Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.353");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (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: | \(20.8866761420\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.19 | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.4.c.b.353.20 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 2.99142 | − | 4.24869i | 0.575699 | − | 0.817662i | ||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 19.3201i | 1.72805i | 0.503452 | + | 0.864023i | \(0.332063\pi\) | ||||
−0.503452 | + | 0.864023i | \(0.667937\pi\) | |||||||
\(6\) | 5.98284 | − | 8.49739i | 0.407081 | − | 0.578174i | ||||
\(7\) | 6.85976 | 0.370392 | 0.185196 | − | 0.982702i | \(-0.440708\pi\) | ||||
0.185196 | + | 0.982702i | \(0.440708\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −9.10280 | − | 25.4193i | −0.337141 | − | 0.941454i | ||||
\(10\) | 38.6403i | 1.22191i | ||||||||
\(11\) | 4.18926 | 0.114828 | 0.0574140 | − | 0.998350i | \(-0.481715\pi\) | ||||
0.0574140 | + | 0.998350i | \(0.481715\pi\) | |||||||
\(12\) | 11.9657 | − | 16.9948i | 0.287850 | − | 0.408831i | ||||
\(13\) | − | 24.0853i | − | 0.513850i | −0.966431 | − | 0.256925i | \(-0.917291\pi\) | ||
0.966431 | − | 0.256925i | \(-0.0827093\pi\) | |||||||
\(14\) | 13.7195 | 0.261907 | ||||||||
\(15\) | 82.0854 | + | 57.7947i | 1.41296 | + | 0.994835i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 81.9283i | 1.16885i | 0.811446 | + | 0.584427i | \(0.198681\pi\) | ||||
−0.811446 | + | 0.584427i | \(0.801319\pi\) | |||||||
\(18\) | −18.2056 | − | 50.8385i | −0.238395 | − | 0.665709i | ||||
\(19\) | 122.854 | 1.48340 | 0.741702 | − | 0.670729i | \(-0.234019\pi\) | ||||
0.741702 | + | 0.670729i | \(0.234019\pi\) | |||||||
\(20\) | 77.2806i | 0.864023i | ||||||||
\(21\) | 20.5204 | − | 29.1450i | 0.213235 | − | 0.302856i | ||||
\(22\) | 8.37851 | 0.0811957 | ||||||||
\(23\) | 216.823 | 1.96569 | 0.982844 | − | 0.184439i | \(-0.0590468\pi\) | ||||
0.982844 | + | 0.184439i | \(0.0590468\pi\) | |||||||
\(24\) | 23.9314 | − | 33.9896i | 0.203540 | − | 0.289087i | ||||
\(25\) | −248.268 | −1.98615 | ||||||||
\(26\) | − | 48.1705i | − | 0.363347i | ||||||
\(27\) | −135.229 | − | 37.3647i | −0.963883 | − | 0.266327i | ||||
\(28\) | 27.4391 | 0.185196 | ||||||||
\(29\) | 136.479i | 0.873911i | 0.899483 | + | 0.436956i | \(0.143943\pi\) | ||||
−0.899483 | + | 0.436956i | \(0.856057\pi\) | |||||||
\(30\) | 164.171 | + | 115.589i | 0.999112 | + | 0.703455i | ||||
\(31\) | 342.041i | 1.98169i | 0.135002 | + | 0.990845i | \(0.456896\pi\) | ||||
−0.135002 | + | 0.990845i | \(0.543104\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 12.5318 | − | 17.7989i | 0.0661064 | − | 0.0938904i | ||||
\(34\) | 163.857i | 0.826505i | ||||||||
\(35\) | 132.532i | 0.640055i | ||||||||
\(36\) | −36.4112 | − | 101.677i | −0.168570 | − | 0.470727i | ||||
\(37\) | − | 346.028i | − | 1.53748i | −0.639562 | − | 0.768740i | \(-0.720884\pi\) | ||
0.639562 | − | 0.768740i | \(-0.279116\pi\) | |||||||
\(38\) | 245.708 | 1.04893 | ||||||||
\(39\) | −102.331 | − | 72.0492i | −0.420155 | − | 0.295823i | ||||
\(40\) | 154.561i | 0.610957i | ||||||||
\(41\) | 280.955i | 1.07019i | 0.844791 | + | 0.535096i | \(0.179724\pi\) | ||||
−0.844791 | + | 0.535096i | \(0.820276\pi\) | |||||||
\(42\) | 41.0409 | − | 58.2901i | 0.150780 | − | 0.214151i | ||||
\(43\) | − | 353.238i | − | 1.25275i | −0.779522 | − | 0.626375i | \(-0.784538\pi\) | ||
0.779522 | − | 0.626375i | \(-0.215462\pi\) | |||||||
\(44\) | 16.7570 | 0.0574140 | ||||||||
\(45\) | 491.104 | − | 175.868i | 1.62688 | − | 0.582595i | ||||
\(46\) | 433.647 | 1.38995 | ||||||||
\(47\) | 88.0361 | 0.273221 | 0.136610 | − | 0.990625i | \(-0.456379\pi\) | ||||
0.136610 | + | 0.990625i | \(0.456379\pi\) | |||||||
\(48\) | 47.8627 | − | 67.9791i | 0.143925 | − | 0.204415i | ||||
\(49\) | −295.944 | −0.862809 | ||||||||
\(50\) | −496.536 | −1.40442 | ||||||||
\(51\) | 348.088 | + | 245.082i | 0.955728 | + | 0.672909i | ||||
\(52\) | − | 96.3411i | − | 0.256925i | ||||||
\(53\) | 89.3036i | 0.231449i | 0.993281 | + | 0.115724i | \(0.0369190\pi\) | ||||
−0.993281 | + | 0.115724i | \(0.963081\pi\) | |||||||
\(54\) | −270.458 | − | 74.7294i | −0.681568 | − | 0.188322i | ||||
\(55\) | 80.9370i | 0.198428i | ||||||||
\(56\) | 54.8781 | 0.130954 | ||||||||
\(57\) | 367.509 | − | 521.970i | 0.853995 | − | 1.21292i | ||||
\(58\) | 272.957i | 0.617948i | ||||||||
\(59\) | −359.580 | − | 275.828i | −0.793446 | − | 0.608640i | ||||
\(60\) | 328.342 | + | 231.179i | 0.706479 | + | 0.497418i | ||||
\(61\) | − | 198.413i | − | 0.416462i | −0.978080 | − | 0.208231i | \(-0.933229\pi\) | ||
0.978080 | − | 0.208231i | \(-0.0667706\pi\) | |||||||
\(62\) | 684.082i | 1.40127i | ||||||||
\(63\) | −62.4431 | − | 174.370i | −0.124874 | − | 0.348708i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 465.331 | 0.887957 | ||||||||
\(66\) | 25.0637 | − | 35.5977i | 0.0467443 | − | 0.0663906i | ||||
\(67\) | − | 856.105i | − | 1.56104i | −0.625129 | − | 0.780521i | \(-0.714954\pi\) | ||
0.625129 | − | 0.780521i | \(-0.285046\pi\) | |||||||
\(68\) | 327.713i | 0.584427i | ||||||||
\(69\) | 648.610 | − | 921.217i | 1.13164 | − | 1.60727i | ||||
\(70\) | 265.063i | 0.452588i | ||||||||
\(71\) | − | 384.378i | − | 0.642497i | −0.946995 | − | 0.321249i | \(-0.895897\pi\) | ||
0.946995 | − | 0.321249i | \(-0.104103\pi\) | |||||||
\(72\) | −72.8224 | − | 203.354i | −0.119197 | − | 0.332854i | ||||
\(73\) | − | 586.003i | − | 0.939540i | −0.882789 | − | 0.469770i | \(-0.844337\pi\) | ||
0.882789 | − | 0.469770i | \(-0.155663\pi\) | |||||||
\(74\) | − | 692.057i | − | 1.08716i | ||||||
\(75\) | −742.674 | + | 1054.82i | −1.14342 | + | 1.62399i | ||||
\(76\) | 491.417 | 0.741702 | ||||||||
\(77\) | 28.7373 | 0.0425314 | ||||||||
\(78\) | −204.662 | − | 144.098i | −0.297095 | − | 0.209178i | ||||
\(79\) | 417.338 | 0.594357 | 0.297179 | − | 0.954822i | \(-0.403954\pi\) | ||||
0.297179 | + | 0.954822i | \(0.403954\pi\) | |||||||
\(80\) | 309.122i | 0.432012i | ||||||||
\(81\) | −563.278 | + | 462.773i | −0.772672 | + | 0.634805i | ||||
\(82\) | 561.911i | 0.756740i | ||||||||
\(83\) | −1265.56 | −1.67366 | −0.836828 | − | 0.547465i | \(-0.815593\pi\) | ||||
−0.836828 | + | 0.547465i | \(0.815593\pi\) | |||||||
\(84\) | 82.0818 | − | 116.580i | 0.106617 | − | 0.151428i | ||||
\(85\) | −1582.87 | −2.01984 | ||||||||
\(86\) | − | 706.475i | − | 0.885828i | ||||||
\(87\) | 579.855 | + | 408.265i | 0.714564 | + | 0.503110i | ||||
\(88\) | 33.5140 | 0.0405978 | ||||||||
\(89\) | −329.519 | −0.392460 | −0.196230 | − | 0.980558i | \(-0.562870\pi\) | ||||
−0.196230 | + | 0.980558i | \(0.562870\pi\) | |||||||
\(90\) | 982.208 | − | 351.735i | 1.15038 | − | 0.411957i | ||||
\(91\) | − | 165.219i | − | 0.190326i | ||||||
\(92\) | 867.294 | 0.982844 | ||||||||
\(93\) | 1453.23 | + | 1023.19i | 1.62035 | + | 1.14086i | ||||
\(94\) | 176.072 | 0.193196 | ||||||||
\(95\) | 2373.56i | 2.56339i | ||||||||
\(96\) | 95.7255 | − | 135.958i | 0.101770 | − | 0.144544i | ||||
\(97\) | 49.9128i | 0.0522462i | 0.999659 | + | 0.0261231i | \(0.00831618\pi\) | ||||
−0.999659 | + | 0.0261231i | \(0.991684\pi\) | |||||||
\(98\) | −591.887 | −0.610098 | ||||||||
\(99\) | −38.1340 | − | 106.488i | −0.0387132 | − | 0.108105i | ||||
\(100\) | −993.073 | −0.993073 | ||||||||
\(101\) | 351.292 | 0.346088 | 0.173044 | − | 0.984914i | \(-0.444640\pi\) | ||||
0.173044 | + | 0.984914i | \(0.444640\pi\) | |||||||
\(102\) | 696.177 | + | 490.164i | 0.675801 | + | 0.475818i | ||||
\(103\) | 1144.52i | 1.09488i | 0.836844 | + | 0.547441i | \(0.184398\pi\) | ||||
−0.836844 | + | 0.547441i | \(0.815602\pi\) | |||||||
\(104\) | − | 192.682i | − | 0.181673i | ||||||
\(105\) | 563.087 | + | 396.458i | 0.523349 | + | 0.368479i | ||||
\(106\) | 178.607i | 0.163659i | ||||||||
\(107\) | 372.797i | 0.336819i | 0.985717 | + | 0.168409i | \(0.0538630\pi\) | ||||
−0.985717 | + | 0.168409i | \(0.946137\pi\) | |||||||
\(108\) | −540.916 | − | 149.459i | −0.481941 | − | 0.133164i | ||||
\(109\) | − | 1401.55i | − | 1.23160i | −0.787904 | − | 0.615798i | \(-0.788834\pi\) | ||
0.787904 | − | 0.615798i | \(-0.211166\pi\) | |||||||
\(110\) | 161.874i | 0.140310i | ||||||||
\(111\) | −1470.17 | − | 1035.12i | −1.25714 | − | 0.885125i | ||||
\(112\) | 109.756 | 0.0925981 | ||||||||
\(113\) | −1636.81 | −1.36264 | −0.681319 | − | 0.731987i | \(-0.738593\pi\) | ||||
−0.681319 | + | 0.731987i | \(0.738593\pi\) | |||||||
\(114\) | 735.017 | − | 1043.94i | 0.603865 | − | 0.857666i | ||||
\(115\) | 4189.06i | 3.39680i | ||||||||
\(116\) | 545.914i | 0.436956i | ||||||||
\(117\) | −612.230 | + | 219.243i | −0.483766 | + | 0.173240i | ||||
\(118\) | −719.160 | − | 551.657i | −0.561051 | − | 0.430374i | ||||
\(119\) | 562.009i | 0.432935i | ||||||||
\(120\) | 656.683 | + | 462.358i | 0.499556 | + | 0.351727i | ||||
\(121\) | −1313.45 | −0.986815 | ||||||||
\(122\) | − | 396.826i | − | 0.294483i | ||||||
\(123\) | 1193.69 | + | 840.456i | 0.875054 | + | 0.616108i | ||||
\(124\) | 1368.16i | 0.990845i | ||||||||
\(125\) | − | 2381.56i | − | 1.70410i | ||||||
\(126\) | −124.886 | − | 348.740i | −0.0882996 | − | 0.246573i | ||||
\(127\) | −2385.37 | −1.66667 | −0.833337 | − | 0.552765i | \(-0.813573\pi\) | ||||
−0.833337 | + | 0.552765i | \(0.813573\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −1500.80 | − | 1056.68i | −1.02433 | − | 0.721207i | ||||
\(130\) | 930.662 | 0.627880 | ||||||||
\(131\) | 613.343 | 0.409069 | 0.204535 | − | 0.978859i | \(-0.434432\pi\) | ||||
0.204535 | + | 0.978859i | \(0.434432\pi\) | |||||||
\(132\) | 50.1273 | − | 71.1955i | 0.0330532 | − | 0.0469452i | ||||
\(133\) | 842.751 | 0.549442 | ||||||||
\(134\) | − | 1712.21i | − | 1.10382i | ||||||
\(135\) | 721.891 | − | 2612.64i | 0.460226 | − | 1.66563i | ||||
\(136\) | 655.426i | 0.413253i | ||||||||
\(137\) | − | 1818.42i | − | 1.13400i | −0.823716 | − | 0.567002i | \(-0.808103\pi\) | ||
0.823716 | − | 0.567002i | \(-0.191897\pi\) | |||||||
\(138\) | 1297.22 | − | 1842.43i | 0.800194 | − | 1.13651i | ||||
\(139\) | 1979.15 | 1.20769 | 0.603847 | − | 0.797100i | \(-0.293634\pi\) | ||||
0.603847 | + | 0.797100i | \(0.293634\pi\) | |||||||
\(140\) | 530.127i | 0.320028i | ||||||||
\(141\) | 263.353 | − | 374.038i | 0.157293 | − | 0.223402i | ||||
\(142\) | − | 768.757i | − | 0.454314i | ||||||
\(143\) | − | 100.899i | − | 0.0590044i | ||||||
\(144\) | −145.645 | − | 406.708i | −0.0842852 | − | 0.235364i | ||||
\(145\) | −2636.79 | −1.51016 | ||||||||
\(146\) | − | 1172.01i | − | 0.664355i | ||||||
\(147\) | −885.292 | + | 1257.37i | −0.496719 | + | 0.705486i | ||||
\(148\) | − | 1384.11i | − | 0.768740i | ||||||
\(149\) | 2341.67 | 1.28750 | 0.643749 | − | 0.765237i | \(-0.277378\pi\) | ||||
0.643749 | + | 0.765237i | \(0.277378\pi\) | |||||||
\(150\) | −1485.35 | + | 2109.63i | −0.808522 | + | 1.14834i | ||||
\(151\) | − | 58.6798i | − | 0.0316245i | −0.999875 | − | 0.0158122i | \(-0.994967\pi\) | ||
0.999875 | − | 0.0158122i | \(-0.00503340\pi\) | |||||||
\(152\) | 982.834 | 0.524463 | ||||||||
\(153\) | 2082.56 | − | 745.777i | 1.10042 | − | 0.394069i | ||||
\(154\) | 57.4746 | 0.0300743 | ||||||||
\(155\) | −6608.29 | −3.42445 | ||||||||
\(156\) | −409.324 | − | 288.197i | −0.210078 | − | 0.147912i | ||||
\(157\) | 816.575i | 0.415094i | 0.978225 | + | 0.207547i | \(0.0665480\pi\) | ||||
−0.978225 | + | 0.207547i | \(0.933452\pi\) | |||||||
\(158\) | 834.676 | 0.420274 | ||||||||
\(159\) | 379.424 | + | 267.145i | 0.189247 | + | 0.133245i | ||||
\(160\) | 618.245i | 0.305478i | ||||||||
\(161\) | 1487.36 | 0.728076 | ||||||||
\(162\) | −1126.56 | + | 925.546i | −0.546362 | + | 0.448875i | ||||
\(163\) | 743.864 | 0.357447 | 0.178724 | − | 0.983899i | \(-0.442803\pi\) | ||||
0.178724 | + | 0.983899i | \(0.442803\pi\) | |||||||
\(164\) | 1123.82i | 0.535096i | ||||||||
\(165\) | 343.877 | + | 242.117i | 0.162247 | + | 0.114235i | ||||
\(166\) | −2531.12 | −1.18345 | ||||||||
\(167\) | − | 3395.96i | − | 1.57358i | −0.617224 | − | 0.786788i | \(-0.711743\pi\) | ||
0.617224 | − | 0.786788i | \(-0.288257\pi\) | |||||||
\(168\) | 164.164 | − | 233.160i | 0.0753898 | − | 0.107076i | ||||
\(169\) | 1616.90 | 0.735958 | ||||||||
\(170\) | −3165.73 | −1.42824 | ||||||||
\(171\) | −1118.32 | − | 3122.86i | −0.500116 | − | 1.39656i | ||||
\(172\) | − | 1412.95i | − | 0.626375i | ||||||
\(173\) | −3561.30 | −1.56509 | −0.782545 | − | 0.622594i | \(-0.786079\pi\) | ||||
−0.782545 | + | 0.622594i | \(0.786079\pi\) | |||||||
\(174\) | 1159.71 | + | 816.529i | 0.505273 | + | 0.355752i | ||||
\(175\) | −1703.06 | −0.735653 | ||||||||
\(176\) | 67.0281 | 0.0287070 | ||||||||
\(177\) | −2247.57 | + | 702.627i | −0.954448 | + | 0.298377i | ||||
\(178\) | −659.038 | −0.277511 | ||||||||
\(179\) | 439.482 | 0.183511 | 0.0917553 | − | 0.995782i | \(-0.470752\pi\) | ||||
0.0917553 | + | 0.995782i | \(0.470752\pi\) | |||||||
\(180\) | 1964.42 | − | 703.470i | 0.813438 | − | 0.291298i | ||||
\(181\) | −1254.06 | −0.514990 | −0.257495 | − | 0.966280i | \(-0.582897\pi\) | ||||
−0.257495 | + | 0.966280i | \(0.582897\pi\) | |||||||
\(182\) | − | 330.439i | − | 0.134581i | ||||||
\(183\) | −842.996 | − | 593.537i | −0.340525 | − | 0.239757i | ||||
\(184\) | 1734.59 | 0.694976 | ||||||||
\(185\) | 6685.32 | 2.65684 | ||||||||
\(186\) | 2906.46 | + | 2046.38i | 1.14576 | + | 0.806708i | ||||
\(187\) | 343.219i | 0.134217i | ||||||||
\(188\) | 352.144 | 0.136610 | ||||||||
\(189\) | −927.639 | − | 256.313i | −0.357015 | − | 0.0986456i | ||||
\(190\) | 4747.12i | 1.81259i | ||||||||
\(191\) | 1864.36 | 0.706283 | 0.353141 | − | 0.935570i | \(-0.385113\pi\) | ||||
0.353141 | + | 0.935570i | \(0.385113\pi\) | |||||||
\(192\) | 191.451 | − | 271.916i | 0.0719624 | − | 0.102208i | ||||
\(193\) | 2674.19 | 0.997369 | 0.498684 | − | 0.866784i | \(-0.333817\pi\) | ||||
0.498684 | + | 0.866784i | \(0.333817\pi\) | |||||||
\(194\) | 99.8256i | 0.0369436i | ||||||||
\(195\) | 1392.00 | − | 1977.05i | 0.511196 | − | 0.726048i | ||||
\(196\) | −1183.77 | −0.431405 | ||||||||
\(197\) | 1280.49i | 0.463104i | 0.972823 | + | 0.231552i | \(0.0743803\pi\) | ||||
−0.972823 | + | 0.231552i | \(0.925620\pi\) | |||||||
\(198\) | −76.2679 | − | 212.976i | −0.0273744 | − | 0.0764420i | ||||
\(199\) | −1491.41 | −0.531271 | −0.265635 | − | 0.964074i | \(-0.585582\pi\) | ||||
−0.265635 | + | 0.964074i | \(0.585582\pi\) | |||||||
\(200\) | −1986.15 | −0.702208 | ||||||||
\(201\) | −3637.33 | − | 2560.97i | −1.27640 | − | 0.898691i | ||||
\(202\) | 702.584 | 0.244721 | ||||||||
\(203\) | 936.210i | 0.323690i | ||||||||
\(204\) | 1392.35 | + | 980.328i | 0.477864 | + | 0.336454i | ||||
\(205\) | −5428.10 | −1.84934 | ||||||||
\(206\) | 2289.04i | 0.774199i | ||||||||
\(207\) | −1973.70 | − | 5511.49i | −0.662714 | − | 1.85061i | ||||
\(208\) | − | 385.364i | − | 0.128463i | ||||||
\(209\) | 514.668 | 0.170336 | ||||||||
\(210\) | 1126.17 | + | 792.916i | 0.370063 | + | 0.260554i | ||||
\(211\) | 1360.50i | 0.443889i | 0.975059 | + | 0.221945i | \(0.0712404\pi\) | ||||
−0.975059 | + | 0.221945i | \(0.928760\pi\) | |||||||
\(212\) | 357.214i | 0.115724i | ||||||||
\(213\) | −1633.11 | − | 1149.84i | −0.525345 | − | 0.369885i | ||||
\(214\) | 745.593i | 0.238167i | ||||||||
\(215\) | 6824.61 | 2.16481 | ||||||||
\(216\) | −1081.83 | − | 298.917i | −0.340784 | − | 0.0941609i | ||||
\(217\) | 2346.32i | 0.734003i | ||||||||
\(218\) | − | 2803.10i | − | 0.870870i | ||||||
\(219\) | −2489.75 | − | 1752.98i | −0.768226 | − | 0.540892i | ||||
\(220\) | 323.748i | 0.0992141i | ||||||||
\(221\) | 1973.26 | 0.600616 | ||||||||
\(222\) | −2940.34 | − | 2070.23i | −0.888930 | − | 0.625878i | ||||
\(223\) | −4065.57 | −1.22086 | −0.610428 | − | 0.792072i | \(-0.709003\pi\) | ||||
−0.610428 | + | 0.792072i | \(0.709003\pi\) | |||||||
\(224\) | 219.512 | 0.0654768 | ||||||||
\(225\) | 2259.94 | + | 6310.79i | 0.669611 | + | 1.86986i | ||||
\(226\) | −3273.62 | −0.963530 | ||||||||
\(227\) | 1176.48 | 0.343990 | 0.171995 | − | 0.985098i | \(-0.444979\pi\) | ||||
0.171995 | + | 0.985098i | \(0.444979\pi\) | |||||||
\(228\) | 1470.03 | − | 2087.88i | 0.426997 | − | 0.606461i | ||||
\(229\) | 4445.18i | 1.28273i | 0.767235 | + | 0.641367i | \(0.221632\pi\) | ||||
−0.767235 | + | 0.641367i | \(0.778368\pi\) | |||||||
\(230\) | 8378.12i | 2.40190i | ||||||||
\(231\) | 85.9654 | − | 122.096i | 0.0244853 | − | 0.0347763i | ||||
\(232\) | 1091.83i | 0.308974i | ||||||||
\(233\) | 452.890 | 0.127338 | 0.0636691 | − | 0.997971i | \(-0.479720\pi\) | ||||
0.0636691 | + | 0.997971i | \(0.479720\pi\) | |||||||
\(234\) | −1224.46 | + | 438.487i | −0.342074 | + | 0.122499i | ||||
\(235\) | 1700.87i | 0.472138i | ||||||||
\(236\) | −1438.32 | − | 1103.31i | −0.396723 | − | 0.304320i | ||||
\(237\) | 1248.43 | − | 1773.14i | 0.342171 | − | 0.485983i | ||||
\(238\) | 1124.02i | 0.306131i | ||||||||
\(239\) | − | 2596.48i | − | 0.702729i | −0.936239 | − | 0.351364i | \(-0.885718\pi\) | ||
0.936239 | − | 0.351364i | \(-0.114282\pi\) | |||||||
\(240\) | 1313.37 | + | 924.715i | 0.353239 | + | 0.248709i | ||||
\(241\) | 4352.05 | 1.16324 | 0.581618 | − | 0.813462i | \(-0.302420\pi\) | ||||
0.581618 | + | 0.813462i | \(0.302420\pi\) | |||||||
\(242\) | −2626.90 | −0.697783 | ||||||||
\(243\) | 281.180 | + | 3777.54i | 0.0742293 | + | 0.997241i | ||||
\(244\) | − | 793.652i | − | 0.208231i | ||||||
\(245\) | − | 5717.67i | − | 1.49097i | ||||||
\(246\) | 2387.39 | + | 1680.91i | 0.618757 | + | 0.435654i | ||||
\(247\) | − | 2958.98i | − | 0.762247i | ||||||
\(248\) | 2736.33i | 0.700633i | ||||||||
\(249\) | −3785.83 | + | 5376.99i | −0.963523 | + | 1.36848i | ||||
\(250\) | − | 4763.12i | − | 1.20498i | ||||||
\(251\) | 4403.08i | 1.10725i | 0.832766 | + | 0.553625i | \(0.186756\pi\) | ||||
−0.832766 | + | 0.553625i | \(0.813244\pi\) | |||||||
\(252\) | −249.772 | − | 697.481i | −0.0624372 | − | 0.174354i | ||||
\(253\) | 908.329 | 0.225716 | ||||||||
\(254\) | −4770.75 | −1.17852 | ||||||||
\(255\) | −4735.02 | + | 6725.12i | −1.16282 | + | 1.65154i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 883.840i | 0.214523i | 0.994231 | + | 0.107262i | \(0.0342082\pi\) | ||||
−0.994231 | + | 0.107262i | \(0.965792\pi\) | |||||||
\(258\) | −3001.60 | − | 2113.37i | −0.724307 | − | 0.509970i | ||||
\(259\) | − | 2373.67i | − | 0.569471i | ||||||
\(260\) | 1861.32 | 0.443978 | ||||||||
\(261\) | 3469.18 | − | 1242.34i | 0.822747 | − | 0.294631i | ||||
\(262\) | 1226.69 | 0.289256 | ||||||||
\(263\) | − | 4860.77i | − | 1.13965i | −0.821766 | − | 0.569825i | \(-0.807011\pi\) | ||
0.821766 | − | 0.569825i | \(-0.192989\pi\) | |||||||
\(264\) | 100.255 | − | 142.391i | 0.0233721 | − | 0.0331953i | ||||
\(265\) | −1725.36 | −0.399955 | ||||||||
\(266\) | 1685.50 | 0.388514 | ||||||||
\(267\) | −985.731 | + | 1400.03i | −0.225939 | + | 0.320900i | ||||
\(268\) | − | 3424.42i | − | 0.780521i | ||||||
\(269\) | −3635.08 | −0.823921 | −0.411960 | − | 0.911202i | \(-0.635156\pi\) | ||||
−0.411960 | + | 0.911202i | \(0.635156\pi\) | |||||||
\(270\) | 1443.78 | − | 5225.29i | 0.325429 | − | 1.17778i | ||||
\(271\) | −1565.65 | −0.350947 | −0.175473 | − | 0.984484i | \(-0.556146\pi\) | ||||
−0.175473 | + | 0.984484i | \(0.556146\pi\) | |||||||
\(272\) | 1310.85i | 0.292214i | ||||||||
\(273\) | −701.966 | − | 494.240i | −0.155622 | − | 0.109571i | ||||
\(274\) | − | 3636.85i | − | 0.801862i | ||||||
\(275\) | −1040.06 | −0.228065 | ||||||||
\(276\) | 2594.44 | − | 3684.87i | 0.565822 | − | 0.803634i | ||||
\(277\) | 5463.54 | 1.18510 | 0.592549 | − | 0.805534i | \(-0.298122\pi\) | ||||
0.592549 | + | 0.805534i | \(0.298122\pi\) | |||||||
\(278\) | 3958.30 | 0.853968 | ||||||||
\(279\) | 8694.43 | − | 3113.53i | 1.86567 | − | 0.668109i | ||||
\(280\) | 1060.25i | 0.226294i | ||||||||
\(281\) | 2307.25i | 0.489818i | 0.969546 | + | 0.244909i | \(0.0787581\pi\) | ||||
−0.969546 | + | 0.244909i | \(0.921242\pi\) | |||||||
\(282\) | 526.706 | − | 748.077i | 0.111223 | − | 0.157969i | ||||
\(283\) | 1493.24i | 0.313653i | 0.987626 | + | 0.156827i | \(0.0501264\pi\) | ||||
−0.987626 | + | 0.156827i | \(0.949874\pi\) | |||||||
\(284\) | − | 1537.51i | − | 0.321249i | ||||||
\(285\) | 10084.5 | + | 7100.32i | 2.09599 | + | 1.47574i | ||||
\(286\) | − | 201.799i | − | 0.0417224i | ||||||
\(287\) | 1927.29i | 0.396391i | ||||||||
\(288\) | −291.290 | − | 813.416i | −0.0595987 | − | 0.166427i | ||||
\(289\) | −1799.25 | −0.366221 | ||||||||
\(290\) | −5273.57 | −1.06784 | ||||||||
\(291\) | 212.064 | + | 149.310i | 0.0427197 | + | 0.0300781i | ||||
\(292\) | − | 2344.01i | − | 0.469770i | ||||||
\(293\) | − | 34.7500i | − | 0.00692874i | −0.999994 | − | 0.00346437i | \(-0.998897\pi\) | ||
0.999994 | − | 0.00346437i | \(-0.00110274\pi\) | |||||||
\(294\) | −1770.58 | + | 2514.75i | −0.351233 | + | 0.498854i | ||||
\(295\) | 5329.04 | − | 6947.14i | 1.05176 | − | 1.37111i | ||||
\(296\) | − | 2768.23i | − | 0.543581i | ||||||
\(297\) | −566.509 | − | 156.530i | −0.110681 | − | 0.0305818i | ||||
\(298\) | 4683.34 | 0.910399 | ||||||||
\(299\) | − | 5222.25i | − | 1.01007i | ||||||
\(300\) | −2970.70 | + | 4219.26i | −0.571711 | + | 0.811997i | ||||
\(301\) | − | 2423.13i | − | 0.464009i | ||||||
\(302\) | − | 117.360i | − | 0.0223619i | ||||||
\(303\) | 1050.86 | − | 1492.53i | 0.199242 | − | 0.282983i | ||||
\(304\) | 1965.67 | 0.370851 | ||||||||
\(305\) | 3833.37 | 0.719666 | ||||||||
\(306\) | 4165.11 | − | 1491.55i | 0.778117 | − | 0.278649i | ||||
\(307\) | 5355.26 | 0.995573 | 0.497786 | − | 0.867300i | \(-0.334146\pi\) | ||||
0.497786 | + | 0.867300i | \(0.334146\pi\) | |||||||
\(308\) | 114.949 | 0.0212657 | ||||||||
\(309\) | 4862.72 | + | 3423.74i | 0.895244 | + | 0.630323i | ||||
\(310\) | −13216.6 | −2.42145 | ||||||||
\(311\) | − | 6528.18i | − | 1.19029i | −0.803620 | − | 0.595143i | \(-0.797095\pi\) | ||
0.803620 | − | 0.595143i | \(-0.202905\pi\) | |||||||
\(312\) | −818.647 | − | 576.393i | −0.148547 | − | 0.104589i | ||||
\(313\) | − | 528.968i | − | 0.0955240i | −0.998859 | − | 0.0477620i | \(-0.984791\pi\) | ||
0.998859 | − | 0.0477620i | \(-0.0152089\pi\) | |||||||
\(314\) | 1633.15i | 0.293516i | ||||||||
\(315\) | 3368.86 | − | 1206.41i | 0.602583 | − | 0.215789i | ||||
\(316\) | 1669.35 | 0.297179 | ||||||||
\(317\) | 1736.12i | 0.307603i | 0.988102 | + | 0.153802i | \(0.0491516\pi\) | ||||
−0.988102 | + | 0.153802i | \(0.950848\pi\) | |||||||
\(318\) | 758.847 | + | 534.289i | 0.133818 | + | 0.0942184i | ||||
\(319\) | 571.743i | 0.100349i | ||||||||
\(320\) | 1236.49i | 0.216006i | ||||||||
\(321\) | 1583.90 | + | 1115.19i | 0.275404 | + | 0.193906i | ||||
\(322\) | 2974.72 | 0.514827 | ||||||||
\(323\) | 10065.2i | 1.73388i | ||||||||
\(324\) | −2253.11 | + | 1851.09i | −0.386336 | + | 0.317403i | ||||
\(325\) | 5979.60i | 1.02058i | ||||||||
\(326\) | 1487.73 | 0.252754 | ||||||||
\(327\) | −5954.75 | − | 4192.62i | −1.00703 | − | 0.709029i | ||||
\(328\) | 2247.64i | 0.378370i | ||||||||
\(329\) | 603.907 | 0.101199 | ||||||||
\(330\) | 687.753 | + | 484.233i | 0.114726 | + | 0.0807763i | ||||
\(331\) | −4528.41 | −0.751975 | −0.375988 | − | 0.926625i | \(-0.622697\pi\) | ||||
−0.375988 | + | 0.926625i | \(0.622697\pi\) | |||||||
\(332\) | −5062.25 | −0.836828 | ||||||||
\(333\) | −8795.79 | + | 3149.83i | −1.44747 | + | 0.518347i | ||||
\(334\) | − | 6791.92i | − | 1.11269i | ||||||
\(335\) | 16540.1 | 2.69755 | ||||||||
\(336\) | 328.327 | − | 466.321i | 0.0533087 | − | 0.0757139i | ||||
\(337\) | 2199.10i | 0.355467i | 0.984079 | + | 0.177734i | \(0.0568766\pi\) | ||||
−0.984079 | + | 0.177734i | \(0.943123\pi\) | |||||||
\(338\) | 3233.80 | 0.520401 | ||||||||
\(339\) | −4896.38 | + | 6954.30i | −0.784469 | + | 1.11418i | ||||
\(340\) | −6331.47 | −1.00992 | ||||||||
\(341\) | 1432.90i | 0.227554i | ||||||||
\(342\) | −2236.64 | − | 6245.73i | −0.353636 | − | 0.987515i | ||||
\(343\) | −4383.00 | −0.689971 | ||||||||
\(344\) | − | 2825.90i | − | 0.442914i | ||||||
\(345\) | 17798.0 | + | 12531.2i | 2.77743 | + | 1.95554i | ||||
\(346\) | −7122.60 | −1.10669 | ||||||||
\(347\) | −3235.70 | −0.500580 | −0.250290 | − | 0.968171i | \(-0.580526\pi\) | ||||
−0.250290 | + | 0.968171i | \(0.580526\pi\) | |||||||
\(348\) | 2319.42 | + | 1633.06i | 0.357282 | + | 0.251555i | ||||
\(349\) | 3400.91i | 0.521623i | 0.965390 | + | 0.260812i | \(0.0839901\pi\) | ||||
−0.965390 | + | 0.260812i | \(0.916010\pi\) | |||||||
\(350\) | −3406.12 | −0.520185 | ||||||||
\(351\) | −899.938 | + | 3257.03i | −0.136852 | + | 0.495291i | ||||
\(352\) | 134.056 | 0.0202989 | ||||||||
\(353\) | −11542.1 | −1.74029 | −0.870144 | − | 0.492798i | \(-0.835974\pi\) | ||||
−0.870144 | + | 0.492798i | \(0.835974\pi\) | |||||||
\(354\) | −4495.13 | + | 1405.25i | −0.674897 | + | 0.210984i | ||||
\(355\) | 7426.25 | 1.11027 | ||||||||
\(356\) | −1318.08 | −0.196230 | ||||||||
\(357\) | 2387.80 | + | 1681.20i | 0.353994 | + | 0.249240i | ||||
\(358\) | 878.963 | 0.129762 | ||||||||
\(359\) | − | 6857.58i | − | 1.00816i | −0.863657 | − | 0.504079i | \(-0.831832\pi\) | ||
0.863657 | − | 0.504079i | \(-0.168168\pi\) | |||||||
\(360\) | 3928.83 | − | 1406.94i | 0.575188 | − | 0.205979i | ||||
\(361\) | 8234.15 | 1.20049 | ||||||||
\(362\) | −2508.11 | −0.364153 | ||||||||
\(363\) | −3929.08 | + | 5580.45i | −0.568108 | + | 0.806880i | ||||
\(364\) | − | 660.877i | − | 0.0951631i | ||||||
\(365\) | 11321.7 | 1.62357 | ||||||||
\(366\) | −1685.99 | − | 1187.07i | −0.240787 | − | 0.169534i | ||||
\(367\) | − | 5058.19i | − | 0.719443i | −0.933060 | − | 0.359722i | \(-0.882872\pi\) | ||
0.933060 | − | 0.359722i | \(-0.117128\pi\) | |||||||
\(368\) | 3469.18 | 0.491422 | ||||||||
\(369\) | 7141.68 | − | 2557.48i | 1.00754 | − | 0.360805i | ||||
\(370\) | 13370.6 | 1.87867 | ||||||||
\(371\) | 612.602i | 0.0857269i | ||||||||
\(372\) | 5812.91 | + | 4092.76i | 0.810176 | + | 0.570429i | ||||
\(373\) | 11615.2 | 1.61237 | 0.806185 | − | 0.591663i | \(-0.201528\pi\) | ||||
0.806185 | + | 0.591663i | \(0.201528\pi\) | |||||||
\(374\) | 686.437i | 0.0949059i | ||||||||
\(375\) | −10118.5 | − | 7124.24i | −1.39338 | − | 0.981052i | ||||
\(376\) | 704.289 | 0.0965982 | ||||||||
\(377\) | 3287.12 | 0.449059 | ||||||||
\(378\) | −1855.28 | − | 512.626i | −0.252448 | − | 0.0697530i | ||||
\(379\) | 5801.94 | 0.786347 | 0.393174 | − | 0.919464i | \(-0.371377\pi\) | ||||
0.393174 | + | 0.919464i | \(0.371377\pi\) | |||||||
\(380\) | 9494.25i | 1.28170i | ||||||||
\(381\) | −7135.65 | + | 10134.7i | −0.959503 | + | 1.36278i | ||||
\(382\) | 3728.71 | 0.499417 | ||||||||
\(383\) | 7103.14i | 0.947659i | 0.880616 | + | 0.473830i | \(0.157129\pi\) | ||||
−0.880616 | + | 0.473830i | \(0.842871\pi\) | |||||||
\(384\) | 382.902 | − | 543.833i | 0.0508851 | − | 0.0722718i | ||||
\(385\) | 555.209i | 0.0734963i | ||||||||
\(386\) | 5348.37 | 0.705246 | ||||||||
\(387\) | −8979.04 | + | 3215.45i | −1.17941 | + | 0.422353i | ||||
\(388\) | 199.651i | 0.0261231i | ||||||||
\(389\) | − | 10123.9i | − | 1.31954i | −0.751466 | − | 0.659771i | \(-0.770653\pi\) | ||
0.751466 | − | 0.659771i | \(-0.229347\pi\) | |||||||
\(390\) | 2784.00 | − | 3954.10i | 0.361470 | − | 0.513394i | ||||
\(391\) | 17764.0i | 2.29760i | ||||||||
\(392\) | −2367.55 | −0.305049 | ||||||||
\(393\) | 1834.77 | − | 2605.91i | 0.235501 | − | 0.334480i | ||||
\(394\) | 2560.99i | 0.327464i | ||||||||
\(395\) | 8063.04i | 1.02708i | ||||||||
\(396\) | −152.536 | − | 425.951i | −0.0193566 | − | 0.0540527i | ||||
\(397\) | − | 12298.8i | − | 1.55480i | −0.629003 | − | 0.777402i | \(-0.716537\pi\) | ||
0.629003 | − | 0.777402i | \(-0.283463\pi\) | |||||||
\(398\) | −2982.81 | −0.375665 | ||||||||
\(399\) | 2521.02 | − | 3580.59i | 0.316313 | − | 0.449258i | ||||
\(400\) | −3972.29 | −0.496536 | ||||||||
\(401\) | −366.551 | −0.0456476 | −0.0228238 | − | 0.999740i | \(-0.507266\pi\) | ||||
−0.0228238 | + | 0.999740i | \(0.507266\pi\) | |||||||
\(402\) | −7274.65 | − | 5121.94i | −0.902554 | − | 0.635470i | ||||
\(403\) | 8238.15 | 1.01829 | ||||||||
\(404\) | 1405.17 | 0.173044 | ||||||||
\(405\) | −8940.85 | − | 10882.6i | −1.09697 | − | 1.33521i | ||||
\(406\) | 1872.42i | 0.228883i | ||||||||
\(407\) | − | 1449.60i | − | 0.176546i | ||||||
\(408\) | 2784.71 | + | 1960.66i | 0.337901 | + | 0.237909i | ||||
\(409\) | 8767.45i | 1.05996i | 0.848011 | + | 0.529979i | \(0.177800\pi\) | ||||
−0.848011 | + | 0.529979i | \(0.822200\pi\) | |||||||
\(410\) | −10856.2 | −1.30768 | ||||||||
\(411\) | −7725.93 | − | 5439.67i | −0.927231 | − | 0.652845i | ||||
\(412\) | 4578.08i | 0.547441i | ||||||||
\(413\) | −2466.63 | − | 1892.12i | −0.293886 | − | 0.225436i | ||||
\(414\) | −3947.40 | − | 11023.0i | −0.468609 | − | 1.30858i | ||||
\(415\) | − | 24450.9i | − | 2.89216i | ||||||
\(416\) | − | 770.728i | − | 0.0908367i | ||||||
\(417\) | 5920.47 | − | 8408.81i | 0.695268 | − | 0.987485i | ||||
\(418\) | 1029.34 | 0.120446 | ||||||||
\(419\) | −4236.17 | −0.493915 | −0.246958 | − | 0.969026i | \(-0.579431\pi\) | ||||
−0.246958 | + | 0.969026i | \(0.579431\pi\) | |||||||
\(420\) | 2252.35 | + | 1585.83i | 0.261674 | + | 0.184240i | ||||
\(421\) | − | 4501.94i | − | 0.521167i | −0.965451 | − | 0.260583i | \(-0.916085\pi\) | ||
0.965451 | − | 0.260583i | \(-0.0839149\pi\) | |||||||
\(422\) | 2721.00i | 0.313877i | ||||||||
\(423\) | −801.375 | − | 2237.81i | −0.0921139 | − | 0.257225i | ||||
\(424\) | 714.429i | 0.0818295i | ||||||||
\(425\) | − | 20340.2i | − | 2.32152i | ||||||
\(426\) | −3266.21 | − | 2299.67i | −0.371475 | − | 0.261548i | ||||
\(427\) | − | 1361.07i | − | 0.154254i | ||||||
\(428\) | 1491.19i | 0.168409i | ||||||||
\(429\) | −428.690 | − | 301.832i | −0.0482456 | − | 0.0339688i | ||||
\(430\) | 13649.2 | 1.53075 | ||||||||
\(431\) | −11871.0 | −1.32669 | −0.663347 | − | 0.748312i | \(-0.730864\pi\) | ||||
−0.663347 | + | 0.748312i | \(0.730864\pi\) | |||||||
\(432\) | −2163.66 | − | 597.835i | −0.240971 | − | 0.0665818i | ||||
\(433\) | −4824.35 | −0.535435 | −0.267718 | − | 0.963497i | \(-0.586269\pi\) | ||||
−0.267718 | + | 0.963497i | \(0.586269\pi\) | |||||||
\(434\) | 4692.64i | 0.519019i | ||||||||
\(435\) | −7887.73 | + | 11202.9i | −0.869397 | + | 1.23480i | ||||
\(436\) | − | 5606.20i | − | 0.615798i | ||||||
\(437\) | 26637.7 | 2.91591 | ||||||||
\(438\) | −4979.49 | − | 3505.96i | −0.543218 | − | 0.382469i | ||||
\(439\) | −8521.83 | −0.926480 | −0.463240 | − | 0.886233i | \(-0.653313\pi\) | ||||
−0.463240 | + | 0.886233i | \(0.653313\pi\) | |||||||
\(440\) | 647.496i | 0.0701549i | ||||||||
\(441\) | 2693.92 | + | 7522.67i | 0.290888 | + | 0.812296i | ||||
\(442\) | 3946.53 | 0.424700 | ||||||||
\(443\) | 6506.99 | 0.697870 | 0.348935 | − | 0.937147i | \(-0.386543\pi\) | ||||
0.348935 | + | 0.937147i | \(0.386543\pi\) | |||||||
\(444\) | −5880.68 | − | 4140.47i | −0.628569 | − | 0.442563i | ||||
\(445\) | − | 6366.36i | − | 0.678190i | ||||||
\(446\) | −8131.15 | −0.863276 | ||||||||
\(447\) | 7004.93 | − | 9949.05i | 0.741212 | − | 1.05274i | ||||
\(448\) | 439.025 | 0.0462991 | ||||||||
\(449\) | 3008.46i | 0.316210i | 0.987422 | + | 0.158105i | \(0.0505384\pi\) | ||||
−0.987422 | + | 0.158105i | \(0.949462\pi\) | |||||||
\(450\) | 4519.87 | + | 12621.6i | 0.473486 | + | 1.32219i | ||||
\(451\) | 1176.99i | 0.122888i | ||||||||
\(452\) | −6547.24 | −0.681319 | ||||||||
\(453\) | −249.313 | − | 175.536i | −0.0258581 | − | 0.0182062i | ||||
\(454\) | 2352.96 | 0.243238 | ||||||||
\(455\) | 3192.06 | 0.328893 | ||||||||
\(456\) | 2940.07 | − | 4175.76i | 0.301933 | − | 0.428833i | ||||
\(457\) | 6371.84i | 0.652215i | 0.945333 | + | 0.326107i | \(0.105737\pi\) | ||||
−0.945333 | + | 0.326107i | \(0.894263\pi\) | |||||||
\(458\) | 8890.36i | 0.907029i | ||||||||
\(459\) | 3061.22 | − | 11079.1i | 0.311298 | − | 1.12664i | ||||
\(460\) | 16756.2i | 1.69840i | ||||||||
\(461\) | 12246.1i | 1.23722i | 0.785699 | + | 0.618609i | \(0.212304\pi\) | ||||
−0.785699 | + | 0.618609i | \(0.787696\pi\) | |||||||
\(462\) | 171.931 | − | 244.192i | 0.0173137 | − | 0.0245906i | ||||
\(463\) | − | 8205.00i | − | 0.823582i | −0.911278 | − | 0.411791i | \(-0.864903\pi\) | ||
0.911278 | − | 0.411791i | \(-0.135097\pi\) | |||||||
\(464\) | 2183.66i | 0.218478i | ||||||||
\(465\) | −19768.2 | + | 28076.6i | −1.97146 | + | 2.80004i | ||||
\(466\) | 905.780 | 0.0900418 | ||||||||
\(467\) | −6329.50 | −0.627183 | −0.313592 | − | 0.949558i | \(-0.601532\pi\) | ||||
−0.313592 | + | 0.949558i | \(0.601532\pi\) | |||||||
\(468\) | −2448.92 | + | 876.974i | −0.241883 | + | 0.0866199i | ||||
\(469\) | − | 5872.68i | − | 0.578198i | ||||||
\(470\) | 3401.74i | 0.333852i | ||||||||
\(471\) | 3469.38 | + | 2442.72i | 0.339406 | + | 0.238969i | ||||
\(472\) | −2876.64 | − | 2206.63i | −0.280526 | − | 0.215187i | ||||
\(473\) | − | 1479.80i | − | 0.143851i | ||||||
\(474\) | 2496.87 | − | 3546.28i | 0.241951 | − | 0.343642i | ||||
\(475\) | −30500.8 | −2.94626 | ||||||||
\(476\) | 2248.04i | 0.216467i | ||||||||
\(477\) | 2270.03 | − | 812.913i | 0.217899 | − | 0.0780309i | ||||
\(478\) | − | 5192.95i | − | 0.496904i | ||||||
\(479\) | 4833.02i | 0.461015i | 0.973071 | + | 0.230508i | \(0.0740386\pi\) | ||||
−0.973071 | + | 0.230508i | \(0.925961\pi\) | |||||||
\(480\) | 2626.73 | + | 1849.43i | 0.249778 | + | 0.175864i | ||||
\(481\) | −8334.19 | −0.790034 | ||||||||
\(482\) | 8704.10 | 0.822533 | ||||||||
\(483\) | 4449.31 | − | 6319.33i | 0.419153 | − | 0.595320i | ||||
\(484\) | −5253.80 | −0.493407 | ||||||||
\(485\) | −964.323 | −0.0902838 | ||||||||
\(486\) | 562.361 | + | 7555.09i | 0.0524881 | + | 0.705156i | ||||
\(487\) | 16547.6 | 1.53972 | 0.769858 | − | 0.638215i | \(-0.220327\pi\) | ||||
0.769858 | + | 0.638215i | \(0.220327\pi\) | |||||||
\(488\) | − | 1587.30i | − | 0.147242i | ||||||
\(489\) | 2225.21 | − | 3160.45i | 0.205782 | − | 0.292271i | ||||
\(490\) | − | 11435.3i | − | 1.05428i | ||||||
\(491\) | 12716.8i | 1.16884i | 0.811451 | + | 0.584421i | \(0.198678\pi\) | ||||
−0.811451 | + | 0.584421i | \(0.801322\pi\) | |||||||
\(492\) | 4774.77 | + | 3361.82i | 0.437527 | + | 0.308054i | ||||
\(493\) | −11181.5 | −1.02148 | ||||||||
\(494\) | − | 5917.95i | − | 0.538990i | ||||||
\(495\) | 2057.36 | − | 736.754i | 0.186811 | − | 0.0668982i | ||||
\(496\) | 5472.66i | 0.495423i | ||||||||
\(497\) | − | 2636.74i | − | 0.237976i | ||||||
\(498\) | −7571.66 | + | 10754.0i | −0.681314 | + | 0.967665i | ||||
\(499\) | −2473.28 | −0.221883 | −0.110941 | − | 0.993827i | \(-0.535387\pi\) | ||||
−0.110941 | + | 0.993827i | \(0.535387\pi\) | |||||||
\(500\) | − | 9526.24i | − | 0.852052i | ||||||
\(501\) | −14428.4 | − | 10158.7i | −1.28665 | − | 0.905906i | ||||
\(502\) | 8806.16i | 0.782944i | ||||||||
\(503\) | −6251.46 | −0.554153 | −0.277076 | − | 0.960848i | \(-0.589365\pi\) | ||||
−0.277076 | + | 0.960848i | \(0.589365\pi\) | |||||||
\(504\) | −499.545 | − | 1394.96i | −0.0441498 | − | 0.123287i | ||||
\(505\) | 6787.02i | 0.598056i | ||||||||
\(506\) | 1816.66 | 0.159605 | ||||||||
\(507\) | 4836.83 | − | 6869.71i | 0.423690 | − | 0.601765i | ||||
\(508\) | −9541.49 | −0.833337 | ||||||||
\(509\) | −7718.65 | −0.672148 | −0.336074 | − | 0.941836i | \(-0.609099\pi\) | ||||
−0.336074 | + | 0.941836i | \(0.609099\pi\) | |||||||
\(510\) | −9470.04 | + | 13450.2i | −0.822236 | + | 1.16782i | ||||
\(511\) | − | 4019.84i | − | 0.347999i | ||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −16613.4 | − | 4590.41i | −1.42983 | − | 0.395071i | ||||
\(514\) | 1767.68i | 0.151691i | ||||||||
\(515\) | −22112.3 | −1.89201 | ||||||||
\(516\) | −6003.20 | − | 4226.73i | −0.512163 | − | 0.360604i | ||||
\(517\) | 368.806 | 0.0313734 | ||||||||
\(518\) | − | 4747.35i | − | 0.402677i | ||||||
\(519\) | −10653.3 | + | 15130.9i | −0.901021 | + | 1.27971i | ||||
\(520\) | 3722.65 | 0.313940 | ||||||||
\(521\) | − | 8059.77i | − | 0.677745i | −0.940832 | − | 0.338872i | \(-0.889955\pi\) | ||
0.940832 | − | 0.338872i | \(-0.110045\pi\) | |||||||
\(522\) | 6938.37 | − | 2484.67i | 0.581770 | − | 0.208336i | ||||
\(523\) | 12070.8 | 1.00922 | 0.504608 | − | 0.863349i | \(-0.331637\pi\) | ||||
0.504608 | + | 0.863349i | \(0.331637\pi\) | |||||||
\(524\) | 2453.37 | 0.204535 | ||||||||
\(525\) | −5094.57 | + | 7235.79i | −0.423515 | + | 0.601515i | ||||
\(526\) | − | 9721.54i | − | 0.805854i | ||||||
\(527\) | −28022.8 | −2.31631 | ||||||||
\(528\) | 200.509 | − | 284.782i | 0.0165266 | − | 0.0234726i | ||||
\(529\) | 34845.4 | 2.86393 | ||||||||
\(530\) | −3450.72 | −0.282811 | ||||||||
\(531\) | −3738.17 | + | 11651.1i | −0.305504 | + | 0.952191i | ||||
\(532\) | 3371.00 | 0.274721 | ||||||||
\(533\) | 6766.88 | 0.549918 | ||||||||
\(534\) | −1971.46 | + | 2800.05i | −0.159763 | + | 0.226910i | ||||
\(535\) | −7202.48 | −0.582038 | ||||||||
\(536\) | − | 6848.84i | − | 0.551912i | ||||||
\(537\) | 1314.67 | − | 1867.22i | 0.105647 | − | 0.150050i | ||||
\(538\) | −7270.16 | −0.582600 | ||||||||
\(539\) | −1239.78 | −0.0990747 | ||||||||
\(540\) | 2887.56 | − | 10450.6i | 0.230113 | − | 0.832817i | ||||
\(541\) | 18578.4i | 1.47643i | 0.674568 | + | 0.738213i | \(0.264330\pi\) | ||||
−0.674568 | + | 0.738213i | \(0.735670\pi\) | |||||||
\(542\) | −3131.30 | −0.248157 | ||||||||
\(543\) | −3751.41 | + | 5328.10i | −0.296480 | + | 0.421088i | ||||
\(544\) | 2621.71i | 0.206626i | ||||||||
\(545\) | 27078.1 | 2.12826 | ||||||||
\(546\) | −1403.93 | − | 988.481i | −0.110042 | − | 0.0774781i | ||||
\(547\) | −22992.7 | −1.79725 | −0.898627 | − | 0.438714i | \(-0.855434\pi\) | ||||
−0.898627 | + | 0.438714i | \(0.855434\pi\) | |||||||
\(548\) | − | 7273.70i | − | 0.567002i | ||||||
\(549\) | −5043.51 | + | 1806.11i | −0.392080 | + | 0.140406i | ||||
\(550\) | −2080.12 | −0.161266 | ||||||||
\(551\) | 16767.0i | 1.29636i | ||||||||
\(552\) | 5188.88 | − | 7369.73i | 0.400097 | − | 0.568255i | ||||
\(553\) | 2862.84 | 0.220145 | ||||||||
\(554\) | 10927.1 | 0.837991 | ||||||||
\(555\) | 19998.6 | − | 28403.9i | 1.52954 | − | 2.17239i | ||||
\(556\) | 7916.60 | 0.603847 | ||||||||
\(557\) | − | 6008.06i | − | 0.457037i | −0.973540 | − | 0.228519i | \(-0.926612\pi\) | ||
0.973540 | − | 0.228519i | \(-0.0733882\pi\) | |||||||
\(558\) | 17388.9 | − | 6227.07i | 1.31923 | − | 0.472424i | ||||
\(559\) | −8507.82 | −0.643726 | ||||||||
\(560\) | 2120.51i | 0.160014i | ||||||||
\(561\) | 1458.23 | + | 1026.71i | 0.109744 | + | 0.0772688i | ||||
\(562\) | 4614.50i | 0.346354i | ||||||||
\(563\) | 17932.4 | 1.34238 | 0.671189 | − | 0.741286i | \(-0.265784\pi\) | ||||
0.671189 | + | 0.741286i | \(0.265784\pi\) | |||||||
\(564\) | 1053.41 | − | 1496.15i | 0.0786465 | − | 0.111701i | ||||
\(565\) | − | 31623.4i | − | 2.35470i | ||||||
\(566\) | 2986.48i | 0.221786i | ||||||||
\(567\) | −3863.95 | + | 3174.51i | −0.286192 | + | 0.235127i | ||||
\(568\) | − | 3075.03i | − | 0.227157i | ||||||
\(569\) | −9814.15 | −0.723077 | −0.361538 | − | 0.932357i | \(-0.617748\pi\) | ||||
−0.361538 | + | 0.932357i | \(0.617748\pi\) | |||||||
\(570\) | 20169.1 | + | 14200.6i | 1.48209 | + | 1.04351i | ||||
\(571\) | − | 23326.3i | − | 1.70959i | −0.518969 | − | 0.854793i | \(-0.673684\pi\) | ||
0.518969 | − | 0.854793i | \(-0.326316\pi\) | |||||||
\(572\) | − | 403.597i | − | 0.0295022i | ||||||
\(573\) | 5577.07 | − | 7921.08i | 0.406607 | − | 0.577500i | ||||
\(574\) | 3854.57i | 0.280291i | ||||||||
\(575\) | −53830.4 | −3.90414 | ||||||||
\(576\) | −582.579 | − | 1626.83i | −0.0421426 | − | 0.117682i | ||||
\(577\) | 4534.05 | 0.327132 | 0.163566 | − | 0.986532i | \(-0.447700\pi\) | ||||
0.163566 | + | 0.986532i | \(0.447700\pi\) | |||||||
\(578\) | −3598.49 | −0.258958 | ||||||||
\(579\) | 7999.62 | − | 11361.8i | 0.574184 | − | 0.815510i | ||||
\(580\) | −10547.1 | −0.755080 | ||||||||
\(581\) | −8681.46 | −0.619910 | ||||||||
\(582\) | 424.129 | + | 298.620i | 0.0302074 | + | 0.0212684i | ||||
\(583\) | 374.116i | 0.0265768i | ||||||||
\(584\) | − | 4688.02i | − | 0.332178i | ||||||
\(585\) | −4235.82 | − | 11828.4i | −0.299367 | − | 0.835971i | ||||
\(586\) | − | 69.5001i | − | 0.00489936i | ||||||
\(587\) | −14774.7 | −1.03887 | −0.519437 | − | 0.854509i | \(-0.673858\pi\) | ||||
−0.519437 | + | 0.854509i | \(0.673858\pi\) | |||||||
\(588\) | −3541.17 | + | 5029.50i | −0.248359 | + | 0.352743i | ||||
\(589\) | 42021.2i | 2.93965i | ||||||||
\(590\) | 10658.1 | − | 13894.3i | 0.743706 | − | 0.969523i | ||||
\(591\) | 5440.43 | + | 3830.50i | 0.378662 | + | 0.266608i | ||||
\(592\) | − | 5536.46i | − | 0.384370i | ||||||
\(593\) | 810.843i | 0.0561507i | 0.999606 | + | 0.0280753i | \(0.00893783\pi\) | ||||
−0.999606 | + | 0.0280753i | \(0.991062\pi\) | |||||||
\(594\) | −1133.02 | − | 313.060i | −0.0782631 | − | 0.0216246i | ||||
\(595\) | −10858.1 | −0.748132 | ||||||||
\(596\) | 9366.69 | 0.643749 | ||||||||
\(597\) | −4461.42 | + | 6336.52i | −0.305852 | + | 0.434400i | ||||
\(598\) | − | 10444.5i | − | 0.714227i | ||||||
\(599\) | 10769.4i | 0.734600i | 0.930103 | + | 0.367300i | \(0.119718\pi\) | ||||
−0.930103 | + | 0.367300i | \(0.880282\pi\) | |||||||
\(600\) | −5941.40 | + | 8438.52i | −0.404261 | + | 0.574169i | ||||
\(601\) | − | 8354.78i | − | 0.567052i | −0.958965 | − | 0.283526i | \(-0.908496\pi\) | ||
0.958965 | − | 0.283526i | \(-0.0915043\pi\) | |||||||
\(602\) | − | 4846.26i | − | 0.328104i | ||||||
\(603\) | −21761.5 | + | 7792.95i | −1.46965 | + | 0.526291i | ||||
\(604\) | − | 234.719i | − | 0.0158122i | ||||||
\(605\) | − | 25376.1i | − | 1.70526i | ||||||
\(606\) | 2101.72 | − | 2985.07i | 0.140886 | − | 0.200099i | ||||
\(607\) | 8150.29 | 0.544992 | 0.272496 | − | 0.962157i | \(-0.412151\pi\) | ||||
0.272496 | + | 0.962157i | \(0.412151\pi\) | |||||||
\(608\) | 3931.33 | 0.262231 | ||||||||
\(609\) | 3977.67 | + | 2800.60i | 0.264669 | + | 0.186348i | ||||
\(610\) | 7666.74 | 0.508880 | ||||||||
\(611\) | − | 2120.37i | − | 0.140395i | ||||||
\(612\) | 8330.23 | − | 2983.11i | 0.550212 | − | 0.197034i | ||||
\(613\) | − | 10034.8i | − | 0.661180i | −0.943774 | − | 0.330590i | \(-0.892752\pi\) | ||
0.943774 | − | 0.330590i | \(-0.107248\pi\) | |||||||
\(614\) | 10710.5 | 0.703976 | ||||||||
\(615\) | −16237.7 | + | 23062.3i | −1.06466 | + | 1.51213i | ||||
\(616\) | 229.898 | 0.0150371 | ||||||||
\(617\) | − | 16348.2i | − | 1.06670i | −0.845895 | − | 0.533350i | \(-0.820933\pi\) | ||
0.845895 | − | 0.533350i | \(-0.179067\pi\) | |||||||
\(618\) | 9725.43 | + | 6847.48i | 0.633033 | + | 0.445706i | ||||
\(619\) | 14628.1 | 0.949843 | 0.474922 | − | 0.880028i | \(-0.342476\pi\) | ||||
0.474922 | + | 0.880028i | \(0.342476\pi\) | |||||||
\(620\) | −26433.1 | −1.71223 | ||||||||
\(621\) | −29320.8 | − | 8101.54i | −1.89469 | − | 0.523516i | ||||
\(622\) | − | 13056.4i | − | 0.841659i | ||||||
\(623\) | −2260.42 | −0.145364 | ||||||||
\(624\) | −1637.29 | − | 1152.79i | −0.105039 | − | 0.0739558i | ||||
\(625\) | 14978.6 | 0.958627 | ||||||||
\(626\) | − | 1057.94i | − | 0.0675457i | ||||||
\(627\) | 1539.59 | − | 2186.67i | 0.0980625 | − | 0.139278i | ||||
\(628\) | 3266.30i | 0.207547i | ||||||||
\(629\) | 28349.5 | 1.79709 | ||||||||
\(630\) | 6737.72 | − | 2412.82i | 0.426090 | − | 0.152586i | ||||
\(631\) | −3561.61 | −0.224700 | −0.112350 | − | 0.993669i | \(-0.535838\pi\) | ||||
−0.112350 | + | 0.993669i | \(0.535838\pi\) | |||||||
\(632\) | 3338.71 | 0.210137 | ||||||||
\(633\) | 5780.34 | + | 4069.82i | 0.362951 | + | 0.255547i | ||||
\(634\) | 3472.24i | 0.217508i | ||||||||
\(635\) | − | 46085.8i | − | 2.88009i | ||||||
\(636\) | 1517.69 | + | 1068.58i | 0.0946234 | + | 0.0666225i | ||||
\(637\) | 7127.88i | 0.443355i | ||||||||
\(638\) | 1143.49i | 0.0709578i | ||||||||
\(639\) | −9770.61 | + | 3498.92i | −0.604882 | + | 0.216612i | ||||
\(640\) | 2472.98i | 0.152739i | ||||||||
\(641\) | 14739.1i | 0.908205i | 0.890949 | + | 0.454103i | \(0.150040\pi\) | ||||
−0.890949 | + | 0.454103i | \(0.849960\pi\) | |||||||
\(642\) | 3167.80 | + | 2230.38i | 0.194740 | + | 0.137112i | ||||
\(643\) | 15120.1 | 0.927340 | 0.463670 | − | 0.886008i | \(-0.346532\pi\) | ||||
0.463670 | + | 0.886008i | \(0.346532\pi\) | |||||||
\(644\) | 5949.43 | 0.364038 | ||||||||
\(645\) | 20415.3 | − | 28995.7i | 1.24628 | − | 1.77008i | ||||
\(646\) | 20130.5i | 1.22604i | ||||||||
\(647\) | − | 16479.3i | − | 1.00134i | −0.865637 | − | 0.500672i | \(-0.833086\pi\) | ||
0.865637 | − | 0.500672i | \(-0.166914\pi\) | |||||||
\(648\) | −4506.22 | + | 3702.19i | −0.273181 | + | 0.224438i | ||||
\(649\) | −1506.37 | − | 1155.52i | −0.0911098 | − | 0.0698890i | ||||
\(650\) | 11959.2i | 0.721660i | ||||||||
\(651\) | 9968.80 | + | 7018.84i | 0.600166 | + | 0.422565i | ||||
\(652\) | 2975.46 | 0.178724 | ||||||||
\(653\) | − | 2442.19i | − | 0.146356i | −0.997319 | − | 0.0731779i | \(-0.976686\pi\) | ||
0.997319 | − | 0.0731779i | \(-0.0233141\pi\) | |||||||
\(654\) | −11909.5 | − | 8385.25i | −0.712077 | − | 0.501359i | ||||
\(655\) | 11849.9i | 0.706891i | ||||||||
\(656\) | 4495.29i | 0.267548i | ||||||||
\(657\) | −14895.8 | + | 5334.27i | −0.884534 | + | 0.316757i | ||||
\(658\) | 1207.81 | 0.0715585 | ||||||||
\(659\) | 16334.4 | 0.965549 | 0.482774 | − | 0.875745i | \(-0.339629\pi\) | ||||
0.482774 | + | 0.875745i | \(0.339629\pi\) | |||||||
\(660\) | 1375.51 | + | 968.467i | 0.0811235 | + | 0.0571175i | ||||
\(661\) | −1213.17 | −0.0713870 | −0.0356935 | − | 0.999363i | \(-0.511364\pi\) | ||||
−0.0356935 | + | 0.999363i | \(0.511364\pi\) | |||||||
\(662\) | −9056.82 | −0.531727 | ||||||||
\(663\) | 5902.86 | − | 8383.80i | 0.345774 | − | 0.491101i | ||||
\(664\) | −10124.5 | −0.591727 | ||||||||
\(665\) | 16282.1i | 0.949461i | ||||||||
\(666\) | −17591.6 | + | 6299.66i | −1.02351 | + | 0.366527i | ||||
\(667\) | 29591.7i | 1.71784i | ||||||||
\(668\) | − | 13583.8i | − | 0.786788i | ||||||
\(669\) | −12161.8 | + | 17273.4i | −0.702846 | + | 0.998247i | ||||
\(670\) | 33080.1 | 1.90746 | ||||||||
\(671\) | − | 831.203i | − | 0.0478215i | ||||||
\(672\) | 656.654 | − | 932.641i | 0.0376949 | − | 0.0535378i | ||||
\(673\) | − | 7012.56i | − | 0.401656i | −0.979627 | − | 0.200828i | \(-0.935637\pi\) | ||
0.979627 | − | 0.200828i | \(-0.0643632\pi\) | |||||||
\(674\) | 4398.20i | 0.251353i | ||||||||
\(675\) | 33573.1 | + | 9276.46i | 1.91441 | + | 0.528965i | ||||
\(676\) | 6467.60 | 0.367979 | ||||||||
\(677\) | − | 13576.6i | − | 0.770739i | −0.922762 | − | 0.385370i | \(-0.874074\pi\) | ||
0.922762 | − | 0.385370i | \(-0.125926\pi\) | |||||||
\(678\) | −9792.77 | + | 13908.6i | −0.554704 | + | 0.787842i | ||||
\(679\) | 342.390i | 0.0193516i | ||||||||
\(680\) | −12662.9 | −0.714120 | ||||||||
\(681\) | 3519.35 | − | 4998.51i | 0.198035 | − | 0.281268i | ||||
\(682\) | 2865.80i | 0.160905i | ||||||||
\(683\) | 35104.8 | 1.96669 | 0.983345 | − | 0.181749i | \(-0.0581758\pi\) | ||||
0.983345 | + | 0.181749i | \(0.0581758\pi\) | |||||||
\(684\) | −4473.27 | − | 12491.5i | −0.250058 | − | 0.698279i | ||||
\(685\) | 35132.2 | 1.95961 | ||||||||
\(686\) | −8766.01 | −0.487883 | ||||||||
\(687\) | 18886.2 | + | 13297.4i | 1.04884 | + | 0.738468i | ||||
\(688\) | − | 5651.80i | − | 0.313187i | ||||||
\(689\) | 2150.90 | 0.118930 | ||||||||
\(690\) | 35596.1 | + | 25062.5i | 1.96394 | + | 1.38277i | ||||
\(691\) | 13636.1i | 0.750713i | 0.926881 | + | 0.375356i | \(0.122480\pi\) | ||||
−0.926881 | + | 0.375356i | \(0.877520\pi\) | |||||||
\(692\) | −14245.2 | −0.782545 | ||||||||
\(693\) | −261.590 | − | 730.481i | −0.0143391 | − | 0.0400414i | ||||
\(694\) | −6471.40 | −0.353964 | ||||||||
\(695\) | 38237.5i | 2.08695i | ||||||||
\(696\) | 4638.84 | + | 3266.12i | 0.252636 | + | 0.177876i | ||||
\(697\) | −23018.2 | −1.25090 | ||||||||
\(698\) | 6801.82i | 0.368843i | ||||||||
\(699\) | 1354.78 | − | 1924.19i | 0.0733085 | − | 0.104120i | ||||
\(700\) | −6812.24 | −0.367827 | ||||||||
\(701\) | −20921.4 | −1.12723 | −0.563616 | − | 0.826037i | \(-0.690590\pi\) | ||||
−0.563616 | + | 0.826037i | \(0.690590\pi\) | |||||||
\(702\) | −1799.88 | + | 6514.05i | −0.0967692 | + | 0.350224i | ||||
\(703\) | − | 42511.0i | − | 2.28070i | ||||||
\(704\) | 268.112 | 0.0143535 | ||||||||
\(705\) | 7226.48 | + | 5088.02i | 0.386049 | + | 0.271810i | ||||
\(706\) | −23084.1 | −1.23057 | ||||||||
\(707\) | 2409.78 | 0.128188 | ||||||||
\(708\) | −8990.26 | + | 2810.51i | −0.477224 | + | 0.149188i | ||||
\(709\) | −12409.7 | −0.657341 | −0.328671 | − | 0.944445i | \(-0.606601\pi\) | ||||
−0.328671 | + | 0.944445i | \(0.606601\pi\) | |||||||
\(710\) | 14852.5 | 0.785076 | ||||||||
\(711\) | −3798.95 | − | 10608.4i | −0.200382 | − | 0.559560i | ||||
\(712\) | −2636.15 | −0.138756 | ||||||||
\(713\) | 74162.6i | 3.89539i | ||||||||
\(714\) | 4775.61 | + | 3362.41i | 0.250312 | + | 0.176240i | ||||
\(715\) | 1949.39 | 0.101962 | ||||||||
\(716\) | 1757.93 | 0.0917553 | ||||||||
\(717\) | −11031.6 | − | 7767.15i | −0.574594 | − | 0.404560i | ||||
\(718\) | − | 13715.2i | − | 0.712876i | ||||||
\(719\) | 31979.3 | 1.65873 | 0.829365 | − | 0.558707i | \(-0.188702\pi\) | ||||
0.829365 | + | 0.558707i | \(0.188702\pi\) | |||||||
\(720\) | 7857.66 | − | 2813.88i | 0.406719 | − | 0.145649i | ||||
\(721\) | 7851.14i | 0.405536i | ||||||||
\(722\) | 16468.3 | 0.848874 | ||||||||
\(723\) | 13018.8 | − | 18490.5i | 0.669674 | − | 0.951134i | ||||
\(724\) | −5016.23 | −0.257495 | ||||||||
\(725\) | − | 33883.3i | − | 1.73571i | ||||||
\(726\) | −7858.16 | + | 11160.9i | −0.401713 | + | 0.570551i | ||||
\(727\) | −10864.9 | −0.554275 | −0.277137 | − | 0.960830i | \(-0.589386\pi\) | ||||
−0.277137 | + | 0.960830i | \(0.589386\pi\) | |||||||
\(728\) | − | 1321.75i | − | 0.0672905i | ||||||
\(729\) | 16890.8 | + | 10105.6i | 0.858140 | + | 0.513416i | ||||
\(730\) | 22643.3 | 1.14804 | ||||||||
\(731\) | 28940.2 | 1.46428 | ||||||||
\(732\) | −3371.98 | − | 2374.15i | −0.170262 | − | 0.119878i | ||||
\(733\) | −4862.94 | −0.245044 | −0.122522 | − | 0.992466i | \(-0.539098\pi\) | ||||
−0.122522 | + | 0.992466i | \(0.539098\pi\) | |||||||
\(734\) | − | 10116.4i | − | 0.508723i | ||||||
\(735\) | −24292.7 | − | 17104.0i | −1.21911 | − | 0.858353i | ||||
\(736\) | 6938.35 | 0.347488 | ||||||||
\(737\) | − | 3586.44i | − | 0.179251i | ||||||
\(738\) | 14283.4 | − | 5114.96i | 0.712436 | − | 0.255128i | ||||
\(739\) | − | 20365.8i | − | 1.01376i | −0.862017 | − | 0.506879i | \(-0.830799\pi\) | ||
0.862017 | − | 0.506879i | \(-0.169201\pi\) | |||||||
\(740\) | 26741.3 | 1.32842 | ||||||||
\(741\) | −12571.8 | − | 8851.54i | −0.623260 | − | 0.438825i | ||||
\(742\) | 1225.20i | 0.0606181i | ||||||||
\(743\) | 35272.0i | 1.74160i | 0.491641 | + | 0.870798i | \(0.336397\pi\) | ||||
−0.491641 | + | 0.870798i | \(0.663603\pi\) | |||||||
\(744\) | 11625.8 | + | 8185.51i | 0.572881 | + | 0.403354i | ||||
\(745\) | 45241.5i | 2.22486i | ||||||||
\(746\) | 23230.5 | 1.14012 | ||||||||
\(747\) | 11520.2 | + | 32169.7i | 0.564258 | + | 1.57567i | ||||
\(748\) | 1372.87i | 0.0671086i | ||||||||
\(749\) | 2557.30i | 0.124755i | ||||||||
\(750\) | −20237.0 | − | 14248.5i | −0.985269 | − | 0.693708i | ||||
\(751\) | 5331.76i | 0.259066i | 0.991575 | + | 0.129533i | \(0.0413478\pi\) | ||||
−0.991575 | + | 0.129533i | \(0.958652\pi\) | |||||||
\(752\) | 1408.58 | 0.0683052 | ||||||||
\(753\) | 18707.3 | + | 13171.5i | 0.905356 | + | 0.637443i | ||||
\(754\) | 6574.24 | 0.317533 | ||||||||
\(755\) | 1133.70 | 0.0546486 | ||||||||
\(756\) | −3710.56 | − | 1025.25i | −0.178507 | − | 0.0493228i | ||||
\(757\) | −7086.43 | −0.340239 | −0.170119 | − | 0.985423i | \(-0.554415\pi\) | ||||
−0.170119 | + | 0.985423i | \(0.554415\pi\) | |||||||
\(758\) | 11603.9 | 0.556032 | ||||||||
\(759\) | 2717.19 | − | 3859.21i | 0.129945 | − | 0.184559i | ||||
\(760\) | 18988.5i | 0.906296i | ||||||||
\(761\) | 4581.22i | 0.218225i | 0.994029 | + | 0.109112i | \(0.0348008\pi\) | ||||
−0.994029 | + | 0.109112i | \(0.965199\pi\) | |||||||
\(762\) | −14271.3 | + | 20269.4i | −0.678471 | + | 0.963628i | ||||
\(763\) | − | 9614.30i | − | 0.456174i | ||||||
\(764\) | 7457.42 | 0.353141 | ||||||||
\(765\) | 14408.5 | + | 40235.3i | 0.680969 | + | 1.90158i | ||||
\(766\) | 14206.3i | 0.670096i | ||||||||
\(767\) | −6643.40 | + | 8660.58i | −0.312750 | + | 0.407712i | ||||
\(768\) | 765.804 | − | 1087.67i | 0.0359812 | − | 0.0511038i | ||||
\(769\) | 11328.6i | 0.531235i | 0.964079 | + | 0.265617i | \(0.0855758\pi\) | ||||
−0.964079 | + | 0.265617i | \(0.914424\pi\) | |||||||
\(770\) | 1110.42i | 0.0519697i | ||||||||
\(771\) | 3755.17 | + | 2643.94i | 0.175407 | + | 0.123501i | ||||
\(772\) | 10696.7 | 0.498684 | ||||||||
\(773\) | 17160.9 | 0.798491 | 0.399245 | − | 0.916844i | \(-0.369272\pi\) | ||||
0.399245 | + | 0.916844i | \(0.369272\pi\) | |||||||
\(774\) | −17958.1 | + | 6430.91i | −0.833966 | + | 0.298649i | ||||
\(775\) | − | 84917.9i | − | 3.93593i | ||||||
\(776\) | 399.303i | 0.0184718i | ||||||||
\(777\) | −10085.0 | − | 7100.66i | −0.465634 | − | 0.327844i | ||||
\(778\) | − | 20247.8i | − | 0.933058i | ||||||
\(779\) | 34516.5i | 1.58753i | ||||||||
\(780\) | 5568.00 | − | 7908.19i | 0.255598 | − | 0.363024i | ||||
\(781\) | − | 1610.26i | − | 0.0737767i | ||||||
\(782\) | 35528.0i | 1.62465i | ||||||||
\(783\) | 5099.48 | − | 18455.9i | 0.232746 | − | 0.842348i | ||||
\(784\) | −4735.10 | −0.215702 | ||||||||
\(785\) | −15776.3 | −0.717302 | ||||||||
\(786\) | 3669.54 | − | 5211.82i | 0.166524 | − | 0.236513i | ||||
\(787\) | −26544.8 | −1.20231 | −0.601157 | − | 0.799131i | \(-0.705293\pi\) | ||||
−0.601157 | + | 0.799131i | \(0.705293\pi\) | |||||||
\(788\) | 5121.98i | 0.231552i | ||||||||
\(789\) | −20651.9 | − | 14540.6i | −0.931848 | − | 0.656096i | ||||
\(790\) | 16126.1i | 0.726253i | ||||||||
\(791\) | −11228.1 | −0.504711 | ||||||||
\(792\) | −305.072 | − | 851.902i | −0.0136872 | − | 0.0382210i | ||||
\(793\) | −4778.83 | −0.213999 | ||||||||
\(794\) | − | 24597.5i | − | 1.09941i | ||||||
\(795\) | −5161.27 | + | 7330.52i | −0.230253 | + | 0.327027i | ||||
\(796\) | −5965.62 | −0.265635 | ||||||||
\(797\) | 6602.21 | 0.293428 | 0.146714 | − | 0.989179i | \(-0.453130\pi\) | ||||
0.146714 | + | 0.989179i | \(0.453130\pi\) | |||||||
\(798\) | 5042.04 | − | 7161.18i | 0.223667 | − | 0.317673i | ||||
\(799\) | 7212.64i | 0.319355i | ||||||||
\(800\) | −7944.58 | −0.351104 | ||||||||
\(801\) | 2999.55 | + | 8376.14i | 0.132314 | + | 0.369483i | ||||
\(802\) | −733.103 | −0.0322778 | ||||||||
\(803\) | − | 2454.91i | − | 0.107885i | ||||||
\(804\) | −14549.3 | − | 10243.9i | −0.638202 | − | 0.449345i | ||||
\(805\) | 28736.0i | 1.25815i | ||||||||
\(806\) | 16476.3 | 0.720041 | ||||||||
\(807\) | −10874.1 | + | 15444.3i | −0.474331 | + | 0.673688i | ||||
\(808\) | 2810.34 | 0.122361 | ||||||||
\(809\) | −27228.8 | −1.18333 | −0.591665 | − | 0.806184i | \(-0.701529\pi\) | ||||
−0.591665 | + | 0.806184i | \(0.701529\pi\) | |||||||
\(810\) | −17881.7 | − | 21765.2i | −0.775677 | − | 0.944138i | ||||
\(811\) | − | 7065.46i | − | 0.305921i | −0.988232 | − | 0.152960i | \(-0.951119\pi\) | ||
0.988232 | − | 0.152960i | \(-0.0488807\pi\) | |||||||
\(812\) | 3744.84i | 0.161845i | ||||||||
\(813\) | −4683.52 | + | 6651.97i | −0.202040 | + | 0.286955i | ||||
\(814\) | − | 2899.20i | − | 0.124837i | ||||||
\(815\) | 14371.6i | 0.617686i | ||||||||
\(816\) | 5569.41 | + | 3921.31i | 0.238932 | + | 0.168227i | ||||
\(817\) | − | 43396.7i | − | 1.85833i | ||||||
\(818\) | 17534.9i | 0.749503i | ||||||||
\(819\) | −4199.75 | + | 1503.96i | −0.179183 | + | 0.0641667i | ||||
\(820\) | −21712.4 | −0.924670 | ||||||||
\(821\) | 14983.1 | 0.636924 | 0.318462 | − | 0.947936i | \(-0.396834\pi\) | ||||
0.318462 | + | 0.947936i | \(0.396834\pi\) | |||||||
\(822\) | −15451.9 | − | 10879.3i | −0.655652 | − | 0.461631i | ||||
\(823\) | 26292.3i | 1.11360i | 0.830647 | + | 0.556800i | \(0.187971\pi\) | ||||
−0.830647 | + | 0.556800i | \(0.812029\pi\) | |||||||
\(824\) | 9156.16i | 0.387100i | ||||||||
\(825\) | −3111.25 | + | 4418.89i | −0.131297 | + | 0.186480i | ||||
\(826\) | −4933.27 | − | 3784.23i | −0.207809 | − | 0.159407i | ||||
\(827\) | 24569.6i | 1.03310i | 0.856258 | + | 0.516548i | \(0.172783\pi\) | ||||
−0.856258 | + | 0.516548i | \(0.827217\pi\) | |||||||
\(828\) | −7894.81 | − | 22046.0i | −0.331357 | − | 0.925303i | ||||
\(829\) | 30899.9 | 1.29457 | 0.647285 | − | 0.762248i | \(-0.275904\pi\) | ||||
0.647285 | + | 0.762248i | \(0.275904\pi\) | |||||||
\(830\) | − | 48901.7i | − | 2.04506i | ||||||
\(831\) | 16343.7 | − | 23212.9i | 0.682260 | − | 0.969009i | ||||
\(832\) | − | 1541.46i | − | 0.0642313i | ||||||
\(833\) | − | 24246.2i | − | 1.00850i | ||||||
\(834\) | 11840.9 | − | 16817.6i | 0.491629 | − | 0.698257i | ||||
\(835\) | 65610.4 | 2.71921 | ||||||||
\(836\) | 2058.67 | 0.0851682 | ||||||||
\(837\) | 12780.3 | − | 46253.9i | 0.527778 | − | 1.91012i | ||||
\(838\) | −8472.34 | −0.349251 | ||||||||
\(839\) | 4412.75 | 0.181579 | 0.0907897 | − | 0.995870i | \(-0.471061\pi\) | ||||
0.0907897 | + | 0.995870i | \(0.471061\pi\) | |||||||
\(840\) | 4504.69 | + | 3171.66i | 0.185032 | + | 0.130277i | ||||
\(841\) | 5762.62 | 0.236279 | ||||||||
\(842\) | − | 9003.89i | − | 0.368521i | ||||||
\(843\) | 9802.79 | + | 6901.95i | 0.400505 | + | 0.281988i | ||||
\(844\) | 5442.00i | 0.221945i | ||||||||
\(845\) | 31238.7i | 1.27177i | ||||||||
\(846\) | −1602.75 | − | 4475.62i | −0.0651344 | − | 0.181885i | ||||
\(847\) | −9009.96 | −0.365509 | ||||||||
\(848\) | 1428.86i | 0.0578622i | ||||||||
\(849\) | 6344.32 | + | 4466.91i | 0.256462 | + | 0.180570i | ||||
\(850\) | − | 40680.4i | − | 1.64156i | ||||||
\(851\) | − | 75027.1i | − | 3.02220i | ||||||
\(852\) | −6532.42 | − | 4599.35i | −0.262673 | − | 0.184943i | ||||
\(853\) | 1603.41 | 0.0643607 | 0.0321803 | − | 0.999482i | \(-0.489755\pi\) | ||||
0.0321803 | + | 0.999482i | \(0.489755\pi\) | |||||||
\(854\) | − | 2722.13i | − | 0.109074i | ||||||
\(855\) | 60334.2 | − | 21606.1i | 2.41332 | − | 0.864224i | ||||
\(856\) | 2982.37i | 0.119083i | ||||||||
\(857\) | −38885.4 | −1.54994 | −0.774970 | − | 0.631998i | \(-0.782235\pi\) | ||||
−0.774970 | + | 0.631998i | \(0.782235\pi\) | |||||||
\(858\) | −857.381 | − | 603.665i | −0.0341148 | − | 0.0240195i | ||||
\(859\) | 23506.4i | 0.933678i | 0.884342 | + | 0.466839i | \(0.154607\pi\) | ||||
−0.884342 | + | 0.466839i | \(0.845393\pi\) | |||||||
\(860\) | 27298.4 | 1.08241 | ||||||||
\(861\) | 8188.46 | + | 5765.33i | 0.324114 | + | 0.228202i | ||||
\(862\) | −23742.0 | −0.938114 | ||||||||
\(863\) | −35138.2 | −1.38600 | −0.693001 | − | 0.720937i | \(-0.743712\pi\) | ||||
−0.693001 | + | 0.720937i | \(0.743712\pi\) | |||||||
\(864\) | −4327.33 | − | 1195.67i | −0.170392 | − | 0.0470805i | ||||
\(865\) | − | 68804.8i | − | 2.70455i | ||||||
\(866\) | −9648.70 | −0.378610 | ||||||||
\(867\) | −5382.30 | + | 7644.44i | −0.210833 | + | 0.299445i | ||||
\(868\) | 9385.29i | 0.367002i | ||||||||
\(869\) | 1748.34 | 0.0682488 | ||||||||
\(870\) | −15775.5 | + | 22405.8i | −0.614757 | + | 0.873135i | ||||
\(871\) | −20619.5 | −0.802142 | ||||||||
\(872\) | − | 11212.4i | − | 0.435435i | ||||||
\(873\) | 1268.75 | − | 454.347i | 0.0491874 | − | 0.0176143i | ||||
\(874\) | 53275.4 | 2.06186 | ||||||||
\(875\) | − | 16336.9i | − | 0.631188i | ||||||
\(876\) | −9958.98 | − | 7011.92i | −0.384113 | − | 0.270446i | ||||
\(877\) | −10671.1 | −0.410876 | −0.205438 | − | 0.978670i | \(-0.565862\pi\) | ||||
−0.205438 | + | 0.978670i | \(0.565862\pi\) | |||||||
\(878\) | −17043.7 | −0.655121 | ||||||||
\(879\) | −147.642 | − | 103.952i | −0.00566536 | − | 0.00398887i | ||||
\(880\) | 1294.99i | 0.0496070i | ||||||||
\(881\) | 27854.9 | 1.06522 | 0.532609 | − | 0.846362i | \(-0.321212\pi\) | ||||
0.532609 | + | 0.846362i | \(0.321212\pi\) | |||||||
\(882\) | 5387.83 | + | 15045.3i | 0.205689 | + | 0.574380i | ||||
\(883\) | −17898.9 | −0.682160 | −0.341080 | − | 0.940034i | \(-0.610793\pi\) | ||||
−0.341080 | + | 0.940034i | \(0.610793\pi\) | |||||||
\(884\) | 7893.06 | 0.300308 | ||||||||
\(885\) | −13574.9 | − | 43423.3i | −0.515609 | − | 1.64933i | ||||
\(886\) | 13014.0 | 0.493469 | ||||||||
\(887\) | −131.720 | −0.00498618 | −0.00249309 | − | 0.999997i | \(-0.500794\pi\) | ||||
−0.00249309 | + | 0.999997i | \(0.500794\pi\) | |||||||
\(888\) | −11761.4 | − | 8280.93i | −0.444465 | − | 0.312939i | ||||
\(889\) | −16363.1 | −0.617324 | ||||||||
\(890\) | − | 12732.7i | − | 0.479553i | ||||||
\(891\) | −2359.71 | + | 1938.67i | −0.0887244 | + | 0.0728934i | ||||
\(892\) | −16262.3 | −0.610428 | ||||||||
\(893\) | 10815.6 | 0.405297 | ||||||||
\(894\) | 14009.9 | − | 19898.1i | 0.524116 | − | 0.744398i | ||||
\(895\) | 8490.85i | 0.317115i | ||||||||
\(896\) | 878.050 | 0.0327384 | ||||||||
\(897\) | −22187.7 | − | 15622.0i | −0.825894 | − | 0.581496i | ||||
\(898\) | 6016.93i | 0.223594i | ||||||||
\(899\) | −46681.3 | −1.73182 | ||||||||
\(900\) | 9039.75 | + | 25243.2i | 0.334805 | + | 0.934932i | ||||
\(901\) | −7316.49 | −0.270530 | ||||||||
\(902\) | 2353.99i | 0.0868949i | ||||||||
\(903\) | −10295.1 | − | 7248.59i | −0.379402 | − | 0.267130i | ||||
\(904\) | −13094.5 | −0.481765 | ||||||||
\(905\) | − | 24228.6i | − | 0.889928i | ||||||
\(906\) | −498.625 | − | 351.072i | −0.0182844 | − | 0.0128737i | ||||
\(907\) | −29776.4 | −1.09009 | −0.545043 | − | 0.838408i | \(-0.683487\pi\) | ||||
−0.545043 | + | 0.838408i | \(0.683487\pi\) | |||||||
\(908\) | 4705.92 | 0.171995 | ||||||||
\(909\) | −3197.74 | − | 8929.59i | −0.116680 | − | 0.325826i | ||||
\(910\) | 6384.12 | 0.232562 | ||||||||
\(911\) | 1619.23i | 0.0588886i | 0.999566 | + | 0.0294443i | \(0.00937376\pi\) | ||||
−0.999566 | + | 0.0294443i | \(0.990626\pi\) | |||||||
\(912\) | 5880.14 | − | 8351.52i | 0.213499 | − | 0.303231i | ||||
\(913\) | −5301.76 | −0.192183 | ||||||||
\(914\) | 12743.7i | 0.461185i | ||||||||
\(915\) | 11467.2 | − | 16286.8i | 0.414311 | − | 0.588443i | ||||
\(916\) | 17780.7i | 0.641367i | ||||||||
\(917\) | 4207.39 | 0.151516 | ||||||||
\(918\) | 6122.45 | − | 22158.2i | 0.220121 | − | 0.796654i | ||||
\(919\) | − | 17813.8i | − | 0.639416i | −0.947516 | − | 0.319708i | \(-0.896415\pi\) | ||
0.947516 | − | 0.319708i | \(-0.103585\pi\) | |||||||
\(920\) | 33512.5i | 1.20095i | ||||||||
\(921\) | 16019.8 | − | 22752.9i | 0.573150 | − | 0.814042i | ||||
\(922\) | 24492.2i | 0.874846i | ||||||||
\(923\) | −9257.85 | −0.330147 | ||||||||
\(924\) | 343.861 | − | 488.384i | 0.0122427 | − | 0.0173882i | ||||
\(925\) | 85907.8i | 3.05366i | ||||||||
\(926\) | − | 16410.0i | − | 0.582361i | ||||||
\(927\) | 29092.9 | − | 10418.3i | 1.03078 | − | 0.369130i | ||||
\(928\) | 4367.31i | 0.154487i | ||||||||
\(929\) | 15087.4 | 0.532831 | 0.266416 | − | 0.963858i | \(-0.414161\pi\) | ||||
0.266416 | + | 0.963858i | \(0.414161\pi\) | |||||||
\(930\) | −39536.3 | + | 56153.2i | −1.39403 | + | 1.97993i | ||||
\(931\) | −36357.9 | −1.27990 | ||||||||
\(932\) | 1811.56 | 0.0636691 | ||||||||
\(933\) | −27736.2 | − | 19528.5i | −0.973251 | − | 0.685247i | ||||
\(934\) | −12659.0 | −0.443485 | ||||||||
\(935\) | −6631.03 | −0.231934 | ||||||||
\(936\) | −4897.84 | + | 1753.95i | −0.171037 | + | 0.0612495i | ||||
\(937\) | − | 150.028i | − | 0.00523072i | −0.999997 | − | 0.00261536i | \(-0.999168\pi\) | ||
0.999997 | − | 0.00261536i | \(-0.000832497\pi\) | |||||||
\(938\) | − | 11745.4i | − | 0.408848i | ||||||
\(939\) | −2247.42 | − | 1582.36i | −0.0781063 | − | 0.0549931i | ||||
\(940\) | 6803.48i | 0.236069i | ||||||||
\(941\) | −22210.1 | −0.769423 | −0.384711 | − | 0.923037i | \(-0.625699\pi\) | ||||
−0.384711 | + | 0.923037i | \(0.625699\pi\) | |||||||
\(942\) | 6938.75 | + | 4885.44i | 0.239997 | + | 0.168977i | ||||
\(943\) | 60917.7i | 2.10366i | ||||||||
\(944\) | −5753.28 | − | 4413.25i | −0.198362 | − | 0.152160i | ||||
\(945\) | 4952.00 | − | 17922.1i | 0.170464 | − | 0.616938i | ||||
\(946\) | − | 2959.61i | − | 0.101718i | ||||||
\(947\) | 16355.4i | 0.561223i | 0.959822 | + | 0.280611i | \(0.0905372\pi\) | ||||
−0.959822 | + | 0.280611i | \(0.909463\pi\) | |||||||
\(948\) | 4993.74 | − | 7092.57i | 0.171085 | − | 0.242992i | ||||
\(949\) | −14114.0 | −0.482783 | ||||||||
\(950\) | −61001.6 | −2.08332 | ||||||||
\(951\) | 7376.24 | + | 5193.46i | 0.251515 | + | 0.177087i | ||||
\(952\) | 4496.07i | 0.153066i | ||||||||
\(953\) | 42907.8i | 1.45847i | 0.684264 | + | 0.729235i | \(0.260124\pi\) | ||||
−0.684264 | + | 0.729235i | \(0.739876\pi\) | |||||||
\(954\) | 4540.06 | − | 1625.83i | 0.154078 | − | 0.0551762i | ||||
\(955\) | 36019.6i | 1.22049i | ||||||||
\(956\) | − | 10385.9i | − | 0.351364i | ||||||
\(957\) | 2429.16 | + | 1710.32i | 0.0820519 | + | 0.0577711i | ||||
\(958\) | 9666.04i | 0.325987i | ||||||||
\(959\) | − | 12474.0i | − | 0.420026i | ||||||
\(960\) | 5253.47 | + | 3698.86i | 0.176620 | + | 0.124354i | ||||
\(961\) | −87201.2 | −2.92710 | ||||||||
\(962\) | −16668.4 | −0.558638 | ||||||||
\(963\) | 9476.21 | − | 3393.49i | 0.317099 | − | 0.113555i | ||||
\(964\) | 17408.2 | 0.581618 | ||||||||
\(965\) | 51665.7i | 1.72350i | ||||||||
\(966\) | 8898.63 | − | 12638.7i | 0.296386 | − | 0.420955i | ||||
\(967\) | 23064.3i | 0.767009i | 0.923539 | + | 0.383505i | \(0.125283\pi\) | ||||
−0.923539 | + | 0.383505i | \(0.874717\pi\) | |||||||
\(968\) | −10507.6 | −0.348892 | ||||||||
\(969\) | 42764.1 | + | 30109.4i | 1.41773 | + | 0.998196i | ||||
\(970\) | −1928.65 | −0.0638403 | ||||||||
\(971\) | 4903.81i | 0.162071i | 0.996711 | + | 0.0810355i | \(0.0258227\pi\) | ||||
−0.996711 | + | 0.0810355i | \(0.974177\pi\) | |||||||
\(972\) | 1124.72 | + | 15110.2i | 0.0371147 | + | 0.498621i | ||||
\(973\) | 13576.5 | 0.447321 | ||||||||
\(974\) | 33095.1 | 1.08874 | ||||||||
\(975\) | 25405.5 | + | 17887.5i | 0.834490 | + | 0.587548i | ||||
\(976\) | − | 3174.61i | − | 0.104115i | ||||||
\(977\) | 25816.5 | 0.845386 | 0.422693 | − | 0.906273i | \(-0.361085\pi\) | ||||
0.422693 | + | 0.906273i | \(0.361085\pi\) | |||||||
\(978\) | 4450.42 | − | 6320.90i | 0.145510 | − | 0.206667i | ||||
\(979\) | −1380.44 | −0.0450654 | ||||||||
\(980\) | − | 22870.7i | − | 0.745487i | ||||||
\(981\) | −35626.3 | + | 12758.0i | −1.15949 | + | 0.415222i | ||||
\(982\) | 25433.6i | 0.826496i | ||||||||
\(983\) | −2380.07 | −0.0772252 | −0.0386126 | − | 0.999254i | \(-0.512294\pi\) | ||||
−0.0386126 | + | 0.999254i | \(0.512294\pi\) | |||||||
\(984\) | 9549.55 | + | 6723.64i | 0.309378 | + | 0.217827i | ||||
\(985\) | −24739.3 | −0.800265 | ||||||||
\(986\) | −22362.9 | −0.722292 | ||||||||
\(987\) | 1806.54 | − | 2565.81i | 0.0582602 | − | 0.0827465i | ||||
\(988\) | − | 11835.9i | − | 0.381124i | ||||||
\(989\) | − | 76590.2i | − | 2.46252i | ||||||
\(990\) | 4114.72 | − | 1473.51i | 0.132095 | − | 0.0473042i | ||||
\(991\) | 35380.6i | 1.13411i | 0.823680 | + | 0.567054i | \(0.191917\pi\) | ||||
−0.823680 | + | 0.567054i | \(0.808083\pi\) | |||||||
\(992\) | 10945.3i | 0.350317i | ||||||||
\(993\) | −13546.4 | + | 19239.8i | −0.432912 | + | 0.614861i | ||||
\(994\) | − | 5273.49i | − | 0.168275i | ||||||
\(995\) | − | 28814.2i | − | 0.918061i | ||||||
\(996\) | −15143.3 | + | 21508.0i | −0.481761 | + | 0.684242i | ||||
\(997\) | 16910.4 | 0.537169 | 0.268584 | − | 0.963256i | \(-0.413444\pi\) | ||||
0.268584 | + | 0.963256i | \(0.413444\pi\) | |||||||
\(998\) | −4946.57 | −0.156895 | ||||||||
\(999\) | −12929.2 | + | 46793.1i | −0.409473 | + | 1.48195i |
(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 | 354.4.c.b.353.19 | yes | 30 | |
3.2 | odd | 2 | 354.4.c.a.353.20 | yes | 30 | ||
59.58 | odd | 2 | 354.4.c.a.353.19 | ✓ | 30 | ||
177.176 | even | 2 | inner | 354.4.c.b.353.20 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.c.a.353.19 | ✓ | 30 | 59.58 | odd | 2 | ||
354.4.c.a.353.20 | yes | 30 | 3.2 | odd | 2 | ||
354.4.c.b.353.19 | yes | 30 | 1.1 | even | 1 | trivial | |
354.4.c.b.353.20 | yes | 30 | 177.176 | even | 2 | inner |