Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(5,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1316x^{16} + 520390x^{12} + 64668772x^{8} + 2536036097x^{4} + 8509693504 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.5 | ||
Root | \(-0.980238 - 0.980238i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.8 |
Dual form | 39.4.f.b.5.5 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.980238 | + | 0.980238i | −0.346566 | + | 0.346566i | −0.858829 | − | 0.512263i | \(-0.828807\pi\) |
0.512263 | + | 0.858829i | \(0.328807\pi\) | |||||||
\(3\) | −2.50090 | − | 4.55472i | −0.481299 | − | 0.876556i | ||||
\(4\) | 6.07827i | 0.759783i | ||||||||
\(5\) | 12.5563 | − | 12.5563i | 1.12307 | − | 1.12307i | 0.131790 | − | 0.991278i | \(-0.457928\pi\) |
0.991278 | − | 0.131790i | \(-0.0420724\pi\) | |||||||
\(6\) | 6.91619 | + | 2.01323i | 0.470587 | + | 0.136983i | ||||
\(7\) | 21.4578 | − | 21.4578i | 1.15861 | − | 1.15861i | 0.173836 | − | 0.984775i | \(-0.444384\pi\) |
0.984775 | − | 0.173836i | \(-0.0556164\pi\) | |||||||
\(8\) | −13.8001 | − | 13.8001i | −0.609882 | − | 0.609882i | ||||
\(9\) | −14.4909 | + | 22.7818i | −0.536702 | + | 0.843772i | ||||
\(10\) | 24.6163i | 0.778435i | ||||||||
\(11\) | −8.34980 | − | 8.34980i | −0.228869 | − | 0.228869i | 0.583351 | − | 0.812220i | \(-0.301741\pi\) |
−0.812220 | + | 0.583351i | \(0.801741\pi\) | |||||||
\(12\) | 27.6848 | − | 15.2012i | 0.665993 | − | 0.365683i | ||||
\(13\) | 29.3793 | + | 36.5220i | 0.626796 | + | 0.779184i | ||||
\(14\) | 42.0674i | 0.803071i | ||||||||
\(15\) | −88.5924 | − | 25.7883i | −1.52496 | − | 0.443900i | ||||
\(16\) | −21.5715 | −0.337054 | ||||||||
\(17\) | −39.5799 | −0.564678 | −0.282339 | − | 0.959315i | \(-0.591110\pi\) | ||||
−0.282339 | + | 0.959315i | \(0.591110\pi\) | |||||||
\(18\) | −8.12705 | − | 36.5362i | −0.106420 | − | 0.478426i | ||||
\(19\) | 9.15970 | + | 9.15970i | 0.110599 | + | 0.110599i | 0.760241 | − | 0.649642i | \(-0.225081\pi\) |
−0.649642 | + | 0.760241i | \(0.725081\pi\) | |||||||
\(20\) | 76.3204 | + | 76.3204i | 0.853288 | + | 0.853288i | ||||
\(21\) | −151.398 | − | 44.0703i | −1.57323 | − | 0.457949i | ||||
\(22\) | 16.3696 | 0.158637 | ||||||||
\(23\) | 2.83931 | 0.0257408 | 0.0128704 | − | 0.999917i | \(-0.495903\pi\) | ||||
0.0128704 | + | 0.999917i | \(0.495903\pi\) | |||||||
\(24\) | −28.3428 | + | 97.3680i | −0.241060 | + | 0.828131i | ||||
\(25\) | − | 190.320i | − | 1.52256i | ||||||
\(26\) | −64.5989 | − | 7.00158i | −0.487265 | − | 0.0528124i | ||||
\(27\) | 140.005 | + | 9.02699i | 0.997928 | + | 0.0643424i | ||||
\(28\) | 130.426 | + | 130.426i | 0.880293 | + | 0.880293i | ||||
\(29\) | 175.398i | 1.12312i | 0.827435 | + | 0.561562i | \(0.189799\pi\) | ||||
−0.827435 | + | 0.561562i | \(0.810201\pi\) | |||||||
\(30\) | 112.120 | − | 61.5630i | 0.682342 | − | 0.374660i | ||||
\(31\) | 95.0010 | + | 95.0010i | 0.550409 | + | 0.550409i | 0.926559 | − | 0.376150i | \(-0.122752\pi\) |
−0.376150 | + | 0.926559i | \(0.622752\pi\) | |||||||
\(32\) | 131.546 | − | 131.546i | 0.726694 | − | 0.726694i | ||||
\(33\) | −17.1489 | + | 58.9130i | −0.0904621 | + | 0.310771i | ||||
\(34\) | 38.7977 | − | 38.7977i | 0.195699 | − | 0.195699i | ||||
\(35\) | − | 538.859i | − | 2.60240i | ||||||
\(36\) | −138.474 | − | 88.0799i | −0.641084 | − | 0.407777i | ||||
\(37\) | −92.4719 | + | 92.4719i | −0.410873 | + | 0.410873i | −0.882043 | − | 0.471170i | \(-0.843832\pi\) |
0.471170 | + | 0.882043i | \(0.343832\pi\) | |||||||
\(38\) | −17.9574 | −0.0766597 | ||||||||
\(39\) | 92.8728 | − | 225.152i | 0.381322 | − | 0.924442i | ||||
\(40\) | −346.554 | −1.36988 | ||||||||
\(41\) | −187.117 | + | 187.117i | −0.712749 | + | 0.712749i | −0.967110 | − | 0.254360i | \(-0.918135\pi\) |
0.254360 | + | 0.967110i | \(0.418135\pi\) | |||||||
\(42\) | 191.605 | − | 105.207i | 0.703937 | − | 0.386518i | ||||
\(43\) | 52.5720i | 0.186445i | 0.995645 | + | 0.0932227i | \(0.0297168\pi\) | ||||
−0.995645 | + | 0.0932227i | \(0.970283\pi\) | |||||||
\(44\) | 50.7523 | − | 50.7523i | 0.173891 | − | 0.173891i | ||||
\(45\) | 104.103 | + | 468.007i | 0.344861 | + | 1.55037i | ||||
\(46\) | −2.78320 | + | 2.78320i | −0.00892089 | + | 0.00892089i | ||||
\(47\) | 194.887 | + | 194.887i | 0.604835 | + | 0.604835i | 0.941592 | − | 0.336756i | \(-0.109330\pi\) |
−0.336756 | + | 0.941592i | \(0.609330\pi\) | |||||||
\(48\) | 53.9482 | + | 98.2520i | 0.162224 | + | 0.295447i | ||||
\(49\) | − | 577.872i | − | 1.68476i | ||||||
\(50\) | 186.559 | + | 186.559i | 0.527668 | + | 0.527668i | ||||
\(51\) | 98.9855 | + | 180.275i | 0.271779 | + | 0.494972i | ||||
\(52\) | −221.991 | + | 178.575i | −0.592011 | + | 0.476229i | ||||
\(53\) | 473.173i | 1.22633i | 0.789957 | + | 0.613163i | \(0.210103\pi\) | ||||
−0.789957 | + | 0.613163i | \(0.789897\pi\) | |||||||
\(54\) | −146.087 | + | 128.390i | −0.368147 | + | 0.323549i | ||||
\(55\) | −209.685 | −0.514071 | ||||||||
\(56\) | −592.237 | −1.41323 | ||||||||
\(57\) | 18.8123 | − | 64.6274i | 0.0437150 | − | 0.150177i | ||||
\(58\) | −171.932 | − | 171.932i | −0.389237 | − | 0.389237i | ||||
\(59\) | −395.766 | − | 395.766i | −0.873294 | − | 0.873294i | 0.119536 | − | 0.992830i | \(-0.461859\pi\) |
−0.992830 | + | 0.119536i | \(0.961859\pi\) | |||||||
\(60\) | 156.748 | − | 538.488i | 0.337268 | − | 1.15864i | ||||
\(61\) | 104.515 | 0.219374 | 0.109687 | − | 0.993966i | \(-0.465015\pi\) | ||||
0.109687 | + | 0.993966i | \(0.465015\pi\) | |||||||
\(62\) | −186.247 | −0.381506 | ||||||||
\(63\) | 177.904 | + | 799.791i | 0.355775 | + | 1.59943i | ||||
\(64\) | 85.3201i | 0.166641i | ||||||||
\(65\) | 827.475 | + | 89.6862i | 1.57901 | + | 0.171142i | ||||
\(66\) | −40.9388 | − | 74.5588i | −0.0763517 | − | 0.139054i | ||||
\(67\) | −473.452 | − | 473.452i | −0.863305 | − | 0.863305i | 0.128416 | − | 0.991720i | \(-0.459011\pi\) |
−0.991720 | + | 0.128416i | \(0.959011\pi\) | |||||||
\(68\) | − | 240.577i | − | 0.429033i | ||||||
\(69\) | −7.10085 | − | 12.9323i | −0.0123890 | − | 0.0225632i | ||||
\(70\) | 528.210 | + | 528.210i | 0.901903 | + | 0.901903i | ||||
\(71\) | 313.305 | − | 313.305i | 0.523697 | − | 0.523697i | −0.394989 | − | 0.918686i | \(-0.629252\pi\) |
0.918686 | + | 0.394989i | \(0.129252\pi\) | |||||||
\(72\) | 514.366 | − | 114.415i | 0.841926 | − | 0.187277i | ||||
\(73\) | −84.4987 | + | 84.4987i | −0.135477 | + | 0.135477i | −0.771593 | − | 0.636116i | \(-0.780540\pi\) |
0.636116 | + | 0.771593i | \(0.280540\pi\) | |||||||
\(74\) | − | 181.289i | − | 0.284789i | ||||||
\(75\) | −866.855 | + | 475.973i | −1.33461 | + | 0.732808i | ||||
\(76\) | −55.6751 | + | 55.6751i | −0.0840312 | + | 0.0840312i | ||||
\(77\) | −358.336 | −0.530340 | ||||||||
\(78\) | 129.666 | + | 311.740i | 0.188227 | + | 0.452534i | ||||
\(79\) | 651.078 | 0.927240 | 0.463620 | − | 0.886034i | \(-0.346550\pi\) | ||||
0.463620 | + | 0.886034i | \(0.346550\pi\) | |||||||
\(80\) | −270.857 | + | 270.857i | −0.378535 | + | 0.378535i | ||||
\(81\) | −309.025 | − | 660.261i | −0.423902 | − | 0.905708i | ||||
\(82\) | − | 366.838i | − | 0.494030i | ||||||
\(83\) | 311.890 | − | 311.890i | 0.412462 | − | 0.412462i | −0.470133 | − | 0.882595i | \(-0.655794\pi\) |
0.882595 | + | 0.470133i | \(0.155794\pi\) | |||||||
\(84\) | 267.871 | − | 920.238i | 0.347942 | − | 1.19531i | ||||
\(85\) | −496.976 | + | 496.976i | −0.634172 | + | 0.634172i | ||||
\(86\) | −51.5330 | − | 51.5330i | −0.0646157 | − | 0.0646157i | ||||
\(87\) | 798.889 | − | 438.654i | 0.984481 | − | 0.540559i | ||||
\(88\) | 230.455i | 0.279166i | ||||||||
\(89\) | 617.346 | + | 617.346i | 0.735264 | + | 0.735264i | 0.971658 | − | 0.236393i | \(-0.0759653\pi\) |
−0.236393 | + | 0.971658i | \(0.575965\pi\) | |||||||
\(90\) | −560.804 | − | 356.713i | −0.656822 | − | 0.417787i | ||||
\(91\) | 1414.10 | + | 153.267i | 1.62898 | + | 0.176558i | ||||
\(92\) | 17.2581i | 0.0195574i | ||||||||
\(93\) | 195.114 | − | 670.291i | 0.217553 | − | 0.747376i | ||||
\(94\) | −382.072 | −0.419231 | ||||||||
\(95\) | 230.023 | 0.248420 | ||||||||
\(96\) | −928.136 | − | 270.170i | −0.986745 | − | 0.287231i | ||||
\(97\) | 177.855 | + | 177.855i | 0.186169 | + | 0.186169i | 0.794038 | − | 0.607868i | \(-0.207975\pi\) |
−0.607868 | + | 0.794038i | \(0.707975\pi\) | |||||||
\(98\) | 566.452 | + | 566.452i | 0.583881 | + | 0.583881i | ||||
\(99\) | 311.220 | − | 69.2273i | 0.315948 | − | 0.0702788i | ||||
\(100\) | 1156.82 | 1.15682 | ||||||||
\(101\) | −1181.17 | −1.16368 | −0.581838 | − | 0.813305i | \(-0.697666\pi\) | ||||
−0.581838 | + | 0.813305i | \(0.697666\pi\) | |||||||
\(102\) | −273.742 | − | 79.6833i | −0.265730 | − | 0.0773512i | ||||
\(103\) | 227.818i | 0.217938i | 0.994045 | + | 0.108969i | \(0.0347549\pi\) | ||||
−0.994045 | + | 0.108969i | \(0.965245\pi\) | |||||||
\(104\) | 98.5702 | − | 909.441i | 0.0929385 | − | 0.857481i | ||||
\(105\) | −2454.35 | + | 1347.64i | −2.28115 | + | 1.25253i | ||||
\(106\) | −463.822 | − | 463.822i | −0.425003 | − | 0.425003i | ||||
\(107\) | 571.489i | 0.516336i | 0.966100 | + | 0.258168i | \(0.0831188\pi\) | ||||
−0.966100 | + | 0.258168i | \(0.916881\pi\) | |||||||
\(108\) | −54.8684 | + | 850.990i | −0.0488863 | + | 0.758209i | ||||
\(109\) | −29.9579 | − | 29.9579i | −0.0263252 | − | 0.0263252i | 0.693822 | − | 0.720147i | \(-0.255926\pi\) |
−0.720147 | + | 0.693822i | \(0.755926\pi\) | |||||||
\(110\) | 205.541 | − | 205.541i | 0.178160 | − | 0.178160i | ||||
\(111\) | 652.447 | + | 189.920i | 0.557906 | + | 0.162400i | ||||
\(112\) | −462.876 | + | 462.876i | −0.390515 | + | 0.390515i | ||||
\(113\) | − | 18.7115i | − | 0.0155773i | −0.999970 | − | 0.00778864i | \(-0.997521\pi\) | ||
0.999970 | − | 0.00778864i | \(-0.00247923\pi\) | |||||||
\(114\) | 44.9097 | + | 81.7908i | 0.0368963 | + | 0.0671966i | ||||
\(115\) | 35.6512 | − | 35.6512i | 0.0289086 | − | 0.0289086i | ||||
\(116\) | −1066.12 | −0.853331 | ||||||||
\(117\) | −1257.77 | + | 140.075i | −0.993856 | + | 0.110684i | ||||
\(118\) | 775.889 | 0.605309 | ||||||||
\(119\) | −849.296 | + | 849.296i | −0.654243 | + | 0.654243i | ||||
\(120\) | 866.700 | + | 1578.46i | 0.659321 | + | 1.20077i | ||||
\(121\) | − | 1191.56i | − | 0.895238i | ||||||
\(122\) | −102.450 | + | 102.450i | −0.0760277 | + | 0.0760277i | ||||
\(123\) | 1320.23 | + | 384.303i | 0.967811 | + | 0.281719i | ||||
\(124\) | −577.441 | + | 577.441i | −0.418192 | + | 0.418192i | ||||
\(125\) | −820.177 | − | 820.177i | −0.586871 | − | 0.586871i | ||||
\(126\) | −958.374 | − | 609.597i | −0.677609 | − | 0.431010i | ||||
\(127\) | − | 1382.85i | − | 0.966207i | −0.875563 | − | 0.483103i | \(-0.839510\pi\) | ||
0.875563 | − | 0.483103i | \(-0.160490\pi\) | |||||||
\(128\) | 968.731 | + | 968.731i | 0.668941 | + | 0.668941i | ||||
\(129\) | 239.451 | − | 131.477i | 0.163430 | − | 0.0897360i | ||||
\(130\) | −899.036 | + | 723.208i | −0.606544 | + | 0.487920i | ||||
\(131\) | − | 1018.32i | − | 0.679169i | −0.940576 | − | 0.339585i | \(-0.889714\pi\) | ||
0.940576 | − | 0.339585i | \(-0.110286\pi\) | |||||||
\(132\) | −358.089 | − | 104.236i | −0.236119 | − | 0.0687316i | ||||
\(133\) | 393.093 | 0.256282 | ||||||||
\(134\) | 928.192 | 0.598385 | ||||||||
\(135\) | 1871.29 | − | 1644.60i | 1.19300 | − | 1.04848i | ||||
\(136\) | 546.205 | + | 546.205i | 0.344387 | + | 0.344387i | ||||
\(137\) | −1113.93 | − | 1113.93i | −0.694670 | − | 0.694670i | 0.268586 | − | 0.963256i | \(-0.413444\pi\) |
−0.963256 | + | 0.268586i | \(0.913444\pi\) | |||||||
\(138\) | 19.6372 | + | 5.71618i | 0.0121133 | + | 0.00352604i | ||||
\(139\) | −1755.93 | −1.07148 | −0.535742 | − | 0.844382i | \(-0.679968\pi\) | ||||
−0.535742 | + | 0.844382i | \(0.679968\pi\) | |||||||
\(140\) | 3275.33 | 1.97726 | ||||||||
\(141\) | 400.263 | − | 1375.05i | 0.239065 | − | 0.821279i | ||||
\(142\) | 614.227i | 0.362991i | ||||||||
\(143\) | 59.6404 | − | 550.263i | 0.0348768 | − | 0.321785i | ||||
\(144\) | 312.591 | − | 491.438i | 0.180898 | − | 0.284397i | ||||
\(145\) | 2202.35 | + | 2202.35i | 1.26134 | + | 1.26134i | ||||
\(146\) | − | 165.658i | − | 0.0939036i | ||||||
\(147\) | −2632.05 | + | 1445.20i | −1.47679 | + | 0.810873i | ||||
\(148\) | −562.069 | − | 562.069i | −0.312174 | − | 0.312174i | ||||
\(149\) | −1917.05 | + | 1917.05i | −1.05403 | + | 1.05403i | −0.0555800 | + | 0.998454i | \(0.517701\pi\) |
−0.998454 | + | 0.0555800i | \(0.982299\pi\) | |||||||
\(150\) | 383.158 | − | 1316.29i | 0.208565 | − | 0.716498i | ||||
\(151\) | 969.318 | − | 969.318i | 0.522397 | − | 0.522397i | −0.395897 | − | 0.918295i | \(-0.629566\pi\) |
0.918295 | + | 0.395897i | \(0.129566\pi\) | |||||||
\(152\) | − | 252.809i | − | 0.134904i | ||||||
\(153\) | 573.550 | − | 901.703i | 0.303064 | − | 0.476460i | ||||
\(154\) | 351.255 | − | 351.255i | 0.183798 | − | 0.183798i | ||||
\(155\) | 2385.72 | 1.23629 | ||||||||
\(156\) | 1368.54 | + | 564.506i | 0.702376 | + | 0.289722i | ||||
\(157\) | −187.932 | −0.0955324 | −0.0477662 | − | 0.998859i | \(-0.515210\pi\) | ||||
−0.0477662 | + | 0.998859i | \(0.515210\pi\) | |||||||
\(158\) | −638.211 | + | 638.211i | −0.321350 | + | 0.321350i | ||||
\(159\) | 2155.17 | − | 1183.36i | 1.07494 | − | 0.590230i | ||||
\(160\) | − | 3303.45i | − | 1.63225i | ||||||
\(161\) | 60.9254 | − | 60.9254i | 0.0298235 | − | 0.0298235i | ||||
\(162\) | 950.131 | + | 344.295i | 0.460798 | + | 0.166978i | ||||
\(163\) | −2353.70 | + | 2353.70i | −1.13102 | + | 1.13102i | −0.141010 | + | 0.990008i | \(0.545035\pi\) |
−0.990008 | + | 0.141010i | \(0.954965\pi\) | |||||||
\(164\) | −1137.35 | − | 1137.35i | −0.541535 | − | 0.541535i | ||||
\(165\) | 524.402 | + | 955.055i | 0.247422 | + | 0.450612i | ||||
\(166\) | 611.453i | 0.285891i | ||||||||
\(167\) | −1595.37 | − | 1595.37i | −0.739244 | − | 0.739244i | 0.233188 | − | 0.972432i | \(-0.425084\pi\) |
−0.972432 | + | 0.233188i | \(0.925084\pi\) | |||||||
\(168\) | 1481.13 | + | 2697.47i | 0.680187 | + | 1.23878i | ||||
\(169\) | −470.716 | + | 2145.98i | −0.214254 | + | 0.976778i | ||||
\(170\) | − | 974.309i | − | 0.439565i | ||||||
\(171\) | −341.407 | + | 75.9421i | −0.152679 | + | 0.0339616i | ||||
\(172\) | −319.546 | −0.141658 | ||||||||
\(173\) | 3479.34 | 1.52907 | 0.764535 | − | 0.644582i | \(-0.222968\pi\) | ||||
0.764535 | + | 0.644582i | \(0.222968\pi\) | |||||||
\(174\) | −353.116 | + | 1213.09i | −0.153849 | + | 0.528528i | ||||
\(175\) | −4083.85 | − | 4083.85i | −1.76406 | − | 1.76406i | ||||
\(176\) | 180.118 | + | 180.118i | 0.0771413 | + | 0.0771413i | ||||
\(177\) | −812.830 | + | 2792.38i | −0.345175 | + | 1.18581i | ||||
\(178\) | −1210.29 | −0.509636 | ||||||||
\(179\) | −2074.00 | −0.866023 | −0.433012 | − | 0.901388i | \(-0.642549\pi\) | ||||
−0.433012 | + | 0.901388i | \(0.642549\pi\) | |||||||
\(180\) | −2844.67 | + | 632.764i | −1.17794 | + | 0.262019i | ||||
\(181\) | − | 4030.51i | − | 1.65517i | −0.561341 | − | 0.827585i | \(-0.689714\pi\) | ||
0.561341 | − | 0.827585i | \(-0.310286\pi\) | |||||||
\(182\) | −1536.39 | + | 1235.91i | −0.625740 | + | 0.503362i | ||||
\(183\) | −261.383 | − | 476.038i | −0.105585 | − | 0.192294i | ||||
\(184\) | −39.1827 | − | 39.1827i | −0.0156988 | − | 0.0156988i | ||||
\(185\) | 2322.21i | 0.922876i | ||||||||
\(186\) | 465.786 | + | 848.303i | 0.183619 | + | 0.334412i | ||||
\(187\) | 330.484 | + | 330.484i | 0.129237 | + | 0.129237i | ||||
\(188\) | −1184.58 | + | 1184.58i | −0.459544 | + | 0.459544i | ||||
\(189\) | 3197.90 | − | 2810.51i | 1.23076 | − | 1.08166i | ||||
\(190\) | −225.478 | + | 225.478i | −0.0860940 | + | 0.0860940i | ||||
\(191\) | 1624.37i | 0.615366i | 0.951489 | + | 0.307683i | \(0.0995536\pi\) | ||||
−0.951489 | + | 0.307683i | \(0.900446\pi\) | |||||||
\(192\) | 388.609 | − | 213.377i | 0.146070 | − | 0.0802041i | ||||
\(193\) | 589.677 | − | 589.677i | 0.219927 | − | 0.219927i | −0.588541 | − | 0.808468i | \(-0.700297\pi\) |
0.808468 | + | 0.588541i | \(0.200297\pi\) | |||||||
\(194\) | −348.680 | −0.129040 | ||||||||
\(195\) | −1660.94 | − | 3993.21i | −0.609961 | − | 1.46646i | ||||
\(196\) | 3512.46 | 1.28005 | ||||||||
\(197\) | 3290.58 | − | 3290.58i | 1.19007 | − | 1.19007i | 0.213023 | − | 0.977047i | \(-0.431669\pi\) |
0.977047 | − | 0.213023i | \(-0.0683309\pi\) | |||||||
\(198\) | −237.211 | + | 372.929i | −0.0851406 | + | 0.133853i | ||||
\(199\) | 4033.81i | 1.43693i | 0.695563 | + | 0.718466i | \(0.255155\pi\) | ||||
−0.695563 | + | 0.718466i | \(0.744845\pi\) | |||||||
\(200\) | −2626.43 | + | 2626.43i | −0.928582 | + | 0.928582i | ||||
\(201\) | −972.383 | + | 3340.50i | −0.341227 | + | 1.17224i | ||||
\(202\) | 1157.83 | − | 1157.83i | 0.403291 | − | 0.403291i | ||||
\(203\) | 3763.65 | + | 3763.65i | 1.30126 | + | 1.30126i | ||||
\(204\) | −1095.76 | + | 601.661i | −0.376072 | + | 0.206493i | ||||
\(205\) | 4698.98i | 1.60093i | ||||||||
\(206\) | −223.316 | − | 223.316i | −0.0755299 | − | 0.0755299i | ||||
\(207\) | −41.1444 | + | 64.6848i | −0.0138151 | + | 0.0217193i | ||||
\(208\) | −633.755 | − | 787.834i | −0.211264 | − | 0.262627i | ||||
\(209\) | − | 152.963i | − | 0.0506253i | ||||||
\(210\) | 1084.85 | − | 3726.85i | 0.356483 | − | 1.22465i | ||||
\(211\) | −5146.04 | −1.67899 | −0.839497 | − | 0.543364i | \(-0.817150\pi\) | ||||
−0.839497 | + | 0.543364i | \(0.817150\pi\) | |||||||
\(212\) | −2876.07 | −0.931742 | ||||||||
\(213\) | −2210.56 | − | 643.471i | −0.711104 | − | 0.206995i | ||||
\(214\) | −560.196 | − | 560.196i | −0.178945 | − | 0.178945i | ||||
\(215\) | 660.108 | + | 660.108i | 0.209391 | + | 0.209391i | ||||
\(216\) | −1807.51 | − | 2056.65i | −0.569377 | − | 0.647859i | ||||
\(217\) | 4077.02 | 1.27542 | ||||||||
\(218\) | 58.7318 | 0.0182469 | ||||||||
\(219\) | 596.191 | + | 173.545i | 0.183958 | + | 0.0535483i | ||||
\(220\) | − | 1274.52i | − | 0.390582i | ||||||
\(221\) | −1162.83 | − | 1445.54i | −0.353938 | − | 0.439988i | ||||
\(222\) | −825.720 | + | 453.386i | −0.249634 | + | 0.137069i | ||||
\(223\) | 1830.37 | + | 1830.37i | 0.549645 | + | 0.549645i | 0.926338 | − | 0.376693i | \(-0.122939\pi\) |
−0.376693 | + | 0.926338i | \(0.622939\pi\) | |||||||
\(224\) | − | 5645.35i | − | 1.68391i | ||||||
\(225\) | 4335.84 | + | 2757.92i | 1.28469 | + | 0.817161i | ||||
\(226\) | 18.3417 | + | 18.3417i | 0.00539856 | + | 0.00539856i | ||||
\(227\) | 2496.64 | − | 2496.64i | 0.729990 | − | 0.729990i | −0.240628 | − | 0.970617i | \(-0.577353\pi\) |
0.970617 | + | 0.240628i | \(0.0773533\pi\) | |||||||
\(228\) | 392.823 | + | 114.346i | 0.114102 | + | 0.0332139i | ||||
\(229\) | −1298.02 | + | 1298.02i | −0.374565 | + | 0.374565i | −0.869137 | − | 0.494572i | \(-0.835325\pi\) |
0.494572 | + | 0.869137i | \(0.335325\pi\) | |||||||
\(230\) | 69.8933i | 0.0200375i | ||||||||
\(231\) | 896.165 | + | 1632.12i | 0.255252 | + | 0.464873i | ||||
\(232\) | 2420.50 | − | 2420.50i | 0.684973 | − | 0.684973i | ||||
\(233\) | −374.174 | −0.105206 | −0.0526028 | − | 0.998616i | \(-0.516752\pi\) | ||||
−0.0526028 | + | 0.998616i | \(0.516752\pi\) | |||||||
\(234\) | 1095.61 | − | 1370.22i | 0.306078 | − | 0.382796i | ||||
\(235\) | 4894.12 | 1.35854 | ||||||||
\(236\) | 2405.57 | − | 2405.57i | 0.663514 | − | 0.663514i | ||||
\(237\) | −1628.28 | − | 2965.48i | −0.446280 | − | 0.812778i | ||||
\(238\) | − | 1665.02i | − | 0.453477i | ||||||
\(239\) | −14.5400 | + | 14.5400i | −0.00393522 | + | 0.00393522i | −0.709072 | − | 0.705136i | \(-0.750886\pi\) |
0.705136 | + | 0.709072i | \(0.250886\pi\) | |||||||
\(240\) | 1911.07 | + | 556.291i | 0.513996 | + | 0.149618i | ||||
\(241\) | −418.110 | + | 418.110i | −0.111755 | + | 0.111755i | −0.760773 | − | 0.649018i | \(-0.775180\pi\) |
0.649018 | + | 0.760773i | \(0.275180\pi\) | |||||||
\(242\) | 1168.01 | + | 1168.01i | 0.310259 | + | 0.310259i | ||||
\(243\) | −2234.46 | + | 3058.77i | −0.589880 | + | 0.807491i | ||||
\(244\) | 635.273i | 0.166677i | ||||||||
\(245\) | −7255.92 | − | 7255.92i | −1.89210 | − | 1.89210i | ||||
\(246\) | −1670.84 | + | 917.426i | −0.433045 | + | 0.237776i | ||||
\(247\) | −65.4253 | + | 603.636i | −0.0168539 | + | 0.155500i | ||||
\(248\) | − | 2622.04i | − | 0.671369i | ||||||
\(249\) | −2200.58 | − | 640.564i | −0.560064 | − | 0.163029i | ||||
\(250\) | 1607.94 | 0.406780 | ||||||||
\(251\) | −3640.15 | −0.915396 | −0.457698 | − | 0.889108i | \(-0.651326\pi\) | ||||
−0.457698 | + | 0.889108i | \(0.651326\pi\) | |||||||
\(252\) | −4861.34 | + | 1081.35i | −1.21522 | + | 0.270312i | ||||
\(253\) | −23.7077 | − | 23.7077i | −0.00589127 | − | 0.00589127i | ||||
\(254\) | 1355.52 | + | 1355.52i | 0.334855 | + | 0.334855i | ||||
\(255\) | 3506.48 | + | 1020.70i | 0.861114 | + | 0.250661i | ||||
\(256\) | −2581.73 | −0.630306 | ||||||||
\(257\) | 8045.83 | 1.95286 | 0.976430 | − | 0.215832i | \(-0.0692464\pi\) | ||||
0.976430 | + | 0.215832i | \(0.0692464\pi\) | |||||||
\(258\) | −105.839 | + | 363.598i | −0.0255398 | + | 0.0877388i | ||||
\(259\) | 3968.48i | 0.952083i | ||||||||
\(260\) | −545.137 | + | 5029.61i | −0.130031 | + | 1.19971i | ||||
\(261\) | −3995.89 | − | 2541.68i | −0.947660 | − | 0.602782i | ||||
\(262\) | 998.197 | + | 998.197i | 0.235377 | + | 0.235377i | ||||
\(263\) | 2164.94i | 0.507588i | 0.967258 | + | 0.253794i | \(0.0816786\pi\) | ||||
−0.967258 | + | 0.253794i | \(0.918321\pi\) | |||||||
\(264\) | 1049.66 | − | 576.347i | 0.244705 | − | 0.134362i | ||||
\(265\) | 5941.29 | + | 5941.29i | 1.37725 | + | 1.37725i | ||||
\(266\) | −385.325 | + | 385.325i | −0.0888188 | + | 0.0888188i | ||||
\(267\) | 1267.91 | − | 4355.76i | 0.290618 | − | 0.998383i | ||||
\(268\) | 2877.77 | − | 2877.77i | 0.655924 | − | 0.655924i | ||||
\(269\) | 8484.29i | 1.92304i | 0.274743 | + | 0.961518i | \(0.411407\pi\) | ||||
−0.274743 | + | 0.961518i | \(0.588593\pi\) | |||||||
\(270\) | −222.211 | + | 3446.41i | −0.0500864 | + | 0.776822i | ||||
\(271\) | 2258.21 | − | 2258.21i | 0.506186 | − | 0.506186i | −0.407167 | − | 0.913354i | \(-0.633483\pi\) |
0.913354 | + | 0.407167i | \(0.133483\pi\) | |||||||
\(272\) | 853.797 | 0.190327 | ||||||||
\(273\) | −2838.43 | − | 6824.11i | −0.629266 | − | 1.51287i | ||||
\(274\) | 2183.84 | 0.481498 | ||||||||
\(275\) | −1589.13 | + | 1589.13i | −0.348467 | + | 0.348467i | ||||
\(276\) | 78.6059 | − | 43.1609i | 0.0171432 | − | 0.00941297i | ||||
\(277\) | − | 7018.23i | − | 1.52233i | −0.648559 | − | 0.761164i | \(-0.724628\pi\) | ||
0.648559 | − | 0.761164i | \(-0.275372\pi\) | |||||||
\(278\) | 1721.23 | − | 1721.23i | 0.371340 | − | 0.371340i | ||||
\(279\) | −3540.95 | + | 787.643i | −0.759825 | + | 0.169014i | ||||
\(280\) | −7436.29 | + | 7436.29i | −1.58715 | + | 1.58715i | ||||
\(281\) | 98.2745 | + | 98.2745i | 0.0208632 | + | 0.0208632i | 0.717461 | − | 0.696598i | \(-0.245304\pi\) |
−0.696598 | + | 0.717461i | \(0.745304\pi\) | |||||||
\(282\) | 955.526 | + | 1740.23i | 0.201776 | + | 0.367480i | ||||
\(283\) | − | 8008.21i | − | 1.68212i | −0.540945 | − | 0.841058i | \(-0.681933\pi\) | ||
0.540945 | − | 0.841058i | \(-0.318067\pi\) | |||||||
\(284\) | 1904.35 | + | 1904.35i | 0.397896 | + | 0.397896i | ||||
\(285\) | −575.267 | − | 1047.69i | −0.119564 | − | 0.217754i | ||||
\(286\) | 480.926 | + | 597.850i | 0.0994328 | + | 0.123607i | ||||
\(287\) | 8030.22i | 1.65160i | ||||||||
\(288\) | 1090.63 | + | 4903.07i | 0.223146 | + | 1.00318i | ||||
\(289\) | −3346.43 | −0.681138 | ||||||||
\(290\) | −4317.64 | −0.874279 | ||||||||
\(291\) | 365.281 | − | 1254.88i | 0.0735847 | − | 0.252791i | ||||
\(292\) | −513.606 | − | 513.606i | −0.102933 | − | 0.102933i | ||||
\(293\) | −5325.57 | − | 5325.57i | −1.06185 | − | 1.06185i | −0.997957 | − | 0.0638968i | \(-0.979647\pi\) |
−0.0638968 | − | 0.997957i | \(-0.520353\pi\) | |||||||
\(294\) | 1163.39 | − | 3996.67i | 0.230783 | − | 0.792826i | ||||
\(295\) | −9938.69 | −1.96154 | ||||||||
\(296\) | 2552.23 | 0.501168 | ||||||||
\(297\) | −1093.64 | − | 1244.39i | −0.213669 | − | 0.243121i | ||||
\(298\) | − | 3758.34i | − | 0.730586i | ||||||
\(299\) | 83.4170 | + | 103.697i | 0.0161342 | + | 0.0200568i | ||||
\(300\) | −2893.09 | − | 5268.98i | −0.556775 | − | 1.01401i | ||||
\(301\) | 1128.08 | + | 1128.08i | 0.216018 | + | 0.216018i | ||||
\(302\) | 1900.32i | 0.362091i | ||||||||
\(303\) | 2954.01 | + | 5379.92i | 0.560077 | + | 1.02003i | ||||
\(304\) | −197.588 | − | 197.588i | −0.0372778 | − | 0.0372778i | ||||
\(305\) | 1312.32 | − | 1312.32i | 0.246372 | − | 0.246372i | ||||
\(306\) | 321.668 | + | 1446.10i | 0.0600932 | + | 0.270157i | ||||
\(307\) | −4466.27 | + | 4466.27i | −0.830304 | + | 0.830304i | −0.987558 | − | 0.157254i | \(-0.949736\pi\) |
0.157254 | + | 0.987558i | \(0.449736\pi\) | |||||||
\(308\) | − | 2178.06i | − | 0.402944i | ||||||
\(309\) | 1037.65 | − | 569.752i | 0.191035 | − | 0.104893i | ||||
\(310\) | −2338.57 | + | 2338.57i | −0.428457 | + | 0.428457i | ||||
\(311\) | −3306.43 | −0.602863 | −0.301432 | − | 0.953488i | \(-0.597464\pi\) | ||||
−0.301432 | + | 0.953488i | \(0.597464\pi\) | |||||||
\(312\) | −4388.76 | + | 1825.47i | −0.796362 | + | 0.331239i | ||||
\(313\) | −572.860 | −0.103450 | −0.0517252 | − | 0.998661i | \(-0.516472\pi\) | ||||
−0.0517252 | + | 0.998661i | \(0.516472\pi\) | |||||||
\(314\) | 184.218 | − | 184.218i | 0.0331083 | − | 0.0331083i | ||||
\(315\) | 12276.2 | + | 7808.58i | 2.19583 | + | 1.39671i | ||||
\(316\) | 3957.42i | 0.704502i | ||||||||
\(317\) | 2376.21 | − | 2376.21i | 0.421014 | − | 0.421014i | −0.464539 | − | 0.885553i | \(-0.653780\pi\) |
0.885553 | + | 0.464539i | \(0.153780\pi\) | |||||||
\(318\) | −952.604 | + | 3272.55i | −0.167985 | + | 0.577093i | ||||
\(319\) | 1464.54 | − | 1464.54i | 0.257048 | − | 0.257048i | ||||
\(320\) | 1071.30 | + | 1071.30i | 0.187149 | + | 0.187149i | ||||
\(321\) | 2602.97 | − | 1429.24i | 0.452598 | − | 0.248512i | ||||
\(322\) | 119.443i | 0.0206717i | ||||||||
\(323\) | −362.540 | − | 362.540i | −0.0624528 | − | 0.0624528i | ||||
\(324\) | 4013.24 | − | 1878.34i | 0.688142 | − | 0.322074i | ||||
\(325\) | 6950.87 | − | 5591.47i | 1.18635 | − | 0.954335i | ||||
\(326\) | − | 4614.37i | − | 0.783946i | ||||||
\(327\) | −61.5280 | + | 211.372i | −0.0104052 | + | 0.0357458i | ||||
\(328\) | 5164.44 | 0.869386 | ||||||||
\(329\) | 8363.70 | 1.40154 | ||||||||
\(330\) | −1450.22 | − | 422.143i | −0.241915 | − | 0.0704188i | ||||
\(331\) | −1458.54 | − | 1458.54i | −0.242201 | − | 0.242201i | 0.575559 | − | 0.817760i | \(-0.304785\pi\) |
−0.817760 | + | 0.575559i | \(0.804785\pi\) | |||||||
\(332\) | 1895.75 | + | 1895.75i | 0.313382 | + | 0.313382i | ||||
\(333\) | −766.675 | − | 3446.69i | −0.126167 | − | 0.567199i | ||||
\(334\) | 3127.69 | 0.512394 | ||||||||
\(335\) | −11889.6 | −1.93910 | ||||||||
\(336\) | 3265.88 | + | 950.661i | 0.530263 | + | 0.154354i | ||||
\(337\) | 9456.34i | 1.52855i | 0.644893 | + | 0.764273i | \(0.276902\pi\) | ||||
−0.644893 | + | 0.764273i | \(0.723098\pi\) | |||||||
\(338\) | −1642.16 | − | 2564.99i | −0.264265 | − | 0.412772i | ||||
\(339\) | −85.2257 | + | 46.7957i | −0.0136544 | + | 0.00749733i | ||||
\(340\) | −3020.75 | − | 3020.75i | −0.481833 | − | 0.481833i | ||||
\(341\) | − | 1586.48i | − | 0.251943i | ||||||
\(342\) | 260.219 | − | 409.102i | 0.0411434 | − | 0.0646833i | ||||
\(343\) | −5039.83 | − | 5039.83i | −0.793368 | − | 0.793368i | ||||
\(344\) | 725.496 | − | 725.496i | 0.113710 | − | 0.113710i | ||||
\(345\) | −251.542 | − | 73.2210i | −0.0392537 | − | 0.0114263i | ||||
\(346\) | −3410.58 | + | 3410.58i | −0.529925 | + | 0.529925i | ||||
\(347\) | − | 12663.0i | − | 1.95903i | −0.201366 | − | 0.979516i | \(-0.564538\pi\) | ||
0.201366 | − | 0.979516i | \(-0.435462\pi\) | |||||||
\(348\) | 2666.25 | + | 4855.86i | 0.410708 | + | 0.747992i | ||||
\(349\) | 756.113 | − | 756.113i | 0.115971 | − | 0.115971i | −0.646740 | − | 0.762711i | \(-0.723868\pi\) |
0.762711 | + | 0.646740i | \(0.223868\pi\) | |||||||
\(350\) | 8006.28 | 1.22272 | ||||||||
\(351\) | 3783.57 | + | 5378.49i | 0.575363 | + | 0.817898i | ||||
\(352\) | −2196.76 | −0.332635 | ||||||||
\(353\) | 3714.43 | − | 3714.43i | 0.560054 | − | 0.560054i | −0.369268 | − | 0.929323i | \(-0.620392\pi\) |
0.929323 | + | 0.369268i | \(0.120392\pi\) | |||||||
\(354\) | −1940.43 | − | 3533.96i | −0.291335 | − | 0.530587i | ||||
\(355\) | − | 7867.89i | − | 1.17629i | ||||||
\(356\) | −3752.39 | + | 3752.39i | −0.558642 | + | 0.558642i | ||||
\(357\) | 5992.32 | + | 1744.30i | 0.888367 | + | 0.258594i | ||||
\(358\) | 2033.01 | − | 2033.01i | 0.300135 | − | 0.300135i | ||||
\(359\) | −6824.51 | − | 6824.51i | −1.00330 | − | 1.00330i | −0.999995 | − | 0.00330378i | \(-0.998948\pi\) |
−0.00330378 | − | 0.999995i | \(-0.501052\pi\) | |||||||
\(360\) | 5021.90 | − | 7895.15i | 0.735215 | − | 1.15586i | ||||
\(361\) | − | 6691.20i | − | 0.975536i | ||||||
\(362\) | 3950.86 | + | 3950.86i | 0.573626 | + | 0.573626i | ||||
\(363\) | −5427.23 | + | 2979.98i | −0.784726 | + | 0.430877i | ||||
\(364\) | −931.600 | + | 8595.25i | −0.134146 | + | 1.23767i | ||||
\(365\) | 2121.98i | 0.304300i | ||||||||
\(366\) | 722.849 | + | 210.413i | 0.103235 | + | 0.0300505i | ||||
\(367\) | −5558.09 | −0.790545 | −0.395272 | − | 0.918564i | \(-0.629350\pi\) | ||||
−0.395272 | + | 0.918564i | \(0.629350\pi\) | |||||||
\(368\) | −61.2482 | −0.00867604 | ||||||||
\(369\) | −1551.37 | − | 6974.36i | −0.218864 | − | 0.983932i | ||||
\(370\) | −2276.31 | − | 2276.31i | −0.319838 | − | 0.319838i | ||||
\(371\) | 10153.2 | + | 10153.2i | 1.42083 | + | 1.42083i | ||||
\(372\) | 4074.21 | + | 1185.96i | 0.567844 | + | 0.165293i | ||||
\(373\) | 10353.4 | 1.43721 | 0.718607 | − | 0.695416i | \(-0.244780\pi\) | ||||
0.718607 | + | 0.695416i | \(0.244780\pi\) | |||||||
\(374\) | −647.906 | −0.0895787 | ||||||||
\(375\) | −1684.49 | + | 5786.86i | −0.231965 | + | 0.796886i | ||||
\(376\) | − | 5378.91i | − | 0.737756i | ||||||
\(377\) | −6405.89 | + | 5153.07i | −0.875119 | + | 0.703969i | ||||
\(378\) | −379.742 | + | 5889.67i | −0.0516715 | + | 0.801407i | ||||
\(379\) | −590.187 | − | 590.187i | −0.0799891 | − | 0.0799891i | 0.665980 | − | 0.745969i | \(-0.268013\pi\) |
−0.745969 | + | 0.665980i | \(0.768013\pi\) | |||||||
\(380\) | 1398.14i | 0.188745i | ||||||||
\(381\) | −6298.50 | + | 3458.38i | −0.846934 | + | 0.465035i | ||||
\(382\) | −1592.26 | − | 1592.26i | −0.213265 | − | 0.213265i | ||||
\(383\) | −5620.17 | + | 5620.17i | −0.749811 | + | 0.749811i | −0.974443 | − | 0.224633i | \(-0.927882\pi\) |
0.224633 | + | 0.974443i | \(0.427882\pi\) | |||||||
\(384\) | 1989.59 | − | 6835.00i | 0.264404 | − | 0.908326i | ||||
\(385\) | −4499.37 | + | 4499.37i | −0.595608 | + | 0.595608i | ||||
\(386\) | 1156.05i | 0.152439i | ||||||||
\(387\) | −1197.69 | − | 761.818i | −0.157317 | − | 0.100066i | ||||
\(388\) | −1081.05 | + | 1081.05i | −0.141448 | + | 0.141448i | ||||
\(389\) | −907.219 | −0.118246 | −0.0591232 | − | 0.998251i | \(-0.518830\pi\) | ||||
−0.0591232 | + | 0.998251i | \(0.518830\pi\) | |||||||
\(390\) | 5542.42 | + | 2286.18i | 0.719618 | + | 0.296834i | ||||
\(391\) | −112.380 | −0.0145353 | ||||||||
\(392\) | −7974.66 | + | 7974.66i | −1.02750 | + | 1.02750i | ||||
\(393\) | −4638.17 | + | 2546.73i | −0.595330 | + | 0.326884i | ||||
\(394\) | 6451.09i | 0.824877i | ||||||||
\(395\) | 8175.11 | − | 8175.11i | 1.04135 | − | 1.04135i | ||||
\(396\) | 420.782 | + | 1891.68i | 0.0533967 | + | 0.240052i | ||||
\(397\) | −39.8753 | + | 39.8753i | −0.00504102 | + | 0.00504102i | −0.709623 | − | 0.704582i | \(-0.751135\pi\) |
0.704582 | + | 0.709623i | \(0.251135\pi\) | |||||||
\(398\) | −3954.09 | − | 3954.09i | −0.497992 | − | 0.497992i | ||||
\(399\) | −983.089 | − | 1790.43i | −0.123348 | − | 0.224646i | ||||
\(400\) | 4105.49i | 0.513186i | ||||||||
\(401\) | 8973.42 | + | 8973.42i | 1.11748 | + | 1.11748i | 0.992109 | + | 0.125375i | \(0.0400136\pi\) |
0.125375 | + | 0.992109i | \(0.459986\pi\) | |||||||
\(402\) | −2321.32 | − | 4227.65i | −0.288002 | − | 0.524518i | ||||
\(403\) | −678.567 | + | 6260.69i | −0.0838755 | + | 0.773864i | ||||
\(404\) | − | 7179.50i | − | 0.884142i | ||||||
\(405\) | −12170.6 | − | 4410.22i | −1.49324 | − | 0.541100i | ||||
\(406\) | −7378.54 | −0.901948 | ||||||||
\(407\) | 1544.24 | 0.188072 | ||||||||
\(408\) | 1121.80 | − | 3853.81i | 0.136121 | − | 0.467628i | ||||
\(409\) | 1155.75 | + | 1155.75i | 0.139726 | + | 0.139726i | 0.773510 | − | 0.633784i | \(-0.218499\pi\) |
−0.633784 | + | 0.773510i | \(0.718499\pi\) | |||||||
\(410\) | −4606.12 | − | 4606.12i | −0.554829 | − | 0.554829i | ||||
\(411\) | −2287.81 | + | 7859.50i | −0.274573 | + | 0.943261i | ||||
\(412\) | −1384.74 | −0.165586 | ||||||||
\(413\) | −16984.5 | −2.02362 | ||||||||
\(414\) | −23.0752 | − | 103.738i | −0.00273934 | − | 0.0123151i | ||||
\(415\) | − | 7832.35i | − | 0.926446i | ||||||
\(416\) | 8669.02 | + | 939.596i | 1.02172 | + | 0.110739i | ||||
\(417\) | 4391.42 | + | 7997.78i | 0.515704 | + | 0.939215i | ||||
\(418\) | 149.940 | + | 149.940i | 0.0175450 | + | 0.0175450i | ||||
\(419\) | − | 1498.58i | − | 0.174726i | −0.996177 | − | 0.0873630i | \(-0.972156\pi\) | ||
0.996177 | − | 0.0873630i | \(-0.0278440\pi\) | |||||||
\(420\) | −8191.29 | − | 14918.2i | −0.951653 | − | 1.73318i | ||||
\(421\) | 9941.27 | + | 9941.27i | 1.15085 | + | 1.15085i | 0.986382 | + | 0.164468i | \(0.0525907\pi\) |
0.164468 | + | 0.986382i | \(0.447409\pi\) | |||||||
\(422\) | 5044.34 | − | 5044.34i | 0.581883 | − | 0.581883i | ||||
\(423\) | −7264.00 | + | 1615.79i | −0.834959 | + | 0.185727i | ||||
\(424\) | 6529.81 | − | 6529.81i | 0.747914 | − | 0.747914i | ||||
\(425\) | 7532.85i | 0.859757i | ||||||||
\(426\) | 2797.63 | − | 1536.12i | 0.318182 | − | 0.174708i | ||||
\(427\) | 2242.67 | − | 2242.67i | 0.254169 | − | 0.254169i | ||||
\(428\) | −3473.67 | −0.392304 | ||||||||
\(429\) | −2655.45 | + | 1104.51i | −0.298849 | + | 0.124303i | ||||
\(430\) | −1294.13 | −0.145136 | ||||||||
\(431\) | 3711.54 | − | 3711.54i | 0.414800 | − | 0.414800i | −0.468607 | − | 0.883407i | \(-0.655244\pi\) |
0.883407 | + | 0.468607i | \(0.155244\pi\) | |||||||
\(432\) | −3020.12 | − | 194.725i | −0.336356 | − | 0.0216869i | ||||
\(433\) | − | 5222.54i | − | 0.579628i | −0.957083 | − | 0.289814i | \(-0.906407\pi\) | ||
0.957083 | − | 0.289814i | \(-0.0935935\pi\) | |||||||
\(434\) | −3996.45 | + | 3996.45i | −0.442018 | + | 0.442018i | ||||
\(435\) | 4523.21 | − | 15538.9i | 0.498555 | − | 1.71272i | ||||
\(436\) | 182.092 | − | 182.092i | 0.0200015 | − | 0.0200015i | ||||
\(437\) | 26.0073 | + | 26.0073i | 0.00284690 | + | 0.00284690i | ||||
\(438\) | −754.524 | + | 414.294i | −0.0823118 | + | 0.0451958i | ||||
\(439\) | 5028.80i | 0.546724i | 0.961911 | + | 0.273362i | \(0.0881357\pi\) | ||||
−0.961911 | + | 0.273362i | \(0.911864\pi\) | |||||||
\(440\) | 2893.66 | + | 2893.66i | 0.313522 | + | 0.313522i | ||||
\(441\) | 13165.0 | + | 8373.91i | 1.42155 | + | 0.904213i | ||||
\(442\) | 2556.82 | + | 277.122i | 0.275148 | + | 0.0298220i | ||||
\(443\) | 14535.3i | 1.55890i | 0.626466 | + | 0.779448i | \(0.284501\pi\) | ||||
−0.626466 | + | 0.779448i | \(0.715499\pi\) | |||||||
\(444\) | −1154.39 | + | 3965.75i | −0.123389 | + | 0.423888i | ||||
\(445\) | 15503.1 | 1.65150 | ||||||||
\(446\) | −3588.40 | −0.380977 | ||||||||
\(447\) | 13526.0 | + | 3937.27i | 1.43123 | + | 0.416614i | ||||
\(448\) | 1830.78 | + | 1830.78i | 0.193072 | + | 0.193072i | ||||
\(449\) | 1392.85 | + | 1392.85i | 0.146398 | + | 0.146398i | 0.776507 | − | 0.630109i | \(-0.216990\pi\) |
−0.630109 | + | 0.776507i | \(0.716990\pi\) | |||||||
\(450\) | −6953.57 | + | 1546.74i | −0.728432 | + | 0.162031i | ||||
\(451\) | 3124.77 | 0.326252 | ||||||||
\(452\) | 113.734 | 0.0118354 | ||||||||
\(453\) | −6839.15 | − | 1990.80i | −0.709340 | − | 0.206481i | ||||
\(454\) | 4894.60i | 0.505980i | ||||||||
\(455\) | 19680.2 | − | 15831.3i | 2.02774 | − | 1.63117i | ||||
\(456\) | −1151.47 | + | 632.250i | −0.118251 | + | 0.0649294i | ||||
\(457\) | −1525.73 | − | 1525.73i | −0.156172 | − | 0.156172i | 0.624696 | − | 0.780868i | \(-0.285223\pi\) |
−0.780868 | + | 0.624696i | \(0.785223\pi\) | |||||||
\(458\) | − | 2544.73i | − | 0.259624i | ||||||
\(459\) | −5541.40 | − | 357.287i | −0.563508 | − | 0.0363328i | ||||
\(460\) | 216.698 | + | 216.698i | 0.0219643 | + | 0.0219643i | ||||
\(461\) | 1822.95 | − | 1822.95i | 0.184172 | − | 0.184172i | −0.608999 | − | 0.793171i | \(-0.708429\pi\) |
0.793171 | + | 0.608999i | \(0.208429\pi\) | |||||||
\(462\) | −2478.32 | − | 721.412i | −0.249571 | − | 0.0726475i | ||||
\(463\) | 11841.6 | − | 11841.6i | 1.18860 | − | 1.18860i | 0.211151 | − | 0.977454i | \(-0.432279\pi\) |
0.977454 | − | 0.211151i | \(-0.0677211\pi\) | |||||||
\(464\) | − | 3783.59i | − | 0.378554i | ||||||
\(465\) | −5966.45 | − | 10866.3i | −0.595027 | − | 1.08368i | ||||
\(466\) | 366.779 | − | 366.779i | 0.0364608 | − | 0.0364608i | ||||
\(467\) | −9399.73 | −0.931408 | −0.465704 | − | 0.884941i | \(-0.654199\pi\) | ||||
−0.465704 | + | 0.884941i | \(0.654199\pi\) | |||||||
\(468\) | −851.416 | − | 7645.08i | −0.0840956 | − | 0.755115i | ||||
\(469\) | −20318.5 | −2.00047 | ||||||||
\(470\) | −4797.40 | + | 4797.40i | −0.470825 | + | 0.470825i | ||||
\(471\) | 470.000 | + | 855.977i | 0.0459797 | + | 0.0837396i | ||||
\(472\) | 10923.2i | 1.06521i | ||||||||
\(473\) | 438.965 | − | 438.965i | 0.0426716 | − | 0.0426716i | ||||
\(474\) | 4502.98 | + | 1310.77i | 0.436347 | + | 0.127016i | ||||
\(475\) | 1743.27 | − | 1743.27i | 0.168394 | − | 0.168394i | ||||
\(476\) | −5162.25 | − | 5162.25i | −0.497083 | − | 0.497083i | ||||
\(477\) | −10779.7 | − | 6856.72i | −1.03474 | − | 0.658171i | ||||
\(478\) | − | 28.5054i | − | 0.00272763i | ||||||
\(479\) | 4069.42 | + | 4069.42i | 0.388177 | + | 0.388177i | 0.874037 | − | 0.485860i | \(-0.161494\pi\) |
−0.485860 | + | 0.874037i | \(0.661494\pi\) | |||||||
\(480\) | −15046.3 | + | 8261.60i | −1.43076 | + | 0.785602i | ||||
\(481\) | −6094.02 | − | 660.503i | −0.577679 | − | 0.0626119i | ||||
\(482\) | − | 819.695i | − | 0.0774607i | ||||||
\(483\) | −429.866 | − | 125.129i | −0.0404961 | − | 0.0117880i | ||||
\(484\) | 7242.63 | 0.680187 | ||||||||
\(485\) | 4466.39 | 0.418161 | ||||||||
\(486\) | −808.019 | − | 5188.63i | −0.0754166 | − | 0.484282i | ||||
\(487\) | 9498.10 | + | 9498.10i | 0.883778 | + | 0.883778i | 0.993916 | − | 0.110138i | \(-0.0351294\pi\) |
−0.110138 | + | 0.993916i | \(0.535129\pi\) | |||||||
\(488\) | −1442.32 | − | 1442.32i | −0.133792 | − | 0.133792i | ||||
\(489\) | 16606.8 | + | 4834.06i | 1.53576 | + | 0.447043i | ||||
\(490\) | 14225.1 | 1.31147 | ||||||||
\(491\) | 10110.3 | 0.929269 | 0.464634 | − | 0.885503i | \(-0.346186\pi\) | ||||
0.464634 | + | 0.885503i | \(0.346186\pi\) | |||||||
\(492\) | −2335.90 | + | 8024.68i | −0.214045 | + | 0.735327i | ||||
\(493\) | − | 6942.23i | − | 0.634204i | ||||||
\(494\) | −527.574 | − | 655.839i | −0.0480500 | − | 0.0597320i | ||||
\(495\) | 3038.53 | − | 4777.01i | 0.275903 | − | 0.433758i | ||||
\(496\) | −2049.31 | − | 2049.31i | −0.185518 | − | 0.185518i | ||||
\(497\) | − | 13445.7i | − | 1.21352i | ||||||
\(498\) | 2785.00 | − | 1529.19i | 0.250600 | − | 0.137599i | ||||
\(499\) | 859.012 | + | 859.012i | 0.0770635 | + | 0.0770635i | 0.744588 | − | 0.667524i | \(-0.232646\pi\) |
−0.667524 | + | 0.744588i | \(0.732646\pi\) | |||||||
\(500\) | 4985.26 | − | 4985.26i | 0.445895 | − | 0.445895i | ||||
\(501\) | −3276.60 | + | 11256.4i | −0.292191 | + | 1.00379i | ||||
\(502\) | 3568.21 | − | 3568.21i | 0.317245 | − | 0.317245i | ||||
\(503\) | − | 5309.97i | − | 0.470695i | −0.971911 | − | 0.235348i | \(-0.924377\pi\) | ||
0.971911 | − | 0.235348i | \(-0.0756229\pi\) | |||||||
\(504\) | 8582.07 | − | 13492.2i | 0.758484 | − | 1.19245i | ||||
\(505\) | −14831.2 | + | 14831.2i | −1.30689 | + | 1.30689i | ||||
\(506\) | 46.4784 | 0.00408343 | ||||||||
\(507\) | 10951.6 | − | 3222.92i | 0.959321 | − | 0.282317i | ||||
\(508\) | 8405.34 | 0.734108 | ||||||||
\(509\) | −11449.6 | + | 11449.6i | −0.997046 | + | 0.997046i | −0.999996 | − | 0.00294997i | \(-0.999061\pi\) |
0.00294997 | + | 0.999996i | \(0.499061\pi\) | |||||||
\(510\) | −4437.71 | + | 2436.66i | −0.385304 | + | 0.211563i | ||||
\(511\) | 3626.31i | 0.313930i | ||||||||
\(512\) | −5219.13 | + | 5219.13i | −0.450499 | + | 0.450499i | ||||
\(513\) | 1199.72 | + | 1365.09i | 0.103254 | + | 0.117486i | ||||
\(514\) | −7886.83 | + | 7886.83i | −0.676796 | + | 0.676796i | ||||
\(515\) | 2860.55 | + | 2860.55i | 0.244759 | + | 0.244759i | ||||
\(516\) | 799.155 | + | 1455.44i | 0.0681799 | + | 0.124171i | ||||
\(517\) | − | 3254.54i | − | 0.276856i | ||||||
\(518\) | −3890.06 | − | 3890.06i | −0.329960 | − | 0.329960i | ||||
\(519\) | −8701.50 | − | 15847.4i | −0.735941 | − | 1.34032i | ||||
\(520\) | −10181.5 | − | 12656.9i | −0.858633 | − | 1.06739i | ||||
\(521\) | − | 4751.09i | − | 0.399518i | −0.979845 | − | 0.199759i | \(-0.935984\pi\) | ||
0.979845 | − | 0.199759i | \(-0.0640160\pi\) | |||||||
\(522\) | 6408.38 | − | 1425.47i | 0.537331 | − | 0.119523i | ||||
\(523\) | −13699.2 | −1.14536 | −0.572682 | − | 0.819778i | \(-0.694097\pi\) | ||||
−0.572682 | + | 0.819778i | \(0.694097\pi\) | |||||||
\(524\) | 6189.63 | 0.516021 | ||||||||
\(525\) | −8387.46 | + | 28814.1i | −0.697255 | + | 2.39533i | ||||
\(526\) | −2122.15 | − | 2122.15i | −0.175913 | − | 0.175913i | ||||
\(527\) | −3760.13 | − | 3760.13i | −0.310804 | − | 0.310804i | ||||
\(528\) | 369.928 | − | 1270.84i | 0.0304906 | − | 0.104747i | ||||
\(529\) | −12158.9 | −0.999337 | ||||||||
\(530\) | −11647.7 | −0.954615 | ||||||||
\(531\) | 14751.3 | − | 3281.25i | 1.20556 | − | 0.268162i | ||||
\(532\) | 2389.33i | 0.194719i | ||||||||
\(533\) | −12331.2 | − | 1336.53i | −1.00211 | − | 0.108614i | ||||
\(534\) | 3026.82 | + | 5512.54i | 0.245287 | + | 0.446725i | ||||
\(535\) | 7175.78 | + | 7175.78i | 0.579880 | + | 0.579880i | ||||
\(536\) | 13067.3i | 1.05303i | ||||||||
\(537\) | 5186.88 | + | 9446.50i | 0.416816 | + | 0.759118i | ||||
\(538\) | −8316.62 | − | 8316.62i | −0.666459 | − | 0.666459i | ||||
\(539\) | −4825.12 | + | 4825.12i | −0.385589 | + | 0.385589i | ||||
\(540\) | 9996.33 | + | 11374.2i | 0.796617 | + | 0.906423i | ||||
\(541\) | 7488.89 | − | 7488.89i | 0.595143 | − | 0.595143i | −0.343873 | − | 0.939016i | \(-0.611739\pi\) |
0.939016 | + | 0.343873i | \(0.111739\pi\) | |||||||
\(542\) | 4427.17i | 0.350854i | ||||||||
\(543\) | −18357.9 | + | 10079.9i | −1.45085 | + | 0.796632i | ||||
\(544\) | −5206.56 | + | 5206.56i | −0.410348 | + | 0.410348i | ||||
\(545\) | −752.320 | −0.0591300 | ||||||||
\(546\) | 9471.59 | + | 3906.92i | 0.742393 | + | 0.306228i | ||||
\(547\) | −3941.66 | −0.308105 | −0.154052 | − | 0.988063i | \(-0.549232\pi\) | ||||
−0.154052 | + | 0.988063i | \(0.549232\pi\) | |||||||
\(548\) | 6770.79 | − | 6770.79i | 0.527799 | − | 0.527799i | ||||
\(549\) | −1514.53 | + | 2381.05i | −0.117739 | + | 0.185102i | ||||
\(550\) | − | 3115.46i | − | 0.241534i | ||||||
\(551\) | −1606.59 | + | 1606.59i | −0.124216 | + | 0.124216i | ||||
\(552\) | −80.4740 | + | 276.458i | −0.00620507 | + | 0.0213167i | ||||
\(553\) | 13970.7 | − | 13970.7i | 1.07431 | − | 1.07431i | ||||
\(554\) | 6879.54 | + | 6879.54i | 0.527588 | + | 0.527588i | ||||
\(555\) | 10577.0 | − | 5807.62i | 0.808952 | − | 0.444179i | ||||
\(556\) | − | 10673.0i | − | 0.814095i | ||||||
\(557\) | 9204.93 | + | 9204.93i | 0.700225 | + | 0.700225i | 0.964459 | − | 0.264234i | \(-0.0851190\pi\) |
−0.264234 | + | 0.964459i | \(0.585119\pi\) | |||||||
\(558\) | 2698.90 | − | 4243.05i | 0.204755 | − | 0.321904i | ||||
\(559\) | −1920.03 | + | 1544.53i | −0.145275 | + | 0.116863i | ||||
\(560\) | 11624.0i | 0.877149i | ||||||||
\(561\) | 678.753 | − | 2331.77i | 0.0510820 | − | 0.175486i | ||||
\(562\) | −192.665 | −0.0144610 | ||||||||
\(563\) | −18033.2 | −1.34993 | −0.674963 | − | 0.737852i | \(-0.735840\pi\) | ||||
−0.674963 | + | 0.737852i | \(0.735840\pi\) | |||||||
\(564\) | 8357.94 | + | 2432.90i | 0.623994 | + | 0.181638i | ||||
\(565\) | −234.947 | − | 234.947i | −0.0174943 | − | 0.0174943i | ||||
\(566\) | 7849.95 | + | 7849.95i | 0.582965 | + | 0.582965i | ||||
\(567\) | −20798.7 | − | 7536.75i | −1.54050 | − | 0.558225i | ||||
\(568\) | −8647.25 | −0.638786 | ||||||||
\(569\) | 11148.1 | 0.821361 | 0.410680 | − | 0.911779i | \(-0.365291\pi\) | ||||
0.410680 | + | 0.911779i | \(0.365291\pi\) | |||||||
\(570\) | 1590.89 | + | 463.089i | 0.116903 | + | 0.0340293i | ||||
\(571\) | 5351.31i | 0.392199i | 0.980584 | + | 0.196099i | \(0.0628275\pi\) | ||||
−0.980584 | + | 0.196099i | \(0.937173\pi\) | |||||||
\(572\) | 3344.64 | + | 362.511i | 0.244487 | + | 0.0264988i | ||||
\(573\) | 7398.53 | − | 4062.38i | 0.539403 | − | 0.296175i | ||||
\(574\) | −7871.52 | − | 7871.52i | −0.572388 | − | 0.572388i | ||||
\(575\) | − | 540.379i | − | 0.0391919i | ||||||
\(576\) | −1943.75 | − | 1236.37i | −0.140607 | − | 0.0894364i | ||||
\(577\) | −13728.6 | − | 13728.6i | −0.990515 | − | 0.990515i | 0.00944038 | − | 0.999955i | \(-0.496995\pi\) |
−0.999955 | + | 0.00944038i | \(0.996995\pi\) | |||||||
\(578\) | 3280.30 | − | 3280.30i | 0.236060 | − | 0.236060i | ||||
\(579\) | −4160.54 | − | 1211.09i | −0.298629 | − | 0.0869276i | ||||
\(580\) | −13386.4 | + | 13386.4i | −0.958348 | + | 0.958348i | ||||
\(581\) | − | 13384.9i | − | 0.955767i | ||||||
\(582\) | 872.015 | + | 1588.14i | 0.0621069 | + | 0.113111i | ||||
\(583\) | 3950.90 | − | 3950.90i | 0.280668 | − | 0.280668i | ||||
\(584\) | 2332.17 | 0.165250 | ||||||||
\(585\) | −14034.1 | + | 17551.8i | −0.991862 | + | 1.24047i | ||||
\(586\) | 10440.6 | 0.736005 | ||||||||
\(587\) | 1912.64 | − | 1912.64i | 0.134486 | − | 0.134486i | −0.636659 | − | 0.771145i | \(-0.719684\pi\) |
0.771145 | + | 0.636659i | \(0.219684\pi\) | |||||||
\(588\) | −8784.33 | − | 15998.3i | −0.616088 | − | 1.12204i | ||||
\(589\) | 1740.36i | 0.121749i | ||||||||
\(590\) | 9742.28 | − | 9742.28i | 0.679802 | − | 0.679802i | ||||
\(591\) | −23217.1 | − | 6758.23i | −1.61594 | − | 0.470383i | ||||
\(592\) | 1994.76 | − | 1994.76i | 0.138486 | − | 0.138486i | ||||
\(593\) | 11122.4 | + | 11122.4i | 0.770223 | + | 0.770223i | 0.978145 | − | 0.207922i | \(-0.0666701\pi\) |
−0.207922 | + | 0.978145i | \(0.566670\pi\) | |||||||
\(594\) | 2291.83 | + | 147.768i | 0.158308 | + | 0.0102071i | ||||
\(595\) | 21328.0i | 1.46952i | ||||||||
\(596\) | −11652.4 | − | 11652.4i | −0.800838 | − | 0.800838i | ||||
\(597\) | 18372.9 | − | 10088.2i | 1.25955 | − | 0.691594i | ||||
\(598\) | −183.417 | − | 19.8797i | −0.0125426 | − | 0.00135943i | ||||
\(599\) | − | 6287.08i | − | 0.428853i | −0.976740 | − | 0.214427i | \(-0.931212\pi\) | ||
0.976740 | − | 0.214427i | \(-0.0687882\pi\) | |||||||
\(600\) | 18531.1 | + | 5394.20i | 1.26088 | + | 0.367029i | ||||
\(601\) | −4651.42 | −0.315700 | −0.157850 | − | 0.987463i | \(-0.550456\pi\) | ||||
−0.157850 | + | 0.987463i | \(0.550456\pi\) | |||||||
\(602\) | −2211.57 | −0.149729 | ||||||||
\(603\) | 17646.9 | − | 3925.34i | 1.19177 | − | 0.265095i | ||||
\(604\) | 5891.78 | + | 5891.78i | 0.396909 | + | 0.396909i | ||||
\(605\) | −14961.6 | − | 14961.6i | −1.00541 | − | 1.00541i | ||||
\(606\) | −8169.23 | − | 2377.97i | −0.547611 | − | 0.159404i | ||||
\(607\) | 5225.96 | 0.349448 | 0.174724 | − | 0.984617i | \(-0.444097\pi\) | ||||
0.174724 | + | 0.984617i | \(0.444097\pi\) | |||||||
\(608\) | 2409.84 | 0.160743 | ||||||||
\(609\) | 7729.84 | − | 26554.9i | 0.514333 | − | 1.76693i | ||||
\(610\) | 2572.78i | 0.170769i | ||||||||
\(611\) | −1392.03 | + | 12843.3i | −0.0921694 | + | 0.850386i | ||||
\(612\) | 5480.79 | + | 3486.19i | 0.362006 | + | 0.230263i | ||||
\(613\) | −9977.15 | − | 9977.15i | −0.657379 | − | 0.657379i | 0.297380 | − | 0.954759i | \(-0.403887\pi\) |
−0.954759 | + | 0.297380i | \(0.903887\pi\) | |||||||
\(614\) | − | 8756.01i | − | 0.575511i | ||||||
\(615\) | 21402.5 | − | 11751.7i | 1.40331 | − | 0.770527i | ||||
\(616\) | 4945.06 | + | 4945.06i | 0.323445 | + | 0.323445i | ||||
\(617\) | −3883.63 | + | 3883.63i | −0.253402 | + | 0.253402i | −0.822364 | − | 0.568962i | \(-0.807345\pi\) |
0.568962 | + | 0.822364i | \(0.307345\pi\) | |||||||
\(618\) | −458.650 | + | 1575.63i | −0.0298537 | + | 0.102559i | ||||
\(619\) | −11697.3 | + | 11697.3i | −0.759537 | + | 0.759537i | −0.976238 | − | 0.216701i | \(-0.930470\pi\) |
0.216701 | + | 0.976238i | \(0.430470\pi\) | |||||||
\(620\) | 14501.0i | 0.939315i | ||||||||
\(621\) | 397.519 | + | 25.6305i | 0.0256874 | + | 0.00165622i | ||||
\(622\) | 3241.09 | − | 3241.09i | 0.208932 | − | 0.208932i | ||||
\(623\) | 26493.7 | 1.70377 | ||||||||
\(624\) | −2003.40 | + | 4856.87i | −0.128526 | + | 0.311587i | ||||
\(625\) | 3193.27 | 0.204369 | ||||||||
\(626\) | 561.539 | − | 561.539i | 0.0358524 | − | 0.0358524i | ||||
\(627\) | −696.705 | + | 382.547i | −0.0443759 | + | 0.0243659i | ||||
\(628\) | − | 1142.30i | − | 0.0725840i | ||||||
\(629\) | 3660.03 | − | 3660.03i | 0.232011 | − | 0.232011i | ||||
\(630\) | −19687.9 | + | 4379.34i | −1.24505 | + | 0.276948i | ||||
\(631\) | 16669.7 | − | 16669.7i | 1.05168 | − | 1.05168i | 0.0530933 | − | 0.998590i | \(-0.483092\pi\) |
0.998590 | − | 0.0530933i | \(-0.0169081\pi\) | |||||||
\(632\) | −8984.90 | − | 8984.90i | −0.565507 | − | 0.565507i | ||||
\(633\) | 12869.8 | + | 23438.8i | 0.808099 | + | 1.47173i | ||||
\(634\) | 4658.51i | 0.291818i | ||||||||
\(635\) | −17363.5 | − | 17363.5i | −1.08512 | − | 1.08512i | ||||
\(636\) | 7192.78 | + | 13099.7i | 0.448447 | + | 0.816724i | ||||
\(637\) | 21105.1 | − | 16977.5i | 1.31274 | − | 1.05600i | ||||
\(638\) | 2871.19i | 0.178169i | ||||||||
\(639\) | 2597.58 | + | 11677.8i | 0.160812 | + | 0.722949i | ||||
\(640\) | 24327.3 | 1.50253 | ||||||||
\(641\) | −16769.7 | −1.03333 | −0.516663 | − | 0.856189i | \(-0.672826\pi\) | ||||
−0.516663 | + | 0.856189i | \(0.672826\pi\) | |||||||
\(642\) | −1150.54 | + | 3952.53i | −0.0707292 | + | 0.242981i | ||||
\(643\) | 9637.04 | + | 9637.04i | 0.591054 | + | 0.591054i | 0.937916 | − | 0.346862i | \(-0.112753\pi\) |
−0.346862 | + | 0.937916i | \(0.612753\pi\) | |||||||
\(644\) | 370.321 | + | 370.321i | 0.0226594 | + | 0.0226594i | ||||
\(645\) | 1355.74 | − | 4657.47i | 0.0827631 | − | 0.284322i | ||||
\(646\) | 710.751 | 0.0432881 | ||||||||
\(647\) | 15564.9 | 0.945781 | 0.472890 | − | 0.881121i | \(-0.343211\pi\) | ||||
0.472890 | + | 0.881121i | \(0.343211\pi\) | |||||||
\(648\) | −4847.08 | + | 13376.2i | −0.293844 | + | 0.810905i | ||||
\(649\) | 6609.13i | 0.399740i | ||||||||
\(650\) | −1332.54 | + | 12294.5i | −0.0804102 | + | 0.741891i | ||||
\(651\) | −10196.2 | − | 18569.7i | −0.613859 | − | 1.11798i | ||||
\(652\) | −14306.4 | − | 14306.4i | −0.859329 | − | 0.859329i | ||||
\(653\) | 26562.0i | 1.59181i | 0.605424 | + | 0.795903i | \(0.293004\pi\) | ||||
−0.605424 | + | 0.795903i | \(0.706996\pi\) | |||||||
\(654\) | −146.883 | − | 267.507i | −0.00878221 | − | 0.0159944i | ||||
\(655\) | −12786.3 | − | 12786.3i | −0.762753 | − | 0.762753i | ||||
\(656\) | 4036.38 | − | 4036.38i | 0.240235 | − | 0.240235i | ||||
\(657\) | −700.570 | − | 3149.50i | −0.0416010 | − | 0.187023i | ||||
\(658\) | −8198.42 | + | 8198.42i | −0.485726 | + | 0.485726i | ||||
\(659\) | − | 16494.7i | − | 0.975026i | −0.873116 | − | 0.487513i | \(-0.837904\pi\) | ||
0.873116 | − | 0.487513i | \(-0.162096\pi\) | |||||||
\(660\) | −5805.08 | + | 3187.45i | −0.342367 | + | 0.187987i | ||||
\(661\) | −22055.3 | + | 22055.3i | −1.29781 | + | 1.29781i | −0.367968 | + | 0.929839i | \(0.619946\pi\) |
−0.929839 | + | 0.367968i | \(0.880054\pi\) | |||||||
\(662\) | 2859.43 | 0.167878 | ||||||||
\(663\) | −3675.89 | + | 8911.51i | −0.215324 | + | 0.522013i | ||||
\(664\) | −8608.19 | −0.503107 | ||||||||
\(665\) | 4935.79 | − | 4935.79i | 0.287822 | − | 0.287822i | ||||
\(666\) | 4130.10 | + | 2627.05i | 0.240297 | + | 0.152847i | ||||
\(667\) | 498.010i | 0.0289101i | ||||||||
\(668\) | 9697.11 | − | 9697.11i | 0.561665 | − | 0.561665i | ||||
\(669\) | 3759.25 | − | 12914.4i | 0.217251 | − | 0.746338i | ||||
\(670\) | 11654.6 | − | 11654.6i | 0.672026 | − | 0.672026i | ||||
\(671\) | −872.683 | − | 872.683i | −0.0502080 | − | 0.0502080i | ||||
\(672\) | −25713.0 | + | 14118.5i | −1.47604 | + | 0.810465i | ||||
\(673\) | 19116.7i | 1.09494i | 0.836825 | + | 0.547471i | \(0.184409\pi\) | ||||
−0.836825 | + | 0.547471i | \(0.815591\pi\) | |||||||
\(674\) | −9269.46 | − | 9269.46i | −0.529742 | − | 0.529742i | ||||
\(675\) | 1718.02 | − | 26645.8i | 0.0979652 | − | 1.51941i | ||||
\(676\) | −13043.8 | − | 2861.14i | −0.742140 | − | 0.162787i | ||||
\(677\) | − | 10209.1i | − | 0.579567i | −0.957092 | − | 0.289783i | \(-0.906417\pi\) | ||
0.957092 | − | 0.289783i | \(-0.0935833\pi\) | |||||||
\(678\) | 37.6705 | − | 129.412i | 0.00213382 | − | 0.00733046i | ||||
\(679\) | 7632.73 | 0.431395 | ||||||||
\(680\) | 13716.6 | 0.773540 | ||||||||
\(681\) | −17615.3 | − | 5127.63i | −0.991221 | − | 0.288533i | ||||
\(682\) | 1555.13 | + | 1555.13i | 0.0873150 | + | 0.0873150i | ||||
\(683\) | 3196.97 | + | 3196.97i | 0.179105 | + | 0.179105i | 0.790966 | − | 0.611861i | \(-0.209579\pi\) |
−0.611861 | + | 0.790966i | \(0.709579\pi\) | |||||||
\(684\) | −461.596 | − | 2075.17i | −0.0258035 | − | 0.116003i | ||||
\(685\) | −27973.7 | −1.56032 | ||||||||
\(686\) | 9880.47 | 0.549910 | ||||||||
\(687\) | 9158.33 | + | 2665.89i | 0.508606 | + | 0.148050i | ||||
\(688\) | − | 1134.05i | − | 0.0628422i | ||||||
\(689\) | −17281.2 | + | 13901.5i | −0.955533 | + | 0.768656i | ||||
\(690\) | 318.345 | − | 174.797i | 0.0175640 | − | 0.00964405i | ||||
\(691\) | 23607.5 | + | 23607.5i | 1.29967 | + | 1.29967i | 0.928608 | + | 0.371063i | \(0.121007\pi\) |
0.371063 | + | 0.928608i | \(0.378993\pi\) | |||||||
\(692\) | 21148.4i | 1.16176i | ||||||||
\(693\) | 5192.63 | − | 8163.56i | 0.284635 | − | 0.447486i | ||||
\(694\) | 12412.7 | + | 12412.7i | 0.678935 | + | 0.678935i | ||||
\(695\) | −22048.0 | + | 22048.0i | −1.20335 | + | 1.20335i | ||||
\(696\) | −17078.1 | − | 4971.26i | −0.930094 | − | 0.270740i | ||||
\(697\) | 7406.06 | − | 7406.06i | 0.402474 | − | 0.402474i | ||||
\(698\) | 1482.34i | 0.0803832i | ||||||||
\(699\) | 935.772 | + | 1704.26i | 0.0506354 | + | 0.0922187i | ||||
\(700\) | 24822.7 | − | 24822.7i | 1.34030 | − | 1.34030i | ||||
\(701\) | −23768.5 | −1.28063 | −0.640316 | − | 0.768111i | \(-0.721197\pi\) | ||||
−0.640316 | + | 0.768111i | \(0.721197\pi\) | |||||||
\(702\) | −8981.00 | − | 1563.39i | −0.482857 | − | 0.0840548i | ||||
\(703\) | −1694.03 | −0.0908841 | ||||||||
\(704\) | 712.406 | − | 712.406i | 0.0381389 | − | 0.0381389i | ||||
\(705\) | −12239.7 | − | 22291.4i | −0.653865 | − | 1.19084i | ||||
\(706\) | 7282.05i | 0.388192i | ||||||||
\(707\) | −25345.4 | + | 25345.4i | −1.34825 | + | 1.34825i | ||||
\(708\) | −16972.8 | − | 4940.60i | −0.900956 | − | 0.262259i | ||||
\(709\) | −6842.97 | + | 6842.97i | −0.362473 | + | 0.362473i | −0.864723 | − | 0.502250i | \(-0.832506\pi\) |
0.502250 | + | 0.864723i | \(0.332506\pi\) | |||||||
\(710\) | 7712.40 | + | 7712.40i | 0.407664 | + | 0.407664i | ||||
\(711\) | −9434.73 | + | 14832.7i | −0.497651 | + | 0.782379i | ||||
\(712\) | − | 17038.8i | − | 0.896849i | ||||||
\(713\) | 269.738 | + | 269.738i | 0.0141680 | + | 0.0141680i | ||||
\(714\) | −7583.72 | + | 4164.07i | −0.397498 | + | 0.218258i | ||||
\(715\) | −6160.39 | − | 7658.11i | −0.322217 | − | 0.400555i | ||||
\(716\) | − | 12606.3i | − | 0.657990i | ||||||
\(717\) | 102.589 | + | 29.8626i | 0.00534346 | + | 0.00155542i | ||||
\(718\) | 13379.3 | 0.695419 | ||||||||
\(719\) | 14543.7 | 0.754365 | 0.377183 | − | 0.926139i | \(-0.376893\pi\) | ||||
0.377183 | + | 0.926139i | \(0.376893\pi\) | |||||||
\(720\) | −2245.65 | − | 10095.6i | −0.116237 | − | 0.522557i | ||||
\(721\) | 4888.47 | + | 4888.47i | 0.252505 | + | 0.252505i | ||||
\(722\) | 6558.97 | + | 6558.97i | 0.338088 | + | 0.338088i | ||||
\(723\) | 2950.03 | + | 858.721i | 0.151747 | + | 0.0441718i | ||||
\(724\) | 24498.5 | 1.25757 | ||||||||
\(725\) | 33381.8 | 1.71002 | ||||||||
\(726\) | 2398.88 | − | 8241.07i | 0.122632 | − | 0.421287i | ||||
\(727\) | 37001.0i | 1.88761i | 0.330508 | + | 0.943803i | \(0.392780\pi\) | ||||
−0.330508 | + | 0.943803i | \(0.607220\pi\) | |||||||
\(728\) | −17399.5 | − | 21629.7i | −0.885808 | − | 1.10117i | ||||
\(729\) | 19520.0 | + | 2527.65i | 0.991720 | + | 0.128418i | ||||
\(730\) | −2080.04 | − | 2080.04i | −0.105460 | − | 0.105460i | ||||
\(731\) | − | 2080.79i | − | 0.105282i | ||||||
\(732\) | 2893.49 | − | 1588.76i | 0.146102 | − | 0.0802215i | ||||
\(733\) | −25498.3 | − | 25498.3i | −1.28486 | − | 1.28486i | −0.937870 | − | 0.346987i | \(-0.887205\pi\) |
−0.346987 | − | 0.937870i | \(-0.612795\pi\) | |||||||
\(734\) | 5448.25 | − | 5448.25i | 0.273976 | − | 0.273976i | ||||
\(735\) | −14902.3 | + | 51195.1i | −0.747864 | + | 2.56919i | ||||
\(736\) | 373.499 | − | 373.499i | 0.0187057 | − | 0.0187057i | ||||
\(737\) | 7906.46i | 0.395167i | ||||||||
\(738\) | 8357.24 | + | 5315.83i | 0.416849 | + | 0.265147i | ||||
\(739\) | 19940.2 | − | 19940.2i | 0.992574 | − | 0.992574i | −0.00739871 | − | 0.999973i | \(-0.502355\pi\) |
0.999973 | + | 0.00739871i | \(0.00235511\pi\) | |||||||
\(740\) | −14115.0 | −0.701186 | ||||||||
\(741\) | 2913.02 | − | 1211.64i | 0.144416 | − | 0.0600685i | ||||
\(742\) | −19905.2 | −0.984827 | ||||||||
\(743\) | 14891.9 | − | 14891.9i | 0.735302 | − | 0.735302i | −0.236363 | − | 0.971665i | \(-0.575955\pi\) |
0.971665 | + | 0.236363i | \(0.0759555\pi\) | |||||||
\(744\) | −11942.6 | + | 6557.46i | −0.588492 | + | 0.323129i | ||||
\(745\) | 48142.1i | 2.36750i | ||||||||
\(746\) | −10148.8 | + | 10148.8i | −0.498090 | + | 0.498090i | ||||
\(747\) | 2585.85 | + | 11625.0i | 0.126655 | + | 0.569393i | ||||
\(748\) | −2008.77 | + | 2008.77i | −0.0981924 | + | 0.0981924i | ||||
\(749\) | 12262.9 | + | 12262.9i | 0.598233 | + | 0.598233i | ||||
\(750\) | −4021.30 | − | 7323.71i | −0.195783 | − | 0.356565i | ||||
\(751\) | − | 29500.0i | − | 1.43338i | −0.697391 | − | 0.716691i | \(-0.745656\pi\) | ||
0.697391 | − | 0.716691i | \(-0.254344\pi\) | |||||||
\(752\) | −4204.01 | − | 4204.01i | −0.203862 | − | 0.203862i | ||||
\(753\) | 9103.67 | + | 16579.9i | 0.440579 | + | 0.802396i | ||||
\(754\) | 1228.06 | − | 11330.5i | 0.0593149 | − | 0.547259i | ||||
\(755\) | − | 24342.1i | − | 1.17337i | ||||||
\(756\) | 17083.0 | + | 19437.7i | 0.821829 | + | 0.935109i | ||||
\(757\) | 33559.2 | 1.61127 | 0.805634 | − | 0.592414i | \(-0.201825\pi\) | ||||
0.805634 | + | 0.592414i | \(0.201825\pi\) | |||||||
\(758\) | 1157.05 | 0.0554431 | ||||||||
\(759\) | −48.6912 | + | 167.273i | −0.00232856 | + | 0.00799949i | ||||
\(760\) | −3174.33 | − | 3174.33i | −0.151507 | − | 0.151507i | ||||
\(761\) | −7495.37 | − | 7495.37i | −0.357039 | − | 0.357039i | 0.505681 | − | 0.862720i | \(-0.331241\pi\) |
−0.862720 | + | 0.505681i | \(0.831241\pi\) | |||||||
\(762\) | 2783.99 | − | 9564.06i | 0.132354 | − | 0.454684i | ||||
\(763\) | −1285.66 | −0.0610014 | ||||||||
\(764\) | −9873.33 | −0.467545 | ||||||||
\(765\) | −4120.38 | − | 18523.7i | −0.194735 | − | 0.875458i | ||||
\(766\) | − | 11018.2i | − | 0.519718i | ||||||
\(767\) | 2826.85 | − | 26081.5i | 0.133079 | − | 1.22783i | ||||
\(768\) | 6456.67 | + | 11759.1i | 0.303366 | + | 0.552499i | ||||
\(769\) | 3499.00 | + | 3499.00i | 0.164080 | + | 0.164080i | 0.784371 | − | 0.620292i | \(-0.212986\pi\) |
−0.620292 | + | 0.784371i | \(0.712986\pi\) | |||||||
\(770\) | − | 8820.90i | − | 0.412835i | ||||||
\(771\) | −20121.9 | − | 36646.5i | −0.939911 | − | 1.71179i | ||||
\(772\) | 3584.22 | + | 3584.22i | 0.167097 | + | 0.167097i | ||||
\(773\) | 21389.3 | − | 21389.3i | 0.995240 | − | 0.995240i | −0.00474920 | − | 0.999989i | \(-0.501512\pi\) |
0.999989 | + | 0.00474920i | \(0.00151172\pi\) | |||||||
\(774\) | 1920.78 | − | 427.255i | 0.0892003 | − | 0.0198416i | ||||
\(775\) | 18080.6 | − | 18080.6i | 0.838031 | − | 0.838031i | ||||
\(776\) | − | 4908.81i | − | 0.227082i | ||||||
\(777\) | 18075.3 | − | 9924.80i | 0.834554 | − | 0.458237i | ||||
\(778\) | 889.290 | − | 889.290i | 0.0409802 | − | 0.0409802i | ||||
\(779\) | −3427.86 | −0.157659 | ||||||||
\(780\) | 24271.8 | − | 10095.6i | 1.11419 | − | 0.463438i | ||||
\(781\) | −5232.07 | −0.239716 | ||||||||
\(782\) | 110.159 | − | 110.159i | 0.00503743 | − | 0.00503743i | ||||
\(783\) | −1583.32 | + | 24556.7i | −0.0722645 | + | 1.12080i | ||||
\(784\) | 12465.6i | 0.567855i | ||||||||
\(785\) | −2359.72 | + | 2359.72i | −0.107289 | + | 0.107289i | ||||
\(786\) | 2050.11 | − | 7042.91i | 0.0930345 | − | 0.319608i | ||||
\(787\) | −18104.8 | + | 18104.8i | −0.820033 | + | 0.820033i | −0.986112 | − | 0.166079i | \(-0.946889\pi\) |
0.166079 | + | 0.986112i | \(0.446889\pi\) | |||||||
\(788\) | 20001.0 | + | 20001.0i | 0.904196 | + | 0.904196i | ||||
\(789\) | 9860.68 | − | 5414.30i | 0.444930 | − | 0.244302i | ||||
\(790\) | 16027.1i | 0.721796i | ||||||||
\(791\) | −401.508 | − | 401.508i | −0.0180480 | − | 0.0180480i | ||||
\(792\) | −5250.20 | − | 3339.52i | −0.235553 | − | 0.149829i | ||||
\(793\) | 3070.59 | + | 3817.11i | 0.137503 | + | 0.170933i | ||||
\(794\) | − | 78.1746i | − | 0.00349409i | ||||||
\(795\) | 12202.3 | − | 41919.5i | 0.544366 | − | 1.87010i | ||||
\(796\) | −24518.6 | −1.09176 | ||||||||
\(797\) | 33484.2 | 1.48817 | 0.744086 | − | 0.668084i | \(-0.232885\pi\) | ||||
0.744086 | + | 0.668084i | \(0.232885\pi\) | |||||||
\(798\) | 2718.71 | + | 791.386i | 0.120603 | + | 0.0351062i | ||||
\(799\) | −7713.62 | − | 7713.62i | −0.341537 | − | 0.341537i | ||||
\(800\) | −25035.8 | − | 25035.8i | −1.10644 | − | 1.10644i | ||||
\(801\) | −23010.2 | + | 5118.35i | −1.01501 | + | 0.225778i | ||||
\(802\) | −17592.2 | −0.774565 | ||||||||
\(803\) | 1411.09 | 0.0620130 | ||||||||
\(804\) | −20304.5 | − | 5910.41i | −0.890651 | − | 0.259259i | ||||
\(805\) | − | 1529.99i | − | 0.0669877i | ||||||
\(806\) | −5471.80 | − | 6802.12i | −0.239127 | − | 0.297264i | ||||
\(807\) | 38643.6 | − | 21218.4i | 1.68565 | − | 0.925556i | ||||
\(808\) | 16300.3 | + | 16300.3i | 0.709705 | + | 0.709705i | ||||
\(809\) | − | 17431.9i | − | 0.757568i | −0.925485 | − | 0.378784i | \(-0.876342\pi\) | ||
0.925485 | − | 0.378784i | \(-0.123658\pi\) | |||||||
\(810\) | 16253.2 | − | 7607.04i | 0.705035 | − | 0.329980i | ||||
\(811\) | 27929.2 | + | 27929.2i | 1.20928 | + | 1.20928i | 0.971261 | + | 0.238019i | \(0.0764980\pi\) |
0.238019 | + | 0.971261i | \(0.423502\pi\) | |||||||
\(812\) | −22876.5 | + | 22876.5i | −0.988678 | + | 0.988678i | ||||
\(813\) | −15933.1 | − | 4637.95i | −0.687328 | − | 0.200074i | ||||
\(814\) | −1513.73 | + | 1513.73i | −0.0651795 | + | 0.0651795i | ||||
\(815\) | 59107.4i | 2.54042i | ||||||||
\(816\) | −2135.26 | − | 3888.81i | −0.0916044 | − | 0.166833i | ||||
\(817\) | −481.543 | + | 481.543i | −0.0206206 | + | 0.0206206i | ||||
\(818\) | −2265.82 | −0.0968489 | ||||||||
\(819\) | −23983.3 | + | 29994.7i | −1.02325 | + | 1.27973i | ||||
\(820\) | −28561.6 | −1.21636 | ||||||||
\(821\) | −977.281 | + | 977.281i | −0.0415437 | + | 0.0415437i | −0.727573 | − | 0.686030i | \(-0.759352\pi\) |
0.686030 | + | 0.727573i | \(0.259352\pi\) | |||||||
\(822\) | −5461.58 | − | 9946.78i | −0.231745 | − | 0.422060i | ||||
\(823\) | − | 18625.0i | − | 0.788856i | −0.918927 | − | 0.394428i | \(-0.870943\pi\) | ||
0.918927 | − | 0.394428i | \(-0.129057\pi\) | |||||||
\(824\) | 3143.90 | − | 3143.90i | 0.132916 | − | 0.132916i | ||||
\(825\) | 11212.3 | + | 3263.79i | 0.473168 | + | 0.137734i | ||||
\(826\) | 16648.9 | − | 16648.9i | 0.701317 | − | 0.701317i | ||||
\(827\) | −18545.6 | − | 18545.6i | −0.779799 | − | 0.779799i | 0.199997 | − | 0.979796i | \(-0.435907\pi\) |
−0.979796 | + | 0.199997i | \(0.935907\pi\) | |||||||
\(828\) | −393.172 | − | 250.086i | −0.0165020 | − | 0.0104965i | ||||
\(829\) | 30011.6i | 1.25735i | 0.777667 | + | 0.628676i | \(0.216403\pi\) | ||||
−0.777667 | + | 0.628676i | \(0.783597\pi\) | |||||||
\(830\) | 7677.57 | + | 7677.57i | 0.321075 | + | 0.321075i | ||||
\(831\) | −31966.1 | + | 17551.9i | −1.33441 | + | 0.732696i | ||||
\(832\) | −3116.06 | + | 2506.64i | −0.129844 | + | 0.104450i | ||||
\(833\) | 22872.1i | 0.951347i | ||||||||
\(834\) | −12144.4 | − | 3535.09i | −0.504226 | − | 0.146775i | ||||
\(835\) | −40063.9 | −1.66044 | ||||||||
\(836\) | 929.752 | 0.0384643 | ||||||||
\(837\) | 12443.1 | + | 14158.2i | 0.513854 | + | 0.584683i | ||||
\(838\) | 1468.96 | + | 1468.96i | 0.0605542 | + | 0.0605542i | ||||
\(839\) | 29877.0 | + | 29877.0i | 1.22940 | + | 1.22940i | 0.964190 | + | 0.265211i | \(0.0854415\pi\) |
0.265211 | + | 0.964190i | \(0.414558\pi\) | |||||||
\(840\) | 52467.7 | + | 15272.8i | 2.15513 | + | 0.627334i | ||||
\(841\) | −6375.44 | −0.261407 | ||||||||
\(842\) | −19489.6 | −0.797692 | ||||||||
\(843\) | 201.838 | − | 693.388i | 0.00824633 | − | 0.0283293i | ||||
\(844\) | − | 31279.0i | − | 1.27567i | ||||||
\(845\) | 21035.1 | + | 32856.0i | 0.856366 | + | 1.33761i | ||||
\(846\) | 5536.59 | − | 8704.31i | 0.225002 | − | 0.353736i | ||||
\(847\) | −25568.3 | − | 25568.3i | −1.03723 | − | 1.03723i | ||||
\(848\) | − | 10207.0i | − | 0.413338i | ||||||
\(849\) | −36475.2 | + | 20027.8i | −1.47447 | + | 0.809601i | ||||
\(850\) | −7383.98 | − | 7383.98i | −0.297963 | − | 0.297963i | ||||
\(851\) | −262.557 | + | 262.557i | −0.0105762 | + | 0.0105762i | ||||
\(852\) | 3911.19 | − | 13436.4i | 0.157271 | − | 0.540285i | ||||
\(853\) | −2542.34 | + | 2542.34i | −0.102049 | + | 0.102049i | −0.756288 | − | 0.654239i | \(-0.772989\pi\) |
0.654239 | + | 0.756288i | \(0.272989\pi\) | |||||||
\(854\) | 4396.70i | 0.176173i | ||||||||
\(855\) | −3333.26 | + | 5240.36i | −0.133327 | + | 0.209610i | ||||
\(856\) | 7886.58 | − | 7886.58i | 0.314904 | − | 0.314904i | ||||
\(857\) | −670.949 | −0.0267435 | −0.0133717 | − | 0.999911i | \(-0.504256\pi\) | ||||
−0.0133717 | + | 0.999911i | \(0.504256\pi\) | |||||||
\(858\) | 1520.29 | − | 3685.65i | 0.0604916 | − | 0.146650i | ||||
\(859\) | −21485.2 | −0.853396 | −0.426698 | − | 0.904394i | \(-0.640323\pi\) | ||||
−0.426698 | + | 0.904394i | \(0.640323\pi\) | |||||||
\(860\) | −4012.31 | + | 4012.31i | −0.159092 | + | 0.159092i | ||||
\(861\) | 36575.4 | − | 20082.8i | 1.44772 | − | 0.794913i | ||||
\(862\) | 7276.39i | 0.287511i | ||||||||
\(863\) | 5985.24 | − | 5985.24i | 0.236084 | − | 0.236084i | −0.579143 | − | 0.815226i | \(-0.696613\pi\) |
0.815226 | + | 0.579143i | \(0.196613\pi\) | |||||||
\(864\) | 19604.6 | − | 17229.6i | 0.771945 | − | 0.678431i | ||||
\(865\) | 43687.5 | − | 43687.5i | 1.71725 | − | 1.71725i | ||||
\(866\) | 5119.33 | + | 5119.33i | 0.200880 | + | 0.200880i | ||||
\(867\) | 8369.11 | + | 15242.1i | 0.327831 | + | 0.597056i | ||||
\(868\) | 24781.2i | 0.969043i | ||||||||
\(869\) | −5436.37 | − | 5436.37i | −0.212216 | − | 0.212216i | ||||
\(870\) | 10798.0 | + | 19665.7i | 0.420790 | + | 0.766354i | ||||
\(871\) | 3381.75 | − | 31201.1i | 0.131557 | − | 1.21379i | ||||
\(872\) | 826.842i | 0.0321105i | ||||||||
\(873\) | −6629.14 | + | 1474.58i | −0.257002 | + | 0.0571670i | ||||
\(874\) | −50.9866 | −0.00197328 | ||||||||
\(875\) | −35198.4 | −1.35991 | ||||||||
\(876\) | −1054.85 | + | 3623.81i | −0.0406851 | + | 0.139768i | ||||
\(877\) | −15989.8 | − | 15989.8i | −0.615664 | − | 0.615664i | 0.328752 | − | 0.944416i | \(-0.393372\pi\) |
−0.944416 | + | 0.328752i | \(0.893372\pi\) | |||||||
\(878\) | −4929.42 | − | 4929.42i | −0.189476 | − | 0.189476i | ||||
\(879\) | −10937.7 | + | 37575.2i | −0.419705 | + | 1.44184i | ||||
\(880\) | 4523.21 | 0.173270 | ||||||||
\(881\) | 4784.23 | 0.182957 | 0.0914784 | − | 0.995807i | \(-0.470841\pi\) | ||||
0.0914784 | + | 0.995807i | \(0.470841\pi\) | |||||||
\(882\) | −21113.3 | + | 4696.39i | −0.806032 | + | 0.179292i | ||||
\(883\) | 14740.6i | 0.561792i | 0.959738 | + | 0.280896i | \(0.0906316\pi\) | ||||
−0.959738 | + | 0.280896i | \(0.909368\pi\) | |||||||
\(884\) | 8786.36 | − | 7067.98i | 0.334296 | − | 0.268916i | ||||
\(885\) | 24855.7 | + | 45268.0i | 0.944086 | + | 1.71940i | ||||
\(886\) | −14248.0 | − | 14248.0i | −0.540261 | − | 0.540261i | ||||
\(887\) | − | 33315.4i | − | 1.26113i | −0.776137 | − | 0.630564i | \(-0.782824\pi\) | ||
0.776137 | − | 0.630564i | \(-0.217176\pi\) | |||||||
\(888\) | −6382.90 | − | 11624.7i | −0.241212 | − | 0.439302i | ||||
\(889\) | −29672.9 | − | 29672.9i | −1.11946 | − | 1.11946i | ||||
\(890\) | −15196.8 | + | 15196.8i | −0.572356 | + | 0.572356i | ||||
\(891\) | −2932.75 | + | 8093.34i | −0.110270 | + | 0.304307i | ||||
\(892\) | −11125.5 | + | 11125.5i | −0.417611 | + | 0.417611i | ||||
\(893\) | 3570.22i | 0.133788i | ||||||||
\(894\) | −17118.2 | + | 9399.24i | −0.640400 | + | 0.351630i | ||||
\(895\) | −26041.7 | + | 26041.7i | −0.972603 | + | 0.972603i | ||||
\(896\) | 41573.6 | 1.55009 | ||||||||
\(897\) | 263.695 | − | 639.279i | 0.00981552 | − | 0.0237959i | ||||
\(898\) | −2730.65 | −0.101473 | ||||||||
\(899\) | −16663.0 | + | 16663.0i | −0.618177 | + | 0.618177i | ||||
\(900\) | −16763.4 | + | 26354.4i | −0.620866 | + | 0.976089i | ||||
\(901\) | − | 18728.1i | − | 0.692480i | ||||||
\(902\) | −3063.02 | + | 3063.02i | −0.113068 | + | 0.113068i | ||||
\(903\) | 2316.86 | − | 7959.29i | 0.0853824 | − | 0.293321i | ||||
\(904\) | −258.220 | + | 258.220i | −0.00950030 | + | 0.00950030i | ||||
\(905\) | −50608.2 | − | 50608.2i | −1.85887 | − | 1.85887i | ||||
\(906\) | 8655.45 | − | 4752.53i | 0.317393 | − | 0.174274i | ||||
\(907\) | 1739.58i | 0.0636844i | 0.999493 | + | 0.0318422i | \(0.0101374\pi\) | ||||
−0.999493 | + | 0.0318422i | \(0.989863\pi\) | |||||||
\(908\) | 15175.2 | + | 15175.2i | 0.554634 | + | 0.554634i | ||||
\(909\) | 17116.3 | − | 26909.3i | 0.624547 | − | 0.981877i | ||||
\(910\) | −3772.87 | + | 34809.8i | −0.137439 | + | 1.26806i | ||||
\(911\) | − | 20866.1i | − | 0.758864i | −0.925220 | − | 0.379432i | \(-0.876119\pi\) | ||
0.925220 | − | 0.379432i | \(-0.123881\pi\) | |||||||
\(912\) | −405.810 | + | 1394.11i | −0.0147343 | + | 0.0506179i | ||||
\(913\) | −5208.44 | −0.188800 | ||||||||
\(914\) | 2991.16 | 0.108248 | ||||||||
\(915\) | −9259.27 | − | 2695.27i | −0.334538 | − | 0.0973803i | ||||
\(916\) | −7889.70 | − | 7889.70i | −0.284589 | − | 0.284589i | ||||
\(917\) | −21850.9 | − | 21850.9i | −0.786893 | − | 0.786893i | ||||
\(918\) | 5782.12 | − | 5081.66i | 0.207885 | − | 0.182701i | ||||
\(919\) | 36900.1 | 1.32451 | 0.662254 | − | 0.749280i | \(-0.269600\pi\) | ||||
0.662254 | + | 0.749280i | \(0.269600\pi\) | |||||||
\(920\) | −983.977 | −0.0352617 | ||||||||
\(921\) | 31512.3 | + | 9172.89i | 1.12743 | + | 0.328184i | ||||
\(922\) | 3573.85i | 0.127656i | ||||||||
\(923\) | 20647.2 | + | 2237.86i | 0.736307 | + | 0.0798049i | ||||
\(924\) | −9920.47 | + | 5447.13i | −0.353203 | + | 0.193937i | ||||
\(925\) | 17599.3 | + | 17599.3i | 0.625579 | + | 0.625579i | ||||
\(926\) | 23215.1i | 0.823861i | ||||||||
\(927\) | −5190.12 | − | 3301.30i | −0.183890 | − | 0.116968i | ||||
\(928\) | 23072.8 | + | 23072.8i | 0.816167 | + | 0.816167i | ||||
\(929\) | 13969.2 | − | 13969.2i | 0.493340 | − | 0.493340i | −0.416017 | − | 0.909357i | \(-0.636574\pi\) |
0.909357 | + | 0.416017i | \(0.136574\pi\) | |||||||
\(930\) | 16500.1 | + | 4802.99i | 0.581783 | + | 0.169351i | ||||
\(931\) | 5293.13 | − | 5293.13i | 0.186332 | − | 0.186332i | ||||
\(932\) | − | 2274.33i | − | 0.0799335i | ||||||
\(933\) | 8269.07 | + | 15059.9i | 0.290158 | + | 0.528444i | ||||
\(934\) | 9213.97 | − | 9213.97i | 0.322795 | − | 0.322795i | ||||
\(935\) | 8299.30 | 0.290285 | ||||||||
\(936\) | 19290.4 | + | 15424.3i | 0.673638 | + | 0.538631i | ||||
\(937\) | 13597.8 | 0.474088 | 0.237044 | − | 0.971499i | \(-0.423821\pi\) | ||||
0.237044 | + | 0.971499i | \(0.423821\pi\) | |||||||
\(938\) | 19916.9 | − | 19916.9i | 0.693295 | − | 0.693295i | ||||
\(939\) | 1432.67 | + | 2609.22i | 0.0497906 | + | 0.0906801i | ||||
\(940\) | 29747.8i | 1.03220i | ||||||||
\(941\) | −18089.6 | + | 18089.6i | −0.626678 | + | 0.626678i | −0.947231 | − | 0.320553i | \(-0.896131\pi\) |
0.320553 | + | 0.947231i | \(0.396131\pi\) | |||||||
\(942\) | −1299.77 | − | 378.349i | −0.0449563 | − | 0.0130863i | ||||
\(943\) | −531.283 | + | 531.283i | −0.0183467 | + | 0.0183467i | ||||
\(944\) | 8537.26 | + | 8537.26i | 0.294347 | + | 0.294347i | ||||
\(945\) | 4864.28 | − | 75443.2i | 0.167444 | − | 2.59700i | ||||
\(946\) | 860.581i | 0.0295771i | ||||||||
\(947\) | 1830.89 | + | 1830.89i | 0.0628257 | + | 0.0628257i | 0.737822 | − | 0.674996i | \(-0.235855\pi\) |
−0.674996 | + | 0.737822i | \(0.735855\pi\) | |||||||
\(948\) | 18025.0 | − | 9897.14i | 0.617535 | − | 0.339076i | ||||
\(949\) | −5568.58 | − | 603.552i | −0.190478 | − | 0.0206450i | ||||
\(950\) | 3417.65i | 0.116719i | ||||||||
\(951\) | −16765.7 | − | 4880.30i | −0.571676 | − | 0.166409i | ||||
\(952\) | 23440.7 | 0.798021 | ||||||||
\(953\) | 10645.7 | 0.361855 | 0.180927 | − | 0.983496i | \(-0.442090\pi\) | ||||
0.180927 | + | 0.983496i | \(0.442090\pi\) | |||||||
\(954\) | 17287.9 | − | 3845.50i | 0.586706 | − | 0.130506i | ||||
\(955\) | 20396.0 | + | 20396.0i | 0.691098 | + | 0.691098i | ||||
\(956\) | −88.3783 | − | 88.3783i | −0.00298991 | − | 0.00298991i | ||||
\(957\) | −10333.2 | − | 3007.89i | −0.349034 | − | 0.101600i | ||||
\(958\) | −7978.00 | −0.269058 | ||||||||
\(959\) | −47805.1 | −1.60970 | ||||||||
\(960\) | 2200.26 | − | 7558.71i | 0.0739719 | − | 0.254121i | ||||
\(961\) | − | 11740.6i | − | 0.394100i | ||||||
\(962\) | 6621.04 | − | 5326.14i | 0.221903 | − | 0.178505i | ||||
\(963\) | −13019.6 | − | 8281.42i | −0.435670 | − | 0.277119i | ||||
\(964\) | −2541.39 | − | 2541.39i | −0.0849093 | − | 0.0849093i | ||||
\(965\) | − | 14808.3i | − | 0.493985i | ||||||
\(966\) | 544.028 | − | 298.715i | 0.0181199 | − | 0.00994927i | ||||
\(967\) | 2868.25 | + | 2868.25i | 0.0953843 | + | 0.0953843i | 0.753189 | − | 0.657804i | \(-0.228515\pi\) |
−0.657804 | + | 0.753189i | \(0.728515\pi\) | |||||||
\(968\) | −16443.6 | + | 16443.6i | −0.545989 | + | 0.545989i | ||||
\(969\) | −744.590 | + | 2557.95i | −0.0246849 | + | 0.0848019i | ||||
\(970\) | −4378.12 | + | 4378.12i | −0.144921 | + | 0.144921i | ||||
\(971\) | − | 28264.0i | − | 0.934123i | −0.884225 | − | 0.467062i | \(-0.845313\pi\) | ||
0.884225 | − | 0.467062i | \(-0.154687\pi\) | |||||||
\(972\) | −18592.0 | − | 13581.7i | −0.613518 | − | 0.448181i | ||||
\(973\) | −37678.4 | + | 37678.4i | −1.24143 | + | 1.24143i | ||||
\(974\) | −18620.8 | −0.612575 | ||||||||
\(975\) | −42851.0 | − | 17675.6i | −1.40752 | − | 0.580586i | ||||
\(976\) | −2254.55 | −0.0739410 | ||||||||
\(977\) | 9578.62 | − | 9578.62i | 0.313661 | − | 0.313661i | −0.532665 | − | 0.846326i | \(-0.678809\pi\) |
0.846326 | + | 0.532665i | \(0.178809\pi\) | |||||||
\(978\) | −21017.2 | + | 11540.1i | −0.687173 | + | 0.377313i | ||||
\(979\) | − | 10309.4i | − | 0.336559i | ||||||
\(980\) | 44103.4 | − | 44103.4i | 1.43758 | − | 1.43758i | ||||
\(981\) | 1116.62 | − | 248.378i | 0.0363413 | − | 0.00808369i | ||||
\(982\) | −9910.49 | + | 9910.49i | −0.322053 | + | 0.322053i | ||||
\(983\) | 3628.32 | + | 3628.32i | 0.117727 | + | 0.117727i | 0.763516 | − | 0.645789i | \(-0.223471\pi\) |
−0.645789 | + | 0.763516i | \(0.723471\pi\) | |||||||
\(984\) | −12915.8 | − | 23522.6i | −0.418435 | − | 0.762065i | ||||
\(985\) | − | 82634.8i | − | 2.67306i | ||||||
\(986\) | 6805.04 | + | 6805.04i | 0.219794 | + | 0.219794i | ||||
\(987\) | −20916.8 | − | 38094.3i | −0.674559 | − | 1.22853i | ||||
\(988\) | −3669.06 | − | 397.673i | −0.118146 | − | 0.0128053i | ||||
\(989\) | 149.268i | 0.00479925i | ||||||||
\(990\) | 1704.12 | + | 7661.08i | 0.0547075 | + | 0.245945i | ||||
\(991\) | −5968.73 | −0.191325 | −0.0956624 | − | 0.995414i | \(-0.530497\pi\) | ||||
−0.0956624 | + | 0.995414i | \(0.530497\pi\) | |||||||
\(992\) | 24993.9 | 0.799957 | ||||||||
\(993\) | −2995.57 | + | 10290.9i | −0.0957317 | + | 0.328874i | ||||
\(994\) | 13179.9 | + | 13179.9i | 0.420566 | + | 0.420566i | ||||
\(995\) | 50649.6 | + | 50649.6i | 1.61377 | + | 1.61377i | ||||
\(996\) | 3893.52 | − | 13375.7i | 0.123866 | − | 0.425528i | ||||
\(997\) | 7785.95 | 0.247325 | 0.123663 | − | 0.992324i | \(-0.460536\pi\) | ||||
0.123663 | + | 0.992324i | \(0.460536\pi\) | |||||||
\(998\) | −1684.07 | −0.0534152 | ||||||||
\(999\) | −13781.3 | + | 12111.8i | −0.436458 | + | 0.383585i |
(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 | 39.4.f.b.8.5 | yes | 20 | |
3.2 | odd | 2 | inner | 39.4.f.b.8.6 | yes | 20 | |
13.5 | odd | 4 | inner | 39.4.f.b.5.6 | yes | 20 | |
39.5 | even | 4 | inner | 39.4.f.b.5.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.f.b.5.5 | ✓ | 20 | 39.5 | even | 4 | inner | |
39.4.f.b.5.6 | yes | 20 | 13.5 | odd | 4 | inner | |
39.4.f.b.8.5 | yes | 20 | 1.1 | even | 1 | trivial | |
39.4.f.b.8.6 | yes | 20 | 3.2 | odd | 2 | inner |