Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 27x^{6} + 10x^{5} + 446x^{4} + 62x^{3} + 3061x^{2} + 2142x + 14161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.4 | ||
Root | \(1.44795 + 2.50793i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.373 |
Dual form | 588.4.i.k.361.4 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.32734 | − | 14.4234i | 0.744820 | − | 1.29007i | −0.205459 | − | 0.978666i | \(-0.565869\pi\) |
0.950279 | − | 0.311401i | \(-0.100798\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 35.8800 | + | 62.1460i | 0.983475 | + | 1.70343i | 0.648526 | + | 0.761192i | \(0.275386\pi\) |
0.334949 | + | 0.942236i | \(0.391281\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −65.3878 | −1.39502 | −0.697512 | − | 0.716573i | \(-0.745709\pi\) | ||||
−0.697512 | + | 0.716573i | \(0.745709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −49.9641 | −0.860044 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −45.2158 | − | 78.3160i | −0.645085 | − | 1.11732i | −0.984282 | − | 0.176604i | \(-0.943489\pi\) |
0.339197 | − | 0.940715i | \(-0.389845\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −81.9092 | + | 141.871i | −0.989014 | + | 1.71302i | −0.366488 | + | 0.930423i | \(0.619440\pi\) |
−0.622526 | + | 0.782599i | \(0.713893\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.6144 | + | 68.6142i | −0.359138 | + | 0.622045i | −0.987817 | − | 0.155619i | \(-0.950263\pi\) |
0.628679 | + | 0.777665i | \(0.283596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −76.1893 | − | 131.964i | −0.609514 | − | 1.05571i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −43.2995 | −0.277259 | −0.138630 | − | 0.990344i | \(-0.544270\pi\) | ||||
−0.138630 | + | 0.990344i | \(0.544270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −67.8179 | − | 117.464i | −0.392918 | − | 0.680554i | 0.599915 | − | 0.800064i | \(-0.295201\pi\) |
−0.992833 | + | 0.119510i | \(0.961868\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 107.640 | − | 186.438i | 0.567810 | − | 0.983475i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −135.370 | + | 234.468i | −0.601479 | + | 1.04179i | 0.391118 | + | 0.920340i | \(0.372088\pi\) |
−0.992597 | + | 0.121452i | \(0.961245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 98.0817 | + | 169.882i | 0.402709 | + | 0.697512i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 152.241 | 0.579902 | 0.289951 | − | 0.957041i | \(-0.406361\pi\) | ||||
0.289951 | + | 0.957041i | \(0.406361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −177.641 | −0.630001 | −0.315001 | − | 0.949091i | \(-0.602005\pi\) | ||||
−0.315001 | + | 0.949091i | \(0.602005\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 74.9461 | + | 129.810i | 0.248273 | + | 0.430022i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22.8166 | − | 39.5194i | 0.0708114 | − | 0.122649i | −0.828446 | − | 0.560069i | \(-0.810774\pi\) |
0.899257 | + | 0.437420i | \(0.144108\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −135.647 | + | 234.948i | −0.372440 | + | 0.645085i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79.2188 | + | 137.211i | 0.205312 | + | 0.355611i | 0.950232 | − | 0.311543i | \(-0.100846\pi\) |
−0.744920 | + | 0.667154i | \(0.767512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1195.14 | 2.93005 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 491.455 | 1.14201 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 195.884 | + | 339.282i | 0.432237 | + | 0.748656i | 0.997066 | − | 0.0765519i | \(-0.0243911\pi\) |
−0.564829 | + | 0.825208i | \(0.691058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −275.647 | + | 477.435i | −0.578574 | + | 1.00212i | 0.417069 | + | 0.908875i | \(0.363057\pi\) |
−0.995643 | + | 0.0932450i | \(0.970276\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −544.506 | + | 943.113i | −1.03904 | + | 1.79967i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −229.315 | − | 397.185i | −0.418139 | − | 0.724237i | 0.577614 | − | 0.816310i | \(-0.303984\pi\) |
−0.995752 | + | 0.0920729i | \(0.970651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 237.687 | 0.414697 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −486.786 | −0.813674 | −0.406837 | − | 0.913501i | \(-0.633368\pi\) | ||||
−0.406837 | + | 0.913501i | \(0.633368\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −287.446 | − | 497.871i | −0.460863 | − | 0.798238i | 0.538141 | − | 0.842855i | \(-0.319127\pi\) |
−0.999004 | + | 0.0446164i | \(0.985793\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −228.568 | + | 395.891i | −0.351903 | + | 0.609514i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 334.160 | − | 578.782i | 0.475897 | − | 0.824279i | −0.523721 | − | 0.851890i | \(-0.675457\pi\) |
0.999619 | + | 0.0276111i | \(0.00878999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.2450 | 0.100831 | 0.0504155 | − | 0.998728i | \(-0.483945\pi\) | ||||
0.0504155 | + | 0.998728i | \(0.483945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1506.11 | −1.92189 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 64.9493 | + | 112.495i | 0.0800379 | + | 0.138630i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −683.401 | + | 1183.69i | −0.813937 | + | 1.40978i | 0.0961518 | + | 0.995367i | \(0.469347\pi\) |
−0.910089 | + | 0.414413i | \(0.863987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −203.454 | + | 352.392i | −0.226851 | + | 0.392918i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1364.17 | + | 2362.82i | 1.47327 | + | 2.55179i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 242.655 | 0.253999 | 0.127000 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127000 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −645.840 | −0.655650 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −347.371 | − | 601.665i | −0.342225 | − | 0.592751i | 0.642620 | − | 0.766185i | \(-0.277847\pi\) |
−0.984846 | + | 0.173433i | \(0.944514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 87.1089 | − | 150.877i | 0.0833310 | − | 0.144334i | −0.821348 | − | 0.570428i | \(-0.806777\pi\) |
0.904679 | + | 0.426094i | \(0.140111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −23.8025 | + | 41.2272i | −0.0215054 | + | 0.0372485i | −0.876578 | − | 0.481260i | \(-0.840179\pi\) |
0.855072 | + | 0.518509i | \(0.173513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 816.549 | + | 1414.30i | 0.717534 | + | 1.24281i | 0.961974 | + | 0.273141i | \(0.0880626\pi\) |
−0.244440 | + | 0.969664i | \(0.578604\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 812.221 | 0.694528 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1127.29 | −0.938464 | −0.469232 | − | 0.883075i | \(-0.655469\pi\) | ||||
−0.469232 | + | 0.883075i | \(0.655469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 659.766 | + | 1142.75i | 0.534987 | + | 0.926624i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 294.245 | − | 509.647i | 0.232504 | − | 0.402709i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1909.25 | + | 3306.91i | −1.43445 | + | 2.48453i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −228.361 | − | 395.533i | −0.167403 | − | 0.289951i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −455.982 | −0.326274 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2398.66 | 1.67596 | 0.837979 | − | 0.545702i | \(-0.183737\pi\) | ||||
0.837979 | + | 0.545702i | \(0.183737\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 266.462 | + | 461.526i | 0.181866 | + | 0.315001i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −774.482 | + | 1341.44i | −0.516541 | + | 0.894675i | 0.483275 | + | 0.875469i | \(0.339447\pi\) |
−0.999816 | + | 0.0192062i | \(0.993886\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 224.838 | − | 389.431i | 0.143341 | − | 0.248273i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −761.634 | − | 1319.19i | −0.474969 | − | 0.822671i | 0.524620 | − | 0.851337i | \(-0.324207\pi\) |
−0.999589 | + | 0.0286657i | \(0.990874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 551.445 | 0.336496 | 0.168248 | − | 0.985745i | \(-0.446189\pi\) | ||||
0.168248 | + | 0.985745i | \(0.446189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −136.899 | −0.0817660 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2346.11 | − | 4063.59i | −1.37197 | − | 2.37632i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −360.570 | + | 624.526i | −0.206508 | + | 0.357683i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1200.12 | − | 2078.67i | 0.659851 | − | 1.14290i | −0.320803 | − | 0.947146i | \(-0.603953\pi\) |
0.980654 | − | 0.195749i | \(-0.0627139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −310.780 | − | 538.287i | −0.167490 | − | 0.290100i | 0.770047 | − | 0.637987i | \(-0.220233\pi\) |
−0.937537 | + | 0.347887i | \(0.886899\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 813.884 | 0.430056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2258.97 | −1.17061 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1345.79 | + | 2330.97i | 0.684112 | + | 1.18492i | 0.973715 | + | 0.227770i | \(0.0731433\pi\) |
−0.289603 | + | 0.957147i | \(0.593523\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 237.657 | − | 411.633i | 0.118537 | − | 0.205312i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −528.653 | + | 915.654i | −0.254032 | + | 0.439997i | −0.964632 | − | 0.263599i | \(-0.915090\pi\) |
0.710600 | + | 0.703596i | \(0.248424\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1792.71 | − | 3105.06i | −0.845832 | − | 1.46502i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −243.840 | −0.112987 | −0.0564937 | − | 0.998403i | \(-0.517992\pi\) | ||||
−0.0564937 | + | 0.998403i | \(0.517992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2078.56 | 0.946090 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −737.183 | − | 1276.84i | −0.329671 | − | 0.571007i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 843.632 | − | 1461.21i | 0.370753 | − | 0.642162i | −0.618929 | − | 0.785447i | \(-0.712433\pi\) |
0.989682 | + | 0.143285i | \(0.0457665\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 587.653 | − | 1017.85i | 0.249552 | − | 0.432237i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 179.570 | + | 311.024i | 0.0749814 | + | 0.129872i | 0.901078 | − | 0.433657i | \(-0.142777\pi\) |
−0.826097 | + | 0.563528i | \(0.809444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2982.58 | 1.22483 | 0.612413 | − | 0.790538i | \(-0.290199\pi\) | ||||
0.612413 | + | 0.790538i | \(0.290199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1653.88 | 0.668080 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2254.55 | + | 3904.99i | 0.895988 | + | 1.55190i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3244.68 | − | 5619.96i | 1.26885 | − | 2.19771i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1745.39 | + | 3023.10i | −0.661213 | + | 1.14525i | 0.319084 | + | 0.947726i | \(0.396625\pi\) |
−0.980297 | + | 0.197528i | \(0.936709\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −802.114 | − | 1389.30i | −0.299158 | − | 0.518156i | 0.676786 | − | 0.736180i | \(-0.263372\pi\) |
−0.975943 | + | 0.218024i | \(0.930039\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3267.04 | 1.19978 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −455.935 | −0.164893 | −0.0824467 | − | 0.996595i | \(-0.526273\pi\) | ||||
−0.0824467 | + | 0.996595i | \(0.526273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1042.08 | − | 1804.94i | −0.371212 | − | 0.642958i | 0.618541 | − | 0.785753i | \(-0.287724\pi\) |
−0.989752 | + | 0.142795i | \(0.954391\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −687.945 | + | 1191.56i | −0.241412 | + | 0.418139i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1267.76 | − | 2195.83i | 0.431923 | − | 0.748113i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −356.530 | − | 617.528i | −0.119713 | − | 0.207348i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11755.6 | −3.89068 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2568.06 | 0.837880 | 0.418940 | − | 0.908014i | \(-0.362402\pi\) | ||||
0.418940 | + | 0.908014i | \(0.362402\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 730.178 | + | 1264.71i | 0.234887 | + | 0.406837i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1479.28 | + | 2562.19i | −0.469238 | + | 0.812743i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −862.338 | + | 1493.61i | −0.266079 | + | 0.460863i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2956.56 | + | 5120.91i | 0.899908 | + | 1.55869i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4659.55 | −1.39922 | −0.699612 | − | 0.714523i | \(-0.746644\pi\) | ||||
−0.699612 | + | 0.714523i | \(0.746644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1371.41 | 0.406343 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2414.39 | − | 4181.84i | −0.705940 | − | 1.22272i | −0.966351 | − | 0.257227i | \(-0.917191\pi\) |
0.260411 | − | 0.965498i | \(-0.416142\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1611.29 | − | 2790.84i | 0.464966 | − | 0.805345i | −0.534234 | − | 0.845337i | \(-0.679400\pi\) |
0.999200 | + | 0.0399917i | \(0.0127331\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2851.21 | − | 4938.44i | 0.801670 | − | 1.38853i | −0.116847 | − | 0.993150i | \(-0.537279\pi\) |
0.918517 | − | 0.395383i | \(-0.129388\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −380.003 | − | 658.184i | −0.105484 | − | 0.182703i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2004.96 | −0.549519 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1994.47 | 0.539796 | 0.269898 | − | 0.962889i | \(-0.413010\pi\) | ||||
0.269898 | + | 0.962889i | \(0.413010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 710.443 | + | 1230.52i | 0.189891 | + | 0.328900i | 0.945214 | − | 0.326452i | \(-0.105853\pi\) |
−0.755323 | + | 0.655353i | \(0.772520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5355.86 | − | 9276.62i | 1.37970 | − | 2.38971i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −114.367 | − | 198.090i | −0.0291074 | − | 0.0504155i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3855.44 | −0.969534 | −0.484767 | − | 0.874643i | \(-0.661096\pi\) | ||||
−0.484767 | + | 0.874643i | \(0.661096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5685.46 | −1.41281 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2259.16 | + | 3912.99i | 0.554801 | + | 0.960944i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2026.64 | + | 3510.24i | −0.491900 | + | 0.851996i | −0.999956 | − | 0.00932793i | \(-0.997031\pi\) |
0.508056 | + | 0.861324i | \(0.330364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 194.848 | − | 337.486i | 0.0462099 | − | 0.0800379i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 250.393 | + | 433.694i | 0.0587069 | + | 0.101683i | 0.893885 | − | 0.448296i | \(-0.147969\pi\) |
−0.835178 | + | 0.549979i | \(0.814636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2638.73 | 0.611683 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4100.41 | 0.939853 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1640.87 | − | 2842.07i | −0.371917 | − | 0.644179i | 0.617943 | − | 0.786223i | \(-0.287966\pi\) |
−0.989860 | + | 0.142043i | \(0.954633\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1662.18 | + | 2878.98i | −0.372584 | + | 0.645334i | −0.989962 | − | 0.141332i | \(-0.954861\pi\) |
0.617378 | + | 0.786666i | \(0.288195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5467.34 | − | 9469.71i | 1.19888 | − | 2.07653i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4309.87 | − | 7464.92i | −0.934856 | − | 1.61922i | −0.774890 | − | 0.632096i | \(-0.782195\pi\) |
−0.159966 | − | 0.987122i | \(-0.551139\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1220.72 | 0.261945 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7710.80 | −1.63697 | −0.818484 | − | 0.574529i | \(-0.805185\pi\) | ||||
−0.818484 | + | 0.574529i | \(0.805185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 69.6354 | + | 120.612i | 0.0146268 | + | 0.0253344i | 0.873246 | − | 0.487279i | \(-0.162011\pi\) |
−0.858619 | + | 0.512614i | \(0.828677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4092.52 | − | 7088.45i | 0.850596 | − | 1.47327i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1632.43 | + | 2827.46i | −0.332268 | + | 0.575506i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −363.983 | − | 630.437i | −0.0733232 | − | 0.127000i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4437.09 | −0.884702 | −0.442351 | − | 0.896842i | \(-0.645855\pi\) | ||||
−0.442351 | + | 0.896842i | \(0.645855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6524.79 | 1.28776 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 968.760 | + | 1677.94i | 0.189270 | + | 0.327825i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2590.30 | − | 4486.53i | 0.501006 | − | 0.867768i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1042.11 | + | 1804.99i | −0.197584 | + | 0.342225i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4590.82 | + | 7951.53i | 0.861867 | + | 1.49280i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −299.480 | −0.0556749 | −0.0278375 | − | 0.999612i | \(-0.508862\pi\) | ||||
−0.0278375 | + | 0.999612i | \(0.508862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −522.654 | −0.0962224 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −456.972 | − | 791.498i | −0.0833199 | − | 0.144314i | 0.821354 | − | 0.570419i | \(-0.193219\pi\) |
−0.904674 | + | 0.426104i | \(0.859886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1943.69 | + | 3366.57i | −0.351002 | + | 0.607954i | −0.986425 | − | 0.164210i | \(-0.947492\pi\) |
0.635423 | + | 0.772164i | \(0.280826\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1439.65 | + | 2493.55i | −0.255075 | + | 0.441803i | −0.964916 | − | 0.262559i | \(-0.915434\pi\) |
0.709841 | + | 0.704362i | \(0.248767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1553.59 | − | 2690.89i | −0.272678 | − | 0.472291i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 142.815 | 0.0248323 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14814.4 | 2.55199 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4981.85 | + | 8628.81i | 0.850287 | + | 1.47274i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2449.65 | − | 4242.91i | 0.414269 | − | 0.717534i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1405.39 | − | 2434.21i | 0.233376 | − | 0.404219i | −0.725424 | − | 0.688303i | \(-0.758356\pi\) |
0.958799 | + | 0.284084i | \(0.0916894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1218.33 | − | 2110.21i | −0.200493 | − | 0.347264i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7638.34 | −1.24575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2960.90 | 0.478607 | 0.239303 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239303 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1690.93 | + | 2928.78i | 0.270911 | + | 0.469232i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4866.61 | − | 8429.22i | 0.772850 | − | 1.33862i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1979.30 | − | 3428.24i | 0.308875 | − | 0.534987i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2142.26 | + | 3710.50i | 0.331419 | + | 0.574034i | 0.982790 | − | 0.184725i | \(-0.0591393\pi\) |
−0.651371 | + | 0.758759i | \(0.725806\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3295.36 | 0.505434 | 0.252717 | − | 0.967540i | \(-0.418676\pi\) | ||||
0.252717 | + | 0.967540i | \(0.418676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1765.47 | −0.268472 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5314.83 | + | 9205.56i | 0.801360 | + | 1.38800i | 0.918721 | + | 0.394906i | \(0.129223\pi\) |
−0.117362 | + | 0.993089i | \(0.537444\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4053.63 | + | 7021.09i | −0.606040 | + | 1.04969i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1592.51 | + | 2758.30i | −0.234121 | + | 0.405509i | −0.959017 | − | 0.283349i | \(-0.908554\pi\) |
0.724896 | + | 0.688858i | \(0.241888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9988.74 | − | 17301.0i | −1.45630 | − | 2.52238i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11455.5 | 1.65636 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9574.65 | −1.37304 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3801.52 | − | 6584.42i | −0.540702 | − | 0.936523i | −0.998864 | − | 0.0476544i | \(-0.984825\pi\) |
0.458162 | − | 0.888869i | \(-0.348508\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −685.083 | + | 1186.60i | −0.0966504 | + | 0.167403i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −755.978 | + | 1309.39i | −0.104941 | + | 0.181763i | −0.913714 | − | 0.406358i | \(-0.866799\pi\) |
0.808773 | + | 0.588121i | \(0.200132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 683.972 | + | 1184.67i | 0.0941871 | + | 0.163137i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2831.26 | 0.386783 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8848.36 | 1.19923 | 0.599617 | − | 0.800287i | \(-0.295320\pi\) | ||||
0.599617 | + | 0.800287i | \(0.295320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3597.99 | − | 6231.90i | −0.483807 | − | 0.837979i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2067.05 | + | 3580.24i | −0.275774 | + | 0.477654i | −0.970330 | − | 0.241784i | \(-0.922267\pi\) |
0.694556 | + | 0.719438i | \(0.255601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 799.386 | − | 1384.58i | 0.105000 | − | 0.181866i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3815.30 | − | 6608.30i | −0.497284 | − | 0.861322i | 0.502711 | − | 0.864455i | \(-0.332336\pi\) |
−0.999995 | + | 0.00313295i | \(0.999003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7164.79 | 0.926698 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4646.89 | 0.596450 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5565.32 | − | 9639.43i | −0.708916 | − | 1.22788i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5809.25 | − | 10061.9i | 0.734403 | − | 1.27202i | −0.220582 | − | 0.975368i | \(-0.570796\pi\) |
0.954985 | − | 0.296654i | \(-0.0958709\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1523.51 | + | 2638.79i | −0.189726 | + | 0.328616i | −0.945159 | − | 0.326611i | \(-0.894093\pi\) |
0.755433 | + | 0.655226i | \(0.227427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4434.46 | + | 7680.71i | 0.548130 | + | 0.949388i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1349.03 | −0.165516 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19428.3 | −2.36616 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5791.42 | − | 10031.0i | −0.700164 | − | 1.21272i | −0.968408 | − | 0.249369i | \(-0.919777\pi\) |
0.268244 | − | 0.963351i | \(-0.413557\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2284.90 | + | 3957.57i | −0.274224 | + | 0.474969i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 634.918 | − | 1099.71i | 0.0751010 | − | 0.130079i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −827.167 | − | 1432.70i | −0.0971380 | − | 0.168248i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1318.83 | −0.153768 | −0.0768841 | − | 0.997040i | \(-0.524497\pi\) | ||||
−0.0768841 | + | 0.997040i | \(0.524497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9733.56 | −1.12680 | −0.563402 | − | 0.826183i | \(-0.690508\pi\) | ||||
−0.563402 | + | 0.826183i | \(0.690508\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 205.349 | + | 355.675i | 0.0236038 | + | 0.0408830i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6889.92 | + | 11933.7i | −0.786377 | + | 1.36204i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7038.34 | + | 12190.8i | −0.792108 | + | 1.37197i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7214.47 | + | 12495.8i | 0.806284 | + | 1.39653i | 0.915421 | + | 0.402499i | \(0.131858\pi\) |
−0.109136 | + | 0.994027i | \(0.534808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16620.3 | −1.84463 | −0.922313 | − | 0.386444i | \(-0.873703\pi\) | ||||
−0.922313 | + | 0.386444i | \(0.873703\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2163.42 | 0.238455 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6489.57 | − | 11240.3i | −0.710385 | − | 1.23042i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 257.783 | − | 446.493i | 0.0280257 | − | 0.0485420i | −0.851672 | − | 0.524075i | \(-0.824411\pi\) |
0.879698 | + | 0.475533i | \(0.157745\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4488.05 | + | 7773.52i | −0.481340 | + | 0.833705i | −0.999771 | − | 0.0214146i | \(-0.993183\pi\) |
0.518431 | + | 0.855120i | \(0.326516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11381.8 | + | 19713.9i | 1.21247 | + | 2.10007i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7200.73 | −0.761930 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2106.83 | 0.221442 | 0.110721 | − | 0.993852i | \(-0.464684\pi\) | ||||
0.110721 | + | 0.993852i | \(0.464684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5462.39 | + | 9461.14i | 0.570319 | + | 0.987822i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −932.340 | + | 1614.86i | −0.0967001 | + | 0.167490i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7863.08 | + | 13619.3i | −0.804857 | + | 1.39405i | 0.111531 | + | 0.993761i | \(0.464425\pi\) |
−0.916388 | + | 0.400292i | \(0.868909\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1220.83 | − | 2114.53i | −0.124147 | − | 0.215028i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7921.16 | −0.800272 | −0.400136 | − | 0.916456i | \(-0.631037\pi\) | ||||
−0.400136 | + | 0.916456i | \(0.631037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5821.20 | −0.584306 | −0.292153 | − | 0.956372i | \(-0.594372\pi\) | ||||
−0.292153 | + | 0.956372i | \(0.594372\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3388.46 | + | 5868.98i | 0.337927 | + | 0.585306i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5893.94 | + | 10208.6i | −0.584024 | + | 1.01156i | 0.410973 | + | 0.911648i | \(0.365189\pi\) |
−0.994996 | + | 0.0999112i | \(0.968144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4037.36 | − | 6992.92i | 0.394972 | − | 0.684112i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6373.77 | − | 11039.7i | −0.619590 | − | 1.07316i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24962.4 | 2.41127 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1425.94 | −0.136875 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2657.21 | + | 4602.43i | 0.253468 | + | 0.439020i | 0.964478 | − | 0.264162i | \(-0.0850954\pi\) |
−0.711010 | + | 0.703182i | \(0.751762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8851.56 | − | 15331.3i | 0.839078 | − | 1.45332i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2020.67 | − | 3499.91i | 0.189184 | − | 0.327676i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9331.34 | + | 16162.4i | 0.868261 | + | 1.50387i | 0.863772 | + | 0.503883i | \(0.168096\pi\) |
0.00448933 | + | 0.999990i | \(0.498571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3171.92 | 0.293331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13519.1 | 1.24259 | 0.621293 | − | 0.783578i | \(-0.286608\pi\) | ||||
0.621293 | + | 0.783578i | \(0.286608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1957.82 | + | 3391.05i | 0.178856 | + | 0.309787i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5378.13 | + | 9315.19i | −0.488341 | + | 0.845832i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6916.17 | + | 11979.2i | −0.620462 | + | 1.07467i | 0.368938 | + | 0.929454i | \(0.379721\pi\) |
−0.989400 | + | 0.145217i | \(0.953612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 365.760 | + | 633.515i | 0.0326167 | + | 0.0564937i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13469.0 | 1.19394 | 0.596970 | − | 0.802264i | \(-0.296371\pi\) | ||||
0.596970 | + | 0.802264i | \(0.296371\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11570.7 | −1.01958 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3117.84 | − | 5400.26i | −0.273113 | − | 0.473045i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4387.62 | + | 7599.59i | −0.382079 | + | 0.661779i | −0.991359 | − | 0.131175i | \(-0.958125\pi\) |
0.609281 | + | 0.792955i | \(0.291458\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2211.55 | + | 3830.51i | −0.190336 | + | 0.329671i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1450.77 | − | 2512.81i | −0.124133 | − | 0.215005i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3274.63 | 0.278565 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5061.79 | −0.428108 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 830.382 | + | 1438.26i | 0.0698267 | + | 0.120943i | 0.898825 | − | 0.438308i | \(-0.144422\pi\) |
−0.828998 | + | 0.559251i | \(0.811089\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3162.41 | + | 5477.45i | −0.264402 | + | 0.457958i | −0.967407 | − | 0.253227i | \(-0.918508\pi\) |
0.703005 | + | 0.711185i | \(0.251841\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6132.88 | + | 10622.5i | −0.506931 | + | 0.878030i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2944.90 | + | 5100.71i | 0.242040 | + | 0.419225i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3525.92 | −0.288158 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9954.68 | −0.808977 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 396.424 | + | 686.626i | 0.0320353 | + | 0.0554868i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 538.709 | − | 933.071i | 0.0432905 | − | 0.0749814i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2233.94 | + | 3869.30i | −0.177532 | + | 0.307494i | −0.941034 | − | 0.338311i | \(-0.890145\pi\) |
0.763503 | + | 0.645804i | \(0.223478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4473.87 | − | 7748.97i | −0.353577 | − | 0.612413i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27198.7 | 2.13774 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10939.0 | −0.855063 | −0.427531 | − | 0.904000i | \(-0.640617\pi\) | ||||
−0.427531 | + | 0.904000i | \(0.640617\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2480.83 | − | 4296.92i | −0.192858 | − | 0.334040i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3546.63 | − | 6142.94i | 0.274213 | − | 0.474951i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6763.65 | − | 11715.0i | 0.517299 | − | 0.895988i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7162.57 | + | 12405.9i | 0.544862 | + | 0.943728i | 0.998616 | + | 0.0526011i | \(0.0167512\pi\) |
−0.453754 | + | 0.891127i | \(0.649915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11615.6 | 0.878867 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19468.1 | −1.46514 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10201.4 | − | 17669.4i | −0.763656 | − | 1.32269i | −0.940954 | − | 0.338533i | \(-0.890069\pi\) |
0.177299 | − | 0.984157i | \(-0.443264\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9387.32 | + | 16259.3i | −0.698987 | + | 1.21068i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3625.21 | − | 6279.05i | 0.267095 | − | 0.462622i | −0.701016 | − | 0.713146i | \(-0.747270\pi\) |
0.968110 | + | 0.250524i | \(0.0806030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12447.4 | − | 21559.5i | −0.912272 | − | 1.58010i | −0.810847 | − | 0.585258i | \(-0.800993\pi\) |
−0.101424 | − | 0.994843i | \(-0.532340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10472.3 | 0.763503 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12072.8 | 0.875599 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −681.723 | − | 1180.78i | −0.0491863 | − | 0.0851932i | 0.840384 | − | 0.541991i | \(-0.182329\pi\) |
−0.889570 | + | 0.456798i | \(0.848996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2406.34 | + | 4167.90i | −0.172719 | + | 0.299158i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5684.74 | + | 9846.26i | −0.403839 | + | 0.699469i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4900.56 | − | 8488.01i | −0.346347 | − | 0.599891i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23854.8 | 1.67733 | 0.838666 | − | 0.544647i | \(-0.183336\pi\) | ||||
0.838666 | + | 0.544647i | \(0.183336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22219.6 | 1.55440 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 683.902 | + | 1184.55i | 0.0476006 | + | 0.0824467i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1718.60 | + | 2976.71i | −0.119013 | + | 0.206136i | −0.919377 | − | 0.393378i | \(-0.871306\pi\) |
0.800364 | + | 0.599514i | \(0.204640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3126.24 | + | 5414.81i | −0.214319 | + | 0.371212i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8255.87 | − | 14299.6i | −0.563148 | − | 0.975401i | −0.997219 | − | 0.0745226i | \(-0.976257\pi\) |
0.434071 | − | 0.900879i | \(-0.357077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11148.3 | −0.756656 | −0.378328 | − | 0.925672i | \(-0.623501\pi\) | ||||
−0.378328 | + | 0.925672i | \(0.623501\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4127.67 | 0.278759 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31797.9 | + | 55075.6i | 2.13681 | + | 3.70106i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 195.791 | − | 339.121i | 0.0130921 | − | 0.0226763i | −0.859405 | − | 0.511295i | \(-0.829166\pi\) |
0.872497 | + | 0.488619i | \(0.162499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1491.92 | + | 2584.09i | −0.0987836 | + | 0.171098i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5870.25 | + | 10167.6i | 0.386782 | + | 0.669925i | 0.992015 | − | 0.126123i | \(-0.0402534\pi\) |
−0.605233 | + | 0.796048i | \(0.706920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7606.56 | −0.498742 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8818.95 | −0.575426 | −0.287713 | − | 0.957717i | \(-0.592895\pi\) | ||||
−0.287713 | + | 0.957717i | \(0.592895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7962.35 | + | 13791.2i | 0.517018 | + | 0.895501i | 0.999805 | + | 0.0197631i | \(0.00629120\pi\) |
−0.482787 | + | 0.875738i | \(0.660375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1069.59 | + | 1852.58i | −0.0691162 | + | 0.119713i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5726.55 | − | 9918.67i | 0.366499 | − | 0.634795i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17633.4 | + | 30542.0i | 1.12314 | + | 1.94534i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24483.5 | 1.55202 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29206.4 | 1.84261 | 0.921307 | − | 0.388836i | \(-0.127123\pi\) | ||||
0.921307 | + | 0.388836i | \(0.127123\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3852.09 | − | 6672.02i | −0.241875 | − | 0.418940i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19974.5 | − | 34596.8i | 1.24829 | − | 2.16210i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2190.54 | − | 3794.12i | 0.135612 | − | 0.234887i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2806.51 | − | 4861.01i | −0.172933 | − | 0.299530i | 0.766511 | − | 0.642232i | \(-0.221991\pi\) |
−0.939444 | + | 0.342702i | \(0.888658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18995.0 | −1.16499 | −0.582496 | − | 0.812834i | \(-0.697924\pi\) | ||||
−0.582496 | + | 0.812834i | \(0.697924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8875.68 | 0.541829 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11332.5 | − | 19628.5i | −0.688604 | − | 1.19270i | −0.972290 | − | 0.233779i | \(-0.924891\pi\) |
0.283686 | − | 0.958917i | \(-0.408443\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14056.7 | + | 24346.9i | −0.850188 | + | 1.47257i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13263.9 | + | 22973.7i | −0.794879 | + | 1.37677i | 0.128037 | + | 0.991769i | \(0.459132\pi\) |
−0.922916 | + | 0.385001i | \(0.874201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12898.8 | + | 22341.3i | 0.769460 | + | 1.33274i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5174.03 | 0.307242 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17114.8 | −1.01168 | −0.505839 | − | 0.862628i | \(-0.668817\pi\) | ||||
−0.505839 | + | 0.862628i | \(0.668817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 595.908 | + | 1032.14i | 0.0350653 | + | 0.0607348i | 0.883025 | − | 0.469325i | \(-0.155503\pi\) |
−0.847960 | + | 0.530060i | \(0.822169\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8869.68 | − | 15362.7i | 0.519562 | − | 0.899908i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1715.29 | − | 2970.96i | 0.0995744 | − | 0.172468i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6989.33 | + | 12105.9i | 0.403921 | + | 0.699612i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39560.9 | −2.27605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9415.20 | −0.539271 | −0.269636 | − | 0.962962i | \(-0.586903\pi\) | ||||
−0.269636 | + | 0.962962i | \(0.586903\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2057.11 | − | 3563.02i | −0.117301 | − | 0.203171i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3958.56 | + | 6856.43i | −0.224727 | + | 0.389238i | −0.956237 | − | 0.292592i | \(-0.905482\pi\) |
0.731511 | + | 0.681830i | \(0.238816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7243.16 | + | 12545.5i | −0.407575 | + | 0.705940i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14617.2 | − | 25317.7i | −0.818904 | − | 1.41838i | −0.906490 | − | 0.422227i | \(-0.861249\pi\) |
0.0875859 | − | 0.996157i | \(-0.472085\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25369.6 | −1.41507 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9667.76 | −0.536897 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5179.94 | − | 8971.93i | −0.286415 | − | 0.496086i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 611.228 | − | 1058.68i | 0.0336501 | − | 0.0582836i | −0.848710 | − | 0.528859i | \(-0.822620\pi\) |
0.882360 | + | 0.470575i | \(0.155953\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4592.07 | − | 7953.70i | 0.250629 | − | 0.434102i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6883.68 | − | 11922.9i | −0.374086 | − | 0.647936i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17107.3 | −0.925688 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13054.6 | 0.703372 | 0.351686 | − | 0.936118i | \(-0.385608\pi\) | ||||
0.351686 | + | 0.936118i | \(0.385608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22176.1 | − | 38410.2i | −1.18974 | − | 2.06069i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1140.01 | + | 1974.55i | −0.0609010 | + | 0.105484i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9987.87 | − | 17299.5i | 0.529058 | − | 0.916356i | −0.470367 | − | 0.882471i | \(-0.655879\pi\) |
0.999426 | − | 0.0338854i | \(-0.0107881\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3007.44 | + | 5209.03i | 0.158632 | + | 0.274760i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10746.3 | 0.564447 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −78147.5 | −4.08749 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2991.70 | − | 5181.77i | −0.155826 | − | 0.269898i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3256.13 | + | 5639.78i | −0.168892 | + | 0.292529i | −0.938030 | − | 0.346553i | \(-0.887352\pi\) |
0.769139 | + | 0.639082i | \(0.220685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2131.33 | − | 3691.57i | 0.109633 | − | 0.189891i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3298.96 | + | 5713.97i | 0.168994 | + | 0.292705i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11437.1 | 0.583467 | 0.291733 | − | 0.956500i | \(-0.405768\pi\) | ||||
0.291733 | + | 0.956500i | \(0.405768\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8032.19 | + | 13912.2i | 0.406404 | + | 0.703913i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6138.02 | − | 10631.4i | 0.309295 | − | 0.535714i | −0.668914 | − | 0.743340i | \(-0.733240\pi\) |
0.978208 | + | 0.207626i | \(0.0665738\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16455.6 | − | 28502.0i | 0.822458 | − | 1.42454i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6046.91 | − | 10473.5i | −0.301000 | − | 0.521347i | 0.675363 | − | 0.737486i | \(-0.263987\pi\) |
−0.976363 | + | 0.216138i | \(0.930654\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32135.2 | −1.59314 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34331.6 | 1.69516 | 0.847580 | − | 0.530668i | \(-0.178059\pi\) | ||||
0.847580 | + | 0.530668i | \(0.178059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19987.6 | − | 34619.6i | −0.982940 | − | 1.70250i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −343.102 | + | 594.271i | −0.0168052 | + | 0.0291074i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7278.96 | − | 12607.5i | 0.353679 | − | 0.612590i | −0.633212 | − | 0.773979i | \(-0.718264\pi\) |
0.986891 | + | 0.161388i | \(0.0515971\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5783.16 | + | 10016.7i | 0.279880 | + | 0.484767i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10351.9 | −0.498998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27115.5 | 1.30189 | 0.650944 | − | 0.759126i | \(-0.274373\pi\) | ||||
0.650944 | + | 0.759126i | \(0.274373\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8528.19 | + | 14771.3i | 0.407844 | + | 0.706407i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5481.98 | − | 9495.06i | 0.261132 | − | 0.452294i | −0.705411 | − | 0.708799i | \(-0.749238\pi\) |
0.966543 | + | 0.256504i | \(0.0825708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6777.49 | − | 11739.0i | 0.320315 | − | 0.554801i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12808.4 | − | 22184.9i | −0.602981 | − | 1.04439i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7835.53 | −0.367434 | −0.183717 | − | 0.982979i | \(-0.558813\pi\) | ||||
−0.183717 | + | 0.982979i | \(0.558813\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12159.8 | 0.567997 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14383.9 | + | 24913.6i | 0.669278 | + | 1.15922i | 0.978106 | + | 0.208106i | \(0.0667298\pi\) |
−0.308828 | + | 0.951118i | \(0.599937\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10334.0 | + | 17899.0i | −0.478978 | + | 0.829614i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12469.9 | + | 21598.5i | −0.573531 | + | 0.993386i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17465.9 | − | 30251.8i | −0.800228 | − | 1.38603i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1169.09 | −0.0533586 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44827.3 | 2.03816 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1347.91 | + | 2334.65i | 0.0610520 | + | 0.105745i | 0.894936 | − | 0.446195i | \(-0.147221\pi\) |
−0.833884 | + | 0.551940i | \(0.813888\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 751.180 | − | 1301.08i | 0.0338944 | − | 0.0587069i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18024.0 | − | 31218.4i | 0.807125 | − | 1.39798i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3958.09 | − | 6855.62i | −0.176578 | − | 0.305841i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12592.1 | 0.559643 | 0.279822 | − | 0.960052i | \(-0.409725\pi\) | ||||
0.279822 | + | 0.960052i | \(0.409725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4126.67 | −0.182717 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6150.61 | − | 10653.2i | −0.271312 | − | 0.469927i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20627.1 | − | 35727.2i | 0.906495 | − | 1.57009i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4922.62 | + | 8526.22i | −0.214726 | + | 0.371917i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3899.74 | + | 6754.56i | 0.169478 | + | 0.293545i | 0.938236 | − | 0.345995i | \(-0.112458\pi\) |
−0.768758 | + | 0.639539i | \(0.779125\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19323.5 | −0.836669 | −0.418335 | − | 0.908293i | \(-0.637386\pi\) | ||||
−0.418335 | + | 0.908293i | \(0.637386\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9973.08 | 0.430223 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8804.55 | + | 15249.9i | 0.378417 | + | 0.655438i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14550.5 | − | 25202.1i | 0.623080 | − | 1.07921i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −542.649 | + | 939.896i | −0.0230677 | + | 0.0399545i | −0.877329 | − | 0.479890i | \(-0.840677\pi\) |
0.854261 | + | 0.519844i | \(0.174010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12175.4 | + | 21088.4i | 0.515683 | + | 0.893190i | 0.999834 | + | 0.0182053i | \(0.00579524\pi\) |
−0.484151 | + | 0.874985i | \(0.660871\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32804.1 | −1.38435 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31664.9 | 1.33143 | 0.665716 | − | 0.746205i | \(-0.268126\pi\) | ||||
0.665716 | + | 0.746205i | \(0.268126\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1709.01 | + | 2960.09i | 0.0716000 | + | 0.124015i | 0.899603 | − | 0.436709i | \(-0.143856\pi\) |
−0.828003 | + | 0.560724i | \(0.810523\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12929.6 | + | 22394.8i | −0.539740 | + | 0.934856i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2030.54 | + | 3517.00i | −0.0841554 | + | 0.145761i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1831.08 | − | 3171.53i | −0.0756171 | − | 0.130973i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9114.25 | 0.375040 | 0.187520 | − | 0.982261i | \(-0.439955\pi\) | ||||
0.187520 | + | 0.982261i | \(0.439955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22514.2 | −0.923127 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11566.2 | + | 20033.3i | 0.472552 | + | 0.818484i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17308.9 | − | 29979.9i | 0.704667 | − | 1.22052i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 208.906 | − | 361.836i | 0.00844481 | − | 0.0146268i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10725.2 | − | 18576.6i | −0.432028 | − | 0.748295i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36229.5 | −1.45425 | −0.727124 | − | 0.686506i | \(-0.759143\pi\) | ||||
−0.727124 | + | 0.686506i | \(0.759143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24555.1 | −0.982183 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4322.59 | − | 7486.95i | −0.172295 | − | 0.298424i | 0.766927 | − | 0.641735i | \(-0.221785\pi\) |
−0.939222 | + | 0.343311i | \(0.888452\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4106.29 | − | 7112.31i | 0.163102 | − | 0.282501i | −0.772877 | − | 0.634555i | \(-0.781183\pi\) |
0.935980 | + | 0.352054i | \(0.114517\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1305.80 | − | 2261.72i | 0.0515065 | − | 0.0892119i | −0.839123 | − | 0.543942i | \(-0.816931\pi\) |
0.890629 | + | 0.454730i | \(0.150264\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14050.4 | − | 24336.1i | −0.552288 | − | 0.956591i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9794.61 | 0.383670 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47958.6 | 1.87213 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14994.4 | + | 25971.1i | 0.583313 | + | 1.01033i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1091.95 | + | 1891.31i | −0.0423332 | + | 0.0733232i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3223.29 | − | 5582.90i | 0.124108 | − | 0.214961i | −0.797276 | − | 0.603615i | \(-0.793726\pi\) |
0.921384 | + | 0.388654i | \(0.127060\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6655.64 | + | 11527.9i | 0.255392 | + | 0.442351i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37166.3 | 1.42130 | 0.710649 | − | 0.703547i | \(-0.248401\pi\) | ||||
0.710649 | + | 0.703547i | \(0.248401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24377.3 | 0.929060 | 0.464530 | − | 0.885557i | \(-0.346223\pi\) | ||||
0.464530 | + | 0.885557i | \(0.346223\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9787.18 | − | 16951.9i | −0.371743 | − | 0.643878i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18172.2 | − | 31475.2i | 0.687896 | − | 1.19147i | −0.284621 | − | 0.958640i | \(-0.591868\pi\) |
0.972517 | − | 0.232831i | \(-0.0747989\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2906.28 | − | 5033.82i | 0.109275 | − | 0.189270i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3737.77 | + | 6474.01i | 0.140067 | + | 0.242603i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5981.35 | 0.223391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15541.8 | −0.578512 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2936.48 | + | 5086.14i | 0.108940 | + | 0.188690i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7163.88 | − | 12408.2i | 0.264887 | − | 0.458798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24837.0 | − | 43018.9i | 0.912275 | − | 1.58011i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −163.437 | − | 283.082i | −0.00598329 | − | 0.0103634i | 0.863018 | − | 0.505173i | \(-0.168571\pi\) |
−0.869002 | + | 0.494809i | \(0.835238\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6252.68 | 0.228150 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38230.7 | −1.39038 | −0.695191 | − | 0.718825i | \(-0.744680\pi\) | ||||
−0.695191 | + | 0.718825i | \(0.744680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2735.67 | + | 4738.32i | 0.0991648 | + | 0.171758i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13772.5 | − | 23854.6i | 0.497599 | − | 0.861867i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10024.7 | − | 17363.2i | 0.359829 | − | 0.623243i | −0.628103 | − | 0.778130i | \(-0.716168\pi\) |
0.987932 | + | 0.154888i | \(0.0495016\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 449.219 | + | 778.071i | 0.0160720 | + | 0.0278375i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31829.8 | 1.13509 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41255.0 | 1.46644 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 783.980 | + | 1357.89i | 0.0277770 | + | 0.0481112i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21670.7 | + | 37534.8i | −0.765332 | + | 1.32559i | 0.174738 | + | 0.984615i | \(0.444092\pi\) |
−0.940071 | + | 0.340980i | \(0.889241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1370.92 | + | 2374.49i | −0.0481048 | + | 0.0833199i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −54039.2 | − | 93598.6i | −1.89013 | − | 3.27380i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17530.0 | 0.611185 | 0.305592 | − | 0.952162i | \(-0.401146\pi\) | ||||
0.305592 | + | 0.952162i | \(0.401146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11662.1 | 0.405303 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16312.5 | + | 28254.1i | 0.565115 | + | 0.978807i | 0.997039 | + | 0.0768974i | \(0.0245014\pi\) |
−0.431924 | + | 0.901910i | \(0.642165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6030.93 | + | 10445.9i | −0.208265 | + | 0.360726i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9697.09 | − | 16795.8i | 0.332749 | − | 0.576338i | −0.650301 | − | 0.759677i | \(-0.725357\pi\) |
0.983050 | + | 0.183339i | \(0.0586906\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18795.5 | + | 32554.7i | 0.642915 | + | 1.11356i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8637.91 | 0.294536 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49618.5 | −1.68657 | −0.843285 | − | 0.537467i | \(-0.819381\pi\) | ||||
−0.843285 | + | 0.537467i | \(0.819381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29068.9 | + | 50348.7i | 0.984970 | + | 1.70602i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4660.76 | + | 8072.67i | −0.157430 | + | 0.272678i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5696.96 | − | 9867.43i | 0.191231 | − | 0.331222i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −214.223 | − | 371.045i | −0.00716847 | − | 0.0124162i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26717.9 | −0.891274 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28432.8 | 0.945538 | 0.472769 | − | 0.881186i | \(-0.343254\pi\) | ||||
0.472769 | + | 0.881186i | \(0.343254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22221.5 | − | 38488.8i | −0.736696 | − | 1.27600i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21345.1 | + | 36970.8i | −0.705455 | + | 1.22188i | 0.261072 | + | 0.965319i | \(0.415924\pi\) |
−0.966527 | + | 0.256565i | \(0.917409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14945.5 | − | 25886.4i | 0.490913 | − | 0.850287i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11367.5 | − | 19689.1i | −0.372241 | − | 0.644740i | 0.617669 | − | 0.786438i | \(-0.288077\pi\) |
−0.989910 | + | 0.141698i | \(0.954744\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −98081.7 | −3.20195 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14697.9 | −0.478356 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2821.91 | − | 4887.70i | −0.0915616 | − | 0.158589i | 0.816607 | − | 0.577194i | \(-0.195853\pi\) |
−0.908168 | + | 0.418605i | \(0.862519\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3796.73 | + | 6576.12i | −0.122816 | + | 0.212724i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7037.16 | − | 12188.7i | 0.226257 | − | 0.391889i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27422.3 | + | 47496.8i | 0.879009 | + | 1.52249i | 0.852430 | + | 0.522841i | \(0.175128\pi\) |
0.0265782 | + | 0.999647i | \(0.491539\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8432.36 | −0.269479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34711.0 | −1.10594 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22440.6 | − | 38868.2i | −0.712838 | − | 1.23467i | −0.963787 | − | 0.266672i | \(-0.914076\pi\) |
0.250949 | − | 0.968000i | \(-0.419257\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3655.00 | + | 6330.64i | −0.115755 | + | 0.200493i |
(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 | 588.4.i.k.373.4 | 8 | ||
3.2 | odd | 2 | 1764.4.k.bd.1549.1 | 8 | |||
7.2 | even | 3 | 588.4.a.k.1.1 | yes | 4 | ||
7.3 | odd | 6 | 588.4.i.l.361.1 | 8 | |||
7.4 | even | 3 | inner | 588.4.i.k.361.4 | 8 | ||
7.5 | odd | 6 | 588.4.a.j.1.4 | ✓ | 4 | ||
7.6 | odd | 2 | 588.4.i.l.373.1 | 8 | |||
21.2 | odd | 6 | 1764.4.a.ba.1.4 | 4 | |||
21.5 | even | 6 | 1764.4.a.bc.1.1 | 4 | |||
21.11 | odd | 6 | 1764.4.k.bd.361.1 | 8 | |||
21.17 | even | 6 | 1764.4.k.bb.361.4 | 8 | |||
21.20 | even | 2 | 1764.4.k.bb.1549.4 | 8 | |||
28.19 | even | 6 | 2352.4.a.cq.1.4 | 4 | |||
28.23 | odd | 6 | 2352.4.a.cl.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.j.1.4 | ✓ | 4 | 7.5 | odd | 6 | ||
588.4.a.k.1.1 | yes | 4 | 7.2 | even | 3 | ||
588.4.i.k.361.4 | 8 | 7.4 | even | 3 | inner | ||
588.4.i.k.373.4 | 8 | 1.1 | even | 1 | trivial | ||
588.4.i.l.361.1 | 8 | 7.3 | odd | 6 | |||
588.4.i.l.373.1 | 8 | 7.6 | odd | 2 | |||
1764.4.a.ba.1.4 | 4 | 21.2 | odd | 6 | |||
1764.4.a.bc.1.1 | 4 | 21.5 | even | 6 | |||
1764.4.k.bb.361.4 | 8 | 21.17 | even | 6 | |||
1764.4.k.bb.1549.4 | 8 | 21.20 | even | 2 | |||
1764.4.k.bd.361.1 | 8 | 21.11 | odd | 6 | |||
1764.4.k.bd.1549.1 | 8 | 3.2 | odd | 2 | |||
2352.4.a.cl.1.1 | 4 | 28.23 | odd | 6 | |||
2352.4.a.cq.1.4 | 4 | 28.19 | even | 6 |