Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(4,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.g (of order \(3\), 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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 4.22 | ||
Character | \(\chi\) | \(=\) | 63.4 |
Dual form | 63.4.g.a.16.22 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54715 | − | 4.41178i | 0.900552 | − | 1.55980i | 0.0737725 | − | 0.997275i | \(-0.476496\pi\) |
0.826779 | − | 0.562526i | \(-0.190171\pi\) | |||||||
\(3\) | −3.72363 | − | 3.62416i | −0.716614 | − | 0.697470i | ||||
\(4\) | −8.97590 | − | 15.5467i | −1.12199 | − | 1.94334i | ||||
\(5\) | 6.84046 | 0.611829 | 0.305915 | − | 0.952059i | \(-0.401038\pi\) | ||||
0.305915 | + | 0.952059i | \(0.401038\pi\) | |||||||
\(6\) | −25.4737 | + | 7.19661i | −1.73326 | + | 0.489667i | ||||
\(7\) | 16.1584 | + | 9.05014i | 0.872474 | + | 0.488661i | ||||
\(8\) | −50.6973 | −2.24053 | ||||||||
\(9\) | 0.730904 | + | 26.9901i | 0.0270705 | + | 0.999634i | ||||
\(10\) | 17.4236 | − | 30.1786i | 0.550984 | − | 0.954333i | ||||
\(11\) | −41.0518 | −1.12523 | −0.562617 | − | 0.826718i | \(-0.690205\pi\) | ||||
−0.562617 | + | 0.826718i | \(0.690205\pi\) | |||||||
\(12\) | −22.9208 | + | 90.4204i | −0.551390 | + | 2.17518i | ||||
\(13\) | 31.8869 | − | 55.2298i | 0.680296 | − | 1.17831i | −0.294595 | − | 0.955622i | \(-0.595185\pi\) |
0.974891 | − | 0.222685i | \(-0.0714820\pi\) | |||||||
\(14\) | 81.0851 | − | 48.2355i | 1.54792 | − | 0.920821i | ||||
\(15\) | −25.4714 | − | 24.7909i | −0.438445 | − | 0.426733i | ||||
\(16\) | −57.3263 | + | 99.2920i | −0.895723 | + | 1.55144i | ||||
\(17\) | 38.0175 | − | 65.8483i | 0.542389 | − | 0.939445i | −0.456378 | − | 0.889786i | \(-0.650853\pi\) |
0.998766 | − | 0.0496584i | \(-0.0158133\pi\) | |||||||
\(18\) | 120.936 | + | 65.5231i | 1.58361 | + | 0.857997i | ||||
\(19\) | 46.7854 | + | 81.0346i | 0.564911 | + | 0.978454i | 0.997058 | + | 0.0766508i | \(0.0244227\pi\) |
−0.432147 | + | 0.901803i | \(0.642244\pi\) | |||||||
\(20\) | −61.3993 | − | 106.347i | −0.686465 | − | 1.18899i | ||||
\(21\) | −27.3689 | − | 92.2602i | −0.284400 | − | 0.958706i | ||||
\(22\) | −104.565 | + | 181.112i | −1.01333 | + | 1.75514i | ||||
\(23\) | 42.1281 | 0.381927 | 0.190963 | − | 0.981597i | \(-0.438839\pi\) | ||||
0.190963 | + | 0.981597i | \(0.438839\pi\) | |||||||
\(24\) | 188.778 | + | 183.735i | 1.60559 | + | 1.56270i | ||||
\(25\) | −78.2081 | −0.625665 | ||||||||
\(26\) | −162.441 | − | 281.357i | −1.22528 | − | 2.12225i | ||||
\(27\) | 95.0949 | − | 103.150i | 0.677816 | − | 0.735232i | ||||
\(28\) | −4.33661 | − | 332.444i | −0.0292694 | − | 2.24378i | ||||
\(29\) | 21.9258 | + | 37.9765i | 0.140397 | + | 0.243175i | 0.927646 | − | 0.373460i | \(-0.121829\pi\) |
−0.787249 | + | 0.616635i | \(0.788495\pi\) | |||||||
\(30\) | −174.252 | + | 49.2281i | −1.06046 | + | 0.299593i | ||||
\(31\) | 100.068 | + | 173.322i | 0.579765 | + | 1.00418i | 0.995506 | + | 0.0946989i | \(0.0301888\pi\) |
−0.415741 | + | 0.909483i | \(0.636478\pi\) | |||||||
\(32\) | 89.2474 | + | 154.581i | 0.493027 | + | 0.853948i | ||||
\(33\) | 152.862 | + | 148.778i | 0.806358 | + | 0.784817i | ||||
\(34\) | −193.672 | − | 335.450i | −0.976898 | − | 1.69204i | ||||
\(35\) | 110.531 | + | 61.9071i | 0.533805 | + | 0.298977i | ||||
\(36\) | 413.047 | − | 253.624i | 1.91225 | − | 1.17418i | ||||
\(37\) | −52.1566 | − | 90.3379i | −0.231743 | − | 0.401391i | 0.726578 | − | 0.687084i | \(-0.241110\pi\) |
−0.958321 | + | 0.285693i | \(0.907776\pi\) | |||||||
\(38\) | 476.677 | 2.03492 | ||||||||
\(39\) | −318.897 | + | 90.0921i | −1.30934 | + | 0.369905i | ||||
\(40\) | −346.793 | −1.37082 | ||||||||
\(41\) | −108.674 | + | 188.229i | −0.413951 | + | 0.716984i | −0.995318 | − | 0.0966575i | \(-0.969185\pi\) |
0.581367 | + | 0.813642i | \(0.302518\pi\) | |||||||
\(42\) | −476.745 | − | 114.254i | −1.75151 | − | 0.419757i | ||||
\(43\) | 236.154 | + | 409.031i | 0.837515 | + | 1.45062i | 0.891966 | + | 0.452102i | \(0.149326\pi\) |
−0.0544516 | + | 0.998516i | \(0.517341\pi\) | |||||||
\(44\) | 368.476 | + | 638.220i | 1.26250 | + | 2.18671i | ||||
\(45\) | 4.99972 | + | 184.625i | 0.0165625 | + | 0.611605i | ||||
\(46\) | 107.306 | − | 185.860i | 0.343945 | − | 0.595730i | ||||
\(47\) | 8.94210 | − | 15.4882i | 0.0277519 | − | 0.0480677i | −0.851816 | − | 0.523841i | \(-0.824498\pi\) |
0.879568 | + | 0.475774i | \(0.157832\pi\) | |||||||
\(48\) | 573.312 | − | 161.967i | 1.72397 | − | 0.487042i | ||||
\(49\) | 179.190 | + | 292.472i | 0.522420 | + | 0.852688i | ||||
\(50\) | −199.207 | + | 345.037i | −0.563443 | + | 0.975913i | ||||
\(51\) | −380.208 | + | 107.413i | −1.04392 | + | 0.294919i | ||||
\(52\) | −1144.86 | −3.05313 | ||||||||
\(53\) | 211.151 | − | 365.724i | 0.547241 | − | 0.947850i | −0.451221 | − | 0.892412i | \(-0.649011\pi\) |
0.998462 | − | 0.0554374i | \(-0.0176553\pi\) | |||||||
\(54\) | −212.856 | − | 682.277i | −0.536408 | − | 1.71937i | ||||
\(55\) | −280.813 | −0.688451 | ||||||||
\(56\) | −819.190 | − | 458.818i | −1.95480 | − | 1.09486i | ||||
\(57\) | 119.471 | − | 471.301i | 0.277620 | − | 1.09518i | ||||
\(58\) | 223.392 | 0.505739 | ||||||||
\(59\) | −145.516 | − | 252.042i | −0.321095 | − | 0.556153i | 0.659619 | − | 0.751600i | \(-0.270718\pi\) |
−0.980714 | + | 0.195447i | \(0.937384\pi\) | |||||||
\(60\) | −156.789 | + | 618.517i | −0.337356 | + | 1.33084i | ||||
\(61\) | 77.0146 | − | 133.393i | 0.161651 | − | 0.279988i | −0.773810 | − | 0.633418i | \(-0.781651\pi\) |
0.935461 | + | 0.353430i | \(0.114985\pi\) | |||||||
\(62\) | 1019.55 | 2.08843 | ||||||||
\(63\) | −232.454 | + | 442.733i | −0.464864 | + | 0.885382i | ||||
\(64\) | −7.91610 | −0.0154611 | ||||||||
\(65\) | 218.121 | − | 377.797i | 0.416225 | − | 0.720923i | ||||
\(66\) | 1045.74 | − | 295.433i | 1.95033 | − | 0.550990i | ||||
\(67\) | 419.175 | + | 726.033i | 0.764335 | + | 1.32387i | 0.940598 | + | 0.339524i | \(0.110266\pi\) |
−0.176263 | + | 0.984343i | \(0.556401\pi\) | |||||||
\(68\) | −1364.97 | −2.43421 | ||||||||
\(69\) | −156.870 | − | 152.679i | −0.273694 | − | 0.266383i | ||||
\(70\) | 554.660 | − | 329.953i | 0.947065 | − | 0.563385i | ||||
\(71\) | −940.646 | −1.57231 | −0.786156 | − | 0.618028i | \(-0.787932\pi\) | ||||
−0.786156 | + | 0.618028i | \(0.787932\pi\) | |||||||
\(72\) | −37.0549 | − | 1368.33i | −0.0606522 | − | 2.23971i | ||||
\(73\) | 65.8171 | − | 113.998i | 0.105525 | − | 0.182774i | −0.808428 | − | 0.588595i | \(-0.799681\pi\) |
0.913952 | + | 0.405821i | \(0.133014\pi\) | |||||||
\(74\) | −531.402 | −0.834787 | ||||||||
\(75\) | 291.218 | + | 283.439i | 0.448360 | + | 0.436383i | ||||
\(76\) | 839.881 | − | 1454.72i | 1.26764 | − | 2.19563i | ||||
\(77\) | −663.332 | − | 371.524i | −0.981737 | − | 0.549858i | ||||
\(78\) | −414.810 | + | 1636.38i | −0.602153 | + | 2.37543i | ||||
\(79\) | −310.182 | + | 537.251i | −0.441749 | + | 0.765132i | −0.997819 | − | 0.0660030i | \(-0.978975\pi\) |
0.556070 | + | 0.831135i | \(0.312309\pi\) | |||||||
\(80\) | −392.138 | + | 679.203i | −0.548030 | + | 0.949215i | ||||
\(81\) | −727.932 | + | 39.4543i | −0.998534 | + | 0.0541212i | ||||
\(82\) | 553.616 | + | 958.891i | 0.745569 | + | 1.29136i | ||||
\(83\) | 102.235 | + | 177.076i | 0.135201 | + | 0.234176i | 0.925674 | − | 0.378321i | \(-0.123499\pi\) |
−0.790473 | + | 0.612497i | \(0.790165\pi\) | |||||||
\(84\) | −1188.68 | + | 1253.61i | −1.54400 | + | 1.62834i | ||||
\(85\) | 260.057 | − | 450.433i | 0.331849 | − | 0.574780i | ||||
\(86\) | 2406.07 | 3.01690 | ||||||||
\(87\) | 55.9896 | − | 220.873i | 0.0689967 | − | 0.272185i | ||||
\(88\) | 2081.21 | 2.52112 | ||||||||
\(89\) | 432.859 | + | 749.734i | 0.515539 | + | 0.892940i | 0.999837 | + | 0.0180370i | \(0.00574166\pi\) |
−0.484298 | + | 0.874903i | \(0.660925\pi\) | |||||||
\(90\) | 827.260 | + | 448.208i | 0.968898 | + | 0.524948i | ||||
\(91\) | 1015.08 | − | 603.846i | 1.16933 | − | 0.695607i | ||||
\(92\) | −378.138 | − | 654.953i | −0.428517 | − | 0.742213i | ||||
\(93\) | 255.533 | − | 1008.05i | 0.284920 | − | 1.12398i | ||||
\(94\) | −45.5536 | − | 78.9012i | −0.0499840 | − | 0.0865749i | ||||
\(95\) | 320.034 | + | 554.314i | 0.345629 | + | 0.598647i | ||||
\(96\) | 227.902 | − | 899.050i | 0.242293 | − | 0.955822i | ||||
\(97\) | 331.039 | + | 573.377i | 0.346515 | + | 0.600182i | 0.985628 | − | 0.168931i | \(-0.0540316\pi\) |
−0.639113 | + | 0.769113i | \(0.720698\pi\) | |||||||
\(98\) | 1746.75 | − | 45.5792i | 1.80049 | − | 0.0469815i | ||||
\(99\) | −30.0049 | − | 1107.99i | −0.0304606 | − | 1.12482i | ||||
\(100\) | 701.988 | + | 1215.88i | 0.701988 | + | 1.21588i | ||||
\(101\) | −240.380 | −0.236819 | −0.118410 | − | 0.992965i | \(-0.537780\pi\) | ||||
−0.118410 | + | 0.992965i | \(0.537780\pi\) | |||||||
\(102\) | −494.561 | + | 1950.99i | −0.480087 | + | 1.89389i | ||||
\(103\) | −406.366 | −0.388742 | −0.194371 | − | 0.980928i | \(-0.562267\pi\) | ||||
−0.194371 | + | 0.980928i | \(0.562267\pi\) | |||||||
\(104\) | −1616.58 | + | 2800.00i | −1.52422 | + | 2.64003i | ||||
\(105\) | −187.216 | − | 631.102i | −0.174004 | − | 0.586564i | ||||
\(106\) | −1075.66 | − | 1863.10i | −0.985638 | − | 1.70718i | ||||
\(107\) | −855.526 | − | 1481.81i | −0.772961 | − | 1.33881i | −0.935933 | − | 0.352177i | \(-0.885442\pi\) |
0.162972 | − | 0.986631i | \(-0.447892\pi\) | |||||||
\(108\) | −2457.21 | − | 552.547i | −2.18931 | − | 0.492304i | ||||
\(109\) | 298.924 | − | 517.751i | 0.262676 | − | 0.454968i | −0.704276 | − | 0.709926i | \(-0.748728\pi\) |
0.966952 | + | 0.254958i | \(0.0820616\pi\) | |||||||
\(110\) | −715.271 | + | 1238.89i | −0.619986 | + | 1.07385i | ||||
\(111\) | −133.187 | + | 525.409i | −0.113888 | + | 0.449276i | ||||
\(112\) | −1824.91 | + | 1085.59i | −1.53962 | + | 0.915883i | ||||
\(113\) | 374.893 | − | 649.334i | 0.312097 | − | 0.540568i | −0.666719 | − | 0.745309i | \(-0.732302\pi\) |
0.978816 | + | 0.204741i | \(0.0656352\pi\) | |||||||
\(114\) | −1774.97 | − | 1727.55i | −1.45826 | − | 1.41930i | ||||
\(115\) | 288.176 | 0.233674 | ||||||||
\(116\) | 393.607 | − | 681.747i | 0.315047 | − | 0.545678i | ||||
\(117\) | 1513.96 | + | 820.264i | 1.19629 | + | 0.648149i | ||||
\(118\) | −1482.61 | −1.15665 | ||||||||
\(119\) | 1210.24 | − | 719.942i | 0.932290 | − | 0.554596i | ||||
\(120\) | 1291.33 | + | 1256.83i | 0.982349 | + | 0.956106i | ||||
\(121\) | 354.247 | 0.266151 | ||||||||
\(122\) | −392.335 | − | 679.543i | −0.291150 | − | 0.504287i | ||||
\(123\) | 1086.83 | − | 307.043i | 0.796718 | − | 0.225082i | ||||
\(124\) | 1796.40 | − | 3111.45i | 1.30098 | − | 2.25336i | ||||
\(125\) | −1390.04 | −0.994630 | ||||||||
\(126\) | 1361.15 | + | 2153.24i | 0.962386 | + | 1.52243i | ||||
\(127\) | −2519.73 | −1.76055 | −0.880275 | − | 0.474463i | \(-0.842642\pi\) | ||||
−0.880275 | + | 0.474463i | \(0.842642\pi\) | |||||||
\(128\) | −734.143 | + | 1271.57i | −0.506950 | + | 0.878064i | ||||
\(129\) | 603.042 | − | 2378.94i | 0.411588 | − | 1.62367i | ||||
\(130\) | −1111.17 | − | 1924.61i | −0.749664 | − | 1.29846i | ||||
\(131\) | −415.123 | −0.276866 | −0.138433 | − | 0.990372i | \(-0.544207\pi\) | ||||
−0.138433 | + | 0.990372i | \(0.544207\pi\) | |||||||
\(132\) | 940.941 | − | 3711.92i | 0.620442 | − | 2.44758i | ||||
\(133\) | 22.6039 | + | 1732.81i | 0.0147369 | + | 1.12973i | ||||
\(134\) | 4270.80 | 2.75329 | ||||||||
\(135\) | 650.493 | − | 705.595i | 0.414708 | − | 0.449837i | ||||
\(136\) | −1927.39 | + | 3338.33i | −1.21524 | + | 2.10485i | ||||
\(137\) | −1154.04 | −0.719683 | −0.359842 | − | 0.933013i | \(-0.617169\pi\) | ||||
−0.359842 | + | 0.933013i | \(0.617169\pi\) | |||||||
\(138\) | −1073.16 | + | 303.179i | −0.661980 | + | 0.187017i | ||||
\(139\) | 644.637 | − | 1116.54i | 0.393362 | − | 0.681323i | −0.599528 | − | 0.800354i | \(-0.704645\pi\) |
0.992891 | + | 0.119030i | \(0.0379785\pi\) | |||||||
\(140\) | −29.6644 | − | 2274.07i | −0.0179079 | − | 1.37281i | ||||
\(141\) | −89.4287 | + | 25.2647i | −0.0534132 | + | 0.0150898i | ||||
\(142\) | −2395.96 | + | 4149.93i | −1.41595 | + | 2.45249i | ||||
\(143\) | −1309.01 | + | 2267.28i | −0.765492 | + | 1.32587i | ||||
\(144\) | −2721.80 | − | 1474.67i | −1.57512 | − | 0.853397i | ||||
\(145\) | 149.982 | + | 259.777i | 0.0858990 | + | 0.148781i | ||||
\(146\) | −335.291 | − | 580.741i | −0.190061 | − | 0.329195i | ||||
\(147\) | 392.728 | − | 1738.47i | 0.220351 | − | 0.975421i | ||||
\(148\) | −936.305 | + | 1621.73i | −0.520026 | + | 0.900711i | ||||
\(149\) | 1637.22 | 0.900174 | 0.450087 | − | 0.892985i | \(-0.351393\pi\) | ||||
0.450087 | + | 0.892985i | \(0.351393\pi\) | |||||||
\(150\) | 1992.25 | − | 562.833i | 1.08444 | − | 0.306367i | ||||
\(151\) | 380.806 | 0.205229 | 0.102615 | − | 0.994721i | \(-0.467279\pi\) | ||||
0.102615 | + | 0.994721i | \(0.467279\pi\) | |||||||
\(152\) | −2371.89 | − | 4108.24i | −1.26570 | − | 2.19225i | ||||
\(153\) | 1805.04 | + | 977.968i | 0.953783 | + | 0.516759i | ||||
\(154\) | −3328.69 | + | 1980.15i | −1.74177 | + | 1.03614i | ||||
\(155\) | 684.510 | + | 1185.61i | 0.354717 | + | 0.614388i | ||||
\(156\) | 4263.02 | + | 4149.14i | 2.18792 | + | 2.12947i | ||||
\(157\) | −795.841 | − | 1378.44i | −0.404554 | − | 0.700708i | 0.589715 | − | 0.807611i | \(-0.299240\pi\) |
−0.994269 | + | 0.106903i | \(0.965907\pi\) | |||||||
\(158\) | 1580.16 | + | 2736.91i | 0.795637 | + | 1.37808i | ||||
\(159\) | −2111.69 | + | 596.577i | −1.05326 | + | 0.297558i | ||||
\(160\) | 610.493 | + | 1057.41i | 0.301648 | + | 0.522470i | ||||
\(161\) | 680.724 | + | 381.265i | 0.333221 | + | 0.186633i | ||||
\(162\) | −1680.08 | + | 3311.97i | −0.814814 | + | 1.60625i | ||||
\(163\) | −460.445 | − | 797.514i | −0.221257 | − | 0.383228i | 0.733933 | − | 0.679222i | \(-0.237683\pi\) |
−0.955190 | + | 0.295994i | \(0.904349\pi\) | |||||||
\(164\) | 3901.78 | 1.85779 | ||||||||
\(165\) | 1045.64 | + | 1017.71i | 0.493354 | + | 0.480174i | ||||
\(166\) | 1041.63 | 0.487024 | ||||||||
\(167\) | −1489.89 | + | 2580.57i | −0.690367 | + | 1.19575i | 0.281350 | + | 0.959605i | \(0.409218\pi\) |
−0.971718 | + | 0.236146i | \(0.924116\pi\) | |||||||
\(168\) | 1387.53 | + | 4677.34i | 0.637205 | + | 2.14801i | ||||
\(169\) | −935.053 | − | 1619.56i | −0.425605 | − | 0.737169i | ||||
\(170\) | −1324.81 | − | 2294.64i | −0.597695 | − | 1.03524i | ||||
\(171\) | −2152.94 | + | 1321.97i | −0.962803 | + | 0.591191i | ||||
\(172\) | 4239.39 | − | 7342.83i | 1.87936 | − | 3.25515i | ||||
\(173\) | −853.321 | + | 1477.99i | −0.375010 | + | 0.649537i | −0.990329 | − | 0.138742i | \(-0.955694\pi\) |
0.615318 | + | 0.788279i | \(0.289027\pi\) | |||||||
\(174\) | −831.832 | − | 809.610i | −0.362419 | − | 0.352738i | ||||
\(175\) | −1263.72 | − | 707.794i | −0.545876 | − | 0.305738i | ||||
\(176\) | 2353.34 | − | 4076.11i | 1.00790 | − | 1.74573i | ||||
\(177\) | −371.590 | + | 1465.89i | −0.157799 | + | 0.622501i | ||||
\(178\) | 4410.22 | 1.85708 | ||||||||
\(179\) | −1526.74 | + | 2644.39i | −0.637507 | + | 1.10419i | 0.348471 | + | 0.937320i | \(0.386701\pi\) |
−0.985978 | + | 0.166875i | \(0.946632\pi\) | |||||||
\(180\) | 2825.43 | − | 1734.90i | 1.16997 | − | 0.718400i | ||||
\(181\) | 418.264 | 0.171764 | 0.0858821 | − | 0.996305i | \(-0.472629\pi\) | ||||
0.0858821 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(182\) | −78.4818 | − | 6016.40i | −0.0319641 | − | 2.45036i | ||||
\(183\) | −770.212 | + | 217.594i | −0.311124 | + | 0.0878962i | ||||
\(184\) | −2135.78 | −0.855717 | ||||||||
\(185\) | −356.775 | − | 617.953i | −0.141787 | − | 0.245583i | ||||
\(186\) | −3796.43 | − | 3695.01i | −1.49660 | − | 1.45662i | ||||
\(187\) | −1560.69 | + | 2703.19i | −0.610314 | + | 1.05709i | ||||
\(188\) | −321.053 | −0.124549 | ||||||||
\(189\) | 2470.11 | − | 806.124i | 0.950656 | − | 0.310248i | ||||
\(190\) | 3260.69 | 1.24503 | ||||||||
\(191\) | 1043.03 | − | 1806.58i | 0.395136 | − | 0.684396i | −0.597982 | − | 0.801509i | \(-0.704031\pi\) |
0.993119 | + | 0.117113i | \(0.0373641\pi\) | |||||||
\(192\) | 29.4767 | + | 28.6892i | 0.0110797 | + | 0.0107837i | ||||
\(193\) | 634.473 | + | 1098.94i | 0.236634 | + | 0.409862i | 0.959746 | − | 0.280868i | \(-0.0906224\pi\) |
−0.723112 | + | 0.690731i | \(0.757289\pi\) | |||||||
\(194\) | 3372.82 | 1.24822 | ||||||||
\(195\) | −2181.40 | + | 616.272i | −0.801095 | + | 0.226319i | ||||
\(196\) | 2938.59 | − | 5411.02i | 1.07091 | − | 1.97194i | ||||
\(197\) | −789.856 | −0.285660 | −0.142830 | − | 0.989747i | \(-0.545620\pi\) | ||||
−0.142830 | + | 0.989747i | \(0.545620\pi\) | |||||||
\(198\) | −4964.65 | − | 2689.84i | −1.78193 | − | 0.965447i | ||||
\(199\) | 2735.94 | − | 4738.78i | 0.974600 | − | 1.68806i | 0.293349 | − | 0.956005i | \(-0.405230\pi\) |
0.681250 | − | 0.732051i | \(-0.261437\pi\) | |||||||
\(200\) | 3964.94 | 1.40182 | ||||||||
\(201\) | 1070.41 | − | 4222.64i | 0.375625 | − | 1.48180i | ||||
\(202\) | −612.284 | + | 1060.51i | −0.213268 | + | 0.369391i | ||||
\(203\) | 10.5932 | + | 812.072i | 0.00366255 | + | 0.280770i | ||||
\(204\) | 5082.63 | + | 4946.86i | 1.74439 | + | 1.69779i | ||||
\(205\) | −743.379 | + | 1287.57i | −0.253267 | + | 0.438672i | ||||
\(206\) | −1035.07 | + | 1792.80i | −0.350082 | + | 0.606360i | ||||
\(207\) | 30.7916 | + | 1137.04i | 0.0103390 | + | 0.381787i | ||||
\(208\) | 3655.92 | + | 6332.24i | 1.21871 | + | 2.11087i | ||||
\(209\) | −1920.62 | − | 3326.62i | −0.635656 | − | 1.10099i | ||||
\(210\) | −3261.15 | − | 781.551i | −1.07162 | − | 0.256820i | ||||
\(211\) | −835.844 | + | 1447.72i | −0.272710 | + | 0.472348i | −0.969555 | − | 0.244874i | \(-0.921253\pi\) |
0.696844 | + | 0.717222i | \(0.254587\pi\) | |||||||
\(212\) | −7581.07 | −2.45599 | ||||||||
\(213\) | 3502.62 | + | 3409.05i | 1.12674 | + | 1.09664i | ||||
\(214\) | −8716.60 | −2.78437 | ||||||||
\(215\) | 1615.40 | + | 2797.96i | 0.512416 | + | 0.887531i | ||||
\(216\) | −4821.06 | + | 5229.44i | −1.51866 | + | 1.64731i | ||||
\(217\) | 48.3467 | + | 3706.25i | 0.0151244 | + | 1.15943i | ||||
\(218\) | −1522.80 | − | 2637.57i | −0.473107 | − | 0.819445i | ||||
\(219\) | −658.228 | + | 185.957i | −0.203100 | + | 0.0573781i | ||||
\(220\) | 2520.55 | + | 4365.72i | 0.772433 | + | 1.33789i | ||||
\(221\) | −2424.53 | − | 4199.40i | −0.737969 | − | 1.27820i | ||||
\(222\) | 1978.75 | + | 1925.89i | 0.598220 | + | 0.582239i | ||||
\(223\) | 1354.96 | + | 2346.87i | 0.406884 | + | 0.704743i | 0.994539 | − | 0.104368i | \(-0.0332821\pi\) |
−0.587655 | + | 0.809112i | \(0.699949\pi\) | |||||||
\(224\) | 43.1190 | + | 3305.49i | 0.0128616 | + | 0.985970i | ||||
\(225\) | −57.1626 | − | 2110.84i | −0.0169371 | − | 0.625435i | ||||
\(226\) | −1909.81 | − | 3307.90i | −0.562119 | − | 0.973619i | ||||
\(227\) | −296.947 | −0.0868240 | −0.0434120 | − | 0.999057i | \(-0.513823\pi\) | ||||
−0.0434120 | + | 0.999057i | \(0.513823\pi\) | |||||||
\(228\) | −8399.54 | + | 2372.97i | −2.43979 | + | 0.689271i | ||||
\(229\) | 3020.31 | 0.871563 | 0.435781 | − | 0.900053i | \(-0.356472\pi\) | ||||
0.435781 | + | 0.900053i | \(0.356472\pi\) | |||||||
\(230\) | 734.025 | − | 1271.37i | 0.210436 | − | 0.364485i | ||||
\(231\) | 1123.54 | + | 3787.44i | 0.320016 | + | 1.07877i | ||||
\(232\) | −1111.58 | − | 1925.31i | −0.314563 | − | 0.544839i | ||||
\(233\) | −150.838 | − | 261.259i | −0.0424108 | − | 0.0734577i | 0.844041 | − | 0.536279i | \(-0.180170\pi\) |
−0.886452 | + | 0.462821i | \(0.846837\pi\) | |||||||
\(234\) | 7475.12 | − | 4589.95i | 2.08831 | − | 1.28228i | ||||
\(235\) | 61.1681 | − | 105.946i | 0.0169794 | − | 0.0294092i | ||||
\(236\) | −2612.28 | + | 4524.60i | −0.720529 | + | 1.24799i | ||||
\(237\) | 3102.09 | − | 876.377i | 0.850221 | − | 0.240197i | ||||
\(238\) | −93.5708 | − | 7173.11i | −0.0254844 | − | 1.95363i | ||||
\(239\) | −1040.51 | + | 1802.22i | −0.281611 | + | 0.487765i | −0.971782 | − | 0.235882i | \(-0.924202\pi\) |
0.690171 | + | 0.723647i | \(0.257535\pi\) | |||||||
\(240\) | 3921.72 | − | 1107.93i | 1.05478 | − | 0.297986i | ||||
\(241\) | −3469.12 | −0.927243 | −0.463622 | − | 0.886033i | \(-0.653450\pi\) | ||||
−0.463622 | + | 0.886033i | \(0.653450\pi\) | |||||||
\(242\) | 902.319 | − | 1562.86i | 0.239683 | − | 0.415143i | ||||
\(243\) | 2853.54 | + | 2491.23i | 0.753311 | + | 0.657664i | ||||
\(244\) | −2765.10 | −0.725481 | ||||||||
\(245\) | 1225.74 | + | 2000.64i | 0.319632 | + | 0.521700i | ||||
\(246\) | 1413.71 | − | 5576.95i | 0.366402 | − | 1.44542i | ||||
\(247\) | 5967.37 | 1.53723 | ||||||||
\(248\) | −5073.17 | − | 8786.99i | −1.29898 | − | 2.24990i | ||||
\(249\) | 261.066 | − | 1029.88i | 0.0664434 | − | 0.262113i | ||||
\(250\) | −3540.63 | + | 6132.54i | −0.895715 | + | 1.55142i | ||||
\(251\) | 5185.82 | 1.30409 | 0.652044 | − | 0.758181i | \(-0.273912\pi\) | ||||
0.652044 | + | 0.758181i | \(0.273912\pi\) | |||||||
\(252\) | 8969.52 | − | 360.030i | 2.24217 | − | 0.0899990i | ||||
\(253\) | −1729.43 | −0.429757 | ||||||||
\(254\) | −6418.12 | + | 11116.5i | −1.58547 | + | 2.74611i | ||||
\(255\) | −2600.80 | + | 734.756i | −0.638700 | + | 0.180440i | ||||
\(256\) | 3708.27 | + | 6422.92i | 0.905340 | + | 1.56809i | ||||
\(257\) | 173.080 | 0.0420094 | 0.0210047 | − | 0.999779i | \(-0.493314\pi\) | ||||
0.0210047 | + | 0.999779i | \(0.493314\pi\) | |||||||
\(258\) | −8959.34 | − | 8720.00i | −2.16195 | − | 2.10420i | ||||
\(259\) | −25.1989 | − | 1931.74i | −0.00604550 | − | 0.463447i | ||||
\(260\) | −7831.34 | −1.86800 | ||||||||
\(261\) | −1008.96 | + | 619.536i | −0.239285 | + | 0.146928i | ||||
\(262\) | −1057.38 | + | 1831.44i | −0.249333 | + | 0.431857i | ||||
\(263\) | 3048.54 | 0.714758 | 0.357379 | − | 0.933960i | \(-0.383671\pi\) | ||||
0.357379 | + | 0.933960i | \(0.383671\pi\) | |||||||
\(264\) | −7749.68 | − | 7542.66i | −1.80667 | − | 1.75840i | ||||
\(265\) | 1444.37 | − | 2501.72i | 0.334818 | − | 0.579922i | ||||
\(266\) | 7702.35 | + | 4313.99i | 1.77542 | + | 0.994389i | ||||
\(267\) | 1105.35 | − | 4360.49i | 0.253357 | − | 0.999466i | ||||
\(268\) | 7524.95 | − | 13033.6i | 1.71515 | − | 2.97072i | ||||
\(269\) | 1564.23 | − | 2709.33i | 0.354547 | − | 0.614093i | −0.632494 | − | 0.774566i | \(-0.717969\pi\) |
0.987040 | + | 0.160473i | \(0.0513019\pi\) | |||||||
\(270\) | −1456.03 | − | 4667.09i | −0.328190 | − | 1.05196i | ||||
\(271\) | −2322.28 | − | 4022.30i | −0.520547 | − | 0.901614i | −0.999715 | − | 0.0238903i | \(-0.992395\pi\) |
0.479168 | − | 0.877723i | \(-0.340939\pi\) | |||||||
\(272\) | 4358.81 | + | 7549.68i | 0.971660 | + | 1.68296i | ||||
\(273\) | −5968.22 | − | 1430.31i | −1.32313 | − | 0.317093i | ||||
\(274\) | −2939.52 | + | 5091.39i | −0.648112 | + | 1.12256i | ||||
\(275\) | 3210.58 | 0.704019 | ||||||||
\(276\) | −965.611 | + | 3809.24i | −0.210590 | + | 0.830758i | ||||
\(277\) | −2334.16 | −0.506303 | −0.253152 | − | 0.967427i | \(-0.581467\pi\) | ||||
−0.253152 | + | 0.967427i | \(0.581467\pi\) | |||||||
\(278\) | −3283.97 | − | 5688.00i | −0.708486 | − | 1.22713i | ||||
\(279\) | −4604.85 | + | 2827.52i | −0.988119 | + | 0.606736i | ||||
\(280\) | −5603.63 | − | 3138.53i | −1.19600 | − | 0.669867i | ||||
\(281\) | 3471.31 | + | 6012.48i | 0.736943 | + | 1.27642i | 0.953866 | + | 0.300233i | \(0.0970646\pi\) |
−0.216923 | + | 0.976189i | \(0.569602\pi\) | |||||||
\(282\) | −116.326 | + | 458.893i | −0.0245642 | + | 0.0969031i | ||||
\(283\) | −1943.74 | − | 3366.65i | −0.408280 | − | 0.707161i | 0.586418 | − | 0.810009i | \(-0.300538\pi\) |
−0.994697 | + | 0.102848i | \(0.967204\pi\) | |||||||
\(284\) | 8443.14 | + | 14623.9i | 1.76411 | + | 3.05553i | ||||
\(285\) | 817.237 | − | 3223.92i | 0.169856 | − | 0.670064i | ||||
\(286\) | 6668.50 | + | 11550.2i | 1.37873 | + | 2.38803i | ||||
\(287\) | −3459.49 | + | 2057.97i | −0.711524 | + | 0.423268i | ||||
\(288\) | −4106.93 | + | 2521.78i | −0.840288 | + | 0.515963i | ||||
\(289\) | −434.166 | − | 751.997i | −0.0883708 | − | 0.153063i | ||||
\(290\) | 1528.11 | 0.309426 | ||||||||
\(291\) | 845.342 | − | 3334.79i | 0.170291 | − | 0.671782i | ||||
\(292\) | −2363.07 | −0.473589 | ||||||||
\(293\) | 2927.47 | − | 5070.52i | 0.583701 | − | 1.01100i | −0.411335 | − | 0.911484i | \(-0.634937\pi\) |
0.995036 | − | 0.0995159i | \(-0.0317294\pi\) | |||||||
\(294\) | −6669.43 | − | 6160.77i | −1.32302 | − | 1.22212i | ||||
\(295\) | −995.399 | − | 1724.08i | −0.196456 | − | 0.340271i | ||||
\(296\) | 2644.20 | + | 4579.89i | 0.519227 | + | 0.899327i | ||||
\(297\) | −3903.81 | + | 4234.50i | −0.762701 | + | 0.827308i | ||||
\(298\) | 4170.23 | − | 7223.05i | 0.810654 | − | 1.40409i | ||||
\(299\) | 1343.34 | − | 2326.73i | 0.259823 | − | 0.450027i | ||||
\(300\) | 1792.59 | − | 7071.60i | 0.344985 | − | 1.36093i | ||||
\(301\) | 114.095 | + | 8746.52i | 0.0218483 | + | 1.67489i | ||||
\(302\) | 969.969 | − | 1680.04i | 0.184819 | − | 0.320117i | ||||
\(303\) | 895.089 | + | 871.178i | 0.169708 | + | 0.165174i | ||||
\(304\) | −10728.1 | −2.02401 | ||||||||
\(305\) | 526.815 | − | 912.471i | 0.0989028 | − | 0.171305i | ||||
\(306\) | 8912.28 | − | 5472.42i | 1.66497 | − | 1.02234i | ||||
\(307\) | 366.420 | 0.0681196 | 0.0340598 | − | 0.999420i | \(-0.489156\pi\) | ||||
0.0340598 | + | 0.999420i | \(0.489156\pi\) | |||||||
\(308\) | 178.026 | + | 13647.4i | 0.0329349 | + | 2.52478i | ||||
\(309\) | 1513.16 | + | 1472.74i | 0.278578 | + | 0.271136i | ||||
\(310\) | 6974.18 | 1.27776 | ||||||||
\(311\) | −4791.47 | − | 8299.07i | −0.873632 | − | 1.51317i | −0.858213 | − | 0.513293i | \(-0.828425\pi\) |
−0.0154185 | − | 0.999881i | \(-0.504908\pi\) | |||||||
\(312\) | 16167.2 | − | 4567.43i | 2.93362 | − | 0.828782i | ||||
\(313\) | 4344.98 | − | 7525.73i | 0.784641 | − | 1.35904i | −0.144572 | − | 0.989494i | \(-0.546180\pi\) |
0.929213 | − | 0.369545i | \(-0.120486\pi\) | |||||||
\(314\) | −8108.49 | −1.45729 | ||||||||
\(315\) | −1590.09 | + | 3028.50i | −0.284418 | + | 0.541703i | ||||
\(316\) | 11136.6 | 1.98255 | ||||||||
\(317\) | 2773.36 | − | 4803.60i | 0.491380 | − | 0.851095i | −0.508571 | − | 0.861020i | \(-0.669826\pi\) |
0.999951 | + | 0.00992548i | \(0.00315943\pi\) | |||||||
\(318\) | −2746.81 | + | 10835.9i | −0.484382 | + | 1.91084i | ||||
\(319\) | −900.091 | − | 1559.00i | −0.157979 | − | 0.273628i | ||||
\(320\) | −54.1498 | −0.00945958 | ||||||||
\(321\) | −2184.67 | + | 8618.30i | −0.379864 | + | 1.49853i | ||||
\(322\) | 3415.96 | − | 2032.07i | 0.591193 | − | 0.351686i | ||||
\(323\) | 7114.66 | 1.22560 | ||||||||
\(324\) | 7147.22 | + | 10962.8i | 1.22552 | + | 1.87977i | ||||
\(325\) | −2493.82 | + | 4319.42i | −0.425637 | + | 0.737225i | ||||
\(326\) | −4691.28 | −0.797013 | ||||||||
\(327\) | −2989.49 | + | 844.567i | −0.505564 | + | 0.142828i | ||||
\(328\) | 5509.47 | − | 9542.68i | 0.927468 | − | 1.60642i | ||||
\(329\) | 284.660 | − | 169.337i | 0.0477016 | − | 0.0283765i | ||||
\(330\) | 7153.33 | − | 2020.90i | 1.19327 | − | 0.337112i | ||||
\(331\) | 1173.11 | − | 2031.88i | 0.194803 | − | 0.337409i | −0.752033 | − | 0.659126i | \(-0.770927\pi\) |
0.946836 | + | 0.321717i | \(0.104260\pi\) | |||||||
\(332\) | 1835.30 | − | 3178.83i | 0.303388 | − | 0.525484i | ||||
\(333\) | 2400.11 | − | 1473.74i | 0.394970 | − | 0.242524i | ||||
\(334\) | 7589.95 | + | 13146.2i | 1.24342 | + | 2.15367i | ||||
\(335\) | 2867.35 | + | 4966.40i | 0.467643 | + | 0.809981i | ||||
\(336\) | 10729.7 | + | 2571.41i | 1.74212 | + | 0.417506i | ||||
\(337\) | −2875.53 | + | 4980.56i | −0.464807 | + | 0.805070i | −0.999193 | − | 0.0401712i | \(-0.987210\pi\) |
0.534386 | + | 0.845241i | \(0.320543\pi\) | |||||||
\(338\) | −9526.87 | −1.53312 | ||||||||
\(339\) | −3749.26 | + | 1059.21i | −0.600683 | + | 0.169700i | ||||
\(340\) | −9337.00 | −1.48932 | ||||||||
\(341\) | −4107.96 | − | 7115.19i | −0.652371 | − | 1.12994i | ||||
\(342\) | 348.405 | + | 12865.6i | 0.0550864 | + | 2.03418i | ||||
\(343\) | 248.519 | + | 6347.59i | 0.0391218 | + | 0.999234i | ||||
\(344\) | −11972.4 | − | 20736.8i | −1.87647 | − | 3.25015i | ||||
\(345\) | −1073.06 | − | 1044.40i | −0.167454 | − | 0.162981i | ||||
\(346\) | 4347.06 | + | 7529.34i | 0.675432 | + | 1.16988i | ||||
\(347\) | 853.487 | + | 1478.28i | 0.132039 | + | 0.228698i | 0.924462 | − | 0.381273i | \(-0.124514\pi\) |
−0.792423 | + | 0.609971i | \(0.791181\pi\) | |||||||
\(348\) | −3936.41 | + | 1112.08i | −0.606361 | + | 0.171304i | ||||
\(349\) | 1098.11 | + | 1901.98i | 0.168425 | + | 0.291720i | 0.937866 | − | 0.346997i | \(-0.112799\pi\) |
−0.769441 | + | 0.638717i | \(0.779465\pi\) | |||||||
\(350\) | −6341.51 | + | 3772.41i | −0.968480 | + | 0.576125i | ||||
\(351\) | −2664.68 | − | 8541.21i | −0.405214 | − | 1.29885i | ||||
\(352\) | −3663.76 | − | 6345.82i | −0.554771 | − | 0.960891i | ||||
\(353\) | −10646.6 | −1.60527 | −0.802637 | − | 0.596468i | \(-0.796570\pi\) | ||||
−0.802637 | + | 0.596468i | \(0.796570\pi\) | |||||||
\(354\) | 5520.68 | + | 5373.20i | 0.828872 | + | 0.806730i | ||||
\(355\) | −6434.45 | −0.961986 | ||||||||
\(356\) | 7770.60 | − | 13459.1i | 1.15686 | − | 2.00373i | ||||
\(357\) | −7115.68 | − | 1705.31i | −1.05491 | − | 0.252813i | ||||
\(358\) | 7777.65 | + | 13471.3i | 1.14822 | + | 1.98877i | ||||
\(359\) | −1648.66 | − | 2855.56i | −0.242375 | − | 0.419806i | 0.719015 | − | 0.694994i | \(-0.244593\pi\) |
−0.961390 | + | 0.275188i | \(0.911260\pi\) | |||||||
\(360\) | −253.472 | − | 9359.98i | −0.0371088 | − | 1.37032i | ||||
\(361\) | −948.242 | + | 1642.40i | −0.138248 | + | 0.239452i | ||||
\(362\) | 1065.38 | − | 1845.29i | 0.154683 | − | 0.267918i | ||||
\(363\) | −1319.09 | − | 1283.85i | −0.190728 | − | 0.185633i | ||||
\(364\) | −18499.1 | − | 10361.1i | −2.66378 | − | 1.49195i | ||||
\(365\) | 450.219 | − | 779.802i | 0.0645631 | − | 0.111827i | ||||
\(366\) | −1001.86 | + | 3952.25i | −0.143083 | + | 0.564447i | ||||
\(367\) | 1684.74 | 0.239626 | 0.119813 | − | 0.992796i | \(-0.461771\pi\) | ||||
0.119813 | + | 0.992796i | \(0.461771\pi\) | |||||||
\(368\) | −2415.05 | + | 4182.99i | −0.342101 | + | 0.592536i | ||||
\(369\) | −5159.74 | − | 2795.54i | −0.727927 | − | 0.394390i | ||||
\(370\) | −3635.03 | −0.510747 | ||||||||
\(371\) | 6721.72 | − | 3998.58i | 0.940631 | − | 0.559558i | ||||
\(372\) | −17965.5 | + | 5075.47i | −2.50395 | + | 0.707395i | ||||
\(373\) | 4840.97 | 0.672000 | 0.336000 | − | 0.941862i | \(-0.390926\pi\) | ||||
0.336000 | + | 0.941862i | \(0.390926\pi\) | |||||||
\(374\) | 7950.59 | + | 13770.8i | 1.09924 | + | 1.90394i | ||||
\(375\) | 5175.99 | + | 5037.72i | 0.712765 | + | 0.693725i | ||||
\(376\) | −453.340 | + | 785.209i | −0.0621788 | + | 0.107697i | ||||
\(377\) | 2796.58 | 0.382046 | ||||||||
\(378\) | 2735.28 | − | 12950.9i | 0.372189 | − | 1.76223i | ||||
\(379\) | −4006.74 | −0.543040 | −0.271520 | − | 0.962433i | \(-0.587526\pi\) | ||||
−0.271520 | + | 0.962433i | \(0.587526\pi\) | |||||||
\(380\) | 5745.18 | − | 9950.94i | 0.775582 | − | 1.34335i | ||||
\(381\) | 9382.55 | + | 9131.91i | 1.26163 | + | 1.22793i | ||||
\(382\) | −5313.50 | − | 9203.25i | −0.711681 | − | 1.23267i | ||||
\(383\) | −2661.13 | −0.355033 | −0.177516 | − | 0.984118i | \(-0.556806\pi\) | ||||
−0.177516 | + | 0.984118i | \(0.556806\pi\) | |||||||
\(384\) | 7342.06 | − | 2074.22i | 0.975711 | − | 0.275650i | ||||
\(385\) | −4537.50 | − | 2541.40i | −0.600655 | − | 0.336420i | ||||
\(386\) | 6464.38 | 0.852405 | ||||||||
\(387\) | −10867.2 | + | 6672.78i | −1.42741 | + | 0.876477i | ||||
\(388\) | 5942.75 | − | 10293.1i | 0.777571 | − | 1.34679i | ||||
\(389\) | 6825.12 | 0.889582 | 0.444791 | − | 0.895634i | \(-0.353278\pi\) | ||||
0.444791 | + | 0.895634i | \(0.353278\pi\) | |||||||
\(390\) | −2837.49 | + | 11193.6i | −0.368415 | + | 1.45336i | ||||
\(391\) | 1601.61 | − | 2774.06i | 0.207153 | − | 0.358799i | ||||
\(392\) | −9084.46 | − | 14827.6i | −1.17050 | − | 1.91047i | ||||
\(393\) | 1545.77 | + | 1504.47i | 0.198406 | + | 0.193106i | ||||
\(394\) | −2011.88 | + | 3484.68i | −0.257251 | + | 0.445572i | ||||
\(395\) | −2121.79 | + | 3675.05i | −0.270275 | + | 0.468131i | ||||
\(396\) | −16956.3 | + | 10411.7i | −2.15173 | + | 1.32123i | ||||
\(397\) | −1988.98 | − | 3445.01i | −0.251446 | − | 0.435516i | 0.712478 | − | 0.701694i | \(-0.247573\pi\) |
−0.963924 | + | 0.266178i | \(0.914239\pi\) | |||||||
\(398\) | −13937.6 | − | 24140.7i | −1.75535 | − | 3.04036i | ||||
\(399\) | 6195.80 | − | 6534.26i | 0.777389 | − | 0.819855i | ||||
\(400\) | 4483.38 | − | 7765.44i | 0.560422 | − | 0.970680i | ||||
\(401\) | −7984.65 | −0.994350 | −0.497175 | − | 0.867650i | \(-0.665629\pi\) | ||||
−0.497175 | + | 0.867650i | \(0.665629\pi\) | |||||||
\(402\) | −15902.9 | − | 15478.1i | −1.97305 | − | 1.92034i | ||||
\(403\) | 12763.4 | 1.57765 | ||||||||
\(404\) | 2157.63 | + | 3737.13i | 0.265708 | + | 0.460220i | ||||
\(405\) | −4979.39 | + | 269.886i | −0.610933 | + | 0.0331129i | ||||
\(406\) | 3609.67 | + | 2021.73i | 0.441244 | + | 0.247135i | ||||
\(407\) | 2141.12 | + | 3708.53i | 0.260765 | + | 0.451659i | ||||
\(408\) | 19275.5 | − | 5445.57i | 2.33893 | − | 0.660774i | ||||
\(409\) | −1535.45 | − | 2659.48i | −0.185631 | − | 0.321522i | 0.758158 | − | 0.652071i | \(-0.226100\pi\) |
−0.943789 | + | 0.330549i | \(0.892766\pi\) | |||||||
\(410\) | 3786.99 | + | 6559.25i | 0.456161 | + | 0.790094i | ||||
\(411\) | 4297.24 | + | 4182.44i | 0.515735 | + | 0.501958i | ||||
\(412\) | 3647.50 | + | 6317.65i | 0.436163 | + | 0.755457i | ||||
\(413\) | −70.3047 | − | 5389.54i | −0.00837644 | − | 0.642136i | ||||
\(414\) | 5094.82 | + | 2760.37i | 0.604822 | + | 0.327692i | ||||
\(415\) | 699.333 | + | 1211.28i | 0.0827202 | + | 0.143276i | ||||
\(416\) | 11383.3 | 1.34162 | ||||||||
\(417\) | −6446.92 | + | 1821.33i | −0.757092 | + | 0.213887i | ||||
\(418\) | −19568.4 | −2.28977 | ||||||||
\(419\) | −1945.50 | + | 3369.70i | −0.226835 | + | 0.392889i | −0.956868 | − | 0.290522i | \(-0.906171\pi\) |
0.730034 | + | 0.683411i | \(0.239504\pi\) | |||||||
\(420\) | −8131.13 | + | 8575.30i | −0.944663 | + | 0.996267i | ||||
\(421\) | −2847.38 | − | 4931.81i | −0.329627 | − | 0.570930i | 0.652811 | − | 0.757521i | \(-0.273590\pi\) |
−0.982438 | + | 0.186591i | \(0.940256\pi\) | |||||||
\(422\) | 4258.03 | + | 7375.13i | 0.491180 | + | 0.850748i | ||||
\(423\) | 424.563 | + | 230.028i | 0.0488013 | + | 0.0264405i | ||||
\(424\) | −10704.8 | + | 18541.2i | −1.22611 | + | 2.12368i | ||||
\(425\) | −2973.28 | + | 5149.87i | −0.339353 | + | 0.587777i | ||||
\(426\) | 23961.7 | − | 6769.46i | 2.72523 | − | 0.769909i | ||||
\(427\) | 2451.66 | − | 1458.43i | 0.277855 | − | 0.165289i | ||||
\(428\) | −15358.2 | + | 26601.2i | −1.73450 | + | 3.00425i | ||||
\(429\) | 13091.3 | − | 3698.44i | 1.47332 | − | 0.416229i | ||||
\(430\) | 16458.7 | 1.84583 | ||||||||
\(431\) | −4029.23 | + | 6978.82i | −0.450304 | + | 0.779949i | −0.998405 | − | 0.0564630i | \(-0.982018\pi\) |
0.548101 | + | 0.836412i | \(0.315351\pi\) | |||||||
\(432\) | 4790.56 | + | 15355.4i | 0.533532 | + | 1.71015i | ||||
\(433\) | 504.156 | 0.0559542 | 0.0279771 | − | 0.999609i | \(-0.491093\pi\) | ||||
0.0279771 | + | 0.999609i | \(0.491093\pi\) | |||||||
\(434\) | 16474.3 | + | 9227.05i | 1.82210 | + | 1.02054i | ||||
\(435\) | 382.995 | − | 1510.87i | 0.0422142 | − | 0.166531i | ||||
\(436\) | −10732.4 | −1.17888 | ||||||||
\(437\) | 1970.98 | + | 3413.84i | 0.215755 | + | 0.373698i | ||||
\(438\) | −856.199 | + | 3377.62i | −0.0934036 | + | 0.368468i | ||||
\(439\) | 3713.45 | − | 6431.89i | 0.403721 | − | 0.699265i | −0.590451 | − | 0.807074i | \(-0.701050\pi\) |
0.994172 | + | 0.107809i | \(0.0343834\pi\) | |||||||
\(440\) | 14236.5 | 1.54249 | ||||||||
\(441\) | −7762.88 | + | 5050.13i | −0.838234 | + | 0.545311i | ||||
\(442\) | −24702.5 | −2.65832 | ||||||||
\(443\) | 7650.95 | − | 13251.8i | 0.820559 | − | 1.42125i | −0.0847073 | − | 0.996406i | \(-0.526996\pi\) |
0.905266 | − | 0.424844i | \(-0.139671\pi\) | |||||||
\(444\) | 9363.86 | − | 2645.40i | 1.00088 | − | 0.282759i | ||||
\(445\) | 2960.96 | + | 5128.53i | 0.315422 | + | 0.546327i | ||||
\(446\) | 13805.2 | 1.46568 | ||||||||
\(447\) | −6096.39 | − | 5933.54i | −0.645077 | − | 0.627845i | ||||
\(448\) | −127.912 | − | 71.6418i | −0.0134894 | − | 0.00755526i | ||||
\(449\) | 8469.43 | 0.890194 | 0.445097 | − | 0.895482i | \(-0.353169\pi\) | ||||
0.445097 | + | 0.895482i | \(0.353169\pi\) | |||||||
\(450\) | −9458.19 | − | 5124.44i | −0.990808 | − | 0.536819i | ||||
\(451\) | 4461.25 | − | 7727.11i | 0.465792 | − | 0.806775i | ||||
\(452\) | −13460.0 | −1.40068 | ||||||||
\(453\) | −1417.98 | − | 1380.10i | −0.147070 | − | 0.143141i | ||||
\(454\) | −756.367 | + | 1310.07i | −0.0781895 | + | 0.135428i | ||||
\(455\) | 6943.62 | − | 4130.58i | 0.715432 | − | 0.425593i | ||||
\(456\) | −6056.86 | + | 23893.7i | −0.622014 | + | 2.45378i | ||||
\(457\) | −7461.42 | + | 12923.6i | −0.763743 | + | 1.32284i | 0.177166 | + | 0.984181i | \(0.443307\pi\) |
−0.940909 | + | 0.338661i | \(0.890026\pi\) | |||||||
\(458\) | 7693.17 | − | 13325.0i | 0.784887 | − | 1.35946i | ||||
\(459\) | −3176.99 | − | 10183.4i | −0.323070 | − | 1.03555i | ||||
\(460\) | −2586.64 | − | 4480.18i | −0.262179 | − | 0.454108i | ||||
\(461\) | 6078.32 | + | 10528.0i | 0.614091 | + | 1.06364i | 0.990543 | + | 0.137200i | \(0.0438104\pi\) |
−0.376453 | + | 0.926436i | \(0.622856\pi\) | |||||||
\(462\) | 19571.2 | + | 4690.34i | 1.97086 | + | 0.472325i | ||||
\(463\) | 7641.92 | − | 13236.2i | 0.767063 | − | 1.32859i | −0.172086 | − | 0.985082i | \(-0.555051\pi\) |
0.939149 | − | 0.343510i | \(-0.111616\pi\) | |||||||
\(464\) | −5027.69 | −0.503027 | ||||||||
\(465\) | 1747.96 | − | 6895.54i | 0.174322 | − | 0.687684i | ||||
\(466\) | −1536.82 | −0.152773 | ||||||||
\(467\) | 9121.63 | + | 15799.1i | 0.903852 | + | 1.56552i | 0.822451 | + | 0.568836i | \(0.192606\pi\) |
0.0814004 | + | 0.996681i | \(0.474061\pi\) | |||||||
\(468\) | −836.779 | − | 30899.8i | −0.0826498 | − | 3.05201i | ||||
\(469\) | 202.520 | + | 15525.2i | 0.0199393 | + | 1.52854i | ||||
\(470\) | −311.608 | − | 539.721i | −0.0305817 | − | 0.0529691i | ||||
\(471\) | −2032.26 | + | 8017.05i | −0.198814 | + | 0.784302i | ||||
\(472\) | 7377.29 | + | 12777.8i | 0.719422 | + | 1.24608i | ||||
\(473\) | −9694.53 | − | 16791.4i | −0.942400 | − | 1.63228i | ||||
\(474\) | 4035.09 | − | 15918.0i | 0.391008 | − | 1.54249i | ||||
\(475\) | −3658.99 | − | 6337.56i | −0.353445 | − | 0.612184i | ||||
\(476\) | −22055.7 | − | 12353.1i | −2.12379 | − | 1.18951i | ||||
\(477\) | 10025.3 | + | 5431.67i | 0.962316 | + | 0.521382i | ||||
\(478\) | 5300.67 | + | 9181.02i | 0.507211 | + | 0.878515i | ||||
\(479\) | −3032.42 | −0.289258 | −0.144629 | − | 0.989486i | \(-0.546199\pi\) | ||||
−0.144629 | + | 0.989486i | \(0.546199\pi\) | |||||||
\(480\) | 1558.95 | − | 6149.92i | 0.148242 | − | 0.584800i | ||||
\(481\) | −6652.46 | −0.630615 | ||||||||
\(482\) | −8836.35 | + | 15305.0i | −0.835031 | + | 1.44632i | ||||
\(483\) | −1153.00 | − | 3886.75i | −0.108620 | − | 0.366155i | ||||
\(484\) | −3179.69 | − | 5507.38i | −0.298618 | − | 0.517222i | ||||
\(485\) | 2264.46 | + | 3922.16i | 0.212008 | + | 0.367209i | ||||
\(486\) | 18259.1 | − | 6243.68i | 1.70422 | − | 0.582756i | ||||
\(487\) | 2783.79 | − | 4821.67i | 0.259026 | − | 0.448646i | −0.706955 | − | 0.707258i | \(-0.749932\pi\) |
0.965981 | + | 0.258612i | \(0.0832652\pi\) | |||||||
\(488\) | −3904.43 | + | 6762.68i | −0.362183 | + | 0.627320i | ||||
\(489\) | −1175.79 | + | 4638.38i | −0.108734 | + | 0.428946i | ||||
\(490\) | 11948.6 | − | 311.783i | 1.10159 | − | 0.0287447i | ||||
\(491\) | 2266.08 | − | 3924.96i | 0.208283 | − | 0.360756i | −0.742891 | − | 0.669412i | \(-0.766546\pi\) |
0.951174 | + | 0.308656i | \(0.0998793\pi\) | |||||||
\(492\) | −14528.8 | − | 14140.7i | −1.33132 | − | 1.29575i | ||||
\(493\) | 3334.25 | 0.304599 | ||||||||
\(494\) | 15199.8 | − | 26326.7i | 1.38435 | − | 2.39777i | ||||
\(495\) | −205.247 | − | 7579.17i | −0.0186367 | − | 0.688199i | ||||
\(496\) | −22946.1 | −2.07723 | ||||||||
\(497\) | −15199.4 | − | 8512.97i | −1.37180 | − | 0.768328i | ||||
\(498\) | −3878.64 | − | 3775.02i | −0.349008 | − | 0.339684i | ||||
\(499\) | −20637.4 | −1.85141 | −0.925707 | − | 0.378241i | \(-0.876529\pi\) | ||||
−0.925707 | + | 0.378241i | \(0.876529\pi\) | |||||||
\(500\) | 12476.8 | + | 21610.5i | 1.11596 | + | 1.93290i | ||||
\(501\) | 14900.2 | − | 4209.49i | 1.32873 | − | 0.375381i | ||||
\(502\) | 13209.0 | − | 22878.7i | 1.17440 | − | 2.03412i | ||||
\(503\) | −8789.60 | −0.779143 | −0.389572 | − | 0.920996i | \(-0.627377\pi\) | ||||
−0.389572 | + | 0.920996i | \(0.627377\pi\) | |||||||
\(504\) | 11784.8 | − | 22445.4i | 1.04154 | − | 1.98372i | ||||
\(505\) | −1644.31 | −0.144893 | ||||||||
\(506\) | −4405.12 | + | 7629.89i | −0.387018 | + | 0.670336i | ||||
\(507\) | −2387.75 | + | 9419.43i | −0.209159 | + | 0.825112i | ||||
\(508\) | 22616.8 | + | 39173.5i | 1.97532 | + | 3.42135i | ||||
\(509\) | −5818.46 | −0.506677 | −0.253338 | − | 0.967378i | \(-0.581529\pi\) | ||||
−0.253338 | + | 0.967378i | \(0.581529\pi\) | |||||||
\(510\) | −3383.03 | + | 13345.7i | −0.293731 | + | 1.15874i | ||||
\(511\) | 2095.20 | − | 1246.38i | 0.181382 | − | 0.107900i | ||||
\(512\) | 26035.7 | 2.24732 | ||||||||
\(513\) | 12807.8 | + | 2880.06i | 1.10230 | + | 0.247871i | ||||
\(514\) | 440.859 | − | 763.590i | 0.0378316 | − | 0.0655263i | ||||
\(515\) | −2779.73 | −0.237844 | ||||||||
\(516\) | −42397.5 | + | 11977.8i | −3.61715 | + | 1.02189i | ||||
\(517\) | −367.089 | + | 635.816i | −0.0312274 | + | 0.0540874i | ||||
\(518\) | −8586.62 | − | 4809.26i | −0.728329 | − | 0.407928i | ||||
\(519\) | 8533.95 | − | 2410.94i | 0.721770 | − | 0.203909i | ||||
\(520\) | −11058.2 | + | 19153.3i | −0.932563 | + | 1.61525i | ||||
\(521\) | −11685.2 | + | 20239.4i | −0.982609 | + | 1.70193i | −0.330493 | + | 0.943808i | \(0.607215\pi\) |
−0.652115 | + | 0.758120i | \(0.726118\pi\) | |||||||
\(522\) | 163.278 | + | 6029.38i | 0.0136906 | + | 0.505554i | ||||
\(523\) | 2340.45 | + | 4053.77i | 0.195680 | + | 0.338927i | 0.947123 | − | 0.320870i | \(-0.103975\pi\) |
−0.751443 | + | 0.659798i | \(0.770642\pi\) | |||||||
\(524\) | 3726.11 | + | 6453.80i | 0.310641 | + | 0.538045i | ||||
\(525\) | 2140.47 | + | 7215.49i | 0.177939 | + | 0.599828i | ||||
\(526\) | 7765.08 | − | 13449.5i | 0.643676 | − | 1.11488i | ||||
\(527\) | 15217.3 | 1.25783 | ||||||||
\(528\) | −23535.5 | + | 6649.05i | −1.93987 | + | 0.548036i | ||||
\(529\) | −10392.2 | −0.854132 | ||||||||
\(530\) | −7358.03 | − | 12744.5i | −0.603043 | − | 1.04450i | ||||
\(531\) | 6696.27 | − | 4111.72i | 0.547257 | − | 0.336033i | ||||
\(532\) | 26736.6 | − | 15904.9i | 2.17890 | − | 1.29618i | ||||
\(533\) | 6930.55 | + | 12004.1i | 0.563218 | + | 0.975523i | ||||
\(534\) | −16422.0 | − | 15983.4i | −1.33081 | − | 1.29526i | ||||
\(535\) | −5852.19 | − | 10136.3i | −0.472920 | − | 0.819122i | ||||
\(536\) | −21251.1 | − | 36807.9i | −1.71251 | − | 2.96616i | ||||
\(537\) | 15268.7 | − | 4313.59i | 1.22699 | − | 0.346639i | ||||
\(538\) | −7968.66 | − | 13802.1i | −0.638575 | − | 1.10604i | ||||
\(539\) | −7356.07 | − | 12006.5i | −0.587845 | − | 0.959474i | ||||
\(540\) | −16808.4 | − | 3779.68i | −1.33948 | − | 0.301206i | ||||
\(541\) | 347.398 | + | 601.711i | 0.0276078 | + | 0.0478181i | 0.879499 | − | 0.475900i | \(-0.157878\pi\) |
−0.851891 | + | 0.523718i | \(0.824544\pi\) | |||||||
\(542\) | −23660.7 | −1.87512 | ||||||||
\(543\) | −1557.46 | − | 1515.86i | −0.123089 | − | 0.119800i | ||||
\(544\) | 13571.9 | 1.06965 | ||||||||
\(545\) | 2044.78 | − | 3541.65i | 0.160713 | − | 0.278363i | ||||
\(546\) | −21512.2 | + | 22687.3i | −1.68615 | + | 1.77825i | ||||
\(547\) | −1795.35 | − | 3109.64i | −0.140336 | − | 0.243069i | 0.787287 | − | 0.616586i | \(-0.211485\pi\) |
−0.927623 | + | 0.373518i | \(0.878152\pi\) | |||||||
\(548\) | 10358.6 | + | 17941.6i | 0.807475 | + | 1.39859i | ||||
\(549\) | 3656.58 | + | 1981.13i | 0.284261 | + | 0.154012i | ||||
\(550\) | 8177.81 | − | 14164.4i | 0.634006 | − | 1.09813i | ||||
\(551\) | −2051.61 | + | 3553.49i | −0.158623 | + | 0.274744i | ||||
\(552\) | 7952.87 | + | 7740.42i | 0.613219 | + | 0.596837i | ||||
\(553\) | −9874.25 | + | 5873.95i | −0.759305 | + | 0.451692i | ||||
\(554\) | −5945.44 | + | 10297.8i | −0.455952 | + | 0.789733i | ||||
\(555\) | −911.061 | + | 3594.04i | −0.0696800 | + | 0.274880i | ||||
\(556\) | −23144.8 | −1.76539 | ||||||||
\(557\) | −7640.68 | + | 13234.1i | −0.581232 | + | 1.00672i | 0.414102 | + | 0.910231i | \(0.364096\pi\) |
−0.995334 | + | 0.0964925i | \(0.969238\pi\) | |||||||
\(558\) | 745.192 | + | 27517.7i | 0.0565349 | + | 2.08767i | ||||
\(559\) | 30120.9 | 2.27903 | ||||||||
\(560\) | −12483.2 | + | 7425.96i | −0.941986 | + | 0.560364i | ||||
\(561\) | 15608.2 | − | 4409.50i | 1.17465 | − | 0.331853i | ||||
\(562\) | 35367.7 | 2.65462 | ||||||||
\(563\) | 10341.4 | + | 17911.9i | 0.774138 | + | 1.34085i | 0.935277 | + | 0.353915i | \(0.115150\pi\) |
−0.161139 | + | 0.986932i | \(0.551517\pi\) | |||||||
\(564\) | 1195.49 | + | 1163.55i | 0.0892536 | + | 0.0868692i | ||||
\(565\) | 2564.44 | − | 4441.74i | 0.190950 | − | 0.330735i | ||||
\(566\) | −19803.9 | −1.47071 | ||||||||
\(567\) | −12119.3 | − | 5950.36i | −0.897642 | − | 0.440726i | ||||
\(568\) | 47688.2 | 3.52281 | ||||||||
\(569\) | 5304.47 | − | 9187.62i | 0.390817 | − | 0.676915i | −0.601740 | − | 0.798692i | \(-0.705526\pi\) |
0.992558 | + | 0.121776i | \(0.0388591\pi\) | |||||||
\(570\) | −12141.6 | − | 11817.3i | −0.892203 | − | 0.868369i | ||||
\(571\) | −5574.04 | − | 9654.52i | −0.408523 | − | 0.707582i | 0.586202 | − | 0.810165i | \(-0.300623\pi\) |
−0.994724 | + | 0.102583i | \(0.967289\pi\) | |||||||
\(572\) | 46998.3 | 3.43549 | ||||||||
\(573\) | −10431.2 | + | 2946.94i | −0.760506 | + | 0.214852i | ||||
\(574\) | 267.474 | + | 20504.5i | 0.0194497 | + | 1.49101i | ||||
\(575\) | −3294.76 | −0.238958 | ||||||||
\(576\) | −5.78591 | − | 213.656i | −0.000418541 | − | 0.0154555i | ||||
\(577\) | −5630.45 | + | 9752.22i | −0.406237 | + | 0.703623i | −0.994465 | − | 0.105073i | \(-0.966492\pi\) |
0.588228 | + | 0.808695i | \(0.299826\pi\) | |||||||
\(578\) | −4423.53 | −0.318330 | ||||||||
\(579\) | 1620.19 | − | 6391.49i | 0.116292 | − | 0.458758i | ||||
\(580\) | 2692.45 | − | 4663.46i | 0.192755 | − | 0.333862i | ||||
\(581\) | 49.3936 | + | 3786.50i | 0.00352701 | + | 0.270380i | ||||
\(582\) | −12559.2 | − | 12223.7i | −0.894491 | − | 0.870596i | ||||
\(583\) | −8668.11 | + | 15013.6i | −0.615774 | + | 1.06655i | ||||
\(584\) | −3336.75 | + | 5779.42i | −0.236431 | + | 0.409510i | ||||
\(585\) | 10356.2 | + | 5610.98i | 0.731926 | + | 0.396557i | ||||
\(586\) | −14913.4 | − | 25830.7i | −1.05131 | − | 1.82092i | ||||
\(587\) | −2580.61 | − | 4469.74i | −0.181453 | − | 0.314286i | 0.760922 | − | 0.648843i | \(-0.224747\pi\) |
−0.942376 | + | 0.334557i | \(0.891413\pi\) | |||||||
\(588\) | −30552.6 | + | 9498.73i | −2.14280 | + | 0.666192i | ||||
\(589\) | −9363.42 | + | 16217.9i | −0.655030 | + | 1.13455i | ||||
\(590\) | −10141.7 | −0.707673 | ||||||||
\(591\) | 2941.14 | + | 2862.57i | 0.204708 | + | 0.199239i | ||||
\(592\) | 11959.8 | 0.830311 | ||||||||
\(593\) | −8750.90 | − | 15157.0i | −0.605998 | − | 1.04962i | −0.991893 | − | 0.127076i | \(-0.959441\pi\) |
0.385895 | − | 0.922543i | \(-0.373893\pi\) | |||||||
\(594\) | 8738.11 | + | 28008.7i | 0.603584 | + | 1.93470i | ||||
\(595\) | 8278.60 | − | 4924.73i | 0.570402 | − | 0.339318i | ||||
\(596\) | −14695.5 | − | 25453.3i | −1.00998 | − | 1.74934i | ||||
\(597\) | −27361.7 | + | 7730.01i | −1.87578 | + | 0.529930i | ||||
\(598\) | −6843.34 | − | 11853.0i | −0.467969 | − | 0.810545i | ||||
\(599\) | 8401.61 | + | 14552.0i | 0.573089 | + | 0.992619i | 0.996246 | + | 0.0865631i | \(0.0275884\pi\) |
−0.423157 | + | 0.906056i | \(0.639078\pi\) | |||||||
\(600\) | −14764.0 | − | 14369.6i | −1.00456 | − | 0.977727i | ||||
\(601\) | −6448.81 | − | 11169.7i | −0.437692 | − | 0.758104i | 0.559819 | − | 0.828615i | \(-0.310870\pi\) |
−0.997511 | + | 0.0705106i | \(0.977537\pi\) | |||||||
\(602\) | 38878.4 | + | 21775.3i | 2.63217 | + | 1.47424i | ||||
\(603\) | −19289.3 | + | 11844.3i | −1.30269 | + | 0.799892i | ||||
\(604\) | −3418.08 | − | 5920.29i | −0.230264 | − | 0.398829i | ||||
\(605\) | 2423.21 | 0.162839 | ||||||||
\(606\) | 6123.37 | − | 1729.92i | 0.410470 | − | 0.115963i | ||||
\(607\) | 17809.6 | 1.19089 | 0.595445 | − | 0.803396i | \(-0.296976\pi\) | ||||
0.595445 | + | 0.803396i | \(0.296976\pi\) | |||||||
\(608\) | −8350.95 | + | 14464.3i | −0.557032 | + | 0.964808i | ||||
\(609\) | 2903.64 | − | 3062.25i | 0.193204 | − | 0.203758i | ||||
\(610\) | −2683.75 | − | 4648.39i | −0.178134 | − | 0.308537i | ||||
\(611\) | −570.272 | − | 987.740i | −0.0377590 | − | 0.0654005i | ||||
\(612\) | −997.658 | − | 36840.6i | −0.0658953 | − | 2.43332i | ||||
\(613\) | 1507.76 | − | 2611.52i | 0.0993439 | − | 0.172069i | −0.812069 | − | 0.583561i | \(-0.801659\pi\) |
0.911413 | + | 0.411492i | \(0.134992\pi\) | |||||||
\(614\) | 933.326 | − | 1616.57i | 0.0613452 | − | 0.106253i | ||||
\(615\) | 7434.43 | − | 2100.31i | 0.487456 | − | 0.137712i | ||||
\(616\) | 33629.2 | + | 18835.3i | 2.19961 | + | 1.23197i | ||||
\(617\) | −9570.31 | + | 16576.3i | −0.624451 | + | 1.08158i | 0.364196 | + | 0.931322i | \(0.381344\pi\) |
−0.988647 | + | 0.150258i | \(0.951989\pi\) | |||||||
\(618\) | 10351.6 | − | 2924.45i | 0.673792 | − | 0.190354i | ||||
\(619\) | 17605.8 | 1.14319 | 0.571597 | − | 0.820535i | \(-0.306324\pi\) | ||||
0.571597 | + | 0.820535i | \(0.306324\pi\) | |||||||
\(620\) | 12288.2 | − | 21283.7i | 0.795976 | − | 1.37867i | ||||
\(621\) | 4006.17 | − | 4345.52i | 0.258876 | − | 0.280805i | ||||
\(622\) | −48818.3 | −3.14700 | ||||||||
\(623\) | 209.131 | + | 16032.0i | 0.0134489 | + | 1.03099i | ||||
\(624\) | 9335.75 | − | 36828.6i | 0.598925 | − | 2.36270i | ||||
\(625\) | 267.516 | 0.0171210 | ||||||||
\(626\) | −22134.6 | − | 38338.2i | −1.41322 | − | 2.44777i | ||||
\(627\) | −4904.50 | + | 19347.7i | −0.312387 | + | 1.23234i | ||||
\(628\) | −14286.8 | + | 24745.4i | −0.907809 | + | 1.57237i | ||||
\(629\) | −7931.46 | −0.502779 | ||||||||
\(630\) | 9310.88 | + | 14729.2i | 0.588816 | + | 0.931466i | ||||
\(631\) | −8362.46 | −0.527582 | −0.263791 | − | 0.964580i | \(-0.584973\pi\) | ||||
−0.263791 | + | 0.964580i | \(0.584973\pi\) | |||||||
\(632\) | 15725.4 | − | 27237.2i | 0.989751 | − | 1.71430i | ||||
\(633\) | 8359.17 | − | 2361.56i | 0.524877 | − | 0.148284i | ||||
\(634\) | −14128.3 | − | 24470.9i | −0.885026 | − | 1.53291i | ||||
\(635\) | −17236.1 | −1.07716 | ||||||||
\(636\) | 28229.1 | + | 27475.0i | 1.76000 | + | 1.71298i | ||||
\(637\) | 21867.0 | − | 570.592i | 1.36013 | − | 0.0354908i | ||||
\(638\) | −9170.65 | −0.569075 | ||||||||
\(639\) | −687.521 | − | 25388.1i | −0.0425633 | − | 1.57174i | ||||
\(640\) | −5021.87 | + | 8698.14i | −0.310167 | + | 0.537225i | ||||
\(641\) | −26848.3 | −1.65436 | −0.827178 | − | 0.561940i | \(-0.810055\pi\) | ||||
−0.827178 | + | 0.561940i | \(0.810055\pi\) | |||||||
\(642\) | 32457.4 | + | 31590.4i | 1.99531 | + | 1.94201i | ||||
\(643\) | −7757.71 | + | 13436.7i | −0.475792 | + | 0.824096i | −0.999615 | − | 0.0277312i | \(-0.991172\pi\) |
0.523824 | + | 0.851827i | \(0.324505\pi\) | |||||||
\(644\) | −182.693 | − | 14005.2i | −0.0111788 | − | 0.856961i | ||||
\(645\) | 4125.09 | − | 16273.0i | 0.251822 | − | 0.993412i | ||||
\(646\) | 18122.1 | − | 31388.3i | 1.10372 | − | 1.91170i | ||||
\(647\) | 10083.1 | − | 17464.4i | 0.612685 | − | 1.06120i | −0.378101 | − | 0.925765i | \(-0.623423\pi\) |
0.990786 | − | 0.135438i | \(-0.0432440\pi\) | |||||||
\(648\) | 36904.2 | − | 2000.23i | 2.23724 | − | 0.121260i | ||||
\(649\) | 5973.70 | + | 10346.8i | 0.361307 | + | 0.625802i | ||||
\(650\) | 12704.2 | + | 22004.4i | 0.766616 | + | 1.32782i | ||||
\(651\) | 13252.0 | − | 13975.9i | 0.797830 | − | 0.841413i | ||||
\(652\) | −8265.82 | + | 14316.8i | −0.496494 | + | 0.859954i | ||||
\(653\) | 8801.94 | 0.527483 | 0.263742 | − | 0.964593i | \(-0.415043\pi\) | ||||
0.263742 | + | 0.964593i | \(0.415043\pi\) | |||||||
\(654\) | −3888.63 | + | 15340.2i | −0.232504 | + | 0.917203i | ||||
\(655\) | −2839.64 | −0.169395 | ||||||||
\(656\) | −12459.7 | − | 21580.9i | −0.741571 | − | 1.28444i | ||||
\(657\) | 3124.94 | + | 1693.09i | 0.185564 | + | 0.100538i | ||||
\(658\) | −22.0088 | − | 1687.19i | −0.00130394 | − | 0.0999595i | ||||
\(659\) | −7010.77 | − | 12143.0i | −0.414417 | − | 0.717791i | 0.580950 | − | 0.813939i | \(-0.302681\pi\) |
−0.995367 | + | 0.0961482i | \(0.969348\pi\) | |||||||
\(660\) | 6436.47 | − | 25391.2i | 0.379605 | − | 1.49750i | ||||
\(661\) | −9586.86 | − | 16604.9i | −0.564123 | − | 0.977090i | −0.997131 | − | 0.0756998i | \(-0.975881\pi\) |
0.433007 | − | 0.901390i | \(-0.357452\pi\) | |||||||
\(662\) | −5976.15 | − | 10351.0i | −0.350861 | − | 0.607708i | ||||
\(663\) | −6191.26 | + | 24423.9i | −0.362668 | + | 1.43069i | ||||
\(664\) | −5183.03 | − | 8977.27i | −0.302922 | − | 0.524677i | ||||
\(665\) | 154.621 | + | 11853.2i | 0.00901645 | + | 0.691199i | ||||
\(666\) | −388.404 | − | 14342.6i | −0.0225981 | − | 0.834481i | ||||
\(667\) | 923.691 | + | 1599.88i | 0.0536214 | + | 0.0928749i | ||||
\(668\) | 53492.5 | 3.09833 | ||||||||
\(669\) | 3460.03 | − | 13649.5i | 0.199959 | − | 0.788818i | ||||
\(670\) | 29214.3 | 1.68455 | ||||||||
\(671\) | −3161.58 | + | 5476.02i | −0.181895 | + | 0.315051i | ||||
\(672\) | 11819.1 | − | 12464.7i | 0.678468 | − | 0.715530i | ||||
\(673\) | 4962.05 | + | 8594.52i | 0.284209 | + | 0.492265i | 0.972417 | − | 0.233249i | \(-0.0749356\pi\) |
−0.688208 | + | 0.725514i | \(0.741602\pi\) | |||||||
\(674\) | 14648.8 | + | 25372.4i | 0.837166 | + | 1.45001i | ||||
\(675\) | −7437.19 | + | 8067.18i | −0.424085 | + | 0.460009i | ||||
\(676\) | −16785.9 | + | 29074.0i | −0.955046 | + | 1.65419i | ||||
\(677\) | 1575.95 | − | 2729.62i | 0.0894660 | − | 0.154960i | −0.817820 | − | 0.575475i | \(-0.804817\pi\) |
0.907286 | + | 0.420515i | \(0.138151\pi\) | |||||||
\(678\) | −4876.90 | + | 19238.9i | −0.276248 | + | 1.08977i | ||||
\(679\) | 159.938 | + | 12260.8i | 0.00903957 | + | 0.692971i | ||||
\(680\) | −13184.2 | + | 22835.7i | −0.743517 | + | 1.28781i | ||||
\(681\) | 1105.72 | + | 1076.18i | 0.0622193 | + | 0.0605572i | ||||
\(682\) | −41854.3 | −2.34997 | ||||||||
\(683\) | −99.2937 | + | 171.982i | −0.00556276 | + | 0.00963499i | −0.868793 | − | 0.495175i | \(-0.835104\pi\) |
0.863231 | + | 0.504810i | \(0.168437\pi\) | |||||||
\(684\) | 39876.8 | + | 21605.2i | 2.22914 | + | 1.20774i | ||||
\(685\) | −7894.19 | −0.440323 | ||||||||
\(686\) | 28637.2 | + | 15071.8i | 1.59384 | + | 0.838840i | ||||
\(687\) | −11246.5 | − | 10946.1i | −0.624574 | − | 0.607889i | ||||
\(688\) | −54151.3 | −3.00073 | ||||||||
\(689\) | −13465.9 | − | 23323.6i | −0.744572 | − | 1.28964i | ||||
\(690\) | −7340.89 | + | 2073.89i | −0.405019 | + | 0.114423i | ||||
\(691\) | −10880.0 | + | 18844.8i | −0.598981 | + | 1.03747i | 0.393991 | + | 0.919114i | \(0.371094\pi\) |
−0.992972 | + | 0.118351i | \(0.962239\pi\) | |||||||
\(692\) | 30637.3 | 1.68303 | ||||||||
\(693\) | 9542.64 | − | 18175.0i | 0.523081 | − | 0.996262i | ||||
\(694\) | 8695.82 | 0.475632 | ||||||||
\(695\) | 4409.61 | − | 7637.67i | 0.240671 | − | 0.416854i | ||||
\(696\) | −2838.52 | + | 11197.7i | −0.154589 | + | 0.609838i | ||||
\(697\) | 8263.02 | + | 14312.0i | 0.449045 | + | 0.777768i | ||||
\(698\) | 11188.1 | 0.606701 | ||||||||
\(699\) | −385.179 | + | 1519.49i | −0.0208424 | + | 0.0822211i | ||||
\(700\) | 339.158 | + | 25999.8i | 0.0183128 | + | 1.40386i | ||||
\(701\) | 1686.04 | 0.0908427 | 0.0454213 | − | 0.998968i | \(-0.485537\pi\) | ||||
0.0454213 | + | 0.998968i | \(0.485537\pi\) | |||||||
\(702\) | −44469.3 | − | 9999.72i | −2.39086 | − | 0.537629i | ||||
\(703\) | 4880.33 | − | 8452.99i | 0.261828 | − | 0.453500i | ||||
\(704\) | 324.970 | 0.0173974 | ||||||||
\(705\) | −611.734 | + | 172.822i | −0.0326797 | + | 0.00923241i | ||||
\(706\) | −27118.4 | + | 46970.5i | −1.44563 | + | 2.50391i | ||||
\(707\) | −3884.17 | − | 2175.48i | −0.206619 | − | 0.115724i | ||||
\(708\) | 26125.1 | − | 7380.64i | 1.38678 | − | 0.391781i | ||||
\(709\) | 4991.21 | − | 8645.04i | 0.264385 | − | 0.457928i | −0.703017 | − | 0.711173i | \(-0.748164\pi\) |
0.967402 | + | 0.253244i | \(0.0814977\pi\) | |||||||
\(710\) | −16389.5 | + | 28387.4i | −0.866319 | + | 1.50051i | ||||
\(711\) | −14727.2 | − | 7979.17i | −0.776810 | − | 0.420875i | ||||
\(712\) | −21944.8 | − | 38009.5i | −1.15508 | − | 2.00066i | ||||
\(713\) | 4215.67 | + | 7301.75i | 0.221428 | + | 0.383524i | ||||
\(714\) | −25648.1 | + | 27049.2i | −1.34434 | + | 1.41777i | ||||
\(715\) | −8954.27 | + | 15509.2i | −0.468350 | + | 0.811207i | ||||
\(716\) | 54815.4 | 2.86110 | ||||||||
\(717\) | 10406.0 | − | 2939.82i | 0.542008 | − | 0.153124i | ||||
\(718\) | −16797.5 | −0.873086 | ||||||||
\(719\) | 13757.6 | + | 23828.8i | 0.713591 | + | 1.23598i | 0.963501 | + | 0.267706i | \(0.0862656\pi\) |
−0.249910 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(720\) | −18618.4 | − | 10087.4i | −0.963703 | − | 0.522133i | ||||
\(721\) | −6566.24 | − | 3677.67i | −0.339167 | − | 0.189963i | ||||
\(722\) | 4830.62 | + | 8366.88i | 0.248999 | + | 0.431279i | ||||
\(723\) | 12917.7 | + | 12572.7i | 0.664475 | + | 0.646725i | ||||
\(724\) | −3754.30 | − | 6502.63i | −0.192717 | − | 0.333796i | ||||
\(725\) | −1714.77 | − | 2970.07i | −0.0878414 | − | 0.152146i | ||||
\(726\) | −9023.97 | + | 2549.38i | −0.461310 | + | 0.130325i | ||||
\(727\) | −14734.5 | − | 25521.0i | −0.751683 | − | 1.30195i | −0.947006 | − | 0.321215i | \(-0.895909\pi\) |
0.195323 | − | 0.980739i | \(-0.437424\pi\) | |||||||
\(728\) | −51461.9 | + | 30613.4i | −2.61992 | + | 1.55853i | ||||
\(729\) | −1596.92 | − | 19618.1i | −0.0811322 | − | 0.996703i | ||||
\(730\) | −2293.55 | − | 3972.54i | −0.116285 | − | 0.201411i | ||||
\(731\) | 35912.0 | 1.81703 | ||||||||
\(732\) | 10296.2 | + | 10021.2i | 0.519890 | + | 0.506001i | ||||
\(733\) | 9512.71 | 0.479345 | 0.239673 | − | 0.970854i | \(-0.422960\pi\) | ||||
0.239673 | + | 0.970854i | \(0.422960\pi\) | |||||||
\(734\) | 4291.28 | − | 7432.71i | 0.215796 | − | 0.373769i | ||||
\(735\) | 2686.44 | − | 11892.0i | 0.134817 | − | 0.596791i | ||||
\(736\) | 3759.82 | + | 6512.21i | 0.188300 | + | 0.326146i | ||||
\(737\) | −17207.9 | − | 29804.9i | −0.860055 | − | 1.48966i | ||||
\(738\) | −25475.9 | + | 15643.0i | −1.27071 | + | 0.780253i | ||||
\(739\) | −1612.42 | + | 2792.80i | −0.0802624 | + | 0.139019i | −0.903363 | − | 0.428878i | \(-0.858909\pi\) |
0.823100 | + | 0.567896i | \(0.192242\pi\) | |||||||
\(740\) | −6404.76 | + | 11093.4i | −0.318167 | + | 0.551081i | ||||
\(741\) | −22220.3 | − | 21626.7i | −1.10160 | − | 1.07217i | ||||
\(742\) | −519.696 | − | 39839.7i | −0.0257124 | − | 1.97111i | ||||
\(743\) | −8219.64 | + | 14236.8i | −0.405854 | + | 0.702960i | −0.994420 | − | 0.105489i | \(-0.966359\pi\) |
0.588566 | + | 0.808449i | \(0.299693\pi\) | |||||||
\(744\) | −12954.8 | + | 51105.5i | −0.638370 | + | 2.51830i | ||||
\(745\) | 11199.3 | 0.550753 | ||||||||
\(746\) | 12330.7 | − | 21357.3i | 0.605171 | − | 1.04819i | ||||
\(747\) | −4704.57 | + | 2888.75i | −0.230430 | + | 0.141491i | ||||
\(748\) | 56034.3 | 2.73906 | ||||||||
\(749\) | −413.338 | − | 31686.4i | −0.0201643 | − | 1.54579i | ||||
\(750\) | 35409.3 | − | 10003.6i | 1.72395 | − | 0.487037i | ||||
\(751\) | −8160.99 | −0.396536 | −0.198268 | − | 0.980148i | \(-0.563532\pi\) | ||||
−0.198268 | + | 0.980148i | \(0.563532\pi\) | |||||||
\(752\) | 1025.23 | + | 1775.76i | 0.0497160 | + | 0.0861107i | ||||
\(753\) | −19310.1 | − | 18794.3i | −0.934528 | − | 0.909563i | ||||
\(754\) | 7123.30 | − | 12337.9i | 0.344052 | − | 0.595916i | ||||
\(755\) | 2604.89 | 0.125565 | ||||||||
\(756\) | −34704.0 | − | 31166.4i | −1.66954 | − | 1.49935i | ||||
\(757\) | 18136.9 | 0.870801 | 0.435401 | − | 0.900237i | \(-0.356607\pi\) | ||||
0.435401 | + | 0.900237i | \(0.356607\pi\) | |||||||
\(758\) | −10205.7 | + | 17676.9i | −0.489036 | + | 0.847035i | ||||
\(759\) | 6439.78 | + | 6267.74i | 0.307970 | + | 0.299743i | ||||
\(760\) | −16224.8 | − | 28102.3i | −0.774391 | − | 1.34128i | ||||
\(761\) | 17339.3 | 0.825950 | 0.412975 | − | 0.910742i | \(-0.364490\pi\) | ||||
0.412975 | + | 0.910742i | \(0.364490\pi\) | |||||||
\(762\) | 64186.8 | − | 18133.5i | 3.05150 | − | 0.862084i | ||||
\(763\) | 9515.85 | − | 5660.74i | 0.451503 | − | 0.268588i | ||||
\(764\) | −37448.5 | −1.77335 | ||||||||
\(765\) | 12347.3 | + | 6689.76i | 0.583553 | + | 0.316168i | ||||
\(766\) | −6778.29 | + | 11740.3i | −0.319725 | + | 0.553780i | ||||
\(767\) | −18560.3 | −0.873759 | ||||||||
\(768\) | 9469.44 | − | 37356.0i | 0.444920 | − | 1.75517i | ||||
\(769\) | 17102.1 | − | 29621.7i | 0.801974 | − | 1.38906i | −0.116341 | − | 0.993209i | \(-0.537116\pi\) |
0.918315 | − | 0.395851i | \(-0.129550\pi\) | |||||||
\(770\) | −22769.8 | + | 13545.2i | −1.06567 | + | 0.633940i | ||||
\(771\) | −644.485 | − | 627.268i | −0.0301045 | − | 0.0293003i | ||||
\(772\) | 11389.9 | − | 19728.0i | 0.531001 | − | 0.919721i | ||||
\(773\) | 14432.8 | − | 24998.4i | 0.671556 | − | 1.16317i | −0.305907 | − | 0.952061i | \(-0.598960\pi\) |
0.977463 | − | 0.211108i | \(-0.0677070\pi\) | |||||||
\(774\) | 1758.61 | + | 64940.2i | 0.0816690 | + | 3.01580i | ||||
\(775\) | −7826.11 | − | 13555.2i | −0.362738 | − | 0.628281i | ||||
\(776\) | −16782.8 | − | 29068.7i | −0.776376 | − | 1.34472i | ||||
\(777\) | −6907.12 | + | 7284.43i | −0.318908 | + | 0.336329i | ||||
\(778\) | 17384.6 | − | 30111.0i | 0.801115 | − | 1.38757i | ||||
\(779\) | −20337.4 | −0.935381 | ||||||||
\(780\) | 29161.0 | + | 28382.0i | 1.33863 | + | 1.30287i | ||||
\(781\) | 38615.2 | 1.76922 | ||||||||
\(782\) | −8159.05 | − | 14131.9i | −0.373104 | − | 0.646234i | ||||
\(783\) | 6002.31 | + | 1349.73i | 0.273953 | + | 0.0616032i | ||||
\(784\) | −39312.4 | + | 1025.81i | −1.79084 | + | 0.0467296i | ||||
\(785\) | −5443.92 | − | 9429.14i | −0.247518 | − | 0.428714i | ||||
\(786\) | 10574.7 | − | 2987.48i | 0.479882 | − | 0.135572i | ||||
\(787\) | −4734.23 | − | 8199.93i | −0.214431 | − | 0.371405i | 0.738666 | − | 0.674072i | \(-0.235456\pi\) |
−0.953096 | + | 0.302667i | \(0.902123\pi\) | |||||||
\(788\) | 7089.67 | + | 12279.7i | 0.320506 | + | 0.555133i | ||||
\(789\) | −11351.7 | − | 11048.4i | −0.512205 | − | 0.498522i | ||||
\(790\) | 10809.0 | + | 18721.7i | 0.486794 | + | 0.843152i | ||||
\(791\) | 11934.2 | − | 7099.39i | 0.536451 | − | 0.319121i | ||||
\(792\) | 1521.17 | + | 56172.2i | 0.0682479 | + | 2.52019i | ||||
\(793\) | −4911.52 | − | 8507.00i | −0.219941 | − | 0.380949i | ||||
\(794\) | −20264.8 | −0.905759 | ||||||||
\(795\) | −14444.9 | + | 4080.86i | −0.644414 | + | 0.182055i | ||||
\(796\) | −98229.9 | −4.37395 | ||||||||
\(797\) | 4604.83 | − | 7975.81i | 0.204657 | − | 0.354476i | −0.745366 | − | 0.666655i | \(-0.767725\pi\) |
0.950023 | + | 0.312179i | \(0.101059\pi\) | |||||||
\(798\) | −13046.1 | − | 43978.3i | −0.578732 | − | 1.95089i | ||||
\(799\) | −679.913 | − | 1177.64i | −0.0301046 | − | 0.0521427i | ||||
\(800\) | −6979.87 | − | 12089.5i | −0.308470 | − | 0.534285i | ||||
\(801\) | −19919.0 | + | 12230.9i | −0.878657 | + | 0.539523i | ||||
\(802\) | −20338.1 | + | 35226.6i | −0.895464 | + | 1.55099i | ||||
\(803\) | −2701.91 | + | 4679.84i | −0.118740 | + | 0.205664i | ||||
\(804\) | −75256.0 | + | 21260.7i | −3.30109 | + | 0.932596i | ||||
\(805\) | 4656.47 | + | 2608.03i | 0.203874 | + | 0.114188i | ||||
\(806\) | 32510.3 | − | 56309.5i | 1.42075 | − | 2.46081i | ||||
\(807\) | −15643.7 | + | 4419.53i | −0.682385 | + | 0.192782i | ||||
\(808\) | 12186.6 | 0.530600 | ||||||||
\(809\) | 16520.1 | − | 28613.7i | 0.717944 | − | 1.24352i | −0.243869 | − | 0.969808i | \(-0.578417\pi\) |
0.961813 | − | 0.273708i | \(-0.0882500\pi\) | |||||||
\(810\) | −11492.5 | + | 22655.4i | −0.498527 | + | 0.982754i | ||||
\(811\) | 2036.06 | 0.0881575 | 0.0440788 | − | 0.999028i | \(-0.485965\pi\) | ||||
0.0440788 | + | 0.999028i | \(0.485965\pi\) | |||||||
\(812\) | 12530.0 | − | 7453.77i | 0.541522 | − | 0.322138i | ||||
\(813\) | −5930.16 | + | 23393.9i | −0.255818 | + | 1.00917i | ||||
\(814\) | 21815.0 | 0.939330 | ||||||||
\(815\) | −3149.66 | − | 5455.37i | −0.135371 | − | 0.234470i | ||||
\(816\) | 11130.6 | − | 43909.3i | 0.477513 | − | 1.88374i | ||||
\(817\) | −22097.1 | + | 38273.3i | −0.946242 | + | 1.63894i | ||||
\(818\) | −15644.0 | −0.668681 | ||||||||
\(819\) | 17039.8 | + | 26955.8i | 0.727007 | + | 1.15007i | ||||
\(820\) | 26690.0 | 1.13665 | ||||||||
\(821\) | −21807.8 | + | 37772.2i | −0.927036 | + | 1.60567i | −0.138781 | + | 0.990323i | \(0.544318\pi\) |
−0.788254 | + | 0.615350i | \(0.789015\pi\) | |||||||
\(822\) | 29397.7 | − | 8305.20i | 1.24740 | − | 0.352405i | ||||
\(823\) | 18536.5 | + | 32106.1i | 0.785105 | + | 1.35984i | 0.928936 | + | 0.370239i | \(0.120724\pi\) |
−0.143832 | + | 0.989602i | \(0.545942\pi\) | |||||||
\(824\) | 20601.7 | 0.870986 | ||||||||
\(825\) | −11955.0 | − | 11635.7i | −0.504510 | − | 0.491032i | ||||
\(826\) | −23956.6 | − | 13417.8i | −1.00915 | − | 0.565211i | ||||
\(827\) | −33864.7 | −1.42393 | −0.711965 | − | 0.702215i | \(-0.752194\pi\) | ||||
−0.711965 | + | 0.702215i | \(0.752194\pi\) | |||||||
\(828\) | 17400.9 | − | 10684.7i | 0.730341 | − | 0.448452i | ||||
\(829\) | −19513.9 | + | 33799.1i | −0.817548 | + | 1.41603i | 0.0899363 | + | 0.995948i | \(0.471334\pi\) |
−0.907484 | + | 0.420087i | \(0.862000\pi\) | |||||||
\(830\) | 7125.21 | 0.297975 | ||||||||
\(831\) | 8691.56 | + | 8459.37i | 0.362824 | + | 0.353132i | ||||
\(832\) | −252.420 | + | 437.205i | −0.0105181 | + | 0.0182180i | ||||
\(833\) | 26071.2 | − | 680.294i | 1.08441 | − | 0.0282963i | ||||
\(834\) | −8385.93 | + | 33081.6i | −0.348179 | + | 1.37353i | ||||
\(835\) | −10191.6 | + | 17652.3i | −0.422387 | + | 0.731596i | ||||
\(836\) | −34478.6 | + | 59718.7i | −1.42640 | + | 2.47059i | ||||
\(837\) | 27394.2 | + | 6160.07i | 1.13128 | + | 0.254389i | ||||
\(838\) | 9910.93 | + | 17166.2i | 0.408553 | + | 0.707635i | ||||
\(839\) | −12277.2 | − | 21264.7i | −0.505192 | − | 0.875019i | −0.999982 | − | 0.00600582i | \(-0.998088\pi\) |
0.494790 | − | 0.869013i | \(-0.335245\pi\) | |||||||
\(840\) | 9491.36 | + | 31995.2i | 0.389861 | + | 1.31421i | ||||
\(841\) | 11233.0 | − | 19456.2i | 0.460577 | − | 0.797743i | ||||
\(842\) | −29010.8 | −1.18738 | ||||||||
\(843\) | 8864.33 | − | 34968.9i | 0.362163 | − | 1.42870i | ||||
\(844\) | 30009.8 | 1.22391 | ||||||||
\(845\) | −6396.20 | − | 11078.5i | −0.260397 | − | 0.451022i | ||||
\(846\) | 2096.26 | − | 1287.17i | 0.0851900 | − | 0.0523093i | ||||
\(847\) | 5724.08 | + | 3205.99i | 0.232210 | + | 0.130058i | ||||
\(848\) | 24209.0 | + | 41931.2i | 0.980353 | + | 1.69802i | ||||
\(849\) | −4963.52 | + | 19580.6i | −0.200645 | + | 0.791524i | ||||
\(850\) | 15146.7 | + | 26234.9i | 0.611211 | + | 1.05865i | ||||
\(851\) | −2197.26 | − | 3805.77i | −0.0885089 | − | 0.153302i | ||||
\(852\) | 21560.4 | − | 85053.5i | 0.866956 | − | 3.42005i | ||||
\(853\) | 14782.4 | + | 25603.8i | 0.593363 | + | 1.02774i | 0.993776 | + | 0.111400i | \(0.0355336\pi\) |
−0.400412 | + | 0.916335i | \(0.631133\pi\) | |||||||
\(854\) | −189.552 | − | 14531.0i | −0.00759525 | − | 0.582250i | ||||
\(855\) | −14727.1 | + | 9042.89i | −0.589071 | + | 0.361708i | ||||
\(856\) | 43372.9 | + | 75124.0i | 1.73184 | + | 2.99963i | ||||
\(857\) | 37084.4 | 1.47816 | 0.739078 | − | 0.673619i | \(-0.235261\pi\) | ||||
0.739078 | + | 0.673619i | \(0.235261\pi\) | |||||||
\(858\) | 17028.7 | − | 67176.4i | 0.677563 | − | 2.67292i | ||||
\(859\) | 36849.0 | 1.46365 | 0.731823 | − | 0.681495i | \(-0.238670\pi\) | ||||
0.731823 | + | 0.681495i | \(0.238670\pi\) | |||||||
\(860\) | 28999.4 | − | 50228.4i | 1.14985 | − | 1.99160i | ||||
\(861\) | 20340.3 | + | 4874.65i | 0.805104 | + | 0.192947i | ||||
\(862\) | 20526.0 | + | 35552.2i | 0.811044 | + | 1.40477i | ||||
\(863\) | 2623.49 | + | 4544.03i | 0.103482 | + | 0.179236i | 0.913117 | − | 0.407698i | \(-0.133668\pi\) |
−0.809635 | + | 0.586934i | \(0.800335\pi\) | |||||||
\(864\) | 24432.0 | + | 5493.98i | 0.962031 | + | 0.216330i | ||||
\(865\) | −5837.11 | + | 10110.2i | −0.229442 | + | 0.397406i | ||||
\(866\) | 1284.16 | − | 2224.23i | 0.0503897 | − | 0.0872775i | ||||
\(867\) | −1108.68 | + | 4373.65i | −0.0434289 | + | 0.171323i | ||||
\(868\) | 57186.0 | − | 34018.5i | 2.23620 | − | 1.33026i | ||||
\(869\) | 12733.5 | − | 22055.1i | 0.497071 | − | 0.860953i | ||||
\(870\) | −5690.11 | − | 5538.11i | −0.221739 | − | 0.215815i | ||||
\(871\) | 53464.9 | 2.07990 | ||||||||
\(872\) | −15154.6 | + | 26248.6i | −0.588533 | + | 1.01937i | ||||
\(873\) | −15233.5 | + | 9353.87i | −0.590581 | + | 0.362635i | ||||
\(874\) | 20081.5 | 0.777192 | ||||||||
\(875\) | −22460.8 | − | 12580.0i | −0.867788 | − | 0.486037i | ||||
\(876\) | 8799.20 | + | 8564.14i | 0.339381 | + | 0.330315i | ||||
\(877\) | 11314.5 | 0.435647 | 0.217824 | − | 0.975988i | \(-0.430104\pi\) | ||||
0.217824 | + | 0.975988i | \(0.430104\pi\) | |||||||
\(878\) | −18917.4 | − | 32765.9i | −0.727143 | − | 1.25945i | ||||
\(879\) | −29277.2 | + | 8271.16i | −1.12343 | + | 0.317382i | ||||
\(880\) | 16098.0 | − | 27882.5i | 0.616662 | − | 1.06809i | ||||
\(881\) | 35730.9 | 1.36641 | 0.683203 | − | 0.730229i | \(-0.260586\pi\) | ||||
0.683203 | + | 0.730229i | \(0.260586\pi\) | |||||||
\(882\) | 2506.89 | + | 47111.6i | 0.0957045 | + | 1.79856i | ||||
\(883\) | −31697.4 | −1.20804 | −0.604021 | − | 0.796968i | \(-0.706436\pi\) | ||||
−0.604021 | + | 0.796968i | \(0.706436\pi\) | |||||||
\(884\) | −43524.6 | + | 75386.8i | −1.65598 | + | 2.86825i | ||||
\(885\) | −2541.85 | + | 10027.3i | −0.0965461 | + | 0.380865i | ||||
\(886\) | −38976.2 | − | 67508.7i | −1.47791 | − | 2.55982i | ||||
\(887\) | 8754.31 | 0.331388 | 0.165694 | − | 0.986177i | \(-0.447014\pi\) | ||||
0.165694 | + | 0.986177i | \(0.447014\pi\) | |||||||
\(888\) | 6752.23 | − | 26636.9i | 0.255169 | − | 1.00662i | ||||
\(889\) | −40714.9 | − | 22803.9i | −1.53603 | − | 0.860313i | ||||
\(890\) | 30167.9 | 1.13622 | ||||||||
\(891\) | 29882.9 | − | 1619.67i | 1.12358 | − | 0.0608990i | ||||
\(892\) | 24324.0 | − | 42130.5i | 0.913037 | − | 1.58143i | ||||
\(893\) | 1673.44 | 0.0627093 | ||||||||
\(894\) | −41705.9 | + | 11782.4i | −1.56024 | + | 0.440786i | ||||
\(895\) | −10443.6 | + | 18088.8i | −0.390046 | + | 0.675579i | ||||
\(896\) | −23370.5 | + | 13902.5i | −0.871377 | + | 0.518360i | ||||
\(897\) | −13434.5 | + | 3795.41i | −0.500073 | + | 0.141277i | ||||
\(898\) | 21572.9 | − | 37365.3i | 0.801666 | − | 1.38853i | ||||
\(899\) | −4388.12 | + | 7600.45i | −0.162794 | + | 0.281968i | ||||
\(900\) | −32303.6 | + | 19835.4i | −1.19643 | + | 0.734645i | ||||
\(901\) | −16054.9 | − | 27807.8i | −0.593635 | − | 1.02821i | ||||
\(902\) | −22726.9 | − | 39364.2i | −0.838939 | − | 1.45309i | ||||
\(903\) | 31274.0 | − | 32982.3i | 1.15253 | − | 1.21549i | ||||
\(904\) | −19006.1 | + | 32919.5i | −0.699262 | + | 1.21116i | ||||
\(905\) | 2861.12 | 0.105090 | ||||||||
\(906\) | −9700.53 | + | 2740.51i | −0.355716 | + | 0.100494i | ||||
\(907\) | −30737.3 | −1.12527 | −0.562633 | − | 0.826707i | \(-0.690211\pi\) | ||||
−0.562633 | + | 0.826707i | \(0.690211\pi\) | |||||||
\(908\) | 2665.36 | + | 4616.55i | 0.0974154 | + | 0.168728i | ||||
\(909\) | −175.695 | − | 6487.89i | −0.00641082 | − | 0.236733i | ||||
\(910\) | −536.852 | − | 41154.9i | −0.0195566 | − | 1.49920i | ||||
\(911\) | 22221.2 | + | 38488.3i | 0.808146 | + | 1.39975i | 0.914146 | + | 0.405385i | \(0.132862\pi\) |
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(912\) | 39947.6 | + | 38880.5i | 1.45044 | + | 1.41169i | ||||
\(913\) | −4196.92 | − | 7269.27i | −0.152133 | − | 0.263502i | ||||
\(914\) | 38010.6 | + | 65836.4i | 1.37558 | + | 2.38258i | ||||
\(915\) | −5268.61 | + | 1488.44i | −0.190355 | + | 0.0537775i | ||||
\(916\) | −27110.0 | − | 46955.9i | −0.977882 | − | 1.69374i | ||||
\(917\) | −6707.74 | − | 3756.92i | −0.241559 | − | 0.135294i | ||||
\(918\) | −53019.0 | − | 11922.3i | −1.90620 | − | 0.428642i | ||||
\(919\) | −19611.8 | − | 33968.7i | −0.703954 | − | 1.21928i | −0.967068 | − | 0.254520i | \(-0.918083\pi\) |
0.263113 | − | 0.964765i | \(-0.415251\pi\) | |||||||
\(920\) | −14609.7 | −0.523553 | ||||||||
\(921\) | −1364.42 | − | 1327.97i | −0.0488154 | − | 0.0475114i | ||||
\(922\) | 61929.5 | 2.21208 | ||||||||
\(923\) | −29994.3 | + | 51951.7i | −1.06964 | + | 1.85267i | ||||
\(924\) | 48797.5 | − | 51463.1i | 1.73736 | − | 1.83226i | ||||
\(925\) | 4079.07 | + | 7065.16i | 0.144993 | + | 0.251136i | ||||
\(926\) | −38930.2 | − | 67429.0i | −1.38156 | − | 2.39293i | ||||
\(927\) | −297.014 | − | 10967.9i | −0.0105234 | − | 0.388599i | ||||
\(928\) | −3913.63 | + | 6778.61i | −0.138439 | + | 0.239783i | ||||
\(929\) | −18970.2 | + | 32857.3i | −0.669958 | + | 1.16040i | 0.307957 | + | 0.951400i | \(0.400355\pi\) |
−0.977915 | + | 0.209001i | \(0.932979\pi\) | |||||||
\(930\) | −25969.3 | − | 25275.6i | −0.915664 | − | 0.891203i | ||||
\(931\) | −15316.9 | + | 28204.0i | −0.539196 | + | 0.992857i | ||||
\(932\) | −2707.81 | + | 4690.07i | −0.0951688 | + | 0.164837i | ||||
\(933\) | −12235.5 | + | 48267.8i | −0.429338 | + | 1.69369i | ||||
\(934\) | 92936.5 | 3.25586 | ||||||||
\(935\) | −10675.8 | + | 18491.1i | −0.373408 | + | 0.646762i | ||||
\(936\) | −76753.9 | − | 41585.2i | −2.68032 | − | 1.45220i | ||||
\(937\) | 24646.9 | 0.859316 | 0.429658 | − | 0.902992i | \(-0.358634\pi\) | ||||
0.429658 | + | 0.902992i | \(0.358634\pi\) | |||||||
\(938\) | 69009.5 | + | 38651.4i | 2.40217 | + | 1.34543i | ||||
\(939\) | −43453.6 | + | 12276.1i | −1.51017 | + | 0.426642i | ||||
\(940\) | −2196.15 | −0.0762028 | ||||||||
\(941\) | 23340.3 | + | 40426.5i | 0.808577 | + | 1.40050i | 0.913849 | + | 0.406053i | \(0.133095\pi\) |
−0.105272 | + | 0.994443i | \(0.533571\pi\) | |||||||
\(942\) | 30193.0 | + | 29386.5i | 1.04431 | + | 1.01641i | ||||
\(943\) | −4578.22 | + | 7929.71i | −0.158099 | + | 0.273836i | ||||
\(944\) | 33367.7 | 1.15045 | ||||||||
\(945\) | 16896.7 | − | 5514.26i | 0.581639 | − | 0.189819i | ||||
\(946\) | −98773.6 | −3.39472 | ||||||||
\(947\) | 20872.4 | − | 36152.0i | 0.716220 | − | 1.24053i | −0.246267 | − | 0.969202i | \(-0.579204\pi\) |
0.962487 | − | 0.271328i | \(-0.0874627\pi\) | |||||||
\(948\) | −41468.8 | − | 40361.0i | −1.42072 | − | 1.38277i | ||||
\(949\) | −4197.41 | − | 7270.12i | −0.143576 | − | 0.248681i | ||||
\(950\) | −37280.0 | −1.27318 | ||||||||
\(951\) | −27736.0 | + | 7835.74i | −0.945743 | + | 0.267183i | ||||
\(952\) | −61355.9 | + | 36499.1i | −2.08882 | + | 1.24259i | ||||
\(953\) | −2401.94 | −0.0816439 | −0.0408219 | − | 0.999166i | \(-0.512998\pi\) | ||||
−0.0408219 | + | 0.999166i | \(0.512998\pi\) | |||||||
\(954\) | 49499.2 | − | 30394.0i | 1.67987 | − | 1.03149i | ||||
\(955\) | 7134.81 | − | 12357.8i | 0.241756 | − | 0.418733i | ||||
\(956\) | 37358.1 | 1.26386 | ||||||||
\(957\) | −2298.47 | + | 9067.23i | −0.0776374 | + | 0.306272i | ||||
\(958\) | −7724.01 | + | 13378.4i | −0.260492 | + | 0.451185i | ||||
\(959\) | −18647.5 | − | 10444.3i | −0.627905 | − | 0.351681i | ||||
\(960\) | 201.634 | + | 196.248i | 0.00677887 | + | 0.00659778i | ||||
\(961\) | −5131.62 | + | 8888.23i | −0.172254 | + | 0.298353i | ||||
\(962\) | −16944.8 | + | 29349.2i | −0.567902 | + | 0.983635i | ||||
\(963\) | 39369.0 | − | 24173.8i | 1.31739 | − | 0.808920i | ||||
\(964\) | 31138.5 | + | 53933.4i | 1.04036 | + | 1.80195i | ||||
\(965\) | 4340.09 | + | 7517.26i | 0.144780 | + | 0.250766i | ||||
\(966\) | −20084.4 | − | 4813.31i | −0.668948 | − | 0.160317i | ||||
\(967\) | 18468.8 | − | 31988.9i | 0.614184 | − | 1.06380i | −0.376343 | − | 0.926480i | \(-0.622819\pi\) |
0.990527 | − | 0.137318i | \(-0.0438481\pi\) | |||||||
\(968\) | −17959.4 | −0.596319 | ||||||||
\(969\) | −26492.4 | − | 25784.7i | −0.878285 | − | 0.854822i | ||||
\(970\) | 23071.7 | 0.763697 | ||||||||
\(971\) | 690.662 | + | 1196.26i | 0.0228264 | + | 0.0395364i | 0.877213 | − | 0.480102i | \(-0.159400\pi\) |
−0.854387 | + | 0.519638i | \(0.826067\pi\) | |||||||
\(972\) | 13117.3 | − | 66724.2i | 0.432858 | − | 2.20183i | ||||
\(973\) | 20521.2 | − | 12207.5i | 0.676135 | − | 0.402216i | ||||
\(974\) | −14181.4 | − | 24563.0i | −0.466532 | − | 0.808058i | ||||
\(975\) | 24940.3 | − | 7045.93i | 0.819210 | − | 0.231436i | ||||
\(976\) | 8829.92 | + | 15293.9i | 0.289589 | + | 0.501583i | ||||
\(977\) | 14924.9 | + | 25850.7i | 0.488730 | + | 0.846505i | 0.999916 | − | 0.0129649i | \(-0.00412697\pi\) |
−0.511186 | + | 0.859470i | \(0.670794\pi\) | |||||||
\(978\) | 17468.6 | + | 17002.0i | 0.571150 | + | 0.555893i | ||||
\(979\) | −17769.6 | − | 30777.9i | −0.580102 | − | 1.00477i | ||||
\(980\) | 20101.3 | − | 37013.8i | 0.655217 | − | 1.20649i | ||||
\(981\) | 14192.6 | + | 7689.55i | 0.461912 | + | 0.250264i | ||||
\(982\) | −11544.1 | − | 19994.9i | −0.375138 | − | 0.649759i | ||||
\(983\) | −17268.6 | −0.560309 | −0.280154 | − | 0.959955i | \(-0.590386\pi\) | ||||
−0.280154 | + | 0.959955i | \(0.590386\pi\) | |||||||
\(984\) | −55099.5 | + | 15566.2i | −1.78507 | + | 0.504303i | ||||
\(985\) | −5402.98 | −0.174775 | ||||||||
\(986\) | 8492.83 | − | 14710.0i | 0.274307 | − | 0.475114i | ||||
\(987\) | −1673.68 | − | 401.105i | −0.0539754 | − | 0.0129355i | ||||
\(988\) | −53562.5 | − | 92773.0i | −1.72475 | − | 2.98735i | ||||
\(989\) | 9948.72 | + | 17231.7i | 0.319869 | + | 0.554030i | ||||
\(990\) | −33960.5 | − | 18399.7i | −1.09024 | − | 0.590689i | ||||
\(991\) | −24523.9 | + | 42476.6i | −0.786101 | + | 1.36157i | 0.142238 | + | 0.989833i | \(0.454570\pi\) |
−0.928339 | + | 0.371735i | \(0.878763\pi\) | |||||||
\(992\) | −17861.6 | + | 30937.2i | −0.571679 | + | 0.990177i | ||||
\(993\) | −11732.1 | + | 3314.45i | −0.374931 | + | 0.105922i | ||||
\(994\) | −76272.4 | + | 45372.5i | −2.43382 | + | 1.44782i | ||||
\(995\) | 18715.1 | − | 32415.4i | 0.596289 | − | 1.03280i | ||||
\(996\) | −18354.6 | + | 5185.38i | −0.583922 | + | 0.164965i | ||||
\(997\) | −45483.8 | −1.44482 | −0.722411 | − | 0.691464i | \(-0.756966\pi\) | ||||
−0.722411 | + | 0.691464i | \(0.756966\pi\) | |||||||
\(998\) | −52566.4 | + | 91047.7i | −1.66729 | + | 2.88784i | ||||
\(999\) | −14278.2 | − | 3210.71i | −0.452194 | − | 0.101684i |
(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 | 63.4.g.a.4.22 | ✓ | 44 | |
3.2 | odd | 2 | 189.4.g.a.172.1 | 44 | |||
7.2 | even | 3 | 63.4.h.a.58.1 | yes | 44 | ||
9.2 | odd | 6 | 189.4.h.a.46.22 | 44 | |||
9.7 | even | 3 | 63.4.h.a.25.1 | yes | 44 | ||
21.2 | odd | 6 | 189.4.h.a.37.22 | 44 | |||
63.2 | odd | 6 | 189.4.g.a.100.1 | 44 | |||
63.16 | even | 3 | inner | 63.4.g.a.16.22 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.g.a.4.22 | ✓ | 44 | 1.1 | even | 1 | trivial | |
63.4.g.a.16.22 | yes | 44 | 63.16 | even | 3 | inner | |
63.4.h.a.25.1 | yes | 44 | 9.7 | even | 3 | ||
63.4.h.a.58.1 | yes | 44 | 7.2 | even | 3 | ||
189.4.g.a.100.1 | 44 | 63.2 | odd | 6 | |||
189.4.g.a.172.1 | 44 | 3.2 | odd | 2 | |||
189.4.h.a.37.22 | 44 | 21.2 | odd | 6 | |||
189.4.h.a.46.22 | 44 | 9.2 | odd | 6 |