Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.353");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (of order \(2\), degree \(1\), 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: | \(20.8866761420\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.6 | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.4.c.b.353.5 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −4.66792 | + | 2.28265i | −0.898342 | + | 0.439296i | ||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 8.40010i | 0.751328i | 0.926756 | + | 0.375664i | \(0.122585\pi\) | ||||
−0.926756 | + | 0.375664i | \(0.877415\pi\) | |||||||
\(6\) | −9.33585 | + | 4.56530i | −0.635224 | + | 0.310629i | ||||
\(7\) | 31.0296 | 1.67544 | 0.837720 | − | 0.546100i | \(-0.183888\pi\) | ||||
0.837720 | + | 0.546100i | \(0.183888\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 16.5790 | − | 21.3105i | 0.614037 | − | 0.789277i | ||||
\(10\) | 16.8002i | 0.531269i | ||||||||
\(11\) | −8.36506 | −0.229287 | −0.114644 | − | 0.993407i | \(-0.536573\pi\) | ||||
−0.114644 | + | 0.993407i | \(0.536573\pi\) | |||||||
\(12\) | −18.6717 | + | 9.13060i | −0.449171 | + | 0.219648i | ||||
\(13\) | 33.8590i | 0.722368i | 0.932494 | + | 0.361184i | \(0.117627\pi\) | ||||
−0.932494 | + | 0.361184i | \(0.882373\pi\) | |||||||
\(14\) | 62.0592 | 1.18471 | ||||||||
\(15\) | −19.1745 | − | 39.2110i | −0.330055 | − | 0.674949i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 52.8462i | − | 0.753946i | −0.926224 | − | 0.376973i | \(-0.876965\pi\) | ||
0.926224 | − | 0.376973i | \(-0.123035\pi\) | |||||||
\(18\) | 33.1580 | − | 42.6210i | 0.434190 | − | 0.558103i | ||||
\(19\) | −13.4852 | −0.162827 | −0.0814135 | − | 0.996680i | \(-0.525943\pi\) | ||||
−0.0814135 | + | 0.996680i | \(0.525943\pi\) | |||||||
\(20\) | 33.6004i | 0.375664i | ||||||||
\(21\) | −144.844 | + | 70.8297i | −1.50512 | + | 0.736015i | ||||
\(22\) | −16.7301 | −0.162131 | ||||||||
\(23\) | 124.185 | 1.12584 | 0.562921 | − | 0.826511i | \(-0.309677\pi\) | ||||
0.562921 | + | 0.826511i | \(0.309677\pi\) | |||||||
\(24\) | −37.3434 | + | 18.2612i | −0.317612 | + | 0.155315i | ||||
\(25\) | 54.4384 | 0.435507 | ||||||||
\(26\) | 67.7180i | 0.510792i | ||||||||
\(27\) | −28.7452 | + | 137.320i | −0.204889 | + | 0.978785i | ||||
\(28\) | 124.118 | 0.837720 | ||||||||
\(29\) | − | 146.756i | − | 0.939722i | −0.882740 | − | 0.469861i | \(-0.844304\pi\) | ||
0.882740 | − | 0.469861i | \(-0.155696\pi\) | |||||||
\(30\) | −38.3490 | − | 78.4220i | −0.233384 | − | 0.477261i | ||||
\(31\) | 205.242i | 1.18911i | 0.804054 | + | 0.594556i | \(0.202672\pi\) | ||||
−0.804054 | + | 0.594556i | \(0.797328\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 39.0475 | − | 19.0945i | 0.205979 | − | 0.100725i | ||||
\(34\) | − | 105.692i | − | 0.533120i | ||||||
\(35\) | 260.651i | 1.25880i | ||||||||
\(36\) | 66.3160 | − | 85.2419i | 0.307019 | − | 0.394638i | ||||
\(37\) | 278.619i | 1.23796i | 0.785405 | + | 0.618982i | \(0.212455\pi\) | ||||
−0.785405 | + | 0.618982i | \(0.787545\pi\) | |||||||
\(38\) | −26.9704 | −0.115136 | ||||||||
\(39\) | −77.2882 | − | 158.051i | −0.317334 | − | 0.648934i | ||||
\(40\) | 67.2008i | 0.265634i | ||||||||
\(41\) | 402.984i | 1.53501i | 0.641040 | + | 0.767507i | \(0.278503\pi\) | ||||
−0.641040 | + | 0.767507i | \(0.721497\pi\) | |||||||
\(42\) | −289.687 | + | 141.659i | −1.06428 | + | 0.520441i | ||||
\(43\) | 466.280i | 1.65365i | 0.562457 | + | 0.826826i | \(0.309856\pi\) | ||||
−0.562457 | + | 0.826826i | \(0.690144\pi\) | |||||||
\(44\) | −33.4602 | −0.114644 | ||||||||
\(45\) | 179.010 | + | 139.265i | 0.593006 | + | 0.461343i | ||||
\(46\) | 248.370 | 0.796091 | ||||||||
\(47\) | −513.624 | −1.59404 | −0.797019 | − | 0.603954i | \(-0.793591\pi\) | ||||
−0.797019 | + | 0.603954i | \(0.793591\pi\) | |||||||
\(48\) | −74.6868 | + | 36.5224i | −0.224586 | + | 0.109824i | ||||
\(49\) | 619.835 | 1.80710 | ||||||||
\(50\) | 108.877 | 0.307950 | ||||||||
\(51\) | 120.629 | + | 246.682i | 0.331206 | + | 0.677301i | ||||
\(52\) | 135.436i | 0.361184i | ||||||||
\(53\) | − | 100.658i | − | 0.260877i | −0.991456 | − | 0.130438i | \(-0.958361\pi\) | ||
0.991456 | − | 0.130438i | \(-0.0416385\pi\) | |||||||
\(54\) | −57.4903 | + | 274.640i | −0.144879 | + | 0.692106i | ||||
\(55\) | − | 70.2673i | − | 0.172270i | ||||||
\(56\) | 248.237 | 0.592357 | ||||||||
\(57\) | 62.9478 | − | 30.7820i | 0.146274 | − | 0.0715293i | ||||
\(58\) | − | 293.512i | − | 0.664484i | ||||||
\(59\) | 339.656 | − | 300.022i | 0.749481 | − | 0.662026i | ||||
\(60\) | −76.6980 | − | 156.844i | −0.165028 | − | 0.337475i | ||||
\(61\) | 413.290i | 0.867481i | 0.901038 | + | 0.433740i | \(0.142807\pi\) | ||||
−0.901038 | + | 0.433740i | \(0.857193\pi\) | |||||||
\(62\) | 410.483i | 0.840829i | ||||||||
\(63\) | 514.440 | − | 661.255i | 1.02878 | − | 1.32239i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −284.419 | −0.542735 | ||||||||
\(66\) | 78.0949 | − | 38.1890i | 0.145649 | − | 0.0712234i | ||||
\(67\) | − | 771.385i | − | 1.40656i | −0.710911 | − | 0.703282i | \(-0.751717\pi\) | ||
0.710911 | − | 0.703282i | \(-0.248283\pi\) | |||||||
\(68\) | − | 211.385i | − | 0.376973i | ||||||
\(69\) | −579.686 | + | 283.471i | −1.01139 | + | 0.494578i | ||||
\(70\) | 521.303i | 0.890109i | ||||||||
\(71\) | − | 262.065i | − | 0.438048i | −0.975720 | − | 0.219024i | \(-0.929713\pi\) | ||
0.975720 | − | 0.219024i | \(-0.0702873\pi\) | |||||||
\(72\) | 132.632 | − | 170.484i | 0.217095 | − | 0.279052i | ||||
\(73\) | − | 355.978i | − | 0.570740i | −0.958417 | − | 0.285370i | \(-0.907883\pi\) | ||
0.958417 | − | 0.285370i | \(-0.0921166\pi\) | |||||||
\(74\) | 557.238i | 0.875373i | ||||||||
\(75\) | −254.114 | + | 124.264i | −0.391234 | + | 0.191317i | ||||
\(76\) | −53.9408 | −0.0814135 | ||||||||
\(77\) | −259.564 | −0.384157 | ||||||||
\(78\) | −154.576 | − | 316.102i | −0.224389 | − | 0.458866i | ||||
\(79\) | 942.458 | 1.34221 | 0.671106 | − | 0.741361i | \(-0.265819\pi\) | ||||
0.671106 | + | 0.741361i | \(0.265819\pi\) | |||||||
\(80\) | 134.402i | 0.187832i | ||||||||
\(81\) | −179.273 | − | 706.613i | −0.245916 | − | 0.969291i | ||||
\(82\) | 805.969i | 1.08542i | ||||||||
\(83\) | −1153.17 | −1.52502 | −0.762510 | − | 0.646976i | \(-0.776033\pi\) | ||||
−0.762510 | + | 0.646976i | \(0.776033\pi\) | |||||||
\(84\) | −579.375 | + | 283.319i | −0.752559 | + | 0.368007i | ||||
\(85\) | 443.913 | 0.566460 | ||||||||
\(86\) | 932.560i | 1.16931i | ||||||||
\(87\) | 334.993 | + | 685.046i | 0.412816 | + | 0.844192i | ||||
\(88\) | −66.9205 | −0.0810653 | ||||||||
\(89\) | −109.139 | −0.129985 | −0.0649925 | − | 0.997886i | \(-0.520702\pi\) | ||||
−0.0649925 | + | 0.997886i | \(0.520702\pi\) | |||||||
\(90\) | 358.020 | + | 278.531i | 0.419318 | + | 0.326219i | ||||
\(91\) | 1050.63i | 1.21028i | ||||||||
\(92\) | 496.740 | 0.562921 | ||||||||
\(93\) | −468.495 | − | 958.052i | −0.522373 | − | 1.06823i | ||||
\(94\) | −1027.25 | −1.12716 | ||||||||
\(95\) | − | 113.277i | − | 0.122336i | ||||||
\(96\) | −149.374 | + | 73.0448i | −0.158806 | + | 0.0776574i | ||||
\(97\) | − | 1052.48i | − | 1.10168i | −0.834610 | − | 0.550842i | \(-0.814307\pi\) | ||
0.834610 | − | 0.550842i | \(-0.185693\pi\) | |||||||
\(98\) | 1239.67 | 1.27781 | ||||||||
\(99\) | −138.684 | + | 178.263i | −0.140791 | + | 0.180971i | ||||
\(100\) | 217.753 | 0.217753 | ||||||||
\(101\) | 525.404 | 0.517621 | 0.258810 | − | 0.965928i | \(-0.416670\pi\) | ||||
0.258810 | + | 0.965928i | \(0.416670\pi\) | |||||||
\(102\) | 241.259 | + | 493.364i | 0.234198 | + | 0.478924i | ||||
\(103\) | − | 1421.58i | − | 1.35993i | −0.733245 | − | 0.679964i | \(-0.761995\pi\) | ||
0.733245 | − | 0.679964i | \(-0.238005\pi\) | |||||||
\(104\) | 270.872i | 0.255396i | ||||||||
\(105\) | −594.976 | − | 1216.70i | −0.552988 | − | 1.13084i | ||||
\(106\) | − | 201.317i | − | 0.184468i | ||||||
\(107\) | − | 1116.93i | − | 1.00914i | −0.863370 | − | 0.504571i | \(-0.831651\pi\) | ||
0.863370 | − | 0.504571i | \(-0.168349\pi\) | |||||||
\(108\) | −114.981 | + | 549.279i | −0.102445 | + | 0.489393i | ||||
\(109\) | 981.827i | 0.862771i | 0.902168 | + | 0.431385i | \(0.141975\pi\) | ||||
−0.902168 | + | 0.431385i | \(0.858025\pi\) | |||||||
\(110\) | − | 140.535i | − | 0.121813i | ||||||
\(111\) | −635.990 | − | 1300.57i | −0.543833 | − | 1.11212i | ||||
\(112\) | 496.473 | 0.418860 | ||||||||
\(113\) | −408.043 | −0.339694 | −0.169847 | − | 0.985470i | \(-0.554327\pi\) | ||||
−0.169847 | + | 0.985470i | \(0.554327\pi\) | |||||||
\(114\) | 125.896 | − | 61.5640i | 0.103432 | − | 0.0505789i | ||||
\(115\) | 1043.17i | 0.845876i | ||||||||
\(116\) | − | 587.025i | − | 0.469861i | ||||||
\(117\) | 721.551 | + | 561.348i | 0.570149 | + | 0.443561i | ||||
\(118\) | 679.311 | − | 600.044i | 0.529963 | − | 0.468123i | ||||
\(119\) | − | 1639.79i | − | 1.26319i | ||||||
\(120\) | −153.396 | − | 313.688i | −0.116692 | − | 0.238631i | ||||
\(121\) | −1261.03 | −0.947427 | ||||||||
\(122\) | 826.580i | 0.613402i | ||||||||
\(123\) | −919.873 | − | 1881.10i | −0.674326 | − | 1.37897i | ||||
\(124\) | 820.966i | 0.594556i | ||||||||
\(125\) | 1507.30i | 1.07854i | ||||||||
\(126\) | 1028.88 | − | 1322.51i | 0.727459 | − | 0.935068i | ||||
\(127\) | 1285.44 | 0.898147 | 0.449073 | − | 0.893495i | \(-0.351754\pi\) | ||||
0.449073 | + | 0.893495i | \(0.351754\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −1064.35 | − | 2176.56i | −0.726444 | − | 1.48555i | ||||
\(130\) | −568.837 | −0.383772 | ||||||||
\(131\) | −258.622 | −0.172488 | −0.0862439 | − | 0.996274i | \(-0.527486\pi\) | ||||
−0.0862439 | + | 0.996274i | \(0.527486\pi\) | |||||||
\(132\) | 156.190 | − | 76.3781i | 0.102989 | − | 0.0503626i | ||||
\(133\) | −418.440 | −0.272807 | ||||||||
\(134\) | − | 1542.77i | − | 0.994590i | ||||||
\(135\) | −1153.50 | − | 241.462i | −0.735388 | − | 0.153939i | ||||
\(136\) | − | 422.769i | − | 0.266560i | ||||||
\(137\) | 1367.24i | 0.852635i | 0.904574 | + | 0.426317i | \(0.140189\pi\) | ||||
−0.904574 | + | 0.426317i | \(0.859811\pi\) | |||||||
\(138\) | −1159.37 | + | 566.942i | −0.715162 | + | 0.349720i | ||||
\(139\) | −610.063 | −0.372265 | −0.186133 | − | 0.982525i | \(-0.559595\pi\) | ||||
−0.186133 | + | 0.982525i | \(0.559595\pi\) | |||||||
\(140\) | 1042.61i | 0.629402i | ||||||||
\(141\) | 2397.56 | − | 1172.43i | 1.43199 | − | 0.700255i | ||||
\(142\) | − | 524.130i | − | 0.309747i | ||||||
\(143\) | − | 283.232i | − | 0.165630i | ||||||
\(144\) | 265.264 | − | 340.968i | 0.153509 | − | 0.197319i | ||||
\(145\) | 1232.77 | 0.706039 | ||||||||
\(146\) | − | 711.956i | − | 0.403574i | ||||||
\(147\) | −2893.34 | + | 1414.87i | −1.62339 | + | 0.793852i | ||||
\(148\) | 1114.48i | 0.618982i | ||||||||
\(149\) | 1743.66 | 0.958697 | 0.479348 | − | 0.877625i | \(-0.340873\pi\) | ||||
0.479348 | + | 0.877625i | \(0.340873\pi\) | |||||||
\(150\) | −508.228 | + | 248.528i | −0.276644 | + | 0.135281i | ||||
\(151\) | − | 1657.12i | − | 0.893075i | −0.894765 | − | 0.446538i | \(-0.852657\pi\) | ||
0.894765 | − | 0.446538i | \(-0.147343\pi\) | |||||||
\(152\) | −107.882 | −0.0575681 | ||||||||
\(153\) | −1126.18 | − | 876.137i | −0.595072 | − | 0.462951i | ||||
\(154\) | −519.129 | −0.271640 | ||||||||
\(155\) | −1724.05 | −0.893413 | ||||||||
\(156\) | −309.153 | − | 632.204i | −0.158667 | − | 0.324467i | ||||
\(157\) | 2682.20i | 1.36346i | 0.731605 | + | 0.681729i | \(0.238772\pi\) | ||||
−0.731605 | + | 0.681729i | \(0.761228\pi\) | |||||||
\(158\) | 1884.92 | 0.949088 | ||||||||
\(159\) | 229.768 | + | 469.865i | 0.114602 | + | 0.234357i | ||||
\(160\) | 268.803i | 0.132817i | ||||||||
\(161\) | 3853.41 | 1.88628 | ||||||||
\(162\) | −358.546 | − | 1413.23i | −0.173889 | − | 0.685392i | ||||
\(163\) | 1503.49 | 0.722471 | 0.361236 | − | 0.932475i | \(-0.382355\pi\) | ||||
0.361236 | + | 0.932475i | \(0.382355\pi\) | |||||||
\(164\) | 1611.94i | 0.767507i | ||||||||
\(165\) | 160.396 | + | 328.002i | 0.0756775 | + | 0.154757i | ||||
\(166\) | −2306.34 | −1.07835 | ||||||||
\(167\) | − | 1242.64i | − | 0.575799i | −0.957661 | − | 0.287899i | \(-0.907043\pi\) | ||
0.957661 | − | 0.287899i | \(-0.0929569\pi\) | |||||||
\(168\) | −1158.75 | + | 566.638i | −0.532140 | + | 0.260220i | ||||
\(169\) | 1050.57 | 0.478184 | ||||||||
\(170\) | 887.826 | 0.400548 | ||||||||
\(171\) | −223.571 | + | 287.376i | −0.0999819 | + | 0.128516i | ||||
\(172\) | 1865.12i | 0.826826i | ||||||||
\(173\) | 2533.15 | 1.11325 | 0.556624 | − | 0.830764i | \(-0.312096\pi\) | ||||
0.556624 | + | 0.830764i | \(0.312096\pi\) | |||||||
\(174\) | 669.986 | + | 1370.09i | 0.291905 | + | 0.596934i | ||||
\(175\) | 1689.20 | 0.729666 | ||||||||
\(176\) | −133.841 | −0.0573218 | ||||||||
\(177\) | −900.641 | + | 2175.79i | −0.382465 | + | 0.923970i | ||||
\(178\) | −218.277 | −0.0919133 | ||||||||
\(179\) | −1900.69 | −0.793656 | −0.396828 | − | 0.917893i | \(-0.629889\pi\) | ||||
−0.396828 | + | 0.917893i | \(0.629889\pi\) | |||||||
\(180\) | 716.040 | + | 557.061i | 0.296503 | + | 0.230672i | ||||
\(181\) | −3907.44 | −1.60463 | −0.802313 | − | 0.596903i | \(-0.796398\pi\) | ||||
−0.802313 | + | 0.596903i | \(0.796398\pi\) | |||||||
\(182\) | 2101.26i | 0.855801i | ||||||||
\(183\) | −943.396 | − | 1929.20i | −0.381081 | − | 0.779295i | ||||
\(184\) | 993.480 | 0.398045 | ||||||||
\(185\) | −2340.43 | −0.930117 | ||||||||
\(186\) | −936.990 | − | 1916.10i | −0.369373 | − | 0.755353i | ||||
\(187\) | 442.061i | 0.172870i | ||||||||
\(188\) | −2054.50 | −0.797019 | ||||||||
\(189\) | −891.950 | + | 4260.97i | −0.343279 | + | 1.63990i | ||||
\(190\) | − | 226.554i | − | 0.0865049i | ||||||
\(191\) | −1208.73 | −0.457909 | −0.228954 | − | 0.973437i | \(-0.573531\pi\) | ||||
−0.228954 | + | 0.973437i | \(0.573531\pi\) | |||||||
\(192\) | −298.747 | + | 146.090i | −0.112293 | + | 0.0549120i | ||||
\(193\) | −520.796 | −0.194237 | −0.0971184 | − | 0.995273i | \(-0.530963\pi\) | ||||
−0.0971184 | + | 0.995273i | \(0.530963\pi\) | |||||||
\(194\) | − | 2104.96i | − | 0.779008i | ||||||
\(195\) | 1327.64 | − | 649.229i | 0.487562 | − | 0.238422i | ||||
\(196\) | 2479.34 | 0.903549 | ||||||||
\(197\) | 199.705i | 0.0722253i | 0.999348 | + | 0.0361126i | \(0.0114975\pi\) | ||||
−0.999348 | + | 0.0361126i | \(0.988502\pi\) | |||||||
\(198\) | −277.369 | + | 356.527i | −0.0995543 | + | 0.127966i | ||||
\(199\) | 3735.08 | 1.33052 | 0.665258 | − | 0.746614i | \(-0.268322\pi\) | ||||
0.665258 | + | 0.746614i | \(0.268322\pi\) | |||||||
\(200\) | 435.507 | 0.153975 | ||||||||
\(201\) | 1760.80 | + | 3600.77i | 0.617898 | + | 1.26357i | ||||
\(202\) | 1050.81 | 0.366013 | ||||||||
\(203\) | − | 4553.78i | − | 1.57445i | ||||||
\(204\) | 482.517 | + | 986.727i | 0.165603 | + | 0.338651i | ||||
\(205\) | −3385.11 | −1.15330 | ||||||||
\(206\) | − | 2843.16i | − | 0.961615i | ||||||
\(207\) | 2058.86 | − | 2646.44i | 0.691309 | − | 0.888601i | ||||
\(208\) | 541.744i | 0.180592i | ||||||||
\(209\) | 112.804 | 0.0373342 | ||||||||
\(210\) | −1189.95 | − | 2433.40i | −0.391022 | − | 0.799622i | ||||
\(211\) | − | 5577.94i | − | 1.81991i | −0.414707 | − | 0.909955i | \(-0.636116\pi\) | ||
0.414707 | − | 0.909955i | \(-0.363884\pi\) | |||||||
\(212\) | − | 402.633i | − | 0.130438i | ||||||
\(213\) | 598.203 | + | 1223.30i | 0.192433 | + | 0.393517i | ||||
\(214\) | − | 2233.87i | − | 0.713571i | ||||||
\(215\) | −3916.80 | −1.24243 | ||||||||
\(216\) | −229.961 | + | 1098.56i | −0.0724393 | + | 0.346053i | ||||
\(217\) | 6368.56i | 1.99229i | ||||||||
\(218\) | 1963.65i | 0.610071i | ||||||||
\(219\) | 812.573 | + | 1661.68i | 0.250724 | + | 0.512720i | ||||
\(220\) | − | 281.069i | − | 0.0861350i | ||||||
\(221\) | 1789.32 | 0.544627 | ||||||||
\(222\) | −1271.98 | − | 2601.14i | −0.384548 | − | 0.786384i | ||||
\(223\) | 645.411 | 0.193811 | 0.0969056 | − | 0.995294i | \(-0.469106\pi\) | ||||
0.0969056 | + | 0.995294i | \(0.469106\pi\) | |||||||
\(224\) | 992.947 | 0.296179 | ||||||||
\(225\) | 902.534 | − | 1160.11i | 0.267418 | − | 0.343736i | ||||
\(226\) | −816.086 | −0.240200 | ||||||||
\(227\) | −4962.92 | −1.45111 | −0.725553 | − | 0.688167i | \(-0.758416\pi\) | ||||
−0.725553 | + | 0.688167i | \(0.758416\pi\) | |||||||
\(228\) | 251.791 | − | 123.128i | 0.0731372 | − | 0.0357647i | ||||
\(229\) | − | 1665.45i | − | 0.480594i | −0.970699 | − | 0.240297i | \(-0.922755\pi\) | ||
0.970699 | − | 0.240297i | \(-0.0772448\pi\) | |||||||
\(230\) | 2086.33i | 0.598125i | ||||||||
\(231\) | 1211.63 | − | 592.495i | 0.345105 | − | 0.168759i | ||||
\(232\) | − | 1174.05i | − | 0.332242i | ||||||
\(233\) | −1081.65 | −0.304126 | −0.152063 | − | 0.988371i | \(-0.548592\pi\) | ||||
−0.152063 | + | 0.988371i | \(0.548592\pi\) | |||||||
\(234\) | 1443.10 | + | 1122.70i | 0.403156 | + | 0.313645i | ||||
\(235\) | − | 4314.50i | − | 1.19765i | ||||||
\(236\) | 1358.62 | − | 1200.09i | 0.374741 | − | 0.331013i | ||||
\(237\) | −4399.32 | + | 2151.30i | −1.20577 | + | 0.589629i | ||||
\(238\) | − | 3279.59i | − | 0.893211i | ||||||
\(239\) | − | 3631.44i | − | 0.982837i | −0.870923 | − | 0.491419i | \(-0.836478\pi\) | ||
0.870923 | − | 0.491419i | \(-0.163522\pi\) | |||||||
\(240\) | −306.792 | − | 627.376i | −0.0825139 | − | 0.168737i | ||||
\(241\) | −196.304 | −0.0524692 | −0.0262346 | − | 0.999656i | \(-0.508352\pi\) | ||||
−0.0262346 | + | 0.999656i | \(0.508352\pi\) | |||||||
\(242\) | −2522.05 | −0.669932 | ||||||||
\(243\) | 2449.78 | + | 2889.20i | 0.646723 | + | 0.762725i | ||||
\(244\) | 1653.16i | 0.433740i | ||||||||
\(245\) | 5206.67i | 1.35772i | ||||||||
\(246\) | −1839.75 | − | 3762.20i | −0.476821 | − | 0.975078i | ||||
\(247\) | − | 456.595i | − | 0.117621i | ||||||
\(248\) | 1641.93i | 0.420415i | ||||||||
\(249\) | 5382.90 | − | 2632.28i | 1.36999 | − | 0.669936i | ||||
\(250\) | 3014.60i | 0.762640i | ||||||||
\(251\) | − | 4710.90i | − | 1.18466i | −0.805696 | − | 0.592330i | \(-0.798208\pi\) | ||
0.805696 | − | 0.592330i | \(-0.201792\pi\) | |||||||
\(252\) | 2057.76 | − | 2645.02i | 0.514391 | − | 0.661193i | ||||
\(253\) | −1038.82 | −0.258141 | ||||||||
\(254\) | 2570.89 | 0.635086 | ||||||||
\(255\) | −2072.15 | + | 1013.30i | −0.508875 | + | 0.248844i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 7251.98i | − | 1.76018i | −0.474807 | − | 0.880090i | \(-0.657482\pi\) | ||
0.474807 | − | 0.880090i | \(-0.342518\pi\) | |||||||
\(258\) | −2128.71 | − | 4353.12i | −0.513673 | − | 1.05044i | ||||
\(259\) | 8645.43i | 2.07413i | ||||||||
\(260\) | −1137.67 | −0.271368 | ||||||||
\(261\) | −3127.44 | − | 2433.07i | −0.741701 | − | 0.577024i | ||||
\(262\) | −517.244 | −0.121967 | ||||||||
\(263\) | − | 5336.53i | − | 1.25119i | −0.780146 | − | 0.625597i | \(-0.784855\pi\) | ||
0.780146 | − | 0.625597i | \(-0.215145\pi\) | |||||||
\(264\) | 312.380 | − | 152.756i | 0.0728244 | − | 0.0356117i | ||||
\(265\) | 845.539 | 0.196004 | ||||||||
\(266\) | −836.879 | −0.192904 | ||||||||
\(267\) | 509.451 | − | 249.125i | 0.116771 | − | 0.0571020i | ||||
\(268\) | − | 3085.54i | − | 0.703282i | ||||||
\(269\) | 4621.19 | 1.04743 | 0.523715 | − | 0.851893i | \(-0.324546\pi\) | ||||
0.523715 | + | 0.851893i | \(0.324546\pi\) | |||||||
\(270\) | −2307.00 | − | 482.924i | −0.519998 | − | 0.108851i | ||||
\(271\) | −1948.39 | −0.436740 | −0.218370 | − | 0.975866i | \(-0.570074\pi\) | ||||
−0.218370 | + | 0.975866i | \(0.570074\pi\) | |||||||
\(272\) | − | 845.539i | − | 0.188486i | ||||||
\(273\) | −2398.22 | − | 4904.26i | −0.531674 | − | 1.08725i | ||||
\(274\) | 2734.47i | 0.602904i | ||||||||
\(275\) | −455.380 | −0.0998562 | ||||||||
\(276\) | −2318.74 | + | 1133.88i | −0.505696 | + | 0.247289i | ||||
\(277\) | 6091.03 | 1.32121 | 0.660603 | − | 0.750735i | \(-0.270300\pi\) | ||||
0.660603 | + | 0.750735i | \(0.270300\pi\) | |||||||
\(278\) | −1220.13 | −0.263231 | ||||||||
\(279\) | 4373.80 | + | 3402.70i | 0.938539 | + | 0.730159i | ||||
\(280\) | 2085.21i | 0.445054i | ||||||||
\(281\) | 236.625i | 0.0502343i | 0.999685 | + | 0.0251172i | \(0.00799588\pi\) | ||||
−0.999685 | + | 0.0251172i | \(0.992004\pi\) | |||||||
\(282\) | 4795.12 | − | 2344.85i | 1.01257 | − | 0.495155i | ||||
\(283\) | − | 4957.63i | − | 1.04135i | −0.853756 | − | 0.520673i | \(-0.825681\pi\) | ||
0.853756 | − | 0.520673i | \(-0.174319\pi\) | |||||||
\(284\) | − | 1048.26i | − | 0.219024i | ||||||
\(285\) | 258.572 | + | 528.768i | 0.0537420 | + | 0.109900i | ||||
\(286\) | − | 566.465i | − | 0.117118i | ||||||
\(287\) | 12504.4i | 2.57182i | ||||||||
\(288\) | 530.528 | − | 681.935i | 0.108547 | − | 0.139526i | ||||
\(289\) | 2120.28 | 0.431566 | ||||||||
\(290\) | 2465.53 | 0.499245 | ||||||||
\(291\) | 2402.45 | + | 4912.90i | 0.483966 | + | 0.989689i | ||||
\(292\) | − | 1423.91i | − | 0.285370i | ||||||
\(293\) | 697.323i | 0.139038i | 0.997581 | + | 0.0695188i | \(0.0221464\pi\) | ||||
−0.997581 | + | 0.0695188i | \(0.977854\pi\) | |||||||
\(294\) | −5786.68 | + | 2829.73i | −1.14791 | + | 0.561338i | ||||
\(295\) | 2520.21 | + | 2853.14i | 0.497398 | + | 0.563106i | ||||
\(296\) | 2228.95i | 0.437686i | ||||||||
\(297\) | 240.455 | − | 1148.69i | 0.0469785 | − | 0.224423i | ||||
\(298\) | 3487.31 | 0.677901 | ||||||||
\(299\) | 4204.78i | 0.813273i | ||||||||
\(300\) | −1016.46 | + | 497.055i | −0.195617 | + | 0.0956583i | ||||
\(301\) | 14468.5i | 2.77060i | ||||||||
\(302\) | − | 3314.24i | − | 0.631499i | ||||||
\(303\) | −2452.55 | + | 1199.31i | −0.465001 | + | 0.227389i | ||||
\(304\) | −215.763 | −0.0407068 | ||||||||
\(305\) | −3471.67 | −0.651762 | ||||||||
\(306\) | −2252.35 | − | 1752.27i | −0.420780 | − | 0.327356i | ||||
\(307\) | 4472.31 | 0.831428 | 0.415714 | − | 0.909495i | \(-0.363532\pi\) | ||||
0.415714 | + | 0.909495i | \(0.363532\pi\) | |||||||
\(308\) | −1038.26 | −0.192079 | ||||||||
\(309\) | 3244.98 | + | 6635.84i | 0.597412 | + | 1.22168i | ||||
\(310\) | −3448.10 | −0.631738 | ||||||||
\(311\) | 1640.56i | 0.299125i | 0.988752 | + | 0.149562i | \(0.0477865\pi\) | ||||
−0.988752 | + | 0.149562i | \(0.952214\pi\) | |||||||
\(312\) | −618.306 | − | 1264.41i | −0.112194 | − | 0.229433i | ||||
\(313\) | 1328.32i | 0.239875i | 0.992781 | + | 0.119938i | \(0.0382695\pi\) | ||||
−0.992781 | + | 0.119938i | \(0.961731\pi\) | |||||||
\(314\) | 5364.40i | 0.964110i | ||||||||
\(315\) | 5554.61 | + | 4321.34i | 0.993545 | + | 0.772953i | ||||
\(316\) | 3769.83 | 0.671106 | ||||||||
\(317\) | 4577.13i | 0.810970i | 0.914102 | + | 0.405485i | \(0.132897\pi\) | ||||
−0.914102 | + | 0.405485i | \(0.867103\pi\) | |||||||
\(318\) | 459.535 | + | 939.730i | 0.0810361 | + | 0.165715i | ||||
\(319\) | 1227.62i | 0.215466i | ||||||||
\(320\) | 537.606i | 0.0939159i | ||||||||
\(321\) | 2549.57 | + | 5213.76i | 0.443312 | + | 0.906554i | ||||
\(322\) | 7706.82 | 1.33380 | ||||||||
\(323\) | 712.641i | 0.122763i | ||||||||
\(324\) | −717.092 | − | 2826.45i | −0.122958 | − | 0.484646i | ||||
\(325\) | 1843.23i | 0.314596i | ||||||||
\(326\) | 3006.99 | 0.510864 | ||||||||
\(327\) | −2241.17 | − | 4583.09i | −0.379012 | − | 0.775063i | ||||
\(328\) | 3223.88i | 0.542710i | ||||||||
\(329\) | −15937.5 | −2.67072 | ||||||||
\(330\) | 320.792 | + | 656.005i | 0.0535121 | + | 0.109430i | ||||
\(331\) | −3063.70 | −0.508751 | −0.254375 | − | 0.967106i | \(-0.581870\pi\) | ||||
−0.254375 | + | 0.967106i | \(0.581870\pi\) | |||||||
\(332\) | −4612.68 | −0.762510 | ||||||||
\(333\) | 5937.50 | + | 4619.23i | 0.977097 | + | 0.760156i | ||||
\(334\) | − | 2485.28i | − | 0.407151i | ||||||
\(335\) | 6479.71 | 1.05679 | ||||||||
\(336\) | −2317.50 | + | 1133.28i | −0.376280 | + | 0.184004i | ||||
\(337\) | − | 1397.94i | − | 0.225966i | −0.993597 | − | 0.112983i | \(-0.963959\pi\) | ||
0.993597 | − | 0.112983i | \(-0.0360405\pi\) | |||||||
\(338\) | 2101.14 | 0.338127 | ||||||||
\(339\) | 1904.71 | − | 931.420i | 0.305162 | − | 0.149227i | ||||
\(340\) | 1775.65 | 0.283230 | ||||||||
\(341\) | − | 1716.86i | − | 0.272648i | ||||||
\(342\) | −447.142 | + | 574.752i | −0.0706979 | + | 0.0908743i | ||||
\(343\) | 8590.07 | 1.35224 | ||||||||
\(344\) | 3730.24i | 0.584654i | ||||||||
\(345\) | −2381.18 | − | 4869.42i | −0.371590 | − | 0.759886i | ||||
\(346\) | 5066.31 | 0.787186 | ||||||||
\(347\) | −5532.97 | −0.855982 | −0.427991 | − | 0.903783i | \(-0.640778\pi\) | ||||
−0.427991 | + | 0.903783i | \(0.640778\pi\) | |||||||
\(348\) | 1339.97 | + | 2740.19i | 0.206408 | + | 0.422096i | ||||
\(349\) | − | 5299.70i | − | 0.812856i | −0.913683 | − | 0.406428i | \(-0.866774\pi\) | ||
0.913683 | − | 0.406428i | \(-0.133226\pi\) | |||||||
\(350\) | 3378.40 | 0.515952 | ||||||||
\(351\) | −4649.51 | − | 973.282i | −0.707044 | − | 0.148005i | ||||
\(352\) | −267.682 | −0.0405327 | ||||||||
\(353\) | −9723.93 | −1.46615 | −0.733077 | − | 0.680145i | \(-0.761917\pi\) | ||||
−0.733077 | + | 0.680145i | \(0.761917\pi\) | |||||||
\(354\) | −1801.28 | + | 4351.59i | −0.270444 | + | 0.653345i | ||||
\(355\) | 2201.37 | 0.329117 | ||||||||
\(356\) | −436.555 | −0.0649925 | ||||||||
\(357\) | 3743.08 | + | 7654.43i | 0.554915 | + | 1.13478i | ||||
\(358\) | −3801.39 | −0.561200 | ||||||||
\(359\) | − | 1512.83i | − | 0.222407i | −0.993798 | − | 0.111204i | \(-0.964529\pi\) | ||
0.993798 | − | 0.111204i | \(-0.0354705\pi\) | |||||||
\(360\) | 1432.08 | + | 1114.12i | 0.209659 | + | 0.163109i | ||||
\(361\) | −6677.15 | −0.973487 | ||||||||
\(362\) | −7814.87 | −1.13464 | ||||||||
\(363\) | 5886.37 | − | 2878.48i | 0.851114 | − | 0.416201i | ||||
\(364\) | 4202.52i | 0.605142i | ||||||||
\(365\) | 2990.25 | 0.428813 | ||||||||
\(366\) | −1886.79 | − | 3858.41i | −0.269465 | − | 0.551045i | ||||
\(367\) | 4626.41i | 0.658029i | 0.944325 | + | 0.329014i | \(0.106716\pi\) | ||||
−0.944325 | + | 0.329014i | \(0.893284\pi\) | |||||||
\(368\) | 1986.96 | 0.281461 | ||||||||
\(369\) | 8587.79 | + | 6681.08i | 1.21155 | + | 0.942556i | ||||
\(370\) | −4680.85 | −0.657692 | ||||||||
\(371\) | − | 3123.38i | − | 0.437084i | ||||||
\(372\) | −1873.98 | − | 3832.21i | −0.261186 | − | 0.534115i | ||||
\(373\) | −3438.22 | −0.477277 | −0.238638 | − | 0.971109i | \(-0.576701\pi\) | ||||
−0.238638 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(374\) | 884.123i | 0.122238i | ||||||||
\(375\) | −3440.64 | − | 7035.96i | −0.473797 | − | 0.968894i | ||||
\(376\) | −4109.00 | −0.563578 | ||||||||
\(377\) | 4969.01 | 0.678825 | ||||||||
\(378\) | −1783.90 | + | 8521.95i | −0.242735 | + | 1.15958i | ||||
\(379\) | −13480.0 | −1.82697 | −0.913485 | − | 0.406871i | \(-0.866620\pi\) | ||||
−0.913485 | + | 0.406871i | \(0.866620\pi\) | |||||||
\(380\) | − | 453.108i | − | 0.0611682i | ||||||
\(381\) | −6000.35 | + | 2934.22i | −0.806843 | + | 0.394553i | ||||
\(382\) | −2417.46 | −0.323791 | ||||||||
\(383\) | 4288.91i | 0.572202i | 0.958200 | + | 0.286101i | \(0.0923592\pi\) | ||||
−0.958200 | + | 0.286101i | \(0.907641\pi\) | |||||||
\(384\) | −597.494 | + | 292.179i | −0.0794030 | + | 0.0388287i | ||||
\(385\) | − | 2180.37i | − | 0.288628i | ||||||
\(386\) | −1041.59 | −0.137346 | ||||||||
\(387\) | 9936.65 | + | 7730.46i | 1.30519 | + | 1.01540i | ||||
\(388\) | − | 4209.93i | − | 0.550842i | ||||||
\(389\) | 2244.88i | 0.292596i | 0.989241 | + | 0.146298i | \(0.0467359\pi\) | ||||
−0.989241 | + | 0.146298i | \(0.953264\pi\) | |||||||
\(390\) | 2655.29 | − | 1298.46i | 0.344758 | − | 0.168590i | ||||
\(391\) | − | 6562.70i | − | 0.848824i | ||||||
\(392\) | 4958.68 | 0.638906 | ||||||||
\(393\) | 1207.23 | − | 590.344i | 0.154953 | − | 0.0757733i | ||||
\(394\) | 399.410i | 0.0510710i | ||||||||
\(395\) | 7916.74i | 1.00844i | ||||||||
\(396\) | −554.738 | + | 713.054i | −0.0703955 | + | 0.0904856i | ||||
\(397\) | 10293.5i | 1.30131i | 0.759375 | + | 0.650653i | \(0.225505\pi\) | ||||
−0.759375 | + | 0.650653i | \(0.774495\pi\) | |||||||
\(398\) | 7470.16 | 0.940817 | ||||||||
\(399\) | 1953.24 | − | 955.152i | 0.245074 | − | 0.119843i | ||||
\(400\) | 871.014 | 0.108877 | ||||||||
\(401\) | 14430.6 | 1.79708 | 0.898540 | − | 0.438892i | \(-0.144629\pi\) | ||||
0.898540 | + | 0.438892i | \(0.144629\pi\) | |||||||
\(402\) | 3521.61 | + | 7201.54i | 0.436920 | + | 0.893482i | ||||
\(403\) | −6949.27 | −0.858977 | ||||||||
\(404\) | 2101.62 | 0.258810 | ||||||||
\(405\) | 5935.62 | − | 1505.91i | 0.728255 | − | 0.184764i | ||||
\(406\) | − | 9107.56i | − | 1.11330i | ||||||
\(407\) | − | 2330.66i | − | 0.283850i | ||||||
\(408\) | 965.035 | + | 1973.45i | 0.117099 | + | 0.239462i | ||||
\(409\) | − | 7892.13i | − | 0.954133i | −0.878867 | − | 0.477067i | \(-0.841700\pi\) | ||
0.878867 | − | 0.477067i | \(-0.158300\pi\) | |||||||
\(410\) | −6770.22 | −0.815505 | ||||||||
\(411\) | −3120.93 | − | 6382.16i | −0.374559 | − | 0.765958i | ||||
\(412\) | − | 5686.33i | − | 0.679964i | ||||||
\(413\) | 10539.4 | − | 9309.55i | 1.25571 | − | 1.10918i | ||||
\(414\) | 4117.73 | − | 5292.88i | 0.488829 | − | 0.628336i | ||||
\(415\) | − | 9686.73i | − | 1.14579i | ||||||
\(416\) | 1083.49i | 0.127698i | ||||||||
\(417\) | 2847.73 | − | 1392.56i | 0.334422 | − | 0.163535i | ||||
\(418\) | 225.609 | 0.0263993 | ||||||||
\(419\) | 2953.47 | 0.344359 | 0.172180 | − | 0.985066i | \(-0.444919\pi\) | ||||
0.172180 | + | 0.985066i | \(0.444919\pi\) | |||||||
\(420\) | −2379.91 | − | 4866.80i | −0.276494 | − | 0.565418i | ||||
\(421\) | − | 13002.4i | − | 1.50522i | −0.658465 | − | 0.752611i | \(-0.728794\pi\) | ||
0.658465 | − | 0.752611i | \(-0.271206\pi\) | |||||||
\(422\) | − | 11155.9i | − | 1.28687i | ||||||
\(423\) | −8515.38 | + | 10945.6i | −0.978799 | + | 1.25814i | ||||
\(424\) | − | 805.266i | − | 0.0922339i | ||||||
\(425\) | − | 2876.86i | − | 0.328349i | ||||||
\(426\) | 1196.41 | + | 2446.60i | 0.136071 | + | 0.278258i | ||||
\(427\) | 12824.2i | 1.45341i | ||||||||
\(428\) | − | 4467.74i | − | 0.504571i | ||||||
\(429\) | 646.521 | + | 1322.11i | 0.0727606 | + | 0.148792i | ||||
\(430\) | −7833.60 | −0.878534 | ||||||||
\(431\) | 10132.3 | 1.13238 | 0.566192 | − | 0.824273i | \(-0.308416\pi\) | ||||
0.566192 | + | 0.824273i | \(0.308416\pi\) | |||||||
\(432\) | −459.922 | + | 2197.12i | −0.0512223 | + | 0.244696i | ||||
\(433\) | −4114.22 | −0.456621 | −0.228310 | − | 0.973588i | \(-0.573320\pi\) | ||||
−0.228310 | + | 0.973588i | \(0.573320\pi\) | |||||||
\(434\) | 12737.1i | 1.40876i | ||||||||
\(435\) | −5754.46 | + | 2813.97i | −0.634265 | + | 0.310160i | ||||
\(436\) | 3927.31i | 0.431385i | ||||||||
\(437\) | −1674.66 | −0.183318 | ||||||||
\(438\) | 1625.15 | + | 3323.35i | 0.177289 | + | 0.362548i | ||||
\(439\) | −5508.75 | −0.598902 | −0.299451 | − | 0.954112i | \(-0.596804\pi\) | ||||
−0.299451 | + | 0.954112i | \(0.596804\pi\) | |||||||
\(440\) | − | 562.139i | − | 0.0609066i | ||||||
\(441\) | 10276.2 | − | 13209.0i | 1.10963 | − | 1.42630i | ||||
\(442\) | 3578.63 | 0.385109 | ||||||||
\(443\) | −1630.71 | −0.174893 | −0.0874464 | − | 0.996169i | \(-0.527871\pi\) | ||||
−0.0874464 | + | 0.996169i | \(0.527871\pi\) | |||||||
\(444\) | −2543.96 | − | 5202.29i | −0.271917 | − | 0.556058i | ||||
\(445\) | − | 916.775i | − | 0.0976614i | ||||||
\(446\) | 1290.82 | 0.137045 | ||||||||
\(447\) | −8139.25 | + | 3980.16i | −0.861238 | + | 0.421152i | ||||
\(448\) | 1985.89 | 0.209430 | ||||||||
\(449\) | 4257.32i | 0.447473i | 0.974650 | + | 0.223736i | \(0.0718254\pi\) | ||||
−0.974650 | + | 0.223736i | \(0.928175\pi\) | |||||||
\(450\) | 1805.07 | − | 2320.22i | 0.189093 | − | 0.243058i | ||||
\(451\) | − | 3370.99i | − | 0.351959i | ||||||
\(452\) | −1632.17 | −0.169847 | ||||||||
\(453\) | 3782.62 | + | 7735.30i | 0.392325 | + | 0.802287i | ||||
\(454\) | −9925.85 | −1.02609 | ||||||||
\(455\) | −8825.39 | −0.909320 | ||||||||
\(456\) | 503.583 | − | 246.256i | 0.0517158 | − | 0.0252894i | ||||
\(457\) | − | 3275.73i | − | 0.335300i | −0.985847 | − | 0.167650i | \(-0.946382\pi\) | ||
0.985847 | − | 0.167650i | \(-0.0536179\pi\) | |||||||
\(458\) | − | 3330.90i | − | 0.339831i | ||||||
\(459\) | 7256.82 | + | 1519.07i | 0.737951 | + | 0.154475i | ||||
\(460\) | 4172.67i | 0.422938i | ||||||||
\(461\) | 6732.01i | 0.680132i | 0.940402 | + | 0.340066i | \(0.110449\pi\) | ||||
−0.940402 | + | 0.340066i | \(0.889551\pi\) | |||||||
\(462\) | 2423.25 | − | 1184.99i | 0.244026 | − | 0.119331i | ||||
\(463\) | − | 4773.68i | − | 0.479161i | −0.970876 | − | 0.239581i | \(-0.922990\pi\) | ||
0.970876 | − | 0.239581i | \(-0.0770100\pi\) | |||||||
\(464\) | − | 2348.10i | − | 0.234930i | ||||||
\(465\) | 8047.73 | − | 3935.40i | 0.802590 | − | 0.392473i | ||||
\(466\) | −2163.30 | −0.215050 | ||||||||
\(467\) | 18623.8 | 1.84541 | 0.922704 | − | 0.385509i | \(-0.125974\pi\) | ||||
0.922704 | + | 0.385509i | \(0.125974\pi\) | |||||||
\(468\) | 2886.20 | + | 2245.39i | 0.285074 | + | 0.221781i | ||||
\(469\) | − | 23935.8i | − | 2.35661i | ||||||
\(470\) | − | 8628.99i | − | 0.846863i | ||||||
\(471\) | −6122.52 | − | 12520.3i | −0.598962 | − | 1.22485i | ||||
\(472\) | 2717.24 | − | 2400.17i | 0.264982 | − | 0.234061i | ||||
\(473\) | − | 3900.46i | − | 0.379162i | ||||||
\(474\) | −8798.64 | + | 4302.61i | −0.852606 | + | 0.416931i | ||||
\(475\) | −734.112 | −0.0709123 | ||||||||
\(476\) | − | 6559.18i | − | 0.631595i | ||||||
\(477\) | −2145.08 | − | 1668.81i | −0.205904 | − | 0.160188i | ||||
\(478\) | − | 7262.87i | − | 0.694971i | ||||||
\(479\) | 2379.76i | 0.227002i | 0.993538 | + | 0.113501i | \(0.0362066\pi\) | ||||
−0.993538 | + | 0.113501i | \(0.963793\pi\) | |||||||
\(480\) | −613.584 | − | 1254.75i | −0.0583461 | − | 0.119315i | ||||
\(481\) | −9433.75 | −0.894266 | ||||||||
\(482\) | −392.609 | −0.0371013 | ||||||||
\(483\) | −17987.4 | + | 8795.99i | −1.69453 | + | 0.828636i | ||||
\(484\) | −5044.10 | −0.473714 | ||||||||
\(485\) | 8840.95 | 0.827725 | ||||||||
\(486\) | 4899.57 | + | 5778.40i | 0.457302 | + | 0.539328i | ||||
\(487\) | −14744.7 | −1.37196 | −0.685982 | − | 0.727618i | \(-0.740627\pi\) | ||||
−0.685982 | + | 0.727618i | \(0.740627\pi\) | |||||||
\(488\) | 3306.32i | 0.306701i | ||||||||
\(489\) | −7018.20 | + | 3431.95i | −0.649026 | + | 0.317379i | ||||
\(490\) | 10413.3i | 0.960055i | ||||||||
\(491\) | − | 19027.8i | − | 1.74891i | −0.485111 | − | 0.874453i | \(-0.661221\pi\) | ||
0.485111 | − | 0.874453i | \(-0.338779\pi\) | |||||||
\(492\) | −3679.49 | − | 7524.40i | −0.337163 | − | 0.689484i | ||||
\(493\) | −7755.50 | −0.708499 | ||||||||
\(494\) | − | 913.189i | − | 0.0831707i | ||||||
\(495\) | −1497.43 | − | 1164.96i | −0.135969 | − | 0.105780i | ||||
\(496\) | 3283.87i | 0.297278i | ||||||||
\(497\) | − | 8131.76i | − | 0.733923i | ||||||
\(498\) | 10765.8 | − | 5264.56i | 0.968730 | − | 0.473716i | ||||
\(499\) | −17377.1 | −1.55893 | −0.779465 | − | 0.626446i | \(-0.784509\pi\) | ||||
−0.779465 | + | 0.626446i | \(0.784509\pi\) | |||||||
\(500\) | 6029.20i | 0.539268i | ||||||||
\(501\) | 2836.51 | + | 5800.55i | 0.252946 | + | 0.517264i | ||||
\(502\) | − | 9421.81i | − | 0.837681i | ||||||
\(503\) | −12024.8 | −1.06592 | −0.532960 | − | 0.846140i | \(-0.678920\pi\) | ||||
−0.532960 | + | 0.846140i | \(0.678920\pi\) | |||||||
\(504\) | 4115.52 | − | 5290.04i | 0.363730 | − | 0.467534i | ||||
\(505\) | 4413.45i | 0.388903i | ||||||||
\(506\) | −2077.63 | −0.182534 | ||||||||
\(507\) | −4903.98 | + | 2398.08i | −0.429573 | + | 0.210064i | ||||
\(508\) | 5141.77 | 0.449073 | ||||||||
\(509\) | 306.241 | 0.0266677 | 0.0133339 | − | 0.999911i | \(-0.495756\pi\) | ||||
0.0133339 | + | 0.999911i | \(0.495756\pi\) | |||||||
\(510\) | −4144.30 | + | 2026.60i | −0.359829 | + | 0.175959i | ||||
\(511\) | − | 11045.8i | − | 0.956241i | ||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 387.634 | − | 1851.78i | 0.0333615 | − | 0.159373i | ||||
\(514\) | − | 14504.0i | − | 1.24463i | ||||||
\(515\) | 11941.4 | 1.02175 | ||||||||
\(516\) | −4257.42 | − | 8706.24i | −0.363222 | − | 0.742773i | ||||
\(517\) | 4296.50 | 0.365493 | ||||||||
\(518\) | 17290.9i | 1.46663i | ||||||||
\(519\) | −11824.6 | + | 5782.30i | −1.00008 | + | 0.489046i | ||||
\(520\) | −2275.35 | −0.191886 | ||||||||
\(521\) | − | 3176.70i | − | 0.267128i | −0.991040 | − | 0.133564i | \(-0.957358\pi\) | ||
0.991040 | − | 0.133564i | \(-0.0426421\pi\) | |||||||
\(522\) | −6254.89 | − | 4866.14i | −0.524462 | − | 0.408018i | ||||
\(523\) | −2353.51 | −0.196772 | −0.0983861 | − | 0.995148i | \(-0.531368\pi\) | ||||
−0.0983861 | + | 0.995148i | \(0.531368\pi\) | |||||||
\(524\) | −1034.49 | −0.0862439 | ||||||||
\(525\) | −7885.05 | + | 3855.85i | −0.655489 | + | 0.320539i | ||||
\(526\) | − | 10673.1i | − | 0.884728i | ||||||
\(527\) | 10846.2 | 0.896526 | ||||||||
\(528\) | 624.759 | − | 305.512i | 0.0514946 | − | 0.0251813i | ||||
\(529\) | 3254.92 | 0.267520 | ||||||||
\(530\) | 1691.08 | 0.138596 | ||||||||
\(531\) | −762.454 | − | 12212.3i | −0.0623121 | − | 0.998057i | ||||
\(532\) | −1673.76 | −0.136403 | ||||||||
\(533\) | −13644.6 | −1.10885 | ||||||||
\(534\) | 1018.90 | − | 498.251i | 0.0825696 | − | 0.0403772i | ||||
\(535\) | 9382.36 | 0.758196 | ||||||||
\(536\) | − | 6171.08i | − | 0.497295i | ||||||
\(537\) | 8872.29 | − | 4338.62i | 0.712975 | − | 0.348650i | ||||
\(538\) | 9242.38 | 0.740645 | ||||||||
\(539\) | −5184.96 | −0.414345 | ||||||||
\(540\) | −4614.00 | − | 965.848i | −0.367694 | − | 0.0769694i | ||||
\(541\) | − | 402.038i | − | 0.0319500i | −0.999872 | − | 0.0159750i | \(-0.994915\pi\) | ||
0.999872 | − | 0.0159750i | \(-0.00508522\pi\) | |||||||
\(542\) | −3896.79 | −0.308822 | ||||||||
\(543\) | 18239.6 | − | 8919.31i | 1.44150 | − | 0.704907i | ||||
\(544\) | − | 1691.08i | − | 0.133280i | ||||||
\(545\) | −8247.44 | −0.648223 | ||||||||
\(546\) | −4796.44 | − | 9808.52i | −0.375950 | − | 0.768802i | ||||
\(547\) | 3875.34 | 0.302920 | 0.151460 | − | 0.988463i | \(-0.451602\pi\) | ||||
0.151460 | + | 0.988463i | \(0.451602\pi\) | |||||||
\(548\) | 5468.95i | 0.426317i | ||||||||
\(549\) | 8807.40 | + | 6851.94i | 0.684683 | + | 0.532666i | ||||
\(550\) | −910.761 | −0.0706090 | ||||||||
\(551\) | 1979.03i | 0.153012i | ||||||||
\(552\) | −4637.49 | + | 2267.77i | −0.357581 | + | 0.174860i | ||||
\(553\) | 29244.1 | 2.24880 | ||||||||
\(554\) | 12182.1 | 0.934234 | ||||||||
\(555\) | 10924.9 | − | 5342.38i | 0.835563 | − | 0.408597i | ||||
\(556\) | −2440.25 | −0.186133 | ||||||||
\(557\) | 14688.1i | 1.11733i | 0.829392 | + | 0.558667i | \(0.188687\pi\) | ||||
−0.829392 | + | 0.558667i | \(0.811313\pi\) | |||||||
\(558\) | 8747.59 | + | 6805.41i | 0.663647 | + | 0.516301i | ||||
\(559\) | −15787.8 | −1.19455 | ||||||||
\(560\) | 4170.42i | 0.314701i | ||||||||
\(561\) | −1009.07 | − | 2063.51i | −0.0759413 | − | 0.155297i | ||||
\(562\) | 473.249i | 0.0355210i | ||||||||
\(563\) | −26307.9 | −1.96935 | −0.984676 | − | 0.174392i | \(-0.944204\pi\) | ||||
−0.984676 | + | 0.174392i | \(0.944204\pi\) | |||||||
\(564\) | 9590.24 | − | 4689.70i | 0.715996 | − | 0.350128i | ||||
\(565\) | − | 3427.60i | − | 0.255222i | ||||||
\(566\) | − | 9915.27i | − | 0.736343i | ||||||
\(567\) | −5562.76 | − | 21925.9i | −0.412018 | − | 1.62399i | ||||
\(568\) | − | 2096.52i | − | 0.154873i | ||||||
\(569\) | 7713.03 | 0.568272 | 0.284136 | − | 0.958784i | \(-0.408293\pi\) | ||||
0.284136 | + | 0.958784i | \(0.408293\pi\) | |||||||
\(570\) | 517.143 | + | 1057.54i | 0.0380013 | + | 0.0777110i | ||||
\(571\) | 17912.5i | 1.31281i | 0.754409 | + | 0.656405i | \(0.227924\pi\) | ||||
−0.754409 | + | 0.656405i | \(0.772076\pi\) | |||||||
\(572\) | − | 1132.93i | − | 0.0828150i | ||||||
\(573\) | 5642.26 | − | 2759.11i | 0.411359 | − | 0.201158i | ||||
\(574\) | 25008.9i | 1.81855i | ||||||||
\(575\) | 6760.43 | 0.490312 | ||||||||
\(576\) | 1061.06 | − | 1363.87i | 0.0767547 | − | 0.0986596i | ||||
\(577\) | −21753.0 | −1.56948 | −0.784740 | − | 0.619825i | \(-0.787204\pi\) | ||||
−0.784740 | + | 0.619825i | \(0.787204\pi\) | |||||||
\(578\) | 4240.56 | 0.305163 | ||||||||
\(579\) | 2431.03 | − | 1188.79i | 0.174491 | − | 0.0853275i | ||||
\(580\) | 4931.06 | 0.353019 | ||||||||
\(581\) | −35782.3 | −2.55508 | ||||||||
\(582\) | 4804.90 | + | 9825.81i | 0.342215 | + | 0.699816i | ||||
\(583\) | 842.013i | 0.0598158i | ||||||||
\(584\) | − | 2847.82i | − | 0.201787i | ||||||
\(585\) | −4715.38 | + | 6061.10i | −0.333260 | + | 0.428368i | ||||
\(586\) | 1394.65i | 0.0983145i | ||||||||
\(587\) | −9628.83 | −0.677043 | −0.338522 | − | 0.940959i | \(-0.609927\pi\) | ||||
−0.338522 | + | 0.940959i | \(0.609927\pi\) | |||||||
\(588\) | −11573.4 | + | 5659.47i | −0.811696 | + | 0.396926i | ||||
\(589\) | − | 2767.72i | − | 0.193620i | ||||||
\(590\) | 5040.42 | + | 5706.28i | 0.351714 | + | 0.398176i | ||||
\(591\) | −455.856 | − | 932.207i | −0.0317283 | − | 0.0648830i | ||||
\(592\) | 4457.90i | 0.309491i | ||||||||
\(593\) | 21483.0i | 1.48769i | 0.668352 | + | 0.743846i | \(0.267000\pi\) | ||||
−0.668352 | + | 0.743846i | \(0.733000\pi\) | |||||||
\(594\) | 480.910 | − | 2297.38i | 0.0332188 | − | 0.158691i | ||||
\(595\) | 13774.4 | 0.949070 | ||||||||
\(596\) | 6974.62 | 0.479348 | ||||||||
\(597\) | −17435.1 | + | 8525.88i | −1.19526 | + | 0.584491i | ||||
\(598\) | 8409.56i | 0.575071i | ||||||||
\(599\) | − | 19057.7i | − | 1.29996i | −0.759951 | − | 0.649980i | \(-0.774777\pi\) | ||
0.759951 | − | 0.649980i | \(-0.225223\pi\) | |||||||
\(600\) | −2032.91 | + | 994.110i | −0.138322 | + | 0.0676406i | ||||
\(601\) | − | 5559.07i | − | 0.377303i | −0.982044 | − | 0.188651i | \(-0.939588\pi\) | ||
0.982044 | − | 0.188651i | \(-0.0604116\pi\) | |||||||
\(602\) | 28937.0i | 1.95911i | ||||||||
\(603\) | −16438.6 | − | 12788.8i | −1.11017 | − | 0.863682i | ||||
\(604\) | − | 6628.47i | − | 0.446538i | ||||||
\(605\) | − | 10592.7i | − | 0.711828i | ||||||
\(606\) | −4905.09 | + | 2398.63i | −0.328805 | + | 0.160788i | ||||
\(607\) | 15577.0 | 1.04160 | 0.520801 | − | 0.853678i | \(-0.325633\pi\) | ||||
0.520801 | + | 0.853678i | \(0.325633\pi\) | |||||||
\(608\) | −431.526 | −0.0287840 | ||||||||
\(609\) | 10394.7 | + | 21256.7i | 0.691649 | + | 1.41439i | ||||
\(610\) | −6943.35 | −0.460866 | ||||||||
\(611\) | − | 17390.8i | − | 1.15148i | ||||||
\(612\) | −4504.71 | − | 3504.55i | −0.297536 | − | 0.231475i | ||||
\(613\) | 4461.15i | 0.293938i | 0.989141 | + | 0.146969i | \(0.0469518\pi\) | ||||
−0.989141 | + | 0.146969i | \(0.953048\pi\) | |||||||
\(614\) | 8944.62 | 0.587908 | ||||||||
\(615\) | 15801.4 | − | 7727.02i | 1.03606 | − | 0.506640i | ||||
\(616\) | −2076.51 | −0.135820 | ||||||||
\(617\) | − | 6488.60i | − | 0.423373i | −0.977338 | − | 0.211687i | \(-0.932104\pi\) | ||
0.977338 | − | 0.211687i | \(-0.0678956\pi\) | |||||||
\(618\) | 6489.95 | + | 13271.7i | 0.422434 | + | 0.863859i | ||||
\(619\) | 6925.70 | 0.449705 | 0.224853 | − | 0.974393i | \(-0.427810\pi\) | ||||
0.224853 | + | 0.974393i | \(0.427810\pi\) | |||||||
\(620\) | −6896.20 | −0.446706 | ||||||||
\(621\) | −3569.72 | + | 17053.1i | −0.230673 | + | 1.10196i | ||||
\(622\) | 3281.13i | 0.211513i | ||||||||
\(623\) | −3386.53 | −0.217782 | ||||||||
\(624\) | −1236.61 | − | 2528.82i | −0.0793335 | − | 0.162234i | ||||
\(625\) | −5856.67 | −0.374827 | ||||||||
\(626\) | 2656.64i | 0.169617i | ||||||||
\(627\) | −526.562 | + | 257.493i | −0.0335389 | + | 0.0164008i | ||||
\(628\) | 10728.8i | 0.681729i | ||||||||
\(629\) | 14723.9 | 0.933358 | ||||||||
\(630\) | 11109.2 | + | 8642.69i | 0.702542 | + | 0.546560i | ||||
\(631\) | 657.435 | 0.0414772 | 0.0207386 | − | 0.999785i | \(-0.493398\pi\) | ||||
0.0207386 | + | 0.999785i | \(0.493398\pi\) | |||||||
\(632\) | 7539.66 | 0.474544 | ||||||||
\(633\) | 12732.5 | + | 26037.4i | 0.799480 | + | 1.63490i | ||||
\(634\) | 9154.27i | 0.573442i | ||||||||
\(635\) | 10797.9i | 0.674803i | ||||||||
\(636\) | 919.071 | + | 1879.46i | 0.0573012 | + | 0.117178i | ||||
\(637\) | 20987.0i | 1.30539i | ||||||||
\(638\) | 2455.25i | 0.152358i | ||||||||
\(639\) | −5584.73 | − | 4344.78i | −0.345741 | − | 0.268978i | ||||
\(640\) | 1075.21i | 0.0664086i | ||||||||
\(641\) | − | 9656.95i | − | 0.595049i | −0.954714 | − | 0.297525i | \(-0.903839\pi\) | ||
0.954714 | − | 0.297525i | \(-0.0961610\pi\) | |||||||
\(642\) | 5099.14 | + | 10427.5i | 0.313469 | + | 0.641031i | ||||
\(643\) | 28412.0 | 1.74255 | 0.871275 | − | 0.490796i | \(-0.163294\pi\) | ||||
0.871275 | + | 0.490796i | \(0.163294\pi\) | |||||||
\(644\) | 15413.6 | 0.943140 | ||||||||
\(645\) | 18283.3 | − | 8940.68i | 1.11613 | − | 0.545797i | ||||
\(646\) | 1425.28i | 0.0868064i | ||||||||
\(647\) | 26332.7i | 1.60007i | 0.599955 | + | 0.800034i | \(0.295185\pi\) | ||||
−0.599955 | + | 0.800034i | \(0.704815\pi\) | |||||||
\(648\) | −1434.18 | − | 5652.91i | −0.0869445 | − | 0.342696i | ||||
\(649\) | −2841.24 | + | 2509.70i | −0.171847 | + | 0.151794i | ||||
\(650\) | 3686.45i | 0.222453i | ||||||||
\(651\) | −14537.2 | − | 29728.0i | −0.875204 | − | 1.78975i | ||||
\(652\) | 6013.98 | 0.361236 | ||||||||
\(653\) | − | 15577.3i | − | 0.933516i | −0.884385 | − | 0.466758i | \(-0.845422\pi\) | ||
0.884385 | − | 0.466758i | \(-0.154578\pi\) | |||||||
\(654\) | −4482.34 | − | 9166.19i | −0.268002 | − | 0.548052i | ||||
\(655\) | − | 2172.45i | − | 0.129595i | ||||||
\(656\) | 6447.75i | 0.383754i | ||||||||
\(657\) | −7586.06 | − | 5901.76i | −0.450472 | − | 0.350456i | ||||
\(658\) | −31875.1 | −1.88848 | ||||||||
\(659\) | −6819.10 | −0.403087 | −0.201543 | − | 0.979480i | \(-0.564596\pi\) | ||||
−0.201543 | + | 0.979480i | \(0.564596\pi\) | |||||||
\(660\) | 641.583 | + | 1312.01i | 0.0378388 | + | 0.0773787i | ||||
\(661\) | −1640.37 | −0.0965252 | −0.0482626 | − | 0.998835i | \(-0.515368\pi\) | ||||
−0.0482626 | + | 0.998835i | \(0.515368\pi\) | |||||||
\(662\) | −6127.41 | −0.359741 | ||||||||
\(663\) | −8352.39 | + | 4084.39i | −0.489261 | + | 0.239253i | ||||
\(664\) | −9225.35 | −0.539176 | ||||||||
\(665\) | − | 3514.93i | − | 0.204967i | ||||||
\(666\) | 11875.0 | + | 9238.45i | 0.690912 | + | 0.537512i | ||||
\(667\) | − | 18224.9i | − | 1.05798i | ||||||
\(668\) | − | 4970.56i | − | 0.287899i | ||||||
\(669\) | −3012.73 | + | 1473.25i | −0.174109 | + | 0.0851406i | ||||
\(670\) | 12959.4 | 0.747263 | ||||||||
\(671\) | − | 3457.19i | − | 0.198902i | ||||||
\(672\) | −4635.00 | + | 2266.55i | −0.266070 | + | 0.130110i | ||||
\(673\) | 13220.3i | 0.757214i | 0.925557 | + | 0.378607i | \(0.123597\pi\) | ||||
−0.925557 | + | 0.378607i | \(0.876403\pi\) | |||||||
\(674\) | − | 2795.87i | − | 0.159782i | ||||||
\(675\) | −1564.84 | + | 7475.46i | −0.0892307 | + | 0.426268i | ||||
\(676\) | 4202.28 | 0.239092 | ||||||||
\(677\) | − | 11227.9i | − | 0.637403i | −0.947855 | − | 0.318702i | \(-0.896753\pi\) | ||
0.947855 | − | 0.318702i | \(-0.103247\pi\) | |||||||
\(678\) | 3809.43 | − | 1862.84i | 0.215782 | − | 0.105519i | ||||
\(679\) | − | 32658.1i | − | 1.84580i | ||||||
\(680\) | 3551.30 | 0.200274 | ||||||||
\(681\) | 23166.5 | − | 11328.6i | 1.30359 | − | 0.637465i | ||||
\(682\) | − | 3433.72i | − | 0.192792i | ||||||
\(683\) | −22495.5 | −1.26027 | −0.630136 | − | 0.776485i | \(-0.717001\pi\) | ||||
−0.630136 | + | 0.776485i | \(0.717001\pi\) | |||||||
\(684\) | −894.284 | + | 1149.50i | −0.0499910 | + | 0.0642578i | ||||
\(685\) | −11484.9 | −0.640608 | ||||||||
\(686\) | 17180.1 | 0.956182 | ||||||||
\(687\) | 3801.64 | + | 7774.19i | 0.211123 | + | 0.431738i | ||||
\(688\) | 7460.48i | 0.413413i | ||||||||
\(689\) | 3408.19 | 0.188449 | ||||||||
\(690\) | −4762.37 | − | 9738.84i | −0.262754 | − | 0.537321i | ||||
\(691\) | − | 23380.9i | − | 1.28719i | −0.765364 | − | 0.643597i | \(-0.777441\pi\) | ||
0.765364 | − | 0.643597i | \(-0.222559\pi\) | |||||||
\(692\) | 10132.6 | 0.556624 | ||||||||
\(693\) | −4303.32 | + | 5531.44i | −0.235887 | + | 0.303206i | ||||
\(694\) | −11065.9 | −0.605270 | ||||||||
\(695\) | − | 5124.59i | − | 0.279693i | ||||||
\(696\) | 2679.94 | + | 5480.37i | 0.145953 | + | 0.298467i | ||||
\(697\) | 21296.2 | 1.15732 | ||||||||
\(698\) | − | 10599.4i | − | 0.574776i | ||||||
\(699\) | 5049.07 | − | 2469.03i | 0.273209 | − | 0.133601i | ||||
\(700\) | 6756.80 | 0.364833 | ||||||||
\(701\) | −7108.69 | −0.383012 | −0.191506 | − | 0.981491i | \(-0.561337\pi\) | ||||
−0.191506 | + | 0.981491i | \(0.561337\pi\) | |||||||
\(702\) | −9299.01 | − | 1946.56i | −0.499955 | − | 0.104656i | ||||
\(703\) | − | 3757.23i | − | 0.201574i | ||||||
\(704\) | −535.364 | −0.0286609 | ||||||||
\(705\) | 9848.49 | + | 20139.7i | 0.526121 | + | 1.07590i | ||||
\(706\) | −19447.9 | −1.03673 | ||||||||
\(707\) | 16303.1 | 0.867242 | ||||||||
\(708\) | −3602.56 | + | 8703.18i | −0.191233 | + | 0.461985i | ||||
\(709\) | −26463.3 | −1.40177 | −0.700883 | − | 0.713276i | \(-0.747210\pi\) | ||||
−0.700883 | + | 0.713276i | \(0.747210\pi\) | |||||||
\(710\) | 4402.74 | 0.232721 | ||||||||
\(711\) | 15625.0 | − | 20084.2i | 0.824169 | − | 1.05938i | ||||
\(712\) | −873.109 | −0.0459567 | ||||||||
\(713\) | 25487.9i | 1.33875i | ||||||||
\(714\) | 7486.16 | + | 15308.9i | 0.392384 | + | 0.802409i | ||||
\(715\) | 2379.18 | 0.124442 | ||||||||
\(716\) | −7602.77 | −0.396828 | ||||||||
\(717\) | 8289.30 | + | 16951.3i | 0.431757 | + | 0.882924i | ||||
\(718\) | − | 3025.66i | − | 0.157266i | ||||||
\(719\) | −10353.4 | −0.537022 | −0.268511 | − | 0.963277i | \(-0.586531\pi\) | ||||
−0.268511 | + | 0.963277i | \(0.586531\pi\) | |||||||
\(720\) | 2864.16 | + | 2228.24i | 0.148251 | + | 0.115336i | ||||
\(721\) | − | 44111.1i | − | 2.27848i | ||||||
\(722\) | −13354.3 | −0.688360 | ||||||||
\(723\) | 916.333 | − | 448.094i | 0.0471353 | − | 0.0230495i | ||||
\(724\) | −15629.7 | −0.802313 | ||||||||
\(725\) | − | 7989.17i | − | 0.409255i | ||||||
\(726\) | 11772.7 | − | 5756.96i | 0.601828 | − | 0.294299i | ||||
\(727\) | 9760.73 | 0.497944 | 0.248972 | − | 0.968511i | \(-0.419907\pi\) | ||||
0.248972 | + | 0.968511i | \(0.419907\pi\) | |||||||
\(728\) | 8405.04i | 0.427900i | ||||||||
\(729\) | −18030.4 | − | 7894.56i | −0.916041 | − | 0.401085i | ||||
\(730\) | 5980.50 | 0.303217 | ||||||||
\(731\) | 24641.1 | 1.24676 | ||||||||
\(732\) | −3773.59 | − | 7716.82i | −0.190541 | − | 0.389647i | ||||
\(733\) | 25960.4 | 1.30814 | 0.654071 | − | 0.756433i | \(-0.273060\pi\) | ||||
0.654071 | + | 0.756433i | \(0.273060\pi\) | |||||||
\(734\) | 9252.82i | 0.465297i | ||||||||
\(735\) | −11885.0 | − | 24304.3i | −0.596443 | − | 1.21970i | ||||
\(736\) | 3973.92 | 0.199023 | ||||||||
\(737\) | 6452.69i | 0.322507i | ||||||||
\(738\) | 17175.6 | + | 13362.2i | 0.856696 | + | 0.666488i | ||||
\(739\) | − | 14687.1i | − | 0.731090i | −0.930794 | − | 0.365545i | \(-0.880883\pi\) | ||
0.930794 | − | 0.365545i | \(-0.119117\pi\) | |||||||
\(740\) | −9361.71 | −0.465058 | ||||||||
\(741\) | 1042.25 | + | 2131.35i | 0.0516705 | + | 0.105664i | ||||
\(742\) | − | 6246.77i | − | 0.309065i | ||||||
\(743\) | 14225.4i | 0.702397i | 0.936301 | + | 0.351198i | \(0.114226\pi\) | ||||
−0.936301 | + | 0.351198i | \(0.885774\pi\) | |||||||
\(744\) | −3747.96 | − | 7664.42i | −0.184687 | − | 0.377676i | ||||
\(745\) | 14646.9i | 0.720295i | ||||||||
\(746\) | −6876.44 | −0.337486 | ||||||||
\(747\) | −19118.4 | + | 24574.6i | −0.936420 | + | 1.20366i | ||||
\(748\) | 1768.25i | 0.0864351i | ||||||||
\(749\) | − | 34658.0i | − | 1.69076i | ||||||
\(750\) | −6881.28 | − | 14071.9i | −0.335025 | − | 0.685112i | ||||
\(751\) | 38067.6i | 1.84967i | 0.380364 | + | 0.924837i | \(0.375799\pi\) | ||||
−0.380364 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(752\) | −8217.99 | −0.398510 | ||||||||
\(753\) | 10753.3 | + | 21990.1i | 0.520417 | + | 1.06423i | ||||
\(754\) | 9938.03 | 0.480002 | ||||||||
\(755\) | 13920.0 | 0.670992 | ||||||||
\(756\) | −3567.80 | + | 17043.9i | −0.171640 | + | 0.819948i | ||||
\(757\) | −8768.72 | −0.421010 | −0.210505 | − | 0.977593i | \(-0.567511\pi\) | ||||
−0.210505 | + | 0.977593i | \(0.567511\pi\) | |||||||
\(758\) | −26960.0 | −1.29186 | ||||||||
\(759\) | 4849.11 | − | 2371.25i | 0.231899 | − | 0.113401i | ||||
\(760\) | − | 906.215i | − | 0.0432525i | ||||||
\(761\) | 29912.6i | 1.42487i | 0.701736 | + | 0.712437i | \(0.252409\pi\) | ||||
−0.701736 | + | 0.712437i | \(0.747591\pi\) | |||||||
\(762\) | −12000.7 | + | 5868.44i | −0.570524 | + | 0.278991i | ||||
\(763\) | 30465.7i | 1.44552i | ||||||||
\(764\) | −4834.92 | −0.228954 | ||||||||
\(765\) | 7359.64 | − | 9460.00i | 0.347828 | − | 0.447094i | ||||
\(766\) | 8577.82i | 0.404608i | ||||||||
\(767\) | 10158.4 | + | 11500.4i | 0.478226 | + | 0.541402i | ||||
\(768\) | −1194.99 | + | 584.359i | −0.0561464 | + | 0.0274560i | ||||
\(769\) | 27505.9i | 1.28984i | 0.764250 | + | 0.644920i | \(0.223109\pi\) | ||||
−0.764250 | + | 0.644920i | \(0.776891\pi\) | |||||||
\(770\) | − | 4360.73i | − | 0.204091i | ||||||
\(771\) | 16553.7 | + | 33851.7i | 0.773241 | + | 1.58124i | ||||
\(772\) | −2083.18 | −0.0971184 | ||||||||
\(773\) | 10827.2 | 0.503787 | 0.251893 | − | 0.967755i | \(-0.418947\pi\) | ||||
0.251893 | + | 0.967755i | \(0.418947\pi\) | |||||||
\(774\) | 19873.3 | + | 15460.9i | 0.922909 | + | 0.717999i | ||||
\(775\) | 11173.0i | 0.517867i | ||||||||
\(776\) | − | 8419.85i | − | 0.389504i | ||||||
\(777\) | −19734.5 | − | 40356.2i | −0.911160 | − | 1.86328i | ||||
\(778\) | 4489.76i | 0.206897i | ||||||||
\(779\) | − | 5434.32i | − | 0.249942i | ||||||
\(780\) | 5310.58 | − | 2596.91i | 0.243781 | − | 0.119211i | ||||
\(781\) | 2192.19i | 0.100439i | ||||||||
\(782\) | − | 13125.4i | − | 0.600209i | ||||||
\(783\) | 20152.5 | + | 4218.53i | 0.919786 | + | 0.192539i | ||||
\(784\) | 9917.36 | 0.451775 | ||||||||
\(785\) | −22530.7 | −1.02440 | ||||||||
\(786\) | 2414.46 | − | 1180.69i | 0.109568 | − | 0.0535798i | ||||
\(787\) | 14752.6 | 0.668201 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(788\) | 798.819i | 0.0361126i | ||||||||
\(789\) | 12181.4 | + | 24910.5i | 0.549645 | + | 1.12400i | ||||
\(790\) | 15833.5i | 0.713076i | ||||||||
\(791\) | −12661.4 | −0.569137 | ||||||||
\(792\) | −1109.48 | + | 1426.11i | −0.0497771 | + | 0.0639830i | ||||
\(793\) | −13993.6 | −0.626641 | ||||||||
\(794\) | 20587.1i | 0.920162i | ||||||||
\(795\) | −3946.91 | + | 1930.07i | −0.176079 | + | 0.0861039i | ||||
\(796\) | 14940.3 | 0.665258 | ||||||||
\(797\) | −32488.0 | −1.44389 | −0.721947 | − | 0.691948i | \(-0.756753\pi\) | ||||
−0.721947 | + | 0.691948i | \(0.756753\pi\) | |||||||
\(798\) | 3906.49 | − | 1910.30i | 0.173293 | − | 0.0847419i | ||||
\(799\) | 27143.1i | 1.20182i | ||||||||
\(800\) | 1742.03 | 0.0769875 | ||||||||
\(801\) | −1809.41 | + | 2325.80i | −0.0798157 | + | 0.102594i | ||||
\(802\) | 28861.2 | 1.27073 | ||||||||
\(803\) | 2977.78i | 0.130864i | ||||||||
\(804\) | 7043.21 | + | 14403.1i | 0.308949 | + | 0.631787i | ||||
\(805\) | 32369.0i | 1.41721i | ||||||||
\(806\) | −13898.5 | −0.607389 | ||||||||
\(807\) | −21571.3 | + | 10548.6i | −0.940951 | + | 0.460132i | ||||
\(808\) | 4203.24 | 0.183007 | ||||||||
\(809\) | −17534.8 | −0.762042 | −0.381021 | − | 0.924566i | \(-0.624427\pi\) | ||||
−0.381021 | + | 0.924566i | \(0.624427\pi\) | |||||||
\(810\) | 11871.2 | − | 3011.82i | 0.514954 | − | 0.130648i | ||||
\(811\) | − | 8326.69i | − | 0.360530i | −0.983618 | − | 0.180265i | \(-0.942305\pi\) | ||
0.983618 | − | 0.180265i | \(-0.0576955\pi\) | |||||||
\(812\) | − | 18215.1i | − | 0.787224i | ||||||
\(813\) | 9094.95 | − | 4447.50i | 0.392342 | − | 0.191858i | ||||
\(814\) | − | 4661.33i | − | 0.200712i | ||||||
\(815\) | 12629.5i | 0.542812i | ||||||||
\(816\) | 1930.07 | + | 3946.91i | 0.0828014 | + | 0.169325i | ||||
\(817\) | − | 6287.88i | − | 0.269259i | ||||||
\(818\) | − | 15784.3i | − | 0.674674i | ||||||
\(819\) | 22389.4 | + | 17418.4i | 0.955250 | + | 0.743160i | ||||
\(820\) | −13540.4 | −0.576649 | ||||||||
\(821\) | 13785.7 | 0.586021 | 0.293010 | − | 0.956109i | \(-0.405343\pi\) | ||||
0.293010 | + | 0.956109i | \(0.405343\pi\) | |||||||
\(822\) | −6241.85 | − | 12764.3i | −0.264853 | − | 0.541614i | ||||
\(823\) | 1766.43i | 0.0748164i | 0.999300 | + | 0.0374082i | \(0.0119102\pi\) | ||||
−0.999300 | + | 0.0374082i | \(0.988090\pi\) | |||||||
\(824\) | − | 11372.7i | − | 0.480807i | ||||||
\(825\) | 2125.68 | − | 1039.47i | 0.0897051 | − | 0.0438665i | ||||
\(826\) | 21078.7 | − | 18619.1i | 0.887922 | − | 0.784312i | ||||
\(827\) | − | 32816.5i | − | 1.37985i | −0.723878 | − | 0.689927i | \(-0.757642\pi\) | ||
0.723878 | − | 0.689927i | \(-0.242358\pi\) | |||||||
\(828\) | 8235.46 | − | 10585.8i | 0.345655 | − | 0.444301i | ||||
\(829\) | 32527.6 | 1.36276 | 0.681382 | − | 0.731928i | \(-0.261379\pi\) | ||||
0.681382 | + | 0.731928i | \(0.261379\pi\) | |||||||
\(830\) | − | 19373.5i | − | 0.810196i | ||||||
\(831\) | −28432.4 | + | 13903.7i | −1.18690 | + | 0.580401i | ||||
\(832\) | 2166.97i | 0.0902961i | ||||||||
\(833\) | − | 32755.9i | − | 1.36245i | ||||||
\(834\) | 5695.46 | − | 2785.12i | 0.236472 | − | 0.115637i | ||||
\(835\) | 10438.3 | 0.432613 | ||||||||
\(836\) | 451.218 | 0.0186671 | ||||||||
\(837\) | −28183.7 | − | 5899.70i | −1.16389 | − | 0.243636i | ||||
\(838\) | 5906.95 | 0.243499 | ||||||||
\(839\) | −16461.3 | −0.677364 | −0.338682 | − | 0.940901i | \(-0.609981\pi\) | ||||
−0.338682 | + | 0.940901i | \(0.609981\pi\) | |||||||
\(840\) | −4759.81 | − | 9733.61i | −0.195511 | − | 0.399811i | ||||
\(841\) | 2851.63 | 0.116923 | ||||||||
\(842\) | − | 26004.8i | − | 1.06435i | ||||||
\(843\) | −540.132 | − | 1104.55i | −0.0220678 | − | 0.0451276i | ||||
\(844\) | − | 22311.8i | − | 0.909955i | ||||||
\(845\) | 8824.89i | 0.359273i | ||||||||
\(846\) | −17030.8 | + | 21891.2i | −0.692116 | + | 0.889638i | ||||
\(847\) | −39129.1 | −1.58736 | ||||||||
\(848\) | − | 1610.53i | − | 0.0652192i | ||||||
\(849\) | 11316.6 | + | 23141.9i | 0.457459 | + | 0.935485i | ||||
\(850\) | − | 5753.72i | − | 0.232178i | ||||||
\(851\) | 34600.3i | 1.39375i | ||||||||
\(852\) | 2392.81 | + | 4893.20i | 0.0962164 | + | 0.196758i | ||||
\(853\) | 34952.5 | 1.40299 | 0.701496 | − | 0.712674i | \(-0.252516\pi\) | ||||
0.701496 | + | 0.712674i | \(0.252516\pi\) | |||||||
\(854\) | 25648.4i | 1.02772i | ||||||||
\(855\) | −2413.98 | − | 1878.02i | −0.0965574 | − | 0.0751192i | ||||
\(856\) | − | 8935.47i | − | 0.356785i | ||||||
\(857\) | 48998.5 | 1.95304 | 0.976521 | − | 0.215423i | \(-0.0691129\pi\) | ||||
0.976521 | + | 0.215423i | \(0.0691129\pi\) | |||||||
\(858\) | 1293.04 | + | 2644.21i | 0.0514495 | + | 0.105212i | ||||
\(859\) | 3465.97i | 0.137669i | 0.997628 | + | 0.0688343i | \(0.0219280\pi\) | ||||
−0.997628 | + | 0.0688343i | \(0.978072\pi\) | |||||||
\(860\) | −15667.2 | −0.621217 | ||||||||
\(861\) | −28543.3 | − | 58369.8i | −1.12979 | − | 2.31038i | ||||
\(862\) | 20264.7 | 0.800717 | ||||||||
\(863\) | 47401.2 | 1.86970 | 0.934852 | − | 0.355037i | \(-0.115532\pi\) | ||||
0.934852 | + | 0.355037i | \(0.115532\pi\) | |||||||
\(864\) | −919.845 | + | 4394.23i | −0.0362196 | + | 0.173026i | ||||
\(865\) | 21278.7i | 0.836414i | ||||||||
\(866\) | −8228.44 | −0.322880 | ||||||||
\(867\) | −9897.31 | + | 4839.86i | −0.387694 | + | 0.189585i | ||||
\(868\) | 25474.2i | 0.996143i | ||||||||
\(869\) | −7883.72 | −0.307752 | ||||||||
\(870\) | −11508.9 | + | 5627.95i | −0.448493 | + | 0.219316i | ||||
\(871\) | 26118.3 | 1.01606 | ||||||||
\(872\) | 7854.62i | 0.305035i | ||||||||
\(873\) | −22428.9 | − | 17449.1i | −0.869533 | − | 0.676475i | ||||
\(874\) | −3349.32 | −0.129625 | ||||||||
\(875\) | 46770.9i | 1.80702i | ||||||||
\(876\) | 3250.29 | + | 6646.71i | 0.125362 | + | 0.256360i | ||||
\(877\) | −35986.2 | −1.38559 | −0.692797 | − | 0.721132i | \(-0.743622\pi\) | ||||
−0.692797 | + | 0.721132i | \(0.743622\pi\) | |||||||
\(878\) | −11017.5 | −0.423488 | ||||||||
\(879\) | −1591.74 | − | 3255.05i | −0.0610787 | − | 0.124903i | ||||
\(880\) | − | 1124.28i | − | 0.0430675i | ||||||
\(881\) | −41577.0 | −1.58997 | −0.794986 | − | 0.606627i | \(-0.792522\pi\) | ||||
−0.794986 | + | 0.606627i | \(0.792522\pi\) | |||||||
\(882\) | 20552.5 | − | 26417.9i | 0.784624 | − | 1.00855i | ||||
\(883\) | −27141.5 | −1.03441 | −0.517206 | − | 0.855861i | \(-0.673028\pi\) | ||||
−0.517206 | + | 0.855861i | \(0.673028\pi\) | |||||||
\(884\) | 7157.27 | 0.272313 | ||||||||
\(885\) | −18276.9 | − | 7565.47i | −0.694204 | − | 0.287357i | ||||
\(886\) | −3261.43 | −0.123668 | ||||||||
\(887\) | 16474.1 | 0.623616 | 0.311808 | − | 0.950145i | \(-0.399065\pi\) | ||||
0.311808 | + | 0.950145i | \(0.399065\pi\) | |||||||
\(888\) | −5087.92 | − | 10404.6i | −0.192274 | − | 0.393192i | ||||
\(889\) | 39886.8 | 1.50479 | ||||||||
\(890\) | − | 1833.55i | − | 0.0690570i | ||||||
\(891\) | 1499.63 | + | 5910.86i | 0.0563855 | + | 0.222246i | ||||
\(892\) | 2581.64 | 0.0969056 | ||||||||
\(893\) | 6926.32 | 0.259553 | ||||||||
\(894\) | −16278.5 | + | 7960.31i | −0.608987 | + | 0.297799i | ||||
\(895\) | − | 15966.0i | − | 0.596296i | ||||||
\(896\) | 3971.79 | 0.148089 | ||||||||
\(897\) | −9598.04 | − | 19627.6i | −0.357268 | − | 0.730597i | ||||
\(898\) | 8514.63i | 0.316411i | ||||||||
\(899\) | 30120.5 | 1.11743 | ||||||||
\(900\) | 3610.14 | − | 4640.43i | 0.133709 | − | 0.171868i | ||||
\(901\) | −5319.41 | −0.196687 | ||||||||
\(902\) | − | 6741.98i | − | 0.248873i | ||||||
\(903\) | −33026.5 | − | 67537.7i | −1.21711 | − | 2.48894i | ||||
\(904\) | −3264.34 | −0.120100 | ||||||||
\(905\) | − | 32822.8i | − | 1.20560i | ||||||
\(906\) | 7565.24 | + | 15470.6i | 0.277415 | + | 0.567303i | ||||
\(907\) | 7623.06 | 0.279073 | 0.139537 | − | 0.990217i | \(-0.455439\pi\) | ||||
0.139537 | + | 0.990217i | \(0.455439\pi\) | |||||||
\(908\) | −19851.7 | −0.725553 | ||||||||
\(909\) | 8710.69 | − | 11196.6i | 0.317838 | − | 0.408546i | ||||
\(910\) | −17650.8 | −0.642987 | ||||||||
\(911\) | − | 41097.5i | − | 1.49465i | −0.664461 | − | 0.747323i | \(-0.731339\pi\) | ||
0.664461 | − | 0.747323i | \(-0.268661\pi\) | |||||||
\(912\) | 1007.17 | − | 492.512i | 0.0365686 | − | 0.0178823i | ||||
\(913\) | 9646.33 | 0.349668 | ||||||||
\(914\) | − | 6551.46i | − | 0.237093i | ||||||
\(915\) | 16205.5 | − | 7924.62i | 0.585506 | − | 0.286317i | ||||
\(916\) | − | 6661.80i | − | 0.240297i | ||||||
\(917\) | −8024.93 | −0.288993 | ||||||||
\(918\) | 14513.6 | + | 3038.14i | 0.521810 | + | 0.109231i | ||||
\(919\) | − | 16473.5i | − | 0.591307i | −0.955295 | − | 0.295653i | \(-0.904463\pi\) | ||
0.955295 | − | 0.295653i | \(-0.0955373\pi\) | |||||||
\(920\) | 8345.33i | 0.299062i | ||||||||
\(921\) | −20876.4 | + | 10208.7i | −0.746907 | + | 0.365243i | ||||
\(922\) | 13464.0i | 0.480926i | ||||||||
\(923\) | 8873.25 | 0.316432 | ||||||||
\(924\) | 4846.51 | − | 2369.98i | 0.172552 | − | 0.0843794i | ||||
\(925\) | 15167.6i | 0.539142i | ||||||||
\(926\) | − | 9547.36i | − | 0.338818i | ||||||
\(927\) | −30294.6 | − | 23568.4i | −1.07336 | − | 0.835047i | ||||
\(928\) | − | 4696.20i | − | 0.166121i | ||||||
\(929\) | 41311.2 | 1.45896 | 0.729482 | − | 0.684000i | \(-0.239761\pi\) | ||||
0.729482 | + | 0.684000i | \(0.239761\pi\) | |||||||
\(930\) | 16095.5 | − | 7870.81i | 0.567517 | − | 0.277520i | ||||
\(931\) | −8358.59 | −0.294245 | ||||||||
\(932\) | −4326.61 | −0.152063 | ||||||||
\(933\) | −3744.83 | − | 7658.02i | −0.131404 | − | 0.268716i | ||||
\(934\) | 37247.5 | 1.30490 | ||||||||
\(935\) | −3713.36 | −0.129882 | ||||||||
\(936\) | 5772.41 | + | 4490.79i | 0.201578 | + | 0.156823i | ||||
\(937\) | 4002.69i | 0.139554i | 0.997563 | + | 0.0697771i | \(0.0222288\pi\) | ||||
−0.997563 | + | 0.0697771i | \(0.977771\pi\) | |||||||
\(938\) | − | 47871.5i | − | 1.66638i | ||||||
\(939\) | −3032.09 | − | 6200.49i | −0.105376 | − | 0.215490i | ||||
\(940\) | − | 17258.0i | − | 0.598823i | ||||||
\(941\) | −9974.29 | −0.345539 | −0.172770 | − | 0.984962i | \(-0.555272\pi\) | ||||
−0.172770 | + | 0.984962i | \(0.555272\pi\) | |||||||
\(942\) | −12245.0 | − | 25040.6i | −0.423530 | − | 0.866101i | ||||
\(943\) | 50044.6i | 1.72818i | ||||||||
\(944\) | 5434.49 | − | 4800.35i | 0.187370 | − | 0.165506i | ||||
\(945\) | −35792.6 | − | 7492.47i | −1.23210 | − | 0.257915i | ||||
\(946\) | − | 7800.92i | − | 0.268108i | ||||||
\(947\) | 52622.0i | 1.80569i | 0.429969 | + | 0.902844i | \(0.358524\pi\) | ||||
−0.429969 | + | 0.902844i | \(0.641476\pi\) | |||||||
\(948\) | −17597.3 | + | 8605.21i | −0.602883 | + | 0.294815i | ||||
\(949\) | 12053.0 | 0.412285 | ||||||||
\(950\) | −1468.22 | −0.0501426 | ||||||||
\(951\) | −10448.0 | − | 21365.7i | −0.356256 | − | 0.728528i | ||||
\(952\) | − | 13118.4i | − | 0.446605i | ||||||
\(953\) | 29557.9i | 1.00470i | 0.864665 | + | 0.502348i | \(0.167530\pi\) | ||||
−0.864665 | + | 0.502348i | \(0.832470\pi\) | |||||||
\(954\) | −4290.15 | − | 3337.63i | −0.145596 | − | 0.113270i | ||||
\(955\) | − | 10153.4i | − | 0.344040i | ||||||
\(956\) | − | 14525.7i | − | 0.491419i | ||||||
\(957\) | −2802.24 | − | 5730.46i | −0.0946536 | − | 0.193563i | ||||
\(958\) | 4759.53i | 0.160515i | ||||||||
\(959\) | 42424.8i | 1.42854i | ||||||||
\(960\) | −1227.17 | − | 2509.50i | −0.0412569 | − | 0.0843687i | ||||
\(961\) | −12333.1 | −0.413988 | ||||||||
\(962\) | −18867.5 | −0.632342 | ||||||||
\(963\) | −23802.4 | − | 18517.7i | −0.796492 | − | 0.619650i | ||||
\(964\) | −785.217 | −0.0262346 | ||||||||
\(965\) | − | 4374.73i | − | 0.145935i | ||||||
\(966\) | −35974.8 | + | 17592.0i | −1.19821 | + | 0.585934i | ||||
\(967\) | − | 2245.69i | − | 0.0746810i | −0.999303 | − | 0.0373405i | \(-0.988111\pi\) | ||
0.999303 | − | 0.0373405i | \(-0.0118886\pi\) | |||||||
\(968\) | −10088.2 | −0.334966 | ||||||||
\(969\) | −1626.71 | − | 3326.55i | −0.0539293 | − | 0.110283i | ||||
\(970\) | 17681.9 | 0.585290 | ||||||||
\(971\) | − | 44353.4i | − | 1.46588i | −0.680294 | − | 0.732939i | \(-0.738148\pi\) | ||
0.680294 | − | 0.732939i | \(-0.261852\pi\) | |||||||
\(972\) | 9799.13 | + | 11556.8i | 0.323361 | + | 0.381362i | ||||
\(973\) | −18930.0 | −0.623708 | ||||||||
\(974\) | −29489.4 | −0.970125 | ||||||||
\(975\) | −4207.44 | − | 8604.04i | −0.138201 | − | 0.282615i | ||||
\(976\) | 6612.64i | 0.216870i | ||||||||
\(977\) | 1724.31 | 0.0564643 | 0.0282321 | − | 0.999601i | \(-0.491012\pi\) | ||||
0.0282321 | + | 0.999601i | \(0.491012\pi\) | |||||||
\(978\) | −14036.4 | + | 6863.91i | −0.458931 | + | 0.224421i | ||||
\(979\) | 912.951 | 0.0298039 | ||||||||
\(980\) | 20826.7i | 0.678861i | ||||||||
\(981\) | 20923.2 | + | 16277.7i | 0.680965 | + | 0.529773i | ||||
\(982\) | − | 38055.6i | − | 1.23666i | ||||||
\(983\) | 4199.15 | 0.136248 | 0.0681241 | − | 0.997677i | \(-0.478299\pi\) | ||||
0.0681241 | + | 0.997677i | \(0.478299\pi\) | |||||||
\(984\) | −7358.98 | − | 15048.8i | −0.238410 | − | 0.487539i | ||||
\(985\) | −1677.54 | −0.0542648 | ||||||||
\(986\) | −15511.0 | −0.500985 | ||||||||
\(987\) | 74395.3 | − | 36379.9i | 2.39922 | − | 1.17324i | ||||
\(988\) | − | 1826.38i | − | 0.0588106i | ||||||
\(989\) | 57905.0i | 1.86175i | ||||||||
\(990\) | −2994.86 | − | 2329.93i | −0.0961444 | − | 0.0747979i | ||||
\(991\) | 18156.4i | 0.581994i | 0.956724 | + | 0.290997i | \(0.0939869\pi\) | ||||
−0.956724 | + | 0.290997i | \(0.906013\pi\) | |||||||
\(992\) | 6567.73i | 0.210207i | ||||||||
\(993\) | 14301.1 | − | 6993.37i | 0.457032 | − | 0.223492i | ||||
\(994\) | − | 16263.5i | − | 0.518962i | ||||||
\(995\) | 31375.0i | 0.999653i | ||||||||
\(996\) | 21531.6 | − | 10529.1i | 0.684995 | − | 0.334968i | ||||
\(997\) | 20085.1 | 0.638017 | 0.319008 | − | 0.947752i | \(-0.396650\pi\) | ||||
0.319008 | + | 0.947752i | \(0.396650\pi\) | |||||||
\(998\) | −34754.2 | −1.10233 | ||||||||
\(999\) | −38259.9 | − | 8008.95i | −1.21170 | − | 0.253645i |
(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 | 354.4.c.b.353.6 | yes | 30 | |
3.2 | odd | 2 | 354.4.c.a.353.5 | ✓ | 30 | ||
59.58 | odd | 2 | 354.4.c.a.353.6 | yes | 30 | ||
177.176 | even | 2 | inner | 354.4.c.b.353.5 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.c.a.353.5 | ✓ | 30 | 3.2 | odd | 2 | ||
354.4.c.a.353.6 | yes | 30 | 59.58 | odd | 2 | ||
354.4.c.b.353.5 | yes | 30 | 177.176 | even | 2 | inner | |
354.4.c.b.353.6 | yes | 30 | 1.1 | even | 1 | trivial |