Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 60 x^{18} - 25 x^{17} + 2336 x^{16} - 645 x^{15} + 52478 x^{14} - 2415 x^{13} + \cdots + 589824 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 6.7 | ||
Root | \(-0.961392 + 1.66518i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.4.c.a.36.7 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92278 | 0.679807 | 0.339903 | − | 0.940460i | \(-0.389606\pi\) | ||||
0.339903 | + | 0.940460i | \(0.389606\pi\) | |||||||
\(3\) | −4.18916 | + | 7.25584i | −0.806205 | + | 1.39639i | 0.109270 | + | 0.994012i | \(0.465149\pi\) |
−0.915475 | + | 0.402375i | \(0.868185\pi\) | |||||||
\(4\) | −4.30290 | −0.537862 | ||||||||
\(5\) | −0.0351129 | + | 0.0608173i | −0.00314059 | + | 0.00543966i | −0.867591 | − | 0.497278i | \(-0.834333\pi\) |
0.864451 | + | 0.502717i | \(0.167666\pi\) | |||||||
\(6\) | −8.05486 | + | 13.9514i | −0.548063 | + | 0.949274i | ||||
\(7\) | 11.7213 | + | 20.3018i | 0.632888 | + | 1.09619i | 0.986958 | + | 0.160975i | \(0.0514640\pi\) |
−0.354070 | + | 0.935219i | \(0.615203\pi\) | |||||||
\(8\) | −23.6558 | −1.04545 | ||||||||
\(9\) | −21.5982 | − | 37.4091i | −0.799932 | − | 1.38552i | ||||
\(10\) | −0.0675145 | + | 0.116939i | −0.00213500 | + | 0.00369792i | ||||
\(11\) | 55.0459 | 1.50881 | 0.754407 | − | 0.656407i | \(-0.227925\pi\) | ||||
0.754407 | + | 0.656407i | \(0.227925\pi\) | |||||||
\(12\) | 18.0255 | − | 31.2212i | 0.433627 | − | 0.751064i | ||||
\(13\) | 13.8919 | + | 24.0615i | 0.296378 | + | 0.513342i | 0.975305 | − | 0.220864i | \(-0.0708878\pi\) |
−0.678926 | + | 0.734206i | \(0.737554\pi\) | |||||||
\(14\) | 22.5374 | + | 39.0360i | 0.430242 | + | 0.745200i | ||||
\(15\) | −0.294187 | − | 0.509547i | −0.00506392 | − | 0.00877096i | ||||
\(16\) | −11.0619 | −0.172841 | ||||||||
\(17\) | −14.7103 | − | 25.4791i | −0.209870 | − | 0.363505i | 0.741804 | − | 0.670617i | \(-0.233971\pi\) |
−0.951673 | + | 0.307112i | \(0.900637\pi\) | |||||||
\(18\) | −41.5286 | − | 71.9296i | −0.543799 | − | 0.941888i | ||||
\(19\) | 22.9265 | − | 39.7099i | 0.276826 | − | 0.479478i | −0.693768 | − | 0.720199i | \(-0.744051\pi\) |
0.970594 | + | 0.240721i | \(0.0773839\pi\) | |||||||
\(20\) | 0.151087 | − | 0.261691i | 0.00168921 | − | 0.00292579i | ||||
\(21\) | −196.409 | −2.04095 | ||||||||
\(22\) | 105.841 | 1.02570 | ||||||||
\(23\) | −63.3970 | + | 109.807i | −0.574747 | + | 0.995491i | 0.421322 | + | 0.906911i | \(0.361566\pi\) |
−0.996069 | + | 0.0885798i | \(0.971767\pi\) | |||||||
\(24\) | 99.0981 | − | 171.643i | 0.842846 | − | 1.45985i | ||||
\(25\) | 62.4975 | + | 108.249i | 0.499980 | + | 0.865991i | ||||
\(26\) | 26.7111 | + | 46.2650i | 0.201480 | + | 0.348974i | ||||
\(27\) | 135.698 | 0.967225 | ||||||||
\(28\) | −50.4354 | − | 87.3566i | −0.340407 | − | 0.589602i | ||||
\(29\) | −67.6217 | − | 117.124i | −0.433001 | − | 0.749980i | 0.564129 | − | 0.825687i | \(-0.309212\pi\) |
−0.997130 | + | 0.0757067i | \(0.975879\pi\) | |||||||
\(30\) | −0.565658 | − | 0.979749i | −0.00344249 | − | 0.00596256i | ||||
\(31\) | 109.025 | − | 188.838i | 0.631663 | − | 1.09407i | −0.355549 | − | 0.934658i | \(-0.615706\pi\) |
0.987212 | − | 0.159415i | \(-0.0509607\pi\) | |||||||
\(32\) | 167.977 | 0.927951 | ||||||||
\(33\) | −230.596 | + | 399.404i | −1.21641 | + | 2.10689i | ||||
\(34\) | −28.2848 | − | 48.9907i | −0.142671 | − | 0.247113i | ||||
\(35\) | −1.64627 | −0.00795057 | ||||||||
\(36\) | 92.9347 | + | 160.968i | 0.430253 | + | 0.745220i | ||||
\(37\) | −185.007 | + | 320.441i | −0.822025 | + | 1.42379i | 0.0821464 | + | 0.996620i | \(0.473822\pi\) |
−0.904172 | + | 0.427169i | \(0.859511\pi\) | |||||||
\(38\) | 44.0827 | − | 76.3536i | 0.188189 | − | 0.325952i | ||||
\(39\) | −232.781 | −0.955766 | ||||||||
\(40\) | 0.830624 | − | 1.43868i | 0.00328333 | − | 0.00568689i | ||||
\(41\) | 357.357 | 1.36121 | 0.680606 | − | 0.732649i | \(-0.261716\pi\) | ||||
0.680606 | + | 0.732649i | \(0.261716\pi\) | |||||||
\(42\) | −377.652 | −1.38745 | ||||||||
\(43\) | −256.869 | − | 116.299i | −0.910980 | − | 0.412451i | ||||
\(44\) | −236.857 | −0.811534 | ||||||||
\(45\) | 3.03349 | 0.0100490 | ||||||||
\(46\) | −121.899 | + | 211.135i | −0.390717 | + | 0.676742i | ||||
\(47\) | 442.020 | 1.37181 | 0.685907 | − | 0.727689i | \(-0.259406\pi\) | ||||
0.685907 | + | 0.727689i | \(0.259406\pi\) | |||||||
\(48\) | 46.3399 | − | 80.2631i | 0.139346 | − | 0.241354i | ||||
\(49\) | −103.275 | + | 178.878i | −0.301094 | + | 0.521511i | ||||
\(50\) | 120.169 | + | 208.139i | 0.339890 | + | 0.588707i | ||||
\(51\) | 246.496 | 0.676791 | ||||||||
\(52\) | −59.7754 | − | 103.534i | −0.159411 | − | 0.276107i | ||||
\(53\) | 139.624 | − | 241.836i | 0.361865 | − | 0.626769i | −0.626403 | − | 0.779500i | \(-0.715473\pi\) |
0.988268 | + | 0.152731i | \(0.0488067\pi\) | |||||||
\(54\) | 260.918 | 0.657526 | ||||||||
\(55\) | −1.93282 | + | 3.34774i | −0.00473857 | + | 0.00820744i | ||||
\(56\) | −277.276 | − | 480.256i | −0.661653 | − | 1.14602i | ||||
\(57\) | 192.086 | + | 332.702i | 0.446358 | + | 0.773114i | ||||
\(58\) | −130.022 | − | 225.205i | −0.294357 | − | 0.509842i | ||||
\(59\) | 413.803 | 0.913095 | 0.456547 | − | 0.889699i | \(-0.349086\pi\) | ||||
0.456547 | + | 0.889699i | \(0.349086\pi\) | |||||||
\(60\) | 1.26586 | + | 2.19253i | 0.00272369 | + | 0.00471757i | ||||
\(61\) | −280.281 | − | 485.462i | −0.588301 | − | 1.01897i | −0.994455 | − | 0.105163i | \(-0.966464\pi\) |
0.406154 | − | 0.913805i | \(-0.366870\pi\) | |||||||
\(62\) | 209.633 | − | 363.094i | 0.429409 | − | 0.743758i | ||||
\(63\) | 506.315 | − | 876.963i | 1.01253 | − | 1.75376i | ||||
\(64\) | 411.478 | 0.803669 | ||||||||
\(65\) | −1.95114 | −0.00372321 | ||||||||
\(66\) | −443.386 | + | 767.968i | −0.826926 | + | 1.43228i | ||||
\(67\) | −89.6639 | + | 155.302i | −0.163495 | + | 0.283182i | −0.936120 | − | 0.351681i | \(-0.885610\pi\) |
0.772625 | + | 0.634863i | \(0.218944\pi\) | |||||||
\(68\) | 63.2971 | + | 109.634i | 0.112881 | + | 0.195516i | ||||
\(69\) | −531.160 | − | 919.996i | −0.926727 | − | 1.60514i | ||||
\(70\) | −3.16542 | −0.00540485 | ||||||||
\(71\) | −295.903 | − | 512.519i | −0.494608 | − | 0.856687i | 0.505372 | − | 0.862901i | \(-0.331355\pi\) |
−0.999981 | + | 0.00621447i | \(0.998022\pi\) | |||||||
\(72\) | 510.922 | + | 884.943i | 0.836288 | + | 1.44849i | ||||
\(73\) | −352.364 | − | 610.312i | −0.564946 | − | 0.978515i | −0.997055 | − | 0.0766932i | \(-0.975564\pi\) |
0.432109 | − | 0.901821i | \(-0.357770\pi\) | |||||||
\(74\) | −355.728 | + | 616.139i | −0.558819 | + | 0.967902i | ||||
\(75\) | −1047.25 | −1.61235 | ||||||||
\(76\) | −98.6505 | + | 170.868i | −0.148895 | + | 0.257893i | ||||
\(77\) | 645.206 | + | 1117.53i | 0.954910 | + | 1.65395i | ||||
\(78\) | −447.589 | −0.649736 | ||||||||
\(79\) | 298.886 | + | 517.685i | 0.425661 | + | 0.737267i | 0.996482 | − | 0.0838076i | \(-0.0267081\pi\) |
−0.570820 | + | 0.821075i | \(0.693375\pi\) | |||||||
\(80\) | 0.388413 | − | 0.672752i | 0.000542824 | − | 0.000940199i | ||||
\(81\) | 14.6898 | − | 25.4435i | 0.0201507 | − | 0.0349020i | ||||
\(82\) | 687.120 | 0.925362 | ||||||||
\(83\) | −18.9456 | + | 32.8147i | −0.0250548 | + | 0.0433962i | −0.878281 | − | 0.478145i | \(-0.841309\pi\) |
0.853226 | + | 0.521541i | \(0.174643\pi\) | |||||||
\(84\) | 845.128 | 1.09775 | ||||||||
\(85\) | 2.06609 | 0.00263646 | ||||||||
\(86\) | −493.903 | − | 223.617i | −0.619290 | − | 0.280387i | ||||
\(87\) | 1133.11 | 1.39635 | ||||||||
\(88\) | −1302.16 | −1.57739 | ||||||||
\(89\) | 188.195 | − | 325.963i | 0.224142 | − | 0.388225i | −0.731920 | − | 0.681391i | \(-0.761375\pi\) |
0.956062 | + | 0.293166i | \(0.0947088\pi\) | |||||||
\(90\) | 5.83275 | 0.00683140 | ||||||||
\(91\) | −325.661 | + | 564.061i | −0.375148 | + | 0.649776i | ||||
\(92\) | 272.791 | − | 472.487i | 0.309135 | − | 0.535437i | ||||
\(93\) | 913.451 | + | 1582.14i | 1.01850 | + | 1.76409i | ||||
\(94\) | 849.909 | 0.932569 | ||||||||
\(95\) | 1.61003 | + | 2.78866i | 0.00173880 | + | 0.00301169i | ||||
\(96\) | −703.683 | + | 1218.81i | −0.748118 | + | 1.29578i | ||||
\(97\) | −1659.85 | −1.73745 | −0.868723 | − | 0.495298i | \(-0.835059\pi\) | ||||
−0.868723 | + | 0.495298i | \(0.835059\pi\) | |||||||
\(98\) | −198.576 | + | 343.944i | −0.204686 | + | 0.354527i | ||||
\(99\) | −1188.89 | − | 2059.22i | −1.20695 | − | 2.09049i | ||||
\(100\) | −268.921 | − | 465.784i | −0.268921 | − | 0.465784i | ||||
\(101\) | 511.226 | + | 885.469i | 0.503652 | + | 0.872351i | 0.999991 | + | 0.00422218i | \(0.00134396\pi\) |
−0.496339 | + | 0.868129i | \(0.665323\pi\) | |||||||
\(102\) | 473.959 | 0.460087 | ||||||||
\(103\) | 33.3182 | + | 57.7087i | 0.0318732 | + | 0.0552059i | 0.881522 | − | 0.472143i | \(-0.156519\pi\) |
−0.849649 | + | 0.527349i | \(0.823186\pi\) | |||||||
\(104\) | −328.624 | − | 569.194i | −0.309848 | − | 0.536673i | ||||
\(105\) | 6.89648 | − | 11.9450i | 0.00640978 | − | 0.0111021i | ||||
\(106\) | 268.467 | − | 464.999i | 0.245998 | − | 0.426082i | ||||
\(107\) | 1282.02 | 1.15830 | 0.579148 | − | 0.815222i | \(-0.303385\pi\) | ||||
0.579148 | + | 0.815222i | \(0.303385\pi\) | |||||||
\(108\) | −583.894 | −0.520234 | ||||||||
\(109\) | −793.527 | + | 1374.43i | −0.697303 | + | 1.20776i | 0.272095 | + | 0.962271i | \(0.412284\pi\) |
−0.969398 | + | 0.245494i | \(0.921050\pi\) | |||||||
\(110\) | −3.71639 | + | 6.43698i | −0.00322131 | + | 0.00557947i | ||||
\(111\) | −1550.05 | − | 2684.76i | −1.32544 | − | 2.29573i | ||||
\(112\) | −129.659 | − | 224.576i | −0.109389 | − | 0.189468i | ||||
\(113\) | 999.212 | 0.831840 | 0.415920 | − | 0.909401i | \(-0.363460\pi\) | ||||
0.415920 | + | 0.909401i | \(0.363460\pi\) | |||||||
\(114\) | 369.340 | + | 639.715i | 0.303437 | + | 0.525568i | ||||
\(115\) | −4.45210 | − | 7.71126i | −0.00361009 | − | 0.00625286i | ||||
\(116\) | 290.969 | + | 503.974i | 0.232895 | + | 0.403386i | ||||
\(117\) | 600.078 | − | 1039.37i | 0.474165 | − | 0.821277i | ||||
\(118\) | 795.654 | 0.620728 | ||||||||
\(119\) | 344.847 | − | 597.293i | 0.265648 | − | 0.460115i | ||||
\(120\) | 6.95924 | + | 12.0537i | 0.00529407 | + | 0.00916960i | ||||
\(121\) | 1699.05 | 1.27652 | ||||||||
\(122\) | −538.921 | − | 933.438i | −0.399931 | − | 0.692701i | ||||
\(123\) | −1497.02 | + | 2592.92i | −1.09742 | + | 1.90078i | ||||
\(124\) | −469.126 | + | 812.550i | −0.339748 | + | 0.588461i | ||||
\(125\) | −17.5561 | −0.0125621 | ||||||||
\(126\) | 973.534 | − | 1686.21i | 0.688328 | − | 1.19222i | ||||
\(127\) | 1275.21 | 0.890994 | 0.445497 | − | 0.895284i | \(-0.353027\pi\) | ||||
0.445497 | + | 0.895284i | \(0.353027\pi\) | |||||||
\(128\) | −552.632 | −0.381611 | ||||||||
\(129\) | 1919.91 | − | 1376.61i | 1.31038 | − | 0.939561i | ||||
\(130\) | −3.75161 | −0.00253106 | ||||||||
\(131\) | −1567.29 | −1.04530 | −0.522651 | − | 0.852547i | \(-0.675057\pi\) | ||||
−0.522651 | + | 0.852547i | \(0.675057\pi\) | |||||||
\(132\) | 992.232 | − | 1718.60i | 0.654263 | − | 1.13322i | ||||
\(133\) | 1074.91 | 0.700801 | ||||||||
\(134\) | −172.404 | + | 298.613i | −0.111145 | + | 0.192509i | ||||
\(135\) | −4.76474 | + | 8.25277i | −0.00303766 | + | 0.00526137i | ||||
\(136\) | 347.985 | + | 602.728i | 0.219408 | + | 0.380026i | ||||
\(137\) | −630.037 | −0.392903 | −0.196452 | − | 0.980514i | \(-0.562942\pi\) | ||||
−0.196452 | + | 0.980514i | \(0.562942\pi\) | |||||||
\(138\) | −1021.31 | − | 1768.95i | −0.629996 | − | 1.09118i | ||||
\(139\) | −299.762 | + | 519.203i | −0.182917 | + | 0.316822i | −0.942873 | − | 0.333153i | \(-0.891887\pi\) |
0.759956 | + | 0.649975i | \(0.225221\pi\) | |||||||
\(140\) | 7.08372 | 0.00427631 | ||||||||
\(141\) | −1851.69 | + | 3207.23i | −1.10596 | + | 1.91558i | ||||
\(142\) | −568.957 | − | 985.463i | −0.336238 | − | 0.582382i | ||||
\(143\) | 764.691 | + | 1324.48i | 0.447180 | + | 0.774538i | ||||
\(144\) | 238.916 | + | 413.814i | 0.138261 | + | 0.239476i | ||||
\(145\) | 9.49757 | 0.00543952 | ||||||||
\(146\) | −677.519 | − | 1173.50i | −0.384054 | − | 0.665201i | ||||
\(147\) | −865.275 | − | 1498.70i | −0.485487 | − | 0.840889i | ||||
\(148\) | 796.066 | − | 1378.83i | 0.442137 | − | 0.765803i | ||||
\(149\) | −1237.33 | + | 2143.12i | −0.680309 | + | 1.17833i | 0.294578 | + | 0.955628i | \(0.404821\pi\) |
−0.974887 | + | 0.222702i | \(0.928512\pi\) | |||||||
\(150\) | −2013.63 | −1.09608 | ||||||||
\(151\) | 2083.60 | 1.12292 | 0.561459 | − | 0.827504i | \(-0.310240\pi\) | ||||
0.561459 | + | 0.827504i | \(0.310240\pi\) | |||||||
\(152\) | −542.346 | + | 939.370i | −0.289408 | + | 0.501270i | ||||
\(153\) | −635.432 | + | 1100.60i | −0.335762 | + | 0.581558i | ||||
\(154\) | 1240.59 | + | 2148.77i | 0.649155 | + | 1.12437i | ||||
\(155\) | 7.65640 | + | 13.2613i | 0.00396759 | + | 0.00687207i | ||||
\(156\) | 1001.64 | 0.514071 | ||||||||
\(157\) | −1327.94 | − | 2300.07i | −0.675042 | − | 1.16921i | −0.976457 | − | 0.215713i | \(-0.930792\pi\) |
0.301415 | − | 0.953493i | \(-0.402541\pi\) | |||||||
\(158\) | 574.693 | + | 995.397i | 0.289368 | + | 0.501199i | ||||
\(159\) | 1169.82 | + | 2026.18i | 0.583475 | + | 1.01061i | ||||
\(160\) | −5.89816 | + | 10.2159i | −0.00291431 | + | 0.00504774i | ||||
\(161\) | −2972.37 | −1.45500 | ||||||||
\(162\) | 28.2454 | − | 48.9224i | 0.0136986 | − | 0.0237266i | ||||
\(163\) | −590.172 | − | 1022.21i | −0.283594 | − | 0.491199i | 0.688673 | − | 0.725072i | \(-0.258193\pi\) |
−0.972267 | + | 0.233873i | \(0.924860\pi\) | |||||||
\(164\) | −1537.67 | −0.732145 | ||||||||
\(165\) | −16.1938 | − | 28.0484i | −0.00764051 | − | 0.0132337i | ||||
\(166\) | −36.4283 | + | 63.0956i | −0.0170324 | + | 0.0295010i | ||||
\(167\) | 1430.44 | − | 2477.59i | 0.662819 | − | 1.14804i | −0.317053 | − | 0.948408i | \(-0.602693\pi\) |
0.979872 | − | 0.199628i | \(-0.0639734\pi\) | |||||||
\(168\) | 4646.21 | 2.13371 | ||||||||
\(169\) | 712.531 | − | 1234.14i | 0.324320 | − | 0.561739i | ||||
\(170\) | 3.97264 | 0.00179228 | ||||||||
\(171\) | −1980.68 | −0.885769 | ||||||||
\(172\) | 1105.28 | + | 500.422i | 0.489982 | + | 0.221842i | ||||
\(173\) | −315.057 | −0.138459 | −0.0692293 | − | 0.997601i | \(-0.522054\pi\) | ||||
−0.0692293 | + | 0.997601i | \(0.522054\pi\) | |||||||
\(174\) | 2178.73 | 0.949248 | ||||||||
\(175\) | −1465.10 | + | 2537.62i | −0.632863 | + | 1.09615i | ||||
\(176\) | −608.909 | −0.260786 | ||||||||
\(177\) | −1733.49 | + | 3002.49i | −0.736141 | + | 1.27503i | ||||
\(178\) | 361.858 | − | 626.757i | 0.152373 | − | 0.263918i | ||||
\(179\) | −118.762 | − | 205.703i | −0.0495906 | − | 0.0858935i | 0.840165 | − | 0.542332i | \(-0.182458\pi\) |
−0.889755 | + | 0.456438i | \(0.849125\pi\) | |||||||
\(180\) | −13.0528 | −0.00540500 | ||||||||
\(181\) | 106.932 | + | 185.212i | 0.0439127 | + | 0.0760591i | 0.887146 | − | 0.461488i | \(-0.152684\pi\) |
−0.843234 | + | 0.537547i | \(0.819351\pi\) | |||||||
\(182\) | −626.175 | + | 1084.57i | −0.255029 | + | 0.441722i | ||||
\(183\) | 4696.58 | 1.89716 | ||||||||
\(184\) | 1499.71 | − | 2597.57i | 0.600869 | − | 1.04074i | ||||
\(185\) | −12.9922 | − | 22.5032i | −0.00516329 | − | 0.00894308i | ||||
\(186\) | 1756.37 | + | 3042.12i | 0.692383 | + | 1.19924i | ||||
\(187\) | −809.743 | − | 1402.52i | −0.316654 | − | 0.548461i | ||||
\(188\) | −1901.97 | −0.737847 | ||||||||
\(189\) | 1590.55 | + | 2754.91i | 0.612145 | + | 1.06027i | ||||
\(190\) | 3.09574 | + | 5.36198i | 0.00118205 | + | 0.00204736i | ||||
\(191\) | −816.795 | + | 1414.73i | −0.309430 | + | 0.535949i | −0.978238 | − | 0.207487i | \(-0.933472\pi\) |
0.668808 | + | 0.743436i | \(0.266805\pi\) | |||||||
\(192\) | −1723.75 | + | 2985.62i | −0.647922 | + | 1.12223i | ||||
\(193\) | −4902.71 | −1.82852 | −0.914261 | − | 0.405126i | \(-0.867228\pi\) | ||||
−0.914261 | + | 0.405126i | \(0.867228\pi\) | |||||||
\(194\) | −3191.53 | −1.18113 | ||||||||
\(195\) | 8.17362 | − | 14.1571i | 0.00300167 | − | 0.00519904i | ||||
\(196\) | 444.384 | − | 769.695i | 0.161947 | − | 0.280501i | ||||
\(197\) | −2215.52 | − | 3837.39i | −0.801265 | − | 1.38783i | −0.918784 | − | 0.394761i | \(-0.870827\pi\) |
0.117518 | − | 0.993071i | \(-0.462506\pi\) | |||||||
\(198\) | −2285.98 | − | 3959.43i | −0.820492 | − | 1.42113i | ||||
\(199\) | 961.504 | 0.342508 | 0.171254 | − | 0.985227i | \(-0.445218\pi\) | ||||
0.171254 | + | 0.985227i | \(0.445218\pi\) | |||||||
\(200\) | −1478.43 | − | 2560.72i | −0.522704 | − | 0.905350i | ||||
\(201\) | −751.233 | − | 1301.17i | −0.263621 | − | 0.456605i | ||||
\(202\) | 982.977 | + | 1702.57i | 0.342386 | + | 0.593030i | ||||
\(203\) | 1585.22 | − | 2745.68i | 0.548082 | − | 0.949307i | ||||
\(204\) | −1060.65 | −0.364020 | ||||||||
\(205\) | −12.5478 | + | 21.7335i | −0.00427501 | + | 0.00740454i | ||||
\(206\) | 64.0636 | + | 110.961i | 0.0216676 | + | 0.0375294i | ||||
\(207\) | 5477.03 | 1.83903 | ||||||||
\(208\) | −153.670 | − | 266.164i | −0.0512264 | − | 0.0887268i | ||||
\(209\) | 1262.01 | − | 2185.87i | 0.417680 | − | 0.723442i | ||||
\(210\) | 13.2604 | − | 22.9678i | 0.00435742 | − | 0.00754727i | ||||
\(211\) | −3416.62 | −1.11474 | −0.557370 | − | 0.830264i | \(-0.688189\pi\) | ||||
−0.557370 | + | 0.830264i | \(0.688189\pi\) | |||||||
\(212\) | −600.789 | + | 1040.60i | −0.194634 | + | 0.337115i | ||||
\(213\) | 4958.34 | 1.59502 | ||||||||
\(214\) | 2465.05 | 0.787418 | ||||||||
\(215\) | 16.0924 | − | 11.5385i | 0.00510461 | − | 0.00366008i | ||||
\(216\) | −3210.04 | −1.01118 | ||||||||
\(217\) | 5111.66 | 1.59909 | ||||||||
\(218\) | −1525.78 | + | 2642.73i | −0.474032 | + | 0.821047i | ||||
\(219\) | 5904.43 | 1.82185 | ||||||||
\(220\) | 8.31672 | − | 14.4050i | 0.00254870 | − | 0.00441447i | ||||
\(221\) | 408.709 | − | 707.904i | 0.124401 | − | 0.215470i | ||||
\(222\) | −2980.41 | − | 5162.22i | −0.901044 | − | 1.56065i | ||||
\(223\) | 4025.40 | 1.20879 | 0.604396 | − | 0.796684i | \(-0.293415\pi\) | ||||
0.604396 | + | 0.796684i | \(0.293415\pi\) | |||||||
\(224\) | 1968.90 | + | 3410.24i | 0.587289 | + | 1.01721i | ||||
\(225\) | 2699.66 | − | 4675.95i | 0.799900 | − | 1.38547i | ||||
\(226\) | 1921.27 | 0.565491 | ||||||||
\(227\) | 1351.97 | − | 2341.69i | 0.395303 | − | 0.684684i | −0.597837 | − | 0.801618i | \(-0.703973\pi\) |
0.993140 | + | 0.116933i | \(0.0373064\pi\) | |||||||
\(228\) | −826.526 | − | 1431.58i | −0.240079 | − | 0.415829i | ||||
\(229\) | −1438.15 | − | 2490.95i | −0.415004 | − | 0.718807i | 0.580425 | − | 0.814314i | \(-0.302886\pi\) |
−0.995429 | + | 0.0955062i | \(0.969553\pi\) | |||||||
\(230\) | −8.56042 | − | 14.8271i | −0.00245416 | − | 0.00425074i | ||||
\(231\) | −10811.5 | −3.07941 | ||||||||
\(232\) | 1599.65 | + | 2770.67i | 0.452681 | + | 0.784066i | ||||
\(233\) | 668.312 | + | 1157.55i | 0.187908 | + | 0.325466i | 0.944553 | − | 0.328360i | \(-0.106496\pi\) |
−0.756645 | + | 0.653826i | \(0.773163\pi\) | |||||||
\(234\) | 1153.82 | − | 1998.48i | 0.322340 | − | 0.558310i | ||||
\(235\) | −15.5206 | + | 26.8825i | −0.00430831 | + | 0.00746221i | ||||
\(236\) | −1780.55 | −0.491119 | ||||||||
\(237\) | −5008.32 | −1.37268 | ||||||||
\(238\) | 663.067 | − | 1148.47i | 0.180589 | − | 0.312790i | ||||
\(239\) | −1722.37 | + | 2983.23i | −0.466154 | + | 0.807402i | −0.999253 | − | 0.0386508i | \(-0.987694\pi\) |
0.533099 | + | 0.846053i | \(0.321027\pi\) | |||||||
\(240\) | 3.25425 | + | 5.63653i | 0.000875255 | + | 0.00151599i | ||||
\(241\) | −370.298 | − | 641.375i | −0.0989750 | − | 0.171430i | 0.812286 | − | 0.583260i | \(-0.198223\pi\) |
−0.911261 | + | 0.411830i | \(0.864890\pi\) | |||||||
\(242\) | 3266.90 | 0.867787 | ||||||||
\(243\) | 1955.00 | + | 3386.15i | 0.516103 | + | 0.893917i | ||||
\(244\) | 1206.02 | + | 2088.89i | 0.316425 | + | 0.548064i | ||||
\(245\) | −7.25259 | − | 12.5619i | −0.00189123 | − | 0.00327570i | ||||
\(246\) | −2878.46 | + | 4985.63i | −0.746031 | + | 1.29216i | ||||
\(247\) | 1273.97 | 0.328181 | ||||||||
\(248\) | −2579.09 | + | 4467.11i | −0.660372 | + | 1.14380i | ||||
\(249\) | −158.732 | − | 274.932i | −0.0403986 | − | 0.0699724i | ||||
\(250\) | −33.7566 | −0.00853981 | ||||||||
\(251\) | −656.541 | − | 1137.16i | −0.165102 | − | 0.285964i | 0.771590 | − | 0.636121i | \(-0.219462\pi\) |
−0.936691 | + | 0.350156i | \(0.886129\pi\) | |||||||
\(252\) | −2178.62 | + | 3773.48i | −0.544604 | + | 0.943282i | ||||
\(253\) | −3489.74 | + | 6044.41i | −0.867186 | + | 1.50201i | ||||
\(254\) | 2451.95 | 0.605704 | ||||||||
\(255\) | −8.65518 | + | 14.9912i | −0.00212552 | + | 0.00368151i | ||||
\(256\) | −4354.42 | −1.06309 | ||||||||
\(257\) | 4405.40 | 1.06927 | 0.534633 | − | 0.845084i | \(-0.320450\pi\) | ||||
0.534633 | + | 0.845084i | \(0.320450\pi\) | |||||||
\(258\) | 3691.57 | − | 2646.92i | 0.890804 | − | 0.638720i | ||||
\(259\) | −8674.05 | −2.08100 | ||||||||
\(260\) | 8.39554 | 0.00200258 | ||||||||
\(261\) | −2921.01 | + | 5059.33i | −0.692743 | + | 1.19987i | ||||
\(262\) | −3013.56 | −0.710604 | ||||||||
\(263\) | 150.475 | − | 260.630i | 0.0352802 | − | 0.0611070i | −0.847846 | − | 0.530242i | \(-0.822101\pi\) |
0.883126 | + | 0.469135i | \(0.155434\pi\) | |||||||
\(264\) | 5454.94 | − | 9448.23i | 1.27170 | − | 2.20265i | ||||
\(265\) | 9.80521 | + | 16.9831i | 0.00227294 | + | 0.00393685i | ||||
\(266\) | 2066.82 | 0.476409 | ||||||||
\(267\) | 1576.76 | + | 2731.02i | 0.361408 | + | 0.625977i | ||||
\(268\) | 385.815 | − | 668.250i | 0.0879380 | − | 0.152313i | ||||
\(269\) | −2216.51 | −0.502389 | −0.251195 | − | 0.967937i | \(-0.580823\pi\) | ||||
−0.251195 | + | 0.967937i | \(0.580823\pi\) | |||||||
\(270\) | −9.16157 | + | 15.8683i | −0.00206502 | + | 0.00357672i | ||||
\(271\) | −64.6236 | − | 111.931i | −0.0144856 | − | 0.0250898i | 0.858692 | − | 0.512492i | \(-0.171278\pi\) |
−0.873177 | + | 0.487403i | \(0.837944\pi\) | |||||||
\(272\) | 162.724 | + | 281.846i | 0.0362742 | + | 0.0628287i | ||||
\(273\) | −2728.49 | − | 4725.88i | −0.604893 | − | 1.04770i | ||||
\(274\) | −1211.43 | −0.267098 | ||||||||
\(275\) | 3440.23 | + | 5958.65i | 0.754377 | + | 1.30662i | ||||
\(276\) | 2285.53 | + | 3958.65i | 0.498452 | + | 0.863344i | ||||
\(277\) | 603.242 | − | 1044.85i | 0.130849 | − | 0.226638i | −0.793155 | − | 0.609020i | \(-0.791563\pi\) |
0.924004 | + | 0.382382i | \(0.124896\pi\) | |||||||
\(278\) | −576.377 | + | 998.315i | −0.124348 | + | 0.215378i | ||||
\(279\) | −9419.00 | −2.02115 | ||||||||
\(280\) | 38.9438 | 0.00831192 | ||||||||
\(281\) | 3971.04 | − | 6878.05i | 0.843034 | − | 1.46018i | −0.0442833 | − | 0.999019i | \(-0.514100\pi\) |
0.887318 | − | 0.461159i | \(-0.152566\pi\) | |||||||
\(282\) | −3560.41 | + | 6166.81i | −0.751841 | + | 1.30223i | ||||
\(283\) | 1753.25 | + | 3036.71i | 0.368267 | + | 0.637858i | 0.989295 | − | 0.145931i | \(-0.0466178\pi\) |
−0.621027 | + | 0.783789i | \(0.713284\pi\) | |||||||
\(284\) | 1273.24 | + | 2205.32i | 0.266031 | + | 0.460780i | ||||
\(285\) | −26.9787 | −0.00560730 | ||||||||
\(286\) | 1470.34 | + | 2546.70i | 0.303996 | + | 0.526536i | ||||
\(287\) | 4188.67 | + | 7254.98i | 0.861495 | + | 1.49215i | ||||
\(288\) | −3627.99 | − | 6283.87i | −0.742297 | − | 1.28570i | ||||
\(289\) | 2023.71 | − | 3505.17i | 0.411910 | − | 0.713448i | ||||
\(290\) | 18.2618 | 0.00369782 | ||||||||
\(291\) | 6953.38 | − | 12043.6i | 1.40074 | − | 2.42615i | ||||
\(292\) | 1516.18 | + | 2626.11i | 0.303863 | + | 0.526306i | ||||
\(293\) | 5419.92 | 1.08067 | 0.540333 | − | 0.841451i | \(-0.318298\pi\) | ||||
0.540333 | + | 0.841451i | \(0.318298\pi\) | |||||||
\(294\) | −1663.74 | − | 2881.68i | −0.330038 | − | 0.571642i | ||||
\(295\) | −14.5298 | + | 25.1664i | −0.00286766 | + | 0.00496693i | ||||
\(296\) | 4376.49 | − | 7580.30i | 0.859386 | − | 1.48850i | ||||
\(297\) | 7469.61 | 1.45936 | ||||||||
\(298\) | −2379.12 | + | 4120.75i | −0.462479 | + | 0.801037i | ||||
\(299\) | −3522.81 | −0.681370 | ||||||||
\(300\) | 4506.21 | 0.867220 | ||||||||
\(301\) | −649.750 | − | 6578.07i | −0.124422 | − | 1.25965i | ||||
\(302\) | 4006.31 | 0.763368 | ||||||||
\(303\) | −8566.43 | −1.62419 | ||||||||
\(304\) | −253.610 | + | 439.265i | −0.0478471 | + | 0.0828736i | ||||
\(305\) | 39.3659 | 0.00739045 | ||||||||
\(306\) | −1221.80 | + | 2116.22i | −0.228254 | + | 0.395347i | ||||
\(307\) | −2878.08 | + | 4984.98i | −0.535051 | + | 0.926735i | 0.464110 | + | 0.885778i | \(0.346374\pi\) |
−0.999161 | + | 0.0409579i | \(0.986959\pi\) | |||||||
\(308\) | −2776.26 | − | 4808.62i | −0.513610 | − | 0.889599i | ||||
\(309\) | −558.301 | −0.102785 | ||||||||
\(310\) | 14.7216 | + | 25.4986i | 0.00269720 | + | 0.00467168i | ||||
\(311\) | 244.854 | − | 424.100i | 0.0446444 | − | 0.0773264i | −0.842840 | − | 0.538165i | \(-0.819118\pi\) |
0.887484 | + | 0.460838i | \(0.152451\pi\) | |||||||
\(312\) | 5506.64 | 0.999205 | ||||||||
\(313\) | 4038.86 | − | 6995.51i | 0.729361 | − | 1.26329i | −0.227793 | − | 0.973710i | \(-0.573151\pi\) |
0.957154 | − | 0.289580i | \(-0.0935156\pi\) | |||||||
\(314\) | −2553.35 | − | 4422.53i | −0.458898 | − | 0.794835i | ||||
\(315\) | 35.5563 | + | 61.5854i | 0.00635991 | + | 0.0110157i | ||||
\(316\) | −1286.07 | − | 2227.55i | −0.228947 | − | 0.396548i | ||||
\(317\) | −4400.14 | −0.779610 | −0.389805 | − | 0.920897i | \(-0.627458\pi\) | ||||
−0.389805 | + | 0.920897i | \(0.627458\pi\) | |||||||
\(318\) | 2249.30 | + | 3895.91i | 0.396650 | + | 0.687018i | ||||
\(319\) | −3722.29 | − | 6447.20i | −0.653318 | − | 1.13158i | ||||
\(320\) | −14.4482 | + | 25.0250i | −0.00252399 | + | 0.00437169i | ||||
\(321\) | −5370.60 | + | 9302.15i | −0.933824 | + | 1.61743i | ||||
\(322\) | −5715.22 | −0.989120 | ||||||||
\(323\) | −1349.03 | −0.232390 | ||||||||
\(324\) | −63.2089 | + | 109.481i | −0.0108383 | + | 0.0187725i | ||||
\(325\) | −1736.42 | + | 3007.56i | −0.296367 | + | 0.513322i | ||||
\(326\) | −1134.77 | − | 1965.48i | −0.192789 | − | 0.333921i | ||||
\(327\) | −6648.42 | − | 11515.4i | −1.12434 | − | 1.94741i | ||||
\(328\) | −8453.57 | −1.42308 | ||||||||
\(329\) | 5181.03 | + | 8973.80i | 0.868205 | + | 1.50377i | ||||
\(330\) | −31.1371 | − | 53.9311i | −0.00519407 | − | 0.00899639i | ||||
\(331\) | 4491.19 | + | 7778.97i | 0.745795 | + | 1.29175i | 0.949822 | + | 0.312789i | \(0.101263\pi\) |
−0.204028 | + | 0.978965i | \(0.565403\pi\) | |||||||
\(332\) | 81.5210 | − | 141.198i | 0.0134760 | − | 0.0233412i | ||||
\(333\) | 15983.2 | 2.63026 | ||||||||
\(334\) | 2750.43 | − | 4763.88i | 0.450589 | − | 0.780443i | ||||
\(335\) | −6.29671 | − | 10.9062i | −0.00102694 | − | 0.00177872i | ||||
\(336\) | 2172.65 | 0.352761 | ||||||||
\(337\) | −1756.82 | − | 3042.90i | −0.283976 | − | 0.491861i | 0.688384 | − | 0.725346i | \(-0.258320\pi\) |
−0.972360 | + | 0.233485i | \(0.924987\pi\) | |||||||
\(338\) | 1370.04 | − | 2372.98i | 0.220475 | − | 0.381874i | ||||
\(339\) | −4185.86 | + | 7250.12i | −0.670633 | + | 1.16157i | ||||
\(340\) | −8.89017 | −0.00141805 | ||||||||
\(341\) | 6001.40 | − | 10394.7i | 0.953062 | − | 1.65075i | ||||
\(342\) | −3808.42 | −0.602152 | ||||||||
\(343\) | 3198.71 | 0.503540 | ||||||||
\(344\) | 6076.44 | + | 2751.14i | 0.952384 | + | 0.431197i | ||||
\(345\) | 74.6022 | 0.0116419 | ||||||||
\(346\) | −605.787 | −0.0941251 | ||||||||
\(347\) | 1504.62 | − | 2606.08i | 0.232773 | − | 0.403175i | −0.725850 | − | 0.687853i | \(-0.758553\pi\) |
0.958623 | + | 0.284678i | \(0.0918867\pi\) | |||||||
\(348\) | −4875.67 | −0.751044 | ||||||||
\(349\) | −2916.80 | + | 5052.04i | −0.447371 | + | 0.774869i | −0.998214 | − | 0.0597396i | \(-0.980973\pi\) |
0.550843 | + | 0.834609i | \(0.314306\pi\) | |||||||
\(350\) | −2817.07 | + | 4879.31i | −0.430225 | + | 0.745171i | ||||
\(351\) | 1885.10 | + | 3265.09i | 0.286664 | + | 0.496517i | ||||
\(352\) | 9246.44 | 1.40011 | ||||||||
\(353\) | −3091.77 | − | 5355.11i | −0.466171 | − | 0.807432i | 0.533082 | − | 0.846063i | \(-0.321034\pi\) |
−0.999254 | + | 0.0386313i | \(0.987700\pi\) | |||||||
\(354\) | −3333.13 | + | 5773.14i | −0.500434 | + | 0.866777i | ||||
\(355\) | 41.5600 | 0.00621345 | ||||||||
\(356\) | −809.784 | + | 1402.59i | −0.120557 | + | 0.208812i | ||||
\(357\) | 2889.24 | + | 5004.31i | 0.428333 | + | 0.741894i | ||||
\(358\) | −228.355 | − | 395.522i | −0.0337121 | − | 0.0583910i | ||||
\(359\) | 2154.46 | + | 3731.64i | 0.316736 | + | 0.548603i | 0.979805 | − | 0.199955i | \(-0.0640797\pi\) |
−0.663069 | + | 0.748558i | \(0.730746\pi\) | |||||||
\(360\) | −71.7598 | −0.0105058 | ||||||||
\(361\) | 2378.25 | + | 4119.25i | 0.346734 | + | 0.600561i | ||||
\(362\) | 205.607 | + | 356.122i | 0.0298522 | + | 0.0517055i | ||||
\(363\) | −7117.58 | + | 12328.0i | −1.02914 | + | 1.78252i | ||||
\(364\) | 1401.28 | − | 2427.10i | 0.201778 | − | 0.349490i | ||||
\(365\) | 49.4900 | 0.00709705 | ||||||||
\(366\) | 9030.51 | 1.28971 | ||||||||
\(367\) | 347.868 | − | 602.524i | 0.0494783 | − | 0.0856990i | −0.840226 | − | 0.542237i | \(-0.817577\pi\) |
0.889704 | + | 0.456538i | \(0.150911\pi\) | |||||||
\(368\) | 701.288 | − | 1214.67i | 0.0993401 | − | 0.172062i | ||||
\(369\) | −7718.24 | − | 13368.4i | −1.08888 | − | 1.88599i | ||||
\(370\) | −24.9813 | − | 43.2688i | −0.00351004 | − | 0.00607957i | ||||
\(371\) | 6546.28 | 0.916081 | ||||||||
\(372\) | −3930.49 | − | 6807.80i | −0.547813 | − | 0.948839i | ||||
\(373\) | −539.937 | − | 935.198i | −0.0749514 | − | 0.129820i | 0.826114 | − | 0.563503i | \(-0.190547\pi\) |
−0.901065 | + | 0.433684i | \(0.857213\pi\) | |||||||
\(374\) | −1556.96 | − | 2696.74i | −0.215264 | − | 0.372848i | ||||
\(375\) | 73.5453 | − | 127.384i | 0.0101276 | − | 0.0175416i | ||||
\(376\) | −10456.4 | −1.43416 | ||||||||
\(377\) | 1878.79 | − | 3254.15i | 0.256664 | − | 0.444555i | ||||
\(378\) | 3058.28 | + | 5297.10i | 0.416140 | + | 0.720776i | ||||
\(379\) | −5259.67 | −0.712853 | −0.356426 | − | 0.934323i | \(-0.616005\pi\) | ||||
−0.356426 | + | 0.934323i | \(0.616005\pi\) | |||||||
\(380\) | −6.92780 | − | 11.9993i | −0.000935234 | − | 0.00161987i | ||||
\(381\) | −5342.04 | + | 9252.69i | −0.718323 | + | 1.24417i | ||||
\(382\) | −1570.52 | + | 2720.22i | −0.210353 | + | 0.364342i | ||||
\(383\) | −9371.54 | −1.25030 | −0.625148 | − | 0.780506i | \(-0.714961\pi\) | ||||
−0.625148 | + | 0.780506i | \(0.714961\pi\) | |||||||
\(384\) | 2315.06 | − | 4009.81i | 0.307657 | − | 0.532877i | ||||
\(385\) | −90.6202 | −0.0119959 | ||||||||
\(386\) | −9426.85 | −1.24304 | ||||||||
\(387\) | 1197.26 | + | 12121.1i | 0.157262 | + | 1.59212i | ||||
\(388\) | 7142.17 | 0.934507 | ||||||||
\(389\) | −3732.64 | −0.486510 | −0.243255 | − | 0.969962i | \(-0.578215\pi\) | ||||
−0.243255 | + | 0.969962i | \(0.578215\pi\) | |||||||
\(390\) | 15.7161 | − | 27.2211i | 0.00204056 | − | 0.00353435i | ||||
\(391\) | 3730.36 | 0.482487 | ||||||||
\(392\) | 2443.07 | − | 4231.51i | 0.314779 | − | 0.545213i | ||||
\(393\) | 6565.62 | − | 11372.0i | 0.842727 | − | 1.45965i | ||||
\(394\) | −4259.97 | − | 7378.48i | −0.544706 | − | 0.943458i | ||||
\(395\) | −41.9789 | −0.00534731 | ||||||||
\(396\) | 5115.67 | + | 8860.60i | 0.649172 | + | 1.12440i | ||||
\(397\) | −2453.43 | + | 4249.47i | −0.310161 | + | 0.537215i | −0.978397 | − | 0.206734i | \(-0.933716\pi\) |
0.668236 | + | 0.743950i | \(0.267050\pi\) | |||||||
\(398\) | 1848.76 | 0.232840 | ||||||||
\(399\) | −4502.97 | + | 7799.37i | −0.564989 | + | 0.978589i | ||||
\(400\) | −691.339 | − | 1197.43i | −0.0864173 | − | 0.149679i | ||||
\(401\) | 935.972 | + | 1621.15i | 0.116559 | + | 0.201886i | 0.918402 | − | 0.395649i | \(-0.129480\pi\) |
−0.801843 | + | 0.597535i | \(0.796147\pi\) | |||||||
\(402\) | −1444.46 | − | 2501.88i | −0.179212 | − | 0.310404i | ||||
\(403\) | 6058.28 | 0.748845 | ||||||||
\(404\) | −2199.75 | − | 3810.08i | −0.270896 | − | 0.469205i | ||||
\(405\) | 1.03160 | + | 1.78679i | 0.000126570 | + | 0.000219226i | ||||
\(406\) | 3048.04 | − | 5279.36i | 0.372590 | − | 0.645345i | ||||
\(407\) | −10183.9 | + | 17639.0i | −1.24028 | + | 2.14823i | ||||
\(408\) | −5831.07 | −0.707551 | ||||||||
\(409\) | 1917.96 | 0.231875 | 0.115937 | − | 0.993257i | \(-0.463013\pi\) | ||||
0.115937 | + | 0.993257i | \(0.463013\pi\) | |||||||
\(410\) | −24.1267 | + | 41.7887i | −0.00290618 | + | 0.00503366i | ||||
\(411\) | 2639.33 | − | 4571.45i | 0.316760 | − | 0.548645i | ||||
\(412\) | −143.365 | − | 248.315i | −0.0171434 | − | 0.0296932i | ||||
\(413\) | 4850.29 | + | 8400.95i | 0.577887 | + | 1.00093i | ||||
\(414\) | 10531.1 | 1.25019 | ||||||||
\(415\) | −1.33047 | − | 2.30444i | −0.000157374 | − | 0.000272579i | ||||
\(416\) | 2333.52 | + | 4041.77i | 0.275024 | + | 0.476356i | ||||
\(417\) | −2511.50 | − | 4350.05i | −0.294937 | − | 0.510846i | ||||
\(418\) | 2426.57 | − | 4202.95i | 0.283942 | − | 0.491801i | ||||
\(419\) | 9353.24 | 1.09054 | 0.545269 | − | 0.838261i | \(-0.316427\pi\) | ||||
0.545269 | + | 0.838261i | \(0.316427\pi\) | |||||||
\(420\) | −29.6749 | + | 51.3984i | −0.00344758 | + | 0.00597139i | ||||
\(421\) | −1738.45 | − | 3011.08i | −0.201251 | − | 0.348577i | 0.747681 | − | 0.664058i | \(-0.231167\pi\) |
−0.948932 | + | 0.315481i | \(0.897834\pi\) | |||||||
\(422\) | −6569.43 | −0.757808 | ||||||||
\(423\) | −9546.82 | − | 16535.6i | −1.09736 | − | 1.90068i | ||||
\(424\) | −3302.92 | + | 5720.83i | −0.378312 | + | 0.655255i | ||||
\(425\) | 1838.72 | − | 3184.76i | 0.209861 | − | 0.363490i | ||||
\(426\) | 9533.82 | 1.08431 | ||||||||
\(427\) | 6570.50 | − | 11380.4i | 0.744657 | − | 1.28978i | ||||
\(428\) | −5516.41 | −0.623004 | ||||||||
\(429\) | −12813.7 | −1.44207 | ||||||||
\(430\) | 30.9422 | − | 22.1860i | 0.00347015 | − | 0.00248815i | ||||
\(431\) | −4840.83 | −0.541008 | −0.270504 | − | 0.962719i | \(-0.587190\pi\) | ||||
−0.270504 | + | 0.962719i | \(0.587190\pi\) | |||||||
\(432\) | −1501.07 | −0.167177 | ||||||||
\(433\) | −5795.79 | + | 10038.6i | −0.643251 | + | 1.11414i | 0.341451 | + | 0.939899i | \(0.389082\pi\) |
−0.984702 | + | 0.174244i | \(0.944252\pi\) | |||||||
\(434\) | 9828.62 | 1.08707 | ||||||||
\(435\) | −39.7868 | + | 68.9128i | −0.00438536 | + | 0.00759567i | ||||
\(436\) | 3414.47 | − | 5914.03i | 0.375053 | − | 0.649611i | ||||
\(437\) | 2906.94 | + | 5034.97i | 0.318210 | + | 0.551156i | ||||
\(438\) | 11352.9 | 1.23850 | ||||||||
\(439\) | 2238.86 | + | 3877.82i | 0.243405 | + | 0.421591i | 0.961682 | − | 0.274167i | \(-0.0884021\pi\) |
−0.718277 | + | 0.695758i | \(0.755069\pi\) | |||||||
\(440\) | 45.7224 | − | 79.1935i | 0.00495393 | − | 0.00858046i | ||||
\(441\) | 8922.23 | 0.963420 | ||||||||
\(442\) | 785.859 | − | 1361.15i | 0.0845690 | − | 0.146478i | ||||
\(443\) | −2209.22 | − | 3826.47i | −0.236937 | − | 0.410387i | 0.722897 | − | 0.690956i | \(-0.242810\pi\) |
−0.959834 | + | 0.280569i | \(0.909477\pi\) | |||||||
\(444\) | 6669.70 | + | 11552.3i | 0.712905 | + | 1.23479i | ||||
\(445\) | 13.2161 | + | 22.8910i | 0.00140787 | + | 0.00243851i | ||||
\(446\) | 7739.97 | 0.821745 | ||||||||
\(447\) | −10366.7 | − | 17955.7i | −1.09694 | − | 1.89995i | ||||
\(448\) | 4823.04 | + | 8353.75i | 0.508632 | + | 0.880977i | ||||
\(449\) | 5519.82 | − | 9560.61i | 0.580170 | − | 1.00488i | −0.415288 | − | 0.909690i | \(-0.636319\pi\) |
0.995459 | − | 0.0951945i | \(-0.0303473\pi\) | |||||||
\(450\) | 5190.87 | − | 8990.85i | 0.543778 | − | 0.941850i | ||||
\(451\) | 19671.0 | 2.05382 | ||||||||
\(452\) | −4299.51 | −0.447416 | ||||||||
\(453\) | −8728.53 | + | 15118.3i | −0.905302 | + | 1.56803i | ||||
\(454\) | 2599.56 | − | 4502.56i | 0.268729 | − | 0.465453i | ||||
\(455\) | −22.8698 | − | 39.6116i | −0.00235638 | − | 0.00408136i | ||||
\(456\) | −4543.95 | − | 7870.35i | −0.466644 | − | 0.808252i | ||||
\(457\) | −12619.7 | −1.29174 | −0.645870 | − | 0.763447i | \(-0.723505\pi\) | ||||
−0.645870 | + | 0.763447i | \(0.723505\pi\) | |||||||
\(458\) | −2765.26 | − | 4789.57i | −0.282122 | − | 0.488650i | ||||
\(459\) | −1996.16 | − | 3457.45i | −0.202991 | − | 0.351591i | ||||
\(460\) | 19.1569 | + | 33.1808i | 0.00194173 | + | 0.00336318i | ||||
\(461\) | 3432.48 | − | 5945.23i | 0.346782 | − | 0.600644i | −0.638894 | − | 0.769295i | \(-0.720608\pi\) |
0.985676 | + | 0.168651i | \(0.0539410\pi\) | |||||||
\(462\) | −20788.2 | −2.09341 | ||||||||
\(463\) | 147.484 | − | 255.449i | 0.0148038 | − | 0.0256409i | −0.858529 | − | 0.512766i | \(-0.828621\pi\) |
0.873332 | + | 0.487125i | \(0.161954\pi\) | |||||||
\(464\) | 748.021 | + | 1295.61i | 0.0748406 | + | 0.129628i | ||||
\(465\) | −128.296 | −0.0127948 | ||||||||
\(466\) | 1285.02 | + | 2225.72i | 0.127741 | + | 0.221254i | ||||
\(467\) | 2799.34 | − | 4848.59i | 0.277383 | − | 0.480441i | −0.693351 | − | 0.720600i | \(-0.743866\pi\) |
0.970734 | + | 0.240159i | \(0.0771996\pi\) | |||||||
\(468\) | −2582.08 | + | 4472.29i | −0.255035 | + | 0.441734i | ||||
\(469\) | −4203.89 | −0.413897 | ||||||||
\(470\) | −29.8428 | + | 51.6892i | −0.00292882 | + | 0.00507286i | ||||
\(471\) | 22251.9 | 2.17689 | ||||||||
\(472\) | −9788.86 | −0.954595 | ||||||||
\(473\) | −14139.6 | − | 6401.76i | −1.37450 | − | 0.622312i | ||||
\(474\) | −9629.92 | −0.933158 | ||||||||
\(475\) | 5731.40 | 0.553631 | ||||||||
\(476\) | −1483.84 | + | 2570.09i | −0.142882 | + | 0.247479i | ||||
\(477\) | −12062.5 | −1.15787 | ||||||||
\(478\) | −3311.74 | + | 5736.11i | −0.316895 | + | 0.548878i | ||||
\(479\) | −3186.39 | + | 5518.99i | −0.303946 | + | 0.526449i | −0.977026 | − | 0.213120i | \(-0.931637\pi\) |
0.673080 | + | 0.739569i | \(0.264971\pi\) | |||||||
\(480\) | −49.4167 | − | 85.5922i | −0.00469907 | − | 0.00813902i | ||||
\(481\) | −10280.4 | −0.974522 | ||||||||
\(482\) | −712.003 | − | 1233.23i | −0.0672839 | − | 0.116539i | ||||
\(483\) | 12451.7 | − | 21567.0i | 1.17303 | − | 2.03175i | ||||
\(484\) | −7310.83 | −0.686592 | ||||||||
\(485\) | 58.2821 | − | 100.948i | 0.00545661 | − | 0.00945112i | ||||
\(486\) | 3759.04 | + | 6510.85i | 0.350851 | + | 0.607691i | ||||
\(487\) | 7983.31 | + | 13827.5i | 0.742830 | + | 1.28662i | 0.951202 | + | 0.308570i | \(0.0998503\pi\) |
−0.208372 | + | 0.978050i | \(0.566816\pi\) | |||||||
\(488\) | 6630.29 | + | 11484.0i | 0.615039 | + | 1.06528i | ||||
\(489\) | 9889.30 | 0.914539 | ||||||||
\(490\) | −13.9452 | − | 24.1537i | −0.00128567 | − | 0.00222685i | ||||
\(491\) | −5722.04 | − | 9910.86i | −0.525931 | − | 0.910939i | −0.999544 | − | 0.0302059i | \(-0.990384\pi\) |
0.473613 | − | 0.880733i | \(-0.342950\pi\) | |||||||
\(492\) | 6441.55 | − | 11157.1i | 0.590259 | − | 1.02236i | ||||
\(493\) | −1989.48 | + | 3445.87i | −0.181747 | + | 0.314796i | ||||
\(494\) | 2449.57 | 0.223100 | ||||||||
\(495\) | 166.981 | 0.0151621 | ||||||||
\(496\) | −1206.02 | + | 2088.90i | −0.109178 | + | 0.189101i | ||||
\(497\) | 6936.70 | − | 12014.7i | 0.626064 | − | 1.08437i | ||||
\(498\) | −305.208 | − | 528.636i | −0.0274632 | − | 0.0475677i | ||||
\(499\) | −690.385 | − | 1195.78i | −0.0619356 | − | 0.107276i | 0.833395 | − | 0.552678i | \(-0.186394\pi\) |
−0.895331 | + | 0.445402i | \(0.853061\pi\) | |||||||
\(500\) | 75.5421 | 0.00675669 | ||||||||
\(501\) | 11984.7 | + | 20758.1i | 1.06874 | + | 1.85110i | ||||
\(502\) | −1262.39 | − | 2186.52i | −0.112237 | − | 0.194401i | ||||
\(503\) | 4831.72 | + | 8368.79i | 0.428302 | + | 0.741840i | 0.996722 | − | 0.0808977i | \(-0.0257787\pi\) |
−0.568421 | + | 0.822738i | \(0.692445\pi\) | |||||||
\(504\) | −11977.3 | + | 20745.3i | −1.05855 | + | 1.83347i | ||||
\(505\) | −71.8024 | −0.00632706 | ||||||||
\(506\) | −6710.02 | + | 11622.1i | −0.589519 | + | 1.02108i | ||||
\(507\) | 5969.81 | + | 10340.0i | 0.522936 | + | 0.905752i | ||||
\(508\) | −5487.08 | −0.479232 | ||||||||
\(509\) | 3783.15 | + | 6552.61i | 0.329441 | + | 0.570608i | 0.982401 | − | 0.186784i | \(-0.0598066\pi\) |
−0.652960 | + | 0.757392i | \(0.726473\pi\) | |||||||
\(510\) | −16.6420 | + | 28.8249i | −0.00144495 | + | 0.00250272i | ||||
\(511\) | 8260.28 | − | 14307.2i | 0.715095 | − | 1.23858i | ||||
\(512\) | −3951.56 | −0.341085 | ||||||||
\(513\) | 3111.08 | − | 5388.55i | 0.267753 | − | 0.463762i | ||||
\(514\) | 8470.64 | 0.726894 | ||||||||
\(515\) | −4.67958 | −0.000400402 | ||||||||
\(516\) | −8261.18 | + | 5923.39i | −0.704803 | + | 0.505354i | ||||
\(517\) | 24331.4 | 2.06981 | ||||||||
\(518\) | −16678.3 | −1.41468 | ||||||||
\(519\) | 1319.82 | − | 2286.00i | 0.111626 | − | 0.193342i | ||||
\(520\) | 46.1557 | 0.00389243 | ||||||||
\(521\) | −2358.61 | + | 4085.23i | −0.198335 | + | 0.343526i | −0.947989 | − | 0.318304i | \(-0.896887\pi\) |
0.749654 | + | 0.661830i | \(0.230220\pi\) | |||||||
\(522\) | −5616.47 | + | 9728.01i | −0.470931 | + | 0.815677i | ||||
\(523\) | 3443.03 | + | 5963.51i | 0.287865 | + | 0.498597i | 0.973300 | − | 0.229537i | \(-0.0737213\pi\) |
−0.685435 | + | 0.728134i | \(0.740388\pi\) | |||||||
\(524\) | 6743.88 | 0.562229 | ||||||||
\(525\) | −12275.1 | − | 21261.0i | −1.02043 | − | 1.76744i | ||||
\(526\) | 289.331 | − | 501.136i | 0.0239837 | − | 0.0415410i | ||||
\(527\) | −6415.21 | −0.530267 | ||||||||
\(528\) | 2550.82 | − | 4418.15i | 0.210247 | − | 0.364158i | ||||
\(529\) | −1954.85 | − | 3385.89i | −0.160668 | − | 0.278285i | ||||
\(530\) | 18.8533 | + | 32.6549i | 0.00154516 | + | 0.00267630i | ||||
\(531\) | −8937.38 | − | 15480.0i | −0.730413 | − | 1.26511i | ||||
\(532\) | −4625.23 | −0.376934 | ||||||||
\(533\) | 4964.36 | + | 8598.52i | 0.403434 | + | 0.698768i | ||||
\(534\) | 3031.76 | + | 5251.17i | 0.245688 | + | 0.425544i | ||||
\(535\) | −45.0155 | + | 77.9691i | −0.00363774 | + | 0.00630074i | ||||
\(536\) | 2121.07 | − | 3673.81i | 0.170926 | − | 0.296053i | ||||
\(537\) | 1990.06 | 0.159921 | ||||||||
\(538\) | −4261.86 | −0.341528 | ||||||||
\(539\) | −5684.88 | + | 9846.51i | −0.454296 | + | 0.786863i | ||||
\(540\) | 20.5022 | − | 35.5109i | 0.00163384 | − | 0.00282990i | ||||
\(541\) | −530.306 | − | 918.518i | −0.0421435 | − | 0.0729947i | 0.844184 | − | 0.536053i | \(-0.180085\pi\) |
−0.886328 | + | 0.463058i | \(0.846752\pi\) | |||||||
\(542\) | −124.257 | − | 215.220i | −0.00984743 | − | 0.0170562i | ||||
\(543\) | −1791.82 | −0.141611 | ||||||||
\(544\) | −2471.00 | − | 4279.90i | −0.194749 | − | 0.337314i | ||||
\(545\) | −55.7260 | − | 96.5203i | −0.00437989 | − | 0.00758619i | ||||
\(546\) | −5246.30 | − | 9086.85i | −0.411210 | − | 0.712237i | ||||
\(547\) | −6561.53 | + | 11364.9i | −0.512890 | + | 0.888351i | 0.486998 | + | 0.873403i | \(0.338092\pi\) |
−0.999888 | + | 0.0149486i | \(0.995242\pi\) | |||||||
\(548\) | 2710.99 | 0.211328 | ||||||||
\(549\) | −12107.1 | + | 20970.2i | −0.941201 | + | 1.63021i | ||||
\(550\) | 6614.82 | + | 11457.2i | 0.512831 | + | 0.888249i | ||||
\(551\) | −6201.32 | −0.479465 | ||||||||
\(552\) | 12565.0 | + | 21763.3i | 0.968847 | + | 1.67809i | ||||
\(553\) | −7006.63 | + | 12135.8i | −0.538792 | + | 0.933215i | ||||
\(554\) | 1159.90 | − | 2009.01i | 0.0889524 | − | 0.154070i | ||||
\(555\) | 217.706 | 0.0166507 | ||||||||
\(556\) | 1289.85 | − | 2234.08i | 0.0983842 | − | 0.170406i | ||||
\(557\) | −10395.9 | −0.790826 | −0.395413 | − | 0.918504i | \(-0.629398\pi\) | ||||
−0.395413 | + | 0.918504i | \(0.629398\pi\) | |||||||
\(558\) | −18110.7 | −1.37399 | ||||||||
\(559\) | −770.076 | − | 7796.25i | −0.0582661 | − | 0.589886i | ||||
\(560\) | 18.2108 | 0.00137419 | ||||||||
\(561\) | 13568.6 | 1.02115 | ||||||||
\(562\) | 7635.46 | − | 13225.0i | 0.573101 | − | 0.992639i | ||||
\(563\) | −10043.6 | −0.751844 | −0.375922 | − | 0.926651i | \(-0.622674\pi\) | ||||
−0.375922 | + | 0.926651i | \(0.622674\pi\) | |||||||
\(564\) | 7967.65 | − | 13800.4i | 0.594856 | − | 1.03032i | ||||
\(565\) | −35.0852 | + | 60.7693i | −0.00261247 | + | 0.00452493i | ||||
\(566\) | 3371.11 | + | 5838.94i | 0.250351 | + | 0.433620i | ||||
\(567\) | 688.733 | 0.0510124 | ||||||||
\(568\) | 6999.82 | + | 12124.1i | 0.517088 | + | 0.895623i | ||||
\(569\) | −3187.79 | + | 5521.41i | −0.234867 | + | 0.406801i | −0.959234 | − | 0.282613i | \(-0.908799\pi\) |
0.724367 | + | 0.689414i | \(0.242132\pi\) | |||||||
\(570\) | −51.8743 | −0.00381188 | ||||||||
\(571\) | 1520.80 | − | 2634.10i | 0.111459 | − | 0.193053i | −0.804899 | − | 0.593411i | \(-0.797781\pi\) |
0.916359 | + | 0.400358i | \(0.131114\pi\) | |||||||
\(572\) | −3290.39 | − | 5699.12i | −0.240521 | − | 0.416595i | ||||
\(573\) | −6843.37 | − | 11853.1i | −0.498928 | − | 0.864169i | ||||
\(574\) | 8053.90 | + | 13949.8i | 0.585651 | + | 1.01438i | ||||
\(575\) | −15848.6 | −1.14945 | ||||||||
\(576\) | −8887.17 | − | 15393.0i | −0.642880 | − | 1.11350i | ||||
\(577\) | −11217.2 | − | 19428.7i | −0.809319 | − | 1.40178i | −0.913336 | − | 0.407207i | \(-0.866503\pi\) |
0.104017 | − | 0.994576i | \(-0.466831\pi\) | |||||||
\(578\) | 3891.16 | − | 6739.69i | 0.280019 | − | 0.485007i | ||||
\(579\) | 20538.2 | − | 35573.3i | 1.47416 | − | 2.55332i | ||||
\(580\) | −40.8671 | −0.00292571 | ||||||||
\(581\) | −888.264 | −0.0634275 | ||||||||
\(582\) | 13369.9 | − | 23157.3i | 0.952231 | − | 1.64931i | ||||
\(583\) | 7685.73 | − | 13312.1i | 0.545987 | − | 0.945678i | ||||
\(584\) | 8335.45 | + | 14437.4i | 0.590622 | + | 1.02299i | ||||
\(585\) | 42.1409 | + | 72.9902i | 0.00297831 | + | 0.00515859i | ||||
\(586\) | 10421.3 | 0.734644 | ||||||||
\(587\) | −13562.7 | − | 23491.3i | −0.953650 | − | 1.65177i | −0.737428 | − | 0.675426i | \(-0.763960\pi\) |
−0.216222 | − | 0.976344i | \(-0.569374\pi\) | |||||||
\(588\) | 3723.19 | + | 6448.76i | 0.261126 | + | 0.452283i | ||||
\(589\) | −4999.15 | − | 8658.78i | −0.349722 | − | 0.605737i | ||||
\(590\) | −27.9377 | + | 48.3895i | −0.00194945 | + | 0.00337655i | ||||
\(591\) | 37124.7 | 2.58393 | ||||||||
\(592\) | 2046.52 | − | 3544.67i | 0.142080 | − | 0.246090i | ||||
\(593\) | 5824.98 | + | 10089.2i | 0.403378 | + | 0.698671i | 0.994131 | − | 0.108181i | \(-0.0345026\pi\) |
−0.590753 | + | 0.806852i | \(0.701169\pi\) | |||||||
\(594\) | 14362.4 | 0.992084 | ||||||||
\(595\) | 24.2171 | + | 41.9453i | 0.00166858 | + | 0.00289007i | ||||
\(596\) | 5324.11 | − | 9221.62i | 0.365913 | − | 0.633779i | ||||
\(597\) | −4027.89 | + | 6976.52i | −0.276132 | + | 0.478274i | ||||
\(598\) | −6773.61 | −0.463200 | ||||||||
\(599\) | −10171.0 | + | 17616.8i | −0.693786 | + | 1.20167i | 0.276803 | + | 0.960927i | \(0.410725\pi\) |
−0.970588 | + | 0.240745i | \(0.922608\pi\) | |||||||
\(600\) | 24773.5 | 1.68563 | ||||||||
\(601\) | 14226.2 | 0.965553 | 0.482777 | − | 0.875744i | \(-0.339628\pi\) | ||||
0.482777 | + | 0.875744i | \(0.339628\pi\) | |||||||
\(602\) | −1249.33 | − | 12648.2i | −0.0845828 | − | 0.856316i | ||||
\(603\) | 7746.29 | 0.523140 | ||||||||
\(604\) | −8965.51 | −0.603976 | ||||||||
\(605\) | −59.6584 | + | 103.331i | −0.00400902 | + | 0.00694383i | ||||
\(606\) | −16471.4 | −1.10413 | ||||||||
\(607\) | −9265.16 | + | 16047.7i | −0.619541 | + | 1.07308i | 0.370028 | + | 0.929020i | \(0.379348\pi\) |
−0.989570 | + | 0.144056i | \(0.953985\pi\) | |||||||
\(608\) | 3851.13 | − | 6670.35i | 0.256881 | − | 0.444932i | ||||
\(609\) | 13281.5 | + | 23004.2i | 0.883733 | + | 1.53067i | ||||
\(610\) | 75.6922 | 0.00502408 | ||||||||
\(611\) | 6140.49 | + | 10635.6i | 0.406576 | + | 0.704210i | ||||
\(612\) | 2734.20 | − | 4735.78i | 0.180594 | − | 0.312798i | ||||
\(613\) | −10295.0 | −0.678321 | −0.339160 | − | 0.940729i | \(-0.610143\pi\) | ||||
−0.339160 | + | 0.940729i | \(0.610143\pi\) | |||||||
\(614\) | −5533.93 | + | 9585.04i | −0.363731 | + | 0.630001i | ||||
\(615\) | −105.130 | − | 182.090i | −0.00689307 | − | 0.0119391i | ||||
\(616\) | −15262.9 | − | 26436.1i | −0.998311 | − | 1.72912i | ||||
\(617\) | −3394.51 | − | 5879.46i | −0.221487 | − | 0.383628i | 0.733772 | − | 0.679395i | \(-0.237758\pi\) |
−0.955260 | + | 0.295768i | \(0.904425\pi\) | |||||||
\(618\) | −1073.49 | −0.0698741 | ||||||||
\(619\) | −14423.5 | − | 24982.2i | −0.936557 | − | 1.62216i | −0.771833 | − | 0.635825i | \(-0.780660\pi\) |
−0.164724 | − | 0.986340i | \(-0.552673\pi\) | |||||||
\(620\) | −32.9447 | − | 57.0619i | −0.00213402 | − | 0.00369623i | ||||
\(621\) | −8602.83 | + | 14900.5i | −0.555909 | + | 0.962863i | ||||
\(622\) | 470.802 | − | 815.453i | 0.0303496 | − | 0.0525670i | ||||
\(623\) | 8823.52 | 0.567426 | ||||||||
\(624\) | 2574.99 | 0.165196 | ||||||||
\(625\) | −7811.58 | + | 13530.0i | −0.499941 | + | 0.865923i | ||||
\(626\) | 7765.86 | − | 13450.9i | 0.495824 | − | 0.858793i | ||||
\(627\) | 10573.5 | + | 18313.9i | 0.673470 | + | 1.16649i | ||||
\(628\) | 5714.01 | + | 9896.96i | 0.363080 | + | 0.628872i | ||||
\(629\) | 10886.1 | 0.690072 | ||||||||
\(630\) | 68.3671 | + | 118.415i | 0.00432351 | + | 0.00748854i | ||||
\(631\) | 7108.11 | + | 12311.6i | 0.448446 | + | 0.776731i | 0.998285 | − | 0.0585392i | \(-0.0186443\pi\) |
−0.549839 | + | 0.835271i | \(0.685311\pi\) | |||||||
\(632\) | −7070.38 | − | 12246.3i | −0.445008 | − | 0.770776i | ||||
\(633\) | 14312.8 | − | 24790.5i | 0.898708 | − | 1.55661i | ||||
\(634\) | −8460.51 | −0.529984 | ||||||||
\(635\) | −44.7761 | + | 77.5545i | −0.00279825 | + | 0.00484670i | ||||
\(636\) | −5033.60 | − | 8718.46i | −0.313829 | − | 0.543568i | ||||
\(637\) | −5738.76 | −0.356951 | ||||||||
\(638\) | −7157.17 | − | 12396.6i | −0.444130 | − | 0.769256i | ||||
\(639\) | −12781.9 | + | 22138.9i | −0.791306 | + | 1.37058i | ||||
\(640\) | 19.4045 | − | 33.6096i | 0.00119848 | − | 0.00207584i | ||||
\(641\) | −21448.7 | −1.32164 | −0.660821 | − | 0.750543i | \(-0.729792\pi\) | ||||
−0.660821 | + | 0.750543i | \(0.729792\pi\) | |||||||
\(642\) | −10326.5 | + | 17886.0i | −0.634820 | + | 1.09954i | ||||
\(643\) | −26733.7 | −1.63961 | −0.819807 | − | 0.572639i | \(-0.805920\pi\) | ||||
−0.819807 | + | 0.572639i | \(0.805920\pi\) | |||||||
\(644\) | 12789.8 | 0.782591 | ||||||||
\(645\) | 16.3078 | + | 165.100i | 0.000995534 | + | 0.0100788i | ||||
\(646\) | −2593.89 | −0.157980 | ||||||||
\(647\) | −535.525 | −0.0325404 | −0.0162702 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162702 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(648\) | −347.500 | + | 601.888i | −0.0210665 | + | 0.0364882i | ||||
\(649\) | 22778.2 | 1.37769 | ||||||||
\(650\) | −3338.76 | + | 5782.90i | −0.201472 | + | 0.348960i | ||||
\(651\) | −21413.6 | + | 37089.4i | −1.28919 | + | 2.23295i | ||||
\(652\) | 2539.45 | + | 4398.45i | 0.152535 | + | 0.264198i | ||||
\(653\) | 130.350 | 0.00781159 | 0.00390580 | − | 0.999992i | \(-0.498757\pi\) | ||||
0.00390580 | + | 0.999992i | \(0.498757\pi\) | |||||||
\(654\) | −12783.5 | − | 22141.6i | −0.764333 | − | 1.32386i | ||||
\(655\) | 55.0320 | − | 95.3182i | 0.00328287 | − | 0.00568609i | ||||
\(656\) | −3953.03 | −0.235274 | ||||||||
\(657\) | −15220.8 | + | 26363.2i | −0.903836 | + | 1.56549i | ||||
\(658\) | 9962.00 | + | 17254.7i | 0.590212 | + | 1.02228i | ||||
\(659\) | −13894.5 | − | 24065.9i | −0.821323 | − | 1.42257i | −0.904698 | − | 0.426054i | \(-0.859903\pi\) |
0.0833751 | − | 0.996518i | \(-0.473430\pi\) | |||||||
\(660\) | 69.6802 | + | 120.690i | 0.00410954 | + | 0.00711794i | ||||
\(661\) | 21026.7 | 1.23729 | 0.618643 | − | 0.785673i | \(-0.287683\pi\) | ||||
0.618643 | + | 0.785673i | \(0.287683\pi\) | |||||||
\(662\) | 8635.59 | + | 14957.3i | 0.506997 | + | 0.878144i | ||||
\(663\) | 3424.29 | + | 5931.05i | 0.200586 | + | 0.347425i | ||||
\(664\) | 448.174 | − | 776.259i | 0.0261935 | − | 0.0453685i | ||||
\(665\) | −37.7432 | + | 65.3731i | −0.00220093 | + | 0.00381212i | ||||
\(666\) | 30732.3 | 1.78807 | ||||||||
\(667\) | 17148.0 | 0.995464 | ||||||||
\(668\) | −6155.04 | + | 10660.8i | −0.356505 | + | 0.617485i | ||||
\(669\) | −16863.0 | + | 29207.6i | −0.974533 | + | 1.68794i | ||||
\(670\) | −12.1072 | − | 20.9703i | −0.000698123 | − | 0.00120918i | ||||
\(671\) | −15428.3 | − | 26722.7i | −0.887637 | − | 1.53743i | ||||
\(672\) | −32992.2 | −1.89390 | ||||||||
\(673\) | 5338.07 | + | 9245.81i | 0.305747 | + | 0.529569i | 0.977427 | − | 0.211272i | \(-0.0677606\pi\) |
−0.671681 | + | 0.740841i | \(0.734427\pi\) | |||||||
\(674\) | −3377.98 | − | 5850.84i | −0.193049 | − | 0.334371i | ||||
\(675\) | 8480.78 | + | 14689.1i | 0.483593 | + | 0.837608i | ||||
\(676\) | −3065.95 | + | 5310.38i | −0.174440 | + | 0.302138i | ||||
\(677\) | −6422.42 | −0.364599 | −0.182300 | − | 0.983243i | \(-0.558354\pi\) | ||||
−0.182300 | + | 0.983243i | \(0.558354\pi\) | |||||||
\(678\) | −8048.50 | + | 13940.4i | −0.455901 | + | 0.789644i | ||||
\(679\) | −19455.5 | − | 33697.9i | −1.09961 | − | 1.90458i | ||||
\(680\) | −48.8750 | −0.00275628 | ||||||||
\(681\) | 11327.3 | + | 19619.4i | 0.637390 | + | 1.10399i | ||||
\(682\) | 11539.4 | − | 19986.8i | 0.647898 | − | 1.12219i | ||||
\(683\) | 1347.81 | − | 2334.47i | 0.0755087 | − | 0.130785i | −0.825799 | − | 0.563965i | \(-0.809275\pi\) |
0.901307 | + | 0.433180i | \(0.142609\pi\) | |||||||
\(684\) | 8522.67 | 0.476422 | ||||||||
\(685\) | 22.1224 | − | 38.3171i | 0.00123395 | − | 0.00213726i | ||||
\(686\) | 6150.43 | 0.342310 | ||||||||
\(687\) | 24098.6 | 1.33831 | ||||||||
\(688\) | 2841.45 | + | 1286.48i | 0.157455 | + | 0.0712886i | ||||
\(689\) | 7758.57 | 0.428996 | ||||||||
\(690\) | 143.444 | 0.00791423 | ||||||||
\(691\) | −4323.87 | + | 7489.17i | −0.238043 | + | 0.412303i | −0.960153 | − | 0.279476i | \(-0.909839\pi\) |
0.722109 | + | 0.691779i | \(0.243173\pi\) | |||||||
\(692\) | 1355.66 | 0.0744717 | ||||||||
\(693\) | 27870.5 | − | 48273.2i | 1.52773 | − | 2.64610i | ||||
\(694\) | 2893.06 | − | 5010.93i | 0.158241 | − | 0.274081i | ||||
\(695\) | −21.0510 | − | 36.4614i | −0.00114893 | − | 0.00199001i | ||||
\(696\) | −26804.7 | −1.45981 | ||||||||
\(697\) | −5256.84 | − | 9105.11i | −0.285677 | − | 0.494807i | ||||
\(698\) | −5608.37 | + | 9713.98i | −0.304126 | + | 0.526762i | ||||
\(699\) | −11198.7 | −0.605969 | ||||||||
\(700\) | 6304.17 | − | 10919.1i | 0.340393 | − | 0.589578i | ||||
\(701\) | 6754.48 | + | 11699.1i | 0.363927 | + | 0.630341i | 0.988603 | − | 0.150543i | \(-0.0481023\pi\) |
−0.624676 | + | 0.780884i | \(0.714769\pi\) | |||||||
\(702\) | 3624.64 | + | 6278.06i | 0.194876 | + | 0.337536i | ||||
\(703\) | 8483.12 | + | 14693.2i | 0.455117 | + | 0.788285i | ||||
\(704\) | 22650.2 | 1.21259 | ||||||||
\(705\) | −130.037 | − | 225.230i | −0.00694675 | − | 0.0120321i | ||||
\(706\) | −5944.81 | − | 10296.7i | −0.316906 | − | 0.548898i | ||||
\(707\) | −11984.4 | + | 20757.6i | −0.637511 | + | 1.10420i | ||||
\(708\) | 7459.03 | − | 12919.4i | 0.395943 | − | 0.685793i | ||||
\(709\) | −5130.31 | −0.271753 | −0.135877 | − | 0.990726i | \(-0.543385\pi\) | ||||
−0.135877 | + | 0.990726i | \(0.543385\pi\) | |||||||
\(710\) | 79.9109 | 0.00422395 | ||||||||
\(711\) | 12910.8 | − | 22362.1i | 0.681000 | − | 1.17953i | ||||
\(712\) | −4451.90 | + | 7710.92i | −0.234329 | + | 0.405870i | ||||
\(713\) | 13823.8 | + | 23943.5i | 0.726093 | + | 1.25763i | ||||
\(714\) | 5555.39 | + | 9622.21i | 0.291184 | + | 0.504345i | ||||
\(715\) | −107.402 | −0.00561763 | ||||||||
\(716\) | 511.023 | + | 885.118i | 0.0266729 | + | 0.0461989i | ||||
\(717\) | −14430.6 | − | 24994.5i | −0.751631 | − | 1.30186i | ||||
\(718\) | 4142.57 | + | 7175.14i | 0.215319 | + | 0.372944i | ||||
\(719\) | 13293.6 | − | 23025.1i | 0.689521 | − | 1.19429i | −0.282472 | − | 0.959276i | \(-0.591154\pi\) |
0.971993 | − | 0.235010i | \(-0.0755124\pi\) | |||||||
\(720\) | −33.5560 | −0.00173689 | ||||||||
\(721\) | −781.061 | + | 1352.84i | −0.0403443 | + | 0.0698784i | ||||
\(722\) | 4572.86 | + | 7920.43i | 0.235712 | + | 0.408266i | ||||
\(723\) | 6204.95 | 0.319176 | ||||||||
\(724\) | −460.118 | − | 796.948i | −0.0236190 | − | 0.0409093i | ||||
\(725\) | 8452.38 | − | 14639.9i | 0.432984 | − | 0.749950i | ||||
\(726\) | −13685.6 | + | 23704.1i | −0.699614 | + | 1.21177i | ||||
\(727\) | 23833.0 | 1.21584 | 0.607920 | − | 0.793999i | \(-0.292004\pi\) | ||||
0.607920 | + | 0.793999i | \(0.292004\pi\) | |||||||
\(728\) | 7703.77 | − | 13343.3i | 0.392199 | − | 0.679308i | ||||
\(729\) | −31965.9 | −1.62404 | ||||||||
\(730\) | 95.1586 | 0.00482462 | ||||||||
\(731\) | 815.446 | + | 8255.57i | 0.0412590 | + | 0.417706i | ||||
\(732\) | −20208.9 | −1.02041 | ||||||||
\(733\) | 1707.21 | 0.0860261 | 0.0430130 | − | 0.999075i | \(-0.486304\pi\) | ||||
0.0430130 | + | 0.999075i | \(0.486304\pi\) | |||||||
\(734\) | 668.875 | − | 1158.52i | 0.0336357 | − | 0.0582588i | ||||
\(735\) | 121.529 | 0.00609887 | ||||||||
\(736\) | −10649.2 | + | 18445.0i | −0.533337 | + | 0.923767i | ||||
\(737\) | −4935.62 | + | 8548.75i | −0.246684 | + | 0.427269i | ||||
\(738\) | −14840.5 | − | 25704.5i | −0.740226 | − | 1.28211i | ||||
\(739\) | −17540.3 | −0.873111 | −0.436556 | − | 0.899677i | \(-0.643802\pi\) | ||||
−0.436556 | + | 0.899677i | \(0.643802\pi\) | |||||||
\(740\) | 55.9043 | + | 96.8291i | 0.00277714 | + | 0.00481015i | ||||
\(741\) | −5336.87 | + | 9243.73i | −0.264581 | + | 0.458268i | ||||
\(742\) | 12587.1 | 0.622758 | ||||||||
\(743\) | 4355.47 | − | 7543.89i | 0.215056 | − | 0.372488i | −0.738234 | − | 0.674545i | \(-0.764340\pi\) |
0.953290 | + | 0.302057i | \(0.0976733\pi\) | |||||||
\(744\) | −21608.4 | − | 37426.9i | −1.06479 | − | 1.84427i | ||||
\(745\) | −86.8924 | − | 150.502i | −0.00427314 | − | 0.00740130i | ||||
\(746\) | −1038.18 | − | 1798.18i | −0.0509525 | − | 0.0882522i | ||||
\(747\) | 1636.76 | 0.0801685 | ||||||||
\(748\) | 3484.24 | + | 6034.89i | 0.170316 | + | 0.294997i | ||||
\(749\) | 15026.9 | + | 26027.4i | 0.733072 | + | 1.26972i | ||||
\(750\) | 141.412 | − | 244.932i | 0.00688484 | − | 0.0119249i | ||||
\(751\) | −12765.5 | + | 22110.4i | −0.620264 | + | 1.07433i | 0.369172 | + | 0.929361i | \(0.379641\pi\) |
−0.989436 | + | 0.144968i | \(0.953692\pi\) | |||||||
\(752\) | −4889.56 | −0.237106 | ||||||||
\(753\) | 11001.4 | 0.532423 | ||||||||
\(754\) | 3612.50 | − | 6257.03i | 0.174482 | − | 0.302212i | ||||
\(755\) | −73.1611 | + | 126.719i | −0.00352663 | + | 0.00610830i | ||||
\(756\) | −6843.97 | − | 11854.1i | −0.329250 | − | 0.570277i | ||||
\(757\) | 18328.4 | + | 31745.8i | 0.879998 | + | 1.52420i | 0.851342 | + | 0.524612i | \(0.175790\pi\) |
0.0286563 | + | 0.999589i | \(0.490877\pi\) | |||||||
\(758\) | −10113.2 | −0.484602 | ||||||||
\(759\) | −29238.2 | − | 50642.0i | −1.39826 | − | 2.42186i | ||||
\(760\) | −38.0866 | − | 65.9680i | −0.00181782 | − | 0.00314857i | ||||
\(761\) | −7587.33 | − | 13141.6i | −0.361420 | − | 0.625998i | 0.626775 | − | 0.779200i | \(-0.284375\pi\) |
−0.988195 | + | 0.153203i | \(0.951041\pi\) | |||||||
\(762\) | −10271.6 | + | 17790.9i | −0.488321 | + | 0.845797i | ||||
\(763\) | −37204.5 | −1.76526 | ||||||||
\(764\) | 3514.59 | − | 6087.44i | 0.166431 | − | 0.288267i | ||||
\(765\) | −44.6237 | − | 77.2905i | −0.00210898 | − | 0.00365287i | ||||
\(766\) | −18019.4 | −0.849959 | ||||||||
\(767\) | 5748.51 | + | 9956.71i | 0.270621 | + | 0.468730i | ||||
\(768\) | 18241.4 | − | 31595.0i | 0.857069 | − | 1.48449i | ||||
\(769\) | 5637.67 | − | 9764.72i | 0.264369 | − | 0.457900i | −0.703029 | − | 0.711161i | \(-0.748170\pi\) |
0.967398 | + | 0.253261i | \(0.0815031\pi\) | |||||||
\(770\) | −174.243 | −0.00815492 | ||||||||
\(771\) | −18454.9 | + | 31964.9i | −0.862047 | + | 1.49311i | ||||
\(772\) | 21095.9 | 0.983493 | ||||||||
\(773\) | 7328.29 | 0.340983 | 0.170492 | − | 0.985359i | \(-0.445464\pi\) | ||||
0.170492 | + | 0.985359i | \(0.445464\pi\) | |||||||
\(774\) | 2302.08 | + | 23306.2i | 0.106908 | + | 1.08233i | ||||
\(775\) | 27255.3 | 1.26328 | ||||||||
\(776\) | 39265.1 | 1.81641 | ||||||||
\(777\) | 36337.0 | − | 62937.5i | 1.67771 | − | 2.90588i | ||||
\(778\) | −7177.06 | −0.330733 | ||||||||
\(779\) | 8192.94 | − | 14190.6i | 0.376820 | − | 0.652671i | ||||
\(780\) | −35.1703 | + | 60.9167i | −0.00161449 | + | 0.00279637i | ||||
\(781\) | −16288.2 | − | 28212.0i | −0.746272 | − | 1.29258i | ||||
\(782\) | 7172.68 | 0.327998 | ||||||||
\(783\) | −9176.12 | − | 15893.5i | −0.418809 | − | 0.725399i | ||||
\(784\) | 1142.42 | − | 1978.73i | 0.0520416 | − | 0.0901387i | ||||
\(785\) | 186.512 | 0.00848012 | ||||||||
\(786\) | 12624.3 | − | 21865.9i | 0.572892 | − | 0.992278i | ||||
\(787\) | 5754.50 | + | 9967.08i | 0.260642 | + | 0.451446i | 0.966413 | − | 0.256995i | \(-0.0827323\pi\) |
−0.705770 | + | 0.708441i | \(0.749399\pi\) | |||||||
\(788\) | 9533.16 | + | 16511.9i | 0.430971 | + | 0.746463i | ||||
\(789\) | 1260.73 | + | 2183.65i | 0.0568861 | + | 0.0985296i | ||||
\(790\) | −80.7164 | −0.00363514 | ||||||||
\(791\) | 11712.0 | + | 20285.8i | 0.526462 | + | 0.911858i | ||||
\(792\) | 28124.1 | + | 48712.5i | 1.26180 | + | 2.18551i | ||||
\(793\) | 7787.28 | − | 13488.0i | 0.348719 | − | 0.603999i | ||||
\(794\) | −4717.42 | + | 8170.81i | −0.210850 | + | 0.365203i | ||||
\(795\) | −164.302 | −0.00732982 | ||||||||
\(796\) | −4137.25 | −0.184222 | ||||||||
\(797\) | −3815.51 | + | 6608.66i | −0.169576 | + | 0.293715i | −0.938271 | − | 0.345901i | \(-0.887573\pi\) |
0.768695 | + | 0.639616i | \(0.220907\pi\) | |||||||
\(798\) | −8658.24 | + | 14996.5i | −0.384083 | + | 0.665252i | ||||
\(799\) | −6502.27 | − | 11262.3i | −0.287902 | − | 0.498661i | ||||
\(800\) | 10498.2 | + | 18183.3i | 0.463957 | + | 0.803597i | ||||
\(801\) | −16258.6 | −0.717192 | ||||||||
\(802\) | 1799.67 | + | 3117.12i | 0.0792377 | + | 0.137244i | ||||
\(803\) | −19396.2 | − | 33595.1i | −0.852398 | − | 1.47640i | ||||
\(804\) | 3232.48 | + | 5598.82i | 0.141792 | + | 0.245591i | ||||
\(805\) | 104.368 | − | 180.771i | 0.00456956 | − | 0.00791472i | ||||
\(806\) | 11648.8 | 0.509070 | ||||||||
\(807\) | 9285.30 | − | 16082.6i | 0.405028 | − | 0.701530i | ||||
\(808\) | −12093.5 | − | 20946.5i | −0.526543 | − | 0.911999i | ||||
\(809\) | 7806.54 | 0.339262 | 0.169631 | − | 0.985508i | \(-0.445742\pi\) | ||||
0.169631 | + | 0.985508i | \(0.445742\pi\) | |||||||
\(810\) | 1.98355 | + | 3.43561i | 8.60431e−5 | + | 0.000149031i | ||||
\(811\) | 10102.7 | − | 17498.3i | 0.437426 | − | 0.757644i | −0.560064 | − | 0.828449i | \(-0.689224\pi\) |
0.997490 | + | 0.0708052i | \(0.0225569\pi\) | |||||||
\(812\) | −6821.05 | + | 11814.4i | −0.294793 | + | 0.510596i | ||||
\(813\) | 1082.87 | 0.0467135 | ||||||||
\(814\) | −19581.4 | + | 33915.9i | −0.843153 | + | 1.46038i | ||||
\(815\) | 82.8905 | 0.00356261 | ||||||||
\(816\) | −2726.70 | −0.116978 | ||||||||
\(817\) | −10507.3 | + | 7533.91i | −0.449944 | + | 0.322617i | ||||
\(818\) | 3687.82 | 0.157630 | ||||||||
\(819\) | 28134.7 | 1.20037 | ||||||||
\(820\) | 53.9920 | − | 93.5169i | 0.00229937 | − | 0.00398262i | ||||
\(821\) | 9050.07 | 0.384713 | 0.192357 | − | 0.981325i | \(-0.438387\pi\) | ||||
0.192357 | + | 0.981325i | \(0.438387\pi\) | |||||||
\(822\) | 5074.86 | − | 8789.91i | 0.215336 | − | 0.372973i | ||||
\(823\) | 15775.7 | − | 27324.2i | 0.668171 | − | 1.15731i | −0.310244 | − | 0.950657i | \(-0.600411\pi\) |
0.978415 | − | 0.206649i | \(-0.0662559\pi\) | |||||||
\(824\) | −788.169 | − | 1365.15i | −0.0333218 | − | 0.0577150i | ||||
\(825\) | −57646.7 | −2.43273 | ||||||||
\(826\) | 9326.06 | + | 16153.2i | 0.392851 | + | 0.680439i | ||||
\(827\) | −12709.6 | + | 22013.7i | −0.534410 | + | 0.925625i | 0.464782 | + | 0.885425i | \(0.346133\pi\) |
−0.999192 | + | 0.0401997i | \(0.987201\pi\) | |||||||
\(828\) | −23567.1 | −0.989147 | ||||||||
\(829\) | −18258.4 | + | 31624.5i | −0.764947 | + | 1.32493i | 0.175327 | + | 0.984510i | \(0.443902\pi\) |
−0.940274 | + | 0.340417i | \(0.889432\pi\) | |||||||
\(830\) | −2.55820 | − | 4.43094i | −0.000106984 | − | 0.000185301i | ||||
\(831\) | 5054.16 | + | 8754.05i | 0.210983 | + | 0.365433i | ||||
\(832\) | 5716.21 | + | 9900.77i | 0.238190 | + | 0.412557i | ||||
\(833\) | 6076.87 | 0.252762 | ||||||||
\(834\) | −4829.08 | − | 8364.21i | −0.200500 | − | 0.347277i | ||||
\(835\) | 100.454 | + | 173.991i | 0.00416328 | + | 0.00721102i | ||||
\(836\) | −5430.30 | + | 9405.56i | −0.224654 | + | 0.389113i | ||||
\(837\) | 14794.5 | − | 25624.9i | 0.610960 | − | 1.05821i | ||||
\(838\) | 17984.3 | 0.741355 | ||||||||
\(839\) | −9085.26 | −0.373847 | −0.186924 | − | 0.982374i | \(-0.559852\pi\) | ||||
−0.186924 | + | 0.982374i | \(0.559852\pi\) | |||||||
\(840\) | −163.142 | + | 282.570i | −0.00670111 | + | 0.0116067i | ||||
\(841\) | 3049.11 | − | 5281.22i | 0.125020 | − | 0.216541i | ||||
\(842\) | −3342.66 | − | 5789.65i | −0.136812 | − | 0.236965i | ||||
\(843\) | 33270.7 | + | 57626.5i | 1.35932 | + | 2.35440i | ||||
\(844\) | 14701.4 | 0.599577 | ||||||||
\(845\) | 50.0380 | + | 86.6684i | 0.00203711 | + | 0.00352838i | ||||
\(846\) | −18356.5 | − | 31794.3i | −0.745991 | − | 1.29209i | ||||
\(847\) | 19915.0 | + | 34493.7i | 0.807894 | + | 1.39931i | ||||
\(848\) | −1544.50 | + | 2675.16i | −0.0625453 | + | 0.108332i | ||||
\(849\) | −29378.5 | −1.18760 | ||||||||
\(850\) | 3535.46 | − | 6123.60i | 0.142665 | − | 0.247103i | ||||
\(851\) | −23457.7 | − | 40630.0i | −0.944913 | − | 1.63664i | ||||
\(852\) | −21335.2 | −0.857903 | ||||||||
\(853\) | −11268.4 | − | 19517.4i | −0.452313 | − | 0.783429i | 0.546217 | − | 0.837644i | \(-0.316068\pi\) |
−0.998529 | + | 0.0542154i | \(0.982734\pi\) | |||||||
\(854\) | 12633.7 | − | 21882.1i | 0.506223 | − | 0.876804i | ||||
\(855\) | 69.5474 | − | 120.460i | 0.00278184 | − | 0.00481828i | ||||
\(856\) | −30327.3 | −1.21094 | ||||||||
\(857\) | 13650.0 | − | 23642.6i | 0.544080 | − | 0.942375i | −0.454584 | − | 0.890704i | \(-0.650212\pi\) |
0.998664 | − | 0.0516708i | \(-0.0164547\pi\) | |||||||
\(858\) | −24637.9 | −0.980331 | ||||||||
\(859\) | 2423.33 | 0.0962549 | 0.0481275 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481275 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(860\) | −69.2439 | + | 49.6489i | −0.00274558 | + | 0.00196862i | ||||
\(861\) | −70188.0 | −2.77817 | ||||||||
\(862\) | −9307.86 | −0.367781 | ||||||||
\(863\) | −429.835 | + | 744.497i | −0.0169545 | + | 0.0293661i | −0.874378 | − | 0.485245i | \(-0.838730\pi\) |
0.857424 | + | 0.514611i | \(0.172064\pi\) | |||||||
\(864\) | 22794.1 | 0.897537 | ||||||||
\(865\) | 11.0626 | − | 19.1609i | 0.000434842 | − | 0.000753168i | ||||
\(866\) | −11144.0 | + | 19302.1i | −0.437287 | + | 0.757403i | ||||
\(867\) | 16955.3 | + | 29367.5i | 0.664167 | + | 1.15037i | ||||
\(868\) | −21995.0 | −0.860089 | ||||||||
\(869\) | 16452.4 | + | 28496.4i | 0.642244 | + | 1.11240i | ||||
\(870\) | −76.5015 | + | 132.505i | −0.00298120 | + | 0.00516359i | ||||
\(871\) | −4982.40 | −0.193826 | ||||||||
\(872\) | 18771.5 | − | 32513.2i | 0.728996 | − | 1.26266i | ||||
\(873\) | 35849.7 | + | 62093.5i | 1.38984 | + | 2.40727i | ||||
\(874\) | 5589.42 | + | 9681.17i | 0.216322 | + | 0.374680i | ||||
\(875\) | −205.779 | − | 356.420i | −0.00795041 | − | 0.0137705i | ||||
\(876\) | −25406.2 | −0.979903 | ||||||||
\(877\) | 8783.41 | + | 15213.3i | 0.338192 | + | 0.585766i | 0.984093 | − | 0.177655i | \(-0.0568512\pi\) |
−0.645900 | + | 0.763422i | \(0.723518\pi\) | |||||||
\(878\) | 4304.85 | + | 7456.21i | 0.165469 | + | 0.286600i | ||||
\(879\) | −22704.9 | + | 39326.1i | −0.871238 | + | 1.50903i | ||||
\(880\) | 21.3806 | − | 37.0322i | 0.000819021 | − | 0.00141859i | ||||
\(881\) | −25664.9 | −0.981469 | −0.490734 | − | 0.871309i | \(-0.663271\pi\) | ||||
−0.490734 | + | 0.871309i | \(0.663271\pi\) | |||||||
\(882\) | 17155.5 | 0.654940 | ||||||||
\(883\) | 19408.6 | − | 33616.7i | 0.739695 | − | 1.28119i | −0.212937 | − | 0.977066i | \(-0.568303\pi\) |
0.952632 | − | 0.304124i | \(-0.0983637\pi\) | |||||||
\(884\) | −1758.63 | + | 3046.04i | −0.0669109 | + | 0.115893i | ||||
\(885\) | −121.736 | − | 210.852i | −0.00462384 | − | 0.00800872i | ||||
\(886\) | −4247.85 | − | 7357.48i | −0.161071 | − | 0.278984i | ||||
\(887\) | 19118.6 | 0.723721 | 0.361861 | − | 0.932232i | \(-0.382142\pi\) | ||||
0.361861 | + | 0.932232i | \(0.382142\pi\) | |||||||
\(888\) | 36667.6 | + | 63510.2i | 1.38568 | + | 2.40007i | ||||
\(889\) | 14947.0 | + | 25889.0i | 0.563899 | + | 0.976702i | ||||
\(890\) | 25.4118 | + | 44.0144i | 0.000957083 | + | 0.00165772i | ||||
\(891\) | 808.614 | − | 1400.56i | 0.0304036 | − | 0.0526606i | ||||
\(892\) | −17320.9 | −0.650164 | ||||||||
\(893\) | 10134.0 | − | 17552.6i | 0.379754 | − | 0.657754i | ||||
\(894\) | −19933.0 | − | 34525.0i | −0.745705 | − | 1.29160i | ||||
\(895\) | 16.6804 | 0.000622975 | ||||||||
\(896\) | −6477.54 | − | 11219.4i | −0.241517 | − | 0.418320i | ||||
\(897\) | 14757.6 | − | 25561.0i | 0.549323 | − | 0.951456i | ||||
\(898\) | 10613.4 | − | 18383.0i | 0.394404 | − | 0.683127i | ||||
\(899\) | −29490.0 | −1.09404 | ||||||||
\(900\) | −11616.4 | + | 20120.2i | −0.430236 | + | 0.745191i | ||||
\(901\) | −8215.68 | −0.303778 | ||||||||
\(902\) | 37823.1 | 1.39620 | ||||||||
\(903\) | 50451.3 | + | 22842.1i | 1.85926 | + | 0.841791i | ||||
\(904\) | −23637.2 | −0.869647 | ||||||||
\(905\) | −15.0188 | −0.000551647 | ||||||||
\(906\) | −16783.1 | + | 29069.1i | −0.615431 | + | 1.06596i | ||||
\(907\) | −9172.98 | −0.335814 | −0.167907 | − | 0.985803i | \(-0.553701\pi\) | ||||
−0.167907 | + | 0.985803i | \(0.553701\pi\) | |||||||
\(908\) | −5817.41 | + | 10076.1i | −0.212618 | + | 0.368266i | ||||
\(909\) | 22083.1 | − | 38249.0i | 0.805774 | − | 1.39564i | ||||
\(910\) | −43.9736 | − | 76.1645i | −0.00160188 | − | 0.00277454i | ||||
\(911\) | 18316.9 | 0.666154 | 0.333077 | − | 0.942900i | \(-0.391913\pi\) | ||||
0.333077 | + | 0.942900i | \(0.391913\pi\) | |||||||
\(912\) | −2124.82 | − | 3680.30i | −0.0771491 | − | 0.133626i | ||||
\(913\) | −1042.88 | + | 1806.31i | −0.0378030 | + | 0.0654768i | ||||
\(914\) | −24265.0 | −0.878134 | ||||||||
\(915\) | −164.910 | + | 285.633i | −0.00595821 | + | 0.0103199i | ||||
\(916\) | 6188.23 | + | 10718.3i | 0.223215 | + | 0.386620i | ||||
\(917\) | −18370.6 | − | 31818.8i | −0.661559 | − | 1.14585i | ||||
\(918\) | −3838.19 | − | 6647.94i | −0.137995 | − | 0.239014i | ||||
\(919\) | 23462.4 | 0.842168 | 0.421084 | − | 0.907022i | \(-0.361650\pi\) | ||||
0.421084 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(920\) | 105.318 | + | 182.416i | 0.00377417 | + | 0.00653705i | ||||
\(921\) | −24113.5 | − | 41765.8i | −0.862721 | − | 1.49428i | ||||
\(922\) | 6599.92 | − | 11431.4i | 0.235745 | − | 0.408322i | ||||
\(923\) | 8221.30 | − | 14239.7i | 0.293182 | − | 0.507807i | ||||
\(924\) | 46520.8 | 1.65630 | ||||||||
\(925\) | −46249.9 | −1.64399 | ||||||||
\(926\) | 283.580 | − | 491.174i | 0.0100637 | − | 0.0174309i | ||||
\(927\) | 1439.22 | − | 2492.80i | 0.0509927 | − | 0.0883219i | ||||
\(928\) | −11358.9 | − | 19674.2i | −0.401804 | − | 0.695945i | ||||
\(929\) | 19668.8 | + | 34067.4i | 0.694631 | + | 1.20314i | 0.970305 | + | 0.241885i | \(0.0777657\pi\) |
−0.275674 | + | 0.961251i | \(0.588901\pi\) | |||||||
\(930\) | −246.685 | −0.00869796 | ||||||||
\(931\) | 4735.49 | + | 8202.11i | 0.166702 | + | 0.288736i | ||||
\(932\) | −2875.68 | − | 4980.82i | −0.101069 | − | 0.175056i | ||||
\(933\) | 2051.47 | + | 3553.25i | 0.0719851 | + | 0.124682i | ||||
\(934\) | 5382.52 | − | 9322.80i | 0.188567 | − | 0.326607i | ||||
\(935\) | 113.730 | 0.00397792 | ||||||||
\(936\) | −14195.3 | + | 24587.1i | −0.495715 | + | 0.858604i | ||||
\(937\) | −20538.7 | − | 35574.0i | −0.716082 | − | 1.24029i | −0.962541 | − | 0.271137i | \(-0.912600\pi\) |
0.246459 | − | 0.969153i | \(-0.420733\pi\) | |||||||
\(938\) | −8083.17 | −0.281370 | ||||||||
\(939\) | 33838.9 | + | 58610.6i | 1.17603 | + | 2.03694i | ||||
\(940\) | 66.7836 | − | 115.673i | 0.00231728 | − | 0.00401364i | ||||
\(941\) | 19244.2 | − | 33331.9i | 0.666675 | − | 1.15472i | −0.312153 | − | 0.950032i | \(-0.601050\pi\) |
0.978828 | − | 0.204684i | \(-0.0656166\pi\) | |||||||
\(942\) | 42785.6 | 1.47986 | ||||||||
\(943\) | −22655.3 | + | 39240.2i | −0.782353 | + | 1.35507i | ||||
\(944\) | −4577.43 | −0.157821 | ||||||||
\(945\) | −223.395 | −0.00768998 | ||||||||
\(946\) | −27187.3 | − | 12309.2i | −0.934394 | − | 0.423052i | ||||
\(947\) | 24162.6 | 0.829122 | 0.414561 | − | 0.910022i | \(-0.363935\pi\) | ||||
0.414561 | + | 0.910022i | \(0.363935\pi\) | |||||||
\(948\) | 21550.3 | 0.738313 | ||||||||
\(949\) | 9789.99 | − | 16956.8i | 0.334875 | − | 0.580021i | ||||
\(950\) | 11020.3 | 0.376362 | ||||||||
\(951\) | 18432.9 | − | 31926.7i | 0.628525 | − | 1.08864i | ||||
\(952\) | −8157.64 | + | 14129.5i | −0.277721 | + | 0.481028i | ||||
\(953\) | −12928.6 | − | 22393.0i | −0.439453 | − | 0.761155i | 0.558194 | − | 0.829710i | \(-0.311494\pi\) |
−0.997647 | + | 0.0685550i | \(0.978161\pi\) | |||||||
\(954\) | −23193.6 | −0.787128 | ||||||||
\(955\) | −57.3600 | − | 99.3504i | −0.00194359 | − | 0.00336639i | ||||
\(956\) | 7411.18 | − | 12836.5i | 0.250727 | − | 0.434271i | ||||
\(957\) | 62373.2 | 2.10683 | ||||||||
\(958\) | −6126.74 | + | 10611.8i | −0.206624 | + | 0.357884i | ||||
\(959\) | −7384.82 | − | 12790.9i | −0.248664 | − | 0.430698i | ||||
\(960\) | −121.052 | − | 209.668i | −0.00406971 | − | 0.00704895i | ||||
\(961\) | −8877.62 | − | 15376.5i | −0.297997 | − | 0.516145i | ||||
\(962\) | −19766.9 | −0.662487 | ||||||||
\(963\) | −27689.3 | − | 47959.3i | −0.926558 | − | 1.60485i | ||||
\(964\) | 1593.35 | + | 2759.77i | 0.0532350 | + | 0.0922057i | ||||
\(965\) | 172.148 | − | 298.169i | 0.00574264 | − | 0.00994654i | ||||
\(966\) | 23942.0 | − | 41468.7i | 0.797433 | − | 1.38119i | ||||
\(967\) | −42638.6 | −1.41796 | −0.708979 | − | 0.705230i | \(-0.750844\pi\) | ||||
−0.708979 | + | 0.705230i | \(0.750844\pi\) | |||||||
\(968\) | −40192.4 | −1.33454 | ||||||||
\(969\) | 5651.29 | − | 9788.33i | 0.187354 | − | 0.324506i | ||||
\(970\) | 112.064 | − | 194.100i | 0.00370944 | − | 0.00642494i | ||||
\(971\) | 24599.3 | + | 42607.3i | 0.813007 | + | 1.40817i | 0.910750 | + | 0.412958i | \(0.135504\pi\) |
−0.0977432 | + | 0.995212i | \(0.531162\pi\) | |||||||
\(972\) | −8412.16 | − | 14570.3i | −0.277593 | − | 0.480805i | ||||
\(973\) | −14054.3 | −0.463064 | ||||||||
\(974\) | 15350.2 | + | 26587.3i | 0.504981 | + | 0.874653i | ||||
\(975\) | −14548.3 | − | 25198.3i | −0.477864 | − | 0.827685i | ||||
\(976\) | 3100.43 | + | 5370.11i | 0.101683 | + | 0.176120i | ||||
\(977\) | −21000.7 | + | 36374.3i | −0.687688 | + | 1.19111i | 0.284895 | + | 0.958559i | \(0.408041\pi\) |
−0.972584 | + | 0.232553i | \(0.925292\pi\) | |||||||
\(978\) | 19015.0 | 0.621710 | ||||||||
\(979\) | 10359.3 | − | 17942.9i | 0.338188 | − | 0.585759i | ||||
\(980\) | 31.2072 | + | 54.0524i | 0.00101722 | + | 0.00176188i | ||||
\(981\) | 68554.8 | 2.23118 | ||||||||
\(982\) | −11002.3 | − | 19056.5i | −0.357531 | − | 0.619263i | ||||
\(983\) | −11537.6 | + | 19983.7i | −0.374356 | + | 0.648403i | −0.990230 | − | 0.139441i | \(-0.955469\pi\) |
0.615875 | + | 0.787844i | \(0.288803\pi\) | |||||||
\(984\) | 35413.4 | − | 61337.7i | 1.14729 | − | 1.98717i | ||||
\(985\) | 311.173 | 0.0100658 | ||||||||
\(986\) | −3825.33 | + | 6625.67i | −0.123553 | + | 0.214000i | ||||
\(987\) | −86816.7 | −2.79980 | ||||||||
\(988\) | −5481.77 | −0.176516 | ||||||||
\(989\) | 29055.1 | − | 20832.9i | 0.934174 | − | 0.669817i | ||||
\(990\) | 321.069 | 0.0103073 | ||||||||
\(991\) | −23753.3 | −0.761401 | −0.380701 | − | 0.924698i | \(-0.624317\pi\) | ||||
−0.380701 | + | 0.924698i | \(0.624317\pi\) | |||||||
\(992\) | 18313.8 | − | 31720.4i | 0.586152 | − | 1.01525i | ||||
\(993\) | −75257.3 | −2.40505 | ||||||||
\(994\) | 13337.8 | − | 23101.7i | 0.425602 | − | 0.737165i | ||||
\(995\) | −33.7611 | + | 58.4760i | −0.00107568 | + | 0.00186313i | ||||
\(996\) | 683.009 | + | 1183.01i | 0.0217289 | + | 0.0376355i | ||||
\(997\) | −881.578 | −0.0280039 | −0.0140019 | − | 0.999902i | \(-0.504457\pi\) | ||||
−0.0140019 | + | 0.999902i | \(0.504457\pi\) | |||||||
\(998\) | −1327.46 | − | 2299.23i | −0.0421043 | − | 0.0729267i | ||||
\(999\) | −25105.0 | + | 43483.2i | −0.795083 | + | 1.37712i |
(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 | 43.4.c.a.6.7 | ✓ | 20 | |
43.6 | even | 3 | 1849.4.a.d.1.7 | 10 | |||
43.36 | even | 3 | inner | 43.4.c.a.36.7 | yes | 20 | |
43.37 | odd | 6 | 1849.4.a.f.1.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.c.a.6.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
43.4.c.a.36.7 | yes | 20 | 43.36 | even | 3 | inner | |
1849.4.a.d.1.7 | 10 | 43.6 | even | 3 | |||
1849.4.a.f.1.4 | 10 | 43.37 | odd | 6 |