Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,3,Mod(46,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.46");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.65941252056\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.19163381760000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 177x^{4} - 266x^{2} + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(-3.05907 + 1.76616i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 171.145 |
Dual form | 171.3.p.f.46.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.05907 | + | 1.76616i | −1.52954 | + | 0.883078i | −0.530155 | + | 0.847901i | \(0.677866\pi\) |
−0.999381 | + | 0.0351770i | \(0.988801\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.23861 | − | 7.34149i | 1.05965 | − | 1.83537i | ||||
\(5\) | 0.533068 | + | 0.923301i | 0.106614 | + | 0.184660i | 0.914396 | − | 0.404820i | \(-0.132666\pi\) |
−0.807783 | + | 0.589480i | \(0.799333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.477226 | 0.0681751 | 0.0340875 | − | 0.999419i | \(-0.489147\pi\) | ||||
0.0340875 | + | 0.999419i | \(0.489147\pi\) | |||||||
\(8\) | 15.8150i | 1.97687i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.26139 | − | 1.88296i | −0.326139 | − | 0.188296i | ||||
\(11\) | −11.1702 | −1.01547 | −0.507734 | − | 0.861514i | \(-0.669517\pi\) | ||||
−0.507734 | + | 0.861514i | \(0.669517\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.9772 | − | 7.49240i | −0.998248 | − | 0.576339i | −0.0905186 | − | 0.995895i | \(-0.528852\pi\) |
−0.907729 | + | 0.419556i | \(0.862186\pi\) | |||||||
\(14\) | −1.45987 | + | 0.842855i | −0.104276 | + | 0.0602039i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −10.9772 | − | 19.0131i | −0.686077 | − | 1.18832i | ||||
\(17\) | −6.11814 | − | 10.5969i | −0.359891 | − | 0.623349i | 0.628051 | − | 0.778172i | \(-0.283853\pi\) |
−0.987942 | + | 0.154823i | \(0.950519\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.52277 | + | 17.8453i | −0.343304 | + | 0.939224i | ||||
\(20\) | 9.03788 | 0.451894 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 34.1703 | − | 19.7282i | 1.55319 | − | 0.896738i | ||||
\(23\) | 20.7411 | − | 35.9246i | 0.901787 | − | 1.56194i | 0.0766135 | − | 0.997061i | \(-0.475589\pi\) |
0.825173 | − | 0.564880i | \(-0.191077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.9317 | − | 20.6663i | 0.477267 | − | 0.826651i | ||||
\(26\) | 52.9310 | 2.03581 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.02277 | − | 3.50355i | 0.0722419 | − | 0.125127i | ||||
\(29\) | −30.5907 | − | 17.6616i | −1.05485 | − | 0.609019i | −0.130848 | − | 0.991402i | \(-0.541770\pi\) |
−0.924004 | + | 0.382383i | \(0.875103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 15.8903i | − | 0.512590i | −0.966599 | − | 0.256295i | \(-0.917498\pi\) | ||
0.966599 | − | 0.256295i | \(-0.0825018\pi\) | |||||||
\(32\) | 12.3756 | + | 7.14507i | 0.386738 | + | 0.223283i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 37.4317 | + | 21.6112i | 1.10093 | + | 0.635623i | ||||
\(35\) | 0.254394 | + | 0.440623i | 0.00726839 | + | 0.0125892i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24.3276i | 0.657503i | 0.944416 | + | 0.328751i | \(0.106628\pi\) | ||||
−0.944416 | + | 0.328751i | \(0.893372\pi\) | |||||||
\(38\) | −11.5639 | − | 66.1102i | −0.304313 | − | 1.73974i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −14.6020 | + | 8.43045i | −0.365049 | + | 0.210761i | ||||
\(41\) | −5.83947 | + | 3.37142i | −0.142426 | + | 0.0822297i | −0.569520 | − | 0.821978i | \(-0.692871\pi\) |
0.427094 | + | 0.904207i | \(0.359537\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.6703 | − | 54.8546i | −0.736518 | − | 1.27569i | −0.954054 | − | 0.299635i | \(-0.903135\pi\) |
0.217536 | − | 0.976052i | \(-0.430198\pi\) | |||||||
\(44\) | −47.3459 | + | 82.0056i | −1.07604 | + | 1.86376i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 146.528i | 3.18539i | ||||||||
\(47\) | 20.2080 | − | 35.0013i | 0.429958 | − | 0.744709i | −0.566911 | − | 0.823779i | \(-0.691862\pi\) |
0.996869 | + | 0.0790699i | \(0.0251950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.7723 | −0.995352 | ||||||||
\(50\) | 84.2928i | 1.68586i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −110.011 | + | 63.5148i | −2.11559 | + | 1.22144i | ||||
\(53\) | 26.3505 | + | 15.2134i | 0.497178 | + | 0.287046i | 0.727548 | − | 0.686057i | \(-0.240660\pi\) |
−0.230369 | + | 0.973103i | \(0.573993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.95445 | − | 10.3134i | −0.108263 | − | 0.187517i | ||||
\(56\) | 7.54730i | 0.134773i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 124.772 | 2.15125 | ||||||||
\(59\) | −69.1775 | + | 39.9396i | −1.17250 | + | 0.676943i | −0.954267 | − | 0.298954i | \(-0.903362\pi\) |
−0.218232 | + | 0.975897i | \(0.570029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35.8861 | + | 62.1566i | −0.588297 | + | 1.01896i | 0.406158 | + | 0.913803i | \(0.366868\pi\) |
−0.994456 | + | 0.105158i | \(0.966465\pi\) | |||||||
\(62\) | 28.0647 | + | 48.6095i | 0.452657 | + | 0.784024i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 37.3406 | 0.583447 | ||||||||
\(65\) | − | 15.9758i | − | 0.245782i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.62474 | + | 4.40215i | 0.113802 | + | 0.0657037i | 0.555821 | − | 0.831302i | \(-0.312404\pi\) |
−0.442019 | + | 0.897006i | \(0.645737\pi\) | |||||||
\(68\) | −103.730 | −1.52544 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.55642 | − | 0.898598i | −0.0222345 | − | 0.0128371i | ||||
\(71\) | −42.2697 | + | 24.4044i | −0.595347 | + | 0.343724i | −0.767209 | − | 0.641397i | \(-0.778355\pi\) |
0.171862 | + | 0.985121i | \(0.445022\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −56.7950 | − | 98.3719i | −0.778014 | − | 1.34756i | −0.933085 | − | 0.359657i | \(-0.882894\pi\) |
0.155071 | − | 0.987903i | \(-0.450439\pi\) | |||||||
\(74\) | −42.9663 | − | 74.4199i | −0.580626 | − | 1.00567i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 103.363 | + | 123.526i | 1.36004 | + | 1.62534i | ||||
\(77\) | −5.33068 | −0.0692296 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 104.534 | − | 60.3525i | 1.32321 | − | 0.763956i | 0.338971 | − | 0.940797i | \(-0.389921\pi\) |
0.984239 | + | 0.176841i | \(0.0565877\pi\) | |||||||
\(80\) | 11.7032 | − | 20.2706i | 0.146290 | − | 0.253382i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.9089 | − | 20.6268i | 0.145231 | − | 0.251547i | ||||
\(83\) | 65.4460 | 0.788506 | 0.394253 | − | 0.919002i | \(-0.371003\pi\) | ||||
0.394253 | + | 0.919002i | \(0.371003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.52277 | − | 11.2978i | 0.0767385 | − | 0.132915i | ||||
\(86\) | 193.763 | + | 111.869i | 2.25306 | + | 1.30081i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 176.655i | − | 2.00745i | ||||||
\(89\) | 133.279 | + | 76.9484i | 1.49751 | + | 0.864589i | 0.999996 | − | 0.00286509i | \(-0.000911989\pi\) |
0.497517 | + | 0.867454i | \(0.334245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.19306 | − | 3.57557i | −0.0680556 | − | 0.0392919i | ||||
\(92\) | −175.827 | − | 304.541i | −1.91116 | − | 3.31023i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 142.762i | 1.51875i | ||||||||
\(95\) | −19.9536 | + | 3.49026i | −0.210038 | + | 0.0367395i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −83.0911 | + | 47.9727i | −0.856609 | + | 0.494564i | −0.862875 | − | 0.505417i | \(-0.831339\pi\) |
0.00626610 | + | 0.999980i | \(0.498005\pi\) | |||||||
\(98\) | 149.198 | − | 86.1394i | 1.52243 | − | 0.878974i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −101.148 | − | 175.193i | −1.01148 | − | 1.75193i | ||||
\(101\) | −13.5811 | + | 23.5232i | −0.134466 | + | 0.232902i | −0.925393 | − | 0.379008i | \(-0.876265\pi\) |
0.790927 | + | 0.611910i | \(0.209599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 43.4453i | 0.421799i | 0.977508 | + | 0.210900i | \(0.0676393\pi\) | ||||
−0.977508 | + | 0.210900i | \(0.932361\pi\) | |||||||
\(104\) | 118.492 | − | 205.234i | 1.13935 | − | 1.97341i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −107.477 | −1.01394 | ||||||||
\(107\) | 35.9667i | 0.336137i | 0.985775 | + | 0.168069i | \(0.0537530\pi\) | ||||
−0.985775 | + | 0.168069i | \(0.946247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −70.0455 | + | 40.4408i | −0.642620 | + | 0.371017i | −0.785623 | − | 0.618706i | \(-0.787657\pi\) |
0.143003 | + | 0.989722i | \(0.454324\pi\) | |||||||
\(110\) | 36.4302 | + | 21.0330i | 0.331184 | + | 0.191209i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.23861 | − | 9.07354i | −0.0467733 | − | 0.0810138i | ||||
\(113\) | − | 19.9908i | − | 0.176910i | −0.996080 | − | 0.0884550i | \(-0.971807\pi\) | ||
0.996080 | − | 0.0884550i | \(-0.0281930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 44.2257 | 0.384571 | ||||||||
\(116\) | −259.324 | + | 149.721i | −2.23556 | + | 1.29070i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 141.079 | − | 244.356i | 1.19559 | − | 2.07082i | ||||
\(119\) | −2.91973 | − | 5.05713i | −0.0245356 | − | 0.0424969i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.77226 | 0.0311757 | ||||||||
\(122\) | − | 253.522i | − | 2.07805i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −116.658 | − | 67.3527i | −0.940793 | − | 0.543167i | ||||
\(125\) | 52.0950 | 0.416760 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −35.7267 | − | 20.6268i | −0.281313 | − | 0.162416i | 0.352705 | − | 0.935735i | \(-0.385262\pi\) |
−0.634018 | + | 0.773319i | \(0.718595\pi\) | |||||||
\(128\) | −163.730 | + | 94.5296i | −1.27914 | + | 0.738512i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 28.2158 | + | 48.8713i | 0.217045 | + | 0.375933i | ||||
\(131\) | 102.942 | + | 178.301i | 0.785819 | + | 1.36108i | 0.928509 | + | 0.371311i | \(0.121092\pi\) |
−0.142689 | + | 0.989768i | \(0.545575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.11283 | + | 8.51622i | −0.0234048 | + | 0.0640317i | ||||
\(134\) | −31.0995 | −0.232086 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 167.590 | − | 96.7582i | 1.23228 | − | 0.711457i | ||||
\(137\) | −90.1487 | + | 156.142i | −0.658019 | + | 1.13972i | 0.323108 | + | 0.946362i | \(0.395272\pi\) |
−0.981128 | + | 0.193361i | \(0.938061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 35.8525 | − | 62.0983i | 0.257932 | − | 0.446751i | −0.707756 | − | 0.706457i | \(-0.750292\pi\) |
0.965688 | + | 0.259706i | \(0.0836258\pi\) | |||||||
\(140\) | 4.31311 | 0.0308079 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 86.2039 | − | 149.310i | 0.607070 | − | 1.05148i | ||||
\(143\) | 144.958 | + | 83.6913i | 1.01369 | + | 0.585254i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 37.6593i | − | 0.259719i | ||||||
\(146\) | 347.480 | + | 200.618i | 2.38000 | + | 1.37409i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 178.601 | + | 103.115i | 1.20676 | + | 0.696725i | ||||
\(149\) | −109.036 | − | 188.856i | −0.731786 | − | 1.26749i | −0.956119 | − | 0.292978i | \(-0.905354\pi\) |
0.224333 | − | 0.974513i | \(-0.427980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 26.1899i | − | 0.173443i | −0.996233 | − | 0.0867217i | \(-0.972361\pi\) | ||
0.996233 | − | 0.0867217i | \(-0.0276391\pi\) | |||||||
\(152\) | −282.222 | − | 103.157i | −1.85672 | − | 0.678667i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.3069 | − | 9.41481i | 0.105889 | − | 0.0611352i | ||||
\(155\) | 14.6715 | − | 8.47060i | 0.0946549 | − | 0.0546490i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 59.8861 | + | 103.726i | 0.381440 | + | 0.660674i | 0.991268 | − | 0.131860i | \(-0.0420948\pi\) |
−0.609828 | + | 0.792534i | \(0.708762\pi\) | |||||||
\(158\) | −213.184 | + | 369.245i | −1.34927 | + | 2.33700i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.2352i | 0.0952202i | ||||||||
\(161\) | 9.89818 | − | 17.1442i | 0.0614794 | − | 0.106485i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 252.885 | 1.55144 | 0.775721 | − | 0.631076i | \(-0.217386\pi\) | ||||
0.775721 | + | 0.631076i | \(0.217386\pi\) | |||||||
\(164\) | 57.1606i | 0.348540i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −200.204 | + | 115.588i | −1.20605 | + | 0.696312i | ||||
\(167\) | −163.312 | − | 94.2882i | −0.977916 | − | 0.564600i | −0.0762758 | − | 0.997087i | \(-0.524303\pi\) |
−0.901640 | + | 0.432487i | \(0.857636\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.7723 | + | 48.1030i | 0.164333 | + | 0.284633i | ||||
\(170\) | 46.0809i | 0.271064i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −536.952 | −3.12182 | ||||||||
\(173\) | −168.946 | + | 97.5408i | −0.976564 | + | 0.563820i | −0.901231 | − | 0.433339i | \(-0.857335\pi\) |
−0.0753332 | + | 0.997158i | \(0.524002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.69410 | − | 9.86247i | 0.0325377 | − | 0.0563570i | ||||
\(176\) | 122.617 | + | 212.379i | 0.696689 | + | 1.20670i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −543.612 | −3.05400 | ||||||||
\(179\) | − | 170.754i | − | 0.953933i | −0.878921 | − | 0.476966i | \(-0.841736\pi\) | ||
0.878921 | − | 0.476966i | \(-0.158264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70497 | + | 0.984365i | 0.00941972 | + | 0.00543848i | 0.504702 | − | 0.863293i | \(-0.331602\pi\) |
−0.495283 | + | 0.868732i | \(0.664936\pi\) | |||||||
\(182\) | 25.2600 | 0.138791 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 568.146 | + | 328.020i | 3.08775 | + | 1.78271i | ||||
\(185\) | −22.4617 | + | 12.9683i | −0.121415 | + | 0.0700988i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 68.3406 | + | 118.369i | 0.365458 | + | 0.632991i | ||||
\(188\) | −171.308 | − | 296.714i | −0.911213 | − | 1.57827i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 54.8753 | − | 45.9182i | 0.288817 | − | 0.241675i | ||||
\(191\) | −12.1877 | −0.0638101 | −0.0319050 | − | 0.999491i | \(-0.510157\pi\) | ||||
−0.0319050 | + | 0.999491i | \(0.510157\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −245.884 | + | 141.961i | −1.27401 | + | 0.735550i | −0.975740 | − | 0.218931i | \(-0.929743\pi\) |
−0.298270 | + | 0.954481i | \(0.596410\pi\) | |||||||
\(194\) | 169.454 | − | 293.504i | 0.873476 | − | 1.51291i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −206.727 | + | 358.061i | −1.05473 | + | 1.82684i | ||||
\(197\) | 306.876 | 1.55775 | 0.778874 | − | 0.627181i | \(-0.215791\pi\) | ||||
0.778874 | + | 0.627181i | \(0.215791\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −76.7376 | + | 132.913i | −0.385616 | + | 0.667906i | −0.991854 | − | 0.127376i | \(-0.959344\pi\) |
0.606238 | + | 0.795283i | \(0.292678\pi\) | |||||||
\(200\) | 326.836 | + | 188.699i | 1.63418 | + | 0.943495i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 95.9453i | − | 0.474977i | ||||||
\(203\) | −14.5987 | − | 8.42855i | −0.0719146 | − | 0.0415199i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.22567 | − | 3.59439i | −0.0303691 | − | 0.0175336i | ||||
\(206\) | −76.7312 | − | 132.902i | −0.372481 | − | 0.645157i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 328.983i | 1.58165i | ||||||||
\(209\) | 72.8604 | − | 199.334i | 0.348614 | − | 0.953752i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 238.078 | − | 137.454i | 1.12833 | − | 0.651443i | 0.184817 | − | 0.982773i | \(-0.440831\pi\) |
0.943515 | + | 0.331330i | \(0.107497\pi\) | |||||||
\(212\) | 223.379 | − | 128.968i | 1.05367 | − | 0.608339i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −63.5228 | − | 110.025i | −0.296835 | − | 0.514134i | ||||
\(215\) | 33.7648 | − | 58.4824i | 0.157046 | − | 0.272011i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 7.58325i | − | 0.0349458i | ||||||
\(218\) | 142.850 | − | 247.423i | 0.655273 | − | 1.13497i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −100.954 | −0.458884 | ||||||||
\(221\) | 183.358i | 0.829676i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 347.646 | − | 200.714i | 1.55895 | − | 0.900062i | 0.561595 | − | 0.827412i | \(-0.310188\pi\) |
0.997358 | − | 0.0726498i | \(-0.0231455\pi\) | |||||||
\(224\) | 5.90596 | + | 3.40981i | 0.0263659 | + | 0.0152224i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 35.3069 | + | 61.1534i | 0.156225 | + | 0.270590i | ||||
\(227\) | − | 338.864i | − | 1.49279i | −0.665501 | − | 0.746397i | \(-0.731782\pi\) | ||
0.665501 | − | 0.746397i | \(-0.268218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −222.453 | −0.971412 | −0.485706 | − | 0.874122i | \(-0.661437\pi\) | ||||
−0.485706 | + | 0.874122i | \(0.661437\pi\) | |||||||
\(230\) | −135.289 | + | 78.1094i | −0.588215 | + | 0.339606i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 279.317 | − | 483.791i | 1.20395 | − | 2.08531i | ||||
\(233\) | −116.802 | − | 202.307i | −0.501296 | − | 0.868271i | −0.999999 | − | 0.00149765i | \(-0.999523\pi\) |
0.498702 | − | 0.866773i | \(-0.333810\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 43.0890 | 0.183358 | ||||||||
\(236\) | 677.154i | 2.86930i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.8634 | + | 10.3134i | 0.0750561 | + | 0.0433337i | ||||
\(239\) | −322.917 | −1.35112 | −0.675558 | − | 0.737307i | \(-0.736097\pi\) | ||||
−0.675558 | + | 0.737307i | \(0.736097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 201.841 | + | 116.533i | 0.837513 | + | 0.483538i | 0.856418 | − | 0.516283i | \(-0.172685\pi\) |
−0.0189052 | + | 0.999821i | \(0.506018\pi\) | |||||||
\(242\) | −11.5396 | + | 6.66239i | −0.0476843 | + | 0.0275305i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 304.215 | + | 526.915i | 1.24678 | + | 2.15949i | ||||
\(245\) | −25.9989 | − | 45.0315i | −0.106118 | − | 0.183802i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 218.351 | − | 182.711i | 0.884014 | − | 0.739720i | ||||
\(248\) | 251.304 | 1.01332 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −159.362 | + | 92.0079i | −0.637449 | + | 0.368032i | ||||
\(251\) | 134.042 | − | 232.167i | 0.534031 | − | 0.924969i | −0.465178 | − | 0.885217i | \(-0.654010\pi\) |
0.999210 | − | 0.0397521i | \(-0.0126568\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −231.681 | + | 401.284i | −0.915736 | + | 1.58610i | ||||
\(254\) | 145.721 | 0.573704 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 259.227 | − | 448.994i | 1.01260 | − | 1.75388i | ||||
\(257\) | −414.568 | − | 239.351i | −1.61310 | − | 0.931326i | −0.988645 | − | 0.150267i | \(-0.951987\pi\) |
−0.624458 | − | 0.781059i | \(-0.714680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6098i | 0.0448253i | ||||||||
\(260\) | −117.287 | − | 67.7154i | −0.451102 | − | 0.260444i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −629.816 | − | 363.624i | −2.40388 | − | 1.38788i | ||||
\(263\) | 133.812 | + | 231.769i | 0.508790 | + | 0.881250i | 0.999948 | + | 0.0101794i | \(0.00324025\pi\) |
−0.491158 | + | 0.871070i | \(0.663426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.4392i | 0.122412i | ||||||||
\(266\) | −5.51858 | − | 31.5495i | −0.0207465 | − | 0.118607i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 64.6366 | − | 37.3180i | 0.241182 | − | 0.139246i | ||||
\(269\) | −16.7552 | + | 9.67363i | −0.0622871 | + | 0.0359615i | −0.530820 | − | 0.847485i | \(-0.678116\pi\) |
0.468533 | + | 0.883446i | \(0.344783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 117.499 | + | 203.514i | 0.433576 | + | 0.750975i | 0.997178 | − | 0.0750712i | \(-0.0239184\pi\) |
−0.563603 | + | 0.826046i | \(0.690585\pi\) | |||||||
\(272\) | −134.320 | + | 232.650i | −0.493825 | + | 0.855330i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 636.866i | − | 2.32433i | ||||||
\(275\) | −133.279 | + | 230.845i | −0.484650 | + | 0.839438i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −107.636 | −0.388576 | −0.194288 | − | 0.980945i | \(-0.562240\pi\) | ||||
−0.194288 | + | 0.980945i | \(0.562240\pi\) | |||||||
\(278\) | 253.284i | 0.911095i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.96843 | + | 4.02323i | −0.0248873 | + | 0.0143687i | ||||
\(281\) | 364.932 | + | 210.694i | 1.29869 | + | 0.749799i | 0.980178 | − | 0.198119i | \(-0.0634833\pi\) |
0.318513 | + | 0.947919i | \(0.396817\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4772 | − | 18.1471i | −0.0370220 | − | 0.0641240i | 0.846921 | − | 0.531719i | \(-0.178454\pi\) |
−0.883943 | + | 0.467595i | \(0.845120\pi\) | |||||||
\(284\) | 413.763i | 1.45691i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −591.247 | −2.06730 | ||||||||
\(287\) | −2.78674 | + | 1.60893i | −0.00970991 | + | 0.00560602i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 69.6366 | − | 120.614i | 0.240957 | − | 0.417350i | ||||
\(290\) | 66.5121 | + | 115.202i | 0.229352 | + | 0.397250i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −962.929 | −3.29770 | ||||||||
\(293\) | − | 308.437i | − | 1.05269i | −0.850272 | − | 0.526344i | \(-0.823563\pi\) | ||
0.850272 | − | 0.526344i | \(-0.176437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −73.7526 | − | 42.5811i | −0.250009 | − | 0.144343i | ||||
\(296\) | −384.740 | −1.29980 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 667.099 | + | 385.150i | 2.23859 | + | 1.29245i | ||||
\(299\) | −538.324 | + | 310.801i | −1.80041 | + | 1.03947i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.1139 | − | 26.1780i | −0.0502122 | − | 0.0869701i | ||||
\(302\) | 46.2555 | + | 80.1169i | 0.153164 | + | 0.265288i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 410.896 | − | 71.8732i | 1.35163 | − | 0.236425i | ||||
\(305\) | −76.5190 | −0.250882 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8634 | + | 10.3134i | −0.0581868 | + | 0.0335942i | −0.528811 | − | 0.848739i | \(-0.677362\pi\) |
0.470624 | + | 0.882334i | \(0.344029\pi\) | |||||||
\(308\) | −22.5947 | + | 39.1352i | −0.0733594 | + | 0.127062i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −29.9208 | + | 51.8244i | −0.0965187 | + | 0.167175i | ||||
\(311\) | 294.737 | 0.947707 | 0.473854 | − | 0.880604i | \(-0.342863\pi\) | ||||
0.473854 | + | 0.880604i | \(0.342863\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.7267 | − | 44.5600i | 0.0821940 | − | 0.142364i | −0.821998 | − | 0.569490i | \(-0.807141\pi\) |
0.904192 | + | 0.427126i | \(0.140474\pi\) | |||||||
\(314\) | −366.392 | − | 211.536i | −1.16685 | − | 0.673683i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 1023.24i | − | 3.23811i | ||||||
\(317\) | −42.0638 | − | 24.2856i | −0.132693 | − | 0.0766106i | 0.432184 | − | 0.901786i | \(-0.357743\pi\) |
−0.564877 | + | 0.825175i | \(0.691076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 341.703 | + | 197.282i | 1.07117 | + | 0.618440i | ||||
\(320\) | 19.9051 | + | 34.4766i | 0.0622034 | + | 0.107739i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 69.9269i | 0.217164i | ||||||||
\(323\) | 229.012 | − | 40.0585i | 0.709017 | − | 0.124020i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −309.680 | + | 178.794i | −0.952862 | + | 0.550135i | ||||
\(326\) | −773.594 | + | 446.634i | −2.37299 | + | 1.37004i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −53.3188 | − | 92.3509i | −0.162557 | − | 0.281558i | ||||
\(329\) | 9.64379 | − | 16.7035i | 0.0293124 | − | 0.0507706i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 351.908i | − | 1.06317i | −0.847006 | − | 0.531583i | \(-0.821597\pi\) | ||
0.847006 | − | 0.531583i | \(-0.178403\pi\) | |||||||
\(332\) | 277.400 | − | 480.471i | 0.835543 | − | 1.44720i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 666.111 | 1.99434 | ||||||||
\(335\) | 9.38658i | 0.0280196i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 85.1791 | − | 49.1782i | 0.252757 | − | 0.145929i | −0.368269 | − | 0.929719i | \(-0.620049\pi\) |
0.621026 | + | 0.783790i | \(0.286716\pi\) | |||||||
\(338\) | −169.915 | − | 98.1003i | −0.502706 | − | 0.290237i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −55.2950 | − | 95.7738i | −0.162632 | − | 0.281688i | ||||
\(341\) | 177.497i | 0.520519i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −46.6594 | −0.136033 | ||||||||
\(344\) | 867.522 | − | 500.864i | 2.52187 | − | 1.45600i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 344.545 | − | 596.769i | 0.995793 | − | 1.72476i | ||||
\(347\) | −42.8027 | − | 74.1365i | −0.123351 | − | 0.213650i | 0.797736 | − | 0.603006i | \(-0.206031\pi\) |
−0.921087 | + | 0.389357i | \(0.872697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 146.137 | 0.418730 | 0.209365 | − | 0.977838i | \(-0.432860\pi\) | ||||
0.209365 | + | 0.977838i | \(0.432860\pi\) | |||||||
\(350\) | 40.2267i | 0.114933i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −138.238 | − | 79.8115i | −0.392720 | − | 0.226737i | ||||
\(353\) | 517.025 | 1.46466 | 0.732330 | − | 0.680949i | \(-0.238433\pi\) | ||||
0.732330 | + | 0.680949i | \(0.238433\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −45.0652 | − | 26.0184i | −0.126944 | − | 0.0732913i | ||||
\(356\) | 1129.83 | − | 652.309i | 3.17369 | − | 1.83233i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 301.578 | + | 522.349i | 0.842397 | + | 1.45907i | ||||
\(359\) | 112.210 | + | 194.354i | 0.312563 | + | 0.541376i | 0.978917 | − | 0.204261i | \(-0.0654790\pi\) |
−0.666353 | + | 0.745636i | \(0.732146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −275.907 | − | 232.801i | −0.764285 | − | 0.644879i | ||||
\(362\) | −6.95417 | −0.0192104 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −52.5000 | + | 30.3109i | −0.144231 | + | 0.0832717i | ||||
\(365\) | 60.5512 | − | 104.878i | 0.165894 | − | 0.287337i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 171.714 | − | 297.417i | 0.467885 | − | 0.810400i | −0.531442 | − | 0.847095i | \(-0.678350\pi\) |
0.999327 | + | 0.0366945i | \(0.0116828\pi\) | |||||||
\(368\) | −910.719 | −2.47478 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 45.8080 | − | 79.3417i | 0.123805 | − | 0.214437i | ||||
\(371\) | 12.5751 | + | 7.26024i | 0.0338952 | + | 0.0195694i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 497.699i | 1.33431i | 0.744918 | + | 0.667156i | \(0.232489\pi\) | ||||
−0.744918 | + | 0.667156i | \(0.767511\pi\) | |||||||
\(374\) | −418.117 | − | 241.400i | −1.11796 | − | 0.645455i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 553.545 | + | 319.589i | 1.47219 | + | 0.849971i | ||||
\(377\) | 264.655 | + | 458.396i | 0.702003 | + | 1.21590i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 73.4149i | 0.193707i | 0.995299 | + | 0.0968535i | \(0.0308778\pi\) | ||||
−0.995299 | + | 0.0968535i | \(0.969122\pi\) | |||||||
\(380\) | −58.9520 | + | 161.283i | −0.155137 | + | 0.424430i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 37.2831 | − | 21.5254i | 0.0975998 | − | 0.0563493i | ||||
\(383\) | 228.528 | − | 131.941i | 0.596678 | − | 0.344492i | −0.171055 | − | 0.985261i | \(-0.554718\pi\) |
0.767734 | + | 0.640769i | \(0.221384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.84162 | − | 4.92182i | −0.00738082 | − | 0.0127840i | ||||
\(386\) | 501.451 | − | 868.539i | 1.29910 | − | 2.25010i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 813.350i | 2.09626i | ||||||||
\(389\) | −193.951 | + | 335.933i | −0.498589 | + | 0.863582i | −0.999999 | − | 0.00162809i | \(-0.999482\pi\) |
0.501409 | + | 0.865210i | \(0.332815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −507.588 | −1.29818 | ||||||||
\(392\) | − | 771.331i | − | 1.96768i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −938.756 | + | 541.991i | −2.38263 | + | 1.37561i | ||||
\(395\) | 111.447 | + | 64.3440i | 0.282145 | + | 0.162896i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −207.294 | − | 359.044i | −0.522151 | − | 0.904392i | −0.999668 | − | 0.0257696i | \(-0.991796\pi\) |
0.477517 | − | 0.878623i | \(-0.341537\pi\) | |||||||
\(398\) | − | 542.122i | − | 1.36212i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −523.907 | −1.30977 | ||||||||
\(401\) | −359.226 | + | 207.399i | −0.895824 | + | 0.517204i | −0.875843 | − | 0.482596i | \(-0.839694\pi\) |
−0.0199812 | + | 0.999800i | \(0.506361\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −119.056 | + | 206.212i | −0.295425 | + | 0.511692i | ||||
\(404\) | 115.130 | + | 199.411i | 0.284975 | + | 0.493592i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 59.5445 | 0.146661 | ||||||||
\(407\) | − | 271.743i | − | 0.667673i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −385.954 | − | 222.831i | −0.943654 | − | 0.544819i | −0.0525501 | − | 0.998618i | \(-0.516735\pi\) |
−0.891104 | + | 0.453799i | \(0.850068\pi\) | |||||||
\(410\) | 25.3930 | 0.0619342 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 318.953 | + | 184.148i | 0.774159 | + | 0.446961i | ||||
\(413\) | −33.0133 | + | 19.0602i | −0.0799352 | + | 0.0461506i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.8872 | + | 60.4263i | 0.0840655 | + | 0.145606i | ||||
\(416\) | −107.068 | − | 185.446i | −0.257374 | − | 0.445785i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 129.170 | + | 738.461i | 0.309020 | + | 1.76665i | ||||
\(419\) | −352.866 | −0.842162 | −0.421081 | − | 0.907023i | \(-0.638349\pi\) | ||||
−0.421081 | + | 0.907023i | \(0.638349\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 281.887 | − | 162.748i | 0.669566 | − | 0.386574i | −0.126346 | − | 0.991986i | \(-0.540325\pi\) |
0.795912 | + | 0.605412i | \(0.206992\pi\) | |||||||
\(422\) | −485.532 | + | 840.966i | −1.15055 | + | 1.99281i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −240.600 | + | 416.731i | −0.567453 | + | 0.982857i | ||||
\(425\) | −291.999 | −0.687056 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.1258 | + | 29.6627i | −0.0401072 | + | 0.0694677i | ||||
\(428\) | 264.049 | + | 152.449i | 0.616937 | + | 0.356189i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 238.536i | 0.554735i | ||||||||
\(431\) | 166.026 | + | 95.8551i | 0.385211 | + | 0.222402i | 0.680083 | − | 0.733135i | \(-0.261944\pi\) |
−0.294872 | + | 0.955537i | \(0.595277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −253.975 | − | 146.633i | −0.586548 | − | 0.338643i | 0.177184 | − | 0.984178i | \(-0.443301\pi\) |
−0.763731 | + | 0.645534i | \(0.776635\pi\) | |||||||
\(434\) | 13.3932 | + | 23.1977i | 0.0308599 | + | 0.0534509i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 685.652i | 1.57260i | ||||||||
\(437\) | 505.795 | + | 604.459i | 1.15743 | + | 1.38320i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 202.351 | − | 116.828i | 0.460937 | − | 0.266122i | −0.251501 | − | 0.967857i | \(-0.580924\pi\) |
0.712438 | + | 0.701735i | \(0.247591\pi\) | |||||||
\(440\) | 163.106 | − | 94.1694i | 0.370696 | − | 0.214021i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −323.840 | − | 560.907i | −0.732669 | − | 1.26902i | ||||
\(443\) | 200.275 | − | 346.887i | 0.452089 | − | 0.783040i | −0.546427 | − | 0.837507i | \(-0.684012\pi\) |
0.998516 | + | 0.0544663i | \(0.0173458\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 164.075i | 0.368708i | ||||||||
\(446\) | −708.984 | + | 1228.00i | −1.58965 | + | 2.75335i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.8199 | 0.0397765 | ||||||||
\(449\) | 243.737i | 0.542844i | 0.962460 | + | 0.271422i | \(0.0874939\pi\) | ||||
−0.962460 | + | 0.271422i | \(0.912506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 65.2277 | − | 37.6593i | 0.144629 | − | 0.0835017i | ||||
\(452\) | −146.763 | − | 84.7334i | −0.324696 | − | 0.187463i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 598.487 | + | 1036.61i | 1.31825 | + | 2.28328i | ||||
\(455\) | − | 7.62408i | − | 0.0167562i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.08902 | 0.00894753 | 0.00447377 | − | 0.999990i | \(-0.498576\pi\) | ||||
0.00447377 | + | 0.999990i | \(0.498576\pi\) | |||||||
\(458\) | 680.501 | − | 392.887i | 1.48581 | − | 0.857833i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 187.455 | − | 324.682i | 0.407512 | − | 0.705831i | ||||
\(461\) | −391.718 | − | 678.476i | −0.849715 | − | 1.47175i | −0.881463 | − | 0.472253i | \(-0.843441\pi\) |
0.0317484 | − | 0.999496i | \(-0.489892\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −219.978 | −0.475115 | −0.237558 | − | 0.971373i | \(-0.576347\pi\) | ||||
−0.237558 | + | 0.971373i | \(0.576347\pi\) | |||||||
\(464\) | 775.500i | 1.67134i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 714.612 | + | 412.581i | 1.53350 | + | 0.885368i | ||||
\(467\) | 445.983 | 0.954995 | 0.477498 | − | 0.878633i | \(-0.341544\pi\) | ||||
0.477498 | + | 0.878633i | \(0.341544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.63872 | + | 2.10082i | 0.00775847 | + | 0.00447935i | ||||
\(470\) | −131.812 | + | 76.1019i | −0.280452 | + | 0.161919i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −631.643 | − | 1094.04i | −1.33823 | − | 2.31788i | ||||
\(473\) | 353.762 | + | 612.734i | 0.747911 | + | 1.29542i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 290.967 | + | 347.725i | 0.612563 | + | 0.732053i | ||||
\(476\) | −49.5025 | −0.103997 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 987.826 | − | 570.321i | 2.06658 | − | 1.19314i | ||||
\(479\) | −315.684 | + | 546.781i | −0.659048 | + | 1.14150i | 0.321815 | + | 0.946803i | \(0.395707\pi\) |
−0.980862 | + | 0.194702i | \(0.937626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 182.272 | − | 315.705i | 0.378944 | − | 0.656351i | ||||
\(482\) | −823.260 | −1.70801 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.9891 | − | 27.6940i | 0.0330354 | − | 0.0572190i | ||||
\(485\) | −88.5864 | − | 51.1454i | −0.182652 | − | 0.105454i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 792.723i | − | 1.62777i | −0.581027 | − | 0.813884i | \(-0.697349\pi\) | ||
0.581027 | − | 0.813884i | \(-0.302651\pi\) | |||||||
\(488\) | −983.004 | − | 567.538i | −2.01435 | − | 1.16299i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 159.065 | + | 91.8363i | 0.324623 | + | 0.187421i | ||||
\(491\) | 67.9055 | + | 117.616i | 0.138300 | + | 0.239543i | 0.926853 | − | 0.375424i | \(-0.122503\pi\) |
−0.788553 | + | 0.614967i | \(0.789169\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 432.224i | 0.876722i | ||||||||
\(494\) | −345.257 | + | 944.568i | −0.698901 | + | 1.91208i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −302.124 | + | 174.431i | −0.609120 | + | 0.351676i | ||||
\(497\) | −20.1722 | + | 11.6464i | −0.0405878 | + | 0.0234334i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −236.577 | − | 409.764i | −0.474102 | − | 0.821170i | 0.525458 | − | 0.850820i | \(-0.323894\pi\) |
−0.999560 | + | 0.0296501i | \(0.990561\pi\) | |||||||
\(500\) | 220.811 | − | 382.455i | 0.441621 | − | 0.764910i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 946.955i | 1.88636i | ||||||||
\(503\) | −359.444 | + | 622.575i | −0.714601 | + | 1.23772i | 0.248513 | + | 0.968629i | \(0.420058\pi\) |
−0.963113 | + | 0.269096i | \(0.913275\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.9586 | −0.0573438 | ||||||||
\(506\) | − | 1636.74i | − | 3.23466i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −302.863 | + | 174.858i | −0.596188 | + | 0.344209i | ||||
\(509\) | −578.570 | − | 334.037i | −1.13668 | − | 0.656262i | −0.191073 | − | 0.981576i | \(-0.561197\pi\) |
−0.945606 | + | 0.325314i | \(0.894530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.1040 | − | 46.9456i | −0.0530412 | − | 0.0918700i | ||||
\(512\) | 1075.10i | 2.09981i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1690.92 | 3.28973 | ||||||||
\(515\) | −40.1131 | + | 23.1593i | −0.0778895 | + | 0.0449695i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −225.727 | + | 390.970i | −0.436609 | + | 0.756228i | ||||
\(518\) | −20.5046 | − | 35.5151i | −0.0395842 | − | 0.0685619i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 252.657 | 0.485880 | ||||||||
\(521\) | − | 772.856i | − | 1.48341i | −0.670727 | − | 0.741704i | \(-0.734018\pi\) | ||
0.670727 | − | 0.741704i | \(-0.265982\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −599.415 | − | 346.072i | −1.14611 | − | 0.661706i | −0.198172 | − | 0.980167i | \(-0.563501\pi\) |
−0.947936 | + | 0.318461i | \(0.896834\pi\) | |||||||
\(524\) | 1745.33 | 3.33078 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −818.679 | − | 472.665i | −1.55642 | − | 0.898602i | ||||
\(527\) | −168.388 | + | 97.2190i | −0.319522 | + | 0.184476i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −595.886 | − | 1032.11i | −1.12644 | − | 1.95105i | ||||
\(530\) | −57.2927 | − | 99.2338i | −0.108099 | − | 0.187234i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 49.3276 | + | 58.9498i | 0.0927211 | + | 0.110808i | ||||
\(533\) | 101.040 | 0.189569 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.2081 | + | 19.1727i | −0.0620712 | + | 0.0358368i | ||||
\(536\) | −69.6197 | + | 120.585i | −0.129888 | + | 0.224972i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.1703 | − | 59.1847i | 0.0635135 | − | 0.110009i | ||||
\(539\) | 544.793 | 1.01075 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −488.635 | + | 846.340i | −0.903206 | + | 1.56440i | −0.0798991 | + | 0.996803i | \(0.525460\pi\) |
−0.823307 | + | 0.567596i | \(0.807874\pi\) | |||||||
\(542\) | −718.875 | − | 415.043i | −1.32634 | − | 0.765762i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 174.858i | − | 0.321431i | ||||||
\(545\) | −74.6781 | − | 43.1154i | −0.137024 | − | 0.0791109i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 166.215 | + | 95.9642i | 0.303866 | + | 0.175437i | 0.644178 | − | 0.764875i | \(-0.277199\pi\) |
−0.340312 | + | 0.940312i | \(0.610533\pi\) | |||||||
\(548\) | 764.211 | + | 1323.65i | 1.39454 | + | 2.41542i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 941.563i | − | 1.71193i | ||||||
\(551\) | 514.711 | − | 430.697i | 0.934141 | − | 0.781664i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 49.8861 | − | 28.8018i | 0.0902100 | − | 0.0520828i | ||||
\(554\) | 329.265 | − | 190.101i | 0.594341 | − | 0.343143i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −303.930 | − | 526.422i | −0.546636 | − | 0.946801i | ||||
\(557\) | 161.531 | − | 279.780i | 0.290002 | − | 0.502299i | −0.683808 | − | 0.729662i | \(-0.739677\pi\) |
0.973810 | + | 0.227364i | \(0.0730106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 949.147i | 1.69794i | ||||||||
\(560\) | 5.58508 | − | 9.67363i | 0.00997335 | − | 0.0172743i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1488.47 | −2.64852 | ||||||||
\(563\) | − | 328.512i | − | 0.583503i | −0.956494 | − | 0.291752i | \(-0.905762\pi\) | ||
0.956494 | − | 0.291752i | \(-0.0942381\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.4576 | − | 10.6565i | 0.0326683 | − | 0.0188610i | ||||
\(566\) | 64.1012 | + | 37.0088i | 0.113253 | + | 0.0653866i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −385.954 | − | 668.493i | −0.679497 | − | 1.17692i | ||||
\(569\) | − | 1069.96i | − | 1.88042i | −0.340590 | − | 0.940212i | \(-0.610627\pi\) | ||
0.340590 | − | 0.940212i | \(-0.389373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 226.109 | 0.395987 | 0.197994 | − | 0.980203i | \(-0.436557\pi\) | ||||
0.197994 | + | 0.980203i | \(0.436557\pi\) | |||||||
\(572\) | 1228.84 | − | 709.470i | 2.14832 | − | 1.24033i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.68323 | − | 9.84365i | 0.00990110 | − | 0.0171492i | ||||
\(575\) | −494.952 | − | 857.282i | −0.860786 | − | 1.49093i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 563.905 | 0.977305 | 0.488652 | − | 0.872479i | \(-0.337489\pi\) | ||||
0.488652 | + | 0.872479i | \(0.337489\pi\) | |||||||
\(578\) | 491.957i | 0.851136i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −276.475 | − | 159.623i | −0.476681 | − | 0.275212i | ||||
\(581\) | 31.2325 | 0.0537564 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −294.339 | − | 169.936i | −0.504869 | − | 0.291486i | ||||
\(584\) | 1555.75 | − | 898.211i | 2.66395 | − | 1.53803i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 544.748 | + | 943.532i | 0.929605 | + | 1.61012i | ||||
\(587\) | 138.379 | + | 239.680i | 0.235740 | + | 0.408313i | 0.959487 | − | 0.281752i | \(-0.0909154\pi\) |
−0.723748 | + | 0.690065i | \(0.757582\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 283.566 | + | 103.649i | 0.481437 | + | 0.175974i | ||||
\(590\) | 300.819 | 0.509863 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 462.543 | − | 267.050i | 0.781323 | − | 0.451097i | ||||
\(593\) | −130.080 | + | 225.306i | −0.219360 | + | 0.379942i | −0.954612 | − | 0.297851i | \(-0.903730\pi\) |
0.735253 | + | 0.677793i | \(0.237063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.11283 | − | 5.39159i | 0.00523166 | − | 0.00906149i | ||||
\(596\) | −1848.65 | −3.10176 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1097.85 | − | 1901.53i | 1.83587 | − | 3.17981i | ||||
\(599\) | −660.820 | − | 381.524i | −1.10320 | − | 0.636936i | −0.166144 | − | 0.986102i | \(-0.553132\pi\) |
−0.937061 | + | 0.349166i | \(0.886465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 628.679i | − | 1.04606i | −0.852316 | − | 0.523028i | \(-0.824802\pi\) | ||
0.852316 | − | 0.523028i | \(-0.175198\pi\) | |||||||
\(602\) | 92.4688 | + | 53.3869i | 0.153603 | + | 0.0886826i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −192.273 | − | 111.009i | −0.318333 | − | 0.183790i | ||||
\(605\) | 2.01087 | + | 3.48293i | 0.00332375 | + | 0.00575691i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 56.3825i | 0.0928871i | 0.998921 | + | 0.0464436i | \(0.0147888\pi\) | ||||
−0.998921 | + | 0.0464436i | \(0.985211\pi\) | |||||||
\(608\) | −208.229 | + | 174.241i | −0.342482 | + | 0.286580i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 234.077 | − | 135.144i | 0.383733 | − | 0.221548i | ||||
\(611\) | −524.488 | + | 302.813i | −0.858410 | + | 0.495603i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0673 | + | 24.3653i | 0.0229483 | + | 0.0397476i | 0.877271 | − | 0.479995i | \(-0.159361\pi\) |
−0.854323 | + | 0.519742i | \(0.826028\pi\) | |||||||
\(614\) | 36.4302 | − | 63.0989i | 0.0593325 | − | 0.102767i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 84.3045i | − | 0.136858i | ||||||
\(617\) | 66.9966 | − | 116.042i | 0.108584 | − | 0.188074i | −0.806613 | − | 0.591081i | \(-0.798702\pi\) |
0.915197 | + | 0.403007i | \(0.132035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 586.929 | 0.948188 | 0.474094 | − | 0.880474i | \(-0.342776\pi\) | ||||
0.474094 | + | 0.880474i | \(0.342776\pi\) | |||||||
\(620\) | − | 143.614i | − | 0.231636i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −901.622 | + | 520.551i | −1.44955 | + | 0.836900i | ||||
\(623\) | 63.6040 | + | 36.7218i | 0.102093 | + | 0.0589434i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −270.522 | − | 468.557i | −0.432835 | − | 0.749692i | ||||
\(626\) | 181.749i | 0.290335i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1015.34 | 1.61678 | ||||||||
\(629\) | 257.798 | − | 148.840i | 0.409854 | − | 0.236629i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −163.649 | + | 283.448i | −0.259348 | + | 0.449204i | −0.966067 | − | 0.258290i | \(-0.916841\pi\) |
0.706719 | + | 0.707494i | \(0.250174\pi\) | |||||||
\(632\) | 954.473 | + | 1653.19i | 1.51024 | + | 2.61581i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 171.568 | 0.270612 | ||||||||
\(635\) | − | 43.9820i | − | 0.0692630i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 632.929 | + | 365.421i | 0.993608 | + | 0.573660i | ||||
\(638\) | −1393.72 | −2.18452 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −174.558 | − | 100.781i | −0.272748 | − | 0.157471i | ||||
\(641\) | −234.307 | + | 135.277i | −0.365534 | + | 0.211041i | −0.671506 | − | 0.741000i | \(-0.734352\pi\) |
0.305972 | + | 0.952041i | \(0.401019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −402.896 | − | 697.836i | −0.626588 | − | 1.08528i | −0.988232 | − | 0.152966i | \(-0.951118\pi\) |
0.361644 | − | 0.932316i | \(-0.382216\pi\) | |||||||
\(644\) | −83.9091 | − | 145.335i | −0.130294 | − | 0.225675i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −629.816 | + | 527.013i | −0.974947 | + | 0.815810i | ||||
\(647\) | −590.952 | −0.913372 | −0.456686 | − | 0.889628i | \(-0.650964\pi\) | ||||
−0.456686 | + | 0.889628i | \(0.650964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 772.723 | − | 446.132i | 1.19064 | − | 0.687414i | ||||
\(650\) | 631.556 | − | 1093.89i | 0.971624 | − | 1.68290i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1071.88 | − | 1856.55i | 1.64399 | − | 2.84748i | ||||
\(653\) | 990.945 | 1.51753 | 0.758763 | − | 0.651366i | \(-0.225804\pi\) | ||||
0.758763 | + | 0.651366i | \(0.225804\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −109.751 | + | 190.093i | −0.167558 | + | 0.290219i | ||||
\(656\) | 128.202 | + | 74.0177i | 0.195430 | + | 0.112832i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 68.1297i | 0.103541i | ||||||||
\(659\) | −446.552 | − | 257.817i | −0.677620 | − | 0.391224i | 0.121338 | − | 0.992611i | \(-0.461282\pi\) |
−0.798958 | + | 0.601387i | \(0.794615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1142.22 | + | 659.462i | 1.72802 | + | 0.997673i | 0.898100 | + | 0.439791i | \(0.144948\pi\) |
0.829921 | + | 0.557882i | \(0.188386\pi\) | |||||||
\(662\) | 621.525 | + | 1076.51i | 0.938859 | + | 1.62615i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1035.03i | 1.55877i | ||||||||
\(665\) | −9.52238 | + | 1.66564i | −0.0143194 | + | 0.00250472i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1268.97 | + | 732.640i | −1.90250 | + | 1.09841i | ||||
\(668\) | −1384.43 | + | 799.303i | −2.07250 | + | 1.19656i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.5782 | − | 28.7142i | −0.0247435 | − | 0.0428570i | ||||
\(671\) | 400.853 | − | 694.299i | 0.597397 | − | 1.03472i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 569.028i | − | 0.845510i | −0.906244 | − | 0.422755i | \(-0.861063\pi\) | ||
0.906244 | − | 0.422755i | \(-0.138937\pi\) | |||||||
\(674\) | −173.713 | + | 300.879i | −0.257734 | + | 0.446408i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 470.863 | 0.696543 | ||||||||
\(677\) | 909.084i | 1.34281i | 0.741090 | + | 0.671406i | \(0.234309\pi\) | ||||
−0.741090 | + | 0.671406i | \(0.765691\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.6532 | + | 22.8938i | −0.0583994 | + | 0.0337169i | ||||
\(680\) | 178.674 | + | 103.157i | 0.262756 | + | 0.151702i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −313.487 | − | 542.976i | −0.459658 | − | 0.796152i | ||||
\(683\) | 85.6567i | 0.125412i | 0.998032 | + | 0.0627062i | \(0.0199731\pi\) | ||||
−0.998032 | + | 0.0627062i | \(0.980027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −192.222 | −0.280615 | ||||||||
\(686\) | 142.735 | − | 82.4078i | 0.208068 | − | 0.120128i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −695.304 | + | 1204.30i | −1.01062 | + | 1.75044i | ||||
\(689\) | −227.971 | − | 394.856i | −0.330872 | − | 0.573086i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0911 | −0.0174980 | −0.00874899 | − | 0.999962i | \(-0.502785\pi\) | ||||
−0.00874899 | + | 0.999962i | \(0.502785\pi\) | |||||||
\(692\) | 1653.75i | 2.38981i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 261.873 | + | 151.193i | 0.377339 | + | 0.217857i | ||||
\(695\) | 76.4473 | 0.109996 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 71.4534 | + | 41.2536i | 0.102516 | + | 0.0591874i | ||||
\(698\) | −447.042 | + | 258.100i | −0.640462 | + | 0.369771i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −48.2702 | − | 83.6064i | −0.0689574 | − | 0.119438i | ||||
\(701\) | 13.8355 | + | 23.9638i | 0.0197368 | + | 0.0341851i | 0.875725 | − | 0.482810i | \(-0.160384\pi\) |
−0.855988 | + | 0.516995i | \(0.827051\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −434.132 | − | 158.683i | −0.617543 | − | 0.225723i | ||||
\(704\) | −417.100 | −0.592471 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1581.62 | + | 913.147i | −2.24025 | + | 1.29341i | ||||
\(707\) | −6.48125 | + | 11.2258i | −0.00916725 | + | 0.0158781i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −330.042 | + | 571.650i | −0.465504 | + | 0.806277i | −0.999224 | − | 0.0393844i | \(-0.987460\pi\) |
0.533720 | + | 0.845661i | \(0.320794\pi\) | |||||||
\(710\) | 183.810 | 0.258888 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1216.94 | + | 2107.80i | −1.70918 | + | 2.96039i | ||||
\(713\) | −570.853 | − | 329.582i | −0.800635 | − | 0.462247i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 178.453i | 0.249584i | ||||||||
\(716\) | −1253.59 | − | 723.760i | −1.75082 | − | 1.01084i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −686.519 | − | 396.362i | −0.956154 | − | 0.552036i | ||||
\(719\) | 216.159 | + | 374.398i | 0.300638 | + | 0.520720i | 0.976281 | − | 0.216509i | \(-0.0694671\pi\) |
−0.675643 | + | 0.737229i | \(0.736134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.7332i | 0.0287562i | ||||||||
\(722\) | 1255.18 | + | 224.861i | 1.73848 | + | 0.311442i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.4534 | − | 8.34468i | 0.0199633 | − | 0.0115258i | ||||
\(725\) | −729.997 | + | 421.464i | −1.00689 | + | 0.581330i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 517.896 | + | 897.022i | 0.712374 | + | 1.23387i | 0.963964 | + | 0.266034i | \(0.0857134\pi\) |
−0.251590 | + | 0.967834i | \(0.580953\pi\) | |||||||
\(728\) | 56.5474 | − | 97.9430i | 0.0776751 | − | 0.134537i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 427.772i | 0.585989i | ||||||||
\(731\) | −387.527 | + | 671.216i | −0.530132 | + | 0.918216i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 416.182 | 0.567779 | 0.283890 | − | 0.958857i | \(-0.408375\pi\) | ||||
0.283890 | + | 0.958857i | \(0.408375\pi\) | |||||||
\(734\) | 1213.09i | 1.65272i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 513.368 | − | 296.393i | 0.697511 | − | 0.402708i | ||||
\(737\) | −85.1695 | − | 49.1726i | −0.115562 | − | 0.0667200i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 330.536 | + | 572.505i | 0.447274 | + | 0.774702i | 0.998208 | − | 0.0598475i | \(-0.0190614\pi\) |
−0.550933 | + | 0.834549i | \(0.685728\pi\) | |||||||
\(740\) | 219.870i | 0.297122i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −51.2909 | −0.0691252 | ||||||||
\(743\) | −99.0651 | + | 57.1953i | −0.133331 | + | 0.0769788i | −0.565182 | − | 0.824966i | \(-0.691194\pi\) |
0.431851 | + | 0.901945i | \(0.357861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 116.247 | − | 201.346i | 0.156037 | − | 0.270264i | ||||
\(746\) | −879.013 | − | 1522.50i | −1.17830 | − | 2.04088i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1158.68 | 1.54903 | ||||||||
\(749\) | 17.1642i | 0.0229162i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −118.013 | − | 68.1348i | −0.157141 | − | 0.0907254i | 0.419367 | − | 0.907817i | \(-0.362252\pi\) |
−0.576509 | + | 0.817091i | \(0.695585\pi\) | |||||||
\(752\) | −887.312 | −1.17994 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1619.20 | − | 934.844i | −2.14748 | − | 1.23985i | ||||
\(755\) | 24.1812 | − | 13.9610i | 0.0320281 | − | 0.0184914i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 101.860 | + | 176.427i | 0.134558 | + | 0.233061i | 0.925428 | − | 0.378922i | \(-0.123705\pi\) |
−0.790871 | + | 0.611983i | \(0.790372\pi\) | |||||||
\(758\) | −129.662 | − | 224.582i | −0.171058 | − | 0.296282i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −55.1983 | − | 315.566i | −0.0726293 | − | 0.415218i | ||||
\(761\) | 976.891 | 1.28369 | 0.641847 | − | 0.766833i | \(-0.278168\pi\) | ||||
0.641847 | + | 0.766833i | \(0.278168\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.4275 | + | 19.2994i | −0.0438107 | + | 0.0252941i | ||||
\(764\) | −51.6590 | + | 89.4761i | −0.0676166 | + | 0.117115i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −466.055 | + | 807.232i | −0.608427 | + | 1.05383i | ||||
\(767\) | 1196.98 | 1.56059 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 357.908 | − | 619.915i | 0.465420 | − | 0.806131i | −0.533801 | − | 0.845610i | \(-0.679237\pi\) |
0.999220 | + | 0.0394796i | \(0.0125700\pi\) | |||||||
\(770\) | 17.3854 | + | 10.0375i | 0.0225785 | + | 0.0130357i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2406.87i | 3.11771i | ||||||||
\(773\) | 320.373 | + | 184.967i | 0.414454 | + | 0.239285i | 0.692702 | − | 0.721224i | \(-0.256420\pi\) |
−0.278248 | + | 0.960509i | \(0.589754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −328.393 | − | 189.598i | −0.423733 | − | 0.244642i | ||||
\(776\) | −758.686 | − | 1314.08i | −0.977688 | − | 1.69340i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 1370.19i | − | 1.76117i | ||||||
\(779\) | −22.0743 | − | 126.198i | −0.0283367 | − | 0.162000i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 472.158 | − | 272.601i | 0.604556 | − | 0.349041i | ||||
\(782\) | 1552.75 | − | 896.479i | 1.98561 | − | 1.14639i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 535.384 | + | 927.312i | 0.682888 | + | 1.18280i | ||||
\(785\) | −63.8468 | + | 110.586i | −0.0813335 | + | 0.140874i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 162.672i | − | 0.206699i | −0.994645 | − | 0.103350i | \(-0.967044\pi\) | ||
0.994645 | − | 0.103350i | \(-0.0329561\pi\) | |||||||
\(788\) | 1300.73 | − | 2252.93i | 1.65067 | − | 2.85905i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −454.566 | −0.575400 | ||||||||
\(791\) | − | 9.54014i | − | 0.0120609i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 931.405 | − | 537.747i | 1.17453 | − | 0.678117i | ||||
\(794\) | 1268.25 | + | 732.227i | 1.59730 | + | 0.922200i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 650.522 | + | 1126.74i | 0.817238 | + | 1.41550i | ||||
\(797\) | − | 103.395i | − | 0.129730i | −0.997894 | − | 0.0648652i | \(-0.979338\pi\) | ||
0.997894 | − | 0.0648652i | \(-0.0206617\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −494.542 | −0.618952 | ||||||||
\(800\) | 295.324 | − | 170.505i | 0.369155 | − | 0.213132i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 732.598 | − | 1268.90i | 0.913464 | − | 1.58217i | ||||
\(803\) | 634.409 | + | 1098.83i | 0.790049 | + | 1.36840i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.1056 | 0.0262182 | ||||||||
\(806\) | − | 841.089i | − | 1.04353i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −372.018 | − | 214.784i | −0.460418 | − | 0.265822i | ||||
\(809\) | −940.571 | −1.16263 | −0.581317 | − | 0.813677i | \(-0.697462\pi\) | ||||
−0.581317 | + | 0.813677i | \(0.697462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 884.720 | + | 510.794i | 1.09090 | + | 0.629832i | 0.933816 | − | 0.357753i | \(-0.116457\pi\) |
0.157085 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(812\) | −123.756 | + | 71.4507i | −0.152409 | + | 0.0879935i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 479.940 | + | 831.281i | 0.589607 | + | 1.02123i | ||||
\(815\) | 134.805 | + | 233.489i | 0.165405 | + | 0.286490i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1185.47 | − | 207.361i | 1.45101 | − | 0.253808i | ||||
\(818\) | 1574.22 | 1.92447 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −52.7764 | + | 30.4705i | −0.0643615 | + | 0.0371591i | ||||
\(821\) | 638.601 | − | 1106.09i | 0.777833 | − | 1.34725i | −0.155356 | − | 0.987859i | \(-0.549652\pi\) |
0.933188 | − | 0.359387i | \(-0.117014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −242.137 | + | 419.393i | −0.294212 | + | 0.509590i | −0.974801 | − | 0.223075i | \(-0.928391\pi\) |
0.680589 | + | 0.732665i | \(0.261724\pi\) | |||||||
\(824\) | −687.086 | −0.833842 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 67.3266 | − | 116.613i | 0.0815092 | − | 0.141178i | ||||
\(827\) | −769.904 | − | 444.504i | −0.930961 | − | 0.537490i | −0.0438453 | − | 0.999038i | \(-0.513961\pi\) |
−0.887115 | + | 0.461548i | \(0.847294\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 188.951i | − | 0.227927i | −0.993485 | − | 0.113963i | \(-0.963645\pi\) | ||
0.993485 | − | 0.113963i | \(-0.0363547\pi\) | |||||||
\(830\) | −213.445 | − | 123.232i | −0.257162 | − | 0.148473i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −484.577 | − | 279.771i | −0.582424 | − | 0.336263i | ||||
\(833\) | 298.396 | + | 516.836i | 0.358218 | + | 0.620452i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 201.048i | − | 0.240776i | ||||||
\(836\) | −1154.58 | − | 1379.80i | −1.38108 | − | 1.65048i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1079.44 | − | 623.216i | 1.28812 | − | 0.743694i | ||||
\(839\) | 146.484 | − | 84.5725i | 0.174593 | − | 0.100802i | −0.410157 | − | 0.912015i | \(-0.634526\pi\) |
0.584750 | + | 0.811214i | \(0.301193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 203.361 | + | 352.232i | 0.241809 | + | 0.418825i | ||||
\(842\) | −574.875 | + | 995.713i | −0.682750 | + | 1.18256i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 2330.47i | − | 2.76121i | ||||||
\(845\) | −29.6090 | + | 51.2843i | −0.0350402 | + | 0.0606915i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.80022 | 0.00212540 | ||||||||
\(848\) | − | 668.005i | − | 0.787742i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 893.245 | − | 515.715i | 1.05088 | − | 0.606724i | ||||
\(851\) | 873.960 | + | 504.581i | 1.02698 | + | 0.592927i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 253.769 | + | 439.541i | 0.297502 | + | 0.515288i | 0.975564 | − | 0.219716i | \(-0.0705132\pi\) |
−0.678062 | + | 0.735005i | \(0.737180\pi\) | |||||||
\(854\) | − | 120.987i | − | 0.141671i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −568.812 | −0.664500 | ||||||||
\(857\) | −761.557 | + | 439.685i | −0.888631 | + | 0.513051i | −0.873494 | − | 0.486834i | \(-0.838152\pi\) |
−0.0151366 | + | 0.999885i | \(0.504818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −584.193 | + | 1011.85i | −0.680085 | + | 1.17794i | 0.294869 | + | 0.955538i | \(0.404724\pi\) |
−0.974955 | + | 0.222404i | \(0.928609\pi\) | |||||||
\(860\) | −286.232 | − | 495.769i | −0.332828 | − | 0.576475i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −677.180 | −0.785592 | ||||||||
\(863\) | − | 1078.16i | − | 1.24932i | −0.780899 | − | 0.624658i | \(-0.785238\pi\) | ||
0.780899 | − | 0.624658i | \(-0.214762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −180.119 | − | 103.992i | −0.208230 | − | 0.120222i | ||||
\(866\) | 1035.90 | 1.19619 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −55.6724 | − | 32.1425i | −0.0641387 | − | 0.0370305i | ||||
\(869\) | −1167.66 | + | 674.147i | −1.34368 | + | 0.775773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −65.9653 | − | 114.255i | −0.0757352 | − | 0.131177i | ||||
\(872\) | −639.570 | − | 1107.77i | −0.733452 | − | 1.27038i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2614.83 | − | 955.769i | −2.99180 | − | 1.09356i | ||||
\(875\) | 24.8611 | 0.0284126 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −884.225 | + | 510.507i | −1.00824 | + | 0.582106i | −0.910675 | − | 0.413123i | \(-0.864438\pi\) |
−0.0975626 | + | 0.995229i | \(0.531105\pi\) | |||||||
\(878\) | −412.672 | + | 714.768i | −0.470013 | + | 0.814087i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −130.727 | + | 226.425i | −0.148553 | + | 0.257301i | ||||
\(881\) | 111.944 | 0.127065 | 0.0635325 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635325 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −670.488 | + | 1161.32i | −0.759330 | + | 1.31520i | 0.183863 | + | 0.982952i | \(0.441140\pi\) |
−0.943193 | + | 0.332246i | \(0.892194\pi\) | |||||||
\(884\) | 1346.12 | + | 777.185i | 1.52277 | + | 0.879169i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1414.87i | 1.59692i | ||||||||
\(887\) | 1218.13 | + | 703.287i | 1.37331 | + | 0.792882i | 0.991344 | − | 0.131293i | \(-0.0419129\pi\) |
0.381969 | + | 0.924175i | \(0.375246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.0497 | − | 9.84365i | −0.0191785 | − | 0.0110727i | ||||
\(890\) | −289.782 | − | 501.917i | −0.325598 | − | 0.563952i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 3402.99i | − | 3.81501i | ||||||
\(893\) | 492.796 | + | 588.923i | 0.551843 | + | 0.659489i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 157.657 | − | 91.0235i | 0.176153 | − | 0.101702i | ||||
\(896\) | −78.1361 | + | 45.1119i | −0.0872055 | + | 0.0503481i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −430.477 | − | 745.608i | −0.479373 | − | 0.830299i | ||||
\(899\) | −280.647 | + | 486.095i | −0.312177 | + | 0.540706i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 372.312i | − | 0.413221i | ||||||
\(902\) | −133.024 | + | 230.405i | −0.147477 | + | 0.255438i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 316.154 | 0.349728 | ||||||||
\(905\) | 2.09893i | 0.00231926i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1155.56 | − | 667.165i | 1.27405 | − | 0.735574i | 0.298303 | − | 0.954471i | \(-0.403579\pi\) |
0.975748 | + | 0.218898i | \(0.0702461\pi\) | |||||||
\(908\) | −2487.77 | − | 1436.31i | −2.73983 | − | 1.58184i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.4653 | + | 23.3226i | 0.0147971 | + | 0.0256293i | ||||
\(911\) | 378.747i | 0.415749i | 0.978156 | + | 0.207874i | \(0.0666545\pi\) | ||||
−0.978156 | + | 0.207874i | \(0.933345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −731.041 | −0.800703 | ||||||||
\(914\) | −12.5086 | + | 7.22185i | −0.0136856 | + | 0.00790137i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −942.894 | + | 1633.14i | −1.02936 | + | 1.78290i | ||||
\(917\) | 49.1267 | + | 85.0899i | 0.0535733 | + | 0.0927916i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −452.655 | −0.492552 | −0.246276 | − | 0.969200i | \(-0.579207\pi\) | ||||
−0.246276 | + | 0.969200i | \(0.579207\pi\) | |||||||
\(920\) | 699.427i | 0.760247i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2396.59 | + | 1383.67i | 2.59934 | + | 1.50073i | ||||
\(923\) | 731.390 | 0.792406 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 502.761 | + | 290.269i | 0.543525 | + | 0.313804i | ||||
\(926\) | 672.929 | − | 388.516i | 0.726705 | − | 0.419564i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −252.386 | − | 437.146i | −0.271968 | − | 0.471062i | ||||
\(929\) | 823.417 | + | 1426.20i | 0.886348 | + | 1.53520i | 0.844161 | + | 0.536089i | \(0.180099\pi\) |
0.0421865 | + | 0.999110i | \(0.486568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 318.130 | − | 870.354i | 0.341708 | − | 0.934859i | ||||
\(932\) | −1980.31 | −2.12480 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1364.29 | + | 787.675i | −1.46070 | + | 0.843335i | ||||
\(935\) | −72.8604 | + | 126.198i | −0.0779255 | + | 0.134971i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 558.953 | − | 968.136i | 0.596535 | − | 1.03323i | −0.396793 | − | 0.917908i | \(-0.629877\pi\) |
0.993328 | − | 0.115321i | \(-0.0367897\pi\) | |||||||
\(938\) | −14.8415 | −0.0158225 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 182.638 | − | 316.338i | 0.194295 | − | 0.336530i | ||||
\(941\) | 1529.54 | + | 883.078i | 1.62544 | + | 0.938446i | 0.985431 | + | 0.170076i | \(0.0544013\pi\) |
0.640006 | + | 0.768370i | \(0.278932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 279.708i | 0.296615i | ||||||||
\(944\) | 1518.75 | + | 876.852i | 1.60885 | + | 0.928869i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2164.37 | − | 1249.60i | −2.28791 | − | 1.32093i | ||||
\(947\) | −650.983 | − | 1127.54i | −0.687416 | − | 1.19064i | −0.972671 | − | 0.232187i | \(-0.925412\pi\) |
0.285255 | − | 0.958452i | \(-0.407922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1702.13i | 1.79360i | ||||||||
\(950\) | −1504.23 | − | 549.823i | −1.58340 | − | 0.578761i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 79.9783 | − | 46.1755i | 0.0840108 | − | 0.0485036i | ||||
\(953\) | 727.416 | − | 419.974i | 0.763291 | − | 0.440686i | −0.0671852 | − | 0.997741i | \(-0.521402\pi\) |
0.830476 | + | 0.557054i | \(0.188069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.49689 | − | 11.2529i | −0.00680302 | − | 0.0117832i | ||||
\(956\) | −1368.72 | + | 2370.69i | −1.43171 | + | 2.47980i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2230.19i | − | 2.32796i | ||||||
\(959\) | −43.0212 | + | 74.5150i | −0.0448605 | + | 0.0777007i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 708.499 | 0.737252 | ||||||||
\(962\) | 1287.68i | 1.33855i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1711.05 | − | 987.874i | 1.77495 | − | 1.02477i | ||||
\(965\) | −262.146 | − | 151.350i | −0.271654 | − | 0.156839i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −370.759 | − | 642.174i | −0.383412 | − | 0.664089i | 0.608136 | − | 0.793833i | \(-0.291918\pi\) |
−0.991547 | + | 0.129744i | \(0.958584\pi\) | |||||||
\(968\) | 59.6581i | 0.0616302i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 361.323 | 0.372498 | ||||||||
\(971\) | −1265.77 | + | 730.790i | −1.30357 | + | 0.752616i | −0.981014 | − | 0.193935i | \(-0.937875\pi\) |
−0.322554 | + | 0.946551i | \(0.604542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.1097 | − | 29.6349i | 0.0175845 | − | 0.0304573i | ||||
\(974\) | 1400.07 | + | 2425.00i | 1.43745 | + | 2.48973i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1575.72 | 1.61447 | ||||||||
\(977\) | − | 340.557i | − | 0.348574i | −0.984695 | − | 0.174287i | \(-0.944238\pi\) | ||
0.984695 | − | 0.174287i | \(-0.0557621\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1488.74 | − | 859.526i | −1.52068 | − | 0.877963i | ||||
\(980\) | −440.798 | −0.449794 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −415.455 | − | 239.863i | −0.423071 | − | 0.244260i | ||||
\(983\) | −397.752 | + | 229.642i | −0.404631 | + | 0.233614i | −0.688480 | − | 0.725255i | \(-0.741722\pi\) |
0.283849 | + | 0.958869i | \(0.408388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 163.586 | + | 283.339i | 0.166077 | + | 0.287654i | ||||
\(986\) | −763.375 | − | 1322.20i | −0.774214 | − | 1.34098i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −415.862 | − | 2377.47i | −0.420913 | − | 2.40634i | ||||
\(989\) | −2627.51 | −2.65673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 108.241 | − | 62.4928i | 0.109224 | − | 0.0630603i | −0.444393 | − | 0.895832i | \(-0.646581\pi\) |
0.553617 | + | 0.832772i | \(0.313247\pi\) | |||||||
\(992\) | 113.537 | − | 196.652i | 0.114453 | − | 0.198238i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 41.1387 | − | 71.2544i | 0.0413870 | − | 0.0716845i | ||||
\(995\) | −163.625 | −0.164448 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −122.478 | + | 212.139i | −0.122847 | + | 0.212777i | −0.920889 | − | 0.389824i | \(-0.872536\pi\) |
0.798042 | + | 0.602601i | \(0.205869\pi\) | |||||||
\(998\) | 1447.41 | + | 835.664i | 1.45031 | + | 0.837339i | ||||
\(999\) | 0 | 0 |
(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 | 171.3.p.f.145.1 | yes | 8 | |
3.2 | odd | 2 | inner | 171.3.p.f.145.4 | yes | 8 | |
19.8 | odd | 6 | inner | 171.3.p.f.46.1 | ✓ | 8 | |
57.8 | even | 6 | inner | 171.3.p.f.46.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.3.p.f.46.1 | ✓ | 8 | 19.8 | odd | 6 | inner | |
171.3.p.f.46.4 | yes | 8 | 57.8 | even | 6 | inner | |
171.3.p.f.145.1 | yes | 8 | 1.1 | even | 1 | trivial | |
171.3.p.f.145.4 | yes | 8 | 3.2 | odd | 2 | inner |