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 | 5.6 | ||
Root | \(0.980238 - 0.980238i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.5 |
Dual form | 39.4.f.b.8.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | \(-0.171193\pi\) |
−0.512263 | + | 0.858829i | \(0.671193\pi\) | |||||||
\(3\) | −2.50090 | − | 4.55472i | −0.481299 | − | 0.876556i | ||||
\(4\) | − | 6.07827i | − | 0.759783i | ||||||
\(5\) | −12.5563 | − | 12.5563i | −1.12307 | − | 1.12307i | −0.991278 | − | 0.131790i | \(-0.957928\pi\) |
−0.131790 | − | 0.991278i | \(-0.542072\pi\) | |||||||
\(6\) | 2.01323 | − | 6.91619i | 0.136983 | − | 0.470587i | ||||
\(7\) | 21.4578 | + | 21.4578i | 1.15861 | + | 1.15861i | 0.984775 | + | 0.173836i | \(0.0556164\pi\) |
0.173836 | + | 0.984775i | \(0.444384\pi\) | |||||||
\(8\) | 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 | \(-0.698259\pi\) |
0.812220 | + | 0.583351i | \(0.198259\pi\) | |||||||
\(12\) | −27.6848 | + | 15.2012i | −0.665993 | + | 0.365683i | ||||
\(13\) | 29.3793 | − | 36.5220i | 0.626796 | − | 0.779184i | ||||
\(14\) | 42.0674i | 0.803071i | ||||||||
\(15\) | −25.7883 | + | 88.5924i | −0.443900 | + | 1.52496i | ||||
\(16\) | −21.5715 | −0.337054 | ||||||||
\(17\) | 39.5799 | 0.564678 | 0.282339 | − | 0.959315i | \(-0.408890\pi\) | ||||
0.282339 | + | 0.959315i | \(0.408890\pi\) | |||||||
\(18\) | −36.5362 | + | 8.12705i | −0.478426 | + | 0.106420i | ||||
\(19\) | 9.15970 | − | 9.15970i | 0.110599 | − | 0.110599i | −0.649642 | − | 0.760241i | \(-0.725081\pi\) |
0.760241 | + | 0.649642i | \(0.225081\pi\) | |||||||
\(20\) | −76.3204 | + | 76.3204i | −0.853288 | + | 0.853288i | ||||
\(21\) | 44.0703 | − | 151.398i | 0.457949 | − | 1.57323i | ||||
\(22\) | 16.3696 | 0.158637 | ||||||||
\(23\) | −2.83931 | −0.0257408 | −0.0128704 | − | 0.999917i | \(-0.504097\pi\) | ||||
−0.0128704 | + | 0.999917i | \(0.504097\pi\) | |||||||
\(24\) | −97.3680 | − | 28.3428i | −0.828131 | − | 0.241060i | ||||
\(25\) | 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 | −0.376150 | − | 0.926559i | \(-0.622752\pi\) |
0.926559 | + | 0.376150i | \(0.122752\pi\) | |||||||
\(32\) | −131.546 | − | 131.546i | −0.726694 | − | 0.726694i | ||||
\(33\) | −58.9130 | − | 17.1489i | −0.310771 | − | 0.0904621i | ||||
\(34\) | 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 | 0.471170 | − | 0.882043i | \(-0.343832\pi\) |
−0.882043 | + | 0.471170i | \(0.843832\pi\) | |||||||
\(38\) | 17.9574 | 0.0766597 | ||||||||
\(39\) | −239.822 | − | 42.4763i | −0.984675 | − | 0.174401i | ||||
\(40\) | −346.554 | −1.36988 | ||||||||
\(41\) | 187.117 | + | 187.117i | 0.712749 | + | 0.712749i | 0.967110 | − | 0.254360i | \(-0.0818649\pi\) |
−0.254360 | + | 0.967110i | \(0.581865\pi\) | |||||||
\(42\) | 191.605 | − | 105.207i | 0.703937 | − | 0.386518i | ||||
\(43\) | − | 52.5720i | − | 0.186445i | −0.995645 | − | 0.0932227i | \(-0.970283\pi\) | ||
0.995645 | − | 0.0932227i | \(-0.0297168\pi\) | |||||||
\(44\) | −50.7523 | − | 50.7523i | −0.173891 | − | 0.173891i | ||||
\(45\) | 468.007 | − | 104.103i | 1.55037 | − | 0.344861i | ||||
\(46\) | −2.78320 | − | 2.78320i | −0.00892089 | − | 0.00892089i | ||||
\(47\) | −194.887 | + | 194.887i | −0.604835 | + | 0.604835i | −0.941592 | − | 0.336756i | \(-0.890670\pi\) |
0.336756 | + | 0.941592i | \(0.390670\pi\) | |||||||
\(48\) | 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 | \(0.789897\pi\) | |||||||
\(54\) | 128.390 | + | 146.087i | 0.323549 | + | 0.368147i | ||||
\(55\) | −209.685 | −0.514071 | ||||||||
\(56\) | 592.237 | 1.41323 | ||||||||
\(57\) | −64.6274 | − | 18.8123i | −0.150177 | − | 0.0437150i | ||||
\(58\) | −171.932 | + | 171.932i | −0.389237 | + | 0.389237i | ||||
\(59\) | 395.766 | − | 395.766i | 0.873294 | − | 0.873294i | −0.119536 | − | 0.992830i | \(-0.538141\pi\) |
0.992830 | + | 0.119536i | \(0.0381407\pi\) | |||||||
\(60\) | 538.488 | + | 156.748i | 1.15864 | + | 0.337268i | ||||
\(61\) | 104.515 | 0.219374 | 0.109687 | − | 0.993966i | \(-0.465015\pi\) | ||||
0.109687 | + | 0.993966i | \(0.465015\pi\) | |||||||
\(62\) | 186.247 | 0.381506 | ||||||||
\(63\) | −799.791 | + | 177.904i | −1.59943 | + | 0.355775i | ||||
\(64\) | − | 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 | −0.991720 | − | 0.128416i | \(-0.959011\pi\) |
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(68\) | − | 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 | \(-0.370748\pi\) |
−0.918686 | + | 0.394989i | \(0.870748\pi\) | |||||||
\(72\) | 114.415 | + | 514.366i | 0.187277 | + | 0.841926i | ||||
\(73\) | −84.4987 | − | 84.4987i | −0.135477 | − | 0.135477i | 0.636116 | − | 0.771593i | \(-0.280540\pi\) |
−0.771593 | + | 0.636116i | \(0.780540\pi\) | |||||||
\(74\) | − | 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 | ||||||||
\(78\) | −193.446 | − | 276.720i | −0.280814 | − | 0.401697i | ||||
\(79\) | 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 | \(-0.344206\pi\) |
−0.882595 | + | 0.470133i | \(0.844206\pi\) | |||||||
\(84\) | −920.238 | − | 267.871i | −1.19531 | − | 0.347942i | ||||
\(85\) | −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 | \(-0.924035\pi\) |
0.236393 | + | 0.971658i | \(0.424035\pi\) | |||||||
\(90\) | 560.804 | + | 356.713i | 0.656822 | + | 0.417787i | ||||
\(91\) | 1414.10 | − | 153.267i | 1.62898 | − | 0.176558i | ||||
\(92\) | 17.2581i | 0.0195574i | ||||||||
\(93\) | −670.291 | − | 195.114i | −0.747376 | − | 0.217553i | ||||
\(94\) | −382.072 | −0.419231 | ||||||||
\(95\) | −230.023 | −0.248420 | ||||||||
\(96\) | −270.170 | + | 928.136i | −0.287231 | + | 0.986745i | ||||
\(97\) | 177.855 | − | 177.855i | 0.186169 | − | 0.186169i | −0.607868 | − | 0.794038i | \(-0.707975\pi\) |
0.794038 | + | 0.607868i | \(0.207975\pi\) | |||||||
\(98\) | −566.452 | + | 566.452i | −0.583881 | + | 0.583881i | ||||
\(99\) | 69.2273 | + | 311.220i | 0.0702788 | + | 0.315948i | ||||
\(100\) | 1156.82 | 1.15682 | ||||||||
\(101\) | 1181.17 | 1.16368 | 0.581838 | − | 0.813305i | \(-0.302334\pi\) | ||||
0.581838 | + | 0.813305i | \(0.302334\pi\) | |||||||
\(102\) | 79.6833 | − | 273.742i | 0.0773512 | − | 0.265730i | ||||
\(103\) | − | 227.818i | − | 0.217938i | −0.994045 | − | 0.108969i | \(-0.965245\pi\) | ||
0.994045 | − | 0.108969i | \(-0.0347549\pi\) | |||||||
\(104\) | −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 | −0.720147 | − | 0.693822i | \(-0.755926\pi\) |
0.693822 | + | 0.720147i | \(0.255926\pi\) | |||||||
\(110\) | −205.541 | − | 205.541i | −0.178160 | − | 0.178160i | ||||
\(111\) | −189.920 | + | 652.447i | −0.162400 | + | 0.557906i | ||||
\(112\) | −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 | ||||||||
\(117\) | 406.305 | + | 1198.55i | 0.321051 | + | 0.947062i | ||||
\(118\) | 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 | ||||
\(123\) | 384.303 | − | 1320.23i | 0.281719 | − | 0.967811i | ||||
\(124\) | −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 | \(0.160490\pi\) | ||||
−0.875563 | + | 0.483103i | \(0.839510\pi\) | |||||||
\(128\) | −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 | \(-0.110286\pi\) | |||||||
\(132\) | −104.236 | + | 358.089i | −0.0687316 | + | 0.236119i | ||||
\(133\) | 393.093 | 0.256282 | ||||||||
\(134\) | −928.192 | −0.598385 | ||||||||
\(135\) | −1644.60 | − | 1871.29i | −1.04848 | − | 1.19300i | ||||
\(136\) | 546.205 | − | 546.205i | 0.344387 | − | 0.344387i | ||||
\(137\) | 1113.93 | − | 1113.93i | 0.694670 | − | 0.694670i | −0.268586 | − | 0.963256i | \(-0.586556\pi\) |
0.963256 | + | 0.268586i | \(0.0865563\pi\) | |||||||
\(138\) | −5.71618 | + | 19.6372i | −0.00352604 | + | 0.0121133i | ||||
\(139\) | −1755.93 | −1.07148 | −0.535742 | − | 0.844382i | \(-0.679968\pi\) | ||||
−0.535742 | + | 0.844382i | \(0.679968\pi\) | |||||||
\(140\) | −3275.33 | −1.97726 | ||||||||
\(141\) | 1375.05 | + | 400.263i | 0.821279 | + | 0.239065i | ||||
\(142\) | − | 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 | 0.998454 | + | 0.0555800i | \(0.0177008\pi\) |
0.0555800 | + | 0.998454i | \(0.482299\pi\) | |||||||
\(150\) | 1316.29 | + | 383.158i | 0.716498 | + | 0.208565i | ||||
\(151\) | 969.318 | + | 969.318i | 0.522397 | + | 0.522397i | 0.918295 | − | 0.395897i | \(-0.129566\pi\) |
−0.395897 | + | 0.918295i | \(0.629566\pi\) | |||||||
\(152\) | − | 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 | ||||||||
\(156\) | −258.182 | + | 1457.70i | −0.132507 | + | 0.748140i | ||||
\(157\) | −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 | ||||
\(162\) | 344.295 | − | 950.131i | 0.166978 | − | 0.460798i | ||||
\(163\) | −2353.70 | − | 2353.70i | −1.13102 | − | 1.13102i | −0.990008 | − | 0.141010i | \(-0.954965\pi\) |
−0.141010 | − | 0.990008i | \(-0.545035\pi\) | |||||||
\(164\) | 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 | \(-0.574916\pi\) |
0.972432 | + | 0.233188i | \(0.0749156\pi\) | |||||||
\(168\) | −1481.13 | − | 2697.47i | −0.680187 | − | 1.23878i | ||||
\(169\) | −470.716 | − | 2145.98i | −0.214254 | − | 0.976778i | ||||
\(170\) | − | 974.309i | − | 0.439565i | ||||||
\(171\) | 75.9421 | + | 341.407i | 0.0339616 | + | 0.152679i | ||||
\(172\) | −319.546 | −0.141658 | ||||||||
\(173\) | −3479.34 | −1.52907 | −0.764535 | − | 0.644582i | \(-0.777032\pi\) | ||||
−0.764535 | + | 0.644582i | \(0.777032\pi\) | |||||||
\(174\) | 1213.09 | + | 353.116i | 0.528528 | + | 0.153849i | ||||
\(175\) | −4083.85 | + | 4083.85i | −1.76406 | + | 1.76406i | ||||
\(176\) | −180.118 | + | 180.118i | −0.0771413 | + | 0.0771413i | ||||
\(177\) | −2792.38 | − | 812.830i | −1.18581 | − | 0.345175i | ||||
\(178\) | −1210.29 | −0.509636 | ||||||||
\(179\) | 2074.00 | 0.866023 | 0.433012 | − | 0.901388i | \(-0.357451\pi\) | ||||
0.433012 | + | 0.901388i | \(0.357451\pi\) | |||||||
\(180\) | −632.764 | − | 2844.67i | −0.262019 | − | 1.17794i | ||||
\(181\) | 4030.51i | 1.65517i | 0.561341 | + | 0.827585i | \(0.310286\pi\) | ||||
−0.561341 | + | 0.827585i | \(0.689714\pi\) | |||||||
\(182\) | 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 | ||||
\(189\) | 2810.51 | + | 3197.90i | 1.08166 | + | 1.23076i | ||||
\(190\) | −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 | 0.808468 | − | 0.588541i | \(-0.200297\pi\) |
−0.588541 | + | 0.808468i | \(0.700297\pi\) | |||||||
\(194\) | 348.680 | 0.129040 | ||||||||
\(195\) | 2477.93 | + | 3544.62i | 0.909992 | + | 1.30172i | ||||
\(196\) | 3512.46 | 1.28005 | ||||||||
\(197\) | −3290.58 | − | 3290.58i | −1.19007 | − | 1.19007i | −0.977047 | − | 0.213023i | \(-0.931669\pi\) |
−0.213023 | − | 0.977047i | \(-0.568331\pi\) | |||||||
\(198\) | −237.211 | + | 372.929i | −0.0851406 | + | 0.133853i | ||||
\(199\) | − | 4033.81i | − | 1.43693i | −0.695563 | − | 0.718466i | \(-0.744845\pi\) | ||
0.695563 | − | 0.718466i | \(-0.255155\pi\) | |||||||
\(200\) | 2626.43 | + | 2626.43i | 0.928582 | + | 0.928582i | ||||
\(201\) | 3340.50 | + | 972.383i | 1.17224 | + | 0.341227i | ||||
\(202\) | 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 | ||||||
\(210\) | −3726.85 | − | 1084.85i | −1.22465 | − | 0.356483i | ||||
\(211\) | −5146.04 | −1.67899 | −0.839497 | − | 0.543364i | \(-0.817150\pi\) | ||||
−0.839497 | + | 0.543364i | \(0.817150\pi\) | |||||||
\(212\) | 2876.07 | 0.931742 | ||||||||
\(213\) | −643.471 | + | 2210.56i | −0.206995 | + | 0.711104i | ||||
\(214\) | −560.196 | + | 560.196i | −0.178945 | + | 0.178945i | ||||
\(215\) | −660.108 | + | 660.108i | −0.209391 | + | 0.209391i | ||||
\(216\) | 2056.65 | − | 1807.51i | 0.647859 | − | 0.569377i | ||||
\(217\) | 4077.02 | 1.27542 | ||||||||
\(218\) | −58.7318 | −0.0182469 | ||||||||
\(219\) | −173.545 | + | 596.191i | −0.0535483 | + | 0.183958i | ||||
\(220\) | 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 | −0.376693 | − | 0.926338i | \(-0.622939\pi\) |
0.926338 | + | 0.376693i | \(0.122939\pi\) | |||||||
\(224\) | − | 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 | \(-0.422647\pi\) |
−0.970617 | + | 0.240628i | \(0.922647\pi\) | |||||||
\(228\) | −114.346 | + | 392.823i | −0.0332139 | + | 0.114102i | ||||
\(229\) | −1298.02 | − | 1298.02i | −0.374565 | − | 0.374565i | 0.494572 | − | 0.869137i | \(-0.335325\pi\) |
−0.869137 | + | 0.494572i | \(0.835325\pi\) | |||||||
\(230\) | 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 | \(-0.483248\pi\) | ||||
0.0526028 | + | 0.998616i | \(0.483248\pi\) | |||||||
\(234\) | −776.591 | + | 1573.14i | −0.216954 | + | 0.439485i | ||||
\(235\) | 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 | \(-0.249114\pi\) |
−0.705136 | + | 0.709072i | \(0.749114\pi\) | |||||||
\(240\) | 556.291 | − | 1911.07i | 0.149618 | − | 0.513996i | ||||
\(241\) | −418.110 | − | 418.110i | −0.111755 | − | 0.111755i | 0.649018 | − | 0.760773i | \(-0.275180\pi\) |
−0.760773 | + | 0.649018i | \(0.775180\pi\) | |||||||
\(242\) | −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 | ||||||
\(249\) | −640.564 | + | 2200.58i | −0.163029 | + | 0.560064i | ||||
\(250\) | 1607.94 | 0.406780 | ||||||||
\(251\) | 3640.15 | 0.915396 | 0.457698 | − | 0.889108i | \(-0.348674\pi\) | ||||
0.457698 | + | 0.889108i | \(0.348674\pi\) | |||||||
\(252\) | 1081.35 | + | 4861.34i | 0.270312 | + | 1.21522i | ||||
\(253\) | −23.7077 | + | 23.7077i | −0.00589127 | + | 0.00589127i | ||||
\(254\) | −1355.52 | + | 1355.52i | −0.334855 | + | 0.334855i | ||||
\(255\) | −1020.70 | + | 3506.48i | −0.250661 | + | 0.861114i | ||||
\(256\) | −2581.73 | −0.630306 | ||||||||
\(257\) | −8045.83 | −1.95286 | −0.976430 | − | 0.215832i | \(-0.930754\pi\) | ||||
−0.976430 | + | 0.215832i | \(0.930754\pi\) | |||||||
\(258\) | −363.598 | − | 105.839i | −0.0877388 | − | 0.0255398i | ||||
\(259\) | − | 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 | ||||
\(267\) | 4355.76 | + | 1267.91i | 0.998383 | + | 0.290618i | ||||
\(268\) | 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 | 0.913354 | − | 0.407167i | \(-0.133483\pi\) |
−0.407167 | + | 0.913354i | \(0.633483\pi\) | |||||||
\(272\) | −853.797 | −0.190327 | ||||||||
\(273\) | −4234.61 | − | 6057.50i | −0.938792 | − | 1.34292i | ||||
\(274\) | 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 | \(0.275372\pi\) | ||||
−0.648559 | + | 0.761164i | \(0.724628\pi\) | |||||||
\(278\) | −1721.23 | − | 1721.23i | −0.371340 | − | 0.371340i | ||||
\(279\) | 787.643 | + | 3540.95i | 0.169014 | + | 0.759825i | ||||
\(280\) | −7436.29 | − | 7436.29i | −1.58715 | − | 1.58715i | ||||
\(281\) | −98.2745 | + | 98.2745i | −0.0208632 | + | 0.0208632i | −0.717461 | − | 0.696598i | \(-0.754696\pi\) |
0.696598 | + | 0.717461i | \(0.254696\pi\) | |||||||
\(282\) | 955.526 | + | 1740.23i | 0.201776 | + | 0.367480i | ||||
\(283\) | 8008.21i | 1.68212i | 0.540945 | + | 0.841058i | \(0.318067\pi\) | ||||
−0.540945 | + | 0.841058i | \(0.681933\pi\) | |||||||
\(284\) | −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 | ||||||||
\(288\) | 4903.07 | − | 1090.63i | 1.00318 | − | 0.223146i | ||||
\(289\) | −3346.43 | −0.681138 | ||||||||
\(290\) | 4317.64 | 0.874279 | ||||||||
\(291\) | −1254.88 | − | 365.281i | −0.252791 | − | 0.0735847i | ||||
\(292\) | −513.606 | + | 513.606i | −0.102933 | + | 0.102933i | ||||
\(293\) | 5325.57 | − | 5325.57i | 1.06185 | − | 1.06185i | 0.0638968 | − | 0.997957i | \(-0.479647\pi\) |
0.997957 | − | 0.0638968i | \(-0.0203528\pi\) | |||||||
\(294\) | 3996.67 | + | 1163.39i | 0.792826 | + | 0.230783i | ||||
\(295\) | −9938.69 | −1.96154 | ||||||||
\(296\) | −2552.23 | −0.501168 | ||||||||
\(297\) | 1244.39 | − | 1093.64i | 0.243121 | − | 0.213669i | ||||
\(298\) | 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 | ||||
\(306\) | −1446.10 | + | 321.668i | −0.270157 | + | 0.0600932i | ||||
\(307\) | −4466.27 | − | 4466.27i | −0.830304 | − | 0.830304i | 0.157254 | − | 0.987558i | \(-0.449736\pi\) |
−0.987558 | + | 0.157254i | \(0.949736\pi\) | |||||||
\(308\) | − | 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 | \(-0.402536\pi\) | ||||
0.301432 | + | 0.953488i | \(0.402536\pi\) | |||||||
\(312\) | −3895.74 | + | 2723.39i | −0.706899 | + | 0.494171i | ||||
\(313\) | −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 | \(-0.346220\pi\) |
−0.885553 | + | 0.464539i | \(0.846220\pi\) | |||||||
\(318\) | 3272.55 | + | 952.604i | 0.577093 | + | 0.167985i | ||||
\(319\) | 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 | ||||||
\(327\) | 211.372 | + | 61.5280i | 0.0357458 | + | 0.0104052i | ||||
\(328\) | 5164.44 | 0.869386 | ||||||||
\(329\) | −8363.70 | −1.40154 | ||||||||
\(330\) | −422.143 | + | 1450.22i | −0.0704188 | + | 0.241915i | ||||
\(331\) | −1458.54 | + | 1458.54i | −0.242201 | + | 0.242201i | −0.817760 | − | 0.575559i | \(-0.804785\pi\) |
0.575559 | + | 0.817760i | \(0.304785\pi\) | |||||||
\(332\) | −1895.75 | + | 1895.75i | −0.313382 | + | 0.313382i | ||||
\(333\) | 3446.69 | − | 766.675i | 0.567199 | − | 0.126167i | ||||
\(334\) | 3127.69 | 0.512394 | ||||||||
\(335\) | 11889.6 | 1.93910 | ||||||||
\(336\) | −950.661 | + | 3265.88i | −0.154354 | + | 0.530263i | ||||
\(337\) | − | 9456.34i | − | 1.52855i | −0.644893 | − | 0.764273i | \(-0.723098\pi\) | ||
0.644893 | − | 0.764273i | \(-0.276902\pi\) | |||||||
\(338\) | 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 | ||||
\(345\) | 73.2210 | − | 251.542i | 0.0114263 | − | 0.0392537i | ||||
\(346\) | −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 | 0.762711 | − | 0.646740i | \(-0.223868\pi\) |
−0.646740 | + | 0.762711i | \(0.723868\pi\) | |||||||
\(350\) | −8006.28 | −1.22272 | ||||||||
\(351\) | 4442.94 | − | 4848.07i | 0.675632 | − | 0.737239i | ||||
\(352\) | −2196.76 | −0.332635 | ||||||||
\(353\) | −3714.43 | − | 3714.43i | −0.560054 | − | 0.560054i | 0.369268 | − | 0.929323i | \(-0.379608\pi\) |
−0.929323 | + | 0.369268i | \(0.879608\pi\) | |||||||
\(354\) | −1940.43 | − | 3533.96i | −0.291335 | − | 0.530587i | ||||
\(355\) | 7867.89i | 1.17629i | ||||||||
\(356\) | 3752.39 | + | 3752.39i | 0.558642 | + | 0.558642i | ||||
\(357\) | 1744.30 | − | 5992.32i | 0.258594 | − | 0.888367i | ||||
\(358\) | 2033.01 | + | 2033.01i | 0.300135 | + | 0.300135i | ||||
\(359\) | 6824.51 | − | 6824.51i | 1.00330 | − | 1.00330i | 0.00330378 | − | 0.999995i | \(-0.498948\pi\) |
0.999995 | − | 0.00330378i | \(-0.00105163\pi\) | |||||||
\(360\) | 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 | ||||||||
\(366\) | 210.413 | − | 722.849i | 0.0300505 | − | 0.103235i | ||||
\(367\) | −5558.09 | −0.790545 | −0.395272 | − | 0.918564i | \(-0.629350\pi\) | ||||
−0.395272 | + | 0.918564i | \(0.629350\pi\) | |||||||
\(368\) | 61.2482 | 0.00867604 | ||||||||
\(369\) | −6974.36 | + | 1551.37i | −0.983932 | + | 0.218864i | ||||
\(370\) | −2276.31 | + | 2276.31i | −0.319838 | + | 0.319838i | ||||
\(371\) | −10153.2 | + | 10153.2i | −1.42083 | + | 1.42083i | ||||
\(372\) | −1185.96 | + | 4074.21i | −0.165293 | + | 0.567844i | ||||
\(373\) | 10353.4 | 1.43721 | 0.718607 | − | 0.695416i | \(-0.244780\pi\) | ||||
0.718607 | + | 0.695416i | \(0.244780\pi\) | |||||||
\(374\) | 647.906 | 0.0895787 | ||||||||
\(375\) | −5786.86 | − | 1684.49i | −0.796886 | − | 0.231965i | ||||
\(376\) | 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 | −0.745969 | − | 0.665980i | \(-0.768013\pi\) |
0.665980 | + | 0.745969i | \(0.268013\pi\) | |||||||
\(380\) | 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 | \(-0.0721182\pi\) |
−0.224633 | + | 0.974443i | \(0.572118\pi\) | |||||||
\(384\) | 6835.00 | + | 1989.59i | 0.908326 | + | 0.264404i | ||||
\(385\) | −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 | \(-0.481170\pi\) | ||||
0.0591232 | + | 0.998251i | \(0.481170\pi\) | |||||||
\(390\) | −1045.61 | + | 5903.53i | −0.135760 | + | 0.766505i | ||||
\(391\) | −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 | ||||
\(396\) | 1891.68 | − | 420.782i | 0.240052 | − | 0.0533967i | ||||
\(397\) | −39.8753 | − | 39.8753i | −0.00504102 | − | 0.00504102i | 0.704582 | − | 0.709623i | \(-0.251135\pi\) |
−0.709623 | + | 0.704582i | \(0.751135\pi\) | |||||||
\(398\) | 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 | −0.125375 | + | 0.992109i | \(0.540014\pi\) |
−0.992109 | + | 0.125375i | \(0.959986\pi\) | |||||||
\(402\) | 2321.32 | + | 4227.65i | 0.288002 | + | 0.524518i | ||||
\(403\) | −678.567 | − | 6260.69i | −0.0838755 | − | 0.773864i | ||||
\(404\) | − | 7179.50i | − | 0.884142i | ||||||
\(405\) | −4410.22 | + | 12170.6i | −0.541100 | + | 1.49324i | ||||
\(406\) | −7378.54 | −0.901948 | ||||||||
\(407\) | −1544.24 | −0.188072 | ||||||||
\(408\) | −3853.81 | − | 1121.80i | −0.467628 | − | 0.136121i | ||||
\(409\) | 1155.75 | − | 1155.75i | 0.139726 | − | 0.139726i | −0.633784 | − | 0.773510i | \(-0.718499\pi\) |
0.773510 | + | 0.633784i | \(0.218499\pi\) | |||||||
\(410\) | 4606.12 | − | 4606.12i | 0.554829 | − | 0.554829i | ||||
\(411\) | −7859.50 | − | 2287.81i | −0.943261 | − | 0.274573i | ||||
\(412\) | −1384.74 | −0.165586 | ||||||||
\(413\) | 16984.5 | 2.02362 | ||||||||
\(414\) | 103.738 | − | 23.0752i | 0.0123151 | − | 0.00273934i | ||||
\(415\) | 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 | 0.164468 | − | 0.986382i | \(-0.447409\pi\) |
0.986382 | − | 0.164468i | \(-0.0525907\pi\) | |||||||
\(422\) | −5044.34 | − | 5044.34i | −0.581883 | − | 0.581883i | ||||
\(423\) | −1615.79 | − | 7264.00i | −0.185727 | − | 0.834959i | ||||
\(424\) | 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 | ||||||||
\(429\) | −2357.14 | + | 1647.80i | −0.265277 | + | 0.185446i | ||||
\(430\) | −1294.13 | −0.145136 | ||||||||
\(431\) | −3711.54 | − | 3711.54i | −0.414800 | − | 0.414800i | 0.468607 | − | 0.883407i | \(-0.344756\pi\) |
−0.883407 | + | 0.468607i | \(0.844756\pi\) | |||||||
\(432\) | −3020.12 | − | 194.725i | −0.336356 | − | 0.0216869i | ||||
\(433\) | 5222.54i | 0.579628i | 0.957083 | + | 0.289814i | \(0.0935935\pi\) | ||||
−0.957083 | + | 0.289814i | \(0.906407\pi\) | |||||||
\(434\) | 3996.45 | + | 3996.45i | 0.442018 | + | 0.442018i | ||||
\(435\) | −15538.9 | − | 4523.21i | −1.71272 | − | 0.498555i | ||||
\(436\) | 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 | \(-0.911864\pi\) | ||
0.961911 | − | 0.273362i | \(-0.0881357\pi\) | |||||||
\(440\) | −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 | \(0.715499\pi\) | |||||||
\(444\) | 3965.75 | + | 1154.39i | 0.423888 | + | 0.123389i | ||||
\(445\) | 15503.1 | 1.65150 | ||||||||
\(446\) | 3588.40 | 0.380977 | ||||||||
\(447\) | 3937.27 | − | 13526.0i | 0.416614 | − | 1.43123i | ||||
\(448\) | 1830.78 | − | 1830.78i | 0.193072 | − | 0.193072i | ||||
\(449\) | −1392.85 | + | 1392.85i | −0.146398 | + | 0.146398i | −0.776507 | − | 0.630109i | \(-0.783010\pi\) |
0.630109 | + | 0.776507i | \(0.283010\pi\) | |||||||
\(450\) | −1546.74 | − | 6953.57i | −0.162031 | − | 0.728432i | ||||
\(451\) | 3124.77 | 0.326252 | ||||||||
\(452\) | −113.734 | −0.0118354 | ||||||||
\(453\) | 1990.80 | − | 6839.15i | 0.206481 | − | 0.709340i | ||||
\(454\) | − | 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 | −0.780868 | − | 0.624696i | \(-0.785223\pi\) |
0.624696 | + | 0.780868i | \(0.285223\pi\) | |||||||
\(458\) | − | 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 | \(-0.291571\pi\) |
−0.793171 | + | 0.608999i | \(0.791571\pi\) | |||||||
\(462\) | 721.412 | − | 2478.32i | 0.0726475 | − | 0.249571i | ||||
\(463\) | 11841.6 | + | 11841.6i | 1.18860 | + | 1.18860i | 0.977454 | + | 0.211151i | \(0.0677211\pi\) |
0.211151 | + | 0.977454i | \(0.432279\pi\) | |||||||
\(464\) | − | 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 | \(-0.345801\pi\) | ||||
0.465704 | + | 0.884941i | \(0.345801\pi\) | |||||||
\(468\) | 7285.13 | − | 2469.63i | 0.719562 | − | 0.243929i | ||||
\(469\) | −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 | ||||
\(474\) | 1310.77 | − | 4502.98i | 0.127016 | − | 0.436347i | ||||
\(475\) | 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 | \(-0.838506\pi\) |
0.485860 | + | 0.874037i | \(0.338506\pi\) | |||||||
\(480\) | 15046.3 | − | 8261.60i | 1.43076 | − | 0.785602i | ||||
\(481\) | −6094.02 | + | 660.503i | −0.577679 | + | 0.0626119i | ||||
\(482\) | − | 819.695i | − | 0.0774607i | ||||||
\(483\) | −125.129 | + | 429.866i | −0.0117880 | + | 0.0404961i | ||||
\(484\) | 7242.63 | 0.680187 | ||||||||
\(485\) | −4466.39 | −0.418161 | ||||||||
\(486\) | −5188.63 | + | 808.019i | −0.484282 | + | 0.0754166i | ||||
\(487\) | 9498.10 | − | 9498.10i | 0.883778 | − | 0.883778i | −0.110138 | − | 0.993916i | \(-0.535129\pi\) |
0.993916 | + | 0.110138i | \(0.0351294\pi\) | |||||||
\(488\) | 1442.32 | − | 1442.32i | 0.133792 | − | 0.133792i | ||||
\(489\) | −4834.06 | + | 16606.8i | −0.447043 | + | 1.53576i | ||||
\(490\) | 14225.1 | 1.31147 | ||||||||
\(491\) | −10110.3 | −0.929269 | −0.464634 | − | 0.885503i | \(-0.653814\pi\) | ||||
−0.464634 | + | 0.885503i | \(0.653814\pi\) | |||||||
\(492\) | −8024.68 | − | 2335.90i | −0.735327 | − | 0.214045i | ||||
\(493\) | 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 | −0.667524 | − | 0.744588i | \(-0.732646\pi\) |
0.744588 | + | 0.667524i | \(0.232646\pi\) | |||||||
\(500\) | −4985.26 | − | 4985.26i | −0.445895 | − | 0.445895i | ||||
\(501\) | −11256.4 | − | 3276.60i | −1.00379 | − | 0.292191i | ||||
\(502\) | 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 | ||||||||
\(507\) | −8597.13 | + | 7510.87i | −0.753081 | + | 0.657928i | ||||
\(508\) | 8405.34 | 0.734108 | ||||||||
\(509\) | 11449.6 | + | 11449.6i | 0.997046 | + | 0.997046i | 0.999996 | − | 0.00294997i | \(-0.000939007\pi\) |
−0.00294997 | + | 0.999996i | \(0.500939\pi\) | |||||||
\(510\) | −4437.71 | + | 2436.66i | −0.385304 | + | 0.211563i | ||||
\(511\) | − | 3626.31i | − | 0.313930i | ||||||
\(512\) | 5219.13 | + | 5219.13i | 0.450499 | + | 0.450499i | ||||
\(513\) | 1365.09 | − | 1199.72i | 0.117486 | − | 0.103254i | ||||
\(514\) | −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 | \(-0.0640160\pi\) | |||||||
\(522\) | −1425.47 | − | 6408.38i | −0.119523 | − | 0.537331i | ||||
\(523\) | −13699.2 | −1.14536 | −0.572682 | − | 0.819778i | \(-0.694097\pi\) | ||||
−0.572682 | + | 0.819778i | \(0.694097\pi\) | |||||||
\(524\) | −6189.63 | −0.516021 | ||||||||
\(525\) | 28814.1 | + | 8387.46i | 2.39533 | + | 0.697255i | ||||
\(526\) | −2122.15 | + | 2122.15i | −0.175913 | + | 0.175913i | ||||
\(527\) | 3760.13 | − | 3760.13i | 0.310804 | − | 0.310804i | ||||
\(528\) | 1270.84 | + | 369.928i | 0.104747 | + | 0.0304906i | ||||
\(529\) | −12158.9 | −0.999337 | ||||||||
\(530\) | 11647.7 | 0.954615 | ||||||||
\(531\) | 3281.25 | + | 14751.3i | 0.268162 | + | 1.20556i | ||||
\(532\) | − | 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 | ||||
\(540\) | −11374.2 | + | 9996.33i | −0.906423 | + | 0.796617i | ||||
\(541\) | 7488.89 | + | 7488.89i | 0.595143 | + | 0.595143i | 0.939016 | − | 0.343873i | \(-0.111739\pi\) |
−0.343873 | + | 0.939016i | \(0.611739\pi\) | |||||||
\(542\) | 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 | ||||||||
\(546\) | 1786.87 | − | 10088.7i | 0.140057 | − | 0.790764i | ||||
\(547\) | −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 | ||||
\(552\) | 276.458 | + | 80.4740i | 0.0213167 | + | 0.00620507i | ||||
\(553\) | 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 | \(-0.914881\pi\) |
0.264234 | + | 0.964459i | \(0.414881\pi\) | |||||||
\(558\) | −2698.90 | + | 4243.05i | −0.204755 | + | 0.321904i | ||||
\(559\) | −1920.03 | − | 1544.53i | −0.145275 | − | 0.116863i | ||||
\(560\) | 11624.0i | 0.877149i | ||||||||
\(561\) | −2331.77 | − | 678.753i | −0.175486 | − | 0.0510820i | ||||
\(562\) | −192.665 | −0.0144610 | ||||||||
\(563\) | 18033.2 | 1.34993 | 0.674963 | − | 0.737852i | \(-0.264160\pi\) | ||||
0.674963 | + | 0.737852i | \(0.264160\pi\) | |||||||
\(564\) | 2432.90 | − | 8357.94i | 0.181638 | − | 0.623994i | ||||
\(565\) | −234.947 | + | 234.947i | −0.0174943 | + | 0.0174943i | ||||
\(566\) | −7849.95 | + | 7849.95i | −0.582965 | + | 0.582965i | ||||
\(567\) | 7536.75 | − | 20798.7i | 0.558225 | − | 1.54050i | ||||
\(568\) | −8647.25 | −0.638786 | ||||||||
\(569\) | −11148.1 | −0.821361 | −0.410680 | − | 0.911779i | \(-0.634709\pi\) | ||||
−0.410680 | + | 0.911779i | \(0.634709\pi\) | |||||||
\(570\) | −463.089 | + | 1590.89i | −0.0340293 | + | 0.116903i | ||||
\(571\) | − | 5351.31i | − | 0.392199i | −0.980584 | − | 0.196099i | \(-0.937173\pi\) | ||
0.980584 | − | 0.196099i | \(-0.0628275\pi\) | |||||||
\(572\) | −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 | −0.999955 | − | 0.00944038i | \(-0.996995\pi\) |
0.00944038 | + | 0.999955i | \(0.496995\pi\) | |||||||
\(578\) | −3280.30 | − | 3280.30i | −0.236060 | − | 0.236060i | ||||
\(579\) | 1211.09 | − | 4160.54i | 0.0869276 | − | 0.298629i | ||||
\(580\) | −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 | ||||||||
\(585\) | 9947.68 | − | 20151.0i | 0.703053 | − | 1.42418i | ||||
\(586\) | 10440.6 | 0.736005 | ||||||||
\(587\) | −1912.64 | − | 1912.64i | −0.134486 | − | 0.134486i | 0.636659 | − | 0.771145i | \(-0.280316\pi\) |
−0.771145 | + | 0.636659i | \(0.780316\pi\) | |||||||
\(588\) | −8784.33 | − | 15998.3i | −0.616088 | − | 1.12204i | ||||
\(589\) | − | 1740.36i | − | 0.121749i | ||||||
\(590\) | −9742.28 | − | 9742.28i | −0.679802 | − | 0.679802i | ||||
\(591\) | −6758.23 | + | 23217.1i | −0.470383 | + | 1.61594i | ||||
\(592\) | 1994.76 | + | 1994.76i | 0.138486 | + | 0.138486i | ||||
\(593\) | −11122.4 | + | 11122.4i | −0.770223 | + | 0.770223i | −0.978145 | − | 0.207922i | \(-0.933330\pi\) |
0.207922 | + | 0.978145i | \(0.433330\pi\) | |||||||
\(594\) | 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 | \(-0.0687882\pi\) | |||||||
\(600\) | 5394.20 | − | 18531.1i | 0.367029 | − | 1.26088i | ||||
\(601\) | −4651.42 | −0.315700 | −0.157850 | − | 0.987463i | \(-0.550456\pi\) | ||||
−0.157850 | + | 0.987463i | \(0.550456\pi\) | |||||||
\(602\) | 2211.57 | 0.149729 | ||||||||
\(603\) | −3925.34 | − | 17646.9i | −0.265095 | − | 1.19177i | ||||
\(604\) | 5891.78 | − | 5891.78i | 0.396909 | − | 0.396909i | ||||
\(605\) | 14961.6 | − | 14961.6i | 1.00541 | − | 1.00541i | ||||
\(606\) | 2377.97 | − | 8169.23i | 0.159404 | − | 0.547611i | ||||
\(607\) | 5225.96 | 0.349448 | 0.174724 | − | 0.984617i | \(-0.444097\pi\) | ||||
0.174724 | + | 0.984617i | \(0.444097\pi\) | |||||||
\(608\) | −2409.84 | −0.160743 | ||||||||
\(609\) | 26554.9 | + | 7729.84i | 1.76693 | + | 0.514333i | ||||
\(610\) | − | 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 | −0.954759 | − | 0.297380i | \(-0.903887\pi\) |
0.297380 | + | 0.954759i | \(0.403887\pi\) | |||||||
\(614\) | − | 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 | \(-0.192655\pi\) |
−0.568962 | + | 0.822364i | \(0.692655\pi\) | |||||||
\(618\) | −1575.63 | − | 458.650i | −0.102559 | − | 0.0298537i | ||||
\(619\) | −11697.3 | − | 11697.3i | −0.759537 | − | 0.759537i | 0.216701 | − | 0.976238i | \(-0.430470\pi\) |
−0.976238 | + | 0.216701i | \(0.930470\pi\) | |||||||
\(620\) | 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 | ||||||||
\(624\) | 5173.32 | + | 916.276i | 0.331889 | + | 0.0587827i | ||||
\(625\) | 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 | ||||
\(630\) | 4379.34 | + | 19687.9i | 0.276948 | + | 1.24505i | ||||
\(631\) | 16669.7 | + | 16669.7i | 1.05168 | + | 1.05168i | 0.998590 | + | 0.0530933i | \(0.0169081\pi\) |
0.0530933 | + | 0.998590i | \(0.483092\pi\) | |||||||
\(632\) | 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 | ||||||||
\(639\) | 11677.8 | − | 2597.58i | 0.722949 | − | 0.160812i | ||||
\(640\) | 24327.3 | 1.50253 | ||||||||
\(641\) | 16769.7 | 1.03333 | 0.516663 | − | 0.856189i | \(-0.327174\pi\) | ||||
0.516663 | + | 0.856189i | \(0.327174\pi\) | |||||||
\(642\) | 3952.53 | + | 1150.54i | 0.242981 | + | 0.0707292i | ||||
\(643\) | 9637.04 | − | 9637.04i | 0.591054 | − | 0.591054i | −0.346862 | − | 0.937916i | \(-0.612753\pi\) |
0.937916 | + | 0.346862i | \(0.112753\pi\) | |||||||
\(644\) | −370.321 | + | 370.321i | −0.0226594 | + | 0.0226594i | ||||
\(645\) | 4657.47 | + | 1355.74i | 0.284322 | + | 0.0827631i | ||||
\(646\) | 710.751 | 0.0432881 | ||||||||
\(647\) | −15564.9 | −0.945781 | −0.472890 | − | 0.881121i | \(-0.656789\pi\) | ||||
−0.472890 | + | 0.881121i | \(0.656789\pi\) | |||||||
\(648\) | −13376.2 | − | 4847.08i | −0.810905 | − | 0.293844i | ||||
\(649\) | − | 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 | ||||
\(657\) | 3149.50 | − | 700.570i | 0.187023 | − | 0.0416010i | ||||
\(658\) | −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 | −0.929839 | − | 0.367968i | \(-0.880054\pi\) |
−0.367968 | − | 0.929839i | \(-0.619946\pi\) | |||||||
\(662\) | −2859.43 | −0.167878 | ||||||||
\(663\) | −9492.14 | − | 1681.21i | −0.556025 | − | 0.0984807i | ||||
\(664\) | −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 | ||||
\(669\) | −12914.4 | − | 3759.25i | −0.746338 | − | 0.217251i | ||||
\(670\) | 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 | \(-0.815591\pi\) | ||
0.836825 | − | 0.547471i | \(-0.184409\pi\) | |||||||
\(674\) | 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 | \(-0.0935833\pi\) | |||||||
\(678\) | −129.412 | − | 37.6705i | −0.00733046 | − | 0.00213382i | ||||
\(679\) | 7632.73 | 0.431395 | ||||||||
\(680\) | −13716.6 | −0.773540 | ||||||||
\(681\) | −5127.63 | + | 17615.3i | −0.288533 | + | 0.991221i | ||||
\(682\) | 1555.13 | − | 1555.13i | 0.0873150 | − | 0.0873150i | ||||
\(683\) | −3196.97 | + | 3196.97i | −0.179105 | + | 0.179105i | −0.790966 | − | 0.611861i | \(-0.790421\pi\) |
0.611861 | + | 0.790966i | \(0.290421\pi\) | |||||||
\(684\) | 2075.17 | − | 461.596i | 0.116003 | − | 0.0258035i | ||||
\(685\) | −27973.7 | −1.56032 | ||||||||
\(686\) | −9880.47 | −0.549910 | ||||||||
\(687\) | −2665.89 | + | 9158.33i | −0.148050 | + | 0.508606i | ||||
\(688\) | 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 | 0.371063 | − | 0.928608i | \(-0.378993\pi\) |
0.928608 | − | 0.371063i | \(-0.121007\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | 4971.26 | − | 17078.1i | 0.270740 | − | 0.930094i | ||||
\(697\) | 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 | \(-0.278803\pi\) | ||||
0.640316 | + | 0.768111i | \(0.278803\pi\) | |||||||
\(702\) | 9107.40 | − | 397.126i | 0.489654 | − | 0.0213512i | ||||
\(703\) | −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 | ||||
\(708\) | −4940.60 | + | 16972.8i | −0.262259 | + | 0.900956i | ||||
\(709\) | −6842.97 | − | 6842.97i | −0.362473 | − | 0.362473i | 0.502250 | − | 0.864723i | \(-0.332506\pi\) |
−0.864723 | + | 0.502250i | \(0.832506\pi\) | |||||||
\(710\) | −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 | ||||||
\(717\) | 29.8626 | − | 102.589i | 0.00155542 | − | 0.00534346i | ||||
\(718\) | 13379.3 | 0.695419 | ||||||||
\(719\) | −14543.7 | −0.754365 | −0.377183 | − | 0.926139i | \(-0.623107\pi\) | ||||
−0.377183 | + | 0.926139i | \(0.623107\pi\) | |||||||
\(720\) | −10095.6 | + | 2245.65i | −0.522557 | + | 0.116237i | ||||
\(721\) | 4888.47 | − | 4888.47i | 0.252505 | − | 0.252505i | ||||
\(722\) | −6558.97 | + | 6558.97i | −0.338088 | + | 0.338088i | ||||
\(723\) | −858.721 | + | 2950.03i | −0.0441718 | + | 0.151747i | ||||
\(724\) | 24498.5 | 1.25757 | ||||||||
\(725\) | −33381.8 | −1.71002 | ||||||||
\(726\) | 8241.07 | + | 2398.88i | 0.421287 | + | 0.122632i | ||||
\(727\) | − | 37001.0i | − | 1.88761i | −0.330508 | − | 0.943803i | \(-0.607220\pi\) | ||
0.330508 | − | 0.943803i | \(-0.392780\pi\) | |||||||
\(728\) | 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 | −0.346987 | + | 0.937870i | \(0.612795\pi\) |
−0.937870 | + | 0.346987i | \(0.887205\pi\) | |||||||
\(734\) | −5448.25 | − | 5448.25i | −0.273976 | − | 0.273976i | ||||
\(735\) | −51195.1 | − | 14902.3i | −2.56919 | − | 0.747864i | ||||
\(736\) | 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 | 0.999973 | − | 0.00739871i | \(-0.00235511\pi\) |
−0.00739871 | + | 0.999973i | \(0.502355\pi\) | |||||||
\(740\) | 14115.0 | 0.701186 | ||||||||
\(741\) | −2585.77 | + | 1807.63i | −0.128193 | + | 0.0896153i | ||||
\(742\) | −19905.2 | −0.984827 | ||||||||
\(743\) | −14891.9 | − | 14891.9i | −0.735302 | − | 0.735302i | 0.236363 | − | 0.971665i | \(-0.424045\pi\) |
−0.971665 | + | 0.236363i | \(0.924045\pi\) | |||||||
\(744\) | −11942.6 | + | 6557.46i | −0.588492 | + | 0.323129i | ||||
\(745\) | − | 48142.1i | − | 2.36750i | ||||||
\(746\) | 10148.8 | + | 10148.8i | 0.498090 | + | 0.498090i | ||||
\(747\) | 11625.0 | − | 2585.85i | 0.569393 | − | 0.126655i | ||||
\(748\) | −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 | \(0.254344\pi\) | ||||
−0.697391 | + | 0.716691i | \(0.745656\pi\) | |||||||
\(752\) | 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 | ||||||
\(756\) | 19437.7 | − | 17083.0i | 0.935109 | − | 0.821829i | ||||
\(757\) | 33559.2 | 1.61127 | 0.805634 | − | 0.592414i | \(-0.201825\pi\) | ||||
0.805634 | + | 0.592414i | \(0.201825\pi\) | |||||||
\(758\) | −1157.05 | −0.0554431 | ||||||||
\(759\) | 167.273 | + | 48.6912i | 0.00799949 | + | 0.00232856i | ||||
\(760\) | −3174.33 | + | 3174.33i | −0.151507 | + | 0.151507i | ||||
\(761\) | 7495.37 | − | 7495.37i | 0.357039 | − | 0.357039i | −0.505681 | − | 0.862720i | \(-0.668759\pi\) |
0.862720 | + | 0.505681i | \(0.168759\pi\) | |||||||
\(762\) | 9564.06 | + | 2783.99i | 0.454684 | + | 0.132354i | ||||
\(763\) | −1285.66 | −0.0610014 | ||||||||
\(764\) | 9873.33 | 0.467545 | ||||||||
\(765\) | 18523.7 | − | 4120.38i | 0.875458 | − | 0.194735i | ||||
\(766\) | 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 | −0.620292 | − | 0.784371i | \(-0.712986\pi\) |
0.784371 | + | 0.620292i | \(0.212986\pi\) | |||||||
\(770\) | − | 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 | \(-0.498488\pi\) |
−0.999989 | + | 0.00474920i | \(0.998488\pi\) | |||||||
\(774\) | 427.255 | + | 1920.78i | 0.0198416 | + | 0.0892003i | ||||
\(775\) | 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 | ||||||||
\(780\) | 21545.1 | − | 15061.5i | 0.989026 | − | 0.691397i | ||||
\(781\) | −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 | ||||
\(786\) | −7042.91 | − | 2050.11i | −0.319608 | − | 0.0930345i | ||||
\(787\) | −18104.8 | − | 18104.8i | −0.820033 | − | 0.820033i | 0.166079 | − | 0.986112i | \(-0.446889\pi\) |
−0.986112 | + | 0.166079i | \(0.946889\pi\) | |||||||
\(788\) | −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 | ||||||
\(795\) | −41919.5 | − | 12202.3i | −1.87010 | − | 0.544366i | ||||
\(796\) | −24518.6 | −1.09176 | ||||||||
\(797\) | −33484.2 | −1.48817 | −0.744086 | − | 0.668084i | \(-0.767115\pi\) | ||||
−0.744086 | + | 0.668084i | \(0.767115\pi\) | |||||||
\(798\) | 791.386 | − | 2718.71i | 0.0351062 | − | 0.120603i | ||||
\(799\) | −7713.62 | + | 7713.62i | −0.341537 | + | 0.341537i | ||||
\(800\) | 25035.8 | − | 25035.8i | 1.10644 | − | 1.10644i | ||||
\(801\) | −5118.35 | − | 23010.2i | −0.225778 | − | 1.01501i | ||||
\(802\) | −17592.2 | −0.774565 | ||||||||
\(803\) | −1411.09 | −0.0620130 | ||||||||
\(804\) | 5910.41 | − | 20304.5i | 0.259259 | − | 0.890651i | ||||
\(805\) | 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 | 0.238019 | − | 0.971261i | \(-0.423502\pi\) |
0.971261 | − | 0.238019i | \(-0.0764980\pi\) | |||||||
\(812\) | 22876.5 | + | 22876.5i | 0.988678 | + | 0.988678i | ||||
\(813\) | 4637.95 | − | 15933.1i | 0.200074 | − | 0.687328i | ||||
\(814\) | −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 | ||||||||
\(819\) | −16999.9 | + | 34436.7i | −0.725303 | + | 1.46925i | ||||
\(820\) | −28561.6 | −1.21636 | ||||||||
\(821\) | 977.281 | + | 977.281i | 0.0415437 | + | 0.0415437i | 0.727573 | − | 0.686030i | \(-0.240648\pi\) |
−0.686030 | + | 0.727573i | \(0.740648\pi\) | |||||||
\(822\) | −5461.58 | − | 9946.78i | −0.231745 | − | 0.422060i | ||||
\(823\) | 18625.0i | 0.788856i | 0.918927 | + | 0.394428i | \(0.129057\pi\) | ||||
−0.918927 | + | 0.394428i | \(0.870943\pi\) | |||||||
\(824\) | −3143.90 | − | 3143.90i | −0.132916 | − | 0.132916i | ||||
\(825\) | 3263.79 | − | 11212.3i | 0.137734 | − | 0.473168i | ||||
\(826\) | 16648.9 | + | 16648.9i | 0.701317 | + | 0.701317i | ||||
\(827\) | 18545.6 | − | 18545.6i | 0.779799 | − | 0.779799i | −0.199997 | − | 0.979796i | \(-0.564093\pi\) |
0.979796 | + | 0.199997i | \(0.0640933\pi\) | |||||||
\(828\) | −393.172 | − | 250.086i | −0.0165020 | − | 0.0104965i | ||||
\(829\) | − | 30011.6i | − | 1.25735i | −0.777667 | − | 0.628676i | \(-0.783597\pi\) | ||
0.777667 | − | 0.628676i | \(-0.216403\pi\) | |||||||
\(830\) | −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 | ||||||||
\(834\) | −3535.09 | + | 12144.4i | −0.146775 | + | 0.504226i | ||||
\(835\) | −40063.9 | −1.66044 | ||||||||
\(836\) | −929.752 | −0.0384643 | ||||||||
\(837\) | 14158.2 | − | 12443.1i | 0.584683 | − | 0.513854i | ||||
\(838\) | 1468.96 | − | 1468.96i | 0.0605542 | − | 0.0605542i | ||||
\(839\) | −29877.0 | + | 29877.0i | −1.22940 | + | 1.22940i | −0.265211 | + | 0.964190i | \(0.585442\pi\) |
−0.964190 | + | 0.265211i | \(0.914558\pi\) | |||||||
\(840\) | −15272.8 | + | 52467.7i | −0.627334 | + | 2.15513i | ||||
\(841\) | −6375.44 | −0.261407 | ||||||||
\(842\) | 19489.6 | 0.797692 | ||||||||
\(843\) | 693.388 | + | 201.838i | 0.0283293 | + | 0.00824633i | ||||
\(844\) | 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 | ||||
\(852\) | 13436.4 | + | 3911.19i | 0.540285 | + | 0.157271i | ||||
\(853\) | −2542.34 | − | 2542.34i | −0.102049 | − | 0.102049i | 0.654239 | − | 0.756288i | \(-0.272989\pi\) |
−0.756288 | + | 0.654239i | \(0.772989\pi\) | |||||||
\(854\) | 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 | \(-0.495744\pi\) | ||||
0.0133717 | + | 0.999911i | \(0.495744\pi\) | |||||||
\(858\) | −3925.79 | − | 695.319i | −0.156205 | − | 0.0276664i | ||||
\(859\) | −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 | \(-0.303387\pi\) |
−0.815226 | + | 0.579143i | \(0.803387\pi\) | |||||||
\(864\) | −17229.6 | − | 19604.6i | −0.678431 | − | 0.771945i | ||||
\(865\) | 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 | ||||||||
\(873\) | 1474.58 | + | 6629.14i | 0.0571670 | + | 0.257002i | ||||
\(874\) | −50.9866 | −0.00197328 | ||||||||
\(875\) | 35198.4 | 1.35991 | ||||||||
\(876\) | 3623.81 | + | 1054.85i | 0.139768 | + | 0.0406851i | ||||
\(877\) | −15989.8 | + | 15989.8i | −0.615664 | + | 0.615664i | −0.944416 | − | 0.328752i | \(-0.893372\pi\) |
0.328752 | + | 0.944416i | \(0.393372\pi\) | |||||||
\(878\) | 4929.42 | − | 4929.42i | 0.189476 | − | 0.189476i | ||||
\(879\) | −37575.2 | − | 10937.7i | −1.44184 | − | 0.419705i | ||||
\(880\) | 4523.21 | 0.173270 | ||||||||
\(881\) | −4784.23 | −0.182957 | −0.0914784 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914784 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(882\) | −4696.39 | − | 21113.3i | −0.179292 | − | 0.806032i | ||||
\(883\) | − | 14740.6i | − | 0.561792i | −0.959738 | − | 0.280896i | \(-0.909368\pi\) | ||
0.959738 | − | 0.280896i | \(-0.0906316\pi\) | |||||||
\(884\) | −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 | ||||
\(891\) | −8093.34 | − | 2932.75i | −0.304307 | − | 0.110270i | ||||
\(892\) | −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 | ||||||||
\(897\) | 680.931 | + | 120.604i | 0.0253463 | + | 0.00448923i | ||||
\(898\) | −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 | ||||
\(903\) | −7959.29 | − | 2316.86i | −0.293321 | − | 0.0853824i | ||||
\(904\) | −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 | \(-0.989863\pi\) | ||
0.999493 | − | 0.0318422i | \(-0.0101374\pi\) | |||||||
\(908\) | −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 | \(-0.123881\pi\) | |||||||
\(912\) | 1394.11 | + | 405.810i | 0.0506179 | + | 0.0147343i | ||||
\(913\) | −5208.44 | −0.188800 | ||||||||
\(914\) | −2991.16 | −0.108248 | ||||||||
\(915\) | −2695.27 | + | 9259.27i | −0.0973803 | + | 0.334538i | ||||
\(916\) | −7889.70 | + | 7889.70i | −0.284589 | + | 0.284589i | ||||
\(917\) | 21850.9 | − | 21850.9i | 0.786893 | − | 0.786893i | ||||
\(918\) | 5081.66 | + | 5782.12i | 0.182701 | + | 0.207885i | ||||
\(919\) | 36900.1 | 1.32451 | 0.662254 | − | 0.749280i | \(-0.269600\pi\) | ||||
0.662254 | + | 0.749280i | \(0.269600\pi\) | |||||||
\(920\) | 983.977 | 0.0352617 | ||||||||
\(921\) | −9172.89 | + | 31512.3i | −0.328184 | + | 1.12743i | ||||
\(922\) | − | 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 | \(-0.363426\pi\) |
−0.909357 | + | 0.416017i | \(0.863426\pi\) | |||||||
\(930\) | −4802.99 | + | 16500.1i | −0.169351 | + | 0.581783i | ||||
\(931\) | 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 | ||||||||
\(936\) | 22147.1 | + | 10933.1i | 0.773399 | + | 0.381793i | ||||
\(937\) | 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 | \(-0.103869\pi\) |
−0.320553 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(942\) | −378.349 | + | 1299.77i | −0.0130863 | + | 0.0449563i | ||||
\(943\) | −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 | \(-0.764145\pi\) |
0.674996 | + | 0.737822i | \(0.264145\pi\) | |||||||
\(948\) | −18025.0 | + | 9897.14i | −0.617535 | + | 0.339076i | ||||
\(949\) | −5568.58 | + | 603.552i | −0.190478 | + | 0.0206450i | ||||
\(950\) | 3417.65i | 0.116719i | ||||||||
\(951\) | −4880.30 | + | 16765.7i | −0.166409 | + | 0.571676i | ||||
\(952\) | 23440.7 | 0.798021 | ||||||||
\(953\) | −10645.7 | −0.361855 | −0.180927 | − | 0.983496i | \(-0.557910\pi\) | ||||
−0.180927 | + | 0.983496i | \(0.557910\pi\) | |||||||
\(954\) | −3845.50 | − | 17287.9i | −0.130506 | − | 0.586706i | ||||
\(955\) | 20396.0 | − | 20396.0i | 0.691098 | − | 0.691098i | ||||
\(956\) | 88.3783 | − | 88.3783i | 0.00298991 | − | 0.00298991i | ||||
\(957\) | 3007.89 | − | 10333.2i | 0.101600 | − | 0.349034i | ||||
\(958\) | −7978.00 | −0.269058 | ||||||||
\(959\) | 47805.1 | 1.60970 | ||||||||
\(960\) | 7558.71 | + | 2200.26i | 0.254121 | + | 0.0739719i | ||||
\(961\) | 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 | −0.657804 | − | 0.753189i | \(-0.728515\pi\) |
0.753189 | + | 0.657804i | \(0.228515\pi\) | |||||||
\(968\) | 16443.6 | + | 16443.6i | 0.545989 | + | 0.545989i | ||||
\(969\) | −2557.95 | − | 744.590i | −0.0848019 | − | 0.0246849i | ||||
\(970\) | −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 | ||||||||
\(975\) | 8084.09 | − | 45643.0i | 0.265537 | − | 1.49923i | ||||
\(976\) | −2254.55 | −0.0739410 | ||||||||
\(977\) | −9578.62 | − | 9578.62i | −0.313661 | − | 0.313661i | 0.532665 | − | 0.846326i | \(-0.321191\pi\) |
−0.846326 | + | 0.532665i | \(0.821191\pi\) | |||||||
\(978\) | −21017.2 | + | 11540.1i | −0.687173 | + | 0.377313i | ||||
\(979\) | 10309.4i | 0.336559i | ||||||||
\(980\) | −44103.4 | − | 44103.4i | −1.43758 | − | 1.43758i | ||||
\(981\) | −248.378 | − | 1116.62i | −0.00808369 | − | 0.0363413i | ||||
\(982\) | −9910.49 | − | 9910.49i | −0.322053 | − | 0.322053i | ||||
\(983\) | −3628.32 | + | 3628.32i | −0.117727 | + | 0.117727i | −0.763516 | − | 0.645789i | \(-0.776529\pi\) |
0.645789 | + | 0.763516i | \(0.276529\pi\) | |||||||
\(984\) | −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 | ||||||||
\(990\) | 7661.08 | − | 1704.12i | 0.245945 | − | 0.0547075i | ||||
\(991\) | −5968.73 | −0.191325 | −0.0956624 | − | 0.995414i | \(-0.530497\pi\) | ||||
−0.0956624 | + | 0.995414i | \(0.530497\pi\) | |||||||
\(992\) | −24993.9 | −0.799957 | ||||||||
\(993\) | 10290.9 | + | 2995.57i | 0.328874 | + | 0.0957317i | ||||
\(994\) | 13179.9 | − | 13179.9i | 0.420566 | − | 0.420566i | ||||
\(995\) | −50649.6 | + | 50649.6i | −1.61377 | + | 1.61377i | ||||
\(996\) | 13375.7 | + | 3893.52i | 0.425528 | + | 0.123866i | ||||
\(997\) | 7785.95 | 0.247325 | 0.123663 | − | 0.992324i | \(-0.460536\pi\) | ||||
0.123663 | + | 0.992324i | \(0.460536\pi\) | |||||||
\(998\) | 1684.07 | 0.0534152 | ||||||||
\(999\) | −12111.8 | − | 13781.3i | −0.383585 | − | 0.436458i |
(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.5.6 | yes | 20 | |
3.2 | odd | 2 | inner | 39.4.f.b.5.5 | ✓ | 20 | |
13.8 | odd | 4 | inner | 39.4.f.b.8.5 | yes | 20 | |
39.8 | even | 4 | inner | 39.4.f.b.8.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.f.b.5.5 | ✓ | 20 | 3.2 | odd | 2 | inner | |
39.4.f.b.5.6 | yes | 20 | 1.1 | even | 1 | trivial | |
39.4.f.b.8.5 | yes | 20 | 13.8 | odd | 4 | inner | |
39.4.f.b.8.6 | yes | 20 | 39.8 | even | 4 | inner |