Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(49,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([15, 26]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("775.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.ck (of order \(30\), degree \(8\), 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: | \(6.18840615665\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{30})\) |
Twist minimal: | no (minimal twist has level 155) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 324.3 | ||
Character | \(\chi\) | \(=\) | 775.324 |
Dual form | 775.2.ck.b.299.3 |
$q$-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 \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(652\) |
\(\chi(n)\) | \(e\left(\frac{11}{15}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34623 | − | 0.437416i | −0.951927 | − | 0.309300i | −0.208429 | − | 0.978038i | \(-0.566835\pi\) |
−0.743498 | + | 0.668738i | \(0.766835\pi\) | |||||||
\(3\) | −2.31753 | − | 2.08671i | −1.33803 | − | 1.20476i | −0.960341 | − | 0.278830i | \(-0.910054\pi\) |
−0.377685 | − | 0.925934i | \(-0.623280\pi\) | |||||||
\(4\) | 0.00296283 | + | 0.00215262i | 0.00148141 | + | 0.00107631i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.20716 | + | 3.82291i | 0.901069 | + | 1.56070i | ||||
\(7\) | −0.944642 | − | 0.0992859i | −0.357041 | − | 0.0375265i | −0.0756900 | − | 0.997131i | \(-0.524116\pi\) |
−0.281351 | + | 0.959605i | \(0.590783\pi\) | |||||||
\(8\) | 1.66098 | + | 2.28615i | 0.587246 | + | 0.808275i | ||||
\(9\) | 0.702986 | + | 6.68846i | 0.234329 | + | 2.22949i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.64680 | − | 1.17843i | 0.798039 | − | 0.355310i | 0.0331325 | − | 0.999451i | \(-0.489452\pi\) |
0.764907 | + | 0.644141i | \(0.222785\pi\) | |||||||
\(12\) | −0.00237454 | − | 0.0111713i | −0.000685470 | − | 0.00322488i | ||||
\(13\) | 0.844492 | − | 3.97302i | 0.234220 | − | 1.10192i | −0.691108 | − | 0.722751i | \(-0.742877\pi\) |
0.925328 | − | 0.379167i | \(-0.123789\pi\) | |||||||
\(14\) | 1.22827 | + | 0.546863i | 0.328270 | + | 0.146155i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.23833 | − | 3.81118i | −0.309582 | − | 0.952795i | ||||
\(17\) | 2.40356 | − | 5.39849i | 0.582949 | − | 1.30933i | −0.345692 | − | 0.938348i | \(-0.612356\pi\) |
0.928642 | − | 0.370978i | \(-0.120977\pi\) | |||||||
\(18\) | 1.97926 | − | 9.31169i | 0.466516 | − | 2.19479i | ||||
\(19\) | 3.85426 | − | 0.819249i | 0.884229 | − | 0.187949i | 0.256653 | − | 0.966504i | \(-0.417380\pi\) |
0.627576 | + | 0.778555i | \(0.284047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.98205 | + | 2.20129i | 0.432520 | + | 0.480362i | ||||
\(22\) | −4.07866 | + | 0.428684i | −0.869572 | + | 0.0913957i | ||||
\(23\) | 4.17178 | + | 5.74196i | 0.869876 | + | 1.19728i | 0.979123 | + | 0.203267i | \(0.0651559\pi\) |
−0.109247 | + | 0.994015i | \(0.534844\pi\) | |||||||
\(24\) | 0.921154 | − | 8.76420i | 0.188030 | − | 1.78898i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.87474 | + | 4.97920i | −0.563783 | + | 0.976501i | ||||
\(27\) | 6.82861 | − | 9.39877i | 1.31417 | − | 1.80879i | ||||
\(28\) | −0.00258509 | − | 0.00232762i | −0.000488536 | − | 0.000439879i | ||||
\(29\) | 0.690565 | − | 2.12534i | 0.128235 | − | 0.394666i | −0.866242 | − | 0.499625i | \(-0.833471\pi\) |
0.994477 | + | 0.104959i | \(0.0334712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68304 | − | 3.01150i | 0.841099 | − | 0.540882i | ||||
\(32\) | 0.0207168i | 0.00366225i | ||||||||
\(33\) | −8.59307 | − | 2.79206i | −1.49586 | − | 0.486035i | ||||
\(34\) | −5.59713 | + | 6.21624i | −0.959899 | + | 1.06608i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0123149 | + | 0.0213300i | −0.00205248 | + | 0.00355500i | ||||
\(37\) | −1.26106 | + | 0.728076i | −0.207318 | + | 0.119695i | −0.600064 | − | 0.799952i | \(-0.704858\pi\) |
0.392746 | + | 0.919647i | \(0.371525\pi\) | |||||||
\(38\) | −5.54707 | − | 0.583021i | −0.899854 | − | 0.0945784i | ||||
\(39\) | −10.2477 | + | 7.44538i | −1.64094 | + | 1.19222i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.928592 | + | 1.03131i | 0.145022 | + | 0.161063i | 0.811279 | − | 0.584659i | \(-0.198772\pi\) |
−0.666258 | + | 0.745722i | \(0.732105\pi\) | |||||||
\(42\) | −1.70542 | − | 3.83043i | −0.263151 | − | 0.591048i | ||||
\(43\) | 2.66625 | + | 12.5437i | 0.406599 | + | 1.91290i | 0.408186 | + | 0.912899i | \(0.366162\pi\) |
−0.00158676 | + | 0.999999i | \(0.500505\pi\) | |||||||
\(44\) | 0.0103787 | + | 0.00220606i | 0.00156465 | + | 0.000332577i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.10454 | − | 9.55479i | −0.457739 | − | 1.40878i | ||||
\(47\) | 1.42464 | − | 0.462894i | 0.207805 | − | 0.0675201i | −0.203265 | − | 0.979124i | \(-0.565155\pi\) |
0.411070 | + | 0.911604i | \(0.365155\pi\) | |||||||
\(48\) | −5.08297 | + | 11.4165i | −0.733664 | + | 1.64784i | ||||
\(49\) | −5.96454 | − | 1.26780i | −0.852077 | − | 0.181115i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8354 | + | 7.49561i | −2.35743 | + | 1.04960i | ||||
\(52\) | 0.0110545 | − | 0.00995351i | 0.00153298 | − | 0.00138030i | ||||
\(53\) | −2.69114 | + | 0.282850i | −0.369657 | + | 0.0388525i | −0.287536 | − | 0.957770i | \(-0.592836\pi\) |
−0.0821209 | + | 0.996622i | \(0.526169\pi\) | |||||||
\(54\) | −13.3040 | + | 9.66595i | −1.81045 | + | 1.31537i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.34205 | − | 2.32450i | −0.179339 | − | 0.310625i | ||||
\(57\) | −10.6419 | − | 6.14411i | −1.40955 | − | 0.813807i | ||||
\(58\) | −1.85931 | + | 2.55913i | −0.244140 | + | 0.336030i | ||||
\(59\) | 2.76666 | − | 3.07268i | 0.360188 | − | 0.400029i | −0.535628 | − | 0.844454i | \(-0.679925\pi\) |
0.895816 | + | 0.444425i | \(0.146592\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.75919 | 0.737389 | 0.368695 | − | 0.929551i | \(-0.379805\pi\) | ||||
0.368695 | + | 0.929551i | \(0.379805\pi\) | |||||||
\(62\) | −7.62172 | + | 2.00573i | −0.967959 | + | 0.254728i | ||||
\(63\) | − | 6.38800i | − | 0.804813i | ||||||
\(64\) | −2.46759 | + | 7.59447i | −0.308449 | + | 0.949309i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.3469 | + | 7.51749i | 1.27362 | + | 0.925339i | ||||
\(67\) | 7.95257 | + | 4.59142i | 0.971561 | + | 0.560931i | 0.899712 | − | 0.436484i | \(-0.143777\pi\) |
0.0718494 | + | 0.997415i | \(0.477110\pi\) | |||||||
\(68\) | 0.0187422 | − | 0.0108208i | 0.00227283 | − | 0.00131222i | ||||
\(69\) | 2.31360 | − | 22.0125i | 0.278525 | − | 2.64999i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.16123 | − | 11.0483i | −0.137812 | − | 1.31119i | −0.816747 | − | 0.576996i | \(-0.804225\pi\) |
0.678935 | − | 0.734198i | \(-0.262442\pi\) | |||||||
\(72\) | −14.1232 | + | 12.7165i | −1.66443 | + | 1.49866i | ||||
\(73\) | −2.19480 | − | 4.92960i | −0.256882 | − | 0.576966i | 0.738359 | − | 0.674407i | \(-0.235601\pi\) |
−0.995241 | + | 0.0974413i | \(0.968934\pi\) | |||||||
\(74\) | 2.01615 | − | 0.428546i | 0.234373 | − | 0.0498175i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0131831 | + | 0.00586947i | 0.00151220 | + | 0.000673275i | ||||
\(77\) | −2.61728 | + | 0.850405i | −0.298267 | + | 0.0969127i | ||||
\(78\) | 17.0525 | − | 5.54068i | 1.93081 | − | 0.627358i | ||||
\(79\) | −3.76376 | − | 1.67573i | −0.423456 | − | 0.188535i | 0.183934 | − | 0.982939i | \(-0.441117\pi\) |
−0.607390 | + | 0.794404i | \(0.707783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −15.7030 | + | 3.33777i | −1.74478 | + | 0.370864i | ||||
\(82\) | −0.798986 | − | 1.79455i | −0.0882333 | − | 0.198175i | ||||
\(83\) | 12.5706 | − | 11.3186i | 1.37981 | − | 1.24238i | 0.441192 | − | 0.897413i | \(-0.354556\pi\) |
0.938614 | − | 0.344970i | \(-0.112111\pi\) | |||||||
\(84\) | 0.00113393 | + | 0.0107887i | 0.000123722 | + | 0.00117714i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.89744 | − | 18.0529i | 0.204606 | − | 1.94670i | ||||
\(87\) | −6.03537 | + | 3.48452i | −0.647060 | + | 0.373580i | ||||
\(88\) | 7.09035 | + | 4.09361i | 0.755833 | + | 0.436381i | ||||
\(89\) | −6.19419 | − | 4.50034i | −0.656583 | − | 0.477036i | 0.208924 | − | 0.977932i | \(-0.433004\pi\) |
−0.865507 | + | 0.500896i | \(0.833004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.19221 | + | 3.66924i | −0.124977 | + | 0.384641i | ||||
\(92\) | 0.0259927i | 0.00270992i | ||||||||
\(93\) | −17.1372 | − | 2.79291i | −1.77705 | − | 0.289611i | ||||
\(94\) | −2.12037 | −0.218700 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0432300 | − | 0.0480118i | 0.00441215 | − | 0.00490019i | ||||
\(97\) | −0.00200089 | + | 0.00275399i | −0.000203160 | + | 0.000279625i | −0.809119 | − | 0.587645i | \(-0.800055\pi\) |
0.808915 | + | 0.587925i | \(0.200055\pi\) | |||||||
\(98\) | 7.47508 | + | 4.31574i | 0.755097 | + | 0.435955i | ||||
\(99\) | 9.74255 | + | 16.8746i | 0.979163 | + | 1.69596i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.87721 | + | 2.81696i | −0.385797 | + | 0.280298i | −0.763731 | − | 0.645535i | \(-0.776635\pi\) |
0.377934 | + | 0.925833i | \(0.376635\pi\) | |||||||
\(102\) | 25.9430 | − | 2.72672i | 2.56874 | − | 0.269985i | ||||
\(103\) | −6.14194 | + | 5.53023i | −0.605183 | + | 0.544909i | −0.913741 | − | 0.406296i | \(-0.866820\pi\) |
0.308558 | + | 0.951205i | \(0.400153\pi\) | |||||||
\(104\) | 10.4856 | − | 4.66849i | 1.02820 | − | 0.457783i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.74661 | + | 0.796367i | 0.363903 | + | 0.0773500i | ||||
\(107\) | −6.53269 | + | 14.6727i | −0.631539 | + | 1.41846i | 0.260042 | + | 0.965597i | \(0.416264\pi\) |
−0.891580 | + | 0.452862i | \(0.850403\pi\) | |||||||
\(108\) | 0.0404640 | − | 0.0131475i | 0.00389365 | − | 0.00126512i | ||||
\(109\) | −2.11356 | − | 6.50487i | −0.202442 | − | 0.623054i | −0.999809 | − | 0.0195581i | \(-0.993774\pi\) |
0.797366 | − | 0.603496i | \(-0.206226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.44184 | + | 0.944142i | 0.421601 | + | 0.0896140i | ||||
\(112\) | 0.791380 | + | 3.72315i | 0.0747784 | + | 0.351805i | ||||
\(113\) | −5.79099 | − | 13.0068i | −0.544770 | − | 1.22357i | −0.950826 | − | 0.309725i | \(-0.899763\pi\) |
0.406056 | − | 0.913848i | \(-0.366904\pi\) | |||||||
\(114\) | 11.6389 | + | 12.9263i | 1.09008 | + | 1.21066i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.00662107 | − | 0.00481049i | 0.000614751 | − | 0.000446643i | ||||
\(117\) | 27.1671 | + | 2.85538i | 2.51160 | + | 0.263980i | ||||
\(118\) | −5.06859 | + | 2.92635i | −0.466602 | + | 0.269393i | ||||
\(119\) | −2.80650 | + | 4.86100i | −0.257271 | + | 0.445607i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.74360 | + | 1.93646i | −0.158509 | + | 0.176042i | ||||
\(122\) | −7.75319 | − | 2.51916i | −0.701941 | − | 0.228074i | ||||
\(123\) | − | 4.32778i | − | 0.390223i | ||||||
\(124\) | 0.0203577 | + | 0.00115824i | 0.00182817 | + | 0.000104013i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.79421 | + | 8.59971i | −0.248928 | + | 0.766123i | ||||
\(127\) | −4.87763 | − | 4.39184i | −0.432820 | − | 0.389713i | 0.423720 | − | 0.905793i | \(-0.360724\pi\) |
−0.856540 | + | 0.516080i | \(0.827391\pi\) | |||||||
\(128\) | 6.66824 | − | 9.17804i | 0.589395 | − | 0.811232i | ||||
\(129\) | 19.9960 | − | 34.6341i | 1.76055 | − | 3.04936i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.929302 | − | 8.84171i | 0.0811935 | − | 0.772504i | −0.875855 | − | 0.482575i | \(-0.839702\pi\) |
0.957048 | − | 0.289929i | \(-0.0936318\pi\) | |||||||
\(132\) | −0.0194495 | − | 0.0267700i | −0.00169287 | − | 0.00233003i | ||||
\(133\) | −3.72224 | + | 0.391223i | −0.322759 | + | 0.0339234i | ||||
\(134\) | −8.69761 | − | 9.65968i | −0.751359 | − | 0.834469i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.3340 | − | 3.47190i | 1.40063 | − | 0.297713i | ||||
\(137\) | 3.66411 | − | 17.2383i | 0.313046 | − | 1.47277i | −0.487304 | − | 0.873233i | \(-0.662020\pi\) |
0.800350 | − | 0.599533i | \(-0.204647\pi\) | |||||||
\(138\) | −12.7432 | + | 28.6218i | −1.08478 | + | 2.43645i | ||||
\(139\) | 5.13638 | + | 15.8081i | 0.435662 | + | 1.34083i | 0.892407 | + | 0.451232i | \(0.149015\pi\) |
−0.456745 | + | 0.889598i | \(0.650985\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.26758 | − | 1.90005i | −0.359395 | − | 0.160013i | ||||
\(142\) | −3.26944 | + | 15.3815i | −0.274365 | + | 1.29079i | ||||
\(143\) | −2.44673 | − | 11.5110i | −0.204606 | − | 0.962595i | ||||
\(144\) | 24.6204 | − | 10.9617i | 2.05170 | − | 0.913476i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.798415 | + | 7.59641i | 0.0660773 | + | 0.628683i | ||||
\(147\) | 11.1775 | + | 15.3844i | 0.921901 | + | 1.26889i | ||||
\(148\) | −0.00530359 | 0.000557429i | −0.000435952 | 4.58204e-5i | ||||||
\(149\) | 2.06741 | + | 3.58085i | 0.169369 | + | 0.293355i | 0.938198 | − | 0.346099i | \(-0.112494\pi\) |
−0.768829 | + | 0.639454i | \(0.779161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.12460 | + | 5.90287i | 0.661171 | + | 0.480369i | 0.867058 | − | 0.498207i | \(-0.166008\pi\) |
−0.205887 | + | 0.978576i | \(0.566008\pi\) | |||||||
\(152\) | 8.27479 | + | 7.45065i | 0.671174 | + | 0.604328i | ||||
\(153\) | 37.7973 | + | 12.2811i | 3.05573 | + | 0.992866i | ||||
\(154\) | 3.89543 | 0.313903 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0463892 | −0.00371411 | ||||||||
\(157\) | −22.2287 | − | 7.22255i | −1.77404 | − | 0.576422i | −0.775551 | − | 0.631285i | \(-0.782528\pi\) |
−0.998494 | + | 0.0548631i | \(0.982528\pi\) | |||||||
\(158\) | 4.33388 | + | 3.90224i | 0.344785 | + | 0.310446i | ||||
\(159\) | 6.82702 | + | 4.96012i | 0.541418 | + | 0.393363i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.37074 | − | 5.83830i | −0.265652 | − | 0.460122i | ||||
\(162\) | 22.5998 | + | 2.37533i | 1.77561 | + | 0.186624i | ||||
\(163\) | −0.145566 | − | 0.200354i | −0.0114016 | − | 0.0156929i | 0.803278 | − | 0.595604i | \(-0.203087\pi\) |
−0.814680 | + | 0.579911i | \(0.803087\pi\) | |||||||
\(164\) | 0.000531248 | 0.00505448i | 4.14835e−5 | 0.000394689i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.8739 | + | 9.73888i | −1.69774 | + | 0.755884i | ||||
\(167\) | 0.0119197 | + | 0.0560777i | 0.000922373 | + | 0.00433943i | 0.978606 | − | 0.205741i | \(-0.0659606\pi\) |
−0.977684 | + | 0.210081i | \(0.932627\pi\) | |||||||
\(168\) | −1.74032 | + | 8.18758i | −0.134269 | + | 0.631685i | ||||
\(169\) | −3.19565 | − | 1.42280i | −0.245819 | − | 0.109446i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.18901 | + | 25.2032i | 0.626229 | + | 1.92734i | ||||
\(172\) | −0.0191022 | + | 0.0429043i | −0.00145653 | + | 0.00327142i | ||||
\(173\) | 2.79938 | − | 13.1701i | 0.212833 | − | 1.00130i | −0.733894 | − | 0.679264i | \(-0.762299\pi\) |
0.946727 | − | 0.322037i | \(-0.104368\pi\) | |||||||
\(174\) | 9.64918 | − | 2.05100i | 0.731502 | − | 0.155486i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.76881 | − | 8.62814i | −0.585596 | − | 0.650370i | ||||
\(177\) | −12.8236 | + | 1.34782i | −0.963881 | + | 0.101308i | ||||
\(178\) | 6.37027 | + | 8.76793i | 0.477472 | + | 0.657184i | ||||
\(179\) | −0.316693 | + | 3.01313i | −0.0236707 | + | 0.225212i | 0.976291 | + | 0.216462i | \(0.0694518\pi\) |
−0.999962 | + | 0.00874979i | \(0.997215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.39081 | + | 5.87305i | −0.252037 | + | 0.436540i | −0.964086 | − | 0.265589i | \(-0.914434\pi\) |
0.712050 | + | 0.702129i | \(0.247767\pi\) | |||||||
\(182\) | 3.20997 | − | 4.41814i | 0.237939 | − | 0.327494i | ||||
\(183\) | −13.3471 | − | 12.0178i | −0.986646 | − | 0.888380i | ||||
\(184\) | −6.19771 | + | 19.0746i | −0.456901 | + | 1.40620i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 21.8489 | + | 11.2560i | 1.60204 | + | 0.825329i | ||||
\(187\) | − | 17.1211i | − | 1.25202i | ||||||
\(188\) | 0.00521741 | + | 0.00169524i | 0.000380518 | + | 0.000123638i | ||||
\(189\) | −7.38376 | + | 8.20049i | −0.537089 | + | 0.596498i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.60468 | − | 9.70760i | 0.405541 | − | 0.702417i | −0.588843 | − | 0.808247i | \(-0.700417\pi\) |
0.994384 | + | 0.105830i | \(0.0337499\pi\) | |||||||
\(192\) | 21.5662 | − | 12.4512i | 1.55641 | − | 0.898591i | ||||
\(193\) | 4.64346 | + | 0.488048i | 0.334244 | + | 0.0351304i | 0.270164 | − | 0.962814i | \(-0.412922\pi\) |
0.0640799 | + | 0.997945i | \(0.479589\pi\) | |||||||
\(194\) | 0.00389829 | − | 0.00283228i | 0.000279881 | − | 0.000203346i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0149428 | − | 0.0165957i | −0.00106734 | − | 0.00118541i | ||||
\(197\) | 5.52524 | + | 12.4099i | 0.393657 | + | 0.884168i | 0.996283 | + | 0.0861438i | \(0.0274545\pi\) |
−0.602626 | + | 0.798024i | \(0.705879\pi\) | |||||||
\(198\) | −5.73447 | − | 26.9786i | −0.407531 | − | 1.91728i | ||||
\(199\) | 7.46756 | + | 1.58728i | 0.529361 | + | 0.112519i | 0.464836 | − | 0.885397i | \(-0.346113\pi\) |
0.0645254 | + | 0.997916i | \(0.479447\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.84934 | − | 27.2355i | −0.624184 | − | 1.92104i | ||||
\(202\) | 6.45180 | − | 2.09632i | 0.453947 | − | 0.147496i | ||||
\(203\) | −0.863353 | + | 1.93912i | −0.0605955 | + | 0.136100i | ||||
\(204\) | −0.0660156 | − | 0.0140321i | −0.00462202 | − | 0.000982440i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.6875 | − | 4.75836i | 0.744630 | − | 0.331531i | ||||
\(207\) | −35.4722 | + | 31.9393i | −2.46549 | + | 2.21993i | ||||
\(208\) | −16.1877 | + | 1.70139i | −1.12241 | + | 0.117970i | ||||
\(209\) | 9.23603 | − | 6.71037i | 0.638869 | − | 0.464166i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.30466 | − | 16.1161i | −0.640559 | − | 1.10948i | −0.985308 | − | 0.170786i | \(-0.945369\pi\) |
0.344749 | − | 0.938695i | \(-0.387964\pi\) | |||||||
\(212\) | −0.00858225 | − | 0.00495497i | −0.000589432 | − | 0.000340308i | ||||
\(213\) | −20.3635 | + | 28.0279i | −1.39528 | + | 1.92044i | ||||
\(214\) | 15.2125 | − | 16.8952i | 1.03991 | − | 1.15494i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 32.8292 | 2.23374 | ||||||||
\(217\) | −4.72280 | + | 2.37983i | −0.320604 | + | 0.161554i | ||||
\(218\) | 9.68155i | 0.655717i | ||||||||
\(219\) | −5.20015 | + | 16.0044i | −0.351393 | + | 1.08148i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.4185 | − | 14.1084i | −1.30623 | − | 0.949033i | ||||
\(222\) | −5.56674 | − | 3.21396i | −0.373615 | − | 0.215707i | ||||
\(223\) | 17.0611 | − | 9.85023i | 1.14250 | − | 0.659620i | 0.195448 | − | 0.980714i | \(-0.437384\pi\) |
0.947047 | + | 0.321094i | \(0.104051\pi\) | |||||||
\(224\) | 0.00205689 | − | 0.0195700i | 0.000137432 | − | 0.00130757i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.10662 | + | 20.0431i | 0.140130 | + | 1.33325i | ||||
\(227\) | 19.1662 | − | 17.2574i | 1.27211 | − | 1.14541i | 0.290014 | − | 0.957022i | \(-0.406340\pi\) |
0.982094 | − | 0.188389i | \(-0.0603266\pi\) | |||||||
\(228\) | −0.0183042 | − | 0.0411119i | −0.00121222 | − | 0.00272270i | ||||
\(229\) | 0.296092 | − | 0.0629363i | 0.0195663 | − | 0.00415895i | −0.198118 | − | 0.980178i | \(-0.563483\pi\) |
0.217684 | + | 0.976019i | \(0.430150\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.84017 | + | 3.49067i | 0.515845 | + | 0.229669i | ||||
\(232\) | 6.00585 | − | 1.95142i | 0.394303 | − | 0.128117i | ||||
\(233\) | 0.419673 | − | 0.136360i | 0.0274937 | − | 0.00893324i | −0.295238 | − | 0.955424i | \(-0.595399\pi\) |
0.322732 | + | 0.946491i | \(0.395399\pi\) | |||||||
\(234\) | −35.3241 | − | 15.7273i | −2.30921 | − | 1.02813i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.0148114 | − | 0.00314827i | 0.000964143 | − | 0.000204935i | ||||
\(237\) | 5.22584 | + | 11.7374i | 0.339455 | + | 0.762428i | ||||
\(238\) | 5.90447 | − | 5.31641i | 0.382730 | − | 0.344612i | ||||
\(239\) | −1.37323 | − | 13.0654i | −0.0888270 | − | 0.845133i | −0.944698 | − | 0.327943i | \(-0.893645\pi\) |
0.855871 | − | 0.517190i | \(-0.173022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.71749 | + | 25.8552i | −0.175049 | + | 1.66548i | 0.456185 | + | 0.889885i | \(0.349216\pi\) |
−0.631234 | + | 0.775593i | \(0.717451\pi\) | |||||||
\(242\) | 3.19432 | − | 1.84424i | 0.205339 | − | 0.118552i | ||||
\(243\) | 13.1739 | + | 7.60596i | 0.845106 | + | 0.487922i | ||||
\(244\) | 0.0170635 | + | 0.0123974i | 0.00109238 | + | 0.000793659i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.89304 | + | 5.82618i | −0.120696 | + | 0.371464i | ||||
\(247\) | − | 16.0049i | − | 1.01837i | ||||||
\(248\) | 14.6632 | + | 5.70406i | 0.931113 | + | 0.362208i | ||||
\(249\) | −52.7515 | −3.34299 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3115 | + | 12.5627i | −0.713976 | + | 0.792951i | −0.985535 | − | 0.169471i | \(-0.945794\pi\) |
0.271559 | + | 0.962422i | \(0.412461\pi\) | |||||||
\(252\) | 0.0137509 | − | 0.0189265i | 0.000866228 | − | 0.00119226i | ||||
\(253\) | 17.8083 | + | 10.2817i | 1.11960 | + | 0.646402i | ||||
\(254\) | 4.64534 | + | 8.04597i | 0.291475 | + | 0.504849i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.0711076 | + | 0.0516627i | −0.00444423 | + | 0.00322892i | ||||
\(257\) | 4.15731 | − | 0.436951i | 0.259326 | − | 0.0272562i | 0.0260267 | − | 0.999661i | \(-0.491715\pi\) |
0.233299 | + | 0.972405i | \(0.425048\pi\) | |||||||
\(258\) | −42.0687 | + | 37.8788i | −2.61908 | + | 2.35823i | ||||
\(259\) | 1.26354 | − | 0.562566i | 0.0785127 | − | 0.0349561i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.7007 | + | 3.12473i | 0.909951 | + | 0.193416i | ||||
\(262\) | −5.11856 | + | 11.4965i | −0.316226 | + | 0.710254i | ||||
\(263\) | −17.4868 | + | 5.68182i | −1.07828 | + | 0.350356i | −0.793709 | − | 0.608298i | \(-0.791853\pi\) |
−0.284575 | + | 0.958654i | \(0.591853\pi\) | |||||||
\(264\) | −7.88989 | − | 24.2826i | −0.485589 | − | 1.49449i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.18211 | + | 1.10149i | 0.317736 | + | 0.0675368i | ||||
\(267\) | 4.96429 | + | 23.3552i | 0.303810 | + | 1.42931i | ||||
\(268\) | 0.0136785 | + | 0.0307224i | 0.000835548 | + | 0.00187667i | ||||
\(269\) | −15.0877 | − | 16.7566i | −0.919911 | − | 1.02167i | −0.999691 | − | 0.0248525i | \(-0.992088\pi\) |
0.0797798 | − | 0.996813i | \(-0.474578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.89808 | + | 5.73829i | −0.479774 | + | 0.348576i | −0.801238 | − | 0.598345i | \(-0.795825\pi\) |
0.321464 | + | 0.946922i | \(0.395825\pi\) | |||||||
\(272\) | −23.5510 | − | 2.47531i | −1.42799 | − | 0.150088i | ||||
\(273\) | 10.4196 | − | 6.01577i | 0.630624 | − | 0.364091i | ||||
\(274\) | −12.4730 | + | 21.6039i | −0.753523 | + | 1.30514i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0542392 | − | 0.0602388i | 0.00326482 | − | 0.00362595i | ||||
\(277\) | 24.4535 | + | 7.94542i | 1.46927 | + | 0.477394i | 0.930887 | − | 0.365308i | \(-0.119036\pi\) |
0.538381 | + | 0.842702i | \(0.319036\pi\) | |||||||
\(278\) | − | 23.5281i | − | 1.41112i | ||||||
\(279\) | 23.4344 | + | 29.2053i | 1.40298 | + | 1.74847i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0465029 | − | 0.143121i | 0.00277413 | − | 0.00853790i | −0.949660 | − | 0.313283i | \(-0.898571\pi\) |
0.952434 | + | 0.304745i | \(0.0985712\pi\) | |||||||
\(282\) | 4.91402 | + | 4.42460i | 0.292626 | + | 0.263481i | ||||
\(283\) | −8.86651 | + | 12.2037i | −0.527059 | + | 0.725435i | −0.986679 | − | 0.162681i | \(-0.947986\pi\) |
0.459620 | + | 0.888116i | \(0.347986\pi\) | |||||||
\(284\) | 0.0203423 | − | 0.0352339i | 0.00120709 | − | 0.00209075i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.74122 | + | 16.5666i | −0.102961 | + | 0.979604i | ||||
\(287\) | −0.774793 | − | 1.06641i | −0.0457346 | − | 0.0629482i | ||||
\(288\) | −0.138564 | + | 0.0145636i | −0.00816494 | + | 0.000858170i | ||||
\(289\) | −11.9914 | − | 13.3177i | −0.705374 | − | 0.783397i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0103839 | − | 0.00220717i | 0.000608715 | − | 0.000129386i | ||||
\(292\) | 0.00410875 | − | 0.0193301i | 0.000240446 | − | 0.00113121i | ||||
\(293\) | −1.68196 | + | 3.77774i | −0.0982610 | + | 0.220698i | −0.955987 | − | 0.293410i | \(-0.905210\pi\) |
0.857726 | + | 0.514107i | \(0.171877\pi\) | |||||||
\(294\) | −8.31800 | − | 25.6002i | −0.485116 | − | 1.49303i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.75909 | − | 1.67366i | −0.218493 | − | 0.0972793i | ||||
\(297\) | 6.99814 | − | 32.9237i | 0.406073 | − | 1.91043i | ||||
\(298\) | −1.21688 | − | 5.72496i | −0.0704919 | − | 0.331638i | ||||
\(299\) | 26.3360 | − | 11.7255i | 1.52305 | − | 0.678105i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.27324 | − | 12.1140i | −0.0733882 | − | 0.698242i | ||||
\(302\) | −8.35556 | − | 11.5004i | −0.480808 | − | 0.661776i | ||||
\(303\) | 14.8637 | + | 1.56224i | 0.853899 | + | 0.0897484i | ||||
\(304\) | −7.89515 | − | 13.6748i | −0.452818 | − | 0.784303i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −45.5118 | − | 33.0662i | −2.60174 | − | 1.89027i | ||||
\(307\) | −7.72660 | − | 6.95706i | −0.440980 | − | 0.397060i | 0.418510 | − | 0.908212i | \(-0.362552\pi\) |
−0.859491 | + | 0.511152i | \(0.829219\pi\) | |||||||
\(308\) | −0.00958514 | − | 0.00311440i | −0.000546164 | − | 0.000177459i | ||||
\(309\) | 25.7741 | 1.46624 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.5627 | −1.22271 | −0.611353 | − | 0.791358i | \(-0.709375\pi\) | ||||
−0.611353 | + | 0.791358i | \(0.709375\pi\) | |||||||
\(312\) | −34.0425 | − | 11.0611i | −1.92727 | − | 0.626209i | ||||
\(313\) | 1.53286 | + | 1.38020i | 0.0866426 | + | 0.0780134i | 0.711314 | − | 0.702874i | \(-0.248100\pi\) |
−0.624671 | + | 0.780888i | \(0.714767\pi\) | |||||||
\(314\) | 26.7657 | + | 19.4464i | 1.51047 | + | 1.09742i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.00754414 | − | 0.0130668i | −0.000424391 | − | 0.000735067i | ||||
\(317\) | 21.6026 | + | 2.27052i | 1.21332 | + | 0.127525i | 0.689490 | − | 0.724295i | \(-0.257835\pi\) |
0.523833 | + | 0.851821i | \(0.324501\pi\) | |||||||
\(318\) | −7.02109 | − | 9.66370i | −0.393723 | − | 0.541914i | ||||
\(319\) | −0.676779 | − | 6.43912i | −0.0378924 | − | 0.360522i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.7573 | − | 20.3725i | 2.55392 | − | 1.13708i | ||||
\(322\) | 1.98402 | + | 9.33410i | 0.110565 | + | 0.520169i | ||||
\(323\) | 4.84126 | − | 22.7763i | 0.269375 | − | 1.26731i | ||||
\(324\) | −0.0537102 | − | 0.0239133i | −0.00298390 | − | 0.00132852i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.108327 | + | 0.333395i | 0.00599966 | + | 0.0184650i | ||||
\(327\) | −8.67556 | + | 19.4856i | −0.479759 | + | 1.07756i | ||||
\(328\) | −0.815340 | + | 3.83588i | −0.0450196 | + | 0.211801i | ||||
\(329\) | −1.39174 | + | 0.295823i | −0.0767289 | + | 0.0163092i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3089 | − | 12.5598i | −0.621594 | − | 0.690350i | 0.347320 | − | 0.937747i | \(-0.387092\pi\) |
−0.968914 | + | 0.247396i | \(0.920425\pi\) | |||||||
\(332\) | 0.0616093 | − | 0.00647540i | 0.00338125 | − | 0.000355384i | ||||
\(333\) | −5.75622 | − | 7.92276i | −0.315439 | − | 0.434164i | ||||
\(334\) | 0.00848268 | − | 0.0807073i | 0.000464151 | − | 0.00441611i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.93510 | − | 10.2799i | 0.323786 | − | 0.560814i | ||||
\(337\) | 2.54993 | − | 3.50967i | 0.138903 | − | 0.191184i | −0.733898 | − | 0.679260i | \(-0.762301\pi\) |
0.872801 | + | 0.488076i | \(0.162301\pi\) | |||||||
\(338\) | 3.67972 | + | 3.31324i | 0.200150 | + | 0.180216i | ||||
\(339\) | −13.7206 | + | 42.2277i | −0.745201 | + | 2.29349i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.84621 | − | 13.4895i | 0.479049 | − | 0.730496i | ||||
\(342\) | − | 37.5112i | − | 2.02837i | ||||||
\(343\) | 11.8320 | + | 3.84444i | 0.638867 | + | 0.207580i | ||||
\(344\) | −24.2482 | + | 26.9303i | −1.30737 | + | 1.45198i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.52940 | + | 16.5054i | −0.512304 | + | 0.887336i | ||||
\(347\) | 9.08535 | − | 5.24543i | 0.487727 | − | 0.281589i | −0.235904 | − | 0.971776i | \(-0.575805\pi\) |
0.723631 | + | 0.690187i | \(0.242472\pi\) | |||||||
\(348\) | −0.0253826 | − | 0.00266782i | −0.00136065 | − | 0.000143010i | ||||
\(349\) | 4.52158 | − | 3.28512i | 0.242035 | − | 0.175849i | −0.460155 | − | 0.887839i | \(-0.652206\pi\) |
0.702189 | + | 0.711990i | \(0.252206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.5748 | − | 35.0674i | −1.68534 | − | 1.87176i | ||||
\(352\) | 0.0244133 | + | 0.0548332i | 0.00130123 | + | 0.00292262i | ||||
\(353\) | −6.21600 | − | 29.2440i | −0.330844 | − | 1.55650i | −0.757959 | − | 0.652302i | \(-0.773803\pi\) |
0.427115 | − | 0.904197i | \(-0.359530\pi\) | |||||||
\(354\) | 17.8531 | + | 3.79478i | 0.948879 | + | 0.201691i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.00866479 | − | 0.0266675i | −0.000459233 | − | 0.00141337i | ||||
\(357\) | 16.6477 | − | 5.40915i | 0.881087 | − | 0.286283i | ||||
\(358\) | 1.74433 | − | 3.91784i | 0.0921909 | − | 0.207064i | ||||
\(359\) | 4.53424 | + | 0.963782i | 0.239308 | + | 0.0508665i | 0.326004 | − | 0.945368i | \(-0.394298\pi\) |
−0.0866962 | + | 0.996235i | \(0.527631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.17318 | + | 1.41279i | −0.167009 | + | 0.0743574i | ||||
\(362\) | 7.13377 | − | 6.42327i | 0.374942 | − | 0.337600i | ||||
\(363\) | 8.08168 | − | 0.849419i | 0.424178 | − | 0.0445829i | ||||
\(364\) | −0.0114308 | + | 0.00830495i | −0.000599136 | + | 0.000435298i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.7115 | + | 22.0169i | 0.664439 | + | 1.15084i | ||||
\(367\) | −22.9593 | − | 13.2555i | −1.19846 | − | 0.691934i | −0.238252 | − | 0.971203i | \(-0.576574\pi\) |
−0.960213 | + | 0.279270i | \(0.909908\pi\) | |||||||
\(368\) | 16.7176 | − | 23.0098i | 0.871466 | − | 1.19947i | ||||
\(369\) | −6.24506 | + | 6.93584i | −0.325105 | + | 0.361066i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.57025 | 0.133441 | ||||||||
\(372\) | −0.0447625 | − | 0.0451648i | −0.00232083 | − | 0.00234169i | ||||
\(373\) | 1.86550i | 0.0965919i | 0.998833 | + | 0.0482959i | \(0.0153791\pi\) | ||||
−0.998833 | + | 0.0482959i | \(0.984621\pi\) | |||||||
\(374\) | −7.48906 | + | 23.0489i | −0.387250 | + | 1.19183i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.42455 | + | 2.48808i | 0.176608 | + | 0.128313i | ||||
\(377\) | −7.86085 | − | 4.53846i | −0.404854 | − | 0.233743i | ||||
\(378\) | 13.5272 | − | 7.80996i | 0.695766 | − | 0.401701i | ||||
\(379\) | 0.152228 | − | 1.44835i | 0.00781942 | − | 0.0743968i | −0.989916 | − | 0.141654i | \(-0.954758\pi\) |
0.997736 | + | 0.0672569i | \(0.0214247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.13955 | + | 20.3564i | 0.109612 | + | 1.04289i | ||||
\(382\) | −11.7914 | + | 10.6171i | −0.603303 | + | 0.543216i | ||||
\(383\) | 5.60769 | + | 12.5951i | 0.286539 | + | 0.643578i | 0.998265 | − | 0.0588794i | \(-0.0187527\pi\) |
−0.711726 | + | 0.702458i | \(0.752086\pi\) | |||||||
\(384\) | −34.6058 | + | 7.35568i | −1.76597 | + | 0.375368i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.03768 | − | 2.68815i | −0.307310 | − | 0.136823i | ||||
\(387\) | −82.0238 | + | 26.6511i | −4.16950 | + | 1.35475i | ||||
\(388\) | −1.18566e−5 | 0 | 3.85244e-6i | −6.01927e−7 | 0 | 1.95578e-7i | ||||
\(389\) | 14.7869 | + | 6.58357i | 0.749727 | + | 0.333800i | 0.745780 | − | 0.666192i | \(-0.232077\pi\) |
0.00394702 | + | 0.999992i | \(0.498744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.0250 | − | 8.72014i | 2.07473 | − | 0.440996i | ||||
\(392\) | −7.00862 | − | 15.7416i | −0.353989 | − | 0.795071i | ||||
\(393\) | −20.6038 | + | 18.5517i | −1.03932 | + | 0.935812i | ||||
\(394\) | −2.00995 | − | 19.1234i | −0.101260 | − | 0.963421i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.00745909 | + | 0.0709685i | −0.000374833 | + | 0.00356630i | ||||
\(397\) | −21.1560 | + | 12.2144i | −1.06179 | + | 0.613023i | −0.925926 | − | 0.377705i | \(-0.876713\pi\) |
−0.135861 | + | 0.990728i | \(0.543380\pi\) | |||||||
\(398\) | −9.35874 | − | 5.40327i | −0.469111 | − | 0.270841i | ||||
\(399\) | 9.44277 | + | 6.86057i | 0.472730 | + | 0.343458i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.02856 | + | 6.24326i | −0.101301 | + | 0.311774i | −0.988845 | − | 0.148951i | \(-0.952410\pi\) |
0.887543 | + | 0.460725i | \(0.152410\pi\) | |||||||
\(402\) | 40.5360i | 2.02175i | ||||||||
\(403\) | −8.00998 | − | 21.1490i | −0.399006 | − | 1.05351i | ||||
\(404\) | −0.0175514 | −0.000873213 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.01047 | − | 2.23286i | 0.0997781 | − | 0.110815i | ||||
\(407\) | −2.47980 | + | 3.41315i | −0.122919 | + | 0.169183i | ||||
\(408\) | −45.0994 | − | 26.0381i | −2.23275 | − | 1.28908i | ||||
\(409\) | 13.9181 | + | 24.1069i | 0.688208 | + | 1.19201i | 0.972417 | + | 0.233248i | \(0.0749355\pi\) |
−0.284210 | + | 0.958762i | \(0.591731\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −44.4630 | + | 32.3043i | −2.19320 | + | 1.59345i | ||||
\(412\) | −0.0301020 | + | 0.00316384i | −0.00148302 | + | 0.000155871i | ||||
\(413\) | −2.91857 | + | 2.62790i | −0.143614 | + | 0.129310i | ||||
\(414\) | 61.7244 | − | 27.4815i | 3.03359 | − | 1.35064i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.0823084 | + | 0.0174952i | 0.00403550 | + | 0.000857772i | ||||
\(417\) | 21.0833 | − | 47.3540i | 1.03246 | − | 2.31893i | ||||
\(418\) | −15.3690 | + | 4.99370i | −0.751723 | + | 0.244250i | ||||
\(419\) | 6.28700 | + | 19.3494i | 0.307140 | + | 0.945279i | 0.978870 | + | 0.204483i | \(0.0655514\pi\) |
−0.671730 | + | 0.740796i | \(0.734449\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0345 | + | 2.77056i | 0.635262 | + | 0.135029i | 0.514275 | − | 0.857625i | \(-0.328061\pi\) |
0.120986 | + | 0.992654i | \(0.461394\pi\) | |||||||
\(422\) | 5.47673 | + | 25.7660i | 0.266603 | + | 1.25427i | ||||
\(423\) | 4.09756 | + | 9.20326i | 0.199230 | + | 0.447478i | ||||
\(424\) | −5.11657 | − | 5.68253i | −0.248483 | − | 0.275968i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 39.6738 | − | 28.8247i | 1.92220 | − | 1.39656i | ||||
\(427\) | −5.44038 | − | 0.571807i | −0.263278 | − | 0.0276717i | ||||
\(428\) | −0.0509399 | + | 0.0294102i | −0.00246227 | + | 0.00142159i | ||||
\(429\) | −18.3497 | + | 31.7826i | −0.885931 | + | 1.53448i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3433 | + | 17.0405i | −0.739062 | + | 0.820812i | −0.989072 | − | 0.147431i | \(-0.952899\pi\) |
0.250010 | + | 0.968243i | \(0.419566\pi\) | |||||||
\(432\) | −44.2764 | − | 14.3863i | −2.13025 | − | 0.692161i | ||||
\(433\) | − | 6.35044i | − | 0.305183i | −0.988289 | − | 0.152591i | \(-0.951238\pi\) | ||
0.988289 | − | 0.152591i | \(-0.0487618\pi\) | |||||||
\(434\) | 7.39894 | − | 1.13797i | 0.355160 | − | 0.0546244i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.00774040 | − | 0.0238225i | 0.000370698 | − | 0.00114089i | ||||
\(437\) | 20.7832 | + | 18.7133i | 0.994197 | + | 0.895179i | ||||
\(438\) | 14.0012 | − | 19.2710i | 0.669002 | − | 0.920802i | ||||
\(439\) | 5.60915 | − | 9.71534i | 0.267710 | − | 0.463688i | −0.700560 | − | 0.713594i | \(-0.747066\pi\) |
0.968270 | + | 0.249906i | \(0.0803997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.28666 | − | 40.7849i | 0.204127 | − | 1.94214i | ||||
\(442\) | 19.9705 | + | 27.4871i | 0.949901 | + | 1.30743i | ||||
\(443\) | −1.92826 | + | 0.202669i | −0.0916146 | + | 0.00962908i | −0.150225 | − | 0.988652i | \(-0.548000\pi\) |
0.0586102 | + | 0.998281i | \(0.481333\pi\) | |||||||
\(444\) | 0.0111280 | + | 0.0123589i | 0.000528112 | + | 0.000586528i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −27.2768 | + | 5.79786i | −1.29159 | + | 0.274536i | ||||
\(447\) | 2.68094 | − | 12.6128i | 0.126804 | − | 0.596566i | ||||
\(448\) | 3.08502 | − | 6.92906i | 0.145753 | − | 0.327367i | ||||
\(449\) | −3.70576 | − | 11.4052i | −0.174886 | − | 0.538243i | 0.824743 | − | 0.565508i | \(-0.191320\pi\) |
−0.999628 | + | 0.0272656i | \(0.991320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.67311 | + | 1.63538i | 0.172960 | + | 0.0770068i | ||||
\(452\) | 0.0108409 | − | 0.0510026i | 0.000509915 | − | 0.00239896i | ||||
\(453\) | −6.51141 | − | 30.6338i | −0.305933 | − | 1.43930i | ||||
\(454\) | −33.3508 | + | 14.8487i | −1.56523 | + | 0.696885i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.62969 | − | 34.5342i | −0.169976 | − | 1.61721i | ||||
\(457\) | −13.7224 | − | 18.8873i | −0.641908 | − | 0.883510i | 0.356808 | − | 0.934178i | \(-0.383865\pi\) |
−0.998716 | + | 0.0506677i | \(0.983865\pi\) | |||||||
\(458\) | −0.426137 | − | 0.0447888i | −0.0199121 | − | 0.00209284i | ||||
\(459\) | −34.3262 | − | 59.4547i | −1.60221 | − | 2.77511i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.2238 | + | 19.7792i | 1.26794 | + | 0.921210i | 0.999118 | − | 0.0419810i | \(-0.0133669\pi\) |
0.268818 | + | 0.963191i | \(0.413367\pi\) | |||||||
\(462\) | −9.02778 | − | 8.12865i | −0.420010 | − | 0.378179i | ||||
\(463\) | −26.2572 | − | 8.53149i | −1.22028 | − | 0.396492i | −0.373094 | − | 0.927793i | \(-0.621703\pi\) |
−0.847183 | + | 0.531301i | \(0.821703\pi\) | |||||||
\(464\) | −8.95519 | −0.415734 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.624622 | −0.0289350 | ||||||||
\(467\) | 32.6305 | + | 10.6023i | 1.50996 | + | 0.490615i | 0.942904 | − | 0.333065i | \(-0.108083\pi\) |
0.567055 | + | 0.823680i | \(0.308083\pi\) | |||||||
\(468\) | 0.0743448 | + | 0.0669404i | 0.00343659 | + | 0.00309432i | ||||
\(469\) | −7.05647 | − | 5.12683i | −0.325838 | − | 0.236735i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.4443 | + | 63.1234i | 1.67926 | + | 2.90857i | ||||
\(472\) | 11.6200 | + | 1.22131i | 0.534852 | + | 0.0562153i | ||||
\(473\) | 21.8389 | + | 30.0587i | 1.00415 | + | 1.38210i | ||||
\(474\) | −1.90103 | − | 18.0871i | −0.0873173 | − | 0.830769i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.0187791 | + | 0.00836098i | −0.000860737 | + | 0.000383225i | ||||
\(477\) | −3.78367 | − | 17.8008i | −0.173242 | − | 0.815041i | ||||
\(478\) | −3.86635 | + | 18.1897i | −0.176843 | + | 0.831979i | ||||
\(479\) | −22.0079 | − | 9.79853i | −1.00556 | − | 0.447706i | −0.163188 | − | 0.986595i | \(-0.552178\pi\) |
−0.842377 | + | 0.538889i | \(0.818844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.82770 | + | 5.62509i | 0.0833361 | + | 0.256482i | ||||
\(482\) | 14.9678 | − | 33.6183i | 0.681766 | − | 1.53127i | ||||
\(483\) | −4.37105 | + | 20.5642i | −0.198890 | + | 0.935703i | ||||
\(484\) | −0.00933445 | + | 0.00198410i | −0.000424293 | + | 9.01863e-5i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.4081 | − | 16.0018i | −0.653565 | − | 0.725858i | ||||
\(487\) | 3.79482 | − | 0.398851i | 0.171960 | − | 0.0180737i | −0.0181573 | − | 0.999835i | \(-0.505780\pi\) |
0.190117 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(488\) | 9.56592 | + | 13.1664i | 0.433029 | + | 0.596013i | ||||
\(489\) | −0.0807285 | + | 0.768080i | −0.00365067 | + | 0.0347338i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.42799 | + | 2.47336i | −0.0644445 | + | 0.111621i | −0.896447 | − | 0.443150i | \(-0.853861\pi\) |
0.832003 | + | 0.554771i | \(0.187194\pi\) | |||||||
\(492\) | 0.00931607 | − | 0.0128225i | 0.000420001 | − | 0.000578082i | ||||
\(493\) | −9.81381 | − | 8.83639i | −0.441992 | − | 0.397971i | ||||
\(494\) | −7.00081 | + | 21.5463i | −0.314981 | + | 0.969413i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.2765 | − | 14.1187i | −0.775738 | − | 0.633947i | ||||
\(497\) | 10.5520i | 0.473322i | ||||||||
\(498\) | 71.0156 | + | 23.0744i | 3.18229 | + | 1.03399i | ||||
\(499\) | 11.4047 | − | 12.6662i | 0.510545 | − | 0.567018i | −0.431667 | − | 0.902033i | \(-0.642075\pi\) |
0.942213 | + | 0.335015i | \(0.108741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0893939 | − | 0.154835i | 0.00399382 | − | 0.00691750i | ||||
\(502\) | 20.7230 | − | 11.9644i | 0.924912 | − | 0.533998i | ||||
\(503\) | 19.8213 | + | 2.08330i | 0.883786 | + | 0.0928897i | 0.535536 | − | 0.844512i | \(-0.320109\pi\) |
0.348250 | + | 0.937402i | \(0.386776\pi\) | |||||||
\(504\) | 14.6039 | − | 10.6104i | 0.650510 | − | 0.472623i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.4767 | − | 21.6311i | −0.865846 | − | 0.961620i | ||||
\(507\) | 4.43705 | + | 9.96577i | 0.197056 | + | 0.442596i | ||||
\(508\) | −0.00499762 | − | 0.0235120i | −0.000221734 | − | 0.00104317i | ||||
\(509\) | −22.1274 | − | 4.70332i | −0.980780 | − | 0.208471i | −0.310495 | − | 0.950575i | \(-0.600495\pi\) |
−0.670285 | + | 0.742104i | \(0.733828\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.58386 | + | 4.87462i | 0.0700659 | + | 0.215641i | ||||
\(512\) | −21.4605 | + | 6.97295i | −0.948431 | + | 0.308164i | ||||
\(513\) | 18.6193 | − | 41.8197i | 0.822063 | − | 1.84638i | ||||
\(514\) | −5.78782 | − | 1.23024i | −0.255290 | − | 0.0542635i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.133799 | − | 0.0595710i | 0.00589016 | − | 0.00262247i | ||||
\(517\) | 3.22525 | − | 2.90403i | 0.141846 | − | 0.127719i | ||||
\(518\) | −1.94709 | + | 0.204648i | −0.0855503 | + | 0.00899170i | ||||
\(519\) | −33.9698 | + | 24.6805i | −1.49111 | + | 1.08335i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.76098 | − | 3.05010i | −0.0771499 | − | 0.133628i | 0.824869 | − | 0.565324i | \(-0.191249\pi\) |
−0.902019 | + | 0.431696i | \(0.857915\pi\) | |||||||
\(522\) | −18.4237 | − | 10.6369i | −0.806383 | − | 0.465566i | ||||
\(523\) | −23.1228 | + | 31.8259i | −1.01109 | + | 1.39165i | −0.0928261 | + | 0.995682i | \(0.529590\pi\) |
−0.918265 | + | 0.395966i | \(0.870410\pi\) | |||||||
\(524\) | 0.0217862 | − | 0.0241960i | 0.000951735 | − | 0.00105701i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.0266 | 1.13481 | ||||||||
\(527\) | −5.00159 | − | 32.5197i | −0.217873 | − | 1.41658i | ||||
\(528\) | 36.2072i | 1.57572i | ||||||||
\(529\) | −8.45898 | + | 26.0341i | −0.367782 | + | 1.13192i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.4964 | + | 16.3446i | 0.976263 | + | 0.709296i | ||||
\(532\) | −0.0118705 | − | 0.00685344i | −0.000514652 | − | 0.000297134i | ||||
\(533\) | 4.88159 | − | 2.81839i | 0.211445 | − | 0.122078i | ||||
\(534\) | 3.53285 | − | 33.6128i | 0.152881 | − | 1.45457i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.71243 | + | 25.8070i | 0.117159 | + | 1.11469i | ||||
\(537\) | 7.02148 | − | 6.32217i | 0.302999 | − | 0.272822i | ||||
\(538\) | 12.9819 | + | 29.1577i | 0.559688 | + | 1.25708i | ||||
\(539\) | −17.2809 | + | 3.67318i | −0.744343 | + | 0.158215i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.04711 | + | 0.466202i | 0.0450186 | + | 0.0200436i | 0.429122 | − | 0.903246i | \(-0.358823\pi\) |
−0.384104 | + | 0.923290i | \(0.625490\pi\) | |||||||
\(542\) | 13.1426 | − | 4.27030i | 0.564525 | − | 0.183425i | ||||
\(543\) | 20.1137 | − | 6.53532i | 0.863160 | − | 0.280458i | ||||
\(544\) | 0.111840 | + | 0.0497942i | 0.00479508 | + | 0.00213491i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.6586 | + | 3.54089i | −0.712921 | + | 0.151536i | ||||
\(547\) | 10.9514 | + | 24.5971i | 0.468246 | + | 1.05170i | 0.981149 | + | 0.193251i | \(0.0619033\pi\) |
−0.512903 | + | 0.858446i | \(0.671430\pi\) | |||||||
\(548\) | 0.0479636 | − | 0.0431866i | 0.00204890 | − | 0.00184484i | ||||
\(549\) | 4.04863 | + | 38.5202i | 0.172791 | + | 1.64400i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.920436 | − | 8.75736i | 0.0392119 | − | 0.373076i | ||||
\(552\) | 54.1665 | − | 31.2731i | 2.30548 | − | 1.33107i | ||||
\(553\) | 3.38903 | + | 1.95666i | 0.144116 | + | 0.0832054i | ||||
\(554\) | −29.4445 | − | 21.3927i | −1.25098 | − | 0.908888i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0188107 | + | 0.0578935i | −0.000797753 | + | 0.00245523i | ||||
\(557\) | 5.09359i | 0.215822i | 0.994161 | + | 0.107911i | \(0.0344162\pi\) | ||||
−0.994161 | + | 0.107911i | \(0.965584\pi\) | |||||||
\(558\) | −18.7732 | − | 49.5676i | −0.794734 | − | 2.09836i | ||||
\(559\) | 52.0881 | 2.20309 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.7269 | + | 39.6787i | −1.50839 | + | 1.67524i | ||||
\(562\) | −0.125207 | + | 0.172333i | −0.00528154 | + | 0.00726942i | ||||
\(563\) | −25.8636 | − | 14.9324i | −1.09002 | − | 0.629325i | −0.156440 | − | 0.987688i | \(-0.550002\pi\) |
−0.933582 | + | 0.358363i | \(0.883335\pi\) | |||||||
\(564\) | −0.00855401 | − | 0.0148160i | −0.000360189 | − | 0.000623866i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.2744 | − | 12.5506i | 0.726098 | − | 0.527541i | ||||
\(567\) | 15.1651 | − | 1.59392i | 0.636875 | − | 0.0669382i | ||||
\(568\) | 23.3293 | − | 21.0058i | 0.978876 | − | 0.881384i | ||||
\(569\) | 12.6321 | − | 5.62416i | 0.529564 | − | 0.235777i | −0.124496 | − | 0.992220i | \(-0.539731\pi\) |
0.654059 | + | 0.756443i | \(0.273065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9925 | + | 2.33652i | 0.460020 | + | 0.0977803i | 0.432092 | − | 0.901830i | \(-0.357776\pi\) |
0.0279284 | + | 0.999610i | \(0.491109\pi\) | |||||||
\(572\) | 0.0175295 | − | 0.0393719i | 0.000732944 | − | 0.00164622i | ||||
\(573\) | −33.2460 | + | 10.8023i | −1.38887 | + | 0.451271i | ||||
\(574\) | 0.576583 | + | 1.77454i | 0.0240661 | + | 0.0740678i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −52.5300 | − | 11.1656i | −2.18875 | − | 0.465233i | ||||
\(577\) | 4.85267 | + | 22.8300i | 0.202020 | + | 0.950427i | 0.955963 | + | 0.293488i | \(0.0948159\pi\) |
−0.753943 | + | 0.656939i | \(0.771851\pi\) | |||||||
\(578\) | 10.3177 | + | 23.1739i | 0.429160 | + | 0.963908i | ||||
\(579\) | −9.74295 | − | 10.8206i | −0.404903 | − | 0.449690i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.9985 | + | 9.44399i | −0.539270 | + | 0.391803i | ||||
\(582\) | −0.0149446 | − | 0.00157074i | −0.000619472 | − | 6.51091e-5i | ||||
\(583\) | −6.78958 | + | 3.91997i | −0.281196 | + | 0.162348i | ||||
\(584\) | 7.62426 | − | 13.2056i | 0.315494 | − | 0.546452i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.91674 | − | 4.34998i | 0.161799 | − | 0.179696i | ||||
\(587\) | 0.0287292 | + | 0.00933469i | 0.00118578 | + | 0.000385284i | 0.309610 | − | 0.950864i | \(-0.399802\pi\) |
−0.308424 | + | 0.951249i | \(0.599802\pi\) | |||||||
\(588\) | 0.0696423i | 0.00287200i | ||||||||
\(589\) | 15.5825 | − | 15.4437i | 0.642066 | − | 0.636347i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0910 | − | 40.2898i | 0.538490 | − | 1.65730i | ||||
\(592\) | 4.33644 | + | 3.90455i | 0.178227 | + | 0.160476i | ||||
\(593\) | 4.48509 | − | 6.17320i | 0.184181 | − | 0.253503i | −0.706936 | − | 0.707278i | \(-0.749923\pi\) |
0.891116 | + | 0.453775i | \(0.149923\pi\) | |||||||
\(594\) | −23.8224 | + | 41.2617i | −0.977446 | + | 1.69299i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.00158285 | + | 0.0150598i | −6.48360e−5 | + | 0.000616873i | ||||
\(597\) | −13.9941 | − | 19.2612i | −0.572740 | − | 0.788309i | ||||
\(598\) | −40.5832 | + | 4.26546i | −1.65957 | + | 0.174428i | ||||
\(599\) | 5.47027 | + | 6.07535i | 0.223509 | + | 0.248232i | 0.844462 | − | 0.535616i | \(-0.179921\pi\) |
−0.620952 | + | 0.783848i | \(0.713254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.823421 | + | 0.175024i | −0.0335880 | + | 0.00713936i | −0.224675 | − | 0.974434i | \(-0.572132\pi\) |
0.191087 | + | 0.981573i | \(0.438799\pi\) | |||||||
\(602\) | −3.58481 | + | 16.8652i | −0.146106 | + | 0.687374i | ||||
\(603\) | −25.1190 | + | 56.4182i | −1.02292 | + | 2.29753i | ||||
\(604\) | 0.0113652 | + | 0.0349784i | 0.000462442 | + | 0.00142325i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.3266 | − | 8.60477i | −0.785091 | − | 0.349545i | ||||
\(607\) | 9.36525 | − | 44.0600i | 0.380124 | − | 1.78834i | −0.206462 | − | 0.978455i | \(-0.566195\pi\) |
0.586586 | − | 0.809887i | \(-0.300472\pi\) | |||||||
\(608\) | 0.0169722 | + | 0.0798481i | 0.000688315 | + | 0.00323827i | ||||
\(609\) | 6.04723 | − | 2.69240i | 0.245046 | − | 0.109102i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.635991 | − | 6.05105i | −0.0257294 | − | 0.244799i | ||||
\(612\) | 0.0855503 | + | 0.117750i | 0.00345816 | + | 0.00475975i | ||||
\(613\) | −39.3673 | − | 4.13767i | −1.59003 | − | 0.167119i | −0.732213 | − | 0.681075i | \(-0.761513\pi\) |
−0.857816 | + | 0.513956i | \(0.828179\pi\) | |||||||
\(614\) | 7.35863 | + | 12.7455i | 0.296970 | + | 0.514368i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.29140 | − | 4.57097i | −0.253488 | − | 0.184170i | ||||
\(617\) | 22.0382 | + | 19.8433i | 0.887226 | + | 0.798862i | 0.980447 | − | 0.196783i | \(-0.0630496\pi\) |
−0.0932207 | + | 0.995645i | \(0.529716\pi\) | |||||||
\(618\) | −34.6978 | − | 11.2740i | −1.39575 | − | 0.453507i | ||||
\(619\) | 19.6256 | 0.788820 | 0.394410 | − | 0.918934i | \(-0.370949\pi\) | ||||
0.394410 | + | 0.918934i | \(0.370949\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 82.4548 | 3.30880 | ||||||||
\(622\) | 29.0283 | + | 9.43185i | 1.16393 | + | 0.378183i | ||||
\(623\) | 5.40448 | + | 4.86621i | 0.216526 | + | 0.194961i | ||||
\(624\) | 41.0657 | + | 29.8360i | 1.64394 | + | 1.19439i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.45986 | − | 2.52856i | −0.0583479 | − | 0.101062i | ||||
\(627\) | −35.4074 | − | 3.72146i | −1.41403 | − | 0.148621i | ||||
\(628\) | −0.0503124 | − | 0.0692491i | −0.00200769 | − | 0.00276334i | ||||
\(629\) | 0.899463 | + | 8.55782i | 0.0358639 | + | 0.341223i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0599 | − | 8.04080i | 0.718955 | − | 0.320099i | −0.0144462 | − | 0.999896i | \(-0.504599\pi\) |
0.733401 | + | 0.679796i | \(0.237932\pi\) | |||||||
\(632\) | −2.42056 | − | 11.3879i | −0.0962848 | − | 0.452985i | ||||
\(633\) | −12.0659 | + | 56.7658i | −0.479578 | + | 2.25624i | ||||
\(634\) | −28.0889 | − | 12.5060i | −1.11555 | − | 0.496675i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.00955003 | + | 0.0293920i | 0.000378683 | + | 0.00116547i | ||||
\(637\) | −10.0740 | + | 22.6266i | −0.399147 | + | 0.896499i | ||||
\(638\) | −1.90548 | + | 8.96456i | −0.0754385 | + | 0.354910i | ||||
\(639\) | 73.0800 | − | 15.5336i | 2.89100 | − | 0.614501i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.0021 | + | 29.9889i | 1.06652 | + | 1.18449i | 0.982158 | + | 0.188056i | \(0.0602187\pi\) |
0.0843623 | + | 0.996435i | \(0.473115\pi\) | |||||||
\(642\) | −70.5110 | + | 7.41101i | −2.78285 | + | 0.292489i | ||||
\(643\) | 16.8980 | + | 23.2581i | 0.666391 | + | 0.917208i | 0.999672 | − | 0.0256194i | \(-0.00815579\pi\) |
−0.333281 | + | 0.942828i | \(0.608156\pi\) | |||||||
\(644\) | 0.00258071 | − | 0.0245538i | 0.000101694 | − | 0.000967555i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.4802 | + | 28.5445i | −0.648403 | + | 1.12307i | ||||
\(647\) | −22.8229 | + | 31.4131i | −0.897262 | + | 1.23498i | 0.0740708 | + | 0.997253i | \(0.476401\pi\) |
−0.971333 | + | 0.237723i | \(0.923599\pi\) | |||||||
\(648\) | −33.7130 | − | 30.3553i | −1.32437 | − | 1.19247i | ||||
\(649\) | 3.70184 | − | 11.3931i | 0.145310 | − | 0.447217i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.9112 | + | 4.33978i | 0.623611 | + | 0.170090i | ||||
\(652\) | 0 | 0.000906962i | 0 | 3.55194e-5i | ||||||
\(653\) | 41.4492 | + | 13.4677i | 1.62203 | + | 0.527030i | 0.972420 | − | 0.233235i | \(-0.0749312\pi\) |
0.649612 | + | 0.760266i | \(0.274931\pi\) | |||||||
\(654\) | 20.2026 | − | 22.4373i | 0.789984 | − | 0.877366i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.78059 | − | 4.81612i | 0.108564 | − | 0.188038i | ||||
\(657\) | 31.4285 | − | 18.1453i | 1.22614 | − | 0.707915i | ||||
\(658\) | 2.00299 | + | 0.210523i | 0.0780848 | + | 0.00820704i | ||||
\(659\) | −1.37480 | + | 0.998853i | −0.0535548 | + | 0.0389098i | −0.614241 | − | 0.789119i | \(-0.710538\pi\) |
0.560686 | + | 0.828029i | \(0.310538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.18741 | + | 2.42937i | 0.0850804 | + | 0.0944914i | 0.784182 | − | 0.620531i | \(-0.213083\pi\) |
−0.699101 | + | 0.715023i | \(0.746416\pi\) | |||||||
\(662\) | 9.73051 | + | 21.8551i | 0.378187 | + | 0.849422i | ||||
\(663\) | 15.5629 | + | 73.2175i | 0.604411 | + | 2.84353i | ||||
\(664\) | 46.7557 | + | 9.93822i | 1.81447 | + | 0.385678i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.28364 | + | 13.1837i | 0.165988 | + | 0.510858i | ||||
\(667\) | 15.0845 | − | 4.90125i | 0.584074 | − | 0.189777i | ||||
\(668\) | −8.53981e−5 | 0 | 0.000191807i | −3.30415e−6 | 0 | 7.42124e-6i | ||||
\(669\) | −60.0942 | − | 12.7734i | −2.32337 | − | 0.493849i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.2434 | − | 6.78681i | 0.588466 | − | 0.262002i | ||||
\(672\) | −0.0456038 | + | 0.0410619i | −0.00175921 | + | 0.00158400i | ||||
\(673\) | −18.4625 | + | 1.94049i | −0.711678 | + | 0.0748004i | −0.453448 | − | 0.891283i | \(-0.649806\pi\) |
−0.258231 | + | 0.966083i | \(0.583139\pi\) | |||||||
\(674\) | −4.96797 | + | 3.60944i | −0.191359 | + | 0.139031i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.00640542 | − | 0.0110945i | −0.000246362 | − | 0.000426712i | ||||
\(677\) | −21.9558 | − | 12.6762i | −0.843831 | − | 0.487186i | 0.0147335 | − | 0.999891i | \(-0.495310\pi\) |
−0.858565 | + | 0.512705i | \(0.828643\pi\) | |||||||
\(678\) | 36.9421 | − | 50.8465i | 1.41875 | − | 1.95275i | ||||
\(679\) | 0.00216356 | − | 0.00240288i | 8.30298e−5 | − | 9.22139e-5i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −80.4295 | −3.08206 | ||||||||
\(682\) | −17.8095 | + | 14.2904i | −0.681962 | + | 0.547209i | ||||
\(683\) | − | 19.8387i | − | 0.759106i | −0.925170 | − | 0.379553i | \(-0.876078\pi\) | ||
0.925170 | − | 0.379553i | \(-0.123922\pi\) | |||||||
\(684\) | −0.0299902 | + | 0.0923005i | −0.00114671 | + | 0.00352920i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14.2469 | − | 10.3510i | −0.543950 | − | 0.395203i | ||||
\(687\) | −0.817532 | − | 0.472002i | −0.0311908 | − | 0.0180080i | ||||
\(688\) | 44.5046 | − | 25.6948i | 1.69672 | − | 0.979604i | ||||
\(689\) | −1.14888 | + | 10.9308i | −0.0437687 | + | 0.416431i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.77024 | + | 26.3571i | 0.105385 | + | 1.00267i | 0.911608 | + | 0.411060i | \(0.134841\pi\) |
−0.806223 | + | 0.591612i | \(0.798492\pi\) | |||||||
\(692\) | 0.0366442 | − | 0.0329946i | 0.00139300 | − | 0.00125427i | ||||
\(693\) | −7.52781 | − | 16.9077i | −0.285958 | − | 0.642272i | ||||
\(694\) | −14.5254 | + | 3.08747i | −0.551376 | + | 0.117199i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −17.9908 | − | 8.01001i | −0.681939 | − | 0.303619i | ||||
\(697\) | 7.79942 | − | 2.53418i | 0.295424 | − | 0.0959891i | ||||
\(698\) | −7.52404 | + | 2.44471i | −0.284789 | + | 0.0925336i | ||||
\(699\) | −1.25715 | − | 0.559718i | −0.0475497 | − | 0.0211705i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.2362 | + | 2.17576i | −0.386615 | + | 0.0821775i | −0.397119 | − | 0.917767i | \(-0.629990\pi\) |
0.0105038 | + | 0.999945i | \(0.496656\pi\) | |||||||
\(702\) | 27.1679 | + | 61.0200i | 1.02539 | + | 2.30305i | ||||
\(703\) | −4.26400 | + | 3.83932i | −0.160820 | + | 0.144803i | ||||
\(704\) | 2.41833 | + | 23.0089i | 0.0911444 | + | 0.867181i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.42363 | + | 42.0880i | −0.166486 | + | 1.58400i | ||||
\(707\) | 3.94226 | − | 2.27607i | 0.148264 | − | 0.0856003i | ||||
\(708\) | −0.0408955 | − | 0.0236110i | −0.00153695 | − | 0.000887356i | ||||
\(709\) | −0.951875 | − | 0.691578i | −0.0357484 | − | 0.0259728i | 0.569768 | − | 0.821806i | \(-0.307033\pi\) |
−0.605516 | + | 0.795833i | \(0.707033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.56220 | − | 26.3518i | 0.321108 | − | 0.988268i | ||||
\(712\) | − | 21.6358i | − | 0.810837i | ||||||
\(713\) | 36.8285 | + | 14.3265i | 1.37924 | + | 0.536532i | ||||
\(714\) | −24.7776 | −0.927278 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.00742444 | + | 0.00824567i | −0.000277464 | + | 0.000308155i | ||||
\(717\) | −24.0813 | + | 33.1451i | −0.899333 | + | 1.23783i | ||||
\(718\) | −5.68255 | − | 3.28082i | −0.212071 | − | 0.122439i | ||||
\(719\) | −19.4477 | − | 33.6843i | −0.725276 | − | 1.25621i | −0.958860 | − | 0.283878i | \(-0.908379\pi\) |
0.233585 | − | 0.972336i | \(-0.424954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.35101 | − | 4.61428i | 0.236524 | − | 0.171845i | ||||
\(722\) | 4.88980 | − | 0.513939i | 0.181980 | − | 0.0191268i | ||||
\(723\) | 60.2501 | − | 54.2495i | 2.24073 | − | 2.01756i | ||||
\(724\) | −0.0226888 | + | 0.0101017i | −0.000843223 | + | 0.000375427i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.2513 | − | 2.39155i | −0.417576 | − | 0.0887586i | ||||
\(727\) | 3.41823 | − | 7.67746i | 0.126775 | − | 0.284741i | −0.838996 | − | 0.544138i | \(-0.816857\pi\) |
0.965771 | + | 0.259396i | \(0.0835236\pi\) | |||||||
\(728\) | −10.3687 | + | 3.36898i | −0.384288 | + | 0.124863i | ||||
\(729\) | 0.223240 | + | 0.687063i | 0.00826816 | + | 0.0254468i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74.1256 | + | 15.7559i | 2.74163 | + | 0.582752i | ||||
\(732\) | −0.0136754 | − | 0.0643378i | −0.000505458 | − | 0.00237799i | ||||
\(733\) | −16.3468 | − | 36.7154i | −0.603781 | − | 1.35611i | −0.914102 | − | 0.405483i | \(-0.867103\pi\) |
0.310321 | − | 0.950632i | \(-0.399563\pi\) | |||||||
\(734\) | 25.1102 | + | 27.8877i | 0.926835 | + | 1.02935i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.118955 | + | 0.0864260i | −0.00438475 | + | 0.00318570i | ||||
\(737\) | 26.4595 | + | 2.78101i | 0.974649 | + | 0.102440i | ||||
\(738\) | 11.4411 | − | 6.60554i | 0.421154 | − | 0.243153i | ||||
\(739\) | 4.55735 | − | 7.89357i | 0.167645 | − | 0.290370i | −0.769946 | − | 0.638109i | \(-0.779717\pi\) |
0.937591 | + | 0.347739i | \(0.113050\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.3977 | + | 37.0919i | −1.22689 | + | 1.36260i | ||||
\(742\) | −3.46014 | − | 1.12427i | −0.127026 | − | 0.0412732i | ||||
\(743\) | 6.65317i | 0.244081i | 0.992525 | + | 0.122041i | \(0.0389438\pi\) | ||||
−0.992525 | + | 0.122041i | \(0.961056\pi\) | |||||||
\(744\) | −22.0796 | − | 43.8171i | −0.809478 | − | 1.60641i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.815999 | − | 2.51139i | 0.0298759 | − | 0.0919484i | ||||
\(747\) | 84.5413 | + | 76.1213i | 3.09321 | + | 2.78513i | ||||
\(748\) | 0.0368553 | − | 0.0507270i | 0.00134756 | − | 0.00185476i | ||||
\(749\) | 7.62784 | − | 13.2118i | 0.278715 | − | 0.482749i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.14886 | − | 39.4738i | 0.151394 | − | 1.44042i | −0.610139 | − | 0.792294i | \(-0.708887\pi\) |
0.761534 | − | 0.648125i | \(-0.224447\pi\) | |||||||
\(752\) | −3.52835 | − | 4.85635i | −0.128666 | − | 0.177093i | ||||
\(753\) | 52.4295 | − | 5.51056i | 1.91064 | − | 0.200816i | ||||
\(754\) | 8.59729 | + | 9.54826i | 0.313095 | + | 0.347727i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.0395293 | + | 0.00840222i | −0.00143767 | + | 0.000305586i | ||||
\(757\) | 2.91405 | − | 13.7095i | 0.105913 | − | 0.498281i | −0.892930 | − | 0.450195i | \(-0.851354\pi\) |
0.998843 | − | 0.0480862i | \(-0.0153122\pi\) | |||||||
\(758\) | −0.838465 | + | 1.88322i | −0.0304544 | + | 0.0684017i | ||||
\(759\) | −19.8165 | − | 60.9889i | −0.719293 | − | 2.21376i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.5132 | − | 14.0306i | −1.14235 | − | 0.508609i | −0.253743 | − | 0.967272i | \(-0.581662\pi\) |
−0.888610 | + | 0.458663i | \(0.848328\pi\) | |||||||
\(762\) | 6.02391 | − | 28.3403i | 0.218223 | − | 1.02666i | ||||
\(763\) | 1.35072 | + | 6.35463i | 0.0488993 | + | 0.230053i | ||||
\(764\) | 0.0375025 | − | 0.0166972i | 0.00135679 | − | 0.000604083i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.03994 | − | 19.4087i | −0.0737060 | − | 0.701266i | ||||
\(767\) | −9.87142 | − | 13.5868i | −0.356436 | − | 0.490593i | ||||
\(768\) | 0.272599 | + | 0.0286513i | 0.00983657 | + | 0.00103387i | ||||
\(769\) | −13.5658 | − | 23.4966i | −0.489195 | − | 0.847310i | 0.510728 | − | 0.859742i | \(-0.329376\pi\) |
−0.999923 | + | 0.0124321i | \(0.996043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5465 | − | 7.66246i | −0.379822 | − | 0.275957i | ||||
\(772\) | 0.0127072 | + | 0.0114416i | 0.000457342 | + | 0.000411793i | ||||
\(773\) | 26.8373 | + | 8.71995i | 0.965269 | + | 0.313635i | 0.748905 | − | 0.662678i | \(-0.230580\pi\) |
0.216364 | + | 0.976313i | \(0.430580\pi\) | |||||||
\(774\) | 122.080 | 4.38809 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.00961947 | −0.000345319 | ||||||||
\(777\) | −4.10221 | − | 1.33289i | −0.147166 | − | 0.0478171i | ||||
\(778\) | −17.0268 | − | 15.3310i | −0.610441 | − | 0.549644i | ||||
\(779\) | 4.42393 | + | 3.21418i | 0.158504 | + | 0.115160i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0932 | − | 27.8742i | −0.575860 | − | 0.997419i | ||||
\(782\) | −59.0434 | − | 6.20571i | −2.11139 | − | 0.221916i | ||||
\(783\) | −15.2600 | − | 21.0036i | −0.545347 | − | 0.750606i | ||||
\(784\) | 2.55423 | + | 24.3019i | 0.0912226 | + | 0.867925i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 35.8522 | − | 15.9624i | 1.27881 | − | 0.569361i | ||||
\(787\) | −0.164770 | − | 0.775181i | −0.00587341 | − | 0.0276322i | 0.975113 | − | 0.221707i | \(-0.0711629\pi\) |
−0.980987 | + | 0.194075i | \(0.937830\pi\) | |||||||
\(788\) | −0.0103434 | + | 0.0486621i | −0.000368470 | + | 0.00173351i | ||||
\(789\) | 52.3825 | + | 23.3222i | 1.86487 | + | 0.830293i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.17902 | + | 12.8617i | 0.148589 | + | 0.457310i | ||||
\(792\) | −22.3956 | + | 50.3013i | −0.795792 | + | 1.78738i | ||||
\(793\) | 4.86359 | − | 22.8814i | 0.172711 | − | 0.812543i | ||||
\(794\) | 33.8235 | − | 7.18941i | 1.20035 | − | 0.255143i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.0187083 | + | 0.0207777i | 0.000663097 | + | 0.000736444i | ||||
\(797\) | 26.5598 | − | 2.79155i | 0.940796 | − | 0.0988817i | 0.378301 | − | 0.925682i | \(-0.376508\pi\) |
0.562495 | + | 0.826801i | \(0.309842\pi\) | |||||||
\(798\) | −9.71120 | − | 13.3663i | −0.343773 | − | 0.473162i | ||||
\(799\) | 0.925287 | − | 8.80351i | 0.0327343 | − | 0.311446i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.7460 | − | 44.5933i | 0.909689 | − | 1.57563i | ||||
\(802\) | 5.46181 | − | 7.51753i | 0.192863 | − | 0.265453i | ||||
\(803\) | −11.6184 | − | 10.4612i | −0.410004 | − | 0.369169i | ||||
\(804\) | 0.0324086 | − | 0.0997433i | 0.00114296 | − | 0.00351767i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.53235 | + | 31.9751i | 0.0539746 | + | 1.12627i | ||||
\(807\) | 70.3174i | 2.47529i | ||||||||
\(808\) | −12.8800 | − | 4.18495i | −0.453116 | − | 0.147226i | ||||
\(809\) | 22.5806 | − | 25.0783i | 0.793890 | − | 0.881705i | −0.201313 | − | 0.979527i | \(-0.564521\pi\) |
0.995204 | + | 0.0978222i | \(0.0311876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.46711 | − | 7.73726i | 0.156861 | − | 0.271692i | −0.776874 | − | 0.629656i | \(-0.783196\pi\) |
0.933735 | + | 0.357964i | \(0.116529\pi\) | |||||||
\(812\) | −0.00673216 | + | 0.00388681i | −0.000236252 | + | 0.000136400i | ||||
\(813\) | 30.2782 | + | 3.18237i | 1.06190 | + | 0.111610i | ||||
\(814\) | 4.83133 | − | 3.51017i | 0.169338 | − | 0.123031i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 49.4149 | + | 54.8808i | 1.72987 | + | 1.92121i | ||||
\(817\) | 20.5528 | + | 46.1624i | 0.719053 | + | 1.61502i | ||||
\(818\) | −8.19223 | − | 38.5414i | −0.286435 | − | 1.34757i | ||||
\(819\) | −25.3797 | − | 5.39462i | −0.886838 | − | 0.188503i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.15729 | − | 15.8725i | −0.179991 | − | 0.553955i | 0.819835 | − | 0.572599i | \(-0.194065\pi\) |
−0.999826 | + | 0.0186447i | \(0.994065\pi\) | |||||||
\(822\) | 73.9878 | − | 24.0401i | 2.58062 | − | 0.838494i | ||||
\(823\) | −19.0195 | + | 42.7184i | −0.662977 | + | 1.48907i | 0.197881 | + | 0.980226i | \(0.436594\pi\) |
−0.860858 | + | 0.508845i | \(0.830073\pi\) | |||||||
\(824\) | −22.8446 | − | 4.85576i | −0.795828 | − | 0.169158i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.07855 | − | 2.26112i | 0.176705 | − | 0.0786743i | ||||
\(827\) | −17.0531 | + | 15.3547i | −0.592994 | + | 0.533935i | −0.910064 | − | 0.414468i | \(-0.863968\pi\) |
0.317070 | + | 0.948402i | \(0.397301\pi\) | |||||||
\(828\) | −0.173851 | + | 0.0182725i | −0.00604174 | + | 0.000635013i | ||||
\(829\) | −10.9766 | + | 7.97494i | −0.381232 | + | 0.276981i | −0.761853 | − | 0.647750i | \(-0.775710\pi\) |
0.380621 | + | 0.924731i | \(0.375710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.0918 | − | 69.4411i | −1.39077 | − | 2.40889i | ||||
\(832\) | 28.0891 | + | 16.2173i | 0.973816 | + | 0.562233i | ||||
\(833\) | −21.1804 | + | 29.1523i | −0.733856 | + | 1.01007i | ||||
\(834\) | −49.0964 | + | 54.5270i | −1.70007 | + | 1.88812i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.0418096 | 0.00144602 | ||||||||
\(837\) | 3.67420 | − | 64.5792i | 0.126999 | − | 2.23218i | ||||
\(838\) | − | 28.7987i | − | 0.994835i | ||||||
\(839\) | 5.03944 | − | 15.5098i | 0.173981 | − | 0.535458i | −0.825605 | − | 0.564249i | \(-0.809166\pi\) |
0.999585 | + | 0.0287910i | \(0.00916571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.4213 | + | 14.1104i | 0.669700 | + | 0.486566i | ||||
\(842\) | −16.3355 | − | 9.43130i | −0.562958 | − | 0.325024i | ||||
\(843\) | −0.406425 | + | 0.234649i | −0.0139980 | + | 0.00808176i | ||||
\(844\) | 0.00712383 | − | 0.0677787i | 0.000245212 | − | 0.00233304i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.49059 | − | 14.1820i | −0.0512476 | − | 0.487588i | ||||
\(847\) | 1.83934 | − | 1.65615i | 0.0632005 | − | 0.0569060i | ||||
\(848\) | 4.41051 | + | 9.90616i | 0.151457 | + | 0.340179i | ||||
\(849\) | 46.0140 | − | 9.78057i | 1.57920 | − | 0.335668i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.44147 | − | 4.20361i | −0.323649 | − | 0.144098i | ||||
\(852\) | −0.120667 | + | 0.0392071i | −0.00413398 | + | 0.00134321i | ||||
\(853\) | −41.3684 | + | 13.4414i | −1.41643 | + | 0.460225i | −0.914465 | − | 0.404665i | \(-0.867388\pi\) |
−0.501961 | + | 0.864890i | \(0.667388\pi\) | |||||||
\(854\) | 7.07387 | + | 3.14949i | 0.242063 | + | 0.107773i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −44.3945 | + | 9.43635i | −1.51737 | + | 0.322528i | ||||
\(857\) | 1.21881 | + | 2.73749i | 0.0416338 | + | 0.0935110i | 0.933165 | − | 0.359448i | \(-0.117035\pi\) |
−0.891531 | + | 0.452959i | \(0.850368\pi\) | |||||||
\(858\) | 38.6051 | − | 34.7602i | 1.31796 | − | 1.18669i | ||||
\(859\) | 3.97319 | + | 37.8023i | 0.135563 | + | 1.28980i | 0.824867 | + | 0.565327i | \(0.191250\pi\) |
−0.689304 | + | 0.724472i | \(0.742083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.429688 | + | 4.08821i | −0.0146437 | + | 0.139326i | ||||
\(862\) | 28.1094 | − | 16.2290i | 0.957410 | − | 0.552761i | ||||
\(863\) | 3.72036 | + | 2.14795i | 0.126642 | + | 0.0731170i | 0.561983 | − | 0.827149i | \(-0.310039\pi\) |
−0.435340 | + | 0.900266i | \(0.643372\pi\) | |||||||
\(864\) | 0.194713 | + | 0.141467i | 0.00662426 | + | 0.00481281i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.77778 | + | 8.54914i | −0.0943929 | + | 0.290512i | ||||
\(867\) | 55.8867i | 1.89801i | ||||||||
\(868\) | −0.0191157 | − | 0.00311535i | −0.000648829 | − | 0.000105742i | ||||
\(869\) | −11.9366 | −0.404922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.9577 | − | 27.7183i | 0.845659 | − | 0.939200i | ||||
\(872\) | 11.3605 | − | 15.6364i | 0.384715 | − | 0.529515i | ||||
\(873\) | −0.0198266 | − | 0.0114469i | −0.000671027 | − | 0.000387418i | ||||
\(874\) | −19.7935 | − | 34.2833i | −0.669524 | − | 1.15965i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0498585 | + | 0.0362243i | −0.00168456 | + | 0.00122391i | ||||
\(877\) | −8.29006 | + | 0.871320i | −0.279935 | + | 0.0294224i | −0.243456 | − | 0.969912i | \(-0.578281\pi\) |
−0.0364796 | + | 0.999334i | \(0.511614\pi\) | |||||||
\(878\) | −11.8008 | + | 10.6255i | −0.398259 | + | 0.358594i | ||||
\(879\) | 11.7810 | − | 5.24525i | 0.397364 | − | 0.176918i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.6695 | − | 2.90554i | −0.460537 | − | 0.0978903i | −0.0282003 | − | 0.999602i | \(-0.508978\pi\) |
−0.432337 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(882\) | −23.6108 | + | 53.0307i | −0.795016 | + | 1.78564i | ||||
\(883\) | 5.07760 | − | 1.64981i | 0.170875 | − | 0.0555206i | −0.222330 | − | 0.974971i | \(-0.571366\pi\) |
0.393205 | + | 0.919451i | \(0.371366\pi\) | |||||||
\(884\) | −0.0271637 | − | 0.0836014i | −0.000913616 | − | 0.00281182i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.68453 | + | 0.570615i | 0.0901887 | + | 0.0191702i | ||||
\(887\) | 1.46021 | + | 6.86974i | 0.0490290 | + | 0.230663i | 0.995839 | − | 0.0911297i | \(-0.0290478\pi\) |
−0.946810 | + | 0.321793i | \(0.895714\pi\) | |||||||
\(888\) | 5.21937 | + | 11.7229i | 0.175151 | + | 0.393395i | ||||
\(889\) | 4.17157 | + | 4.63300i | 0.139910 | + | 0.155386i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −37.6293 | + | 27.3393i | −1.26063 | + | 0.915901i | ||||
\(892\) | 0.0717529 | + | 0.00754153i | 0.00240246 | + | 0.000252509i | ||||
\(893\) | 5.11172 | − | 2.95125i | 0.171057 | − | 0.0987600i | ||||
\(894\) | −9.12620 | + | 15.8070i | −0.305226 | + | 0.528666i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.21035 | + | 8.00791i | −0.240881 | + | 0.267525i | ||||
\(897\) | −85.5022 | − | 27.7813i | −2.85483 | − | 0.927592i | ||||
\(898\) | 16.9749i | 0.566460i | ||||||||
\(899\) | −3.16653 | − | 12.0327i | −0.105610 | − | 0.401312i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.94136 | + | 15.2079i | −0.164621 | + | 0.506650i | ||||
\(902\) | −4.22951 | − | 3.80827i | −0.140827 | − | 0.126801i | ||||
\(903\) | −22.3277 | + | 30.7315i | −0.743021 | + | 1.02268i | ||||
\(904\) | 20.1166 | − | 34.8430i | 0.669069 | − | 1.15886i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.63386 | + | 44.0882i | −0.153950 | + | 1.46473i | ||||
\(907\) | 16.3662 | + | 22.5261i | 0.543429 | + | 0.747966i | 0.989102 | − | 0.147230i | \(-0.0470356\pi\) |
−0.445673 | + | 0.895196i | \(0.647036\pi\) | |||||||
\(908\) | 0.0939348 | − | 0.00987295i | 0.00311734 | − | 0.000327645i | ||||
\(909\) | −21.5668 | − | 23.9523i | −0.715324 | − | 0.794448i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1754 | + | 4.28841i | −0.668440 | + | 0.142081i | −0.529618 | − | 0.848236i | \(-0.677665\pi\) |
−0.138822 | + | 0.990317i | \(0.544331\pi\) | |||||||
\(912\) | −10.2381 | + | 48.1666i | −0.339018 | + | 1.59496i | ||||
\(913\) | 19.9337 | − | 44.7718i | 0.659708 | − | 1.48173i | ||||
\(914\) | 10.2119 | + | 31.4290i | 0.337780 | + | 1.03958i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.00101275 | 0.000450904i | 3.34621e−5 | 1.48983e-5i | ||||||
\(917\) | −1.75572 | + | 8.25999i | −0.0579788 | + | 0.272769i | ||||
\(918\) | 20.2044 | + | 95.0544i | 0.666846 | + | 3.13726i | ||||
\(919\) | −3.16738 | + | 1.41021i | −0.104482 | + | 0.0465185i | −0.458312 | − | 0.888791i | \(-0.651546\pi\) |
0.353830 | + | 0.935310i | \(0.384879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.38923 | + | 32.2464i | 0.111679 | + | 1.06255i | ||||
\(922\) | −27.9976 | − | 38.5354i | −0.922053 | − | 1.26910i | ||||
\(923\) | −44.8759 | − | 4.71664i | −1.47711 | − | 0.155250i | ||||
\(924\) | 0.0157150 | + | 0.0272191i | 0.000516985 | + | 0.000895444i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.6164 | + | 22.9707i | 1.03898 | + | 0.754863i | ||||
\(927\) | −41.3064 | − | 37.1925i | −1.35668 | − | 1.22156i | ||||
\(928\) | 0.0440303 | + | 0.0143063i | 0.00144536 | + | 0.000469627i | ||||
\(929\) | 16.0952 | 0.528066 | 0.264033 | − | 0.964514i | \(-0.414947\pi\) | ||||
0.264033 | + | 0.964514i | \(0.414947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0276 | −0.787472 | ||||||||
\(932\) | 0.00153695 | 0.000499385i | 5.03445e−5 | 1.63579e-5i | ||||||
\(933\) | 49.9721 | + | 44.9951i | 1.63601 | + | 1.47307i | ||||
\(934\) | −39.2905 | − | 28.5462i | −1.28562 | − | 0.934060i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 38.5962 | + | 66.8506i | 1.26156 | + | 2.18508i | ||||
\(937\) | 2.90279 | + | 0.305096i | 0.0948300 | + | 0.00996704i | 0.151825 | − | 0.988407i | \(-0.451485\pi\) |
−0.0569946 | + | 0.998374i | \(0.518152\pi\) | |||||||
\(938\) | 7.25707 | + | 9.98849i | 0.236952 | + | 0.326136i | ||||
\(939\) | −0.672383 | − | 6.39729i | −0.0219424 | − | 0.208768i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.6925 | + | 19.4531i | −1.42433 | + | 0.634154i | −0.966915 | − | 0.255097i | \(-0.917892\pi\) |
−0.457418 | + | 0.889252i | \(0.651226\pi\) | |||||||
\(942\) | −21.4512 | − | 100.920i | −0.698917 | − | 3.28814i | ||||
\(943\) | −2.04784 | + | 9.63431i | −0.0666867 | + | 0.313736i | ||||
\(944\) | −15.1366 | − | 6.73924i | −0.492653 | − | 0.219343i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.2520 | − | 50.0185i | −0.528398 | − | 1.62624i | ||||
\(947\) | 14.4237 | − | 32.3961i | 0.468706 | − | 1.05273i | −0.512309 | − | 0.858801i | \(-0.671210\pi\) |
0.981015 | − | 0.193931i | \(-0.0621236\pi\) | |||||||
\(948\) | −0.00978296 | + | 0.0460252i | −0.000317736 | + | 0.00149483i | ||||
\(949\) | −21.4389 | + | 4.55698i | −0.695936 | + | 0.147926i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.3267 | − | 50.3404i | −1.46982 | − | 1.63240i | ||||
\(952\) | −15.7745 | + | 1.65797i | −0.511255 | + | 0.0537350i | ||||
\(953\) | −16.5362 | − | 22.7601i | −0.535660 | − | 0.737273i | 0.452319 | − | 0.891856i | \(-0.350597\pi\) |
−0.987980 | + | 0.154583i | \(0.950597\pi\) | |||||||
\(954\) | −2.69266 | + | 25.6189i | −0.0871780 | + | 0.829443i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.0240563 | − | 0.0416667i | 0.000778035 | − | 0.00134760i | ||||
\(957\) | −11.8681 | + | 16.3351i | −0.383643 | + | 0.528039i | ||||
\(958\) | 25.3416 | + | 22.8176i | 0.818749 | + | 0.737204i | ||||
\(959\) | −5.17279 | + | 15.9202i | −0.167038 | + | 0.514091i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8617 | − | 28.2060i | 0.414894 | − | 0.909870i | ||||
\(962\) | − | 8.37212i | − | 0.269928i | ||||||
\(963\) | −102.730 | − | 33.3790i | −3.31043 | − | 1.07562i | ||||
\(964\) | −0.0637078 | + | 0.0707547i | −0.00205189 | + | 0.00227885i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.8795 | − | 25.7721i | 0.478741 | − | 0.829204i | ||||
\(967\) | −45.2698 | + | 26.1365i | −1.45578 | + | 0.840494i | −0.998800 | − | 0.0489843i | \(-0.984402\pi\) |
−0.456978 | + | 0.889478i | \(0.651068\pi\) | |||||||
\(968\) | −7.32313 | − | 0.769691i | −0.235374 | − | 0.0247388i | ||||
\(969\) | −58.7474 | + | 42.6825i | −1.88724 | + | 1.37116i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.2859 | − | 23.6404i | −0.683097 | − | 0.758656i | 0.297493 | − | 0.954724i | \(-0.403849\pi\) |
−0.980590 | + | 0.196068i | \(0.937183\pi\) | |||||||
\(972\) | 0.0226593 | + | 0.0508935i | 0.000726796 | + | 0.00163241i | ||||
\(973\) | −3.28251 | − | 15.4430i | −0.105233 | − | 0.495080i | ||||
\(974\) | −5.28315 | − | 1.12297i | −0.169283 | − | 0.0359822i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.13177 | − | 21.9493i | −0.228282 | − | 0.702581i | ||||
\(977\) | −37.6768 | + | 12.2419i | −1.20539 | + | 0.391654i | −0.841741 | − | 0.539882i | \(-0.818469\pi\) |
−0.363648 | + | 0.931537i | \(0.618469\pi\) | |||||||
\(978\) | 0.444649 | − | 0.998699i | 0.0142183 | − | 0.0319349i | ||||
\(979\) | −21.6981 | − | 4.61208i | −0.693475 | − | 0.147403i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.0218 | − | 18.7093i | 1.34165 | − | 0.597342i | ||||
\(982\) | 3.00429 | − | 2.70508i | 0.0958708 | − | 0.0863225i | ||||
\(983\) | −13.6615 | + | 1.43588i | −0.435734 | + | 0.0457975i | −0.319856 | − | 0.947466i | \(-0.603635\pi\) |
−0.115878 | + | 0.993264i | \(0.536968\pi\) | |||||||
\(984\) | 9.89394 | − | 7.18837i | 0.315407 | − | 0.229157i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.34644 | + | 16.1885i | 0.297651 | + | 0.515547i | ||||
\(987\) | 3.84269 | + | 2.21858i | 0.122314 | + | 0.0706181i | ||||
\(988\) | 0.0344525 | − | 0.0474198i | 0.00109608 | − | 0.00150863i | ||||
\(989\) | −60.9025 | + | 67.6391i | −1.93659 | + | 2.15080i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.43802 | 0.0774461 | 0.0387231 | − | 0.999250i | \(-0.487671\pi\) | ||||
0.0387231 | + | 0.999250i | \(0.487671\pi\) | |||||||
\(992\) | 0.0623888 | + | 0.0970177i | 0.00198085 | + | 0.00308031i | ||||
\(993\) | 52.7062i | 1.67258i | ||||||||
\(994\) | 4.61562 | − | 14.2054i | 0.146398 | − | 0.450568i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.156294 | − | 0.113554i | −0.00495236 | − | 0.00359810i | ||||
\(997\) | −25.1800 | − | 14.5377i | −0.797458 | − | 0.460413i | 0.0451235 | − | 0.998981i | \(-0.485632\pi\) |
−0.842582 | + | 0.538569i | \(0.818965\pi\) | |||||||
\(998\) | −20.8938 | + | 12.0630i | −0.661381 | + | 0.381848i | ||||
\(999\) | −1.76829 | + | 16.8242i | −0.0559464 | + | 0.532294i |
(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 | 775.2.ck.b.324.3 | 80 | ||
5.2 | odd | 4 | 775.2.bl.b.76.4 | 40 | |||
5.3 | odd | 4 | 155.2.q.b.76.2 | yes | 40 | ||
5.4 | even | 2 | inner | 775.2.ck.b.324.8 | 80 | ||
31.20 | even | 15 | inner | 775.2.ck.b.299.8 | 80 | ||
155.43 | even | 60 | 4805.2.a.z.1.6 | 20 | |||
155.82 | odd | 60 | 775.2.bl.b.51.4 | 40 | |||
155.113 | odd | 60 | 155.2.q.b.51.2 | ✓ | 40 | ||
155.143 | odd | 60 | 4805.2.a.ba.1.6 | 20 | |||
155.144 | even | 30 | inner | 775.2.ck.b.299.3 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
155.2.q.b.51.2 | ✓ | 40 | 155.113 | odd | 60 | ||
155.2.q.b.76.2 | yes | 40 | 5.3 | odd | 4 | ||
775.2.bl.b.51.4 | 40 | 155.82 | odd | 60 | |||
775.2.bl.b.76.4 | 40 | 5.2 | odd | 4 | |||
775.2.ck.b.299.3 | 80 | 155.144 | even | 30 | inner | ||
775.2.ck.b.299.8 | 80 | 31.20 | even | 15 | inner | ||
775.2.ck.b.324.3 | 80 | 1.1 | even | 1 | trivial | ||
775.2.ck.b.324.8 | 80 | 5.4 | even | 2 | inner | ||
4805.2.a.z.1.6 | 20 | 155.43 | even | 60 | |||
4805.2.a.ba.1.6 | 20 | 155.143 | odd | 60 |