Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(101,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.l (of order \(9\), degree \(6\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} - 12862 x^{9} + 77397 x^{8} - 24822 x^{7} + 178501 x^{6} - 39408 x^{5} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 651.1 | ||
Root | \(-1.58985 + 2.75370i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.651 |
Dual form | 950.2.l.i.251.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{8}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.939693 | + | 0.342020i | −0.664463 | + | 0.241845i | ||||
\(3\) | −0.552148 | + | 3.13139i | −0.318783 | + | 1.80791i | 0.231396 | + | 0.972860i | \(0.425671\pi\) |
−0.550178 | + | 0.835047i | \(0.685440\pi\) | |||||||
\(4\) | 0.766044 | − | 0.642788i | 0.383022 | − | 0.321394i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.552148 | − | 3.13139i | −0.225413 | − | 1.27838i | ||||
\(7\) | −1.67305 | − | 2.89781i | −0.632354 | − | 1.09527i | −0.987069 | − | 0.160295i | \(-0.948755\pi\) |
0.354715 | − | 0.934975i | \(-0.384578\pi\) | |||||||
\(8\) | −0.500000 | + | 0.866025i | −0.176777 | + | 0.306186i | ||||
\(9\) | −6.68164 | − | 2.43192i | −2.22721 | − | 0.810639i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.09216 | + | 5.35578i | −0.932322 | + | 1.61483i | −0.152981 | + | 0.988229i | \(0.548887\pi\) |
−0.779341 | + | 0.626600i | \(0.784446\pi\) | |||||||
\(12\) | 1.58985 | + | 2.75370i | 0.458949 | + | 0.794923i | ||||
\(13\) | 0.128260 | + | 0.727397i | 0.0355729 | + | 0.201744i | 0.997415 | − | 0.0718630i | \(-0.0228944\pi\) |
−0.961842 | + | 0.273607i | \(0.911783\pi\) | |||||||
\(14\) | 2.56327 | + | 2.15083i | 0.685061 | + | 0.574835i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.173648 | − | 0.984808i | 0.0434120 | − | 0.246202i | ||||
\(17\) | 0.815778 | − | 0.296919i | 0.197855 | − | 0.0720134i | −0.241192 | − | 0.970477i | \(-0.577538\pi\) |
0.439047 | + | 0.898464i | \(0.355316\pi\) | |||||||
\(18\) | 7.11045 | 1.67595 | ||||||||
\(19\) | −2.59916 | − | 3.49919i | −0.596289 | − | 0.802770i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.99794 | − | 3.63895i | 2.18173 | − | 0.794085i | ||||
\(22\) | 1.07390 | − | 6.09037i | 0.228956 | − | 1.29847i | ||||
\(23\) | 0.875950 | − | 0.735009i | 0.182648 | − | 0.153260i | −0.546879 | − | 0.837211i | \(-0.684184\pi\) |
0.729528 | + | 0.683951i | \(0.239740\pi\) | |||||||
\(24\) | −2.43579 | − | 2.04387i | −0.497203 | − | 0.417203i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.369309 | − | 0.639662i | −0.0724275 | − | 0.125448i | ||||
\(27\) | 6.53498 | − | 11.3189i | 1.25766 | − | 2.17833i | ||||
\(28\) | −3.14431 | − | 1.14444i | −0.594219 | − | 0.216278i | ||||
\(29\) | 7.32010 | + | 2.66430i | 1.35931 | + | 0.494748i | 0.915840 | − | 0.401543i | \(-0.131526\pi\) |
0.443468 | + | 0.896290i | \(0.353748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.23887 | − | 5.60988i | −0.581718 | − | 1.00756i | −0.995276 | − | 0.0970869i | \(-0.969048\pi\) |
0.413558 | − | 0.910478i | \(-0.364286\pi\) | |||||||
\(32\) | 0.173648 | + | 0.984808i | 0.0306970 | + | 0.174091i | ||||
\(33\) | −15.0637 | − | 12.6399i | −2.62225 | − | 2.20033i | ||||
\(34\) | −0.665029 | + | 0.558025i | −0.114051 | + | 0.0957005i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.68164 | + | 2.43192i | −1.11361 | + | 0.405319i | ||||
\(37\) | −1.68113 | −0.276377 | −0.138188 | − | 0.990406i | \(-0.544128\pi\) | ||||
−0.138188 | + | 0.990406i | \(0.544128\pi\) | |||||||
\(38\) | 3.63921 | + | 2.39920i | 0.590357 | + | 0.389202i | ||||
\(39\) | −2.34858 | −0.376074 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.68282 | − | 9.54373i | 0.262812 | − | 1.49048i | −0.512383 | − | 0.858757i | \(-0.671237\pi\) |
0.775194 | − | 0.631723i | \(-0.217652\pi\) | |||||||
\(42\) | −8.15040 | + | 6.83899i | −1.25763 | + | 1.05528i | ||||
\(43\) | −1.42354 | − | 1.19449i | −0.217088 | − | 0.182158i | 0.527758 | − | 0.849395i | \(-0.323033\pi\) |
−0.744846 | + | 0.667236i | \(0.767477\pi\) | |||||||
\(44\) | 1.07390 | + | 6.09037i | 0.161896 | + | 0.918158i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.571736 | + | 0.990275i | −0.0842978 | + | 0.146008i | ||||
\(47\) | 0.311691 | + | 0.113446i | 0.0454649 | + | 0.0165479i | 0.364652 | − | 0.931144i | \(-0.381188\pi\) |
−0.319188 | + | 0.947692i | \(0.603410\pi\) | |||||||
\(48\) | 2.98793 | + | 1.08752i | 0.431271 | + | 0.156970i | ||||
\(49\) | −2.09821 | + | 3.63420i | −0.299744 | + | 0.519172i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.479338 | + | 2.71846i | 0.0671207 | + | 0.380661i | ||||
\(52\) | 0.565815 | + | 0.474775i | 0.0784644 | + | 0.0658394i | ||||
\(53\) | 5.44265 | − | 4.56693i | 0.747606 | − | 0.627316i | −0.187263 | − | 0.982310i | \(-0.559962\pi\) |
0.934868 | + | 0.354994i | \(0.115517\pi\) | |||||||
\(54\) | −2.26958 | + | 12.8714i | −0.308850 | + | 1.75158i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.34610 | 0.447142 | ||||||||
\(57\) | 12.3925 | − | 6.20691i | 1.64142 | − | 0.822125i | ||||
\(58\) | −7.78988 | −1.02286 | ||||||||
\(59\) | −4.56719 | + | 1.66232i | −0.594597 | + | 0.216416i | −0.621750 | − | 0.783216i | \(-0.713578\pi\) |
0.0271531 | + | 0.999631i | \(0.491356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.53664 | − | 4.64579i | 0.708894 | − | 0.594833i | −0.215394 | − | 0.976527i | \(-0.569104\pi\) |
0.924289 | + | 0.381694i | \(0.124659\pi\) | |||||||
\(62\) | 4.96223 | + | 4.16381i | 0.630204 | + | 0.528804i | ||||
\(63\) | 4.13149 | + | 23.4308i | 0.520519 | + | 2.95201i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 18.4784 | + | 6.72557i | 2.27453 | + | 0.827861i | ||||
\(67\) | 2.74854 | + | 1.00039i | 0.335787 | + | 0.122217i | 0.504410 | − | 0.863464i | \(-0.331710\pi\) |
−0.168623 | + | 0.985681i | \(0.553932\pi\) | |||||||
\(68\) | 0.434067 | − | 0.751825i | 0.0526383 | − | 0.0911722i | ||||
\(69\) | 1.81794 | + | 3.14877i | 0.218855 | + | 0.379068i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.27849 | − | 4.42918i | −0.626442 | − | 0.525647i | 0.273379 | − | 0.961906i | \(-0.411859\pi\) |
−0.899821 | + | 0.436259i | \(0.856303\pi\) | |||||||
\(72\) | 5.44692 | − | 4.57051i | 0.641926 | − | 0.538640i | ||||
\(73\) | −1.35735 | + | 7.69790i | −0.158866 | + | 0.900972i | 0.796301 | + | 0.604901i | \(0.206787\pi\) |
−0.955166 | + | 0.296070i | \(0.904324\pi\) | |||||||
\(74\) | 1.57975 | − | 0.574982i | 0.183642 | − | 0.0668403i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.24031 | − | 1.00983i | −0.486397 | − | 0.115835i | ||||
\(77\) | 20.6934 | 2.35823 | ||||||||
\(78\) | 2.20694 | − | 0.803262i | 0.249887 | − | 0.0909515i | ||||
\(79\) | −0.399207 | + | 2.26401i | −0.0449143 | + | 0.254721i | −0.998995 | − | 0.0448292i | \(-0.985726\pi\) |
0.954080 | + | 0.299551i | \(0.0968368\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.4949 | + | 13.0018i | 1.72165 | + | 1.44464i | ||||
\(82\) | 1.68282 | + | 9.54373i | 0.185836 | + | 1.05393i | ||||
\(83\) | −5.72338 | − | 9.91318i | −0.628223 | − | 1.08811i | −0.987908 | − | 0.155040i | \(-0.950449\pi\) |
0.359686 | − | 0.933074i | \(-0.382884\pi\) | |||||||
\(84\) | 5.31979 | − | 9.21415i | 0.580437 | − | 1.00535i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.74623 | + | 0.635576i | 0.188301 | + | 0.0685359i | ||||
\(87\) | −12.3847 | + | 21.4510i | −1.32778 | + | 2.29978i | ||||
\(88\) | −3.09216 | − | 5.35578i | −0.329626 | − | 0.570928i | ||||
\(89\) | 0.404290 | + | 2.29284i | 0.0428546 | + | 0.243041i | 0.998709 | − | 0.0508007i | \(-0.0161773\pi\) |
−0.955854 | + | 0.293841i | \(0.905066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.89328 | − | 1.58865i | 0.198469 | − | 0.166535i | ||||
\(92\) | 0.198562 | − | 1.12610i | 0.0207015 | − | 0.117404i | ||||
\(93\) | 19.3550 | − | 7.04466i | 2.00702 | − | 0.730497i | ||||
\(94\) | −0.331695 | −0.0342117 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.17969 | −0.324526 | ||||||||
\(97\) | −6.43131 | + | 2.34081i | −0.653000 | + | 0.237673i | −0.647211 | − | 0.762311i | \(-0.724065\pi\) |
−0.00578901 | + | 0.999983i | \(0.501843\pi\) | |||||||
\(98\) | 0.728700 | − | 4.13266i | 0.0736098 | − | 0.417462i | ||||
\(99\) | 33.6855 | − | 28.2655i | 3.38552 | − | 2.84079i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.76892 | + | 10.0321i | 0.176015 | + | 0.998228i | 0.936966 | + | 0.349420i | \(0.113621\pi\) |
−0.760952 | + | 0.648809i | \(0.775268\pi\) | |||||||
\(102\) | −1.38020 | − | 2.39057i | −0.136660 | − | 0.236702i | ||||
\(103\) | 1.03525 | − | 1.79310i | 0.102006 | − | 0.176680i | −0.810505 | − | 0.585732i | \(-0.800807\pi\) |
0.912511 | + | 0.409052i | \(0.134141\pi\) | |||||||
\(104\) | −0.694074 | − | 0.252622i | −0.0680596 | − | 0.0247717i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.55244 | + | 6.15300i | −0.345043 | + | 0.597632i | ||||
\(107\) | −7.31857 | − | 12.6761i | −0.707513 | − | 1.22545i | −0.965777 | − | 0.259374i | \(-0.916484\pi\) |
0.258264 | − | 0.966075i | \(-0.416850\pi\) | |||||||
\(108\) | −2.26958 | − | 12.8714i | −0.218390 | − | 1.23855i | ||||
\(109\) | −6.66091 | − | 5.58917i | −0.637999 | − | 0.535345i | 0.265404 | − | 0.964137i | \(-0.414495\pi\) |
−0.903403 | + | 0.428792i | \(0.858939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.928235 | − | 5.26428i | 0.0881041 | − | 0.499663i | ||||
\(112\) | −3.14431 | + | 1.14444i | −0.297109 | + | 0.108139i | ||||
\(113\) | −10.8308 | −1.01888 | −0.509439 | − | 0.860507i | \(-0.670147\pi\) | ||||
−0.509439 | + | 0.860507i | \(0.670147\pi\) | |||||||
\(114\) | −9.52221 | + | 10.0711i | −0.891836 | + | 0.943240i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.32010 | − | 2.66430i | 0.679654 | − | 0.247374i | ||||
\(117\) | 0.911985 | − | 5.17212i | 0.0843130 | − | 0.478163i | ||||
\(118\) | 3.72320 | − | 3.12414i | 0.342749 | − | 0.287600i | ||||
\(119\) | −2.22526 | − | 1.86721i | −0.203989 | − | 0.171167i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.6229 | − | 23.5956i | −1.23845 | − | 2.14506i | ||||
\(122\) | −3.61379 | + | 6.25926i | −0.327177 | + | 0.566687i | ||||
\(123\) | 28.9559 | + | 10.5391i | 2.61087 | + | 0.950279i | ||||
\(124\) | −6.08708 | − | 2.21552i | −0.546636 | − | 0.198959i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.8962 | − | 20.6047i | −1.05979 | − | 1.83562i | ||||
\(127\) | 1.94911 | + | 11.0540i | 0.172956 | + | 0.980880i | 0.940477 | + | 0.339857i | \(0.110379\pi\) |
−0.767522 | + | 0.641023i | \(0.778510\pi\) | |||||||
\(128\) | 0.766044 | + | 0.642788i | 0.0677094 | + | 0.0568149i | ||||
\(129\) | 4.52642 | − | 3.79812i | 0.398529 | − | 0.334406i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2703 | + | 5.19396i | −1.24680 | + | 0.453798i | −0.879319 | − | 0.476233i | \(-0.842002\pi\) |
−0.367481 | + | 0.930031i | \(0.619780\pi\) | |||||||
\(132\) | −19.6643 | −1.71155 | ||||||||
\(133\) | −5.79147 | + | 13.3862i | −0.502184 | + | 1.16073i | ||||
\(134\) | −2.92493 | −0.252676 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.150750 | + | 0.854944i | −0.0129267 | + | 0.0733109i | ||||
\(137\) | 6.54988 | − | 5.49600i | 0.559594 | − | 0.469555i | −0.318580 | − | 0.947896i | \(-0.603206\pi\) |
0.878174 | + | 0.478341i | \(0.158762\pi\) | |||||||
\(138\) | −2.78525 | − | 2.33710i | −0.237096 | − | 0.198948i | ||||
\(139\) | 1.52883 | + | 8.67044i | 0.129674 | + | 0.735417i | 0.978421 | + | 0.206619i | \(0.0662460\pi\) |
−0.848748 | + | 0.528798i | \(0.822643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.527344 | + | 0.913387i | −0.0444104 | + | 0.0769210i | ||||
\(142\) | 6.47503 | + | 2.35672i | 0.543372 | + | 0.197771i | ||||
\(143\) | −4.29238 | − | 1.56230i | −0.358947 | − | 0.130646i | ||||
\(144\) | −3.55522 | + | 6.15783i | −0.296269 | + | 0.513152i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.35735 | − | 7.69790i | −0.112335 | − | 0.637083i | ||||
\(147\) | −10.2216 | − | 8.57692i | −0.843061 | − | 0.707413i | ||||
\(148\) | −1.28782 | + | 1.08061i | −0.105858 | + | 0.0888258i | ||||
\(149\) | 0.132240 | − | 0.749969i | 0.0108335 | − | 0.0614398i | −0.978912 | − | 0.204284i | \(-0.934514\pi\) |
0.989745 | + | 0.142844i | \(0.0456246\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.08784 | −0.495421 | −0.247711 | − | 0.968834i | \(-0.579678\pi\) | ||||
−0.247711 | + | 0.968834i | \(0.579678\pi\) | |||||||
\(152\) | 4.32997 | − | 0.501343i | 0.351207 | − | 0.0406643i | ||||
\(153\) | −6.17282 | −0.499043 | ||||||||
\(154\) | −19.4454 | + | 7.07756i | −1.56696 | + | 0.570326i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.79912 | + | 1.50964i | −0.144045 | + | 0.120868i | ||||
\(157\) | −18.6728 | − | 15.6683i | −1.49025 | − | 1.25047i | −0.894317 | − | 0.447434i | \(-0.852338\pi\) |
−0.595933 | − | 0.803034i | \(-0.703218\pi\) | |||||||
\(158\) | −0.399207 | − | 2.26401i | −0.0317592 | − | 0.180115i | ||||
\(159\) | 11.2957 | + | 19.5647i | 0.895804 | + | 1.55158i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.59543 | − | 1.30863i | −0.283360 | − | 0.103134i | ||||
\(162\) | −19.0073 | − | 6.91809i | −1.49335 | − | 0.543536i | ||||
\(163\) | −2.15496 | + | 3.73250i | −0.168789 | + | 0.292352i | −0.937994 | − | 0.346650i | \(-0.887319\pi\) |
0.769205 | + | 0.639002i | \(0.220652\pi\) | |||||||
\(164\) | −4.84548 | − | 8.39261i | −0.378368 | − | 0.655353i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.76873 | + | 7.35783i | 0.680585 | + | 0.571079i | ||||
\(167\) | −3.99229 | + | 3.34993i | −0.308933 | + | 0.259225i | −0.784051 | − | 0.620697i | \(-0.786850\pi\) |
0.475118 | + | 0.879922i | \(0.342405\pi\) | |||||||
\(168\) | −1.84754 | + | 10.4779i | −0.142541 | + | 0.808391i | ||||
\(169\) | 11.7033 | − | 4.25967i | 0.900258 | − | 0.327667i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.85690 | + | 29.7013i | 0.677304 | + | 2.27131i | ||||
\(172\) | −1.85830 | −0.141694 | ||||||||
\(173\) | 6.61144 | − | 2.40637i | 0.502658 | − | 0.182953i | −0.0782309 | − | 0.996935i | \(-0.524927\pi\) |
0.580889 | + | 0.813983i | \(0.302705\pi\) | |||||||
\(174\) | 4.30117 | − | 24.3931i | 0.326071 | − | 1.84924i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.73747 | + | 3.97521i | 0.357100 | + | 0.299642i | ||||
\(177\) | −2.68360 | − | 15.2195i | −0.201712 | − | 1.14397i | ||||
\(178\) | −1.16411 | − | 2.01629i | −0.0872534 | − | 0.151127i | ||||
\(179\) | −1.59972 | + | 2.77080i | −0.119569 | + | 0.207099i | −0.919597 | − | 0.392863i | \(-0.871485\pi\) |
0.800028 | + | 0.599963i | \(0.204818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.44963 | + | 1.61953i | 0.330738 | + | 0.120379i | 0.502052 | − | 0.864838i | \(-0.332579\pi\) |
−0.171313 | + | 0.985217i | \(0.554801\pi\) | |||||||
\(182\) | −1.23575 | + | 2.14038i | −0.0915997 | + | 0.158655i | ||||
\(183\) | 11.4907 | + | 19.9025i | 0.849419 | + | 1.47124i | ||||
\(184\) | 0.198562 | + | 1.12610i | 0.0146382 | + | 0.0830172i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.7784 | + | 13.2396i | −1.15693 | + | 0.970777i | ||||
\(187\) | −0.932285 | + | 5.28725i | −0.0681754 | + | 0.386642i | ||||
\(188\) | 0.311691 | − | 0.113446i | 0.0227324 | − | 0.00827393i | ||||
\(189\) | −43.7335 | −3.18114 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.4307 | −1.33360 | −0.666800 | − | 0.745237i | \(-0.732336\pi\) | ||||
−0.666800 | + | 0.745237i | \(0.732336\pi\) | |||||||
\(192\) | 2.98793 | − | 1.08752i | 0.215636 | − | 0.0784849i | ||||
\(193\) | 2.35285 | − | 13.3437i | 0.169362 | − | 0.960501i | −0.775090 | − | 0.631851i | \(-0.782295\pi\) |
0.944452 | − | 0.328649i | \(-0.106593\pi\) | |||||||
\(194\) | 5.24285 | − | 4.39927i | 0.376415 | − | 0.315849i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.728700 | + | 4.13266i | 0.0520500 | + | 0.295190i | ||||
\(197\) | 4.09550 | + | 7.09361i | 0.291792 | + | 0.505399i | 0.974234 | − | 0.225541i | \(-0.0724151\pi\) |
−0.682441 | + | 0.730940i | \(0.739082\pi\) | |||||||
\(198\) | −21.9867 | + | 38.0820i | −1.56252 | + | 2.70637i | ||||
\(199\) | −5.58408 | − | 2.03244i | −0.395845 | − | 0.144076i | 0.136425 | − | 0.990650i | \(-0.456439\pi\) |
−0.532270 | + | 0.846575i | \(0.678661\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.65019 | + | 8.05437i | −0.327999 | + | 0.568112i | ||||
\(202\) | −5.09342 | − | 8.82205i | −0.358371 | − | 0.620718i | ||||
\(203\) | −4.52627 | − | 25.6698i | −0.317682 | − | 1.80166i | ||||
\(204\) | 2.11459 | + | 1.77435i | 0.148051 | + | 0.124229i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.359538 | + | 2.03904i | −0.0250502 | + | 0.142067i | ||||
\(207\) | −7.64026 | + | 2.78083i | −0.531035 | + | 0.193281i | ||||
\(208\) | 0.738619 | 0.0512140 | ||||||||
\(209\) | 26.7779 | − | 3.10047i | 1.85227 | − | 0.214464i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.63846 | − | 0.596352i | 0.112796 | − | 0.0410545i | −0.285005 | − | 0.958526i | \(-0.591995\pi\) |
0.397802 | + | 0.917471i | \(0.369773\pi\) | |||||||
\(212\) | 1.23375 | − | 6.99694i | 0.0847342 | − | 0.480552i | ||||
\(213\) | 16.7840 | − | 14.0834i | 1.15002 | − | 0.964981i | ||||
\(214\) | 11.2127 | + | 9.40858i | 0.766485 | + | 0.643157i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.53498 | + | 11.3189i | 0.444649 | + | 0.770155i | ||||
\(217\) | −10.8376 | + | 18.7713i | −0.735703 | + | 1.27428i | ||||
\(218\) | 8.17082 | + | 2.97393i | 0.553397 | + | 0.201420i | ||||
\(219\) | −23.3557 | − | 8.50076i | −1.57823 | − | 0.574428i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.320610 | + | 0.555312i | 0.0215665 | + | 0.0373543i | ||||
\(222\) | 0.928235 | + | 5.26428i | 0.0622990 | + | 0.353315i | ||||
\(223\) | −20.2549 | − | 16.9959i | −1.35637 | − | 1.13813i | −0.977085 | − | 0.212848i | \(-0.931726\pi\) |
−0.379283 | − | 0.925281i | \(-0.623829\pi\) | |||||||
\(224\) | 2.56327 | − | 2.15083i | 0.171265 | − | 0.143709i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.1777 | − | 3.70436i | 0.677007 | − | 0.246411i | ||||
\(227\) | 27.4472 | 1.82174 | 0.910869 | − | 0.412697i | \(-0.135413\pi\) | ||||
0.910869 | + | 0.412697i | \(0.135413\pi\) | |||||||
\(228\) | 5.50345 | − | 12.7205i | 0.364475 | − | 0.842434i | ||||
\(229\) | −11.5722 | −0.764711 | −0.382355 | − | 0.924015i | \(-0.624887\pi\) | ||||
−0.382355 | + | 0.924015i | \(0.624887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.4258 | + | 64.7990i | −0.751764 | + | 4.26346i | ||||
\(232\) | −5.96740 | + | 5.00724i | −0.391779 | + | 0.328741i | ||||
\(233\) | −9.84970 | − | 8.26488i | −0.645275 | − | 0.541450i | 0.260358 | − | 0.965512i | \(-0.416159\pi\) |
−0.905633 | + | 0.424062i | \(0.860604\pi\) | |||||||
\(234\) | 0.911985 | + | 5.17212i | 0.0596183 | + | 0.338112i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.43015 | + | 4.20914i | −0.158189 | + | 0.273992i | ||||
\(237\) | −6.86908 | − | 2.50014i | −0.446195 | − | 0.162402i | ||||
\(238\) | 2.72968 | + | 0.993522i | 0.176939 | + | 0.0644005i | ||||
\(239\) | 5.65708 | − | 9.79836i | 0.365926 | − | 0.633803i | −0.622998 | − | 0.782223i | \(-0.714086\pi\) |
0.988924 | + | 0.148420i | \(0.0474189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.13196 | − | 23.4335i | −0.266163 | − | 1.50948i | −0.765704 | − | 0.643193i | \(-0.777609\pi\) |
0.499541 | − | 0.866290i | \(-0.333502\pi\) | |||||||
\(242\) | 20.8715 | + | 17.5133i | 1.34167 | + | 1.12580i | ||||
\(243\) | −19.2325 | + | 16.1379i | −1.23376 | + | 1.03525i | ||||
\(244\) | 1.25506 | − | 7.11777i | 0.0803467 | − | 0.455669i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −30.8143 | −1.96465 | ||||||||
\(247\) | 2.21194 | − | 2.33943i | 0.140742 | − | 0.148854i | ||||
\(248\) | 6.47773 | 0.411337 | ||||||||
\(249\) | 34.2022 | − | 12.4486i | 2.16747 | − | 0.788896i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9736 | − | 16.7599i | 1.26072 | − | 1.05787i | 0.265120 | − | 0.964215i | \(-0.414588\pi\) |
0.995604 | − | 0.0936578i | \(-0.0298560\pi\) | |||||||
\(252\) | 18.2260 | + | 15.2934i | 1.14813 | + | 0.963394i | ||||
\(253\) | 1.22797 | + | 6.96417i | 0.0772018 | + | 0.437833i | ||||
\(254\) | −5.61224 | − | 9.72069i | −0.352143 | − | 0.609930i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | − | 0.342020i | −0.0587308 | − | 0.0213763i | ||||
\(257\) | −9.54054 | − | 3.47247i | −0.595122 | − | 0.216607i | 0.0268585 | − | 0.999639i | \(-0.491450\pi\) |
−0.621981 | + | 0.783032i | \(0.713672\pi\) | |||||||
\(258\) | −2.95441 | + | 5.11719i | −0.183934 | + | 0.318582i | ||||
\(259\) | 2.81263 | + | 4.87161i | 0.174768 | + | 0.302707i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −42.4309 | − | 35.6037i | −2.62641 | − | 2.20382i | ||||
\(262\) | 11.6332 | − | 9.76144i | 0.718704 | − | 0.603064i | ||||
\(263\) | −2.97399 | + | 16.8663i | −0.183384 | + | 1.04002i | 0.744630 | + | 0.667477i | \(0.232626\pi\) |
−0.928014 | + | 0.372545i | \(0.878485\pi\) | |||||||
\(264\) | 18.4784 | − | 6.72557i | 1.13726 | − | 0.413930i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.863848 | − | 14.5597i | 0.0529659 | − | 0.892714i | ||||
\(267\) | −7.40300 | −0.453056 | ||||||||
\(268\) | 2.74854 | − | 1.00039i | 0.167894 | − | 0.0611083i | ||||
\(269\) | 3.96080 | − | 22.4628i | 0.241495 | − | 1.36958i | −0.587000 | − | 0.809587i | \(-0.699691\pi\) |
0.828495 | − | 0.559997i | \(-0.189198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6282 | + | 11.4354i | 0.827852 | + | 0.694650i | 0.954797 | − | 0.297260i | \(-0.0960727\pi\) |
−0.126945 | + | 0.991910i | \(0.540517\pi\) | |||||||
\(272\) | −0.150750 | − | 0.854944i | −0.00914054 | − | 0.0518386i | ||||
\(273\) | 3.92930 | + | 6.80574i | 0.237812 | + | 0.411902i | ||||
\(274\) | −4.27513 | + | 7.40475i | −0.258270 | + | 0.447337i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.41662 | + | 1.24355i | 0.205656 | + | 0.0748527i | ||||
\(277\) | −10.4365 | + | 18.0765i | −0.627066 | + | 1.08611i | 0.361071 | + | 0.932538i | \(0.382411\pi\) |
−0.988137 | + | 0.153572i | \(0.950922\pi\) | |||||||
\(278\) | −4.40210 | − | 7.62466i | −0.264020 | − | 0.457296i | ||||
\(279\) | 7.99817 | + | 45.3598i | 0.478838 | + | 2.71562i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.8354 | + | 17.4830i | −1.24294 | + | 1.04295i | −0.245650 | + | 0.969359i | \(0.579001\pi\) |
−0.997289 | + | 0.0735907i | \(0.976554\pi\) | |||||||
\(282\) | 0.183145 | − | 1.03867i | 0.0109061 | − | 0.0618516i | ||||
\(283\) | −18.5060 | + | 6.73563i | −1.10007 | + | 0.400392i | −0.827341 | − | 0.561700i | \(-0.810148\pi\) |
−0.272726 | + | 0.962092i | \(0.587925\pi\) | |||||||
\(284\) | −6.89058 | −0.408881 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.56786 | 0.270103 | ||||||||
\(287\) | −30.4714 | + | 11.0907i | −1.79867 | + | 0.654662i | ||||
\(288\) | 1.23472 | − | 7.00242i | 0.0727564 | − | 0.412622i | ||||
\(289\) | −12.4454 | + | 10.4429i | −0.732084 | + | 0.614291i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.77893 | − | 21.4314i | −0.221525 | − | 1.25633i | ||||
\(292\) | 3.90833 | + | 6.76942i | 0.228718 | + | 0.396151i | ||||
\(293\) | −7.38854 | + | 12.7973i | −0.431643 | + | 0.747628i | −0.997015 | − | 0.0772085i | \(-0.975399\pi\) |
0.565372 | + | 0.824836i | \(0.308733\pi\) | |||||||
\(294\) | 12.5386 | + | 4.56368i | 0.731267 | + | 0.266159i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.840567 | − | 1.45590i | 0.0488570 | − | 0.0846227i | ||||
\(297\) | 40.4145 | + | 69.9999i | 2.34508 | + | 4.06181i | ||||
\(298\) | 0.132240 | + | 0.749969i | 0.00766044 | + | 0.0434445i | ||||
\(299\) | 0.646993 | + | 0.542892i | 0.0374166 | + | 0.0313962i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07976 | + | 6.12360i | −0.0622361 | + | 0.352958i | ||||
\(302\) | 5.72070 | − | 2.08216i | 0.329189 | − | 0.119815i | ||||
\(303\) | −32.3910 | −1.86081 | ||||||||
\(304\) | −3.89737 | + | 1.95205i | −0.223530 | + | 0.111958i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.80055 | − | 2.11123i | 0.331595 | − | 0.120691i | ||||
\(307\) | 0.736086 | − | 4.17455i | 0.0420106 | − | 0.238254i | −0.956571 | − | 0.291500i | \(-0.905846\pi\) |
0.998581 | + | 0.0532459i | \(0.0169567\pi\) | |||||||
\(308\) | 15.8521 | − | 13.3015i | 0.903255 | − | 0.757921i | ||||
\(309\) | 5.04328 | + | 4.23182i | 0.286902 | + | 0.240740i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.49343 | + | 6.05079i | 0.198094 | + | 0.343109i | 0.947910 | − | 0.318537i | \(-0.103192\pi\) |
−0.749816 | + | 0.661646i | \(0.769858\pi\) | |||||||
\(312\) | 1.17429 | − | 2.03393i | 0.0664811 | − | 0.115149i | ||||
\(313\) | −7.16016 | − | 2.60608i | −0.404716 | − | 0.147305i | 0.131638 | − | 0.991298i | \(-0.457976\pi\) |
−0.536354 | + | 0.843993i | \(0.680199\pi\) | |||||||
\(314\) | 22.9056 | + | 8.33694i | 1.29264 | + | 0.470481i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.14947 | + | 1.99094i | 0.0646627 | + | 0.111999i | ||||
\(317\) | −2.38566 | − | 13.5297i | −0.133992 | − | 0.759905i | −0.975557 | − | 0.219749i | \(-0.929476\pi\) |
0.841565 | − | 0.540156i | \(-0.181635\pi\) | |||||||
\(318\) | −17.3060 | − | 14.5214i | −0.970470 | − | 0.814321i | ||||
\(319\) | −36.9043 | + | 30.9664i | −2.06625 | + | 1.73379i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 43.7348 | − | 15.9182i | 2.44104 | − | 0.888466i | ||||
\(322\) | 3.82618 | 0.213224 | ||||||||
\(323\) | −3.15932 | − | 2.08283i | −0.175789 | − | 0.115892i | ||||
\(324\) | 20.2271 | 1.12373 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.748409 | − | 4.24444i | 0.0414506 | − | 0.235078i | ||||
\(327\) | 21.1796 | − | 17.7718i | 1.17124 | − | 0.982785i | ||||
\(328\) | 7.42370 | + | 6.22923i | 0.409905 | + | 0.343952i | ||||
\(329\) | −0.192730 | − | 1.09302i | −0.0106255 | − | 0.0602604i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.32212 | − | 5.75409i | 0.182600 | − | 0.316273i | −0.760165 | − | 0.649730i | \(-0.774882\pi\) |
0.942765 | + | 0.333457i | \(0.108215\pi\) | |||||||
\(332\) | −10.7564 | − | 3.91502i | −0.590336 | − | 0.214865i | ||||
\(333\) | 11.2327 | + | 4.08838i | 0.615550 | + | 0.224042i | ||||
\(334\) | 2.60578 | − | 4.51335i | 0.142582 | − | 0.246959i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.84754 | − | 10.4779i | −0.100792 | − | 0.571619i | ||||
\(337\) | 14.1012 | + | 11.8323i | 0.768139 | + | 0.644545i | 0.940232 | − | 0.340536i | \(-0.110608\pi\) |
−0.172093 | + | 0.985081i | \(0.555053\pi\) | |||||||
\(338\) | −9.54066 | + | 8.00556i | −0.518943 | + | 0.435445i | ||||
\(339\) | 5.98022 | − | 33.9155i | 0.324801 | − | 1.84204i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.0604 | 2.16939 | ||||||||
\(342\) | −18.4812 | − | 24.8808i | −0.999349 | − | 1.34540i | ||||
\(343\) | −9.38108 | −0.506531 | ||||||||
\(344\) | 1.74623 | − | 0.635576i | 0.0941504 | − | 0.0342680i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.38969 | + | 4.52249i | −0.289752 | + | 0.243131i | ||||
\(347\) | −5.68212 | − | 4.76787i | −0.305032 | − | 0.255952i | 0.477403 | − | 0.878684i | \(-0.341578\pi\) |
−0.782435 | + | 0.622732i | \(0.786023\pi\) | |||||||
\(348\) | 4.30117 | + | 24.3931i | 0.230567 | + | 1.30761i | ||||
\(349\) | −9.57581 | − | 16.5858i | −0.512581 | − | 0.887817i | −0.999894 | − | 0.0145891i | \(-0.995356\pi\) |
0.487312 | − | 0.873228i | \(-0.337977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.07153 | + | 3.30177i | 0.484202 | + | 0.176235i | ||||
\(352\) | −5.81136 | − | 2.11516i | −0.309747 | − | 0.112739i | ||||
\(353\) | −0.801691 | + | 1.38857i | −0.0426697 | + | 0.0739061i | −0.886572 | − | 0.462592i | \(-0.846920\pi\) |
0.843902 | + | 0.536498i | \(0.180253\pi\) | |||||||
\(354\) | 7.72713 | + | 13.3838i | 0.410692 | + | 0.711340i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.78351 | + | 1.49655i | 0.0945261 | + | 0.0793168i | ||||
\(357\) | 7.07563 | − | 5.93716i | 0.374482 | − | 0.314228i | ||||
\(358\) | 0.555577 | − | 3.15084i | 0.0293632 | − | 0.166527i | ||||
\(359\) | 20.2961 | − | 7.38717i | 1.07119 | − | 0.389880i | 0.254566 | − | 0.967055i | \(-0.418067\pi\) |
0.816620 | + | 0.577175i | \(0.195845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.48872 | + | 18.1899i | −0.288880 | + | 0.957365i | ||||
\(362\) | −4.73520 | −0.248876 | ||||||||
\(363\) | 81.4089 | − | 29.6304i | 4.27286 | − | 1.55519i | ||||
\(364\) | 0.429171 | − | 2.43395i | 0.0224947 | − | 0.127574i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −17.6048 | − | 14.7722i | −0.920219 | − | 0.772155i | ||||
\(367\) | −3.42815 | − | 19.4420i | −0.178948 | − | 1.01486i | −0.933488 | − | 0.358610i | \(-0.883251\pi\) |
0.754540 | − | 0.656255i | \(-0.227860\pi\) | |||||||
\(368\) | −0.571736 | − | 0.990275i | −0.0298038 | − | 0.0516217i | ||||
\(369\) | −34.4535 | + | 59.6753i | −1.79358 | + | 3.10657i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.3399 | − | 8.13107i | −1.15983 | − | 0.422144i | ||||
\(372\) | 10.2986 | − | 17.8377i | 0.533958 | − | 0.924842i | ||||
\(373\) | −11.5800 | − | 20.0572i | −0.599592 | − | 1.03852i | −0.992881 | − | 0.119109i | \(-0.961996\pi\) |
0.393289 | − | 0.919415i | \(-0.371337\pi\) | |||||||
\(374\) | −0.932285 | − | 5.28725i | −0.0482073 | − | 0.273397i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.254093 | + | 0.213209i | −0.0131039 | + | 0.0109954i | ||||
\(377\) | −0.999129 | + | 5.66634i | −0.0514578 | + | 0.291831i | ||||
\(378\) | 41.0960 | − | 14.9577i | 2.11375 | − | 0.769343i | ||||
\(379\) | −3.52957 | −0.181302 | −0.0906508 | − | 0.995883i | \(-0.528895\pi\) | ||||
−0.0906508 | + | 0.995883i | \(0.528895\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.6904 | −1.82847 | ||||||||
\(382\) | 17.3192 | − | 6.30368i | 0.886128 | − | 0.322524i | ||||
\(383\) | −6.36973 | + | 36.1246i | −0.325478 | + | 1.84588i | 0.180815 | + | 0.983517i | \(0.442127\pi\) |
−0.506293 | + | 0.862362i | \(0.668985\pi\) | |||||||
\(384\) | −2.43579 | + | 2.04387i | −0.124301 | + | 0.104301i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.35285 | + | 13.3437i | 0.119757 | + | 0.679176i | ||||
\(387\) | 6.60667 | + | 11.4431i | 0.335836 | + | 0.581685i | ||||
\(388\) | −3.42203 | + | 5.92713i | −0.173727 | + | 0.300904i | ||||
\(389\) | 23.1021 | + | 8.40847i | 1.17132 | + | 0.426327i | 0.853129 | − | 0.521699i | \(-0.174702\pi\) |
0.318193 | + | 0.948026i | \(0.396924\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.496343 | − | 0.859691i | 0.0251011 | − | 0.0434764i | ||||
\(392\) | −2.09821 | − | 3.63420i | −0.105976 | − | 0.183555i | ||||
\(393\) | −8.38498 | − | 47.5536i | −0.422966 | − | 2.39876i | ||||
\(394\) | −6.27467 | − | 5.26507i | −0.316113 | − | 0.265251i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.63589 | − | 43.3053i | 0.383718 | − | 2.17617i | ||||
\(397\) | 19.1282 | − | 6.96208i | 0.960015 | − | 0.349417i | 0.185976 | − | 0.982554i | \(-0.440455\pi\) |
0.774039 | + | 0.633137i | \(0.218233\pi\) | |||||||
\(398\) | 5.94246 | 0.297868 | ||||||||
\(399\) | −38.7197 | − | 25.5265i | −1.93841 | − | 1.27792i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.9313 | + | 6.89045i | −0.945386 | + | 0.344092i | −0.768291 | − | 0.640101i | \(-0.778892\pi\) |
−0.177096 | + | 0.984194i | \(0.556670\pi\) | |||||||
\(402\) | 1.61500 | − | 9.15910i | 0.0805487 | − | 0.456814i | ||||
\(403\) | 3.66520 | − | 3.07547i | 0.182576 | − | 0.153200i | ||||
\(404\) | 7.80356 | + | 6.54797i | 0.388242 | + | 0.325774i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.0329 | + | 22.5736i | 0.646811 | + | 1.12031i | ||||
\(407\) | 5.19834 | − | 9.00379i | 0.257672 | − | 0.446301i | ||||
\(408\) | −2.59392 | − | 0.944111i | −0.128418 | − | 0.0467405i | ||||
\(409\) | −12.1073 | − | 4.40670i | −0.598668 | − | 0.217897i | 0.0248698 | − | 0.999691i | \(-0.492083\pi\) |
−0.623537 | + | 0.781794i | \(0.714305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5936 | + | 23.5448i | 0.670523 | + | 1.16138i | ||||
\(412\) | −0.359538 | − | 2.03904i | −0.0177132 | − | 0.100456i | ||||
\(413\) | 12.4582 | + | 10.4537i | 0.613030 | + | 0.514393i | ||||
\(414\) | 6.22840 | − | 5.22625i | 0.306109 | − | 0.256856i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.694074 | + | 0.252622i | −0.0340298 | + | 0.0123858i | ||||
\(417\) | −27.9946 | −1.37090 | ||||||||
\(418\) | −24.1026 | + | 12.0721i | −1.17890 | + | 0.590465i | ||||
\(419\) | 20.0166 | 0.977876 | 0.488938 | − | 0.872319i | \(-0.337384\pi\) | ||||
0.488938 | + | 0.872319i | \(0.337384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.16311 | − | 6.59634i | 0.0566867 | − | 0.321486i | −0.943257 | − | 0.332062i | \(-0.892256\pi\) |
0.999944 | + | 0.0105764i | \(0.00336662\pi\) | |||||||
\(422\) | −1.33569 | + | 1.12077i | −0.0650202 | + | 0.0545585i | ||||
\(423\) | −1.80672 | − | 1.51601i | −0.0878455 | − | 0.0737112i | ||||
\(424\) | 1.23375 | + | 6.99694i | 0.0599161 | + | 0.339801i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.9550 | + | 18.9746i | −0.530770 | + | 0.919321i | ||||
\(427\) | −22.7257 | − | 8.27149i | −1.09978 | − | 0.400285i | ||||
\(428\) | −13.7544 | − | 5.00620i | −0.664845 | − | 0.241984i | ||||
\(429\) | 7.26219 | − | 12.5785i | 0.350622 | − | 0.607295i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.86528 | − | 27.5924i | −0.234352 | − | 1.32908i | −0.843974 | − | 0.536385i | \(-0.819790\pi\) |
0.609621 | − | 0.792693i | \(-0.291321\pi\) | |||||||
\(432\) | −10.0122 | − | 8.40121i | −0.481711 | − | 0.404203i | ||||
\(433\) | 17.3262 | − | 14.5384i | 0.832646 | − | 0.698673i | −0.123251 | − | 0.992376i | \(-0.539332\pi\) |
0.955897 | + | 0.293702i | \(0.0948875\pi\) | |||||||
\(434\) | 3.76386 | − | 21.3459i | 0.180671 | − | 1.02464i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.69520 | −0.416425 | ||||||||
\(437\) | −4.84868 | − | 1.15471i | −0.231944 | − | 0.0552373i | ||||
\(438\) | 24.8546 | 1.18760 | ||||||||
\(439\) | 3.88563 | − | 1.41425i | 0.185451 | − | 0.0674986i | −0.247626 | − | 0.968856i | \(-0.579650\pi\) |
0.433076 | + | 0.901357i | \(0.357428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.8575 | − | 19.1798i | 1.08845 | − | 0.913322i | ||||
\(442\) | −0.491202 | − | 0.412168i | −0.0233641 | − | 0.0196048i | ||||
\(443\) | 5.02534 | + | 28.5001i | 0.238761 | + | 1.35408i | 0.834547 | + | 0.550937i | \(0.185730\pi\) |
−0.595786 | + | 0.803144i | \(0.703159\pi\) | |||||||
\(444\) | −2.67274 | − | 4.62933i | −0.126843 | − | 0.219698i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.8463 | + | 9.04332i | 1.17651 | + | 0.428214i | ||||
\(447\) | 2.27543 | + | 0.828187i | 0.107624 | + | 0.0391719i | ||||
\(448\) | −1.67305 | + | 2.89781i | −0.0790443 | + | 0.136909i | ||||
\(449\) | 2.78070 | + | 4.81632i | 0.131229 | + | 0.227296i | 0.924151 | − | 0.382028i | \(-0.124774\pi\) |
−0.792921 | + | 0.609324i | \(0.791441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 45.9106 | + | 38.5236i | 2.16185 | + | 1.81400i | ||||
\(452\) | −8.29690 | + | 6.96192i | −0.390253 | + | 0.327461i | ||||
\(453\) | 3.36139 | − | 19.0634i | 0.157932 | − | 0.895676i | ||||
\(454\) | −25.7920 | + | 9.38751i | −1.21048 | + | 0.440578i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.820886 | + | 13.8356i | −0.0384415 | + | 0.647913i | ||||
\(457\) | 3.44090 | 0.160959 | 0.0804793 | − | 0.996756i | \(-0.474355\pi\) | ||||
0.0804793 | + | 0.996756i | \(0.474355\pi\) | |||||||
\(458\) | 10.8743 | − | 3.95792i | 0.508122 | − | 0.184941i | ||||
\(459\) | 1.97029 | − | 11.1741i | 0.0919654 | − | 0.521562i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.88985 | − | 3.26397i | −0.181169 | − | 0.152018i | 0.547693 | − | 0.836679i | \(-0.315506\pi\) |
−0.728862 | + | 0.684661i | \(0.759950\pi\) | |||||||
\(462\) | −11.4258 | − | 64.7990i | −0.531577 | − | 3.01472i | ||||
\(463\) | −2.56405 | − | 4.44107i | −0.119162 | − | 0.206394i | 0.800274 | − | 0.599634i | \(-0.204687\pi\) |
−0.919436 | + | 0.393240i | \(0.871354\pi\) | |||||||
\(464\) | 3.89494 | − | 6.74624i | 0.180818 | − | 0.313186i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0824 | + | 4.39765i | 0.559708 | + | 0.203717i | ||||
\(467\) | 14.8110 | − | 25.6535i | 0.685373 | − | 1.18710i | −0.287947 | − | 0.957646i | \(-0.592973\pi\) |
0.973320 | − | 0.229454i | \(-0.0736940\pi\) | |||||||
\(468\) | −2.62595 | − | 4.54829i | −0.121385 | − | 0.210245i | ||||
\(469\) | −1.69952 | − | 9.63844i | −0.0784764 | − | 0.445062i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 59.3737 | − | 49.8205i | 2.73580 | − | 2.29561i | ||||
\(472\) | 0.843982 | − | 4.78646i | 0.0388474 | − | 0.220315i | ||||
\(473\) | 10.7993 | − | 3.93061i | 0.496550 | − | 0.180729i | ||||
\(474\) | 7.30992 | 0.335756 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.90486 | −0.133144 | ||||||||
\(477\) | −47.4722 | + | 17.2785i | −2.17360 | + | 0.791127i | ||||
\(478\) | −1.96468 | + | 11.1423i | −0.0898626 | + | 0.509636i | ||||
\(479\) | −28.8677 | + | 24.2229i | −1.31900 | + | 1.10677i | −0.332485 | + | 0.943109i | \(0.607887\pi\) |
−0.986516 | + | 0.163664i | \(0.947669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.215622 | − | 1.22285i | −0.00983151 | − | 0.0557573i | ||||
\(482\) | 11.8975 | + | 20.6071i | 0.541916 | + | 0.938626i | ||||
\(483\) | 6.08303 | − | 10.5361i | 0.276788 | − | 0.479410i | ||||
\(484\) | −25.6027 | − | 9.31863i | −1.16376 | − | 0.423574i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.5531 | − | 21.7426i | 0.569420 | − | 0.986264i | ||||
\(487\) | −8.87714 | − | 15.3757i | −0.402262 | − | 0.696738i | 0.591737 | − | 0.806131i | \(-0.298442\pi\) |
−0.993999 | + | 0.109393i | \(0.965109\pi\) | |||||||
\(488\) | 1.25506 | + | 7.11777i | 0.0568137 | + | 0.322206i | ||||
\(489\) | −10.4980 | − | 8.80890i | −0.474738 | − | 0.398352i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.87201 | + | 21.9592i | −0.174741 | + | 0.991006i | 0.763701 | + | 0.645570i | \(0.223380\pi\) |
−0.938442 | + | 0.345436i | \(0.887731\pi\) | |||||||
\(492\) | 28.9559 | − | 10.5391i | 1.30543 | − | 0.475139i | ||||
\(493\) | 6.76266 | 0.304575 | ||||||||
\(494\) | −1.27841 | + | 2.95487i | −0.0575183 | + | 0.132946i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.08708 | + | 2.21552i | −0.273318 | + | 0.0994796i | ||||
\(497\) | −4.00374 | + | 22.7063i | −0.179592 | + | 1.01852i | ||||
\(498\) | −27.8819 | + | 23.3957i | −1.24942 | + | 1.04838i | ||||
\(499\) | −14.4603 | − | 12.1337i | −0.647334 | − | 0.543177i | 0.258927 | − | 0.965897i | \(-0.416631\pi\) |
−0.906261 | + | 0.422719i | \(0.861076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.28559 | − | 14.3511i | −0.370173 | − | 0.641158i | ||||
\(502\) | −13.0369 | + | 22.5805i | −0.581864 | + | 1.00782i | ||||
\(503\) | 38.3963 | + | 13.9751i | 1.71201 | + | 0.623119i | 0.997100 | − | 0.0761023i | \(-0.0242476\pi\) |
0.714905 | + | 0.699221i | \(0.246470\pi\) | |||||||
\(504\) | −22.3575 | − | 8.13745i | −0.995880 | − | 0.362471i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.53580 | − | 6.12418i | −0.157185 | − | 0.272253i | ||||
\(507\) | 6.87669 | + | 38.9997i | 0.305405 | + | 1.73204i | ||||
\(508\) | 8.59845 | + | 7.21496i | 0.381495 | + | 0.320112i | ||||
\(509\) | −10.1977 | + | 8.55692i | −0.452007 | + | 0.379279i | −0.840180 | − | 0.542308i | \(-0.817551\pi\) |
0.388173 | + | 0.921586i | \(0.373106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.5780 | − | 8.94566i | 1.08727 | − | 0.395733i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −56.5926 | + | 6.55254i | −2.49862 | + | 0.289302i | ||||
\(514\) | 10.1528 | 0.447822 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.02606 | − | 5.81905i | 0.0451696 | − | 0.256170i | ||||
\(517\) | −1.57139 | + | 1.31856i | −0.0691098 | + | 0.0579900i | ||||
\(518\) | −4.30919 | − | 3.61584i | −0.189335 | − | 0.158871i | ||||
\(519\) | 3.88477 | + | 22.0316i | 0.170523 | + | 0.967082i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8343 | − | 23.9617i | 0.606091 | − | 1.04978i | −0.385787 | − | 0.922588i | \(-0.626070\pi\) |
0.991878 | − | 0.127193i | \(-0.0405968\pi\) | |||||||
\(522\) | 52.0492 | + | 18.9443i | 2.27813 | + | 0.829172i | ||||
\(523\) | −1.00974 | − | 0.367514i | −0.0441527 | − | 0.0160703i | 0.319849 | − | 0.947468i | \(-0.396368\pi\) |
−0.364002 | + | 0.931398i | \(0.618590\pi\) | |||||||
\(524\) | −7.59305 | + | 13.1516i | −0.331704 | + | 0.574528i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.97399 | − | 16.8663i | −0.129672 | − | 0.735407i | ||||
\(527\) | −4.30788 | − | 3.61474i | −0.187654 | − | 0.157460i | ||||
\(528\) | −15.0637 | + | 12.6399i | −0.655563 | + | 0.550083i | ||||
\(529\) | −3.76686 | + | 21.3629i | −0.163776 | + | 0.928822i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 34.5589 | 1.49973 | ||||||||
\(532\) | 4.16797 | + | 13.9771i | 0.180704 | + | 0.605985i | ||||
\(533\) | 7.15792 | 0.310044 | ||||||||
\(534\) | 6.95655 | − | 2.53198i | 0.301039 | − | 0.109569i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.24063 | + | 1.88011i | −0.0967804 | + | 0.0812084i | ||||
\(537\) | −7.79316 | − | 6.53924i | −0.336300 | − | 0.282189i | ||||
\(538\) | 3.96080 | + | 22.4628i | 0.170762 | + | 0.968442i | ||||
\(539\) | −12.9760 | − | 22.4751i | −0.558916 | − | 0.968071i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5180 | − | 5.28411i | −0.624177 | − | 0.227182i | 0.0105181 | − | 0.999945i | \(-0.496652\pi\) |
−0.634695 | + | 0.772763i | \(0.718874\pi\) | |||||||
\(542\) | −16.7174 | − | 6.08464i | −0.718074 | − | 0.261358i | ||||
\(543\) | −7.52824 | + | 13.0393i | −0.323068 | + | 0.559569i | ||||
\(544\) | 0.434067 | + | 0.751825i | 0.0186104 | + | 0.0322342i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.02003 | − | 5.05141i | −0.257634 | − | 0.216180i | ||||
\(547\) | 25.7407 | − | 21.5990i | 1.10059 | − | 0.923508i | 0.103129 | − | 0.994668i | \(-0.467115\pi\) |
0.997465 | + | 0.0711601i | \(0.0226701\pi\) | |||||||
\(548\) | 1.48474 | − | 8.42037i | 0.0634248 | − | 0.359700i | ||||
\(549\) | −48.2920 | + | 17.5769i | −2.06105 | + | 0.750162i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.70322 | − | 32.5394i | −0.413371 | − | 1.38622i | ||||
\(552\) | −3.63589 | −0.154754 | ||||||||
\(553\) | 7.22858 | − | 2.63099i | 0.307391 | − | 0.111881i | ||||
\(554\) | 3.62454 | − | 20.5558i | 0.153992 | − | 0.873333i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.74440 | + | 5.65923i | 0.286026 | + | 0.240005i | ||||
\(557\) | 2.47429 | + | 14.0324i | 0.104839 | + | 0.594571i | 0.991285 | + | 0.131739i | \(0.0420559\pi\) |
−0.886446 | + | 0.462833i | \(0.846833\pi\) | |||||||
\(558\) | −23.0298 | − | 39.8888i | −0.974929 | − | 1.68863i | ||||
\(559\) | 0.686287 | − | 1.18868i | 0.0290269 | − | 0.0502760i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0417 | − | 5.83869i | −0.677280 | − | 0.246510i | ||||
\(562\) | 13.5994 | − | 23.5548i | 0.573655 | − | 0.993599i | ||||
\(563\) | 7.38607 | + | 12.7930i | 0.311286 | + | 0.539163i | 0.978641 | − | 0.205577i | \(-0.0659070\pi\) |
−0.667355 | + | 0.744740i | \(0.732574\pi\) | |||||||
\(564\) | 0.183145 | + | 1.03867i | 0.00771178 | + | 0.0437357i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.0862 | − | 12.6588i | 0.634122 | − | 0.532091i | ||||
\(567\) | 11.7529 | − | 66.6539i | 0.493574 | − | 2.79920i | ||||
\(568\) | 6.47503 | − | 2.35672i | 0.271686 | − | 0.0988857i | ||||
\(569\) | 19.4550 | 0.815598 | 0.407799 | − | 0.913072i | \(-0.366296\pi\) | ||||
0.407799 | + | 0.913072i | \(0.366296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.3956 | −1.64866 | −0.824328 | − | 0.566112i | \(-0.808447\pi\) | ||||
−0.824328 | + | 0.566112i | \(0.808447\pi\) | |||||||
\(572\) | −4.29238 | + | 1.56230i | −0.179473 | + | 0.0653230i | ||||
\(573\) | 10.1765 | − | 57.7137i | 0.425129 | − | 2.41102i | ||||
\(574\) | 24.8405 | − | 20.8436i | 1.03682 | − | 0.869997i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.23472 | + | 7.00242i | 0.0514465 | + | 0.291768i | ||||
\(577\) | −7.94763 | − | 13.7657i | −0.330864 | − | 0.573073i | 0.651818 | − | 0.758376i | \(-0.274007\pi\) |
−0.982682 | + | 0.185303i | \(0.940673\pi\) | |||||||
\(578\) | 8.12317 | − | 14.0697i | 0.337879 | − | 0.585224i | ||||
\(579\) | 40.4852 | + | 14.7354i | 1.68251 | + | 0.612382i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.1510 | + | 33.1706i | −0.794519 | + | 1.37615i | ||||
\(582\) | 10.8810 | + | 18.8464i | 0.451032 | + | 0.781210i | ||||
\(583\) | 7.62990 | + | 43.2713i | 0.315998 | + | 1.79212i | ||||
\(584\) | −5.98791 | − | 5.02445i | −0.247781 | − | 0.207913i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.56601 | − | 14.5526i | 0.106001 | − | 0.601161i | ||||
\(587\) | −12.0891 | + | 4.40009i | −0.498973 | + | 0.181611i | −0.579232 | − | 0.815163i | \(-0.696647\pi\) |
0.0802592 | + | 0.996774i | \(0.474425\pi\) | |||||||
\(588\) | −13.3433 | −0.550269 | ||||||||
\(589\) | −11.2117 | + | 25.9144i | −0.461971 | + | 1.06778i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.4742 | + | 8.90787i | −1.00673 | + | 0.366421i | ||||
\(592\) | −0.291926 | + | 1.65559i | −0.0119981 | + | 0.0680445i | ||||
\(593\) | −1.66829 | + | 1.39986i | −0.0685086 | + | 0.0574855i | −0.676399 | − | 0.736535i | \(-0.736460\pi\) |
0.607890 | + | 0.794021i | \(0.292016\pi\) | |||||||
\(594\) | −61.9185 | − | 51.9558i | −2.54055 | − | 2.13177i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.380769 | − | 0.659512i | −0.0155969 | − | 0.0270146i | ||||
\(597\) | 9.44759 | − | 16.3637i | 0.386664 | − | 0.669722i | ||||
\(598\) | −0.793654 | − | 0.288867i | −0.0324549 | − | 0.0118126i | ||||
\(599\) | −3.32108 | − | 1.20877i | −0.135696 | − | 0.0493891i | 0.273280 | − | 0.961935i | \(-0.411892\pi\) |
−0.408975 | + | 0.912545i | \(0.634114\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2019 | − | 19.4022i | −0.456935 | − | 0.791434i | 0.541863 | − | 0.840467i | \(-0.317719\pi\) |
−0.998797 | + | 0.0490333i | \(0.984386\pi\) | |||||||
\(602\) | −1.07976 | − | 6.12360i | −0.0440076 | − | 0.249579i | ||||
\(603\) | −15.9319 | − | 13.3684i | −0.648796 | − | 0.544405i | ||||
\(604\) | −4.66356 | + | 3.91319i | −0.189757 | + | 0.159225i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 30.4376 | − | 11.0784i | 1.23644 | − | 0.450028i | ||||
\(607\) | 12.5717 | 0.510269 | 0.255134 | − | 0.966906i | \(-0.417880\pi\) | ||||
0.255134 | + | 0.966906i | \(0.417880\pi\) | |||||||
\(608\) | 2.99469 | − | 3.16730i | 0.121451 | − | 0.128451i | ||||
\(609\) | 82.8812 | 3.35851 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0425431 | + | 0.241274i | −0.00172111 | + | 0.00976090i | ||||
\(612\) | −4.72865 | + | 3.96781i | −0.191144 | + | 0.160389i | ||||
\(613\) | 35.9199 | + | 30.1404i | 1.45079 | + | 1.21736i | 0.932000 | + | 0.362458i | \(0.118062\pi\) |
0.518791 | + | 0.854901i | \(0.326382\pi\) | |||||||
\(614\) | 0.736086 | + | 4.17455i | 0.0297060 | + | 0.168471i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.3467 | + | 17.9210i | −0.416880 | + | 0.722058i | ||||
\(617\) | 0.496525 | + | 0.180720i | 0.0199893 | + | 0.00727553i | 0.351995 | − | 0.936002i | \(-0.385503\pi\) |
−0.332006 | + | 0.943277i | \(0.607725\pi\) | |||||||
\(618\) | −6.18650 | − | 2.25170i | −0.248858 | − | 0.0905768i | ||||
\(619\) | −10.9317 | + | 18.9343i | −0.439383 | + | 0.761034i | −0.997642 | − | 0.0686330i | \(-0.978136\pi\) |
0.558259 | + | 0.829667i | \(0.311470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.59520 | − | 14.7181i | −0.104142 | − | 0.590616i | ||||
\(622\) | −5.35224 | − | 4.49106i | −0.214605 | − | 0.180075i | ||||
\(623\) | 5.96783 | − | 5.00760i | 0.239096 | − | 0.200625i | ||||
\(624\) | −0.407827 | + | 2.31290i | −0.0163261 | + | 0.0925901i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.61968 | 0.304544 | ||||||||
\(627\) | −5.07663 | + | 85.5640i | −0.202741 | + | 3.41710i | ||||
\(628\) | −24.3756 | −0.972692 | ||||||||
\(629\) | −1.37143 | + | 0.499161i | −0.0546826 | + | 0.0199028i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.0776 | − | 19.3644i | 0.918705 | − | 0.770885i | −0.0550497 | − | 0.998484i | \(-0.517532\pi\) |
0.973755 | + | 0.227598i | \(0.0730873\pi\) | |||||||
\(632\) | −1.76109 | − | 1.47773i | −0.0700524 | − | 0.0587810i | ||||
\(633\) | 0.962734 | + | 5.45993i | 0.0382652 | + | 0.217013i | ||||
\(634\) | 6.86922 | + | 11.8978i | 0.272812 | + | 0.472524i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 21.2289 | + | 7.72669i | 0.841781 | + | 0.306383i | ||||
\(637\) | −2.91263 | − | 1.06011i | −0.115402 | − | 0.0420031i | ||||
\(638\) | 24.0876 | − | 41.7209i | 0.953637 | − | 1.65175i | ||||
\(639\) | 24.4976 | + | 42.4310i | 0.969109 | + | 1.67855i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.6653 | + | 20.6967i | 0.974223 | + | 0.817470i | 0.983208 | − | 0.182490i | \(-0.0584156\pi\) |
−0.00898505 | + | 0.999960i | \(0.502860\pi\) | |||||||
\(642\) | −35.6530 | + | 29.9164i | −1.40711 | + | 1.18071i | ||||
\(643\) | 4.44391 | − | 25.2027i | 0.175251 | − | 0.993896i | −0.762604 | − | 0.646866i | \(-0.776079\pi\) |
0.937854 | − | 0.347030i | \(-0.112810\pi\) | |||||||
\(644\) | −3.59543 | + | 1.30863i | −0.141680 | + | 0.0515672i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.68115 | + | 0.876666i | 0.144833 | + | 0.0344920i | ||||
\(647\) | 18.8860 | 0.742483 | 0.371242 | − | 0.928536i | \(-0.378932\pi\) | ||||
0.371242 | + | 0.928536i | \(0.378932\pi\) | |||||||
\(648\) | −19.0073 | + | 6.91809i | −0.746677 | + | 0.271768i | ||||
\(649\) | 5.21946 | − | 29.6010i | 0.204882 | − | 1.16194i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −52.7961 | − | 44.3012i | −2.06924 | − | 1.73630i | ||||
\(652\) | 0.748409 | + | 4.24444i | 0.0293100 | + | 0.166225i | ||||
\(653\) | 12.4152 | + | 21.5038i | 0.485846 | + | 0.841510i | 0.999868 | − | 0.0162674i | \(-0.00517829\pi\) |
−0.514022 | + | 0.857777i | \(0.671845\pi\) | |||||||
\(654\) | −13.8240 | + | 23.9439i | −0.540562 | + | 0.936282i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.10652 | − | 3.31450i | −0.355550 | − | 0.129410i | ||||
\(657\) | 27.7900 | − | 48.1336i | 1.08419 | − | 1.87787i | ||||
\(658\) | 0.554943 | + | 0.961190i | 0.0216339 | + | 0.0374711i | ||||
\(659\) | 5.44946 | + | 30.9054i | 0.212281 | + | 1.20391i | 0.885563 | + | 0.464519i | \(0.153773\pi\) |
−0.673282 | + | 0.739386i | \(0.735116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2738 | + | 11.9771i | −0.555186 | + | 0.465857i | −0.876693 | − | 0.481051i | \(-0.840255\pi\) |
0.321506 | + | 0.946907i | \(0.395811\pi\) | |||||||
\(662\) | −1.15376 | + | 6.54331i | −0.0448422 | + | 0.254313i | ||||
\(663\) | −1.91592 | + | 0.697338i | −0.0744082 | + | 0.0270824i | ||||
\(664\) | 11.4468 | 0.444220 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11.9536 | −0.463193 | ||||||||
\(667\) | 8.37032 | − | 3.04655i | 0.324100 | − | 0.117963i | ||||
\(668\) | −0.904979 | + | 5.13239i | −0.0350147 | + | 0.198578i | ||||
\(669\) | 64.4044 | − | 54.0417i | 2.49002 | − | 2.08937i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.76167 | + | 44.0186i | 0.299636 | + | 1.69932i | ||||
\(672\) | 5.31979 | + | 9.21415i | 0.205215 | + | 0.355444i | ||||
\(673\) | −7.28810 | + | 12.6234i | −0.280935 | + | 0.486594i | −0.971615 | − | 0.236566i | \(-0.923978\pi\) |
0.690680 | + | 0.723161i | \(0.257311\pi\) | |||||||
\(674\) | −17.2976 | − | 6.29582i | −0.666280 | − | 0.242506i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.22722 | − | 10.7859i | 0.239509 | − | 0.414841i | ||||
\(677\) | 1.21821 | + | 2.11001i | 0.0468197 | + | 0.0810941i | 0.888486 | − | 0.458905i | \(-0.151758\pi\) |
−0.841666 | + | 0.539999i | \(0.818425\pi\) | |||||||
\(678\) | 5.98022 | + | 33.9155i | 0.229669 | + | 1.30252i | ||||
\(679\) | 17.5431 | + | 14.7204i | 0.673244 | + | 0.564918i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.1549 | + | 85.9479i | −0.580738 | + | 3.29353i | ||||
\(682\) | −37.6445 | + | 13.7015i | −1.44148 | + | 0.524656i | ||||
\(683\) | −15.0962 | −0.577639 | −0.288820 | − | 0.957384i | \(-0.593263\pi\) | ||||
−0.288820 | + | 0.957384i | \(0.593263\pi\) | |||||||
\(684\) | 25.8764 | + | 17.0594i | 0.989409 | + | 0.652282i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.81533 | − | 3.20852i | 0.336571 | − | 0.122502i | ||||
\(687\) | 6.38955 | − | 36.2370i | 0.243777 | − | 1.38253i | ||||
\(688\) | −1.42354 | + | 1.19449i | −0.0542720 | + | 0.0455396i | ||||
\(689\) | 4.02004 | + | 3.37322i | 0.153151 | + | 0.128509i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.12019 | + | 10.6005i | 0.232823 | + | 0.403261i | 0.958638 | − | 0.284629i | \(-0.0918704\pi\) |
−0.725815 | + | 0.687890i | \(0.758537\pi\) | |||||||
\(692\) | 3.51787 | − | 6.09314i | 0.133729 | − | 0.231626i | ||||
\(693\) | −138.266 | − | 50.3246i | −5.25228 | − | 1.91167i | ||||
\(694\) | 6.97015 | + | 2.53693i | 0.264583 | + | 0.0963005i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.3847 | − | 21.4510i | −0.469442 | − | 0.813097i | ||||
\(697\) | −1.46091 | − | 8.28523i | −0.0553359 | − | 0.313825i | ||||
\(698\) | 14.6710 | + | 12.3104i | 0.555305 | + | 0.465956i | ||||
\(699\) | 31.3190 | − | 26.2798i | 1.18459 | − | 0.993992i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.9967 | + | 15.2856i | −1.58620 | + | 0.577328i | −0.976539 | − | 0.215339i | \(-0.930914\pi\) |
−0.609656 | + | 0.792666i | \(0.708692\pi\) | |||||||
\(702\) | −9.65372 | −0.364356 | ||||||||
\(703\) | 4.36954 | + | 5.88261i | 0.164800 | + | 0.221867i | ||||
\(704\) | 6.18432 | 0.233080 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.278424 | − | 1.57902i | 0.0104786 | − | 0.0594273i | ||||
\(707\) | 26.1115 | − | 21.9102i | 0.982026 | − | 0.824017i | ||||
\(708\) | −11.8386 | − | 9.93381i | −0.444924 | − | 0.373335i | ||||
\(709\) | −2.78707 | − | 15.8063i | −0.104671 | − | 0.593617i | −0.991351 | − | 0.131235i | \(-0.958106\pi\) |
0.886681 | − | 0.462382i | \(-0.153005\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.17325 | − | 14.1565i | 0.306521 | − | 0.530910i | ||||
\(712\) | −2.18780 | − | 0.796295i | −0.0819914 | − | 0.0298424i | ||||
\(713\) | −6.96040 | − | 2.53338i | −0.260669 | − | 0.0948758i | ||||
\(714\) | −4.61829 | + | 7.99911i | −0.172835 | + | 0.299359i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.555577 | + | 3.15084i | 0.0207629 | + | 0.117752i | ||||
\(717\) | 27.5589 | + | 23.1247i | 1.02921 | + | 0.863606i | ||||
\(718\) | −16.5455 | + | 13.8833i | −0.617474 | + | 0.518122i | ||||
\(719\) | −0.265213 | + | 1.50410i | −0.00989079 | + | 0.0560934i | −0.989354 | − | 0.145531i | \(-0.953511\pi\) |
0.979463 | + | 0.201624i | \(0.0646221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.92809 | −0.258016 | ||||||||
\(722\) | −1.06362 | − | 18.9702i | −0.0395838 | − | 0.705998i | ||||
\(723\) | 75.6608 | 2.81385 | ||||||||
\(724\) | 4.44963 | − | 1.61953i | 0.165369 | − | 0.0601894i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −66.3651 | + | 55.6869i | −2.46304 | + | 2.06674i | ||||
\(727\) | 29.0850 | + | 24.4052i | 1.07870 | + | 0.905139i | 0.995812 | − | 0.0914199i | \(-0.0291405\pi\) |
0.0828900 | + | 0.996559i | \(0.473585\pi\) | |||||||
\(728\) | 0.429171 | + | 2.43395i | 0.0159061 | + | 0.0902081i | ||||
\(729\) | −9.57428 | − | 16.5831i | −0.354603 | − | 0.614190i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.51596 | − | 0.551764i | −0.0560698 | − | 0.0204077i | ||||
\(732\) | 21.5955 | + | 7.86012i | 0.798193 | + | 0.290519i | ||||
\(733\) | −16.0110 | + | 27.7319i | −0.591381 | + | 1.02430i | 0.402666 | + | 0.915347i | \(0.368084\pi\) |
−0.994047 | + | 0.108955i | \(0.965250\pi\) | |||||||
\(734\) | 9.87097 | + | 17.0970i | 0.364344 | + | 0.631062i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.875950 | + | 0.735009i | 0.0322879 | + | 0.0270928i | ||||
\(737\) | −13.8568 | + | 11.6272i | −0.510421 | + | 0.428294i | ||||
\(738\) | 11.9656 | − | 67.8602i | 0.440459 | − | 2.49797i | ||||
\(739\) | 36.3892 | − | 13.2446i | 1.33860 | − | 0.487210i | 0.429228 | − | 0.903196i | \(-0.358786\pi\) |
0.909371 | + | 0.415986i | \(0.136564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.10434 | + | 8.21814i | 0.224249 | + | 0.301901i | ||||
\(742\) | 23.7737 | 0.872758 | ||||||||
\(743\) | −29.3436 | + | 10.6802i | −1.07651 | + | 0.391819i | −0.818609 | − | 0.574351i | \(-0.805254\pi\) |
−0.257905 | + | 0.966170i | \(0.583032\pi\) | |||||||
\(744\) | −3.57667 | + | 20.2843i | −0.131127 | + | 0.743658i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.7417 | + | 14.8870i | 0.649568 | + | 0.545052i | ||||
\(747\) | 14.1335 | + | 80.1551i | 0.517118 | + | 2.93272i | ||||
\(748\) | 2.68441 | + | 4.64953i | 0.0981517 | + | 0.170004i | ||||
\(749\) | −24.4887 | + | 42.4157i | −0.894798 | + | 1.54984i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.3847 | + | 11.7871i | 1.18173 | + | 0.430116i | 0.856814 | − | 0.515625i | \(-0.172440\pi\) |
0.324920 | + | 0.945741i | \(0.394663\pi\) | |||||||
\(752\) | 0.165847 | − | 0.287256i | 0.00604784 | − | 0.0104752i | ||||
\(753\) | 41.4532 | + | 71.7991i | 1.51064 | + | 2.61650i | ||||
\(754\) | −0.999129 | − | 5.66634i | −0.0363861 | − | 0.206356i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −33.5018 | + | 28.1113i | −1.21845 | + | 1.02240i | ||||
\(757\) | 0.469366 | − | 2.66191i | 0.0170594 | − | 0.0967487i | −0.975089 | − | 0.221813i | \(-0.928803\pi\) |
0.992149 | + | 0.125064i | \(0.0399137\pi\) | |||||||
\(758\) | 3.31671 | − | 1.20718i | 0.120468 | − | 0.0438468i | ||||
\(759\) | −22.4855 | −0.816173 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.19327 | 0.333256 | 0.166628 | − | 0.986020i | \(-0.446712\pi\) | ||||
0.166628 | + | 0.986020i | \(0.446712\pi\) | |||||||
\(762\) | 33.5380 | − | 12.2068i | 1.21495 | − | 0.442207i | ||||
\(763\) | −5.05230 | + | 28.6530i | −0.182906 | + | 1.03731i | ||||
\(764\) | −14.1187 | + | 11.8470i | −0.510798 | + | 0.428611i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.36973 | − | 36.1246i | −0.230148 | − | 1.30523i | ||||
\(767\) | −1.79495 | − | 3.10895i | −0.0648120 | − | 0.112258i | ||||
\(768\) | 1.58985 | − | 2.75370i | 0.0573686 | − | 0.0993654i | ||||
\(769\) | −0.0570740 | − | 0.0207732i | −0.00205814 | − | 0.000749102i | 0.340991 | − | 0.940067i | \(-0.389237\pi\) |
−0.343049 | + | 0.939318i | \(0.611460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.1414 | − | 27.9578i | 0.581320 | − | 1.00688i | ||||
\(772\) | −6.77477 | − | 11.7343i | −0.243829 | − | 0.422325i | ||||
\(773\) | −1.71922 | − | 9.75016i | −0.0618359 | − | 0.350689i | −0.999990 | − | 0.00447097i | \(-0.998577\pi\) |
0.938154 | − | 0.346218i | \(-0.112534\pi\) | |||||||
\(774\) | −10.1220 | − | 8.49337i | −0.363828 | − | 0.305288i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.18846 | − | 6.74008i | 0.0426632 | − | 0.241955i | ||||
\(777\) | −16.8079 | + | 6.11757i | −0.602979 | + | 0.219466i | ||||
\(778\) | −24.5847 | −0.881405 | ||||||||
\(779\) | −37.7693 | + | 18.9172i | −1.35322 | + | 0.677779i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.0437 | − | 14.5747i | 1.43288 | − | 0.521524i | ||||
\(782\) | −0.172378 | + | 0.977604i | −0.00616423 | + | 0.0349591i | ||||
\(783\) | 77.9937 | − | 65.4445i | 2.78727 | − | 2.33879i | ||||
\(784\) | 3.21464 | + | 2.69741i | 0.114809 | + | 0.0963359i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.1436 | + | 41.8179i | 0.861173 | + | 1.49160i | ||||
\(787\) | 5.59115 | − | 9.68415i | 0.199303 | − | 0.345203i | −0.749000 | − | 0.662570i | \(-0.769466\pi\) |
0.948303 | + | 0.317368i | \(0.102799\pi\) | |||||||
\(788\) | 7.69702 | + | 2.80149i | 0.274195 | + | 0.0997988i | ||||
\(789\) | −51.1729 | − | 18.6254i | −1.82180 | − | 0.663082i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.1205 | + | 31.3857i | 0.644293 | + | 1.11595i | ||||
\(792\) | 7.63589 | + | 43.3053i | 0.271329 | + | 1.53879i | ||||
\(793\) | 4.08947 | + | 3.43147i | 0.145221 | + | 0.121855i | ||||
\(794\) | −15.5934 | + | 13.0844i | −0.553390 | + | 0.464349i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.58408 | + | 2.03244i | −0.197923 | + | 0.0720379i | ||||
\(797\) | −16.8348 | −0.596320 | −0.298160 | − | 0.954516i | \(-0.596373\pi\) | ||||
−0.298160 | + | 0.954516i | \(0.596373\pi\) | |||||||
\(798\) | 45.1152 | + | 10.7442i | 1.59706 | + | 0.380339i | ||||
\(799\) | 0.287955 | 0.0101871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.87468 | − | 16.3031i | 0.101572 | − | 0.576043i | ||||
\(802\) | 15.4330 | − | 12.9498i | 0.544957 | − | 0.457273i | ||||
\(803\) | −37.0312 | − | 31.0728i | −1.30680 | − | 1.09654i | ||||
\(804\) | 1.61500 | + | 9.15910i | 0.0569565 | + | 0.323016i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.39229 | + | 4.14356i | −0.0842647 | + | 0.145951i | ||||
\(807\) | 68.1529 | + | 24.8056i | 2.39910 | + | 0.873199i | ||||
\(808\) | −9.57249 | − | 3.48410i | −0.336759 | − | 0.122570i | ||||
\(809\) | −13.1217 | + | 22.7275i | −0.461335 | + | 0.799056i | −0.999028 | − | 0.0440848i | \(-0.985963\pi\) |
0.537692 | + | 0.843141i | \(0.319296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.65768 | + | 43.4288i | 0.268897 | + | 1.52499i | 0.757703 | + | 0.652600i | \(0.226322\pi\) |
−0.488805 | + | 0.872393i | \(0.662567\pi\) | |||||||
\(812\) | −19.9675 | − | 16.7548i | −0.700723 | − | 0.587977i | ||||
\(813\) | −43.3334 | + | 36.3610i | −1.51977 | + | 1.27524i | ||||
\(814\) | −1.80536 | + | 10.2387i | −0.0632780 | + | 0.358867i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.76040 | 0.0966332 | ||||||||
\(817\) | −0.479748 | + | 8.08592i | −0.0167843 | + | 0.282891i | ||||
\(818\) | 12.8843 | 0.450490 | ||||||||
\(819\) | −16.5136 | + | 6.01047i | −0.577033 | + | 0.210023i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.5474 | + | 29.8278i | −1.24061 | + | 1.04100i | −0.243138 | + | 0.969992i | \(0.578177\pi\) |
−0.997476 | + | 0.0710073i | \(0.977379\pi\) | |||||||
\(822\) | −20.8266 | − | 17.4756i | −0.726412 | − | 0.609532i | ||||
\(823\) | −5.43149 | − | 30.8035i | −0.189330 | − | 1.07374i | −0.920265 | − | 0.391296i | \(-0.872027\pi\) |
0.730935 | − | 0.682447i | \(-0.239084\pi\) | |||||||
\(824\) | 1.03525 | + | 1.79310i | 0.0360646 | + | 0.0624656i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.2823 | − | 5.56230i | −0.531739 | − | 0.193537i | ||||
\(827\) | −18.5253 | − | 6.74267i | −0.644189 | − | 0.234466i | −0.000793747 | − | 1.00000i | \(-0.500253\pi\) |
−0.643395 | + | 0.765534i | \(0.722475\pi\) | |||||||
\(828\) | −4.06530 | + | 7.04130i | −0.141279 | + | 0.244702i | ||||
\(829\) | 27.3133 | + | 47.3081i | 0.948632 | + | 1.64308i | 0.748311 | + | 0.663348i | \(0.230865\pi\) |
0.200320 | + | 0.979730i | \(0.435802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.8420 | − | 42.6615i | −1.76369 | − | 1.47991i | ||||
\(832\) | 0.565815 | − | 0.474775i | 0.0196161 | − | 0.0164599i | ||||
\(833\) | −0.632609 | + | 3.58770i | −0.0219186 | + | 0.124307i | ||||
\(834\) | 26.3064 | − | 9.57473i | 0.910915 | − | 0.331546i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.5202 | − | 19.5876i | 0.640533 | − | 0.677452i | ||||
\(837\) | −84.6638 | −2.92641 | ||||||||
\(838\) | −18.8095 | + | 6.84609i | −0.649762 | + | 0.236494i | ||||
\(839\) | 6.63032 | − | 37.6024i | 0.228904 | − | 1.29818i | −0.626175 | − | 0.779682i | \(-0.715381\pi\) |
0.855079 | − | 0.518497i | \(-0.173508\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.2700 | + | 20.3650i | 0.836898 | + | 0.702241i | ||||
\(842\) | 1.16311 | + | 6.59634i | 0.0400835 | + | 0.227325i | ||||
\(843\) | −43.2418 | − | 74.8970i | −1.48933 | − | 2.57959i | ||||
\(844\) | 0.871808 | − | 1.51002i | 0.0300089 | − | 0.0519769i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.21627 | + | 0.806655i | 0.0761968 | + | 0.0277334i | ||||
\(847\) | −45.5838 | + | 78.9534i | −1.56628 | + | 2.71287i | ||||
\(848\) | −3.55244 | − | 6.15300i | −0.121991 | − | 0.211295i | ||||
\(849\) | −10.8738 | − | 61.6685i | −0.373189 | − | 2.11646i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.47259 | + | 1.23565i | −0.0504797 | + | 0.0423575i | ||||
\(852\) | 3.80462 | − | 21.5771i | 0.130344 | − | 0.739219i | ||||
\(853\) | −31.2888 | + | 11.3882i | −1.07131 | + | 0.389925i | −0.816666 | − | 0.577111i | \(-0.804180\pi\) |
−0.254643 | + | 0.967035i | \(0.581958\pi\) | |||||||
\(854\) | 24.1842 | 0.827567 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.6371 | 0.500287 | ||||||||
\(857\) | −37.9460 | + | 13.8112i | −1.29621 | + | 0.471782i | −0.895761 | − | 0.444537i | \(-0.853368\pi\) |
−0.400450 | + | 0.916319i | \(0.631146\pi\) | |||||||
\(858\) | −2.52213 | + | 14.3037i | −0.0861042 | + | 0.488321i | ||||
\(859\) | −5.94441 | + | 4.98795i | −0.202821 | + | 0.170187i | −0.738541 | − | 0.674209i | \(-0.764485\pi\) |
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.9045 | − | 101.541i | −0.610183 | − | 3.46052i | ||||
\(862\) | 14.0090 | + | 24.2643i | 0.477149 | + | 0.826446i | ||||
\(863\) | −23.2056 | + | 40.1932i | −0.789926 | + | 1.36819i | 0.136085 | + | 0.990697i | \(0.456548\pi\) |
−0.926011 | + | 0.377495i | \(0.876785\pi\) | |||||||
\(864\) | 12.2818 | + | 4.47019i | 0.417834 | + | 0.152079i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.3089 | + | 19.5876i | −0.384292 | + | 0.665614i | ||||
\(867\) | −25.8292 | − | 44.7375i | −0.877205 | − | 1.51936i | ||||
\(868\) | 3.76386 | + | 21.3459i | 0.127754 | + | 0.724526i | ||||
\(869\) | −10.8912 | − | 9.13876i | −0.369457 | − | 0.310011i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.375151 | + | 2.12759i | −0.0127115 | + | 0.0720906i | ||||
\(872\) | 8.17082 | − | 2.97393i | 0.276699 | − | 0.100710i | ||||
\(873\) | 48.6643 | 1.64704 | ||||||||
\(874\) | 4.95120 | − | 0.573271i | 0.167477 | − | 0.0193912i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −23.3557 | + | 8.50076i | −0.789115 | + | 0.287214i | ||||
\(877\) | 4.69718 | − | 26.6390i | 0.158612 | − | 0.899536i | −0.796796 | − | 0.604248i | \(-0.793473\pi\) |
0.955408 | − | 0.295288i | \(-0.0954155\pi\) | |||||||
\(878\) | −3.16759 | + | 2.65793i | −0.106901 | + | 0.0897006i | ||||
\(879\) | −35.9938 | − | 30.2024i | −1.21404 | − | 1.01870i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.1018 | − | 17.4968i | −0.340338 | − | 0.589482i | 0.644158 | − | 0.764893i | \(-0.277208\pi\) |
−0.984495 | + | 0.175410i | \(0.943875\pi\) | |||||||
\(882\) | −14.9192 | + | 25.8408i | −0.502356 | + | 0.870106i | ||||
\(883\) | −14.1304 | − | 5.14304i | −0.475525 | − | 0.173077i | 0.0931285 | − | 0.995654i | \(-0.470313\pi\) |
−0.568654 | + | 0.822577i | \(0.692535\pi\) | |||||||
\(884\) | 0.602549 | + | 0.219310i | 0.0202659 | + | 0.00737619i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.4699 | − | 25.0626i | −0.486125 | − | 0.841994i | ||||
\(887\) | −5.06838 | − | 28.7442i | −0.170180 | − | 0.965137i | −0.943562 | − | 0.331197i | \(-0.892548\pi\) |
0.773382 | − | 0.633940i | \(-0.218563\pi\) | |||||||
\(888\) | 4.09488 | + | 3.43601i | 0.137415 | + | 0.115305i | ||||
\(889\) | 28.7713 | − | 24.1420i | 0.964959 | − | 0.809697i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −117.547 | + | 42.7837i | −3.93798 | + | 1.43331i | ||||
\(892\) | −26.4409 | −0.885307 | ||||||||
\(893\) | −0.413165 | − | 1.38553i | −0.0138260 | − | 0.0463651i | ||||
\(894\) | −2.42146 | −0.0809857 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.581045 | − | 3.29527i | 0.0194114 | − | 0.110087i | ||||
\(897\) | −2.05724 | + | 1.72623i | −0.0686892 | + | 0.0576371i | ||||
\(898\) | −4.26028 | − | 3.57480i | −0.142167 | − | 0.119293i | ||||
\(899\) | −8.76243 | − | 49.6942i | −0.292243 | − | 1.65739i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.08399 | − | 5.34162i | 0.102743 | − | 0.177955i | ||||
\(902\) | −56.3177 | − | 20.4980i | −1.87517 | − | 0.682507i | ||||
\(903\) | −18.5792 | − | 6.76226i | −0.618276 | − | 0.225034i | ||||
\(904\) | 5.41542 | − | 9.37977i | 0.180114 | − | 0.311967i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.36139 | + | 19.0634i | 0.111675 | + | 0.633338i | ||||
\(907\) | −40.2537 | − | 33.7769i | −1.33660 | − | 1.12154i | −0.982485 | − | 0.186343i | \(-0.940336\pi\) |
−0.354119 | − | 0.935200i | \(-0.615219\pi\) | |||||||
\(908\) | 21.0258 | − | 17.6427i | 0.697766 | − | 0.585495i | ||||
\(909\) | 12.5778 | − | 71.3325i | 0.417181 | − | 2.36595i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5338 | −0.945366 | −0.472683 | − | 0.881233i | \(-0.656714\pi\) | ||||
−0.472683 | + | 0.881233i | \(0.656714\pi\) | |||||||
\(912\) | −3.96068 | − | 13.2820i | −0.131151 | − | 0.439811i | ||||
\(913\) | 70.7905 | 2.34282 | ||||||||
\(914\) | −3.23339 | + | 1.17686i | −0.106951 | + | 0.0389270i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.86480 | + | 7.43845i | −0.292901 | + | 0.245773i | ||||
\(917\) | 38.9260 | + | 32.6628i | 1.28545 | + | 1.07862i | ||||
\(918\) | 1.97029 | + | 11.1741i | 0.0650294 | + | 0.368800i | ||||
\(919\) | −13.5016 | − | 23.3855i | −0.445378 | − | 0.771418i | 0.552700 | − | 0.833380i | \(-0.313597\pi\) |
−0.998078 | + | 0.0619624i | \(0.980264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6657 | + | 4.60994i | 0.417349 | + | 0.151903i | ||||
\(922\) | 4.77161 | + | 1.73672i | 0.157145 | + | 0.0571960i | ||||
\(923\) | 2.54476 | − | 4.40765i | 0.0837617 | − | 0.145079i | ||||
\(924\) | 32.8993 | + | 56.9833i | 1.08231 | + | 1.87461i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.92835 | + | 3.29628i | 0.129094 | + | 0.108323i | ||||
\(927\) | −11.2778 | + | 9.46322i | −0.370412 | + | 0.310813i | ||||
\(928\) | −1.35270 | + | 7.67154i | −0.0444045 | + | 0.251831i | ||||
\(929\) | 10.4901 | − | 3.81810i | 0.344170 | − | 0.125268i | −0.164151 | − | 0.986435i | \(-0.552488\pi\) |
0.508321 | + | 0.861168i | \(0.330266\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.1704 | − | 2.10384i | 0.595510 | − | 0.0689507i | ||||
\(932\) | −12.8579 | −0.421173 | ||||||||
\(933\) | −20.8763 | + | 7.59834i | −0.683458 | + | 0.248758i | ||||
\(934\) | −5.14382 | + | 29.1720i | −0.168311 | + | 0.954538i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.02320 | + | 3.37586i | 0.131502 | + | 0.110344i | ||||
\(937\) | −2.37497 | − | 13.4691i | −0.0775869 | − | 0.440017i | −0.998711 | − | 0.0507491i | \(-0.983839\pi\) |
0.921125 | − | 0.389268i | \(-0.127272\pi\) | |||||||
\(938\) | 4.89357 | + | 8.47591i | 0.159781 | + | 0.276748i | ||||
\(939\) | 12.1141 | − | 20.9823i | 0.395330 | − | 0.684731i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.22980 | + | 1.17555i | 0.105288 | + | 0.0383218i | 0.394127 | − | 0.919056i | \(-0.371047\pi\) |
−0.288839 | + | 0.957378i | \(0.593269\pi\) | |||||||
\(942\) | −38.7534 | + | 67.1229i | −1.26266 | + | 2.18698i | ||||
\(943\) | −5.54067 | − | 9.59672i | −0.180429 | − | 0.312512i | ||||
\(944\) | 0.843982 | + | 4.78646i | 0.0274693 | + | 0.155786i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.80363 | + | 7.38712i | −0.286231 | + | 0.240176i | ||||
\(947\) | −7.09857 | + | 40.2580i | −0.230673 | + | 1.30821i | 0.620866 | + | 0.783917i | \(0.286781\pi\) |
−0.851538 | + | 0.524292i | \(0.824330\pi\) | |||||||
\(948\) | −6.86908 | + | 2.50014i | −0.223097 | + | 0.0812008i | ||||
\(949\) | −5.77353 | −0.187417 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.6840 | 1.41655 | ||||||||
\(952\) | 2.72968 | − | 0.993522i | 0.0884694 | − | 0.0322002i | ||||
\(953\) | 7.57113 | − | 42.9380i | 0.245253 | − | 1.39090i | −0.574652 | − | 0.818398i | \(-0.694862\pi\) |
0.819905 | − | 0.572500i | \(-0.194026\pi\) | |||||||
\(954\) | 38.6997 | − | 32.4729i | 1.25295 | − | 1.05135i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.96468 | − | 11.1423i | −0.0635424 | − | 0.360367i | ||||
\(957\) | −76.5911 | − | 132.660i | −2.47584 | − | 4.28828i | ||||
\(958\) | 18.8421 | − | 32.6354i | 0.608760 | − | 1.05440i | ||||
\(959\) | −26.8847 | − | 9.78522i | −0.868152 | − | 0.315981i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.48052 | + | 9.49254i | −0.176791 | + | 0.306211i | ||||
\(962\) | 0.620858 | + | 1.07536i | 0.0200173 | + | 0.0346709i | ||||
\(963\) | 18.0727 | + | 102.496i | 0.582386 | + | 3.30287i | ||||
\(964\) | −18.2280 | − | 15.2951i | −0.587085 | − | 0.492623i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.11262 | + | 11.9812i | −0.0679723 | + | 0.385490i | ||||
\(967\) | 21.6746 | − | 7.88890i | 0.697008 | − | 0.253690i | 0.0308750 | − | 0.999523i | \(-0.490171\pi\) |
0.666133 | + | 0.745833i | \(0.267948\pi\) | |||||||
\(968\) | 27.2459 | 0.875715 | ||||||||
\(969\) | 8.26654 | − | 8.74301i | 0.265560 | − | 0.280866i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.8948 | − | 11.2448i | 0.991462 | − | 0.360863i | 0.205176 | − | 0.978725i | \(-0.434223\pi\) |
0.786286 | + | 0.617862i | \(0.212001\pi\) | |||||||
\(972\) | −4.35964 | + | 24.7248i | −0.139836 | + | 0.793047i | ||||
\(973\) | 22.5675 | − | 18.9364i | 0.723480 | − | 0.607072i | ||||
\(974\) | 13.6006 | + | 11.4122i | 0.435790 | + | 0.365672i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.61379 | − | 6.25926i | −0.115675 | − | 0.200354i | ||||
\(977\) | 28.1552 | − | 48.7663i | 0.900765 | − | 1.56017i | 0.0742618 | − | 0.997239i | \(-0.476340\pi\) |
0.826503 | − | 0.562932i | \(-0.190327\pi\) | |||||||
\(978\) | 12.8777 | + | 4.68712i | 0.411785 | + | 0.149877i | ||||
\(979\) | −13.5301 | − | 4.92455i | −0.432424 | − | 0.157389i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.9134 | + | 53.5436i | 0.986988 | + | 1.70951i | ||||
\(982\) | −3.87201 | − | 21.9592i | −0.123561 | − | 0.700747i | ||||
\(983\) | 26.4336 | + | 22.1804i | 0.843100 | + | 0.707445i | 0.958259 | − | 0.285902i | \(-0.0922933\pi\) |
−0.115159 | + | 0.993347i | \(0.536738\pi\) | |||||||
\(984\) | −23.6051 | + | 19.8070i | −0.752503 | + | 0.631425i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.35482 | + | 2.31296i | −0.202379 | + | 0.0736598i | ||||
\(987\) | 3.52910 | 0.112332 | ||||||||
\(988\) | 0.190686 | − | 3.21391i | 0.00606652 | − | 0.102248i | ||||
\(989\) | −2.12491 | −0.0675683 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.27532 | − | 41.2604i | 0.231108 | − | 1.31068i | −0.619549 | − | 0.784958i | \(-0.712684\pi\) |
0.850657 | − | 0.525721i | \(-0.176205\pi\) | |||||||
\(992\) | 4.96223 | − | 4.16381i | 0.157551 | − | 0.132201i | ||||
\(993\) | 16.1840 | + | 13.5800i | 0.513583 | + | 0.430947i | ||||
\(994\) | −4.00374 | − | 22.7063i | −0.126991 | − | 0.720201i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18.1986 | − | 31.5209i | 0.576644 | − | 0.998777i | ||||
\(997\) | −30.8447 | − | 11.2266i | −0.976862 | − | 0.355549i | −0.196243 | − | 0.980555i | \(-0.562874\pi\) |
−0.780619 | + | 0.625007i | \(0.785096\pi\) | |||||||
\(998\) | 17.7382 | + | 6.45619i | 0.561494 | + | 0.204367i | ||||
\(999\) | −10.9862 | + | 19.0286i | −0.347587 | + | 0.602039i |
(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 | 950.2.l.i.651.1 | 18 | ||
5.2 | odd | 4 | 950.2.u.g.499.3 | 36 | |||
5.3 | odd | 4 | 950.2.u.g.499.4 | 36 | |||
5.4 | even | 2 | 190.2.k.d.81.3 | yes | 18 | ||
19.4 | even | 9 | inner | 950.2.l.i.251.1 | 18 | ||
95.4 | even | 18 | 190.2.k.d.61.3 | ✓ | 18 | ||
95.23 | odd | 36 | 950.2.u.g.99.3 | 36 | |||
95.42 | odd | 36 | 950.2.u.g.99.4 | 36 | |||
95.59 | odd | 18 | 3610.2.a.bj.1.2 | 9 | |||
95.74 | even | 18 | 3610.2.a.bi.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.d.61.3 | ✓ | 18 | 95.4 | even | 18 | ||
190.2.k.d.81.3 | yes | 18 | 5.4 | even | 2 | ||
950.2.l.i.251.1 | 18 | 19.4 | even | 9 | inner | ||
950.2.l.i.651.1 | 18 | 1.1 | even | 1 | trivial | ||
950.2.u.g.99.3 | 36 | 95.23 | odd | 36 | |||
950.2.u.g.99.4 | 36 | 95.42 | odd | 36 | |||
950.2.u.g.499.3 | 36 | 5.2 | odd | 4 | |||
950.2.u.g.499.4 | 36 | 5.3 | odd | 4 | |||
3610.2.a.bi.1.8 | 9 | 95.74 | even | 18 | |||
3610.2.a.bj.1.2 | 9 | 95.59 | odd | 18 |