||||||
\(299\) | −2320.07 | − | 4018.48i | −0.448739 | − | 0.777240i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 69.5327 | − | 120.434i | 0.0133149 | − | 0.0230622i | ||||
\(302\) | −1773.51 | + | 3071.81i | −0.337927 | + | 0.585307i | ||||
\(303\) | −1040.47 | − | 392.322i | −0.197272 | − | 0.0743839i | ||||
\(304\) | 4698.18 | + | 8137.49i | 0.886379 | + | 1.53525i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8484.50 | + | 2868.69i | −1.58506 | + | 0.535921i | ||||
\(307\) | 4912.68 | 0.913296 | 0.456648 | − | 0.889648i | \(-0.349050\pi\) | ||||
0.456648 | + | 0.889648i | \(0.349050\pi\) | |||||||
\(308\) | −273.066 | − | 472.964i | −0.0505174 | − | 0.0874988i | ||||
\(309\) | 1410.33 | + | 8574.42i | 0.259647 | + | 1.57858i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 414.430 | − | 717.813i | 0.0755632 | − | 0.130879i | −0.825768 | − | 0.564010i | \(-0.809258\pi\) |
0.901331 | + | 0.433131i | \(0.142591\pi\) | |||||||
\(312\) | 1008.16 | + | 6129.36i | 0.182936 | + | 1.11220i | ||||
\(313\) | 4618.60 | + | 7999.66i | 0.834054 | + | 1.44462i | 0.894798 | + | 0.446471i | \(0.147319\pi\) |
−0.0607442 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(314\) | −10571.9 | −1.90003 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1465.72 | 0.260928 | ||||||||
\(317\) | −4549.20 | − | 7879.45i | −0.806021 | − | 1.39607i | −0.915599 | − | 0.402091i | \(-0.868283\pi\) |
0.109578 | − | 0.993978i | \(-0.465050\pi\) | |||||||
\(318\) | −8778.88 | − | 3310.18i | −1.54810 | − | 0.583729i | ||||
\(319\) | −143.693 | + | 248.884i | −0.0252203 | + | 0.0436828i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2414.01 | + | 1978.69i | −0.419741 | + | 0.344049i | ||||
\(322\) | −1661.45 | − | 2877.71i | −0.287543 | − | 0.498039i | ||||
\(323\) | −14143.9 | −2.43649 | ||||||||
\(324\) | 725.548 | − | 553.955i | 0.124408 | − | 0.0949855i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3381.38 | + | 5856.72i | 0.574470 | + | 0.995011i | ||||
\(327\) | 3100.68 | − | 2541.54i | 0.524368 | − | 0.429808i | ||||
\(328\) | −1249.36 | + | 2163.95i | −0.210318 | + | 0.364281i | ||||
\(329\) | −3026.92 | + | 5242.78i | −0.507233 | + | 0.878553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2981.73 | − | 5164.50i | −0.495137 | − | 0.857603i | 0.504847 | − | 0.863209i | \(-0.331549\pi\) |
−0.999984 | + | 0.00560570i | \(0.998216\pi\) | |||||||
\(332\) | 530.982 | 0.0877754 | ||||||||
\(333\) | 117.458 | − | 586.801i | 0.0193294 | − | 0.0965661i | ||||
\(334\) | −4830.23 | −0.791313 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 837.807 | + | 5093.65i | 0.136030 | + | 0.827027i | ||||
\(337\) | 298.427 | − | 516.890i | 0.0482384 | − | 0.0835514i | −0.840898 | − | 0.541194i | \(-0.817973\pi\) |
0.889136 | + | 0.457642i | \(0.151306\pi\) | |||||||
\(338\) | 1817.84 | − | 3148.60i | 0.292537 | − | 0.506690i | ||||
\(339\) | −983.901 | − | 5981.85i | −0.157635 | − | 0.958377i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1061.74 | −0.168611 | ||||||||
\(342\) | 10090.3 | − | 3411.63i | 1.59539 | − | 0.539415i | ||||
\(343\) | −6828.34 | −1.07492 | ||||||||
\(344\) | 104.080 | + | 180.272i | 0.0163128 | + | 0.0282546i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2293.16 | + | 3971.87i | −0.356304 | + | 0.617137i | ||||
\(347\) | −2281.05 | + | 3950.90i | −0.352891 | + | 0.611226i | −0.986755 | − | 0.162219i | \(-0.948135\pi\) |
0.633863 | + | 0.773445i | \(0.281468\pi\) | |||||||
\(348\) | −45.4671 | + | 37.2680i | −0.00700372 | + | 0.00574074i | ||||
\(349\) | −337.633 | − | 584.798i | −0.0517854 | − | 0.0896949i | 0.838971 | − | 0.544177i | \(-0.183158\pi\) |
−0.890756 | + | 0.454482i | \(0.849825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8166.42 | + | 282.140i | 1.24185 | + | 0.0429046i | ||||
\(352\) | 1786.65 | 0.270536 | ||||||||
\(353\) | −1680.91 | − | 2911.43i | −0.253445 | − | 0.438979i | 0.711027 | − | 0.703165i | \(-0.248230\pi\) |
−0.964472 | + | 0.264185i | \(0.914897\pi\) | |||||||
\(354\) | 5408.52 | − | 4433.20i | 0.812033 | − | 0.665598i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −645.732 | + | 1118.44i | −0.0961341 | + | 0.166509i | ||||
\(357\) | −7270.57 | − | 2741.46i | −1.07787 | − | 0.406424i | ||||
\(358\) | 2391.81 | + | 4142.74i | 0.353104 | + | 0.611594i | ||||
\(359\) | 7701.61 | 1.13224 | 0.566122 | − | 0.824322i | \(-0.308443\pi\) | ||||
0.566122 | + | 0.824322i | \(0.308443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9961.87 | 1.45238 | ||||||||
\(362\) | 3018.03 | + | 5227.39i | 0.438189 | + | 0.758965i | ||||
\(363\) | 269.300 | + | 1637.27i | 0.0389382 | + | 0.236734i | ||||
\(364\) | 500.026 | − | 866.070i | 0.0720013 | − | 0.124710i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 370.868 | + | 2254.78i | 0.0529661 | + | 0.322020i | ||||
\(367\) | 2954.75 | + | 5117.77i | 0.420263 | + | 0.727917i | 0.995965 | − | 0.0897425i | \(-0.0286044\pi\) |
−0.575702 | + | 0.817660i | \(0.695271\pi\) | |||||||
\(368\) | 5771.94 | 0.817617 | ||||||||
\(369\) | 2468.66 | + | 2170.23i | 0.348274 | + | 0.306172i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4069.86 | − | 7049.20i | −0.569532 | − | 0.986459i | ||||
\(372\) | −203.228 | − | 76.6295i | −0.0283249 | − | 0.0106803i | ||||
\(373\) | −4212.19 | + | 7295.73i | −0.584716 | + | 1.01276i | 0.410195 | + | 0.911998i | \(0.365461\pi\) |
−0.994911 | + | 0.100760i | \(0.967873\pi\) | |||||||
\(374\) | −5275.42 | + | 9137.30i | −0.729374 | + | 1.26331i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4530.84 | − | 7847.64i | −0.621436 | − | 1.07636i | ||||
\(377\) | −526.249 | −0.0718917 | ||||||||
\(378\) | 5848.13 | + | 202.046i | 0.795754 | + | 0.0274923i | ||||
\(379\) | −3510.24 | −0.475749 | −0.237875 | − | 0.971296i | \(-0.576451\pi\) | ||||
−0.237875 | + | 0.971296i | \(0.576451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6550.81 | − | 5369.50i | 0.880862 | − | 0.722016i | ||||
\(382\) | −3571.54 | + | 6186.09i | −0.478367 | + | 0.828555i | ||||
\(383\) | 2866.01 | − | 4964.08i | 0.382367 | − | 0.662279i | −0.609033 | − | 0.793145i | \(-0.708442\pi\) |
0.991400 | + | 0.130866i | \(0.0417758\pi\) | |||||||
\(384\) | −8229.64 | − | 3103.09i | −1.09366 | − | 0.412380i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −712.283 | −0.0939229 | ||||||||
\(387\) | 259.400 | − | 87.7056i | 0.0340725 | − | 0.0115202i | ||||
\(388\) | −2001.89 | −0.261934 | ||||||||
\(389\) | −7183.60 | − | 12442.4i | −0.936306 | − | 1.62173i | −0.772288 | − | 0.635273i | \(-0.780888\pi\) |
−0.164019 | − | 0.986457i | \(-0.552446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4344.11 | + | 7524.23i | −0.561870 | + | 0.973188i | ||||
\(392\) | 1590.44 | − | 2754.72i | 0.204922 | − | 0.354934i | ||||
\(393\) | −218.276 | − | 1327.06i | −0.0280167 | − | 0.170334i | ||||
\(394\) | 1091.75 | + | 1890.97i | 0.139598 | + | 0.241791i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 211.065 | − | 1054.44i | 0.0267838 | − | 0.133807i | ||||
\(397\) | 9014.42 | 1.13960 | 0.569800 | − | 0.821784i | \(-0.307021\pi\) | ||||
0.569800 | + | 0.821784i | \(0.307021\pi\) | |||||||
\(398\) | 2587.69 | + | 4482.01i | 0.325902 | + | 0.564479i | ||||
\(399\) | 8646.64 | + | 3260.32i | 1.08490 | + | 0.409073i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5255.55 | + | 9102.87i | −0.654487 | + | 1.13361i | 0.327535 | + | 0.944839i | \(0.393782\pi\) |
−0.982022 | + | 0.188766i | \(0.939551\pi\) | |||||||
\(402\) | −10545.7 | + | 8643.97i | −1.30839 | + | 1.07244i | ||||
\(403\) | −972.104 | − | 1683.73i | −0.120159 | − | 0.208121i | ||||
\(404\) | −267.969 | −0.0329998 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −376.857 | −0.0460667 | ||||||||
\(407\) | −352.491 | − | 610.533i | −0.0429296 | − | 0.0743562i | ||||
\(408\) | 8995.23 | − | 7373.12i | 1.09150 | − | 0.894666i | ||||
\(409\) | −1659.10 | + | 2873.65i | −0.200580 | + | 0.347415i | −0.948715 | − | 0.316131i | \(-0.897616\pi\) |
0.748135 | + | 0.663546i | \(0.230949\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5118.57 | − | 1930.02i | −0.614308 | − | 0.231632i | ||||
\(412\) | 1047.03 | + | 1813.51i | 0.125203 | + | 0.216857i | ||||
\(413\) | 6067.11 | 0.722864 | ||||||||
\(414\) | 1284.20 | − | 6415.66i | 0.152452 | − | 0.761625i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1635.81 | + | 2833.31i | 0.192794 | + | 0.333929i | ||||
\(417\) | −2010.93 | − | 12225.9i | −0.236153 | − | 1.43575i | ||||
\(418\) | 6273.89 | − | 10866.7i | 0.734129 | − | 1.27155i | ||||
\(419\) | 243.069 | − | 421.008i | 0.0283406 | − | 0.0490873i | −0.851507 | − | 0.524343i | \(-0.824311\pi\) |
0.879848 | + | 0.475255i | \(0.157644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2525.96 | − | 4375.10i | −0.292418 | − | 0.506482i | 0.681963 | − | 0.731387i | \(-0.261126\pi\) |
−0.974381 | + | 0.224904i | \(0.927793\pi\) | |||||||
\(422\) | 15022.1 | 1.73286 | ||||||||
\(423\) | −11292.3 | + | 3818.03i | −1.29799 | + | 0.438863i | ||||
\(424\) | 12183.9 | 1.39553 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12105.4 | + | 4564.48i | 1.37678 | + | 0.519130i | ||||
\(427\) | −991.230 | + | 1716.86i | −0.112340 | + | 0.194578i | ||||
\(428\) | −376.094 | + | 651.414i | −0.0424747 | + | 0.0735684i | ||||
\(429\) | 7444.70 | − | 6102.19i | 0.837840 | − | 0.686752i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6944.24 | 0.776084 | 0.388042 | − | 0.921642i | \(-0.373152\pi\) | ||||
0.388042 | + | 0.921642i | \(0.373152\pi\) | |||||||
\(432\) | −5383.10 | + | 8621.89i | −0.599525 | + | 0.960234i | ||||
\(433\) | 13738.3 | 1.52476 | 0.762378 | − | 0.647131i | \(-0.224032\pi\) | ||||
0.762378 | + | 0.647131i | \(0.224032\pi\) | |||||||
\(434\) | −696.142 | − | 1205.75i | −0.0769952 | − | 0.133360i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 483.075 | − | 836.711i | 0.0530622 | − | 0.0919064i | ||||
\(437\) | 5166.31 | − | 8948.31i | 0.565533 | − | 0.979533i | ||||
\(438\) | 7321.31 | + | 2760.59i | 0.798688 | + | 0.301155i | ||||
\(439\) | −4240.92 | − | 7345.48i | −0.461066 | − | 0.798589i | 0.537949 | − | 0.842978i | \(-0.319199\pi\) |
−0.999014 | + | 0.0443883i | \(0.985866\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3142.61 | − | 2762.71i | −0.339338 | − | 0.298317i | ||||
\(442\) | −19320.2 | −2.07912 | ||||||||
\(443\) | −279.098 | − | 483.411i | −0.0299330 | − | 0.0518455i | 0.850671 | − | 0.525699i | \(-0.176196\pi\) |
−0.880604 | + | 0.473853i | \(0.842863\pi\) | |||||||
\(444\) | −23.4061 | − | 142.303i | −0.00250181 | − | 0.0152103i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4643.44 | − | 8042.67i | 0.492989 | − | 0.853882i | ||||
\(447\) | −966.707 | − | 5877.32i | −0.102290 | − | 0.621896i | ||||
\(448\) | −2802.34 | − | 4853.79i | −0.295531 | − | 0.511875i | ||||
\(449\) | 14775.0 | 1.55295 | 0.776476 | − | 0.630147i | \(-0.217005\pi\) | ||||
0.776476 | + | 0.630147i | \(0.217005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3872.15 | 0.404285 | ||||||||
\(452\) | −730.449 | − | 1265.17i | −0.0760120 | − | 0.131657i | ||||
\(453\) | −5669.66 | − | 2137.82i | −0.588044 | − | 0.221729i | ||||
\(454\) | 1277.46 | − | 2212.62i | 0.132058 | − | 0.228730i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10697.7 | + | 8768.60i | −1.09861 | + | 0.900499i | ||||
\(457\) | −7103.97 | − | 12304.4i | −0.727154 | − | 1.25947i | −0.958081 | − | 0.286497i | \(-0.907509\pi\) |
0.230927 | − | 0.972971i | \(-0.425824\pi\) | |||||||
\(458\) | −4263.02 | −0.434930 | ||||||||
\(459\) | −7187.92 | − | 13506.4i | −0.730944 | − | 1.37347i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3851.26 | + | 6670.57i | 0.389091 | + | 0.673925i | 0.992328 | − | 0.123637i | \(-0.0394558\pi\) |
−0.603237 | + | 0.797562i | \(0.706123\pi\) | |||||||
\(462\) | 5331.29 | − | 4369.90i | 0.536870 | − | 0.440056i | ||||
\(463\) | 3954.53 | − | 6849.45i | 0.396939 | − | 0.687518i | −0.596408 | − | 0.802682i | \(-0.703406\pi\) |
0.993347 | + | 0.115163i | \(0.0367391\pi\) | |||||||
\(464\) | 327.304 | − | 566.908i | 0.0327472 | − | 0.0567199i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4345.11 | + | 7525.96i | 0.431939 | + | 0.748140i | ||||
\(467\) | −11639.8 | −1.15337 | −0.576685 | − | 0.816967i | \(-0.695654\pi\) | ||||
−0.576685 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(468\) | 1865.41 | − | 630.711i | 0.184249 | − | 0.0622962i | ||||
\(469\) | −11829.8 | −1.16471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2931.11 | − | 17820.4i | −0.286749 | − | 1.74336i | ||||
\(472\) | −4540.77 | + | 7864.84i | −0.442809 | + | 0.766967i | ||||
\(473\) | 161.288 | − | 279.359i | 0.0156787 | − | 0.0271563i | ||||
\(474\) | 3002.65 | + | 18255.3i | 0.290962 | + | 1.76897i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1872.50 | −0.180307 | ||||||||
\(477\) | 3145.77 | − | 15715.7i | 0.301960 | − | 1.50854i | ||||
\(478\) | 5200.87 | 0.497662 | ||||||||
\(479\) | 9347.93 | + | 16191.1i | 0.891687 | + | 1.54445i | 0.837853 | + | 0.545897i | \(0.183811\pi\) |
0.0538341 | + | 0.998550i | \(0.482856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 645.465 | − | 1117.98i | 0.0611865 | − | 0.105978i | ||||
\(482\) | −6589.10 | + | 11412.7i | −0.622667 | + | 1.07849i | ||||
\(483\) | 4390.12 | − | 3598.45i | 0.413576 | − | 0.338996i | ||||
\(484\) | 199.928 | + | 346.286i | 0.0187761 | + | 0.0325212i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8385.77 | + | 7901.75i | 0.782687 | + | 0.737512i | ||||
\(487\) | 2249.54 | 0.209315 | 0.104658 | − | 0.994508i | \(-0.466625\pi\) | ||||
0.104658 | + | 0.994508i | \(0.466625\pi\) | |||||||
\(488\) | −1483.72 | − | 2569.88i | −0.137633 | − | 0.238387i | ||||
\(489\) | −8934.78 | + | 7323.57i | −0.826267 | + | 0.677266i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −994.175 | + | 1721.96i | −0.0913778 | + | 0.158271i | −0.908091 | − | 0.418773i | \(-0.862460\pi\) |
0.816713 | + | 0.577044i | \(0.195794\pi\) | |||||||
\(492\) | 741.168 | + | 279.466i | 0.0679155 | + | 0.0256084i | ||||
\(493\) | 492.676 | + | 853.339i | 0.0450081 | + | 0.0779563i | ||||
\(494\) | 22976.9 | 2.09267 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2418.43 | 0.218933 | ||||||||
\(497\) | 5612.01 | + | 9720.28i | 0.506505 | + | 0.877292i | ||||
\(498\) | 1087.76 | + | 6613.29i | 0.0978790 | + | 0.595078i | ||||
\(499\) | −1206.95 | + | 2090.50i | −0.108278 | + | 0.187543i | −0.915073 | − | 0.403289i | \(-0.867867\pi\) |
0.806795 | + | 0.590832i | \(0.201200\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1339.20 | − | 8142.00i | −0.119423 | − | 0.726063i | ||||
\(502\) | −2623.10 | − | 4543.34i | −0.233216 | − | 0.403942i | ||||
\(503\) | 8758.56 | 0.776391 | 0.388196 | − | 0.921577i | \(-0.373098\pi\) | ||||
0.388196 | + | 0.921577i | \(0.373098\pi\) | |||||||
\(504\) | −7198.67 | + | 2433.94i | −0.636219 | + | 0.215111i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3853.88 | − | 6675.12i | −0.338589 | − | 0.586453i | ||||
\(507\) | 5811.38 | + | 2191.25i | 0.509058 | + | 0.191947i | ||||
\(508\) | 1020.59 | − | 1767.72i | 0.0891368 | − | 0.154389i | ||||
\(509\) | 5924.01 | − | 10260.7i | 0.515869 | − | 0.893511i | −0.483961 | − | 0.875089i | \(-0.660802\pi\) |
0.999830 | − | 0.0184220i | \(-0.00586422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3394.13 | + | 5878.81i | 0.293831 | + | 0.508930i | ||||
\(512\) | 7826.64 | 0.675570 | ||||||||
\(513\) | 8548.36 | + | 16062.7i | 0.735710 | + | 1.38243i | ||||
\(514\) | −17804.1 | −1.52783 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 51.0344 | − | 41.8313i | 0.00435400 | − | 0.00356884i | ||||
\(517\) | −7021.23 | + | 12161.1i | −0.597279 | + | 1.03452i | ||||
\(518\) | 462.230 | − | 800.606i | 0.0392070 | − | 0.0679085i | ||||
\(519\) | −7330.91 | − | 2764.21i | −0.620022 | − | 0.233787i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3816.55 | 0.320933 | 0.160466 | − | 0.987041i | \(-0.448700\pi\) | ||||
0.160466 | + | 0.987041i | \(0.448700\pi\) | |||||||
\(522\) | −557.310 | − | 489.939i | −0.0467295 | − | 0.0410806i | ||||
\(523\) | 12158.9 | 1.01658 | 0.508288 | − | 0.861187i | \(-0.330278\pi\) | ||||
0.508288 | + | 0.861187i | \(0.330278\pi\) | |||||||
\(524\) | −162.049 | − | 280.676i | −0.0135098 | − | 0.0233996i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −596.729 | + | 1033.57i | −0.0494651 | + | 0.0856761i | ||||
\(527\) | −1820.17 | + | 3152.63i | −0.150452 | + | 0.260590i | ||||
\(528\) | 1943.37 | + | 11815.2i | 0.160179 | + | 0.973846i | ||||
\(529\) | 2909.97 | + | 5040.22i | 0.239169 | + | 0.414253i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8972.28 | + | 7887.65i | 0.733265 | + | 0.644623i | ||||
\(532\) | 2226.90 | 0.181482 | ||||||||
\(533\) | 3545.25 | + | 6140.55i | 0.288108 | + | 0.499018i | ||||
\(534\) | −15252.8 | − | 5751.27i | −1.23606 | − | 0.466071i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8853.71 | − | 15335.1i | 0.713474 | − | 1.23577i | ||||
\(537\) | −6320.00 | + | 5180.31i | −0.507874 | + | 0.416289i | ||||
\(538\) | −7011.72 | − | 12144.7i | −0.561890 | − | 0.973222i | ||||
\(539\) | −4929.26 | −0.393911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14919.8 | 1.18568 | 0.592840 | − | 0.805321i | \(-0.298007\pi\) | ||||
0.592840 | + | 0.805321i | \(0.298007\pi\) | |||||||
\(542\) | −1757.69 | − | 3044.42i | −0.139298 | − | 0.241271i | ||||
\(543\) | −7974.69 | + | 6536.61i | −0.630252 | + | 0.516598i | ||||
\(544\) | 3062.91 | − | 5305.12i | 0.241399 | − | 0.418116i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11811.1 | + | 4453.52i | 0.925766 | + | 0.349072i | ||||
\(547\) | −513.578 | − | 889.543i | −0.0401444 | − | 0.0695322i | 0.845255 | − | 0.534363i | \(-0.179448\pi\) |
−0.885400 | + | 0.464831i | \(0.846115\pi\) | |||||||
\(548\) | −1318.27 | −0.102762 | ||||||||
\(549\) | −3697.91 | + | 1250.30i | −0.287473 | + | 0.0971973i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −585.923 | − | 1014.85i | −0.0453015 | − | 0.0784646i | ||||
\(552\) | 1379.02 | + | 8384.10i | 0.106332 | + | 0.646469i | ||||
\(553\) | −8025.26 | + | 13900.2i | −0.617123 | + | 1.06889i | ||||
\(554\) | 925.313 | − | 1602.69i | 0.0709617 | − | 0.122909i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1492.92 | − | 2585.81i | −0.113874 | − | 0.197235i | ||||
\(557\) | 10590.8 | 0.805648 | 0.402824 | − | 0.915277i | \(-0.368029\pi\) | ||||
0.402824 | + | 0.915277i | \(0.368029\pi\) | |||||||
\(558\) | 538.079 | − | 2688.15i | 0.0408220 | − | 0.203940i | ||||
\(559\) | 590.685 | 0.0446929 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16864.8 | − | 6359.07i | −1.26922 | − | 0.478574i | ||||
\(562\) | 4181.23 | − | 7242.11i | 0.313834 | − | 0.543576i | ||||
\(563\) | −1096.03 | + | 1898.38i | −0.0820467 | + | 0.142109i | −0.904129 | − | 0.427260i | \(-0.859479\pi\) |
0.822082 | + | 0.569369i | \(0.192812\pi\) | |||||||
\(564\) | −2221.64 | + | 1821.01i | −0.165865 | + | 0.135955i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3107.32 | 0.230761 | ||||||||
\(567\) | 1280.84 | + | 9913.81i | 0.0948684 | + | 0.734287i | ||||
\(568\) | −16800.6 | −1.24109 | ||||||||
\(569\) | 8284.89 | + | 14349.8i | 0.610405 | + | 1.05725i | 0.991172 | + | 0.132582i | \(0.0423267\pi\) |
−0.380767 | + | 0.924671i | \(0.624340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3639.66 | + | 6304.08i | −0.266752 | + | 0.462027i | −0.968021 | − | 0.250869i | \(-0.919284\pi\) |
0.701269 | + | 0.712896i | \(0.252617\pi\) | |||||||
\(572\) | 1159.86 | − | 2008.93i | 0.0847833 | − | 0.146849i | ||||
\(573\) | −11417.7 | − | 4305.19i | −0.832429 | − | 0.313878i | ||||
\(574\) | 2538.82 | + | 4397.36i | 0.184614 | + | 0.319760i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2166.05 | − | 10821.2i | 0.156688 | − | 0.782784i | ||||
\(577\) | 17938.0 | 1.29422 | 0.647112 | − | 0.762395i | \(-0.275976\pi\) | ||||
0.647112 | + | 0.762395i | \(0.275976\pi\) | |||||||
\(578\) | 10615.6 | + | 18386.8i | 0.763930 | + | 1.32317i | ||||
\(579\) | −197.484 | − | 1200.65i | −0.0141747 | − | 0.0861782i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2907.29 | + | 5035.57i | −0.207598 | + | 0.359571i | ||||
\(582\) | −4101.03 | − | 24933.2i | −0.292085 | − | 1.77580i | ||||
\(583\) | −9440.42 | − | 16351.3i | −0.670639 | − | 1.16158i | ||||
\(584\) | −10161.0 | −0.719974 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15915.9 | −1.12198 | ||||||||
\(587\) | 5754.83 | + | 9967.67i | 0.404646 | + | 0.700868i | 0.994280 | − | 0.106803i | \(-0.0340613\pi\) |
−0.589634 | + | 0.807671i | \(0.700728\pi\) | |||||||
\(588\) | −943.509 | − | 355.762i | −0.0661729 | − | 0.0249513i | ||||
\(589\) | 2164.67 | − | 3749.32i | 0.151433 | − | 0.262289i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2884.79 | + | 2364.57i | −0.200785 | + | 0.164578i | ||||
\(592\) | 802.904 | + | 1390.67i | 0.0557418 | + | 0.0965476i | ||||
\(593\) | 9612.80 | 0.665684 | 0.332842 | − | 0.942983i | \(-0.391992\pi\) | ||||
0.332842 | + | 0.942983i | \(0.391992\pi\) | |||||||
\(594\) | 13565.3 | + | 468.664i | 0.937021 | + | 0.0323729i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −717.684 | − | 1243.07i | −0.0493247 | − | 0.0854328i | ||||
\(597\) | −6837.57 | + | 5604.55i | −0.468749 | + | 0.384219i | ||||
\(598\) | 7057.05 | − | 12223.2i | 0.482582 | − | 0.835857i | ||||
\(599\) | −3686.00 | + | 6384.33i | −0.251429 | + | 0.435487i | −0.963919 | − | 0.266194i | \(-0.914234\pi\) |
0.712491 | + | 0.701681i | \(0.247567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12095.3 | + | 20949.7i | 0.820927 | + | 1.42189i | 0.904993 | + | 0.425427i | \(0.139876\pi\) |
−0.0840654 | + | 0.996460i | \(0.526790\pi\) | |||||||
\(602\) | 423.001 | 0.0286383 | ||||||||
\(603\) | −17494.4 | − | 15379.6i | −1.18147 | − | 1.03865i | ||||
\(604\) | −1460.20 | −0.0983684 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −548.956 | − | 3337.50i | −0.0367984 | − | 0.223724i | ||||
\(607\) | −658.866 | + | 1141.19i | −0.0440569 | + | 0.0763088i | −0.887213 | − | 0.461360i | \(-0.847362\pi\) |
0.843156 | + | 0.537669i | \(0.180695\pi\) | |||||||
\(608\) | −3642.62 | + | 6309.20i | −0.242973 | + | 0.420842i | ||||
\(609\) | −104.485 | − | 635.242i | −0.00695230 | − | 0.0422681i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25713.9 | −1.70257 | ||||||||
\(612\) | −2769.13 | − | 2434.38i | −0.182901 | − | 0.160791i | ||||
\(613\) | 4137.52 | 0.272615 | 0.136307 | − | 0.990667i | \(-0.456477\pi\) | ||||
0.136307 | + | 0.990667i | \(0.456477\pi\) | |||||||
\(614\) | 7471.56 | + | 12941.1i | 0.491087 | + | 0.850588i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4475.93 | + | 7752.54i | −0.292760 | + | 0.507076i | ||||
\(617\) | −3895.81 | + | 6747.74i | −0.254197 | + | 0.440281i | −0.964677 | − | 0.263436i | \(-0.915144\pi\) |
0.710480 | + | 0.703717i | \(0.248478\pi\) | |||||||
\(618\) | −20442.0 | + | 16755.7i | −1.33058 | + | 1.09064i | ||||
\(619\) | −10978.2 | − | 19014.8i | −0.712844 | − | 1.23468i | −0.963785 | − | 0.266680i | \(-0.914073\pi\) |
0.250941 | − | 0.968002i | \(-0.419260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11170.5 | + | 385.927i | 0.721831 | + | 0.0249384i | ||||
\(622\) | 2521.18 | 0.162524 | ||||||||
\(623\) | −7071.17 | − | 12247.6i | −0.454736 | − | 0.787625i | ||||
\(624\) | −16957.5 | + | 13899.6i | −1.08789 | + | 0.891712i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14048.6 | + | 24332.9i | −0.896957 | + | 1.55357i | ||||
\(627\) | 20056.7 | + | 7562.63i | 1.27749 | + | 0.481694i | ||||
\(628\) | −2176.06 | − | 3769.05i | −0.138271 | − | 0.239493i | ||||
\(629\) | −2417.15 | −0.153224 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11152.7 | −0.703618 | −0.351809 | − | 0.936072i | \(-0.614433\pi\) | ||||
−0.351809 | + | 0.936072i | \(0.614433\pi\) | |||||||
\(632\) | −12012.6 | − | 20806.4i | −0.756068 | − | 1.30955i | ||||
\(633\) | 4164.95 | + | 25321.8i | 0.261520 | + | 1.58997i | ||||
\(634\) | 13837.5 | − | 23967.2i | 0.866810 | − | 1.50136i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −626.861 | − | 3811.15i | −0.0390828 | − | 0.237613i | ||||
\(637\) | −4513.11 | − | 7816.94i | −0.280716 | − | 0.486214i | ||||
\(638\) | −874.155 | −0.0542447 | ||||||||
\(639\) | −4337.77 | + | 21670.7i | −0.268544 | + | 1.34160i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2404.72 | − | 4165.10i | −0.148176 | − | 0.256648i | 0.782377 | − | 0.622805i | \(-0.214007\pi\) |
−0.930553 | + | 0.366156i | \(0.880674\pi\) | |||||||
\(642\) | −8883.71 | − | 3349.71i | −0.546125 | − | 0.205923i | ||||
\(643\) | −1276.51 | + | 2210.98i | −0.0782904 | + | 0.135603i | −0.902512 | − | 0.430664i | \(-0.858279\pi\) |
0.824222 | + | 0.566267i | \(0.191613\pi\) | |||||||
\(644\) | 683.964 | − | 1184.66i | 0.0418509 | − | 0.0724879i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21511.0 | − | 37258.2i | −1.31013 | − | 2.26920i | ||||
\(647\) | −8446.00 | −0.513210 | −0.256605 | − | 0.966516i | \(-0.582604\pi\) | ||||
−0.256605 | + | 0.966516i | \(0.582604\pi\) | |||||||
\(648\) | −13810.0 | − | 5759.36i | −0.837201 | − | 0.349150i | ||||
\(649\) | 14073.2 | 0.851191 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1839.45 | − | 1507.74i | 0.110743 | − | 0.0907727i | ||||
\(652\) | −1392.01 | + | 2411.02i | −0.0836122 | + | 0.144821i | ||||
\(653\) | 4047.44 | − | 7010.37i | 0.242555 | − | 0.420118i | −0.718886 | − | 0.695128i | \(-0.755348\pi\) |
0.961441 | + | 0.275010i | \(0.0886812\pi\) | |||||||
\(654\) | 11410.7 | + | 4302.55i | 0.682254 | + | 0.257252i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8819.97 | −0.524942 | ||||||||
\(657\) | −2623.47 | + | 13106.4i | −0.155786 | + | 0.778280i | ||||
\(658\) | −18414.2 | −1.09097 | ||||||||
\(659\) | −1087.67 | − | 1883.89i | −0.0642936 | − | 0.111360i | 0.832087 | − | 0.554645i | \(-0.187146\pi\) |
−0.896380 | + | 0.443286i | \(0.853813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4438.47 | − | 7687.66i | 0.261175 | − | 0.452368i | −0.705379 | − | 0.708830i | \(-0.749223\pi\) |
0.966554 | + | 0.256462i | \(0.0825567\pi\) | |||||||
\(662\) | 9069.64 | − | 15709.1i | 0.532480 | − | 0.922282i | ||||
\(663\) | −5356.62 | − | 32566.8i | −0.313776 | − | 1.90768i | ||||
\(664\) | −4351.77 | − | 7537.48i | −0.254339 | − | 0.440529i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1724.41 | − | 583.037i | 0.100329 | − | 0.0339223i | ||||
\(667\) | −719.834 | −0.0417872 | ||||||||
\(668\) | −994.226 | − | 1722.05i | −0.0575865 | − | 0.0997427i | ||||
\(669\) | 14844.4 | + | 5597.27i | 0.857874 | + | 0.323472i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2299.25 | + | 3982.42i | −0.132283 | + | 0.229120i | ||||
\(672\) | −3095.35 | + | 2537.16i | −0.177687 | + | 0.145645i | ||||
\(673\) | −4583.96 | − | 7939.65i | −0.262554 | − | 0.454757i | 0.704366 | − | 0.709837i | \(-0.251231\pi\) |
−0.966920 | + | 0.255080i | \(0.917898\pi\) | |||||||
\(674\) | 1815.47 | 0.103753 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1496.70 | 0.0851557 | ||||||||
\(677\) | −9438.93 | − | 16348.7i | −0.535846 | − | 0.928112i | −0.999122 | − | 0.0418983i | \(-0.986659\pi\) |
0.463276 | − | 0.886214i | \(-0.346674\pi\) | |||||||
\(678\) | 14261.2 | − | 11689.4i | 0.807812 | − | 0.662139i | ||||
\(679\) | 10961.0 | − | 18984.9i | 0.619503 | − | 1.07301i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4083.85 | + | 1539.87i | 0.229800 | + | 0.0866488i | ||||
\(682\) | −1614.77 | − | 2796.86i | −0.0906638 | − | 0.157034i | ||||
\(683\) | 27207.5 | 1.52426 | 0.762128 | − | 0.647426i | \(-0.224155\pi\) | ||||
0.762128 | + | 0.647426i | \(0.224155\pi\) | |||||||
\(684\) | 3293.23 | + | 2895.13i | 0.184094 | + | 0.161839i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10385.0 | − | 17987.4i | −0.577991 | − | 1.00111i | ||||
\(687\) | −1181.94 | − | 7185.89i | −0.0656388 | − | 0.399067i | ||||
\(688\) | −367.381 | + | 636.323i | −0.0203580 | + | 0.0352610i | ||||
\(689\) | 17286.9 | − | 29941.7i | 0.955845 | − | 1.65557i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8703.62 | + | 15075.1i | 0.479162 | + | 0.829934i | 0.999714 | − | 0.0238963i | \(-0.00760715\pi\) |
−0.520552 | + | 0.853830i | \(0.674274\pi\) | |||||||
\(692\) | −1888.04 | −0.103718 | ||||||||
\(693\) | 8844.17 | + | 7775.03i | 0.484794 | + | 0.426189i | ||||
\(694\) | −13876.7 | −0.759011 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 901.668 | + | 339.985i | 0.0491058 | + | 0.0185159i | ||||
\(697\) | 6638.15 | − | 11497.6i | 0.360743 | − | 0.624825i | ||||
\(698\) | 1026.99 | − | 1778.80i | 0.0556909 | − | 0.0964595i | ||||
\(699\) | −11481.3 | + | 9410.87i | −0.621263 | + | 0.509230i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18543.0 | 0.999086 | 0.499543 | − | 0.866289i | \(-0.333501\pi\) | ||||
0.499543 | + | 0.866289i | \(0.333501\pi\) | |||||||
\(702\) | 11676.8 | + | 21941.3i | 0.627798 | + | 1.17966i | ||||
\(703\) | 2874.63 | 0.154223 | ||||||||
\(704\) | −6500.29 | − | 11258.8i | −0.347996 | − | 0.602746i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5112.91 | − | 8855.81i | 0.272559 | − | 0.472086i | ||||
\(707\) | 1467.21 | − | 2541.28i | 0.0780482 | − | 0.135184i | ||||
\(708\) | 2693.76 | + | 1015.72i | 0.142991 | + | 0.0539165i | ||||
\(709\) | −13116.9 | − | 22719.1i | −0.694803 | − | 1.20343i | −0.970247 | − | 0.242117i | \(-0.922158\pi\) |
0.275444 | − | 0.961317i | \(-0.411175\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29939.2 | + | 10122.7i | −1.57920 | + | 0.533941i | ||||
\(712\) | 21168.9 | 1.11424 | ||||||||
\(713\) | −1329.70 | − | 2303.11i | −0.0698425 | − | 0.120971i | ||||
\(714\) | −3835.98 | − | 23321.7i | −0.201061 | − | 1.22240i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −984.633 | + | 1705.43i | −0.0513931 | + | 0.0890155i | ||||
\(717\) | 1441.96 | + | 8766.76i | 0.0751062 | + | 0.456626i | ||||
\(718\) | 11713.2 | + | 20287.8i | 0.608817 | + | 1.05450i | ||||
\(719\) | −3043.06 | −0.157840 | −0.0789199 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789199 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22931.2 | −1.18447 | ||||||||
\(722\) | 15150.7 | + | 26241.8i | 0.780958 | + | 1.35266i | ||||
\(723\) | −21064.4 | − | 7942.60i | −1.08353 | − | 0.408559i | ||||
\(724\) | −1242.43 | + | 2151.95i | −0.0637769 | + | 0.110465i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3903.37 | + | 3199.47i | −0.199542 | + | 0.163559i | ||||
\(727\) | 10971.2 | + | 19002.7i | 0.559698 | + | 0.969426i | 0.997521 | + | 0.0703647i | \(0.0224163\pi\) |
−0.437823 | + | 0.899061i | \(0.644250\pi\) | |||||||
\(728\) | −16392.2 | −0.834528 | ||||||||
\(729\) | −10994.5 | + | 16326.1i | −0.558577 | + | 0.829453i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −553.002 | − | 957.827i | −0.0279802 | − | 0.0484631i | ||||
\(732\) | −727.525 | + | 596.330i | −0.0367351 | + | 0.0301107i | ||||
\(733\) | −13288.4 | + | 23016.2i | −0.669604 | + | 1.15979i | 0.308411 | + | 0.951253i | \(0.400203\pi\) |
−0.978015 | + | 0.208535i | \(0.933131\pi\) | |||||||
\(734\) | −8987.58 | + | 15566.9i | −0.451959 | + | 0.782815i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2237.56 | + | 3875.57i | 0.112062 | + | 0.194097i | ||||
\(737\) | −27440.4 | −1.37148 | ||||||||
\(738\) | −1962.37 | + | 9803.63i | −0.0978803 | + | 0.488993i | ||||
\(739\) | 28787.7 | 1.43298 | 0.716489 | − | 0.697598i | \(-0.245748\pi\) | ||||
0.716489 | + | 0.697598i | \(0.245748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6370.45 | + | 38730.6i | 0.315822 | + | 1.92011i | ||||
\(742\) | 12379.5 | − | 21441.8i | 0.612485 | − | 1.06086i | ||||
\(743\) | −2251.51 | + | 3899.73i | −0.111171 | + | 0.192553i | −0.916243 | − | 0.400624i | \(-0.868793\pi\) |
0.805072 | + | 0.593177i | \(0.202127\pi\) | |||||||
\(744\) | 577.808 | + | 3512.92i | 0.0284724 | + | 0.173105i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −25624.8 | −1.25763 | ||||||||
\(747\) | −10846.0 | + | 3667.13i | −0.531238 | + | 0.179616i | ||||
\(748\) | −4343.45 | −0.212316 | ||||||||
\(749\) | −4118.46 | − | 7133.38i | −0.200915 | − | 0.347995i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2852.83 | + | 4941.24i | −0.138617 | + | 0.240091i | −0.926973 | − | 0.375128i | \(-0.877599\pi\) |
0.788357 | + | 0.615219i | \(0.210932\pi\) | |||||||
\(752\) | 15993.0 | − | 27700.6i | 0.775536 | − | 1.34327i | ||||
\(753\) | 6931.13 | − | 5681.24i | 0.335438 | − | 0.274948i | ||||
\(754\) | −800.356 | − | 1386.26i | −0.0386568 | − | 0.0669556i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1131.71 | + | 2126.53i | 0.0544444 | + | 0.102303i | ||||
\(757\) | −17397.6 | −0.835305 | −0.417652 | − | 0.908607i | \(-0.637147\pi\) | ||||
−0.417652 | + | 0.908607i | \(0.637147\pi\) | |||||||
\(758\) | −5338.62 | − | 9246.77i | −0.255815 | − | 0.443084i | ||||
\(759\) | 10183.3 | − | 8346.94i | 0.486996 | − | 0.399176i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17757.2 | − | 30756.3i | 0.845857 | − | 1.46507i | −0.0390179 | − | 0.999239i | \(-0.512423\pi\) |
0.884875 | − | 0.465829i | \(-0.154244\pi\) | |||||||
\(762\) | 24107.4 | + | 9090.00i | 1.14609 | + | 0.432147i | ||||
\(763\) | 5289.97 | + | 9162.50i | 0.250996 | + | 0.434737i | ||||
\(764\) | −2940.58 | −0.139249 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17435.3 | 0.822408 | ||||||||
\(767\) | 12885.1 | + | 22317.7i | 0.606591 | + | 1.05065i | ||||
\(768\) | −1584.37 | − | 9632.57i | −0.0744416 | − | 0.452585i | ||||
\(769\) | −15631.8 | + | 27075.1i | −0.733027 | + | 1.26964i | 0.222556 | + | 0.974920i | \(0.428560\pi\) |
−0.955583 | + | 0.294721i | \(0.904773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4936.26 | − | 30011.2i | −0.230577 | − | 1.40185i | ||||
\(772\) | −146.612 | − | 253.940i | −0.00683508 | − | 0.0118387i | ||||
\(773\) | 6676.47 | 0.310654 | 0.155327 | − | 0.987863i | \(-0.450357\pi\) | ||||
0.155327 | + | 0.987863i | \(0.450357\pi\) | |||||||
\(774\) | 625.551 | + | 549.930i | 0.0290503 | + | 0.0255385i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16406.9 | + | 28417.5i | 0.758985 | + | 1.31460i | ||||
\(777\) | 1477.68 | + | 557.179i | 0.0682260 | + | 0.0257254i | ||||
\(778\) | 21850.7 | − | 37846.5i | 1.00692 | − | 1.74404i | ||||
\(779\) | −7894.53 | + | 13673.7i | −0.363095 | + | 0.628898i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13017.6 | + | 22547.1i | 0.596422 | + | 1.03303i | ||||
\(782\) | −26427.3 | −1.20849 | ||||||||
\(783\) | 671.341 | − | 1075.26i | 0.0306408 | − | 0.0490761i | ||||
\(784\) | 11227.9 | 0.511473 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3163.81 | − | 2593.28i | 0.143574 | − | 0.117683i | ||||
\(787\) | 4716.91 | − | 8169.93i | 0.213646 | − | 0.370047i | −0.739207 | − | 0.673479i | \(-0.764799\pi\) |
0.952853 | + | 0.303432i | \(0.0981326\pi\) | |||||||
\(788\) | −449.439 | + | 778.451i | −0.0203180 | + | 0.0351919i | ||||
\(789\) | −1907.66 | − | 719.306i | −0.0860766 | − | 0.0324562i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15997.7 | 0.719107 | ||||||||
\(792\) | −16698.0 | + | 5645.75i | −0.749164 | + | 0.253299i | ||||
\(793\) | −8420.57 | −0.377078 | ||||||||
\(794\) | 13709.8 | + | 23746.0i | 0.612773 | + | 1.06135i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1065.27 | + | 1845.10i | −0.0474340 | + | 0.0821580i | ||||
\(797\) | −11738.1 | + | 20331.1i | −0.521689 | + | 0.903592i | 0.477992 | + | 0.878364i | \(0.341365\pi\) |
−0.999682 | + | 0.0252283i | \(0.991969\pi\) | |||||||
\(798\) | 4562.00 | + | 27735.7i | 0.202372 | + | 1.23037i | ||||
\(799\) | 24073.4 | + | 41696.4i | 1.06590 | + | 1.84620i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5465.61 | − | 27305.3i | 0.241096 | − | 1.20447i | ||||
\(802\) | −31972.0 | −1.40769 | ||||||||
\(803\) | 7873.02 | + | 13636.5i | 0.345993 | + | 0.599278i | ||||
\(804\) | −5252.37 | − | 1980.47i | −0.230394 | − | 0.0868729i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2956.89 | − | 5121.48i | 0.129221 | − | 0.223817i | ||||
\(807\) | 18527.4 | − | 15186.3i | 0.808173 | − | 0.662435i | ||||
\(808\) | 2196.19 | + | 3803.91i | 0.0956208 | + | 0.165620i | ||||
\(809\) | −33269.8 | −1.44586 | −0.722932 | − | 0.690919i | \(-0.757206\pi\) | ||||
−0.722932 | + | 0.690919i | \(0.757206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27892.8 | 1.20771 | 0.603853 | − | 0.797096i | \(-0.293631\pi\) | ||||
0.603853 | + | 0.797096i | \(0.293631\pi\) | |||||||
\(812\) | −77.5699 | − | 134.355i | −0.00335243 | − | 0.00580657i | ||||
\(813\) | 4644.44 | − | 3806.91i | 0.200354 | − | 0.164224i | ||||
\(814\) | 1072.19 | − | 1857.08i | 0.0461672 | − | 0.0799640i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 38414.6 | + | 14484.7i | 1.64801 | + | 0.621404i | ||||
\(817\) | 657.666 | + | 1139.11i | 0.0281626 | + | 0.0487790i | ||||
\(818\) | −10093.1 | −0.431415 | ||||||||
\(819\) | −4232.32 | + | 21143.9i | −0.180573 | + | 0.902111i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1848.66 | + | 3201.98i | 0.0785856 | + | 0.136114i | 0.902640 | − | 0.430397i | \(-0.141626\pi\) |
−0.824054 | + | 0.566511i | \(0.808293\pi\) | |||||||
\(822\) | −2700.58 | − | 16418.8i | −0.114591 | − | 0.696680i | ||||
\(823\) | 3572.25 | − | 6187.32i | 0.151301 | − | 0.262061i | −0.780405 | − | 0.625275i | \(-0.784987\pi\) |
0.931706 | + | 0.363213i | \(0.118320\pi\) | |||||||
\(824\) | 17162.3 | − | 29725.9i | 0.725578 | − | 1.25674i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9227.29 | + | 15982.1i | 0.388691 | + | 0.673232i | ||||
\(827\) | −19866.9 | −0.835357 | −0.417679 | − | 0.908595i | \(-0.637156\pi\) | ||||
−0.417679 | + | 0.908595i | \(0.637156\pi\) | |||||||
\(828\) | 2551.61 | − | 862.723i | 0.107095 | − | 0.0362098i | ||||
\(829\) | −36736.5 | −1.53910 | −0.769548 | − | 0.638589i | \(-0.779518\pi\) | ||||
−0.769548 | + | 0.638589i | \(0.779518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2958.09 | + | 1115.39i | 0.123484 | + | 0.0465611i | ||||
\(832\) | 11903.0 | − | 20616.7i | 0.495990 | − | 0.859079i | ||||
\(833\) | −8450.38 | + | 14636.5i | −0.351487 | + | 0.608793i | ||||
\(834\) | 29147.5 | − | 23891.3i | 1.21018 | − | 0.991952i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5165.52 | 0.213700 | ||||||||
\(837\) | 4680.42 | + | 161.703i | 0.193284 | + | 0.00667773i | ||||
\(838\) | 1478.71 | 0.0609560 | ||||||||
\(839\) | −15006.1 | − | 25991.4i | −0.617485 | − | 1.06951i | −0.989943 | − | 0.141466i | \(-0.954818\pi\) |
0.372458 | − | 0.928049i | \(-0.378515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12153.7 | − | 21050.8i | 0.498326 | − | 0.863127i | ||||
\(842\) | 7683.32 | − | 13307.9i | 0.314471 | − | 0.544680i | ||||
\(843\) | 13366.8 | + | 5040.12i | 0.546117 | + | 0.205920i | ||||
\(844\) | 3092.07 | + | 5355.62i | 0.126106 | + | 0.218422i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27231.7 | − | 23939.7i | −1.10667 | − | 0.972890i | ||||
\(847\) | −4378.68 | −0.177631 | ||||||||
\(848\) | 21503.4 | + | 37245.0i | 0.870789 | + | 1.50825i | ||||
\(849\) | 861.519 | + | 5237.80i | 0.0348260 | + | 0.211733i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 882.905 | − | 1529.24i | 0.0355648 | − | 0.0616000i | ||||
\(852\) | 864.391 | + | 5255.27i | 0.0347577 | + | 0.211318i | ||||
\(853\) | −2690.51 | − | 4660.10i | −0.107997 | − | 0.187056i | 0.806962 | − | 0.590604i | \(-0.201110\pi\) |
−0.914959 | + | 0.403548i | \(0.867777\pi\) | |||||||
\(854\) | −6030.13 | −0.241624 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12329.4 | 0.492302 | ||||||||
\(857\) | 7319.88 | + | 12678.4i | 0.291765 | + | 0.505352i | 0.974227 | − | 0.225569i | \(-0.0724242\pi\) |
−0.682462 | + | 0.730921i | \(0.739091\pi\) | |||||||
\(858\) | 27397.0 | + | 10330.4i | 1.09011 | + | 0.411041i | ||||
\(859\) | −14770.0 | + | 25582.4i | −0.586667 | + | 1.01614i | 0.407999 | + | 0.912983i | \(0.366227\pi\) |
−0.994665 | + | 0.103154i | \(0.967107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6708.44 | + | 5498.71i | −0.265532 | + | 0.217649i | ||||
\(862\) | 10561.3 | + | 18292.7i | 0.417307 | + | 0.722797i | ||||
\(863\) | −3387.63 | −0.133622 | −0.0668112 | − | 0.997766i | \(-0.521283\pi\) | ||||
−0.0668112 | + | 0.997766i | \(0.521283\pi\) | |||||||
\(864\) | −7876.00 | − | 272.106i | −0.310124 | − | 0.0107144i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20894.1 | + | 36189.7i | 0.819875 | + | 1.42007i | ||||
\(867\) | −28050.2 | + | 22991.9i | −1.09877 | + | 0.900628i | ||||
\(868\) | 286.580 | − | 496.370i | 0.0112064 | − | 0.0194100i | ||||
\(869\) | −18615.4 | + | 32242.8i | −0.726678 | + | 1.25864i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25123.8 | − | 43515.7i | −0.977368 | − | 1.69285i | ||||
\(872\) | −15836.5 | −0.615015 | ||||||||
\(873\) | 40891.2 | − | 13825.7i | 1.58529 | − | 0.536000i | ||||
\(874\) | 31429.2 | 1.21637 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 522.783 | + | 3178.38i | 0.0201635 | + | 0.122588i | ||||
\(877\) | −122.052 | + | 211.400i | −0.00469944 | + | 0.00813967i | −0.868366 | − | 0.495925i | \(-0.834829\pi\) |
0.863666 | + | 0.504064i | \(0.168163\pi\) | |||||||
\(878\) | 12899.8 | − | 22343.1i | 0.495838 | − | 0.858817i | ||||
\(879\) | −4412.75 | − | 26828.4i | −0.169327 | − | 1.02946i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13910.2 | 0.531948 | 0.265974 | − | 0.963980i | \(-0.414307\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414307\pi\) | |||||||
\(882\) | 2498.10 | − | 12480.1i | 0.0953689 | − | 0.476446i | ||||
\(883\) | 8805.87 | 0.335607 | 0.167803 | − | 0.985820i | \(-0.446333\pi\) | ||||
0.167803 | + | 0.985820i | \(0.446333\pi\) | |||||||
\(884\) | −3976.76 | − | 6887.95i | −0.151304 | − | 0.262067i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 848.943 | − | 1470.41i | 0.0321905 | − | 0.0557556i | ||||
\(887\) | 6640.41 | − | 11501.5i | 0.251368 | − | 0.435381i | −0.712535 | − | 0.701637i | \(-0.752453\pi\) |
0.963903 | + | 0.266255i | \(0.0857864\pi\) | |||||||
\(888\) | −1828.21 | + | 1498.53i | −0.0690885 | + | 0.0566298i | ||||
\(889\) | 11176.1 | + | 19357.6i | 0.421637 | + | 0.730296i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2971.04 | + | 22996.0i | 0.111710 | + | 0.864642i | ||||
\(892\) | 3823.11 | 0.143506 | ||||||||
\(893\) | −28629.7 | − | 49588.2i | −1.07285 | − | 1.85824i | ||||
\(894\) | 14011.9 | − | 11485.2i | 0.524194 | − | 0.429666i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11605.0 | − | 20100.4i | 0.432695 | − | 0.749449i | ||||
\(897\) | 22560.4 | + | 8506.67i | 0.839765 | + | 0.316644i | ||||
\(898\) | 22470.9 | + | 38920.7i | 0.835036 | + | 1.44633i | ||||
\(899\) | −301.609 | −0.0111893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64736.1 | −2.39364 | ||||||||
\(902\) | 5889.04 | + | 10200.1i | 0.217387 | + | 0.376526i | ||||
\(903\) | 117.279 | + | 713.025i | 0.00432204 | + | 0.0262768i | ||||
\(904\) | −11973.1 | + | 20738.0i | −0.440507 | + | 0.762981i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2991.33 | − | 18186.5i | −0.109691 | − | 0.666894i | ||||
\(907\) | −542.122 | − | 938.982i | −0.0198466 | − | 0.0343753i | 0.855932 | − | 0.517089i | \(-0.172984\pi\) |
−0.875778 | + | 0.482714i | \(0.839651\pi\) | |||||||
\(908\) | 1051.78 | 0.0384411 | ||||||||
\(909\) | 5473.61 | − | 1850.68i | 0.199723 | − | 0.0675281i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25094.4 | − | 43464.7i | −0.912638 | − | 1.58073i | −0.810324 | − | 0.585983i | \(-0.800709\pi\) |
−0.102314 | − | 0.994752i | \(-0.532625\pi\) | |||||||
\(912\) | −45685.2 | − | 17226.2i | −1.65876 | − | 0.625455i | ||||
\(913\) | −6743.74 | + | 11680.5i | −0.244452 | + | 0.423404i | ||||
\(914\) | 21608.4 | − | 37426.9i | 0.781995 | − | 1.35445i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −877.475 | − | 1519.83i | −0.0316513 | − | 0.0548216i | ||||
\(917\) | 3549.06 | 0.127808 | ||||||||
\(918\) | 24647.0 | − | 39476.1i | 0.886136 | − | 1.41929i | ||||
\(919\) | 30376.1 | 1.09033 | 0.545166 | − | 0.838328i | \(-0.316467\pi\) | ||||
0.545166 | + | 0.838328i | \(0.316467\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19742.5 | + | 16182.3i | −0.706336 | + | 0.578962i | ||||
\(922\) | −11714.5 | + | 20290.2i | −0.418435 | + | 0.724751i | ||||
\(923\) | −23837.2 | + | 41287.2i | −0.850066 | + | 1.47236i | ||||
\(924\) | 2655.30 | + | 1001.21i | 0.0945377 | + | 0.0356466i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24057.3 | 0.853750 | ||||||||
\(927\) | −33911.6 | − | 29812.2i | −1.20151 | − | 1.05627i | ||||
\(928\) | 507.534 | 0.0179533 | ||||||||
\(929\) | 23098.8 | + | 40008.3i | 0.815766 | + | 1.41295i | 0.908776 | + | 0.417283i | \(0.137018\pi\) |
−0.0930102 | + | 0.995665i | \(0.529649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10049.8 | − | 17406.7i | 0.353778 | − | 0.612762i | ||||
\(932\) | −1788.74 | + | 3098.20i | −0.0628672 | + | 0.108889i | ||||
\(933\) | 699.007 | + | 4249.78i | 0.0245278 | + | 0.149123i | ||||
\(934\) | −17702.6 | − | 30661.7i | −0.620177 | − | 1.07418i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −24241.5 | − | 21311.0i | −0.846536 | − | 0.744201i | ||||
\(937\) | −37004.7 | −1.29017 | −0.645085 | − | 0.764111i | \(-0.723178\pi\) | ||||
−0.645085 | + | 0.764111i | \(0.723178\pi\) | |||||||
\(938\) | −17991.6 | − | 31162.4i | −0.626277 | − | 1.08474i | ||||
\(939\) | −44911.3 | − | 16934.4i | −1.56084 | − | 0.588533i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21907.2 | + | 37944.4i | −0.758932 | + | 1.31451i | 0.184464 | + | 0.982839i | \(0.440945\pi\) |
−0.943396 | + | 0.331669i | \(0.892388\pi\) | |||||||
\(942\) | 42485.1 | − | 34823.7i | 1.46947 | − | 1.20448i | ||||
\(943\) | 4849.40 | + | 8399.41i | 0.167464 | + | 0.290055i | ||||
\(944\) | −32056.0 | −1.10523 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 981.191 | 0.0337223 | ||||||||
\(947\) | 2304.86 | + | 3992.14i | 0.0790898 | + | 0.136988i | 0.902857 | − | 0.429940i | \(-0.141465\pi\) |
−0.823768 | + | 0.566928i | \(0.808132\pi\) | |||||||
\(948\) | −5890.24 | + | 4828.05i | −0.201800 | + | 0.165409i | ||||
\(949\) | −14416.7 | + | 24970.5i | −0.493136 | + | 0.854136i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44236.5 | + | 16679.9i | 1.50838 | + | 0.568752i | ||||
\(952\) | 15346.5 | + | 26580.8i | 0.522460 | + | 0.904927i | ||||
\(953\) | −4281.80 | −0.145542 | −0.0727708 | − | 0.997349i | \(-0.523184\pi\) | ||||
−0.0727708 | + | 0.997349i | \(0.523184\pi\) | |||||||
\(954\) | 46183.1 | − | 15614.9i | 1.56733 | − | 0.529928i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1070.52 | + | 1854.19i | 0.0362165 | + | 0.0627288i | ||||
\(957\) | −242.363 | − | 1473.50i | −0.00818651 | − | 0.0497718i | ||||
\(958\) | −28434.0 | + | 49249.1i | −0.958936 | + | 1.66093i | ||||
\(959\) | 7217.91 | − | 12501.8i | 0.243043 | − | 0.420963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14338.4 | + | 24834.8i | 0.481298 | + | 0.833633i | ||||
\(962\) | 3926.68 | 0.131602 | ||||||||
\(963\) | 3183.34 | − | 15903.4i | 0.106523 | − | 0.532170i | ||||
\(964\) | −5425.05 | −0.181254 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16155.9 | + | 6091.79i | 0.538104 | + | 0.202899i | ||||
\(967\) | −18114.9 | + | 31375.9i | −0.602416 | + | 1.04341i | 0.390038 | + | 0.920799i | \(0.372462\pi\) |
−0.992454 | + | 0.122616i | \(0.960872\pi\) | |||||||
\(968\) | 3277.10 | − | 5676.11i | 0.108812 | − | 0.188468i | ||||
\(969\) | 56839.7 | − | 46589.7i | 1.88437 | − | 1.54456i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 844.928 | 0.0279249 | 0.0139624 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139624 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(972\) | −1091.02 | + | 4616.10i | −0.0360025 | + | 0.152327i | ||||
\(973\) | 32696.7 | 1.07730 | ||||||||
\(974\) | 3421.26 | + | 5925.80i | 0.112551 | + | 0.194943i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5237.24 | − | 9071.16i | 0.171762 | − | 0.297501i | ||||
\(977\) | 22922.5 | − | 39702.9i | 0.750619 | − | 1.30011i | −0.196904 | − | 0.980423i | \(-0.563089\pi\) |
0.947523 | − | 0.319687i | \(-0.103578\pi\) | |||||||
\(978\) | −32880.6 | − | 12398.0i | −1.07506 | − | 0.405363i | ||||
\(979\) | −16402.2 | − | 28409.5i | −0.535463 | − | 0.927449i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4088.85 | + | 20427.2i | −0.133075 | + | 0.664821i | ||||
\(982\) | −6048.05 | −0.196539 | ||||||||
\(983\) | −20101.0 | − | 34815.9i | −0.652210 | − | 1.12966i | −0.982586 | − | 0.185811i | \(-0.940509\pi\) |
0.330376 | − | 0.943849i | \(-0.392824\pi\) | |||||||
\(984\) | −2107.26 | − | 12811.6i | −0.0682692 | − | 0.415059i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1498.59 | + | 2595.64i | −0.0484025 | + | 0.0838356i | ||||
\(987\) | −5105.42 | − | 31039.6i | −0.164648 | − | 1.00101i | ||||
\(988\) | 4729.43 | + | 8191.61i | 0.152291 | + | 0.263775i | ||||
\(989\) | 807.974 | 0.0259778 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1797.91 | 0.0576313 | 0.0288157 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288157 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(992\) | 937.534 | + | 1623.86i | 0.0300068 | + | 0.0519733i | ||||
\(993\) | 28994.3 | + | 10932.7i | 0.926594 | + | 0.349384i | ||||
\(994\) | −17070.3 | + | 29566.6i | −0.544704 | + | 0.943455i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2133.84 | + | 1749.04i | −0.0678849 | + | 0.0556432i | ||||
\(997\) | 4566.04 | + | 7908.61i | 0.145043 | + | 0.251222i | 0.929389 | − | 0.369102i | \(-0.120335\pi\) |
−0.784346 | + | 0.620324i | \(0.787001\pi\) | |||||||
\(998\) | −7342.47 | −0.232888 | ||||||||
\(999\) | 1460.89 | + | 2745.07i | 0.0462667 | + | 0.0869370i |
(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 | 225.4.e.d.76.6 | 14 | ||
5.2 | odd | 4 | 225.4.k.d.49.4 | 28 | |||
5.3 | odd | 4 | 225.4.k.d.49.11 | 28 | |||
5.4 | even | 2 | 45.4.e.c.31.2 | yes | 14 | ||
9.4 | even | 3 | 2025.4.a.bb.1.2 | 7 | |||
9.5 | odd | 6 | 2025.4.a.ba.1.6 | 7 | |||
9.7 | even | 3 | inner | 225.4.e.d.151.6 | 14 | ||
15.14 | odd | 2 | 135.4.e.c.91.6 | 14 | |||
45.4 | even | 6 | 405.4.a.m.1.6 | 7 | |||
45.7 | odd | 12 | 225.4.k.d.124.11 | 28 | |||
45.14 | odd | 6 | 405.4.a.n.1.2 | 7 | |||
45.29 | odd | 6 | 135.4.e.c.46.6 | 14 | |||
45.34 | even | 6 | 45.4.e.c.16.2 | ✓ | 14 | ||
45.43 | odd | 12 | 225.4.k.d.124.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.2 | ✓ | 14 | 45.34 | even | 6 | ||
45.4.e.c.31.2 | yes | 14 | 5.4 | even | 2 | ||
135.4.e.c.46.6 | 14 | 45.29 | odd | 6 | |||
135.4.e.c.91.6 | 14 | 15.14 | odd | 2 | |||
225.4.e.d.76.6 | 14 | 1.1 | even | 1 | trivial | ||
225.4.e.d.151.6 | 14 | 9.7 | even | 3 | inner | ||
225.4.k.d.49.4 | 28 | 5.2 | odd | 4 | |||
225.4.k.d.49.11 | 28 | 5.3 | odd | 4 | |||
225.4.k.d.124.4 | 28 | 45.43 | odd | 12 | |||
225.4.k.d.124.11 | 28 | 45.7 | odd | 12 | |||
405.4.a.m.1.6 | 7 | 45.4 | even | 6 | |||
405.4.a.n.1.2 | 7 | 45.14 | odd | 6 | |||
2025.4.a.ba.1.6 | 7 | 9.5 | odd | 6 | |||
2025.4.a.bb.1.2 | 7 | 9.4 | even | 3 |