Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,4,Mod(38,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.38");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.8593839112\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Relative dimension: | \(66\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 38.2 | ||
Character | \(\chi\) | \(=\) | 201.38 |
Dual form | 201.4.f.a.164.2 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64802 | + | 4.58651i | −0.936217 | + | 1.62158i | −0.163768 | + | 0.986499i | \(0.552365\pi\) |
−0.772449 | + | 0.635077i | \(0.780968\pi\) | |||||||
\(3\) | 2.08276 | − | 4.76047i | 0.400828 | − | 0.916153i | ||||
\(4\) | −10.0240 | − | 17.3621i | −1.25301 | − | 2.17027i | ||||
\(5\) | −19.9728 | −1.78642 | −0.893209 | − | 0.449642i | \(-0.851552\pi\) | ||||
−0.893209 | + | 0.449642i | \(0.851552\pi\) | |||||||
\(6\) | 16.3187 | + | 22.1584i | 1.11035 | + | 1.50769i | ||||
\(7\) | −22.9190 | + | 13.2323i | −1.23751 | + | 0.714476i | −0.968584 | − | 0.248685i | \(-0.920002\pi\) |
−0.268925 | + | 0.963161i | \(0.586668\pi\) | |||||||
\(8\) | 63.8072 | 2.81991 | ||||||||
\(9\) | −18.3242 | − | 19.8299i | −0.678674 | − | 0.734440i | ||||
\(10\) | 52.8883 | − | 91.6052i | 1.67248 | − | 2.89681i | ||||
\(11\) | 5.59972 | + | 9.69900i | 0.153489 | + | 0.265851i | 0.932508 | − | 0.361150i | \(-0.117616\pi\) |
−0.779019 | + | 0.627001i | \(0.784282\pi\) | |||||||
\(12\) | −103.530 | + | 11.5579i | −2.49054 | + | 0.278041i | ||||
\(13\) | −27.1150 | − | 15.6548i | −0.578488 | − | 0.333990i | 0.182044 | − | 0.983290i | \(-0.441729\pi\) |
−0.760532 | + | 0.649300i | \(0.775062\pi\) | |||||||
\(14\) | − | 140.158i | − | 2.67562i | ||||||
\(15\) | −41.5985 | + | 95.0798i | −0.716046 | + | 1.63663i | ||||
\(16\) | −88.7705 | + | 153.755i | −1.38704 | + | 2.40242i | ||||
\(17\) | 29.4712 | + | 17.0152i | 0.420460 | + | 0.242753i | 0.695274 | − | 0.718745i | \(-0.255283\pi\) |
−0.274814 | + | 0.961497i | \(0.588616\pi\) | |||||||
\(18\) | 139.473 | − | 31.5342i | 1.82634 | − | 0.412927i | ||||
\(19\) | 45.4378 | − | 78.7006i | 0.548639 | − | 0.950271i | −0.449729 | − | 0.893165i | \(-0.648479\pi\) |
0.998368 | − | 0.0571057i | \(-0.0181872\pi\) | |||||||
\(20\) | 200.208 | + | 346.770i | 2.23839 | + | 3.87701i | ||||
\(21\) | 15.2571 | + | 136.665i | 0.158542 | + | 1.42013i | ||||
\(22\) | −59.3127 | −0.574796 | ||||||||
\(23\) | 138.390 | + | 79.8993i | 1.25462 | + | 0.724355i | 0.972023 | − | 0.234884i | \(-0.0754712\pi\) |
0.282596 | + | 0.959239i | \(0.408805\pi\) | |||||||
\(24\) | 132.895 | − | 303.752i | 1.13030 | − | 2.58347i | ||||
\(25\) | 273.911 | 2.19129 | ||||||||
\(26\) | 143.602 | − | 82.9087i | 1.08318 | − | 0.625374i | ||||
\(27\) | −132.564 | + | 45.9310i | −0.944891 | + | 0.327386i | ||||
\(28\) | 459.482 | + | 265.282i | 3.10121 | + | 1.79048i | ||||
\(29\) | −265.236 | + | 153.134i | −1.69838 | + | 0.980562i | −0.751086 | + | 0.660205i | \(0.770470\pi\) |
−0.947297 | + | 0.320357i | \(0.896197\pi\) | |||||||
\(30\) | −325.930 | − | 442.565i | −1.98355 | − | 2.69337i | ||||
\(31\) | 152.420 | − | 87.9997i | 0.883079 | − | 0.509846i | 0.0114066 | − | 0.999935i | \(-0.496369\pi\) |
0.871672 | + | 0.490089i | \(0.163036\pi\) | |||||||
\(32\) | −214.904 | − | 372.224i | −1.18719 | − | 2.05627i | ||||
\(33\) | 57.8347 | − | 6.45660i | 0.305083 | − | 0.0340591i | ||||
\(34\) | −156.081 | + | 90.1133i | −0.787284 | + | 0.454538i | ||||
\(35\) | 457.755 | − | 264.285i | 2.21071 | − | 1.27635i | ||||
\(36\) | −160.607 | + | 516.923i | −0.743549 | + | 2.39316i | ||||
\(37\) | 17.2119 | − | 29.8119i | 0.0764762 | − | 0.132461i | −0.825251 | − | 0.564766i | \(-0.808966\pi\) |
0.901727 | + | 0.432305i | \(0.142300\pi\) | |||||||
\(38\) | 240.641 | + | 416.802i | 1.02729 | + | 1.77932i | ||||
\(39\) | −130.998 | + | 96.4748i | −0.537860 | + | 0.396111i | ||||
\(40\) | −1274.41 | −5.03753 | ||||||||
\(41\) | 24.4688 | + | 42.3812i | 0.0932046 | + | 0.161435i | 0.908858 | − | 0.417106i | \(-0.136956\pi\) |
−0.815653 | + | 0.578541i | \(0.803622\pi\) | |||||||
\(42\) | −667.216 | − | 291.915i | −2.45128 | − | 1.07246i | ||||
\(43\) | − | 58.7928i | − | 0.208507i | −0.994551 | − | 0.104254i | \(-0.966755\pi\) | ||
0.994551 | − | 0.104254i | \(-0.0332454\pi\) | |||||||
\(44\) | 112.264 | − | 194.446i | 0.384645 | − | 0.666225i | ||||
\(45\) | 365.985 | + | 396.057i | 1.21240 | + | 1.31202i | ||||
\(46\) | −732.918 | + | 423.150i | −2.34919 | + | 1.35631i | ||||
\(47\) | 65.2777 | − | 37.6881i | 0.202590 | − | 0.116965i | −0.395273 | − | 0.918564i | \(-0.629350\pi\) |
0.597863 | + | 0.801598i | \(0.296017\pi\) | |||||||
\(48\) | 547.059 | + | 742.825i | 1.64502 | + | 2.23370i | ||||
\(49\) | 178.687 | − | 309.495i | 0.520953 | − | 0.902316i | ||||
\(50\) | −725.323 | + | 1256.30i | −2.05152 | + | 3.55334i | ||||
\(51\) | 142.382 | − | 104.858i | 0.390931 | − | 0.287904i | ||||
\(52\) | 627.699i | 1.67396i | ||||||||
\(53\) | −469.309 | −1.21631 | −0.608157 | − | 0.793817i | \(-0.708091\pi\) | ||||
−0.608157 | + | 0.793817i | \(0.708091\pi\) | |||||||
\(54\) | 140.371 | − | 729.634i | 0.353742 | − | 1.83872i | ||||
\(55\) | −111.842 | − | 193.716i | −0.274195 | − | 0.474920i | ||||
\(56\) | −1462.40 | + | 844.315i | −3.48966 | + | 2.01476i | ||||
\(57\) | −280.016 | − | 380.220i | −0.650684 | − | 0.883533i | ||||
\(58\) | − | 1622.01i | − | 3.67207i | ||||||
\(59\) | − | 326.866i | − | 0.721259i | −0.932709 | − | 0.360630i | \(-0.882562\pi\) | ||
0.932709 | − | 0.360630i | \(-0.117438\pi\) | |||||||
\(60\) | 2067.77 | − | 230.844i | 4.44914 | − | 0.496697i | ||||
\(61\) | 63.6744 | + | 36.7625i | 0.133650 | + | 0.0771631i | 0.565334 | − | 0.824862i | \(-0.308747\pi\) |
−0.431684 | + | 0.902025i | \(0.642080\pi\) | |||||||
\(62\) | 932.101i | 1.90931i | ||||||||
\(63\) | 682.367 | + | 212.009i | 1.36461 | + | 0.423979i | ||||
\(64\) | 855.951 | 1.67178 | ||||||||
\(65\) | 541.561 | + | 312.670i | 1.03342 | + | 0.596646i | ||||
\(66\) | −123.534 | + | 282.357i | −0.230394 | + | 0.526601i | ||||
\(67\) | 319.774 | − | 445.542i | 0.583085 | − | 0.812411i | ||||
\(68\) | − | 682.245i | − | 1.21668i | ||||||
\(69\) | 668.591 | − | 492.389i | 1.16651 | − | 0.859082i | ||||
\(70\) | 2799.33i | 4.77977i | ||||||||
\(71\) | 129.218 | − | 74.6041i | 0.215991 | − | 0.124703i | −0.388102 | − | 0.921617i | \(-0.626869\pi\) |
0.604093 | + | 0.796914i | \(0.293536\pi\) | |||||||
\(72\) | −1169.22 | − | 1265.29i | −1.91380 | − | 2.07105i | ||||
\(73\) | −106.110 | + | 183.788i | −0.170126 | + | 0.294668i | −0.938464 | − | 0.345377i | \(-0.887751\pi\) |
0.768337 | + | 0.640045i | \(0.221084\pi\) | |||||||
\(74\) | 91.1550 | + | 157.885i | 0.143197 | + | 0.248024i | ||||
\(75\) | 570.492 | − | 1303.95i | 0.878330 | − | 2.00756i | ||||
\(76\) | −1821.88 | −2.74979 | ||||||||
\(77\) | −256.680 | − | 148.194i | −0.379888 | − | 0.219328i | ||||
\(78\) | −95.5956 | − | 856.293i | −0.138770 | − | 1.24303i | ||||
\(79\) | −83.6573 | + | 48.2996i | −0.119142 | + | 0.0687864i | −0.558386 | − | 0.829581i | \(-0.688579\pi\) |
0.439245 | + | 0.898367i | \(0.355246\pi\) | |||||||
\(80\) | 1772.99 | − | 3070.91i | 2.47783 | − | 4.29173i | ||||
\(81\) | −57.4472 | + | 726.733i | −0.0788028 | + | 0.996890i | ||||
\(82\) | −259.176 | −0.349039 | ||||||||
\(83\) | 983.038 | + | 567.557i | 1.30003 | + | 0.750573i | 0.980409 | − | 0.196973i | \(-0.0631111\pi\) |
0.319621 | + | 0.947546i | \(0.396444\pi\) | |||||||
\(84\) | 2219.86 | − | 1634.83i | 2.88341 | − | 2.12351i | ||||
\(85\) | −588.621 | − | 339.841i | −0.751117 | − | 0.433658i | ||||
\(86\) | 269.654 | + | 155.685i | 0.338110 | + | 0.195208i | ||||
\(87\) | 176.567 | + | 1581.59i | 0.217586 | + | 1.94902i | ||||
\(88\) | 357.302 | + | 618.866i | 0.432824 | + | 0.749674i | ||||
\(89\) | − | 351.119i | − | 0.418186i | −0.977896 | − | 0.209093i | \(-0.932949\pi\) | ||
0.977896 | − | 0.209093i | \(-0.0670511\pi\) | |||||||
\(90\) | −2785.66 | + | 629.825i | −3.26260 | + | 0.737659i | ||||
\(91\) | 828.597 | 0.954512 | ||||||||
\(92\) | − | 3203.66i | − | 3.63048i | ||||||
\(93\) | −101.466 | − | 908.874i | −0.113134 | − | 1.01340i | ||||
\(94\) | 399.196i | 0.438020i | ||||||||
\(95\) | −907.518 | + | 1571.87i | −0.980099 | + | 1.69758i | ||||
\(96\) | −2219.56 | + | 247.789i | −2.35971 | + | 0.263436i | ||||
\(97\) | 1049.72 | + | 606.059i | 1.09880 | + | 0.634391i | 0.935905 | − | 0.352252i | \(-0.114584\pi\) |
0.162893 | + | 0.986644i | \(0.447917\pi\) | |||||||
\(98\) | 946.333 | + | 1639.10i | 0.975450 | + | 1.68953i | ||||
\(99\) | 89.7195 | − | 288.768i | 0.0910823 | − | 0.293154i | ||||
\(100\) | −2745.70 | − | 4755.69i | −2.74570 | − | 4.75569i | ||||
\(101\) | −450.651 | − | 780.551i | −0.443975 | − | 0.768987i | 0.554005 | − | 0.832513i | \(-0.313099\pi\) |
−0.997980 | + | 0.0635258i | \(0.979765\pi\) | |||||||
\(102\) | 103.903 | + | 930.703i | 0.100862 | + | 0.903464i | ||||
\(103\) | 634.361 | + | 1098.75i | 0.606849 | + | 1.05109i | 0.991756 | + | 0.128138i | \(0.0409000\pi\) |
−0.384908 | + | 0.922955i | \(0.625767\pi\) | |||||||
\(104\) | −1730.13 | − | 998.891i | −1.63128 | − | 0.941820i | ||||
\(105\) | −304.727 | − | 2729.58i | −0.283222 | − | 2.53695i | ||||
\(106\) | 1242.74 | − | 2152.49i | 1.13873 | − | 1.97234i | ||||
\(107\) | − | 171.267i | − | 0.154738i | −0.997003 | − | 0.0773691i | \(-0.975348\pi\) | ||
0.997003 | − | 0.0773691i | \(-0.0246520\pi\) | |||||||
\(108\) | 2126.29 | + | 1841.19i | 1.89447 | + | 1.64045i | ||||
\(109\) | 1833.84i | 1.61147i | 0.592275 | + | 0.805736i | \(0.298230\pi\) | ||||
−0.592275 | + | 0.805736i | \(0.701770\pi\) | |||||||
\(110\) | 1184.64 | 1.02683 | ||||||||
\(111\) | −106.070 | − | 144.028i | −0.0907005 | − | 0.123158i | ||||
\(112\) | − | 4698.55i | − | 3.96402i | ||||||
\(113\) | −346.023 | − | 599.329i | −0.288063 | − | 0.498939i | 0.685285 | − | 0.728275i | \(-0.259678\pi\) |
−0.973347 | + | 0.229336i | \(0.926344\pi\) | |||||||
\(114\) | 2485.37 | − | 277.464i | 2.04190 | − | 0.227955i | ||||
\(115\) | −2764.02 | − | 1595.81i | −2.24127 | − | 1.29400i | ||||
\(116\) | 5317.47 | + | 3070.05i | 4.25616 | + | 2.45730i | ||||
\(117\) | 186.427 | + | 824.549i | 0.147309 | + | 0.651535i | ||||
\(118\) | 1499.17 | + | 865.547i | 1.16958 | + | 0.675255i | ||||
\(119\) | −900.600 | −0.693764 | ||||||||
\(120\) | −2654.28 | + | 6066.77i | −2.01918 | + | 4.61515i | ||||
\(121\) | 602.786 | − | 1044.06i | 0.452882 | − | 0.784415i | ||||
\(122\) | −337.223 | + | 194.696i | −0.250252 | + | 0.144483i | ||||
\(123\) | 252.718 | − | 28.2131i | 0.185258 | − | 0.0206820i | ||||
\(124\) | −3055.73 | − | 1764.23i | −2.21300 | − | 1.27768i | ||||
\(125\) | −2974.17 | −2.12814 | ||||||||
\(126\) | −2779.31 | + | 2568.27i | −1.96508 | + | 1.81587i | ||||
\(127\) | 85.1449 | + | 147.475i | 0.0594912 | + | 0.103042i | 0.894237 | − | 0.447593i | \(-0.147719\pi\) |
−0.834746 | + | 0.550635i | \(0.814385\pi\) | |||||||
\(128\) | −547.347 | + | 948.033i | −0.377962 | + | 0.654649i | ||||
\(129\) | −279.881 | − | 122.451i | −0.191025 | − | 0.0835755i | ||||
\(130\) | −2868.13 | + | 1655.92i | −1.93501 | + | 1.11718i | ||||
\(131\) | 1503.32i | 1.00264i | 0.865263 | + | 0.501318i | \(0.167151\pi\) | ||||
−0.865263 | + | 0.501318i | \(0.832849\pi\) | |||||||
\(132\) | −691.838 | − | 939.413i | −0.456188 | − | 0.619435i | ||||
\(133\) | 2404.98i | 1.56796i | ||||||||
\(134\) | 1196.71 | + | 2646.45i | 0.771493 | + | 1.70611i | ||||
\(135\) | 2647.68 | − | 917.368i | 1.68797 | − | 0.584848i | ||||
\(136\) | 1880.47 | + | 1085.69i | 1.18566 | + | 0.684539i | ||||
\(137\) | 1624.81 | 1.01326 | 0.506632 | − | 0.862162i | \(-0.330890\pi\) | ||||
0.506632 | + | 0.862162i | \(0.330890\pi\) | |||||||
\(138\) | 487.902 | + | 4370.36i | 0.300963 | + | 2.69587i | ||||
\(139\) | 3082.76i | 1.88112i | 0.339622 | + | 0.940562i | \(0.389701\pi\) | ||||
−0.339622 | + | 0.940562i | \(0.610299\pi\) | |||||||
\(140\) | −9177.12 | − | 5298.41i | −5.54006 | − | 3.19855i | ||||
\(141\) | −43.4552 | − | 389.248i | −0.0259545 | − | 0.232486i | ||||
\(142\) | 790.213i | 0.466995i | ||||||||
\(143\) | − | 350.651i | − | 0.205055i | ||||||
\(144\) | 4675.59 | − | 1057.13i | 2.70578 | − | 0.611765i | ||||
\(145\) | 5297.50 | − | 3058.51i | 3.03402 | − | 1.75169i | ||||
\(146\) | −561.963 | − | 973.348i | −0.318551 | − | 0.551746i | ||||
\(147\) | −1101.18 | − | 1495.24i | −0.617848 | − | 0.838946i | ||||
\(148\) | −690.131 | −0.383300 | ||||||||
\(149\) | − | 1443.40i | − | 0.793609i | −0.917903 | − | 0.396805i | \(-0.870119\pi\) | ||
0.917903 | − | 0.396805i | \(-0.129881\pi\) | |||||||
\(150\) | 4469.89 | + | 6069.44i | 2.43310 | + | 3.30379i | ||||
\(151\) | 1685.28 | − | 2919.00i | 0.908255 | − | 1.57314i | 0.0917667 | − | 0.995781i | \(-0.470749\pi\) |
0.816488 | − | 0.577363i | \(-0.195918\pi\) | |||||||
\(152\) | 2899.26 | − | 5021.66i | 1.54711 | − | 2.67967i | ||||
\(153\) | −202.627 | − | 896.200i | −0.107068 | − | 0.473552i | ||||
\(154\) | 1359.39 | − | 784.843i | 0.711315 | − | 0.410678i | ||||
\(155\) | −3044.25 | + | 1757.60i | −1.57755 | + | 0.910798i | ||||
\(156\) | 2988.14 | + | 1307.35i | 1.53361 | + | 0.670972i | ||||
\(157\) | −137.831 | + | 238.730i | −0.0700643 | + | 0.121355i | −0.898929 | − | 0.438094i | \(-0.855654\pi\) |
0.828865 | + | 0.559449i | \(0.188987\pi\) | |||||||
\(158\) | − | 511.593i | − | 0.257596i | ||||||
\(159\) | −977.460 | + | 2234.13i | −0.487532 | + | 1.11433i | ||||
\(160\) | 4292.22 | + | 7434.34i | 2.12081 | + | 3.67335i | ||||
\(161\) | −4229.00 | −2.07014 | ||||||||
\(162\) | −3181.05 | − | 2187.89i | −1.54276 | − | 1.06109i | ||||
\(163\) | 408.772 | + | 708.014i | 0.196426 | + | 0.340221i | 0.947367 | − | 0.320149i | \(-0.103733\pi\) |
−0.750941 | + | 0.660370i | \(0.770400\pi\) | |||||||
\(164\) | 490.553 | − | 849.663i | 0.233572 | − | 0.404558i | ||||
\(165\) | −1155.12 | + | 128.956i | −0.545005 | + | 0.0608438i | ||||
\(166\) | −5206.21 | + | 3005.81i | −2.43422 | + | 1.40540i | ||||
\(167\) | 1748.21 | − | 1009.33i | 0.810063 | − | 0.467690i | −0.0369147 | − | 0.999318i | \(-0.511753\pi\) |
0.846978 | + | 0.531628i | \(0.178420\pi\) | |||||||
\(168\) | 973.514 | + | 8720.20i | 0.447073 | + | 4.00463i | ||||
\(169\) | −608.352 | − | 1053.70i | −0.276901 | − | 0.479607i | ||||
\(170\) | 3117.36 | − | 1799.81i | 1.40642 | − | 0.811995i | ||||
\(171\) | −2393.23 | + | 541.100i | −1.07026 | + | 0.241982i | ||||
\(172\) | −1020.77 | + | 589.341i | −0.452517 | + | 0.261261i | ||||
\(173\) | −181.311 | − | 104.680i | −0.0796811 | − | 0.0460039i | 0.459630 | − | 0.888110i | \(-0.347982\pi\) |
−0.539311 | + | 0.842107i | \(0.681315\pi\) | |||||||
\(174\) | −7721.53 | − | 3378.26i | −3.36418 | − | 1.47187i | ||||
\(175\) | −6277.77 | + | 3624.47i | −2.71174 | + | 1.56562i | ||||
\(176\) | −1988.36 | −0.851581 | ||||||||
\(177\) | −1556.04 | − | 680.783i | −0.660784 | − | 0.289101i | ||||
\(178\) | 1610.41 | + | 929.770i | 0.678120 | + | 0.391513i | ||||
\(179\) | 134.646 | 0.0562231 | 0.0281116 | − | 0.999605i | \(-0.491051\pi\) | ||||
0.0281116 | + | 0.999605i | \(0.491051\pi\) | |||||||
\(180\) | 3207.76 | − | 10324.4i | 1.32829 | − | 4.27519i | ||||
\(181\) | −970.249 | − | 1680.52i | −0.398442 | − | 0.690122i | 0.595092 | − | 0.803658i | \(-0.297116\pi\) |
−0.993534 | + | 0.113536i | \(0.963782\pi\) | |||||||
\(182\) | −2194.14 | + | 3800.37i | −0.893630 | + | 1.54781i | ||||
\(183\) | 307.625 | − | 226.553i | 0.124264 | − | 0.0915152i | ||||
\(184\) | 8830.25 | + | 5098.15i | 3.53791 | + | 2.04261i | ||||
\(185\) | −343.769 | + | 595.426i | −0.136618 | + | 0.236630i | ||||
\(186\) | 4437.24 | + | 1941.35i | 1.74922 | + | 0.765303i | ||||
\(187\) | 381.122i | 0.149039i | ||||||||
\(188\) | −1308.69 | − | 755.574i | −0.507693 | − | 0.293116i | ||||
\(189\) | 2430.47 | − | 2806.82i | 0.935402 | − | 1.08024i | ||||
\(190\) | −4806.25 | − | 8324.68i | −1.83517 | − | 3.17861i | ||||
\(191\) | −1075.63 | + | 1863.05i | −0.407488 | + | 0.705789i | −0.994608 | − | 0.103711i | \(-0.966928\pi\) |
0.587120 | + | 0.809500i | \(0.300262\pi\) | |||||||
\(192\) | 1782.74 | − | 4074.73i | 0.670095 | − | 1.53161i | ||||
\(193\) | 1374.61 | 0.512676 | 0.256338 | − | 0.966587i | \(-0.417484\pi\) | ||||
0.256338 | + | 0.966587i | \(0.417484\pi\) | |||||||
\(194\) | −5559.39 | + | 3209.71i | −2.05743 | + | 1.18786i | ||||
\(195\) | 2616.40 | − | 1926.87i | 0.960843 | − | 0.707620i | ||||
\(196\) | −7164.65 | −2.61103 | ||||||||
\(197\) | 1745.11 | + | 3022.62i | 0.631136 | + | 1.09316i | 0.987320 | + | 0.158744i | \(0.0507445\pi\) |
−0.356183 | + | 0.934416i | \(0.615922\pi\) | |||||||
\(198\) | 1086.86 | + | 1176.16i | 0.390099 | + | 0.422153i | ||||
\(199\) | 1259.49 | − | 2181.51i | 0.448659 | − | 0.777099i | −0.549640 | − | 0.835401i | \(-0.685235\pi\) |
0.998299 | + | 0.0583019i | \(0.0185686\pi\) | |||||||
\(200\) | 17477.5 | 6.17923 | ||||||||
\(201\) | −1454.97 | − | 2450.23i | −0.510577 | − | 0.859832i | ||||
\(202\) | 4773.34 | 1.66263 | ||||||||
\(203\) | 4052.63 | − | 7019.36i | 1.40118 | − | 2.42691i | ||||
\(204\) | −3247.81 | − | 1420.95i | −1.11467 | − | 0.487680i | ||||
\(205\) | −488.710 | − | 846.470i | −0.166502 | − | 0.288391i | ||||
\(206\) | −6719.21 | −2.27257 | ||||||||
\(207\) | −951.487 | − | 4208.34i | −0.319483 | − | 1.41304i | ||||
\(208\) | 4814.02 | − | 2779.37i | 1.60477 | − | 0.926514i | ||||
\(209\) | 1017.76 | 0.336840 | ||||||||
\(210\) | 13326.1 | + | 5830.34i | 4.37901 | + | 1.91587i | ||||
\(211\) | −485.474 | + | 840.866i | −0.158395 | + | 0.274349i | −0.934290 | − | 0.356514i | \(-0.883965\pi\) |
0.775895 | + | 0.630862i | \(0.217299\pi\) | |||||||
\(212\) | 4704.38 | + | 8148.22i | 1.52405 | + | 2.63973i | ||||
\(213\) | −86.0202 | − | 770.522i | −0.0276714 | − | 0.247865i | ||||
\(214\) | 785.517 | + | 453.519i | 0.250920 | + | 0.144869i | ||||
\(215\) | 1174.25i | 0.372481i | ||||||||
\(216\) | −8458.57 | + | 2930.73i | −2.66450 | + | 0.923197i | ||||
\(217\) | −2328.88 | + | 4033.73i | −0.728545 | + | 1.26188i | ||||
\(218\) | −8410.94 | − | 4856.06i | −2.61312 | − | 1.50869i | ||||
\(219\) | 653.915 | + | 887.920i | 0.201769 | + | 0.273973i | ||||
\(220\) | −2242.21 | + | 3883.63i | −0.687137 | + | 1.19016i | ||||
\(221\) | −532.741 | − | 922.734i | −0.162154 | − | 0.280859i | ||||
\(222\) | 941.462 | − | 105.104i | 0.284625 | − | 0.0317752i | ||||
\(223\) | 2852.91 | 0.856703 | 0.428351 | − | 0.903612i | \(-0.359095\pi\) | ||||
0.428351 | + | 0.903612i | \(0.359095\pi\) | |||||||
\(224\) | 9850.75 | + | 5687.33i | 2.93831 | + | 1.69643i | ||||
\(225\) | −5019.20 | − | 5431.62i | −1.48717 | − | 1.60937i | ||||
\(226\) | 3665.10 | 1.07876 | ||||||||
\(227\) | 2765.82 | − | 1596.85i | 0.808696 | − | 0.466901i | −0.0378066 | − | 0.999285i | \(-0.512037\pi\) |
0.846503 | + | 0.532384i | \(0.178704\pi\) | |||||||
\(228\) | −3794.54 | + | 8673.01i | −1.10219 | + | 2.51923i | ||||
\(229\) | 1046.97 | + | 604.467i | 0.302120 | + | 0.174429i | 0.643395 | − | 0.765534i | \(-0.277525\pi\) |
−0.341275 | + | 0.939964i | \(0.610859\pi\) | |||||||
\(230\) | 14638.4 | − | 8451.48i | 4.19664 | − | 2.42293i | ||||
\(231\) | −1240.08 | + | 913.264i | −0.353208 | + | 0.260123i | ||||
\(232\) | −16924.0 | + | 9771.05i | −4.78928 | + | 2.76509i | ||||
\(233\) | 264.135 | + | 457.496i | 0.0742664 | + | 0.128633i | 0.900767 | − | 0.434303i | \(-0.143005\pi\) |
−0.826501 | + | 0.562936i | \(0.809672\pi\) | |||||||
\(234\) | −4275.46 | − | 1328.37i | −1.19443 | − | 0.371105i | ||||
\(235\) | −1303.78 | + | 752.735i | −0.361910 | + | 0.208949i | ||||
\(236\) | −5675.09 | + | 3276.51i | −1.56533 | + | 0.903741i | ||||
\(237\) | 55.6905 | + | 498.845i | 0.0152637 | + | 0.136723i | ||||
\(238\) | 2384.81 | − | 4130.61i | 0.649514 | − | 1.12499i | ||||
\(239\) | −819.001 | − | 1418.55i | −0.221660 | − | 0.383927i | 0.733652 | − | 0.679525i | \(-0.237814\pi\) |
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(240\) | −10926.3 | − | 14836.3i | −2.93870 | − | 3.99032i | ||||
\(241\) | 4839.72 | 1.29358 | 0.646792 | − | 0.762667i | \(-0.276110\pi\) | ||||
0.646792 | + | 0.762667i | \(0.276110\pi\) | |||||||
\(242\) | 3192.38 | + | 5529.37i | 0.847992 | + | 1.46877i | ||||
\(243\) | 3339.94 | + | 1787.09i | 0.881718 | + | 0.471777i | ||||
\(244\) | − | 1474.03i | − | 0.386743i | ||||||
\(245\) | −3568.87 | + | 6181.46i | −0.930639 | + | 1.61191i | ||||
\(246\) | −539.802 | + | 1233.80i | −0.139905 | + | 0.319773i | ||||
\(247\) | −2464.09 | + | 1422.64i | −0.634762 | + | 0.366480i | ||||
\(248\) | 9725.49 | − | 5615.02i | 2.49020 | − | 1.43772i | ||||
\(249\) | 4749.28 | − | 3497.64i | 1.20873 | − | 0.890176i | ||||
\(250\) | 7875.66 | − | 13641.0i | 1.99240 | − | 3.45094i | ||||
\(251\) | −3264.94 | + | 5655.04i | −0.821040 | + | 1.42208i | 0.0838690 | + | 0.996477i | \(0.473272\pi\) |
−0.904909 | + | 0.425606i | \(0.860061\pi\) | |||||||
\(252\) | −3159.13 | − | 13972.5i | −0.789709 | − | 3.49281i | ||||
\(253\) | 1789.65i | 0.444722i | ||||||||
\(254\) | −901.862 | −0.222787 | ||||||||
\(255\) | −2843.76 | + | 2094.31i | −0.698366 | + | 0.514316i | ||||
\(256\) | 525.027 | + | 909.374i | 0.128181 | + | 0.222015i | ||||
\(257\) | 1270.71 | − | 733.648i | 0.308424 | − | 0.178069i | −0.337797 | − | 0.941219i | \(-0.609682\pi\) |
0.646221 | + | 0.763150i | \(0.276348\pi\) | |||||||
\(258\) | 1302.76 | − | 959.425i | 0.314365 | − | 0.231516i | ||||
\(259\) | 911.011i | 0.218562i | ||||||||
\(260\) | − | 12536.9i | − | 2.99040i | ||||||
\(261\) | 7896.87 | + | 2453.54i | 1.87281 | + | 0.581877i | ||||
\(262\) | −6894.97 | − | 3980.81i | −1.62585 | − | 0.938685i | ||||
\(263\) | − | 1224.64i | − | 0.287126i | −0.989641 | − | 0.143563i | \(-0.954144\pi\) | ||
0.989641 | − | 0.143563i | \(-0.0458560\pi\) | |||||||
\(264\) | 3690.27 | − | 411.978i | 0.860304 | − | 0.0960434i | ||||
\(265\) | 9373.40 | 2.17284 | ||||||||
\(266\) | −11030.5 | − | 6368.45i | −2.54256 | − | 1.46795i | ||||
\(267\) | −1671.49 | − | 731.297i | −0.383122 | − | 0.167620i | ||||
\(268\) | −10941.0 | − | 1085.85i | −2.49376 | − | 0.247495i | ||||
\(269\) | 6608.27i | 1.49782i | 0.662672 | + | 0.748910i | \(0.269422\pi\) | ||||
−0.662672 | + | 0.748910i | \(0.730578\pi\) | |||||||
\(270\) | −2803.60 | + | 14572.8i | −0.631931 | + | 3.28472i | ||||
\(271\) | − | 1851.85i | − | 0.415098i | −0.978225 | − | 0.207549i | \(-0.933451\pi\) | ||
0.978225 | − | 0.207549i | \(-0.0665487\pi\) | |||||||
\(272\) | −5232.35 | + | 3020.90i | −1.16639 | + | 0.673415i | ||||
\(273\) | 1725.77 | − | 3944.51i | 0.382595 | − | 0.874479i | ||||
\(274\) | −4302.54 | + | 7452.22i | −0.948635 | + | 1.64308i | ||||
\(275\) | 1533.83 | + | 2656.66i | 0.336339 | + | 0.582556i | ||||
\(276\) | −15250.9 | − | 6672.45i | −3.32608 | − | 1.45520i | ||||
\(277\) | −1095.88 | −0.237708 | −0.118854 | − | 0.992912i | \(-0.537922\pi\) | ||||
−0.118854 | + | 0.992912i | \(0.537922\pi\) | |||||||
\(278\) | −14139.1 | − | 8163.22i | −3.05039 | − | 1.76114i | ||||
\(279\) | −4538.00 | − | 1409.94i | −0.973774 | − | 0.302549i | ||||
\(280\) | 29208.1 | − | 16863.3i | 6.23399 | − | 3.59920i | ||||
\(281\) | −2100.12 | + | 3637.52i | −0.445847 | + | 0.772229i | −0.998111 | − | 0.0614402i | \(-0.980431\pi\) |
0.552264 | + | 0.833669i | \(0.313764\pi\) | |||||||
\(282\) | 1900.36 | + | 831.429i | 0.401294 | + | 0.175571i | ||||
\(283\) | −7421.06 | −1.55879 | −0.779393 | − | 0.626535i | \(-0.784472\pi\) | ||||
−0.779393 | + | 0.626535i | \(0.784472\pi\) | |||||||
\(284\) | −2590.58 | − | 1495.67i | −0.541276 | − | 0.312506i | ||||
\(285\) | 5592.69 | + | 7594.04i | 1.16239 | + | 1.57836i | ||||
\(286\) | 1608.26 | + | 928.531i | 0.332512 | + | 0.191976i | ||||
\(287\) | −1121.60 | − | 647.557i | −0.230683 | − | 0.133185i | ||||
\(288\) | −3443.22 | + | 11082.2i | −0.704491 | + | 2.26745i | ||||
\(289\) | −1877.47 | − | 3251.87i | −0.382142 | − | 0.661890i | ||||
\(290\) | 32396.0i | 6.55986i | ||||||||
\(291\) | 5071.45 | − | 3734.91i | 1.02163 | − | 0.752386i | ||||
\(292\) | 4254.60 | 0.852677 | ||||||||
\(293\) | 4841.97i | 0.965431i | 0.875777 | + | 0.482715i | \(0.160349\pi\) | ||||
−0.875777 | + | 0.482715i | \(0.839651\pi\) | |||||||
\(294\) | 9773.86 | − | 1091.14i | 1.93885 | − | 0.216452i | ||||
\(295\) | 6528.41i | 1.28847i | ||||||||
\(296\) | 1098.24 | − | 1902.21i | 0.215656 | − | 0.373527i | ||||
\(297\) | −1187.81 | − | 1028.54i | −0.232066 | − | 0.200950i | ||||
\(298\) | 6620.16 | + | 3822.15i | 1.28690 | + | 0.742991i | ||||
\(299\) | −2501.62 | − | 4332.93i | −0.483854 | − | 0.838061i | ||||
\(300\) | −28357.9 | + | 3165.85i | −5.45749 | + | 0.609268i | ||||
\(301\) | 777.963 | + | 1347.47i | 0.148974 | + | 0.258030i | ||||
\(302\) | 8925.34 | + | 15459.1i | 1.70065 | + | 2.94561i | ||||
\(303\) | −4654.39 | + | 519.611i | −0.882468 | + | 0.0985178i | ||||
\(304\) | 8067.07 | + | 13972.6i | 1.52197 | + | 2.63612i | ||||
\(305\) | −1271.75 | − | 734.248i | −0.238756 | − | 0.137846i | ||||
\(306\) | 4646.99 | + | 1443.81i | 0.868140 | + | 0.269729i | ||||
\(307\) | −833.560 | + | 1443.77i | −0.154963 | + | 0.268405i | −0.933046 | − | 0.359758i | \(-0.882859\pi\) |
0.778082 | + | 0.628162i | \(0.216193\pi\) | |||||||
\(308\) | 5942.02i | 1.09928i | ||||||||
\(309\) | 6551.77 | − | 731.432i | 1.20620 | − | 0.134659i | ||||
\(310\) | − | 18616.6i | − | 3.41082i | ||||||
\(311\) | 7209.90 | 1.31459 | 0.657293 | − | 0.753635i | \(-0.271701\pi\) | ||||
0.657293 | + | 0.753635i | \(0.271701\pi\) | |||||||
\(312\) | −8358.64 | + | 6155.78i | −1.51671 | + | 1.11700i | ||||
\(313\) | − | 1732.91i | − | 0.312939i | −0.987683 | − | 0.156469i | \(-0.949989\pi\) | ||
0.987683 | − | 0.156469i | \(-0.0500113\pi\) | |||||||
\(314\) | −729.958 | − | 1264.32i | −0.131191 | − | 0.227229i | ||||
\(315\) | −13628.7 | − | 4234.41i | −2.43775 | − | 0.757404i | ||||
\(316\) | 1677.17 | + | 968.314i | 0.298570 | + | 0.172379i | ||||
\(317\) | −487.567 | − | 281.497i | −0.0863864 | − | 0.0498752i | 0.456185 | − | 0.889885i | \(-0.349216\pi\) |
−0.542571 | + | 0.840010i | \(0.682549\pi\) | |||||||
\(318\) | −7658.54 | − | 10399.2i | −1.35053 | − | 1.83382i | ||||
\(319\) | −2970.49 | − | 1715.02i | −0.521366 | − | 0.301011i | ||||
\(320\) | −17095.7 | −2.98650 | ||||||||
\(321\) | −815.311 | − | 356.708i | −0.141764 | − | 0.0620234i | ||||
\(322\) | 11198.5 | − | 19396.4i | 1.93810 | − | 3.35688i | ||||
\(323\) | 2678.21 | − | 1546.27i | 0.461361 | − | 0.266367i | ||||
\(324\) | 13193.5 | − | 6287.39i | 2.26226 | − | 1.07809i | ||||
\(325\) | −7427.09 | − | 4288.03i | −1.26763 | − | 0.731869i | ||||
\(326\) | −4329.75 | −0.735591 | ||||||||
\(327\) | 8729.96 | + | 3819.46i | 1.47636 | + | 0.645923i | ||||
\(328\) | 1561.29 | + | 2704.23i | 0.262828 | + | 0.455232i | ||||
\(329\) | −997.399 | + | 1727.55i | −0.167138 | + | 0.289491i | ||||
\(330\) | 2467.32 | − | 5639.44i | 0.411580 | − | 0.940730i | ||||
\(331\) | −8007.32 | + | 4623.03i | −1.32967 | + | 0.767688i | −0.985249 | − | 0.171126i | \(-0.945259\pi\) |
−0.344425 | + | 0.938814i | \(0.611926\pi\) | |||||||
\(332\) | − | 22756.9i | − | 3.76189i | ||||||
\(333\) | −906.560 | + | 204.969i | −0.149187 | + | 0.0337305i | ||||
\(334\) | 10690.9i | 1.75144i | ||||||||
\(335\) | −6386.78 | + | 8898.69i | −1.04163 | + | 1.45131i | ||||
\(336\) | −22367.3 | − | 9785.95i | −3.63165 | − | 1.58889i | ||||
\(337\) | 5120.31 | + | 2956.21i | 0.827659 | + | 0.477849i | 0.853050 | − | 0.521829i | \(-0.174750\pi\) |
−0.0253916 | + | 0.999678i | \(0.508083\pi\) | |||||||
\(338\) | 6443.72 | 1.03696 | ||||||||
\(339\) | −3573.77 | + | 398.972i | −0.572568 | + | 0.0639209i | ||||
\(340\) | 13626.3i | 2.17350i | ||||||||
\(341\) | 1707.02 | + | 985.548i | 0.271086 | + | 0.156511i | ||||
\(342\) | 3855.57 | − | 12409.4i | 0.609607 | − | 1.96206i | ||||
\(343\) | 380.388i | 0.0598806i | ||||||||
\(344\) | − | 3751.40i | − | 0.587971i | ||||||
\(345\) | −13353.6 | + | 9834.37i | −2.08387 | + | 1.53468i | ||||
\(346\) | 960.232 | − | 554.390i | 0.149198 | − | 0.0861393i | ||||
\(347\) | −1974.70 | − | 3420.28i | −0.305497 | − | 0.529136i | 0.671875 | − | 0.740665i | \(-0.265489\pi\) |
−0.977372 | + | 0.211528i | \(0.932156\pi\) | |||||||
\(348\) | 25689.9 | − | 18919.5i | 3.95725 | − | 2.91435i | ||||
\(349\) | 7980.53 | 1.22403 | 0.612017 | − | 0.790844i | \(-0.290358\pi\) | ||||
0.612017 | + | 0.790844i | \(0.290358\pi\) | |||||||
\(350\) | − | 38390.7i | − | 5.86306i | ||||||
\(351\) | 4313.52 | + | 829.859i | 0.655951 | + | 0.126195i | ||||
\(352\) | 2406.80 | − | 4168.70i | 0.364440 | − | 0.631229i | ||||
\(353\) | 4612.86 | − | 7989.70i | 0.695517 | − | 1.20467i | −0.274489 | − | 0.961590i | \(-0.588509\pi\) |
0.970006 | − | 0.243081i | \(-0.0781580\pi\) | |||||||
\(354\) | 7242.83 | − | 5334.04i | 1.08744 | − | 0.800850i | ||||
\(355\) | −2580.84 | + | 1490.05i | −0.385850 | + | 0.222771i | ||||
\(356\) | −6096.18 | + | 3519.63i | −0.907575 | + | 0.523989i | ||||
\(357\) | −1875.74 | + | 4287.28i | −0.278080 | + | 0.635594i | ||||
\(358\) | −356.546 | + | 617.556i | −0.0526370 | + | 0.0911700i | ||||
\(359\) | − | 939.431i | − | 0.138109i | −0.997613 | − | 0.0690547i | \(-0.978002\pi\) | ||
0.997613 | − | 0.0690547i | \(-0.0219983\pi\) | |||||||
\(360\) | 23352.5 | + | 25271.3i | 3.41884 | + | 3.69976i | ||||
\(361\) | −699.684 | − | 1211.89i | −0.102010 | − | 0.176686i | ||||
\(362\) | 10277.0 | 1.49211 | ||||||||
\(363\) | −3714.74 | − | 5044.07i | −0.537117 | − | 0.729325i | ||||
\(364\) | −8305.89 | − | 14386.2i | −1.19601 | − | 2.07155i | ||||
\(365\) | 2119.31 | − | 3670.75i | 0.303917 | − | 0.526399i | ||||
\(366\) | 224.488 | + | 2010.84i | 0.0320606 | + | 0.287182i | ||||
\(367\) | 8964.74 | − | 5175.79i | 1.27508 | − | 0.736169i | 0.299143 | − | 0.954208i | \(-0.403299\pi\) |
0.975940 | + | 0.218039i | \(0.0699660\pi\) | |||||||
\(368\) | −24569.8 | + | 14185.4i | −3.48041 | + | 2.00942i | ||||
\(369\) | 392.043 | − | 1261.82i | 0.0553088 | − | 0.178015i | ||||
\(370\) | −1820.62 | − | 3153.40i | −0.255809 | − | 0.443074i | ||||
\(371\) | 10756.1 | − | 6210.04i | 1.50520 | − | 0.869027i | ||||
\(372\) | −14762.9 | + | 10872.3i | −2.05758 | + | 1.51532i | ||||
\(373\) | −1260.00 | + | 727.463i | −0.174907 | + | 0.100983i | −0.584898 | − | 0.811107i | \(-0.698865\pi\) |
0.409990 | + | 0.912090i | \(0.365532\pi\) | |||||||
\(374\) | −1748.02 | − | 1009.22i | −0.241679 | − | 0.139533i | ||||
\(375\) | −6194.48 | + | 14158.4i | −0.853018 | + | 1.94970i | ||||
\(376\) | 4165.18 | − | 2404.77i | 0.571285 | − | 0.329831i | ||||
\(377\) | 9589.16 | 1.30999 | ||||||||
\(378\) | 6437.57 | + | 18579.9i | 0.875960 | + | 2.52817i | ||||
\(379\) | 3877.18 | + | 2238.49i | 0.525481 | + | 0.303387i | 0.739174 | − | 0.673514i | \(-0.235216\pi\) |
−0.213693 | + | 0.976901i | \(0.568549\pi\) | |||||||
\(380\) | 36388.0 | 4.91227 | ||||||||
\(381\) | 879.388 | − | 98.1740i | 0.118248 | − | 0.0132011i | ||||
\(382\) | −5696.61 | − | 9866.81i | −0.762994 | − | 1.32154i | ||||
\(383\) | 102.787 | − | 178.032i | 0.0137132 | − | 0.0237520i | −0.859087 | − | 0.511829i | \(-0.828968\pi\) |
0.872801 | + | 0.488077i | \(0.162301\pi\) | |||||||
\(384\) | 3373.09 | + | 4580.16i | 0.448262 | + | 0.608673i | ||||
\(385\) | 5126.60 | + | 2959.85i | 0.678639 | + | 0.391812i | ||||
\(386\) | −3639.99 | + | 6304.66i | −0.479976 | + | 0.831343i | ||||
\(387\) | −1165.85 | + | 1077.33i | −0.153136 | + | 0.141509i | ||||
\(388\) | − | 24300.6i | − | 3.17958i | ||||||
\(389\) | 4985.17 | + | 2878.19i | 0.649764 | + | 0.375141i | 0.788366 | − | 0.615207i | \(-0.210927\pi\) |
−0.138602 | + | 0.990348i | \(0.544261\pi\) | |||||||
\(390\) | 1909.31 | + | 17102.5i | 0.247901 | + | 2.22057i | ||||
\(391\) | 2719.01 | + | 4709.46i | 0.351678 | + | 0.609124i | ||||
\(392\) | 11401.5 | − | 19748.0i | 1.46904 | − | 2.54445i | ||||
\(393\) | 7156.49 | + | 3131.05i | 0.918568 | + | 0.401884i | ||||
\(394\) | −18484.3 | −2.36352 | ||||||||
\(395\) | 1670.87 | − | 964.675i | 0.212837 | − | 0.122881i | ||||
\(396\) | −5912.99 | + | 1336.90i | −0.750350 | + | 0.169651i | ||||
\(397\) | 949.009 | 0.119973 | 0.0599867 | − | 0.998199i | \(-0.480894\pi\) | ||||
0.0599867 | + | 0.998199i | \(0.480894\pi\) | |||||||
\(398\) | 6670.33 | + | 11553.3i | 0.840084 | + | 1.45507i | ||||
\(399\) | 11448.9 | + | 5009.01i | 1.43649 | + | 0.628481i | ||||
\(400\) | −24315.2 | + | 42115.2i | −3.03940 | + | 5.26440i | ||||
\(401\) | −5215.21 | −0.649464 | −0.324732 | − | 0.945806i | \(-0.605274\pi\) | ||||
−0.324732 | + | 0.945806i | \(0.605274\pi\) | |||||||
\(402\) | 15090.8 | − | 184.976i | 1.87229 | − | 0.0229496i | ||||
\(403\) | −5510.49 | −0.681134 | ||||||||
\(404\) | −9034.70 | + | 15648.6i | −1.11261 | + | 1.92709i | ||||
\(405\) | 1147.38 | − | 14514.9i | 0.140775 | − | 1.78086i | ||||
\(406\) | 21462.9 | + | 37174.8i | 2.62361 | + | 4.54423i | ||||
\(407\) | 385.527 | 0.0469530 | ||||||||
\(408\) | 9084.99 | − | 6690.71i | 1.10239 | − | 0.811861i | ||||
\(409\) | −7915.11 | + | 4569.79i | −0.956912 | + | 0.552473i | −0.895221 | − | 0.445622i | \(-0.852982\pi\) |
−0.0616904 | + | 0.998095i | \(0.519649\pi\) | |||||||
\(410\) | 5176.46 | 0.623529 | ||||||||
\(411\) | 3384.10 | − | 7734.88i | 0.406144 | − | 0.928305i | ||||
\(412\) | 12717.7 | − | 22027.7i | 1.52077 | − | 2.63405i | ||||
\(413\) | 4325.18 | + | 7491.43i | 0.515322 | + | 0.892565i | ||||
\(414\) | 21821.1 | + | 6779.77i | 2.59046 | + | 0.804849i | ||||
\(415\) | −19634.0 | − | 11335.7i | −2.32240 | − | 1.34084i | ||||
\(416\) | 13457.1i | 1.58603i | ||||||||
\(417\) | 14675.4 | + | 6420.66i | 1.72340 | + | 0.754007i | ||||
\(418\) | −2695.04 | + | 4667.94i | −0.315356 | + | 0.546212i | ||||
\(419\) | −11894.5 | − | 6867.31i | −1.38684 | − | 0.800692i | −0.393881 | − | 0.919161i | \(-0.628868\pi\) |
−0.992958 | + | 0.118469i | \(0.962201\pi\) | |||||||
\(420\) | −44336.7 | + | 32652.1i | −5.15098 | + | 3.79347i | ||||
\(421\) | −4693.20 | + | 8128.86i | −0.543308 | + | 0.941037i | 0.455403 | + | 0.890285i | \(0.349495\pi\) |
−0.998711 | + | 0.0507518i | \(0.983838\pi\) | |||||||
\(422\) | −2571.09 | − | 4453.26i | −0.296585 | − | 0.513700i | ||||
\(423\) | −1943.51 | − | 603.844i | −0.223397 | − | 0.0694087i | ||||
\(424\) | −29945.3 | −3.42989 | ||||||||
\(425\) | 8072.49 | + | 4660.66i | 0.921349 | + | 0.531941i | ||||
\(426\) | 3761.79 | + | 1645.83i | 0.427839 | + | 0.187184i | ||||
\(427\) | −1945.81 | −0.220525 | ||||||||
\(428\) | −2973.56 | + | 1716.79i | −0.335824 | + | 0.193888i | ||||
\(429\) | −1669.26 | − | 730.322i | −0.187862 | − | 0.0821918i | ||||
\(430\) | −5385.73 | − | 3109.45i | −0.604007 | − | 0.348723i | ||||
\(431\) | −6747.28 | + | 3895.54i | −0.754072 | + | 0.435364i | −0.827163 | − | 0.561962i | \(-0.810047\pi\) |
0.0730914 | + | 0.997325i | \(0.476714\pi\) | |||||||
\(432\) | 4705.70 | − | 24459.8i | 0.524081 | − | 2.72412i | ||||
\(433\) | 12982.6 | − | 7495.52i | 1.44089 | − | 0.831897i | 0.442979 | − | 0.896532i | \(-0.353921\pi\) |
0.997909 | + | 0.0646345i | \(0.0205882\pi\) | |||||||
\(434\) | −12333.8 | − | 21362.8i | −1.36415 | − | 2.36278i | ||||
\(435\) | −3526.53 | − | 31588.7i | −0.388699 | − | 3.48176i | ||||
\(436\) | 31839.5 | − | 18382.5i | 3.49733 | − | 2.01918i | ||||
\(437\) | 12576.2 | − | 7260.89i | 1.37667 | − | 0.794819i | ||||
\(438\) | −5804.03 | + | 647.956i | −0.633168 | + | 0.0706861i | ||||
\(439\) | −2704.02 | + | 4683.50i | −0.293977 | + | 0.509182i | −0.974746 | − | 0.223315i | \(-0.928312\pi\) |
0.680770 | + | 0.732497i | \(0.261645\pi\) | |||||||
\(440\) | −7136.31 | − | 12360.5i | −0.773205 | − | 1.33923i | ||||
\(441\) | −9411.53 | + | 2127.91i | −1.01625 | + | 0.229771i | ||||
\(442\) | 5642.84 | 0.607245 | ||||||||
\(443\) | −4965.16 | − | 8599.92i | −0.532510 | − | 0.922335i | −0.999279 | − | 0.0379558i | \(-0.987915\pi\) |
0.466769 | − | 0.884379i | \(-0.345418\pi\) | |||||||
\(444\) | −1437.38 | + | 3285.35i | −0.153637 | + | 0.351162i | ||||
\(445\) | 7012.81i | 0.747054i | ||||||||
\(446\) | −7554.56 | + | 13084.9i | −0.802060 | + | 1.38921i | ||||
\(447\) | −6871.26 | − | 3006.26i | −0.727068 | − | 0.318101i | ||||
\(448\) | −19617.5 | + | 11326.2i | −2.06884 | + | 1.19445i | ||||
\(449\) | −352.889 | + | 203.741i | −0.0370910 | + | 0.0214145i | −0.518431 | − | 0.855120i | \(-0.673484\pi\) |
0.481340 | + | 0.876534i | \(0.340150\pi\) | |||||||
\(450\) | 38203.1 | − | 8637.56i | 4.00203 | − | 0.904841i | ||||
\(451\) | −274.037 | + | 474.646i | −0.0286118 | + | 0.0495570i | ||||
\(452\) | −6937.09 | + | 12015.4i | −0.721888 | + | 1.25035i | ||||
\(453\) | −10385.8 | − | 14102.3i | −1.07719 | − | 1.46266i | ||||
\(454\) | 16914.0i | 1.74848i | ||||||||
\(455\) | −16549.4 | −1.70516 | ||||||||
\(456\) | −17867.0 | − | 24260.8i | −1.83487 | − | 2.49148i | ||||
\(457\) | 3018.79 | + | 5228.69i | 0.309000 | + | 0.535204i | 0.978144 | − | 0.207929i | \(-0.0666724\pi\) |
−0.669144 | + | 0.743133i | \(0.733339\pi\) | |||||||
\(458\) | −5544.78 | + | 3201.28i | −0.565700 | + | 0.326607i | ||||
\(459\) | −4688.36 | − | 901.972i | −0.476762 | − | 0.0917221i | ||||
\(460\) | 63985.8i | 6.48556i | ||||||||
\(461\) | 1881.34i | 0.190071i | 0.995474 | + | 0.0950353i | \(0.0302964\pi\) | ||||
−0.995474 | + | 0.0950353i | \(0.969704\pi\) | |||||||
\(462\) | −904.941 | − | 8105.97i | −0.0911292 | − | 0.816285i | ||||
\(463\) | −16017.0 | − | 9247.44i | −1.60772 | − | 0.928218i | −0.989879 | − | 0.141915i | \(-0.954674\pi\) |
−0.617842 | − | 0.786302i | \(-0.711993\pi\) | |||||||
\(464\) | − | 54375.1i | − | 5.44031i | ||||||
\(465\) | 2026.55 | + | 18152.7i | 0.202105 | + | 1.81035i | ||||
\(466\) | −2797.74 | −0.278118 | ||||||||
\(467\) | −1198.32 | − | 691.850i | −0.118740 | − | 0.0685546i | 0.439454 | − | 0.898265i | \(-0.355172\pi\) |
−0.558194 | + | 0.829711i | \(0.688505\pi\) | |||||||
\(468\) | 12447.2 | − | 11502.1i | 1.22943 | − | 1.13608i | ||||
\(469\) | −1433.38 | + | 14442.7i | −0.141124 | + | 1.42197i | ||||
\(470\) | − | 7973.04i | − | 0.782487i | ||||||
\(471\) | 849.398 | + | 1153.36i | 0.0830960 | + | 0.112832i | ||||
\(472\) | − | 20856.4i | − | 2.03388i | ||||||
\(473\) | 570.231 | − | 329.223i | 0.0554318 | − | 0.0320036i | ||||
\(474\) | −2435.43 | − | 1065.53i | −0.235997 | − | 0.103252i | ||||
\(475\) | 12445.9 | − | 21557.0i | 1.20223 | − | 2.08232i | ||||
\(476\) | 9027.66 | + | 15636.4i | 0.869290 | + | 1.50565i | ||||
\(477\) | 8599.72 | + | 9306.34i | 0.825480 | + | 0.893308i | ||||
\(478\) | 8674.93 | 0.830088 | ||||||||
\(479\) | 15595.1 | + | 9003.86i | 1.48760 | + | 0.858866i | 0.999900 | − | 0.0141461i | \(-0.00450298\pi\) |
0.487699 | + | 0.873012i | \(0.337836\pi\) | |||||||
\(480\) | 44330.7 | − | 4949.03i | 4.21543 | − | 0.470606i | ||||
\(481\) | −933.401 | + | 538.899i | −0.0884811 | + | 0.0510846i | ||||
\(482\) | −12815.7 | + | 22197.4i | −1.21107 | + | 2.09764i | ||||
\(483\) | −8808.01 | + | 20132.0i | −0.829768 | + | 1.89656i | ||||
\(484\) | −24169.4 | −2.26986 | ||||||||
\(485\) | −20965.9 | − | 12104.7i | −1.96291 | − | 1.13329i | ||||
\(486\) | −17040.7 | + | 10586.4i | −1.59050 | + | 0.988087i | ||||
\(487\) | 4636.64 | + | 2676.97i | 0.431430 | + | 0.249086i | 0.699956 | − | 0.714186i | \(-0.253203\pi\) |
−0.268526 | + | 0.963272i | \(0.586536\pi\) | |||||||
\(488\) | 4062.89 | + | 2345.71i | 0.376882 | + | 0.217593i | ||||
\(489\) | 4221.86 | − | 471.324i | 0.390427 | − | 0.0435869i | ||||
\(490\) | −18900.9 | − | 32737.3i | −1.74256 | − | 3.01820i | ||||
\(491\) | − | 2474.99i | − | 0.227484i | −0.993510 | − | 0.113742i | \(-0.963716\pi\) | ||
0.993510 | − | 0.113742i | \(-0.0362837\pi\) | |||||||
\(492\) | −3023.09 | − | 4104.91i | −0.277015 | − | 0.376146i | ||||
\(493\) | −10422.4 | −0.952136 | ||||||||
\(494\) | − | 15068.8i | − | 1.37242i | ||||||
\(495\) | −1791.95 | + | 5767.50i | −0.162711 | + | 0.523696i | ||||
\(496\) | 31247.1i | 2.82870i | ||||||||
\(497\) | −1974.37 | + | 3419.70i | −0.178194 | + | 0.308641i | ||||
\(498\) | 3465.77 | + | 31044.4i | 0.311857 | + | 2.79344i | ||||
\(499\) | 5672.61 | + | 3275.08i | 0.508900 | + | 0.293813i | 0.732381 | − | 0.680895i | \(-0.238409\pi\) |
−0.223482 | + | 0.974708i | \(0.571742\pi\) | |||||||
\(500\) | 29813.2 | + | 51637.9i | 2.66657 | + | 4.61863i | ||||
\(501\) | −1163.78 | − | 10424.5i | −0.103780 | − | 0.929605i | ||||
\(502\) | −17291.2 | − | 29949.3i | −1.53734 | − | 2.66276i | ||||
\(503\) | 2101.70 | + | 3640.26i | 0.186303 | + | 0.322686i | 0.944015 | − | 0.329903i | \(-0.107016\pi\) |
−0.757712 | + | 0.652589i | \(0.773683\pi\) | |||||||
\(504\) | 43539.9 | + | 13527.7i | 3.84806 | + | 1.19558i | ||||
\(505\) | 9000.75 | + | 15589.8i | 0.793125 | + | 1.37373i | ||||
\(506\) | −8208.27 | − | 4739.04i | −0.721150 | − | 0.416356i | ||||
\(507\) | −6283.15 | + | 701.444i | −0.550383 | + | 0.0614442i | ||||
\(508\) | 1706.99 | − | 2956.60i | 0.149086 | − | 0.258224i | ||||
\(509\) | − | 15816.0i | − | 1.37727i | −0.725109 | − | 0.688634i | \(-0.758211\pi\) | ||
0.725109 | − | 0.688634i | \(-0.241789\pi\) | |||||||
\(510\) | −2075.22 | − | 18588.7i | −0.180181 | − | 1.61396i | ||||
\(511\) | − | 5616.31i | − | 0.486205i | ||||||
\(512\) | −14318.7 | −1.23594 | ||||||||
\(513\) | −2408.65 | + | 12519.9i | −0.207299 | + | 1.07752i | ||||
\(514\) | 7770.86i | 0.666844i | ||||||||
\(515\) | −12669.9 | − | 21945.0i | −1.08409 | − | 1.87769i | ||||
\(516\) | 679.524 | + | 6086.80i | 0.0579736 | + | 0.519296i | ||||
\(517\) | 731.073 | + | 422.085i | 0.0621907 | + | 0.0359058i | ||||
\(518\) | −4178.36 | − | 2412.38i | −0.354414 | − | 0.204621i | ||||
\(519\) | −875.954 | + | 645.103i | −0.0740850 | + | 0.0545605i | ||||
\(520\) | 34555.5 | + | 19950.6i | 2.91415 | + | 1.68248i | ||||
\(521\) | −5317.53 | −0.447150 | −0.223575 | − | 0.974687i | \(-0.571773\pi\) | ||||
−0.223575 | + | 0.974687i | \(0.571773\pi\) | |||||||
\(522\) | −32164.2 | + | 29722.0i | −2.69692 | + | 2.49214i | ||||
\(523\) | 8568.27 | − | 14840.7i | 0.716375 | − | 1.24080i | −0.246051 | − | 0.969257i | \(-0.579133\pi\) |
0.962427 | − | 0.271542i | \(-0.0875334\pi\) | |||||||
\(524\) | 26100.8 | − | 15069.3i | 2.17599 | − | 1.25631i | ||||
\(525\) | 4179.10 | + | 37434.0i | 0.347411 | + | 3.11192i | ||||
\(526\) | 5616.80 | + | 3242.86i | 0.465597 | + | 0.268813i | ||||
\(527\) | 5989.34 | 0.495066 | ||||||||
\(528\) | −4141.28 | + | 9465.53i | −0.341337 | + | 0.780178i | ||||
\(529\) | 6684.30 | + | 11577.5i | 0.549379 | + | 0.951553i | ||||
\(530\) | −24821.0 | + | 42991.2i | −2.03425 | + | 3.52343i | ||||
\(531\) | −6481.70 | + | 5989.55i | −0.529721 | + | 0.489500i | ||||
\(532\) | 41755.7 | − | 24107.6i | 3.40289 | − | 1.96466i | ||||
\(533\) | − | 1532.22i | − | 0.124518i | ||||||
\(534\) | 7780.25 | − | 5729.82i | 0.630495 | − | 0.464333i | ||||
\(535\) | 3420.67i | 0.276427i | ||||||||
\(536\) | 20403.9 | − | 28428.7i | 1.64424 | − | 2.29092i | ||||
\(537\) | 280.436 | − | 640.980i | 0.0225358 | − | 0.0515090i | ||||
\(538\) | −30308.9 | − | 17498.8i | −2.42883 | − | 1.40228i | ||||
\(539\) | 4002.38 | 0.319842 | ||||||||
\(540\) | −42467.9 | − | 36773.7i | −3.38431 | − | 2.93053i | ||||
\(541\) | 4148.64i | 0.329693i | 0.986319 | + | 0.164847i | \(0.0527129\pi\) | ||||
−0.986319 | + | 0.164847i | \(0.947287\pi\) | |||||||
\(542\) | 8493.51 | + | 4903.73i | 0.673113 | + | 0.388622i | ||||
\(543\) | −10020.9 | + | 1118.72i | −0.791965 | + | 0.0884141i | ||||
\(544\) | − | 14626.5i | − | 1.15277i | ||||||
\(545\) | − | 36626.9i | − | 2.87876i | ||||||
\(546\) | 13521.7 | + | 18360.4i | 1.05984 | + | 1.43911i | ||||
\(547\) | 13725.6 | − | 7924.47i | 1.07288 | − | 0.619425i | 0.143910 | − | 0.989591i | \(-0.454032\pi\) |
0.928966 | + | 0.370165i | \(0.120699\pi\) | |||||||
\(548\) | −16287.2 | − | 28210.2i | −1.26962 | − | 2.19905i | ||||
\(549\) | −437.789 | − | 1936.30i | −0.0340335 | − | 0.150527i | ||||
\(550\) | −16246.4 | −1.25954 | ||||||||
\(551\) | 27832.3i | 2.15190i | ||||||||
\(552\) | 42660.9 | − | 31417.9i | 3.28944 | − | 2.42253i | ||||
\(553\) | 1278.23 | − | 2213.95i | 0.0982925 | − | 0.170248i | ||||
\(554\) | 2901.92 | − | 5026.28i | 0.222547 | − | 0.385462i | ||||
\(555\) | 2118.52 | + | 2876.63i | 0.162029 | + | 0.220011i | ||||
\(556\) | 53523.3 | − | 30901.7i | 4.08254 | − | 2.35706i | ||||
\(557\) | 19299.1 | − | 11142.3i | 1.46809 | − | 0.847604i | 0.468731 | − | 0.883341i | \(-0.344711\pi\) |
0.999361 | + | 0.0357370i | \(0.0113779\pi\) | |||||||
\(558\) | 18483.4 | − | 17080.0i | 1.40227 | − | 1.29580i | ||||
\(559\) | −920.391 | + | 1594.16i | −0.0696394 | + | 0.120619i | ||||
\(560\) | 93842.9i | 7.08140i | ||||||||
\(561\) | 1814.32 | + | 793.786i | 0.136543 | + | 0.0597391i | ||||
\(562\) | −11122.3 | − | 19264.5i | −0.834818 | − | 1.44595i | ||||
\(563\) | −3963.01 | −0.296662 | −0.148331 | − | 0.988938i | \(-0.547390\pi\) | ||||
−0.148331 | + | 0.988938i | \(0.547390\pi\) | |||||||
\(564\) | −6322.58 | + | 4656.31i | −0.472037 | + | 0.347635i | ||||
\(565\) | 6911.03 | + | 11970.2i | 0.514600 | + | 0.891314i | ||||
\(566\) | 19651.1 | − | 34036.8i | 1.45936 | − | 2.52769i | ||||
\(567\) | −8299.71 | − | 17416.1i | −0.614735 | − | 1.28996i | ||||
\(568\) | 8245.04 | − | 4760.28i | 0.609075 | − | 0.351649i | ||||
\(569\) | 17625.6 | − | 10176.1i | 1.29860 | − | 0.749745i | 0.318435 | − | 0.947945i | \(-0.396843\pi\) |
0.980162 | + | 0.198199i | \(0.0635093\pi\) | |||||||
\(570\) | −49639.7 | + | 5541.72i | −3.64768 | + | 0.407223i | ||||
\(571\) | 7677.37 | + | 13297.6i | 0.562676 | + | 0.974584i | 0.997262 | + | 0.0739531i | \(0.0235615\pi\) |
−0.434586 | + | 0.900631i | \(0.643105\pi\) | |||||||
\(572\) | −6088.05 | + | 3514.94i | −0.445025 | + | 0.256935i | ||||
\(573\) | 6628.72 | + | 9000.82i | 0.483279 | + | 0.656221i | ||||
\(574\) | 5940.05 | − | 3429.49i | 0.431939 | − | 0.249380i | ||||
\(575\) | 37906.5 | + | 21885.3i | 2.74923 | + | 1.58727i | ||||
\(576\) | −15684.6 | − | 16973.4i | −1.13459 | − | 1.22782i | ||||
\(577\) | −23035.1 | + | 13299.3i | −1.66198 | + | 0.959547i | −0.690217 | + | 0.723603i | \(0.742485\pi\) |
−0.971767 | + | 0.235944i | \(0.924182\pi\) | |||||||
\(578\) | 19886.3 | 1.43107 | ||||||||
\(579\) | 2862.98 | − | 6543.79i | 0.205495 | − | 0.469690i | ||||
\(580\) | −106205. | − | 61317.3i | −7.60329 | − | 4.38976i | ||||
\(581\) | −30040.3 | −2.14507 | ||||||||
\(582\) | 3700.87 | + | 33150.4i | 0.263584 | + | 2.36104i | ||||
\(583\) | −2628.00 | − | 4551.83i | −0.186691 | − | 0.323358i | ||||
\(584\) | −6770.58 | + | 11727.0i | −0.479740 | + | 0.830935i | ||||
\(585\) | −3723.46 | − | 16468.5i | −0.263156 | − | 1.16391i | ||||
\(586\) | −22207.8 | − | 12821.7i | −1.56552 | − | 0.903853i | ||||
\(587\) | −3287.57 | + | 5694.24i | −0.231163 | + | 0.400386i | −0.958151 | − | 0.286264i | \(-0.907586\pi\) |
0.726988 | + | 0.686651i | \(0.240920\pi\) | |||||||
\(588\) | −14922.3 | + | 34107.1i | −1.04657 | + | 2.39210i | ||||
\(589\) | − | 15994.1i | − | 1.11889i | ||||||
\(590\) | −29942.6 | − | 17287.4i | −2.08935 | − | 1.20629i | ||||
\(591\) | 18023.7 | − | 2012.15i | 1.25448 | − | 0.140049i | ||||
\(592\) | 3055.82 | + | 5292.83i | 0.212151 | + | 0.367456i | ||||
\(593\) | −10405.7 | + | 18023.2i | −0.720590 | + | 1.24810i | 0.240174 | + | 0.970730i | \(0.422796\pi\) |
−0.960764 | + | 0.277369i | \(0.910538\pi\) | |||||||
\(594\) | 7862.76 | − | 2724.29i | 0.543119 | − | 0.188180i | ||||
\(595\) | 17987.5 | 1.23935 | ||||||||
\(596\) | −25060.5 | + | 14468.7i | −1.72235 | + | 0.994396i | ||||
\(597\) | −7761.77 | − | 10539.3i | −0.532107 | − | 0.722523i | ||||
\(598\) | 26497.4 | 1.81197 | ||||||||
\(599\) | −5428.89 | − | 9403.11i | −0.370314 | − | 0.641403i | 0.619299 | − | 0.785155i | \(-0.287417\pi\) |
−0.989614 | + | 0.143752i | \(0.954083\pi\) | |||||||
\(600\) | 36401.5 | − | 83201.1i | 2.47681 | − | 5.66112i | ||||
\(601\) | 7046.53 | − | 12204.9i | 0.478259 | − | 0.828370i | −0.521430 | − | 0.853294i | \(-0.674601\pi\) |
0.999689 | + | 0.0249246i | \(0.00793455\pi\) | |||||||
\(602\) | −8240.25 | −0.557886 | ||||||||
\(603\) | −14694.6 | + | 1823.11i | −0.992392 | + | 0.123122i | ||||
\(604\) | −67573.4 | −4.55219 | ||||||||
\(605\) | −12039.3 | + | 20852.7i | −0.809037 | + | 1.40129i | ||||
\(606\) | 9941.73 | − | 22723.4i | 0.666428 | − | 1.52322i | ||||
\(607\) | 13921.7 | + | 24113.2i | 0.930916 | + | 1.61239i | 0.781760 | + | 0.623580i | \(0.214322\pi\) |
0.149156 | + | 0.988814i | \(0.452344\pi\) | |||||||
\(608\) | −39059.0 | −2.60535 | ||||||||
\(609\) | −24974.8 | − | 33912.1i | −1.66179 | − | 2.25646i | ||||
\(610\) | 6735.27 | − | 3888.61i | 0.447054 | − | 0.258107i | ||||
\(611\) | −2360.00 | −0.156261 | ||||||||
\(612\) | −13528.8 | + | 12501.6i | −0.893579 | + | 0.825730i | ||||
\(613\) | −3041.69 | + | 5268.36i | −0.200412 | + | 0.347124i | −0.948661 | − | 0.316294i | \(-0.897562\pi\) |
0.748249 | + | 0.663418i | \(0.230895\pi\) | |||||||
\(614\) | −4414.57 | − | 7646.26i | −0.290159 | − | 0.502570i | ||||
\(615\) | −5047.47 | + | 563.494i | −0.330949 | + | 0.0369468i | ||||
\(616\) | −16378.0 | − | 9455.85i | −1.07125 | − | 0.618486i | ||||
\(617\) | − | 20182.7i | − | 1.31689i | −0.752627 | − | 0.658447i | \(-0.771213\pi\) | ||
0.752627 | − | 0.658447i | \(-0.228787\pi\) | |||||||
\(618\) | −13994.5 | + | 31986.6i | −0.910909 | + | 2.08202i | ||||
\(619\) | −4733.88 | + | 8199.32i | −0.307384 | + | 0.532405i | −0.977789 | − | 0.209590i | \(-0.932787\pi\) |
0.670405 | + | 0.741995i | \(0.266120\pi\) | |||||||
\(620\) | 61031.3 | + | 35236.5i | 3.95335 | + | 2.28247i | ||||
\(621\) | −22015.4 | − | 4235.44i | −1.42262 | − | 0.273691i | ||||
\(622\) | −19092.0 | + | 33068.3i | −1.23074 | + | 2.13170i | ||||
\(623\) | 4646.10 | + | 8047.29i | 0.298784 | + | 0.517509i | ||||
\(624\) | −3204.68 | − | 28705.8i | −0.205593 | − | 1.84159i | ||||
\(625\) | 25163.4 | 1.61046 | ||||||||
\(626\) | 7948.00 | + | 4588.78i | 0.507454 | + | 0.292979i | ||||
\(627\) | 2119.74 | − | 4845.00i | 0.135015 | − | 0.308597i | ||||
\(628\) | 5526.49 | 0.351164 | ||||||||
\(629\) | 1014.51 | − | 585.728i | 0.0643104 | − | 0.0371296i | ||||
\(630\) | 55510.4 | − | 51295.5i | 3.51046 | − | 3.24391i | ||||
\(631\) | 14966.4 | + | 8640.85i | 0.944220 | + | 0.545145i | 0.891281 | − | 0.453452i | \(-0.149808\pi\) |
0.0529390 | + | 0.998598i | \(0.483141\pi\) | |||||||
\(632\) | −5337.94 | + | 3081.86i | −0.335968 | + | 0.193971i | ||||
\(633\) | 2991.79 | + | 4062.41i | 0.187856 | + | 0.255081i | ||||
\(634\) | 2582.18 | − | 1490.82i | 0.161753 | − | 0.0933881i | ||||
\(635\) | −1700.58 | − | 2945.49i | −0.106276 | − | 0.184076i | ||||
\(636\) | 48587.5 | − | 5424.25i | 3.02927 | − | 0.338185i | ||||
\(637\) | −9690.17 | + | 5594.62i | −0.602729 | + | 0.347986i | ||||
\(638\) | 15731.9 | − | 9082.80i | 0.976224 | − | 0.563623i | ||||
\(639\) | −3847.21 | − | 1195.32i | −0.238174 | − | 0.0740000i | ||||
\(640\) | 10932.0 | − | 18934.8i | 0.675198 | − | 1.16948i | ||||
\(641\) | 3384.89 | + | 5862.80i | 0.208573 | + | 0.361259i | 0.951265 | − | 0.308374i | \(-0.0997848\pi\) |
−0.742692 | + | 0.669633i | \(0.766452\pi\) | |||||||
\(642\) | 3795.01 | − | 2794.86i | 0.233298 | − | 0.171814i | ||||
\(643\) | 15442.4 | 0.947105 | 0.473553 | − | 0.880765i | \(-0.342971\pi\) | ||||
0.473553 | + | 0.880765i | \(0.342971\pi\) | |||||||
\(644\) | 42391.7 | + | 73424.6i | 2.59389 | + | 4.49275i | ||||
\(645\) | 5590.00 | + | 2445.69i | 0.341250 | + | 0.149301i | ||||
\(646\) | 16378.2i | 0.997510i | ||||||||
\(647\) | −1990.83 | + | 3448.22i | −0.120970 | + | 0.209526i | −0.920150 | − | 0.391565i | \(-0.871934\pi\) |
0.799180 | + | 0.601091i | \(0.205267\pi\) | |||||||
\(648\) | −3665.55 | + | 46370.8i | −0.222216 | + | 2.81114i | ||||
\(649\) | 3170.27 | − | 1830.36i | 0.191747 | − | 0.110705i | ||||
\(650\) | 39334.2 | − | 22709.6i | 2.37356 | − | 1.37038i | ||||
\(651\) | 14352.0 | + | 19487.9i | 0.864052 | + | 1.17326i | ||||
\(652\) | 8195.10 | − | 14194.3i | 0.492247 | − | 0.852596i | ||||
\(653\) | 5785.68 | − | 10021.1i | 0.346725 | − | 0.600545i | −0.638941 | − | 0.769256i | \(-0.720627\pi\) |
0.985666 | + | 0.168711i | \(0.0539605\pi\) | |||||||
\(654\) | −40635.1 | + | 29926.0i | −2.42960 | + | 1.78930i | ||||
\(655\) | − | 30025.4i | − | 1.79113i | ||||||
\(656\) | −8688.44 | −0.517114 | ||||||||
\(657\) | 5588.87 | − | 1263.62i | 0.331876 | − | 0.0750357i | ||||
\(658\) | −5282.27 | − | 9149.16i | −0.312955 | − | 0.542054i | ||||
\(659\) | 3652.83 | − | 2108.96i | 0.215924 | − | 0.124664i | −0.388137 | − | 0.921602i | \(-0.626881\pi\) |
0.604062 | + | 0.796938i | \(0.293548\pi\) | |||||||
\(660\) | 13817.9 | + | 18762.7i | 0.814942 | + | 1.10657i | ||||
\(661\) | − | 20023.7i | − | 1.17826i | −0.808037 | − | 0.589132i | \(-0.799470\pi\) | ||
0.808037 | − | 0.589132i | \(-0.200530\pi\) | |||||||
\(662\) | − | 48967.5i | − | 2.87489i | ||||||
\(663\) | −5502.22 | + | 614.262i | −0.322306 | + | 0.0359818i | ||||
\(664\) | 62724.9 | + | 36214.2i | 3.66596 | + | 2.11654i | ||||
\(665\) | − | 48034.1i | − | 2.80103i | ||||||
\(666\) | 1460.50 | − | 4700.71i | 0.0849747 | − | 0.273497i | ||||
\(667\) | −48941.2 | −2.84110 | ||||||||
\(668\) | −35048.3 | − | 20235.1i | −2.03003 | − | 1.17204i | ||||
\(669\) | 5941.93 | − | 13581.2i | 0.343390 | − | 0.784871i | ||||
\(670\) | −23901.6 | − | 52857.0i | −1.37821 | − | 3.04782i | ||||
\(671\) | 823.438i | 0.0473747i | ||||||||
\(672\) | 47591.2 | − | 35048.9i | 2.73195 | − | 2.01196i | ||||
\(673\) | − | 8693.63i | − | 0.497942i | −0.968511 | − | 0.248971i | \(-0.919908\pi\) | ||
0.968511 | − | 0.248971i | \(-0.0800923\pi\) | |||||||
\(674\) | −27117.4 | + | 15656.2i | −1.54974 | + | 0.894741i | ||||
\(675\) | −36310.9 | + | 12581.0i | −2.07053 | + | 0.717397i | ||||
\(676\) | −12196.3 | + | 21124.6i | −0.693918 | + | 1.20190i | ||||
\(677\) | −372.596 | − | 645.354i | −0.0211522 | − | 0.0366366i | 0.855256 | − | 0.518206i | \(-0.173400\pi\) |
−0.876408 | + | 0.481570i | \(0.840067\pi\) | |||||||
\(678\) | 7633.54 | − | 17447.6i | 0.432396 | − | 0.988306i | ||||
\(679\) | −32078.2 | −1.81303 | ||||||||
\(680\) | −37558.3 | − | 21684.3i | −2.11808 | − | 1.22287i | ||||
\(681\) | −1841.20 | − | 16492.5i | −0.103605 | − | 0.928037i | ||||
\(682\) | −9040.45 | + | 5219.50i | −0.507590 | + | 0.293057i | ||||
\(683\) | 3118.49 | − | 5401.39i | 0.174708 | − | 0.302604i | −0.765352 | − | 0.643612i | \(-0.777435\pi\) |
0.940060 | + | 0.341008i | \(0.110768\pi\) | |||||||
\(684\) | 33384.5 | + | 36127.7i | 1.86621 | + | 2.01955i | ||||
\(685\) | −32452.0 | −1.81011 | ||||||||
\(686\) | −1744.65 | − | 1007.28i | −0.0971009 | − | 0.0560612i | ||||
\(687\) | 5058.13 | − | 3725.10i | 0.280902 | − | 0.206872i | ||||
\(688\) | 9039.68 | + | 5219.06i | 0.500923 | + | 0.289208i | ||||
\(689\) | 12725.3 | + | 7346.96i | 0.703622 | + | 0.406236i | ||||
\(690\) | −9744.74 | − | 87288.1i | −0.537646 | − | 4.81594i | ||||
\(691\) | 15062.4 | + | 26088.8i | 0.829234 | + | 1.43628i | 0.898640 | + | 0.438687i | \(0.144556\pi\) |
−0.0694064 | + | 0.997588i | \(0.522111\pi\) | |||||||
\(692\) | 4197.27i | 0.230573i | ||||||||
\(693\) | 1764.78 | + | 7805.47i | 0.0967367 | + | 0.427857i | ||||
\(694\) | 20916.2 | 1.14405 | ||||||||
\(695\) | − | 61571.2i | − | 3.36047i | ||||||
\(696\) | 11266.2 | + | 100917.i | 0.613572 | + | 5.49604i | ||||
\(697\) | 1665.37i | 0.0905026i | ||||||||
\(698\) | −21132.6 | + | 36602.8i | −1.14596 | + | 1.98486i | ||||
\(699\) | 2728.03 | − | 304.554i | 0.147616 | − | 0.0164797i | ||||
\(700\) | 125857. | + | 72663.7i | 6.79565 | + | 3.92347i | ||||
\(701\) | 13120.5 | + | 22725.4i | 0.706927 | + | 1.22443i | 0.965992 | + | 0.258574i | \(0.0832524\pi\) |
−0.259065 | + | 0.965860i | \(0.583414\pi\) | |||||||
\(702\) | −15228.5 | + | 17586.5i | −0.818748 | + | 0.945528i | ||||
\(703\) | −1564.14 | − | 2709.17i | −0.0839157 | − | 0.145346i | ||||
\(704\) | 4793.08 | + | 8301.87i | 0.256600 | + | 0.444444i | ||||
\(705\) | 867.921 | + | 7774.36i | 0.0463656 | + | 0.415318i | ||||
\(706\) | 24429.9 | + | 42313.8i | 1.30231 | + | 2.25567i | ||||
\(707\) | 20656.9 | + | 11926.3i | 1.09885 | + | 0.634419i | ||||
\(708\) | 3777.90 | + | 33840.3i | 0.200540 | + | 1.79632i | ||||
\(709\) | 7643.63 | − | 13239.2i | 0.404884 | − | 0.701279i | −0.589424 | − | 0.807824i | \(-0.700645\pi\) |
0.994308 | + | 0.106544i | \(0.0339786\pi\) | |||||||
\(710\) | − | 15782.7i | − | 0.834247i | ||||||
\(711\) | 2490.73 | + | 773.862i | 0.131378 | + | 0.0408187i | ||||
\(712\) | − | 22403.9i | − | 1.17924i | ||||||
\(713\) | 28124.5 | 1.47724 | ||||||||
\(714\) | −14696.7 | − | 19955.9i | −0.770321 | − | 1.04598i | ||||
\(715\) | 7003.46i | 0.366314i | ||||||||
\(716\) | −1349.70 | − | 2337.75i | −0.0704478 | − | 0.122019i | ||||
\(717\) | −8458.76 | + | 944.327i | −0.440583 | + | 0.0491862i | ||||
\(718\) | 4308.71 | + | 2487.63i | 0.223955 | + | 0.129300i | ||||
\(719\) | −20833.7 | − | 12028.3i | −1.08062 | − | 0.623895i | −0.149555 | − | 0.988753i | \(-0.547784\pi\) |
−0.931063 | + | 0.364858i | \(0.881118\pi\) | |||||||
\(720\) | −93384.4 | + | 21113.8i | −4.83365 | + | 1.09287i | ||||
\(721\) | −29077.8 | − | 16788.1i | −1.50196 | − | 0.867158i | ||||
\(722\) | 7411.12 | 0.382013 | ||||||||
\(723\) | 10080.0 | − | 23039.3i | 0.518504 | − | 1.18512i | ||||
\(724\) | −19451.6 | + | 33691.2i | −0.998500 | + | 1.72945i | ||||
\(725\) | −72651.1 | + | 41945.1i | −3.72165 | + | 2.14869i | ||||
\(726\) | 32971.4 | − | 3680.89i | 1.68551 | − | 0.188169i | ||||
\(727\) | −6331.42 | − | 3655.44i | −0.322998 | − | 0.186483i | 0.329730 | − | 0.944075i | \(-0.393042\pi\) |
−0.652728 | + | 0.757592i | \(0.726375\pi\) | |||||||
\(728\) | 52870.4 | 2.69163 | ||||||||
\(729\) | 15463.7 | − | 12177.6i | 0.785637 | − | 0.618688i | ||||
\(730\) | 11224.0 | + | 19440.5i | 0.569064 | + | 0.985648i | ||||
\(731\) | 1000.37 | − | 1732.69i | 0.0506157 | − | 0.0876690i | ||||
\(732\) | −7017.10 | − | 3070.06i | −0.354316 | − | 0.155017i | ||||
\(733\) | 4340.63 | − | 2506.06i | 0.218724 | − | 0.126280i | −0.386635 | − | 0.922233i | \(-0.626363\pi\) |
0.605359 | + | 0.795952i | \(0.293029\pi\) | |||||||
\(734\) | 54822.5i | 2.75686i | ||||||||
\(735\) | 21993.6 | + | 29864.0i | 1.10373 | + | 1.49871i | ||||
\(736\) | − | 68682.6i | − | 3.43978i | ||||||
\(737\) | 6111.95 | + | 606.585i | 0.305477 | + | 0.0303173i | ||||
\(738\) | 4749.19 | + | 5139.42i | 0.236884 | + | 0.256348i | ||||
\(739\) | −4739.07 | − | 2736.11i | −0.235899 | − | 0.136197i | 0.377391 | − | 0.926054i | \(-0.376821\pi\) |
−0.613291 | + | 0.789857i | \(0.710155\pi\) | |||||||
\(740\) | 13783.8 | 0.684735 | ||||||||
\(741\) | 1640.34 | + | 14693.3i | 0.0813216 | + | 0.728435i | ||||
\(742\) | 65777.2i | 3.25439i | ||||||||
\(743\) | 11797.0 | + | 6811.03i | 0.582492 | + | 0.336302i | 0.762123 | − | 0.647432i | \(-0.224157\pi\) |
−0.179631 | + | 0.983734i | \(0.557490\pi\) | |||||||
\(744\) | −6474.24 | − | 57992.7i | −0.319028 | − | 2.85768i | ||||
\(745\) | 28828.6i | 1.41772i | ||||||||
\(746\) | − | 7705.35i | − | 0.378167i | ||||||
\(747\) | −6758.80 | − | 29893.6i | −0.331046 | − | 1.46419i | ||||
\(748\) | 6617.09 | − | 3820.38i | 0.323456 | − | 0.186747i | ||||
\(749\) | 2266.25 | + | 3925.26i | 0.110557 | + | 0.191490i | ||||
\(750\) | −48534.7 | − | 65902.9i | −2.36298 | − | 3.20858i | ||||
\(751\) | −27849.6 | −1.35319 | −0.676595 | − | 0.736355i | \(-0.736545\pi\) | ||||
−0.676595 | + | 0.736355i | \(0.736545\pi\) | |||||||
\(752\) | 13382.4i | 0.648942i | ||||||||
\(753\) | 20120.6 | + | 27320.7i | 0.973750 | + | 1.32221i | ||||
\(754\) | −25392.3 | + | 43980.8i | −1.22644 | + | 2.12425i | ||||
\(755\) | −33659.8 | + | 58300.4i | −1.62252 | + | 2.81029i | ||||
\(756\) | −73095.6 | − | 14062.5i | −3.51648 | − | 0.676520i | ||||
\(757\) | 25383.1 | − | 14654.9i | 1.21871 | − | 0.703623i | 0.254069 | − | 0.967186i | \(-0.418231\pi\) |
0.964642 | + | 0.263563i | \(0.0848978\pi\) | |||||||
\(758\) | −20533.7 | + | 11855.1i | −0.983929 | + | 0.568072i | ||||
\(759\) | 8519.60 | + | 3727.43i | 0.407433 | + | 0.178257i | ||||
\(760\) | −57906.2 | + | 100296.i | −2.76379 | + | 4.78702i | ||||
\(761\) | 21280.1i | 1.01367i | 0.862043 | + | 0.506835i | \(0.169185\pi\) | ||||
−0.862043 | + | 0.506835i | \(0.830815\pi\) | |||||||
\(762\) | −1878.36 | + | 4293.29i | −0.0892992 | + | 0.204107i | ||||
\(763\) | −24265.9 | − | 42029.9i | −1.15136 | − | 1.99421i | ||||
\(764\) | 43128.8 | 2.04234 | ||||||||
\(765\) | 4047.02 | + | 17899.6i | 0.191268 | + | 0.845962i | ||||
\(766\) | 544.363 | + | 942.865i | 0.0256771 | + | 0.0444740i | ||||
\(767\) | −5117.03 | + | 8862.95i | −0.240893 | + | 0.417239i | ||||
\(768\) | 5422.56 | − | 605.368i | 0.254778 | − | 0.0284432i | ||||
\(769\) | 3759.33 | − | 2170.45i | 0.176287 | − | 0.101780i | −0.409260 | − | 0.912418i | \(-0.634213\pi\) |
0.585547 | + | 0.810638i | \(0.300880\pi\) | |||||||
\(770\) | −27150.7 | + | 15675.5i | −1.27071 | + | 0.733643i | ||||
\(771\) | −845.912 | − | 7577.22i | −0.0395133 | − | 0.353939i | ||||
\(772\) | −13779.1 | − | 23866.2i | −0.642386 | − | 1.11265i | ||||
\(773\) | 16846.0 | − | 9726.04i | 0.783840 | − | 0.452550i | −0.0539494 | − | 0.998544i | \(-0.517181\pi\) |
0.837789 | + | 0.545993i | \(0.183848\pi\) | |||||||
\(774\) | −1853.98 | − | 8199.99i | −0.0860982 | − | 0.380804i | ||||
\(775\) | 41749.5 | − | 24104.1i | 1.93508 | − | 1.11722i | ||||
\(776\) | 66980.0 | + | 38670.9i | 3.09851 | + | 1.78892i | ||||
\(777\) | 4336.85 | + | 1897.42i | 0.200236 | + | 0.0876056i | ||||
\(778\) | −26401.7 | + | 15243.0i | −1.21664 | + | 0.702428i | ||||
\(779\) | 4447.24 | 0.204543 | ||||||||
\(780\) | −59681.5 | − | 26111.3i | −2.73967 | − | 1.19864i | ||||
\(781\) | 1447.17 | + | 835.524i | 0.0663045 | + | 0.0382809i | ||||
\(782\) | −28800.0 | −1.31699 | ||||||||
\(783\) | 28127.3 | − | 32482.7i | 1.28376 | − | 1.48255i | ||||
\(784\) | 31724.2 | + | 54948.0i | 1.44516 | + | 2.50310i | ||||
\(785\) | 2752.86 | − | 4768.09i | 0.125164 | − | 0.216791i | ||||
\(786\) | −33311.1 | + | 24532.2i | −1.51167 | + | 1.11328i | ||||
\(787\) | 1525.41 | + | 880.695i | 0.0690914 | + | 0.0398899i | 0.534148 | − | 0.845391i | \(-0.320633\pi\) |
−0.465056 | + | 0.885281i | \(0.653966\pi\) | |||||||
\(788\) | 34986.1 | − | 60597.7i | 1.58163 | − | 2.73947i | ||||
\(789\) | −5829.84 | − | 2550.62i | −0.263052 | − | 0.115088i | ||||
\(790\) | 10217.9i | 0.460174i | ||||||||
\(791\) | 15861.0 | + | 9157.34i | 0.712960 | + | 0.411628i | ||||
\(792\) | 5724.74 | − | 18425.5i | 0.256843 | − | 0.826668i | ||||
\(793\) | −1151.02 | − | 1993.63i | −0.0515434 | − | 0.0892758i | ||||
\(794\) | −2513.00 | + | 4352.64i | −0.112321 | + | 0.194546i | ||||
\(795\) | 19522.6 | − | 44621.8i | 0.870936 | − | 1.99066i | ||||
\(796\) | −50500.8 | −2.24869 | ||||||||
\(797\) | 12690.7 | − | 7327.00i | 0.564026 | − | 0.325641i | −0.190734 | − | 0.981642i | \(-0.561087\pi\) |
0.754760 | + | 0.656001i | \(0.227753\pi\) | |||||||
\(798\) | −53290.7 | + | 39246.3i | −2.36400 | + | 1.74098i | ||||
\(799\) | 2565.08 | 0.113575 | ||||||||
\(800\) | −58864.5 | − | 101956.i | −2.60147 | − | 4.50587i | ||||
\(801\) | −6962.64 | + | 6433.97i | −0.307132 | + | 0.283812i | ||||
\(802\) | 13810.0 | − | 23919.6i | 0.608040 | − | 1.05316i | ||||
\(803\) | −2376.74 | −0.104450 | ||||||||
\(804\) | −27956.6 | + | 49822.7i | −1.22631 | + | 2.18546i | ||||
\(805\) | 84464.8 | 3.69813 | ||||||||
\(806\) | 14591.9 | − | 25273.9i | 0.637689 | − | 1.10451i | ||||
\(807\) | 31458.5 | + | 13763.5i | 1.37223 | + | 0.600368i | ||||
\(808\) | −28754.8 | − | 49804.8i | −1.25197 | − | 2.16847i | ||||
\(809\) | 35548.4 | 1.54489 | 0.772444 | − | 0.635083i | \(-0.219034\pi\) | ||||
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(810\) | 63534.3 | + | 43698.1i | 2.75601 | + | 1.89555i | ||||
\(811\) | 17941.0 | − | 10358.3i | 0.776812 | − | 0.448493i | −0.0584870 | − | 0.998288i | \(-0.518628\pi\) |
0.835299 | + | 0.549795i | \(0.185294\pi\) | |||||||
\(812\) | −162495. | −7.02272 | ||||||||
\(813\) | −8815.66 | − | 3856.95i | −0.380294 | − | 0.166383i | ||||
\(814\) | −1020.88 | + | 1768.22i | −0.0439582 | + | 0.0761379i | ||||
\(815\) | −8164.31 | − | 14141.0i | −0.350900 | − | 0.607776i | ||||
\(816\) | 3483.16 | + | 31200.3i | 0.149430 | + | 1.33851i | ||||
\(817\) | −4627.02 | − | 2671.41i | −0.198138 | − | 0.114395i | ||||
\(818\) | − | 48403.6i | − | 2.06894i | ||||||
\(819\) | −15183.4 | − | 16431.0i | −0.647802 | − | 0.701031i | ||||
\(820\) | −9797.70 | + | 16970.1i | −0.417257 | + | 0.722710i | ||||
\(821\) | −8859.32 | − | 5114.93i | −0.376605 | − | 0.217433i | 0.299735 | − | 0.954022i | \(-0.403102\pi\) |
−0.676340 | + | 0.736590i | \(0.736435\pi\) | |||||||
\(822\) | 26514.9 | + | 36003.3i | 1.12508 | + | 1.52769i | ||||
\(823\) | −11179.9 | + | 19364.2i | −0.473522 | + | 0.820164i | −0.999541 | − | 0.0303091i | \(-0.990351\pi\) |
0.526019 | + | 0.850473i | \(0.323684\pi\) | |||||||
\(824\) | 40476.8 | + | 70107.8i | 1.71126 | + | 2.96398i | ||||
\(825\) | 15841.6 | − | 1768.54i | 0.668524 | − | 0.0746333i | ||||
\(826\) | −45812.7 | −1.92981 | ||||||||
\(827\) | −24944.0 | − | 14401.4i | −1.04884 | − | 0.605546i | −0.126513 | − | 0.991965i | \(-0.540379\pi\) |
−0.922324 | + | 0.386419i | \(0.873712\pi\) | |||||||
\(828\) | −63528.1 | + | 58704.4i | −2.66637 | + | 2.46391i | ||||
\(829\) | 20978.6 | 0.878909 | 0.439455 | − | 0.898265i | \(-0.355172\pi\) | ||||
0.439455 | + | 0.898265i | \(0.355172\pi\) | |||||||
\(830\) | 103982. | − | 60034.3i | 4.34853 | − | 2.51063i | ||||
\(831\) | −2282.46 | + | 5216.92i | −0.0952802 | + | 0.217777i | ||||
\(832\) | −23209.1 | − | 13399.8i | −0.967104 | − | 0.558357i | ||||
\(833\) | 10532.2 | − | 6080.78i | 0.438079 | − | 0.252925i | ||||
\(834\) | −68309.2 | + | 50306.8i | −2.83615 | + | 2.08871i | ||||
\(835\) | −34916.6 | + | 20159.1i | −1.44711 | + | 0.835490i | ||||
\(836\) | −10202.0 | − | 17670.4i | −0.422063 | − | 0.731034i | ||||
\(837\) | −16163.6 | + | 18666.4i | −0.667497 | + | 0.770856i | ||||
\(838\) | 62993.9 | − | 36369.6i | 2.59677 | − | 1.49924i | ||||
\(839\) | −21014.1 | + | 12132.5i | −0.864706 | + | 0.499238i | −0.865586 | − | 0.500761i | \(-0.833054\pi\) |
0.000879119 | 1.00000i | \(0.499720\pi\) | ||||||||
\(840\) | −19443.8 | − | 174167.i | −0.798659 | − | 7.15395i | ||||
\(841\) | 34705.6 | − | 60111.9i | 1.42300 | − | 2.46471i | ||||
\(842\) | −24855.4 | − | 43050.8i | −1.01731 | − | 1.76203i | ||||
\(843\) | 12942.3 | + | 17573.7i | 0.528772 | + | 0.717995i | ||||
\(844\) | 19465.6 | 0.793881 | ||||||||
\(845\) | 12150.5 | + | 21045.2i | 0.494661 | + | 0.856779i | ||||
\(846\) | 7915.99 | − | 7314.94i | 0.321699 | − | 0.297273i | ||||
\(847\) | 31905.0i | 1.29429i | ||||||||
\(848\) | 41660.8 | − | 72158.6i | 1.68707 | − | 2.92210i | ||||
\(849\) | −15456.3 | + | 35327.8i | −0.624805 | + | 1.42809i | ||||
\(850\) | −42752.3 | + | 24683.0i | −1.72517 | + | 0.996025i | ||||
\(851\) | 4763.90 | − | 2750.44i | 0.191897 | − | 0.110792i | ||||
\(852\) | −12515.6 | + | 9217.24i | −0.503262 | + | 0.370631i | ||||
\(853\) | −16577.7 | + | 28713.4i | −0.665426 | + | 1.15255i | 0.313743 | + | 0.949508i | \(0.398417\pi\) |
−0.979170 | + | 0.203044i | \(0.934916\pi\) | |||||||
\(854\) | 5152.53 | − | 8924.45i | 0.206459 | − | 0.357598i | ||||
\(855\) | 47799.5 | − | 10807.3i | 1.91194 | − | 0.432281i | ||||
\(856\) | − | 10928.1i | − | 0.436347i | ||||||
\(857\) | 11924.8 | 0.475313 | 0.237656 | − | 0.971349i | \(-0.423621\pi\) | ||||
0.237656 | + | 0.971349i | \(0.423621\pi\) | |||||||
\(858\) | 7769.87 | − | 5722.18i | 0.309160 | − | 0.227683i | ||||
\(859\) | −3380.18 | − | 5854.65i | −0.134261 | − | 0.232547i | 0.791054 | − | 0.611747i | \(-0.209533\pi\) |
−0.925315 | + | 0.379199i | \(0.876199\pi\) | |||||||
\(860\) | 20387.6 | − | 11770.8i | 0.808384 | − | 0.466721i | ||||
\(861\) | −5418.71 | + | 3990.65i | −0.214482 | + | 0.157957i | ||||
\(862\) | − | 41261.9i | − | 1.63038i | ||||||
\(863\) | 38368.0i | 1.51340i | 0.653763 | + | 0.756700i | \(0.273189\pi\) | ||||
−0.653763 | + | 0.756700i | \(0.726811\pi\) | |||||||
\(864\) | 45585.2 | + | 39473.0i | 1.79495 | + | 1.55428i | ||||
\(865\) | 3621.28 | + | 2090.75i | 0.142344 | + | 0.0821822i | ||||
\(866\) | 79393.2i | 3.11535i | ||||||||
\(867\) | −19390.7 | + | 2164.76i | −0.759566 | + | 0.0847971i | ||||
\(868\) | 93379.0 | 3.65149 | ||||||||
\(869\) | −936.915 | − | 540.928i | −0.0365738 | − | 0.0211159i | ||||
\(870\) | 154220. | + | 67473.2i | 6.00984 | + | 2.62937i | ||||
\(871\) | −15645.6 | + | 7074.83i | −0.608645 | + | 0.275226i | ||||
\(872\) | 117012.i | 4.54420i | ||||||||
\(873\) | −7217.30 | − | 31921.5i | −0.279804 | − | 1.23755i | ||||
\(874\) | 76908.0i | 2.97649i | ||||||||
\(875\) | 68164.9 | − | 39355.0i | 2.63359 | − | 1.52051i | ||||
\(876\) | 8861.32 | − | 20253.9i | 0.341777 | − | 0.781183i | ||||
\(877\) | 22234.7 | − | 38511.6i | 0.856115 | − | 1.48283i | −0.0194918 | − | 0.999810i | \(-0.506205\pi\) |
0.875607 | − | 0.483025i | \(-0.160462\pi\) | |||||||
\(878\) | −14320.6 | − | 24804.0i | −0.550452 | − | 0.953410i | ||||
\(879\) | 23050.1 | + | 10084.7i | 0.884482 | + | 0.386971i | ||||
\(880\) | 39713.0 | 1.52128 | ||||||||
\(881\) | −16640.6 | − | 9607.47i | −0.636364 | − | 0.367405i | 0.146849 | − | 0.989159i | \(-0.453087\pi\) |
−0.783213 | + | 0.621754i | \(0.786420\pi\) | |||||||
\(882\) | 15162.3 | − | 48800.8i | 0.578844 | − | 1.86305i | ||||
\(883\) | −496.314 | + | 286.547i | −0.0189154 | + | 0.0109208i | −0.509428 | − | 0.860513i | \(-0.670143\pi\) |
0.490512 | + | 0.871434i | \(0.336810\pi\) | |||||||
\(884\) | −10680.4 | + | 18499.0i | −0.406359 | + | 0.703835i | ||||
\(885\) | 31078.3 | + | 13597.1i | 1.18044 | + | 0.516455i | ||||
\(886\) | 52591.5 | 1.99418 | ||||||||
\(887\) | −22775.0 | − | 13149.1i | −0.862129 | − | 0.497750i | 0.00259578 | − | 0.999997i | \(-0.499174\pi\) |
−0.864725 | + | 0.502246i | \(0.832507\pi\) | |||||||
\(888\) | −6768.05 | − | 9190.01i | −0.255767 | − | 0.347294i | ||||
\(889\) | −3902.87 | − | 2253.32i | −0.147242 | − | 0.0850101i | ||||
\(890\) | −32164.3 | − | 18570.1i | −1.21141 | − | 0.699405i | ||||
\(891\) | −7370.27 | + | 3512.32i | −0.277119 | + | 0.132062i | ||||
\(892\) | −28597.7 | − | 49532.6i | −1.07345 | − | 1.85928i | ||||
\(893\) | − | 6849.85i | − | 0.256687i | ||||||
\(894\) | 31983.5 | − | 23554.5i | 1.19652 | − | 0.881184i | ||||
\(895\) | −2689.26 | −0.100438 | ||||||||
\(896\) | − | 28970.6i | − | 1.08018i | ||||||
\(897\) | −25837.1 | + | 2884.43i | −0.961734 | + | 0.107367i | ||||
\(898\) | − | 2158.04i | − | 0.0801945i | ||||||
\(899\) | −26951.5 | + | 46681.4i | −0.999871 | + | 1.73183i | ||||
\(900\) | −43991.9 | + | 141591.i | −1.62933 | + | 5.24411i | ||||
\(901\) | −13831.1 | − | 7985.40i | −0.511411 | − | 0.295263i | ||||
\(902\) | −1451.31 | − | 2513.75i | −0.0535736 | − | 0.0927923i | ||||
\(903\) | 8034.91 | − | 897.009i | 0.296108 | − | 0.0330571i | ||||
\(904\) | −22078.7 | − | 38241.5i | −0.812309 | − | 1.40696i | ||||
\(905\) | 19378.6 | + | 33564.6i | 0.711784 | + | 1.23285i | ||||
\(906\) | 92182.2 | − | 10291.1i | 3.38029 | − | 0.377372i | ||||
\(907\) | 8477.02 | + | 14682.6i | 0.310336 | + | 0.537518i | 0.978435 | − | 0.206555i | \(-0.0662251\pi\) |
−0.668099 | + | 0.744072i | \(0.732892\pi\) | |||||||
\(908\) | −55449.4 | − | 32013.7i | −2.02660 | − | 1.17006i | ||||
\(909\) | −7220.40 | + | 23239.3i | −0.263460 | + | 0.847965i | ||||
\(910\) | 43823.1 | − | 75903.8i | 1.59640 | − | 2.76504i | ||||
\(911\) | − | 23047.2i | − | 0.838186i | −0.907943 | − | 0.419093i | \(-0.862348\pi\) | ||
0.907943 | − | 0.419093i | \(-0.137652\pi\) | |||||||
\(912\) | 83317.8 | − | 9301.51i | 3.02514 | − | 0.337723i | ||||
\(913\) | 12712.6i | 0.460818i | ||||||||
\(914\) | −31975.3 | −1.15716 | ||||||||
\(915\) | −6144.13 | + | 4524.89i | −0.221988 | + | 0.163484i | ||||
\(916\) | − | 24236.8i | − | 0.874243i | ||||||
\(917\) | −19892.3 | − | 34454.5i | −0.716360 | − | 1.24077i | ||||
\(918\) | 16551.8 | − | 19114.8i | 0.595087 | − | 0.687235i | ||||
\(919\) | 18797.9 | + | 10853.0i | 0.674740 | + | 0.389561i | 0.797870 | − | 0.602829i | \(-0.205960\pi\) |
−0.123130 | + | 0.992391i | \(0.539293\pi\) | |||||||
\(920\) | −176365. | − | 101824.i | −6.32018 | − | 3.64896i | ||||
\(921\) | 5136.91 | + | 6975.17i | 0.183786 | + | 0.249554i | ||||
\(922\) | −8628.76 | − | 4981.82i | −0.308214 | − | 0.177947i | ||||
\(923\) | −4671.66 | −0.166598 | ||||||||
\(924\) | 28286.8 | + | 12375.8i | 1.00711 | + | 0.440621i | ||||
\(925\) | 4714.53 | − | 8165.81i | 0.167581 | − | 0.290260i | ||||
\(926\) | 84826.9 | − | 48974.8i | 3.01035 | − | 1.73803i | ||||
\(927\) | 10163.8 | − | 32712.9i | 0.360112 | − | 1.15904i | ||||
\(928\) | 114000. | + | 65818.2i | 4.03259 | + | 2.32822i | ||||
\(929\) | −32462.1 | −1.14644 | −0.573222 | − | 0.819400i | \(-0.694307\pi\) | ||||
−0.573222 | + | 0.819400i | \(0.694307\pi\) | |||||||
\(930\) | −88624.0 | − | 38774.0i | −3.12483 | − | 1.36715i | ||||
\(931\) | −16238.3 | − | 28125.5i | −0.571630 | − | 0.990092i | ||||
\(932\) | 5295.41 | − | 9171.91i | 0.186112 | − | 0.322356i | ||||
\(933\) | 15016.5 | − | 34322.6i | 0.526923 | − | 1.20436i | ||||
\(934\) | 6346.35 | − | 3664.07i | 0.222333 | − | 0.128364i | ||||
\(935\) | − | 7612.05i | − | 0.266247i | ||||||
\(936\) | 11895.4 | + | 52612.1i | 0.415398 | + | 1.83727i | ||||
\(937\) | 3834.24i | 0.133681i | 0.997764 | + | 0.0668405i | \(0.0212919\pi\) | ||||
−0.997764 | + | 0.0668405i | \(0.978708\pi\) | |||||||
\(938\) | −62446.0 | − | 44818.8i | −2.17370 | − | 1.56011i | ||||
\(939\) | −8249.47 | − | 3609.24i | −0.286700 | − | 0.125435i | ||||
\(940\) | 26138.2 | + | 15090.9i | 0.906951 | + | 0.523628i | ||||
\(941\) | 29435.5 | 1.01973 | 0.509867 | − | 0.860253i | \(-0.329694\pi\) | ||||
0.509867 | + | 0.860253i | \(0.329694\pi\) | |||||||
\(942\) | −7539.11 | + | 841.658i | −0.260762 | + | 0.0291111i | ||||
\(943\) | 7820.17i | 0.270053i | ||||||||
\(944\) | 50257.2 | + | 29016.0i | 1.73277 | + | 1.00041i | ||||
\(945\) | −48543.2 | + | 56060.0i | −1.67102 | + | 1.92977i | ||||
\(946\) | 3487.16i | 0.119849i | ||||||||
\(947\) | − | 11154.2i | − | 0.382748i | −0.981517 | − | 0.191374i | \(-0.938706\pi\) | ||
0.981517 | − | 0.191374i | \(-0.0612943\pi\) | |||||||
\(948\) | 8102.77 | − | 5967.35i | 0.277601 | − | 0.204441i | ||||
\(949\) | 5754.34 | − | 3322.27i | 0.196832 | − | 0.113641i | ||||
\(950\) | 65914.1 | + | 114167.i | 2.25109 | + | 3.89900i | ||||
\(951\) | −2355.55 | + | 1734.76i | −0.0803195 | + | 0.0591518i | ||||
\(952\) | −57464.8 | −1.95635 | ||||||||
\(953\) | − | 19181.3i | − | 0.651985i | −0.945372 | − | 0.325993i | \(-0.894302\pi\) | ||
0.945372 | − | 0.325993i | \(-0.105698\pi\) | |||||||
\(954\) | −65455.9 | + | 14799.3i | −2.22140 | + | 0.502248i | ||||
\(955\) | 21483.4 | − | 37210.3i | 0.727943 | − | 1.26083i | ||||
\(956\) | −16419.4 | + | 28439.2i | −0.555483 | + | 0.962124i | ||||
\(957\) | −14351.1 | + | 10569.0i | −0.484750 | + | 0.356998i | ||||
\(958\) | −82592.5 | + | 47684.8i | −2.78543 | + | 1.60817i | ||||
\(959\) | −37239.1 | + | 21500.0i | −1.25392 | + | 0.723953i | ||||
\(960\) | −35606.3 | + | 81383.6i | −1.19707 | + | 2.73609i | ||||
\(961\) | 592.411 | − | 1026.09i | 0.0198856 | − | 0.0344428i | ||||
\(962\) | − | 5708.07i | − | 0.191305i | ||||||
\(963\) | −3396.20 | + | 3138.33i | −0.113646 | + | 0.105017i | ||||
\(964\) | −48513.5 | − | 84027.9i | −1.62087 | − | 2.80742i | ||||
\(965\) | −27454.7 | −0.915854 | ||||||||
\(966\) | −69012.0 | − | 93708.1i | −2.29858 | − | 3.12113i | ||||
\(967\) | −685.852 | − | 1187.93i | −0.0228082 | − | 0.0395049i | 0.854396 | − | 0.519622i | \(-0.173927\pi\) |
−0.877204 | + | 0.480117i | \(0.840594\pi\) | |||||||
\(968\) | 38462.1 | − | 66618.3i | 1.27709 | − | 2.21198i | ||||
\(969\) | −1782.88 | − | 15970.1i | −0.0591067 | − | 0.529445i | ||||
\(970\) | 111036. | − | 64106.9i | 3.67542 | − | 2.12201i | ||||
\(971\) | −22768.2 | + | 13145.2i | −0.752489 | + | 0.434450i | −0.826593 | − | 0.562801i | \(-0.809724\pi\) |
0.0741033 | + | 0.997251i | \(0.476391\pi\) | |||||||
\(972\) | −2452.04 | − | 75902.4i | −0.0809149 | − | 2.50470i | ||||
\(973\) | −40792.0 | − | 70653.7i | −1.34402 | − | 2.32791i | ||||
\(974\) | −24555.9 | + | 14177.3i | −0.807824 | + | 0.466397i | ||||
\(975\) | −35881.9 | + | 26425.5i | −1.17861 | + | 0.867994i | ||||
\(976\) | −11304.8 | + | 6526.84i | −0.370757 | + | 0.214056i | ||||
\(977\) | 32216.4 | + | 18600.2i | 1.05496 | + | 0.609081i | 0.924033 | − | 0.382312i | \(-0.124872\pi\) |
0.130925 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(978\) | −9017.84 | + | 20611.7i | −0.294845 | + | 0.673914i | ||||
\(979\) | 3405.50 | − | 1966.17i | 0.111175 | − | 0.0641869i | ||||
\(980\) | 143098. | 4.66438 | ||||||||
\(981\) | 36364.9 | − | 33603.7i | 1.18353 | − | 1.09366i | ||||
\(982\) | 11351.5 | + | 6553.82i | 0.368882 | + | 0.212974i | ||||
\(983\) | 4723.70 | 0.153268 | 0.0766342 | − | 0.997059i | \(-0.475583\pi\) | ||||
0.0766342 | + | 0.997059i | \(0.475583\pi\) | |||||||
\(984\) | 16125.2 | − | 1800.20i | 0.522411 | − | 0.0583214i | ||||
\(985\) | −34854.6 | − | 60370.0i | −1.12747 | − | 1.95284i | ||||
\(986\) | 27598.8 | − | 47802.6i | 0.891406 | − | 1.54396i | ||||
\(987\) | 6146.59 | + | 8346.16i | 0.198225 | + | 0.269160i | ||||
\(988\) | 49400.2 | + | 28521.2i | 1.59072 | + | 0.918403i | ||||
\(989\) | 4697.50 | − | 8136.31i | 0.151033 | − | 0.261597i | ||||
\(990\) | −21707.6 | − | 23491.2i | −0.696880 | − | 0.754142i | ||||
\(991\) | − | 27165.4i | − | 0.870774i | −0.900243 | − | 0.435387i | \(-0.856612\pi\) | ||
0.900243 | − | 0.435387i | \(-0.143388\pi\) | |||||||
\(992\) | −65511.2 | − | 37822.9i | −2.09676 | − | 1.21056i | ||||
\(993\) | 5330.46 | + | 47747.3i | 0.170349 | + | 1.52590i | ||||
\(994\) | −10456.3 | − | 18110.9i | −0.333657 | − | 0.577910i | ||||
\(995\) | −25155.5 | + | 43570.7i | −0.801492 | + | 1.38822i | ||||
\(996\) | −108333. | − | 47397.2i | −3.44646 | − | 1.50787i | ||||
\(997\) | −2117.47 | −0.0672627 | −0.0336313 | − | 0.999434i | \(-0.510707\pi\) | ||||
−0.0336313 | + | 0.999434i | \(0.510707\pi\) | |||||||
\(998\) | −30042.4 | + | 17345.0i | −0.952881 | + | 0.550146i | ||||
\(999\) | −912.399 | + | 4742.56i | −0.0288959 | + | 0.150198i |
(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 | 201.4.f.a.38.2 | ✓ | 132 | |
3.2 | odd | 2 | inner | 201.4.f.a.38.65 | yes | 132 | |
67.30 | odd | 6 | inner | 201.4.f.a.164.65 | yes | 132 | |
201.164 | even | 6 | inner | 201.4.f.a.164.2 | yes | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.4.f.a.38.2 | ✓ | 132 | 1.1 | even | 1 | trivial | |
201.4.f.a.38.65 | yes | 132 | 3.2 | odd | 2 | inner | |
201.4.f.a.164.2 | yes | 132 | 201.164 | even | 6 | inner | |
201.4.f.a.164.65 | yes | 132 | 67.30 | odd | 6 | inner |