Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,4,Mod(125,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("168.125");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.i (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.91232088096\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 125.12 | ||
Character | \(\chi\) | \(=\) | 168.125 |
Dual form | 168.4.i.c.125.10 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60932 | + | 1.09154i | −0.922533 | + | 0.385918i | ||||
\(3\) | 4.05635 | − | 3.24747i | 0.780644 | − | 0.624976i | ||||
\(4\) | 5.61708 | − | 5.69635i | 0.702135 | − | 0.712044i | ||||
\(5\) | − | 13.2397i | − | 1.18419i | −0.805868 | − | 0.592095i | \(-0.798301\pi\) | ||
0.805868 | − | 0.592095i | \(-0.201699\pi\) | |||||||
\(6\) | −7.03955 | + | 12.9013i | −0.478981 | + | 0.877825i | ||||
\(7\) | 18.4748 | + | 1.29729i | 0.997544 | + | 0.0700470i | ||||
\(8\) | −8.43895 | + | 20.9949i | −0.372953 | + | 0.927850i | ||||
\(9\) | 5.90788 | − | 26.3457i | 0.218810 | − | 0.975767i | ||||
\(10\) | 14.4516 | + | 34.5465i | 0.457000 | + | 1.09246i | ||||
\(11\) | 49.5250 | 1.35749 | 0.678743 | − | 0.734376i | \(-0.262525\pi\) | ||||
0.678743 | + | 0.734376i | \(0.262525\pi\) | |||||||
\(12\) | 4.28610 | − | 41.3477i | 0.103107 | − | 0.994670i | ||||
\(13\) | −28.7924 | −0.614276 | −0.307138 | − | 0.951665i | \(-0.599371\pi\) | ||||
−0.307138 | + | 0.951665i | \(0.599371\pi\) | |||||||
\(14\) | −49.6226 | + | 16.7809i | −0.947300 | + | 0.320349i | ||||
\(15\) | −42.9954 | − | 53.7046i | −0.740091 | − | 0.924432i | ||||
\(16\) | −0.896814 | − | 63.9937i | −0.0140127 | − | 0.999902i | ||||
\(17\) | −69.2560 | −0.988061 | −0.494031 | − | 0.869445i | \(-0.664477\pi\) | ||||
−0.494031 | + | 0.869445i | \(0.664477\pi\) | |||||||
\(18\) | 13.3419 | + | 75.1930i | 0.174706 | + | 0.984621i | ||||
\(19\) | 24.7890 | 0.299315 | 0.149658 | − | 0.988738i | \(-0.452183\pi\) | ||||
0.149658 | + | 0.988738i | \(0.452183\pi\) | |||||||
\(20\) | −75.4177 | − | 74.3682i | −0.843196 | − | 0.831462i | ||||
\(21\) | 79.1529 | − | 54.7340i | 0.822504 | − | 0.568759i | ||||
\(22\) | −129.227 | + | 54.0585i | −1.25233 | + | 0.523878i | ||||
\(23\) | 85.5006i | 0.775135i | 0.921841 | + | 0.387568i | \(0.126685\pi\) | ||||
−0.921841 | + | 0.387568i | \(0.873315\pi\) | |||||||
\(24\) | 33.9488 | + | 112.568i | 0.288741 | + | 0.957407i | ||||
\(25\) | −50.2885 | −0.402308 | ||||||||
\(26\) | 75.1286 | − | 31.4281i | 0.566690 | − | 0.237060i | ||||
\(27\) | −61.5925 | − | 126.053i | −0.439018 | − | 0.898478i | ||||
\(28\) | 111.164 | − | 97.9518i | 0.750287 | − | 0.661112i | ||||
\(29\) | −111.594 | −0.714569 | −0.357284 | − | 0.933996i | \(-0.616297\pi\) | ||||
−0.357284 | + | 0.933996i | \(0.616297\pi\) | |||||||
\(30\) | 170.809 | + | 93.2013i | 1.03951 | + | 0.567205i | ||||
\(31\) | − | 236.812i | − | 1.37202i | −0.727592 | − | 0.686010i | \(-0.759360\pi\) | ||
0.727592 | − | 0.686010i | \(-0.240640\pi\) | |||||||
\(32\) | 72.1918 | + | 166.001i | 0.398807 | + | 0.917035i | ||||
\(33\) | 200.891 | − | 160.831i | 1.05971 | − | 0.848396i | ||||
\(34\) | 180.711 | − | 75.5957i | 0.911519 | − | 0.381310i | ||||
\(35\) | 17.1756 | − | 244.600i | 0.0829490 | − | 1.18128i | ||||
\(36\) | −116.889 | − | 181.639i | −0.541155 | − | 0.840923i | ||||
\(37\) | − | 261.434i | − | 1.16161i | −0.814044 | − | 0.580804i | \(-0.802738\pi\) | ||
0.814044 | − | 0.580804i | \(-0.197262\pi\) | |||||||
\(38\) | −64.6825 | + | 27.0582i | −0.276128 | + | 0.115511i | ||||
\(39\) | −116.792 | + | 93.5026i | −0.479531 | + | 0.383908i | ||||
\(40\) | 277.965 | + | 111.729i | 1.09875 | + | 0.441647i | ||||
\(41\) | 471.089 | 1.79443 | 0.897217 | − | 0.441590i | \(-0.145585\pi\) | ||||
0.897217 | + | 0.441590i | \(0.145585\pi\) | |||||||
\(42\) | −146.791 | + | 229.217i | −0.539293 | + | 0.842118i | ||||
\(43\) | 261.133i | 0.926101i | 0.886332 | + | 0.463051i | \(0.153245\pi\) | ||||
−0.886332 | + | 0.463051i | \(0.846755\pi\) | |||||||
\(44\) | 278.186 | − | 282.112i | 0.953139 | − | 0.966590i | ||||
\(45\) | −348.808 | − | 78.2183i | −1.15549 | − | 0.259113i | ||||
\(46\) | −93.3274 | − | 223.098i | −0.299138 | − | 0.715088i | ||||
\(47\) | −217.418 | −0.674757 | −0.337379 | − | 0.941369i | \(-0.609540\pi\) | ||||
−0.337379 | + | 0.941369i | \(0.609540\pi\) | |||||||
\(48\) | −211.455 | − | 256.668i | −0.635853 | − | 0.771810i | ||||
\(49\) | 339.634 | + | 47.9342i | 0.990187 | + | 0.139750i | ||||
\(50\) | 131.219 | − | 54.8919i | 0.371142 | − | 0.155258i | ||||
\(51\) | −280.926 | + | 224.907i | −0.771324 | + | 0.617514i | ||||
\(52\) | −161.729 | + | 164.012i | −0.431305 | + | 0.437391i | ||||
\(53\) | −11.8711 | −0.0307665 | −0.0153832 | − | 0.999882i | \(-0.504897\pi\) | ||||
−0.0153832 | + | 0.999882i | \(0.504897\pi\) | |||||||
\(54\) | 298.306 | + | 261.682i | 0.751747 | + | 0.659451i | ||||
\(55\) | − | 655.694i | − | 1.60752i | ||||||
\(56\) | −183.144 | + | 376.927i | −0.437030 | + | 0.899447i | ||||
\(57\) | 100.553 | − | 80.5016i | 0.233659 | − | 0.187065i | ||||
\(58\) | 291.184 | − | 121.809i | 0.659213 | − | 0.275765i | ||||
\(59\) | 236.528i | 0.521921i | 0.965350 | + | 0.260960i | \(0.0840392\pi\) | ||||
−0.965350 | + | 0.260960i | \(0.915961\pi\) | |||||||
\(60\) | −547.429 | − | 56.7464i | −1.17788 | − | 0.122099i | ||||
\(61\) | −754.519 | −1.58371 | −0.791855 | − | 0.610709i | \(-0.790884\pi\) | ||||
−0.791855 | + | 0.610709i | \(0.790884\pi\) | |||||||
\(62\) | 258.490 | + | 617.917i | 0.529487 | + | 1.26573i | ||||
\(63\) | 143.325 | − | 479.067i | 0.286623 | − | 0.958044i | ||||
\(64\) | −369.568 | − | 354.349i | −0.721813 | − | 0.692088i | ||||
\(65\) | 381.202i | 0.727420i | ||||||||
\(66\) | −348.634 | + | 638.939i | −0.650210 | + | 1.19164i | ||||
\(67\) | − | 163.127i | − | 0.297449i | −0.988879 | − | 0.148725i | \(-0.952483\pi\) | ||
0.988879 | − | 0.148725i | \(-0.0475168\pi\) | |||||||
\(68\) | −389.016 | + | 394.506i | −0.693752 | + | 0.703543i | ||||
\(69\) | 277.661 | + | 346.820i | 0.484441 | + | 0.605105i | ||||
\(70\) | 222.174 | + | 656.986i | 0.379354 | + | 1.12178i | ||||
\(71\) | 478.338i | 0.799554i | 0.916613 | + | 0.399777i | \(0.130912\pi\) | ||||
−0.916613 | + | 0.399777i | \(0.869088\pi\) | |||||||
\(72\) | 503.268 | + | 346.365i | 0.823760 | + | 0.566938i | ||||
\(73\) | 1038.37i | 1.66482i | 0.554157 | + | 0.832412i | \(0.313041\pi\) | ||||
−0.554157 | + | 0.832412i | \(0.686959\pi\) | |||||||
\(74\) | 285.366 | + | 682.164i | 0.448285 | + | 1.07162i | ||||
\(75\) | −203.988 | + | 163.310i | −0.314059 | + | 0.251433i | ||||
\(76\) | 139.242 | − | 141.207i | 0.210160 | − | 0.213126i | ||||
\(77\) | 914.963 | + | 64.2482i | 1.35415 | + | 0.0950878i | ||||
\(78\) | 202.686 | − | 371.461i | 0.294226 | − | 0.539227i | ||||
\(79\) | −148.084 | −0.210895 | −0.105448 | − | 0.994425i | \(-0.533628\pi\) | ||||
−0.105448 | + | 0.994425i | \(0.533628\pi\) | |||||||
\(80\) | −847.255 | + | 11.8735i | −1.18407 | + | 0.0165937i | ||||
\(81\) | −659.194 | − | 311.295i | −0.904244 | − | 0.427016i | ||||
\(82\) | −1229.22 | + | 514.213i | −1.65542 | + | 0.692504i | ||||
\(83\) | − | 739.797i | − | 0.978353i | −0.872185 | − | 0.489176i | \(-0.837297\pi\) | ||
0.872185 | − | 0.489176i | \(-0.162703\pi\) | |||||||
\(84\) | 132.824 | − | 758.328i | 0.172528 | − | 0.985005i | ||||
\(85\) | 916.925i | 1.17005i | ||||||||
\(86\) | −285.037 | − | 681.378i | −0.357399 | − | 0.854359i | ||||
\(87\) | −452.664 | + | 362.398i | −0.557824 | + | 0.446588i | ||||
\(88\) | −417.939 | + | 1039.77i | −0.506278 | + | 1.25954i | ||||
\(89\) | 1347.82 | 1.60527 | 0.802635 | − | 0.596470i | \(-0.203431\pi\) | ||||
0.802635 | + | 0.596470i | \(0.203431\pi\) | |||||||
\(90\) | 995.530 | − | 176.642i | 1.16598 | − | 0.206885i | ||||
\(91\) | −531.934 | − | 37.3521i | −0.612767 | − | 0.0430282i | ||||
\(92\) | 487.042 | + | 480.264i | 0.551930 | + | 0.544250i | ||||
\(93\) | −769.039 | − | 960.590i | −0.857480 | − | 1.07106i | ||||
\(94\) | 567.311 | − | 237.320i | 0.622486 | − | 0.260401i | ||||
\(95\) | − | 328.198i | − | 0.354447i | ||||||
\(96\) | 831.918 | + | 438.917i | 0.884451 | + | 0.466633i | ||||
\(97\) | − | 183.115i | − | 0.191675i | −0.995397 | − | 0.0958375i | \(-0.969447\pi\) | ||
0.995397 | − | 0.0958375i | \(-0.0305529\pi\) | |||||||
\(98\) | −938.535 | + | 245.649i | −0.967412 | + | 0.253207i | ||||
\(99\) | 292.588 | − | 1304.77i | 0.297032 | − | 1.32459i | ||||
\(100\) | −282.475 | + | 286.461i | −0.282475 | + | 0.286461i | ||||
\(101\) | 857.904i | 0.845194i | 0.906318 | + | 0.422597i | \(0.138882\pi\) | ||||
−0.906318 | + | 0.422597i | \(0.861118\pi\) | |||||||
\(102\) | 487.531 | − | 893.495i | 0.473262 | − | 0.867345i | ||||
\(103\) | − | 493.737i | − | 0.472324i | −0.971714 | − | 0.236162i | \(-0.924110\pi\) | ||
0.971714 | − | 0.236162i | \(-0.0758896\pi\) | |||||||
\(104\) | 242.978 | − | 604.493i | 0.229096 | − | 0.569956i | ||||
\(105\) | −724.659 | − | 1047.96i | −0.673519 | − | 0.974002i | ||||
\(106\) | 30.9755 | − | 12.9578i | 0.0283831 | − | 0.0118733i | ||||
\(107\) | −583.614 | −0.527290 | −0.263645 | − | 0.964620i | \(-0.584925\pi\) | ||||
−0.263645 | + | 0.964620i | \(0.584925\pi\) | |||||||
\(108\) | −1064.01 | − | 357.197i | −0.948006 | − | 0.318253i | ||||
\(109\) | 1856.22i | 1.63113i | 0.578665 | + | 0.815565i | \(0.303574\pi\) | ||||
−0.578665 | + | 0.815565i | \(0.696426\pi\) | |||||||
\(110\) | 715.716 | + | 1710.91i | 0.620372 | + | 1.48299i | ||||
\(111\) | −848.999 | − | 1060.47i | −0.725976 | − | 0.906802i | ||||
\(112\) | 66.4498 | − | 1183.43i | 0.0560618 | − | 0.998427i | ||||
\(113\) | 951.492i | 0.792114i | 0.918226 | + | 0.396057i | \(0.129622\pi\) | ||||
−0.918226 | + | 0.396057i | \(0.870378\pi\) | |||||||
\(114\) | −174.504 | + | 319.812i | −0.143366 | + | 0.262747i | ||||
\(115\) | 1132.00 | 0.917908 | ||||||||
\(116\) | −626.833 | + | 635.679i | −0.501724 | + | 0.508804i | ||||
\(117\) | −170.102 | + | 758.558i | −0.134410 | + | 0.599390i | ||||
\(118\) | −258.180 | − | 617.177i | −0.201418 | − | 0.481489i | ||||
\(119\) | −1279.49 | − | 89.8449i | −0.985634 | − | 0.0692107i | ||||
\(120\) | 1490.36 | − | 449.471i | 1.13375 | − | 0.341924i | ||||
\(121\) | 1121.73 | 0.842770 | ||||||||
\(122\) | 1968.78 | − | 823.588i | 1.46102 | − | 0.611182i | ||||
\(123\) | 1910.90 | − | 1529.85i | 1.40081 | − | 1.12148i | ||||
\(124\) | −1348.96 | − | 1330.19i | −0.976939 | − | 0.963344i | ||||
\(125\) | − | 989.155i | − | 0.707781i | ||||||
\(126\) | 148.941 | + | 1406.48i | 0.105307 | + | 0.994440i | ||||
\(127\) | 2550.61 | 1.78213 | 0.891065 | − | 0.453876i | \(-0.149959\pi\) | ||||
0.891065 | + | 0.453876i | \(0.149959\pi\) | |||||||
\(128\) | 1351.11 | + | 521.212i | 0.932985 | + | 0.359914i | ||||
\(129\) | 848.020 | + | 1059.24i | 0.578791 | + | 0.722956i | ||||
\(130\) | −416.097 | − | 994.677i | −0.280724 | − | 0.671069i | ||||
\(131\) | 439.670i | 0.293238i | 0.989193 | + | 0.146619i | \(0.0468391\pi\) | ||||
−0.989193 | + | 0.146619i | \(0.953161\pi\) | |||||||
\(132\) | 212.269 | − | 2047.74i | 0.139967 | − | 1.35025i | ||||
\(133\) | 457.972 | + | 32.1585i | 0.298580 | + | 0.0209661i | ||||
\(134\) | 178.059 | + | 425.650i | 0.114791 | + | 0.274407i | ||||
\(135\) | −1668.90 | + | 815.464i | −1.06397 | + | 0.519881i | ||||
\(136\) | 584.448 | − | 1454.02i | 0.368500 | − | 0.916773i | ||||
\(137\) | − | 1126.88i | − | 0.702745i | −0.936236 | − | 0.351373i | \(-0.885715\pi\) | ||
0.936236 | − | 0.351373i | \(-0.114285\pi\) | |||||||
\(138\) | −1103.07 | − | 601.886i | −0.680434 | − | 0.371275i | ||||
\(139\) | 2419.55 | 1.47643 | 0.738215 | − | 0.674565i | \(-0.235669\pi\) | ||||
0.738215 | + | 0.674565i | \(0.235669\pi\) | |||||||
\(140\) | −1296.85 | − | 1471.77i | −0.782883 | − | 0.888483i | ||||
\(141\) | −881.921 | + | 706.057i | −0.526745 | + | 0.421707i | ||||
\(142\) | −522.125 | − | 1248.14i | −0.308562 | − | 0.737615i | ||||
\(143\) | −1425.95 | −0.833871 | ||||||||
\(144\) | −1691.26 | − | 354.440i | −0.978738 | − | 0.205116i | ||||
\(145\) | 1477.47i | 0.846186i | ||||||||
\(146\) | −1133.42 | − | 2709.44i | −0.642485 | − | 1.53586i | ||||
\(147\) | 1533.34 | − | 908.514i | 0.860324 | − | 0.509748i | ||||
\(148\) | −1489.22 | − | 1468.50i | −0.827115 | − | 0.815605i | ||||
\(149\) | 2049.54 | 1.12688 | 0.563439 | − | 0.826158i | \(-0.309478\pi\) | ||||
0.563439 | + | 0.826158i | \(0.309478\pi\) | |||||||
\(150\) | 354.008 | − | 648.789i | 0.192698 | − | 0.353156i | ||||
\(151\) | 288.181 | 0.155310 | 0.0776551 | − | 0.996980i | \(-0.475257\pi\) | ||||
0.0776551 | + | 0.996980i | \(0.475257\pi\) | |||||||
\(152\) | −209.193 | + | 520.442i | −0.111630 | + | 0.277720i | ||||
\(153\) | −409.156 | + | 1824.60i | −0.216198 | + | 0.964118i | ||||
\(154\) | −2457.56 | + | 831.075i | −1.28595 | + | 0.434870i | ||||
\(155\) | −3135.31 | −1.62473 | ||||||||
\(156\) | −123.407 | + | 1190.50i | −0.0633364 | + | 0.611002i | ||||
\(157\) | 2088.48 | 1.06165 | 0.530824 | − | 0.847482i | \(-0.321883\pi\) | ||||
0.530824 | + | 0.847482i | \(0.321883\pi\) | |||||||
\(158\) | 386.398 | − | 161.639i | 0.194558 | − | 0.0813883i | ||||
\(159\) | −48.1534 | + | 38.5511i | −0.0240177 | + | 0.0192283i | ||||
\(160\) | 2197.80 | − | 955.794i | 1.08594 | − | 0.472264i | ||||
\(161\) | −110.919 | + | 1579.60i | −0.0542959 | + | 0.773231i | ||||
\(162\) | 2059.84 | + | 92.7308i | 0.998988 | + | 0.0449729i | ||||
\(163\) | 4111.75i | 1.97581i | 0.155057 | + | 0.987906i | \(0.450444\pi\) | ||||
−0.155057 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(164\) | 2646.15 | − | 2683.49i | 1.25993 | − | 1.27772i | ||||
\(165\) | −2129.35 | − | 2659.72i | −1.00466 | − | 1.25490i | ||||
\(166\) | 807.518 | + | 1930.37i | 0.377564 | + | 0.902563i | ||||
\(167\) | −1224.94 | −0.567598 | −0.283799 | − | 0.958884i | \(-0.591595\pi\) | ||||
−0.283799 | + | 0.958884i | \(0.591595\pi\) | |||||||
\(168\) | 481.164 | + | 2123.70i | 0.220968 | + | 0.975281i | ||||
\(169\) | −1368.00 | −0.622665 | ||||||||
\(170\) | −1000.86 | − | 2392.55i | −0.451544 | − | 1.07941i | ||||
\(171\) | 146.451 | − | 653.085i | 0.0654934 | − | 0.292062i | ||||
\(172\) | 1487.50 | + | 1466.80i | 0.659425 | + | 0.650248i | ||||
\(173\) | 2451.51i | 1.07737i | 0.842508 | + | 0.538685i | \(0.181079\pi\) | ||||
−0.842508 | + | 0.538685i | \(0.818921\pi\) | |||||||
\(174\) | 785.572 | − | 1439.71i | 0.342265 | − | 0.627267i | ||||
\(175\) | −929.068 | − | 65.2386i | −0.401320 | − | 0.0281804i | ||||
\(176\) | −44.4147 | − | 3169.29i | −0.0190221 | − | 1.35735i | ||||
\(177\) | 768.118 | + | 959.439i | 0.326188 | + | 0.407434i | ||||
\(178\) | −3516.90 | + | 1471.20i | −1.48091 | + | 0.619502i | ||||
\(179\) | 926.214 | 0.386751 | 0.193376 | − | 0.981125i | \(-0.438056\pi\) | ||||
0.193376 | + | 0.981125i | \(0.438056\pi\) | |||||||
\(180\) | −2404.84 | + | 1547.58i | −0.995813 | + | 0.640830i | ||||
\(181\) | 876.720 | 0.360034 | 0.180017 | − | 0.983664i | \(-0.442385\pi\) | ||||
0.180017 | + | 0.983664i | \(0.442385\pi\) | |||||||
\(182\) | 1428.76 | − | 483.163i | 0.581903 | − | 0.196783i | ||||
\(183\) | −3060.59 | + | 2450.28i | −1.23631 | + | 0.989780i | ||||
\(184\) | −1795.07 | − | 721.536i | −0.719210 | − | 0.289089i | ||||
\(185\) | −3461.29 | −1.37556 | ||||||||
\(186\) | 3055.19 | + | 1667.05i | 1.20439 | + | 0.657172i | ||||
\(187\) | −3429.90 | −1.34128 | ||||||||
\(188\) | −1221.25 | + | 1238.49i | −0.473771 | + | 0.480457i | ||||
\(189\) | −974.380 | − | 2408.70i | −0.375004 | − | 0.927023i | ||||
\(190\) | 358.242 | + | 856.374i | 0.136787 | + | 0.326989i | ||||
\(191\) | − | 2476.56i | − | 0.938208i | −0.883143 | − | 0.469104i | \(-0.844577\pi\) | ||
0.883143 | − | 0.469104i | \(-0.155423\pi\) | |||||||
\(192\) | −2649.83 | − | 237.202i | −0.996017 | − | 0.0891593i | ||||
\(193\) | 3130.49 | 1.16755 | 0.583776 | − | 0.811915i | \(-0.301575\pi\) | ||||
0.583776 | + | 0.811915i | \(0.301575\pi\) | |||||||
\(194\) | 199.877 | + | 477.804i | 0.0739708 | + | 0.176827i | ||||
\(195\) | 1237.94 | + | 1546.29i | 0.454620 | + | 0.567856i | ||||
\(196\) | 2180.80 | − | 1665.42i | 0.794753 | − | 0.606933i | ||||
\(197\) | 85.4470 | 0.0309028 | 0.0154514 | − | 0.999881i | \(-0.495081\pi\) | ||||
0.0154514 | + | 0.999881i | \(0.495081\pi\) | |||||||
\(198\) | 660.756 | + | 3723.94i | 0.237161 | + | 1.33661i | ||||
\(199\) | 3536.74i | 1.25986i | 0.776650 | + | 0.629932i | \(0.216917\pi\) | ||||
−0.776650 | + | 0.629932i | \(0.783083\pi\) | |||||||
\(200\) | 424.382 | − | 1055.80i | 0.150042 | − | 0.373282i | ||||
\(201\) | −529.749 | − | 661.699i | −0.185899 | − | 0.232202i | ||||
\(202\) | −936.437 | − | 2238.54i | −0.326176 | − | 0.779720i | ||||
\(203\) | −2061.67 | − | 144.770i | −0.712814 | − | 0.0500534i | ||||
\(204\) | −296.838 | + | 2863.57i | −0.101876 | + | 0.982795i | ||||
\(205\) | − | 6237.06i | − | 2.12495i | ||||||
\(206\) | 538.934 | + | 1288.32i | 0.182278 | + | 0.435735i | ||||
\(207\) | 2252.58 | + | 505.128i | 0.756352 | + | 0.169608i | ||||
\(208\) | 25.8215 | + | 1842.54i | 0.00860767 | + | 0.614216i | ||||
\(209\) | 1227.68 | 0.406317 | ||||||||
\(210\) | 3034.75 | + | 1943.46i | 0.997228 | + | 0.638626i | ||||
\(211\) | − | 1696.15i | − | 0.553403i | −0.960956 | − | 0.276701i | \(-0.910759\pi\) | ||
0.960956 | − | 0.276701i | \(-0.0892413\pi\) | |||||||
\(212\) | −66.6810 | + | 67.6221i | −0.0216022 | + | 0.0219071i | ||||
\(213\) | 1553.39 | + | 1940.31i | 0.499702 | + | 0.624167i | ||||
\(214\) | 1522.83 | − | 637.038i | 0.486443 | − | 0.203491i | ||||
\(215\) | 3457.31 | 1.09668 | ||||||||
\(216\) | 3166.24 | − | 229.370i | 0.997386 | − | 0.0722531i | ||||
\(217\) | 307.213 | − | 4375.04i | 0.0961059 | − | 1.36865i | ||||
\(218\) | −2026.13 | − | 4843.46i | −0.629482 | − | 1.50477i | ||||
\(219\) | 3372.08 | + | 4211.99i | 1.04047 | + | 1.29964i | ||||
\(220\) | −3735.06 | − | 3683.09i | −1.14463 | − | 1.12870i | ||||
\(221\) | 1994.05 | 0.606942 | ||||||||
\(222\) | 3372.85 | + | 1840.38i | 1.01969 | + | 0.556388i | ||||
\(223\) | 3936.51i | 1.18210i | 0.806635 | + | 0.591050i | \(0.201286\pi\) | ||||
−0.806635 | + | 0.591050i | \(0.798714\pi\) | |||||||
\(224\) | 1118.38 | + | 3160.48i | 0.333592 | + | 0.942718i | ||||
\(225\) | −297.099 | + | 1324.89i | −0.0880292 | + | 0.392559i | ||||
\(226\) | −1038.59 | − | 2482.75i | −0.305691 | − | 0.730751i | ||||
\(227\) | 6229.85i | 1.82154i | 0.412912 | + | 0.910771i | \(0.364512\pi\) | ||||
−0.412912 | + | 0.910771i | \(0.635488\pi\) | |||||||
\(228\) | 106.248 | − | 1024.97i | 0.0308617 | − | 0.297720i | ||||
\(229\) | −3973.83 | −1.14672 | −0.573359 | − | 0.819304i | \(-0.694360\pi\) | ||||
−0.573359 | + | 0.819304i | \(0.694360\pi\) | |||||||
\(230\) | −2953.75 | + | 1235.62i | −0.846801 | + | 0.354237i | ||||
\(231\) | 3920.05 | − | 2710.70i | 1.11654 | − | 0.772083i | ||||
\(232\) | 941.737 | − | 2342.90i | 0.266500 | − | 0.663013i | ||||
\(233\) | − | 3401.07i | − | 0.956273i | −0.878285 | − | 0.478137i | \(-0.841312\pi\) | ||
0.878285 | − | 0.478137i | \(-0.158688\pi\) | |||||||
\(234\) | −384.145 | − | 2164.99i | −0.107318 | − | 0.604829i | ||||
\(235\) | 2878.53i | 0.799042i | ||||||||
\(236\) | 1347.35 | + | 1328.60i | 0.371630 | + | 0.366459i | ||||
\(237\) | −600.679 | + | 480.898i | −0.164634 | + | 0.131804i | ||||
\(238\) | 3436.66 | − | 1162.18i | 0.935990 | − | 0.316525i | ||||
\(239\) | − | 4477.57i | − | 1.21184i | −0.795525 | − | 0.605920i | \(-0.792805\pi\) | ||
0.795525 | − | 0.605920i | \(-0.207195\pi\) | |||||||
\(240\) | −3398.20 | + | 2799.60i | −0.913970 | + | 0.752972i | ||||
\(241\) | − | 2312.70i | − | 0.618151i | −0.951037 | − | 0.309076i | \(-0.899980\pi\) | ||
0.951037 | − | 0.309076i | \(-0.100020\pi\) | |||||||
\(242\) | −2926.94 | + | 1224.41i | −0.777483 | + | 0.325240i | ||||
\(243\) | −3684.84 | + | 877.992i | −0.972768 | + | 0.231783i | ||||
\(244\) | −4238.20 | + | 4298.01i | −1.11198 | + | 1.12767i | ||||
\(245\) | 634.632 | − | 4496.64i | 0.165490 | − | 1.17257i | ||||
\(246\) | −3316.26 | + | 6077.69i | −0.859500 | + | 1.57520i | ||||
\(247\) | −713.737 | −0.183862 | ||||||||
\(248\) | 4971.83 | + | 1998.44i | 1.27303 | + | 0.511699i | ||||
\(249\) | −2402.47 | − | 3000.87i | −0.611447 | − | 0.763745i | ||||
\(250\) | 1079.70 | + | 2581.02i | 0.273145 | + | 0.652952i | ||||
\(251\) | − | 4493.21i | − | 1.12992i | −0.825119 | − | 0.564958i | \(-0.808892\pi\) | ||
0.825119 | − | 0.564958i | \(-0.191108\pi\) | |||||||
\(252\) | −1923.87 | − | 3507.38i | −0.480921 | − | 0.876764i | ||||
\(253\) | 4234.42i | 1.05224i | ||||||||
\(254\) | −6655.36 | + | 2784.10i | −1.64407 | + | 0.687755i | ||||
\(255\) | 2977.69 | + | 3719.37i | 0.731255 | + | 0.913395i | ||||
\(256\) | −4094.39 | + | 114.781i | −0.999607 | + | 0.0280227i | ||||
\(257\) | 1431.96 | 0.347562 | 0.173781 | − | 0.984784i | \(-0.444402\pi\) | ||||
0.173781 | + | 0.984784i | \(0.444402\pi\) | |||||||
\(258\) | −3368.96 | − | 1838.26i | −0.812955 | − | 0.443585i | ||||
\(259\) | 339.155 | − | 4829.93i | 0.0813670 | − | 1.15875i | ||||
\(260\) | 2171.46 | + | 2141.24i | 0.517955 | + | 0.510747i | ||||
\(261\) | −659.285 | + | 2940.03i | −0.156355 | + | 0.697253i | ||||
\(262\) | −479.917 | − | 1147.24i | −0.113166 | − | 0.270521i | ||||
\(263\) | 902.626i | 0.211629i | 0.994386 | + | 0.105814i | \(0.0337449\pi\) | ||||
−0.994386 | + | 0.105814i | \(0.966255\pi\) | |||||||
\(264\) | 1681.32 | + | 5574.91i | 0.391962 | + | 1.29967i | ||||
\(265\) | 157.170i | 0.0364334i | ||||||||
\(266\) | −1230.10 | + | 415.983i | −0.283541 | + | 0.0958854i | ||||
\(267\) | 5467.24 | − | 4377.02i | 1.25314 | − | 1.00325i | ||||
\(268\) | −929.227 | − | 916.296i | −0.211797 | − | 0.208850i | ||||
\(269\) | 1889.72i | 0.428321i | 0.976798 | + | 0.214160i | \(0.0687015\pi\) | ||||
−0.976798 | + | 0.214160i | \(0.931298\pi\) | |||||||
\(270\) | 3464.58 | − | 3949.47i | 0.780916 | − | 0.890212i | ||||
\(271\) | − | 7620.90i | − | 1.70825i | −0.520065 | − | 0.854127i | \(-0.674092\pi\) | ||
0.520065 | − | 0.854127i | \(-0.325908\pi\) | |||||||
\(272\) | 62.1097 | + | 4431.95i | 0.0138454 | + | 0.987964i | ||||
\(273\) | −2279.01 | + | 1575.93i | −0.505245 | + | 0.349375i | ||||
\(274\) | 1230.04 | + | 2940.40i | 0.271202 | + | 0.648306i | ||||
\(275\) | −2490.54 | −0.546128 | ||||||||
\(276\) | 3535.25 | + | 366.464i | 0.771004 | + | 0.0799222i | ||||
\(277\) | 2983.80i | 0.647218i | 0.946191 | + | 0.323609i | \(0.104896\pi\) | ||||
−0.946191 | + | 0.323609i | \(0.895104\pi\) | |||||||
\(278\) | −6313.38 | + | 2641.04i | −1.36206 | + | 0.569781i | ||||
\(279\) | −6238.98 | − | 1399.06i | −1.33877 | − | 0.300213i | ||||
\(280\) | 4990.39 | + | 2424.76i | 1.06512 | + | 0.517526i | ||||
\(281\) | − | 2988.80i | − | 0.634508i | −0.948341 | − | 0.317254i | \(-0.897239\pi\) | ||
0.948341 | − | 0.317254i | \(-0.102761\pi\) | |||||||
\(282\) | 1530.52 | − | 2804.98i | 0.323196 | − | 0.592319i | ||||
\(283\) | −3150.99 | −0.661861 | −0.330930 | − | 0.943655i | \(-0.607363\pi\) | ||||
−0.330930 | + | 0.943655i | \(0.607363\pi\) | |||||||
\(284\) | 2724.78 | + | 2686.86i | 0.569317 | + | 0.561395i | ||||
\(285\) | −1065.81 | − | 1331.29i | −0.221521 | − | 0.276697i | ||||
\(286\) | 3720.75 | − | 1556.48i | 0.769274 | − | 0.321806i | ||||
\(287\) | 8703.27 | + | 611.138i | 1.79003 | + | 0.125695i | ||||
\(288\) | 4799.92 | − | 921.230i | 0.982076 | − | 0.188486i | ||||
\(289\) | −116.610 | −0.0237350 | ||||||||
\(290\) | −1612.71 | − | 3855.18i | −0.326558 | − | 0.780635i | ||||
\(291\) | −594.659 | − | 742.776i | −0.119792 | − | 0.149630i | ||||
\(292\) | 5914.93 | + | 5832.62i | 1.18543 | + | 1.16893i | ||||
\(293\) | − | 1635.98i | − | 0.326194i | −0.986610 | − | 0.163097i | \(-0.947852\pi\) | ||
0.986610 | − | 0.163097i | \(-0.0521484\pi\) | |||||||
\(294\) | −3009.29 | + | 4044.30i | −0.596956 | + | 0.802274i | ||||
\(295\) | 3131.55 | 0.618054 | ||||||||
\(296\) | 5488.77 | + | 2206.23i | 1.07780 | + | 0.433224i | ||||
\(297\) | −3050.37 | − | 6242.78i | −0.595961 | − | 1.21967i | ||||
\(298\) | −5347.90 | + | 2237.15i | −1.03958 | + | 0.434882i | ||||
\(299\) | − | 2461.77i | − | 0.476147i | ||||||
\(300\) | −215.541 | + | 2079.31i | −0.0414810 | + | 0.400164i | ||||
\(301\) | −338.764 | + | 4824.37i | −0.0648706 | + | 0.923827i | ||||
\(302\) | −751.956 | + | 314.561i | −0.143279 | + | 0.0599369i | ||||
\(303\) | 2786.02 | + | 3479.96i | 0.528226 | + | 0.659796i | ||||
\(304\) | −22.2311 | − | 1586.34i | −0.00419422 | − | 0.299286i | ||||
\(305\) | 9989.58i | 1.87541i | ||||||||
\(306\) | −924.004 | − | 5207.57i | −0.172620 | − | 0.972865i | ||||
\(307\) | −3788.51 | −0.704305 | −0.352152 | − | 0.935943i | \(-0.614550\pi\) | ||||
−0.352152 | + | 0.935943i | \(0.614550\pi\) | |||||||
\(308\) | 5505.40 | − | 4851.06i | 1.01850 | − | 0.897451i | ||||
\(309\) | −1603.40 | − | 2002.77i | −0.295191 | − | 0.368717i | ||||
\(310\) | 8181.01 | − | 3422.31i | 1.49887 | − | 0.627014i | ||||
\(311\) | 4998.37 | 0.911356 | 0.455678 | − | 0.890145i | \(-0.349397\pi\) | ||||
0.455678 | + | 0.890145i | \(0.349397\pi\) | |||||||
\(312\) | −977.470 | − | 3241.10i | −0.177367 | − | 0.588112i | ||||
\(313\) | − | 1152.65i | − | 0.208152i | −0.994569 | − | 0.104076i | \(-0.966812\pi\) | ||
0.994569 | − | 0.104076i | \(-0.0331885\pi\) | |||||||
\(314\) | −5449.50 | + | 2279.66i | −0.979406 | + | 0.409709i | ||||
\(315\) | −6342.68 | − | 1897.57i | −1.13451 | − | 0.339416i | ||||
\(316\) | −831.799 | + | 843.537i | −0.148077 | + | 0.150167i | ||||
\(317\) | −2738.80 | −0.485256 | −0.242628 | − | 0.970119i | \(-0.578009\pi\) | ||||
−0.242628 | + | 0.970119i | \(0.578009\pi\) | |||||||
\(318\) | 83.5674 | − | 153.153i | 0.0147366 | − | 0.0270076i | ||||
\(319\) | −5526.70 | −0.970018 | ||||||||
\(320\) | −4691.46 | + | 4892.95i | −0.819565 | + | 0.854764i | ||||
\(321\) | −2367.34 | + | 1895.27i | −0.411626 | + | 0.329544i | ||||
\(322\) | −1434.78 | − | 4242.76i | −0.248314 | − | 0.734285i | ||||
\(323\) | −1716.79 | −0.295742 | ||||||||
\(324\) | −5475.99 | + | 2006.43i | −0.938956 | + | 0.344038i | ||||
\(325\) | 1447.93 | 0.247128 | ||||||||
\(326\) | −4488.14 | − | 10728.9i | −0.762500 | − | 1.82275i | ||||
\(327\) | 6028.01 | + | 7529.46i | 1.01942 | + | 1.27333i | ||||
\(328\) | −3975.50 | + | 9890.45i | −0.669239 | + | 1.66497i | ||||
\(329\) | −4016.74 | − | 282.053i | −0.673100 | − | 0.0472647i | ||||
\(330\) | 8459.34 | + | 4615.79i | 1.41112 | + | 0.769973i | ||||
\(331\) | − | 5222.20i | − | 0.867184i | −0.901109 | − | 0.433592i | \(-0.857246\pi\) | ||
0.901109 | − | 0.433592i | \(-0.142754\pi\) | |||||||
\(332\) | −4214.14 | − | 4155.50i | −0.696630 | − | 0.686936i | ||||
\(333\) | −6887.66 | − | 1544.52i | −1.13346 | − | 0.254172i | ||||
\(334\) | 3196.26 | − | 1337.07i | 0.523628 | − | 0.219046i | ||||
\(335\) | −2159.74 | −0.352237 | ||||||||
\(336\) | −3573.62 | − | 5016.21i | −0.580229 | − | 0.814454i | ||||
\(337\) | −2898.62 | −0.468540 | −0.234270 | − | 0.972172i | \(-0.575270\pi\) | ||||
−0.234270 | + | 0.972172i | \(0.575270\pi\) | |||||||
\(338\) | 3569.53 | − | 1493.22i | 0.574429 | − | 0.240297i | ||||
\(339\) | 3089.94 | + | 3859.58i | 0.495052 | + | 0.618359i | ||||
\(340\) | 5223.13 | + | 5150.44i | 0.833129 | + | 0.821535i | ||||
\(341\) | − | 11728.1i | − | 1.86250i | ||||||
\(342\) | 330.732 | + | 1863.96i | 0.0522922 | + | 0.294712i | ||||
\(343\) | 6212.48 | + | 1326.18i | 0.977966 | + | 0.208766i | ||||
\(344\) | −5482.44 | − | 2203.69i | −0.859284 | − | 0.345392i | ||||
\(345\) | 4591.78 | − | 3676.13i | 0.716560 | − | 0.573670i | ||||
\(346\) | −2675.92 | − | 6396.77i | −0.415776 | − | 0.993909i | ||||
\(347\) | −10559.0 | −1.63353 | −0.816765 | − | 0.576970i | \(-0.804235\pi\) | ||||
−0.816765 | + | 0.576970i | \(0.804235\pi\) | |||||||
\(348\) | −478.303 | + | 4614.15i | −0.0736774 | + | 0.710760i | ||||
\(349\) | 4344.86 | 0.666404 | 0.333202 | − | 0.942855i | \(-0.391871\pi\) | ||||
0.333202 | + | 0.942855i | \(0.391871\pi\) | |||||||
\(350\) | 2495.44 | − | 843.887i | 0.381106 | − | 0.128879i | ||||
\(351\) | 1773.40 | + | 3629.37i | 0.269678 | + | 0.551914i | ||||
\(352\) | 3575.30 | + | 8221.20i | 0.541375 | + | 1.24486i | ||||
\(353\) | −9819.24 | −1.48053 | −0.740263 | − | 0.672318i | \(-0.765299\pi\) | ||||
−0.740263 | + | 0.672318i | \(0.765299\pi\) | |||||||
\(354\) | −3051.53 | − | 1665.05i | −0.458155 | − | 0.249990i | ||||
\(355\) | 6333.03 | 0.946824 | ||||||||
\(356\) | 7570.83 | − | 7677.68i | 1.12712 | − | 1.14302i | ||||
\(357\) | −5481.81 | + | 3790.66i | −0.812685 | + | 0.561969i | ||||
\(358\) | −2416.79 | + | 1011.00i | −0.356791 | + | 0.149254i | ||||
\(359\) | − | 728.937i | − | 0.107164i | −0.998563 | − | 0.0535820i | \(-0.982936\pi\) | ||
0.998563 | − | 0.0535820i | \(-0.0170638\pi\) | |||||||
\(360\) | 4585.76 | − | 6663.10i | 0.671363 | − | 0.975489i | ||||
\(361\) | −6244.50 | −0.910410 | ||||||||
\(362\) | −2287.64 | + | 956.975i | −0.332143 | + | 0.138943i | ||||
\(363\) | 4550.11 | − | 3642.77i | 0.657903 | − | 0.526711i | ||||
\(364\) | −3200.68 | + | 2820.27i | −0.460883 | + | 0.406105i | ||||
\(365\) | 13747.7 | 1.97147 | ||||||||
\(366\) | 5311.48 | − | 9734.31i | 0.758567 | − | 1.39022i | ||||
\(367\) | 8207.43i | 1.16737i | 0.811981 | + | 0.583685i | \(0.198390\pi\) | ||||
−0.811981 | + | 0.583685i | \(0.801610\pi\) | |||||||
\(368\) | 5471.50 | − | 76.6782i | 0.775059 | − | 0.0108618i | ||||
\(369\) | 2783.14 | − | 12411.2i | 0.392641 | − | 1.75095i | ||||
\(370\) | 9031.62 | − | 3778.14i | 1.26900 | − | 0.530855i | ||||
\(371\) | −219.316 | − | 15.4003i | −0.0306909 | − | 0.00215510i | ||||
\(372\) | −9791.61 | − | 1015.00i | −1.36471 | − | 0.141466i | ||||
\(373\) | − | 6620.48i | − | 0.919023i | −0.888172 | − | 0.459511i | \(-0.848025\pi\) | ||
0.888172 | − | 0.459511i | \(-0.151975\pi\) | |||||||
\(374\) | 8949.71 | − | 3743.88i | 1.23738 | − | 0.517624i | ||||
\(375\) | −3212.25 | − | 4012.35i | −0.442346 | − | 0.552525i | ||||
\(376\) | 1834.78 | − | 4564.65i | 0.251653 | − | 0.626074i | ||||
\(377\) | 3213.07 | 0.438942 | ||||||||
\(378\) | 5171.66 | + | 5221.50i | 0.703708 | + | 0.710489i | ||||
\(379\) | 2808.73i | 0.380672i | 0.981719 | + | 0.190336i | \(0.0609578\pi\) | ||||
−0.981719 | + | 0.190336i | \(0.939042\pi\) | |||||||
\(380\) | −1869.53 | − | 1843.52i | −0.252382 | − | 0.248869i | ||||
\(381\) | 10346.2 | − | 8283.04i | 1.39121 | − | 1.11379i | ||||
\(382\) | 2703.27 | + | 6462.13i | 0.362071 | + | 0.865528i | ||||
\(383\) | −2395.34 | −0.319573 | −0.159786 | − | 0.987152i | \(-0.551081\pi\) | ||||
−0.159786 | + | 0.987152i | \(0.551081\pi\) | |||||||
\(384\) | 7173.18 | − | 2273.46i | 0.953267 | − | 0.302128i | ||||
\(385\) | 850.624 | − | 12113.8i | 0.112602 | − | 1.60357i | ||||
\(386\) | −8168.44 | + | 3417.05i | −1.07711 | + | 0.450579i | ||||
\(387\) | 6879.73 | + | 1542.74i | 0.903660 | + | 0.202641i | ||||
\(388\) | −1043.09 | − | 1028.57i | −0.136481 | − | 0.134582i | ||||
\(389\) | 12078.7 | 1.57432 | 0.787162 | − | 0.616746i | \(-0.211550\pi\) | ||||
0.787162 | + | 0.616746i | \(0.211550\pi\) | |||||||
\(390\) | −4918.02 | − | 2683.49i | −0.638548 | − | 0.348420i | ||||
\(391\) | − | 5921.43i | − | 0.765881i | ||||||
\(392\) | −3872.53 | + | 6726.06i | −0.498960 | + | 0.866625i | ||||
\(393\) | 1427.81 | + | 1783.45i | 0.183266 | + | 0.228914i | ||||
\(394\) | −222.958 | + | 93.2688i | −0.0285088 | + | 0.0119259i | ||||
\(395\) | 1960.58i | 0.249740i | ||||||||
\(396\) | −5788.95 | − | 8995.69i | −0.734610 | − | 1.14154i | ||||
\(397\) | −5240.22 | −0.662466 | −0.331233 | − | 0.943549i | \(-0.607465\pi\) | ||||
−0.331233 | + | 0.943549i | \(0.607465\pi\) | |||||||
\(398\) | −3860.50 | − | 9228.48i | −0.486204 | − | 1.16227i | ||||
\(399\) | 1962.12 | − | 1356.80i | 0.246188 | − | 0.170238i | ||||
\(400\) | 45.0994 | + | 3218.15i | 0.00563743 | + | 0.402268i | ||||
\(401\) | 10649.8i | 1.32625i | 0.748509 | + | 0.663125i | \(0.230770\pi\) | ||||
−0.748509 | + | 0.663125i | \(0.769230\pi\) | |||||||
\(402\) | 2104.55 | + | 1148.34i | 0.261109 | + | 0.142473i | ||||
\(403\) | 6818.39i | 0.842799i | ||||||||
\(404\) | 4886.92 | + | 4818.92i | 0.601815 | + | 0.593441i | ||||
\(405\) | −4121.44 | + | 8727.50i | −0.505669 | + | 1.07080i | ||||
\(406\) | 5537.59 | − | 1872.65i | 0.676911 | − | 0.228912i | ||||
\(407\) | − | 12947.5i | − | 1.57687i | ||||||
\(408\) | −2351.16 | − | 7795.98i | −0.285294 | − | 0.945977i | ||||
\(409\) | 10197.5i | 1.23284i | 0.787416 | + | 0.616421i | \(0.211418\pi\) | ||||
−0.787416 | + | 0.616421i | \(0.788582\pi\) | |||||||
\(410\) | 6808.00 | + | 16274.5i | 0.820057 | + | 1.96034i | ||||
\(411\) | −3659.52 | − | 4571.03i | −0.439199 | − | 0.548594i | ||||
\(412\) | −2812.50 | − | 2773.36i | −0.336315 | − | 0.331635i | ||||
\(413\) | −306.845 | + | 4369.80i | −0.0365590 | + | 0.520639i | ||||
\(414\) | −6429.05 | + | 1140.74i | −0.763214 | + | 0.135421i | ||||
\(415\) | −9794.66 | −1.15856 | ||||||||
\(416\) | −2078.58 | − | 4779.58i | −0.244978 | − | 0.563312i | ||||
\(417\) | 9814.54 | − | 7857.43i | 1.15257 | − | 0.922733i | ||||
\(418\) | −3203.40 | + | 1340.06i | −0.374841 | + | 0.156805i | ||||
\(419\) | 9402.75i | 1.09631i | 0.836376 | + | 0.548155i | \(0.184670\pi\) | ||||
−0.836376 | + | 0.548155i | \(0.815330\pi\) | |||||||
\(420\) | −10040.0 | − | 1758.55i | −1.16643 | − | 0.204306i | ||||
\(421\) | − | 1525.15i | − | 0.176559i | −0.996096 | − | 0.0882793i | \(-0.971863\pi\) | ||
0.996096 | − | 0.0882793i | \(-0.0281368\pi\) | |||||||
\(422\) | 1851.42 | + | 4425.80i | 0.213568 | + | 0.510532i | ||||
\(423\) | −1284.48 | + | 5728.02i | −0.147644 | + | 0.658406i | ||||
\(424\) | 100.180 | − | 249.233i | 0.0114744 | − | 0.0285467i | ||||
\(425\) | 3482.78 | 0.397505 | ||||||||
\(426\) | −6171.21 | − | 3367.29i | −0.701868 | − | 0.382971i | ||||
\(427\) | −13939.6 | − | 978.829i | −1.57982 | − | 0.110934i | ||||
\(428\) | −3278.20 | + | 3324.47i | −0.370229 | + | 0.375454i | ||||
\(429\) | −5784.13 | + | 4630.72i | −0.650957 | + | 0.521149i | ||||
\(430\) | −9021.21 | + | 3773.79i | −1.01172 | + | 0.423229i | ||||
\(431\) | 7819.69i | 0.873924i | 0.899480 | + | 0.436962i | \(0.143946\pi\) | ||||
−0.899480 | + | 0.436962i | \(0.856054\pi\) | |||||||
\(432\) | −8011.36 | + | 4054.58i | −0.892238 | + | 0.451565i | ||||
\(433\) | 11246.6i | 1.24821i | 0.781340 | + | 0.624106i | \(0.214536\pi\) | ||||
−0.781340 | + | 0.624106i | \(0.785464\pi\) | |||||||
\(434\) | 3973.92 | + | 11751.2i | 0.439526 | + | 1.29971i | ||||
\(435\) | 4798.03 | + | 5993.12i | 0.528846 | + | 0.660570i | ||||
\(436\) | 10573.7 | + | 10426.5i | 1.16144 | + | 1.14527i | ||||
\(437\) | 2119.48i | 0.232010i | ||||||||
\(438\) | −13396.4 | − | 7309.67i | −1.46142 | − | 0.797419i | ||||
\(439\) | − | 5899.62i | − | 0.641397i | −0.947181 | − | 0.320698i | \(-0.896082\pi\) | ||
0.947181 | − | 0.320698i | \(-0.103918\pi\) | |||||||
\(440\) | 13766.2 | + | 5533.37i | 1.49154 | + | 0.599530i | ||||
\(441\) | 3269.38 | − | 8664.71i | 0.353027 | − | 0.935613i | ||||
\(442\) | −5203.11 | + | 2176.58i | −0.559924 | + | 0.234230i | ||||
\(443\) | 991.808 | 0.106371 | 0.0531854 | − | 0.998585i | \(-0.483063\pi\) | ||||
0.0531854 | + | 0.998585i | \(0.483063\pi\) | |||||||
\(444\) | −10809.7 | − | 1120.53i | −1.15542 | − | 0.119770i | ||||
\(445\) | − | 17844.7i | − | 1.90095i | ||||||
\(446\) | −4296.86 | − | 10271.6i | −0.456193 | − | 1.09053i | ||||
\(447\) | 8313.64 | − | 6655.81i | 0.879690 | − | 0.704271i | ||||
\(448\) | −6367.99 | − | 7025.96i | −0.671561 | − | 0.740949i | ||||
\(449\) | − | 13929.7i | − | 1.46411i | −0.681248 | − | 0.732053i | \(-0.738562\pi\) | ||
0.681248 | − | 0.732053i | \(-0.261438\pi\) | |||||||
\(450\) | −670.942 | − | 3781.34i | −0.0702856 | − | 0.396121i | ||||
\(451\) | 23330.7 | 2.43592 | ||||||||
\(452\) | 5420.03 | + | 5344.61i | 0.564020 | + | 0.556171i | ||||
\(453\) | 1168.96 | − | 935.859i | 0.121242 | − | 0.0970651i | ||||
\(454\) | −6800.14 | − | 16255.7i | −0.702965 | − | 1.68043i | ||||
\(455\) | −494.529 | + | 7042.62i | −0.0509535 | + | 0.725633i | ||||
\(456\) | 841.559 | + | 2790.44i | 0.0864246 | + | 0.286567i | ||||
\(457\) | −10005.2 | −1.02412 | −0.512060 | − | 0.858950i | \(-0.671117\pi\) | ||||
−0.512060 | + | 0.858950i | \(0.671117\pi\) | |||||||
\(458\) | 10369.0 | − | 4337.60i | 1.05789 | − | 0.442539i | ||||
\(459\) | 4265.65 | + | 8729.92i | 0.433777 | + | 0.887752i | ||||
\(460\) | 6358.53 | − | 6448.26i | 0.644496 | − | 0.653591i | ||||
\(461\) | 15566.9i | 1.57272i | 0.617770 | + | 0.786359i | \(0.288036\pi\) | ||||
−0.617770 | + | 0.786359i | \(0.711964\pi\) | |||||||
\(462\) | −7269.82 | + | 11352.0i | −0.732084 | + | 1.14316i | ||||
\(463\) | −10866.3 | −1.09071 | −0.545357 | − | 0.838204i | \(-0.683606\pi\) | ||||
−0.545357 | + | 0.838204i | \(0.683606\pi\) | |||||||
\(464\) | 100.079 | + | 7141.32i | 0.0100131 | + | 0.714499i | ||||
\(465\) | −12717.9 | + | 10181.8i | −1.26834 | + | 1.01542i | ||||
\(466\) | 3712.41 | + | 8874.48i | 0.369043 | + | 0.882194i | ||||
\(467\) | − | 2184.04i | − | 0.216414i | −0.994128 | − | 0.108207i | \(-0.965489\pi\) | ||
0.994128 | − | 0.108207i | \(-0.0345109\pi\) | |||||||
\(468\) | 3365.53 | + | 5229.84i | 0.332418 | + | 0.516559i | ||||
\(469\) | 211.622 | − | 3013.73i | 0.0208354 | − | 0.296719i | ||||
\(470\) | −3142.03 | − | 7511.01i | −0.308364 | − | 0.737142i | ||||
\(471\) | 8471.59 | − | 6782.27i | 0.828769 | − | 0.663504i | ||||
\(472\) | −4965.87 | − | 1996.05i | −0.484264 | − | 0.194652i | ||||
\(473\) | 12932.6i | 1.25717i | ||||||||
\(474\) | 1042.44 | − | 1910.48i | 0.101015 | − | 0.185129i | ||||
\(475\) | −1246.60 | −0.120417 | ||||||||
\(476\) | −7698.78 | + | 6783.75i | −0.741329 | + | 0.653219i | ||||
\(477\) | −70.1332 | + | 312.753i | −0.00673203 | + | 0.0300209i | ||||
\(478\) | 4887.45 | + | 11683.4i | 0.467671 | + | 1.11796i | ||||
\(479\) | −7028.43 | −0.670433 | −0.335216 | − | 0.942141i | \(-0.608809\pi\) | ||||
−0.335216 | + | 0.942141i | \(0.608809\pi\) | |||||||
\(480\) | 5811.11 | − | 11014.3i | 0.552583 | − | 1.04736i | ||||
\(481\) | 7527.32i | 0.713547i | ||||||||
\(482\) | 2524.41 | + | 6034.58i | 0.238555 | + | 0.570265i | ||||
\(483\) | 4679.79 | + | 6767.63i | 0.440865 | + | 0.637552i | ||||
\(484\) | 6300.83 | − | 6389.75i | 0.591738 | − | 0.600089i | ||||
\(485\) | −2424.37 | −0.226980 | ||||||||
\(486\) | 8656.55 | − | 6313.11i | 0.807961 | − | 0.589236i | ||||
\(487\) | 3566.36 | 0.331842 | 0.165921 | − | 0.986139i | \(-0.446940\pi\) | ||||
0.165921 | + | 0.986139i | \(0.446940\pi\) | |||||||
\(488\) | 6367.35 | − | 15841.0i | 0.590649 | − | 1.46945i | ||||
\(489\) | 13352.8 | + | 16678.7i | 1.23483 | + | 1.54241i | ||||
\(490\) | 3252.30 | + | 12425.9i | 0.299845 | + | 1.14560i | ||||
\(491\) | −2231.72 | −0.205124 | −0.102562 | − | 0.994727i | \(-0.532704\pi\) | ||||
−0.102562 | + | 0.994727i | \(0.532704\pi\) | |||||||
\(492\) | 2019.13 | − | 19478.4i | 0.185020 | − | 1.78487i | ||||
\(493\) | 7728.56 | 0.706038 | ||||||||
\(494\) | 1862.37 | − | 779.072i | 0.169619 | − | 0.0709557i | ||||
\(495\) | −17274.7 | − | 3873.76i | −1.56857 | − | 0.351743i | ||||
\(496\) | −15154.5 | + | 212.376i | −1.37189 | + | 0.0192257i | ||||
\(497\) | −620.542 | + | 8837.19i | −0.0560063 | + | 0.797590i | ||||
\(498\) | 9544.38 | + | 5207.84i | 0.858823 | + | 0.468612i | ||||
\(499\) | − | 20669.1i | − | 1.85426i | −0.374743 | − | 0.927129i | \(-0.622269\pi\) | ||
0.374743 | − | 0.927129i | \(-0.377731\pi\) | |||||||
\(500\) | −5634.57 | − | 5556.16i | −0.503971 | − | 0.496958i | ||||
\(501\) | −4968.79 | + | 3977.96i | −0.443092 | + | 0.354735i | ||||
\(502\) | 4904.52 | + | 11724.2i | 0.436055 | + | 1.04239i | ||||
\(503\) | −17146.1 | −1.51990 | −0.759948 | − | 0.649984i | \(-0.774775\pi\) | ||||
−0.759948 | + | 0.649984i | \(0.774775\pi\) | |||||||
\(504\) | 8848.43 | + | 7051.91i | 0.782024 | + | 0.623248i | ||||
\(505\) | 11358.4 | 1.00087 | ||||||||
\(506\) | −4622.04 | − | 11048.9i | −0.406076 | − | 0.970723i | ||||
\(507\) | −5549.06 | + | 4442.52i | −0.486080 | + | 0.389151i | ||||
\(508\) | 14327.0 | − | 14529.2i | 1.25130 | − | 1.26895i | ||||
\(509\) | 7036.98i | 0.612787i | 0.951905 | + | 0.306393i | \(0.0991223\pi\) | ||||
−0.951905 | + | 0.306393i | \(0.900878\pi\) | |||||||
\(510\) | −11829.6 | − | 6454.74i | −1.02710 | − | 0.560433i | ||||
\(511\) | −1347.07 | + | 19183.7i | −0.116616 | + | 1.66074i | ||||
\(512\) | 10558.3 | − | 4768.69i | 0.911356 | − | 0.411618i | ||||
\(513\) | −1526.82 | − | 3124.73i | −0.131405 | − | 0.268928i | ||||
\(514\) | −3736.44 | + | 1563.04i | −0.320637 | + | 0.134130i | ||||
\(515\) | −6536.91 | −0.559322 | ||||||||
\(516\) | 10797.2 | + | 1119.24i | 0.921166 | + | 0.0954880i | ||||
\(517\) | −10767.6 | −0.915974 | ||||||||
\(518\) | 4387.10 | + | 12973.0i | 0.372120 | + | 1.10039i | ||||
\(519\) | 7961.20 | + | 9944.17i | 0.673330 | + | 0.841042i | ||||
\(520\) | −8003.28 | − | 3216.95i | −0.674937 | − | 0.271293i | ||||
\(521\) | −5554.16 | −0.467048 | −0.233524 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233524 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(522\) | −1488.87 | − | 8391.10i | −0.124839 | − | 0.703579i | ||||
\(523\) | −1129.07 | −0.0943994 | −0.0471997 | − | 0.998885i | \(-0.515030\pi\) | ||||
−0.0471997 | + | 0.998885i | \(0.515030\pi\) | |||||||
\(524\) | 2504.51 | + | 2469.66i | 0.208798 | + | 0.205892i | ||||
\(525\) | −3980.48 | + | 2752.49i | −0.330900 | + | 0.228816i | ||||
\(526\) | −985.253 | − | 2355.24i | −0.0816712 | − | 0.195234i | ||||
\(527\) | 16400.6i | 1.35564i | ||||||||
\(528\) | −10472.3 | − | 12711.5i | −0.863162 | − | 1.04772i | ||||
\(529\) | 4856.64 | 0.399165 | ||||||||
\(530\) | −171.557 | − | 410.105i | −0.0140603 | − | 0.0336110i | ||||
\(531\) | 6231.50 | + | 1397.38i | 0.509273 | + | 0.114202i | ||||
\(532\) | 2755.65 | − | 2428.13i | 0.224572 | − | 0.197881i | ||||
\(533\) | −13563.8 | −1.10228 | ||||||||
\(534\) | −9488.08 | + | 17388.7i | −0.768894 | + | 1.40915i | ||||
\(535\) | 7726.84i | 0.624412i | ||||||||
\(536\) | 3424.82 | + | 1376.62i | 0.275989 | + | 0.110935i | ||||
\(537\) | 3757.04 | − | 3007.85i | 0.301915 | − | 0.241710i | ||||
\(538\) | −2062.71 | − | 4930.88i | −0.165297 | − | 0.395140i | ||||
\(539\) | 16820.4 | + | 2373.94i | 1.34417 | + | 0.189708i | ||||
\(540\) | −4729.17 | + | 14087.2i | −0.376872 | + | 1.12262i | ||||
\(541\) | 13088.7i | 1.04016i | 0.854118 | + | 0.520079i | \(0.174097\pi\) | ||||
−0.854118 | + | 0.520079i | \(0.825903\pi\) | |||||||
\(542\) | 8318.52 | + | 19885.4i | 0.659245 | + | 1.57592i | ||||
\(543\) | 3556.28 | − | 2847.12i | 0.281058 | − | 0.225012i | ||||
\(544\) | −4999.71 | − | 11496.6i | −0.394046 | − | 0.906087i | ||||
\(545\) | 24575.7 | 1.93157 | ||||||||
\(546\) | 4226.47 | − | 6599.72i | 0.331275 | − | 0.517293i | ||||
\(547\) | − | 134.806i | − | 0.0105373i | −0.999986 | − | 0.00526863i | \(-0.998323\pi\) | ||
0.999986 | − | 0.00526863i | \(-0.00167706\pi\) | |||||||
\(548\) | −6419.12 | − | 6329.79i | −0.500385 | − | 0.493422i | ||||
\(549\) | −4457.61 | + | 19878.4i | −0.346532 | + | 1.54533i | ||||
\(550\) | 6498.61 | − | 2718.52i | 0.503821 | − | 0.210760i | ||||
\(551\) | −2766.31 | −0.213881 | ||||||||
\(552\) | −9624.61 | + | 2902.65i | −0.742120 | + | 0.223813i | ||||
\(553\) | −2735.81 | − | 192.107i | −0.210377 | − | 0.0147726i | ||||
\(554\) | −3256.94 | − | 7785.69i | −0.249773 | − | 0.597080i | ||||
\(555\) | −14040.2 | + | 11240.4i | −1.07383 | + | 0.859695i | ||||
\(556\) | 13590.8 | − | 13782.6i | 1.03665 | − | 1.05128i | ||||
\(557\) | 949.790 | 0.0722512 | 0.0361256 | − | 0.999347i | \(-0.488498\pi\) | ||||
0.0361256 | + | 0.999347i | \(0.488498\pi\) | |||||||
\(558\) | 17806.6 | − | 3159.51i | 1.35092 | − | 0.239700i | ||||
\(559\) | − | 7518.65i | − | 0.568882i | ||||||
\(560\) | −15668.2 | − | 879.773i | −1.18233 | − | 0.0663878i | ||||
\(561\) | −13912.9 | + | 11138.5i | −1.04706 | + | 0.838267i | ||||
\(562\) | 3262.40 | + | 7798.73i | 0.244868 | + | 0.585355i | ||||
\(563\) | 3122.65i | 0.233755i | 0.993146 | + | 0.116877i | \(0.0372884\pi\) | ||||
−0.993146 | + | 0.116877i | \(0.962712\pi\) | |||||||
\(564\) | −931.872 | + | 8989.71i | −0.0695725 | + | 0.671161i | ||||
\(565\) | 12597.4 | 0.938014 | ||||||||
\(566\) | 8221.92 | − | 3439.43i | 0.610589 | − | 0.255424i | ||||
\(567\) | −11774.6 | − | 6606.26i | −0.872112 | − | 0.489307i | ||||
\(568\) | −10042.6 | − | 4036.67i | −0.741866 | − | 0.298196i | ||||
\(569\) | − | 15497.7i | − | 1.14182i | −0.821011 | − | 0.570912i | \(-0.806590\pi\) | ||
0.821011 | − | 0.570912i | \(-0.193410\pi\) | |||||||
\(570\) | 4234.20 | + | 2310.37i | 0.311142 | + | 0.169773i | ||||
\(571\) | − | 11912.4i | − | 0.873063i | −0.899689 | − | 0.436531i | \(-0.856207\pi\) | ||
0.899689 | − | 0.436531i | \(-0.143793\pi\) | |||||||
\(572\) | −8009.65 | + | 8122.69i | −0.585490 | + | 0.593753i | ||||
\(573\) | −8042.56 | − | 10045.8i | −0.586357 | − | 0.732406i | ||||
\(574\) | −23376.7 | + | 7905.31i | −1.69987 | + | 0.574845i | ||||
\(575\) | − | 4299.70i | − | 0.311843i | ||||||
\(576\) | −11519.0 | + | 7643.08i | −0.833258 | + | 0.552885i | ||||
\(577\) | − | 5650.41i | − | 0.407677i | −0.979005 | − | 0.203838i | \(-0.934658\pi\) | ||
0.979005 | − | 0.203838i | \(-0.0653417\pi\) | |||||||
\(578\) | 304.273 | − | 127.285i | 0.0218963 | − | 0.00915977i | ||||
\(579\) | 12698.3 | − | 10166.2i | 0.911443 | − | 0.729692i | ||||
\(580\) | 8416.17 | + | 8299.05i | 0.602521 | + | 0.594137i | ||||
\(581\) | 959.729 | − | 13667.6i | 0.0685306 | − | 0.975949i | ||||
\(582\) | 2362.42 | + | 1289.05i | 0.168257 | + | 0.0918087i | ||||
\(583\) | −587.917 | −0.0417651 | ||||||||
\(584\) | −21800.5 | − | 8762.77i | −1.54471 | − | 0.620901i | ||||
\(585\) | 10043.0 | + | 2252.10i | 0.709793 | + | 0.159167i | ||||
\(586\) | 1785.74 | + | 4268.79i | 0.125884 | + | 0.300925i | ||||
\(587\) | − | 9396.05i | − | 0.660675i | −0.943863 | − | 0.330338i | \(-0.892837\pi\) | ||
0.943863 | − | 0.330338i | \(-0.107163\pi\) | |||||||
\(588\) | 3437.67 | − | 13837.6i | 0.241101 | − | 0.970500i | ||||
\(589\) | − | 5870.33i | − | 0.410667i | ||||||
\(590\) | −8171.21 | + | 3418.21i | −0.570175 | + | 0.238518i | ||||
\(591\) | 346.603 | − | 277.487i | 0.0241241 | − | 0.0193135i | ||||
\(592\) | −16730.1 | + | 234.458i | −1.16149 | + | 0.0162773i | ||||
\(593\) | 5680.51 | 0.393374 | 0.196687 | − | 0.980466i | \(-0.436982\pi\) | ||||
0.196687 | + | 0.980466i | \(0.436982\pi\) | |||||||
\(594\) | 14773.6 | + | 12959.8i | 1.02049 | + | 0.895196i | ||||
\(595\) | −1189.52 | + | 16940.0i | −0.0819587 | + | 1.16718i | ||||
\(596\) | 11512.4 | − | 11674.9i | 0.791220 | − | 0.802386i | ||||
\(597\) | 11485.5 | + | 14346.2i | 0.787385 | + | 0.983506i | ||||
\(598\) | 2687.12 | + | 6423.55i | 0.183754 | + | 0.439261i | ||||
\(599\) | − | 11213.1i | − | 0.764866i | −0.923983 | − | 0.382433i | \(-0.875086\pi\) | ||
0.923983 | − | 0.382433i | \(-0.124914\pi\) | |||||||
\(600\) | −1707.24 | − | 5660.86i | −0.116163 | − | 0.385173i | ||||
\(601\) | − | 4599.55i | − | 0.312179i | −0.987743 | − | 0.156089i | \(-0.950111\pi\) | ||
0.987743 | − | 0.156089i | \(-0.0498888\pi\) | |||||||
\(602\) | −4382.05 | − | 12958.1i | −0.296676 | − | 0.877295i | ||||
\(603\) | −4297.69 | − | 963.734i | −0.290241 | − | 0.0650850i | ||||
\(604\) | 1618.74 | − | 1641.58i | 0.109049 | − | 0.110588i | ||||
\(605\) | − | 14851.3i | − | 0.998000i | ||||||
\(606\) | −11068.1 | − | 6039.26i | −0.741933 | − | 0.404832i | ||||
\(607\) | − | 27115.8i | − | 1.81318i | −0.422017 | − | 0.906588i | \(-0.638678\pi\) | ||
0.422017 | − | 0.906588i | \(-0.361322\pi\) | |||||||
\(608\) | 1789.56 | + | 4115.00i | 0.119369 | + | 0.274483i | ||||
\(609\) | −8833.00 | + | 6107.99i | −0.587736 | + | 0.406417i | ||||
\(610\) | −10904.0 | − | 26066.0i | −0.723756 | − | 1.73013i | ||||
\(611\) | 6259.98 | 0.414487 | ||||||||
\(612\) | 8095.29 | + | 12579.6i | 0.534694 | + | 0.830884i | ||||
\(613\) | 2010.26i | 0.132453i | 0.997805 | + | 0.0662263i | \(0.0210959\pi\) | ||||
−0.997805 | + | 0.0662263i | \(0.978904\pi\) | |||||||
\(614\) | 9885.42 | − | 4135.31i | 0.649745 | − | 0.271804i | ||||
\(615\) | −20254.7 | − | 25299.7i | −1.32804 | − | 1.65883i | ||||
\(616\) | −9070.21 | + | 18667.3i | −0.593262 | + | 1.22099i | ||||
\(617\) | 15659.8i | 1.02178i | 0.859646 | + | 0.510891i | \(0.170684\pi\) | ||||
−0.859646 | + | 0.510891i | \(0.829316\pi\) | |||||||
\(618\) | 6369.87 | + | 3475.69i | 0.414618 | + | 0.226234i | ||||
\(619\) | −27135.8 | −1.76200 | −0.881001 | − | 0.473115i | \(-0.843130\pi\) | ||||
−0.881001 | + | 0.473115i | \(0.843130\pi\) | |||||||
\(620\) | −17611.3 | + | 17859.8i | −1.14078 | + | 1.15688i | ||||
\(621\) | 10777.6 | − | 5266.20i | 0.696442 | − | 0.340298i | ||||
\(622\) | −13042.3 | + | 5455.92i | −0.840756 | + | 0.351708i | ||||
\(623\) | 24900.7 | + | 1748.52i | 1.60133 | + | 0.112444i | ||||
\(624\) | 6088.32 | + | 7390.11i | 0.390589 | + | 0.474104i | ||||
\(625\) | −19382.1 | −1.24046 | ||||||||
\(626\) | 1258.16 | + | 3007.62i | 0.0803294 | + | 0.192027i | ||||
\(627\) | 4979.88 | − | 3986.84i | 0.317189 | − | 0.253938i | ||||
\(628\) | 11731.2 | − | 11896.7i | 0.745420 | − | 0.755940i | ||||
\(629\) | 18105.9i | 1.14774i | ||||||||
\(630\) | 18621.3 | − | 1971.92i | 1.17761 | − | 0.124704i | ||||
\(631\) | 854.200 | 0.0538909 | 0.0269455 | − | 0.999637i | \(-0.491422\pi\) | ||||
0.0269455 | + | 0.999637i | \(0.491422\pi\) | |||||||
\(632\) | 1249.67 | − | 3109.00i | 0.0786540 | − | 0.195679i | ||||
\(633\) | −5508.20 | − | 6880.18i | −0.345863 | − | 0.432011i | ||||
\(634\) | 7146.39 | − | 2989.51i | 0.447665 | − | 0.187269i | ||||
\(635\) | − | 33769.3i | − | 2.11038i | ||||||
\(636\) | −50.8808 | + | 490.843i | −0.00317225 | + | 0.0306025i | ||||
\(637\) | −9778.89 | − | 1380.14i | −0.608248 | − | 0.0858449i | ||||
\(638\) | 14420.9 | − | 6032.61i | 0.894873 | − | 0.374347i | ||||
\(639\) | 12602.2 | + | 2825.97i | 0.780178 | + | 0.174951i | ||||
\(640\) | 6900.66 | − | 17888.2i | 0.426207 | − | 1.10483i | ||||
\(641\) | − | 29337.9i | − | 1.80777i | −0.427779 | − | 0.903884i | \(-0.640704\pi\) | ||
0.427779 | − | 0.903884i | \(-0.359296\pi\) | |||||||
\(642\) | 4108.38 | − | 7529.40i | 0.252562 | − | 0.462869i | ||||
\(643\) | 24076.1 | 1.47662 | 0.738310 | − | 0.674461i | \(-0.235624\pi\) | ||||
0.738310 | + | 0.674461i | \(0.235624\pi\) | |||||||
\(644\) | 8374.94 | + | 9504.60i | 0.512452 | + | 0.581574i | ||||
\(645\) | 14024.0 | − | 11227.5i | 0.856117 | − | 0.685399i | ||||
\(646\) | 4479.65 | − | 1873.94i | 0.272832 | − | 0.114132i | ||||
\(647\) | 9606.99 | 0.583755 | 0.291878 | − | 0.956456i | \(-0.405720\pi\) | ||||
0.291878 | + | 0.956456i | \(0.405720\pi\) | |||||||
\(648\) | 12098.5 | − | 11212.7i | 0.733447 | − | 0.679746i | ||||
\(649\) | 11714.1i | 0.708500i | ||||||||
\(650\) | −3778.11 | + | 1580.47i | −0.227984 | + | 0.0953711i | ||||
\(651\) | −12961.7 | − | 18744.3i | −0.780349 | − | 1.12849i | ||||
\(652\) | 23422.0 | + | 23096.0i | 1.40686 | + | 1.38729i | ||||
\(653\) | 5450.16 | 0.326618 | 0.163309 | − | 0.986575i | \(-0.447783\pi\) | ||||
0.163309 | + | 0.986575i | \(0.447783\pi\) | |||||||
\(654\) | −23947.7 | − | 13066.9i | −1.43185 | − | 0.781281i | ||||
\(655\) | 5821.08 | 0.347249 | ||||||||
\(656\) | −422.479 | − | 30146.8i | −0.0251449 | − | 1.79426i | ||||
\(657\) | 27356.6 | + | 6134.58i | 1.62448 | + | 0.364281i | ||||
\(658\) | 10788.8 | − | 3648.46i | 0.639197 | − | 0.216158i | ||||
\(659\) | −15534.8 | −0.918287 | −0.459144 | − | 0.888362i | \(-0.651844\pi\) | ||||
−0.459144 | + | 0.888362i | \(0.651844\pi\) | |||||||
\(660\) | −27111.4 | − | 2810.37i | −1.59896 | − | 0.165748i | ||||
\(661\) | 10381.1 | 0.610858 | 0.305429 | − | 0.952215i | \(-0.401200\pi\) | ||||
0.305429 | + | 0.952215i | \(0.401200\pi\) | |||||||
\(662\) | 5700.24 | + | 13626.4i | 0.334662 | + | 0.800006i | ||||
\(663\) | 8088.55 | − | 6475.61i | 0.473806 | − | 0.379324i | ||||
\(664\) | 15531.9 | + | 6243.11i | 0.907765 | + | 0.364879i | ||||
\(665\) | 425.768 | − | 6063.39i | 0.0248279 | − | 0.353576i | ||||
\(666\) | 19658.0 | − | 3488.02i | 1.14374 | − | 0.202940i | ||||
\(667\) | − | 9541.36i | − | 0.553888i | ||||||
\(668\) | −6880.59 | + | 6977.69i | −0.398530 | + | 0.404154i | ||||
\(669\) | 12783.7 | + | 15967.9i | 0.738784 | + | 0.922799i | ||||
\(670\) | 5635.46 | − | 2357.45i | 0.324950 | − | 0.135934i | ||||
\(671\) | −37367.6 | −2.14986 | ||||||||
\(672\) | 14800.1 | + | 9188.13i | 0.849592 | + | 0.527440i | ||||
\(673\) | 29748.6 | 1.70390 | 0.851948 | − | 0.523626i | \(-0.175421\pi\) | ||||
0.851948 | + | 0.523626i | \(0.175421\pi\) | |||||||
\(674\) | 7563.42 | − | 3163.96i | 0.432244 | − | 0.180818i | ||||
\(675\) | 3097.39 | + | 6339.02i | 0.176620 | + | 0.361465i | ||||
\(676\) | −7684.14 | + | 7792.58i | −0.437195 | + | 0.443365i | ||||
\(677\) | − | 6845.80i | − | 0.388634i | −0.980939 | − | 0.194317i | \(-0.937751\pi\) | ||
0.980939 | − | 0.194317i | \(-0.0622491\pi\) | |||||||
\(678\) | −12275.5 | − | 6698.08i | −0.695337 | − | 0.379407i | ||||
\(679\) | 237.552 | − | 3383.00i | 0.0134262 | − | 0.191204i | ||||
\(680\) | −19250.7 | − | 7737.89i | −1.08563 | − | 0.436374i | ||||
\(681\) | 20231.3 | + | 25270.4i | 1.13842 | + | 1.42198i | ||||
\(682\) | 12801.7 | + | 30602.4i | 0.718772 | + | 1.71822i | ||||
\(683\) | 13901.9 | 0.778833 | 0.389417 | − | 0.921062i | \(-0.372677\pi\) | ||||
0.389417 | + | 0.921062i | \(0.372677\pi\) | |||||||
\(684\) | −2897.57 | − | 4502.66i | −0.161976 | − | 0.251701i | ||||
\(685\) | −14919.5 | −0.832184 | ||||||||
\(686\) | −17657.9 | + | 3320.75i | −0.982772 | + | 0.184821i | ||||
\(687\) | −16119.2 | + | 12904.9i | −0.895178 | + | 0.716671i | ||||
\(688\) | 16710.9 | − | 234.187i | 0.926011 | − | 0.0129772i | ||||
\(689\) | 341.799 | 0.0188991 | ||||||||
\(690\) | −7968.77 | + | 14604.3i | −0.439661 | + | 0.805763i | ||||
\(691\) | 7713.20 | 0.424637 | 0.212318 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212318 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(692\) | 13964.7 | + | 13770.3i | 0.767134 | + | 0.756459i | ||||
\(693\) | 7098.16 | − | 23725.8i | 0.389086 | − | 1.30053i | ||||
\(694\) | 27551.7 | − | 11525.5i | 1.50699 | − | 0.630408i | ||||
\(695\) | − | 32034.1i | − | 1.74838i | ||||||
\(696\) | −3788.49 | − | 12561.9i | −0.206325 | − | 0.684133i | ||||
\(697\) | −32625.7 | −1.77301 | ||||||||
\(698\) | −11337.1 | + | 4742.59i | −0.614780 | + | 0.257177i | ||||
\(699\) | −11044.9 | − | 13795.9i | −0.597648 | − | 0.746509i | ||||
\(700\) | −5590.27 | + | 4925.85i | −0.301846 | + | 0.265971i | ||||
\(701\) | −28716.9 | −1.54725 | −0.773626 | − | 0.633643i | \(-0.781559\pi\) | ||||
−0.773626 | + | 0.633643i | \(0.781559\pi\) | |||||||
\(702\) | −8588.97 | − | 7534.46i | −0.461780 | − | 0.405085i | ||||
\(703\) | − | 6480.69i | − | 0.347687i | ||||||
\(704\) | −18302.9 | − | 17549.2i | −0.979851 | − | 0.939501i | ||||
\(705\) | 9347.95 | + | 11676.3i | 0.499382 | + | 0.623767i | ||||
\(706\) | 25621.5 | − | 10718.1i | 1.36583 | − | 0.571361i | ||||
\(707\) | −1112.95 | + | 15849.6i | −0.0592033 | + | 0.843118i | ||||
\(708\) | 9779.88 | + | 1013.78i | 0.519139 | + | 0.0538139i | ||||
\(709\) | 6971.08i | 0.369259i | 0.982808 | + | 0.184629i | \(0.0591085\pi\) | ||||
−0.982808 | + | 0.184629i | \(0.940892\pi\) | |||||||
\(710\) | −16524.9 | + | 6912.76i | −0.873477 | + | 0.365396i | ||||
\(711\) | −874.862 | + | 3901.38i | −0.0461461 | + | 0.205785i | ||||
\(712\) | −11374.2 | + | 28297.4i | −0.598690 | + | 1.48945i | ||||
\(713\) | 20247.6 | 1.06350 | ||||||||
\(714\) | 10166.1 | − | 15874.6i | 0.532855 | − | 0.832064i | ||||
\(715\) | 18879.0i | 0.987463i | ||||||||
\(716\) | 5202.62 | − | 5276.04i | 0.271552 | − | 0.275384i | ||||
\(717\) | −14540.8 | − | 18162.6i | −0.757371 | − | 0.946016i | ||||
\(718\) | 795.664 | + | 1902.03i | 0.0413565 | + | 0.0988623i | ||||
\(719\) | −19292.8 | −1.00070 | −0.500348 | − | 0.865825i | \(-0.666795\pi\) | ||||
−0.500348 | + | 0.865825i | \(0.666795\pi\) | |||||||
\(720\) | −4692.67 | + | 22391.7i | −0.242896 | + | 1.15901i | ||||
\(721\) | 640.519 | − | 9121.68i | 0.0330849 | − | 0.471164i | ||||
\(722\) | 16293.9 | − | 6816.13i | 0.839884 | − | 0.351343i | ||||
\(723\) | −7510.44 | − | 9381.13i | −0.386329 | − | 0.482556i | ||||
\(724\) | 4924.61 | − | 4994.10i | 0.252792 | − | 0.256360i | ||||
\(725\) | 5611.90 | 0.287477 | ||||||||
\(726\) | −7896.45 | + | 14471.8i | −0.403671 | + | 0.739805i | ||||
\(727\) | − | 12461.6i | − | 0.635732i | −0.948136 | − | 0.317866i | \(-0.897034\pi\) | ||
0.948136 | − | 0.317866i | \(-0.102966\pi\) | |||||||
\(728\) | 5273.17 | − | 10852.7i | 0.268457 | − | 0.552509i | ||||
\(729\) | −12095.7 | + | 15527.8i | −0.614527 | + | 0.788896i | ||||
\(730\) | −35872.1 | + | 15006.1i | −1.81875 | + | 0.760825i | ||||
\(731\) | − | 18085.0i | − | 0.915045i | ||||||
\(732\) | −3233.94 | + | 31197.6i | −0.163292 | + | 1.57527i | ||||
\(733\) | −26437.4 | −1.33218 | −0.666090 | − | 0.745872i | \(-0.732033\pi\) | ||||
−0.666090 | + | 0.745872i | \(0.732033\pi\) | |||||||
\(734\) | −8958.74 | − | 21415.8i | −0.450508 | − | 1.07694i | ||||
\(735\) | −12028.4 | − | 20300.9i | −0.603639 | − | 1.01879i | ||||
\(736\) | −14193.2 | + | 6172.44i | −0.710826 | + | 0.309129i | ||||
\(737\) | − | 8078.86i | − | 0.403784i | ||||||
\(738\) | 6285.21 | + | 35422.6i | 0.313498 | + | 1.76684i | ||||
\(739\) | − | 24642.5i | − | 1.22664i | −0.789834 | − | 0.613321i | \(-0.789833\pi\) | ||
0.789834 | − | 0.613321i | \(-0.210167\pi\) | |||||||
\(740\) | −19442.4 | + | 19716.7i | −0.965832 | + | 0.979462i | ||||
\(741\) | −2895.16 | + | 2317.84i | −0.143531 | + | 0.114909i | ||||
\(742\) | 589.076 | − | 199.208i | 0.0291451 | − | 0.00985602i | ||||
\(743\) | 29736.2i | 1.46826i | 0.679012 | + | 0.734128i | \(0.262409\pi\) | ||||
−0.679012 | + | 0.734128i | \(0.737591\pi\) | |||||||
\(744\) | 26657.3 | − | 8039.49i | 1.31358 | − | 0.396158i | ||||
\(745\) | − | 27135.2i | − | 1.33444i | ||||||
\(746\) | 7226.52 | + | 17274.9i | 0.354667 | + | 0.847829i | ||||
\(747\) | −19490.5 | − | 4370.63i | −0.954645 | − | 0.214074i | ||||
\(748\) | −19266.0 | + | 19537.9i | −0.941760 | + | 0.955050i | ||||
\(749\) | −10782.1 | − | 757.115i | −0.525995 | − | 0.0369351i | ||||
\(750\) | 12761.4 | + | 6963.21i | 0.621308 | + | 0.339014i | ||||
\(751\) | 8068.95 | 0.392064 | 0.196032 | − | 0.980597i | \(-0.437194\pi\) | ||||
0.196032 | + | 0.980597i | \(0.437194\pi\) | |||||||
\(752\) | 194.983 | + | 13913.4i | 0.00945519 | + | 0.674691i | ||||
\(753\) | −14591.6 | − | 18226.0i | −0.706171 | − | 0.882063i | ||||
\(754\) | −8383.91 | + | 3507.19i | −0.404939 | + | 0.169396i | ||||
\(755\) | − | 3815.42i | − | 0.183917i | ||||||
\(756\) | −19194.0 | − | 7979.47i | −0.923385 | − | 0.383876i | ||||
\(757\) | 10634.4i | 0.510587i | 0.966864 | + | 0.255293i | \(0.0821720\pi\) | ||||
−0.966864 | + | 0.255293i | \(0.917828\pi\) | |||||||
\(758\) | −3065.84 | − | 7328.87i | −0.146908 | − | 0.351183i | ||||
\(759\) | 13751.1 | + | 17176.3i | 0.657622 | + | 0.821422i | ||||
\(760\) | 6890.48 | + | 2769.65i | 0.328873 | + | 0.132192i | ||||
\(761\) | −3296.31 | −0.157019 | −0.0785094 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785094 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(762\) | −17955.2 | + | 32906.4i | −0.853606 | + | 1.56440i | ||||
\(763\) | −2408.05 | + | 34293.2i | −0.114256 | + | 1.62712i | ||||
\(764\) | −14107.4 | − | 13911.0i | −0.668045 | − | 0.658748i | ||||
\(765\) | 24157.1 | + | 5417.09i | 1.14170 | + | 0.256020i | ||||
\(766\) | 6250.21 | − | 2614.61i | 0.294816 | − | 0.123329i | ||||
\(767\) | − | 6810.22i | − | 0.320603i | ||||||
\(768\) | −16235.5 | + | 13762.0i | −0.762824 | + | 0.646606i | ||||
\(769\) | 29295.6i | 1.37376i | 0.726769 | + | 0.686882i | \(0.241021\pi\) | ||||
−0.726769 | + | 0.686882i | \(0.758979\pi\) | |||||||
\(770\) | 11003.1 | + | 32537.2i | 0.514969 | + | 1.52281i | ||||
\(771\) | 5808.53 | − | 4650.25i | 0.271322 | − | 0.217218i | ||||
\(772\) | 17584.2 | − | 17832.4i | 0.819779 | − | 0.831348i | ||||
\(773\) | − | 3337.03i | − | 0.155271i | −0.996982 | − | 0.0776356i | \(-0.975263\pi\) | ||
0.996982 | − | 0.0776356i | \(-0.0247371\pi\) | |||||||
\(774\) | −19635.4 | + | 3484.00i | −0.911859 | + | 0.161795i | ||||
\(775\) | 11908.9i | 0.551975i | ||||||||
\(776\) | 3844.47 | + | 1545.30i | 0.177846 | + | 0.0714857i | ||||
\(777\) | −14309.3 | − | 20693.3i | −0.660674 | − | 0.955427i | ||||
\(778\) | −31517.0 | + | 13184.3i | −1.45237 | + | 0.607559i | ||||
\(779\) | 11677.8 | 0.537102 | ||||||||
\(780\) | 15761.8 | + | 1633.87i | 0.723543 | + | 0.0750024i | ||||
\(781\) | 23689.7i | 1.08538i | ||||||||
\(782\) | 6463.48 | + | 15450.9i | 0.295567 | + | 0.706551i | ||||
\(783\) | 6873.36 | + | 14066.8i | 0.313709 | + | 0.642025i | ||||
\(784\) | 2762.90 | − | 21777.4i | 0.125861 | − | 0.992048i | ||||
\(785\) | − | 27650.7i | − | 1.25719i | ||||||
\(786\) | −5672.33 | − | 3095.08i | −0.257411 | − | 0.140455i | ||||
\(787\) | −643.131 | −0.0291298 | −0.0145649 | − | 0.999894i | \(-0.504636\pi\) | ||||
−0.0145649 | + | 0.999894i | \(0.504636\pi\) | |||||||
\(788\) | 479.963 | − | 486.736i | 0.0216979 | − | 0.0220041i | ||||
\(789\) | 2931.25 | + | 3661.37i | 0.132263 | + | 0.165207i | ||||
\(790\) | −2140.05 | − | 5115.77i | −0.0963792 | − | 0.230394i | ||||
\(791\) | −1234.36 | + | 17578.6i | −0.0554851 | + | 0.790168i | ||||
\(792\) | 24924.4 | + | 17153.8i | 1.11824 | + | 0.769611i | ||||
\(793\) | 21724.5 | 0.972835 | ||||||||
\(794\) | 13673.4 | − | 5719.91i | 0.611147 | − | 0.255657i | ||||
\(795\) | 510.403 | + | 637.534i | 0.0227700 | + | 0.0284415i | ||||
\(796\) | 20146.5 | + | 19866.2i | 0.897079 | + | 0.884595i | ||||
\(797\) | 12470.7i | 0.554248i | 0.960834 | + | 0.277124i | \(0.0893813\pi\) | ||||
−0.960834 | + | 0.277124i | \(0.910619\pi\) | |||||||
\(798\) | −3638.80 | + | 5682.07i | −0.161419 | + | 0.252059i | ||||
\(799\) | 15057.5 | 0.666702 | ||||||||
\(800\) | −3630.42 | − | 8347.94i | −0.160443 | − | 0.368930i | ||||
\(801\) | 7962.79 | − | 35509.4i | 0.351250 | − | 1.56637i | ||||
\(802\) | −11624.7 | − | 27788.7i | −0.511823 | − | 1.22351i | ||||
\(803\) | 51425.4i | 2.25998i | ||||||||
\(804\) | −6744.91 | − | 699.177i | −0.295864 | − | 0.0306693i | ||||
\(805\) | 20913.4 | + | 1468.53i | 0.915654 | + | 0.0642967i | ||||
\(806\) | −7442.54 | − | 17791.3i | −0.325251 | − | 0.777510i | ||||
\(807\) | 6136.81 | + | 7665.36i | 0.267690 | + | 0.334366i | ||||
\(808\) | −18011.6 | − | 7239.81i | −0.784214 | − | 0.315217i | ||||
\(809\) | 36823.8i | 1.60032i | 0.599789 | + | 0.800158i | \(0.295251\pi\) | ||||
−0.599789 | + | 0.800158i | \(0.704749\pi\) | |||||||
\(810\) | 1227.72 | − | 27271.5i | 0.0532566 | − | 1.18299i | ||||
\(811\) | −28331.7 | −1.22671 | −0.613354 | − | 0.789808i | \(-0.710180\pi\) | ||||
−0.613354 | + | 0.789808i | \(0.710180\pi\) | |||||||
\(812\) | −12405.2 | + | 10930.8i | −0.536132 | + | 0.472410i | ||||
\(813\) | −24748.6 | − | 30913.0i | −1.06762 | − | 1.33354i | ||||
\(814\) | 14132.7 | + | 33784.2i | 0.608541 | + | 1.45471i | ||||
\(815\) | 54438.2 | 2.33974 | ||||||||
\(816\) | 14644.6 | + | 17775.8i | 0.628262 | + | 0.762595i | ||||
\(817\) | 6473.23i | 0.277196i | ||||||||
\(818\) | −11131.0 | − | 26608.5i | −0.475776 | − | 1.13734i | ||||
\(819\) | −4126.67 | + | 13793.5i | −0.176065 | + | 0.588503i | ||||
\(820\) | −35528.5 | − | 35034.1i | −1.51306 | − | 1.49200i | ||||
\(821\) | −24314.1 | −1.03358 | −0.516789 | − | 0.856113i | \(-0.672873\pi\) | ||||
−0.516789 | + | 0.856113i | \(0.672873\pi\) | |||||||
\(822\) | 14538.3 | + | 7932.75i | 0.616888 | + | 0.336602i | ||||
\(823\) | −7780.71 | −0.329549 | −0.164774 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164774 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(824\) | 10365.9 | + | 4166.63i | 0.438246 | + | 0.176154i | ||||
\(825\) | −10102.5 | + | 8087.95i | −0.426331 | + | 0.341317i | ||||
\(826\) | −3969.16 | − | 11737.1i | −0.167197 | − | 0.494415i | ||||
\(827\) | 9658.38 | 0.406112 | 0.203056 | − | 0.979167i | \(-0.434913\pi\) | ||||
0.203056 | + | 0.979167i | \(0.434913\pi\) | |||||||
\(828\) | 15530.3 | − | 9994.12i | 0.651829 | − | 0.419468i | ||||
\(829\) | 4178.46 | 0.175059 | 0.0875296 | − | 0.996162i | \(-0.472103\pi\) | ||||
0.0875296 | + | 0.996162i | \(0.472103\pi\) | |||||||
\(830\) | 25557.4 | − | 10691.3i | 1.06881 | − | 0.447107i | ||||
\(831\) | 9689.81 | + | 12103.3i | 0.404496 | + | 0.505247i | ||||
\(832\) | 10640.8 | + | 10202.6i | 0.443392 | + | 0.425133i | ||||
\(833\) | −23521.7 | − | 3319.73i | −0.978365 | − | 0.138081i | ||||
\(834\) | −17032.6 | + | 31215.5i | −0.707182 | + | 1.29605i | ||||
\(835\) | 16217.8i | 0.672144i | ||||||||
\(836\) | 6895.96 | − | 6993.28i | 0.285289 | − | 0.289315i | ||||
\(837\) | −29850.8 | + | 14585.8i | −1.23273 | + | 0.602342i | ||||
\(838\) | −10263.5 | − | 24534.8i | −0.423086 | − | 1.01138i | ||||
\(839\) | 937.651 | 0.0385832 | 0.0192916 | − | 0.999814i | \(-0.493859\pi\) | ||||
0.0192916 | + | 0.999814i | \(0.493859\pi\) | |||||||
\(840\) | 28117.1 | − | 6370.45i | 1.15492 | − | 0.261668i | ||||
\(841\) | −11935.8 | −0.489391 | ||||||||
\(842\) | 1664.76 | + | 3979.60i | 0.0681371 | + | 0.162881i | ||||
\(843\) | −9706.04 | − | 12123.6i | −0.396552 | − | 0.495325i | ||||
\(844\) | −9661.88 | − | 9527.43i | −0.394047 | − | 0.388563i | ||||
\(845\) | 18111.8i | 0.737354i | ||||||||
\(846\) | −2900.75 | − | 16348.3i | −0.117884 | − | 0.664380i | ||||
\(847\) | 20723.6 | + | 1455.20i | 0.840700 | + | 0.0590335i | ||||
\(848\) | 10.6462 | + | 759.677i | 0.000431122 | + | 0.0307635i | ||||
\(849\) | −12781.5 | + | 10232.7i | −0.516678 | + | 0.413647i | ||||
\(850\) | −9087.68 | + | 3801.59i | −0.366711 | + | 0.153404i | ||||
\(851\) | 22352.8 | 0.900403 | ||||||||
\(852\) | 19778.2 | + | 2050.20i | 0.795292 | + | 0.0824399i | ||||
\(853\) | −5791.89 | −0.232486 | −0.116243 | − | 0.993221i | \(-0.537085\pi\) | ||||
−0.116243 | + | 0.993221i | \(0.537085\pi\) | |||||||
\(854\) | 37441.2 | − | 12661.5i | 1.50025 | − | 0.507340i | ||||
\(855\) | −8646.62 | − | 1938.96i | −0.345857 | − | 0.0775566i | ||||
\(856\) | 4925.09 | − | 12252.9i | 0.196654 | − | 0.489246i | ||||
\(857\) | −1880.84 | −0.0749687 | −0.0374843 | − | 0.999297i | \(-0.511934\pi\) | ||||
−0.0374843 | + | 0.999297i | \(0.511934\pi\) | |||||||
\(858\) | 10038.0 | − | 18396.6i | 0.399408 | − | 0.731993i | ||||
\(859\) | 9503.79 | 0.377491 | 0.188746 | − | 0.982026i | \(-0.439558\pi\) | ||||
0.188746 | + | 0.982026i | \(0.439558\pi\) | |||||||
\(860\) | 19420.0 | − | 19694.0i | 0.770018 | − | 0.780885i | ||||
\(861\) | 37288.1 | − | 25784.6i | 1.47593 | − | 1.02060i | ||||
\(862\) | −8535.51 | − | 20404.1i | −0.337263 | − | 0.806224i | ||||
\(863\) | 5322.63i | 0.209947i | 0.994475 | + | 0.104974i | \(0.0334758\pi\) | ||||
−0.994475 | + | 0.104974i | \(0.966524\pi\) | |||||||
\(864\) | 16478.5 | − | 19324.4i | 0.648853 | − | 0.760914i | ||||
\(865\) | 32457.2 | 1.27581 | ||||||||
\(866\) | −12276.1 | − | 29345.9i | −0.481707 | − | 1.15152i | ||||
\(867\) | −473.011 | + | 378.688i | −0.0185286 | + | 0.0148338i | ||||
\(868\) | −23196.1 | − | 26325.0i | −0.907060 | − | 1.02941i | ||||
\(869\) | −7333.85 | −0.286288 | ||||||||
\(870\) | −19061.3 | − | 10400.7i | −0.742803 | − | 0.405307i | ||||
\(871\) | 4696.82i | 0.182716i | ||||||||
\(872\) | −38971.0 | − | 15664.5i | −1.51345 | − | 0.608335i | ||||
\(873\) | −4824.29 | − | 1081.82i | −0.187030 | − | 0.0419405i | ||||
\(874\) | −2313.49 | − | 5530.39i | −0.0895368 | − | 0.214037i | ||||
\(875\) | 1283.22 | − | 18274.4i | 0.0495779 | − | 0.706043i | ||||
\(876\) | 42934.2 | + | 4450.56i | 1.65595 | + | 0.171656i | ||||
\(877\) | − | 15099.1i | − | 0.581369i | −0.956819 | − | 0.290684i | \(-0.906117\pi\) | ||
0.956819 | − | 0.290684i | \(-0.0938829\pi\) | |||||||
\(878\) | 6439.67 | + | 15394.0i | 0.247526 | + | 0.591710i | ||||
\(879\) | −5312.79 | − | 6636.09i | −0.203863 | − | 0.254641i | ||||
\(880\) | −41960.3 | + | 588.036i | −1.60737 | + | 0.0225258i | ||||
\(881\) | −25460.6 | −0.973654 | −0.486827 | − | 0.873498i | \(-0.661846\pi\) | ||||
−0.486827 | + | 0.873498i | \(0.661846\pi\) | |||||||
\(882\) | 927.034 | + | 26177.7i | 0.0353910 | + | 0.999374i | ||||
\(883\) | 29492.7i | 1.12402i | 0.827131 | + | 0.562009i | \(0.189972\pi\) | ||||
−0.827131 | + | 0.562009i | \(0.810028\pi\) | |||||||
\(884\) | 11200.7 | − | 11358.8i | 0.426155 | − | 0.432169i | ||||
\(885\) | 12702.6 | − | 10169.6i | 0.482480 | − | 0.386269i | ||||
\(886\) | −2587.94 | + | 1082.60i | −0.0981305 | + | 0.0410504i | ||||
\(887\) | 11558.8 | 0.437550 | 0.218775 | − | 0.975775i | \(-0.429794\pi\) | ||||
0.218775 | + | 0.975775i | \(0.429794\pi\) | |||||||
\(888\) | 29429.0 | − | 8875.38i | 1.11213 | − | 0.335403i | ||||
\(889\) | 47122.0 | + | 3308.88i | 1.77775 | + | 0.124833i | ||||
\(890\) | 19478.2 | + | 46562.6i | 0.733609 | + | 1.75369i | ||||
\(891\) | −32646.6 | − | 15416.9i | −1.22750 | − | 0.579669i | ||||
\(892\) | 22423.7 | + | 22111.7i | 0.841707 | + | 0.829994i | ||||
\(893\) | −5389.57 | −0.201965 | ||||||||
\(894\) | −14427.8 | + | 26441.8i | −0.539753 | + | 0.989202i | ||||
\(895\) | − | 12262.8i | − | 0.457987i | ||||||
\(896\) | 24285.2 | + | 11382.0i | 0.905483 | + | 0.424383i | ||||
\(897\) | −7994.53 | − | 9985.80i | −0.297580 | − | 0.371701i | ||||
\(898\) | 15204.8 | + | 36347.0i | 0.565024 | + | 1.35069i | ||||
\(899\) | 26426.8i | 0.980403i | ||||||||
\(900\) | 5878.19 | + | 9134.37i | 0.217711 | + | 0.338310i | ||||
\(901\) | 822.146 | 0.0303992 | ||||||||
\(902\) | −60877.2 | + | 25466.4i | −2.24722 | + | 0.940065i | ||||
\(903\) | 14292.8 | + | 20669.4i | 0.526728 | + | 0.761722i | ||||
\(904\) | −19976.4 | − | 8029.60i | −0.734963 | − | 0.295421i | ||||
\(905\) | − | 11607.5i | − | 0.426348i | ||||||
\(906\) | −2028.66 | + | 3717.92i | −0.0743906 | + | 0.136335i | ||||
\(907\) | − | 10190.2i | − | 0.373053i | −0.982450 | − | 0.186527i | \(-0.940277\pi\) | ||
0.982450 | − | 0.186527i | \(-0.0597231\pi\) | |||||||
\(908\) | 35487.4 | + | 34993.6i | 1.29702 | + | 1.27897i | ||||
\(909\) | 22602.1 | + | 5068.40i | 0.824713 | + | 0.184937i | ||||
\(910\) | −6396.92 | − | 18916.2i | −0.233028 | − | 0.689085i | ||||
\(911\) | − | 33432.8i | − | 1.21589i | −0.793978 | − | 0.607947i | \(-0.791993\pi\) | ||
0.793978 | − | 0.607947i | \(-0.208007\pi\) | |||||||
\(912\) | −5241.78 | − | 6362.56i | −0.190321 | − | 0.231015i | ||||
\(913\) | − | 36638.5i | − | 1.32810i | ||||||
\(914\) | 26106.7 | − | 10921.1i | 0.944784 | − | 0.395226i | ||||
\(915\) | 32440.8 | + | 40521.2i | 1.17209 | + | 1.46403i | ||||
\(916\) | −22321.3 | + | 22636.3i | −0.805151 | + | 0.816513i | ||||
\(917\) | −570.378 | + | 8122.80i | −0.0205404 | + | 0.292517i | ||||
\(918\) | −20659.5 | − | 18123.0i | −0.742772 | − | 0.651578i | ||||
\(919\) | −38879.2 | −1.39554 | −0.697772 | − | 0.716320i | \(-0.745825\pi\) | ||||
−0.697772 | + | 0.716320i | \(0.745825\pi\) | |||||||
\(920\) | −9552.89 | + | 23766.2i | −0.342336 | + | 0.851682i | ||||
\(921\) | −15367.5 | + | 12303.1i | −0.549812 | + | 0.440174i | ||||
\(922\) | −16991.9 | − | 40619.0i | −0.606940 | − | 1.45088i | ||||
\(923\) | − | 13772.5i | − | 0.491146i | ||||||
\(924\) | 6578.13 | − | 37556.2i | 0.234204 | − | 1.33713i | ||||
\(925\) | 13147.1i | 0.467324i | ||||||||
\(926\) | 28353.7 | − | 11861.0i | 1.00622 | − | 0.420926i | ||||
\(927\) | −13007.9 | − | 2916.94i | −0.460878 | − | 0.103349i | ||||
\(928\) | −8056.17 | − | 18524.7i | −0.284975 | − | 0.655285i | ||||
\(929\) | −19916.3 | −0.703370 | −0.351685 | − | 0.936118i | \(-0.614391\pi\) | ||||
−0.351685 | + | 0.936118i | \(0.614391\pi\) | |||||||
\(930\) | 22071.2 | − | 40449.7i | 0.778217 | − | 1.42623i | ||||
\(931\) | 8419.20 | + | 1188.24i | 0.296378 | + | 0.0418293i | ||||
\(932\) | −19373.7 | − | 19104.1i | −0.680908 | − | 0.671433i | ||||
\(933\) | 20275.1 | − | 16232.1i | 0.711444 | − | 0.569575i | ||||
\(934\) | 2383.97 | + | 5698.86i | 0.0835180 | + | 0.199649i | ||||
\(935\) | 45410.7i | 1.58833i | ||||||||
\(936\) | −14490.3 | − | 9972.71i | −0.506016 | − | 0.348257i | ||||
\(937\) | 27614.4i | 0.962779i | 0.876507 | + | 0.481390i | \(0.159868\pi\) | ||||
−0.876507 | + | 0.481390i | \(0.840132\pi\) | |||||||
\(938\) | 2737.42 | + | 8094.77i | 0.0952877 | + | 0.281774i | ||||
\(939\) | −3743.19 | − | 4675.54i | −0.130090 | − | 0.162492i | ||||
\(940\) | 16397.1 | + | 16169.0i | 0.568953 | + | 0.561035i | ||||
\(941\) | − | 33189.4i | − | 1.14978i | −0.818231 | − | 0.574890i | \(-0.805045\pi\) | ||
0.818231 | − | 0.574890i | \(-0.194955\pi\) | |||||||
\(942\) | −14702.0 | + | 26944.2i | −0.508509 | + | 0.931942i | ||||
\(943\) | 40278.4i | 1.39093i | ||||||||
\(944\) | 15136.3 | − | 212.122i | 0.521870 | − | 0.00731353i | ||||
\(945\) | −31890.4 | + | 12900.5i | −1.09777 | + | 0.444076i | ||||
\(946\) | −14116.5 | − | 33745.3i | −0.485164 | − | 1.15978i | ||||
\(947\) | −6141.76 | −0.210750 | −0.105375 | − | 0.994433i | \(-0.533604\pi\) | ||||
−0.105375 | + | 0.994433i | \(0.533604\pi\) | |||||||
\(948\) | −634.702 | + | 6122.92i | −0.0217449 | + | 0.209771i | ||||
\(949\) | − | 29897.2i | − | 1.02266i | ||||||
\(950\) | 3252.78 | − | 1360.72i | 0.111089 | − | 0.0464710i | ||||
\(951\) | −11109.5 | + | 8894.16i | −0.378812 | + | 0.303273i | ||||
\(952\) | 12683.8 | − | 26104.5i | 0.431812 | − | 0.888709i | ||||
\(953\) | 7097.85i | 0.241261i | 0.992697 | + | 0.120631i | \(0.0384916\pi\) | ||||
−0.992697 | + | 0.120631i | \(0.961508\pi\) | |||||||
\(954\) | −158.383 | − | 892.626i | −0.00537509 | − | 0.0302933i | ||||
\(955\) | −32788.8 | −1.11102 | ||||||||
\(956\) | −25505.8 | − | 25150.9i | −0.862883 | − | 0.850876i | ||||
\(957\) | −22418.2 | + | 17947.8i | −0.757239 | + | 0.606238i | ||||
\(958\) | 18339.4 | − | 7671.82i | 0.618497 | − | 0.258732i | ||||
\(959\) | 1461.89 | − | 20818.9i | 0.0492252 | − | 0.701019i | ||||
\(960\) | −3140.47 | + | 35082.9i | −0.105582 | + | 1.17947i | ||||
\(961\) | −26288.8 | −0.882441 | ||||||||
\(962\) | −8216.37 | − | 19641.2i | −0.275371 | − | 0.658271i | ||||
\(963\) | −3447.92 | + | 15375.7i | −0.115377 | + | 0.514513i | ||||
\(964\) | −13174.0 | − | 12990.6i | −0.440151 | − | 0.434026i | ||||
\(965\) | − | 41446.6i | − | 1.38260i | ||||||
\(966\) | −19598.2 | − | 12550.7i | −0.652755 | − | 0.418025i | ||||
\(967\) | 10526.5 | 0.350063 | 0.175031 | − | 0.984563i | \(-0.443997\pi\) | ||||
0.175031 | + | 0.984563i | \(0.443997\pi\) | |||||||
\(968\) | −9466.20 | + | 23550.5i | −0.314313 | + | 0.781964i | ||||
\(969\) | −6963.89 | + | 5575.22i | −0.230869 | + | 0.184832i | ||||
\(970\) | 6325.96 | − | 2646.30i | 0.209396 | − | 0.0875955i | ||||
\(971\) | 10918.3i | 0.360848i | 0.983589 | + | 0.180424i | \(0.0577470\pi\) | ||||
−0.983589 | + | 0.180424i | \(0.942253\pi\) | |||||||
\(972\) | −15696.7 | + | 25921.9i | −0.517975 | + | 0.855396i | ||||
\(973\) | 44700.7 | + | 3138.86i | 1.47280 | + | 0.103419i | ||||
\(974\) | −9305.75 | + | 3892.82i | −0.306135 | + | 0.128064i | ||||
\(975\) | 5873.30 | − | 4702.10i | 0.192919 | − | 0.154449i | ||||
\(976\) | 676.663 | + | 48284.5i | 0.0221921 | + | 1.58355i | ||||
\(977\) | − | 23312.8i | − | 0.763400i | −0.924286 | − | 0.381700i | \(-0.875339\pi\) | ||
0.924286 | − | 0.381700i | \(-0.124661\pi\) | |||||||
\(978\) | −53047.1 | − | 28944.9i | −1.73442 | − | 0.946376i | ||||
\(979\) | 66751.0 | 2.17913 | ||||||||
\(980\) | −22049.6 | − | 28873.1i | −0.718725 | − | 0.941139i | ||||
\(981\) | 48903.4 | + | 10966.3i | 1.59160 | + | 0.356909i | ||||
\(982\) | 5823.26 | − | 2436.01i | 0.189234 | − | 0.0791611i | ||||
\(983\) | 17319.7 | 0.561965 | 0.280982 | − | 0.959713i | \(-0.409340\pi\) | ||||
0.280982 | + | 0.959713i | \(0.409340\pi\) | |||||||
\(984\) | 15992.9 | + | 53029.4i | 0.518126 | + | 1.71800i | ||||
\(985\) | − | 1131.29i | − | 0.0365948i | ||||||
\(986\) | −20166.3 | + | 8436.03i | −0.651343 | + | 0.272472i | ||||
\(987\) | −17209.2 | + | 11900.1i | −0.554991 | + | 0.383774i | ||||
\(988\) | −4009.12 | + | 4065.69i | −0.129096 | + | 0.130918i | ||||
\(989\) | −22327.0 | −0.717854 | ||||||||
\(990\) | 49303.6 | − | 8748.18i | 1.58280 | − | 0.280844i | ||||
\(991\) | 20423.3 | 0.654660 | 0.327330 | − | 0.944910i | \(-0.393851\pi\) | ||||
0.327330 | + | 0.944910i | \(0.393851\pi\) | |||||||
\(992\) | 39311.0 | − | 17095.9i | 1.25819 | − | 0.547172i | ||||
\(993\) | −16958.9 | − | 21183.0i | −0.541969 | − | 0.676962i | ||||
\(994\) | −8026.95 | − | 23736.4i | −0.256136 | − | 0.757417i | ||||
\(995\) | 46825.2 | 1.49192 | ||||||||
\(996\) | −30588.9 | − | 3170.84i | −0.973138 | − | 0.100875i | ||||
\(997\) | −47651.1 | −1.51367 | −0.756833 | − | 0.653608i | \(-0.773255\pi\) | ||||
−0.756833 | + | 0.653608i | \(0.773255\pi\) | |||||||
\(998\) | 22561.1 | + | 53932.2i | 0.715591 | + | 1.71061i | ||||
\(999\) | −32954.5 | + | 16102.4i | −1.04368 | + | 0.509966i |
(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 | 168.4.i.c.125.12 | yes | 80 | |
3.2 | odd | 2 | inner | 168.4.i.c.125.70 | yes | 80 | |
4.3 | odd | 2 | 672.4.i.c.209.20 | 80 | |||
7.6 | odd | 2 | inner | 168.4.i.c.125.11 | yes | 80 | |
8.3 | odd | 2 | 672.4.i.c.209.61 | 80 | |||
8.5 | even | 2 | inner | 168.4.i.c.125.71 | yes | 80 | |
12.11 | even | 2 | 672.4.i.c.209.17 | 80 | |||
21.20 | even | 2 | inner | 168.4.i.c.125.69 | yes | 80 | |
24.5 | odd | 2 | inner | 168.4.i.c.125.9 | ✓ | 80 | |
24.11 | even | 2 | 672.4.i.c.209.64 | 80 | |||
28.27 | even | 2 | 672.4.i.c.209.62 | 80 | |||
56.13 | odd | 2 | inner | 168.4.i.c.125.72 | yes | 80 | |
56.27 | even | 2 | 672.4.i.c.209.19 | 80 | |||
84.83 | odd | 2 | 672.4.i.c.209.63 | 80 | |||
168.83 | odd | 2 | 672.4.i.c.209.18 | 80 | |||
168.125 | even | 2 | inner | 168.4.i.c.125.10 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.i.c.125.9 | ✓ | 80 | 24.5 | odd | 2 | inner | |
168.4.i.c.125.10 | yes | 80 | 168.125 | even | 2 | inner | |
168.4.i.c.125.11 | yes | 80 | 7.6 | odd | 2 | inner | |
168.4.i.c.125.12 | yes | 80 | 1.1 | even | 1 | trivial | |
168.4.i.c.125.69 | yes | 80 | 21.20 | even | 2 | inner | |
168.4.i.c.125.70 | yes | 80 | 3.2 | odd | 2 | inner | |
168.4.i.c.125.71 | yes | 80 | 8.5 | even | 2 | inner | |
168.4.i.c.125.72 | yes | 80 | 56.13 | odd | 2 | inner | |
672.4.i.c.209.17 | 80 | 12.11 | even | 2 | |||
672.4.i.c.209.18 | 80 | 168.83 | odd | 2 | |||
672.4.i.c.209.19 | 80 | 56.27 | even | 2 | |||
672.4.i.c.209.20 | 80 | 4.3 | odd | 2 | |||
672.4.i.c.209.61 | 80 | 8.3 | odd | 2 | |||
672.4.i.c.209.62 | 80 | 28.27 | even | 2 | |||
672.4.i.c.209.63 | 80 | 84.83 | odd | 2 | |||
672.4.i.c.209.64 | 80 | 24.11 | even | 2 |