Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(46,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.e (of order \(3\), degree \(2\), not 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: | \(7.96525785077\) |
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: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{13} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.6 | ||
Root | \(-1.52087 - 2.63422i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.46 |
Dual form | 135.4.e.c.91.6 |
$q$-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 \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(82\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | −0.461318 | − | 0.887235i | \(-0.652623\pi\) |
0.999027 | − | 0.0441043i | \(-0.0140434\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.626094 | − | 1.08443i | −0.0782617 | − | 0.135553i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.85611 | − | 11.8751i | 0.370195 | − | 0.641197i | −0.619400 | − | 0.785075i | \(-0.712624\pi\) |
0.989595 | + | 0.143879i | \(0.0459575\pi\) | |||||||
\(8\) | 20.5251 | 0.907090 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −15.2087 | −0.480941 | ||||||||
\(11\) | 15.9034 | − | 27.5455i | 0.435914 | − | 0.755026i | −0.561455 | − | 0.827507i | \(-0.689758\pi\) |
0.997370 | + | 0.0724812i | \(0.0230917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −29.1216 | − | 50.4401i | −0.621298 | − | 1.07612i | −0.989244 | − | 0.146272i | \(-0.953272\pi\) |
0.367946 | − | 0.929847i | \(-0.380061\pi\) | |||||||
\(14\) | −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 | \(0.783731\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 129.695 | 1.56601 | 0.783004 | − | 0.622017i | \(-0.213687\pi\) | ||||
0.783004 | + | 0.622017i | \(0.213687\pi\) | |||||||
\(20\) | −3.13047 | + | 5.42213i | −0.0349997 | + | 0.0606213i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −48.3740 | − | 83.7863i | −0.468790 | − | 0.811968i | ||||
\(23\) | 39.8342 | + | 68.9949i | 0.361131 | + | 0.625497i | 0.988147 | − | 0.153509i | \(-0.0490575\pi\) |
−0.627017 | + | 0.779006i | \(0.715724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −177.161 | −1.33631 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −17.1703 | −0.115888 | ||||||||
\(29\) | 4.51769 | − | 7.82486i | 0.0289280 | − | 0.0501048i | −0.851199 | − | 0.524843i | \(-0.824124\pi\) |
0.880127 | + | 0.474738i | \(0.157457\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.6904 | + | 28.9087i | 0.0966998 | + | 0.167489i | 0.910317 | − | 0.413912i | \(-0.135838\pi\) |
−0.813617 | + | 0.581401i | \(0.802505\pi\) | |||||||
\(32\) | −28.0860 | − | 48.6463i | −0.155154 | − | 0.268735i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −165.858 | + | 287.275i | −0.836602 | + | 1.44904i | ||||
\(35\) | −68.5611 | −0.331113 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −22.1645 | −0.0984817 | −0.0492408 | − | 0.998787i | \(-0.515680\pi\) | ||||
−0.0492408 | + | 0.998787i | \(0.515680\pi\) | |||||||
\(38\) | 197.250 | − | 341.647i | 0.842056 | − | 1.45848i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −51.3127 | − | 88.8763i | −0.202831 | − | 0.351314i | ||||
\(41\) | 60.8698 | + | 105.430i | 0.231860 | + | 0.401593i | 0.958356 | − | 0.285578i | \(-0.0921855\pi\) |
−0.726495 | + | 0.687171i | \(0.758852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.07086 | + | 8.78298i | −0.0179837 | + | 0.0311487i | −0.874877 | − | 0.484345i | \(-0.839058\pi\) |
0.856894 | + | 0.515493i | \(0.172391\pi\) | |||||||
\(44\) | −39.8281 | −0.136462 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 242.331 | 0.776733 | ||||||||
\(47\) | −220.746 | + | 382.343i | −0.685088 | + | 1.18661i | 0.288321 | + | 0.957534i | \(0.406903\pi\) |
−0.973409 | + | 0.229073i | \(0.926430\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 77.4875 | + | 134.212i | 0.225911 | + | 0.391289i | ||||
\(50\) | 38.0218 | + | 65.8556i | 0.107542 | + | 0.186268i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −36.4657 | + | 63.1604i | −0.0972477 | + | 0.168438i | ||||
\(53\) | 593.610 | 1.53846 | 0.769232 | − | 0.638969i | \(-0.220639\pi\) | ||||
0.769232 | + | 0.638969i | \(0.220639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −159.034 | −0.389894 | ||||||||
\(56\) | 140.722 | − | 243.738i | 0.335800 | − | 0.581623i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.7416 | − | 23.8012i | −0.0311097 | − | 0.0538836i | ||||
\(59\) | 221.230 | + | 383.182i | 0.488164 | + | 0.845525i | 0.999907 | − | 0.0136133i | \(-0.00433337\pi\) |
−0.511743 | + | 0.859139i | \(0.671000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.2881 | + | 125.207i | −0.151730 | + | 0.262804i | −0.931864 | − | 0.362809i | \(-0.881818\pi\) |
0.780133 | + | 0.625613i | \(0.215151\pi\) | |||||||
\(62\) | 101.536 | 0.207985 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 408.736 | 0.798312 | ||||||||
\(65\) | −145.608 | + | 252.200i | −0.277853 | + | 0.481255i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −431.360 | − | 747.138i | −0.786553 | − | 1.36235i | −0.928067 | − | 0.372414i | \(-0.878530\pi\) |
0.141514 | − | 0.989936i | \(-0.454803\pi\) | |||||||
\(68\) | 68.2786 | + | 118.262i | 0.121765 | + | 0.210902i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −104.273 | + | 180.605i | −0.178042 | + | 0.308378i | ||||
\(71\) | 818.541 | 1.36821 | 0.684105 | − | 0.729384i | \(-0.260193\pi\) | ||||
0.684105 | + | 0.729384i | \(0.260193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 495.052 | 0.793719 | 0.396859 | − | 0.917879i | \(-0.370100\pi\) | ||||
0.396859 | + | 0.917879i | \(0.370100\pi\) | |||||||
\(74\) | −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 | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −585.263 | + | 1013.71i | −0.833510 | + | 1.44368i | 0.0617284 | + | 0.998093i | \(0.480339\pi\) |
−0.895238 | + | 0.445588i | \(0.852995\pi\) | |||||||
\(80\) | −362.248 | −0.506256 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 370.300 | 0.498693 | ||||||||
\(83\) | −212.022 | + | 367.232i | −0.280390 | + | 0.485651i | −0.971481 | − | 0.237118i | \(-0.923797\pi\) |
0.691090 | + | 0.722768i | \(0.257131\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 272.637 | + | 472.221i | 0.347902 | + | 0.602584i | ||||
\(86\) | 15.4242 | + | 26.7156i | 0.0193400 | + | 0.0334978i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 326.419 | − | 565.374i | 0.395413 | − | 0.684876i | ||||
\(89\) | −1031.37 | −1.22837 | −0.614183 | − | 0.789163i | \(-0.710514\pi\) | ||||
−0.614183 | + | 0.789163i | \(0.710514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −798.643 | −0.920006 | ||||||||
\(92\) | 49.8799 | − | 86.3945i | 0.0565254 | − | 0.0979049i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 671.452 | + | 1162.99i | 0.736756 | + | 1.27610i | ||||
\(95\) | −324.238 | − | 561.597i | −0.350170 | − | 0.606512i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −799.356 | + | 1384.53i | −0.836725 | + | 1.44925i | 0.0558930 | + | 0.998437i | \(0.482199\pi\) |
−0.892618 | + | 0.450814i | \(0.851134\pi\) | |||||||
\(98\) | 471.394 | 0.485897 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 31.3047 | 0.0313047 | ||||||||
\(101\) | −107.000 | + | 185.330i | −0.105415 | + | 0.182584i | −0.913908 | − | 0.405922i | \(-0.866950\pi\) |
0.808493 | + | 0.588506i | \(0.200284\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −836.160 | − | 1448.27i | −0.799897 | − | 1.38546i | −0.919683 | − | 0.392662i | \(-0.871554\pi\) |
0.119786 | − | 0.992800i | \(-0.461779\pi\) | |||||||
\(104\) | −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 | \(0.412525\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −771.570 | −0.678009 | −0.339005 | − | 0.940785i | \(-0.610090\pi\) | ||||
−0.339005 | + | 0.940785i | \(0.610090\pi\) | |||||||
\(110\) | −241.870 | + | 418.931i | −0.209649 | + | 0.363123i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −496.722 | − | 860.348i | −0.419070 | − | 0.725850i | ||||
\(113\) | −583.338 | − | 1010.37i | −0.485627 | − | 0.841131i | 0.514237 | − | 0.857648i | \(-0.328075\pi\) |
−0.999864 | + | 0.0165177i | \(0.994742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 199.171 | − | 344.974i | 0.161503 | − | 0.279731i | ||||
\(116\) | −11.3140 | −0.00905583 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 20.8996 | − | 36.1991i | 0.0151358 | − | 0.0262159i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1630.10 | 1.13896 | 0.569479 | − | 0.822006i | \(-0.307145\pi\) | ||||
0.569479 | + | 0.822006i | \(0.307145\pi\) | |||||||
\(128\) | 846.322 | − | 1465.87i | 0.584414 | − | 1.01223i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 442.901 | + | 767.128i | 0.298808 | + | 0.517550i | ||||
\(131\) | 129.412 | + | 224.149i | 0.0863115 | + | 0.149496i | 0.905949 | − | 0.423386i | \(-0.139159\pi\) |
−0.819638 | + | 0.572882i | \(0.805825\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 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 | −0.653904 | − | 0.756578i | \(-0.726870\pi\) |
0.982167 | + | 0.188009i | \(0.0602033\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1192.25 | − | 2065.03i | −0.727519 | − | 1.26010i | −0.957929 | − | 0.287006i | \(-0.907340\pi\) |
0.230410 | − | 0.973094i | \(-0.425993\pi\) | |||||||
\(140\) | 42.9257 | + | 74.3495i | 0.0259135 | + | 0.0448834i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1244.89 | − | 2156.22i | 0.735699 | − | 1.27427i | ||||
\(143\) | −1852.53 | −1.08333 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −45.1769 | −0.0258740 | ||||||||
\(146\) | 752.910 | − | 1304.08i | 0.426790 | − | 0.739221i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.8771 | + | 24.0358i | 0.00770735 | + | 0.0133495i | ||||
\(149\) | 573.144 | + | 992.715i | 0.315126 | + | 0.545815i | 0.979464 | − | 0.201617i | \(-0.0646198\pi\) |
−0.664338 | + | 0.747432i | \(0.731286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 583.058 | − | 1009.89i | 0.314229 | − | 0.544261i | −0.665044 | − | 0.746804i | \(-0.731587\pi\) |
0.979273 | + | 0.202543i | \(0.0649207\pi\) | |||||||
\(152\) | 2662.01 | 1.42051 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1326.63 | −0.694175 | ||||||||
\(155\) | 83.4522 | − | 144.544i | 0.0432454 | − | 0.0749033i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1737.81 | + | 3009.97i | 0.883390 | + | 1.53008i | 0.847548 | + | 0.530719i | \(0.178078\pi\) |
0.0358423 | + | 0.999357i | \(0.488589\pi\) | |||||||
\(158\) | 1780.22 | + | 3083.43i | 0.896371 | + | 1.55256i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −140.430 | + | 243.232i | −0.0693872 | + | 0.120182i | ||||
\(161\) | 1092.43 | 0.534755 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2223.32 | −1.06837 | −0.534183 | − | 0.845369i | \(-0.679381\pi\) | ||||
−0.534183 | + | 0.845369i | \(0.679381\pi\) | |||||||
\(164\) | 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 | 0.621329 | − | 0.783550i | \(-0.286593\pi\) |
−0.989239 | + | 0.146312i | \(0.953260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −597.632 | + | 1035.13i | −0.272022 | + | 0.471156i | ||||
\(170\) | 1658.58 | 0.748280 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.6993 | 0.00562974 | ||||||||
\(173\) | 753.898 | − | 1305.79i | 0.331317 | − | 0.573857i | −0.651454 | − | 0.758689i | \(-0.725840\pi\) |
0.982770 | + | 0.184831i | \(0.0591738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 171.403 | + | 296.878i | 0.0740390 | + | 0.128239i | ||||
\(176\) | −1152.19 | − | 1995.66i | −0.493465 | − | 0.854707i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1568.58 | + | 2716.85i | −0.660504 | + | 1.14403i | ||||
\(179\) | −1572.66 | −0.656683 | −0.328341 | − | 0.944559i | \(-0.606490\pi\) | ||||
−0.328341 | + | 0.944559i | \(0.606490\pi\) | |||||||
\(180\) | 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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 817.601 | + | 1416.13i | 0.327578 | + | 0.567382i | ||||
\(185\) | 55.4113 | + | 95.9751i | 0.0220212 | + | 0.0381418i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1734.34 | + | 3003.97i | −0.678223 | + | 1.17472i | ||||
\(188\) | 552.831 | 0.214465 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1972.50 | −0.753158 | ||||||||
\(191\) | −1174.18 | + | 2033.73i | −0.444819 | + | 0.770450i | −0.998040 | − | 0.0625853i | \(-0.980065\pi\) |
0.553220 | + | 0.833035i | \(0.313399\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 117.085 | + | 202.797i | 0.0436681 | + | 0.0756354i | 0.887033 | − | 0.461705i | \(-0.152762\pi\) |
−0.843365 | + | 0.537341i | \(0.819429\pi\) | |||||||
\(194\) | 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 | \(0.458564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1701.45 | 0.606094 | 0.303047 | − | 0.952976i | \(-0.401996\pi\) | ||||
0.303047 | + | 0.952976i | \(0.401996\pi\) | |||||||
\(200\) | −256.564 | + | 444.381i | −0.0907090 | + | 0.157113i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 325.467 | + | 563.725i | 0.113365 | + | 0.196354i | ||||
\(203\) | −61.9475 | − | 107.296i | −0.0214180 | − | 0.0370971i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 304.349 | − | 527.148i | 0.103691 | − | 0.179598i | ||||
\(206\) | −5086.77 | −1.72045 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | 0.915840 | + | 0.401544i | \(0.131526\pi\) |
−0.110172 | + | 0.993912i | \(0.535140\pi\) | |||||||
\(212\) | −371.656 | − | 643.727i | −0.120403 | − | 0.208544i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 913.585 | − | 1582.38i | 0.291829 | − | 0.505463i | ||||
\(215\) | 50.7086 | 0.0160851 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 457.726 | 0.143191 | ||||||||
\(218\) | −1173.46 | + | 2032.49i | −0.364572 | + | 0.631456i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 99.5703 | + | 172.461i | 0.0305137 | + | 0.0528514i | ||||
\(221\) | 3175.85 | + | 5500.73i | 0.966655 | + | 1.67430i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1526.57 | − | 2644.10i | 0.458416 | − | 0.794001i | −0.540461 | − | 0.841369i | \(-0.681750\pi\) |
0.998877 | + | 0.0473684i | \(0.0150835\pi\) | |||||||
\(224\) | −770.242 | −0.229750 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3548.73 | −1.04450 | ||||||||
\(227\) | −419.976 | + | 727.420i | −0.122797 | + | 0.212690i | −0.920869 | − | 0.389871i | \(-0.872520\pi\) |
0.798073 | + | 0.602561i | \(0.205853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −700.753 | − | 1213.74i | −0.202214 | − | 0.350245i | 0.747027 | − | 0.664793i | \(-0.231480\pi\) |
−0.949242 | + | 0.314548i | \(0.898147\pi\) | |||||||
\(230\) | −605.827 | − | 1049.32i | −0.173683 | − | 0.300827i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 92.7259 | − | 160.606i | 0.0262403 | − | 0.0454496i | ||||
\(233\) | 2856.99 | 0.803295 | 0.401647 | − | 0.915794i | \(-0.368438\pi\) | ||||
0.401647 | + | 0.915794i | \(0.368438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2207.46 | 0.612761 | ||||||||
\(236\) | 277.021 | − | 479.815i | 0.0764092 | − | 0.132345i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2274.29 | + | 3939.18i | 0.619412 | + | 1.07285i | ||||
\(239\) | −854.917 | − | 1480.76i | −0.231381 | − | 0.400763i | 0.726834 | − | 0.686813i | \(-0.240991\pi\) |
−0.958215 | + | 0.286050i | \(0.907658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2166.23 | − | 3752.02i | 0.579000 | − | 1.00286i | −0.416594 | − | 0.909092i | \(-0.636776\pi\) |
0.995594 | − | 0.0937648i | \(-0.0298902\pi\) | |||||||
\(242\) | 971.309 | 0.258009 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 181.036 | 0.0474987 | ||||||||
\(245\) | 387.437 | − | 671.061i | 0.101030 | − | 0.174990i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3776.93 | − | 6541.84i | −0.972957 | − | 1.68521i | ||||
\(248\) | 342.573 | + | 593.354i | 0.0877154 | + | 0.151927i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 190.109 | − | 329.278i | 0.0480941 | − | 0.0833015i | ||||
\(251\) | 1724.73 | 0.433722 | 0.216861 | − | 0.976202i | \(-0.430418\pi\) | ||||
0.216861 | + | 0.976202i | \(0.430418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | −0.964729 | − | 0.263246i | \(-0.915207\pi\) |
0.254386 | − | 0.967103i | \(-0.418127\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −151.962 | + | 263.206i | −0.0364574 | + | 0.0631462i | ||||
\(260\) | 364.657 | 0.0869810 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 787.277 | 0.185642 | ||||||||
\(263\) | 196.180 | − | 339.794i | 0.0459962 | − | 0.0796677i | −0.842111 | − | 0.539305i | \(-0.818687\pi\) |
0.888107 | + | 0.459637i | \(0.152020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1484.03 | − | 2570.41i | −0.344011 | − | 0.595845i | ||||
\(266\) | −2704.73 | − | 4684.73i | −0.623450 | − | 1.07985i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −540.144 | + | 935.557i | −0.123114 | + | 0.213240i | ||||
\(269\) | 4610.33 | 1.04497 | 0.522485 | − | 0.852648i | \(-0.325005\pi\) | ||||
0.522485 | + | 0.852648i | \(0.325005\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1601.13 | − | 2773.23i | −0.353020 | − | 0.611449i | ||||
\(275\) | 397.585 | + | 688.638i | 0.0871829 | + | 0.151005i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 304.205 | − | 526.898i | 0.0659852 | − | 0.114290i | −0.831145 | − | 0.556055i | \(-0.812314\pi\) |
0.897131 | + | 0.441765i | \(0.145648\pi\) | |||||||
\(278\) | −7253.02 | −1.56477 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1407.22 | −0.300349 | ||||||||
\(281\) | 1374.62 | − | 2380.91i | 0.291825 | − | 0.505456i | −0.682416 | − | 0.730964i | \(-0.739071\pi\) |
0.974241 | + | 0.225508i | \(0.0724042\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −510.780 | − | 884.697i | −0.107289 | − | 0.185830i | 0.807382 | − | 0.590029i | \(-0.200884\pi\) |
−0.914671 | + | 0.404199i | \(0.867550\pi\) | |||||||
\(284\) | −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 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6979.96 | 1.42071 | ||||||||
\(290\) | −68.7082 | + | 119.006i | −0.0139127 | + | 0.0240975i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −309.949 | − | 536.848i | −0.0621178 | − | 0.107591i | ||||
\(293\) | −2616.25 | − | 4531.47i | −0.521648 | − | 0.903521i | −0.999683 | − | 0.0251800i | \(-0.991984\pi\) |
0.478035 | − | 0.878341i | \(-0.341349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1106.15 | − | 1915.91i | 0.218314 | − | 0.378130i | ||||
\(296\) | −454.929 | −0.0893317 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4698.18 | − | 8137.49i | 0.886379 | − | 1.53525i | ||||
\(305\) | 722.881 | 0.135712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4912.68 | −0.913296 | −0.456648 | − | 0.889648i | \(-0.650950\pi\) | ||||
−0.456648 | + | 0.889648i | \(0.650950\pi\) | |||||||
\(308\) | −273.066 | + | 472.964i | −0.0505174 | + | 0.0874988i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −253.840 | − | 439.664i | −0.0465069 | − | 0.0805524i | ||||
\(311\) | −414.430 | − | 717.813i | −0.0755632 | − | 0.130879i | 0.825768 | − | 0.564010i | \(-0.190742\pi\) |
−0.901331 | + | 0.433131i | \(0.857409\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4618.60 | + | 7999.66i | −0.834054 | + | 1.44462i | 0.0607442 | + | 0.998153i | \(0.480653\pi\) |
−0.894798 | + | 0.446471i | \(0.852681\pi\) | |||||||
\(314\) | 10571.9 | 1.90003 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1465.72 | 0.260928 | ||||||||
\(317\) | −4549.20 | + | 7879.45i | −0.806021 | + | 1.39607i | 0.109578 | + | 0.993978i | \(0.465050\pi\) |
−0.915599 | + | 0.402091i | \(0.868283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −143.693 | − | 248.884i | −0.0252203 | − | 0.0436828i | ||||
\(320\) | −1021.84 | − | 1769.88i | −0.178508 | − | 0.309185i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1661.45 | − | 2877.71i | 0.287543 | − | 0.498039i | ||||
\(323\) | −14143.9 | −2.43649 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1456.08 | 0.248519 | ||||||||
\(326\) | −3381.38 | + | 5856.72i | −0.574470 | + | 0.995011i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | −0.999984 | − | 0.00560570i | \(-0.998216\pi\) |
0.504847 | + | 0.863209i | \(0.331549\pi\) | |||||||
\(332\) | 530.982 | 0.0877754 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4830.23 | −0.791313 | ||||||||
\(335\) | −2156.80 | + | 3735.69i | −0.351757 | + | 0.609261i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −298.427 | − | 516.890i | −0.0482384 | − | 0.0835514i | 0.840898 | − | 0.541194i | \(-0.182027\pi\) |
−0.889136 | + | 0.457642i | \(0.848694\pi\) | |||||||
\(338\) | 1817.84 | + | 3148.60i | 0.292537 | + | 0.506690i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 341.393 | − | 591.310i | 0.0544548 | − | 0.0943185i | ||||
\(341\) | 1061.74 | 0.168611 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | 0.633863 | − | 0.773445i | \(-0.281468\pi\) |
−0.986755 | + | 0.162219i | \(0.948135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −337.633 | + | 584.798i | −0.0517854 | + | 0.0896949i | −0.890756 | − | 0.454482i | \(-0.849825\pi\) |
0.838971 | + | 0.544177i | \(0.183158\pi\) | |||||||
\(350\) | 1042.73 | 0.159246 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1786.65 | −0.270536 | ||||||||
\(353\) | −1680.91 | + | 2911.43i | −0.253445 | + | 0.438979i | −0.964472 | − | 0.264185i | \(-0.914897\pi\) |
0.711027 | + | 0.703165i | \(0.248230\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2046.35 | − | 3544.38i | −0.305941 | − | 0.529905i | ||||
\(356\) | 645.732 | + | 1118.44i | 0.0961341 | + | 0.166509i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2391.81 | + | 4142.74i | −0.353104 | + | 0.611594i | ||||
\(359\) | −7701.61 | −1.13224 | −0.566122 | − | 0.824322i | \(-0.691557\pi\) | ||||
−0.566122 | + | 0.824322i | \(0.691557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9961.87 | 1.45238 | ||||||||
\(362\) | 3018.03 | − | 5227.39i | 0.438189 | − | 0.758965i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 500.026 | + | 866.070i | 0.0720013 | + | 0.124710i | ||||
\(365\) | −1237.63 | − | 2143.64i | −0.177481 | − | 0.307406i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2954.75 | + | 5117.77i | −0.420263 | + | 0.727917i | −0.995965 | − | 0.0897425i | \(-0.971396\pi\) |
0.575702 | + | 0.817660i | \(0.304729\pi\) | |||||||
\(368\) | 5771.94 | 0.817617 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 337.093 | 0.0473639 | ||||||||
\(371\) | 4069.86 | − | 7049.20i | 0.569532 | − | 0.986459i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4212.19 | + | 7295.73i | 0.584716 | + | 1.01276i | 0.994911 | + | 0.100760i | \(0.0321273\pi\) |
−0.410195 | + | 0.911998i | \(0.634539\pi\) | |||||||
\(374\) | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3510.24 | −0.475749 | −0.237875 | − | 0.971296i | \(-0.576451\pi\) | ||||
−0.237875 | + | 0.971296i | \(0.576451\pi\) | |||||||
\(380\) | −406.007 | + | 703.225i | −0.0548098 | + | 0.0949334i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3571.54 | + | 6186.09i | 0.478367 | + | 0.828555i | ||||
\(383\) | 2866.01 | + | 4964.08i | 0.382367 | + | 0.662279i | 0.991400 | − | 0.130866i | \(-0.0417758\pi\) |
−0.609033 | + | 0.793145i | \(0.708442\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1090.36 | + | 1888.55i | −0.144337 | + | 0.249999i | ||||
\(386\) | 712.283 | 0.0939229 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2001.89 | 0.261934 | ||||||||
\(389\) | 7183.60 | − | 12442.4i | 0.936306 | − | 1.62173i | 0.164019 | − | 0.986457i | \(-0.447554\pi\) |
0.772288 | − | 0.635273i | \(-0.219112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4344.11 | − | 7524.23i | −0.561870 | − | 0.973188i | ||||
\(392\) | 1590.44 | + | 2754.72i | 0.204922 | + | 0.354934i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1091.75 | − | 1890.97i | 0.139598 | − | 0.241791i | ||||
\(395\) | 5852.63 | 0.745514 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9014.42 | −1.13960 | −0.569800 | − | 0.821784i | \(-0.692979\pi\) | ||||
−0.569800 | + | 0.821784i | \(0.692979\pi\) | |||||||
\(398\) | 2587.69 | − | 4482.01i | 0.325902 | − | 0.564479i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 905.619 | + | 1568.58i | 0.113202 | + | 0.196072i | ||||
\(401\) | 5255.55 | + | 9102.87i | 0.654487 | + | 1.13361i | 0.982022 | + | 0.188766i | \(0.0604488\pi\) |
−0.327535 | + | 0.944839i | \(0.606218\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 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 | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1659.10 | − | 2873.65i | −0.200580 | − | 0.347415i | 0.748135 | − | 0.663546i | \(-0.230949\pi\) |
−0.948715 | + | 0.316131i | \(0.897616\pi\) | |||||||
\(410\) | −925.751 | − | 1603.45i | −0.111511 | − | 0.193143i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1047.03 | + | 1813.51i | −0.125203 | + | 0.216857i | ||||
\(413\) | 6067.11 | 0.722864 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2120.22 | 0.250789 | ||||||||
\(416\) | −1635.81 | + | 2833.31i | −0.192794 | + | 0.333929i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6273.89 | − | 10866.7i | −0.734129 | − | 1.27155i | ||||
\(419\) | −243.069 | − | 421.008i | −0.0283406 | − | 0.0490873i | 0.851507 | − | 0.524343i | \(-0.175689\pi\) |
−0.879848 | + | 0.475255i | \(0.842356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2525.96 | + | 4375.10i | −0.292418 | + | 0.506482i | −0.974381 | − | 0.224904i | \(-0.927793\pi\) |
0.681963 | + | 0.731387i | \(0.261126\pi\) | |||||||
\(422\) | 15022.1 | 1.73286 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12183.9 | 1.39553 | ||||||||
\(425\) | 1363.19 | − | 2361.11i | 0.155586 | − | 0.269484i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 991.230 | + | 1716.86i | 0.112340 | + | 0.194578i | ||||
\(428\) | −376.094 | − | 651.414i | −0.0424747 | − | 0.0735684i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 77.1212 | − | 133.578i | 0.00864910 | − | 0.0149807i | ||||
\(431\) | −6944.24 | −0.776084 | −0.388042 | − | 0.921642i | \(-0.626848\pi\) | ||||
−0.388042 | + | 0.921642i | \(0.626848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13738.3 | −1.52476 | −0.762378 | − | 0.647131i | \(-0.775968\pi\) | ||||
−0.762378 | + | 0.647131i | \(0.775968\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4240.92 | + | 7345.48i | −0.461066 | + | 0.798589i | −0.999014 | − | 0.0443883i | \(-0.985866\pi\) |
0.537949 | + | 0.842978i | \(0.319199\pi\) | |||||||
\(440\) | −3264.19 | −0.353668 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19320.2 | 2.07912 | ||||||||
\(443\) | −279.098 | + | 483.411i | −0.0299330 | + | 0.0518455i | −0.880604 | − | 0.473853i | \(-0.842863\pi\) |
0.850671 | + | 0.525699i | \(0.176196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2578.42 | + | 4465.95i | 0.274671 | + | 0.475744i | ||||
\(446\) | −4643.44 | − | 8042.67i | −0.492989 | − | 0.853882i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2802.34 | − | 4853.79i | 0.295531 | − | 0.511875i | ||||
\(449\) | −14775.0 | −1.55295 | −0.776476 | − | 0.630147i | \(-0.782995\pi\) | ||||
−0.776476 | + | 0.630147i | \(0.782995\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3872.15 | 0.404285 | ||||||||
\(452\) | −730.449 | + | 1265.17i | −0.0760120 | + | 0.131657i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1277.46 | + | 2212.62i | 0.132058 | + | 0.228730i | ||||
\(455\) | 1996.61 | + | 3458.23i | 0.205720 | + | 0.356317i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7103.97 | − | 12304.4i | 0.727154 | − | 1.25947i | −0.230927 | − | 0.972971i | \(-0.574176\pi\) |
0.958081 | − | 0.286497i | \(-0.0924909\pi\) | |||||||
\(458\) | −4263.02 | −0.434930 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −498.799 | −0.0505579 | ||||||||
\(461\) | −3851.26 | + | 6670.57i | −0.389091 | + | 0.673925i | −0.992328 | − | 0.123637i | \(-0.960544\pi\) |
0.603237 | + | 0.797562i | \(0.293877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3954.53 | − | 6849.45i | −0.396939 | − | 0.687518i | 0.596408 | − | 0.802682i | \(-0.296594\pi\) |
−0.993347 | + | 0.115163i | \(0.963261\pi\) | |||||||
\(464\) | −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 | \(0.695654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11829.8 | −1.16471 | ||||||||
\(470\) | 3357.26 | − | 5814.95i | 0.329487 | − | 0.570688i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4540.77 | + | 7864.84i | 0.442809 | + | 0.766967i | ||||
\(473\) | 161.288 | + | 279.359i | 0.0156787 | + | 0.0271563i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1621.19 | + | 2807.99i | −0.156601 | + | 0.271240i | ||||
\(476\) | 1872.50 | 0.180307 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5200.87 | −0.497662 | ||||||||
\(479\) | −9347.93 | + | 16191.1i | −0.891687 | + | 1.54445i | −0.0538341 | + | 0.998550i | \(0.517144\pi\) |
−0.837853 | + | 0.545897i | \(0.816189\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 645.465 | + | 1117.98i | 0.0611865 | + | 0.105978i | ||||
\(482\) | −6589.10 | − | 11412.7i | −0.622667 | − | 1.07849i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 199.928 | − | 346.286i | 0.0187761 | − | 0.0325212i | ||||
\(485\) | 7993.56 | 0.748390 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2249.54 | −0.209315 | −0.104658 | − | 0.994508i | \(-0.533375\pi\) | ||||
−0.104658 | + | 0.994508i | \(0.533375\pi\) | |||||||
\(488\) | −1483.72 | + | 2569.88i | −0.137633 | + | 0.238387i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1178.48 | − | 2041.19i | −0.108650 | − | 0.188187i | ||||
\(491\) | 994.175 | + | 1721.96i | 0.0913778 | + | 0.158271i | 0.908091 | − | 0.418773i | \(-0.137540\pi\) |
−0.816713 | + | 0.577044i | \(0.804206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −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 | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1206.95 | − | 2090.50i | −0.108278 | − | 0.187543i | 0.806795 | − | 0.590832i | \(-0.201200\pi\) |
−0.915073 | + | 0.403289i | \(0.867867\pi\) | |||||||
\(500\) | −78.2617 | − | 135.553i | −0.00699994 | − | 0.0121243i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2623.10 | − | 4543.34i | 0.233216 | − | 0.403942i | ||||
\(503\) | 8758.56 | 0.776391 | 0.388196 | − | 0.921577i | \(-0.373098\pi\) | ||||
0.388196 | + | 0.921577i | \(0.373098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1070.00 | 0.0942860 | ||||||||
\(506\) | 3853.88 | − | 6675.12i | 0.338589 | − | 0.586453i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1020.59 | − | 1767.72i | −0.0891368 | − | 0.154389i | ||||
\(509\) | −5924.01 | − | 10260.7i | −0.515869 | − | 0.893511i | −0.999830 | − | 0.0184220i | \(-0.994136\pi\) |
0.483961 | − | 0.875089i | \(-0.339198\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3394.13 | − | 5878.81i | 0.293831 | − | 0.508930i | ||||
\(512\) | 7826.64 | 0.675570 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17804.1 | −1.52783 | ||||||||
\(515\) | −4180.80 | + | 7241.36i | −0.357725 | + | 0.619597i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7021.23 | + | 12161.1i | 0.597279 | + | 1.03452i | ||||
\(518\) | 462.230 | + | 800.606i | 0.0392070 | + | 0.0679085i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2988.62 | + | 5176.43i | −0.252037 | + | 0.436542i | ||||
\(521\) | −3816.55 | −0.320933 | −0.160466 | − | 0.987041i | \(-0.551300\pi\) | ||||
−0.160466 | + | 0.987041i | \(0.551300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12158.9 | −1.01658 | −0.508288 | − | 0.861187i | \(-0.669722\pi\) | ||||
−0.508288 | + | 0.861187i | \(0.669722\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2909.97 | − | 5040.22i | 0.239169 | − | 0.414253i | ||||
\(530\) | −9028.04 | −0.739911 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2226.90 | −0.181482 | ||||||||
\(533\) | 3545.25 | − | 6140.55i | 0.288108 | − | 0.499018i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1501.75 | − | 2601.10i | −0.121357 | − | 0.210197i | ||||
\(536\) | −8853.71 | − | 15335.1i | −0.713474 | − | 1.23577i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3062.91 | + | 5305.12i | 0.241399 | + | 0.418116i | ||||
\(545\) | 1928.92 | + | 3341.00i | 0.151607 | + | 0.262592i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 513.578 | − | 889.543i | 0.0401444 | − | 0.0695322i | −0.845255 | − | 0.534363i | \(-0.820552\pi\) |
0.885400 | + | 0.464831i | \(0.153885\pi\) | |||||||
\(548\) | −1318.27 | −0.102762 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2418.70 | 0.187516 | ||||||||
\(551\) | 585.923 | − | 1014.85i | 0.0453015 | − | 0.0784646i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.368029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 590.685 | 0.0446929 | ||||||||
\(560\) | −2483.61 | + | 4301.74i | −0.187414 | + | 0.324610i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4181.23 | − | 7242.11i | −0.313834 | − | 0.543576i | ||||
\(563\) | −1096.03 | − | 1898.38i | −0.0820467 | − | 0.142109i | 0.822082 | − | 0.569369i | \(-0.192812\pi\) |
−0.904129 | + | 0.427260i | \(0.859479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2916.69 | + | 5051.86i | −0.217179 | + | 0.376165i | ||||
\(566\) | −3107.32 | −0.230761 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16800.6 | 1.24109 | ||||||||
\(569\) | −8284.89 | + | 14349.8i | −0.610405 | + | 1.05725i | 0.380767 | + | 0.924671i | \(0.375660\pi\) |
−0.991172 | + | 0.132582i | \(0.957673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3639.66 | − | 6304.08i | −0.266752 | − | 0.462027i | 0.701269 | − | 0.712896i | \(-0.252617\pi\) |
−0.968021 | + | 0.250869i | \(0.919284\pi\) | |||||||
\(572\) | 1159.86 | + | 2008.93i | 0.0847833 | + | 0.146849i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2538.82 | − | 4397.36i | 0.184614 | − | 0.319760i | ||||
\(575\) | −1991.71 | −0.144452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17938.0 | −1.29422 | −0.647112 | − | 0.762395i | \(-0.724024\pi\) | ||||
−0.647112 | + | 0.762395i | \(0.724024\pi\) | |||||||
\(578\) | 10615.6 | − | 18386.8i | 0.763930 | − | 1.32317i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 28.2850 | + | 48.9910i | 0.00202495 | + | 0.00350731i | ||||
\(581\) | 2907.29 | + | 5035.57i | 0.207598 | + | 0.359571i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | −0.589634 | − | 0.807671i | \(-0.700728\pi\) |
0.994280 | + | 0.106803i | \(0.0340613\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2164.67 | + | 3749.32i | 0.151433 | + | 0.262289i | ||||
\(590\) | −3364.62 | − | 5827.70i | −0.234778 | − | 0.406648i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −802.904 | + | 1390.67i | −0.0557418 | + | 0.0965476i | ||||
\(593\) | 9612.80 | 0.665684 | 0.332842 | − | 0.942983i | \(-0.391992\pi\) | ||||
0.332842 | + | 0.942983i | \(0.391992\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7476.92 | 0.515166 | ||||||||
\(596\) | 717.684 | − | 1243.07i | 0.0493247 | − | 0.0854328i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7057.05 | − | 12223.2i | −0.482582 | − | 0.835857i | ||||
\(599\) | 3686.00 | + | 6384.33i | 0.251429 | + | 0.435487i | 0.963919 | − | 0.266194i | \(-0.0857663\pi\) |
−0.712491 | + | 0.701681i | \(0.752433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12095.3 | − | 20949.7i | 0.820927 | − | 1.42189i | −0.0840654 | − | 0.996460i | \(-0.526790\pi\) |
0.904993 | − | 0.425427i | \(-0.139876\pi\) | |||||||
\(602\) | 423.001 | 0.0286383 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1460.20 | −0.0983684 | ||||||||
\(605\) | 798.317 | − | 1382.72i | 0.0536466 | − | 0.0929186i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 658.866 | + | 1141.19i | 0.0440569 | + | 0.0763088i | 0.887213 | − | 0.461360i | \(-0.152638\pi\) |
−0.843156 | + | 0.537669i | \(0.819305\pi\) | |||||||
\(608\) | −3642.62 | − | 6309.20i | −0.242973 | − | 0.420842i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1099.41 | − | 1904.23i | 0.0729733 | − | 0.126393i | ||||
\(611\) | 25713.9 | 1.70257 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4137.52 | −0.272615 | −0.136307 | − | 0.990667i | \(-0.543523\pi\) | ||||
−0.136307 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(614\) | −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 | 0.710480 | − | 0.703717i | \(-0.248478\pi\) |
−0.964677 | + | 0.263436i | \(0.915144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10978.2 | + | 19014.8i | −0.712844 | + | 1.23468i | 0.250941 | + | 0.968002i | \(0.419260\pi\) |
−0.963785 | + | 0.266680i | \(0.914073\pi\) | |||||||
\(620\) | −208.996 | −0.0135379 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2521.18 | −0.162524 | ||||||||
\(623\) | −7071.17 | + | 12247.6i | −0.454736 | + | 0.787625i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 14048.6 | + | 24332.9i | 0.896957 | + | 1.55357i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13837.5 | + | 23967.2i | 0.866810 | + | 1.50136i | ||||
\(635\) | −4075.24 | − | 7058.52i | −0.254679 | − | 0.441116i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4513.11 | − | 7816.94i | 0.280716 | − | 0.486214i | ||||
\(638\) | −874.155 | −0.0542447 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8463.22 | −0.522716 | ||||||||
\(641\) | 2404.72 | − | 4165.10i | 0.148176 | − | 0.256648i | −0.782377 | − | 0.622805i | \(-0.785993\pi\) |
0.930553 | + | 0.366156i | \(0.119326\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1276.51 | + | 2210.98i | 0.0782904 | + | 0.135603i | 0.902512 | − | 0.430664i | \(-0.141721\pi\) |
−0.824222 | + | 0.566267i | \(0.808387\pi\) | |||||||
\(644\) | −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 | \(0.582604\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14073.2 | 0.851191 | ||||||||
\(650\) | 2214.51 | − | 3835.64i | 0.133631 | − | 0.231456i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1392.01 | + | 2411.02i | 0.0836122 | + | 0.144821i | ||||
\(653\) | 4047.44 | + | 7010.37i | 0.242555 | + | 0.420118i | 0.961441 | − | 0.275010i | \(-0.0886812\pi\) |
−0.718886 | + | 0.695128i | \(0.755348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 647.062 | − | 1120.74i | 0.0385997 | − | 0.0668566i | ||||
\(656\) | 8819.97 | 0.524942 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18414.2 | 1.09097 | ||||||||
\(659\) | 1087.67 | − | 1883.89i | 0.0642936 | − | 0.111360i | −0.832087 | − | 0.554645i | \(-0.812854\pi\) |
0.896380 | + | 0.443286i | \(0.146187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4438.47 | + | 7687.66i | 0.261175 | + | 0.452368i | 0.966554 | − | 0.256462i | \(-0.0825567\pi\) |
−0.705379 | + | 0.708830i | \(0.749223\pi\) | |||||||
\(662\) | 9069.64 | + | 15709.1i | 0.532480 | + | 0.922282i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4351.77 | + | 7537.48i | −0.254339 | + | 0.440529i | ||||
\(665\) | −8892.06 | −0.518525 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 719.834 | 0.0417872 | ||||||||
\(668\) | −994.226 | + | 1722.05i | −0.0575865 | + | 0.0997427i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6560.43 | + | 11363.0i | 0.378286 | + | 0.655211i | ||||
\(671\) | 2299.25 | + | 3982.42i | 0.132283 | + | 0.229120i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4583.96 | − | 7939.65i | 0.262554 | − | 0.454757i | −0.704366 | − | 0.709837i | \(-0.748769\pi\) |
0.966920 | + | 0.255080i | \(0.0821019\pi\) | |||||||
\(674\) | −1815.47 | −0.103753 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1496.70 | 0.0851557 | ||||||||
\(677\) | −9438.93 | + | 16348.7i | −0.535846 | + | 0.928112i | 0.463276 | + | 0.886214i | \(0.346674\pi\) |
−0.999122 | + | 0.0418983i | \(0.986659\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10961.0 | + | 18984.9i | 0.619503 | + | 1.07301i | ||||
\(680\) | 5595.90 | + | 9692.39i | 0.315578 | + | 0.546597i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1614.77 | − | 2796.86i | 0.0906638 | − | 0.157034i | ||||
\(683\) | 27207.5 | 1.52426 | 0.762128 | − | 0.647426i | \(-0.224155\pi\) | ||||
0.762128 | + | 0.647426i | \(0.224155\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5263.85 | −0.293608 | ||||||||
\(686\) | 10385.0 | − | 17987.4i | 0.577991 | − | 1.00111i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | −0.520552 | − | 0.853830i | \(-0.674274\pi\) |
0.999714 | + | 0.0238963i | \(0.00760715\pi\) | |||||||
\(692\) | −1888.04 | −0.103718 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13876.7 | −0.759011 | ||||||||
\(695\) | −5961.24 | + | 10325.2i | −0.325356 | + | 0.563534i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6638.15 | − | 11497.6i | −0.360743 | − | 0.624825i | ||||
\(698\) | 1026.99 | + | 1778.80i | 0.0556909 | + | 0.0964595i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 214.628 | − | 371.747i | 0.0115888 | − | 0.0200725i | ||||
\(701\) | −18543.0 | −0.999086 | −0.499543 | − | 0.866289i | \(-0.666499\pi\) | ||||
−0.499543 | + | 0.866289i | \(0.666499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −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 | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13116.9 | + | 22719.1i | −0.694803 | + | 1.20343i | 0.275444 | + | 0.961317i | \(0.411175\pi\) |
−0.970247 | + | 0.242117i | \(0.922158\pi\) | |||||||
\(710\) | −12448.9 | −0.658029 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21168.9 | −1.11424 | ||||||||
\(713\) | −1329.70 | + | 2303.11i | −0.0698425 | + | 0.120971i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4631.32 | + | 8021.69i | 0.242240 | + | 0.419572i | ||||
\(716\) | 984.633 | + | 1705.43i | 0.0513931 | + | 0.0890155i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11713.2 | + | 20287.8i | −0.608817 | + | 1.05450i | ||||
\(719\) | 3043.06 | 0.157840 | 0.0789199 | − | 0.996881i | \(-0.474853\pi\) | ||||
0.0789199 | + | 0.996881i | \(0.474853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22931.2 | −1.18447 | ||||||||
\(722\) | 15150.7 | − | 26241.8i | 0.780958 | − | 1.35266i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1242.43 | − | 2151.95i | −0.0637769 | − | 0.110465i | ||||
\(725\) | 112.942 | + | 195.622i | 0.00578561 | + | 0.0100210i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10971.2 | + | 19002.7i | −0.559698 | + | 0.969426i | 0.437823 | + | 0.899061i | \(0.355750\pi\) |
−0.997521 | + | 0.0703647i | \(0.977584\pi\) | |||||||
\(728\) | −16392.2 | −0.834528 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7529.10 | −0.381732 | ||||||||
\(731\) | 553.002 | − | 957.827i | 0.0279802 | − | 0.0484631i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13288.4 | + | 23016.2i | 0.669604 | + | 1.15979i | 0.978015 | + | 0.208535i | \(0.0668694\pi\) |
−0.308411 | + | 0.951253i | \(0.599797\pi\) | |||||||
\(734\) | 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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28787.7 | 1.43298 | 0.716489 | − | 0.697598i | \(-0.245748\pi\) | ||||
0.716489 | + | 0.697598i | \(0.245748\pi\) | |||||||
\(740\) | 69.3853 | − | 120.179i | 0.00344683 | − | 0.00597008i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12379.5 | − | 21441.8i | −0.612485 | − | 1.06086i | ||||
\(743\) | −2251.51 | − | 3899.73i | −0.111171 | − | 0.192553i | 0.805072 | − | 0.593177i | \(-0.202127\pi\) |
−0.916243 | + | 0.400624i | \(0.868793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2865.72 | − | 4963.58i | 0.140929 | − | 0.244096i | ||||
\(746\) | 25624.8 | 1.25763 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | 0.788357 | − | 0.615219i | \(-0.210932\pi\) |
−0.926973 | + | 0.375128i | \(0.877599\pi\) | |||||||
\(752\) | 15993.0 | + | 27700.6i | 0.775536 | + | 1.34327i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −800.356 | + | 1386.26i | −0.0386568 | + | 0.0669556i | ||||
\(755\) | −5830.58 | −0.281055 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17397.6 | 0.835305 | 0.417652 | − | 0.908607i | \(-0.362853\pi\) | ||||
0.417652 | + | 0.908607i | \(0.362853\pi\) | |||||||
\(758\) | −5338.62 | + | 9246.77i | −0.255815 | + | 0.443084i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6655.02 | − | 11526.8i | −0.317636 | − | 0.550161i | ||||
\(761\) | −17757.2 | − | 30756.3i | −0.845857 | − | 1.46507i | −0.884875 | − | 0.465829i | \(-0.845756\pi\) |
0.0390179 | − | 0.999239i | \(-0.487577\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −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 | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15631.8 | − | 27075.1i | −0.733027 | − | 1.26964i | −0.955583 | − | 0.294721i | \(-0.904773\pi\) |
0.222556 | − | 0.974920i | \(-0.428560\pi\) | |||||||
\(770\) | 3316.58 | + | 5744.48i | 0.155222 | + | 0.268853i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 146.612 | − | 253.940i | 0.00683508 | − | 0.0118387i | ||||
\(773\) | 6676.47 | 0.310654 | 0.155327 | − | 0.987863i | \(-0.450357\pi\) | ||||
0.155327 | + | 0.987863i | \(0.450357\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −834.522 | −0.0386799 | ||||||||
\(776\) | −16406.9 | + | 28417.5i | −0.758985 | + | 1.31460i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11227.9 | 0.511473 | ||||||||
\(785\) | 8689.04 | − | 15049.9i | 0.395064 | − | 0.684271i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4716.91 | − | 8169.93i | −0.213646 | − | 0.370047i | 0.739207 | − | 0.673479i | \(-0.235201\pi\) |
−0.952853 | + | 0.303432i | \(0.901867\pi\) | |||||||
\(788\) | −449.439 | − | 778.451i | −0.0203180 | − | 0.0351919i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8901.10 | − | 15417.2i | 0.400869 | − | 0.694326i | ||||
\(791\) | −15997.7 | −0.719107 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | −0.999682 | − | 0.0252283i | \(-0.991969\pi\) |
0.477992 | − | 0.878364i | \(-0.341365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24073.4 | − | 41696.4i | 1.06590 | − | 1.84620i | ||||
\(800\) | 1404.30 | 0.0620618 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31972.0 | 1.40769 | ||||||||
\(803\) | 7873.02 | − | 13636.5i | 0.345993 | − | 0.599278i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2731.08 | − | 4730.37i | −0.119575 | − | 0.207110i | ||||
\(806\) | −2956.89 | − | 5121.48i | −0.129221 | − | 0.223817i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2196.19 | + | 3803.91i | −0.0956208 | + | 0.165620i | ||||
\(809\) | 33269.8 | 1.44586 | 0.722932 | − | 0.690919i | \(-0.242794\pi\) | ||||
0.722932 | + | 0.690919i | \(0.242794\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1072.19 | + | 1857.08i | 0.0461672 | + | 0.0799640i | ||||
\(815\) | 5558.30 | + | 9627.25i | 0.238894 | + | 0.413777i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −657.666 | + | 1139.11i | −0.0281626 | + | 0.0487790i | ||||
\(818\) | −10093.1 | −0.431415 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −762.204 | −0.0324601 | ||||||||
\(821\) | −1848.66 | + | 3201.98i | −0.0785856 | + | 0.136114i | −0.902640 | − | 0.430397i | \(-0.858374\pi\) |
0.824054 | + | 0.566511i | \(0.191707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3572.25 | − | 6187.32i | −0.151301 | − | 0.262061i | 0.780405 | − | 0.625275i | \(-0.215013\pi\) |
−0.931706 | + | 0.363213i | \(0.881680\pi\) | |||||||
\(824\) | −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 | \(0.637156\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36736.5 | −1.53910 | −0.769548 | − | 0.638589i | \(-0.779518\pi\) | ||||
−0.769548 | + | 0.638589i | \(0.779518\pi\) | |||||||
\(830\) | 3224.58 | − | 5585.13i | 0.134851 | − | 0.233569i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11903.0 | − | 20616.7i | −0.495990 | − | 0.859079i | ||||
\(833\) | −8450.38 | − | 14636.5i | −0.351487 | − | 0.608793i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3969.96 | + | 6876.16i | −0.164534 | + | 0.284981i | ||||
\(836\) | −5165.52 | −0.213700 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1478.71 | −0.0609560 | ||||||||
\(839\) | 15006.1 | − | 25991.4i | 0.617485 | − | 1.06951i | −0.372458 | − | 0.928049i | \(-0.621485\pi\) |
0.989943 | − | 0.141466i | \(-0.0451816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12153.7 | + | 21050.8i | 0.498326 | + | 0.863127i | ||||
\(842\) | 7683.32 | + | 13307.9i | 0.314471 | + | 0.544680i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3092.07 | − | 5355.62i | 0.126106 | − | 0.218422i | ||||
\(845\) | 5976.32 | 0.243304 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4378.68 | 0.177631 | ||||||||
\(848\) | 21503.4 | − | 37245.0i | 0.870789 | − | 1.50825i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4146.46 | − | 7181.88i | −0.167320 | − | 0.289807i | ||||
\(851\) | −882.905 | − | 1529.24i | −0.0355648 | − | 0.0616000i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2690.51 | − | 4660.10i | 0.107997 | − | 0.187056i | −0.806962 | − | 0.590604i | \(-0.798890\pi\) |
0.914959 | + | 0.403548i | \(0.132223\pi\) | |||||||
\(854\) | 6030.13 | 0.241624 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12329.4 | 0.492302 | ||||||||
\(857\) | 7319.88 | − | 12678.4i | 0.291765 | − | 0.505352i | −0.682462 | − | 0.730921i | \(-0.739091\pi\) |
0.974227 | + | 0.225569i | \(0.0724242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14770.0 | − | 25582.4i | −0.586667 | − | 1.01614i | −0.994665 | − | 0.103154i | \(-0.967107\pi\) |
0.407999 | − | 0.912983i | \(-0.366227\pi\) | |||||||
\(860\) | −31.7483 | − | 54.9897i | −0.00125885 | − | 0.00218039i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10561.3 | + | 18292.7i | −0.417307 | + | 0.722797i | ||||
\(863\) | −3387.63 | −0.133622 | −0.0668112 | − | 0.997766i | \(-0.521283\pi\) | ||||
−0.0668112 | + | 0.997766i | \(0.521283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7538.98 | −0.296339 | ||||||||
\(866\) | −20894.1 | + | 36189.7i | −0.819875 | + | 1.42007i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 31429.2 | 1.21637 | ||||||||
\(875\) | 857.014 | − | 1484.39i | 0.0331113 | − | 0.0573504i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 122.052 | + | 211.400i | 0.00469944 | + | 0.00813967i | 0.868366 | − | 0.495925i | \(-0.165171\pi\) |
−0.863666 | + | 0.504064i | \(0.831837\pi\) | |||||||
\(878\) | 12899.8 | + | 22343.1i | 0.495838 | + | 0.858817i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5760.97 | + | 9978.30i | −0.220684 | + | 0.382237i | ||||
\(881\) | −13910.2 | −0.531948 | −0.265974 | − | 0.963980i | \(-0.585693\pi\) | ||||
−0.265974 | + | 0.963980i | \(0.585693\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8805.87 | −0.335607 | −0.167803 | − | 0.985820i | \(-0.553667\pi\) | ||||
−0.167803 | + | 0.985820i | \(0.553667\pi\) | |||||||
\(884\) | 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 | 0.963903 | − | 0.266255i | \(-0.0857864\pi\) |
−0.712535 | + | 0.701637i | \(0.752453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11176.1 | − | 19357.6i | 0.421637 | − | 0.730296i | ||||
\(890\) | 15685.8 | 0.590773 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3823.11 | −0.143506 | ||||||||
\(893\) | −28629.7 | + | 49588.2i | −1.07285 | + | 1.85824i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3931.65 | + | 6809.82i | 0.146839 | + | 0.254332i | ||||
\(896\) | −11605.0 | − | 20100.4i | −0.432695 | − | 0.749449i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11973.1 | − | 20738.0i | −0.440507 | − | 0.762981i | ||||
\(905\) | −4961.03 | − | 8592.76i | −0.182221 | − | 0.315616i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 542.122 | − | 938.982i | 0.0198466 | − | 0.0343753i | −0.855932 | − | 0.517089i | \(-0.827016\pi\) |
0.875778 | + | 0.482714i | \(0.160349\pi\) | |||||||
\(908\) | 1051.78 | 0.0384411 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12146.3 | 0.442469 | ||||||||
\(911\) | 25094.4 | − | 43464.7i | 0.912638 | − | 1.58073i | 0.102314 | − | 0.994752i | \(-0.467375\pi\) |
0.810324 | − | 0.585983i | \(-0.199291\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 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 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30376.1 | 1.09033 | 0.545166 | − | 0.838328i | \(-0.316467\pi\) | ||||
0.545166 | + | 0.838328i | \(0.316467\pi\) | |||||||
\(920\) | 4088.00 | − | 7080.63i | 0.146497 | − | 0.253741i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11714.5 | + | 20290.2i | 0.418435 | + | 0.724751i | ||||
\(923\) | −23837.2 | − | 41287.2i | −0.850066 | − | 1.47236i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 277.056 | − | 479.876i | 0.00984817 | − | 0.0170575i | ||||
\(926\) | −24057.3 | −0.853750 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −507.534 | −0.0179533 | ||||||||
\(929\) | −23098.8 | + | 40008.3i | −0.815766 | + | 1.41295i | 0.0930102 | + | 0.995665i | \(0.470351\pi\) |
−0.908776 | + | 0.417283i | \(0.862982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10049.8 | + | 17406.7i | 0.353778 | + | 0.612762i | ||||
\(932\) | −1788.74 | − | 3098.20i | −0.0628672 | − | 0.108889i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17702.6 | + | 30661.7i | −0.620177 | + | 1.07418i | ||||
\(935\) | 17343.4 | 0.606621 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37004.7 | 1.29017 | 0.645085 | − | 0.764111i | \(-0.276822\pi\) | ||||
0.645085 | + | 0.764111i | \(0.276822\pi\) | |||||||
\(938\) | −17991.6 | + | 31162.4i | −0.626277 | + | 1.08474i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1382.08 | − | 2393.83i | −0.0479558 | − | 0.0830618i | ||||
\(941\) | 21907.2 | + | 37944.4i | 0.758932 | + | 1.31451i | 0.943396 | + | 0.331669i | \(0.107612\pi\) |
−0.184464 | + | 0.982839i | \(0.559055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | −0.823768 | − | 0.566928i | \(-0.808132\pi\) |
0.902857 | + | 0.429940i | \(0.141465\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14416.7 | − | 24970.5i | −0.493136 | − | 0.854136i | ||||
\(950\) | 4931.24 | + | 8541.17i | 0.168411 | + | 0.291697i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15346.5 | + | 26580.8i | −0.522460 | + | 0.904927i | ||||
\(953\) | −4281.80 | −0.145542 | −0.0727708 | − | 0.997349i | \(-0.523184\pi\) | ||||
−0.0727708 | + | 0.997349i | \(0.523184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11741.8 | 0.397859 | ||||||||
\(956\) | −1070.52 | + | 1854.19i | −0.0362165 | + | 0.0627288i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5425.05 | −0.181254 | ||||||||
\(965\) | 585.424 | − | 1013.98i | 0.0195290 | − | 0.0338252i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18114.9 | + | 31375.9i | 0.602416 | + | 1.04341i | 0.992454 | + | 0.122616i | \(0.0391284\pi\) |
−0.390038 | + | 0.920799i | \(0.627538\pi\) | |||||||
\(968\) | 3277.10 | + | 5676.11i | 0.108812 | + | 0.188468i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12157.2 | − | 21056.8i | 0.402416 | − | 0.697005i | ||||
\(971\) | −844.928 | −0.0279249 | −0.0139624 | − | 0.999903i | \(-0.504445\pi\) | ||||
−0.0139624 | + | 0.999903i | \(0.504445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −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 | 0.947523 | + | 0.319687i | \(0.103578\pi\) |
−0.196904 | + | 0.980423i | \(0.563089\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16402.2 | + | 28409.5i | −0.535463 | + | 0.927449i | ||||
\(980\) | −970.288 | −0.0316273 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6048.05 | 0.196539 | ||||||||
\(983\) | −20101.0 | + | 34815.9i | −0.652210 | + | 1.12966i | 0.330376 | + | 0.943849i | \(0.392824\pi\) |
−0.982586 | + | 0.185811i | \(0.940509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1794.62 | − | 3108.37i | −0.0580520 | − | 0.100549i | ||||
\(986\) | 1498.59 | + | 2595.64i | 0.0484025 | + | 0.0838356i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17070.3 | − | 29566.6i | −0.544704 | − | 0.943455i | ||||
\(995\) | −4253.63 | − | 7367.50i | −0.135527 | − | 0.234739i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4566.04 | + | 7908.61i | −0.145043 | + | 0.251222i | −0.929389 | − | 0.369102i | \(-0.879665\pi\) |
0.784346 | + | 0.620324i | \(0.212999\pi\) | |||||||
\(998\) | −7342.47 | −0.232888 | ||||||||
\(999\) | 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 | 135.4.e.c.46.6 | 14 | ||
3.2 | odd | 2 | 45.4.e.c.16.2 | ✓ | 14 | ||
9.2 | odd | 6 | 405.4.a.m.1.6 | 7 | |||
9.4 | even | 3 | inner | 135.4.e.c.91.6 | 14 | ||
9.5 | odd | 6 | 45.4.e.c.31.2 | yes | 14 | ||
9.7 | even | 3 | 405.4.a.n.1.2 | 7 | |||
15.2 | even | 4 | 225.4.k.d.124.4 | 28 | |||
15.8 | even | 4 | 225.4.k.d.124.11 | 28 | |||
15.14 | odd | 2 | 225.4.e.d.151.6 | 14 | |||
45.14 | odd | 6 | 225.4.e.d.76.6 | 14 | |||
45.23 | even | 12 | 225.4.k.d.49.4 | 28 | |||
45.29 | odd | 6 | 2025.4.a.bb.1.2 | 7 | |||
45.32 | even | 12 | 225.4.k.d.49.11 | 28 | |||
45.34 | even | 6 | 2025.4.a.ba.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.2 | ✓ | 14 | 3.2 | odd | 2 | ||
45.4.e.c.31.2 | yes | 14 | 9.5 | odd | 6 | ||
135.4.e.c.46.6 | 14 | 1.1 | even | 1 | trivial | ||
135.4.e.c.91.6 | 14 | 9.4 | even | 3 | inner | ||
225.4.e.d.76.6 | 14 | 45.14 | odd | 6 | |||
225.4.e.d.151.6 | 14 | 15.14 | odd | 2 | |||
225.4.k.d.49.4 | 28 | 45.23 | even | 12 | |||
225.4.k.d.49.11 | 28 | 45.32 | even | 12 | |||
225.4.k.d.124.4 | 28 | 15.2 | even | 4 | |||
225.4.k.d.124.11 | 28 | 15.8 | even | 4 | |||
405.4.a.m.1.6 | 7 | 9.2 | odd | 6 | |||
405.4.a.n.1.2 | 7 | 9.7 | even | 3 | |||
2025.4.a.ba.1.6 | 7 | 45.34 | even | 6 | |||
2025.4.a.bb.1.2 | 7 | 45.29 | odd | 6 |