Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(0.396143 - 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.4.k.a.124.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.92048 | − | 1.68614i | 1.03255 | − | 0.596141i | 0.114833 | − | 0.993385i | \(-0.463367\pi\) |
0.917713 | + | 0.397244i | \(0.130033\pi\) | |||||||
\(3\) | −4.97494 | − | 1.50000i | −0.957427 | − | 0.288675i | ||||
\(4\) | 1.68614 | − | 2.92048i | 0.210768 | − | 0.365060i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −17.0584 | + | 4.00772i | −1.16068 | + | 0.272691i | ||||
\(7\) | −1.40965 | + | 0.813859i | −0.0761137 | + | 0.0439443i | −0.537574 | − | 0.843217i | \(-0.680659\pi\) |
0.461460 | + | 0.887161i | \(0.347326\pi\) | |||||||
\(8\) | 15.6060i | 0.689693i | ||||||||
\(9\) | 22.5000 | + | 14.9248i | 0.833333 | + | 0.552771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.4307 | + | 28.4588i | 0.450368 | + | 0.780060i | 0.998409 | − | 0.0563918i | \(-0.0179596\pi\) |
−0.548041 | + | 0.836451i | \(0.684626\pi\) | |||||||
\(12\) | −12.7692 | + | 12.0000i | −0.307178 | + | 0.288675i | ||||
\(13\) | 28.5977 | + | 16.5109i | 0.610121 | + | 0.352253i | 0.773013 | − | 0.634391i | \(-0.218749\pi\) |
−0.162892 | + | 0.986644i | \(0.552082\pi\) | |||||||
\(14\) | −2.74456 | + | 4.75372i | −0.0523939 | + | 0.0907490i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 39.8030 | + | 68.9408i | 0.621922 | + | 1.07720i | ||||
\(17\) | − | 110.307i | − | 1.57373i | −0.617126 | − | 0.786864i | \(-0.711703\pi\) | ||
0.617126 | − | 0.786864i | \(-0.288297\pi\) | |||||||
\(18\) | 90.8762 | + | 5.64947i | 1.18998 | + | 0.0739774i | ||||
\(19\) | 54.3070 | 0.655731 | 0.327865 | − | 0.944724i | \(-0.393671\pi\) | ||||
0.327865 | + | 0.944724i | \(0.393671\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.23369 | − | 1.93443i | 0.0855590 | − | 0.0201013i | ||||
\(22\) | 95.9711 | + | 55.4090i | 0.930051 | + | 0.536965i | ||||
\(23\) | 58.4026 | + | 33.7188i | 0.529469 | + | 0.305689i | 0.740800 | − | 0.671725i | \(-0.234447\pi\) |
−0.211331 | + | 0.977415i | \(0.567780\pi\) | |||||||
\(24\) | 23.4090 | − | 77.6387i | 0.199097 | − | 0.660331i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 111.359 | 0.839970 | ||||||||
\(27\) | −89.5489 | − | 108.000i | −0.638285 | − | 0.769800i | ||||
\(28\) | 5.48913i | 0.0370481i | ||||||||
\(29\) | 137.259 | + | 237.740i | 0.878912 | + | 1.52232i | 0.852536 | + | 0.522668i | \(0.175063\pi\) |
0.0263757 | + | 0.999652i | \(0.491603\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 5.19615i | 0.0173812 | − | 0.0301050i | −0.857204 | − | 0.514977i | \(-0.827800\pi\) |
0.874585 | + | 0.484872i | \(0.161134\pi\) | |||||||
\(32\) | 124.366 | + | 71.8030i | 0.687034 | + | 0.396659i | ||||
\(33\) | −39.0535 | − | 166.227i | −0.206010 | − | 0.876860i | ||||
\(34\) | −185.993 | − | 322.150i | −0.938164 | − | 1.62495i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 81.5258 | − | 40.5455i | 0.377434 | − | 0.187711i | ||||
\(37\) | 347.723i | 1.54501i | 0.635010 | + | 0.772504i | \(0.280996\pi\) | ||||
−0.635010 | + | 0.772504i | \(0.719004\pi\) | |||||||
\(38\) | 158.603 | − | 91.5693i | 0.677072 | − | 0.390908i | ||||
\(39\) | −117.505 | − | 125.037i | −0.482459 | − | 0.513383i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −145.668 | + | 252.305i | −0.554868 | + | 0.961060i | 0.443046 | + | 0.896499i | \(0.353898\pi\) |
−0.997914 | + | 0.0645606i | \(0.979435\pi\) | |||||||
\(42\) | 20.7846 | − | 19.5326i | 0.0763604 | − | 0.0717607i | ||||
\(43\) | 174.408 | − | 100.694i | 0.618533 | − | 0.357110i | −0.157765 | − | 0.987477i | \(-0.550429\pi\) |
0.776297 | + | 0.630367i | \(0.217095\pi\) | |||||||
\(44\) | 110.818 | 0.379692 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 227.418 | 0.728935 | ||||||||
\(47\) | 417.507 | − | 241.048i | 1.29574 | − | 0.748094i | 0.316071 | − | 0.948735i | \(-0.397636\pi\) |
0.979665 | + | 0.200642i | \(0.0643027\pi\) | |||||||
\(48\) | −94.6062 | − | 402.681i | −0.284484 | − | 1.21087i | ||||
\(49\) | −170.175 | + | 294.752i | −0.496138 | + | 0.859336i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −165.461 | + | 548.771i | −0.454296 | + | 1.50673i | ||||
\(52\) | 96.4394 | − | 55.6793i | 0.257187 | − | 0.148487i | ||||
\(53\) | − | 175.228i | − | 0.454140i | −0.973878 | − | 0.227070i | \(-0.927085\pi\) | ||
0.973878 | − | 0.227070i | \(-0.0729147\pi\) | |||||||
\(54\) | −443.629 | − | 164.420i | −1.11797 | − | 0.414347i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.7011 | − | 21.9989i | −0.0303081 | − | 0.0524951i | ||||
\(57\) | −270.174 | − | 81.4605i | −0.627815 | − | 0.189293i | ||||
\(58\) | 801.728 | + | 462.878i | 1.81503 | + | 1.04791i | ||||
\(59\) | −91.6209 | + | 158.692i | −0.202170 | + | 0.350169i | −0.949227 | − | 0.314591i | \(-0.898133\pi\) |
0.747057 | + | 0.664760i | \(0.231466\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −218.297 | − | 378.102i | −0.458199 | − | 0.793623i | 0.540667 | − | 0.841237i | \(-0.318172\pi\) |
−0.998866 | + | 0.0476132i | \(0.984839\pi\) | |||||||
\(62\) | − | 20.2337i | − | 0.0414465i | ||||||
\(63\) | −43.8637 | − | 2.72686i | −0.0877192 | − | 0.00545321i | ||||
\(64\) | −152.568 | −0.297984 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −394.337 | − | 419.613i | −0.735447 | − | 0.782587i | ||||
\(67\) | −720.100 | − | 415.750i | −1.31305 | − | 0.758089i | −0.330448 | − | 0.943824i | \(-0.607200\pi\) |
−0.982600 | + | 0.185736i | \(0.940533\pi\) | |||||||
\(68\) | −322.150 | − | 185.993i | −0.574506 | − | 0.331691i | ||||
\(69\) | −239.971 | − | 255.353i | −0.418683 | − | 0.445520i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −118.951 | −0.198829 | −0.0994146 | − | 0.995046i | \(-0.531697\pi\) | ||||
−0.0994146 | + | 0.995046i | \(0.531697\pi\) | |||||||
\(72\) | −232.916 | + | 351.134i | −0.381242 | + | 0.574744i | ||||
\(73\) | 183.318i | 0.293914i | 0.989143 | + | 0.146957i | \(0.0469479\pi\) | ||||
−0.989143 | + | 0.146957i | \(0.953052\pi\) | |||||||
\(74\) | 586.310 | + | 1015.52i | 0.921042 | + | 1.59529i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 91.5693 | − | 158.603i | 0.138207 | − | 0.239381i | ||||
\(77\) | −46.3229 | − | 26.7446i | −0.0685583 | − | 0.0395822i | ||||
\(78\) | −554.002 | − | 167.038i | −0.804210 | − | 0.242478i | ||||
\(79\) | −319.147 | − | 552.778i | −0.454517 | − | 0.787246i | 0.544144 | − | 0.838992i | \(-0.316855\pi\) |
−0.998660 | + | 0.0517463i | \(0.983521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 283.500 | + | 671.617i | 0.388889 | + | 0.921285i | ||||
\(82\) | 982.470i | 1.32312i | ||||||||
\(83\) | −1294.40 | + | 747.322i | −1.71179 | + | 0.988304i | −0.779647 | + | 0.626219i | \(0.784602\pi\) |
−0.932145 | + | 0.362085i | \(0.882065\pi\) | |||||||
\(84\) | 8.23369 | − | 27.3081i | 0.0106949 | − | 0.0354709i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 339.569 | − | 588.151i | 0.425776 | − | 0.737465i | ||||
\(87\) | −326.247 | − | 1388.63i | −0.402038 | − | 1.71123i | ||||
\(88\) | −444.127 | + | 256.417i | −0.538002 | + | 0.310615i | ||||
\(89\) | 1437.27 | 1.71180 | 0.855900 | − | 0.517142i | \(-0.173004\pi\) | ||||
0.855900 | + | 0.517142i | \(0.173004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −53.7501 | −0.0619181 | ||||||||
\(92\) | 196.950 | − | 113.709i | 0.223190 | − | 0.128859i | ||||
\(93\) | −22.7190 | + | 21.3505i | −0.0253318 | + | 0.0238059i | ||||
\(94\) | 812.880 | − | 1407.95i | 0.891938 | − | 1.54488i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −511.011 | − | 543.765i | −0.543279 | − | 0.578102i | ||||
\(97\) | 772.294 | − | 445.884i | 0.808398 | − | 0.466729i | −0.0380011 | − | 0.999278i | \(-0.512099\pi\) |
0.846399 | + | 0.532549i | \(0.178766\pi\) | |||||||
\(98\) | 1147.76i | 1.18307i | ||||||||
\(99\) | −55.0516 | + | 885.548i | −0.0558878 | + | 0.899000i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 76.8720 | + | 133.146i | 0.0757332 | + | 0.131174i | 0.901405 | − | 0.432977i | \(-0.142537\pi\) |
−0.825672 | + | 0.564151i | \(0.809204\pi\) | |||||||
\(102\) | 442.080 | + | 1881.66i | 0.429142 | + | 1.82659i | ||||
\(103\) | −117.168 | − | 67.6469i | −0.112086 | − | 0.0647131i | 0.442909 | − | 0.896567i | \(-0.353947\pi\) |
−0.554995 | + | 0.831854i | \(0.687280\pi\) | |||||||
\(104\) | −257.668 | + | 446.294i | −0.242947 | + | 0.420796i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −295.459 | − | 511.750i | −0.270732 | − | 0.468921i | ||||
\(107\) | 718.783i | 0.649414i | 0.945815 | + | 0.324707i | \(0.105266\pi\) | ||||
−0.945815 | + | 0.324707i | \(0.894734\pi\) | |||||||
\(108\) | −466.404 | + | 79.4226i | −0.415553 | + | 0.0707634i | ||||
\(109\) | 2010.56 | 1.76676 | 0.883378 | − | 0.468661i | \(-0.155264\pi\) | ||||
0.883378 | + | 0.468661i | \(0.155264\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 521.584 | − | 1729.90i | 0.446005 | − | 1.47923i | ||||
\(112\) | −112.216 | − | 64.7881i | −0.0946735 | − | 0.0546598i | ||||
\(113\) | 196.367 | + | 113.372i | 0.163474 | + | 0.0943820i | 0.579505 | − | 0.814969i | \(-0.303246\pi\) |
−0.416031 | + | 0.909351i | \(0.636579\pi\) | |||||||
\(114\) | −926.392 | + | 217.647i | −0.761093 | + | 0.178812i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 925.755 | 0.740985 | ||||||||
\(117\) | 397.026 | + | 798.310i | 0.313718 | + | 0.630801i | ||||
\(118\) | 617.943i | 0.482087i | ||||||||
\(119\) | 89.7744 | + | 155.494i | 0.0691564 | + | 0.119782i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 125.564 | − | 217.483i | 0.0943381 | − | 0.163398i | ||||
\(122\) | −1275.07 | − | 736.160i | −0.946223 | − | 0.546302i | ||||
\(123\) | 1103.15 | − | 1036.70i | 0.808680 | − | 0.759968i | ||||
\(124\) | −10.1168 | − | 17.5229i | −0.00732677 | − | 0.0126903i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −132.701 | + | 65.9967i | −0.0938250 | + | 0.0466623i | ||||
\(127\) | − | 1132.24i | − | 0.791100i | −0.918444 | − | 0.395550i | \(-0.870554\pi\) | ||
0.918444 | − | 0.395550i | \(-0.129446\pi\) | |||||||
\(128\) | −1440.50 | + | 831.675i | −0.994717 | + | 0.574300i | ||||
\(129\) | −1018.71 | + | 239.336i | −0.695289 | + | 0.163352i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −388.753 | + | 673.339i | −0.259278 | + | 0.449083i | −0.966049 | − | 0.258360i | \(-0.916818\pi\) |
0.706770 | + | 0.707443i | \(0.250151\pi\) | |||||||
\(132\) | −551.312 | − | 166.227i | −0.363527 | − | 0.109608i | ||||
\(133\) | −76.5537 | + | 44.1983i | −0.0499101 | + | 0.0288156i | ||||
\(134\) | −2804.05 | −1.80771 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1721.45 | 1.08539 | ||||||||
\(137\) | −540.087 | + | 311.819i | −0.336808 | + | 0.194456i | −0.658860 | − | 0.752266i | \(-0.728961\pi\) |
0.322052 | + | 0.946722i | \(0.395628\pi\) | |||||||
\(138\) | −1131.39 | − | 341.127i | −0.697902 | − | 0.210425i | ||||
\(139\) | 641.341 | − | 1110.83i | 0.391351 | − | 0.677840i | −0.601277 | − | 0.799041i | \(-0.705341\pi\) |
0.992628 | + | 0.121201i | \(0.0386745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2438.64 | + | 572.937i | −1.45653 | + | 0.342198i | ||||
\(142\) | −347.394 | + | 200.568i | −0.205300 | + | 0.118530i | ||||
\(143\) | 1085.14i | 0.634574i | ||||||||
\(144\) | −133.361 | + | 2145.22i | −0.0771766 | + | 1.24145i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 309.099 | + | 535.376i | 0.175214 | + | 0.303480i | ||||
\(147\) | 1288.74 | − | 1211.11i | 0.723085 | − | 0.679529i | ||||
\(148\) | 1015.52 | + | 586.310i | 0.564021 | + | 0.325638i | ||||
\(149\) | 762.156 | − | 1320.09i | 0.419049 | − | 0.725814i | −0.576795 | − | 0.816889i | \(-0.695697\pi\) |
0.995844 | + | 0.0910749i | \(0.0290303\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1581.28 | − | 2738.86i | −0.852203 | − | 1.47606i | −0.879216 | − | 0.476424i | \(-0.841933\pi\) |
0.0270124 | − | 0.999635i | \(-0.491401\pi\) | |||||||
\(152\) | 847.514i | 0.452253i | ||||||||
\(153\) | 1646.31 | − | 2481.91i | 0.869911 | − | 1.31144i | ||||
\(154\) | −180.380 | −0.0943861 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −563.299 | + | 132.342i | −0.289103 | + | 0.0679220i | ||||
\(157\) | −2068.67 | − | 1194.35i | −1.05158 | − | 0.607131i | −0.128490 | − | 0.991711i | \(-0.541013\pi\) |
−0.923092 | + | 0.384580i | \(0.874346\pi\) | |||||||
\(158\) | −1864.12 | − | 1076.25i | −0.938619 | − | 0.541912i | ||||
\(159\) | −262.842 | + | 871.749i | −0.131099 | + | 0.434806i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −109.769 | −0.0537331 | ||||||||
\(162\) | 1960.40 | + | 1483.42i | 0.950761 | + | 0.719436i | ||||
\(163\) | − | 2544.79i | − | 1.22284i | −0.791305 | − | 0.611422i | \(-0.790598\pi\) | ||
0.791305 | − | 0.611422i | \(-0.209402\pi\) | |||||||
\(164\) | 491.235 | + | 850.844i | 0.233896 | + | 0.405120i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2520.18 | + | 4365.08i | −1.17834 | + | 2.04094i | ||||
\(167\) | −1190.40 | − | 687.279i | −0.551593 | − | 0.318462i | 0.198171 | − | 0.980167i | \(-0.436500\pi\) |
−0.749764 | + | 0.661705i | \(0.769833\pi\) | |||||||
\(168\) | 30.1887 | + | 128.495i | 0.0138637 | + | 0.0590094i | ||||
\(169\) | −553.282 | − | 958.313i | −0.251835 | − | 0.436191i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1221.91 | + | 810.522i | 0.546442 | + | 0.362469i | ||||
\(172\) | − | 679.139i | − | 0.301069i | ||||||
\(173\) | 2044.21 | − | 1180.23i | 0.898372 | − | 0.518675i | 0.0217005 | − | 0.999765i | \(-0.493092\pi\) |
0.876672 | + | 0.481089i | \(0.159759\pi\) | |||||||
\(174\) | −3294.23 | − | 3505.38i | −1.43526 | − | 1.52725i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1307.98 | + | 2265.49i | −0.560187 | + | 0.970272i | ||||
\(177\) | 693.846 | − | 652.052i | 0.294648 | − | 0.276899i | ||||
\(178\) | 4197.52 | − | 2423.44i | 1.76751 | − | 1.02047i | ||||
\(179\) | −1305.11 | −0.544963 | −0.272482 | − | 0.962161i | \(-0.587844\pi\) | ||||
−0.272482 | + | 0.962161i | \(0.587844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3099.43 | 1.27281 | 0.636406 | − | 0.771355i | \(-0.280420\pi\) | ||||
0.636406 | + | 0.771355i | \(0.280420\pi\) | |||||||
\(182\) | −156.976 | + | 90.6303i | −0.0639332 | + | 0.0369119i | ||||
\(183\) | 518.863 | + | 2208.48i | 0.209593 | + | 0.892107i | ||||
\(184\) | −526.214 | + | 911.429i | −0.210832 | + | 0.365171i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −30.3505 | + | 100.661i | −0.0119646 | + | 0.0396820i | ||||
\(187\) | 3139.21 | − | 1812.42i | 1.22760 | − | 0.708756i | ||||
\(188\) | − | 1625.76i | − | 0.630696i | ||||||
\(189\) | 214.129 | + | 79.3616i | 0.0824105 | + | 0.0305434i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −190.356 | − | 329.706i | −0.0721135 | − | 0.124904i | 0.827714 | − | 0.561150i | \(-0.189641\pi\) |
−0.899827 | + | 0.436246i | \(0.856308\pi\) | |||||||
\(192\) | 759.016 | + | 228.852i | 0.285298 | + | 0.0860207i | ||||
\(193\) | −1338.91 | − | 773.020i | −0.499362 | − | 0.288307i | 0.229088 | − | 0.973406i | \(-0.426426\pi\) |
−0.728450 | + | 0.685099i | \(0.759759\pi\) | |||||||
\(194\) | 1503.65 | − | 2604.39i | 0.556472 | − | 0.963838i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 573.879 | + | 993.987i | 0.209140 | + | 0.362240i | ||||
\(197\) | 4284.60i | 1.54957i | 0.632226 | + | 0.774784i | \(0.282141\pi\) | ||||
−0.632226 | + | 0.774784i | \(0.717859\pi\) | |||||||
\(198\) | 1332.38 | + | 2679.05i | 0.478224 | + | 0.961576i | ||||
\(199\) | 1402.85 | 0.499727 | 0.249863 | − | 0.968281i | \(-0.419614\pi\) | ||||
0.249863 | + | 0.968281i | \(0.419614\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2958.83 | + | 3148.48i | 1.03831 | + | 1.10486i | ||||
\(202\) | 449.007 | + | 259.234i | 0.156396 | + | 0.0902953i | ||||
\(203\) | −386.974 | − | 223.420i | −0.133795 | − | 0.0772463i | ||||
\(204\) | 1323.68 | + | 1408.53i | 0.454296 | + | 0.483415i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −456.249 | −0.154312 | ||||||||
\(207\) | 810.813 | + | 1630.32i | 0.272248 | + | 0.547416i | ||||
\(208\) | 2628.73i | 0.876296i | ||||||||
\(209\) | 892.303 | + | 1545.51i | 0.295320 | + | 0.511509i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1075.23 | − | 1862.35i | 0.350814 | − | 0.607628i | −0.635578 | − | 0.772036i | \(-0.719238\pi\) |
0.986392 | + | 0.164409i | \(0.0525716\pi\) | |||||||
\(212\) | −511.750 | − | 295.459i | −0.165789 | − | 0.0957180i | ||||
\(213\) | 591.773 | + | 178.426i | 0.190365 | + | 0.0573971i | ||||
\(214\) | 1211.97 | + | 2099.19i | 0.387142 | + | 0.670550i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1685.44 | − | 1397.50i | 0.530926 | − | 0.440220i | ||||
\(217\) | 9.76631i | 0.00305521i | ||||||||
\(218\) | 5871.79 | − | 3390.08i | 1.82426 | − | 1.05324i | ||||
\(219\) | 274.977 | − | 911.994i | 0.0848456 | − | 0.281401i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1821.27 | − | 3154.52i | 0.554351 | − | 0.960164i | ||||
\(222\) | −1393.58 | − | 5931.60i | −0.421310 | − | 1.79326i | ||||
\(223\) | −2215.42 | + | 1279.07i | −0.665272 | + | 0.384095i | −0.794283 | − | 0.607548i | \(-0.792153\pi\) |
0.129011 | + | 0.991643i | \(0.458820\pi\) | |||||||
\(224\) | −233.750 | −0.0697236 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 764.646 | 0.225060 | ||||||||
\(227\) | 3537.32 | − | 2042.27i | 1.03427 | − | 0.597138i | 0.116067 | − | 0.993241i | \(-0.462971\pi\) |
0.918206 | + | 0.396104i | \(0.129638\pi\) | |||||||
\(228\) | −693.456 | + | 651.684i | −0.201426 | + | 0.189293i | ||||
\(229\) | −1370.95 | + | 2374.56i | −0.395612 | + | 0.685221i | −0.993179 | − | 0.116598i | \(-0.962801\pi\) |
0.597567 | + | 0.801819i | \(0.296134\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 190.337 | + | 202.537i | 0.0542132 | + | 0.0576881i | ||||
\(232\) | −3710.17 | + | 2142.07i | −1.04993 | + | 0.606179i | ||||
\(233\) | 5084.70i | 1.42966i | 0.699300 | + | 0.714828i | \(0.253495\pi\) | ||||
−0.699300 | + | 0.714828i | \(0.746505\pi\) | |||||||
\(234\) | 2505.57 | + | 1662.01i | 0.699975 | + | 0.464311i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 308.971 | + | 535.154i | 0.0852217 | + | 0.147608i | ||||
\(237\) | 758.567 | + | 3228.76i | 0.207908 | + | 0.884938i | ||||
\(238\) | 524.369 | + | 302.745i | 0.142814 | + | 0.0824538i | ||||
\(239\) | 738.236 | − | 1278.66i | 0.199801 | − | 0.346066i | −0.748663 | − | 0.662951i | \(-0.769304\pi\) |
0.948464 | + | 0.316885i | \(0.102637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −881.728 | − | 1527.20i | −0.235673 | − | 0.408197i | 0.723795 | − | 0.690015i | \(-0.242396\pi\) |
−0.959468 | + | 0.281818i | \(0.909063\pi\) | |||||||
\(242\) | − | 846.874i | − | 0.224955i | ||||||
\(243\) | −402.970 | − | 3766.50i | −0.106381 | − | 0.994325i | ||||
\(244\) | −1472.32 | −0.386294 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1473.70 | − | 4887.73i | 0.381951 | − | 1.26679i | ||||
\(247\) | 1553.05 | + | 896.657i | 0.400075 | + | 0.230983i | ||||
\(248\) | 81.0910 | + | 46.8179i | 0.0207632 | + | 0.0119877i | ||||
\(249\) | 7560.54 | − | 1776.28i | 1.92422 | − | 0.452077i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1705.16 | 0.428801 | 0.214400 | − | 0.976746i | \(-0.431220\pi\) | ||||
0.214400 | + | 0.976746i | \(0.431220\pi\) | |||||||
\(252\) | −81.9242 | + | 123.505i | −0.0204791 | + | 0.0308734i | ||||
\(253\) | 2216.09i | 0.550690i | ||||||||
\(254\) | −1909.11 | − | 3306.68i | −0.471607 | − | 0.816848i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2194.37 | + | 3800.76i | −0.535735 | + | 0.927920i | ||||
\(257\) | 197.970 | + | 114.298i | 0.0480507 | + | 0.0277421i | 0.523833 | − | 0.851821i | \(-0.324502\pi\) |
−0.475782 | + | 0.879563i | \(0.657835\pi\) | |||||||
\(258\) | −2571.56 | + | 2416.66i | −0.620537 | + | 0.583158i | ||||
\(259\) | −282.997 | − | 490.166i | −0.0678942 | − | 0.117596i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −459.892 | + | 7397.73i | −0.109068 | + | 1.75444i | ||||
\(262\) | 2621.97i | 0.618266i | ||||||||
\(263\) | −1116.10 | + | 644.380i | −0.261679 | + | 0.151081i | −0.625100 | − | 0.780544i | \(-0.714942\pi\) |
0.363421 | + | 0.931625i | \(0.381609\pi\) | |||||||
\(264\) | 2594.13 | − | 609.468i | 0.604764 | − | 0.142084i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −149.049 | + | 258.161i | −0.0343563 | + | 0.0595069i | ||||
\(267\) | −7150.32 | − | 2155.90i | −1.63892 | − | 0.494154i | ||||
\(268\) | −2428.38 | + | 1402.03i | −0.553496 | + | 0.319561i | ||||
\(269\) | −973.981 | −0.220761 | −0.110380 | − | 0.993889i | \(-0.535207\pi\) | ||||
−0.110380 | + | 0.993889i | \(0.535207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4021.83 | −0.901508 | −0.450754 | − | 0.892648i | \(-0.648845\pi\) | ||||
−0.450754 | + | 0.892648i | \(0.648845\pi\) | |||||||
\(272\) | 7604.65 | − | 4390.55i | 1.69522 | − | 0.978736i | ||||
\(273\) | 267.403 | + | 80.6252i | 0.0592820 | + | 0.0178742i | ||||
\(274\) | −1051.54 | + | 1821.32i | −0.231847 | + | 0.401570i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1150.38 | + | 270.271i | −0.250886 | + | 0.0589435i | ||||
\(277\) | 2926.45 | − | 1689.59i | 0.634777 | − | 0.366489i | −0.147823 | − | 0.989014i | \(-0.547227\pi\) |
0.782600 | + | 0.622525i | \(0.213893\pi\) | |||||||
\(278\) | − | 4325.56i | − | 0.933201i | ||||||
\(279\) | 145.052 | − | 72.1390i | 0.0311255 | − | 0.0154797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −366.654 | − | 635.063i | −0.0778388 | − | 0.134821i | 0.824478 | − | 0.565893i | \(-0.191469\pi\) |
−0.902317 | + | 0.431073i | \(0.858135\pi\) | |||||||
\(282\) | −6155.95 | + | 5785.14i | −1.29993 | + | 1.22163i | ||||
\(283\) | −5983.39 | − | 3454.51i | −1.25680 | − | 0.725617i | −0.284353 | − | 0.958720i | \(-0.591779\pi\) |
−0.972452 | + | 0.233103i | \(0.925112\pi\) | |||||||
\(284\) | −200.568 | + | 347.394i | −0.0419068 | + | 0.0725847i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1829.70 | + | 3169.13i | 0.378295 | + | 0.655227i | ||||
\(287\) | − | 474.214i | − | 0.0975331i | ||||||
\(288\) | 1726.60 | + | 3471.71i | 0.353267 | + | 0.710322i | ||||
\(289\) | −7254.64 | −1.47662 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4510.94 | + | 1059.81i | −0.908715 | + | 0.213494i | ||||
\(292\) | 535.376 | + | 309.099i | 0.107296 | + | 0.0619475i | ||||
\(293\) | 4026.57 | + | 2324.74i | 0.802850 | + | 0.463525i | 0.844467 | − | 0.535608i | \(-0.179918\pi\) |
−0.0416170 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(294\) | 1721.64 | − | 5710.02i | 0.341523 | − | 1.13271i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5426.55 | −1.06558 | ||||||||
\(297\) | 1602.20 | − | 4322.97i | 0.313027 | − | 0.844593i | ||||
\(298\) | − | 5140.41i | − | 0.999248i | ||||||
\(299\) | 1113.45 | + | 1928.56i | 0.215360 | + | 0.373014i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −163.902 | + | 283.886i | −0.0313859 | + | 0.0543619i | ||||
\(302\) | −9236.19 | − | 5332.52i | −1.75988 | − | 1.01607i | ||||
\(303\) | −182.714 | − | 777.702i | −0.0346424 | − | 0.147452i | ||||
\(304\) | 2161.58 | + | 3743.97i | 0.407813 | + | 0.706353i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 623.176 | − | 10024.3i | 0.116420 | − | 1.87271i | ||||
\(307\) | 7361.42i | 1.36853i | 0.729234 | + | 0.684264i | \(0.239877\pi\) | ||||
−0.729234 | + | 0.684264i | \(0.760123\pi\) | |||||||
\(308\) | −156.214 | + | 90.1902i | −0.0288997 | + | 0.0166853i | ||||
\(309\) | 481.433 | + | 512.291i | 0.0886335 | + | 0.0943146i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1354.60 | − | 2346.24i | 0.246986 | − | 0.427792i | −0.715702 | − | 0.698405i | \(-0.753893\pi\) |
0.962688 | + | 0.270614i | \(0.0872266\pi\) | |||||||
\(312\) | 1951.32 | − | 1833.78i | 0.354077 | − | 0.332749i | ||||
\(313\) | −5407.22 | + | 3121.86i | −0.976467 | + | 0.563763i | −0.901202 | − | 0.433400i | \(-0.857314\pi\) |
−0.0752653 | + | 0.997164i | \(0.523980\pi\) | |||||||
\(314\) | −8055.37 | −1.44774 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2152.50 | −0.383189 | ||||||||
\(317\) | −1804.82 | + | 1042.02i | −0.319776 | + | 0.184623i | −0.651293 | − | 0.758827i | \(-0.725773\pi\) |
0.331517 | + | 0.943449i | \(0.392440\pi\) | |||||||
\(318\) | 702.266 | + | 2989.12i | 0.123840 | + | 0.527111i | ||||
\(319\) | −4510.54 | + | 7812.48i | −0.791667 | + | 1.37121i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1078.17 | − | 3575.90i | 0.187470 | − | 0.621767i | ||||
\(322\) | −320.579 | + | 185.087i | −0.0554819 | + | 0.0320325i | ||||
\(323\) | − | 5990.45i | − | 1.03194i | ||||||
\(324\) | 2439.46 | + | 304.483i | 0.418289 | + | 0.0522091i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4290.88 | − | 7432.02i | −0.728987 | − | 1.26264i | ||||
\(327\) | −10002.4 | − | 3015.83i | −1.69154 | − | 0.510018i | ||||
\(328\) | −3937.47 | − | 2273.30i | −0.662836 | − | 0.382689i | ||||
\(329\) | −392.358 | + | 679.583i | −0.0657489 | + | 0.113880i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 113.938 | + | 197.347i | 0.0189203 | + | 0.0327709i | 0.875331 | − | 0.483525i | \(-0.160644\pi\) |
−0.856410 | + | 0.516296i | \(0.827310\pi\) | |||||||
\(332\) | 5040.36i | 0.833210i | ||||||||
\(333\) | −5189.70 | + | 7823.76i | −0.854035 | + | 1.28751i | ||||
\(334\) | −4635.39 | −0.759394 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 461.087 | + | 490.641i | 0.0748641 | + | 0.0796627i | ||||
\(337\) | 2959.62 | + | 1708.74i | 0.478400 | + | 0.276205i | 0.719750 | − | 0.694234i | \(-0.244257\pi\) |
−0.241349 | + | 0.970438i | \(0.577590\pi\) | |||||||
\(338\) | −3231.70 | − | 1865.82i | −0.520063 | − | 0.300259i | ||||
\(339\) | −806.853 | − | 858.570i | −0.129269 | − | 0.137555i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 197.168 | 0.0313116 | ||||||||
\(342\) | 4935.21 | + | 306.806i | 0.780309 | + | 0.0485092i | ||||
\(343\) | − | 1112.30i | − | 0.175098i | ||||||
\(344\) | 1571.43 | + | 2721.80i | 0.246296 | + | 0.426598i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3980.05 | − | 6893.65i | 0.618407 | − | 1.07111i | ||||
\(347\) | 3126.00 | + | 1804.80i | 0.483610 | + | 0.279212i | 0.721920 | − | 0.691977i | \(-0.243260\pi\) |
−0.238310 | + | 0.971189i | \(0.576593\pi\) | |||||||
\(348\) | −4605.57 | − | 1388.63i | −0.709439 | − | 0.213904i | ||||
\(349\) | −4400.42 | − | 7621.74i | −0.674925 | − | 1.16900i | −0.976491 | − | 0.215559i | \(-0.930843\pi\) |
0.301566 | − | 0.953445i | \(-0.402491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −777.715 | − | 4567.08i | −0.118266 | − | 0.694509i | ||||
\(352\) | 4719.09i | 0.714570i | ||||||||
\(353\) | 7370.30 | − | 4255.24i | 1.11128 | − | 0.641597i | 0.172119 | − | 0.985076i | \(-0.444939\pi\) |
0.939160 | + | 0.343479i | \(0.111605\pi\) | |||||||
\(354\) | 926.914 | − | 3074.23i | 0.139166 | − | 0.461563i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2423.44 | − | 4197.52i | 0.360792 | − | 0.624910i | ||||
\(357\) | −213.381 | − | 908.234i | −0.0316340 | − | 0.134647i | ||||
\(358\) | −3811.55 | + | 2200.60i | −0.562700 | + | 0.324875i | ||||
\(359\) | −4320.35 | −0.635152 | −0.317576 | − | 0.948233i | \(-0.602869\pi\) | ||||
−0.317576 | + | 0.948233i | \(0.602869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3909.75 | −0.570017 | ||||||||
\(362\) | 9051.83 | − | 5226.08i | 1.31424 | − | 0.758775i | ||||
\(363\) | −950.898 | + | 893.619i | −0.137491 | + | 0.129209i | ||||
\(364\) | −90.6303 | + | 156.976i | −0.0130503 | + | 0.0226038i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5239.14 | + | 5574.95i | 0.748235 | + | 0.796195i | ||||
\(367\) | −5716.10 | + | 3300.19i | −0.813020 | + | 0.469397i | −0.848003 | − | 0.529991i | \(-0.822195\pi\) |
0.0349838 | + | 0.999388i | \(0.488862\pi\) | |||||||
\(368\) | 5368.43i | 0.760459i | ||||||||
\(369\) | −7043.15 | + | 3502.79i | −0.993636 | + | 0.494168i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 142.611 | + | 247.010i | 0.0199569 | + | 0.0345663i | ||||
\(372\) | 24.0463 | + | 102.351i | 0.00335146 | + | 0.0142651i | ||||
\(373\) | 7455.14 | + | 4304.23i | 1.03489 | + | 0.597492i | 0.918381 | − | 0.395698i | \(-0.129497\pi\) |
0.116506 | + | 0.993190i | \(0.462831\pi\) | |||||||
\(374\) | 6112.00 | − | 10586.3i | 0.845037 | − | 1.46365i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3761.78 | + | 6515.60i | 0.515955 | + | 0.893660i | ||||
\(377\) | 9065.10i | 1.23840i | ||||||||
\(378\) | 759.174 | − | 129.278i | 0.103301 | − | 0.0175908i | ||||
\(379\) | 7129.80 | 0.966314 | 0.483157 | − | 0.875534i | \(-0.339490\pi\) | ||||
0.483157 | + | 0.875534i | \(0.339490\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1698.36 | + | 5632.81i | −0.228371 | + | 0.757421i | ||||
\(382\) | −1111.86 | − | 641.934i | −0.148921 | − | 0.0859796i | ||||
\(383\) | −5133.33 | − | 2963.73i | −0.684859 | − | 0.395404i | 0.116824 | − | 0.993153i | \(-0.462729\pi\) |
−0.801683 | + | 0.597749i | \(0.796062\pi\) | |||||||
\(384\) | 8413.93 | − | 1976.78i | 1.11815 | − | 0.262700i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5213.68 | −0.687486 | ||||||||
\(387\) | 5427.01 | + | 337.379i | 0.712844 | + | 0.0443151i | ||||
\(388\) | − | 3007.30i | − | 0.393485i | ||||||
\(389\) | 519.432 | + | 899.683i | 0.0677024 | + | 0.117264i | 0.897890 | − | 0.440221i | \(-0.145100\pi\) |
−0.830187 | + | 0.557485i | \(0.811766\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3719.42 | − | 6442.22i | 0.481072 | − | 0.833240i | ||||
\(392\) | −4599.89 | − | 2655.75i | −0.592678 | − | 0.342183i | ||||
\(393\) | 2944.03 | − | 2766.69i | 0.377879 | − | 0.355117i | ||||
\(394\) | 7224.43 | + | 12513.1i | 0.923761 | + | 1.60000i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2493.40 | + | 1653.94i | 0.316410 | + | 0.209882i | ||||
\(397\) | − | 13441.4i | − | 1.69926i | −0.527382 | − | 0.849628i | \(-0.676826\pi\) | ||
0.527382 | − | 0.849628i | \(-0.323174\pi\) | |||||||
\(398\) | 4097.01 | − | 2365.41i | 0.515991 | − | 0.297907i | ||||
\(399\) | 447.147 | − | 105.053i | 0.0561037 | − | 0.0131810i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6537.70 | + | 11323.6i | −0.814157 | + | 1.41016i | 0.0957739 | + | 0.995403i | \(0.469467\pi\) |
−0.909931 | + | 0.414759i | \(0.863866\pi\) | |||||||
\(402\) | 13950.0 | + | 4206.08i | 1.73075 | + | 0.521841i | ||||
\(403\) | 171.586 | − | 99.0652i | 0.0212092 | − | 0.0122451i | ||||
\(404\) | 518.468 | 0.0638484 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1506.87 | −0.184199 | ||||||||
\(407\) | −9895.78 | + | 5713.33i | −1.20520 | + | 0.695821i | ||||
\(408\) | −8564.10 | − | 2582.17i | −1.03918 | − | 0.313325i | ||||
\(409\) | −2636.59 | + | 4566.71i | −0.318756 | + | 0.552101i | −0.980229 | − | 0.197868i | \(-0.936598\pi\) |
0.661473 | + | 0.749969i | \(0.269932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3154.63 | − | 741.151i | 0.378604 | − | 0.0889496i | ||||
\(412\) | −395.123 | + | 228.124i | −0.0472484 | + | 0.0272788i | ||||
\(413\) | − | 298.266i | − | 0.0355368i | ||||||
\(414\) | 5116.91 | + | 3394.18i | 0.607446 | + | 0.402934i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2371.06 | + | 4106.80i | 0.279449 | + | 0.484020i | ||||
\(417\) | −4856.88 | + | 4564.32i | −0.570366 | + | 0.536009i | ||||
\(418\) | 5211.91 | + | 3009.10i | 0.609863 | + | 0.352105i | ||||
\(419\) | 6923.06 | − | 11991.1i | 0.807192 | − | 1.39810i | −0.107609 | − | 0.994193i | \(-0.534319\pi\) |
0.914801 | − | 0.403905i | \(-0.132347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −548.684 | − | 950.349i | −0.0635184 | − | 0.110017i | 0.832517 | − | 0.553999i | \(-0.186899\pi\) |
−0.896036 | + | 0.443982i | \(0.853565\pi\) | |||||||
\(422\) | − | 7251.94i | − | 0.836538i | ||||||
\(423\) | 12991.5 | + | 807.637i | 1.49330 | + | 0.0928338i | ||||
\(424\) | 2734.60 | 0.313217 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2029.12 | − | 476.722i | 0.230777 | − | 0.0542189i | ||||
\(427\) | 615.444 | + | 355.327i | 0.0697504 | + | 0.0402704i | ||||
\(428\) | 2099.19 | + | 1211.97i | 0.237075 | + | 0.136875i | ||||
\(429\) | 1627.71 | − | 5398.51i | 0.183186 | − | 0.607558i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15912.8 | 1.77841 | 0.889205 | − | 0.457509i | \(-0.151258\pi\) | ||||
0.889205 | + | 0.457509i | \(0.151258\pi\) | |||||||
\(432\) | 3881.29 | − | 10472.3i | 0.432266 | − | 1.16632i | ||||
\(433\) | 3566.31i | 0.395810i | 0.980221 | + | 0.197905i | \(0.0634138\pi\) | ||||
−0.980221 | + | 0.197905i | \(0.936586\pi\) | |||||||
\(434\) | 16.4674 | + | 28.5223i | 0.00182133 | + | 0.00315464i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3390.08 | − | 5871.79i | 0.372375 | − | 0.644972i | ||||
\(437\) | 3171.67 | + | 1831.17i | 0.347189 | + | 0.200450i | ||||
\(438\) | −734.686 | − | 3127.11i | −0.0801476 | − | 0.341140i | ||||
\(439\) | −290.411 | − | 503.007i | −0.0315730 | − | 0.0546861i | 0.849807 | − | 0.527094i | \(-0.176718\pi\) |
−0.881380 | + | 0.472408i | \(0.843385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8228.06 | + | 4092.09i | −0.888464 | + | 0.441863i | ||||
\(442\) | − | 12283.6i | − | 1.32188i | ||||||
\(443\) | −9346.82 | + | 5396.39i | −1.00244 | + | 0.578759i | −0.908969 | − | 0.416863i | \(-0.863129\pi\) |
−0.0934706 | + | 0.995622i | \(0.529796\pi\) | |||||||
\(444\) | −4172.67 | − | 4440.13i | −0.446005 | − | 0.474593i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4313.40 | + | 7471.03i | −0.457949 | + | 0.793191i | ||||
\(447\) | −5771.82 | + | 5424.15i | −0.610733 | + | 0.573945i | ||||
\(448\) | 215.067 | − | 124.169i | 0.0226807 | − | 0.0130947i | ||||
\(449\) | −2894.01 | −0.304180 | −0.152090 | − | 0.988367i | \(-0.548600\pi\) | ||||
−0.152090 | + | 0.988367i | \(0.548600\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9573.74 | −0.999578 | ||||||||
\(452\) | 662.203 | − | 382.323i | 0.0689102 | − | 0.0397853i | ||||
\(453\) | 3758.48 | + | 15997.6i | 0.389821 | + | 1.65923i | ||||
\(454\) | 6887.11 | − | 11928.8i | 0.711956 | − | 1.23314i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1271.27 | − | 4216.33i | 0.130554 | − | 0.432999i | ||||
\(457\) | −2771.21 | + | 1599.96i | −0.283658 | + | 0.163770i | −0.635078 | − | 0.772448i | \(-0.719032\pi\) |
0.351420 | + | 0.936218i | \(0.385699\pi\) | |||||||
\(458\) | 9246.49i | 0.943363i | ||||||||
\(459\) | −11913.2 | + | 9877.87i | −1.21146 | + | 1.00449i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3658.19 | − | 6336.17i | −0.369585 | − | 0.640141i | 0.619915 | − | 0.784669i | \(-0.287167\pi\) |
−0.989501 | + | 0.144528i | \(0.953834\pi\) | |||||||
\(462\) | 897.381 | + | 270.571i | 0.0903678 | + | 0.0272469i | ||||
\(463\) | −6072.55 | − | 3505.99i | −0.609536 | − | 0.351916i | 0.163248 | − | 0.986585i | \(-0.447803\pi\) |
−0.772784 | + | 0.634669i | \(0.781136\pi\) | |||||||
\(464\) | −10926.7 | + | 18925.6i | −1.09323 | + | 1.89353i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8573.53 | + | 14849.8i | 0.852277 | + | 1.47619i | ||||
\(467\) | 8002.63i | 0.792971i | 0.918041 | + | 0.396485i | \(0.129770\pi\) | ||||
−0.918041 | + | 0.396485i | \(0.870230\pi\) | |||||||
\(468\) | 3000.89 | + | 186.555i | 0.296402 | + | 0.0184263i | ||||
\(469\) | 1353.45 | 0.133255 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8500.00 | + | 9044.83i | 0.831549 | + | 0.884849i | ||||
\(472\) | −2476.54 | − | 1429.83i | −0.241509 | − | 0.139435i | ||||
\(473\) | 5731.28 | + | 3308.95i | 0.557134 | + | 0.321661i | ||||
\(474\) | 7659.52 | + | 8150.47i | 0.742222 | + | 0.789797i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 605.489 | 0.0583037 | ||||||||
\(477\) | 2615.25 | − | 3942.63i | 0.251035 | − | 0.378450i | ||||
\(478\) | − | 4979.08i | − | 0.476439i | ||||||
\(479\) | −1589.42 | − | 2752.96i | −0.151613 | − | 0.262601i | 0.780208 | − | 0.625520i | \(-0.215113\pi\) |
−0.931820 | + | 0.362920i | \(0.881780\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5741.21 | + | 9944.06i | −0.544234 | + | 0.942641i | ||||
\(482\) | −5150.14 | − | 2973.44i | −0.486686 | − | 0.280988i | ||||
\(483\) | 546.096 | + | 164.654i | 0.0514456 | + | 0.0155114i | ||||
\(484\) | −423.437 | − | 733.414i | −0.0397668 | − | 0.0688781i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7527.71 | − | 10320.5i | −0.702601 | − | 0.963269i | ||||
\(487\) | − | 13060.3i | − | 1.21523i | −0.794232 | − | 0.607615i | \(-0.792126\pi\) | ||
0.794232 | − | 0.607615i | \(-0.207874\pi\) | |||||||
\(488\) | 5900.65 | − | 3406.74i | 0.547356 | − | 0.316016i | ||||
\(489\) | −3817.19 | + | 12660.2i | −0.353005 | + | 1.17078i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2200.81 | − | 3811.91i | 0.202283 | − | 0.350365i | −0.746981 | − | 0.664846i | \(-0.768497\pi\) |
0.949264 | + | 0.314481i | \(0.101831\pi\) | |||||||
\(492\) | −1167.60 | − | 4969.75i | −0.106991 | − | 0.455393i | ||||
\(493\) | 26224.4 | − | 15140.7i | 2.39572 | − | 1.38317i | ||||
\(494\) | 6047.56 | 0.550794 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 477.636 | 0.0432389 | ||||||||
\(497\) | 167.679 | − | 96.8093i | 0.0151336 | − | 0.00873741i | ||||
\(498\) | 19085.3 | − | 17935.7i | 1.71734 | − | 1.61389i | ||||
\(499\) | 9362.60 | − | 16216.5i | 0.839935 | − | 1.45481i | −0.0500129 | − | 0.998749i | \(-0.515926\pi\) |
0.889948 | − | 0.456062i | \(-0.150740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4891.26 | + | 5204.77i | 0.436178 | + | 0.464136i | ||||
\(502\) | 4979.90 | − | 2875.15i | 0.442757 | − | 0.255626i | ||||
\(503\) | − | 3811.68i | − | 0.337882i | −0.985626 | − | 0.168941i | \(-0.945965\pi\) | ||
0.985626 | − | 0.168941i | \(-0.0540347\pi\) | |||||||
\(504\) | 42.5553 | − | 684.536i | 0.00376104 | − | 0.0604993i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3736.64 | + | 6472.06i | 0.328289 | + | 0.568613i | ||||
\(507\) | 1315.07 | + | 5597.47i | 0.115196 | + | 0.490320i | ||||
\(508\) | −3306.68 | − | 1909.11i | −0.288799 | − | 0.166738i | ||||
\(509\) | 2247.74 | − | 3893.20i | 0.195735 | − | 0.339024i | −0.751406 | − | 0.659840i | \(-0.770624\pi\) |
0.947141 | + | 0.320816i | \(0.103957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −149.195 | − | 258.413i | −0.0129158 | − | 0.0223709i | ||||
\(512\) | 1493.27i | 0.128894i | ||||||||
\(513\) | −4863.13 | − | 5865.16i | −0.418543 | − | 0.504782i | ||||
\(514\) | 770.891 | 0.0661528 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1018.71 | + | 3378.67i | −0.0869111 | + | 0.288251i | ||||
\(517\) | 13719.9 | + | 7921.16i | 1.16712 | + | 0.673834i | ||||
\(518\) | −1652.98 | − | 954.347i | −0.140208 | − | 0.0809490i | ||||
\(519\) | −11940.2 | + | 2805.23i | −1.00985 | + | 0.237256i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12095.0 | 1.01706 | 0.508531 | − | 0.861043i | \(-0.330189\pi\) | ||||
0.508531 | + | 0.861043i | \(0.330189\pi\) | |||||||
\(522\) | 11130.5 | + | 22380.4i | 0.933274 | + | 1.87656i | ||||
\(523\) | 7385.38i | 0.617476i | 0.951147 | + | 0.308738i | \(0.0999067\pi\) | ||||
−0.951147 | + | 0.308738i | \(0.900093\pi\) | |||||||
\(524\) | 1310.98 | + | 2270.69i | 0.109295 | + | 0.189304i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2173.03 | + | 3763.80i | −0.180131 | + | 0.311995i | ||||
\(527\) | −573.172 | − | 330.921i | −0.0473772 | − | 0.0273532i | ||||
\(528\) | 9905.37 | − | 9308.70i | 0.816431 | − | 0.767253i | ||||
\(529\) | −3809.59 | − | 6598.40i | −0.313108 | − | 0.542320i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4429.92 | + | 2203.15i | −0.362038 | + | 0.180054i | ||||
\(532\) | 298.098i | 0.0242936i | ||||||||
\(533\) | −8331.56 | + | 4810.23i | −0.677073 | + | 0.390908i | ||||
\(534\) | −24517.5 | + | 5760.17i | −1.98685 | + | 0.466792i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6488.18 | − | 11237.9i | 0.522848 | − | 0.905600i | ||||
\(537\) | 6492.83 | + | 1957.66i | 0.521763 | + | 0.157317i | ||||
\(538\) | −2844.49 | + | 1642.27i | −0.227946 | + | 0.131605i | ||||
\(539\) | −11184.4 | −0.893778 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5935.19 | −0.471670 | −0.235835 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235835 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(542\) | −11745.7 | + | 6781.37i | −0.930849 | + | 0.537426i | ||||
\(543\) | −15419.5 | − | 4649.15i | −1.21862 | − | 0.367429i | ||||
\(544\) | 7920.37 | − | 13718.5i | 0.624234 | − | 1.08120i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 916.892 | − | 215.416i | 0.0718670 | − | 0.0168845i | ||||
\(547\) | 8796.41 | − | 5078.61i | 0.687582 | − | 0.396976i | −0.115124 | − | 0.993351i | \(-0.536726\pi\) |
0.802705 | + | 0.596376i | \(0.203393\pi\) | |||||||
\(548\) | 2103.08i | 0.163940i | ||||||||
\(549\) | 731.413 | − | 11765.3i | 0.0568596 | − | 0.914632i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7454.16 | + | 12911.0i | 0.576330 | + | 0.998232i | ||||
\(552\) | 3985.03 | − | 3744.98i | 0.307272 | − | 0.288763i | ||||
\(553\) | 899.768 | + | 519.481i | 0.0691899 | + | 0.0399468i | ||||
\(554\) | 5697.76 | − | 9868.81i | 0.436958 | − | 0.756833i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2162.78 | − | 3746.05i | −0.164968 | − | 0.285733i | ||||
\(557\) | − | 5709.62i | − | 0.434334i | −0.976134 | − | 0.217167i | \(-0.930318\pi\) | ||
0.976134 | − | 0.217167i | \(-0.0696817\pi\) | |||||||
\(558\) | 301.984 | − | 455.258i | 0.0229104 | − | 0.0345387i | ||||
\(559\) | 6650.20 | 0.503173 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18336.0 | + | 4307.88i | −1.37994 | + | 0.324204i | ||||
\(562\) | −2141.61 | − | 1236.46i | −0.160744 | − | 0.0928058i | ||||
\(563\) | −11205.6 | − | 6469.56i | −0.838828 | − | 0.484297i | 0.0180378 | − | 0.999837i | \(-0.494258\pi\) |
−0.856866 | + | 0.515540i | \(0.827591\pi\) | |||||||
\(564\) | −2438.64 | + | 8088.06i | −0.182066 | + | 0.603845i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23299.2 | −1.73028 | ||||||||
\(567\) | −946.236 | − | 716.012i | −0.0700850 | − | 0.0530330i | ||||
\(568\) | − | 1856.34i | − | 0.137131i | ||||||
\(569\) | −3062.71 | − | 5304.77i | −0.225651 | − | 0.390839i | 0.730863 | − | 0.682524i | \(-0.239118\pi\) |
−0.956515 | + | 0.291684i | \(0.905784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9641.20 | − | 16699.0i | 0.706605 | − | 1.22388i | −0.259504 | − | 0.965742i | \(-0.583559\pi\) |
0.966109 | − | 0.258134i | \(-0.0831076\pi\) | |||||||
\(572\) | 3169.13 | + | 1829.70i | 0.231658 | + | 0.133748i | ||||
\(573\) | 452.450 | + | 1925.80i | 0.0329867 | + | 0.140404i | ||||
\(574\) | −799.592 | − | 1384.93i | −0.0581434 | − | 0.100707i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3432.78 | − | 2277.05i | −0.248320 | − | 0.164717i | ||||
\(577\) | 4988.14i | 0.359894i | 0.983676 | + | 0.179947i | \(0.0575927\pi\) | ||||
−0.983676 | + | 0.179947i | \(0.942407\pi\) | |||||||
\(578\) | −21187.0 | + | 12232.3i | −1.52468 | + | 0.880274i | ||||
\(579\) | 5501.46 | + | 5854.09i | 0.394876 | + | 0.420186i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1216.43 | − | 2106.92i | 0.0868606 | − | 0.150447i | ||||
\(582\) | −11387.1 | + | 10701.2i | −0.811018 | + | 0.762165i | ||||
\(583\) | 4986.78 | − | 2879.12i | 0.354256 | − | 0.204530i | ||||
\(584\) | −2860.85 | −0.202710 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15679.4 | 1.10531 | ||||||||
\(587\) | 13245.0 | − | 7647.00i | 0.931311 | − | 0.537693i | 0.0440852 | − | 0.999028i | \(-0.485963\pi\) |
0.887226 | + | 0.461335i | \(0.152629\pi\) | |||||||
\(588\) | −1364.03 | − | 5805.84i | −0.0956661 | − | 0.407192i | ||||
\(589\) | 162.921 | − | 282.188i | 0.0113974 | − | 0.0197408i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6426.90 | − | 21315.6i | 0.447322 | − | 1.48360i | ||||
\(592\) | −23972.3 | + | 13840.4i | −1.66428 | + | 0.960874i | ||||
\(593\) | − | 11090.9i | − | 0.768040i | −0.923325 | − | 0.384020i | \(-0.874539\pi\) | ||
0.923325 | − | 0.384020i | \(-0.125461\pi\) | |||||||
\(594\) | −2609.94 | − | 15326.7i | −0.180281 | − | 1.05869i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2570.21 | − | 4451.73i | −0.176644 | − | 0.305956i | ||||
\(597\) | −6979.10 | − | 2104.28i | −0.478452 | − | 0.144259i | ||||
\(598\) | 6503.63 | + | 3754.88i | 0.444738 | + | 0.256770i | ||||
\(599\) | −14100.8 | + | 24423.3i | −0.961840 | + | 1.66596i | −0.243965 | + | 0.969784i | \(0.578448\pi\) |
−0.717875 | + | 0.696172i | \(0.754885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10572.0 | − | 18311.3i | −0.717539 | − | 1.24281i | −0.961972 | − | 0.273148i | \(-0.911935\pi\) |
0.244433 | − | 0.969666i | \(-0.421398\pi\) | |||||||
\(602\) | 1105.45i | 0.0748416i | ||||||||
\(603\) | −9997.26 | − | 20101.7i | −0.675157 | − | 1.35755i | ||||
\(604\) | −10665.0 | −0.718467 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1844.93 | − | 1963.18i | −0.123672 | − | 0.131599i | ||||
\(607\) | −7620.14 | − | 4399.49i | −0.509542 | − | 0.294184i | 0.223103 | − | 0.974795i | \(-0.428381\pi\) |
−0.732645 | + | 0.680611i | \(0.761715\pi\) | |||||||
\(608\) | 6753.97 | + | 3899.41i | 0.450509 | + | 0.260102i | ||||
\(609\) | 1590.04 | + | 1691.96i | 0.105799 | + | 0.112581i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15919.6 | 1.05407 | ||||||||
\(612\) | −4472.45 | − | 8992.87i | −0.295406 | − | 0.593979i | ||||
\(613\) | 19539.8i | 1.28745i | 0.765257 | + | 0.643724i | \(0.222612\pi\) | ||||
−0.765257 | + | 0.643724i | \(0.777388\pi\) | |||||||
\(614\) | 12412.4 | + | 21498.9i | 0.815836 | + | 1.41307i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 417.375 | − | 722.914i | 0.0272995 | − | 0.0472842i | ||||
\(617\) | −2835.26 | − | 1636.94i | −0.184997 | − | 0.106808i | 0.404641 | − | 0.914475i | \(-0.367396\pi\) |
−0.589638 | + | 0.807667i | \(0.700730\pi\) | |||||||
\(618\) | 2269.81 | + | 684.373i | 0.147743 | + | 0.0445462i | ||||
\(619\) | 4693.24 | + | 8128.92i | 0.304745 | + | 0.527834i | 0.977205 | − | 0.212300i | \(-0.0680954\pi\) |
−0.672460 | + | 0.740134i | \(0.734762\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1588.26 | − | 9326.96i | −0.102632 | − | 0.602702i | ||||
\(622\) | − | 9136.21i | − | 0.588953i | ||||||
\(623\) | −2026.04 | + | 1169.73i | −0.130291 | + | 0.0752238i | ||||
\(624\) | 3943.09 | − | 13077.8i | 0.252965 | − | 0.838989i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10527.8 | + | 18234.7i | −0.672165 | + | 1.16422i | ||||
\(627\) | −2120.88 | − | 9027.29i | −0.135087 | − | 0.574984i | ||||
\(628\) | −6976.15 | + | 4027.68i | −0.443278 | + | 0.255927i | ||||
\(629\) | 38356.3 | 2.43142 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9647.08 | 0.608628 | 0.304314 | − | 0.952572i | \(-0.401573\pi\) | ||||
0.304314 | + | 0.952572i | \(0.401573\pi\) | |||||||
\(632\) | 8626.64 | − | 4980.59i | 0.542958 | − | 0.313477i | ||||
\(633\) | −8142.72 | + | 7652.23i | −0.511286 | + | 0.480488i | ||||
\(634\) | −3513.97 | + | 6086.37i | −0.220122 | + | 0.381263i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2102.74 | + | 2237.52i | 0.131099 | + | 0.139502i | ||||
\(637\) | −9733.23 | + | 5619.48i | −0.605408 | + | 0.349532i | ||||
\(638\) | 30421.6i | 1.88778i | ||||||||
\(639\) | −2676.40 | − | 1775.32i | −0.165691 | − | 0.109907i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3501.88 | + | 6065.44i | 0.215782 | + | 0.373745i | 0.953514 | − | 0.301348i | \(-0.0974367\pi\) |
−0.737732 | + | 0.675093i | \(0.764103\pi\) | |||||||
\(642\) | −2880.68 | − | 12261.3i | −0.177089 | − | 0.753761i | ||||
\(643\) | 5446.34 | + | 3144.44i | 0.334032 | + | 0.192853i | 0.657630 | − | 0.753341i | \(-0.271559\pi\) |
−0.323598 | + | 0.946195i | \(0.604892\pi\) | |||||||
\(644\) | −185.087 | + | 320.579i | −0.0113252 | + | 0.0196158i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10100.7 | − | 17495.0i | −0.615183 | − | 1.06553i | ||||
\(647\) | 5900.85i | 0.358557i | 0.983798 | + | 0.179279i | \(0.0573764\pi\) | ||||
−0.983798 | + | 0.179279i | \(0.942624\pi\) | |||||||
\(648\) | −10481.2 | + | 4424.29i | −0.635404 | + | 0.268214i | ||||
\(649\) | −6021.58 | −0.364203 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.6495 | − | 48.5868i | 0.000881963 | − | 0.00292514i | ||||
\(652\) | −7432.02 | − | 4290.88i | −0.446412 | − | 0.257736i | ||||
\(653\) | 6828.74 | + | 3942.57i | 0.409233 | + | 0.236271i | 0.690460 | − | 0.723370i | \(-0.257408\pi\) |
−0.281227 | + | 0.959641i | \(0.590741\pi\) | |||||||
\(654\) | −34296.9 | + | 8057.75i | −2.05064 | + | 0.481778i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23192.2 | −1.38034 | ||||||||
\(657\) | −2735.98 | + | 4124.65i | −0.162467 | + | 0.244928i | ||||
\(658\) | 2646.28i | 0.156782i | ||||||||
\(659\) | 14378.9 | + | 24905.0i | 0.849959 | + | 1.47217i | 0.881244 | + | 0.472662i | \(0.156707\pi\) |
−0.0312845 | + | 0.999511i | \(0.509960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4130.11 | + | 7153.57i | −0.243030 | + | 0.420940i | −0.961576 | − | 0.274539i | \(-0.911475\pi\) |
0.718546 | + | 0.695479i | \(0.244808\pi\) | |||||||
\(662\) | 665.509 | + | 384.232i | 0.0390721 | + | 0.0225583i | ||||
\(663\) | −13792.5 | + | 12961.7i | −0.807926 | + | 0.759260i | ||||
\(664\) | −11662.7 | − | 20200.4i | −0.681626 | − | 1.18061i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1964.45 | + | 31599.7i | −0.114296 | + | 1.83853i | ||||
\(667\) | 18512.9i | 1.07470i | ||||||||
\(668\) | −4014.37 | + | 2317.70i | −0.232516 | + | 0.134243i | ||||
\(669\) | 12940.2 | − | 3040.18i | 0.747828 | − | 0.175695i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7173.56 | − | 12425.0i | 0.412716 | − | 0.714845i | ||||
\(672\) | 1162.89 | + | 350.625i | 0.0667553 | + | 0.0201275i | ||||
\(673\) | 697.118 | − | 402.481i | 0.0399285 | − | 0.0230528i | −0.479903 | − | 0.877322i | \(-0.659328\pi\) |
0.519831 | + | 0.854269i | \(0.325995\pi\) | |||||||
\(674\) | 11524.7 | 0.658627 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3731.65 | −0.212315 | ||||||||
\(677\) | −1180.63 | + | 681.636i | −0.0670240 | + | 0.0386963i | −0.533137 | − | 0.846029i | \(-0.678987\pi\) |
0.466114 | + | 0.884725i | \(0.345654\pi\) | |||||||
\(678\) | −3804.07 | − | 1146.97i | −0.215478 | − | 0.0649692i | ||||
\(679\) | −725.774 | + | 1257.08i | −0.0410201 | + | 0.0710489i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20661.3 | + | 4854.19i | −1.16262 | + | 0.273147i | ||||
\(682\) | 575.827 | − | 332.454i | 0.0323307 | − | 0.0186661i | ||||
\(683\) | − | 11434.6i | − | 0.640604i | −0.947315 | − | 0.320302i | \(-0.896216\pi\) | ||
0.947315 | − | 0.320302i | \(-0.103784\pi\) | |||||||
\(684\) | 4427.42 | − | 2201.91i | 0.247495 | − | 0.123088i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1875.50 | − | 3248.46i | −0.104383 | − | 0.180797i | ||||
\(687\) | 10382.3 | − | 9756.87i | 0.576576 | − | 0.541845i | ||||
\(688\) | 13883.9 | + | 8015.86i | 0.769358 | + | 0.444189i | ||||
\(689\) | 2893.17 | − | 5011.12i | 0.159972 | − | 0.277080i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9765.29 | + | 16914.0i | 0.537611 | + | 0.931170i | 0.999032 | + | 0.0439884i | \(0.0140065\pi\) |
−0.461421 | + | 0.887181i | \(0.652660\pi\) | |||||||
\(692\) | − | 7960.10i | − | 0.437280i | ||||||
\(693\) | −643.109 | − | 1293.11i | −0.0352521 | − | 0.0708822i | ||||
\(694\) | 12172.6 | 0.665799 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 21671.0 | − | 5091.40i | 1.18022 | − | 0.277283i | ||||
\(697\) | 27831.0 | + | 16068.3i | 1.51245 | + | 0.873212i | ||||
\(698\) | −25702.7 | − | 14839.4i | −1.39378 | − | 0.804701i | ||||
\(699\) | 7627.06 | − | 25296.1i | 0.412706 | − | 1.36879i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11041.4 | −0.594903 | −0.297452 | − | 0.954737i | \(-0.596137\pi\) | ||||
−0.297452 | + | 0.954737i | \(0.596137\pi\) | |||||||
\(702\) | −9972.04 | − | 12026.7i | −0.536140 | − | 0.646609i | ||||
\(703\) | 18883.8i | 1.01311i | ||||||||
\(704\) | −2506.80 | − | 4341.90i | −0.134203 | − | 0.232446i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14349.9 | − | 24854.7i | 0.764964 | − | 1.32496i | ||||
\(707\) | −216.725 | − | 125.126i | −0.0115287 | − | 0.00665608i | ||||
\(708\) | −734.382 | − | 3125.82i | −0.0389827 | − | 0.165926i | ||||
\(709\) | 1969.54 | + | 3411.34i | 0.104327 | + | 0.180699i | 0.913463 | − | 0.406922i | \(-0.133398\pi\) |
−0.809136 | + | 0.587621i | \(0.800065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1069.31 | − | 17200.7i | 0.0564027 | − | 0.907282i | ||||
\(712\) | 22430.0i | 1.18062i | ||||||||
\(713\) | 350.416 | − | 202.313i | 0.0184056 | − | 0.0106265i | ||||
\(714\) | −2154.59 | − | 2292.69i | −0.112932 | − | 0.120170i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2200.60 | + | 3811.55i | −0.114861 | + | 0.198944i | ||||
\(717\) | −5590.67 | + | 5253.91i | −0.291196 | + | 0.273655i | ||||
\(718\) | −12617.5 | + | 7284.72i | −0.655824 | + | 0.378640i | ||||
\(719\) | 23298.2 | 1.20845 | 0.604225 | − | 0.796814i | \(-0.293483\pi\) | ||||
0.604225 | + | 0.796814i | \(0.293483\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 220.220 | 0.0113751 | ||||||||
\(722\) | −11418.3 | + | 6592.38i | −0.588569 | + | 0.339810i | ||||
\(723\) | 2095.75 | + | 8920.31i | 0.107803 | + | 0.458852i | ||||
\(724\) | 5226.08 | − | 9051.83i | 0.268267 | − | 0.464653i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1270.31 | + | 4213.15i | −0.0649389 | + | 0.215378i | ||||
\(727\) | 8231.12 | − | 4752.24i | 0.419911 | − | 0.242436i | −0.275128 | − | 0.961408i | \(-0.588720\pi\) |
0.695039 | + | 0.718972i | \(0.255387\pi\) | |||||||
\(728\) | − | 838.823i | − | 0.0427044i | ||||||
\(729\) | −3645.00 | + | 19342.6i | −0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11107.3 | − | 19238.4i | −0.561994 | − | 0.973402i | ||||
\(732\) | 7324.70 | + | 2208.48i | 0.369848 | + | 0.111513i | ||||
\(733\) | −6340.01 | − | 3660.40i | −0.319473 | − | 0.184448i | 0.331685 | − | 0.943390i | \(-0.392383\pi\) |
−0.651157 | + | 0.758943i | \(0.725716\pi\) | |||||||
\(734\) | −11129.2 | + | 19276.3i | −0.559653 | + | 0.969348i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4842.22 | + | 8386.96i | 0.242509 | + | 0.420037i | ||||
\(737\) | − | 27324.3i | − | 1.36567i | ||||||
\(738\) | −14663.2 | + | 22105.6i | −0.731381 | + | 1.10260i | ||||
\(739\) | 1274.52 | 0.0634424 | 0.0317212 | − | 0.999497i | \(-0.489901\pi\) | ||||
0.0317212 | + | 0.999497i | \(0.489901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6381.37 | − | 6790.39i | −0.316363 | − | 0.336641i | ||||
\(742\) | 832.986 | + | 480.925i | 0.0412128 | + | 0.0237942i | ||||
\(743\) | −1681.09 | − | 970.576i | −0.0830055 | − | 0.0479232i | 0.457923 | − | 0.888992i | \(-0.348594\pi\) |
−0.540928 | + | 0.841069i | \(0.681927\pi\) | |||||||
\(744\) | −333.196 | − | 354.553i | −0.0164187 | − | 0.0174711i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29030.1 | 1.42476 | ||||||||
\(747\) | −40277.6 | − | 2503.93i | −1.97280 | − | 0.122642i | ||||
\(748\) | − | 12224.0i | − | 0.597531i | ||||||
\(749\) | −584.988 | − | 1013.23i | −0.0285380 | − | 0.0494293i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8270.01 | + | 14324.1i | −0.401834 | + | 0.695996i | −0.993947 | − | 0.109858i | \(-0.964960\pi\) |
0.592114 | + | 0.805854i | \(0.298294\pi\) | |||||||
\(752\) | 33236.0 | + | 19188.8i | 1.61169 | + | 0.930511i | ||||
\(753\) | −8483.08 | − | 2557.75i | −0.410545 | − | 0.123784i | ||||
\(754\) | 15285.0 | + | 26474.4i | 0.738260 | + | 1.27870i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 592.826 | − | 491.545i | 0.0285197 | − | 0.0236472i | ||||
\(757\) | − | 21145.7i | − | 1.01526i | −0.861575 | − | 0.507631i | \(-0.830521\pi\) | ||
0.861575 | − | 0.507631i | \(-0.169479\pi\) | |||||||
\(758\) | 20822.4 | − | 12021.8i | 0.997764 | − | 0.576059i | ||||
\(759\) | 3324.14 | − | 11024.9i | 0.158970 | − | 0.527245i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10067.1 | − | 17436.7i | 0.479543 | − | 0.830593i | −0.520181 | − | 0.854056i | \(-0.674136\pi\) |
0.999725 | + | 0.0234624i | \(0.00746901\pi\) | |||||||
\(762\) | 4537.69 | + | 19314.2i | 0.215726 | + | 0.918213i | ||||
\(763\) | −2834.17 | + | 1636.31i | −0.134474 | + | 0.0776388i | ||||
\(764\) | −1283.87 | −0.0607968 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19989.1 | −0.942865 | ||||||||
\(767\) | −5240.29 | + | 3025.48i | −0.246696 | + | 0.142430i | ||||
\(768\) | 16618.0 | − | 15617.0i | 0.780795 | − | 0.733762i | ||||
\(769\) | 1097.36 | − | 1900.68i | 0.0514587 | − | 0.0891291i | −0.839149 | − | 0.543902i | \(-0.816946\pi\) |
0.890607 | + | 0.454773i | \(0.150280\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −813.442 | − | 865.581i | −0.0379966 | − | 0.0404321i | ||||
\(772\) | −4515.18 | + | 2606.84i | −0.210499 | + | 0.121531i | ||||
\(773\) | − | 8327.70i | − | 0.387486i | −0.981052 | − | 0.193743i | \(-0.937937\pi\) | ||
0.981052 | − | 0.193743i | \(-0.0620628\pi\) | |||||||
\(774\) | 16418.4 | − | 8165.40i | 0.762462 | − | 0.379198i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6958.46 | + | 12052.4i | 0.321900 | + | 0.557547i | ||||
\(777\) | 672.646 | + | 2863.04i | 0.0310567 | + | 0.132189i | ||||
\(778\) | 3033.98 | + | 1751.67i | 0.139812 | + | 0.0807204i | ||||
\(779\) | −7910.82 | + | 13701.9i | −0.363844 | + | 0.630196i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1954.45 | − | 3385.20i | −0.0895463 | − | 0.155099i | ||||
\(782\) | − | 25085.8i | − | 1.14715i | ||||||
\(783\) | 13384.5 | − | 36113.4i | 0.610887 | − | 1.64826i | ||||
\(784\) | −27093.9 | −1.23424 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3932.95 | − | 13044.1i | 0.178478 | − | 0.591944i | ||||
\(787\) | −16422.7 | − | 9481.64i | −0.743845 | − | 0.429459i | 0.0796209 | − | 0.996825i | \(-0.474629\pi\) |
−0.823465 | + | 0.567366i | \(0.807962\pi\) | |||||||
\(788\) | 12513.1 | + | 7224.43i | 0.565686 | + | 0.326599i | ||||
\(789\) | 6519.10 | − | 1531.60i | 0.294152 | − | 0.0691084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −369.076 | −0.0165902 | ||||||||
\(792\) | −13819.8 | − | 859.134i | −0.620034 | − | 0.0385454i | ||||
\(793\) | − | 14417.1i | − | 0.645608i | ||||||
\(794\) | −22664.1 | − | 39255.4i | −1.01300 | − | 1.75456i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2365.41 | − | 4097.01i | 0.105326 | − | 0.182430i | ||||
\(797\) | 29674.5 | + | 17132.6i | 1.31885 | + | 0.761439i | 0.983544 | − | 0.180670i | \(-0.0578267\pi\) |
0.335307 | + | 0.942109i | \(0.391160\pi\) | |||||||
\(798\) | 1128.75 | − | 1060.76i | 0.0500718 | − | 0.0470557i | ||||
\(799\) | −26589.2 | − | 46053.9i | −1.17730 | − | 2.03914i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32338.5 | + | 21451.0i | 1.42650 | + | 0.946233i | ||||
\(802\) | 44093.9i | 1.94141i | ||||||||
\(803\) | −5217.00 | + | 3012.04i | −0.229270 | + | 0.132369i | ||||
\(804\) | 14184.1 | − | 3332.42i | 0.622181 | − | 0.146176i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 334.076 | − | 578.636i | 0.0145997 | − | 0.0252873i | ||||
\(807\) | 4845.49 | + | 1460.97i | 0.211362 | + | 0.0637282i | ||||
\(808\) | −2077.88 | + | 1199.66i | −0.0904696 | + | 0.0522327i | ||||
\(809\) | −36425.5 | −1.58300 | −0.791502 | − | 0.611166i | \(-0.790701\pi\) | ||||
−0.791502 | + | 0.611166i | \(0.790701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45174.0 | 1.95595 | 0.977973 | − | 0.208732i | \(-0.0669335\pi\) | ||||
0.977973 | + | 0.208732i | \(0.0669335\pi\) | |||||||
\(812\) | −1304.99 | + | 753.435i | −0.0563991 | + | 0.0325620i | ||||
\(813\) | 20008.3 | + | 6032.74i | 0.863128 | + | 0.260243i | ||||
\(814\) | −19267.0 | + | 33371.3i | −0.829615 | + | 1.43694i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −44418.5 | + | 10435.7i | −1.90559 | + | 0.447700i | ||||
\(817\) | 9471.56 | − | 5468.41i | 0.405591 | − | 0.234168i | ||||
\(818\) | 17782.7i | 0.760093i | ||||||||
\(819\) | −1209.38 | − | 802.210i | −0.0515984 | − | 0.0342265i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3459.65 | + | 5992.29i | 0.147068 | + | 0.254729i | 0.930143 | − | 0.367199i | \(-0.119683\pi\) |
−0.783075 | + | 0.621928i | \(0.786350\pi\) | |||||||
\(822\) | 7963.34 | − | 7483.66i | 0.337900 | − | 0.317546i | ||||
\(823\) | 9871.42 | + | 5699.26i | 0.418100 | + | 0.241390i | 0.694264 | − | 0.719721i | \(-0.255730\pi\) |
−0.276164 | + | 0.961110i | \(0.589063\pi\) | |||||||
\(824\) | 1055.70 | − | 1828.52i | 0.0446322 | − | 0.0773052i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −502.919 | − | 871.080i | −0.0211850 | − | 0.0366934i | ||||
\(827\) | − | 34712.0i | − | 1.45956i | −0.683683 | − | 0.729779i | \(-0.739623\pi\) | ||
0.683683 | − | 0.729779i | \(-0.260377\pi\) | |||||||
\(828\) | 6128.46 | + | 380.986i | 0.257221 | + | 0.0159906i | ||||
\(829\) | −2732.97 | −0.114500 | −0.0572498 | − | 0.998360i | \(-0.518233\pi\) | ||||
−0.0572498 | + | 0.998360i | \(0.518233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17093.3 | + | 4015.91i | −0.713549 | + | 0.167642i | ||||
\(832\) | −4363.09 | − | 2519.03i | −0.181806 | − | 0.104966i | ||||
\(833\) | 32513.2 | + | 18771.5i | 1.35236 | + | 0.780786i | ||||
\(834\) | −6488.34 | + | 21519.4i | −0.269392 | + | 0.893472i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6018.19 | 0.248975 | ||||||||
\(837\) | −829.831 | + | 141.310i | −0.0342690 | + | 0.00583557i | ||||
\(838\) | − | 46693.0i | − | 1.92480i | ||||||
\(839\) | −4787.89 | − | 8292.87i | −0.197016 | − | 0.341242i | 0.750544 | − | 0.660821i | \(-0.229792\pi\) |
−0.947560 | + | 0.319579i | \(0.896458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25485.8 | + | 44142.8i | −1.04497 | + | 1.80995i | ||||
\(842\) | −3204.85 | − | 1850.32i | −0.131171 | − | 0.0757318i | ||||
\(843\) | 871.484 | + | 3709.38i | 0.0356056 | + | 0.151551i | ||||
\(844\) | −3625.97 | − | 6280.37i | −0.147880 | − | 0.256136i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 39303.2 | − | 19546.8i | 1.59725 | − | 0.794364i | ||||
\(847\) | 408.766i | 0.0165825i | ||||||||
\(848\) | 12080.4 | − | 6974.60i | 0.489200 | − | 0.282440i | ||||
\(849\) | 24585.2 | + | 26161.1i | 0.993832 | + | 1.05753i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11724.8 | + | 20307.9i | −0.472292 | + | 0.818034i | ||||
\(852\) | 1518.90 | − | 1427.41i | 0.0610761 | − | 0.0573971i | ||||
\(853\) | 7830.51 | − | 4520.95i | 0.314316 | − | 0.181470i | −0.334540 | − | 0.942381i | \(-0.608581\pi\) |
0.648856 | + | 0.760911i | \(0.275248\pi\) | |||||||
\(854\) | 2396.52 | 0.0960274 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11217.3 | −0.447896 | ||||||||
\(857\) | 2005.09 | − | 1157.64i | 0.0799213 | − | 0.0461426i | −0.459507 | − | 0.888174i | \(-0.651974\pi\) |
0.539428 | + | 0.842032i | \(0.318640\pi\) | |||||||
\(858\) | −4348.94 | − | 18510.8i | −0.173043 | − | 0.736536i | ||||
\(859\) | −15701.6 | + | 27195.9i | −0.623667 | + | 1.08022i | 0.365130 | + | 0.930957i | \(0.381025\pi\) |
−0.988797 | + | 0.149266i | \(0.952309\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −711.322 | + | 2359.19i | −0.0281554 | + | 0.0933808i | ||||
\(862\) | 46473.2 | − | 26831.3i | 1.83629 | − | 1.06018i | ||||
\(863\) | − | 40883.5i | − | 1.61262i | −0.591493 | − | 0.806310i | \(-0.701461\pi\) | ||
0.591493 | − | 0.806310i | \(-0.298539\pi\) | |||||||
\(864\) | −3382.15 | − | 19861.4i | −0.133175 | − | 0.782060i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6013.30 | + | 10415.3i | 0.235959 | + | 0.408692i | ||||
\(867\) | 36091.4 | + | 10882.0i | 1.41376 | + | 0.426264i | ||||
\(868\) | 28.5223 | + | 16.4674i | 0.00111534 | + | 0.000643939i | ||||
\(869\) | 10487.6 | − | 18165.1i | 0.409399 | − | 0.709100i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13728.8 | − | 23779.0i | −0.534078 | − | 0.925051i | ||||
\(872\) | 31376.7i | 1.21852i | ||||||||
\(873\) | 24031.4 | + | 1493.95i | 0.931659 | + | 0.0579182i | ||||
\(874\) | 12350.4 | 0.477985 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2199.81 | − | 2340.81i | −0.0848456 | − | 0.0902840i | ||||
\(877\) | −24521.2 | − | 14157.3i | −0.944154 | − | 0.545107i | −0.0528937 | − | 0.998600i | \(-0.516844\pi\) |
−0.891260 | + | 0.453493i | \(0.850178\pi\) | |||||||
\(878\) | −1696.28 | − | 979.348i | −0.0652013 | − | 0.0376440i | ||||
\(879\) | −16544.8 | − | 17605.3i | −0.634862 | − | 0.675554i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6479.51 | 0.247787 | 0.123893 | − | 0.992296i | \(-0.460462\pi\) | ||||
0.123893 | + | 0.992296i | \(0.460462\pi\) | |||||||
\(882\) | −17130.1 | + | 25824.5i | −0.653968 | + | 0.985893i | ||||
\(883\) | − | 17769.0i | − | 0.677208i | −0.940929 | − | 0.338604i | \(-0.890045\pi\) | ||
0.940929 | − | 0.338604i | \(-0.109955\pi\) | |||||||
\(884\) | −6141.82 | − | 10637.9i | −0.233678 | − | 0.404743i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18198.1 | + | 31520.1i | −0.690044 | + | 1.19519i | ||||
\(887\) | −22419.8 | − | 12944.1i | −0.848684 | − | 0.489988i | 0.0115224 | − | 0.999934i | \(-0.496332\pi\) |
−0.860207 | + | 0.509945i | \(0.829666\pi\) | |||||||
\(888\) | 26996.8 | + | 8139.83i | 1.02022 | + | 0.307607i | ||||
\(889\) | 921.481 | + | 1596.05i | 0.0347643 | + | 0.0602136i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14455.3 | + | 19103.2i | −0.543514 | + | 0.718273i | ||||
\(892\) | 8626.80i | 0.323819i | ||||||||
\(893\) | 22673.5 | − | 13090.6i | 0.849654 | − | 0.490548i | ||||
\(894\) | −7710.62 | + | 25573.2i | −0.288458 | + | 0.956707i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1353.73 | − | 2344.73i | 0.0504744 | − | 0.0874242i | ||||
\(897\) | −2646.52 | − | 11264.6i | −0.0985115 | − | 0.419303i | ||||
\(898\) | −8451.90 | + | 4879.71i | −0.314080 | + | 0.181334i | ||||
\(899\) | 1647.11 | 0.0611060 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19328.9 | −0.714694 | ||||||||
\(902\) | −27959.9 | + | 16142.7i | −1.03211 | + | 0.595889i | ||||
\(903\) | 1241.23 | − | 1166.46i | 0.0457426 | − | 0.0429873i | ||||
\(904\) | −1769.28 | + | 3064.49i | −0.0650946 | + | 0.112747i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 37950.7 | + | 40383.2i | 1.39164 | + | 1.48084i | ||||
\(907\) | 39134.2 | − | 22594.1i | 1.43267 | − | 0.827150i | 0.435343 | − | 0.900265i | \(-0.356627\pi\) |
0.997324 | + | 0.0731143i | \(0.0232938\pi\) | |||||||
\(908\) | − | 13774.2i | − | 0.503429i | ||||||
\(909\) | −257.562 | + | 4143.09i | −0.00939802 | + | 0.151175i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6587.08 | − | 11409.2i | −0.239560 | − | 0.414931i | 0.721028 | − | 0.692906i | \(-0.243670\pi\) |
−0.960588 | + | 0.277975i | \(0.910337\pi\) | |||||||
\(912\) | −5137.78 | − | 21868.4i | −0.186545 | − | 0.794007i | ||||
\(913\) | −42535.8 | − | 24558.0i | −1.54187 | − | 0.890200i | ||||
\(914\) | −5395.51 | + | 9345.29i | −0.195260 | + | 0.338200i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4623.24 | + | 8007.69i | 0.166765 | + | 0.288845i | ||||
\(917\) | − | 1265.56i | − | 0.0455752i | ||||||
\(918\) | −18136.7 | + | 48935.4i | −0.652069 | + | 1.75938i | ||||
\(919\) | 54078.5 | 1.94112 | 0.970558 | − | 0.240867i | \(-0.0774316\pi\) | ||||
0.970558 | + | 0.240867i | \(0.0774316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11042.1 | − | 36622.6i | 0.395060 | − | 1.31027i | ||||
\(922\) | −21367.3 | − | 12336.4i | −0.763228 | − | 0.440650i | ||||
\(923\) | −3401.72 | − | 1963.98i | −0.121310 | − | 0.0700383i | ||||
\(924\) | 912.440 | − | 214.370i | 0.0324860 | − | 0.00763229i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23646.4 | −0.839166 | ||||||||
\(927\) | −1626.66 | − | 3270.76i | −0.0576338 | − | 0.115886i | ||||
\(928\) | 39422.6i | 1.39451i | ||||||||
\(929\) | −22858.9 | − | 39592.8i | −0.807294 | − | 1.39827i | −0.914732 | − | 0.404062i | \(-0.867598\pi\) |
0.107438 | − | 0.994212i | \(-0.465735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9241.71 | + | 16007.1i | −0.325333 | + | 0.563493i | ||||
\(932\) | 14849.8 | + | 8573.53i | 0.521911 | + | 0.301325i | ||||
\(933\) | −10258.4 | + | 9640.50i | −0.359963 | + | 0.338281i | ||||
\(934\) | 13493.6 | + | 23371.5i | 0.472722 | + | 0.818779i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12458.4 | + | 6195.98i | −0.435059 | + | 0.216369i | ||||
\(937\) | 5055.54i | 0.176262i | 0.996109 | + | 0.0881309i | \(0.0280894\pi\) | ||||
−0.996109 | + | 0.0881309i | \(0.971911\pi\) | |||||||
\(938\) | 3952.72 | − | 2282.10i | 0.137592 | − | 0.0794385i | ||||
\(939\) | 31583.4 | − | 7420.23i | 1.09764 | − | 0.257881i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14056.0 | + | 24345.7i | −0.486942 | + | 0.843407i | −0.999887 | − | 0.0150136i | \(-0.995221\pi\) |
0.512946 | + | 0.858421i | \(0.328554\pi\) | |||||||
\(942\) | 40075.0 | + | 12083.1i | 1.38611 | + | 0.417927i | ||||
\(943\) | −17014.8 | + | 9823.52i | −0.587571 | + | 0.339234i | ||||
\(944\) | −14587.1 | −0.502935 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22317.4 | 0.767022 | ||||||||
\(947\) | −26085.0 | + | 15060.2i | −0.895090 | + | 0.516780i | −0.875604 | − | 0.483030i | \(-0.839536\pi\) |
−0.0194859 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(948\) | 10708.6 | + | 3228.76i | 0.366876 | + | 0.110617i | ||||
\(949\) | −3026.74 | + | 5242.46i | −0.103532 | + | 0.179323i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10541.9 | − | 2476.73i | 0.359458 | − | 0.0844514i | ||||
\(952\) | −2426.63 | + | 1401.02i | −0.0826130 | + | 0.0476967i | ||||
\(953\) | 19362.7i | 0.658154i | 0.944303 | + | 0.329077i | \(0.106738\pi\) | ||||
−0.944303 | + | 0.329077i | \(0.893262\pi\) | |||||||
\(954\) | 989.946 | − | 15924.1i | 0.0335961 | − | 0.540420i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2489.54 | − | 4312.01i | −0.0842233 | − | 0.145879i | ||||
\(957\) | 34158.4 | − | 32100.8i | 1.15380 | − | 1.08430i | ||||
\(958\) | −9283.74 | − | 5359.97i | −0.313094 | − | 0.180765i | ||||
\(959\) | 507.554 | − | 879.109i | 0.0170905 | − | 0.0296016i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14877.5 | + | 25768.6i | 0.499396 | + | 0.864979i | ||||
\(962\) | 38721.9i | 1.29776i | ||||||||
\(963\) | −10727.7 | + | 16172.6i | −0.358977 | + | 0.541179i | ||||
\(964\) | −5946.87 | −0.198689 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1872.49 | − | 439.925i | 0.0623669 | − | 0.0146525i | ||||
\(967\) | −26608.2 | − | 15362.3i | −0.884863 | − | 0.510876i | −0.0126043 | − | 0.999921i | \(-0.504012\pi\) |
−0.872259 | + | 0.489045i | \(0.837346\pi\) | |||||||
\(968\) | 3394.04 | + | 1959.55i | 0.112695 | + | 0.0650643i | ||||
\(969\) | −8985.67 | + | 29802.1i | −0.297896 | + | 0.988010i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49791.0 | −1.64559 | −0.822796 | − | 0.568336i | \(-0.807587\pi\) | ||||
−0.822796 | + | 0.568336i | \(0.807587\pi\) | |||||||
\(972\) | −11679.5 | − | 5173.98i | −0.385410 | − | 0.170736i | ||||
\(973\) | 2087.84i | 0.0687906i | ||||||||
\(974\) | −22021.4 | − | 38142.3i | −0.724448 | − | 1.25478i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17377.8 | − | 30099.2i | 0.569927 | − | 0.987143i | ||||
\(977\) | −19391.9 | − | 11195.9i | −0.635008 | − | 0.366622i | 0.147681 | − | 0.989035i | \(-0.452819\pi\) |
−0.782689 | + | 0.622413i | \(0.786153\pi\) | |||||||
\(978\) | 10198.8 | + | 43410.2i | 0.333458 | + | 1.41933i | ||||
\(979\) | 23615.3 | + | 40903.0i | 0.770939 | + | 1.33531i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45237.5 | + | 30007.2i | 1.47230 | + | 0.976611i | ||||
\(982\) | − | 14843.5i | − | 0.482357i | ||||||
\(983\) | −21321.0 | + | 12309.7i | −0.691794 | + | 0.399408i | −0.804284 | − | 0.594245i | \(-0.797451\pi\) |
0.112490 | + | 0.993653i | \(0.464117\pi\) | |||||||
\(984\) | 16178.7 | + | 17215.7i | 0.524144 | + | 0.557741i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 51058.7 | − | 88436.2i | 1.64913 | − | 2.85637i | ||||
\(987\) | 2971.33 | − | 2792.35i | 0.0958242 | − | 0.0900521i | ||||
\(988\) | 5237.34 | − | 3023.78i | 0.168646 | − | 0.0973676i | ||||
\(989\) | 13581.1 | 0.436658 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24540.3 | 0.786629 | 0.393314 | − | 0.919404i | \(-0.371328\pi\) | ||||
0.393314 | + | 0.919404i | \(0.371328\pi\) | |||||||
\(992\) | 746.199 | − | 430.818i | 0.0238829 | − | 0.0137888i | ||||
\(993\) | −270.815 | − | 1152.70i | −0.00865465 | − | 0.0368375i | ||||
\(994\) | 326.468 | − | 565.460i | 0.0104175 | − | 0.0180436i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7560.54 | − | 25075.5i | 0.240527 | − | 0.797737i | ||||
\(997\) | −39799.1 | + | 22978.0i | −1.26424 | + | 0.729912i | −0.973893 | − | 0.227008i | \(-0.927105\pi\) |
−0.290351 | + | 0.956920i | \(0.593772\pi\) | |||||||
\(998\) | − | 63146.7i | − | 2.00288i | ||||||
\(999\) | 37554.1 | − | 31138.2i | 1.18935 | − | 0.986155i |
(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 | 225.4.k.a.49.4 | 8 | ||
5.2 | odd | 4 | 45.4.e.a.31.2 | yes | 4 | ||
5.3 | odd | 4 | 225.4.e.a.76.1 | 4 | |||
5.4 | even | 2 | inner | 225.4.k.a.49.1 | 8 | ||
9.7 | even | 3 | inner | 225.4.k.a.124.1 | 8 | ||
15.2 | even | 4 | 135.4.e.a.91.1 | 4 | |||
45.2 | even | 12 | 135.4.e.a.46.1 | 4 | |||
45.7 | odd | 12 | 45.4.e.a.16.2 | ✓ | 4 | ||
45.13 | odd | 12 | 2025.4.a.l.1.2 | 2 | |||
45.22 | odd | 12 | 405.4.a.d.1.1 | 2 | |||
45.23 | even | 12 | 2025.4.a.j.1.1 | 2 | |||
45.32 | even | 12 | 405.4.a.e.1.2 | 2 | |||
45.34 | even | 6 | inner | 225.4.k.a.124.4 | 8 | ||
45.43 | odd | 12 | 225.4.e.a.151.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.a.16.2 | ✓ | 4 | 45.7 | odd | 12 | ||
45.4.e.a.31.2 | yes | 4 | 5.2 | odd | 4 | ||
135.4.e.a.46.1 | 4 | 45.2 | even | 12 | |||
135.4.e.a.91.1 | 4 | 15.2 | even | 4 | |||
225.4.e.a.76.1 | 4 | 5.3 | odd | 4 | |||
225.4.e.a.151.1 | 4 | 45.43 | odd | 12 | |||
225.4.k.a.49.1 | 8 | 5.4 | even | 2 | inner | ||
225.4.k.a.49.4 | 8 | 1.1 | even | 1 | trivial | ||
225.4.k.a.124.1 | 8 | 9.7 | even | 3 | inner | ||
225.4.k.a.124.4 | 8 | 45.34 | even | 6 | inner | ||
405.4.a.d.1.1 | 2 | 45.22 | odd | 12 | |||
405.4.a.e.1.2 | 2 | 45.32 | even | 12 | |||
2025.4.a.j.1.1 | 2 | 45.23 | even | 12 | |||
2025.4.a.l.1.2 | 2 | 45.13 | odd | 12 |