Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,4,Mod(32,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (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: | \(1.94706303019\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 35x^{6} + 10x^{5} + 2614x^{4} + 16258x^{3} + 120841x^{2} + 205270x + 821047 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 32.2 | ||
Root | \(-0.913072 - 4.51265i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.4.d.b.32.1 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.48911 | −1.58714 | −0.793569 | − | 0.608480i | \(-0.791780\pi\) | ||||
−0.793569 | + | 0.608480i | \(0.791780\pi\) | |||||||
\(3\) | −2.57603 | + | 4.51265i | −0.495758 | + | 0.868461i | ||||
\(4\) | 12.1521 | 1.51901 | ||||||||
\(5\) | − | 12.2625i | − | 1.09679i | −0.836219 | − | 0.548395i | \(-0.815239\pi\) | ||
0.836219 | − | 0.548395i | \(-0.184761\pi\) | |||||||
\(6\) | 11.5641 | − | 20.2578i | 0.786836 | − | 1.37837i | ||||
\(7\) | − | 14.5320i | − | 0.784656i | −0.919825 | − | 0.392328i | \(-0.871670\pi\) | ||
0.919825 | − | 0.392328i | \(-0.128330\pi\) | |||||||
\(8\) | −18.6391 | −0.823738 | ||||||||
\(9\) | −13.7281 | − | 23.2495i | −0.508448 | − | 0.861093i | ||||
\(10\) | 55.0476i | 1.74076i | ||||||||
\(11\) | 27.6173 | − | 23.8387i | 0.756993 | − | 0.653423i | ||||
\(12\) | −31.3041 | + | 54.8381i | −0.753060 | + | 1.31920i | ||||
\(13\) | 14.5320i | 0.310036i | 0.987912 | + | 0.155018i | \(0.0495435\pi\) | ||||
−0.987912 | + | 0.155018i | \(0.950457\pi\) | |||||||
\(14\) | 65.2358i | 1.24536i | ||||||||
\(15\) | 55.3364 | + | 31.5886i | 0.952519 | + | 0.543742i | ||||
\(16\) | −13.5438 | −0.211622 | ||||||||
\(17\) | −92.5127 | −1.31986 | −0.659930 | − | 0.751327i | \(-0.729414\pi\) | ||||
−0.659930 | + | 0.751327i | \(0.729414\pi\) | |||||||
\(18\) | 61.6269 | + | 104.369i | 0.806978 | + | 1.36667i | ||||
\(19\) | − | 162.062i | − | 1.95682i | −0.206667 | − | 0.978411i | \(-0.566262\pi\) | ||
0.206667 | − | 0.978411i | \(-0.433738\pi\) | |||||||
\(20\) | − | 149.015i | − | 1.66603i | ||||||
\(21\) | 65.5781 | + | 37.4350i | 0.681443 | + | 0.389000i | ||||
\(22\) | −123.977 | + | 107.015i | −1.20145 | + | 1.03707i | ||||
\(23\) | 23.8387i | 0.216118i | 0.994144 | + | 0.108059i | \(0.0344636\pi\) | ||||
−0.994144 | + | 0.108059i | \(0.965536\pi\) | |||||||
\(24\) | 48.0149 | − | 84.1117i | 0.408375 | − | 0.715384i | ||||
\(25\) | −25.3686 | −0.202949 | ||||||||
\(26\) | − | 65.2358i | − | 0.492069i | ||||||
\(27\) | 140.281 | − | 2.05868i | 0.999892 | − | 0.0146738i | ||||
\(28\) | − | 176.594i | − | 1.19190i | ||||||
\(29\) | −52.5040 | −0.336198 | −0.168099 | − | 0.985770i | \(-0.553763\pi\) | ||||
−0.168099 | + | 0.985770i | \(0.553763\pi\) | |||||||
\(30\) | −248.411 | − | 141.804i | −1.51178 | − | 0.862995i | ||||
\(31\) | 82.5438 | 0.478236 | 0.239118 | − | 0.970991i | \(-0.423142\pi\) | ||||
0.239118 | + | 0.970991i | \(0.423142\pi\) | |||||||
\(32\) | 209.912 | 1.15961 | ||||||||
\(33\) | 36.4330 | + | 186.037i | 0.192187 | + | 0.981358i | ||||
\(34\) | 415.299 | 2.09480 | ||||||||
\(35\) | −178.199 | −0.860603 | ||||||||
\(36\) | −166.825 | − | 282.529i | −0.772337 | − | 1.30801i | ||||
\(37\) | −276.802 | −1.22989 | −0.614945 | − | 0.788570i | \(-0.710822\pi\) | ||||
−0.614945 | + | 0.788570i | \(0.710822\pi\) | |||||||
\(38\) | 727.515i | 3.10575i | ||||||||
\(39\) | −65.5781 | − | 37.4350i | −0.269254 | − | 0.153703i | ||||
\(40\) | 228.561i | 0.903468i | ||||||||
\(41\) | 175.468 | 0.668379 | 0.334190 | − | 0.942506i | \(-0.391537\pi\) | ||||
0.334190 | + | 0.942506i | \(0.391537\pi\) | |||||||
\(42\) | −294.387 | − | 168.050i | −1.08154 | − | 0.617396i | ||||
\(43\) | 353.189i | 1.25258i | 0.779592 | + | 0.626288i | \(0.215427\pi\) | ||||
−0.779592 | + | 0.626288i | \(0.784573\pi\) | |||||||
\(44\) | 335.607 | − | 289.690i | 1.14988 | − | 0.992555i | ||||
\(45\) | −285.097 | + | 168.341i | −0.944438 | + | 0.557661i | ||||
\(46\) | − | 107.015i | − | 0.343010i | ||||||
\(47\) | − | 387.790i | − | 1.20351i | −0.798681 | − | 0.601755i | \(-0.794468\pi\) | ||
0.798681 | − | 0.601755i | \(-0.205532\pi\) | |||||||
\(48\) | 34.8893 | − | 61.1185i | 0.104913 | − | 0.183785i | ||||
\(49\) | 131.820 | 0.384315 | ||||||||
\(50\) | 113.882 | 0.322108 | ||||||||
\(51\) | 238.316 | − | 417.478i | 0.654331 | − | 1.14625i | ||||
\(52\) | 176.594i | 0.470947i | ||||||||
\(53\) | 79.9449i | 0.207194i | 0.994619 | + | 0.103597i | \(0.0330352\pi\) | ||||
−0.994619 | + | 0.103597i | \(0.966965\pi\) | |||||||
\(54\) | −629.736 | + | 9.24164i | −1.58697 | + | 0.0232894i | ||||
\(55\) | −292.322 | − | 338.657i | −0.716668 | − | 0.830263i | ||||
\(56\) | 270.864i | 0.646351i | ||||||||
\(57\) | 731.331 | + | 417.478i | 1.69942 | + | 0.970110i | ||||
\(58\) | 235.696 | 0.533593 | ||||||||
\(59\) | 291.749i | 0.643770i | 0.946779 | + | 0.321885i | \(0.104317\pi\) | ||||
−0.946779 | + | 0.321885i | \(0.895683\pi\) | |||||||
\(60\) | 672.451 | + | 383.867i | 1.44688 | + | 0.825949i | ||||
\(61\) | 147.530i | 0.309661i | 0.987941 | + | 0.154830i | \(0.0494831\pi\) | ||||
−0.987941 | + | 0.154830i | \(0.950517\pi\) | |||||||
\(62\) | −370.548 | −0.759026 | ||||||||
\(63\) | −337.863 | + | 199.497i | −0.675662 | + | 0.398957i | ||||
\(64\) | −833.967 | −1.62884 | ||||||||
\(65\) | 178.199 | 0.340044 | ||||||||
\(66\) | −163.552 | − | 835.138i | −0.305027 | − | 1.55755i | ||||
\(67\) | 201.106 | 0.366701 | 0.183351 | − | 0.983048i | \(-0.441306\pi\) | ||||
0.183351 | + | 0.983048i | \(0.441306\pi\) | |||||||
\(68\) | −1124.22 | −2.00488 | ||||||||
\(69\) | −107.576 | − | 61.4094i | −0.187690 | − | 0.107142i | ||||
\(70\) | 799.954 | 1.36590 | ||||||||
\(71\) | − | 424.473i | − | 0.709517i | −0.934958 | − | 0.354758i | \(-0.884563\pi\) | ||
0.934958 | − | 0.354758i | \(-0.115437\pi\) | |||||||
\(72\) | 255.879 | + | 433.349i | 0.418828 | + | 0.709315i | ||||
\(73\) | − | 461.542i | − | 0.739992i | −0.929033 | − | 0.369996i | \(-0.879359\pi\) | ||
0.929033 | − | 0.369996i | \(-0.120641\pi\) | |||||||
\(74\) | 1242.59 | 1.95201 | ||||||||
\(75\) | 65.3504 | − | 114.480i | 0.100613 | − | 0.176253i | ||||
\(76\) | − | 1969.39i | − | 2.97243i | ||||||
\(77\) | −346.426 | − | 401.335i | −0.512712 | − | 0.593979i | ||||
\(78\) | 294.387 | + | 168.050i | 0.427343 | + | 0.243947i | ||||
\(79\) | 122.886i | 0.175009i | 0.996164 | + | 0.0875047i | \(0.0278893\pi\) | ||||
−0.996164 | + | 0.0875047i | \(0.972111\pi\) | |||||||
\(80\) | 166.081i | 0.232105i | ||||||||
\(81\) | −352.078 | + | 638.343i | −0.482961 | + | 0.875642i | ||||
\(82\) | −787.696 | −1.06081 | ||||||||
\(83\) | 151.843 | 0.200807 | 0.100403 | − | 0.994947i | \(-0.467987\pi\) | ||||
0.100403 | + | 0.994947i | \(0.467987\pi\) | |||||||
\(84\) | 796.909 | + | 454.913i | 1.03512 | + | 0.590894i | ||||
\(85\) | 1134.44i | 1.44761i | ||||||||
\(86\) | − | 1585.50i | − | 1.98801i | ||||||
\(87\) | 135.252 | − | 236.932i | 0.166673 | − | 0.291975i | ||||
\(88\) | −514.760 | + | 444.332i | −0.623564 | + | 0.538249i | ||||
\(89\) | 764.973i | 0.911090i | 0.890213 | + | 0.455545i | \(0.150556\pi\) | ||||
−0.890213 | + | 0.455545i | \(0.849444\pi\) | |||||||
\(90\) | 1279.83 | − | 755.699i | 1.49895 | − | 0.885085i | ||||
\(91\) | 211.180 | 0.243271 | ||||||||
\(92\) | 289.690i | 0.328286i | ||||||||
\(93\) | −212.636 | + | 372.492i | −0.237089 | + | 0.415329i | ||||
\(94\) | 1740.83i | 1.91014i | ||||||||
\(95\) | −1987.29 | −2.14622 | ||||||||
\(96\) | −540.741 | + | 947.261i | −0.574887 | + | 1.00708i | ||||
\(97\) | 218.967 | 0.229203 | 0.114602 | − | 0.993412i | \(-0.463441\pi\) | ||||
0.114602 | + | 0.993412i | \(0.463441\pi\) | |||||||
\(98\) | −591.753 | −0.609960 | ||||||||
\(99\) | −933.372 | − | 314.827i | −0.947549 | − | 0.319609i | ||||
\(100\) | −308.281 | −0.308281 | ||||||||
\(101\) | −189.536 | −0.186729 | −0.0933643 | − | 0.995632i | \(-0.529762\pi\) | ||||
−0.0933643 | + | 0.995632i | \(0.529762\pi\) | |||||||
\(102\) | −1069.82 | + | 1874.10i | −1.03851 | + | 1.81925i | ||||
\(103\) | 1518.95 | 1.45307 | 0.726536 | − | 0.687128i | \(-0.241129\pi\) | ||||
0.726536 | + | 0.687128i | \(0.241129\pi\) | |||||||
\(104\) | − | 270.864i | − | 0.255388i | ||||||
\(105\) | 459.046 | − | 804.150i | 0.426651 | − | 0.747400i | ||||
\(106\) | − | 358.881i | − | 0.328846i | ||||||
\(107\) | 1296.96 | 1.17179 | 0.585896 | − | 0.810386i | \(-0.300743\pi\) | ||||
0.585896 | + | 0.810386i | \(0.300743\pi\) | |||||||
\(108\) | 1704.70 | − | 25.0172i | 1.51884 | − | 0.0222897i | ||||
\(109\) | 1439.61i | 1.26504i | 0.774544 | + | 0.632521i | \(0.217980\pi\) | ||||
−0.774544 | + | 0.632521i | \(0.782020\pi\) | |||||||
\(110\) | 1312.27 | + | 1520.26i | 1.13745 | + | 1.31774i | ||||
\(111\) | 713.050 | − | 1249.11i | 0.609728 | − | 1.06811i | ||||
\(112\) | 196.819i | 0.166050i | ||||||||
\(113\) | − | 1054.98i | − | 0.878264i | −0.898423 | − | 0.439132i | \(-0.855286\pi\) | ||
0.898423 | − | 0.439132i | \(-0.144714\pi\) | |||||||
\(114\) | −3283.02 | − | 1874.10i | −2.69722 | − | 1.53970i | ||||
\(115\) | 292.322 | 0.237037 | ||||||||
\(116\) | −638.032 | −0.510688 | ||||||||
\(117\) | 337.863 | − | 199.497i | 0.266969 | − | 0.157637i | ||||
\(118\) | − | 1309.69i | − | 1.02175i | ||||||
\(119\) | 1344.40i | 1.03564i | ||||||||
\(120\) | −1031.42 | − | 588.782i | −0.784627 | − | 0.447901i | ||||
\(121\) | 194.428 | − | 1316.72i | 0.146077 | − | 0.989273i | ||||
\(122\) | − | 662.279i | − | 0.491475i | ||||||
\(123\) | −452.012 | + | 791.828i | −0.331354 | + | 0.580461i | ||||
\(124\) | 1003.08 | 0.726444 | ||||||||
\(125\) | − | 1221.73i | − | 0.874198i | ||||||
\(126\) | 1516.70 | − | 895.564i | 1.07237 | − | 0.633200i | ||||
\(127\) | − | 2274.56i | − | 1.58925i | −0.607100 | − | 0.794626i | \(-0.707667\pi\) | ||
0.607100 | − | 0.794626i | \(-0.292333\pi\) | |||||||
\(128\) | 2064.47 | 1.42559 | ||||||||
\(129\) | −1593.82 | − | 909.826i | −1.08781 | − | 0.620974i | ||||
\(130\) | −799.954 | −0.539697 | ||||||||
\(131\) | 1221.78 | 0.814865 | 0.407433 | − | 0.913235i | \(-0.366424\pi\) | ||||
0.407433 | + | 0.913235i | \(0.366424\pi\) | |||||||
\(132\) | 442.736 | + | 2260.73i | 0.291934 | + | 1.49069i | ||||
\(133\) | −2355.09 | −1.53543 | ||||||||
\(134\) | −902.785 | −0.582006 | ||||||||
\(135\) | −25.2446 | − | 1720.19i | −0.0160941 | − | 1.09667i | ||||
\(136\) | 1724.35 | 1.08722 | ||||||||
\(137\) | 404.170i | 0.252048i | 0.992027 | + | 0.126024i | \(0.0402216\pi\) | ||||
−0.992027 | + | 0.126024i | \(0.959778\pi\) | |||||||
\(138\) | 482.920 | + | 275.673i | 0.297891 | + | 0.170050i | ||||
\(139\) | − | 103.934i | − | 0.0634214i | −0.999497 | − | 0.0317107i | \(-0.989904\pi\) | ||
0.999497 | − | 0.0317107i | \(-0.0100955\pi\) | |||||||
\(140\) | −2165.49 | −1.30726 | ||||||||
\(141\) | 1749.96 | + | 998.960i | 1.04520 | + | 0.596650i | ||||
\(142\) | 1905.50i | 1.12610i | ||||||||
\(143\) | 346.426 | + | 401.335i | 0.202584 | + | 0.234695i | ||||
\(144\) | 185.931 | + | 314.887i | 0.107599 | + | 0.182226i | ||||
\(145\) | 643.829i | 0.368739i | ||||||||
\(146\) | 2071.91i | 1.17447i | ||||||||
\(147\) | −339.573 | + | 594.858i | −0.190527 | + | 0.333762i | ||||
\(148\) | −3363.71 | −1.86821 | ||||||||
\(149\) | −335.088 | −0.184238 | −0.0921191 | − | 0.995748i | \(-0.529364\pi\) | ||||
−0.0921191 | + | 0.995748i | \(0.529364\pi\) | |||||||
\(150\) | −293.365 | + | 513.912i | −0.159688 | + | 0.279738i | ||||
\(151\) | − | 1075.03i | − | 0.579371i | −0.957122 | − | 0.289686i | \(-0.906449\pi\) | ||
0.957122 | − | 0.289686i | \(-0.0935508\pi\) | |||||||
\(152\) | 3020.69i | 1.61191i | ||||||||
\(153\) | 1270.02 | + | 2150.87i | 0.671081 | + | 1.13652i | ||||
\(154\) | 1555.14 | + | 1801.64i | 0.813746 | + | 0.942727i | ||||
\(155\) | − | 1012.19i | − | 0.524524i | ||||||
\(156\) | −796.909 | − | 454.913i | −0.408999 | − | 0.233475i | ||||
\(157\) | −454.055 | −0.230812 | −0.115406 | − | 0.993318i | \(-0.536817\pi\) | ||||
−0.115406 | + | 0.993318i | \(0.536817\pi\) | |||||||
\(158\) | − | 551.647i | − | 0.277764i | ||||||
\(159\) | −360.764 | − | 205.941i | −0.179940 | − | 0.102718i | ||||
\(160\) | − | 2574.04i | − | 1.27185i | ||||||
\(161\) | 346.426 | 0.169579 | ||||||||
\(162\) | 1580.52 | − | 2865.59i | 0.766526 | − | 1.38976i | ||||
\(163\) | −1643.97 | −0.789975 | −0.394988 | − | 0.918686i | \(-0.629251\pi\) | ||||
−0.394988 | + | 0.918686i | \(0.629251\pi\) | |||||||
\(164\) | 2132.30 | 1.01527 | ||||||||
\(165\) | 2281.27 | − | 446.759i | 1.07634 | − | 0.210789i | ||||
\(166\) | −681.640 | −0.318708 | ||||||||
\(167\) | 2189.11 | 1.01436 | 0.507181 | − | 0.861840i | \(-0.330688\pi\) | ||||
0.507181 | + | 0.861840i | \(0.330688\pi\) | |||||||
\(168\) | −1222.31 | − | 697.754i | −0.561331 | − | 0.320434i | ||||
\(169\) | 1985.82 | 0.903878 | ||||||||
\(170\) | − | 5092.60i | − | 2.29756i | ||||||
\(171\) | −3767.87 | + | 2224.81i | −1.68501 | + | 0.994943i | ||||
\(172\) | 4291.97i | 1.90267i | ||||||||
\(173\) | 500.257 | 0.219849 | 0.109924 | − | 0.993940i | \(-0.464939\pi\) | ||||
0.109924 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(174\) | −607.160 | + | 1063.61i | −0.264533 | + | 0.463404i | ||||
\(175\) | 368.658i | 0.159245i | ||||||||
\(176\) | −374.043 | + | 322.867i | −0.160196 | + | 0.138279i | ||||
\(177\) | −1316.56 | − | 751.555i | −0.559089 | − | 0.319154i | ||||
\(178\) | − | 3434.05i | − | 1.44603i | ||||||
\(179\) | 1317.47i | 0.550125i | 0.961426 | + | 0.275063i | \(0.0886986\pi\) | ||||
−0.961426 | + | 0.275063i | \(0.911301\pi\) | |||||||
\(180\) | −3464.51 | + | 2045.69i | −1.43461 | + | 0.847092i | ||||
\(181\) | −1747.44 | −0.717602 | −0.358801 | − | 0.933414i | \(-0.616814\pi\) | ||||
−0.358801 | + | 0.933414i | \(0.616814\pi\) | |||||||
\(182\) | −948.010 | −0.386105 | ||||||||
\(183\) | −665.753 | − | 380.043i | −0.268928 | − | 0.153517i | ||||
\(184\) | − | 444.332i | − | 0.178025i | ||||||
\(185\) | 3394.28i | 1.34893i | ||||||||
\(186\) | 954.544 | − | 1672.15i | 0.376293 | − | 0.659184i | ||||
\(187\) | −2554.95 | + | 2205.39i | −0.999125 | + | 0.862427i | ||||
\(188\) | − | 4712.45i | − | 1.82814i | ||||||
\(189\) | −29.9168 | − | 2038.57i | −0.0115139 | − | 0.784572i | ||||
\(190\) | 8921.14 | 3.40635 | ||||||||
\(191\) | 3876.65i | 1.46861i | 0.678820 | + | 0.734304i | \(0.262492\pi\) | ||||
−0.678820 | + | 0.734304i | \(0.737508\pi\) | |||||||
\(192\) | 2148.33 | − | 3763.41i | 0.807511 | − | 1.41459i | ||||
\(193\) | 1017.24i | 0.379392i | 0.981843 | + | 0.189696i | \(0.0607503\pi\) | ||||
−0.981843 | + | 0.189696i | \(0.939250\pi\) | |||||||
\(194\) | −982.966 | −0.363778 | ||||||||
\(195\) | −459.046 | + | 804.150i | −0.168579 | + | 0.295315i | ||||
\(196\) | 1601.88 | 0.583777 | ||||||||
\(197\) | −3483.34 | −1.25978 | −0.629892 | − | 0.776682i | \(-0.716901\pi\) | ||||
−0.629892 | + | 0.776682i | \(0.716901\pi\) | |||||||
\(198\) | 4190.00 | + | 1413.29i | 1.50389 | + | 0.507264i | ||||
\(199\) | 4543.19 | 1.61838 | 0.809191 | − | 0.587546i | \(-0.199906\pi\) | ||||
0.809191 | + | 0.587546i | \(0.199906\pi\) | |||||||
\(200\) | 472.847 | 0.167177 | ||||||||
\(201\) | −518.055 | + | 907.521i | −0.181795 | + | 0.318466i | ||||
\(202\) | 850.849 | 0.296364 | ||||||||
\(203\) | 762.990i | 0.263800i | ||||||||
\(204\) | 2896.03 | − | 5073.22i | 0.993935 | − | 1.74116i | ||||
\(205\) | − | 2151.68i | − | 0.733072i | ||||||
\(206\) | −6818.72 | −2.30623 | ||||||||
\(207\) | 554.239 | − | 327.261i | 0.186098 | − | 0.109885i | ||||
\(208\) | − | 196.819i | − | 0.0656103i | ||||||
\(209\) | −3863.36 | − | 4475.72i | −1.27863 | − | 1.48130i | ||||
\(210\) | −2060.71 | + | 3609.91i | −0.677154 | + | 1.18623i | ||||
\(211\) | 2986.63i | 0.974447i | 0.873277 | + | 0.487224i | \(0.161990\pi\) | ||||
−0.873277 | + | 0.487224i | \(0.838010\pi\) | |||||||
\(212\) | 971.496i | 0.314729i | ||||||||
\(213\) | 1915.50 | + | 1093.46i | 0.616187 | + | 0.351749i | ||||
\(214\) | −5822.18 | −1.85980 | ||||||||
\(215\) | 4330.97 | 1.37381 | ||||||||
\(216\) | −2614.71 | + | 38.3719i | −0.823650 | + | 0.0120874i | ||||
\(217\) | − | 1199.53i | − | 0.375251i | ||||||
\(218\) | − | 6462.55i | − | 2.00780i | ||||||
\(219\) | 2082.78 | + | 1188.95i | 0.642654 | + | 0.366857i | ||||
\(220\) | −3552.32 | − | 4115.38i | −1.08862 | − | 1.26118i | ||||
\(221\) | − | 1344.40i | − | 0.409204i | ||||||
\(222\) | −3200.96 | + | 5607.39i | −0.967722 | + | 1.69524i | ||||
\(223\) | −5317.25 | −1.59672 | −0.798362 | − | 0.602178i | \(-0.794300\pi\) | ||||
−0.798362 | + | 0.602178i | \(0.794300\pi\) | |||||||
\(224\) | − | 3050.45i | − | 0.909896i | ||||||
\(225\) | 348.263 | + | 589.807i | 0.103189 | + | 0.174758i | ||||
\(226\) | 4735.90i | 1.39393i | ||||||||
\(227\) | 5089.65 | 1.48816 | 0.744079 | − | 0.668091i | \(-0.232888\pi\) | ||||
0.744079 | + | 0.668091i | \(0.232888\pi\) | |||||||
\(228\) | 8887.18 | + | 5073.22i | 2.58144 | + | 1.47361i | ||||
\(229\) | 4438.60 | 1.28084 | 0.640418 | − | 0.768027i | \(-0.278761\pi\) | ||||
0.640418 | + | 0.768027i | \(0.278761\pi\) | |||||||
\(230\) | −1312.27 | −0.376210 | ||||||||
\(231\) | 2703.49 | − | 529.446i | 0.770029 | − | 0.150801i | ||||
\(232\) | 978.625 | 0.276939 | ||||||||
\(233\) | 1183.43 | 0.332743 | 0.166372 | − | 0.986063i | \(-0.446795\pi\) | ||||
0.166372 | + | 0.986063i | \(0.446795\pi\) | |||||||
\(234\) | −1516.70 | + | 895.564i | −0.423717 | + | 0.250192i | ||||
\(235\) | −4755.27 | −1.32000 | ||||||||
\(236\) | 3545.35i | 0.977893i | ||||||||
\(237\) | −554.541 | − | 316.558i | −0.151989 | − | 0.0867623i | ||||
\(238\) | − | 6035.14i | − | 1.64370i | ||||||
\(239\) | 1686.66 | 0.456489 | 0.228244 | − | 0.973604i | \(-0.426701\pi\) | ||||
0.228244 | + | 0.973604i | \(0.426701\pi\) | |||||||
\(240\) | −749.465 | − | 427.829i | −0.201574 | − | 0.115068i | ||||
\(241\) | − | 5780.53i | − | 1.54505i | −0.634985 | − | 0.772525i | \(-0.718994\pi\) | ||
0.634985 | − | 0.772525i | \(-0.281006\pi\) | |||||||
\(242\) | −872.809 | + | 5910.91i | −0.231844 | + | 1.57011i | ||||
\(243\) | −1973.66 | − | 3233.20i | −0.521029 | − | 0.853539i | ||||
\(244\) | 1792.80i | 0.470377i | ||||||||
\(245\) | − | 1616.44i | − | 0.421513i | ||||||
\(246\) | 2029.13 | − | 3554.60i | 0.525905 | − | 0.921272i | ||||
\(247\) | 2355.09 | 0.606685 | ||||||||
\(248\) | −1538.54 | −0.393941 | ||||||||
\(249\) | −391.153 | + | 685.216i | −0.0995515 | + | 0.174393i | ||||
\(250\) | 5484.47i | 1.38747i | ||||||||
\(251\) | 1829.21i | 0.459996i | 0.973191 | + | 0.229998i | \(0.0738719\pi\) | ||||
−0.973191 | + | 0.229998i | \(0.926128\pi\) | |||||||
\(252\) | −4105.73 | + | 2424.30i | −1.02634 | + | 0.606019i | ||||
\(253\) | 568.286 | + | 658.361i | 0.141217 | + | 0.163600i | ||||
\(254\) | 10210.8i | 2.52236i | ||||||||
\(255\) | −5119.32 | − | 2922.34i | −1.25719 | − | 0.717664i | ||||
\(256\) | −2595.88 | −0.633761 | ||||||||
\(257\) | − | 4066.01i | − | 0.986891i | −0.869777 | − | 0.493446i | \(-0.835737\pi\) | ||
0.869777 | − | 0.493446i | \(-0.164263\pi\) | |||||||
\(258\) | 7154.82 | + | 4084.30i | 1.72651 | + | 0.985572i | ||||
\(259\) | 4022.49i | 0.965041i | ||||||||
\(260\) | 2165.49 | 0.516530 | ||||||||
\(261\) | 720.780 | + | 1220.69i | 0.170939 | + | 0.289498i | ||||
\(262\) | −5484.70 | −1.29330 | ||||||||
\(263\) | −6812.43 | −1.59723 | −0.798617 | − | 0.601840i | \(-0.794435\pi\) | ||||
−0.798617 | + | 0.601840i | \(0.794435\pi\) | |||||||
\(264\) | −679.077 | − | 3467.55i | −0.158312 | − | 0.808382i | ||||
\(265\) | 980.324 | 0.227248 | ||||||||
\(266\) | 10572.3 | 2.43694 | ||||||||
\(267\) | −3452.06 | − | 1970.60i | −0.791246 | − | 0.451680i | ||||
\(268\) | 2443.85 | 0.557022 | ||||||||
\(269\) | 1591.54i | 0.360736i | 0.983599 | + | 0.180368i | \(0.0577289\pi\) | ||||
−0.983599 | + | 0.180368i | \(0.942271\pi\) | |||||||
\(270\) | 113.326 | + | 7722.13i | 0.0255436 | + | 1.74057i | ||||
\(271\) | 1876.51i | 0.420626i | 0.977634 | + | 0.210313i | \(0.0674483\pi\) | ||||
−0.977634 | + | 0.210313i | \(0.932552\pi\) | |||||||
\(272\) | 1252.97 | 0.279311 | ||||||||
\(273\) | −544.007 | + | 952.983i | −0.120604 | + | 0.211272i | ||||
\(274\) | − | 1814.36i | − | 0.400035i | ||||||
\(275\) | −700.612 | + | 604.756i | −0.153631 | + | 0.132611i | ||||
\(276\) | −1307.27 | − | 746.251i | −0.285103 | − | 0.162750i | ||||
\(277\) | − | 3827.28i | − | 0.830177i | −0.909781 | − | 0.415089i | \(-0.863751\pi\) | ||
0.909781 | − | 0.415089i | \(-0.136249\pi\) | |||||||
\(278\) | 466.571i | 0.100659i | ||||||||
\(279\) | −1133.17 | − | 1919.10i | −0.243158 | − | 0.411805i | ||||
\(280\) | 3321.46 | 0.708912 | ||||||||
\(281\) | 339.184 | 0.0720072 | 0.0360036 | − | 0.999352i | \(-0.488537\pi\) | ||||
0.0360036 | + | 0.999352i | \(0.488537\pi\) | |||||||
\(282\) | −7855.76 | − | 4484.44i | −1.65888 | − | 0.946966i | ||||
\(283\) | 4085.98i | 0.858255i | 0.903244 | + | 0.429127i | \(0.141179\pi\) | ||||
−0.903244 | + | 0.429127i | \(0.858821\pi\) | |||||||
\(284\) | − | 5158.23i | − | 1.07776i | ||||||
\(285\) | 5119.32 | − | 8967.94i | 1.06401 | − | 1.86391i | ||||
\(286\) | −1555.14 | − | 1801.64i | −0.321529 | − | 0.372493i | ||||
\(287\) | − | 2549.91i | − | 0.524448i | ||||||
\(288\) | −2881.69 | − | 4880.35i | −0.589602 | − | 0.998533i | ||||
\(289\) | 3645.60 | 0.742031 | ||||||||
\(290\) | − | 2890.22i | − | 0.585239i | ||||||
\(291\) | −564.067 | + | 988.123i | −0.113629 | + | 0.199054i | ||||
\(292\) | − | 5608.69i | − | 1.12405i | ||||||
\(293\) | −5445.63 | −1.08579 | −0.542896 | − | 0.839800i | \(-0.682672\pi\) | ||||
−0.542896 | + | 0.839800i | \(0.682672\pi\) | |||||||
\(294\) | 1524.38 | − | 2670.38i | 0.302393 | − | 0.529727i | ||||
\(295\) | 3577.57 | 0.706081 | ||||||||
\(296\) | 5159.33 | 1.01311 | ||||||||
\(297\) | 3825.10 | − | 3400.98i | 0.747323 | − | 0.664461i | ||||
\(298\) | 1504.25 | 0.292411 | ||||||||
\(299\) | −346.426 | −0.0670044 | ||||||||
\(300\) | 794.142 | − | 1391.17i | 0.152833 | − | 0.267730i | ||||
\(301\) | 5132.55 | 0.982841 | ||||||||
\(302\) | 4825.94i | 0.919543i | ||||||||
\(303\) | 488.252 | − | 855.313i | 0.0925722 | − | 0.162166i | ||||
\(304\) | 2194.94i | 0.414106i | ||||||||
\(305\) | 1809.09 | 0.339633 | ||||||||
\(306\) | −5701.27 | − | 9655.50i | −1.06510 | − | 1.80382i | ||||
\(307\) | − | 3678.14i | − | 0.683787i | −0.939739 | − | 0.341894i | \(-0.888932\pi\) | ||
0.939739 | − | 0.341894i | \(-0.111068\pi\) | |||||||
\(308\) | −4209.79 | − | 4877.05i | −0.778814 | − | 0.902260i | ||||
\(309\) | −3912.86 | + | 6854.49i | −0.720372 | + | 1.26194i | ||||
\(310\) | 4543.84i | 0.832492i | ||||||||
\(311\) | − | 6388.00i | − | 1.16473i | −0.812929 | − | 0.582363i | \(-0.802128\pi\) | ||
0.812929 | − | 0.582363i | \(-0.197872\pi\) | |||||||
\(312\) | 1222.31 | + | 697.754i | 0.221795 | + | 0.126611i | ||||
\(313\) | 6242.25 | 1.12726 | 0.563631 | − | 0.826027i | \(-0.309404\pi\) | ||||
0.563631 | + | 0.826027i | \(0.309404\pi\) | |||||||
\(314\) | 2038.30 | 0.366331 | ||||||||
\(315\) | 2446.33 | + | 4143.04i | 0.437572 | + | 0.741059i | ||||
\(316\) | 1493.32i | 0.265841i | ||||||||
\(317\) | 268.015i | 0.0474866i | 0.999718 | + | 0.0237433i | \(0.00755844\pi\) | ||||
−0.999718 | + | 0.0237433i | \(0.992442\pi\) | |||||||
\(318\) | 1619.51 | + | 924.490i | 0.285589 | + | 0.163028i | ||||
\(319\) | −1450.02 | + | 1251.63i | −0.254500 | + | 0.219680i | ||||
\(320\) | 10226.5i | 1.78650i | ||||||||
\(321\) | −3341.01 | + | 5852.72i | −0.580925 | + | 1.01765i | ||||
\(322\) | −1555.14 | −0.269145 | ||||||||
\(323\) | 14992.8i | 2.58273i | ||||||||
\(324\) | −4278.48 | + | 7757.19i | −0.733622 | + | 1.33011i | ||||
\(325\) | − | 368.658i | − | 0.0629214i | ||||||
\(326\) | 7379.97 | 1.25380 | ||||||||
\(327\) | −6496.46 | − | 3708.48i | −1.09864 | − | 0.627154i | ||||
\(328\) | −3270.57 | −0.550570 | ||||||||
\(329\) | −5635.38 | −0.944342 | ||||||||
\(330\) | −10240.9 | + | 2005.55i | −1.70831 | + | 0.334551i | ||||
\(331\) | −451.238 | −0.0749313 | −0.0374656 | − | 0.999298i | \(-0.511928\pi\) | ||||
−0.0374656 | + | 0.999298i | \(0.511928\pi\) | |||||||
\(332\) | 1845.21 | 0.305027 | ||||||||
\(333\) | 3799.96 | + | 6435.50i | 0.625335 | + | 1.05905i | ||||
\(334\) | −9827.15 | −1.60993 | ||||||||
\(335\) | − | 2466.06i | − | 0.402194i | ||||||
\(336\) | −888.176 | − | 507.012i | −0.144208 | − | 0.0823208i | ||||
\(337\) | 9096.65i | 1.47040i | 0.677848 | + | 0.735202i | \(0.262913\pi\) | ||||
−0.677848 | + | 0.735202i | \(0.737087\pi\) | |||||||
\(338\) | −8914.55 | −1.43458 | ||||||||
\(339\) | 4760.74 | + | 2717.66i | 0.762738 | + | 0.435406i | ||||
\(340\) | 13785.7i | 2.19893i | ||||||||
\(341\) | 2279.64 | − | 1967.74i | 0.362021 | − | 0.312490i | ||||
\(342\) | 16914.3 | − | 9987.39i | 2.67434 | − | 1.57911i | ||||
\(343\) | − | 6900.10i | − | 1.08621i | ||||||
\(344\) | − | 6583.11i | − | 1.03179i | ||||||
\(345\) | −753.032 | + | 1319.15i | −0.117513 | + | 0.205857i | ||||
\(346\) | −2245.71 | −0.348930 | ||||||||
\(347\) | 6325.38 | 0.978571 | 0.489286 | − | 0.872124i | \(-0.337258\pi\) | ||||
0.489286 | + | 0.872124i | \(0.337258\pi\) | |||||||
\(348\) | 1643.59 | − | 2879.22i | 0.253177 | − | 0.443512i | ||||
\(349\) | − | 5463.97i | − | 0.838051i | −0.907974 | − | 0.419026i | \(-0.862372\pi\) | ||
0.907974 | − | 0.419026i | \(-0.137628\pi\) | |||||||
\(350\) | − | 1654.94i | − | 0.252744i | ||||||
\(351\) | 29.9168 | + | 2038.57i | 0.00454941 | + | 0.310002i | ||||
\(352\) | 5797.20 | − | 5004.04i | 0.877818 | − | 0.757717i | ||||
\(353\) | − | 3331.02i | − | 0.502245i | −0.967955 | − | 0.251123i | \(-0.919200\pi\) | ||
0.967955 | − | 0.251123i | \(-0.0807997\pi\) | |||||||
\(354\) | 5910.18 | + | 3373.81i | 0.887352 | + | 0.506542i | ||||
\(355\) | −5205.10 | −0.778191 | ||||||||
\(356\) | 9296.01i | 1.38395i | ||||||||
\(357\) | −6066.80 | − | 3463.21i | −0.899410 | − | 0.513425i | ||||
\(358\) | − | 5914.27i | − | 0.873125i | ||||||
\(359\) | −2130.28 | −0.313181 | −0.156591 | − | 0.987664i | \(-0.550050\pi\) | ||||
−0.156591 | + | 0.987664i | \(0.550050\pi\) | |||||||
\(360\) | 5313.94 | − | 3137.71i | 0.777970 | − | 0.459367i | ||||
\(361\) | −19405.2 | −2.82915 | ||||||||
\(362\) | 7844.43 | 1.13893 | ||||||||
\(363\) | 5441.06 | + | 4269.31i | 0.786726 | + | 0.617302i | ||||
\(364\) | 2566.27 | 0.369531 | ||||||||
\(365\) | −5659.66 | −0.811617 | ||||||||
\(366\) | 2988.63 | + | 1706.05i | 0.426826 | + | 0.243652i | ||||
\(367\) | 6515.65 | 0.926741 | 0.463370 | − | 0.886165i | \(-0.346640\pi\) | ||||
0.463370 | + | 0.886165i | \(0.346640\pi\) | |||||||
\(368\) | − | 322.867i | − | 0.0457354i | ||||||
\(369\) | −2408.85 | − | 4079.55i | −0.339836 | − | 0.575536i | ||||
\(370\) | − | 15237.3i | − | 2.14094i | ||||||
\(371\) | 1161.76 | 0.162576 | ||||||||
\(372\) | −2583.96 | + | 4526.54i | −0.360140 | + | 0.630888i | ||||
\(373\) | 11019.6i | 1.52969i | 0.644213 | + | 0.764846i | \(0.277185\pi\) | ||||
−0.644213 | + | 0.764846i | \(0.722815\pi\) | |||||||
\(374\) | 11469.4 | − | 9900.21i | 1.58575 | − | 1.36879i | ||||
\(375\) | 5513.24 | + | 3147.21i | 0.759207 | + | 0.433391i | ||||
\(376\) | 7228.04i | 0.991377i | ||||||||
\(377\) | − | 762.990i | − | 0.104233i | ||||||
\(378\) | 134.300 | + | 9151.35i | 0.0182742 | + | 1.24522i | ||||
\(379\) | 57.5809 | 0.00780404 | 0.00390202 | − | 0.999992i | \(-0.498758\pi\) | ||||
0.00390202 | + | 0.999992i | \(0.498758\pi\) | |||||||
\(380\) | −24149.6 | −3.26013 | ||||||||
\(381\) | 10264.3 | + | 5859.35i | 1.38020 | + | 0.787884i | ||||
\(382\) | − | 17402.7i | − | 2.33089i | ||||||
\(383\) | − | 9660.60i | − | 1.28886i | −0.764663 | − | 0.644430i | \(-0.777095\pi\) | ||
0.764663 | − | 0.644430i | \(-0.222905\pi\) | |||||||
\(384\) | −5318.14 | + | 9316.24i | −0.706746 | + | 1.23807i | ||||
\(385\) | −4921.37 | + | 4248.04i | −0.651471 | + | 0.562338i | ||||
\(386\) | − | 4566.51i | − | 0.602148i | ||||||
\(387\) | 8211.46 | − | 4848.61i | 1.07858 | − | 0.636870i | ||||
\(388\) | 2660.90 | 0.348162 | ||||||||
\(389\) | − | 11536.6i | − | 1.50367i | −0.659351 | − | 0.751835i | \(-0.729169\pi\) | ||
0.659351 | − | 0.751835i | \(-0.270831\pi\) | |||||||
\(390\) | 2060.71 | − | 3609.91i | 0.267559 | − | 0.468706i | ||||
\(391\) | − | 2205.39i | − | 0.285246i | ||||||
\(392\) | −2457.00 | −0.316575 | ||||||||
\(393\) | −3147.34 | + | 5513.47i | −0.403976 | + | 0.707678i | ||||
\(394\) | 15637.1 | 1.99945 | ||||||||
\(395\) | 1506.89 | 0.191949 | ||||||||
\(396\) | −11342.4 | − | 3825.80i | −1.43934 | − | 0.485489i | ||||
\(397\) | −6686.34 | −0.845285 | −0.422642 | − | 0.906297i | \(-0.638897\pi\) | ||||
−0.422642 | + | 0.906297i | \(0.638897\pi\) | |||||||
\(398\) | −20394.8 | −2.56860 | ||||||||
\(399\) | 6066.80 | − | 10627.7i | 0.761203 | − | 1.33346i | ||||
\(400\) | 343.587 | 0.0429484 | ||||||||
\(401\) | 5987.05i | 0.745583i | 0.927915 | + | 0.372792i | \(0.121599\pi\) | ||||
−0.927915 | + | 0.372792i | \(0.878401\pi\) | |||||||
\(402\) | 2325.61 | − | 4073.96i | 0.288534 | − | 0.505449i | ||||
\(403\) | 1199.53i | 0.148270i | ||||||||
\(404\) | −2303.26 | −0.283642 | ||||||||
\(405\) | 7827.67 | + | 4317.36i | 0.960396 | + | 0.529707i | ||||
\(406\) | − | 3425.14i | − | 0.418687i | ||||||
\(407\) | −7644.51 | + | 6598.61i | −0.931018 | + | 0.803638i | ||||
\(408\) | −4441.98 | + | 7781.40i | −0.538998 | + | 0.944207i | ||||
\(409\) | − | 6409.23i | − | 0.774856i | −0.921900 | − | 0.387428i | \(-0.873364\pi\) | ||
0.921900 | − | 0.387428i | \(-0.126636\pi\) | |||||||
\(410\) | 9659.11i | 1.16349i | ||||||||
\(411\) | −1823.88 | − | 1041.16i | −0.218894 | − | 0.124955i | ||||
\(412\) | 18458.4 | 2.20723 | ||||||||
\(413\) | 4239.70 | 0.505138 | ||||||||
\(414\) | −2488.04 | + | 1469.11i | −0.295363 | + | 0.174403i | ||||
\(415\) | − | 1861.97i | − | 0.220243i | ||||||
\(416\) | 3050.45i | 0.359521i | ||||||||
\(417\) | 469.019 | + | 267.738i | 0.0550790 | + | 0.0314417i | ||||
\(418\) | 17343.0 | + | 20092.0i | 2.02937 | + | 2.35103i | ||||
\(419\) | 6661.04i | 0.776642i | 0.921524 | + | 0.388321i | \(0.126945\pi\) | ||||
−0.921524 | + | 0.388321i | \(0.873055\pi\) | |||||||
\(420\) | 5578.36 | − | 9772.09i | 0.648086 | − | 1.13531i | ||||
\(421\) | −3531.81 | −0.408860 | −0.204430 | − | 0.978881i | \(-0.565534\pi\) | ||||
−0.204430 | + | 0.978881i | \(0.565534\pi\) | |||||||
\(422\) | − | 13407.3i | − | 1.54658i | ||||||
\(423\) | −9015.92 | + | 5323.62i | −1.03633 | + | 0.611923i | ||||
\(424\) | − | 1490.10i | − | 0.170674i | ||||||
\(425\) | 2346.92 | 0.267864 | ||||||||
\(426\) | −8598.88 | − | 4908.64i | −0.977975 | − | 0.558274i | ||||
\(427\) | 2143.91 | 0.242977 | ||||||||
\(428\) | 15760.7 | 1.77996 | ||||||||
\(429\) | −2703.49 | + | 529.446i | −0.304256 | + | 0.0595848i | ||||
\(430\) | −19442.2 | −2.18043 | ||||||||
\(431\) | 4009.57 | 0.448107 | 0.224053 | − | 0.974577i | \(-0.428071\pi\) | ||||
0.224053 | + | 0.974577i | \(0.428071\pi\) | |||||||
\(432\) | −1899.94 | + | 27.8824i | −0.211599 | + | 0.00310530i | ||||
\(433\) | −7430.09 | −0.824636 | −0.412318 | − | 0.911040i | \(-0.635281\pi\) | ||||
−0.412318 | + | 0.911040i | \(0.635281\pi\) | |||||||
\(434\) | 5384.81i | 0.595575i | ||||||||
\(435\) | −2905.38 | − | 1658.53i | −0.320235 | − | 0.182805i | ||||
\(436\) | 17494.2i | 1.92161i | ||||||||
\(437\) | 3863.36 | 0.422905 | ||||||||
\(438\) | −9349.82 | − | 5337.32i | −1.01998 | − | 0.582253i | ||||
\(439\) | − | 13645.8i | − | 1.48356i | −0.670646 | − | 0.741778i | \(-0.733983\pi\) | ||
0.670646 | − | 0.741778i | \(-0.266017\pi\) | |||||||
\(440\) | 5448.62 | + | 6312.24i | 0.590347 | + | 0.683919i | ||||
\(441\) | −1809.64 | − | 3064.75i | −0.195404 | − | 0.330930i | ||||
\(442\) | 6035.14i | 0.649463i | ||||||||
\(443\) | − | 3300.00i | − | 0.353922i | −0.984218 | − | 0.176961i | \(-0.943373\pi\) | ||
0.984218 | − | 0.176961i | \(-0.0566267\pi\) | |||||||
\(444\) | 8665.04 | − | 15179.3i | 0.926181 | − | 1.62247i | ||||
\(445\) | 9380.48 | 0.999275 | ||||||||
\(446\) | 23869.7 | 2.53422 | ||||||||
\(447\) | 863.198 | − | 1512.14i | 0.0913375 | − | 0.160004i | ||||
\(448\) | 12119.2i | 1.27808i | ||||||||
\(449\) | 9305.54i | 0.978075i | 0.872263 | + | 0.489037i | \(0.162652\pi\) | ||||
−0.872263 | + | 0.489037i | \(0.837348\pi\) | |||||||
\(450\) | −1563.39 | − | 2647.71i | −0.163775 | − | 0.277365i | ||||
\(451\) | 4845.96 | − | 4182.95i | 0.505958 | − | 0.436734i | ||||
\(452\) | − | 12820.1i | − | 1.33409i | ||||||
\(453\) | 4851.26 | + | 2769.33i | 0.503161 | + | 0.287228i | ||||
\(454\) | −22848.0 | −2.36191 | ||||||||
\(455\) | − | 2589.59i | − | 0.266818i | ||||||
\(456\) | −13631.3 | − | 7781.40i | −1.39988 | − | 0.799117i | ||||
\(457\) | 12342.0i | 1.26332i | 0.775246 | + | 0.631659i | \(0.217626\pi\) | ||||
−0.775246 | + | 0.631659i | \(0.782374\pi\) | |||||||
\(458\) | −19925.4 | −2.03286 | ||||||||
\(459\) | −12977.8 | + | 190.454i | −1.31972 | + | 0.0193674i | ||||
\(460\) | 3552.32 | 0.360060 | ||||||||
\(461\) | −2304.33 | −0.232806 | −0.116403 | − | 0.993202i | \(-0.537136\pi\) | ||||
−0.116403 | + | 0.993202i | \(0.537136\pi\) | |||||||
\(462\) | −12136.3 | + | 2376.74i | −1.22214 | + | 0.239342i | ||||
\(463\) | 5178.38 | 0.519783 | 0.259892 | − | 0.965638i | \(-0.416313\pi\) | ||||
0.259892 | + | 0.965638i | \(0.416313\pi\) | |||||||
\(464\) | 711.103 | 0.0711468 | ||||||||
\(465\) | 4567.67 | + | 2607.44i | 0.455529 | + | 0.260037i | ||||
\(466\) | −5312.55 | −0.528110 | ||||||||
\(467\) | − | 10169.0i | − | 1.00763i | −0.863811 | − | 0.503817i | \(-0.831929\pi\) | ||
0.863811 | − | 0.503817i | \(-0.168071\pi\) | |||||||
\(468\) | 4105.73 | − | 2424.30i | 0.405529 | − | 0.239452i | ||||
\(469\) | − | 2922.48i | − | 0.287734i | ||||||
\(470\) | 21346.9 | 2.09502 | ||||||||
\(471\) | 1169.66 | − | 2048.99i | 0.114427 | − | 0.200451i | ||||
\(472\) | − | 5437.92i | − | 0.530298i | ||||||
\(473\) | 8419.57 | + | 9754.11i | 0.818462 | + | 0.948191i | ||||
\(474\) | 2489.39 | + | 1421.06i | 0.241227 | + | 0.137704i | ||||
\(475\) | 4111.29i | 0.397135i | ||||||||
\(476\) | 16337.2i | 1.57314i | ||||||||
\(477\) | 1858.68 | − | 1097.49i | 0.178413 | − | 0.105347i | ||||
\(478\) | −7571.59 | −0.724511 | ||||||||
\(479\) | −17457.5 | −1.66525 | −0.832625 | − | 0.553837i | \(-0.813163\pi\) | ||||
−0.832625 | + | 0.553837i | \(0.813163\pi\) | |||||||
\(480\) | 11615.8 | + | 6630.82i | 1.10455 | + | 0.630530i | ||||
\(481\) | − | 4022.49i | − | 0.381309i | ||||||
\(482\) | 25949.4i | 2.45221i | ||||||||
\(483\) | −892.404 | + | 1563.30i | −0.0840699 | + | 0.147272i | ||||
\(484\) | 2362.70 | − | 16000.9i | 0.221892 | − | 1.50271i | ||||
\(485\) | − | 2685.08i | − | 0.251388i | ||||||
\(486\) | 8859.95 | + | 14514.2i | 0.826945 | + | 1.35468i | ||||
\(487\) | 11525.7 | 1.07245 | 0.536223 | − | 0.844076i | \(-0.319851\pi\) | ||||
0.536223 | + | 0.844076i | \(0.319851\pi\) | |||||||
\(488\) | − | 2749.83i | − | 0.255079i | ||||||
\(489\) | 4234.93 | − | 7418.68i | 0.391636 | − | 0.686062i | ||||
\(490\) | 7256.37i | 0.668999i | ||||||||
\(491\) | −7241.13 | −0.665555 | −0.332777 | − | 0.943005i | \(-0.607986\pi\) | ||||
−0.332777 | + | 0.943005i | \(0.607986\pi\) | |||||||
\(492\) | −5492.88 | + | 9622.35i | −0.503330 | + | 0.881725i | ||||
\(493\) | 4857.28 | 0.443734 | ||||||||
\(494\) | −10572.3 | −0.962892 | ||||||||
\(495\) | −3860.56 | + | 11445.5i | −0.350544 | + | 1.03926i | ||||
\(496\) | −1117.96 | −0.101205 | ||||||||
\(497\) | −6168.46 | −0.556727 | ||||||||
\(498\) | 1755.93 | − | 3076.00i | 0.158002 | − | 0.276785i | ||||
\(499\) | −1625.41 | −0.145818 | −0.0729091 | − | 0.997339i | \(-0.523228\pi\) | ||||
−0.0729091 | + | 0.997339i | \(0.523228\pi\) | |||||||
\(500\) | − | 14846.5i | − | 1.32791i | ||||||
\(501\) | −5639.22 | + | 9878.70i | −0.502878 | + | 0.880934i | ||||
\(502\) | − | 8211.53i | − | 0.730077i | ||||||
\(503\) | 19854.0 | 1.75993 | 0.879966 | − | 0.475037i | \(-0.157565\pi\) | ||||
0.879966 | + | 0.475037i | \(0.157565\pi\) | |||||||
\(504\) | 6297.44 | − | 3718.44i | 0.556568 | − | 0.328636i | ||||
\(505\) | 2324.19i | 0.204802i | ||||||||
\(506\) | −2551.10 | − | 2955.45i | −0.224130 | − | 0.259656i | ||||
\(507\) | −5115.54 | + | 8961.32i | −0.448105 | + | 0.784983i | ||||
\(508\) | − | 27640.7i | − | 2.41409i | ||||||
\(509\) | 16340.1i | 1.42291i | 0.702730 | + | 0.711456i | \(0.251964\pi\) | ||||
−0.702730 | + | 0.711456i | \(0.748036\pi\) | |||||||
\(510\) | 22981.2 | + | 13118.7i | 1.99534 | + | 1.13903i | ||||
\(511\) | −6707.15 | −0.580640 | ||||||||
\(512\) | −4862.56 | −0.419720 | ||||||||
\(513\) | −333.635 | − | 22734.3i | −0.0287141 | − | 1.95661i | ||||
\(514\) | 18252.8i | 1.56633i | ||||||||
\(515\) | − | 18626.1i | − | 1.59372i | ||||||
\(516\) | −19368.2 | − | 11056.3i | −1.65240 | − | 0.943265i | ||||
\(517\) | −9244.43 | − | 10709.7i | −0.786401 | − | 0.911049i | ||||
\(518\) | − | 18057.4i | − | 1.53165i | ||||||
\(519\) | −1288.68 | + | 2257.49i | −0.108992 | + | 0.190930i | ||||
\(520\) | −3321.46 | −0.280107 | ||||||||
\(521\) | 5338.31i | 0.448898i | 0.974486 | + | 0.224449i | \(0.0720582\pi\) | ||||
−0.974486 | + | 0.224449i | \(0.927942\pi\) | |||||||
\(522\) | −3235.66 | − | 5479.81i | −0.271304 | − | 0.459473i | ||||
\(523\) | − | 5078.98i | − | 0.424643i | −0.977200 | − | 0.212322i | \(-0.931898\pi\) | ||
0.977200 | − | 0.212322i | \(-0.0681024\pi\) | |||||||
\(524\) | 14847.1 | 1.23779 | ||||||||
\(525\) | −1663.62 | − | 949.674i | −0.138298 | − | 0.0789470i | ||||
\(526\) | 30581.7 | 2.53503 | ||||||||
\(527\) | −7636.35 | −0.631204 | ||||||||
\(528\) | −493.441 | − | 2519.64i | −0.0406710 | − | 0.207677i | ||||
\(529\) | 11598.7 | 0.953293 | ||||||||
\(530\) | −4400.78 | −0.360675 | ||||||||
\(531\) | 6783.01 | − | 4005.16i | 0.554346 | − | 0.327324i | ||||
\(532\) | −28619.3 | −2.33234 | ||||||||
\(533\) | 2549.91i | 0.207221i | ||||||||
\(534\) | 15496.7 | + | 8846.22i | 1.25582 | + | 0.716879i | ||||
\(535\) | − | 15903.9i | − | 1.28521i | ||||||
\(536\) | −3748.43 | −0.302066 | ||||||||
\(537\) | −5945.29 | − | 3393.85i | −0.477762 | − | 0.272729i | ||||
\(538\) | − | 7144.60i | − | 0.572538i | ||||||
\(539\) | 3640.51 | − | 3142.42i | 0.290923 | − | 0.251120i | ||||
\(540\) | −306.774 | − | 20903.9i | −0.0244471 | − | 1.66585i | ||||
\(541\) | 17212.7i | 1.36789i | 0.729531 | + | 0.683947i | \(0.239738\pi\) | ||||
−0.729531 | + | 0.683947i | \(0.760262\pi\) | |||||||
\(542\) | − | 8423.84i | − | 0.667592i | ||||||
\(543\) | 4501.46 | − | 7885.58i | 0.355757 | − | 0.623209i | ||||
\(544\) | −19419.5 | −1.53052 | ||||||||
\(545\) | 17653.2 | 1.38748 | ||||||||
\(546\) | 2442.10 | − | 4278.04i | 0.191415 | − | 0.335317i | ||||
\(547\) | 12457.6i | 0.973766i | 0.873467 | + | 0.486883i | \(0.161866\pi\) | ||||
−0.873467 | + | 0.486883i | \(0.838134\pi\) | |||||||
\(548\) | 4911.50i | 0.382863i | ||||||||
\(549\) | 3430.00 | − | 2025.31i | 0.266647 | − | 0.157446i | ||||
\(550\) | 3145.12 | − | 2714.81i | 0.243833 | − | 0.210473i | ||||
\(551\) | 8508.91i | 0.657880i | ||||||||
\(552\) | 2005.12 | + | 1144.61i | 0.154608 | + | 0.0882573i | ||||
\(553\) | 1785.78 | 0.137322 | ||||||||
\(554\) | 17181.1i | 1.31761i | ||||||||
\(555\) | −15317.2 | − | 8743.77i | −1.17149 | − | 0.668743i | ||||
\(556\) | − | 1263.01i | − | 0.0963377i | ||||||
\(557\) | −9161.87 | −0.696950 | −0.348475 | − | 0.937318i | \(-0.613300\pi\) | ||||
−0.348475 | + | 0.937318i | \(0.613300\pi\) | |||||||
\(558\) | 5086.92 | + | 8615.05i | 0.385925 | + | 0.653592i | ||||
\(559\) | −5132.55 | −0.388343 | ||||||||
\(560\) | 2413.49 | 0.182122 | ||||||||
\(561\) | −3370.51 | − | 17210.8i | −0.253660 | − | 1.29526i | ||||
\(562\) | −1522.63 | −0.114285 | ||||||||
\(563\) | −12769.3 | −0.955881 | −0.477940 | − | 0.878392i | \(-0.658616\pi\) | ||||
−0.477940 | + | 0.878392i | \(0.658616\pi\) | |||||||
\(564\) | 21265.7 | + | 12139.4i | 1.58767 | + | 0.906316i | ||||
\(565\) | −12936.6 | −0.963272 | ||||||||
\(566\) | − | 18342.4i | − | 1.36217i | ||||||
\(567\) | 9276.42 | + | 5116.42i | 0.687078 | + | 0.378958i | ||||
\(568\) | 7911.78i | 0.584456i | ||||||||
\(569\) | 16454.4 | 1.21231 | 0.606154 | − | 0.795347i | \(-0.292712\pi\) | ||||
0.606154 | + | 0.795347i | \(0.292712\pi\) | |||||||
\(570\) | −22981.2 | + | 40258.0i | −1.68873 | + | 2.95829i | ||||
\(571\) | 8779.22i | 0.643431i | 0.946836 | + | 0.321715i | \(0.104259\pi\) | ||||
−0.946836 | + | 0.321715i | \(0.895741\pi\) | |||||||
\(572\) | 4209.79 | + | 4877.05i | 0.307727 | + | 0.356503i | ||||
\(573\) | −17494.0 | − | 9986.37i | −1.27543 | − | 0.728074i | ||||
\(574\) | 11446.8i | 0.832372i | ||||||||
\(575\) | − | 604.756i | − | 0.0438610i | ||||||
\(576\) | 11448.8 | + | 19389.3i | 0.828182 | + | 1.40258i | ||||
\(577\) | 23766.8 | 1.71478 | 0.857389 | − | 0.514669i | \(-0.172085\pi\) | ||||
0.857389 | + | 0.514669i | \(0.172085\pi\) | |||||||
\(578\) | −16365.5 | −1.17771 | ||||||||
\(579\) | −4590.46 | − | 2620.45i | −0.329487 | − | 0.188087i | ||||
\(580\) | 7823.86i | 0.560117i | ||||||||
\(581\) | − | 2206.59i | − | 0.157564i | ||||||
\(582\) | 2532.15 | − | 4435.79i | 0.180346 | − | 0.315927i | ||||
\(583\) | 1905.79 | + | 2207.86i | 0.135385 | + | 0.156844i | ||||
\(584\) | 8602.72i | 0.609560i | ||||||||
\(585\) | −2446.33 | − | 4143.04i | −0.172895 | − | 0.292809i | ||||
\(586\) | 24446.0 | 1.72330 | ||||||||
\(587\) | 10669.2i | 0.750194i | 0.926986 | + | 0.375097i | \(0.122391\pi\) | ||||
−0.926986 | + | 0.375097i | \(0.877609\pi\) | |||||||
\(588\) | −4126.51 | + | 7228.75i | −0.289412 | + | 0.506988i | ||||
\(589\) | − | 13377.2i | − | 0.935822i | ||||||
\(590\) | −16060.1 | −1.12065 | ||||||||
\(591\) | 8973.20 | − | 15719.1i | 0.624548 | − | 1.09407i | ||||
\(592\) | 3748.95 | 0.260272 | ||||||||
\(593\) | 18602.1 | 1.28819 | 0.644095 | − | 0.764946i | \(-0.277234\pi\) | ||||
0.644095 | + | 0.764946i | \(0.277234\pi\) | |||||||
\(594\) | −17171.3 | + | 15267.4i | −1.18611 | + | 1.05459i | ||||
\(595\) | 16485.7 | 1.13588 | ||||||||
\(596\) | −4072.01 | −0.279859 | ||||||||
\(597\) | −11703.4 | + | 20501.8i | −0.802326 | + | 1.40550i | ||||
\(598\) | 1555.14 | 0.106345 | ||||||||
\(599\) | − | 7674.09i | − | 0.523464i | −0.965141 | − | 0.261732i | \(-0.915706\pi\) | ||
0.965141 | − | 0.261732i | \(-0.0842936\pi\) | |||||||
\(600\) | −1218.07 | + | 2133.80i | −0.0828792 | + | 0.145186i | ||||
\(601\) | 7503.89i | 0.509301i | 0.967033 | + | 0.254651i | \(0.0819604\pi\) | ||||
−0.967033 | + | 0.254651i | \(0.918040\pi\) | |||||||
\(602\) | −23040.6 | −1.55991 | ||||||||
\(603\) | −2760.80 | − | 4675.61i | −0.186449 | − | 0.315764i | ||||
\(604\) | − | 13063.9i | − | 0.880070i | ||||||
\(605\) | −16146.3 | − | 2384.17i | −1.08503 | − | 0.160216i | ||||
\(606\) | −2191.82 | + | 3839.59i | −0.146925 | + | 0.257381i | ||||
\(607\) | 17630.0i | 1.17888i | 0.807812 | + | 0.589441i | \(0.200652\pi\) | ||||
−0.807812 | + | 0.589441i | \(0.799348\pi\) | |||||||
\(608\) | − | 34018.8i | − | 2.26915i | ||||||
\(609\) | −3443.11 | − | 1965.49i | −0.229100 | − | 0.130781i | ||||
\(610\) | −8121.18 | −0.539044 | ||||||||
\(611\) | 5635.38 | 0.373131 | ||||||||
\(612\) | 15433.4 | + | 26137.6i | 1.01938 | + | 1.72639i | ||||
\(613\) | 11241.0i | 0.740654i | 0.928902 | + | 0.370327i | \(0.120754\pi\) | ||||
−0.928902 | + | 0.370327i | \(0.879246\pi\) | |||||||
\(614\) | 16511.6i | 1.08527i | ||||||||
\(615\) | 9709.78 | + | 5542.80i | 0.636644 | + | 0.363426i | ||||
\(616\) | 6457.05 | + | 7480.52i | 0.422341 | + | 0.489283i | ||||
\(617\) | − | 13977.6i | − | 0.912023i | −0.889974 | − | 0.456011i | \(-0.849278\pi\) | ||
0.889974 | − | 0.456011i | \(-0.150722\pi\) | |||||||
\(618\) | 17565.3 | − | 30770.5i | 1.14333 | − | 2.00287i | ||||
\(619\) | −20314.8 | −1.31910 | −0.659548 | − | 0.751662i | \(-0.729252\pi\) | ||||
−0.659548 | + | 0.751662i | \(0.729252\pi\) | |||||||
\(620\) | − | 12300.2i | − | 0.796757i | ||||||
\(621\) | 49.0764 | + | 3344.12i | 0.00317129 | + | 0.216095i | ||||
\(622\) | 28676.4i | 1.84858i | ||||||||
\(623\) | 11116.6 | 0.714893 | ||||||||
\(624\) | 888.176 | + | 507.012i | 0.0569800 | + | 0.0325268i | ||||
\(625\) | −18152.5 | −1.16176 | ||||||||
\(626\) | −28022.1 | −1.78912 | ||||||||
\(627\) | 30149.5 | − | 5904.41i | 1.92034 | − | 0.376076i | ||||
\(628\) | −5517.70 | −0.350606 | ||||||||
\(629\) | 25607.7 | 1.62328 | ||||||||
\(630\) | −10981.8 | − | 18598.5i | −0.694488 | − | 1.17616i | ||||
\(631\) | 3831.37 | 0.241718 | 0.120859 | − | 0.992670i | \(-0.461435\pi\) | ||||
0.120859 | + | 0.992670i | \(0.461435\pi\) | |||||||
\(632\) | − | 2290.48i | − | 0.144162i | ||||||
\(633\) | −13477.6 | − | 7693.67i | −0.846269 | − | 0.483090i | ||||
\(634\) | − | 1203.15i | − | 0.0753678i | ||||||
\(635\) | −27891.8 | −1.74308 | ||||||||
\(636\) | −4384.03 | − | 2502.61i | −0.273330 | − | 0.156030i | ||||
\(637\) | 1915.61i | 0.119151i | ||||||||
\(638\) | 6509.28 | − | 5618.69i | 0.403926 | − | 0.348662i | ||||
\(639\) | −9868.79 | + | 5827.21i | −0.610960 | + | 0.360752i | ||||
\(640\) | − | 25315.5i | − | 1.56357i | ||||||
\(641\) | 18907.4i | 1.16505i | 0.812813 | + | 0.582525i | \(0.197935\pi\) | ||||
−0.812813 | + | 0.582525i | \(0.802065\pi\) | |||||||
\(642\) | 14998.1 | − | 26273.5i | 0.922008 | − | 1.61516i | ||||
\(643\) | −2635.94 | −0.161666 | −0.0808331 | − | 0.996728i | \(-0.525758\pi\) | ||||
−0.0808331 | + | 0.996728i | \(0.525758\pi\) | |||||||
\(644\) | 4209.79 | 0.257591 | ||||||||
\(645\) | −11156.7 | + | 19544.2i | −0.681079 | + | 1.19310i | ||||
\(646\) | − | 67304.3i | − | 4.09915i | ||||||
\(647\) | 10197.9i | 0.619662i | 0.950792 | + | 0.309831i | \(0.100273\pi\) | ||||
−0.950792 | + | 0.309831i | \(0.899727\pi\) | |||||||
\(648\) | 6562.41 | − | 11898.1i | 0.397833 | − | 0.721300i | ||||
\(649\) | 6954.93 | + | 8057.31i | 0.420654 | + | 0.487330i | ||||
\(650\) | 1654.94i | 0.0998649i | ||||||||
\(651\) | 5413.06 | + | 3090.03i | 0.325890 | + | 0.186033i | ||||
\(652\) | −19977.7 | −1.19998 | ||||||||
\(653\) | − | 32680.3i | − | 1.95847i | −0.202731 | − | 0.979234i | \(-0.564982\pi\) | ||
0.202731 | − | 0.979234i | \(-0.435018\pi\) | |||||||
\(654\) | 29163.3 | + | 16647.8i | 1.74369 | + | 0.995381i | ||||
\(655\) | − | 14982.1i | − | 0.893736i | ||||||
\(656\) | −2376.51 | −0.141444 | ||||||||
\(657\) | −10730.6 | + | 6336.10i | −0.637202 | + | 0.376248i | ||||
\(658\) | 25297.8 | 1.49880 | ||||||||
\(659\) | 20357.6 | 1.20337 | 0.601685 | − | 0.798734i | \(-0.294496\pi\) | ||||
0.601685 | + | 0.798734i | \(0.294496\pi\) | |||||||
\(660\) | 27722.2 | − | 5429.05i | 1.63498 | − | 0.320190i | ||||
\(661\) | 8285.93 | 0.487572 | 0.243786 | − | 0.969829i | \(-0.421610\pi\) | ||||
0.243786 | + | 0.969829i | \(0.421610\pi\) | |||||||
\(662\) | 2025.65 | 0.118926 | ||||||||
\(663\) | 6066.80 | + | 3463.21i | 0.355377 | + | 0.202866i | ||||
\(664\) | −2830.21 | −0.165412 | ||||||||
\(665\) | 28879.3i | 1.68405i | ||||||||
\(666\) | −17058.4 | − | 28889.6i | −0.992493 | − | 1.68086i | ||||
\(667\) | − | 1251.63i | − | 0.0726586i | ||||||
\(668\) | 26602.2 | 1.54082 | ||||||||
\(669\) | 13697.4 | − | 23994.9i | 0.791588 | − | 1.38669i | ||||
\(670\) | 11070.4i | 0.638338i | ||||||||
\(671\) | 3516.94 | + | 4074.38i | 0.202339 | + | 0.234411i | ||||
\(672\) | 13765.6 | + | 7858.06i | 0.790209 | + | 0.451088i | ||||
\(673\) | − | 14861.6i | − | 0.851225i | −0.904906 | − | 0.425612i | \(-0.860059\pi\) | ||
0.904906 | − | 0.425612i | \(-0.139941\pi\) | |||||||
\(674\) | − | 40835.8i | − | 2.33373i | ||||||
\(675\) | −3558.73 | + | 52.2259i | −0.202927 | + | 0.00297804i | ||||
\(676\) | 24131.8 | 1.37300 | ||||||||
\(677\) | −18246.3 | −1.03584 | −0.517920 | − | 0.855429i | \(-0.673294\pi\) | ||||
−0.517920 | + | 0.855429i | \(0.673294\pi\) | |||||||
\(678\) | −21371.5 | − | 12199.8i | −1.21057 | − | 0.691050i | ||||
\(679\) | − | 3182.04i | − | 0.179846i | ||||||
\(680\) | − | 21144.8i | − | 1.19245i | ||||||
\(681\) | −13111.1 | + | 22967.8i | −0.737766 | + | 1.29241i | ||||
\(682\) | −10233.5 | + | 8833.40i | −0.574577 | + | 0.495965i | ||||
\(683\) | 32684.8i | 1.83111i | 0.402193 | + | 0.915555i | \(0.368248\pi\) | ||||
−0.402193 | + | 0.915555i | \(0.631752\pi\) | |||||||
\(684\) | −45787.4 | + | 27036.0i | −2.55954 | + | 1.51133i | ||||
\(685\) | 4956.13 | 0.276444 | ||||||||
\(686\) | 30975.3i | 1.72397i | ||||||||
\(687\) | −11434.0 | + | 20029.9i | −0.634984 | + | 1.11235i | ||||
\(688\) | − | 4783.51i | − | 0.265072i | ||||||
\(689\) | −1161.76 | −0.0642375 | ||||||||
\(690\) | 3380.44 | − | 5921.80i | 0.186509 | − | 0.326723i | ||||
\(691\) | −15447.5 | −0.850437 | −0.425219 | − | 0.905091i | \(-0.639803\pi\) | ||||
−0.425219 | + | 0.905091i | \(0.639803\pi\) | |||||||
\(692\) | 6079.15 | 0.333952 | ||||||||
\(693\) | −4575.08 | + | 13563.8i | −0.250783 | + | 0.743501i | ||||
\(694\) | −28395.3 | −1.55313 | ||||||||
\(695\) | −1274.49 | −0.0695600 | ||||||||
\(696\) | −2520.97 | + | 4416.20i | −0.137295 | + | 0.240511i | ||||
\(697\) | −16233.0 | −0.882167 | ||||||||
\(698\) | 24528.4i | 1.33010i | ||||||||
\(699\) | −3048.56 | + | 5340.42i | −0.164960 | + | 0.288974i | ||||
\(700\) | 4479.95i | 0.241895i | ||||||||
\(701\) | −31681.4 | −1.70697 | −0.853487 | − | 0.521114i | \(-0.825516\pi\) | ||||
−0.853487 | + | 0.521114i | \(0.825516\pi\) | |||||||
\(702\) | −134.300 | − | 9151.35i | −0.00722054 | − | 0.492016i | ||||
\(703\) | 44859.1i | 2.40668i | ||||||||
\(704\) | −23031.9 | + | 19880.7i | −1.23302 | + | 1.06432i | ||||
\(705\) | 12249.7 | − | 21458.9i | 0.654400 | − | 1.14637i | ||||
\(706\) | 14953.3i | 0.797133i | ||||||||
\(707\) | 2754.35i | 0.146518i | ||||||||
\(708\) | −15998.9 | − | 9132.94i | −0.849261 | − | 0.484798i | ||||
\(709\) | 11198.2 | 0.593167 | 0.296584 | − | 0.955007i | \(-0.404153\pi\) | ||||
0.296584 | + | 0.955007i | \(0.404153\pi\) | |||||||
\(710\) | 23366.2 | 1.23510 | ||||||||
\(711\) | 2857.03 | − | 1686.99i | 0.150699 | − | 0.0889832i | ||||
\(712\) | − | 14258.4i | − | 0.750500i | ||||||
\(713\) | 1967.74i | 0.103356i | ||||||||
\(714\) | 27234.5 | + | 15546.7i | 1.42749 | + | 0.814877i | ||||
\(715\) | 4921.37 | − | 4248.04i | 0.257411 | − | 0.222193i | ||||
\(716\) | 16010.0i | 0.835645i | ||||||||
\(717\) | −4344.89 | + | 7611.30i | −0.226308 | + | 0.396443i | ||||
\(718\) | 9563.07 | 0.497062 | ||||||||
\(719\) | − | 15023.4i | − | 0.779245i | −0.920975 | − | 0.389622i | \(-0.872605\pi\) | ||
0.920975 | − | 0.389622i | \(-0.127395\pi\) | |||||||
\(720\) | 3861.29 | − | 2279.97i | 0.199864 | − | 0.118013i | ||||
\(721\) | − | 22073.4i | − | 1.14016i | ||||||
\(722\) | 87111.9 | 4.49026 | ||||||||
\(723\) | 26085.5 | + | 14890.8i | 1.34181 | + | 0.765970i | ||||
\(724\) | −21235.0 | −1.09004 | ||||||||
\(725\) | 1331.95 | 0.0682310 | ||||||||
\(726\) | −24425.5 | − | 19165.4i | −1.24864 | − | 0.979744i | ||||
\(727\) | −8061.98 | −0.411283 | −0.205641 | − | 0.978627i | \(-0.565928\pi\) | ||||
−0.205641 | + | 0.978627i | \(0.565928\pi\) | |||||||
\(728\) | −3936.20 | −0.200392 | ||||||||
\(729\) | 19674.5 | − | 577.588i | 0.999569 | − | 0.0293445i | ||||
\(730\) | 25406.8 | 1.28815 | ||||||||
\(731\) | − | 32674.4i | − | 1.65322i | ||||||
\(732\) | −8090.27 | − | 4618.31i | −0.408504 | − | 0.233193i | ||||
\(733\) | − | 32633.9i | − | 1.64442i | −0.569183 | − | 0.822211i | \(-0.692740\pi\) | ||
0.569183 | − | 0.822211i | \(-0.307260\pi\) | |||||||
\(734\) | −29249.4 | −1.47087 | ||||||||
\(735\) | 7294.44 | + | 4164.00i | 0.366067 | + | 0.208968i | ||||
\(736\) | 5004.04i | 0.250613i | ||||||||
\(737\) | 5554.00 | − | 4794.11i | 0.277590 | − | 0.239611i | ||||
\(738\) | 10813.6 | + | 18313.5i | 0.539367 | + | 0.913456i | ||||
\(739\) | − | 5965.10i | − | 0.296928i | −0.988918 | − | 0.148464i | \(-0.952567\pi\) | ||
0.988918 | − | 0.148464i | \(-0.0474329\pi\) | |||||||
\(740\) | 41247.5i | 2.04904i | ||||||||
\(741\) | −6066.80 | + | 10627.7i | −0.300769 | + | 0.526882i | ||||
\(742\) | −5215.28 | −0.258031 | ||||||||
\(743\) | 840.592 | 0.0415051 | 0.0207526 | − | 0.999785i | \(-0.493394\pi\) | ||||
0.0207526 | + | 0.999785i | \(0.493394\pi\) | |||||||
\(744\) | 3963.33 | − | 6942.90i | 0.195299 | − | 0.342122i | ||||
\(745\) | 4109.01i | 0.202071i | ||||||||
\(746\) | − | 49468.3i | − | 2.42783i | ||||||
\(747\) | −2084.52 | − | 3530.28i | −0.102100 | − | 0.172913i | ||||
\(748\) | −31047.9 | + | 26800.0i | −1.51768 | + | 1.31003i | ||||
\(749\) | − | 18847.4i | − | 0.919453i | ||||||
\(750\) | −24749.5 | − | 14128.2i | −1.20497 | − | 0.687851i | ||||
\(751\) | −22433.9 | −1.09005 | −0.545024 | − | 0.838421i | \(-0.683479\pi\) | ||||
−0.545024 | + | 0.838421i | \(0.683479\pi\) | |||||||
\(752\) | 5252.15i | 0.254689i | ||||||||
\(753\) | −8254.61 | − | 4712.12i | −0.399488 | − | 0.228047i | ||||
\(754\) | 3425.14i | 0.165433i | ||||||||
\(755\) | −13182.6 | −0.635449 | ||||||||
\(756\) | −363.552 | − | 24772.8i | −0.0174897 | − | 1.19177i | ||||
\(757\) | 2259.73 | 0.108496 | 0.0542478 | − | 0.998528i | \(-0.482724\pi\) | ||||
0.0542478 | + | 0.998528i | \(0.482724\pi\) | |||||||
\(758\) | −258.487 | −0.0123861 | ||||||||
\(759\) | −4434.88 | + | 868.517i | −0.212090 | + | 0.0415351i | ||||
\(760\) | 37041.2 | 1.76793 | ||||||||
\(761\) | 33640.2 | 1.60244 | 0.801220 | − | 0.598370i | \(-0.204185\pi\) | ||||
0.801220 | + | 0.598370i | \(0.204185\pi\) | |||||||
\(762\) | −46077.6 | − | 26303.3i | −2.19057 | − | 1.25048i | ||||
\(763\) | 20920.4 | 0.992622 | ||||||||
\(764\) | 47109.3i | 2.23083i | ||||||||
\(765\) | 26375.1 | − | 15573.6i | 1.24653 | − | 0.736035i | ||||
\(766\) | 43367.5i | 2.04560i | ||||||||
\(767\) | −4239.70 | −0.199592 | ||||||||
\(768\) | 6687.09 | − | 11714.3i | 0.314192 | − | 0.550396i | ||||
\(769\) | − | 18780.1i | − | 0.880659i | −0.897836 | − | 0.440330i | \(-0.854862\pi\) | ||
0.897836 | − | 0.440330i | \(-0.145138\pi\) | |||||||
\(770\) | 22092.5 | − | 19069.9i | 1.03397 | − | 0.892508i | ||||
\(771\) | 18348.5 | + | 10474.2i | 0.857076 | + | 0.489259i | ||||
\(772\) | 12361.6i | 0.576300i | ||||||||
\(773\) | 22814.4i | 1.06155i | 0.847513 | + | 0.530775i | \(0.178099\pi\) | ||||
−0.847513 | + | 0.530775i | \(0.821901\pi\) | |||||||
\(774\) | −36862.1 | + | 21765.9i | −1.71186 | + | 1.01080i | ||||
\(775\) | −2094.02 | −0.0970574 | ||||||||
\(776\) | −4081.34 | −0.188804 | ||||||||
\(777\) | −18152.1 | − | 10362.1i | −0.838100 | − | 0.478426i | ||||
\(778\) | 51788.9i | 2.38653i | ||||||||
\(779\) | − | 28436.8i | − | 1.30790i | ||||||
\(780\) | −5578.36 | + | 9772.09i | −0.256074 | + | 0.448586i | ||||
\(781\) | −10118.9 | − | 11722.8i | −0.463615 | − | 0.537099i | ||||
\(782\) | 9900.21i | 0.452725i | ||||||||
\(783\) | −7365.31 | + | 108.089i | −0.336162 | + | 0.00493331i | ||||
\(784\) | −1785.34 | −0.0813294 | ||||||||
\(785\) | 5567.84i | 0.253153i | ||||||||
\(786\) | 14128.8 | − | 24750.5i | 0.641166 | − | 1.12318i | ||||
\(787\) | 9762.98i | 0.442202i | 0.975251 | + | 0.221101i | \(0.0709650\pi\) | ||||
−0.975251 | + | 0.221101i | \(0.929035\pi\) | |||||||
\(788\) | −42329.8 | −1.91362 | ||||||||
\(789\) | 17549.0 | − | 30742.1i | 0.791841 | − | 1.38713i | ||||
\(790\) | −6764.57 | −0.304649 | ||||||||
\(791\) | −15331.0 | −0.689135 | ||||||||
\(792\) | 17397.2 | + | 5868.09i | 0.780533 | + | 0.263274i | ||||
\(793\) | −2143.91 | −0.0960058 | ||||||||
\(794\) | 30015.7 | 1.34158 | ||||||||
\(795\) | −2525.35 | + | 4423.86i | −0.112660 | + | 0.197356i | ||||
\(796\) | 55209.1 | 2.45834 | ||||||||
\(797\) | 13025.4i | 0.578902i | 0.957193 | + | 0.289451i | \(0.0934727\pi\) | ||||
−0.957193 | + | 0.289451i | \(0.906527\pi\) | |||||||
\(798\) | −27234.5 | + | 47709.0i | −1.20813 | + | 2.11639i | ||||
\(799\) | 35875.5i | 1.58847i | ||||||||
\(800\) | −5325.18 | −0.235342 | ||||||||
\(801\) | 17785.3 | − | 10501.6i | 0.784533 | − | 0.463242i | ||||
\(802\) | − | 26876.5i | − | 1.18334i | ||||||
\(803\) | −11002.6 | − | 12746.5i | −0.483528 | − | 0.560169i | ||||
\(804\) | −6295.44 | + | 11028.3i | −0.276148 | + | 0.483752i | ||||
\(805\) | − | 4248.04i | − | 0.185992i | ||||||
\(806\) | − | 5384.81i | − | 0.235325i | ||||||
\(807\) | −7182.08 | − | 4099.87i | −0.313285 | − | 0.178838i | ||||
\(808\) | 3532.78 | 0.153815 | ||||||||
\(809\) | −22339.8 | −0.970860 | −0.485430 | − | 0.874276i | \(-0.661337\pi\) | ||||
−0.485430 | + | 0.874276i | \(0.661337\pi\) | |||||||
\(810\) | −35139.2 | − | 19381.1i | −1.52428 | − | 0.840718i | ||||
\(811\) | − | 35155.3i | − | 1.52216i | −0.648659 | − | 0.761079i | \(-0.724670\pi\) | ||
0.648659 | − | 0.761079i | \(-0.275330\pi\) | |||||||
\(812\) | 9271.90i | 0.400714i | ||||||||
\(813\) | −8468.03 | − | 4833.94i | −0.365297 | − | 0.208529i | ||||
\(814\) | 34317.0 | − | 29621.8i | 1.47765 | − | 1.27549i | ||||
\(815\) | 20159.2i | 0.866437i | ||||||||
\(816\) | −3227.70 | + | 5654.24i | −0.138471 | + | 0.242571i | ||||
\(817\) | 57238.5 | 2.45107 | ||||||||
\(818\) | 28771.7i | 1.22980i | ||||||||
\(819\) | −2899.10 | − | 4909.83i | −0.123691 | − | 0.209479i | ||||
\(820\) | − | 26147.3i | − | 1.11354i | ||||||
\(821\) | 34380.7 | 1.46151 | 0.730753 | − | 0.682642i | \(-0.239169\pi\) | ||||
0.730753 | + | 0.682642i | \(0.239169\pi\) | |||||||
\(822\) | 8187.58 | + | 4673.85i | 0.347415 | + | 0.198320i | ||||
\(823\) | −33496.1 | −1.41871 | −0.709357 | − | 0.704850i | \(-0.751014\pi\) | ||||
−0.709357 | + | 0.704850i | \(0.751014\pi\) | |||||||
\(824\) | −28311.8 | −1.19695 | ||||||||
\(825\) | −924.254 | − | 4719.49i | −0.0390041 | − | 0.199166i | ||||
\(826\) | −19032.5 | −0.801725 | ||||||||
\(827\) | 8303.08 | 0.349125 | 0.174562 | − | 0.984646i | \(-0.444149\pi\) | ||||
0.174562 | + | 0.984646i | \(0.444149\pi\) | |||||||
\(828\) | 6735.15 | − | 3976.89i | 0.282684 | − | 0.166916i | ||||
\(829\) | 21903.6 | 0.917665 | 0.458832 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458832 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(830\) | 8358.60i | 0.349556i | ||||||||
\(831\) | 17271.2 | + | 9859.21i | 0.720976 | + | 0.411567i | ||||
\(832\) | − | 12119.2i | − | 0.504999i | ||||||
\(833\) | −12195.0 | −0.507242 | ||||||||
\(834\) | −2105.47 | − | 1201.90i | −0.0874180 | − | 0.0499023i | ||||
\(835\) | − | 26843.9i | − | 1.11254i | ||||||
\(836\) | −46947.8 | − | 54389.2i | −1.94225 | − | 2.25011i | ||||
\(837\) | 11579.3 | − | 169.931i | 0.478184 | − | 0.00701755i | ||||
\(838\) | − | 29902.1i | − | 1.23264i | ||||||
\(839\) | − | 32602.6i | − | 1.34156i | −0.741657 | − | 0.670779i | \(-0.765960\pi\) | ||
0.741657 | − | 0.670779i | \(-0.234040\pi\) | |||||||
\(840\) | −8556.20 | + | 14988.6i | −0.351449 | + | 0.615662i | ||||
\(841\) | −21632.3 | −0.886971 | ||||||||
\(842\) | 15854.7 | 0.648917 | ||||||||
\(843\) | −873.749 | + | 1530.62i | −0.0356981 | + | 0.0625354i | ||||
\(844\) | 36293.8i | 1.48019i | ||||||||
\(845\) | − | 24351.1i | − | 0.991365i | ||||||
\(846\) | 40473.4 | − | 23898.3i | 1.64481 | − | 0.971206i | ||||
\(847\) | −19134.7 | − | 2825.44i | −0.776239 | − | 0.114620i | ||||
\(848\) | − | 1082.76i | − | 0.0438468i | ||||||
\(849\) | −18438.6 | − | 10525.6i | −0.745361 | − | 0.425487i | ||||
\(850\) | −10535.6 | −0.425137 | ||||||||
\(851\) | − | 6598.61i | − | 0.265802i | ||||||
\(852\) | 23277.3 | + | 13287.8i | 0.935994 | + | 0.534309i | ||||
\(853\) | 32544.8i | 1.30635i | 0.757208 | + | 0.653174i | \(0.226563\pi\) | ||||
−0.757208 | + | 0.653174i | \(0.773437\pi\) | |||||||
\(854\) | −9624.26 | −0.385639 | ||||||||
\(855\) | 27281.7 | + | 46203.4i | 1.09124 | + | 1.84810i | ||||
\(856\) | −24174.1 | −0.965249 | ||||||||
\(857\) | 566.319 | 0.0225730 | 0.0112865 | − | 0.999936i | \(-0.496407\pi\) | ||||
0.0112865 | + | 0.999936i | \(0.496407\pi\) | |||||||
\(858\) | 12136.3 | − | 2376.74i | 0.482896 | − | 0.0945693i | ||||
\(859\) | 12811.9 | 0.508888 | 0.254444 | − | 0.967087i | \(-0.418107\pi\) | ||||
0.254444 | + | 0.967087i | \(0.418107\pi\) | |||||||
\(860\) | 52630.2 | 2.08683 | ||||||||
\(861\) | 11506.9 | + | 6568.66i | 0.455462 | + | 0.259999i | ||||
\(862\) | −17999.4 | −0.711208 | ||||||||
\(863\) | − | 10242.5i | − | 0.404009i | −0.979385 | − | 0.202004i | \(-0.935254\pi\) | ||
0.979385 | − | 0.202004i | \(-0.0647456\pi\) | |||||||
\(864\) | 29446.7 | − | 432.142i | 1.15949 | − | 0.0170159i | ||||
\(865\) | − | 6134.39i | − | 0.241128i | ||||||
\(866\) | 33354.5 | 1.30881 | ||||||||
\(867\) | −9391.18 | + | 16451.3i | −0.367868 | + | 0.644425i | ||||
\(868\) | − | 14576.8i | − | 0.570009i | ||||||
\(869\) | 2929.44 | + | 3393.77i | 0.114355 | + | 0.132481i | ||||
\(870\) | 13042.6 | + | 7445.30i | 0.508257 | + | 0.290137i | ||||
\(871\) | 2922.48i | 0.113690i | ||||||||
\(872\) | − | 26833.0i | − | 1.04206i | ||||||
\(873\) | −3006.00 | − | 5090.87i | −0.116538 | − | 0.197365i | ||||
\(874\) | −17343.0 | −0.671209 | ||||||||
\(875\) | −17754.2 | −0.685945 | ||||||||
\(876\) | 25310.1 | + | 14448.2i | 0.976197 | + | 0.557259i | ||||
\(877\) | 14958.4i | 0.575952i | 0.957638 | + | 0.287976i | \(0.0929823\pi\) | ||||
−0.957638 | + | 0.287976i | \(0.907018\pi\) | |||||||
\(878\) | 61257.6i | 2.35461i | ||||||||
\(879\) | 14028.1 | − | 24574.3i | 0.538290 | − | 0.942969i | ||||
\(880\) | 3959.15 | + | 4586.70i | 0.151663 | + | 0.175702i | ||||
\(881\) | − | 26977.7i | − | 1.03167i | −0.856687 | − | 0.515836i | \(-0.827481\pi\) | ||
0.856687 | − | 0.515836i | \(-0.172519\pi\) | |||||||
\(882\) | 8123.65 | + | 13758.0i | 0.310133 | + | 0.525232i | ||||
\(883\) | −38095.3 | −1.45188 | −0.725940 | − | 0.687758i | \(-0.758595\pi\) | ||||
−0.725940 | + | 0.687758i | \(0.758595\pi\) | |||||||
\(884\) | − | 16337.2i | − | 0.621584i | ||||||
\(885\) | −9215.93 | + | 16144.3i | −0.350045 | + | 0.613204i | ||||
\(886\) | 14814.0i | 0.561723i | ||||||||
\(887\) | −24913.9 | −0.943097 | −0.471548 | − | 0.881840i | \(-0.656305\pi\) | ||||
−0.471548 | + | 0.881840i | \(0.656305\pi\) | |||||||
\(888\) | −13290.6 | + | 23282.3i | −0.502256 | + | 0.879844i | ||||
\(889\) | −33054.1 | −1.24702 | ||||||||
\(890\) | −42110.0 | −1.58599 | ||||||||
\(891\) | 5493.85 | + | 26022.4i | 0.206567 | + | 0.978433i | ||||
\(892\) | −64615.6 | −2.42544 | ||||||||
\(893\) | −62846.1 | −2.35506 | ||||||||
\(894\) | −3874.99 | + | 6788.14i | −0.144965 | + | 0.253948i | ||||
\(895\) | 16155.5 | 0.603372 | ||||||||
\(896\) | − | 30000.9i | − | 1.11860i | ||||||
\(897\) | 892.404 | − | 1563.30i | 0.0332179 | − | 0.0581907i | ||||
\(898\) | − | 41773.6i | − | 1.55234i | ||||||
\(899\) | −4333.88 | −0.160782 | ||||||||
\(900\) | 4232.11 | + | 7167.38i | 0.156745 | + | 0.265458i | ||||
\(901\) | − | 7395.92i | − | 0.273467i | ||||||
\(902\) | −21754.0 | + | 18777.7i | −0.803026 | + | 0.693158i | ||||
\(903\) | −13221.6 | + | 23161.4i | −0.487251 | + | 0.853559i | ||||
\(904\) | 19663.8i | 0.723460i | ||||||||
\(905\) | 21427.9i | 0.787059i | ||||||||
\(906\) | −21777.8 | − | 12431.8i | −0.798587 | − | 0.455871i | ||||
\(907\) | 44889.9 | 1.64338 | 0.821690 | − | 0.569934i | \(-0.193031\pi\) | ||||
0.821690 | + | 0.569934i | \(0.193031\pi\) | |||||||
\(908\) | 61849.8 | 2.26053 | ||||||||
\(909\) | 2601.98 | + | 4406.63i | 0.0949418 | + | 0.160791i | ||||
\(910\) | 11625.0i | 0.423476i | ||||||||
\(911\) | 44920.0i | 1.63366i | 0.576876 | + | 0.816832i | \(0.304272\pi\) | ||||
−0.576876 | + | 0.816832i | \(0.695728\pi\) | |||||||
\(912\) | −9905.00 | − | 5654.24i | −0.359635 | − | 0.205297i | ||||
\(913\) | 4193.49 | − | 3619.75i | 0.152009 | − | 0.131212i | ||||
\(914\) | − | 55404.8i | − | 2.00506i | ||||||
\(915\) | −4660.27 | + | 8163.79i | −0.168376 | + | 0.294958i | ||||
\(916\) | 53938.2 | 1.94560 | ||||||||
\(917\) | − | 17754.9i | − | 0.639389i | ||||||
\(918\) | 58258.6 | − | 854.969i | 2.09458 | − | 0.0307388i | ||||
\(919\) | 44178.6i | 1.58577i | 0.609374 | + | 0.792883i | \(0.291421\pi\) | ||||
−0.609374 | + | 0.792883i | \(0.708579\pi\) | |||||||
\(920\) | −5448.62 | −0.195256 | ||||||||
\(921\) | 16598.2 | + | 9475.02i | 0.593842 | + | 0.338993i | ||||
\(922\) | 10344.4 | 0.369495 | ||||||||
\(923\) | 6168.46 | 0.219975 | ||||||||
\(924\) | 32853.0 | − | 6433.86i | 1.16968 | − | 0.229068i | ||||
\(925\) | 7022.07 | 0.249605 | ||||||||
\(926\) | −23246.3 | −0.824968 | ||||||||
\(927\) | −20852.3 | − | 35314.8i | −0.738812 | − | 1.25123i | ||||
\(928\) | −11021.2 | −0.389859 | ||||||||
\(929\) | 36498.3i | 1.28899i | 0.764610 | + | 0.644494i | \(0.222932\pi\) | ||||
−0.764610 | + | 0.644494i | \(0.777068\pi\) | |||||||
\(930\) | −20504.8 | − | 11705.1i | −0.722987 | − | 0.412715i | ||||
\(931\) | − | 21363.0i | − | 0.752036i | ||||||
\(932\) | 14381.1 | 0.505440 | ||||||||
\(933\) | 28826.8 | + | 16455.7i | 1.01152 | + | 0.577422i | ||||
\(934\) | 45649.7i | 1.59925i | ||||||||
\(935\) | 27043.5 | + | 31330.0i | 0.945902 | + | 1.09583i | ||||
\(936\) | −6297.44 | + | 3718.44i | −0.219913 | + | 0.129852i | ||||
\(937\) | 30491.6i | 1.06309i | 0.847030 | + | 0.531545i | \(0.178388\pi\) | ||||
−0.847030 | + | 0.531545i | \(0.821612\pi\) | |||||||
\(938\) | 13119.3i | 0.456674i | ||||||||
\(939\) | −16080.3 | + | 28169.1i | −0.558849 | + | 0.978983i | ||||
\(940\) | −57786.4 | −2.00509 | ||||||||
\(941\) | 9316.95 | 0.322767 | 0.161384 | − | 0.986892i | \(-0.448404\pi\) | ||||
0.161384 | + | 0.986892i | \(0.448404\pi\) | |||||||
\(942\) | −5250.73 | + | 9198.14i | −0.181611 | + | 0.318144i | ||||
\(943\) | 4182.95i | 0.144449i | ||||||||
\(944\) | − | 3951.39i | − | 0.136236i | ||||||
\(945\) | −24997.9 | + | 366.855i | −0.860511 | + | 0.0126284i | ||||
\(946\) | −37796.4 | − | 43787.2i | −1.29901 | − | 1.50491i | ||||
\(947\) | 31678.7i | 1.08703i | 0.839399 | + | 0.543516i | \(0.182907\pi\) | ||||
−0.839399 | + | 0.543516i | \(0.817093\pi\) | |||||||
\(948\) | −6738.82 | − | 3846.83i | −0.230872 | − | 0.131793i | ||||
\(949\) | 6707.15 | 0.229424 | ||||||||
\(950\) | − | 18456.0i | − | 0.630308i | ||||||
\(951\) | −1209.46 | − | 690.417i | −0.0412402 | − | 0.0235419i | ||||
\(952\) | − | 25058.3i | − | 0.853093i | ||||||
\(953\) | 42487.3 | 1.44417 | 0.722087 | − | 0.691802i | \(-0.243183\pi\) | ||||
0.722087 | + | 0.691802i | \(0.243183\pi\) | |||||||
\(954\) | −8343.81 | + | 4926.76i | −0.283166 | + | 0.167201i | ||||
\(955\) | 47537.3 | 1.61076 | ||||||||
\(956\) | 20496.4 | 0.693410 | ||||||||
\(957\) | −1912.88 | − | 9767.66i | −0.0646129 | − | 0.329931i | ||||
\(958\) | 78368.7 | 2.64298 | ||||||||
\(959\) | 5873.41 | 0.197771 | ||||||||
\(960\) | −46148.7 | − | 26343.8i | −1.55150 | − | 0.885670i | ||||
\(961\) | −22977.5 | −0.771291 | ||||||||
\(962\) | 18057.4i | 0.605191i | ||||||||
\(963\) | −17804.8 | − | 30153.6i | −0.595795 | − | 1.00902i | ||||
\(964\) | − | 70245.4i | − | 2.34694i | ||||||
\(965\) | 12473.9 | 0.416114 | ||||||||
\(966\) | 4006.10 | − | 7017.81i | 0.133431 | − | 0.233742i | ||||
\(967\) | − | 19898.2i | − | 0.661721i | −0.943680 | − | 0.330860i | \(-0.892661\pi\) | ||
0.943680 | − | 0.330860i | \(-0.107339\pi\) | |||||||
\(968\) | −3623.96 | + | 24542.5i | −0.120329 | + | 0.814902i | ||||
\(969\) | −67657.4 | − | 38622.0i | −2.24300 | − | 1.28041i | ||||
\(970\) | 12053.6i | 0.398988i | ||||||||
\(971\) | − | 24273.9i | − | 0.802251i | −0.916023 | − | 0.401125i | \(-0.868619\pi\) | ||
0.916023 | − | 0.401125i | \(-0.131381\pi\) | |||||||
\(972\) | −23984.0 | − | 39290.1i | −0.791447 | − | 1.29653i | ||||
\(973\) | −1510.37 | −0.0497640 | ||||||||
\(974\) | −51740.3 | −1.70212 | ||||||||
\(975\) | 1663.62 | + | 949.674i | 0.0546447 | + | 0.0311938i | ||||
\(976\) | − | 1998.12i | − | 0.0655310i | ||||||
\(977\) | − | 8504.73i | − | 0.278496i | −0.990258 | − | 0.139248i | \(-0.955532\pi\) | ||
0.990258 | − | 0.139248i | \(-0.0444685\pi\) | |||||||
\(978\) | −19011.1 | + | 33303.3i | −0.621581 | + | 1.08888i | ||||
\(979\) | 18236.0 | + | 21126.5i | 0.595327 | + | 0.689689i | ||||
\(980\) | − | 19643.1i | − | 0.640281i | ||||||
\(981\) | 33470.2 | − | 19763.1i | 1.08932 | − | 0.643208i | ||||
\(982\) | 32506.2 | 1.05633 | ||||||||
\(983\) | − | 21918.9i | − | 0.711194i | −0.934639 | − | 0.355597i | \(-0.884278\pi\) | ||
0.934639 | − | 0.355597i | \(-0.115722\pi\) | |||||||
\(984\) | 8425.09 | − | 14758.9i | 0.272949 | − | 0.478148i | ||||
\(985\) | 42714.4i | 1.38172i | ||||||||
\(986\) | −21804.9 | −0.704268 | ||||||||
\(987\) | 14516.9 | − | 25430.5i | 0.468165 | − | 0.820124i | ||||
\(988\) | 28619.3 | 0.921559 | ||||||||
\(989\) | −8419.57 | −0.270705 | ||||||||
\(990\) | 17330.5 | − | 51379.9i | 0.556362 | − | 1.64945i | ||||
\(991\) | 6904.12 | 0.221308 | 0.110654 | − | 0.993859i | \(-0.464705\pi\) | ||||
0.110654 | + | 0.993859i | \(0.464705\pi\) | |||||||
\(992\) | 17326.9 | 0.554567 | ||||||||
\(993\) | 1162.40 | − | 2036.28i | 0.0371478 | − | 0.0650749i | ||||
\(994\) | 27690.9 | 0.883602 | ||||||||
\(995\) | − | 55710.8i | − | 1.77503i | ||||||
\(996\) | −4753.32 | + | 8326.79i | −0.151220 | + | 0.264904i | ||||
\(997\) | 22130.0i | 0.702973i | 0.936193 | + | 0.351486i | \(0.114324\pi\) | ||||
−0.936193 | + | 0.351486i | \(0.885676\pi\) | |||||||
\(998\) | 7296.63 | 0.231434 | ||||||||
\(999\) | −38830.0 | + | 569.847i | −1.22976 | + | 0.0180472i |
(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 | 33.4.d.b.32.2 | yes | 8 | |
3.2 | odd | 2 | inner | 33.4.d.b.32.7 | yes | 8 | |
4.3 | odd | 2 | 528.4.b.e.65.6 | 8 | |||
11.10 | odd | 2 | inner | 33.4.d.b.32.8 | yes | 8 | |
12.11 | even | 2 | 528.4.b.e.65.8 | 8 | |||
33.32 | even | 2 | inner | 33.4.d.b.32.1 | ✓ | 8 | |
44.43 | even | 2 | 528.4.b.e.65.5 | 8 | |||
132.131 | odd | 2 | 528.4.b.e.65.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.d.b.32.1 | ✓ | 8 | 33.32 | even | 2 | inner | |
33.4.d.b.32.2 | yes | 8 | 1.1 | even | 1 | trivial | |
33.4.d.b.32.7 | yes | 8 | 3.2 | odd | 2 | inner | |
33.4.d.b.32.8 | yes | 8 | 11.10 | odd | 2 | inner | |
528.4.b.e.65.5 | 8 | 44.43 | even | 2 | |||
528.4.b.e.65.6 | 8 | 4.3 | odd | 2 | |||
528.4.b.e.65.7 | 8 | 132.131 | odd | 2 | |||
528.4.b.e.65.8 | 8 | 12.11 | even | 2 |