Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [272,4,Mod(33,272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(272, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("272.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 272.b (of order \(2\), degree \(1\), 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: | \(16.0485195216\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 95x^{6} + 756x^{4} + 1780x^{2} + 1152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 136) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 33.4 | ||
Root | \(9.30031i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 272.33 |
Dual form | 272.4.b.f.33.5 |
$q$-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 \(\left(\mathbb{Z}/272\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(239\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.62097i | − | 0.504407i | −0.967674 | − | 0.252203i | \(-0.918845\pi\) | ||
0.967674 | − | 0.252203i | \(-0.0811552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 11.5318i | − | 1.03143i | −0.856759 | − | 0.515716i | \(-0.827526\pi\) | ||
0.856759 | − | 0.515716i | \(-0.172474\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 23.0485i | − | 1.24450i | −0.782817 | − | 0.622251i | \(-0.786218\pi\) | ||
0.782817 | − | 0.622251i | \(-0.213782\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 20.1305 | 0.745574 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.19452i | − | 0.0327419i | −0.999866 | − | 0.0163710i | \(-0.994789\pi\) | ||
0.999866 | − | 0.0163710i | \(-0.00521127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 58.3731 | 1.24537 | 0.622684 | − | 0.782474i | \(-0.286042\pi\) | ||||
0.622684 | + | 0.782474i | \(0.286042\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.2245 | −0.520262 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −54.8640 | + | 43.6227i | −0.782734 | + | 0.622357i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −138.971 | −1.67800 | −0.839001 | − | 0.544130i | \(-0.816860\pi\) | ||||
−0.839001 | + | 0.544130i | \(0.816860\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −60.4096 | −0.627736 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 180.911i | − | 1.64011i | −0.572284 | − | 0.820055i | \(-0.693943\pi\) | ||
0.572284 | − | 0.820055i | \(-0.306057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.98158 | −0.0638527 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 123.528i | − | 0.880479i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 115.027i | 0.736551i | 0.929717 | + | 0.368275i | \(0.120052\pi\) | ||||
−0.929717 | + | 0.368275i | \(0.879948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 210.726i | 1.22088i | 0.792061 | + | 0.610442i | \(0.209008\pi\) | ||||
−0.792061 | + | 0.610442i | \(0.790992\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.13080 | −0.0165152 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −265.790 | −1.28362 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 210.661i | − | 0.936010i | −0.883726 | − | 0.468005i | \(-0.844973\pi\) | ||
0.883726 | − | 0.468005i | \(-0.155027\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 152.994i | − | 0.628172i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 297.500i | − | 1.13321i | −0.823989 | − | 0.566605i | \(-0.808257\pi\) | ||
0.823989 | − | 0.566605i | \(-0.191743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −174.746 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 232.140i | − | 0.769009i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 199.717 | 0.619823 | 0.309911 | − | 0.950765i | \(-0.399701\pi\) | ||||
0.309911 | + | 0.950765i | \(0.399701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −188.234 | −0.548787 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 114.334 | + | 143.797i | 0.313921 | + | 0.394816i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −706.217 | −1.83031 | −0.915154 | − | 0.403105i | \(-0.867931\pi\) | ||||
−0.915154 | + | 0.403105i | \(0.867931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.7749 | −0.0337711 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 364.238i | 0.846396i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 182.746 | 0.403247 | 0.201623 | − | 0.979463i | \(-0.435378\pi\) | ||||
0.201623 | + | 0.979463i | \(0.435378\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 489.499i | 1.02744i | 0.857958 | + | 0.513720i | \(0.171733\pi\) | ||||
−0.857958 | + | 0.513720i | \(0.828267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 463.978i | − | 0.927869i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 673.144i | − | 1.28451i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 167.043 | 0.304590 | 0.152295 | − | 0.988335i | \(-0.451334\pi\) | ||||
0.152295 | + | 0.988335i | \(0.451334\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −474.163 | −0.827283 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 818.157i | 1.36757i | 0.729684 | + | 0.683784i | \(0.239667\pi\) | ||||
−0.729684 | + | 0.683784i | \(0.760333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1090.15i | − | 1.74784i | −0.486071 | − | 0.873919i | \(-0.661570\pi\) | ||
0.486071 | − | 0.873919i | \(-0.338430\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.9195i | 0.0322077i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27.5319 | −0.0407474 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 110.196i | 0.156937i | 0.996917 | + | 0.0784685i | \(0.0250030\pi\) | ||||
−0.996917 | + | 0.0784685i | \(0.974997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 219.760 | 0.301454 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −118.672 | −0.156939 | −0.0784696 | − | 0.996917i | \(-0.525003\pi\) | ||||
−0.0784696 | + | 0.996917i | \(0.525003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 503.047 | + | 632.679i | 0.641919 | + | 0.807337i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 301.483 | 0.371521 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 400.332 | 0.476799 | 0.238399 | − | 0.971167i | \(-0.423377\pi\) | ||||
0.238399 | + | 0.971167i | \(0.423377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1345.41i | − | 1.54986i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 552.306 | 0.615823 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1602.58i | 1.73075i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 924.543i | 0.967764i | 0.875133 | + | 0.483882i | \(0.160774\pi\) | ||||
−0.875133 | + | 0.483882i | \(0.839226\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 24.0463i | − | 0.0244115i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 223.816 | 0.220500 | 0.110250 | − | 0.993904i | \(-0.464835\pi\) | ||||
0.110250 | + | 0.993904i | \(0.464835\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1280.06 | 1.22454 | 0.612271 | − | 0.790648i | \(-0.290256\pi\) | ||||
0.612271 | + | 0.790648i | \(0.290256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 696.629i | 0.647467i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1099.03i | − | 0.992969i | −0.868046 | − | 0.496485i | \(-0.834624\pi\) | ||
0.868046 | − | 0.496485i | \(-0.165376\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 733.360i | − | 0.644433i | −0.946666 | − | 0.322216i | \(-0.895572\pi\) | ||
0.946666 | − | 0.322216i | \(-0.104428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −552.136 | −0.472130 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1637.39i | 1.36312i | 0.731761 | + | 0.681561i | \(0.238699\pi\) | ||||
−0.731761 | + | 0.681561i | \(0.761301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2086.22 | −1.69166 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1175.08 | 0.928513 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1005.44 | + | 1264.53i | 0.774525 | + | 0.974115i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1329.57 | 0.998928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −779.739 | −0.571599 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1349.43i | − | 0.965573i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1502.71 | 1.04995 | 0.524977 | − | 0.851117i | \(-0.324074\pi\) | ||||
0.524977 | + | 0.851117i | \(0.324074\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 458.006i | 0.312598i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 702.381i | − | 0.468453i | −0.972182 | − | 0.234226i | \(-0.924744\pi\) | ||
0.972182 | − | 0.234226i | \(-0.0752557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3203.07i | 2.08828i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1424.49 | −0.908155 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.9889 | 0.0118418 | 0.00592092 | − | 0.999982i | \(-0.498115\pi\) | ||||
0.00592092 | + | 0.999982i | \(0.498115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 276.969i | − | 0.169009i | −0.996423 | − | 0.0845043i | \(-0.973069\pi\) | ||
0.996423 | − | 0.0845043i | \(-0.0269307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 523.452i | − | 0.312643i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 69.7277i | − | 0.0407757i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1326.46 | 0.759702 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 493.357i | 0.276812i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128.491 | 0.0706468 | 0.0353234 | − | 0.999376i | \(-0.488754\pi\) | ||||
0.0353234 | + | 0.999376i | \(0.488754\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2097.44 | 1.13038 | 0.565190 | − | 0.824961i | \(-0.308803\pi\) | ||||
0.565190 | + | 0.824961i | \(0.308803\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1104.44 | + | 878.147i | −0.583586 | + | 0.464013i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2430.04 | 1.25926 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2911.59 | 1.48007 | 0.740033 | − | 0.672571i | \(-0.234810\pi\) | ||||
0.740033 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1850.98i | 0.923220i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4169.73 | −2.04112 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1574.26i | 0.756478i | 0.925708 | + | 0.378239i | \(0.123470\pi\) | ||||
−0.925708 | + | 0.378239i | \(0.876530\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 36.1037i | 0.0170344i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1290.10i | − | 0.597788i | −0.954286 | − | 0.298894i | \(-0.903382\pi\) | ||
0.954286 | − | 0.298894i | \(-0.0966177\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1210.41 | 0.550939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2797.55 | −1.25107 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2370.19i | − | 1.04163i | −0.853669 | − | 0.520816i | \(-0.825628\pi\) | ||
0.853669 | − | 0.520816i | \(-0.174372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 183.964i | 0.0794648i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 478.974i | − | 0.203400i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1719.87 | −0.718153 | −0.359077 | − | 0.933308i | \(-0.616908\pi\) | ||||
−0.359077 | + | 0.933308i | \(0.616908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 61.7101i | − | 0.0253418i | −0.999920 | − | 0.0126709i | \(-0.995967\pi\) | ||
0.999920 | − | 0.0126709i | \(-0.00403339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1282.96 | 0.518248 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2429.29 | −0.965431 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 52.1082 | + | 65.5361i | 0.0203771 | + | 0.0256282i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2847.13 | −1.09576 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2565.34 | 0.971839 | 0.485919 | − | 0.874004i | \(-0.338485\pi\) | ||||
0.485919 | + | 0.874004i | \(0.338485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1991.65i | − | 0.742810i | −0.928471 | − | 0.371405i | \(-0.878876\pi\) | ||
0.928471 | − | 0.371405i | \(-0.121124\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1764.29 | −0.647917 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3831.76i | − | 1.38579i | −0.721036 | − | 0.692897i | \(-0.756334\pi\) | ||
0.721036 | − | 0.692897i | \(-0.243666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2171.38i | 0.773492i | 0.922186 | + | 0.386746i | \(0.126401\pi\) | ||||
−0.922186 | + | 0.386746i | \(0.873599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 437.815i | − | 0.153637i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2651.20 | 0.916639 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3430.69 | −1.16883 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3641.83i | − | 1.22282i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 166.003i | 0.0549410i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2069.97i | − | 0.675369i | −0.941259 | − | 0.337685i | \(-0.890356\pi\) | ||
0.941259 | − | 0.337685i | \(-0.109644\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2144.37 | 0.689811 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2015.13i | 0.639214i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4856.91 | 1.51939 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2857.25 | −0.881622 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3202.58 | + | 2546.39i | −0.974791 | + | 0.775062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4297.20 | 1.29041 | 0.645206 | − | 0.764008i | \(-0.276771\pi\) | ||||
0.645206 | + | 0.764008i | \(0.276771\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −160.673 | −0.0476069 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 336.979i | − | 0.0985291i | −0.998786 | − | 0.0492646i | \(-0.984312\pi\) | ||
0.998786 | − | 0.0492646i | \(-0.0156877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3076.57 | −0.887798 | −0.443899 | − | 0.896077i | \(-0.646405\pi\) | ||||
−0.443899 | + | 0.896077i | \(0.646405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 72.1604i | 0.0205533i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6537.86i | − | 1.83824i | −0.393980 | − | 0.919119i | \(-0.628902\pi\) | ||
0.393980 | − | 0.919119i | \(-0.371098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2303.09i | − | 0.639305i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 288.821 | 0.0791601 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3432.31 | 0.928943 | 0.464472 | − | 0.885588i | \(-0.346244\pi\) | ||||
0.464472 | + | 0.885588i | \(0.346244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1312.48i | − | 0.350807i | −0.984497 | − | 0.175404i | \(-0.943877\pi\) | ||
0.984497 | − | 0.175404i | \(-0.0561230\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3911.24i | − | 1.03253i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2170.67i | 0.566037i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8112.14 | −2.08973 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 311.037i | 0.0791612i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6498.55 | −1.63420 | −0.817101 | − | 0.576494i | \(-0.804420\pi\) | ||||
−0.817101 | + | 0.576494i | \(0.804420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −216.102 | −0.0537004 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1658.24 | − | 1318.47i | 0.407226 | − | 0.323788i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4874.66 | −1.18316 | −0.591582 | − | 0.806245i | \(-0.701496\pi\) | ||||
−0.591582 | + | 0.806245i | \(0.701496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4855.41 | −1.16487 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2315.55i | 0.549153i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1482.50 | −0.347584 | −0.173792 | − | 0.984782i | \(-0.555602\pi\) | ||||
−0.173792 | + | 0.984782i | \(0.555602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8143.92i | 1.88784i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1049.26i | − | 0.240501i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5058.75i | − | 1.14661i | −0.819343 | − | 0.573304i | \(-0.805662\pi\) | ||
0.819343 | − | 0.573304i | \(-0.194338\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1133.70 | −0.254122 | −0.127061 | − | 0.991895i | \(-0.540554\pi\) | ||||
−0.127061 | + | 0.991895i | \(0.540554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3526.29 | −0.781761 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.53415i | 0.00209066i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3698.34i | 0.802208i | 0.916033 | + | 0.401104i | \(0.131373\pi\) | ||||
−0.916033 | + | 0.401104i | \(0.868627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4242.01i | 0.910260i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2190.08 | 0.464945 | 0.232472 | − | 0.972603i | \(-0.425318\pi\) | ||||
0.232472 | + | 0.972603i | \(0.425318\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8159.66i | 1.71393i | 0.515378 | + | 0.856963i | \(0.327652\pi\) | ||||
−0.515378 | + | 0.856963i | \(0.672348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4200.31 | 0.873000 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6856.92 | −1.41028 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1107.12 | − | 4786.63i | 0.225345 | − | 0.974279i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2423.20 | 0.488147 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4777.49 | 0.952574 | 0.476287 | − | 0.879290i | \(-0.341982\pi\) | ||||
0.476287 | + | 0.879290i | \(0.341982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2107.39i | − | 0.415922i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −147.556 | −0.0288286 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 10560.3i | − | 2.04254i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4027.65i | 0.771261i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 586.615i | − | 0.111222i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5644.78 | 1.05974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −531.103 | −0.0987351 | −0.0493675 | − | 0.998781i | \(-0.515721\pi\) | ||||
−0.0493675 | + | 0.998781i | \(0.515721\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3355.00i | − | 0.617667i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4767.26i | 0.869217i | 0.900619 | + | 0.434609i | \(0.143113\pi\) | ||||
−0.900619 | + | 0.434609i | \(0.856887\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8613.47i | 1.55547i | 0.628593 | + | 0.777735i | \(0.283631\pi\) | ||||
−0.628593 | + | 0.777735i | \(0.716369\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5350.48 | −0.957034 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2453.20i | 0.434654i | 0.976099 | + | 0.217327i | \(0.0697338\pi\) | ||||
−0.976099 | + | 0.217327i | \(0.930266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 137.402 | 0.0241161 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2880.54 | −0.500860 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7624.48 | − | 6062.27i | 1.31343 | − | 1.04432i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −465.909 | −0.0795200 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1922.12 | −0.325056 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 4603.17i | − | 0.771371i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11003.5 | 1.82721 | 0.913605 | − | 0.406604i | \(-0.133287\pi\) | ||||
0.913605 | + | 0.406604i | \(0.133287\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 4240.70i | − | 0.697865i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1926.30i | − | 0.314164i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3664.37i | − | 0.592318i | −0.955139 | − | 0.296159i | \(-0.904294\pi\) | ||
0.955139 | − | 0.296159i | \(-0.0957058\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4291.56 | 0.687568 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 251.716 | 0.0399741 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3567.12i | − | 0.561535i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5467.94i | 0.853286i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3173.37i | 0.490938i | 0.969404 | + | 0.245469i | \(0.0789419\pi\) | ||||
−0.969404 | + | 0.245469i | \(0.921058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2185.47 | −0.335202 | −0.167601 | − | 0.985855i | \(-0.553602\pi\) | ||||
−0.167601 | + | 0.985855i | \(0.553602\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 7210.70i | − | 1.09652i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1216.36 | 0.183400 | 0.0917002 | − | 0.995787i | \(-0.470770\pi\) | ||||
0.0917002 | + | 0.995787i | \(0.470770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9434.80 | 1.41055 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3314.31 | − | 2635.23i | 0.491350 | − | 0.390675i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7448.93 | 1.09510 | 0.547548 | − | 0.836774i | \(-0.315561\pi\) | ||||
0.547548 | + | 0.836774i | \(0.315561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12453.8 | 1.81569 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3484.78i | − | 0.503866i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12571.3 | −1.80278 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2374.59i | 0.337746i | 0.985638 | + | 0.168873i | \(0.0540128\pi\) | ||||
−0.985638 | + | 0.168873i | \(0.945987\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5988.81i | − | 0.844892i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16277.2i | 2.27782i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12231.7 | 1.69795 | 0.848974 | − | 0.528435i | \(-0.177221\pi\) | ||||
0.848974 | + | 0.528435i | \(0.177221\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3536.82 | −0.487041 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6714.48i | 0.917276i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14129.9i | 1.91505i | 0.288358 | + | 0.957523i | \(0.406891\pi\) | ||||
−0.288358 | + | 0.957523i | \(0.593109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3938.57i | − | 0.529604i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13306.4 | −1.77526 | −0.887631 | − | 0.460556i | \(-0.847650\pi\) | ||||
−0.887631 | + | 0.460556i | \(0.847650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 317.491i | 0.0420282i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3517.73 | −0.462058 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8007.84 | −1.04374 | −0.521868 | − | 0.853026i | \(-0.674765\pi\) | ||||
−0.521868 | + | 0.853026i | \(0.674765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7891.83 | + | 9925.50i | 1.02073 | + | 1.28377i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1840.92 | −0.236291 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1270.76 | 0.161870 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13185.2i | 1.66687i | 0.552619 | + | 0.833434i | \(0.313628\pi\) | ||||
−0.552619 | + | 0.833434i | \(0.686372\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8395.15 | 1.05334 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3205.81i | − | 0.399228i | −0.979875 | − | 0.199614i | \(-0.936031\pi\) | ||
0.979875 | − | 0.199614i | \(-0.0639688\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12300.7i | 1.52045i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 2534.22i | − | 0.310929i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −251.638 | −0.0306468 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15693.3 | −1.89727 | −0.948636 | − | 0.316369i | \(-0.897536\pi\) | ||||
−0.948636 | + | 0.316369i | \(0.897536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 49.7695i | − | 0.00597311i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4212.03i | − | 0.501842i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1368.50i | 0.161872i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −725.929 | −0.0852491 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6910.65i | − | 0.805745i | −0.915256 | − | 0.402873i | \(-0.868012\pi\) | ||
0.915256 | − | 0.402873i | \(-0.131988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9225.05 | 1.06794 | 0.533968 | − | 0.845505i | \(-0.320700\pi\) | ||||
0.533968 | + | 0.845505i | \(0.320700\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4020.40 | 0.462124 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 437.902 | − | 348.178i | 0.0499796 | − | 0.0397391i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11282.2 | 1.27865 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −182.755 | −0.0205675 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8822.74i | 0.986024i | 0.870022 | + | 0.493012i | \(0.164104\pi\) | ||||
−0.870022 | + | 0.493012i | \(0.835896\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3190.95 | −0.354151 | −0.177075 | − | 0.984197i | \(-0.556664\pi\) | ||||
−0.177075 | + | 0.984197i | \(0.556664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3476.63i | − | 0.383199i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25141.3i | 2.75211i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15069.5i | − | 1.63834i | −0.573553 | − | 0.819168i | \(-0.694435\pi\) | ||
0.573553 | − | 0.819168i | \(-0.305565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3789.24 | −0.409161 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3026.24 | 0.324562 | 0.162281 | − | 0.986745i | \(-0.448115\pi\) | ||||
0.162281 | + | 0.986745i | \(0.448115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 4616.53i | − | 0.491786i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 336.771i | − | 0.0356347i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4641.02i | 0.487802i | 0.969800 | + | 0.243901i | \(0.0784272\pi\) | ||||
−0.969800 | + | 0.243901i | \(0.921573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −355.369 | −0.0371035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 5497.34i | − | 0.570171i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15515.0 | −1.59858 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17393.2 | 1.78035 | 0.890174 | − | 0.455620i | \(-0.150582\pi\) | ||||
0.890174 | + | 0.455620i | \(0.150582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5388.62 | + | 6777.23i | 0.547972 | + | 0.689181i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2451.93 | 0.247718 | 0.123859 | − | 0.992300i | \(-0.460473\pi\) | ||||
0.123859 | + | 0.992300i | \(0.460473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14586.3 | 1.46411 | 0.732054 | − | 0.681246i | \(-0.238562\pi\) | ||||
0.732054 | + | 0.681246i | \(0.238562\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 6369.07i | − | 0.635179i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15195.6 | −1.50572 | −0.752859 | − | 0.658182i | \(-0.771326\pi\) | ||||
−0.752859 | + | 0.658182i | \(0.771326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3850.09i | − | 0.379063i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7631.21i | − | 0.746555i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 208.738i | 0.0202913i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1109.21 | 0.107145 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14216.5 | −1.36463 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 4422.10i | − | 0.421819i | −0.977506 | − | 0.210909i | \(-0.932358\pi\) | ||
0.977506 | − | 0.210909i | \(-0.0676425\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 12296.9i | − | 1.16568i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10928.8i | 1.02956i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10661.6 | 0.998183 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17772.7i | − | 1.65371i | −0.562414 | − | 0.826856i | \(-0.690127\pi\) | ||
0.562414 | − | 0.826856i | \(-0.309873\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4126.11 | 0.381573 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4845.34 | −0.445350 | −0.222675 | − | 0.974893i | \(-0.571479\pi\) | ||||
−0.222675 | + | 0.974893i | \(0.571479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5017.79 | − | 6310.84i | −0.458397 | − | 0.576523i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −277.296 | −0.0251788 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18857.3 | 1.70194 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1060.23i | − | 0.0951153i | −0.998868 | − | 0.0475576i | \(-0.984856\pi\) | ||
0.998868 | − | 0.0475576i | \(-0.0151438\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3381.31 | −0.301528 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2803.19i | 0.248485i | 0.992252 | + | 0.124243i | \(0.0396501\pi\) | ||||
−0.992252 | + | 0.124243i | \(0.960350\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2580.99i | − | 0.227431i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3172.46i | − | 0.277898i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1658.97 | 0.144465 | 0.0722323 | − | 0.997388i | \(-0.476988\pi\) | ||||
0.0722323 | + | 0.997388i | \(0.476988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25126.3 | −2.17519 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17166.7i | 1.47745i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 14761.3i | − | 1.26303i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 238.565i | − | 0.0202942i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6212.21 | −0.525406 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12553.6i | 1.05563i | 0.849359 | + | 0.527815i | \(0.176989\pi\) | ||||
−0.849359 | + | 0.527815i | \(0.823011\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12031.6 | 1.00593 | 0.502967 | − | 0.864306i | \(-0.332242\pi\) | ||||
0.502967 | + | 0.864306i | \(0.332242\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 482.164 | 0.0400826 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9192.42 | − | 11561.2i | −0.759826 | − | 0.955628i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20561.8 | −1.68996 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3678.78 | 0.300650 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 17366.0i | − | 1.41126i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12673.8 | −1.02418 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4507.75i | 0.362241i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 224.849i | 0.0179683i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10632.7i | 0.844984i | 0.906367 | + | 0.422492i | \(0.138845\pi\) | ||||
−0.906367 | + | 0.422492i | \(0.861155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −161.741 | −0.0127826 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8456.94 | −0.664689 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17370.0i | 1.35774i | 0.734257 | + | 0.678872i | \(0.237531\pi\) | ||||
−0.734257 | + | 0.678872i | \(0.762469\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9853.85i | 0.766033i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15985.4i | − | 1.23593i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2539.86 | 0.195309 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6367.10i | 0.486970i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1084.77 | 0.0825190 | 0.0412595 | − | 0.999148i | \(-0.486863\pi\) | ||||
0.0412595 | + | 0.999148i | \(0.486863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10200.5 | −0.771797 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 171.768 | − | 136.574i | 0.0129270 | − | 0.0102784i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5494.27 | 0.411289 | 0.205645 | − | 0.978627i | \(-0.434071\pi\) | ||||
0.205645 | + | 0.978627i | \(0.434071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18882.0 | 1.40597 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5065.14i | − | 0.375160i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11612.4 | −0.855569 | −0.427784 | − | 0.903881i | \(-0.640706\pi\) | ||||
−0.427784 | + | 0.903881i | \(0.640706\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3413.97i | 0.250210i | 0.992143 | + | 0.125105i | \(0.0399268\pi\) | ||||
−0.992143 | + | 0.125105i | \(0.960073\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6723.68i | − | 0.490202i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1443.96i | 0.104725i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1355.70 | 0.0978141 | 0.0489070 | − | 0.998803i | \(-0.484426\pi\) | ||||
0.0489070 | + | 0.998803i | \(0.484426\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5220.07 | −0.374678 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2735.22i | 0.195311i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 843.589i | 0.0599278i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 13550.7i | − | 0.957698i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25232.2 | −1.77418 | −0.887092 | − | 0.461593i | \(-0.847278\pi\) | ||||
−0.887092 | + | 0.461593i | \(0.847278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 29284.7i | − | 2.04865i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10042.9 | −0.699004 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14327.4 | −0.992171 | −0.496086 | − | 0.868274i | \(-0.665230\pi\) | ||||
−0.496086 | + | 0.868274i | \(0.665230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14582.3 | − | 11594.5i | 1.00473 | − | 0.798870i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5691.13 | 0.390155 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2523.52 | 0.172134 | 0.0860671 | − | 0.996289i | \(-0.472570\pi\) | ||||
0.0860671 | + | 0.996289i | \(0.472570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17286.6i | 1.17327i | 0.809853 | + | 0.586634i | \(0.199547\pi\) | ||||
−0.809853 | + | 0.586634i | \(0.800453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3362.66 | 0.227095 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 15332.3i | − | 1.03033i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6413.65i | 0.428867i | 0.976739 | + | 0.214433i | \(0.0687905\pi\) | ||||
−0.976739 | + | 0.214433i | \(0.931210\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 6948.73i | − | 0.462359i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11658.1 | 0.771907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 485.788 | 0.0320078 | 0.0160039 | − | 0.999872i | \(-0.494906\pi\) | ||||
0.0160039 | + | 0.999872i | \(0.494906\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8991.76i | 0.589566i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6830.32i | − | 0.445670i | −0.974856 | − | 0.222835i | \(-0.928469\pi\) | ||
0.974856 | − | 0.222835i | \(-0.0715311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10667.8i | − | 0.692689i | −0.938107 | − | 0.346344i | \(-0.887423\pi\) | ||
0.938107 | − | 0.346344i | \(-0.112577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22347.5 | −1.44408 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 9227.05i | − | 0.593377i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16559.0 | −1.05978 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 435.090 | 0.0277126 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9189.58 | + | 11557.7i | 0.582532 | + | 0.732647i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15251.2 | 0.962188 | 0.481094 | − | 0.876669i | \(-0.340240\pi\) | ||||
0.481094 | + | 0.876669i | \(0.340240\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5425.35 | −0.340661 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 17328.9i | − | 1.08296i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10987.8 | −0.683442 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16469.9i | 1.01962i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12000.9i | − | 0.739480i | −0.929135 | − | 0.369740i | \(-0.879447\pi\) | ||
0.929135 | − | 0.369740i | \(-0.120553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5642.30i | − | 0.346051i | −0.984917 | − | 0.173025i | \(-0.944646\pi\) | ||
0.984917 | − | 0.173025i | \(-0.0553543\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5281.62 | 0.322424 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7790.69 | −0.473391 | −0.236695 | − | 0.971584i | \(-0.576064\pi\) | ||||
−0.236695 | + | 0.971584i | \(0.576064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 218.294i | − | 0.0132031i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 12729.8i | − | 0.766393i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6755.02i | 0.404815i | 0.979301 | + | 0.202408i | \(0.0648766\pi\) | ||||
−0.979301 | + | 0.202408i | \(0.935123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8099.69 | −0.483177 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 21945.2i | − | 1.30314i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14303.3 | 0.845492 | 0.422746 | − | 0.906248i | \(-0.361066\pi\) | ||||
0.422746 | + | 0.906248i | \(0.361066\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26136.0 | −1.53793 | −0.768966 | − | 0.639289i | \(-0.779229\pi\) | ||||
−0.768966 | + | 0.639289i | \(0.779229\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6674.03 | + | 8393.88i | 0.390947 | + | 0.491691i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36937.0 | 2.15392 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20809.6 | 1.20802 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 11262.9i | − | 0.650893i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 584.715 | 0.0336404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19026.5i | 1.08977i | 0.838509 | + | 0.544887i | \(0.183428\pi\) | ||||
−0.838509 | + | 0.544887i | \(0.816572\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 985.948i | 0.0562210i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25683.6i | 1.45805i | 0.684486 | + | 0.729026i | \(0.260026\pi\) | ||||
−0.684486 | + | 0.729026i | \(0.739974\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21309.3 | 1.20439 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −883.214 | −0.0496988 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28196.4i | 1.57966i | 0.613327 | + | 0.789829i | \(0.289831\pi\) | ||||
−0.613327 | + | 0.789829i | \(0.710169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 218.976i | − | 0.0122141i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8063.62i | 0.447811i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41224.0 | −2.27941 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35037.4i | 1.92892i | 0.264221 | + | 0.964462i | \(0.414885\pi\) | ||||
−0.264221 | + | 0.964462i | \(0.585115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −554.230 | −0.0303802 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3193.94 | −0.174321 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12977.7 | + | 16322.0i | 0.705261 | + | 0.887002i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17135.6 | −0.927220 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3539.51 | −0.190707 | −0.0953535 | − | 0.995443i | \(-0.530398\pi\) | ||||
−0.0953535 | + | 0.995443i | \(0.530398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29275.6i | 1.57063i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6036.33 | −0.322470 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5158.62i | − | 0.274413i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7264.39i | − | 0.384795i | −0.981317 | − | 0.192398i | \(-0.938374\pi\) | ||
0.981317 | − | 0.192398i | \(-0.0616263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2218.30i | 0.117008i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38122.6 | 2.00239 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −804.084 | −0.0420574 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8995.99i | − | 0.468565i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 9704.92i | − | 0.503383i | −0.967807 | − | 0.251692i | \(-0.919013\pi\) | ||
0.967807 | − | 0.251692i | \(-0.0809869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 29503.4i | − | 1.52395i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3439.99 | −0.176949 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 918.097i | − | 0.0470307i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10937.3 | −0.557967 | −0.278983 | − | 0.960296i | \(-0.589997\pi\) | ||||
−0.278983 | + | 0.960296i | \(0.589997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4317.73 | −0.219364 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9587.29 | − | 7622.91i | 0.485087 | − | 0.385696i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14196.3 | 0.715351 | 0.357675 | − | 0.933846i | \(-0.383569\pi\) | ||||
0.357675 | + | 0.933846i | \(0.383569\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5689.27 | 0.285513 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 199.536i | − | 0.00997287i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8477.05 | −0.421966 | −0.210983 | − | 0.977490i | \(-0.567667\pi\) | ||||
−0.210983 | + | 0.977490i | \(0.567667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21261.7i | 1.05407i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5251.86i | − | 0.259316i | −0.991559 | − | 0.129658i | \(-0.958612\pi\) | ||
0.991559 | − | 0.129658i | \(-0.0413880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1481.72i | − | 0.0728674i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2388.93 | −0.117010 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25331.1 | −1.23575 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 16018.0i | − | 0.778302i | −0.921174 | − | 0.389151i | \(-0.872768\pi\) | ||
0.921174 | − | 0.389151i | \(-0.127232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17032.5i | 0.824303i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 24187.2i | − | 1.16591i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9344.23 | −0.448642 | −0.224321 | − | 0.974515i | \(-0.572016\pi\) | ||||
−0.224321 | + | 0.974515i | \(0.572016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 566.397i | 0.0270868i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35043.1 | 1.66927 | 0.834633 | − | 0.550807i | \(-0.185680\pi\) | ||||
0.834633 | + | 0.550807i | \(0.185680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16902.9 | −0.801998 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10126.6 | + | 12736.1i | 0.478598 | + | 0.601929i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10667.5 | 0.502190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6719.33 | −0.315091 | −0.157546 | − | 0.987512i | \(-0.550358\pi\) | ||||
−0.157546 | + | 0.987512i | \(0.550358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12776.4i | 0.596796i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18716.9 | 0.870892 | 0.435446 | − | 0.900215i | \(-0.356591\pi\) | ||||
0.435446 | + | 0.900215i | \(0.356591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1681.92i | − | 0.0779568i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12725.9i | 0.587567i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41343.7i | 1.90153i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 977.304 | 0.0447768 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14209.0 | 0.648518 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 33575.8i | − | 1.52659i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15916.1i | − | 0.720898i | −0.932779 | − | 0.360449i | \(-0.882623\pi\) | ||
0.932779 | − | 0.360449i | \(-0.117377\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3885.59i | 0.175324i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37739.4 | 1.69641 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28573.5i | 1.27954i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21345.0 | 0.952239 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39802.4 | 1.76898 | 0.884489 | − | 0.466562i | \(-0.154508\pi\) | ||||
0.884489 | + | 0.466562i | \(0.154508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10957.3 | + | 8712.18i | −0.485156 | + | 0.385751i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8058.88 | 0.355489 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1302.20 | −0.0572276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48084.3i | 2.10528i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13258.9 | −0.578357 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 12250.3i | − | 0.532384i | −0.963920 | − | 0.266192i | \(-0.914234\pi\) | ||
0.963920 | − | 0.266192i | \(-0.0857655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15936.1i | − | 0.690002i | −0.938602 | − | 0.345001i | \(-0.887879\pi\) | ||
0.938602 | − | 0.345001i | \(-0.112121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2971.39i | 0.128181i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18154.0 | 0.780256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24284.6 | 1.03992 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 27083.8i | − | 1.15554i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10389.6i | 0.441656i | 0.975313 | + | 0.220828i | \(0.0708759\pi\) | ||||
−0.975313 | + | 0.220828i | \(0.929124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1915.45i | − | 0.0811281i | −0.999177 | − | 0.0405640i | \(-0.987085\pi\) | ||
0.999177 | − | 0.0405640i | \(-0.0129155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.9888 | 0.00105454 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1406.72i | − | 0.0591492i | −0.999563 | − | 0.0295746i | \(-0.990585\pi\) | ||
0.999563 | − | 0.0295746i | \(-0.00941527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22131.8 | −0.927226 | −0.463613 | − | 0.886038i | \(-0.653447\pi\) | ||||
−0.463613 | + | 0.886038i | \(0.653447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9693.25 | 0.404639 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10327.3 | − | 8211.28i | 0.429554 | − | 0.341541i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14877.1 | −0.616578 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26030.5 | 1.07496 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5716.82i | − | 0.235240i | −0.993059 | − | 0.117620i | \(-0.962473\pi\) | ||
0.993059 | − | 0.117620i | \(-0.0375265\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11157.8 | 0.457493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 5740.16i | − | 0.234521i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 13958.2i | − | 0.568257i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30644.7i | − | 1.24317i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21386.3 | 0.864516 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38110.8 | −1.53516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26801.3i | 1.07580i | 0.843008 | + | 0.537900i | \(0.180782\pi\) | ||||
−0.843008 | + | 0.537900i | \(0.819218\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32260.6i | 1.29040i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 6701.95i | − | 0.267135i | −0.991040 | − | 0.133567i | \(-0.957357\pi\) | ||
0.991040 | − | 0.133567i | \(-0.0426432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33950.5 | −1.34852 | −0.674259 | − | 0.738495i | \(-0.735537\pi\) | ||||
−0.674259 | + | 0.738495i | \(0.735537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17971.8i | 0.711357i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43090.0 | 1.69965 | 0.849827 | − | 0.527062i | \(-0.176706\pi\) | ||||
0.849827 | + | 0.527062i | \(0.176706\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27332.5 | −1.07437 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12545.6 | − | 2901.73i | −0.491433 | − | 0.113665i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 131.631 | 0.00513842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9750.81 | 0.379327 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18611.5i | 0.721540i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31102.3 | −1.20166 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 38515.6i | − | 1.48299i | −0.670960 | − | 0.741493i | \(-0.734118\pi\) | ||
0.670960 | − | 0.741493i | \(-0.265882\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 12521.7i | − | 0.480485i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32178.8i | 1.23057i | 0.788305 | + | 0.615284i | \(0.210959\pi\) | ||||
−0.788305 | + | 0.615284i | \(0.789041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33578.7 | 1.27974 | 0.639871 | − | 0.768482i | \(-0.278988\pi\) | ||||
0.639871 | + | 0.768482i | \(0.278988\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5523.41 | −0.209794 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17336.8i | 0.656273i | 0.944630 | + | 0.328137i | \(0.106421\pi\) | ||||
−0.944630 | + | 0.328137i | \(0.893579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 34635.3i | − | 1.30667i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 262.507i | − | 0.00987018i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27754.7 | −1.04006 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19833.2i | 0.740726i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27678.4 | −1.03027 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24239.1 | −0.899244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38745.9 | − | 30807.1i | 1.43264 | − | 1.13910i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10556.4 | 0.389029 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −711.626 | −0.0261384 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2865.79i | 0.104914i | 0.998623 | + | 0.0524570i | \(0.0167052\pi\) | ||||
−0.998623 | + | 0.0524570i | \(0.983295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4505.52 | 0.164399 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23972.0i | 0.871819i | 0.899990 | + | 0.435910i | \(0.143573\pi\) | ||||
−0.899990 | + | 0.435910i | \(0.856427\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 141.756i | 0.00513849i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 14794.8i | − | 0.534538i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16188.8 | −0.582991 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49371.5 | −1.77216 | −0.886081 | − | 0.463530i | \(-0.846582\pi\) | ||||
−0.886081 | + | 0.463530i | \(0.846582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1392.01i | 0.0498026i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47758.3i | 1.70313i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1681.40i | 0.0597668i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25768.2 | 0.912986 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47434.7i | 1.67522i | 0.546266 | + | 0.837612i | \(0.316049\pi\) | ||||
−0.546266 | + | 0.837612i | \(0.683951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26159.0 | 0.920866 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12494.9 | 0.438439 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 755.747 | − | 600.899i | 0.0264338 | − | 0.0210176i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37330.2 | 1.30152 | 0.650760 | − | 0.759283i | \(-0.274450\pi\) | ||||
0.650760 | + | 0.759283i | \(0.274450\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22575.7 | 0.784589 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 32070.6i | − | 1.11102i | −0.831509 | − | 0.555511i | \(-0.812523\pi\) | ||
0.831509 | − | 0.555511i | \(-0.187477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −53820.9 | −1.85859 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32832.5i | 1.13020i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 23171.6i | − | 0.795118i | −0.917577 | − | 0.397559i | \(-0.869857\pi\) | ||
0.917577 | − | 0.397559i | \(-0.130143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 63635.3i | − | 2.17670i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6429.77 | 0.219242 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39914.2 | −1.35671 | −0.678357 | − | 0.734733i | \(-0.737307\pi\) | ||||
−0.678357 | + | 0.734733i | \(0.737307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 29582.8i | − | 1.00239i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 360.127i | − | 0.0121643i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 437.666i | − | 0.0147372i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14614.3 | −0.490560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 22124.1i | − | 0.740332i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22967.3 | −0.766158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40591.6 | 1.34988 | 0.674941 | − | 0.737871i | \(-0.264169\pi\) | ||||
0.674941 | + | 0.737871i | \(0.264169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15889.1 | − | 19983.6i | −0.526760 | − | 0.662503i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29860.5 | −0.986890 | −0.493445 | − | 0.869777i | \(-0.664263\pi\) | ||||
−0.493445 | + | 0.869777i | \(0.664263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6383.73 | −0.210332 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1221.14i | 0.0401104i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35041.0 | −1.14745 | −0.573726 | − | 0.819048i | \(-0.694502\pi\) | ||||
−0.573726 | + | 0.819048i | \(0.694502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 478.204i | − | 0.0156113i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14762.9i | − | 0.480472i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54091.0i | 1.75507i | 0.479513 | + | 0.877535i | \(0.340813\pi\) | ||||
−0.479513 | + | 0.877535i | \(0.659187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44187.0 | −1.42935 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12064.8 | −0.389085 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31613.5i | 1.01643i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15918.2i | − | 0.510251i | −0.966908 | − | 0.255126i | \(-0.917883\pi\) | ||
0.966908 | − | 0.255126i | \(-0.0821168\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 28839.9i | − | 0.921657i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25039.8 | 0.797805 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15294.7i | 0.485845i | 0.970046 | + | 0.242923i | \(0.0781061\pi\) | ||||
−0.970046 | + | 0.242923i | \(0.921894\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26022.4 | −0.824138 |
(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 | 272.4.b.f.33.4 | 8 | ||
4.3 | odd | 2 | 136.4.b.b.33.5 | yes | 8 | ||
12.11 | even | 2 | 1224.4.c.e.577.6 | 8 | |||
17.16 | even | 2 | inner | 272.4.b.f.33.5 | 8 | ||
68.47 | odd | 4 | 2312.4.a.k.1.4 | 8 | |||
68.55 | odd | 4 | 2312.4.a.k.1.5 | 8 | |||
68.67 | odd | 2 | 136.4.b.b.33.4 | ✓ | 8 | ||
204.203 | even | 2 | 1224.4.c.e.577.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.b.b.33.4 | ✓ | 8 | 68.67 | odd | 2 | ||
136.4.b.b.33.5 | yes | 8 | 4.3 | odd | 2 | ||
272.4.b.f.33.4 | 8 | 1.1 | even | 1 | trivial | ||
272.4.b.f.33.5 | 8 | 17.16 | even | 2 | inner | ||
1224.4.c.e.577.3 | 8 | 204.203 | even | 2 | |||
1224.4.c.e.577.6 | 8 | 12.11 | even | 2 | |||
2312.4.a.k.1.4 | 8 | 68.47 | odd | 4 | |||
2312.4.a.k.1.5 | 8 | 68.55 | odd | 4 |