Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(41,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.b (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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + 13209792 x^{2} + 5760000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.6 | ||
Root | \(-1.80256i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.41 |
Dual form | 105.4.b.b.41.11 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.80256i | − | 0.637303i | −0.947872 | − | 0.318651i | \(-0.896770\pi\) | ||
0.947872 | − | 0.318651i | \(-0.103230\pi\) | |||||||
\(3\) | 1.60858 | + | 4.94090i | 0.309571 | + | 0.950876i | ||||
\(4\) | 4.75076 | 0.593845 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 8.90629 | − | 2.89956i | 0.605996 | − | 0.197290i | ||||
\(7\) | 2.01165 | + | 18.4107i | 0.108619 | + | 0.994083i | ||||
\(8\) | − | 22.9841i | − | 1.01576i | ||||||
\(9\) | −21.8250 | + | 15.8956i | −0.808332 | + | 0.588727i | ||||
\(10\) | − | 9.01282i | − | 0.285011i | ||||||
\(11\) | 11.3844i | 0.312047i | 0.987753 | + | 0.156024i | \(0.0498676\pi\) | ||||
−0.987753 | + | 0.156024i | \(0.950132\pi\) | |||||||
\(12\) | 7.64196 | + | 23.4730i | 0.183837 | + | 0.564673i | ||||
\(13\) | 25.5766i | 0.545666i | 0.962061 | + | 0.272833i | \(0.0879607\pi\) | ||||
−0.962061 | + | 0.272833i | \(0.912039\pi\) | |||||||
\(14\) | 33.1865 | − | 3.62613i | 0.633532 | − | 0.0692232i | ||||
\(15\) | 8.04288 | + | 24.7045i | 0.138444 | + | 0.425245i | ||||
\(16\) | −3.42420 | −0.0535031 | ||||||||
\(17\) | 88.9065 | 1.26841 | 0.634205 | − | 0.773165i | \(-0.281327\pi\) | ||||
0.634205 | + | 0.773165i | \(0.281327\pi\) | |||||||
\(18\) | 28.6529 | + | 39.3409i | 0.375197 | + | 0.515152i | ||||
\(19\) | − | 54.2454i | − | 0.654986i | −0.944854 | − | 0.327493i | \(-0.893796\pi\) | ||
0.944854 | − | 0.327493i | \(-0.106204\pi\) | |||||||
\(20\) | 23.7538 | 0.265576 | ||||||||
\(21\) | −87.7294 | + | 39.5544i | −0.911625 | + | 0.411022i | ||||
\(22\) | 20.5211 | 0.198869 | ||||||||
\(23\) | 25.4319i | 0.230561i | 0.993333 | + | 0.115281i | \(0.0367767\pi\) | ||||
−0.993333 | + | 0.115281i | \(0.963223\pi\) | |||||||
\(24\) | 113.562 | − | 36.9716i | 0.965864 | − | 0.314450i | ||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 46.1034 | 0.347755 | ||||||||
\(27\) | −113.646 | − | 82.2656i | −0.810043 | − | 0.586371i | ||||
\(28\) | 9.55687 | + | 87.4647i | 0.0645028 | + | 0.590331i | ||||
\(29\) | − | 231.306i | − | 1.48112i | −0.671991 | − | 0.740559i | \(-0.734561\pi\) | ||
0.671991 | − | 0.740559i | \(-0.265439\pi\) | |||||||
\(30\) | 44.5315 | − | 14.4978i | 0.271010 | − | 0.0882309i | ||||
\(31\) | 117.898i | 0.683068i | 0.939869 | + | 0.341534i | \(0.110947\pi\) | ||||
−0.939869 | + | 0.341534i | \(0.889053\pi\) | |||||||
\(32\) | − | 177.700i | − | 0.981664i | ||||||
\(33\) | −56.2490 | + | 18.3126i | −0.296718 | + | 0.0966007i | ||||
\(34\) | − | 160.260i | − | 0.808362i | ||||||
\(35\) | 10.0583 | + | 92.0534i | 0.0485759 | + | 0.444568i | ||||
\(36\) | −103.685 | + | 75.5163i | −0.480024 | + | 0.349613i | ||||
\(37\) | 392.122 | 1.74228 | 0.871142 | − | 0.491031i | \(-0.163380\pi\) | ||||
0.871142 | + | 0.491031i | \(0.163380\pi\) | |||||||
\(38\) | −97.7808 | −0.417425 | ||||||||
\(39\) | −126.371 | + | 41.1419i | −0.518861 | + | 0.168922i | ||||
\(40\) | − | 114.920i | − | 0.454263i | ||||||
\(41\) | −478.312 | −1.82195 | −0.910973 | − | 0.412466i | \(-0.864667\pi\) | ||||
−0.910973 | + | 0.412466i | \(0.864667\pi\) | |||||||
\(42\) | 71.2993 | + | 158.138i | 0.261946 | + | 0.580981i | ||||
\(43\) | −253.291 | −0.898293 | −0.449146 | − | 0.893458i | \(-0.648272\pi\) | ||||
−0.449146 | + | 0.893458i | \(0.648272\pi\) | |||||||
\(44\) | 54.0844i | 0.185308i | ||||||||
\(45\) | −109.125 | + | 79.4781i | −0.361497 | + | 0.263287i | ||||
\(46\) | 45.8426 | 0.146937 | ||||||||
\(47\) | −313.715 | −0.973617 | −0.486809 | − | 0.873509i | \(-0.661839\pi\) | ||||
−0.486809 | + | 0.873509i | \(0.661839\pi\) | |||||||
\(48\) | −5.50809 | − | 16.9186i | −0.0165630 | − | 0.0508749i | ||||
\(49\) | −334.907 | + | 74.0717i | −0.976404 | + | 0.215953i | ||||
\(50\) | − | 45.0641i | − | 0.127461i | ||||||
\(51\) | 143.013 | + | 439.278i | 0.392663 | + | 1.20610i | ||||
\(52\) | 121.508i | 0.324041i | ||||||||
\(53\) | − | 558.456i | − | 1.44736i | −0.690138 | − | 0.723678i | \(-0.742450\pi\) | ||
0.690138 | − | 0.723678i | \(-0.257550\pi\) | |||||||
\(54\) | −148.289 | + | 204.854i | −0.373696 | + | 0.516242i | ||||
\(55\) | 56.9219i | 0.139552i | ||||||||
\(56\) | 423.152 | − | 46.2359i | 1.00975 | − | 0.110331i | ||||
\(57\) | 268.021 | − | 87.2578i | 0.622811 | − | 0.202765i | ||||
\(58\) | −416.944 | −0.943921 | ||||||||
\(59\) | −258.035 | −0.569377 | −0.284689 | − | 0.958620i | \(-0.591890\pi\) | ||||
−0.284689 | + | 0.958620i | \(0.591890\pi\) | |||||||
\(60\) | 38.2098 | + | 117.365i | 0.0822144 | + | 0.252530i | ||||
\(61\) | − | 457.766i | − | 0.960836i | −0.877040 | − | 0.480418i | \(-0.840485\pi\) | ||
0.877040 | − | 0.480418i | \(-0.159515\pi\) | |||||||
\(62\) | 212.519 | 0.435321 | ||||||||
\(63\) | −336.554 | − | 369.836i | −0.673044 | − | 0.739602i | ||||
\(64\) | −347.710 | −0.679121 | ||||||||
\(65\) | 127.883i | 0.244029i | ||||||||
\(66\) | 33.0097 | + | 101.393i | 0.0615639 | + | 0.189099i | ||||
\(67\) | 751.160 | 1.36968 | 0.684842 | − | 0.728692i | \(-0.259871\pi\) | ||||
0.684842 | + | 0.728692i | \(0.259871\pi\) | |||||||
\(68\) | 422.373 | 0.753239 | ||||||||
\(69\) | −125.656 | + | 40.9091i | −0.219235 | + | 0.0713750i | ||||
\(70\) | 165.932 | − | 18.1307i | 0.283324 | − | 0.0309575i | ||||
\(71\) | − | 297.427i | − | 0.497156i | −0.968612 | − | 0.248578i | \(-0.920037\pi\) | ||
0.968612 | − | 0.248578i | \(-0.0799632\pi\) | |||||||
\(72\) | 365.346 | + | 501.626i | 0.598007 | + | 0.821073i | ||||
\(73\) | − | 302.448i | − | 0.484916i | −0.970162 | − | 0.242458i | \(-0.922046\pi\) | ||
0.970162 | − | 0.242458i | \(-0.0779536\pi\) | |||||||
\(74\) | − | 706.826i | − | 1.11036i | ||||||
\(75\) | 40.2144 | + | 123.522i | 0.0619141 | + | 0.190175i | ||||
\(76\) | − | 257.707i | − | 0.388960i | ||||||
\(77\) | −209.594 | + | 22.9014i | −0.310201 | + | 0.0338942i | ||||
\(78\) | 74.1609 | + | 227.792i | 0.107655 | + | 0.330672i | ||||
\(79\) | −488.855 | −0.696208 | −0.348104 | − | 0.937456i | \(-0.613174\pi\) | ||||
−0.348104 | + | 0.937456i | \(0.613174\pi\) | |||||||
\(80\) | −17.1210 | −0.0239273 | ||||||||
\(81\) | 223.658 | − | 693.843i | 0.306801 | − | 0.951774i | ||||
\(82\) | 862.188i | 1.16113i | ||||||||
\(83\) | 918.367 | 1.21451 | 0.607253 | − | 0.794509i | \(-0.292272\pi\) | ||||
0.607253 | + | 0.794509i | \(0.292272\pi\) | |||||||
\(84\) | −416.781 | + | 187.913i | −0.541364 | + | 0.244084i | ||||
\(85\) | 444.532 | 0.567251 | ||||||||
\(86\) | 456.574i | 0.572484i | ||||||||
\(87\) | 1142.86 | − | 372.073i | 1.40836 | − | 0.458511i | ||||
\(88\) | 261.659 | 0.316966 | ||||||||
\(89\) | 61.4984 | 0.0732451 | 0.0366225 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366225 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(90\) | 143.265 | + | 196.705i | 0.167793 | + | 0.230383i | ||||
\(91\) | −470.882 | + | 51.4511i | −0.542438 | + | 0.0592697i | ||||
\(92\) | 120.821i | 0.136918i | ||||||||
\(93\) | −582.522 | + | 189.648i | −0.649514 | + | 0.211458i | ||||
\(94\) | 565.491i | 0.620489i | ||||||||
\(95\) | − | 271.227i | − | 0.292919i | ||||||
\(96\) | 877.999 | − | 285.844i | 0.933441 | − | 0.303895i | ||||
\(97\) | − | 175.695i | − | 0.183909i | −0.995763 | − | 0.0919545i | \(-0.970689\pi\) | ||
0.995763 | − | 0.0919545i | \(-0.0293114\pi\) | |||||||
\(98\) | 133.519 | + | 603.691i | 0.137627 | + | 0.622265i | ||||
\(99\) | −180.962 | − | 248.464i | −0.183711 | − | 0.252238i | ||||
\(100\) | 118.769 | 0.118769 | ||||||||
\(101\) | −218.123 | −0.214891 | −0.107446 | − | 0.994211i | \(-0.534267\pi\) | ||||
−0.107446 | + | 0.994211i | \(0.534267\pi\) | |||||||
\(102\) | 791.827 | − | 257.790i | 0.768652 | − | 0.250245i | ||||
\(103\) | 344.306i | 0.329374i | 0.986346 | + | 0.164687i | \(0.0526614\pi\) | ||||
−0.986346 | + | 0.164687i | \(0.947339\pi\) | |||||||
\(104\) | 587.854 | 0.554267 | ||||||||
\(105\) | −438.647 | + | 197.772i | −0.407691 | + | 0.183815i | ||||
\(106\) | −1006.65 | −0.922404 | ||||||||
\(107\) | 1799.20i | 1.62557i | 0.582566 | + | 0.812783i | \(0.302049\pi\) | ||||
−0.582566 | + | 0.812783i | \(0.697951\pi\) | |||||||
\(108\) | −539.904 | − | 390.824i | −0.481040 | − | 0.348214i | ||||
\(109\) | −759.911 | −0.667764 | −0.333882 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333882 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(110\) | 102.605 | 0.0889367 | ||||||||
\(111\) | 630.759 | + | 1937.44i | 0.539360 | + | 1.65670i | ||||
\(112\) | −6.88830 | − | 63.0419i | −0.00581145 | − | 0.0531866i | ||||
\(113\) | 1030.58i | 0.857957i | 0.903315 | + | 0.428978i | \(0.141126\pi\) | ||||
−0.903315 | + | 0.428978i | \(0.858874\pi\) | |||||||
\(114\) | −157.288 | − | 483.125i | −0.129222 | − | 0.396919i | ||||
\(115\) | 127.159i | 0.103110i | ||||||||
\(116\) | − | 1098.88i | − | 0.879555i | ||||||
\(117\) | −406.556 | − | 558.208i | −0.321249 | − | 0.441080i | ||||
\(118\) | 465.124i | 0.362866i | ||||||||
\(119\) | 178.849 | + | 1636.83i | 0.137773 | + | 1.26091i | ||||
\(120\) | 567.810 | − | 184.858i | 0.431948 | − | 0.140626i | ||||
\(121\) | 1201.40 | 0.902627 | ||||||||
\(122\) | −825.154 | −0.612344 | ||||||||
\(123\) | −769.401 | − | 2363.29i | −0.564021 | − | 1.73245i | ||||
\(124\) | 560.105i | 0.405637i | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −666.653 | + | 606.660i | −0.471351 | + | 0.428933i | ||||
\(127\) | 789.585 | 0.551688 | 0.275844 | − | 0.961202i | \(-0.411043\pi\) | ||||
0.275844 | + | 0.961202i | \(0.411043\pi\) | |||||||
\(128\) | − | 794.832i | − | 0.548859i | ||||||
\(129\) | −407.439 | − | 1251.49i | −0.278085 | − | 0.854165i | ||||
\(130\) | 230.517 | 0.155521 | ||||||||
\(131\) | −1156.88 | −0.771583 | −0.385792 | − | 0.922586i | \(-0.626072\pi\) | ||||
−0.385792 | + | 0.922586i | \(0.626072\pi\) | |||||||
\(132\) | −267.226 | + | 86.9990i | −0.176205 | + | 0.0573658i | ||||
\(133\) | 998.694 | − | 109.123i | 0.651111 | − | 0.0711439i | ||||
\(134\) | − | 1354.01i | − | 0.872903i | ||||||
\(135\) | −568.229 | − | 411.328i | −0.362262 | − | 0.262233i | ||||
\(136\) | − | 2043.43i | − | 1.28840i | ||||||
\(137\) | − | 127.823i | − | 0.0797125i | −0.999205 | − | 0.0398563i | \(-0.987310\pi\) | ||
0.999205 | − | 0.0398563i | \(-0.0126900\pi\) | |||||||
\(138\) | 73.7413 | + | 226.504i | 0.0454875 | + | 0.139719i | ||||
\(139\) | − | 1296.63i | − | 0.791216i | −0.918420 | − | 0.395608i | \(-0.870534\pi\) | ||
0.918420 | − | 0.395608i | \(-0.129466\pi\) | |||||||
\(140\) | 47.7844 | + | 437.324i | 0.0288465 | + | 0.264004i | ||||
\(141\) | −504.634 | − | 1550.03i | −0.301403 | − | 0.925790i | ||||
\(142\) | −536.131 | −0.316839 | ||||||||
\(143\) | −291.173 | −0.170274 | ||||||||
\(144\) | 74.7331 | − | 54.4298i | 0.0432483 | − | 0.0314987i | ||||
\(145\) | − | 1156.53i | − | 0.662376i | ||||||
\(146\) | −545.182 | −0.309038 | ||||||||
\(147\) | −904.704 | − | 1535.59i | −0.507610 | − | 0.861587i | ||||
\(148\) | 1862.88 | 1.03465 | ||||||||
\(149\) | 2573.40i | 1.41491i | 0.706760 | + | 0.707453i | \(0.250156\pi\) | ||||
−0.706760 | + | 0.707453i | \(0.749844\pi\) | |||||||
\(150\) | 222.657 | − | 72.4891i | 0.121199 | − | 0.0394581i | ||||
\(151\) | 1400.07 | 0.754541 | 0.377271 | − | 0.926103i | \(-0.376863\pi\) | ||||
0.377271 | + | 0.926103i | \(0.376863\pi\) | |||||||
\(152\) | −1246.78 | −0.665310 | ||||||||
\(153\) | −1940.38 | + | 1413.22i | −1.02530 | + | 0.746748i | ||||
\(154\) | 41.2812 | + | 377.807i | 0.0216009 | + | 0.197692i | ||||
\(155\) | 589.490i | 0.305477i | ||||||||
\(156\) | −600.359 | + | 195.455i | −0.308123 | + | 0.100314i | ||||
\(157\) | 2959.00i | 1.50417i | 0.659068 | + | 0.752083i | \(0.270951\pi\) | ||||
−0.659068 | + | 0.752083i | \(0.729049\pi\) | |||||||
\(158\) | 881.192i | 0.443695i | ||||||||
\(159\) | 2759.28 | − | 898.320i | 1.37626 | − | 0.448059i | ||||
\(160\) | − | 888.501i | − | 0.439014i | ||||||
\(161\) | −468.218 | + | 51.1600i | −0.229197 | + | 0.0250433i | ||||
\(162\) | −1250.70 | − | 403.158i | −0.606568 | − | 0.195525i | ||||
\(163\) | −3819.48 | −1.83537 | −0.917684 | − | 0.397312i | \(-0.869943\pi\) | ||||
−0.917684 | + | 0.397312i | \(0.869943\pi\) | |||||||
\(164\) | −2272.35 | −1.08195 | ||||||||
\(165\) | −281.245 | + | 91.5632i | −0.132696 | + | 0.0432011i | ||||
\(166\) | − | 1655.42i | − | 0.774008i | ||||||
\(167\) | 1801.35 | 0.834687 | 0.417343 | − | 0.908749i | \(-0.362961\pi\) | ||||
0.417343 | + | 0.908749i | \(0.362961\pi\) | |||||||
\(168\) | 909.120 | + | 2016.38i | 0.417501 | + | 0.925994i | ||||
\(169\) | 1542.84 | 0.702248 | ||||||||
\(170\) | − | 801.298i | − | 0.361510i | ||||||
\(171\) | 862.264 | + | 1183.90i | 0.385608 | + | 0.529446i | ||||
\(172\) | −1203.33 | −0.533446 | ||||||||
\(173\) | −1586.98 | −0.697434 | −0.348717 | − | 0.937228i | \(-0.613383\pi\) | ||||
−0.348717 | + | 0.937228i | \(0.613383\pi\) | |||||||
\(174\) | −670.686 | − | 2060.08i | −0.292210 | − | 0.897552i | ||||
\(175\) | 50.2913 | + | 460.267i | 0.0217238 | + | 0.198817i | ||||
\(176\) | − | 38.9824i | − | 0.0166955i | ||||||
\(177\) | −415.068 | − | 1274.92i | −0.176262 | − | 0.541407i | ||||
\(178\) | − | 110.855i | − | 0.0466793i | ||||||
\(179\) | − | 1270.55i | − | 0.530531i | −0.964175 | − | 0.265266i | \(-0.914540\pi\) | ||
0.964175 | − | 0.265266i | \(-0.0854596\pi\) | |||||||
\(180\) | −518.426 | + | 377.582i | −0.214673 | + | 0.156352i | ||||
\(181\) | − | 1213.15i | − | 0.498193i | −0.968479 | − | 0.249097i | \(-0.919866\pi\) | ||
0.968479 | − | 0.249097i | \(-0.0801336\pi\) | |||||||
\(182\) | 92.7440 | + | 848.796i | 0.0377728 | + | 0.345697i | ||||
\(183\) | 2261.78 | − | 736.352i | 0.913636 | − | 0.297447i | ||||
\(184\) | 584.528 | 0.234195 | ||||||||
\(185\) | 1960.61 | 0.779173 | ||||||||
\(186\) | 341.853 | + | 1050.03i | 0.134763 | + | 0.413937i | ||||
\(187\) | 1012.14i | 0.395804i | ||||||||
\(188\) | −1490.38 | −0.578178 | ||||||||
\(189\) | 1285.95 | − | 2257.79i | 0.494916 | − | 0.868941i | ||||
\(190\) | −488.904 | −0.186678 | ||||||||
\(191\) | 2654.34i | 1.00555i | 0.864416 | + | 0.502777i | \(0.167688\pi\) | ||||
−0.864416 | + | 0.502777i | \(0.832312\pi\) | |||||||
\(192\) | −559.318 | − | 1718.00i | −0.210236 | − | 0.645760i | ||||
\(193\) | −841.332 | −0.313784 | −0.156892 | − | 0.987616i | \(-0.550148\pi\) | ||||
−0.156892 | + | 0.987616i | \(0.550148\pi\) | |||||||
\(194\) | −316.703 | −0.117206 | ||||||||
\(195\) | −631.856 | + | 205.709i | −0.232042 | + | 0.0755444i | ||||
\(196\) | −1591.06 | + | 351.897i | −0.579833 | + | 0.128242i | ||||
\(197\) | − | 1201.46i | − | 0.434522i | −0.976114 | − | 0.217261i | \(-0.930288\pi\) | ||
0.976114 | − | 0.217261i | \(-0.0697122\pi\) | |||||||
\(198\) | −447.872 | + | 326.195i | −0.160752 | + | 0.117079i | ||||
\(199\) | 4524.30i | 1.61165i | 0.592151 | + | 0.805827i | \(0.298279\pi\) | ||||
−0.592151 | + | 0.805827i | \(0.701721\pi\) | |||||||
\(200\) | − | 574.602i | − | 0.203152i | ||||||
\(201\) | 1208.30 | + | 3711.40i | 0.424014 | + | 1.30240i | ||||
\(202\) | 393.180i | 0.136951i | ||||||||
\(203\) | 4258.50 | − | 465.307i | 1.47236 | − | 0.160878i | ||||
\(204\) | 679.420 | + | 2086.90i | 0.233181 | + | 0.716238i | ||||
\(205\) | −2391.56 | −0.814799 | ||||||||
\(206\) | 620.635 | 0.209911 | ||||||||
\(207\) | −404.255 | − | 555.049i | −0.135738 | − | 0.186370i | ||||
\(208\) | − | 87.5793i | − | 0.0291949i | ||||||
\(209\) | 617.550 | 0.204387 | ||||||||
\(210\) | 356.497 | + | 790.690i | 0.117146 | + | 0.259823i | ||||
\(211\) | 2948.59 | 0.962033 | 0.481017 | − | 0.876711i | \(-0.340268\pi\) | ||||
0.481017 | + | 0.876711i | \(0.340268\pi\) | |||||||
\(212\) | − | 2653.09i | − | 0.859505i | ||||||
\(213\) | 1469.56 | − | 478.434i | 0.472734 | − | 0.153905i | ||||
\(214\) | 3243.18 | 1.03598 | ||||||||
\(215\) | −1266.46 | −0.401729 | ||||||||
\(216\) | −1890.80 | + | 2612.04i | −0.595614 | + | 0.822810i | ||||
\(217\) | −2170.58 | + | 237.170i | −0.679027 | + | 0.0741942i | ||||
\(218\) | 1369.79i | 0.425568i | ||||||||
\(219\) | 1494.36 | − | 486.511i | 0.461095 | − | 0.150116i | ||||
\(220\) | 270.422i | 0.0828721i | ||||||||
\(221\) | 2273.92i | 0.692129i | ||||||||
\(222\) | 3492.36 | − | 1136.98i | 1.05582 | − | 0.343736i | ||||
\(223\) | − | 554.664i | − | 0.166561i | −0.996526 | − | 0.0832804i | \(-0.973460\pi\) | ||
0.996526 | − | 0.0832804i | \(-0.0265397\pi\) | |||||||
\(224\) | 3271.58 | − | 357.471i | 0.975856 | − | 0.106627i | ||||
\(225\) | −545.624 | + | 397.391i | −0.161666 | + | 0.117745i | ||||
\(226\) | 1857.69 | 0.546778 | ||||||||
\(227\) | 5416.25 | 1.58365 | 0.791826 | − | 0.610746i | \(-0.209130\pi\) | ||||
0.791826 | + | 0.610746i | \(0.209130\pi\) | |||||||
\(228\) | 1273.30 | − | 414.541i | 0.369853 | − | 0.120411i | ||||
\(229\) | 681.437i | 0.196640i | 0.995155 | + | 0.0983201i | \(0.0313469\pi\) | ||||
−0.995155 | + | 0.0983201i | \(0.968653\pi\) | |||||||
\(230\) | 229.213 | 0.0657124 | ||||||||
\(231\) | −450.302 | − | 998.745i | −0.128258 | − | 0.284470i | ||||
\(232\) | −5316.35 | −1.50446 | ||||||||
\(233\) | − | 4345.48i | − | 1.22181i | −0.791704 | − | 0.610905i | \(-0.790806\pi\) | ||
0.791704 | − | 0.610905i | \(-0.209194\pi\) | |||||||
\(234\) | −1006.21 | + | 732.843i | −0.281101 | + | 0.204733i | ||||
\(235\) | −1568.57 | −0.435415 | ||||||||
\(236\) | −1225.86 | −0.338122 | ||||||||
\(237\) | −786.360 | − | 2415.38i | −0.215526 | − | 0.662008i | ||||
\(238\) | 2950.49 | − | 322.387i | 0.803579 | − | 0.0878034i | ||||
\(239\) | 1368.95i | 0.370502i | 0.982691 | + | 0.185251i | \(0.0593099\pi\) | ||||
−0.982691 | + | 0.185251i | \(0.940690\pi\) | |||||||
\(240\) | −27.5404 | − | 84.5932i | −0.00740720 | − | 0.0227519i | ||||
\(241\) | − | 4526.16i | − | 1.20978i | −0.796311 | − | 0.604888i | \(-0.793218\pi\) | ||
0.796311 | − | 0.604888i | \(-0.206782\pi\) | |||||||
\(242\) | − | 2165.59i | − | 0.575247i | ||||||
\(243\) | 3787.98 | − | 11.0286i | 0.999996 | − | 0.00291146i | ||||
\(244\) | − | 2174.74i | − | 0.570588i | ||||||
\(245\) | −1674.53 | + | 370.359i | −0.436661 | + | 0.0965769i | ||||
\(246\) | −4259.99 | + | 1386.90i | −1.10409 | + | 0.359452i | ||||
\(247\) | 1387.41 | 0.357404 | ||||||||
\(248\) | 2709.78 | 0.693835 | ||||||||
\(249\) | 1477.26 | + | 4537.56i | 0.375975 | + | 1.15484i | ||||
\(250\) | − | 225.321i | − | 0.0570021i | ||||||
\(251\) | 6278.33 | 1.57882 | 0.789411 | − | 0.613865i | \(-0.210386\pi\) | ||||
0.789411 | + | 0.613865i | \(0.210386\pi\) | |||||||
\(252\) | −1598.89 | − | 1757.00i | −0.399684 | − | 0.439209i | ||||
\(253\) | −289.526 | −0.0719460 | ||||||||
\(254\) | − | 1423.28i | − | 0.351592i | ||||||
\(255\) | 715.064 | + | 2196.39i | 0.175604 | + | 0.539385i | ||||
\(256\) | −4214.42 | −1.02891 | ||||||||
\(257\) | −7065.00 | −1.71480 | −0.857398 | − | 0.514655i | \(-0.827920\pi\) | ||||
−0.857398 | + | 0.514655i | \(0.827920\pi\) | |||||||
\(258\) | −2255.89 | + | 734.435i | −0.544362 | + | 0.177224i | ||||
\(259\) | 788.813 | + | 7219.24i | 0.189245 | + | 1.73198i | ||||
\(260\) | 607.541i | 0.144916i | ||||||||
\(261\) | 3676.75 | + | 5048.24i | 0.871974 | + | 1.19724i | ||||
\(262\) | 2085.36i | 0.491732i | ||||||||
\(263\) | 4457.41i | 1.04508i | 0.852616 | + | 0.522539i | \(0.175015\pi\) | ||||
−0.852616 | + | 0.522539i | \(0.824985\pi\) | |||||||
\(264\) | 420.899 | + | 1292.83i | 0.0981233 | + | 0.301395i | ||||
\(265\) | − | 2792.28i | − | 0.647277i | ||||||
\(266\) | −196.701 | − | 1800.21i | −0.0453402 | − | 0.414955i | ||||
\(267\) | 98.9248 | + | 303.857i | 0.0226745 | + | 0.0696470i | ||||
\(268\) | 3568.58 | 0.813380 | ||||||||
\(269\) | −4733.36 | −1.07286 | −0.536428 | − | 0.843946i | \(-0.680227\pi\) | ||||
−0.536428 | + | 0.843946i | \(0.680227\pi\) | |||||||
\(270\) | −741.445 | + | 1024.27i | −0.167122 | + | 0.230871i | ||||
\(271\) | − | 5052.32i | − | 1.13250i | −0.824234 | − | 0.566249i | \(-0.808394\pi\) | ||
0.824234 | − | 0.566249i | \(-0.191606\pi\) | |||||||
\(272\) | −304.434 | −0.0678640 | ||||||||
\(273\) | −1011.66 | − | 2243.82i | −0.224281 | − | 0.497443i | ||||
\(274\) | −230.408 | −0.0508010 | ||||||||
\(275\) | 284.609i | 0.0624094i | ||||||||
\(276\) | −596.963 | + | 194.349i | −0.130192 | + | 0.0423857i | ||||
\(277\) | −7257.22 | −1.57417 | −0.787084 | − | 0.616846i | \(-0.788410\pi\) | ||||
−0.787084 | + | 0.616846i | \(0.788410\pi\) | |||||||
\(278\) | −2337.26 | −0.504244 | ||||||||
\(279\) | −1874.06 | − | 2573.12i | −0.402141 | − | 0.552146i | ||||
\(280\) | 2115.76 | − | 231.180i | 0.451575 | − | 0.0493415i | ||||
\(281\) | − | 599.316i | − | 0.127232i | −0.997974 | − | 0.0636160i | \(-0.979737\pi\) | ||
0.997974 | − | 0.0636160i | \(-0.0202633\pi\) | |||||||
\(282\) | −2794.03 | + | 909.636i | −0.590008 | + | 0.192085i | ||||
\(283\) | − | 4328.08i | − | 0.909108i | −0.890719 | − | 0.454554i | \(-0.849799\pi\) | ||
0.890719 | − | 0.454554i | \(-0.150201\pi\) | |||||||
\(284\) | − | 1413.00i | − | 0.295234i | ||||||
\(285\) | 1340.10 | − | 436.289i | 0.278530 | − | 0.0906791i | ||||
\(286\) | 524.859i | 0.108516i | ||||||||
\(287\) | −962.197 | − | 8806.05i | −0.197898 | − | 1.81117i | ||||
\(288\) | 2824.66 | + | 3878.30i | 0.577932 | + | 0.793511i | ||||
\(289\) | 2991.36 | 0.608866 | ||||||||
\(290\) | −2084.72 | −0.422134 | ||||||||
\(291\) | 868.094 | − | 282.620i | 0.174875 | − | 0.0569328i | ||||
\(292\) | − | 1436.86i | − | 0.287965i | ||||||
\(293\) | −2719.51 | −0.542236 | −0.271118 | − | 0.962546i | \(-0.587393\pi\) | ||||
−0.271118 | + | 0.962546i | \(0.587393\pi\) | |||||||
\(294\) | −2768.00 | + | 1630.79i | −0.549092 | + | 0.323502i | ||||
\(295\) | −1290.17 | −0.254633 | ||||||||
\(296\) | − | 9012.57i | − | 1.76975i | ||||||
\(297\) | 936.542 | − | 1293.79i | 0.182975 | − | 0.252771i | ||||
\(298\) | 4638.72 | 0.901724 | ||||||||
\(299\) | −650.460 | −0.125810 | ||||||||
\(300\) | 191.049 | + | 586.826i | 0.0367674 | + | 0.112935i | ||||
\(301\) | −509.534 | − | 4663.27i | −0.0975716 | − | 0.892978i | ||||
\(302\) | − | 2523.71i | − | 0.480871i | ||||||
\(303\) | −350.867 | − | 1077.72i | −0.0665241 | − | 0.204335i | ||||
\(304\) | 185.747i | 0.0350438i | ||||||||
\(305\) | − | 2288.83i | − | 0.429699i | ||||||
\(306\) | 2547.43 | + | 3497.66i | 0.475905 | + | 0.653425i | ||||
\(307\) | 7761.41i | 1.44289i | 0.692472 | + | 0.721444i | \(0.256521\pi\) | ||||
−0.692472 | + | 0.721444i | \(0.743479\pi\) | |||||||
\(308\) | −995.731 | + | 108.799i | −0.184211 | + | 0.0201279i | ||||
\(309\) | −1701.18 | + | 553.843i | −0.313194 | + | 0.101965i | ||||
\(310\) | 1062.59 | 0.194682 | ||||||||
\(311\) | −4886.92 | −0.891034 | −0.445517 | − | 0.895273i | \(-0.646980\pi\) | ||||
−0.445517 | + | 0.895273i | \(0.646980\pi\) | |||||||
\(312\) | 945.608 | + | 2904.53i | 0.171585 | + | 0.527040i | ||||
\(313\) | 6512.69i | 1.17610i | 0.808825 | + | 0.588050i | \(0.200104\pi\) | ||||
−0.808825 | + | 0.588050i | \(0.799896\pi\) | |||||||
\(314\) | 5333.79 | 0.958610 | ||||||||
\(315\) | −1682.77 | − | 1849.18i | −0.300994 | − | 0.330760i | ||||
\(316\) | −2322.43 | −0.413440 | ||||||||
\(317\) | 4297.71i | 0.761462i | 0.924686 | + | 0.380731i | \(0.124328\pi\) | ||||
−0.924686 | + | 0.380731i | \(0.875672\pi\) | |||||||
\(318\) | −1619.28 | − | 4973.77i | −0.285549 | − | 0.877092i | ||||
\(319\) | 2633.27 | 0.462179 | ||||||||
\(320\) | −1738.55 | −0.303712 | ||||||||
\(321\) | −8889.68 | + | 2894.16i | −1.54571 | + | 0.503228i | ||||
\(322\) | 92.2193 | + | 843.993i | 0.0159602 | + | 0.146068i | ||||
\(323\) | − | 4822.76i | − | 0.830792i | ||||||
\(324\) | 1062.55 | − | 3296.28i | 0.182192 | − | 0.565206i | ||||
\(325\) | 639.414i | 0.109133i | ||||||||
\(326\) | 6884.86i | 1.16969i | ||||||||
\(327\) | −1222.37 | − | 3754.64i | −0.206720 | − | 0.634961i | ||||
\(328\) | 10993.6i | 1.85066i | ||||||||
\(329\) | −631.085 | − | 5775.70i | −0.105753 | − | 0.967857i | ||||
\(330\) | 165.049 | + | 506.963i | 0.0275322 | + | 0.0845678i | ||||
\(331\) | 3047.66 | 0.506086 | 0.253043 | − | 0.967455i | \(-0.418569\pi\) | ||||
0.253043 | + | 0.967455i | \(0.418569\pi\) | |||||||
\(332\) | 4362.94 | 0.721228 | ||||||||
\(333\) | −8558.06 | + | 6233.03i | −1.40834 | + | 1.02573i | ||||
\(334\) | − | 3247.05i | − | 0.531948i | ||||||
\(335\) | 3755.80 | 0.612541 | ||||||||
\(336\) | 300.403 | − | 135.442i | 0.0487748 | − | 0.0219910i | ||||
\(337\) | 3571.60 | 0.577322 | 0.288661 | − | 0.957431i | \(-0.406790\pi\) | ||||
0.288661 | + | 0.957431i | \(0.406790\pi\) | |||||||
\(338\) | − | 2781.07i | − | 0.447545i | ||||||
\(339\) | −5092.01 | + | 1657.77i | −0.815811 | + | 0.265598i | ||||
\(340\) | 2111.87 | 0.336859 | ||||||||
\(341\) | −1342.20 | −0.213149 | ||||||||
\(342\) | 2134.06 | − | 1554.29i | 0.337418 | − | 0.245749i | ||||
\(343\) | −2037.43 | − | 6016.85i | −0.320731 | − | 0.947170i | ||||
\(344\) | 5821.67i | 0.912451i | ||||||||
\(345\) | −628.281 | + | 204.545i | −0.0980450 | + | 0.0319199i | ||||
\(346\) | 2860.64i | 0.444477i | ||||||||
\(347\) | 11138.9i | 1.72325i | 0.507543 | + | 0.861626i | \(0.330554\pi\) | ||||
−0.507543 | + | 0.861626i | \(0.669446\pi\) | |||||||
\(348\) | 5429.45 | − | 1767.63i | 0.836348 | − | 0.272284i | ||||
\(349\) | − | 10991.7i | − | 1.68587i | −0.538013 | − | 0.842937i | \(-0.680825\pi\) | ||
0.538013 | − | 0.842937i | \(-0.319175\pi\) | |||||||
\(350\) | 829.661 | − | 90.6533i | 0.126706 | − | 0.0138446i | ||||
\(351\) | 2104.07 | − | 2906.67i | 0.319963 | − | 0.442013i | ||||
\(352\) | 2023.01 | 0.306326 | ||||||||
\(353\) | −10085.8 | −1.52072 | −0.760359 | − | 0.649503i | \(-0.774977\pi\) | ||||
−0.760359 | + | 0.649503i | \(0.774977\pi\) | |||||||
\(354\) | −2298.13 | + | 748.188i | −0.345040 | + | 0.112333i | ||||
\(355\) | − | 1487.13i | − | 0.222335i | ||||||
\(356\) | 292.164 | 0.0434962 | ||||||||
\(357\) | −7799.71 | + | 3516.64i | −1.15632 | + | 0.521345i | ||||
\(358\) | −2290.24 | −0.338109 | ||||||||
\(359\) | 640.876i | 0.0942176i | 0.998890 | + | 0.0471088i | \(0.0150007\pi\) | ||||
−0.998890 | + | 0.0471088i | \(0.984999\pi\) | |||||||
\(360\) | 1826.73 | + | 2508.13i | 0.267437 | + | 0.367195i | ||||
\(361\) | 3916.44 | 0.570993 | ||||||||
\(362\) | −2186.79 | −0.317500 | ||||||||
\(363\) | 1932.54 | + | 5935.98i | 0.279427 | + | 0.858286i | ||||
\(364\) | −2237.05 | + | 244.432i | −0.322124 | + | 0.0351970i | ||||
\(365\) | − | 1512.24i | − | 0.216861i | ||||||
\(366\) | −1327.32 | − | 4077.00i | −0.189564 | − | 0.582263i | ||||
\(367\) | − | 4440.20i | − | 0.631544i | −0.948835 | − | 0.315772i | \(-0.897737\pi\) | ||
0.948835 | − | 0.315772i | \(-0.102263\pi\) | |||||||
\(368\) | − | 87.0838i | − | 0.0123358i | ||||||
\(369\) | 10439.1 | − | 7603.07i | 1.47274 | − | 1.07263i | ||||
\(370\) | − | 3534.13i | − | 0.496569i | ||||||
\(371\) | 10281.6 | − | 1123.42i | 1.43879 | − | 0.157210i | ||||
\(372\) | −2767.42 | + | 900.973i | −0.385710 | + | 0.125573i | ||||
\(373\) | −3346.57 | −0.464554 | −0.232277 | − | 0.972650i | \(-0.574618\pi\) | ||||
−0.232277 | + | 0.972650i | \(0.574618\pi\) | |||||||
\(374\) | 1824.46 | 0.252247 | ||||||||
\(375\) | 201.072 | + | 617.612i | 0.0276888 | + | 0.0850490i | ||||
\(376\) | 7210.44i | 0.988963i | ||||||||
\(377\) | 5916.01 | 0.808197 | ||||||||
\(378\) | −4069.81 | − | 2318.01i | −0.553779 | − | 0.315411i | ||||
\(379\) | −5731.50 | −0.776800 | −0.388400 | − | 0.921491i | \(-0.626972\pi\) | ||||
−0.388400 | + | 0.921491i | \(0.626972\pi\) | |||||||
\(380\) | − | 1288.53i | − | 0.173948i | ||||||
\(381\) | 1270.11 | + | 3901.26i | 0.170786 | + | 0.524587i | ||||
\(382\) | 4784.61 | 0.640843 | ||||||||
\(383\) | −2978.01 | −0.397309 | −0.198654 | − | 0.980070i | \(-0.563657\pi\) | ||||
−0.198654 | + | 0.980070i | \(0.563657\pi\) | |||||||
\(384\) | 3927.19 | − | 1278.55i | 0.521897 | − | 0.169911i | ||||
\(385\) | −1047.97 | + | 114.507i | −0.138726 | + | 0.0151580i | ||||
\(386\) | 1516.56i | 0.199976i | ||||||||
\(387\) | 5528.08 | − | 4026.23i | 0.726119 | − | 0.528849i | ||||
\(388\) | − | 834.687i | − | 0.109213i | ||||||
\(389\) | 8663.36i | 1.12918i | 0.825373 | + | 0.564588i | \(0.190965\pi\) | ||||
−0.825373 | + | 0.564588i | \(0.809035\pi\) | |||||||
\(390\) | 370.804 | + | 1138.96i | 0.0481447 | + | 0.147881i | ||||
\(391\) | 2261.06i | 0.292446i | ||||||||
\(392\) | 1702.47 | + | 7697.52i | 0.219356 | + | 0.991794i | ||||
\(393\) | −1860.94 | − | 5716.05i | −0.238860 | − | 0.733680i | ||||
\(394\) | −2165.72 | −0.276922 | ||||||||
\(395\) | −2444.27 | −0.311354 | ||||||||
\(396\) | −859.706 | − | 1180.39i | −0.109096 | − | 0.149790i | ||||
\(397\) | 4560.17i | 0.576494i | 0.957556 | + | 0.288247i | \(0.0930724\pi\) | ||||
−0.957556 | + | 0.288247i | \(0.906928\pi\) | |||||||
\(398\) | 8155.34 | 1.02711 | ||||||||
\(399\) | 2145.64 | + | 4758.92i | 0.269214 | + | 0.597102i | ||||
\(400\) | −85.6050 | −0.0107006 | ||||||||
\(401\) | − | 4033.10i | − | 0.502253i | −0.967954 | − | 0.251127i | \(-0.919199\pi\) | ||
0.967954 | − | 0.251127i | \(-0.0808011\pi\) | |||||||
\(402\) | 6690.05 | − | 2178.04i | 0.830023 | − | 0.270225i | ||||
\(403\) | −3015.43 | −0.372727 | ||||||||
\(404\) | −1036.25 | −0.127612 | ||||||||
\(405\) | 1118.29 | − | 3469.22i | 0.137206 | − | 0.425646i | ||||
\(406\) | −838.746 | − | 7676.22i | −0.102528 | − | 0.938336i | ||||
\(407\) | 4464.07i | 0.543675i | ||||||||
\(408\) | 10096.4 | − | 3287.02i | 1.22511 | − | 0.398852i | ||||
\(409\) | 1829.12i | 0.221135i | 0.993869 | + | 0.110568i | \(0.0352669\pi\) | ||||
−0.993869 | + | 0.110568i | \(0.964733\pi\) | |||||||
\(410\) | 4310.94i | 0.519274i | ||||||||
\(411\) | 631.558 | − | 205.612i | 0.0757968 | − | 0.0246767i | ||||
\(412\) | 1635.72i | 0.195597i | ||||||||
\(413\) | −519.076 | − | 4750.59i | −0.0618451 | − | 0.566008i | ||||
\(414\) | −1000.51 | + | 728.697i | −0.118774 | + | 0.0865060i | ||||
\(415\) | 4591.84 | 0.543143 | ||||||||
\(416\) | 4544.96 | 0.535661 | ||||||||
\(417\) | 6406.53 | − | 2085.73i | 0.752348 | − | 0.244937i | ||||
\(418\) | − | 1113.17i | − | 0.130256i | ||||||
\(419\) | 4125.47 | 0.481008 | 0.240504 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240504 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(420\) | −2083.91 | + | 939.566i | −0.242105 | + | 0.109157i | ||||
\(421\) | 4892.88 | 0.566424 | 0.283212 | − | 0.959057i | \(-0.408600\pi\) | ||||
0.283212 | + | 0.959057i | \(0.408600\pi\) | |||||||
\(422\) | − | 5315.02i | − | 0.613107i | ||||||
\(423\) | 6846.81 | − | 4986.69i | 0.787006 | − | 0.573195i | ||||
\(424\) | −12835.6 | −1.47017 | ||||||||
\(425\) | 2222.66 | 0.253682 | ||||||||
\(426\) | −862.408 | − | 2648.97i | −0.0980841 | − | 0.301275i | ||||
\(427\) | 8427.79 | − | 920.866i | 0.955151 | − | 0.104365i | ||||
\(428\) | 8547.59i | 0.965334i | ||||||||
\(429\) | −468.375 | − | 1438.66i | −0.0527117 | − | 0.161909i | ||||
\(430\) | 2282.87i | 0.256023i | ||||||||
\(431\) | − | 3994.63i | − | 0.446437i | −0.974768 | − | 0.223219i | \(-0.928344\pi\) | ||
0.974768 | − | 0.223219i | \(-0.0716564\pi\) | |||||||
\(432\) | 389.146 | + | 281.694i | 0.0433398 | + | 0.0313727i | ||||
\(433\) | 13895.6i | 1.54221i | 0.636705 | + | 0.771107i | \(0.280297\pi\) | ||||
−0.636705 | + | 0.771107i | \(0.719703\pi\) | |||||||
\(434\) | 427.514 | + | 3912.62i | 0.0472842 | + | 0.432746i | ||||
\(435\) | 5714.30 | − | 1860.37i | 0.629838 | − | 0.205052i | ||||
\(436\) | −3610.15 | −0.396548 | ||||||||
\(437\) | 1379.56 | 0.151014 | ||||||||
\(438\) | −876.967 | − | 2693.69i | −0.0956692 | − | 0.293857i | ||||
\(439\) | 4224.83i | 0.459317i | 0.973271 | + | 0.229658i | \(0.0737609\pi\) | ||||
−0.973271 | + | 0.229658i | \(0.926239\pi\) | |||||||
\(440\) | 1308.30 | 0.141751 | ||||||||
\(441\) | 6131.91 | − | 6940.16i | 0.662121 | − | 0.749397i | ||||
\(442\) | 4098.89 | 0.441096 | ||||||||
\(443\) | 14223.7i | 1.52548i | 0.646706 | + | 0.762739i | \(0.276146\pi\) | ||||
−0.646706 | + | 0.762739i | \(0.723854\pi\) | |||||||
\(444\) | 2996.58 | + | 9204.30i | 0.320296 | + | 0.983821i | ||||
\(445\) | 307.492 | 0.0327562 | ||||||||
\(446\) | −999.818 | −0.106150 | ||||||||
\(447\) | −12714.9 | + | 4139.51i | −1.34540 | + | 0.438013i | ||||
\(448\) | −699.471 | − | 6401.57i | −0.0737654 | − | 0.675103i | ||||
\(449\) | − | 16223.9i | − | 1.70524i | −0.522531 | − | 0.852620i | \(-0.675012\pi\) | ||
0.522531 | − | 0.852620i | \(-0.324988\pi\) | |||||||
\(450\) | 716.323 | + | 983.523i | 0.0750395 | + | 0.103030i | ||||
\(451\) | − | 5445.28i | − | 0.568533i | ||||||
\(452\) | 4896.05i | 0.509493i | ||||||||
\(453\) | 2252.11 | + | 6917.58i | 0.233584 | + | 0.717476i | ||||
\(454\) | − | 9763.14i | − | 1.00927i | ||||||
\(455\) | −2354.41 | + | 257.256i | −0.242586 | + | 0.0265062i | ||||
\(456\) | −2005.54 | − | 6160.21i | −0.205961 | − | 0.632628i | ||||
\(457\) | 4257.18 | 0.435761 | 0.217880 | − | 0.975975i | \(-0.430086\pi\) | ||||
0.217880 | + | 0.975975i | \(0.430086\pi\) | |||||||
\(458\) | 1228.33 | 0.125319 | ||||||||
\(459\) | −10103.8 | − | 7313.94i | −1.02747 | − | 0.743760i | ||||
\(460\) | 604.103i | 0.0612314i | ||||||||
\(461\) | −4912.62 | −0.496320 | −0.248160 | − | 0.968719i | \(-0.579826\pi\) | ||||
−0.248160 | + | 0.968719i | \(0.579826\pi\) | |||||||
\(462\) | −1800.30 | + | 811.698i | −0.181294 | + | 0.0817394i | ||||
\(463\) | −15697.6 | −1.57566 | −0.787830 | − | 0.615893i | \(-0.788795\pi\) | ||||
−0.787830 | + | 0.615893i | \(0.788795\pi\) | |||||||
\(464\) | 792.038i | 0.0792445i | ||||||||
\(465\) | −2912.61 | + | 948.240i | −0.290471 | + | 0.0945669i | ||||
\(466\) | −7833.01 | −0.778663 | ||||||||
\(467\) | −1451.66 | −0.143844 | −0.0719219 | − | 0.997410i | \(-0.522913\pi\) | ||||
−0.0719219 | + | 0.997410i | \(0.522913\pi\) | |||||||
\(468\) | −1931.45 | − | 2651.91i | −0.190772 | − | 0.261933i | ||||
\(469\) | 1511.07 | + | 13829.4i | 0.148774 | + | 1.36158i | ||||
\(470\) | 2827.46i | 0.277491i | ||||||||
\(471\) | −14620.1 | + | 4759.78i | −1.43028 | + | 0.465646i | ||||
\(472\) | 5930.69i | 0.578352i | ||||||||
\(473\) | − | 2883.56i | − | 0.280310i | ||||||
\(474\) | −4353.88 | + | 1417.47i | −0.421900 | + | 0.137355i | ||||
\(475\) | − | 1356.13i | − | 0.130997i | ||||||
\(476\) | 849.668 | + | 7776.18i | 0.0818161 | + | 0.748783i | ||||
\(477\) | 8877.01 | + | 12188.3i | 0.852098 | + | 1.16994i | ||||
\(478\) | 2467.62 | 0.236122 | ||||||||
\(479\) | −12161.8 | −1.16009 | −0.580047 | − | 0.814583i | \(-0.696966\pi\) | ||||
−0.580047 | + | 0.814583i | \(0.696966\pi\) | |||||||
\(480\) | 4389.99 | − | 1429.22i | 0.417448 | − | 0.135906i | ||||
\(481\) | 10029.1i | 0.950706i | ||||||||
\(482\) | −8158.70 | −0.770993 | ||||||||
\(483\) | −1005.94 | − | 2231.12i | −0.0947658 | − | 0.210185i | ||||
\(484\) | 5707.54 | 0.536020 | ||||||||
\(485\) | − | 878.477i | − | 0.0822466i | ||||||
\(486\) | −19.8797 | − | 6828.08i | −0.00185548 | − | 0.637300i | ||||
\(487\) | −699.290 | −0.0650675 | −0.0325337 | − | 0.999471i | \(-0.510358\pi\) | ||||
−0.0325337 | + | 0.999471i | \(0.510358\pi\) | |||||||
\(488\) | −10521.3 | −0.975981 | ||||||||
\(489\) | −6143.93 | − | 18871.7i | −0.568176 | − | 1.74521i | ||||
\(490\) | 667.596 | + | 3018.45i | 0.0615488 | + | 0.278285i | ||||
\(491\) | 15982.5i | 1.46900i | 0.678607 | + | 0.734501i | \(0.262584\pi\) | ||||
−0.678607 | + | 0.734501i | \(0.737416\pi\) | |||||||
\(492\) | −3655.24 | − | 11227.4i | −0.334941 | − | 1.02880i | ||||
\(493\) | − | 20564.6i | − | 1.87867i | ||||||
\(494\) | − | 2500.90i | − | 0.227775i | ||||||
\(495\) | −904.809 | − | 1242.32i | −0.0821579 | − | 0.112804i | ||||
\(496\) | − | 403.707i | − | 0.0365463i | ||||||
\(497\) | 5475.83 | − | 598.319i | 0.494215 | − | 0.0540006i | ||||
\(498\) | 8179.25 | − | 2662.87i | 0.735986 | − | 0.239610i | ||||
\(499\) | −20926.5 | −1.87735 | −0.938675 | − | 0.344804i | \(-0.887946\pi\) | ||||
−0.938675 | + | 0.344804i | \(0.887946\pi\) | |||||||
\(500\) | 593.845 | 0.0531151 | ||||||||
\(501\) | 2897.61 | + | 8900.29i | 0.258395 | + | 0.793684i | ||||
\(502\) | − | 11317.1i | − | 1.00619i | ||||||
\(503\) | −8664.19 | −0.768026 | −0.384013 | − | 0.923328i | \(-0.625458\pi\) | ||||
−0.384013 | + | 0.923328i | \(0.625458\pi\) | |||||||
\(504\) | −8500.34 | + | 7735.37i | −0.751260 | + | 0.683653i | ||||
\(505\) | −1090.61 | −0.0961023 | ||||||||
\(506\) | 521.889i | 0.0458514i | ||||||||
\(507\) | 2481.78 | + | 7623.01i | 0.217395 | + | 0.667751i | ||||
\(508\) | 3751.13 | 0.327617 | ||||||||
\(509\) | 532.494 | 0.0463701 | 0.0231850 | − | 0.999731i | \(-0.492619\pi\) | ||||
0.0231850 | + | 0.999731i | \(0.492619\pi\) | |||||||
\(510\) | 3959.13 | − | 1288.95i | 0.343752 | − | 0.111913i | ||||
\(511\) | 5568.27 | − | 608.420i | 0.482047 | − | 0.0526710i | ||||
\(512\) | 1238.10i | 0.106869i | ||||||||
\(513\) | −4462.53 | + | 6164.76i | −0.384065 | + | 0.530567i | ||||
\(514\) | 12735.1i | 1.09284i | ||||||||
\(515\) | 1721.53i | 0.147301i | ||||||||
\(516\) | −1935.64 | − | 5945.52i | −0.165139 | − | 0.507242i | ||||
\(517\) | − | 3571.45i | − | 0.303814i | ||||||
\(518\) | 13013.1 | − | 1421.89i | 1.10379 | − | 0.120606i | ||||
\(519\) | −2552.79 | − | 7841.13i | −0.215905 | − | 0.663174i | ||||
\(520\) | 2939.27 | 0.247876 | ||||||||
\(521\) | 3128.28 | 0.263056 | 0.131528 | − | 0.991312i | \(-0.458012\pi\) | ||||
0.131528 | + | 0.991312i | \(0.458012\pi\) | |||||||
\(522\) | 9099.79 | − | 6627.59i | 0.763002 | − | 0.555712i | ||||
\(523\) | − | 11087.0i | − | 0.926961i | −0.886107 | − | 0.463480i | \(-0.846600\pi\) | ||
0.886107 | − | 0.463480i | \(-0.153400\pi\) | |||||||
\(524\) | −5496.08 | −0.458201 | ||||||||
\(525\) | −2193.24 | + | 988.859i | −0.182325 | + | 0.0822045i | ||||
\(526\) | 8034.76 | 0.666031 | ||||||||
\(527\) | 10481.9i | 0.866411i | ||||||||
\(528\) | 192.608 | − | 62.7062i | 0.0158754 | − | 0.00516844i | ||||
\(529\) | 11520.2 | 0.946841 | ||||||||
\(530\) | −5033.27 | −0.412512 | ||||||||
\(531\) | 5631.60 | − | 4101.62i | 0.460246 | − | 0.335208i | ||||
\(532\) | 4744.56 | − | 518.416i | 0.386659 | − | 0.0422485i | ||||
\(533\) | − | 12233.6i | − | 0.994175i | ||||||
\(534\) | 547.722 | − | 178.318i | 0.0443863 | − | 0.0144505i | ||||
\(535\) | 8996.02i | 0.726975i | ||||||||
\(536\) | − | 17264.7i | − | 1.39127i | ||||||
\(537\) | 6277.64 | − | 2043.77i | 0.504470 | − | 0.164237i | ||||
\(538\) | 8532.19i | 0.683734i | ||||||||
\(539\) | −843.260 | − | 3812.70i | −0.0673874 | − | 0.304684i | ||||
\(540\) | −2699.52 | − | 1954.12i | −0.215127 | − | 0.155726i | ||||
\(541\) | −14971.8 | −1.18981 | −0.594907 | − | 0.803795i | \(-0.702811\pi\) | ||||
−0.594907 | + | 0.803795i | \(0.702811\pi\) | |||||||
\(542\) | −9107.14 | −0.721744 | ||||||||
\(543\) | 5994.07 | − | 1951.45i | 0.473720 | − | 0.154226i | ||||
\(544\) | − | 15798.7i | − | 1.24515i | ||||||
\(545\) | −3799.55 | −0.298633 | ||||||||
\(546\) | −4044.63 | + | 1823.59i | −0.317022 | + | 0.142935i | ||||
\(547\) | 18296.5 | 1.43017 | 0.715085 | − | 0.699037i | \(-0.246388\pi\) | ||||
0.715085 | + | 0.699037i | \(0.246388\pi\) | |||||||
\(548\) | − | 607.254i | − | 0.0473369i | ||||||
\(549\) | 7276.49 | + | 9990.74i | 0.565670 | + | 0.776674i | ||||
\(550\) | 513.027 | 0.0397737 | ||||||||
\(551\) | −12547.3 | −0.970112 | ||||||||
\(552\) | 940.258 | + | 2888.09i | 0.0725000 | + | 0.222691i | ||||
\(553\) | −983.405 | − | 9000.15i | −0.0756214 | − | 0.692089i | ||||
\(554\) | 13081.6i | 1.00322i | ||||||||
\(555\) | 3153.79 | + | 9687.18i | 0.241209 | + | 0.740897i | ||||
\(556\) | − | 6159.99i | − | 0.469859i | ||||||
\(557\) | − | 20277.9i | − | 1.54255i | −0.636500 | − | 0.771277i | \(-0.719618\pi\) | ||
0.636500 | − | 0.771277i | \(-0.280382\pi\) | |||||||
\(558\) | −4638.22 | + | 3378.12i | −0.351884 | + | 0.256285i | ||||
\(559\) | − | 6478.33i | − | 0.490168i | ||||||
\(560\) | −34.4415 | − | 315.209i | −0.00259896 | − | 0.0237858i | ||||
\(561\) | −5000.90 | + | 1628.11i | −0.376361 | + | 0.122529i | ||||
\(562\) | −1080.31 | −0.0810853 | ||||||||
\(563\) | 11663.5 | 0.873107 | 0.436554 | − | 0.899678i | \(-0.356199\pi\) | ||||
0.436554 | + | 0.899678i | \(0.356199\pi\) | |||||||
\(564\) | −2397.40 | − | 7363.83i | −0.178987 | − | 0.549775i | ||||
\(565\) | 5152.92i | 0.383690i | ||||||||
\(566\) | −7801.65 | −0.579377 | ||||||||
\(567\) | 13224.0 | + | 2721.93i | 0.979467 | + | 0.201605i | ||||
\(568\) | −6836.08 | −0.504992 | ||||||||
\(569\) | − | 4152.37i | − | 0.305934i | −0.988231 | − | 0.152967i | \(-0.951117\pi\) | ||
0.988231 | − | 0.152967i | \(-0.0488828\pi\) | |||||||
\(570\) | −786.440 | − | 2415.63i | −0.0577900 | − | 0.177508i | ||||
\(571\) | −4908.94 | −0.359777 | −0.179889 | − | 0.983687i | \(-0.557574\pi\) | ||||
−0.179889 | + | 0.983687i | \(0.557574\pi\) | |||||||
\(572\) | −1383.29 | −0.101116 | ||||||||
\(573\) | −13114.8 | + | 4269.70i | −0.956158 | + | 0.311290i | ||||
\(574\) | −15873.5 | + | 1734.42i | −1.15426 | + | 0.126121i | ||||
\(575\) | 635.797i | 0.0461123i | ||||||||
\(576\) | 7588.75 | − | 5527.07i | 0.548955 | − | 0.399817i | ||||
\(577\) | − | 19077.9i | − | 1.37647i | −0.725488 | − | 0.688235i | \(-0.758386\pi\) | ||
0.725488 | − | 0.688235i | \(-0.241614\pi\) | |||||||
\(578\) | − | 5392.12i | − | 0.388032i | ||||||
\(579\) | −1353.35 | − | 4156.94i | −0.0971385 | − | 0.298370i | ||||
\(580\) | − | 5494.40i | − | 0.393349i | ||||||
\(581\) | 1847.43 | + | 16907.8i | 0.131918 | + | 1.20732i | ||||
\(582\) | −509.440 | − | 1564.80i | −0.0362835 | − | 0.111448i | ||||
\(583\) | 6357.68 | 0.451643 | ||||||||
\(584\) | −6951.48 | −0.492559 | ||||||||
\(585\) | −2032.78 | − | 2791.04i | −0.143667 | − | 0.197257i | ||||
\(586\) | 4902.09i | 0.345569i | ||||||||
\(587\) | 13746.4 | 0.966570 | 0.483285 | − | 0.875463i | \(-0.339444\pi\) | ||||
0.483285 | + | 0.875463i | \(0.339444\pi\) | |||||||
\(588\) | −4298.03 | − | 7295.22i | −0.301442 | − | 0.511649i | ||||
\(589\) | 6395.42 | 0.447400 | ||||||||
\(590\) | 2325.62i | 0.162278i | ||||||||
\(591\) | 5936.31 | − | 1932.65i | 0.413176 | − | 0.134515i | ||||
\(592\) | −1342.71 | −0.0932177 | ||||||||
\(593\) | 22547.2 | 1.56139 | 0.780693 | − | 0.624914i | \(-0.214866\pi\) | ||||
0.780693 | + | 0.624914i | \(0.214866\pi\) | |||||||
\(594\) | −2332.13 | − | 1688.18i | −0.161092 | − | 0.116611i | ||||
\(595\) | 894.244 | + | 8184.14i | 0.0616142 | + | 0.563894i | ||||
\(596\) | 12225.6i | 0.840235i | ||||||||
\(597\) | −22354.1 | + | 7277.68i | −1.53248 | + | 0.498921i | ||||
\(598\) | 1172.50i | 0.0801788i | ||||||||
\(599\) | 879.555i | 0.0599961i | 0.999550 | + | 0.0299980i | \(0.00955010\pi\) | ||||
−0.999550 | + | 0.0299980i | \(0.990450\pi\) | |||||||
\(600\) | 2839.05 | − | 924.291i | 0.193173 | − | 0.0628900i | ||||
\(601\) | 28491.1i | 1.93374i | 0.255270 | + | 0.966870i | \(0.417836\pi\) | ||||
−0.255270 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(602\) | −8405.84 | + | 918.468i | −0.569097 | + | 0.0621827i | ||||
\(603\) | −16394.0 | + | 11940.2i | −1.10716 | + | 0.806370i | ||||
\(604\) | 6651.38 | 0.448081 | ||||||||
\(605\) | 6006.98 | 0.403667 | ||||||||
\(606\) | −1942.66 | + | 632.461i | −0.130223 | + | 0.0423960i | ||||
\(607\) | − | 1139.02i | − | 0.0761636i | −0.999275 | − | 0.0380818i | \(-0.987875\pi\) | ||
0.999275 | − | 0.0380818i | \(-0.0121247\pi\) | |||||||
\(608\) | −9639.41 | −0.642977 | ||||||||
\(609\) | 9149.16 | + | 20292.3i | 0.608773 | + | 1.35023i | ||||
\(610\) | −4125.77 | −0.273848 | ||||||||
\(611\) | − | 8023.75i | − | 0.531270i | ||||||
\(612\) | −9218.28 | + | 6713.89i | −0.608868 | + | 0.443452i | ||||
\(613\) | 25123.6 | 1.65535 | 0.827676 | − | 0.561206i | \(-0.189663\pi\) | ||||
0.827676 | + | 0.561206i | \(0.189663\pi\) | |||||||
\(614\) | 13990.4 | 0.919557 | ||||||||
\(615\) | −3847.01 | − | 11816.5i | −0.252238 | − | 0.774773i | ||||
\(616\) | 526.367 | + | 4817.33i | 0.0344285 | + | 0.315090i | ||||
\(617\) | − | 22839.2i | − | 1.49023i | −0.666937 | − | 0.745114i | \(-0.732395\pi\) | ||
0.666937 | − | 0.745114i | \(-0.267605\pi\) | |||||||
\(618\) | 998.338 | + | 3066.49i | 0.0649823 | + | 0.199599i | ||||
\(619\) | 16035.4i | 1.04122i | 0.853795 | + | 0.520610i | \(0.174295\pi\) | ||||
−0.853795 | + | 0.520610i | \(0.825705\pi\) | |||||||
\(620\) | 2800.53i | 0.181406i | ||||||||
\(621\) | 2092.17 | − | 2890.22i | 0.135194 | − | 0.186764i | ||||
\(622\) | 8808.99i | 0.567859i | ||||||||
\(623\) | 123.713 | + | 1132.23i | 0.00795580 | + | 0.0728117i | ||||
\(624\) | 432.721 | − | 140.878i | 0.0277607 | − | 0.00903788i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 11739.6 | 0.749532 | ||||||||
\(627\) | 993.376 | + | 3051.25i | 0.0632721 | + | 0.194346i | ||||
\(628\) | 14057.5i | 0.893242i | ||||||||
\(629\) | 34862.2 | 2.20993 | ||||||||
\(630\) | −3333.27 | + | 3033.30i | −0.210794 | + | 0.191825i | ||||
\(631\) | 10777.3 | 0.679932 | 0.339966 | − | 0.940438i | \(-0.389584\pi\) | ||||
0.339966 | + | 0.940438i | \(0.389584\pi\) | |||||||
\(632\) | 11235.9i | 0.707182i | ||||||||
\(633\) | 4743.03 | + | 14568.7i | 0.297817 | + | 0.914775i | ||||
\(634\) | 7746.91 | 0.485282 | ||||||||
\(635\) | 3947.93 | 0.246722 | ||||||||
\(636\) | 13108.7 | − | 4267.70i | 0.817283 | − | 0.266078i | ||||
\(637\) | −1894.50 | − | 8565.76i | −0.117838 | − | 0.532791i | ||||
\(638\) | − | 4746.65i | − | 0.294548i | ||||||
\(639\) | 4727.79 | + | 6491.33i | 0.292689 | + | 0.401867i | ||||
\(640\) | − | 3974.16i | − | 0.245457i | ||||||
\(641\) | − | 16244.6i | − | 1.00097i | −0.865745 | − | 0.500485i | \(-0.833155\pi\) | ||
0.865745 | − | 0.500485i | \(-0.166845\pi\) | |||||||
\(642\) | 5216.91 | + | 16024.2i | 0.320709 | + | 0.985087i | ||||
\(643\) | 15497.6i | 0.950490i | 0.879854 | + | 0.475245i | \(0.157641\pi\) | ||||
−0.879854 | + | 0.475245i | \(0.842359\pi\) | |||||||
\(644\) | −2224.39 | + | 243.049i | −0.136108 | + | 0.0148719i | ||||
\(645\) | −2037.19 | − | 6257.44i | −0.124363 | − | 0.381994i | ||||
\(646\) | −8693.35 | −0.529466 | ||||||||
\(647\) | −19665.2 | −1.19493 | −0.597464 | − | 0.801896i | \(-0.703825\pi\) | ||||
−0.597464 | + | 0.801896i | \(0.703825\pi\) | |||||||
\(648\) | −15947.3 | − | 5140.57i | −0.966776 | − | 0.311637i | ||||
\(649\) | − | 2937.56i | − | 0.177672i | ||||||
\(650\) | 1152.59 | 0.0695510 | ||||||||
\(651\) | −4663.38 | − | 10343.1i | −0.280756 | − | 0.622702i | ||||
\(652\) | −18145.4 | −1.08992 | ||||||||
\(653\) | 22325.5i | 1.33792i | 0.743298 | + | 0.668961i | \(0.233261\pi\) | ||||
−0.743298 | + | 0.668961i | \(0.766739\pi\) | |||||||
\(654\) | −6767.99 | + | 2203.41i | −0.404662 | + | 0.131743i | ||||
\(655\) | −5784.42 | −0.345063 | ||||||||
\(656\) | 1637.84 | 0.0974798 | ||||||||
\(657\) | 4807.60 | + | 6600.91i | 0.285483 | + | 0.391973i | ||||
\(658\) | −10411.1 | + | 1137.57i | −0.616818 | + | 0.0673969i | ||||
\(659\) | − | 14557.3i | − | 0.860505i | −0.902709 | − | 0.430253i | \(-0.858424\pi\) | ||
0.902709 | − | 0.430253i | \(-0.141576\pi\) | |||||||
\(660\) | −1336.13 | + | 434.995i | −0.0788011 | + | 0.0256548i | ||||
\(661\) | 3927.35i | 0.231098i | 0.993302 | + | 0.115549i | \(0.0368628\pi\) | ||||
−0.993302 | + | 0.115549i | \(0.963137\pi\) | |||||||
\(662\) | − | 5493.60i | − | 0.322530i | ||||||
\(663\) | −11235.2 | + | 3657.78i | −0.658129 | + | 0.214263i | ||||
\(664\) | − | 21107.8i | − | 1.23365i | ||||||
\(665\) | 4993.47 | − | 545.614i | 0.291186 | − | 0.0318165i | ||||
\(666\) | 11235.4 | + | 15426.5i | 0.653701 | + | 0.897542i | ||||
\(667\) | 5882.54 | 0.341489 | ||||||||
\(668\) | 8557.78 | 0.495675 | ||||||||
\(669\) | 2740.54 | − | 892.220i | 0.158379 | − | 0.0515623i | ||||
\(670\) | − | 6770.07i | − | 0.390374i | ||||||
\(671\) | 5211.38 | 0.299826 | ||||||||
\(672\) | 7028.82 | + | 15589.5i | 0.403486 | + | 0.894910i | ||||
\(673\) | 2999.78 | 0.171817 | 0.0859086 | − | 0.996303i | \(-0.472621\pi\) | ||||
0.0859086 | + | 0.996303i | \(0.472621\pi\) | |||||||
\(674\) | − | 6438.04i | − | 0.367929i | ||||||
\(675\) | −2841.15 | − | 2056.64i | −0.162009 | − | 0.117274i | ||||
\(676\) | 7329.66 | 0.417027 | ||||||||
\(677\) | 25090.8 | 1.42440 | 0.712200 | − | 0.701977i | \(-0.247699\pi\) | ||||
0.712200 | + | 0.701977i | \(0.247699\pi\) | |||||||
\(678\) | 2988.24 | + | 9178.67i | 0.169267 | + | 0.519919i | ||||
\(679\) | 3234.67 | − | 353.438i | 0.182821 | − | 0.0199760i | ||||
\(680\) | − | 10217.2i | − | 0.576192i | ||||||
\(681\) | 8712.45 | + | 26761.1i | 0.490252 | + | 1.50586i | ||||
\(682\) | 2419.39i | 0.135841i | ||||||||
\(683\) | − | 19494.4i | − | 1.09214i | −0.837738 | − | 0.546072i | \(-0.816123\pi\) | ||
0.837738 | − | 0.546072i | \(-0.183877\pi\) | |||||||
\(684\) | 4096.41 | + | 5624.44i | 0.228991 | + | 0.314409i | ||||
\(685\) | − | 639.113i | − | 0.0356485i | ||||||
\(686\) | −10845.8 | + | 3672.59i | −0.603634 | + | 0.204403i | ||||
\(687\) | −3366.91 | + | 1096.14i | −0.186980 | + | 0.0608740i | ||||
\(688\) | 867.321 | 0.0480615 | ||||||||
\(689\) | 14283.4 | 0.789774 | ||||||||
\(690\) | 368.707 | + | 1132.52i | 0.0203426 | + | 0.0624844i | ||||
\(691\) | − | 359.818i | − | 0.0198091i | −0.999951 | − | 0.00990456i | \(-0.996847\pi\) | ||
0.999951 | − | 0.00990456i | \(-0.00315277\pi\) | |||||||
\(692\) | −7539.38 | −0.414168 | ||||||||
\(693\) | 4210.35 | − | 3831.45i | 0.230791 | − | 0.210021i | ||||
\(694\) | 20078.6 | 1.09823 | ||||||||
\(695\) | − | 6483.16i | − | 0.353842i | ||||||
\(696\) | −8551.76 | − | 26267.6i | −0.465738 | − | 1.43056i | ||||
\(697\) | −42525.0 | −2.31098 | ||||||||
\(698\) | −19813.2 | −1.07441 | ||||||||
\(699\) | 21470.6 | − | 6990.04i | 1.16179 | − | 0.378237i | ||||
\(700\) | 238.922 | + | 2186.62i | 0.0129006 | + | 0.118066i | ||||
\(701\) | − | 29342.5i | − | 1.58096i | −0.612489 | − | 0.790479i | \(-0.709832\pi\) | ||
0.612489 | − | 0.790479i | \(-0.290168\pi\) | |||||||
\(702\) | −5239.46 | − | 3792.73i | −0.281696 | − | 0.203913i | ||||
\(703\) | − | 21270.8i | − | 1.14117i | ||||||
\(704\) | − | 3958.46i | − | 0.211918i | ||||||
\(705\) | −2523.17 | − | 7750.16i | −0.134792 | − | 0.414026i | ||||
\(706\) | 18180.3i | 0.969158i | ||||||||
\(707\) | −438.787 | − | 4015.79i | −0.0233413 | − | 0.213620i | ||||
\(708\) | −1971.89 | − | 6056.85i | −0.104673 | − | 0.321512i | ||||
\(709\) | 6480.14 | 0.343254 | 0.171627 | − | 0.985162i | \(-0.445098\pi\) | ||||
0.171627 | + | 0.985162i | \(0.445098\pi\) | |||||||
\(710\) | −2680.66 | −0.141695 | ||||||||
\(711\) | 10669.2 | − | 7770.65i | 0.562767 | − | 0.409877i | ||||
\(712\) | − | 1413.48i | − | 0.0743996i | ||||||
\(713\) | −2998.37 | −0.157489 | ||||||||
\(714\) | 6338.97 | + | 14059.5i | 0.332255 | + | 0.736923i | ||||
\(715\) | −1455.87 | −0.0761487 | ||||||||
\(716\) | − | 6036.06i | − | 0.315053i | ||||||
\(717\) | −6763.85 | + | 2202.06i | −0.352302 | + | 0.114697i | ||||
\(718\) | 1155.22 | 0.0600452 | ||||||||
\(719\) | −31658.4 | −1.64208 | −0.821042 | − | 0.570868i | \(-0.806607\pi\) | ||||
−0.821042 | + | 0.570868i | \(0.806607\pi\) | |||||||
\(720\) | 373.665 | − | 272.149i | 0.0193412 | − | 0.0140867i | ||||
\(721\) | −6338.92 | + | 692.624i | −0.327425 | + | 0.0357762i | ||||
\(722\) | − | 7059.64i | − | 0.363895i | ||||||
\(723\) | 22363.3 | − | 7280.68i | 1.15035 | − | 0.374511i | ||||
\(724\) | − | 5763.40i | − | 0.295849i | ||||||
\(725\) | − | 5782.65i | − | 0.296224i | ||||||
\(726\) | 10700.0 | − | 3483.52i | 0.546988 | − | 0.178080i | ||||
\(727\) | − | 21956.9i | − | 1.12013i | −0.828447 | − | 0.560067i | \(-0.810775\pi\) | ||
0.828447 | − | 0.560067i | \(-0.189225\pi\) | |||||||
\(728\) | 1182.56 | + | 10822.8i | 0.0602039 | + | 0.550988i | ||||
\(729\) | 6147.75 | + | 18698.3i | 0.312338 | + | 0.949971i | ||||
\(730\) | −2725.91 | −0.138206 | ||||||||
\(731\) | −22519.2 | −1.13940 | ||||||||
\(732\) | 10745.2 | − | 3498.23i | 0.542558 | − | 0.176637i | ||||
\(733\) | 17572.2i | 0.885464i | 0.896654 | + | 0.442732i | \(0.145991\pi\) | ||||
−0.896654 | + | 0.442732i | \(0.854009\pi\) | |||||||
\(734\) | −8003.75 | −0.402485 | ||||||||
\(735\) | −4523.52 | − | 7677.95i | −0.227010 | − | 0.385313i | ||||
\(736\) | 4519.25 | 0.226334 | ||||||||
\(737\) | 8551.49i | 0.427406i | ||||||||
\(738\) | −13705.0 | − | 18817.2i | −0.683589 | − | 0.938580i | ||||
\(739\) | 26316.8 | 1.30999 | 0.654993 | − | 0.755635i | \(-0.272671\pi\) | ||||
0.654993 | + | 0.755635i | \(0.272671\pi\) | |||||||
\(740\) | 9314.40 | 0.462708 | ||||||||
\(741\) | 2231.76 | + | 6855.05i | 0.110642 | + | 0.339847i | ||||
\(742\) | −2025.04 | − | 18533.2i | −0.100191 | − | 0.916947i | ||||
\(743\) | − | 9051.35i | − | 0.446920i | −0.974713 | − | 0.223460i | \(-0.928265\pi\) | ||
0.974713 | − | 0.223460i | \(-0.0717353\pi\) | |||||||
\(744\) | 4358.89 | + | 13388.7i | 0.214791 | + | 0.659751i | ||||
\(745\) | 12867.0i | 0.632765i | ||||||||
\(746\) | 6032.40i | 0.296062i | ||||||||
\(747\) | −20043.3 | + | 14598.0i | −0.981723 | + | 0.715012i | ||||
\(748\) | 4808.46i | 0.235046i | ||||||||
\(749\) | −33124.6 | + | 3619.37i | −1.61595 | + | 0.176567i | ||||
\(750\) | 1113.29 | − | 362.445i | 0.0542020 | − | 0.0176462i | ||||
\(751\) | −8878.79 | −0.431414 | −0.215707 | − | 0.976458i | \(-0.569206\pi\) | ||||
−0.215707 | + | 0.976458i | \(0.569206\pi\) | |||||||
\(752\) | 1074.22 | 0.0520916 | ||||||||
\(753\) | 10099.2 | + | 31020.6i | 0.488757 | + | 1.50127i | ||||
\(754\) | − | 10664.0i | − | 0.515066i | ||||||
\(755\) | 7000.33 | 0.337441 | ||||||||
\(756\) | 6109.24 | − | 10726.2i | 0.293903 | − | 0.516016i | ||||
\(757\) | −24510.4 | −1.17681 | −0.588405 | − | 0.808567i | \(-0.700244\pi\) | ||||
−0.588405 | + | 0.808567i | \(0.700244\pi\) | |||||||
\(758\) | 10331.4i | 0.495057i | ||||||||
\(759\) | −465.725 | − | 1430.52i | −0.0222724 | − | 0.0684117i | ||||
\(760\) | −6233.90 | −0.297536 | ||||||||
\(761\) | 7443.90 | 0.354588 | 0.177294 | − | 0.984158i | \(-0.443266\pi\) | ||||
0.177294 | + | 0.984158i | \(0.443266\pi\) | |||||||
\(762\) | 7032.28 | − | 2289.45i | 0.334321 | − | 0.108843i | ||||
\(763\) | −1528.68 | − | 13990.5i | −0.0725318 | − | 0.663813i | ||||
\(764\) | 12610.1i | 0.597144i | ||||||||
\(765\) | −9701.90 | + | 7066.12i | −0.458527 | + | 0.333956i | ||||
\(766\) | 5368.06i | 0.253206i | ||||||||
\(767\) | − | 6599.64i | − | 0.310690i | ||||||
\(768\) | −6779.21 | − | 20823.0i | −0.318520 | − | 0.978366i | ||||
\(769\) | − | 32340.6i | − | 1.51656i | −0.651930 | − | 0.758279i | \(-0.726040\pi\) | ||
0.651930 | − | 0.758279i | \(-0.273960\pi\) | |||||||
\(770\) | 206.406 | + | 1889.03i | 0.00966021 | + | 0.0884105i | ||||
\(771\) | −11364.6 | − | 34907.4i | −0.530850 | − | 1.63056i | ||||
\(772\) | −3996.97 | −0.186339 | ||||||||
\(773\) | 24198.8 | 1.12596 | 0.562982 | − | 0.826469i | \(-0.309654\pi\) | ||||
0.562982 | + | 0.826469i | \(0.309654\pi\) | |||||||
\(774\) | −7257.53 | − | 9964.71i | −0.337037 | − | 0.462757i | ||||
\(775\) | 2947.45i | 0.136614i | ||||||||
\(776\) | −4038.20 | −0.186808 | ||||||||
\(777\) | −34400.7 | + | 15510.1i | −1.58831 | + | 0.716118i | ||||
\(778\) | 15616.3 | 0.719627 | ||||||||
\(779\) | 25946.2i | 1.19335i | ||||||||
\(780\) | −3001.80 | + | 977.276i | −0.137797 | + | 0.0448617i | ||||
\(781\) | 3386.02 | 0.155136 | ||||||||
\(782\) | 4075.70 | 0.186377 | ||||||||
\(783\) | −19028.5 | + | 26287.0i | −0.868485 | + | 1.19977i | ||||
\(784\) | 1146.79 | − | 253.637i | 0.0522407 | − | 0.0115541i | ||||
\(785\) | 14795.0i | 0.672684i | ||||||||
\(786\) | −10303.5 | + | 3354.46i | −0.467577 | + | 0.152226i | ||||
\(787\) | − | 30214.8i | − | 1.36854i | −0.729228 | − | 0.684271i | \(-0.760121\pi\) | ||
0.729228 | − | 0.684271i | \(-0.239879\pi\) | |||||||
\(788\) | − | 5707.87i | − | 0.258038i | ||||||
\(789\) | −22023.6 | + | 7170.08i | −0.993740 | + | 0.323525i | ||||
\(790\) | 4405.96i | 0.198427i | ||||||||
\(791\) | −18973.7 | + | 2073.17i | −0.852881 | + | 0.0931904i | ||||
\(792\) | −5710.70 | + | 4159.24i | −0.256213 | + | 0.186606i | ||||
\(793\) | 11708.1 | 0.524296 | ||||||||
\(794\) | 8220.00 | 0.367401 | ||||||||
\(795\) | 13796.4 | − | 4491.60i | 0.615481 | − | 0.200378i | ||||
\(796\) | 21493.9i | 0.957073i | ||||||||
\(797\) | −13957.5 | −0.620327 | −0.310163 | − | 0.950683i | \(-0.600384\pi\) | ||||
−0.310163 | + | 0.950683i | \(0.600384\pi\) | |||||||
\(798\) | 8578.25 | − | 3867.66i | 0.380535 | − | 0.171571i | ||||
\(799\) | −27891.3 | −1.23495 | ||||||||
\(800\) | − | 4442.51i | − | 0.196333i | ||||||
\(801\) | −1342.20 | + | 977.555i | −0.0592063 | + | 0.0431214i | ||||
\(802\) | −7269.93 | −0.320087 | ||||||||
\(803\) | 3443.18 | 0.151317 | ||||||||
\(804\) | 5740.34 | + | 17632.0i | 0.251799 | + | 0.773423i | ||||
\(805\) | −2341.09 | + | 255.800i | −0.102500 | + | 0.0111997i | ||||
\(806\) | 5435.50i | 0.237540i | ||||||||
\(807\) | −7613.98 | − | 23387.1i | −0.332125 | − | 1.02015i | ||||
\(808\) | 5013.35i | 0.218278i | ||||||||
\(809\) | 21035.9i | 0.914195i | 0.889416 | + | 0.457098i | \(0.151111\pi\) | ||||
−0.889416 | + | 0.457098i | \(0.848889\pi\) | |||||||
\(810\) | −6253.49 | − | 2015.79i | −0.271266 | − | 0.0874415i | ||||
\(811\) | 12726.2i | 0.551022i | 0.961298 | + | 0.275511i | \(0.0888471\pi\) | ||||
−0.961298 | + | 0.275511i | \(0.911153\pi\) | |||||||
\(812\) | 20231.1 | − | 2210.56i | 0.874351 | − | 0.0955363i | ||||
\(813\) | 24963.0 | − | 8127.05i | 1.07687 | − | 0.350588i | ||||
\(814\) | 8046.77 | 0.346486 | ||||||||
\(815\) | −19097.4 | −0.820801 | ||||||||
\(816\) | −489.705 | − | 1504.18i | −0.0210087 | − | 0.0645302i | ||||
\(817\) | 13739.9i | 0.588369i | ||||||||
\(818\) | 3297.11 | 0.140930 | ||||||||
\(819\) | 9459.14 | − | 8607.89i | 0.403576 | − | 0.367258i | ||||
\(820\) | −11361.7 | −0.483864 | ||||||||
\(821\) | − | 26669.8i | − | 1.13372i | −0.823814 | − | 0.566860i | \(-0.808158\pi\) | ||
0.823814 | − | 0.566860i | \(-0.191842\pi\) | |||||||
\(822\) | −370.630 | − | 1138.42i | −0.0157265 | − | 0.0483055i | ||||
\(823\) | 6265.72 | 0.265382 | 0.132691 | − | 0.991157i | \(-0.457638\pi\) | ||||
0.132691 | + | 0.991157i | \(0.457638\pi\) | |||||||
\(824\) | 7913.56 | 0.334566 | ||||||||
\(825\) | −1406.23 | + | 457.816i | −0.0593436 | + | 0.0193201i | ||||
\(826\) | −8563.25 | + | 935.667i | −0.360719 | + | 0.0394141i | ||||
\(827\) | 33183.6i | 1.39529i | 0.716442 | + | 0.697646i | \(0.245769\pi\) | ||||
−0.716442 | + | 0.697646i | \(0.754231\pi\) | |||||||
\(828\) | −1920.52 | − | 2636.91i | −0.0806071 | − | 0.110675i | ||||
\(829\) | 38711.3i | 1.62183i | 0.585162 | + | 0.810916i | \(0.301031\pi\) | ||||
−0.585162 | + | 0.810916i | \(0.698969\pi\) | |||||||
\(830\) | − | 8277.08i | − | 0.346147i | ||||||
\(831\) | −11673.8 | − | 35857.2i | −0.487316 | − | 1.49684i | ||||
\(832\) | − | 8893.22i | − | 0.370573i | ||||||
\(833\) | −29775.4 | + | 6585.46i | −1.23848 | + | 0.273917i | ||||
\(834\) | −3759.67 | − | 11548.2i | −0.156099 | − | 0.479474i | ||||
\(835\) | 9006.75 | 0.373283 | ||||||||
\(836\) | 2933.83 | 0.121374 | ||||||||
\(837\) | 9698.95 | − | 13398.6i | 0.400532 | − | 0.553314i | ||||
\(838\) | − | 7436.42i | − | 0.306548i | ||||||
\(839\) | −21242.9 | −0.874119 | −0.437060 | − | 0.899432i | \(-0.643980\pi\) | ||||
−0.437060 | + | 0.899432i | \(0.643980\pi\) | |||||||
\(840\) | 4545.60 | + | 10081.9i | 0.186712 | + | 0.414117i | ||||
\(841\) | −29113.4 | −1.19371 | ||||||||
\(842\) | − | 8819.74i | − | 0.360984i | ||||||
\(843\) | 2961.16 | − | 964.045i | 0.120982 | − | 0.0393873i | ||||
\(844\) | 14008.0 | 0.571299 | ||||||||
\(845\) | 7714.20 | 0.314055 | ||||||||
\(846\) | −8988.84 | − | 12341.8i | −0.365299 | − | 0.501561i | ||||
\(847\) | 2416.79 | + | 22118.5i | 0.0980423 | + | 0.897286i | ||||
\(848\) | 1912.27i | 0.0774381i | ||||||||
\(849\) | 21384.6 | − | 6962.05i | 0.864450 | − | 0.281433i | ||||
\(850\) | − | 4006.49i | − | 0.161672i | ||||||
\(851\) | 9972.40i | 0.401703i | ||||||||
\(852\) | 6981.51 | − | 2272.93i | 0.280731 | − | 0.0913957i | ||||
\(853\) | − | 16997.9i | − | 0.682294i | −0.940010 | − | 0.341147i | \(-0.889185\pi\) | ||
0.940010 | − | 0.341147i | \(-0.110815\pi\) | |||||||
\(854\) | −1659.92 | − | 15191.6i | −0.0665121 | − | 0.608721i | ||||
\(855\) | 4311.32 | + | 5919.52i | 0.172449 | + | 0.236776i | ||||
\(856\) | 41353.0 | 1.65119 | ||||||||
\(857\) | −2698.89 | −0.107576 | −0.0537879 | − | 0.998552i | \(-0.517129\pi\) | ||||
−0.0537879 | + | 0.998552i | \(0.517129\pi\) | |||||||
\(858\) | −2593.27 | + | 844.275i | −0.103185 | + | 0.0335933i | ||||
\(859\) | 2431.69i | 0.0965870i | 0.998833 | + | 0.0482935i | \(0.0153783\pi\) | ||||
−0.998833 | + | 0.0482935i | \(0.984622\pi\) | |||||||
\(860\) | −6016.63 | −0.238565 | ||||||||
\(861\) | 41962.0 | − | 18919.3i | 1.66093 | − | 0.748860i | ||||
\(862\) | −7200.57 | −0.284516 | ||||||||
\(863\) | 725.483i | 0.0286161i | 0.999898 | + | 0.0143081i | \(0.00455455\pi\) | ||||
−0.999898 | + | 0.0143081i | \(0.995445\pi\) | |||||||
\(864\) | −14618.6 | + | 20194.9i | −0.575620 | + | 0.795190i | ||||
\(865\) | −7934.92 | −0.311902 | ||||||||
\(866\) | 25047.7 | 0.982858 | ||||||||
\(867\) | 4811.83 | + | 14780.0i | 0.188487 | + | 0.578957i | ||||
\(868\) | −10311.9 | + | 1126.74i | −0.403237 | + | 0.0440598i | ||||
\(869\) | − | 5565.30i | − | 0.217250i | ||||||
\(870\) | −3353.43 | − | 10300.4i | −0.130680 | − | 0.401398i | ||||
\(871\) | 19212.1i | 0.747390i | ||||||||
\(872\) | 17465.8i | 0.678289i | ||||||||
\(873\) | 2792.79 | + | 3834.55i | 0.108272 | + | 0.148660i | ||||
\(874\) | − | 2486.75i | − | 0.0962420i | ||||||
\(875\) | 251.456 | + | 2301.34i | 0.00971517 | + | 0.0889135i | ||||
\(876\) | 7099.37 | − | 2311.30i | 0.273819 | − | 0.0891455i | ||||
\(877\) | 5541.59 | 0.213371 | 0.106685 | − | 0.994293i | \(-0.465976\pi\) | ||||
0.106685 | + | 0.994293i | \(0.465976\pi\) | |||||||
\(878\) | 7615.53 | 0.292724 | ||||||||
\(879\) | −4374.53 | − | 13436.8i | −0.167861 | − | 0.515600i | ||||
\(880\) | − | 194.912i | − | 0.00746645i | ||||||
\(881\) | −13728.4 | −0.524995 | −0.262498 | − | 0.964933i | \(-0.584546\pi\) | ||||
−0.262498 | + | 0.964933i | \(0.584546\pi\) | |||||||
\(882\) | −12510.1 | − | 11053.2i | −0.477593 | − | 0.421972i | ||||
\(883\) | 10444.4 | 0.398053 | 0.199027 | − | 0.979994i | \(-0.436222\pi\) | ||||
0.199027 | + | 0.979994i | \(0.436222\pi\) | |||||||
\(884\) | 10802.9i | 0.411018i | ||||||||
\(885\) | −2075.34 | − | 6374.61i | −0.0788270 | − | 0.242125i | ||||
\(886\) | 25639.1 | 0.972192 | ||||||||
\(887\) | −10785.5 | −0.408278 | −0.204139 | − | 0.978942i | \(-0.565439\pi\) | ||||
−0.204139 | + | 0.978942i | \(0.565439\pi\) | |||||||
\(888\) | 44530.2 | − | 14497.4i | 1.68281 | − | 0.547862i | ||||
\(889\) | 1588.37 | + | 14536.8i | 0.0599238 | + | 0.548424i | ||||
\(890\) | − | 554.274i | − | 0.0208756i | ||||||
\(891\) | 7898.97 | + | 2546.21i | 0.296998 | + | 0.0957364i | ||||
\(892\) | − | 2635.08i | − | 0.0989113i | ||||||
\(893\) | 17017.6i | 0.637706i | ||||||||
\(894\) | 7461.73 | + | 22919.4i | 0.279147 | + | 0.857428i | ||||
\(895\) | − | 6352.73i | − | 0.237261i | ||||||
\(896\) | 14633.4 | − | 1598.93i | 0.545611 | − | 0.0596165i | ||||
\(897\) | −1046.31 | − | 3213.86i | −0.0389470 | − | 0.119629i | ||||
\(898\) | −29244.6 | −1.08675 | ||||||||
\(899\) | 27270.5 | 1.01171 | ||||||||
\(900\) | −2592.13 | + | 1887.91i | −0.0960048 | + | 0.0699225i | ||||
\(901\) | − | 49650.4i | − | 1.83584i | ||||||
\(902\) | −9815.47 | −0.362328 | ||||||||
\(903\) | 22221.1 | − | 10018.8i | 0.818906 | − | 0.369218i | ||||
\(904\) | 23687.0 | 0.871480 | ||||||||
\(905\) | − | 6065.76i | − | 0.222799i | ||||||
\(906\) | 12469.4 | − | 4059.58i | 0.457249 | − | 0.148864i | ||||
\(907\) | 5164.52 | 0.189069 | 0.0945343 | − | 0.995522i | \(-0.469864\pi\) | ||||
0.0945343 | + | 0.995522i | \(0.469864\pi\) | |||||||
\(908\) | 25731.3 | 0.940444 | ||||||||
\(909\) | 4760.52 | − | 3467.20i | 0.173703 | − | 0.126512i | ||||
\(910\) | 463.720 | + | 4243.98i | 0.0168925 | + | 0.154601i | ||||
\(911\) | 47274.3i | 1.71929i | 0.510896 | + | 0.859643i | \(0.329314\pi\) | ||||
−0.510896 | + | 0.859643i | \(0.670686\pi\) | |||||||
\(912\) | −917.757 | + | 298.788i | −0.0333223 | + | 0.0108485i | ||||
\(913\) | 10455.0i | 0.378983i | ||||||||
\(914\) | − | 7673.85i | − | 0.277712i | ||||||
\(915\) | 11308.9 | − | 3681.76i | 0.408591 | − | 0.133022i | ||||
\(916\) | 3237.34i | 0.116774i | ||||||||
\(917\) | −2327.25 | − | 21299.0i | −0.0838086 | − | 0.767018i | ||||
\(918\) | −13183.9 | + | 18212.8i | −0.474000 | + | 0.654808i | ||||
\(919\) | −32724.6 | −1.17463 | −0.587314 | − | 0.809359i | \(-0.699815\pi\) | ||||
−0.587314 | + | 0.809359i | \(0.699815\pi\) | |||||||
\(920\) | 2922.64 | 0.104735 | ||||||||
\(921\) | −38348.3 | + | 12484.8i | −1.37201 | + | 0.446676i | ||||
\(922\) | 8855.32i | 0.316306i | ||||||||
\(923\) | 7607.16 | 0.271281 | ||||||||
\(924\) | −2139.28 | − | 4744.80i | −0.0761656 | − | 0.168931i | ||||
\(925\) | 9803.06 | 0.348457 | ||||||||
\(926\) | 28296.0i | 1.00417i | ||||||||
\(927\) | −5472.97 | − | 7514.47i | −0.193911 | − | 0.266243i | ||||
\(928\) | −41103.1 | −1.45396 | ||||||||
\(929\) | 14232.6 | 0.502642 | 0.251321 | − | 0.967904i | \(-0.419135\pi\) | ||||
0.251321 | + | 0.967904i | \(0.419135\pi\) | |||||||
\(930\) | 1709.26 | + | 5250.17i | 0.0602677 | + | 0.185118i | ||||
\(931\) | 4018.05 | + | 18167.1i | 0.141446 | + | 0.639531i | ||||
\(932\) | − | 20644.3i | − | 0.725566i | ||||||
\(933\) | −7860.98 | − | 24145.8i | −0.275838 | − | 0.847264i | ||||
\(934\) | 2616.72i | 0.0916720i | ||||||||
\(935\) | 5060.72i | 0.177009i | ||||||||
\(936\) | −12829.9 | + | 9344.30i | −0.448032 | + | 0.326312i | ||||
\(937\) | − | 23436.1i | − | 0.817101i | −0.912736 | − | 0.408550i | \(-0.866034\pi\) | ||
0.912736 | − | 0.408550i | \(-0.133966\pi\) | |||||||
\(938\) | 24928.3 | − | 2723.80i | 0.867739 | − | 0.0948138i | ||||
\(939\) | −32178.6 | + | 10476.2i | −1.11833 | + | 0.364086i | ||||
\(940\) | −7451.92 | −0.258569 | ||||||||
\(941\) | 30270.7 | 1.04867 | 0.524333 | − | 0.851513i | \(-0.324315\pi\) | ||||
0.524333 | + | 0.851513i | \(0.324315\pi\) | |||||||
\(942\) | 8579.82 | + | 26353.7i | 0.296757 | + | 0.911519i | ||||
\(943\) | − | 12164.4i | − | 0.420070i | ||||||
\(944\) | 883.562 | 0.0304635 | ||||||||
\(945\) | 6429.75 | − | 11288.9i | 0.221333 | − | 0.388602i | ||||
\(946\) | −5197.81 | −0.178642 | ||||||||
\(947\) | 12968.3i | 0.444997i | 0.974933 | + | 0.222498i | \(0.0714212\pi\) | ||||
−0.974933 | + | 0.222498i | \(0.928579\pi\) | |||||||
\(948\) | −3735.81 | − | 11474.9i | −0.127989 | − | 0.393130i | ||||
\(949\) | 7735.58 | 0.264602 | ||||||||
\(950\) | −2444.52 | −0.0834849 | ||||||||
\(951\) | −21234.6 | + | 6913.20i | −0.724057 | + | 0.235726i | ||||
\(952\) | 37621.0 | − | 4110.67i | 1.28078 | − | 0.139945i | ||||
\(953\) | 25435.7i | 0.864577i | 0.901735 | + | 0.432288i | \(0.142294\pi\) | ||||
−0.901735 | + | 0.432288i | \(0.857706\pi\) | |||||||
\(954\) | 21970.2 | − | 16001.4i | 0.745609 | − | 0.543044i | ||||
\(955\) | 13271.7i | 0.449698i | ||||||||
\(956\) | 6503.56i | 0.220021i | ||||||||
\(957\) | 4235.82 | + | 13010.7i | 0.143077 | + | 0.439475i | ||||
\(958\) | 21922.4i | 0.739331i | ||||||||
\(959\) | 2353.30 | − | 257.134i | 0.0792409 | − | 0.00865829i | ||||
\(960\) | −2796.59 | − | 8589.99i | −0.0940204 | − | 0.288793i | ||||
\(961\) | 15891.0 | 0.533418 | ||||||||
\(962\) | 18078.2 | 0.605888 | ||||||||
\(963\) | −28599.5 | − | 39267.6i | −0.957015 | − | 1.31400i | ||||
\(964\) | − | 21502.7i | − | 0.718419i | ||||||
\(965\) | −4206.66 | −0.140329 | ||||||||
\(966\) | −4021.74 | + | 1813.27i | −0.133952 | + | 0.0603945i | ||||
\(967\) | 23388.3 | 0.777785 | 0.388893 | − | 0.921283i | \(-0.372858\pi\) | ||||
0.388893 | + | 0.921283i | \(0.372858\pi\) | |||||||
\(968\) | − | 27613.0i | − | 0.916854i | ||||||
\(969\) | 23828.8 | − | 7757.79i | 0.789980 | − | 0.257189i | ||||
\(970\) | −1583.51 | −0.0524160 | ||||||||
\(971\) | 20436.8 | 0.675436 | 0.337718 | − | 0.941247i | \(-0.390345\pi\) | ||||
0.337718 | + | 0.941247i | \(0.390345\pi\) | |||||||
\(972\) | 17995.8 | − | 52.3941i | 0.593842 | − | 0.00172895i | ||||
\(973\) | 23871.9 | − | 2608.37i | 0.786534 | − | 0.0859410i | ||||
\(974\) | 1260.52i | 0.0414677i | ||||||||
\(975\) | −3159.28 | + | 1028.55i | −0.103772 | + | 0.0337845i | ||||
\(976\) | 1567.48i | 0.0514077i | ||||||||
\(977\) | 28876.4i | 0.945587i | 0.881173 | + | 0.472793i | \(0.156754\pi\) | ||||
−0.881173 | + | 0.472793i | \(0.843246\pi\) | |||||||
\(978\) | −34017.4 | + | 11074.8i | −1.11223 | + | 0.362100i | ||||
\(979\) | 700.120i | 0.0228559i | ||||||||
\(980\) | −7955.30 | + | 1759.49i | −0.259309 | + | 0.0573517i | ||||
\(981\) | 16585.0 | − | 12079.3i | 0.539775 | − | 0.393131i | ||||
\(982\) | 28809.5 | 0.936199 | ||||||||
\(983\) | −19964.0 | −0.647766 | −0.323883 | − | 0.946097i | \(-0.604988\pi\) | ||||
−0.323883 | + | 0.946097i | \(0.604988\pi\) | |||||||
\(984\) | −54318.0 | + | 17684.0i | −1.75975 | + | 0.572911i | ||||
\(985\) | − | 6007.32i | − | 0.194324i | ||||||
\(986\) | −37069.0 | −1.19728 | ||||||||
\(987\) | 27522.0 | − | 12408.8i | 0.887574 | − | 0.400178i | ||||
\(988\) | 6591.25 | 0.212243 | ||||||||
\(989\) | − | 6441.67i | − | 0.207111i | ||||||
\(990\) | −2239.36 | + | 1630.98i | −0.0718904 | + | 0.0523594i | ||||
\(991\) | −27990.1 | −0.897210 | −0.448605 | − | 0.893730i | \(-0.648079\pi\) | ||||
−0.448605 | + | 0.893730i | \(0.648079\pi\) | |||||||
\(992\) | 20950.5 | 0.670544 | ||||||||
\(993\) | 4902.39 | + | 15058.2i | 0.156669 | + | 0.481225i | ||||
\(994\) | −1078.51 | − | 9870.54i | −0.0344147 | − | 0.314964i | ||||
\(995\) | 22621.5i | 0.720754i | ||||||||
\(996\) | 7018.13 | + | 21556.9i | 0.223271 | + | 0.685799i | ||||
\(997\) | 24576.1i | 0.780676i | 0.920672 | + | 0.390338i | \(0.127642\pi\) | ||||
−0.920672 | + | 0.390338i | \(0.872358\pi\) | |||||||
\(998\) | 37721.3i | 1.19644i | ||||||||
\(999\) | −44563.1 | − | 32258.2i | −1.41132 | − | 1.02163i |
(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 | 105.4.b.b.41.6 | yes | 16 | |
3.2 | odd | 2 | 105.4.b.a.41.11 | yes | 16 | ||
7.6 | odd | 2 | 105.4.b.a.41.6 | ✓ | 16 | ||
21.20 | even | 2 | inner | 105.4.b.b.41.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.b.a.41.6 | ✓ | 16 | 7.6 | odd | 2 | ||
105.4.b.a.41.11 | yes | 16 | 3.2 | odd | 2 | ||
105.4.b.b.41.6 | yes | 16 | 1.1 | even | 1 | trivial | |
105.4.b.b.41.11 | yes | 16 | 21.20 | even | 2 | inner |