Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(25,63)]
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([4, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.h (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 | 25.12 | ||
Character | \(\chi\) | \(=\) | 63.25 |
Dual form | 63.4.h.a.58.12 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.534259 | 0.188889 | 0.0944445 | − | 0.995530i | \(-0.469893\pi\) | ||||
0.0944445 | + | 0.995530i | \(0.469893\pi\) | |||||||
\(3\) | 1.18489 | − | 5.05925i | 0.228031 | − | 0.973654i | ||||
\(4\) | −7.71457 | −0.964321 | ||||||||
\(5\) | 0.696621 | − | 1.20658i | 0.0623077 | − | 0.107920i | −0.833189 | − | 0.552989i | \(-0.813487\pi\) |
0.895497 | + | 0.445068i | \(0.146821\pi\) | |||||||
\(6\) | 0.633036 | − | 2.70295i | 0.0430726 | − | 0.183912i | ||||
\(7\) | −2.10659 | − | 18.4001i | −0.113745 | − | 0.993510i | ||||
\(8\) | −8.39564 | −0.371039 | ||||||||
\(9\) | −24.1921 | − | 11.9893i | −0.896003 | − | 0.444047i | ||||
\(10\) | 0.372176 | − | 0.644627i | 0.0117692 | − | 0.0203849i | ||||
\(11\) | −9.69762 | − | 16.7968i | −0.265813 | − | 0.460402i | 0.701963 | − | 0.712213i | \(-0.252307\pi\) |
−0.967776 | + | 0.251811i | \(0.918974\pi\) | |||||||
\(12\) | −9.14088 | + | 39.0300i | −0.219896 | + | 0.938915i | ||||
\(13\) | 4.05999 | + | 7.03211i | 0.0866184 | + | 0.150027i | 0.906080 | − | 0.423107i | \(-0.139061\pi\) |
−0.819461 | + | 0.573134i | \(0.805727\pi\) | |||||||
\(14\) | −1.12546 | − | 9.83039i | −0.0214852 | − | 0.187663i | ||||
\(15\) | −5.27899 | − | 4.95404i | −0.0908686 | − | 0.0852752i | ||||
\(16\) | 57.2311 | 0.894236 | ||||||||
\(17\) | 28.8598 | − | 49.9867i | 0.411737 | − | 0.713150i | −0.583342 | − | 0.812226i | \(-0.698255\pi\) |
0.995080 | + | 0.0990761i | \(0.0315887\pi\) | |||||||
\(18\) | −12.9248 | − | 6.40538i | −0.169245 | − | 0.0838757i | ||||
\(19\) | 35.7871 | + | 61.9851i | 0.432112 | + | 0.748440i | 0.997055 | − | 0.0766902i | \(-0.0244352\pi\) |
−0.564943 | + | 0.825130i | \(0.691102\pi\) | |||||||
\(20\) | −5.37413 | + | 9.30826i | −0.0600846 | + | 0.104070i | ||||
\(21\) | −95.5866 | − | 11.1442i | −0.993272 | − | 0.115803i | ||||
\(22\) | −5.18104 | − | 8.97382i | −0.0502092 | − | 0.0869648i | ||||
\(23\) | 105.165 | − | 182.151i | 0.953411 | − | 1.65136i | 0.215449 | − | 0.976515i | \(-0.430878\pi\) |
0.737962 | − | 0.674842i | \(-0.235788\pi\) | |||||||
\(24\) | −9.94788 | + | 42.4757i | −0.0846085 | + | 0.361263i | ||||
\(25\) | 61.5294 | + | 106.572i | 0.492236 | + | 0.852577i | ||||
\(26\) | 2.16909 | + | 3.75697i | 0.0163613 | + | 0.0283385i | ||||
\(27\) | −89.3217 | + | 108.188i | −0.636665 | + | 0.771140i | ||||
\(28\) | 16.2514 | + | 141.949i | 0.109687 | + | 0.958062i | ||||
\(29\) | −78.1687 | + | 135.392i | −0.500537 | + | 0.866955i | 0.499463 | + | 0.866335i | \(0.333531\pi\) |
−1.00000 | 0.000619685i | \(0.999803\pi\) | ||||||||
\(30\) | −2.82035 | − | 2.64674i | −0.0171641 | − | 0.0161076i | ||||
\(31\) | 111.132 | 0.643870 | 0.321935 | − | 0.946762i | \(-0.395667\pi\) | ||||
0.321935 | + | 0.946762i | \(0.395667\pi\) | |||||||
\(32\) | 97.7414 | 0.539950 | ||||||||
\(33\) | −96.4697 | + | 29.1605i | −0.508886 | + | 0.153824i | ||||
\(34\) | 15.4186 | − | 26.7058i | 0.0777727 | − | 0.134706i | ||||
\(35\) | −23.6687 | − | 10.2761i | −0.114307 | − | 0.0496279i | ||||
\(36\) | 186.632 | + | 92.4921i | 0.864035 | + | 0.428204i | ||||
\(37\) | 26.2246 | + | 45.4224i | 0.116522 | + | 0.201821i | 0.918387 | − | 0.395683i | \(-0.129492\pi\) |
−0.801865 | + | 0.597505i | \(0.796159\pi\) | |||||||
\(38\) | 19.1196 | + | 33.1161i | 0.0816212 | + | 0.141372i | ||||
\(39\) | 40.3878 | − | 12.2083i | 0.165826 | − | 0.0501253i | ||||
\(40\) | −5.84858 | + | 10.1300i | −0.0231185 | + | 0.0400425i | ||||
\(41\) | −201.952 | − | 349.790i | −0.769257 | − | 1.33239i | −0.937966 | − | 0.346726i | \(-0.887293\pi\) |
0.168709 | − | 0.985666i | \(-0.446040\pi\) | |||||||
\(42\) | −51.0680 | − | 5.95390i | −0.187618 | − | 0.0218740i | ||||
\(43\) | 89.7250 | − | 155.408i | 0.318208 | − | 0.551152i | −0.661906 | − | 0.749586i | \(-0.730252\pi\) |
0.980114 | + | 0.198435i | \(0.0635857\pi\) | |||||||
\(44\) | 74.8130 | + | 129.580i | 0.256329 | + | 0.443975i | ||||
\(45\) | −31.3188 | + | 20.8378i | −0.103749 | + | 0.0690292i | ||||
\(46\) | 56.1854 | − | 97.3160i | 0.180089 | − | 0.311923i | ||||
\(47\) | −92.8201 | −0.288068 | −0.144034 | − | 0.989573i | \(-0.546007\pi\) | ||||
−0.144034 | + | 0.989573i | \(0.546007\pi\) | |||||||
\(48\) | 67.8123 | − | 289.547i | 0.203914 | − | 0.870676i | ||||
\(49\) | −334.125 | + | 77.5226i | −0.974124 | + | 0.226013i | ||||
\(50\) | 32.8726 | + | 56.9371i | 0.0929779 | + | 0.161042i | ||||
\(51\) | −218.700 | − | 205.238i | −0.600472 | − | 0.563510i | ||||
\(52\) | −31.3211 | − | 54.2497i | −0.0835279 | − | 0.144675i | ||||
\(53\) | 214.618 | − | 371.730i | 0.556229 | − | 0.963416i | −0.441578 | − | 0.897223i | \(-0.645581\pi\) |
0.997807 | − | 0.0661934i | \(-0.0210854\pi\) | |||||||
\(54\) | −47.7209 | + | 57.8004i | −0.120259 | + | 0.145660i | ||||
\(55\) | −27.0223 | −0.0662488 | ||||||||
\(56\) | 17.6861 | + | 154.480i | 0.0422037 | + | 0.368631i | ||||
\(57\) | 356.002 | − | 107.611i | 0.827256 | − | 0.250060i | ||||
\(58\) | −41.7623 | + | 72.3344i | −0.0945458 | + | 0.163758i | ||||
\(59\) | −389.746 | −0.860010 | −0.430005 | − | 0.902827i | \(-0.641488\pi\) | ||||
−0.430005 | + | 0.902827i | \(0.641488\pi\) | |||||||
\(60\) | 40.7251 | + | 38.2183i | 0.0876265 | + | 0.0822327i | ||||
\(61\) | −352.315 | −0.739498 | −0.369749 | − | 0.929132i | \(-0.620556\pi\) | ||||
−0.369749 | + | 0.929132i | \(0.620556\pi\) | |||||||
\(62\) | 59.3735 | 0.121620 | ||||||||
\(63\) | −169.641 | + | 470.392i | −0.339250 | + | 0.940696i | ||||
\(64\) | −405.630 | −0.792245 | ||||||||
\(65\) | 11.3131 | 0.0215879 | ||||||||
\(66\) | −51.5398 | + | 15.5792i | −0.0961229 | + | 0.0290556i | ||||
\(67\) | 862.471 | 1.57265 | 0.786325 | − | 0.617813i | \(-0.211981\pi\) | ||||
0.786325 | + | 0.617813i | \(0.211981\pi\) | |||||||
\(68\) | −222.641 | + | 385.626i | −0.397047 | + | 0.687706i | ||||
\(69\) | −796.942 | − | 747.886i | −1.39044 | − | 1.30485i | ||||
\(70\) | −12.6452 | − | 5.49009i | −0.0215913 | − | 0.00937417i | ||||
\(71\) | 377.064 | 0.630272 | 0.315136 | − | 0.949047i | \(-0.397950\pi\) | ||||
0.315136 | + | 0.949047i | \(0.397950\pi\) | |||||||
\(72\) | 203.108 | + | 100.658i | 0.332452 | + | 0.164759i | ||||
\(73\) | 183.741 | − | 318.248i | 0.294592 | − | 0.510248i | −0.680298 | − | 0.732936i | \(-0.738150\pi\) |
0.974890 | + | 0.222688i | \(0.0714830\pi\) | |||||||
\(74\) | 14.0107 | + | 24.2673i | 0.0220097 | + | 0.0381219i | ||||
\(75\) | 612.081 | − | 185.017i | 0.942360 | − | 0.284853i | ||||
\(76\) | −276.082 | − | 478.188i | −0.416694 | − | 0.721736i | ||||
\(77\) | −288.633 | + | 213.821i | −0.427179 | + | 0.316456i | ||||
\(78\) | 21.5776 | − | 6.52237i | 0.0313228 | − | 0.00946812i | ||||
\(79\) | −309.996 | −0.441485 | −0.220742 | − | 0.975332i | \(-0.570848\pi\) | ||||
−0.220742 | + | 0.975332i | \(0.570848\pi\) | |||||||
\(80\) | 39.8684 | − | 69.0540i | 0.0557177 | − | 0.0965060i | ||||
\(81\) | 441.514 | + | 580.091i | 0.605644 | + | 0.795736i | ||||
\(82\) | −107.894 | − | 186.879i | −0.145304 | − | 0.251674i | ||||
\(83\) | 110.580 | − | 191.530i | 0.146237 | − | 0.253291i | −0.783597 | − | 0.621270i | \(-0.786617\pi\) |
0.929834 | + | 0.367980i | \(0.119950\pi\) | |||||||
\(84\) | 737.410 | + | 85.9729i | 0.957833 | + | 0.111672i | ||||
\(85\) | −40.2087 | − | 69.6435i | −0.0513088 | − | 0.0888694i | ||||
\(86\) | 47.9364 | − | 83.0282i | 0.0601059 | − | 0.104107i | ||||
\(87\) | 592.362 | + | 555.899i | 0.729976 | + | 0.685042i | ||||
\(88\) | 81.4178 | + | 141.020i | 0.0986269 | + | 0.170827i | ||||
\(89\) | 712.416 | + | 1233.94i | 0.848494 | + | 1.46963i | 0.882552 | + | 0.470215i | \(0.155824\pi\) |
−0.0340580 | + | 0.999420i | \(0.510843\pi\) | |||||||
\(90\) | −16.7323 | + | 11.1328i | −0.0195971 | + | 0.0130388i | ||||
\(91\) | 120.839 | − | 89.5178i | 0.139201 | − | 0.103121i | ||||
\(92\) | −811.304 | + | 1405.22i | −0.919395 | + | 1.59244i | ||||
\(93\) | 131.679 | − | 562.247i | 0.146823 | − | 0.626907i | ||||
\(94\) | −49.5899 | −0.0544129 | ||||||||
\(95\) | 99.7202 | 0.107696 | ||||||||
\(96\) | 115.812 | − | 494.498i | 0.123126 | − | 0.525724i | ||||
\(97\) | −288.900 | + | 500.389i | −0.302406 | + | 0.523782i | −0.976680 | − | 0.214699i | \(-0.931123\pi\) |
0.674275 | + | 0.738481i | \(0.264456\pi\) | |||||||
\(98\) | −178.509 | + | 41.4171i | −0.184001 | + | 0.0426914i | ||||
\(99\) | 33.2245 | + | 522.617i | 0.0337292 | + | 0.530555i | ||||
\(100\) | −474.673 | − | 822.158i | −0.474673 | − | 0.822158i | ||||
\(101\) | 430.418 | + | 745.506i | 0.424042 | + | 0.734462i | 0.996330 | − | 0.0855905i | \(-0.0272777\pi\) |
−0.572289 | + | 0.820052i | \(0.693944\pi\) | |||||||
\(102\) | −116.842 | − | 109.650i | −0.113423 | − | 0.106441i | ||||
\(103\) | −758.108 | + | 1313.08i | −0.725229 | + | 1.25613i | 0.233651 | + | 0.972321i | \(0.424933\pi\) |
−0.958880 | + | 0.283813i | \(0.908401\pi\) | |||||||
\(104\) | −34.0862 | − | 59.0391i | −0.0321388 | − | 0.0556660i | ||||
\(105\) | −80.0341 | + | 107.570i | −0.0743860 | + | 0.0999785i | ||||
\(106\) | 114.662 | − | 198.600i | 0.105065 | − | 0.181979i | ||||
\(107\) | 636.666 | + | 1102.74i | 0.575223 | + | 0.996315i | 0.996017 | + | 0.0891594i | \(0.0284180\pi\) |
−0.420794 | + | 0.907156i | \(0.638249\pi\) | |||||||
\(108\) | 689.078 | − | 834.623i | 0.613950 | − | 0.743627i | ||||
\(109\) | −148.428 | + | 257.085i | −0.130430 | + | 0.225911i | −0.923842 | − | 0.382773i | \(-0.874969\pi\) |
0.793413 | + | 0.608684i | \(0.208302\pi\) | |||||||
\(110\) | −14.4369 | −0.0125137 | ||||||||
\(111\) | 260.877 | − | 78.8567i | 0.223075 | − | 0.0674301i | ||||
\(112\) | −120.562 | − | 1053.06i | −0.101715 | − | 0.888432i | ||||
\(113\) | −834.841 | − | 1445.99i | −0.695002 | − | 1.20378i | −0.970180 | − | 0.242386i | \(-0.922070\pi\) |
0.275178 | − | 0.961393i | \(-0.411263\pi\) | |||||||
\(114\) | 190.197 | − | 57.4920i | 0.156260 | − | 0.0472335i | ||||
\(115\) | −146.521 | − | 253.781i | −0.118810 | − | 0.205784i | ||||
\(116\) | 603.038 | − | 1044.49i | 0.482678 | − | 0.836023i | ||||
\(117\) | −13.9097 | − | 218.798i | −0.0109911 | − | 0.172888i | ||||
\(118\) | −208.225 | −0.162446 | ||||||||
\(119\) | −980.554 | − | 425.721i | −0.755355 | − | 0.327948i | ||||
\(120\) | 44.3205 | + | 41.5924i | 0.0337158 | + | 0.0316404i | ||||
\(121\) | 477.412 | − | 826.902i | 0.358687 | − | 0.621264i | ||||
\(122\) | −188.228 | −0.139683 | ||||||||
\(123\) | −2008.97 | + | 607.262i | −1.47270 | + | 0.445163i | ||||
\(124\) | −857.339 | −0.620897 | ||||||||
\(125\) | 345.606 | 0.247295 | ||||||||
\(126\) | −90.6321 | + | 251.311i | −0.0640805 | + | 0.177687i | ||||
\(127\) | 1419.40 | 0.991745 | 0.495873 | − | 0.868395i | \(-0.334848\pi\) | ||||
0.495873 | + | 0.868395i | \(0.334848\pi\) | |||||||
\(128\) | −998.642 | −0.689596 | ||||||||
\(129\) | −679.936 | − | 638.083i | −0.464070 | − | 0.435504i | ||||
\(130\) | 6.04412 | 0.00407773 | ||||||||
\(131\) | 628.817 | − | 1089.14i | 0.419389 | − | 0.726404i | −0.576489 | − | 0.817105i | \(-0.695578\pi\) |
0.995878 | + | 0.0907015i | \(0.0289109\pi\) | |||||||
\(132\) | 744.222 | − | 224.960i | 0.490729 | − | 0.148336i | ||||
\(133\) | 1065.14 | − | 789.062i | 0.694432 | − | 0.514439i | ||||
\(134\) | 460.782 | 0.297056 | ||||||||
\(135\) | 68.3144 | + | 183.140i | 0.0435523 | + | 0.116757i | ||||
\(136\) | −242.297 | + | 419.671i | −0.152770 | + | 0.264606i | ||||
\(137\) | −1067.01 | − | 1848.12i | −0.665410 | − | 1.15252i | −0.979174 | − | 0.203023i | \(-0.934923\pi\) |
0.313764 | − | 0.949501i | \(-0.398410\pi\) | |||||||
\(138\) | −425.773 | − | 399.565i | −0.262639 | − | 0.246473i | ||||
\(139\) | 1103.28 | + | 1910.93i | 0.673229 | + | 1.16607i | 0.976983 | + | 0.213317i | \(0.0684266\pi\) |
−0.303754 | + | 0.952751i | \(0.598240\pi\) | |||||||
\(140\) | 182.594 | + | 79.2756i | 0.110228 | + | 0.0478573i | ||||
\(141\) | −109.981 | + | 469.600i | −0.0656886 | + | 0.280479i | ||||
\(142\) | 201.450 | 0.119051 | ||||||||
\(143\) | 78.7445 | − | 136.389i | 0.0460486 | − | 0.0797585i | ||||
\(144\) | −1384.54 | − | 686.160i | −0.801238 | − | 0.397083i | ||||
\(145\) | 108.908 | + | 188.634i | 0.0623745 | + | 0.108036i | ||||
\(146\) | 98.1650 | − | 170.027i | 0.0556452 | − | 0.0963802i | ||||
\(147\) | −3.69320 | + | 1782.28i | −0.00207218 | + | 0.999998i | ||||
\(148\) | −202.312 | − | 350.414i | −0.112364 | − | 0.194621i | ||||
\(149\) | 882.883 | − | 1529.20i | 0.485427 | − | 0.840784i | −0.514433 | − | 0.857531i | \(-0.671998\pi\) |
0.999860 | + | 0.0167467i | \(0.00533090\pi\) | |||||||
\(150\) | 327.009 | − | 98.8470i | 0.178001 | − | 0.0538055i | ||||
\(151\) | 1294.33 | + | 2241.84i | 0.697555 | + | 1.20820i | 0.969312 | + | 0.245834i | \(0.0790619\pi\) |
−0.271757 | + | 0.962366i | \(0.587605\pi\) | |||||||
\(152\) | −300.456 | − | 520.405i | −0.160330 | − | 0.277700i | ||||
\(153\) | −1297.48 | + | 863.274i | −0.685591 | + | 0.456154i | ||||
\(154\) | −154.205 | + | 114.236i | −0.0806894 | + | 0.0597751i | ||||
\(155\) | 77.4172 | − | 134.090i | 0.0401180 | − | 0.0694865i | ||||
\(156\) | −311.575 | + | 94.1815i | −0.159910 | + | 0.0483369i | ||||
\(157\) | −2399.53 | −1.21976 | −0.609882 | − | 0.792492i | \(-0.708783\pi\) | ||||
−0.609882 | + | 0.792492i | \(0.708783\pi\) | |||||||
\(158\) | −165.618 | −0.0833916 | ||||||||
\(159\) | −1626.38 | − | 1526.27i | −0.811196 | − | 0.761263i | ||||
\(160\) | 68.0887 | − | 117.933i | 0.0336430 | − | 0.0582714i | ||||
\(161\) | −3573.14 | − | 1551.33i | −1.74909 | − | 0.759390i | ||||
\(162\) | 235.883 | + | 309.919i | 0.114399 | + | 0.150306i | ||||
\(163\) | 1023.61 | + | 1772.94i | 0.491872 | + | 0.851947i | 0.999956 | − | 0.00936052i | \(-0.00297959\pi\) |
−0.508085 | + | 0.861307i | \(0.669646\pi\) | |||||||
\(164\) | 1557.97 | + | 2698.48i | 0.741811 | + | 1.28485i | ||||
\(165\) | −32.0183 | + | 136.712i | −0.0151068 | + | 0.0645033i | ||||
\(166\) | 59.0782 | − | 102.326i | 0.0276226 | − | 0.0478438i | ||||
\(167\) | 1270.89 | + | 2201.24i | 0.588887 | + | 1.01998i | 0.994379 | + | 0.105884i | \(0.0337672\pi\) |
−0.405491 | + | 0.914099i | \(0.632900\pi\) | |||||||
\(168\) | 802.511 | + | 93.5630i | 0.368542 | + | 0.0429675i | ||||
\(169\) | 1065.53 | − | 1845.56i | 0.484995 | − | 0.840035i | ||||
\(170\) | −21.4819 | − | 37.2077i | −0.00969167 | − | 0.0167865i | ||||
\(171\) | −122.608 | − | 1928.61i | −0.0548310 | − | 0.862483i | ||||
\(172\) | −692.190 | + | 1198.91i | −0.306854 | + | 0.531487i | ||||
\(173\) | 4302.80 | 1.89096 | 0.945479 | − | 0.325683i | \(-0.105594\pi\) | ||||
0.945479 | + | 0.325683i | \(0.105594\pi\) | |||||||
\(174\) | 316.475 | + | 296.994i | 0.137884 | + | 0.129397i | ||||
\(175\) | 1831.32 | − | 1356.65i | 0.791054 | − | 0.586017i | ||||
\(176\) | −555.006 | − | 961.298i | −0.237700 | − | 0.411708i | ||||
\(177\) | −461.805 | + | 1971.82i | −0.196109 | + | 0.837352i | ||||
\(178\) | 380.615 | + | 659.244i | 0.160271 | + | 0.277598i | ||||
\(179\) | 783.675 | − | 1357.37i | 0.327233 | − | 0.566783i | −0.654729 | − | 0.755864i | \(-0.727217\pi\) |
0.981962 | + | 0.189080i | \(0.0605506\pi\) | |||||||
\(180\) | 241.611 | − | 160.754i | 0.100048 | − | 0.0665663i | ||||
\(181\) | 642.368 | 0.263795 | 0.131897 | − | 0.991263i | \(-0.457893\pi\) | ||||
0.131897 | + | 0.991263i | \(0.457893\pi\) | |||||||
\(182\) | 64.5590 | − | 47.8257i | 0.0262936 | − | 0.0194784i | ||||
\(183\) | −417.454 | + | 1782.45i | −0.168629 | + | 0.720015i | ||||
\(184\) | −882.930 | + | 1529.28i | −0.353752 | + | 0.612717i | ||||
\(185\) | 73.0745 | 0.0290408 | ||||||||
\(186\) | 70.3508 | − | 300.385i | 0.0277332 | − | 0.118416i | ||||
\(187\) | −1119.49 | −0.437781 | ||||||||
\(188\) | 716.067 | 0.277790 | ||||||||
\(189\) | 2178.83 | + | 1415.62i | 0.838553 | + | 0.544820i | ||||
\(190\) | 53.2764 | 0.0203425 | ||||||||
\(191\) | −531.028 | −0.201172 | −0.100586 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100586 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(192\) | −480.625 | + | 2052.18i | −0.180657 | + | 0.771373i | ||||
\(193\) | 1417.79 | 0.528782 | 0.264391 | − | 0.964416i | \(-0.414829\pi\) | ||||
0.264391 | + | 0.964416i | \(0.414829\pi\) | |||||||
\(194\) | −154.347 | + | 267.337i | −0.0571211 | + | 0.0989366i | ||||
\(195\) | 13.4047 | − | 57.2358i | 0.00492273 | − | 0.0210192i | ||||
\(196\) | 2577.63 | − | 598.053i | 0.939368 | − | 0.217949i | ||||
\(197\) | −4070.58 | −1.47217 | −0.736084 | − | 0.676891i | \(-0.763327\pi\) | ||||
−0.736084 | + | 0.676891i | \(0.763327\pi\) | |||||||
\(198\) | 17.7505 | + | 279.212i | 0.00637107 | + | 0.100216i | ||||
\(199\) | −154.635 | + | 267.836i | −0.0550844 | + | 0.0954090i | −0.892253 | − | 0.451536i | \(-0.850876\pi\) |
0.837168 | + | 0.546945i | \(0.184209\pi\) | |||||||
\(200\) | −516.579 | − | 894.742i | −0.182638 | − | 0.316339i | ||||
\(201\) | 1021.93 | − | 4363.46i | 0.358614 | − | 1.53122i | ||||
\(202\) | 229.955 | + | 398.293i | 0.0800968 | + | 0.138732i | ||||
\(203\) | 2655.89 | + | 1153.09i | 0.918262 | + | 0.398676i | ||||
\(204\) | 1687.17 | + | 1583.32i | 0.579048 | + | 0.543405i | ||||
\(205\) | −562.735 | −0.191722 | ||||||||
\(206\) | −405.026 | + | 701.525i | −0.136988 | + | 0.237270i | ||||
\(207\) | −4728.03 | + | 3145.77i | −1.58754 | + | 1.05626i | ||||
\(208\) | 232.358 | + | 402.455i | 0.0774572 | + | 0.134160i | ||||
\(209\) | 694.100 | − | 1202.22i | 0.229722 | − | 0.397890i | ||||
\(210\) | −42.7589 | + | 57.4701i | −0.0140507 | + | 0.0188848i | ||||
\(211\) | −1225.67 | − | 2122.93i | −0.399899 | − | 0.692646i | 0.593814 | − | 0.804602i | \(-0.297622\pi\) |
−0.993713 | + | 0.111957i | \(0.964288\pi\) | |||||||
\(212\) | −1655.69 | + | 2867.74i | −0.536383 | + | 0.929042i | ||||
\(213\) | 446.778 | − | 1907.66i | 0.143722 | − | 0.613667i | ||||
\(214\) | 340.145 | + | 589.148i | 0.108653 | + | 0.188193i | ||||
\(215\) | −125.009 | − | 216.521i | −0.0396536 | − | 0.0686820i | ||||
\(216\) | 749.913 | − | 908.308i | 0.236227 | − | 0.286123i | ||||
\(217\) | −234.110 | − | 2044.84i | −0.0732369 | − | 0.639691i | ||||
\(218\) | −79.2990 | + | 137.350i | −0.0246367 | + | 0.0426721i | ||||
\(219\) | −1392.39 | − | 1306.68i | −0.429629 | − | 0.403183i | ||||
\(220\) | 208.465 | 0.0638851 | ||||||||
\(221\) | 468.683 | 0.142656 | ||||||||
\(222\) | 139.376 | − | 42.1299i | 0.0421364 | − | 0.0127368i | ||||
\(223\) | −2312.36 | + | 4005.13i | −0.694383 | + | 1.20271i | 0.276005 | + | 0.961156i | \(0.410989\pi\) |
−0.970388 | + | 0.241550i | \(0.922344\pi\) | |||||||
\(224\) | −205.901 | − | 1798.45i | −0.0614165 | − | 0.536446i | ||||
\(225\) | −210.803 | − | 3315.90i | −0.0624601 | − | 0.982488i | ||||
\(226\) | −446.021 | − | 772.531i | −0.131278 | − | 0.227381i | ||||
\(227\) | −2617.87 | − | 4534.28i | −0.765436 | − | 1.32577i | −0.940016 | − | 0.341131i | \(-0.889190\pi\) |
0.174580 | − | 0.984643i | \(-0.444143\pi\) | |||||||
\(228\) | −2746.40 | + | 830.170i | −0.797740 | + | 0.241138i | ||||
\(229\) | −624.675 | + | 1081.97i | −0.180261 | + | 0.312221i | −0.941969 | − | 0.335699i | \(-0.891027\pi\) |
0.761709 | + | 0.647920i | \(0.224361\pi\) | |||||||
\(230\) | −78.2799 | − | 135.585i | −0.0224418 | − | 0.0388704i | ||||
\(231\) | 739.776 | + | 1713.62i | 0.210709 | + | 0.488086i | ||||
\(232\) | 656.277 | − | 1136.70i | 0.185718 | − | 0.321674i | ||||
\(233\) | 1274.52 | + | 2207.54i | 0.358355 | + | 0.620689i | 0.987686 | − | 0.156448i | \(-0.0500044\pi\) |
−0.629331 | + | 0.777137i | \(0.716671\pi\) | |||||||
\(234\) | −7.43139 | − | 116.895i | −0.00207609 | − | 0.0326566i | ||||
\(235\) | −64.6604 | + | 111.995i | −0.0179489 | + | 0.0310883i | ||||
\(236\) | 3006.72 | 0.829326 | ||||||||
\(237\) | −367.310 | + | 1568.35i | −0.100672 | + | 0.429854i | ||||
\(238\) | −523.870 | − | 227.445i | −0.142678 | − | 0.0619458i | ||||
\(239\) | 565.969 | + | 980.288i | 0.153178 | + | 0.265312i | 0.932394 | − | 0.361443i | \(-0.117716\pi\) |
−0.779216 | + | 0.626755i | \(0.784383\pi\) | |||||||
\(240\) | −302.122 | − | 283.525i | −0.0812580 | − | 0.0762562i | ||||
\(241\) | −3160.46 | − | 5474.09i | −0.844745 | − | 1.46314i | −0.885843 | − | 0.463985i | \(-0.846419\pi\) |
0.0410983 | − | 0.999155i | \(-0.486914\pi\) | |||||||
\(242\) | 255.062 | − | 441.780i | 0.0677520 | − | 0.117350i | ||||
\(243\) | 3457.97 | − | 1546.39i | 0.912877 | − | 0.408235i | ||||
\(244\) | 2717.96 | 0.713113 | ||||||||
\(245\) | −139.221 | + | 457.153i | −0.0363040 | + | 0.119210i | ||||
\(246\) | −1073.31 | + | 324.435i | −0.278177 | + | 0.0840863i | ||||
\(247\) | −290.591 | + | 503.318i | −0.0748576 | + | 0.129657i | ||||
\(248\) | −933.028 | −0.238901 | ||||||||
\(249\) | −837.973 | − | 786.392i | −0.213271 | − | 0.200143i | ||||
\(250\) | 184.643 | 0.0467114 | ||||||||
\(251\) | 1739.84 | 0.437521 | 0.218761 | − | 0.975779i | \(-0.429799\pi\) | ||||
0.218761 | + | 0.975779i | \(0.429799\pi\) | |||||||
\(252\) | 1308.71 | − | 3628.87i | 0.327146 | − | 0.907133i | ||||
\(253\) | −4079.41 | −1.01372 | ||||||||
\(254\) | 758.328 | 0.187330 | ||||||||
\(255\) | −399.987 | + | 120.906i | −0.0982281 | + | 0.0296920i | ||||
\(256\) | 2711.50 | 0.661988 | ||||||||
\(257\) | −3665.25 | + | 6348.39i | −0.889618 | + | 1.54086i | −0.0492900 | + | 0.998785i | \(0.515696\pi\) |
−0.840328 | + | 0.542079i | \(0.817637\pi\) | |||||||
\(258\) | −363.262 | − | 340.901i | −0.0876577 | − | 0.0822619i | ||||
\(259\) | 780.530 | − | 578.221i | 0.187258 | − | 0.138722i | ||||
\(260\) | −87.2756 | −0.0208177 | ||||||||
\(261\) | 3514.32 | − | 2338.23i | 0.833451 | − | 0.554532i | ||||
\(262\) | 335.951 | − | 581.884i | 0.0792180 | − | 0.137210i | ||||
\(263\) | −2016.64 | − | 3492.92i | −0.472818 | − | 0.818945i | 0.526698 | − | 0.850053i | \(-0.323430\pi\) |
−0.999516 | + | 0.0311075i | \(0.990097\pi\) | |||||||
\(264\) | 809.926 | − | 244.821i | 0.188816 | − | 0.0570746i | ||||
\(265\) | −299.015 | − | 517.910i | −0.0693146 | − | 0.120056i | ||||
\(266\) | 569.061 | − | 421.563i | 0.131171 | − | 0.0971718i | ||||
\(267\) | 7086.95 | − | 2142.21i | 1.62440 | − | 0.491016i | ||||
\(268\) | −6653.59 | −1.51654 | ||||||||
\(269\) | −2562.84 | + | 4438.97i | −0.580890 | + | 1.00613i | 0.414485 | + | 0.910056i | \(0.363962\pi\) |
−0.995374 | + | 0.0960740i | \(0.969371\pi\) | |||||||
\(270\) | 36.4976 | + | 97.8441i | 0.00822656 | + | 0.0220541i | ||||
\(271\) | −3560.18 | − | 6166.40i | −0.798027 | − | 1.38222i | −0.920899 | − | 0.389800i | \(-0.872544\pi\) |
0.122873 | − | 0.992422i | \(-0.460789\pi\) | |||||||
\(272\) | 1651.68 | − | 2860.79i | 0.368190 | − | 0.637725i | ||||
\(273\) | −309.713 | − | 717.421i | −0.0686619 | − | 0.159049i | ||||
\(274\) | −570.062 | − | 987.376i | −0.125689 | − | 0.217699i | ||||
\(275\) | 1193.38 | − | 2066.99i | 0.261685 | − | 0.453252i | ||||
\(276\) | 6148.06 | + | 5769.62i | 1.34083 | + | 1.25830i | ||||
\(277\) | 433.555 | + | 750.940i | 0.0940426 | + | 0.162887i | 0.909209 | − | 0.416341i | \(-0.136688\pi\) |
−0.815166 | + | 0.579227i | \(0.803354\pi\) | |||||||
\(278\) | 589.436 | + | 1020.93i | 0.127166 | + | 0.220257i | ||||
\(279\) | −2688.53 | − | 1332.40i | −0.576910 | − | 0.285909i | ||||
\(280\) | 198.714 | + | 86.2745i | 0.0424122 | + | 0.0184139i | ||||
\(281\) | −3122.11 | + | 5407.66i | −0.662811 | + | 1.14802i | 0.317063 | + | 0.948404i | \(0.397303\pi\) |
−0.979874 | + | 0.199617i | \(0.936030\pi\) | |||||||
\(282\) | −58.7584 | + | 250.888i | −0.0124079 | + | 0.0529793i | ||||
\(283\) | 2926.59 | 0.614728 | 0.307364 | − | 0.951592i | \(-0.400553\pi\) | ||||
0.307364 | + | 0.951592i | \(0.400553\pi\) | |||||||
\(284\) | −2908.89 | −0.607784 | ||||||||
\(285\) | 118.157 | − | 504.510i | 0.0245580 | − | 0.104858i | ||||
\(286\) | 42.0699 | − | 72.8673i | 0.00869807 | − | 0.0150655i | ||||
\(287\) | −6010.74 | + | 4452.78i | −1.23625 | + | 0.915817i | ||||
\(288\) | −2364.57 | − | 1171.85i | −0.483797 | − | 0.239763i | ||||
\(289\) | 790.720 | + | 1369.57i | 0.160944 | + | 0.278764i | ||||
\(290\) | 58.1850 | + | 100.779i | 0.0117819 | + | 0.0204068i | ||||
\(291\) | 2189.28 | + | 2054.52i | 0.441024 | + | 0.413877i | ||||
\(292\) | −1417.48 | + | 2455.15i | −0.284081 | + | 0.492043i | ||||
\(293\) | 2992.94 | + | 5183.92i | 0.596755 | + | 1.03361i | 0.993297 | + | 0.115593i | \(0.0368769\pi\) |
−0.396542 | + | 0.918017i | \(0.629790\pi\) | |||||||
\(294\) | −1.97312 | + | 952.197i | −0.000391411 | + | 0.188889i | ||||
\(295\) | −271.505 | + | 470.261i | −0.0535852 | + | 0.0928123i | ||||
\(296\) | −220.173 | − | 381.350i | −0.0432340 | − | 0.0748836i | ||||
\(297\) | 2683.42 | + | 451.150i | 0.524268 | + | 0.0881427i | ||||
\(298\) | 471.688 | − | 816.987i | 0.0916918 | − | 0.158815i | ||||
\(299\) | 1707.88 | 0.330332 | ||||||||
\(300\) | −4721.94 | + | 1427.33i | −0.908737 | + | 0.274689i | ||||
\(301\) | −3048.53 | − | 1323.56i | −0.583769 | − | 0.253452i | ||||
\(302\) | 691.505 | + | 1197.72i | 0.131760 | + | 0.228216i | ||||
\(303\) | 4281.70 | − | 1294.25i | 0.811806 | − | 0.245389i | ||||
\(304\) | 2048.14 | + | 3547.47i | 0.386410 | + | 0.669282i | ||||
\(305\) | −245.430 | + | 425.098i | −0.0460764 | + | 0.0798066i | ||||
\(306\) | −693.192 | + | 461.212i | −0.129501 | + | 0.0861625i | ||||
\(307\) | −3568.44 | −0.663394 | −0.331697 | − | 0.943386i | \(-0.607621\pi\) | ||||
−0.331697 | + | 0.943386i | \(0.607621\pi\) | |||||||
\(308\) | 2226.68 | − | 1649.53i | 0.411937 | − | 0.305165i | ||||
\(309\) | 5744.94 | + | 5391.31i | 1.05766 | + | 0.992560i | ||||
\(310\) | 41.3608 | − | 71.6390i | 0.00757786 | − | 0.0131252i | ||||
\(311\) | 5843.16 | 1.06539 | 0.532694 | − | 0.846308i | \(-0.321180\pi\) | ||||
0.532694 | + | 0.846308i | \(0.321180\pi\) | |||||||
\(312\) | −339.082 | + | 102.496i | −0.0615280 | + | 0.0185984i | ||||
\(313\) | −3900.57 | −0.704388 | −0.352194 | − | 0.935927i | \(-0.614564\pi\) | ||||
−0.352194 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(314\) | −1281.97 | −0.230400 | ||||||||
\(315\) | 449.392 | + | 532.371i | 0.0803821 | + | 0.0952244i | ||||
\(316\) | 2391.49 | 0.425733 | ||||||||
\(317\) | 2538.79 | 0.449819 | 0.224910 | − | 0.974380i | \(-0.427791\pi\) | ||||
0.224910 | + | 0.974380i | \(0.427791\pi\) | |||||||
\(318\) | −868.907 | − | 815.421i | −0.153226 | − | 0.143794i | ||||
\(319\) | 3032.20 | 0.532197 | ||||||||
\(320\) | −282.570 | + | 489.426i | −0.0493629 | + | 0.0854991i | ||||
\(321\) | 6333.41 | − | 1914.44i | 1.10124 | − | 0.332877i | ||||
\(322\) | −1908.98 | − | 828.811i | −0.330383 | − | 0.143440i | ||||
\(323\) | 4131.24 | 0.711667 | ||||||||
\(324\) | −3406.09 | − | 4475.15i | −0.584035 | − | 0.767345i | ||||
\(325\) | −499.618 | + | 865.363i | −0.0852733 | + | 0.147698i | ||||
\(326\) | 546.871 | + | 947.208i | 0.0929091 | + | 0.160923i | ||||
\(327\) | 1124.79 | + | 1055.55i | 0.190217 | + | 0.178508i | ||||
\(328\) | 1695.51 | + | 2936.72i | 0.285424 | + | 0.494369i | ||||
\(329\) | 195.533 | + | 1707.90i | 0.0327663 | + | 0.286199i | ||||
\(330\) | −17.1061 | + | 73.0398i | −0.00285351 | + | 0.0121840i | ||||
\(331\) | 10441.2 | 1.73384 | 0.866921 | − | 0.498446i | \(-0.166096\pi\) | ||||
0.866921 | + | 0.498446i | \(0.166096\pi\) | |||||||
\(332\) | −853.075 | + | 1477.57i | −0.141020 | + | 0.244253i | ||||
\(333\) | −89.8469 | − | 1413.28i | −0.0147855 | − | 0.232574i | ||||
\(334\) | 678.982 | + | 1176.03i | 0.111234 | + | 0.192663i | ||||
\(335\) | 600.815 | − | 1040.64i | 0.0979881 | − | 0.169720i | ||||
\(336\) | −5470.53 | − | 637.797i | −0.888220 | − | 0.103556i | ||||
\(337\) | −2095.75 | − | 3629.94i | −0.338762 | − | 0.586753i | 0.645438 | − | 0.763812i | \(-0.276675\pi\) |
−0.984200 | + | 0.177060i | \(0.943341\pi\) | |||||||
\(338\) | 569.270 | − | 986.005i | 0.0916101 | − | 0.158673i | ||||
\(339\) | −8304.81 | + | 2510.34i | −1.33055 | + | 0.402192i | ||||
\(340\) | 310.193 | + | 537.270i | 0.0494781 | + | 0.0856987i | ||||
\(341\) | −1077.72 | − | 1866.67i | −0.171149 | − | 0.296439i | ||||
\(342\) | −65.5046 | − | 1030.38i | −0.0103570 | − | 0.162913i | ||||
\(343\) | 2130.28 | + | 5984.61i | 0.335348 | + | 0.942094i | ||||
\(344\) | −753.299 | + | 1304.75i | −0.118067 | + | 0.204499i | ||||
\(345\) | −1457.55 | + | 440.583i | −0.227455 | + | 0.0687542i | ||||
\(346\) | 2298.81 | 0.357181 | ||||||||
\(347\) | 1908.52 | 0.295258 | 0.147629 | − | 0.989043i | \(-0.452836\pi\) | ||||
0.147629 | + | 0.989043i | \(0.452836\pi\) | |||||||
\(348\) | −4569.82 | − | 4288.52i | −0.703931 | − | 0.660601i | ||||
\(349\) | 130.338 | − | 225.753i | 0.0199910 | − | 0.0346254i | −0.855857 | − | 0.517213i | \(-0.826970\pi\) |
0.875848 | + | 0.482587i | \(0.160303\pi\) | |||||||
\(350\) | 978.397 | − | 724.801i | 0.149421 | − | 0.110692i | ||||
\(351\) | −1123.43 | − | 188.878i | −0.170839 | − | 0.0287223i | ||||
\(352\) | −947.859 | − | 1641.74i | −0.143526 | − | 0.248594i | ||||
\(353\) | −2875.56 | − | 4980.62i | −0.433571 | − | 0.750968i | 0.563606 | − | 0.826043i | \(-0.309413\pi\) |
−0.997178 | + | 0.0750758i | \(0.976080\pi\) | |||||||
\(354\) | −246.723 | + | 1053.46i | −0.0370429 | + | 0.158167i | ||||
\(355\) | 262.671 | − | 454.959i | 0.0392708 | − | 0.0680190i | ||||
\(356\) | −5495.98 | − | 9519.32i | −0.818221 | − | 1.41720i | ||||
\(357\) | −3315.68 | + | 4456.44i | −0.491553 | + | 0.660672i | ||||
\(358\) | 418.685 | − | 725.184i | 0.0618106 | − | 0.107059i | ||||
\(359\) | −2533.53 | − | 4388.20i | −0.372464 | − | 0.645126i | 0.617480 | − | 0.786586i | \(-0.288153\pi\) |
−0.989944 | + | 0.141461i | \(0.954820\pi\) | |||||||
\(360\) | 262.941 | − | 174.947i | 0.0384951 | − | 0.0256125i | ||||
\(361\) | 868.066 | − | 1503.53i | 0.126559 | − | 0.219206i | ||||
\(362\) | 343.191 | 0.0498279 | ||||||||
\(363\) | −3617.83 | − | 3395.13i | −0.523104 | − | 0.490905i | ||||
\(364\) | −932.217 | + | 690.591i | −0.134235 | + | 0.0994418i | ||||
\(365\) | −255.995 | − | 443.396i | −0.0367107 | − | 0.0635847i | ||||
\(366\) | −223.028 | + | 952.291i | −0.0318521 | + | 0.136003i | ||||
\(367\) | 292.144 | + | 506.008i | 0.0415525 | + | 0.0719711i | 0.886054 | − | 0.463583i | \(-0.153436\pi\) |
−0.844501 | + | 0.535554i | \(0.820103\pi\) | |||||||
\(368\) | 6018.72 | − | 10424.7i | 0.852575 | − | 1.47670i | ||||
\(369\) | 691.896 | + | 10883.4i | 0.0976115 | + | 1.53541i | ||||
\(370\) | 39.0407 | 0.00548548 | ||||||||
\(371\) | −7291.97 | − | 3165.91i | −1.02043 | − | 0.443035i | ||||
\(372\) | −1015.85 | + | 4337.49i | −0.141584 | + | 0.604539i | ||||
\(373\) | −1541.39 | + | 2669.77i | −0.213969 | + | 0.370605i | −0.952953 | − | 0.303118i | \(-0.901972\pi\) |
0.738984 | + | 0.673723i | \(0.235306\pi\) | |||||||
\(374\) | −598.096 | −0.0826920 | ||||||||
\(375\) | 409.504 | − | 1748.51i | 0.0563912 | − | 0.240780i | ||||
\(376\) | 779.284 | 0.106884 | ||||||||
\(377\) | −1269.46 | −0.173423 | ||||||||
\(378\) | 1164.06 | + | 756.306i | 0.158393 | + | 0.102911i | ||||
\(379\) | 2231.91 | 0.302495 | 0.151247 | − | 0.988496i | \(-0.451671\pi\) | ||||
0.151247 | + | 0.988496i | \(0.451671\pi\) | |||||||
\(380\) | −769.298 | −0.103853 | ||||||||
\(381\) | 1681.83 | − | 7181.12i | 0.226149 | − | 0.965616i | ||||
\(382\) | −283.706 | −0.0379992 | ||||||||
\(383\) | −1596.66 | + | 2765.49i | −0.213017 | + | 0.368956i | −0.952657 | − | 0.304046i | \(-0.901662\pi\) |
0.739640 | + | 0.673002i | \(0.234996\pi\) | |||||||
\(384\) | −1183.28 | + | 5052.38i | −0.157250 | + | 0.671428i | ||||
\(385\) | 56.9247 | + | 497.211i | 0.00753546 | + | 0.0658188i | ||||
\(386\) | 757.468 | 0.0998811 | ||||||||
\(387\) | −4033.87 | + | 2683.91i | −0.529853 | + | 0.352535i | ||||
\(388\) | 2228.74 | − | 3860.29i | 0.291616 | − | 0.505094i | ||||
\(389\) | 5149.92 | + | 8919.92i | 0.671237 | + | 1.16262i | 0.977553 | + | 0.210687i | \(0.0675702\pi\) |
−0.306316 | + | 0.951930i | \(0.599096\pi\) | |||||||
\(390\) | 7.16159 | − | 30.5787i | 0.000929850 | − | 0.00397029i | ||||
\(391\) | −6070.10 | − | 10513.7i | −0.785110 | − | 1.35985i | ||||
\(392\) | 2805.19 | − | 650.852i | 0.361438 | − | 0.0838597i | ||||
\(393\) | −4765.17 | − | 4471.86i | −0.611632 | − | 0.573983i | ||||
\(394\) | −2174.74 | −0.278076 | ||||||||
\(395\) | −215.950 | + | 374.036i | −0.0275079 | + | 0.0476451i | ||||
\(396\) | −256.313 | − | 4031.76i | −0.0325258 | − | 0.511625i | ||||
\(397\) | 6193.80 | + | 10728.0i | 0.783018 | + | 1.35623i | 0.930176 | + | 0.367114i | \(0.119654\pi\) |
−0.147158 | + | 0.989113i | \(0.547013\pi\) | |||||||
\(398\) | −82.6152 | + | 143.094i | −0.0104048 | + | 0.0180217i | ||||
\(399\) | −2729.99 | − | 6323.77i | −0.342533 | − | 0.793444i | ||||
\(400\) | 3521.40 | + | 6099.24i | 0.440175 | + | 0.762405i | ||||
\(401\) | 2499.35 | − | 4329.00i | 0.311250 | − | 0.539102i | −0.667383 | − | 0.744715i | \(-0.732586\pi\) |
0.978633 | + | 0.205613i | \(0.0659189\pi\) | |||||||
\(402\) | 545.975 | − | 2331.21i | 0.0677382 | − | 0.289230i | ||||
\(403\) | 451.197 | + | 781.495i | 0.0557710 | + | 0.0965982i | ||||
\(404\) | −3320.49 | − | 5751.26i | −0.408912 | − | 0.708257i | ||||
\(405\) | 1007.50 | − | 128.620i | 0.123612 | − | 0.0157807i | ||||
\(406\) | 1418.93 | + | 616.050i | 0.173450 | + | 0.0753056i | ||||
\(407\) | 508.633 | − | 880.978i | 0.0619460 | − | 0.107294i | ||||
\(408\) | 1836.13 | + | 1723.10i | 0.222798 | + | 0.209084i | ||||
\(409\) | −7898.75 | −0.954934 | −0.477467 | − | 0.878650i | \(-0.658445\pi\) | ||||
−0.477467 | + | 0.878650i | \(0.658445\pi\) | |||||||
\(410\) | −300.646 | −0.0362142 | ||||||||
\(411\) | −10614.4 | + | 3208.48i | −1.27389 | + | 0.385067i | ||||
\(412\) | 5848.47 | − | 10129.9i | 0.699354 | − | 1.21132i | ||||
\(413\) | 821.033 | + | 7171.35i | 0.0978217 | + | 0.854429i | ||||
\(414\) | −2525.99 | + | 1680.66i | −0.299869 | + | 0.199516i | ||||
\(415\) | −154.064 | − | 266.847i | −0.0182234 | − | 0.0315639i | ||||
\(416\) | 396.829 | + | 687.328i | 0.0467696 | + | 0.0810073i | ||||
\(417\) | 10975.2 | − | 3317.53i | 1.28886 | − | 0.389592i | ||||
\(418\) | 370.829 | − | 642.294i | 0.0433919 | − | 0.0751570i | ||||
\(419\) | −5022.29 | − | 8698.86i | −0.585572 | − | 1.01424i | −0.994804 | − | 0.101810i | \(-0.967536\pi\) |
0.409231 | − | 0.912431i | \(-0.365797\pi\) | |||||||
\(420\) | 617.428 | − | 829.855i | 0.0717319 | − | 0.0964114i | ||||
\(421\) | −5.00064 | + | 8.66136i | −0.000578899 | + | 0.00100268i | −0.866315 | − | 0.499499i | \(-0.833518\pi\) |
0.865736 | + | 0.500501i | \(0.166851\pi\) | |||||||
\(422\) | −654.826 | − | 1134.19i | −0.0755366 | − | 0.130833i | ||||
\(423\) | 2245.51 | + | 1112.85i | 0.258110 | + | 0.127916i | ||||
\(424\) | −1801.86 | + | 3120.91i | −0.206382 | + | 0.357465i | ||||
\(425\) | 7102.92 | 0.810687 | ||||||||
\(426\) | 238.695 | − | 1019.19i | 0.0271475 | − | 0.115915i | ||||
\(427\) | 742.182 | + | 6482.62i | 0.0841141 | + | 0.734698i | ||||
\(428\) | −4911.61 | − | 8507.15i | −0.554700 | − | 0.960768i | ||||
\(429\) | −596.726 | − | 559.994i | −0.0671566 | − | 0.0630228i | ||||
\(430\) | −66.7869 | − | 115.678i | −0.00749012 | − | 0.0129733i | ||||
\(431\) | −1362.41 | + | 2359.77i | −0.152262 | + | 0.263726i | −0.932059 | − | 0.362307i | \(-0.881989\pi\) |
0.779796 | + | 0.626033i | \(0.215323\pi\) | |||||||
\(432\) | −5111.98 | + | 6191.72i | −0.569329 | + | 0.689581i | ||||
\(433\) | −4356.92 | −0.483557 | −0.241779 | − | 0.970331i | \(-0.577731\pi\) | ||||
−0.241779 | + | 0.970331i | \(0.577731\pi\) | |||||||
\(434\) | −125.075 | − | 1092.48i | −0.0138337 | − | 0.120831i | ||||
\(435\) | 1083.39 | − | 327.483i | 0.119413 | − | 0.0360956i | ||||
\(436\) | 1145.06 | − | 1983.30i | 0.125776 | − | 0.217851i | ||||
\(437\) | 15054.2 | 1.64792 | ||||||||
\(438\) | −743.894 | − | 698.104i | −0.0811521 | − | 0.0761568i | ||||
\(439\) | 7876.44 | 0.856315 | 0.428157 | − | 0.903704i | \(-0.359163\pi\) | ||||
0.428157 | + | 0.903704i | \(0.359163\pi\) | |||||||
\(440\) | 226.869 | 0.0245808 | ||||||||
\(441\) | 9012.61 | + | 2130.48i | 0.973179 | + | 0.230049i | ||||
\(442\) | 250.398 | 0.0269462 | ||||||||
\(443\) | −4206.13 | −0.451104 | −0.225552 | − | 0.974231i | \(-0.572419\pi\) | ||||
−0.225552 | + | 0.974231i | \(0.572419\pi\) | |||||||
\(444\) | −2012.55 | + | 608.345i | −0.215116 | + | 0.0650243i | ||||
\(445\) | 1985.14 | 0.211471 | ||||||||
\(446\) | −1235.40 | + | 2139.78i | −0.131161 | + | 0.227178i | ||||
\(447\) | −6690.48 | − | 6278.65i | −0.707940 | − | 0.664363i | ||||
\(448\) | 854.493 | + | 7463.61i | 0.0901139 | + | 0.787104i | ||||
\(449\) | 8229.28 | 0.864952 | 0.432476 | − | 0.901645i | \(-0.357640\pi\) | ||||
0.432476 | + | 0.901645i | \(0.357640\pi\) | |||||||
\(450\) | −112.623 | − | 1771.55i | −0.0117980 | − | 0.185581i | ||||
\(451\) | −3916.90 | + | 6784.27i | −0.408957 | + | 0.708334i | ||||
\(452\) | 6440.44 | + | 11155.2i | 0.670205 | + | 1.16083i | ||||
\(453\) | 12875.7 | − | 3892.00i | 1.33543 | − | 0.403669i | ||||
\(454\) | −1398.62 | − | 2422.48i | −0.144582 | − | 0.250424i | ||||
\(455\) | −23.8320 | − | 208.162i | −0.00245552 | − | 0.0214478i | ||||
\(456\) | −2988.87 | + | 903.462i | −0.306944 | + | 0.0927817i | ||||
\(457\) | 786.679 | 0.0805236 | 0.0402618 | − | 0.999189i | \(-0.487181\pi\) | ||||
0.0402618 | + | 0.999189i | \(0.487181\pi\) | |||||||
\(458\) | −333.738 | + | 578.052i | −0.0340493 | + | 0.0589751i | ||||
\(459\) | 2830.15 | + | 7587.18i | 0.287800 | + | 0.771545i | ||||
\(460\) | 1130.34 | + | 1957.81i | 0.114571 | + | 0.198442i | ||||
\(461\) | −9476.59 | + | 16413.9i | −0.957416 | + | 1.65829i | −0.228677 | + | 0.973502i | \(0.573440\pi\) |
−0.728739 | + | 0.684791i | \(0.759893\pi\) | |||||||
\(462\) | 395.232 | + | 915.516i | 0.0398005 | + | 0.0921941i | ||||
\(463\) | 6255.13 | + | 10834.2i | 0.627863 | + | 1.08749i | 0.987980 | + | 0.154583i | \(0.0494036\pi\) |
−0.360117 | + | 0.932907i | \(0.617263\pi\) | |||||||
\(464\) | −4473.68 | + | 7748.64i | −0.447598 | + | 0.775262i | ||||
\(465\) | −586.667 | − | 550.555i | −0.0585076 | − | 0.0549062i | ||||
\(466\) | 680.925 | + | 1179.40i | 0.0676893 | + | 0.117241i | ||||
\(467\) | −6997.28 | − | 12119.6i | −0.693352 | − | 1.20092i | −0.970733 | − | 0.240161i | \(-0.922800\pi\) |
0.277381 | − | 0.960760i | \(-0.410534\pi\) | |||||||
\(468\) | 107.307 | + | 1687.93i | 0.0105989 | + | 0.166719i | ||||
\(469\) | −1816.87 | − | 15869.5i | −0.178881 | − | 1.56244i | ||||
\(470\) | −34.5454 | + | 59.8344i | −0.00339034 | + | 0.00587224i | ||||
\(471\) | −2843.17 | + | 12139.8i | −0.278145 | + | 1.18763i | ||||
\(472\) | 3272.17 | 0.319097 | ||||||||
\(473\) | −3480.48 | −0.338335 | ||||||||
\(474\) | −196.239 | + | 837.905i | −0.0190159 | + | 0.0811946i | ||||
\(475\) | −4403.92 | + | 7627.81i | −0.425402 | + | 0.736817i | ||||
\(476\) | 7564.55 | + | 3284.26i | 0.728405 | + | 0.316247i | ||||
\(477\) | −9648.85 | + | 6419.81i | −0.926185 | + | 0.616232i | ||||
\(478\) | 302.374 | + | 523.727i | 0.0289336 | + | 0.0501145i | ||||
\(479\) | −4638.59 | − | 8034.27i | −0.442469 | − | 0.766378i | 0.555403 | − | 0.831581i | \(-0.312564\pi\) |
−0.997872 | + | 0.0652029i | \(0.979231\pi\) | |||||||
\(480\) | −515.976 | − | 484.215i | −0.0490645 | − | 0.0460444i | ||||
\(481\) | −212.943 | + | 368.829i | −0.0201858 | + | 0.0349629i | ||||
\(482\) | −1688.51 | − | 2924.58i | −0.159563 | − | 0.276371i | ||||
\(483\) | −12082.3 | + | 16239.3i | −1.13823 | + | 1.52984i | ||||
\(484\) | −3683.03 | + | 6379.19i | −0.345889 | + | 0.599098i | ||||
\(485\) | 402.507 | + | 697.163i | 0.0376844 | + | 0.0652712i | ||||
\(486\) | 1847.45 | − | 826.173i | 0.172432 | − | 0.0771110i | ||||
\(487\) | 1909.97 | − | 3308.17i | 0.177719 | − | 0.307819i | −0.763380 | − | 0.645950i | \(-0.776461\pi\) |
0.941099 | + | 0.338131i | \(0.109795\pi\) | |||||||
\(488\) | 2957.91 | 0.274382 | ||||||||
\(489\) | 10182.6 | − | 3077.96i | 0.941663 | − | 0.284642i | ||||
\(490\) | −74.3799 | + | 244.238i | −0.00685743 | + | 0.0225174i | ||||
\(491\) | −4413.32 | − | 7644.10i | −0.405643 | − | 0.702594i | 0.588753 | − | 0.808313i | \(-0.299619\pi\) |
−0.994396 | + | 0.105719i | \(0.966286\pi\) | |||||||
\(492\) | 15498.3 | − | 4684.77i | 1.42016 | − | 0.429280i | ||||
\(493\) | 4511.87 | + | 7814.79i | 0.412179 | + | 0.713916i | ||||
\(494\) | −155.251 | + | 268.902i | −0.0141398 | + | 0.0244908i | ||||
\(495\) | 653.725 | + | 323.977i | 0.0593591 | + | 0.0294176i | ||||
\(496\) | 6360.23 | 0.575772 | ||||||||
\(497\) | −794.318 | − | 6938.01i | −0.0716902 | − | 0.626181i | ||||
\(498\) | −447.694 | − | 420.137i | −0.0402845 | − | 0.0378048i | ||||
\(499\) | 8605.92 | − | 14905.9i | 0.772052 | − | 1.33723i | −0.164384 | − | 0.986396i | \(-0.552564\pi\) |
0.936436 | − | 0.350837i | \(-0.114103\pi\) | |||||||
\(500\) | −2666.20 | −0.238472 | ||||||||
\(501\) | 12642.5 | − | 3821.52i | 1.12739 | − | 0.340784i | ||||
\(502\) | 929.525 | 0.0826429 | ||||||||
\(503\) | 13600.4 | 1.20559 | 0.602797 | − | 0.797895i | \(-0.294053\pi\) | ||||
0.602797 | + | 0.797895i | \(0.294053\pi\) | |||||||
\(504\) | 1424.24 | − | 3949.25i | 0.125875 | − | 0.349035i | ||||
\(505\) | 1199.35 | 0.105684 | ||||||||
\(506\) | −2179.46 | −0.191480 | ||||||||
\(507\) | −8074.61 | − | 7577.58i | −0.707309 | − | 0.663771i | ||||
\(508\) | −10950.1 | −0.956361 | ||||||||
\(509\) | −4805.19 | + | 8322.83i | −0.418440 | + | 0.724760i | −0.995783 | − | 0.0917422i | \(-0.970756\pi\) |
0.577342 | + | 0.816502i | \(0.304090\pi\) | |||||||
\(510\) | −213.697 | + | 64.5953i | −0.0185542 | + | 0.00560849i | ||||
\(511\) | −6242.85 | − | 2710.42i | −0.540445 | − | 0.234642i | ||||
\(512\) | 9437.78 | 0.814639 | ||||||||
\(513\) | −9902.60 | − | 1664.88i | −0.852263 | − | 0.143287i | ||||
\(514\) | −1958.19 | + | 3391.68i | −0.168039 | + | 0.291052i | ||||
\(515\) | 1056.23 | + | 1829.44i | 0.0903746 | + | 0.156533i | ||||
\(516\) | 5245.41 | + | 4922.53i | 0.447512 | + | 0.419966i | ||||
\(517\) | 900.134 | + | 1559.08i | 0.0765723 | + | 0.132627i | ||||
\(518\) | 417.005 | − | 308.920i | 0.0353710 | − | 0.0262030i | ||||
\(519\) | 5098.33 | − | 21769.0i | 0.431198 | − | 1.84114i | ||||
\(520\) | −94.9807 | −0.00800996 | ||||||||
\(521\) | −5228.57 | + | 9056.15i | −0.439670 | + | 0.761530i | −0.997664 | − | 0.0683147i | \(-0.978238\pi\) |
0.557994 | + | 0.829845i | \(0.311571\pi\) | |||||||
\(522\) | 1877.55 | − | 1249.22i | 0.157430 | − | 0.104745i | ||||
\(523\) | −7878.59 | − | 13646.1i | −0.658713 | − | 1.14092i | −0.980949 | − | 0.194265i | \(-0.937768\pi\) |
0.322236 | − | 0.946659i | \(-0.395565\pi\) | |||||||
\(524\) | −4851.05 | + | 8402.27i | −0.404426 | + | 0.700486i | ||||
\(525\) | −4693.73 | − | 10872.6i | −0.390193 | − | 0.903843i | ||||
\(526\) | −1077.41 | − | 1866.12i | −0.0893101 | − | 0.154690i | ||||
\(527\) | 3207.26 | − | 5555.14i | 0.265105 | − | 0.459176i | ||||
\(528\) | −5521.07 | + | 1668.89i | −0.455064 | + | 0.137555i | ||||
\(529\) | −16035.9 | − | 27775.1i | −1.31799 | − | 2.28282i | ||||
\(530\) | −159.752 | − | 276.698i | −0.0130928 | − | 0.0226773i | ||||
\(531\) | 9428.77 | + | 4672.77i | 0.770572 | + | 0.381885i | ||||
\(532\) | −8217.10 | + | 6087.27i | −0.669655 | + | 0.496084i | ||||
\(533\) | 1639.84 | − | 2840.29i | 0.133264 | − | 0.230819i | ||||
\(534\) | 3786.27 | − | 1144.50i | 0.306831 | − | 0.0927476i | ||||
\(535\) | 1774.06 | 0.143363 | ||||||||
\(536\) | −7241.00 | −0.583514 | ||||||||
\(537\) | −5938.69 | − | 5573.13i | −0.477231 | − | 0.447856i | ||||
\(538\) | −1369.22 | + | 2371.56i | −0.109724 | + | 0.190047i | ||||
\(539\) | 4542.34 | + | 4860.43i | 0.362992 | + | 0.388411i | ||||
\(540\) | −527.016 | − | 1412.85i | −0.0419984 | − | 0.112591i | ||||
\(541\) | 592.613 | + | 1026.44i | 0.0470950 | + | 0.0815710i | 0.888612 | − | 0.458660i | \(-0.151670\pi\) |
−0.841517 | + | 0.540231i | \(0.818337\pi\) | |||||||
\(542\) | −1902.05 | − | 3294.46i | −0.150738 | − | 0.261087i | ||||
\(543\) | 761.133 | − | 3249.90i | 0.0601535 | − | 0.256845i | ||||
\(544\) | 2820.80 | − | 4885.77i | 0.222318 | − | 0.385065i | ||||
\(545\) | 206.796 | + | 358.182i | 0.0162535 | + | 0.0281520i | ||||
\(546\) | −165.467 | − | 383.289i | −0.0129695 | − | 0.0300426i | ||||
\(547\) | −2260.79 | + | 3915.81i | −0.176718 | + | 0.306084i | −0.940754 | − | 0.339089i | \(-0.889881\pi\) |
0.764037 | + | 0.645173i | \(0.223215\pi\) | |||||||
\(548\) | 8231.56 | + | 14257.5i | 0.641669 | + | 1.11140i | ||||
\(549\) | 8523.24 | + | 4224.01i | 0.662592 | + | 0.328372i | ||||
\(550\) | 637.573 | − | 1104.31i | 0.0494295 | − | 0.0856143i | ||||
\(551\) | −11189.7 | −0.865151 | ||||||||
\(552\) | 6690.84 | + | 6278.99i | 0.515908 | + | 0.484151i | ||||
\(553\) | 653.034 | + | 5703.95i | 0.0502167 | + | 0.438620i | ||||
\(554\) | 231.631 | + | 401.196i | 0.0177636 | + | 0.0307675i | ||||
\(555\) | 86.5850 | − | 369.702i | 0.00662221 | − | 0.0282757i | ||||
\(556\) | −8511.32 | − | 14742.0i | −0.649209 | − | 1.12446i | ||||
\(557\) | −9190.20 | + | 15917.9i | −0.699104 | + | 1.21088i | 0.269673 | + | 0.962952i | \(0.413084\pi\) |
−0.968777 | + | 0.247932i | \(0.920249\pi\) | |||||||
\(558\) | −1436.37 | − | 711.845i | −0.108972 | − | 0.0540050i | ||||
\(559\) | 1457.13 | 0.110251 | ||||||||
\(560\) | −1354.58 | − | 588.112i | −0.102217 | − | 0.0443791i | ||||
\(561\) | −1326.46 | + | 5663.77i | −0.0998278 | + | 0.426247i | ||||
\(562\) | −1668.02 | + | 2889.09i | −0.125198 | + | 0.216849i | ||||
\(563\) | 8148.85 | 0.610005 | 0.305003 | − | 0.952351i | \(-0.401343\pi\) | ||||
0.305003 | + | 0.952351i | \(0.401343\pi\) | |||||||
\(564\) | 848.458 | − | 3622.76i | 0.0633449 | − | 0.270471i | ||||
\(565\) | −2326.27 | −0.173216 | ||||||||
\(566\) | 1563.56 | 0.116115 | ||||||||
\(567\) | 9743.63 | − | 9345.90i | 0.721683 | − | 0.692224i | ||||
\(568\) | −3165.70 | −0.233855 | ||||||||
\(569\) | −10045.8 | −0.740141 | −0.370070 | − | 0.929004i | \(-0.620666\pi\) | ||||
−0.370070 | + | 0.929004i | \(0.620666\pi\) | |||||||
\(570\) | 63.1264 | − | 269.539i | 0.00463873 | − | 0.0198065i | ||||
\(571\) | −18378.4 | −1.34696 | −0.673478 | − | 0.739208i | \(-0.735200\pi\) | ||||
−0.673478 | + | 0.739208i | \(0.735200\pi\) | |||||||
\(572\) | −607.480 | + | 1052.19i | −0.0444056 | + | 0.0769128i | ||||
\(573\) | −629.208 | + | 2686.61i | −0.0458735 | + | 0.195872i | ||||
\(574\) | −3211.29 | + | 2378.94i | −0.233513 | + | 0.172988i | ||||
\(575\) | 25883.0 | 1.87721 | ||||||||
\(576\) | 9813.03 | + | 4863.21i | 0.709854 | + | 0.351794i | ||||
\(577\) | 7295.68 | − | 12636.5i | 0.526383 | − | 0.911722i | −0.473145 | − | 0.880985i | \(-0.656881\pi\) |
0.999527 | − | 0.0307372i | \(-0.00978551\pi\) | |||||||
\(578\) | 422.449 | + | 731.703i | 0.0304006 | + | 0.0526555i | ||||
\(579\) | 1679.92 | − | 7172.97i | 0.120579 | − | 0.514851i | ||||
\(580\) | −840.177 | − | 1455.23i | −0.0601491 | − | 0.104181i | ||||
\(581\) | −3757.10 | − | 1631.20i | −0.268280 | − | 0.116478i | ||||
\(582\) | 1169.64 | + | 1097.65i | 0.0833046 | + | 0.0781768i | ||||
\(583\) | −8325.16 | −0.591411 | ||||||||
\(584\) | −1542.62 | + | 2671.90i | −0.109305 | + | 0.189322i | ||||
\(585\) | −273.687 | − | 135.636i | −0.0193429 | − | 0.00958607i | ||||
\(586\) | 1599.00 | + | 2769.55i | 0.112720 | + | 0.195238i | ||||
\(587\) | −4804.17 | + | 8321.07i | −0.337801 | + | 0.585089i | −0.984019 | − | 0.178064i | \(-0.943017\pi\) |
0.646218 | + | 0.763153i | \(0.276350\pi\) | |||||||
\(588\) | 28.4914 | − | 13749.5i | 0.00199824 | − | 0.964319i | ||||
\(589\) | 3977.11 | + | 6888.55i | 0.278224 | + | 0.481898i | ||||
\(590\) | −145.054 | + | 251.241i | −0.0101217 | + | 0.0175312i | ||||
\(591\) | −4823.18 | + | 20594.1i | −0.335700 | + | 1.43338i | ||||
\(592\) | 1500.86 | + | 2599.57i | 0.104198 | + | 0.180476i | ||||
\(593\) | −5093.51 | − | 8822.22i | −0.352724 | − | 0.610936i | 0.634001 | − | 0.773332i | \(-0.281411\pi\) |
−0.986726 | + | 0.162395i | \(0.948078\pi\) | |||||||
\(594\) | 1433.64 | + | 241.031i | 0.0990285 | + | 0.0166492i | ||||
\(595\) | −1196.74 | + | 886.553i | −0.0824566 | + | 0.0610842i | ||||
\(596\) | −6811.06 | + | 11797.1i | −0.468107 | + | 0.810785i | ||||
\(597\) | 1171.83 | + | 1099.69i | 0.0803344 | + | 0.0753894i | ||||
\(598\) | 912.449 | 0.0623960 | ||||||||
\(599\) | −21280.9 | −1.45161 | −0.725804 | − | 0.687902i | \(-0.758532\pi\) | ||||
−0.725804 | + | 0.687902i | \(0.758532\pi\) | |||||||
\(600\) | −5138.81 | + | 1553.34i | −0.349652 | + | 0.105691i | ||||
\(601\) | 5973.18 | − | 10345.9i | 0.405410 | − | 0.702190i | −0.588959 | − | 0.808163i | \(-0.700462\pi\) |
0.994369 | + | 0.105973i | \(0.0337956\pi\) | |||||||
\(602\) | −1628.71 | − | 707.126i | −0.110268 | − | 0.0478743i | ||||
\(603\) | −20865.0 | − | 10340.4i | −1.40910 | − | 0.698331i | ||||
\(604\) | −9985.16 | − | 17294.8i | −0.672667 | − | 1.16509i | ||||
\(605\) | −665.151 | − | 1152.07i | −0.0446979 | − | 0.0774190i | ||||
\(606\) | 2287.54 | − | 691.467i | 0.153341 | − | 0.0463514i | ||||
\(607\) | 12041.0 | − | 20855.6i | 0.805155 | − | 1.39457i | −0.111031 | − | 0.993817i | \(-0.535415\pi\) |
0.916186 | − | 0.400753i | \(-0.131251\pi\) | |||||||
\(608\) | 3497.88 | + | 6058.51i | 0.233319 | + | 0.404120i | ||||
\(609\) | 8980.72 | − | 12070.5i | 0.597565 | − | 0.803158i | ||||
\(610\) | −131.123 | + | 227.112i | −0.00870332 | + | 0.0150746i | ||||
\(611\) | −376.849 | − | 652.721i | −0.0249520 | − | 0.0432181i | ||||
\(612\) | 10009.5 | − | 6659.79i | 0.661129 | − | 0.439879i | ||||
\(613\) | −1910.99 | + | 3309.93i | −0.125912 | + | 0.218086i | −0.922089 | − | 0.386978i | \(-0.873519\pi\) |
0.796177 | + | 0.605064i | \(0.206852\pi\) | |||||||
\(614\) | −1906.47 | −0.125308 | ||||||||
\(615\) | −666.777 | + | 2847.02i | −0.0437187 | + | 0.186671i | ||||
\(616\) | 2423.26 | − | 1795.16i | 0.158500 | − | 0.117417i | ||||
\(617\) | −7038.79 | − | 12191.5i | −0.459272 | − | 0.795483i | 0.539650 | − | 0.841889i | \(-0.318556\pi\) |
−0.998923 | + | 0.0464064i | \(0.985223\pi\) | |||||||
\(618\) | 3069.28 | + | 2880.36i | 0.199781 | + | 0.187484i | ||||
\(619\) | 12122.3 | + | 20996.4i | 0.787132 | + | 1.36335i | 0.927717 | + | 0.373285i | \(0.121768\pi\) |
−0.140585 | + | 0.990069i | \(0.544898\pi\) | |||||||
\(620\) | −597.240 | + | 1034.45i | −0.0386867 | + | 0.0670073i | ||||
\(621\) | 10313.1 | + | 27647.7i | 0.666424 | + | 1.78658i | ||||
\(622\) | 3121.76 | 0.201240 | ||||||||
\(623\) | 21203.8 | − | 15707.9i | 1.36358 | − | 1.01015i | ||||
\(624\) | 2311.44 | − | 698.693i | 0.148288 | − | 0.0448239i | ||||
\(625\) | −7450.42 | + | 12904.5i | −0.476827 | + | 0.825889i | ||||
\(626\) | −2083.91 | −0.133051 | ||||||||
\(627\) | −5259.89 | − | 4936.12i | −0.335023 | − | 0.314401i | ||||
\(628\) | 18511.3 | 1.17624 | ||||||||
\(629\) | 3027.35 | 0.191905 | ||||||||
\(630\) | 240.092 | + | 284.424i | 0.0151833 | + | 0.0179868i | ||||
\(631\) | −7470.58 | −0.471314 | −0.235657 | − | 0.971836i | \(-0.575724\pi\) | ||||
−0.235657 | + | 0.971836i | \(0.575724\pi\) | |||||||
\(632\) | 2602.62 | 0.163808 | ||||||||
\(633\) | −12192.7 | + | 3685.56i | −0.765587 | + | 0.231418i | ||||
\(634\) | 1356.37 | 0.0849659 | ||||||||
\(635\) | 988.786 | − | 1712.63i | 0.0617933 | − | 0.107029i | ||||
\(636\) | 12546.8 | + | 11774.5i | 0.782253 | + | 0.734102i | ||||
\(637\) | −1901.69 | − | 2034.86i | −0.118285 | − | 0.126568i | ||||
\(638\) | 1619.98 | 0.100526 | ||||||||
\(639\) | −9121.97 | − | 4520.73i | −0.564726 | − | 0.279871i | ||||
\(640\) | −695.675 | + | 1204.94i | −0.0429671 | + | 0.0744213i | ||||
\(641\) | 7798.13 | + | 13506.8i | 0.480511 | + | 0.832269i | 0.999750 | − | 0.0223597i | \(-0.00711790\pi\) |
−0.519239 | + | 0.854629i | \(0.673785\pi\) | |||||||
\(642\) | 3383.68 | − | 1022.80i | 0.208011 | − | 0.0628767i | ||||
\(643\) | 13714.2 | + | 23753.6i | 0.841109 | + | 1.45684i | 0.888958 | + | 0.457990i | \(0.151430\pi\) |
−0.0478482 | + | 0.998855i | \(0.515236\pi\) | |||||||
\(644\) | 27565.2 | + | 11967.8i | 1.68668 | + | 0.732296i | ||||
\(645\) | −1243.56 | + | 375.897i | −0.0759147 | + | 0.0229472i | ||||
\(646\) | 2207.15 | 0.134426 | ||||||||
\(647\) | 1413.31 | − | 2447.93i | 0.0858780 | − | 0.148745i | −0.819887 | − | 0.572525i | \(-0.805964\pi\) |
0.905765 | + | 0.423780i | \(0.139297\pi\) | |||||||
\(648\) | −3706.80 | − | 4870.24i | −0.224717 | − | 0.295249i | ||||
\(649\) | 3779.61 | + | 6546.47i | 0.228602 | + | 0.395950i | ||||
\(650\) | −266.925 | + | 462.328i | −0.0161072 | + | 0.0278985i | ||||
\(651\) | −10622.8 | − | 1238.49i | −0.639538 | − | 0.0745623i | ||||
\(652\) | −7896.68 | − | 13677.5i | −0.474322 | − | 0.821550i | ||||
\(653\) | 3416.70 | − | 5917.89i | 0.204756 | − | 0.354648i | −0.745299 | − | 0.666730i | \(-0.767693\pi\) |
0.950055 | + | 0.312083i | \(0.101027\pi\) | |||||||
\(654\) | 600.928 | + | 563.938i | 0.0359299 | + | 0.0337182i | ||||
\(655\) | −876.094 | − | 1517.44i | −0.0522623 | − | 0.0905210i | ||||
\(656\) | −11557.9 | − | 20018.9i | −0.687897 | − | 1.19147i | ||||
\(657\) | −8260.63 | + | 5496.17i | −0.490530 | + | 0.326371i | ||||
\(658\) | 104.465 | + | 912.458i | 0.00618919 | + | 0.0540598i | ||||
\(659\) | −2394.72 | + | 4147.77i | −0.141555 | + | 0.245181i | −0.928082 | − | 0.372375i | \(-0.878544\pi\) |
0.786527 | + | 0.617556i | \(0.211877\pi\) | |||||||
\(660\) | 247.007 | − | 1054.68i | 0.0145678 | − | 0.0622019i | ||||
\(661\) | 13763.7 | 0.809903 | 0.404952 | − | 0.914338i | \(-0.367288\pi\) | ||||
0.404952 | + | 0.914338i | \(0.367288\pi\) | |||||||
\(662\) | 5578.32 | 0.327504 | ||||||||
\(663\) | 555.335 | − | 2371.18i | 0.0325301 | − | 0.138898i | ||||
\(664\) | −928.388 | + | 1608.02i | −0.0542597 | + | 0.0939806i | ||||
\(665\) | −210.069 | − | 1834.86i | −0.0122498 | − | 0.106997i | ||||
\(666\) | −48.0015 | − | 755.056i | −0.00279282 | − | 0.0439306i | ||||
\(667\) | 16441.3 | + | 28477.1i | 0.954435 | + | 1.65313i | ||||
\(668\) | −9804.34 | − | 16981.6i | −0.567876 | − | 0.983591i | ||||
\(669\) | 17523.1 | + | 16444.5i | 1.01268 | + | 0.950344i | ||||
\(670\) | 320.991 | − | 555.972i | 0.0185089 | − | 0.0320583i | ||||
\(671\) | 3416.62 | + | 5917.76i | 0.196568 | + | 0.340466i | ||||
\(672\) | −9342.77 | − | 1089.25i | −0.536317 | − | 0.0625280i | ||||
\(673\) | −10042.1 | + | 17393.4i | −0.575176 | + | 0.996233i | 0.420847 | + | 0.907132i | \(0.361733\pi\) |
−0.996023 | + | 0.0891016i | \(0.971600\pi\) | |||||||
\(674\) | −1119.67 | − | 1939.33i | −0.0639884 | − | 0.110831i | ||||
\(675\) | −17025.7 | − | 2862.45i | −0.970846 | − | 0.163224i | ||||
\(676\) | −8220.13 | + | 14237.7i | −0.467690 | + | 0.810063i | ||||
\(677\) | 23113.0 | 1.31212 | 0.656060 | − | 0.754709i | \(-0.272222\pi\) | ||||
0.656060 | + | 0.754709i | \(0.272222\pi\) | |||||||
\(678\) | −4436.92 | + | 1341.17i | −0.251326 | + | 0.0759696i | ||||
\(679\) | 9815.78 | + | 4261.66i | 0.554779 | + | 0.240865i | ||||
\(680\) | 337.578 | + | 584.702i | 0.0190375 | + | 0.0329740i | ||||
\(681\) | −26041.9 | + | 7871.85i | −1.46539 | + | 0.442951i | ||||
\(682\) | −575.782 | − | 997.283i | −0.0323282 | − | 0.0559940i | ||||
\(683\) | 1185.46 | − | 2053.27i | 0.0664132 | − | 0.115031i | −0.830907 | − | 0.556412i | \(-0.812178\pi\) |
0.897320 | + | 0.441381i | \(0.145511\pi\) | |||||||
\(684\) | 945.870 | + | 14878.4i | 0.0528746 | + | 0.831710i | ||||
\(685\) | −2973.22 | −0.165841 | ||||||||
\(686\) | 1138.12 | + | 3197.33i | 0.0633436 | + | 0.177951i | ||||
\(687\) | 4733.79 | + | 4442.40i | 0.262890 | + | 0.246708i | ||||
\(688\) | 5135.06 | − | 8894.18i | 0.284553 | − | 0.492860i | ||||
\(689\) | 3485.40 | 0.192718 | ||||||||
\(690\) | −778.710 | + | 235.385i | −0.0429638 | + | 0.0129869i | ||||
\(691\) | 10628.1 | 0.585111 | 0.292555 | − | 0.956249i | \(-0.405494\pi\) | ||||
0.292555 | + | 0.956249i | \(0.405494\pi\) | |||||||
\(692\) | −33194.2 | −1.82349 | ||||||||
\(693\) | 9546.19 | − | 1712.27i | 0.523275 | − | 0.0938582i | ||||
\(694\) | 1019.64 | 0.0557710 | ||||||||
\(695\) | 3074.27 | 0.167789 | ||||||||
\(696\) | −4973.26 | − | 4667.13i | −0.270849 | − | 0.254177i | ||||
\(697\) | −23313.2 | −1.26693 | ||||||||
\(698\) | 69.6345 | − | 120.610i | 0.00377608 | − | 0.00654036i | ||||
\(699\) | 12678.7 | − | 3832.45i | 0.686052 | − | 0.207377i | ||||
\(700\) | −14127.8 | + | 10466.0i | −0.762830 | + | 0.565109i | ||||
\(701\) | −13584.8 | −0.731942 | −0.365971 | − | 0.930626i | \(-0.619263\pi\) | ||||
−0.365971 | + | 0.930626i | \(0.619263\pi\) | |||||||
\(702\) | −600.205 | − | 100.910i | −0.0322696 | − | 0.00542533i | ||||
\(703\) | −1877.01 | + | 3251.07i | −0.100701 | + | 0.174419i | ||||
\(704\) | 3933.64 | + | 6813.27i | 0.210589 | + | 0.364751i | ||||
\(705\) | 489.996 | + | 459.835i | 0.0261764 | + | 0.0245651i | ||||
\(706\) | −1536.29 | − | 2660.94i | −0.0818969 | − | 0.141850i | ||||
\(707\) | 12810.6 | − | 9490.19i | 0.681462 | − | 0.504831i | ||||
\(708\) | 3562.62 | − | 15211.8i | 0.189112 | − | 0.807476i | ||||
\(709\) | 21284.0 | 1.12741 | 0.563707 | − | 0.825975i | \(-0.309375\pi\) | ||||
0.563707 | + | 0.825975i | \(0.309375\pi\) | |||||||
\(710\) | 140.334 | − | 243.066i | 0.00741781 | − | 0.0128480i | ||||
\(711\) | 7499.46 | + | 3716.63i | 0.395572 | + | 0.196040i | ||||
\(712\) | −5981.19 | − | 10359.7i | −0.314824 | − | 0.545291i | ||||
\(713\) | 11687.3 | − | 20242.9i | 0.613873 | − | 1.06326i | ||||
\(714\) | −1771.43 | + | 2380.89i | −0.0928489 | + | 0.124794i | ||||
\(715\) | −109.710 | − | 190.024i | −0.00573836 | − | 0.00993913i | ||||
\(716\) | −6045.71 | + | 10471.5i | −0.315557 | + | 0.546561i | ||||
\(717\) | 5630.13 | − | 1701.85i | 0.293251 | − | 0.0886428i | ||||
\(718\) | −1353.56 | − | 2344.43i | −0.0703543 | − | 0.121857i | ||||
\(719\) | −13420.8 | − | 23245.5i | −0.696120 | − | 1.20572i | −0.969802 | − | 0.243895i | \(-0.921575\pi\) |
0.273681 | − | 0.961820i | \(-0.411759\pi\) | |||||||
\(720\) | −1792.41 | + | 1192.57i | −0.0927765 | + | 0.0617283i | ||||
\(721\) | 25757.8 | + | 11183.1i | 1.33047 | + | 0.577643i | ||||
\(722\) | 463.772 | − | 803.277i | 0.0239055 | − | 0.0414056i | ||||
\(723\) | −31439.6 | + | 9503.42i | −1.61722 | + | 0.488847i | ||||
\(724\) | −4955.59 | −0.254383 | ||||||||
\(725\) | −19238.7 | −0.985527 | ||||||||
\(726\) | −1932.86 | − | 1813.88i | −0.0988086 | − | 0.0927265i | ||||
\(727\) | 8514.96 | − | 14748.3i | 0.434391 | − | 0.752387i | −0.562855 | − | 0.826556i | \(-0.690297\pi\) |
0.997246 | + | 0.0741684i | \(0.0236302\pi\) | |||||||
\(728\) | −1014.52 | + | 751.560i | −0.0516491 | + | 0.0382619i | ||||
\(729\) | −3726.28 | − | 19327.1i | −0.189314 | − | 0.981917i | ||||
\(730\) | −136.768 | − | 236.888i | −0.00693424 | − | 0.0120105i | ||||
\(731\) | −5178.90 | − | 8970.11i | −0.262036 | − | 0.453860i | ||||
\(732\) | 3220.47 | − | 13750.8i | 0.162612 | − | 0.694325i | ||||
\(733\) | −710.792 | + | 1231.13i | −0.0358168 | + | 0.0620365i | −0.883378 | − | 0.468661i | \(-0.844737\pi\) |
0.847561 | + | 0.530697i | \(0.178070\pi\) | |||||||
\(734\) | 156.080 | + | 270.339i | 0.00784881 | + | 0.0135945i | ||||
\(735\) | 2147.89 | + | 1246.03i | 0.107791 | + | 0.0625312i | ||||
\(736\) | 10279.0 | − | 17803.7i | 0.514794 | − | 0.891650i | ||||
\(737\) | −8363.91 | − | 14486.7i | −0.418031 | − | 0.724051i | ||||
\(738\) | 369.651 | + | 5814.56i | 0.0184377 | + | 0.290023i | ||||
\(739\) | 12068.5 | − | 20903.3i | 0.600742 | − | 1.04052i | −0.391967 | − | 0.919979i | \(-0.628205\pi\) |
0.992709 | − | 0.120537i | \(-0.0384616\pi\) | |||||||
\(740\) | −563.738 | −0.0280046 | ||||||||
\(741\) | 2202.09 | + | 2066.55i | 0.109171 | + | 0.102451i | ||||
\(742\) | −3895.80 | − | 1691.42i | −0.192748 | − | 0.0836844i | ||||
\(743\) | 3732.57 | + | 6465.00i | 0.184300 | + | 0.319216i | 0.943340 | − | 0.331827i | \(-0.107665\pi\) |
−0.759041 | + | 0.651043i | \(0.774332\pi\) | |||||||
\(744\) | −1105.53 | + | 4720.43i | −0.0544769 | + | 0.232607i | ||||
\(745\) | −1230.07 | − | 2130.54i | −0.0604916 | − | 0.104775i | ||||
\(746\) | −823.503 | + | 1426.35i | −0.0404163 | + | 0.0700031i | ||||
\(747\) | −4971.46 | + | 3307.73i | −0.243502 | + | 0.162013i | ||||
\(748\) | 8636.36 | 0.422161 | ||||||||
\(749\) | 18949.3 | − | 14037.7i | 0.924421 | − | 0.684816i | ||||
\(750\) | 218.781 | − | 934.156i | 0.0106517 | − | 0.0454807i | ||||
\(751\) | −12695.5 | + | 21989.2i | −0.616863 | + | 1.06844i | 0.373191 | + | 0.927754i | \(0.378263\pi\) |
−0.990055 | + | 0.140684i | \(0.955070\pi\) | |||||||
\(752\) | −5312.20 | −0.257601 | ||||||||
\(753\) | 2061.51 | − | 8802.30i | 0.0997686 | − | 0.425994i | ||||
\(754\) | −678.218 | −0.0327576 | ||||||||
\(755\) | 3606.62 | 0.173852 | ||||||||
\(756\) | −16808.7 | − | 10920.9i | −0.808634 | − | 0.525381i | ||||
\(757\) | −1908.73 | −0.0916434 | −0.0458217 | − | 0.998950i | \(-0.514591\pi\) | ||||
−0.0458217 | + | 0.998950i | \(0.514591\pi\) | |||||||
\(758\) | 1192.42 | 0.0571379 | ||||||||
\(759\) | −4833.64 | + | 20638.8i | −0.231159 | + | 0.987009i | ||||
\(760\) | −837.215 | −0.0399592 | ||||||||
\(761\) | −11616.9 | + | 20121.0i | −0.553365 | + | 0.958457i | 0.444664 | + | 0.895698i | \(0.353323\pi\) |
−0.998029 | + | 0.0627589i | \(0.980010\pi\) | |||||||
\(762\) | 898.533 | − | 3836.58i | 0.0427171 | − | 0.182394i | ||||
\(763\) | 5043.06 | + | 2189.52i | 0.239280 | + | 0.103887i | ||||
\(764\) | 4096.65 | 0.193994 | ||||||||
\(765\) | 137.757 | + | 2166.90i | 0.00651061 | + | 0.102411i | ||||
\(766\) | −853.029 | + | 1477.49i | −0.0402365 | + | 0.0696917i | ||||
\(767\) | −1582.36 | − | 2740.74i | −0.0744927 | − | 0.129025i | ||||
\(768\) | 3212.82 | − | 13718.2i | 0.150954 | − | 0.644547i | ||||
\(769\) | −13166.1 | − | 22804.4i | −0.617403 | − | 1.06937i | −0.989958 | − | 0.141363i | \(-0.954852\pi\) |
0.372555 | − | 0.928010i | \(-0.378482\pi\) | |||||||
\(770\) | 30.4125 | + | 265.639i | 0.00142336 | + | 0.0124324i | ||||
\(771\) | 27775.2 | + | 26065.5i | 1.29741 | + | 1.21754i | ||||
\(772\) | −10937.7 | −0.509916 | ||||||||
\(773\) | 6385.60 | − | 11060.2i | 0.297120 | − | 0.514628i | −0.678356 | − | 0.734734i | \(-0.737307\pi\) |
0.975476 | + | 0.220106i | \(0.0706404\pi\) | |||||||
\(774\) | −2155.13 | + | 1433.90i | −0.100083 | + | 0.0665899i | ||||
\(775\) | 6837.92 | + | 11843.6i | 0.316936 | + | 0.548949i | ||||
\(776\) | 2425.50 | − | 4201.09i | 0.112204 | − | 0.194343i | ||||
\(777\) | −2000.53 | − | 4634.03i | −0.0923661 | − | 0.213957i | ||||
\(778\) | 2751.39 | + | 4765.55i | 0.126789 | + | 0.219606i | ||||
\(779\) | 14454.5 | − | 25036.0i | 0.664810 | − | 1.15148i | ||||
\(780\) | −103.412 | + | 441.550i | −0.00474709 | + | 0.0202692i | ||||
\(781\) | −3656.63 | − | 6333.47i | −0.167534 | − | 0.290178i | ||||
\(782\) | −3243.00 | − | 5617.05i | −0.148299 | − | 0.256861i | ||||
\(783\) | −7665.64 | − | 20550.4i | −0.349869 | − | 0.937944i | ||||
\(784\) | −19122.3 | + | 4436.70i | −0.871097 | + | 0.202109i | ||||
\(785\) | −1671.56 | + | 2895.23i | −0.0760007 | + | 0.131637i | ||||
\(786\) | −2545.84 | − | 2389.13i | −0.115530 | − | 0.108419i | ||||
\(787\) | 4734.23 | 0.214431 | 0.107215 | − | 0.994236i | \(-0.465807\pi\) | ||||
0.107215 | + | 0.994236i | \(0.465807\pi\) | |||||||
\(788\) | 31402.8 | 1.41964 | ||||||||
\(789\) | −20061.0 | + | 6063.97i | −0.905186 | + | 0.273616i | ||||
\(790\) | −115.373 | + | 199.832i | −0.00519594 | + | 0.00899963i | ||||
\(791\) | −24847.6 | + | 18407.2i | −1.11691 | + | 0.827415i | ||||
\(792\) | −278.941 | − | 4387.70i | −0.0125148 | − | 0.196856i | ||||
\(793\) | −1430.40 | − | 2477.52i | −0.0640541 | − | 0.110945i | ||||
\(794\) | 3309.09 | + | 5731.52i | 0.147903 | + | 0.256176i | ||||
\(795\) | −2974.54 | + | 899.130i | −0.132699 | + | 0.0401118i | ||||
\(796\) | 1192.94 | − | 2066.24i | 0.0531191 | − | 0.0920049i | ||||
\(797\) | 1883.34 | + | 3262.04i | 0.0837031 | + | 0.144978i | 0.904838 | − | 0.425756i | \(-0.139992\pi\) |
−0.821135 | + | 0.570734i | \(0.806659\pi\) | |||||||
\(798\) | −1458.52 | − | 3378.53i | −0.0647007 | − | 0.149873i | ||||
\(799\) | −2678.77 | + | 4639.77i | −0.118608 | + | 0.205436i | ||||
\(800\) | 6013.97 | + | 10416.5i | 0.265783 | + | 0.460349i | ||||
\(801\) | −2440.77 | − | 38393.0i | −0.107666 | − | 1.69357i | ||||
\(802\) | 1335.30 | − | 2312.80i | 0.0587918 | − | 0.101830i | ||||
\(803\) | −7127.39 | −0.313225 | ||||||||
\(804\) | −7883.74 | + | 33662.2i | −0.345819 | + | 1.47658i | ||||
\(805\) | −4360.93 | + | 3230.60i | −0.190935 | + | 0.141446i | ||||
\(806\) | 241.056 | + | 417.521i | 0.0105345 | + | 0.0182463i | ||||
\(807\) | 19421.2 | + | 18225.8i | 0.847161 | + | 0.795015i | ||||
\(808\) | −3613.64 | − | 6259.00i | −0.157336 | − | 0.272514i | ||||
\(809\) | −2426.99 | + | 4203.67i | −0.105474 | + | 0.182686i | −0.913932 | − | 0.405868i | \(-0.866969\pi\) |
0.808458 | + | 0.588554i | \(0.200303\pi\) | |||||||
\(810\) | 538.264 | − | 68.7163i | 0.0233490 | − | 0.00298079i | ||||
\(811\) | 3204.85 | 0.138764 | 0.0693820 | − | 0.997590i | \(-0.477897\pi\) | ||||
0.0693820 | + | 0.997590i | \(0.477897\pi\) | |||||||
\(812\) | −20489.1 | − | 8895.62i | −0.885499 | − | 0.384452i | ||||
\(813\) | −35415.8 | + | 10705.3i | −1.52778 | + | 0.461811i | ||||
\(814\) | 271.742 | − | 470.670i | 0.0117009 | − | 0.0202666i | ||||
\(815\) | 2852.26 | 0.122589 | ||||||||
\(816\) | −12516.4 | − | 11746.0i | −0.536964 | − | 0.503911i | ||||
\(817\) | 12844.0 | 0.550005 | ||||||||
\(818\) | −4219.97 | −0.180376 | ||||||||
\(819\) | −3996.59 | + | 716.856i | −0.170515 | + | 0.0305848i | ||||
\(820\) | 4341.25 | 0.184882 | ||||||||
\(821\) | −11497.3 | −0.488744 | −0.244372 | − | 0.969682i | \(-0.578582\pi\) | ||||
−0.244372 | + | 0.969682i | \(0.578582\pi\) | |||||||
\(822\) | −5670.84 | + | 1714.16i | −0.240625 | + | 0.0727350i | ||||
\(823\) | 26524.5 | 1.12343 | 0.561717 | − | 0.827329i | \(-0.310141\pi\) | ||||
0.561717 | + | 0.827329i | \(0.310141\pi\) | |||||||
\(824\) | 6364.80 | − | 11024.2i | 0.269088 | − | 0.466074i | ||||
\(825\) | −9043.42 | − | 8486.76i | −0.381638 | − | 0.358147i | ||||
\(826\) | 438.644 | + | 3831.36i | 0.0184775 | + | 0.161392i | ||||
\(827\) | 18948.7 | 0.796750 | 0.398375 | − | 0.917223i | \(-0.369574\pi\) | ||||
0.398375 | + | 0.917223i | \(0.369574\pi\) | |||||||
\(828\) | 36474.7 | − | 24268.3i | 1.53090 | − | 1.01858i | ||||
\(829\) | −11676.6 | + | 20224.5i | −0.489198 | + | 0.847316i | −0.999923 | − | 0.0124282i | \(-0.996044\pi\) |
0.510725 | + | 0.859744i | \(0.329377\pi\) | |||||||
\(830\) | −82.3102 | − | 142.565i | −0.00344220 | − | 0.00596207i | ||||
\(831\) | 4312.91 | − | 1303.69i | 0.180040 | − | 0.0544217i | ||||
\(832\) | −1646.85 | − | 2852.43i | −0.0686230 | − | 0.118858i | ||||
\(833\) | −5767.68 | + | 18939.1i | −0.239902 | + | 0.787755i | ||||
\(834\) | 5863.58 | − | 1772.42i | 0.243452 | − | 0.0735897i | ||||
\(835\) | 3541.31 | 0.146769 | ||||||||
\(836\) | −5354.68 | + | 9274.58i | −0.221526 | + | 0.383694i | ||||
\(837\) | −9926.54 | + | 12023.2i | −0.409930 | + | 0.496514i | ||||
\(838\) | −2683.20 | − | 4647.44i | −0.110608 | − | 0.191579i | ||||
\(839\) | 1451.60 | − | 2514.25i | 0.0597316 | − | 0.103458i | −0.834613 | − | 0.550836i | \(-0.814309\pi\) |
0.894345 | + | 0.447378i | \(0.147642\pi\) | |||||||
\(840\) | 671.938 | − | 903.118i | 0.0276001 | − | 0.0370959i | ||||
\(841\) | −26.1867 | − | 45.3567i | −0.00107371 | − | 0.00185972i | ||||
\(842\) | −2.67164 | + | 4.62741i | −0.000109348 | + | 0.000189396i | ||||
\(843\) | 23659.4 | + | 22203.0i | 0.966634 | + | 0.907133i | ||||
\(844\) | 9455.53 | + | 16377.5i | 0.385631 | + | 0.667933i | ||||
\(845\) | −1484.54 | − | 2571.31i | −0.0604377 | − | 0.104681i | ||||
\(846\) | 1199.68 | + | 594.548i | 0.0487541 | + | 0.0241619i | ||||
\(847\) | −16220.8 | − | 7042.47i | −0.658031 | − | 0.285693i | ||||
\(848\) | 12282.8 | − | 21274.5i | 0.497400 | − | 0.861521i | ||||
\(849\) | 3467.68 | − | 14806.4i | 0.140177 | − | 0.598532i | ||||
\(850\) | 3794.80 | 0.153130 | ||||||||
\(851\) | 11031.7 | 0.444372 | ||||||||
\(852\) | −3446.70 | + | 14716.8i | −0.138594 | + | 0.591772i | ||||
\(853\) | −17856.2 | + | 30927.9i | −0.716747 | + | 1.24144i | 0.245535 | + | 0.969388i | \(0.421036\pi\) |
−0.962282 | + | 0.272054i | \(0.912297\pi\) | |||||||
\(854\) | 396.517 | + | 3463.40i | 0.0158882 | + | 0.138776i | ||||
\(855\) | −2412.44 | − | 1195.57i | −0.0964955 | − | 0.0478219i | ||||
\(856\) | −5345.22 | − | 9258.20i | −0.213430 | − | 0.369671i | ||||
\(857\) | 5034.32 | + | 8719.69i | 0.200664 | + | 0.347560i | 0.948743 | − | 0.316050i | \(-0.102357\pi\) |
−0.748079 | + | 0.663610i | \(0.769023\pi\) | |||||||
\(858\) | −318.806 | − | 299.182i | −0.0126851 | − | 0.0119043i | ||||
\(859\) | −9101.61 | + | 15764.4i | −0.361517 | + | 0.626165i | −0.988211 | − | 0.153100i | \(-0.951074\pi\) |
0.626694 | + | 0.779265i | \(0.284408\pi\) | |||||||
\(860\) | 964.387 | + | 1670.37i | 0.0382388 | + | 0.0662315i | ||||
\(861\) | 15405.7 | + | 35685.9i | 0.609786 | + | 1.41251i | ||||
\(862\) | −727.881 | + | 1260.73i | −0.0287607 | + | 0.0498150i | ||||
\(863\) | 11358.5 | + | 19673.5i | 0.448028 | + | 0.776008i | 0.998258 | − | 0.0590059i | \(-0.0187931\pi\) |
−0.550229 | + | 0.835014i | \(0.685460\pi\) | |||||||
\(864\) | −8730.42 | + | 10574.4i | −0.343767 | + | 0.416377i | ||||
\(865\) | 2997.42 | − | 5191.68i | 0.117821 | − | 0.204072i | ||||
\(866\) | −2327.72 | −0.0913387 | ||||||||
\(867\) | 7865.90 | − | 2377.67i | 0.308120 | − | 0.0931372i | ||||
\(868\) | 1806.06 | + | 15775.1i | 0.0706239 | + | 0.616868i | ||||
\(869\) | 3006.23 | + | 5206.94i | 0.117352 | + | 0.203260i | ||||
\(870\) | 578.811 | − | 174.960i | 0.0225558 | − | 0.00681806i | ||||
\(871\) | 3501.62 | + | 6064.99i | 0.136220 | + | 0.235941i | ||||
\(872\) | 1246.15 | − | 2158.40i | 0.0483945 | − | 0.0838217i | ||||
\(873\) | 12988.4 | − | 8641.76i | 0.503540 | − | 0.335028i | ||||
\(874\) | 8042.86 | 0.311274 | ||||||||
\(875\) | −728.048 | − | 6359.17i | −0.0281286 | − | 0.245691i | ||||
\(876\) | 10741.7 | + | 10080.5i | 0.414300 | + | 0.388798i | ||||
\(877\) | 22206.7 | − | 38463.1i | 0.855037 | − | 1.48097i | −0.0215744 | − | 0.999767i | \(-0.506868\pi\) |
0.876611 | − | 0.481200i | \(-0.159799\pi\) | |||||||
\(878\) | 4208.06 | 0.161748 | ||||||||
\(879\) | 29773.0 | − | 8999.67i | 1.14246 | − | 0.345337i | ||||
\(880\) | −1546.51 | −0.0592420 | ||||||||
\(881\) | 372.284 | 0.0142367 | 0.00711837 | − | 0.999975i | \(-0.497734\pi\) | ||||
0.00711837 | + | 0.999975i | \(0.497734\pi\) | |||||||
\(882\) | 4815.07 | + | 1138.23i | 0.183823 | + | 0.0434536i | ||||
\(883\) | 6638.71 | 0.253013 | 0.126507 | − | 0.991966i | \(-0.459624\pi\) | ||||
0.126507 | + | 0.991966i | \(0.459624\pi\) | |||||||
\(884\) | −3615.68 | −0.137566 | ||||||||
\(885\) | 2057.46 | + | 1930.82i | 0.0781479 | + | 0.0733376i | ||||
\(886\) | −2247.16 | −0.0852087 | ||||||||
\(887\) | −19101.1 | + | 33084.1i | −0.723059 | + | 1.25237i | 0.236709 | + | 0.971581i | \(0.423931\pi\) |
−0.959768 | + | 0.280794i | \(0.909402\pi\) | |||||||
\(888\) | −2190.23 | + | 662.053i | −0.0827694 | + | 0.0250192i | ||||
\(889\) | −2990.09 | − | 26117.1i | −0.112806 | − | 0.985309i | ||||
\(890\) | 1060.58 | 0.0399445 | ||||||||
\(891\) | 5462.03 | − | 13041.5i | 0.205370 | − | 0.490356i | ||||
\(892\) | 17838.9 | − | 30897.9i | 0.669608 | − | 1.15980i | ||||
\(893\) | −3321.76 | − | 5753.46i | −0.124478 | − | 0.215602i | ||||
\(894\) | −3574.45 | − | 3354.43i | −0.133722 | − | 0.125491i | ||||
\(895\) | −1091.85 | − | 1891.14i | −0.0407782 | − | 0.0706299i | ||||
\(896\) | 2103.72 | + | 18375.1i | 0.0784381 | + | 0.685121i | ||||
\(897\) | 2023.64 | − | 8640.59i | 0.0753260 | − | 0.321629i | ||||
\(898\) | 4396.56 | 0.163380 | ||||||||
\(899\) | −8687.08 | + | 15046.5i | −0.322281 | + | 0.558206i | ||||
\(900\) | 1626.25 | + | 25580.7i | 0.0602316 | + | 0.947433i | ||||
\(901\) | −12387.7 | − | 21456.1i | −0.458040 | − | 0.793349i | ||||
\(902\) | −2092.64 | + | 3624.56i | −0.0772475 | + | 0.133797i | ||||
\(903\) | −10308.4 | + | 13855.0i | −0.379892 | + | 0.510594i | ||||
\(904\) | 7009.03 | + | 12140.0i | 0.257873 | + | 0.446649i | ||||
\(905\) | 447.487 | − | 775.070i | 0.0164364 | − | 0.0284687i | ||||
\(906\) | 6878.93 | − | 2079.33i | 0.252249 | − | 0.0762486i | ||||
\(907\) | −1524.48 | − | 2640.47i | −0.0558097 | − | 0.0966652i | 0.836771 | − | 0.547553i | \(-0.184441\pi\) |
−0.892580 | + | 0.450888i | \(0.851107\pi\) | |||||||
\(908\) | 20195.7 | + | 34980.0i | 0.738126 | + | 1.27847i | ||||
\(909\) | −1474.63 | − | 23195.8i | −0.0538069 | − | 0.846375i | ||||
\(910\) | −12.7325 | − | 111.212i | −0.000463820 | − | 0.00405126i | ||||
\(911\) | −12782.5 | + | 22139.9i | −0.464876 | + | 0.805189i | −0.999196 | − | 0.0400933i | \(-0.987234\pi\) |
0.534320 | + | 0.845282i | \(0.320568\pi\) | |||||||
\(912\) | 20374.4 | − | 6158.68i | 0.739762 | − | 0.223612i | ||||
\(913\) | −4289.44 | −0.155487 | ||||||||
\(914\) | 420.290 | 0.0152100 | ||||||||
\(915\) | 1859.87 | + | 1745.39i | 0.0671971 | + | 0.0630608i | ||||
\(916\) | 4819.10 | − | 8346.93i | 0.173829 | − | 0.301081i | ||||
\(917\) | −21365.0 | − | 9275.90i | −0.769393 | − | 0.334043i | ||||
\(918\) | 1512.03 | + | 4053.52i | 0.0543622 | + | 0.145736i | ||||
\(919\) | −7508.94 | − | 13005.9i | −0.269529 | − | 0.466838i | 0.699211 | − | 0.714915i | \(-0.253535\pi\) |
−0.968740 | + | 0.248077i | \(0.920201\pi\) | |||||||
\(920\) | 1230.13 | + | 2130.66i | 0.0440830 | + | 0.0763539i | ||||
\(921\) | −4228.20 | + | 18053.7i | −0.151275 | + | 0.645916i | ||||
\(922\) | −5062.95 | + | 8769.29i | −0.180845 | + | 0.313233i | ||||
\(923\) | 1530.88 | + | 2651.56i | 0.0545931 | + | 0.0945580i | ||||
\(924\) | −5707.05 | − | 13219.8i | −0.203191 | − | 0.470672i | ||||
\(925\) | −3227.17 | + | 5589.63i | −0.114712 | + | 0.198687i | ||||
\(926\) | 3341.86 | + | 5788.27i | 0.118596 | + | 0.205415i | ||||
\(927\) | 34083.1 | − | 22677.0i | 1.20759 | − | 0.803464i | ||||
\(928\) | −7640.31 | + | 13233.4i | −0.270265 | + | 0.468112i | ||||
\(929\) | 42240.6 | 1.49179 | 0.745894 | − | 0.666065i | \(-0.232023\pi\) | ||||
0.745894 | + | 0.666065i | \(0.232023\pi\) | |||||||
\(930\) | −313.432 | − | 294.139i | −0.0110514 | − | 0.0103712i | ||||
\(931\) | −16762.6 | − | 17936.4i | −0.590088 | − | 0.631410i | ||||
\(932\) | −9832.39 | − | 17030.2i | −0.345569 | − | 0.598544i | ||||
\(933\) | 6923.49 | − | 29562.0i | 0.242942 | − | 1.03732i | ||||
\(934\) | −3738.36 | − | 6475.03i | −0.130967 | − | 0.226841i | ||||
\(935\) | −779.858 | + | 1350.75i | −0.0272771 | + | 0.0472453i | ||||
\(936\) | 116.781 | + | 1836.95i | 0.00407811 | + | 0.0641480i | ||||
\(937\) | −53310.0 | −1.85866 | −0.929328 | − | 0.369255i | \(-0.879613\pi\) | ||||
−0.929328 | + | 0.369255i | \(0.879613\pi\) | |||||||
\(938\) | −970.677 | − | 8478.43i | −0.0337886 | − | 0.295128i | ||||
\(939\) | −4621.73 | + | 19734.0i | −0.160623 | + | 0.685830i | ||||
\(940\) | 498.827 | − | 863.994i | 0.0173085 | − | 0.0299791i | ||||
\(941\) | 9548.03 | 0.330773 | 0.165386 | − | 0.986229i | \(-0.447113\pi\) | ||||
0.165386 | + | 0.986229i | \(0.447113\pi\) | |||||||
\(942\) | −1518.99 | + | 6485.80i | −0.0525385 | + | 0.224330i | ||||
\(943\) | −84953.1 | −2.93367 | ||||||||
\(944\) | −22305.6 | −0.769052 | ||||||||
\(945\) | 3225.88 | − | 1642.79i | 0.111045 | − | 0.0565502i | ||||
\(946\) | −1859.47 | −0.0639078 | ||||||||
\(947\) | −17781.3 | −0.610154 | −0.305077 | − | 0.952328i | \(-0.598682\pi\) | ||||
−0.305077 | + | 0.952328i | \(0.598682\pi\) | |||||||
\(948\) | 2833.64 | − | 12099.1i | 0.0970806 | − | 0.414517i | ||||
\(949\) | 2983.94 | 0.102068 | ||||||||
\(950\) | −2352.83 | + | 4075.23i | −0.0803537 | + | 0.139177i | ||||
\(951\) | 3008.18 | − | 12844.4i | 0.102573 | − | 0.437968i | ||||
\(952\) | 8232.38 | + | 3574.21i | 0.280266 | + | 0.121681i | ||||
\(953\) | −3414.93 | −0.116076 | −0.0580380 | − | 0.998314i | \(-0.518484\pi\) | ||||
−0.0580380 | + | 0.998314i | \(0.518484\pi\) | |||||||
\(954\) | −5154.98 | + | 3429.84i | −0.174946 | + | 0.116399i | ||||
\(955\) | −369.925 | + | 640.729i | −0.0125346 | + | 0.0217105i | ||||
\(956\) | −4366.21 | − | 7562.50i | −0.147713 | − | 0.255846i | ||||
\(957\) | 3592.81 | − | 15340.7i | 0.121358 | − | 0.518175i | ||||
\(958\) | −2478.21 | − | 4292.38i | −0.0835775 | − | 0.144760i | ||||
\(959\) | −31757.8 | + | 23526.4i | −1.06936 | + | 0.792186i | ||||
\(960\) | 2141.31 | + | 2009.51i | 0.0719902 | + | 0.0675589i | ||||
\(961\) | −17440.6 | −0.585431 | ||||||||
\(962\) | −113.767 | + | 197.050i | −0.00381288 | + | 0.00660411i | ||||
\(963\) | −2181.25 | − | 34310.7i | −0.0729904 | − | 1.14813i | ||||
\(964\) | 24381.6 | + | 42230.2i | 0.814605 | + | 1.41094i | ||||
\(965\) | 987.664 | − | 1710.68i | 0.0329472 | − | 0.0570662i | ||||
\(966\) | −6455.09 | + | 8675.97i | −0.214999 | + | 0.288970i | ||||
\(967\) | 372.673 | + | 645.489i | 0.0123933 | + | 0.0214659i | 0.872156 | − | 0.489229i | \(-0.162722\pi\) |
−0.859762 | + | 0.510695i | \(0.829388\pi\) | |||||||
\(968\) | −4008.18 | + | 6942.38i | −0.133087 | + | 0.230513i | ||||
\(969\) | 4895.05 | − | 20901.0i | 0.162282 | − | 0.692917i | ||||
\(970\) | 215.043 | + | 372.465i | 0.00711816 | + | 0.0123290i | ||||
\(971\) | 10867.8 | + | 18823.6i | 0.359180 | + | 0.622118i | 0.987824 | − | 0.155575i | \(-0.0497231\pi\) |
−0.628644 | + | 0.777693i | \(0.716390\pi\) | |||||||
\(972\) | −26676.8 | + | 11929.7i | −0.880306 | + | 0.393669i | ||||
\(973\) | 32837.2 | − | 24325.9i | 1.08192 | − | 0.801494i | ||||
\(974\) | 1020.42 | − | 1767.42i | 0.0335692 | − | 0.0581435i | ||||
\(975\) | 3786.10 | + | 3553.05i | 0.124361 | + | 0.116706i | ||||
\(976\) | −20163.4 | −0.661285 | ||||||||
\(977\) | −6989.38 | −0.228874 | −0.114437 | − | 0.993430i | \(-0.536506\pi\) | ||||
−0.114437 | + | 0.993430i | \(0.536506\pi\) | |||||||
\(978\) | 5440.15 | − | 1644.42i | 0.177870 | − | 0.0537657i | ||||
\(979\) | 13817.5 | − | 23932.6i | 0.451082 | − | 0.781296i | ||||
\(980\) | 1074.03 | − | 3526.74i | 0.0350087 | − | 0.114957i | ||||
\(981\) | 6673.05 | − | 4439.88i | 0.217181 | − | 0.144500i | ||||
\(982\) | −2357.86 | − | 4083.93i | −0.0766214 | − | 0.132712i | ||||
\(983\) | 11696.8 | + | 20259.5i | 0.379522 | + | 0.657352i | 0.990993 | − | 0.133915i | \(-0.0427550\pi\) |
−0.611470 | + | 0.791267i | \(0.709422\pi\) | |||||||
\(984\) | 16866.6 | − | 5098.36i | 0.546430 | − | 0.165173i | ||||
\(985\) | −2835.65 | + | 4911.49i | −0.0917273 | + | 0.158876i | ||||
\(986\) | 2410.51 | + | 4175.12i | 0.0778561 | + | 0.134851i | ||||
\(987\) | 8872.36 | + | 1034.41i | 0.286130 | + | 0.0333593i | ||||
\(988\) | 2241.78 | − | 3882.88i | 0.0721868 | − | 0.125031i | ||||
\(989\) | −18871.9 | − | 32687.1i | −0.606766 | − | 1.05095i | ||||
\(990\) | 349.258 | + | 173.088i | 0.0112123 | + | 0.00555666i | ||||
\(991\) | 18122.6 | − | 31389.3i | 0.580912 | − | 1.00617i | −0.414460 | − | 0.910068i | \(-0.636029\pi\) |
0.995372 | − | 0.0961013i | \(-0.0306373\pi\) | |||||||
\(992\) | 10862.2 | 0.347658 | ||||||||
\(993\) | 12371.7 | − | 52824.8i | 0.395371 | − | 1.68816i | ||||
\(994\) | −424.371 | − | 3706.69i | −0.0135415 | − | 0.118279i | ||||
\(995\) | 215.444 | + | 373.160i | 0.00686436 | + | 0.0118894i | ||||
\(996\) | 6464.60 | + | 6066.67i | 0.205661 | + | 0.193002i | ||||
\(997\) | −6370.72 | − | 11034.4i | −0.202370 | − | 0.350515i | 0.746922 | − | 0.664912i | \(-0.231531\pi\) |
−0.949292 | + | 0.314397i | \(0.898198\pi\) | |||||||
\(998\) | 4597.79 | − | 7963.60i | 0.145832 | − | 0.252589i | ||||
\(999\) | −7256.58 | − | 1220.01i | −0.229818 | − | 0.0386382i |
(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.h.a.25.12 | yes | 44 | |
3.2 | odd | 2 | 189.4.h.a.46.11 | 44 | |||
7.2 | even | 3 | 63.4.g.a.16.11 | yes | 44 | ||
9.4 | even | 3 | 63.4.g.a.4.11 | ✓ | 44 | ||
9.5 | odd | 6 | 189.4.g.a.172.12 | 44 | |||
21.2 | odd | 6 | 189.4.g.a.100.12 | 44 | |||
63.23 | odd | 6 | 189.4.h.a.37.11 | 44 | |||
63.58 | even | 3 | inner | 63.4.h.a.58.12 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.g.a.4.11 | ✓ | 44 | 9.4 | even | 3 | ||
63.4.g.a.16.11 | yes | 44 | 7.2 | even | 3 | ||
63.4.h.a.25.12 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.h.a.58.12 | yes | 44 | 63.58 | even | 3 | inner | |
189.4.g.a.100.12 | 44 | 21.2 | odd | 6 | |||
189.4.g.a.172.12 | 44 | 9.5 | odd | 6 | |||
189.4.h.a.37.11 | 44 | 63.23 | odd | 6 | |||
189.4.h.a.46.11 | 44 | 3.2 | odd | 2 |