Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(407,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.407");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 743.1 | ||
Root | \(0.297931i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.743 |
Dual form | 1050.2.j.c.407.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.33413 | + | 1.10458i | −0.770258 | + | 0.637732i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.72443 | + | 0.162311i | 0.703995 | + | 0.0662633i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0.559788 | − | 2.94731i | 0.186596 | − | 0.982437i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.780604i | 0.235361i | 0.993052 | + | 0.117681i | \(0.0375459\pi\) | ||||
−0.993052 | + | 0.117681i | \(0.962454\pi\) | |||||||
\(12\) | −1.10458 | − | 1.33413i | −0.318866 | − | 0.385129i | ||||
\(13\) | 3.85292 | + | 3.85292i | 1.06861 | + | 1.06861i | 0.997466 | + | 0.0711428i | \(0.0226646\pi\) |
0.0711428 | + | 0.997466i | \(0.477335\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.97331 | − | 2.97331i | −0.721133 | − | 0.721133i | 0.247703 | − | 0.968836i | \(-0.420324\pi\) |
−0.968836 | + | 0.247703i | \(0.920324\pi\) | |||||||
\(18\) | −2.47989 | + | 1.68823i | −0.584516 | + | 0.397920i | ||||
\(19\) | − | 5.79249i | − | 1.32889i | −0.747338 | − | 0.664444i | \(-0.768668\pi\) | ||
0.747338 | − | 0.664444i | \(-0.231332\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.162311 | + | 1.72443i | −0.0354192 | + | 0.376301i | ||||
\(22\) | 0.551971 | − | 0.551971i | 0.117681 | − | 0.117681i | ||||
\(23\) | −1.74679 | + | 1.74679i | −0.364231 | + | 0.364231i | −0.865368 | − | 0.501137i | \(-0.832915\pi\) |
0.501137 | + | 0.865368i | \(0.332915\pi\) | |||||||
\(24\) | −0.162311 | + | 1.72443i | −0.0331316 | + | 0.351998i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 5.44886i | − | 1.06861i | ||||||
\(27\) | 2.50872 | + | 4.55042i | 0.482804 | + | 0.875728i | ||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | −3.33651 | −0.619574 | −0.309787 | − | 0.950806i | \(-0.600258\pi\) | ||||
−0.309787 | + | 0.950806i | \(0.600258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.20515 | 0.216451 | 0.108225 | − | 0.994126i | \(-0.465483\pi\) | ||||
0.108225 | + | 0.994126i | \(0.465483\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −0.862243 | − | 1.04143i | −0.150097 | − | 0.181289i | ||||
\(34\) | 4.20489i | 0.721133i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.94731 | + | 0.559788i | 0.491218 | + | 0.0932981i | ||||
\(37\) | 6.28770 | − | 6.28770i | 1.03369 | − | 1.03369i | 0.0342797 | − | 0.999412i | \(-0.489086\pi\) |
0.999412 | − | 0.0342797i | \(-0.0109137\pi\) | |||||||
\(38\) | −4.09591 | + | 4.09591i | −0.664444 | + | 0.664444i | ||||
\(39\) | −9.39617 | − | 0.884411i | −1.50459 | − | 0.141619i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.410091i | − | 0.0640455i | −0.999487 | − | 0.0320227i | \(-0.989805\pi\) | ||
0.999487 | − | 0.0320227i | \(-0.0101949\pi\) | |||||||
\(42\) | 1.33413 | − | 1.10458i | 0.205860 | − | 0.170441i | ||||
\(43\) | 0.397015 | + | 0.397015i | 0.0605442 | + | 0.0605442i | 0.736731 | − | 0.676186i | \(-0.236369\pi\) |
−0.676186 | + | 0.736731i | \(0.736369\pi\) | |||||||
\(44\) | −0.780604 | −0.117681 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.47033 | 0.364231 | ||||||||
\(47\) | 4.50070 | + | 4.50070i | 0.656495 | + | 0.656495i | 0.954549 | − | 0.298054i | \(-0.0963376\pi\) |
−0.298054 | + | 0.954549i | \(0.596338\pi\) | |||||||
\(48\) | 1.33413 | − | 1.10458i | 0.192565 | − | 0.159433i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.25104 | + | 0.682501i | 1.01535 | + | 0.0955693i | ||||
\(52\) | −3.85292 | + | 3.85292i | −0.534304 | + | 0.534304i | ||||
\(53\) | 7.69577 | − | 7.69577i | 1.05710 | − | 1.05710i | 0.0588277 | − | 0.998268i | \(-0.481264\pi\) |
0.998268 | − | 0.0588277i | \(-0.0187363\pi\) | |||||||
\(54\) | 1.44370 | − | 4.99157i | 0.196462 | − | 0.679266i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 6.39829 | + | 7.72791i | 0.847474 | + | 1.02359i | ||||
\(58\) | 2.35927 | + | 2.35927i | 0.309787 | + | 0.309787i | ||||
\(59\) | 12.6753 | 1.65019 | 0.825093 | − | 0.564996i | \(-0.191122\pi\) | ||||
0.825093 | + | 0.564996i | \(0.191122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.11230 | 1.16671 | 0.583355 | − | 0.812217i | \(-0.301740\pi\) | ||||
0.583355 | + | 0.812217i | \(0.301740\pi\) | |||||||
\(62\) | −0.852168 | − | 0.852168i | −0.108225 | − | 0.108225i | ||||
\(63\) | −1.68823 | − | 2.47989i | −0.212697 | − | 0.312437i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.126701 | + | 1.34610i | −0.0155958 | + | 0.165693i | ||||
\(67\) | −4.95979 | + | 4.95979i | −0.605934 | + | 0.605934i | −0.941881 | − | 0.335947i | \(-0.890944\pi\) |
0.335947 | + | 0.941881i | \(0.390944\pi\) | |||||||
\(68\) | 2.97331 | − | 2.97331i | 0.360567 | − | 0.360567i | ||||
\(69\) | 0.400963 | − | 4.25991i | 0.0482702 | − | 0.512833i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.88593i | 0.223819i | 0.993718 | + | 0.111910i | \(0.0356967\pi\) | ||||
−0.993718 | + | 0.111910i | \(0.964303\pi\) | |||||||
\(72\) | −1.68823 | − | 2.47989i | −0.198960 | − | 0.292258i | ||||
\(73\) | 8.48507 | + | 8.48507i | 0.993102 | + | 0.993102i | 0.999976 | − | 0.00687462i | \(-0.00218828\pi\) |
−0.00687462 | + | 0.999976i | \(0.502188\pi\) | |||||||
\(74\) | −8.89215 | −1.03369 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.79249 | 0.664444 | ||||||||
\(77\) | 0.551971 | + | 0.551971i | 0.0629029 | + | 0.0629029i | ||||
\(78\) | 6.01872 | + | 7.26947i | 0.681486 | + | 0.823105i | ||||
\(79\) | 12.5532i | 1.41234i | 0.708041 | + | 0.706172i | \(0.249579\pi\) | ||||
−0.708041 | + | 0.706172i | \(0.750421\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.37327 | − | 3.29974i | −0.930364 | − | 0.366638i | ||||
\(82\) | −0.289978 | + | 0.289978i | −0.0320227 | + | 0.0320227i | ||||
\(83\) | 3.60601 | − | 3.60601i | 0.395811 | − | 0.395811i | −0.480942 | − | 0.876753i | \(-0.659705\pi\) |
0.876753 | + | 0.480942i | \(0.159705\pi\) | |||||||
\(84\) | −1.72443 | − | 0.162311i | −0.188151 | − | 0.0177096i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.561464i | − | 0.0605442i | ||||||
\(87\) | 4.45132 | − | 3.68545i | 0.477232 | − | 0.395122i | ||||
\(88\) | 0.551971 | + | 0.551971i | 0.0588403 | + | 0.0588403i | ||||
\(89\) | 18.5847 | 1.96998 | 0.984988 | − | 0.172621i | \(-0.0552236\pi\) | ||||
0.984988 | + | 0.172621i | \(0.0552236\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.44886 | 0.571196 | ||||||||
\(92\) | −1.74679 | − | 1.74679i | −0.182115 | − | 0.182115i | ||||
\(93\) | −1.60782 | + | 1.33119i | −0.166723 | + | 0.138038i | ||||
\(94\) | − | 6.36495i | − | 0.656495i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.72443 | − | 0.162311i | −0.175999 | − | 0.0165658i | ||||
\(97\) | 8.82001 | − | 8.82001i | 0.895536 | − | 0.895536i | −0.0995012 | − | 0.995037i | \(-0.531725\pi\) |
0.995037 | + | 0.0995012i | \(0.0317247\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 2.30068 | + | 0.436973i | 0.231227 | + | 0.0439175i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.52395i | 0.848165i | 0.905624 | + | 0.424083i | \(0.139403\pi\) | ||||
−0.905624 | + | 0.424083i | \(0.860597\pi\) | |||||||
\(102\) | −4.64466 | − | 5.60986i | −0.459890 | − | 0.555459i | ||||
\(103\) | −7.68570 | − | 7.68570i | −0.757294 | − | 0.757294i | 0.218535 | − | 0.975829i | \(-0.429872\pi\) |
−0.975829 | + | 0.218535i | \(0.929872\pi\) | |||||||
\(104\) | 5.44886 | 0.534304 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.8835 | −1.05710 | ||||||||
\(107\) | −8.53379 | − | 8.53379i | −0.824993 | − | 0.824993i | 0.161827 | − | 0.986819i | \(-0.448261\pi\) |
−0.986819 | + | 0.161827i | \(0.948261\pi\) | |||||||
\(108\) | −4.55042 | + | 2.50872i | −0.437864 | + | 0.241402i | ||||
\(109\) | − | 3.67769i | − | 0.352259i | −0.984367 | − | 0.176129i | \(-0.943642\pi\) | ||
0.984367 | − | 0.176129i | \(-0.0563577\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.44330 | + | 15.3339i | −0.136992 | + | 1.45543i | ||||
\(112\) | −0.707107 | + | 0.707107i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | 11.8416 | − | 11.8416i | 1.11396 | − | 1.11396i | 0.121355 | − | 0.992609i | \(-0.461276\pi\) |
0.992609 | − | 0.121355i | \(-0.0387238\pi\) | |||||||
\(114\) | 0.940186 | − | 9.98874i | 0.0880565 | − | 0.935531i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.33651i | − | 0.309787i | ||||||
\(117\) | 13.5126 | − | 9.19894i | 1.24924 | − | 0.850442i | ||||
\(118\) | −8.96281 | − | 8.96281i | −0.825093 | − | 0.825093i | ||||
\(119\) | −4.20489 | −0.385462 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3907 | 0.944605 | ||||||||
\(122\) | −6.44337 | − | 6.44337i | −0.583355 | − | 0.583355i | ||||
\(123\) | 0.452980 | + | 0.547114i | 0.0408438 | + | 0.0493316i | ||||
\(124\) | 1.20515i | 0.108225i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.559788 | + | 2.94731i | −0.0498699 | + | 0.262567i | ||||
\(127\) | −12.5290 | + | 12.5290i | −1.11177 | + | 1.11177i | −0.118863 | + | 0.992911i | \(0.537925\pi\) |
−0.992911 | + | 0.118863i | \(0.962075\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −0.968204 | − | 0.0911319i | −0.0852456 | − | 0.00802372i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.8873i | − | 1.03860i | −0.854591 | − | 0.519301i | \(-0.826192\pi\) | ||
0.854591 | − | 0.519301i | \(-0.173808\pi\) | |||||||
\(132\) | 1.04143 | − | 0.862243i | 0.0906444 | − | 0.0750486i | ||||
\(133\) | −4.09591 | − | 4.09591i | −0.355160 | − | 0.355160i | ||||
\(134\) | 7.01420 | 0.605934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.20489 | −0.360567 | ||||||||
\(137\) | −4.34731 | − | 4.34731i | −0.371416 | − | 0.371416i | 0.496577 | − | 0.867993i | \(-0.334590\pi\) |
−0.867993 | + | 0.496577i | \(0.834590\pi\) | |||||||
\(138\) | −3.29574 | + | 2.72869i | −0.280552 | + | 0.232281i | ||||
\(139\) | − | 11.6395i | − | 0.987250i | −0.869675 | − | 0.493625i | \(-0.835672\pi\) | ||
0.869675 | − | 0.493625i | \(-0.164328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9759 | − | 1.03310i | −0.924338 | − | 0.0870030i | ||||
\(142\) | 1.33356 | − | 1.33356i | 0.111910 | − | 0.111910i | ||||
\(143\) | −3.00761 | + | 3.00761i | −0.251509 | + | 0.251509i | ||||
\(144\) | −0.559788 | + | 2.94731i | −0.0466490 | + | 0.245609i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 11.9997i | − | 0.993102i | ||||||
\(147\) | 1.10458 | + | 1.33413i | 0.0911046 | + | 0.110037i | ||||
\(148\) | 6.28770 | + | 6.28770i | 0.516846 | + | 0.516846i | ||||
\(149\) | −5.78924 | −0.474273 | −0.237137 | − | 0.971476i | \(-0.576209\pi\) | ||||
−0.237137 | + | 0.971476i | \(0.576209\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.326935 | 0.0266056 | 0.0133028 | − | 0.999912i | \(-0.495765\pi\) | ||||
0.0133028 | + | 0.999912i | \(0.495765\pi\) | |||||||
\(152\) | −4.09591 | − | 4.09591i | −0.332222 | − | 0.332222i | ||||
\(153\) | −10.4277 | + | 7.09884i | −0.843028 | + | 0.573907i | ||||
\(154\) | − | 0.780604i | − | 0.0629029i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.884411 | − | 9.39617i | 0.0708095 | − | 0.752296i | ||||
\(157\) | −15.7404 | + | 15.7404i | −1.25622 | + | 1.25622i | −0.303339 | + | 0.952883i | \(0.598101\pi\) |
−0.952883 | + | 0.303339i | \(0.901899\pi\) | |||||||
\(158\) | 8.87644 | − | 8.87644i | 0.706172 | − | 0.706172i | ||||
\(159\) | −1.76651 | + | 18.7678i | −0.140093 | + | 1.48838i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.47033i | 0.194689i | ||||||||
\(162\) | 3.58753 | + | 8.25407i | 0.281863 | + | 0.648501i | ||||
\(163\) | −0.261547 | − | 0.261547i | −0.0204859 | − | 0.0204859i | 0.696790 | − | 0.717276i | \(-0.254611\pi\) |
−0.717276 | + | 0.696790i | \(0.754611\pi\) | |||||||
\(164\) | 0.410091 | 0.0320227 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.09967 | −0.395811 | ||||||||
\(167\) | 7.48816 | + | 7.48816i | 0.579451 | + | 0.579451i | 0.934752 | − | 0.355301i | \(-0.115622\pi\) |
−0.355301 | + | 0.934752i | \(0.615622\pi\) | |||||||
\(168\) | 1.10458 | + | 1.33413i | 0.0852205 | + | 0.102930i | ||||
\(169\) | 16.6901i | 1.28385i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.0723 | − | 3.24257i | −1.30555 | − | 0.247965i | ||||
\(172\) | −0.397015 | + | 0.397015i | −0.0302721 | + | 0.0302721i | ||||
\(173\) | 8.48843 | − | 8.48843i | 0.645363 | − | 0.645363i | −0.306505 | − | 0.951869i | \(-0.599160\pi\) |
0.951869 | + | 0.306505i | \(0.0991598\pi\) | |||||||
\(174\) | −5.75357 | − | 0.541553i | −0.436177 | − | 0.0410550i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.780604i | − | 0.0588403i | ||||||
\(177\) | −16.9105 | + | 14.0010i | −1.27107 | + | 1.05238i | ||||
\(178\) | −13.1414 | − | 13.1414i | −0.984988 | − | 0.984988i | ||||
\(179\) | −2.37051 | −0.177180 | −0.0885902 | − | 0.996068i | \(-0.528236\pi\) | ||||
−0.0885902 | + | 0.996068i | \(0.528236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.15369 | −0.457400 | −0.228700 | − | 0.973497i | \(-0.573447\pi\) | ||||
−0.228700 | + | 0.973497i | \(0.573447\pi\) | |||||||
\(182\) | −3.85292 | − | 3.85292i | −0.285598 | − | 0.285598i | ||||
\(183\) | −12.1570 | + | 10.0653i | −0.898669 | + | 0.744048i | ||||
\(184\) | 2.47033i | 0.182115i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.07819 | + | 0.195609i | 0.152380 | + | 0.0143428i | ||||
\(187\) | 2.32098 | − | 2.32098i | 0.169727 | − | 0.169727i | ||||
\(188\) | −4.50070 | + | 4.50070i | −0.328247 | + | 0.328247i | ||||
\(189\) | 4.99157 | + | 1.44370i | 0.363083 | + | 0.105014i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.64185i | 0.697660i | 0.937186 | + | 0.348830i | \(0.113421\pi\) | ||||
−0.937186 | + | 0.348830i | \(0.886579\pi\) | |||||||
\(192\) | 1.10458 | + | 1.33413i | 0.0797165 | + | 0.0962823i | ||||
\(193\) | 6.77716 | + | 6.77716i | 0.487830 | + | 0.487830i | 0.907621 | − | 0.419791i | \(-0.137896\pi\) |
−0.419791 | + | 0.907621i | \(0.637896\pi\) | |||||||
\(194\) | −12.4734 | −0.895536 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −2.34224 | − | 2.34224i | −0.166878 | − | 0.166878i | 0.618728 | − | 0.785606i | \(-0.287648\pi\) |
−0.785606 | + | 0.618728i | \(0.787648\pi\) | |||||||
\(198\) | −1.31784 | − | 1.93582i | −0.0936549 | − | 0.137572i | ||||
\(199\) | 9.94617i | 0.705066i | 0.935799 | + | 0.352533i | \(0.114680\pi\) | ||||
−0.935799 | + | 0.352533i | \(0.885320\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.13848 | − | 12.0955i | 0.0803024 | − | 0.853150i | ||||
\(202\) | 6.02735 | − | 6.02735i | 0.424083 | − | 0.424083i | ||||
\(203\) | −2.35927 | + | 2.35927i | −0.165588 | + | 0.165588i | ||||
\(204\) | −0.682501 | + | 7.25104i | −0.0477847 | + | 0.507674i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.8692i | 0.757294i | ||||||||
\(207\) | 4.17050 | + | 6.12616i | 0.289869 | + | 0.425797i | ||||
\(208\) | −3.85292 | − | 3.85292i | −0.267152 | − | 0.267152i | ||||
\(209\) | 4.52164 | 0.312768 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9895 | −1.03192 | −0.515960 | − | 0.856613i | \(-0.672565\pi\) | ||||
−0.515960 | + | 0.856613i | \(0.672565\pi\) | |||||||
\(212\) | 7.69577 | + | 7.69577i | 0.528548 | + | 0.528548i | ||||
\(213\) | −2.08317 | − | 2.51607i | −0.142737 | − | 0.172399i | ||||
\(214\) | 12.0686i | 0.824993i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.99157 | + | 1.44370i | 0.339633 | + | 0.0982311i | ||||
\(217\) | 0.852168 | − | 0.852168i | 0.0578489 | − | 0.0578489i | ||||
\(218\) | −2.60052 | + | 2.60052i | −0.176129 | + | 0.176129i | ||||
\(219\) | −20.6926 | − | 1.94769i | −1.39828 | − | 0.131612i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 22.9119i | − | 1.54122i | ||||||
\(222\) | 11.8633 | − | 9.82213i | 0.796210 | − | 0.659218i | ||||
\(223\) | −7.97398 | − | 7.97398i | −0.533977 | − | 0.533977i | 0.387776 | − | 0.921754i | \(-0.373243\pi\) |
−0.921754 | + | 0.387776i | \(0.873243\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.7465 | −1.11396 | ||||||||
\(227\) | 20.3950 | + | 20.3950i | 1.35366 | + | 1.35366i | 0.881526 | + | 0.472135i | \(0.156516\pi\) |
0.472135 | + | 0.881526i | \(0.343484\pi\) | |||||||
\(228\) | −7.72791 | + | 6.39829i | −0.511794 | + | 0.423737i | ||||
\(229\) | − | 19.5317i | − | 1.29069i | −0.763891 | − | 0.645346i | \(-0.776713\pi\) | ||
0.763891 | − | 0.645346i | \(-0.223287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.34610 | − | 0.126701i | −0.0885667 | − | 0.00833630i | ||||
\(232\) | −2.35927 | + | 2.35927i | −0.154893 | + | 0.154893i | ||||
\(233\) | 2.92961 | − | 2.92961i | 0.191925 | − | 0.191925i | −0.604602 | − | 0.796527i | \(-0.706668\pi\) |
0.796527 | + | 0.604602i | \(0.206668\pi\) | |||||||
\(234\) | −16.0595 | − | 3.05021i | −1.04984 | − | 0.199398i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.6753i | 0.825093i | ||||||||
\(237\) | −13.8660 | − | 16.7475i | −0.900696 | − | 1.08787i | ||||
\(238\) | 2.97331 | + | 2.97331i | 0.192731 | + | 0.192731i | ||||
\(239\) | 12.0343 | 0.778432 | 0.389216 | − | 0.921147i | \(-0.372746\pi\) | ||||
0.389216 | + | 0.921147i | \(0.372746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.77972 | 0.372304 | 0.186152 | − | 0.982521i | \(-0.440398\pi\) | ||||
0.186152 | + | 0.982521i | \(0.440398\pi\) | |||||||
\(242\) | −7.34730 | − | 7.34730i | −0.472303 | − | 0.472303i | ||||
\(243\) | 14.8158 | − | 4.84671i | 0.950437 | − | 0.310917i | ||||
\(244\) | 9.11230i | 0.583355i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0665624 | − | 0.707173i | 0.00424386 | − | 0.0450877i | ||||
\(247\) | 22.3180 | − | 22.3180i | 1.42006 | − | 1.42006i | ||||
\(248\) | 0.852168 | − | 0.852168i | 0.0541127 | − | 0.0541127i | ||||
\(249\) | −0.827733 | + | 8.79401i | −0.0524555 | + | 0.557298i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.50663i | − | 0.0950977i | −0.998869 | − | 0.0475489i | \(-0.984859\pi\) | ||
0.998869 | − | 0.0475489i | \(-0.0151410\pi\) | |||||||
\(252\) | 2.47989 | − | 1.68823i | 0.156219 | − | 0.106349i | ||||
\(253\) | −1.36355 | − | 1.36355i | −0.0857257 | − | 0.0857257i | ||||
\(254\) | 17.7188 | 1.11177 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.44942 | − | 3.44942i | −0.215169 | − | 0.215169i | 0.591290 | − | 0.806459i | \(-0.298619\pi\) |
−0.806459 | + | 0.591290i | \(0.798619\pi\) | |||||||
\(258\) | 0.620184 | + | 0.749064i | 0.0386110 | + | 0.0466347i | ||||
\(259\) | − | 8.89215i | − | 0.552532i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.86774 | + | 9.83372i | −0.115610 | + | 0.608692i | ||||
\(262\) | −8.40562 | + | 8.40562i | −0.519301 | + | 0.519301i | ||||
\(263\) | −9.85402 | + | 9.85402i | −0.607625 | + | 0.607625i | −0.942325 | − | 0.334700i | \(-0.891365\pi\) |
0.334700 | + | 0.942325i | \(0.391365\pi\) | |||||||
\(264\) | −1.34610 | − | 0.126701i | −0.0828465 | − | 0.00779790i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.79249i | 0.355160i | ||||||||
\(267\) | −24.7944 | + | 20.5284i | −1.51739 | + | 1.25632i | ||||
\(268\) | −4.95979 | − | 4.95979i | −0.302967 | − | 0.302967i | ||||
\(269\) | −9.17881 | −0.559642 | −0.279821 | − | 0.960052i | \(-0.590275\pi\) | ||||
−0.279821 | + | 0.960052i | \(0.590275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.85752 | −0.477310 | −0.238655 | − | 0.971104i | \(-0.576707\pi\) | ||||
−0.238655 | + | 0.971104i | \(0.576707\pi\) | |||||||
\(272\) | 2.97331 | + | 2.97331i | 0.180283 | + | 0.180283i | ||||
\(273\) | −7.26947 | + | 6.01872i | −0.439968 | + | 0.364270i | ||||
\(274\) | 6.14802i | 0.371416i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.25991 | + | 0.400963i | 0.256417 | + | 0.0241351i | ||||
\(277\) | −2.82887 | + | 2.82887i | −0.169970 | + | 0.169970i | −0.786966 | − | 0.616996i | \(-0.788350\pi\) |
0.616996 | + | 0.786966i | \(0.288350\pi\) | |||||||
\(278\) | −8.23037 | + | 8.23037i | −0.493625 | + | 0.493625i | ||||
\(279\) | 0.674628 | − | 3.55194i | 0.0403889 | − | 0.212649i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.990734i | 0.0591022i | 0.999563 | + | 0.0295511i | \(0.00940778\pi\) | ||||
−0.999563 | + | 0.0295511i | \(0.990592\pi\) | |||||||
\(282\) | 7.03062 | + | 8.49165i | 0.418668 | + | 0.505671i | ||||
\(283\) | 16.0249 | + | 16.0249i | 0.952584 | + | 0.952584i | 0.998926 | − | 0.0463416i | \(-0.0147563\pi\) |
−0.0463416 | + | 0.998926i | \(0.514756\pi\) | |||||||
\(284\) | −1.88593 | −0.111910 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.25340 | 0.251509 | ||||||||
\(287\) | −0.289978 | − | 0.289978i | −0.0171169 | − | 0.0171169i | ||||
\(288\) | 2.47989 | − | 1.68823i | 0.146129 | − | 0.0994801i | ||||
\(289\) | 0.681122i | 0.0400660i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.02457 | + | 21.5095i | −0.118682 | + | 1.26091i | ||||
\(292\) | −8.48507 | + | 8.48507i | −0.496551 | + | 0.496551i | ||||
\(293\) | −0.328091 | + | 0.328091i | −0.0191673 | + | 0.0191673i | −0.716625 | − | 0.697458i | \(-0.754314\pi\) |
0.697458 | + | 0.716625i | \(0.254314\pi\) | |||||||
\(294\) | 0.162311 | − | 1.72443i | 0.00946618 | − | 0.100571i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 8.89215i | − | 0.516846i | ||||||
\(297\) | −3.55208 | + | 1.95832i | −0.206112 | + | 0.113633i | ||||
\(298\) | 4.09361 | + | 4.09361i | 0.237137 | + | 0.237137i | ||||
\(299\) | −13.4605 | −0.778440 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.561464 | 0.0323622 | ||||||||
\(302\) | −0.231178 | − | 0.231178i | −0.0133028 | − | 0.0133028i | ||||
\(303\) | −9.41542 | − | 11.3720i | −0.540902 | − | 0.653306i | ||||
\(304\) | 5.79249i | 0.332222i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 12.3931 | + | 2.35385i | 0.708468 | + | 0.134561i | ||||
\(307\) | 5.29402 | − | 5.29402i | 0.302146 | − | 0.302146i | −0.539707 | − | 0.841853i | \(-0.681465\pi\) |
0.841853 | + | 0.539707i | \(0.181465\pi\) | |||||||
\(308\) | −0.551971 | + | 0.551971i | −0.0314514 | + | 0.0314514i | ||||
\(309\) | 18.7432 | + | 1.76420i | 1.06626 | + | 0.100362i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.1390i | 0.688340i | 0.938907 | + | 0.344170i | \(0.111840\pi\) | ||||
−0.938907 | + | 0.344170i | \(0.888160\pi\) | |||||||
\(312\) | −7.26947 | + | 6.01872i | −0.411553 | + | 0.340743i | ||||
\(313\) | −12.2205 | − | 12.2205i | −0.690745 | − | 0.690745i | 0.271651 | − | 0.962396i | \(-0.412430\pi\) |
−0.962396 | + | 0.271651i | \(0.912430\pi\) | |||||||
\(314\) | 22.2603 | 1.25622 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.5532 | −0.706172 | ||||||||
\(317\) | −2.40772 | − | 2.40772i | −0.135231 | − | 0.135231i | 0.636251 | − | 0.771482i | \(-0.280484\pi\) |
−0.771482 | + | 0.636251i | \(0.780484\pi\) | |||||||
\(318\) | 14.5199 | − | 12.0217i | 0.814237 | − | 0.674144i | ||||
\(319\) | − | 2.60449i | − | 0.145824i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.8114 | + | 1.95887i | 1.16158 | + | 0.109333i | ||||
\(322\) | 1.74679 | − | 1.74679i | 0.0973447 | − | 0.0973447i | ||||
\(323\) | −17.2229 | + | 17.2229i | −0.958305 | + | 0.958305i | ||||
\(324\) | 3.29974 | − | 8.37327i | 0.183319 | − | 0.465182i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.369883i | 0.0204859i | ||||||||
\(327\) | 4.06232 | + | 4.90650i | 0.224647 | + | 0.271330i | ||||
\(328\) | −0.289978 | − | 0.289978i | −0.0160114 | − | 0.0160114i | ||||
\(329\) | 6.36495 | 0.350911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.2790 | −0.839810 | −0.419905 | − | 0.907568i | \(-0.637937\pi\) | ||||
−0.419905 | + | 0.907568i | \(0.637937\pi\) | |||||||
\(332\) | 3.60601 | + | 3.60601i | 0.197905 | + | 0.197905i | ||||
\(333\) | −15.0120 | − | 22.0516i | −0.822654 | − | 1.20842i | ||||
\(334\) | − | 10.5899i | − | 0.579451i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.162311 | − | 1.72443i | 0.00885481 | − | 0.0940753i | ||||
\(337\) | −11.4834 | + | 11.4834i | −0.625541 | + | 0.625541i | −0.946943 | − | 0.321402i | \(-0.895846\pi\) |
0.321402 | + | 0.946943i | \(0.395846\pi\) | |||||||
\(338\) | 11.8016 | − | 11.8016i | 0.641925 | − | 0.641925i | ||||
\(339\) | −2.71815 | + | 28.8782i | −0.147630 | + | 1.56845i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.940744i | 0.0509441i | ||||||||
\(342\) | 9.77907 | + | 14.3648i | 0.528792 | + | 0.776757i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 0.561464 | 0.0302721 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0045 | −0.645363 | ||||||||
\(347\) | −12.0974 | − | 12.0974i | −0.649425 | − | 0.649425i | 0.303429 | − | 0.952854i | \(-0.401868\pi\) |
−0.952854 | + | 0.303429i | \(0.901868\pi\) | |||||||
\(348\) | 3.68545 | + | 4.45132i | 0.197561 | + | 0.238616i | ||||
\(349\) | 0.114169i | 0.00611132i | 0.999995 | + | 0.00305566i | \(0.000972649\pi\) | ||||
−0.999995 | + | 0.00305566i | \(0.999027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.86650 | + | 27.1983i | −0.419883 | + | 1.45174i | ||||
\(352\) | −0.551971 | + | 0.551971i | −0.0294201 | + | 0.0294201i | ||||
\(353\) | 17.4937 | − | 17.4937i | 0.931097 | − | 0.931097i | −0.0666780 | − | 0.997775i | \(-0.521240\pi\) |
0.997775 | + | 0.0666780i | \(0.0212400\pi\) | |||||||
\(354\) | 21.8577 | + | 2.05735i | 1.16172 | + | 0.109347i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.5847i | 0.984988i | ||||||||
\(357\) | 5.60986 | − | 4.64466i | 0.296905 | − | 0.245821i | ||||
\(358\) | 1.67621 | + | 1.67621i | 0.0885902 | + | 0.0885902i | ||||
\(359\) | −25.4743 | −1.34448 | −0.672240 | − | 0.740333i | \(-0.734668\pi\) | ||||
−0.672240 | + | 0.740333i | \(0.734668\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5529 | −0.765944 | ||||||||
\(362\) | 4.35131 | + | 4.35131i | 0.228700 | + | 0.228700i | ||||
\(363\) | −13.8625 | + | 11.4774i | −0.727590 | + | 0.602405i | ||||
\(364\) | 5.44886i | 0.285598i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.7135 | + | 1.47903i | 0.821359 | + | 0.0773101i | ||||
\(367\) | 23.9590 | − | 23.9590i | 1.25065 | − | 1.25065i | 0.295224 | − | 0.955428i | \(-0.404606\pi\) |
0.955428 | − | 0.295224i | \(-0.0953943\pi\) | |||||||
\(368\) | 1.74679 | − | 1.74679i | 0.0910576 | − | 0.0910576i | ||||
\(369\) | −1.20867 | − | 0.229564i | −0.0629206 | − | 0.0119506i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 10.8835i | − | 0.565041i | ||||||
\(372\) | −1.33119 | − | 1.60782i | −0.0690188 | − | 0.0833616i | ||||
\(373\) | −4.14472 | − | 4.14472i | −0.214605 | − | 0.214605i | 0.591615 | − | 0.806221i | \(-0.298491\pi\) |
−0.806221 | + | 0.591615i | \(0.798491\pi\) | |||||||
\(374\) | −3.28236 | −0.169727 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.36495 | 0.328247 | ||||||||
\(377\) | −12.8553 | − | 12.8553i | −0.662082 | − | 0.662082i | ||||
\(378\) | −2.50872 | − | 4.55042i | −0.129035 | − | 0.234048i | ||||
\(379\) | − | 13.5788i | − | 0.697495i | −0.937217 | − | 0.348748i | \(-0.886607\pi\) | ||
0.937217 | − | 0.348748i | \(-0.113393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.87595 | − | 30.5547i | 0.147340 | − | 1.56537i | ||||
\(382\) | 6.81782 | − | 6.81782i | 0.348830 | − | 0.348830i | ||||
\(383\) | −11.0679 | + | 11.0679i | −0.565541 | + | 0.565541i | −0.930876 | − | 0.365335i | \(-0.880954\pi\) |
0.365335 | + | 0.930876i | \(0.380954\pi\) | |||||||
\(384\) | 0.162311 | − | 1.72443i | 0.00828291 | − | 0.0879994i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.58435i | − | 0.487830i | ||||||
\(387\) | 1.39237 | − | 0.947882i | 0.0707782 | − | 0.0481835i | ||||
\(388\) | 8.82001 | + | 8.82001i | 0.447768 | + | 0.447768i | ||||
\(389\) | 29.1746 | 1.47921 | 0.739605 | − | 0.673041i | \(-0.235012\pi\) | ||||
0.739605 | + | 0.673041i | \(0.235012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3875 | 0.525317 | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 13.1306 | + | 15.8592i | 0.662350 | + | 0.799992i | ||||
\(394\) | 3.31243i | 0.166878i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.436973 | + | 2.30068i | −0.0219587 | + | 0.115614i | ||||
\(397\) | 10.4013 | − | 10.4013i | 0.522028 | − | 0.522028i | −0.396155 | − | 0.918183i | \(-0.629656\pi\) |
0.918183 | + | 0.396155i | \(0.129656\pi\) | |||||||
\(398\) | 7.03301 | − | 7.03301i | 0.352533 | − | 0.352533i | ||||
\(399\) | 9.98874 | + | 0.940186i | 0.500062 | + | 0.0470682i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.08489i | 0.154052i | 0.997029 | + | 0.0770260i | \(0.0245425\pi\) | ||||
−0.997029 | + | 0.0770260i | \(0.975458\pi\) | |||||||
\(402\) | −9.35783 | + | 7.74777i | −0.466726 | + | 0.386424i | ||||
\(403\) | 4.64334 | + | 4.64334i | 0.231301 | + | 0.231301i | ||||
\(404\) | −8.52395 | −0.424083 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.33651 | 0.165588 | ||||||||
\(407\) | 4.90821 | + | 4.90821i | 0.243291 | + | 0.243291i | ||||
\(408\) | 5.60986 | − | 4.64466i | 0.277729 | − | 0.229945i | ||||
\(409\) | − | 2.47368i | − | 0.122316i | −0.998128 | − | 0.0611579i | \(-0.980521\pi\) | ||
0.998128 | − | 0.0611579i | \(-0.0194793\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.6018 | + | 0.997893i | 0.522950 | + | 0.0492224i | ||||
\(412\) | 7.68570 | − | 7.68570i | 0.378647 | − | 0.378647i | ||||
\(413\) | 8.96281 | − | 8.96281i | 0.441031 | − | 0.441031i | ||||
\(414\) | 1.38286 | − | 7.28083i | 0.0679640 | − | 0.357833i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.44886i | 0.267152i | ||||||||
\(417\) | 12.8568 | + | 15.5286i | 0.629601 | + | 0.760437i | ||||
\(418\) | −3.19728 | − | 3.19728i | −0.156384 | − | 0.156384i | ||||
\(419\) | −23.6148 | −1.15366 | −0.576828 | − | 0.816865i | \(-0.695710\pi\) | ||||
−0.576828 | + | 0.816865i | \(0.695710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.6409 | −0.957240 | −0.478620 | − | 0.878022i | \(-0.658863\pi\) | ||||
−0.478620 | + | 0.878022i | \(0.658863\pi\) | |||||||
\(422\) | 10.5992 | + | 10.5992i | 0.515960 | + | 0.515960i | ||||
\(423\) | 15.7844 | − | 10.7455i | 0.767464 | − | 0.522465i | ||||
\(424\) | − | 10.8835i | − | 0.528548i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.306108 | + | 3.25216i | −0.0148310 | + | 0.157568i | ||||
\(427\) | 6.44337 | − | 6.44337i | 0.311816 | − | 0.311816i | ||||
\(428\) | 8.53379 | − | 8.53379i | 0.412496 | − | 0.412496i | ||||
\(429\) | 0.690375 | − | 7.33469i | 0.0333316 | − | 0.354122i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 28.9367i | − | 1.39383i | −0.717153 | − | 0.696915i | \(-0.754555\pi\) | ||
0.717153 | − | 0.696915i | \(-0.245445\pi\) | |||||||
\(432\) | −2.50872 | − | 4.55042i | −0.120701 | − | 0.218932i | ||||
\(433\) | −18.0810 | − | 18.0810i | −0.868918 | − | 0.868918i | 0.123434 | − | 0.992353i | \(-0.460609\pi\) |
−0.992353 | + | 0.123434i | \(0.960609\pi\) | |||||||
\(434\) | −1.20515 | −0.0578489 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.67769 | 0.176129 | ||||||||
\(437\) | 10.1183 | + | 10.1183i | 0.484022 | + | 0.484022i | ||||
\(438\) | 13.2547 | + | 16.0091i | 0.633333 | + | 0.764945i | ||||
\(439\) | − | 12.4892i | − | 0.596076i | −0.954554 | − | 0.298038i | \(-0.903668\pi\) | ||
0.954554 | − | 0.298038i | \(-0.0963323\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.94731 | − | 0.559788i | −0.140348 | − | 0.0266566i | ||||
\(442\) | −16.2011 | + | 16.2011i | −0.770609 | + | 0.770609i | ||||
\(443\) | −19.6631 | + | 19.6631i | −0.934224 | + | 0.934224i | −0.997966 | − | 0.0637426i | \(-0.979696\pi\) |
0.0637426 | + | 0.997966i | \(0.479696\pi\) | |||||||
\(444\) | −15.3339 | − | 1.44330i | −0.727714 | − | 0.0684958i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.2769i | 0.533977i | ||||||||
\(447\) | 7.72358 | − | 6.39470i | 0.365313 | − | 0.302459i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | −36.8034 | −1.73686 | −0.868431 | − | 0.495810i | \(-0.834871\pi\) | ||||
−0.868431 | + | 0.495810i | \(0.834871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.320119 | 0.0150738 | ||||||||
\(452\) | 11.8416 | + | 11.8416i | 0.556982 | + | 0.556982i | ||||
\(453\) | −0.436173 | + | 0.361127i | −0.0204932 | + | 0.0169672i | ||||
\(454\) | − | 28.8428i | − | 1.35366i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.98874 | + | 0.940186i | 0.467765 | + | 0.0440283i | ||||
\(457\) | −0.564472 | + | 0.564472i | −0.0264049 | + | 0.0264049i | −0.720186 | − | 0.693781i | \(-0.755944\pi\) |
0.693781 | + | 0.720186i | \(0.255944\pi\) | |||||||
\(458\) | −13.8110 | + | 13.8110i | −0.645346 | + | 0.645346i | ||||
\(459\) | 6.07059 | − | 20.9890i | 0.283351 | − | 0.979683i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.34252i | − | 0.0625275i | −0.999511 | − | 0.0312638i | \(-0.990047\pi\) | ||
0.999511 | − | 0.0312638i | \(-0.00995319\pi\) | |||||||
\(462\) | 0.862243 | + | 1.04143i | 0.0401152 | + | 0.0484515i | ||||
\(463\) | 27.2878 | + | 27.2878i | 1.26817 | + | 1.26817i | 0.947031 | + | 0.321142i | \(0.104067\pi\) |
0.321142 | + | 0.947031i | \(0.395933\pi\) | |||||||
\(464\) | 3.33651 | 0.154893 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.14309 | −0.191925 | ||||||||
\(467\) | −18.9254 | − | 18.9254i | −0.875765 | − | 0.875765i | 0.117328 | − | 0.993093i | \(-0.462567\pi\) |
−0.993093 | + | 0.117328i | \(0.962567\pi\) | |||||||
\(468\) | 9.19894 | + | 13.5126i | 0.425221 | + | 0.624619i | ||||
\(469\) | 7.01420i | 0.323886i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.61310 | − | 38.3863i | 0.166483 | − | 1.76875i | ||||
\(472\) | 8.96281 | − | 8.96281i | 0.412547 | − | 0.412547i | ||||
\(473\) | −0.309911 | + | 0.309911i | −0.0142497 | + | 0.0142497i | ||||
\(474\) | −2.03752 | + | 21.6471i | −0.0935865 | + | 0.994283i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.20489i | − | 0.192731i | ||||||
\(477\) | −18.3738 | − | 26.9898i | −0.841280 | − | 1.23578i | ||||
\(478\) | −8.50951 | − | 8.50951i | −0.389216 | − | 0.389216i | ||||
\(479\) | 15.7320 | 0.718815 | 0.359408 | − | 0.933181i | \(-0.382979\pi\) | ||||
0.359408 | + | 0.933181i | \(0.382979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.4521 | 2.20922 | ||||||||
\(482\) | −4.08688 | − | 4.08688i | −0.186152 | − | 0.186152i | ||||
\(483\) | −2.72869 | − | 3.29574i | −0.124160 | − | 0.149961i | ||||
\(484\) | 10.3907i | 0.472303i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.9035 | − | 7.04924i | −0.630677 | − | 0.319760i | ||||
\(487\) | −1.69131 | + | 1.69131i | −0.0766404 | + | 0.0766404i | −0.744388 | − | 0.667747i | \(-0.767259\pi\) |
0.667747 | + | 0.744388i | \(0.267259\pi\) | |||||||
\(488\) | 6.44337 | − | 6.44337i | 0.291678 | − | 0.291678i | ||||
\(489\) | 0.637837 | + | 0.0600362i | 0.0288440 | + | 0.00271493i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8.25442i | − | 0.372517i | −0.982501 | − | 0.186258i | \(-0.940364\pi\) | ||
0.982501 | − | 0.186258i | \(-0.0596361\pi\) | |||||||
\(492\) | −0.547114 | + | 0.452980i | −0.0246658 | + | 0.0204219i | ||||
\(493\) | 9.92046 | + | 9.92046i | 0.446795 | + | 0.446795i | ||||
\(494\) | −31.5624 | −1.42006 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.20515 | −0.0541127 | ||||||||
\(497\) | 1.33356 | + | 1.33356i | 0.0598182 | + | 0.0598182i | ||||
\(498\) | 6.80360 | − | 5.63301i | 0.304877 | − | 0.252421i | ||||
\(499\) | − | 18.4475i | − | 0.825823i | −0.910771 | − | 0.412912i | \(-0.864512\pi\) | ||
0.910771 | − | 0.412912i | \(-0.135488\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.2615 | − | 1.71885i | −0.815862 | − | 0.0767927i | ||||
\(502\) | −1.06535 | + | 1.06535i | −0.0475489 | + | 0.0475489i | ||||
\(503\) | 6.61830 | − | 6.61830i | 0.295095 | − | 0.295095i | −0.543994 | − | 0.839089i | \(-0.683089\pi\) |
0.839089 | + | 0.543994i | \(0.183089\pi\) | |||||||
\(504\) | −2.94731 | − | 0.559788i | −0.131284 | − | 0.0249350i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.92835i | 0.0857257i | ||||||||
\(507\) | −18.4356 | − | 22.2666i | −0.818752 | − | 0.988896i | ||||
\(508\) | −12.5290 | − | 12.5290i | −0.555887 | − | 0.555887i | ||||
\(509\) | −0.871429 | −0.0386254 | −0.0193127 | − | 0.999813i | \(-0.506148\pi\) | ||||
−0.0193127 | + | 0.999813i | \(0.506148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9997 | 0.530835 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 26.3582 | − | 14.5317i | 1.16375 | − | 0.641592i | ||||
\(514\) | 4.87821i | 0.215169i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0911319 | − | 0.968204i | 0.00401186 | − | 0.0426228i | ||||
\(517\) | −3.51327 | + | 3.51327i | −0.154513 | + | 0.154513i | ||||
\(518\) | −6.28770 | + | 6.28770i | −0.276266 | + | 0.276266i | ||||
\(519\) | −1.94846 | + | 20.7008i | −0.0855278 | + | 0.908666i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.35506i | − | 0.146988i | −0.997296 | − | 0.0734939i | \(-0.976585\pi\) | ||
0.997296 | − | 0.0734939i | \(-0.0234150\pi\) | |||||||
\(522\) | 8.27418 | − | 5.63280i | 0.362151 | − | 0.246541i | ||||
\(523\) | 0.214504 | + | 0.214504i | 0.00937959 | + | 0.00937959i | 0.711781 | − | 0.702401i | \(-0.247889\pi\) |
−0.702401 | + | 0.711781i | \(0.747889\pi\) | |||||||
\(524\) | 11.8873 | 0.519301 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.9357 | 0.607625 | ||||||||
\(527\) | −3.58328 | − | 3.58328i | −0.156090 | − | 0.156090i | ||||
\(528\) | 0.862243 | + | 1.04143i | 0.0375243 | + | 0.0453222i | ||||
\(529\) | 16.8975i | 0.734672i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.09550 | − | 37.3581i | 0.307919 | − | 1.62120i | ||||
\(532\) | 4.09591 | − | 4.09591i | 0.177580 | − | 0.177580i | ||||
\(533\) | 1.58005 | − | 1.58005i | 0.0684396 | − | 0.0684396i | ||||
\(534\) | 32.0480 | + | 3.01651i | 1.38685 | + | 0.130537i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.01420i | 0.302967i | ||||||||
\(537\) | 3.16256 | − | 2.61843i | 0.136475 | − | 0.112994i | ||||
\(538\) | 6.49040 | + | 6.49040i | 0.279821 | + | 0.279821i | ||||
\(539\) | 0.780604 | 0.0336230 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.7416 | 1.62264 | 0.811318 | − | 0.584605i | \(-0.198750\pi\) | ||||
0.811318 | + | 0.584605i | \(0.198750\pi\) | |||||||
\(542\) | 5.55610 | + | 5.55610i | 0.238655 | + | 0.238655i | ||||
\(543\) | 8.20980 | − | 6.79726i | 0.352316 | − | 0.291698i | ||||
\(544\) | − | 4.20489i | − | 0.180283i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.39617 | + | 0.884411i | 0.402119 | + | 0.0378493i | ||||
\(547\) | −13.1372 | + | 13.1372i | −0.561704 | + | 0.561704i | −0.929791 | − | 0.368087i | \(-0.880013\pi\) |
0.368087 | + | 0.929791i | \(0.380013\pi\) | |||||||
\(548\) | 4.34731 | − | 4.34731i | 0.185708 | − | 0.185708i | ||||
\(549\) | 5.10096 | − | 26.8568i | 0.217704 | − | 1.14622i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.3267i | 0.823344i | ||||||||
\(552\) | −2.72869 | − | 3.29574i | −0.116141 | − | 0.140276i | ||||
\(553\) | 8.87644 | + | 8.87644i | 0.377465 | + | 0.377465i | ||||
\(554\) | 4.00063 | 0.169970 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.6395 | 0.493625 | ||||||||
\(557\) | −2.16691 | − | 2.16691i | −0.0918149 | − | 0.0918149i | 0.659708 | − | 0.751522i | \(-0.270680\pi\) |
−0.751522 | + | 0.659708i | \(0.770680\pi\) | |||||||
\(558\) | −2.98864 | + | 2.03457i | −0.126519 | + | 0.0861302i | ||||
\(559\) | 3.05934i | 0.129396i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.532764 | + | 5.66019i | −0.0224933 | + | 0.238973i | ||||
\(562\) | 0.700555 | − | 0.700555i | 0.0295511 | − | 0.0295511i | ||||
\(563\) | −20.7396 | + | 20.7396i | −0.874069 | + | 0.874069i | −0.992913 | − | 0.118844i | \(-0.962081\pi\) |
0.118844 | + | 0.992913i | \(0.462081\pi\) | |||||||
\(564\) | 1.03310 | − | 10.9759i | 0.0435015 | − | 0.462169i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 22.6627i | − | 0.952584i | ||||||
\(567\) | −8.25407 | + | 3.58753i | −0.346638 | + | 0.150662i | ||||
\(568\) | 1.33356 | + | 1.33356i | 0.0559548 | + | 0.0559548i | ||||
\(569\) | 20.8701 | 0.874918 | 0.437459 | − | 0.899238i | \(-0.355879\pi\) | ||||
0.437459 | + | 0.899238i | \(0.355879\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.8812 | 1.45973 | 0.729865 | − | 0.683591i | \(-0.239583\pi\) | ||||
0.729865 | + | 0.683591i | \(0.239583\pi\) | |||||||
\(572\) | −3.00761 | − | 3.00761i | −0.125754 | − | 0.125754i | ||||
\(573\) | −10.6502 | − | 12.8634i | −0.444920 | − | 0.537378i | ||||
\(574\) | 0.410091i | 0.0171169i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.94731 | − | 0.559788i | −0.122805 | − | 0.0233245i | ||||
\(577\) | −33.1884 | + | 33.1884i | −1.38165 | + | 1.38165i | −0.539957 | + | 0.841693i | \(0.681559\pi\) |
−0.841693 | + | 0.539957i | \(0.818441\pi\) | |||||||
\(578\) | 0.481626 | − | 0.481626i | 0.0200330 | − | 0.0200330i | ||||
\(579\) | −16.5275 | − | 1.55565i | −0.686861 | − | 0.0646505i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.09967i | − | 0.211570i | ||||||
\(582\) | 16.6411 | − | 13.7779i | 0.689794 | − | 0.571112i | ||||
\(583\) | 6.00735 | + | 6.00735i | 0.248799 | + | 0.248799i | ||||
\(584\) | 11.9997 | 0.496551 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.463991 | 0.0191673 | ||||||||
\(587\) | −12.2341 | − | 12.2341i | −0.504957 | − | 0.504957i | 0.408017 | − | 0.912974i | \(-0.366220\pi\) |
−0.912974 | + | 0.408017i | \(0.866220\pi\) | |||||||
\(588\) | −1.33413 | + | 1.10458i | −0.0550185 | + | 0.0455523i | ||||
\(589\) | − | 6.98081i | − | 0.287639i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.71205 | + | 0.537645i | 0.234962 | + | 0.0221158i | ||||
\(592\) | −6.28770 | + | 6.28770i | −0.258423 | + | 0.258423i | ||||
\(593\) | −17.2595 | + | 17.2595i | −0.708762 | + | 0.708762i | −0.966275 | − | 0.257513i | \(-0.917097\pi\) |
0.257513 | + | 0.966275i | \(0.417097\pi\) | |||||||
\(594\) | 3.89644 | + | 1.12696i | 0.159873 | + | 0.0462396i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5.78924i | − | 0.237137i | ||||||
\(597\) | −10.9864 | − | 13.2695i | −0.449643 | − | 0.543083i | ||||
\(598\) | 9.51800 | + | 9.51800i | 0.389220 | + | 0.389220i | ||||
\(599\) | 15.9441 | 0.651458 | 0.325729 | − | 0.945463i | \(-0.394390\pi\) | ||||
0.325729 | + | 0.945463i | \(0.394390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.32631 | 0.176474 | 0.0882369 | − | 0.996100i | \(-0.471877\pi\) | ||||
0.0882369 | + | 0.996100i | \(0.471877\pi\) | |||||||
\(602\) | −0.397015 | − | 0.397015i | −0.0161811 | − | 0.0161811i | ||||
\(603\) | 11.8416 | + | 17.3945i | 0.482227 | + | 0.708357i | ||||
\(604\) | 0.326935i | 0.0133028i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.38353 | + | 14.6990i | −0.0562022 | + | 0.597104i | ||||
\(607\) | 11.2179 | − | 11.2179i | 0.455322 | − | 0.455322i | −0.441795 | − | 0.897116i | \(-0.645658\pi\) |
0.897116 | + | 0.441795i | \(0.145658\pi\) | |||||||
\(608\) | 4.09591 | − | 4.09591i | 0.166111 | − | 0.166111i | ||||
\(609\) | 0.541553 | − | 5.75357i | 0.0219448 | − | 0.233146i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.6817i | 1.40307i | ||||||||
\(612\) | −7.09884 | − | 10.4277i | −0.286953 | − | 0.421514i | ||||
\(613\) | 23.2421 | + | 23.2421i | 0.938741 | + | 0.938741i | 0.998229 | − | 0.0594881i | \(-0.0189468\pi\) |
−0.0594881 | + | 0.998229i | \(0.518947\pi\) | |||||||
\(614\) | −7.48687 | −0.302146 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.780604 | 0.0314514 | ||||||||
\(617\) | −18.0762 | − | 18.0762i | −0.727720 | − | 0.727720i | 0.242445 | − | 0.970165i | \(-0.422051\pi\) |
−0.970165 | + | 0.242445i | \(0.922051\pi\) | |||||||
\(618\) | −12.0060 | − | 14.5009i | −0.482951 | − | 0.583312i | ||||
\(619\) | − | 10.0672i | − | 0.404634i | −0.979320 | − | 0.202317i | \(-0.935153\pi\) | ||
0.979320 | − | 0.202317i | \(-0.0648471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.3308 | − | 3.56641i | −0.494819 | − | 0.143115i | ||||
\(622\) | 8.58358 | − | 8.58358i | 0.344170 | − | 0.344170i | ||||
\(623\) | 13.1414 | − | 13.1414i | 0.526498 | − | 0.526498i | ||||
\(624\) | 9.39617 | + | 0.884411i | 0.376148 | + | 0.0354048i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.2824i | 0.690745i | ||||||||
\(627\) | −6.03244 | + | 4.99453i | −0.240913 | + | 0.199462i | ||||
\(628\) | −15.7404 | − | 15.7404i | −0.628111 | − | 0.628111i | ||||
\(629\) | −37.3906 | −1.49086 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7095 | 0.466149 | 0.233075 | − | 0.972459i | \(-0.425121\pi\) | ||||
0.233075 | + | 0.972459i | \(0.425121\pi\) | |||||||
\(632\) | 8.87644 | + | 8.87644i | 0.353086 | + | 0.353086i | ||||
\(633\) | 19.9979 | − | 16.5572i | 0.794845 | − | 0.658088i | ||||
\(634\) | 3.40503i | 0.135231i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.7678 | − | 1.76651i | −0.744190 | − | 0.0700467i | ||||
\(637\) | 3.85292 | − | 3.85292i | 0.152658 | − | 0.152658i | ||||
\(638\) | −1.84165 | + | 1.84165i | −0.0729118 | + | 0.0729118i | ||||
\(639\) | 5.55843 | + | 1.05572i | 0.219888 | + | 0.0417638i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.2227i | 0.680255i | 0.940379 | + | 0.340128i | \(0.110470\pi\) | ||||
−0.940379 | + | 0.340128i | \(0.889530\pi\) | |||||||
\(642\) | −13.3308 | − | 16.1010i | −0.526124 | − | 0.635458i | ||||
\(643\) | 19.6141 | + | 19.6141i | 0.773505 | + | 0.773505i | 0.978717 | − | 0.205213i | \(-0.0657886\pi\) |
−0.205213 | + | 0.978717i | \(0.565789\pi\) | |||||||
\(644\) | −2.47033 | −0.0973447 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.3568 | 0.958305 | ||||||||
\(647\) | 7.71110 | + | 7.71110i | 0.303155 | + | 0.303155i | 0.842247 | − | 0.539092i | \(-0.181233\pi\) |
−0.539092 | + | 0.842247i | \(0.681233\pi\) | |||||||
\(648\) | −8.25407 | + | 3.58753i | −0.324250 | + | 0.140931i | ||||
\(649\) | 9.89441i | 0.388390i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.195609 | + | 2.07819i | −0.00766652 | + | 0.0814508i | ||||
\(652\) | 0.261547 | − | 0.261547i | 0.0102430 | − | 0.0102430i | ||||
\(653\) | −28.8829 | + | 28.8829i | −1.13028 | + | 1.13028i | −0.140145 | + | 0.990131i | \(0.544757\pi\) |
−0.990131 | + | 0.140145i | \(0.955243\pi\) | |||||||
\(654\) | 0.596931 | − | 6.34192i | 0.0233418 | − | 0.247989i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.410091i | 0.0160114i | ||||||||
\(657\) | 29.7580 | − | 20.2583i | 1.16097 | − | 0.790351i | ||||
\(658\) | −4.50070 | − | 4.50070i | −0.175456 | − | 0.175456i | ||||
\(659\) | −46.5136 | −1.81191 | −0.905956 | − | 0.423371i | \(-0.860847\pi\) | ||||
−0.905956 | + | 0.423371i | \(0.860847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.72550 | −0.339383 | −0.169691 | − | 0.985497i | \(-0.554277\pi\) | ||||
−0.169691 | + | 0.985497i | \(0.554277\pi\) | |||||||
\(662\) | 10.8039 | + | 10.8039i | 0.419905 | + | 0.419905i | ||||
\(663\) | 25.3081 | + | 30.5673i | 0.982884 | + | 1.18714i | ||||
\(664\) | − | 5.09967i | − | 0.197905i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.97773 | + | 26.2079i | −0.192883 | + | 1.01554i | ||||
\(667\) | 5.82817 | − | 5.82817i | 0.225668 | − | 0.225668i | ||||
\(668\) | −7.48816 | + | 7.48816i | −0.289726 | + | 0.289726i | ||||
\(669\) | 19.4462 | + | 1.83037i | 0.751835 | + | 0.0707662i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.11310i | 0.274598i | ||||||||
\(672\) | −1.33413 | + | 1.10458i | −0.0514651 | + | 0.0426103i | ||||
\(673\) | −25.1132 | − | 25.1132i | −0.968043 | − | 0.968043i | 0.0314620 | − | 0.999505i | \(-0.489984\pi\) |
−0.999505 | + | 0.0314620i | \(0.989984\pi\) | |||||||
\(674\) | 16.2400 | 0.625541 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.6901 | −0.641925 | ||||||||
\(677\) | 9.97427 | + | 9.97427i | 0.383342 | + | 0.383342i | 0.872305 | − | 0.488962i | \(-0.162624\pi\) |
−0.488962 | + | 0.872305i | \(0.662624\pi\) | |||||||
\(678\) | 22.3420 | − | 18.4980i | 0.858040 | − | 0.710410i | ||||
\(679\) | − | 12.4734i | − | 0.478684i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.7374 | − | 4.68152i | −1.90594 | − | 0.179396i | ||||
\(682\) | 0.665206 | − | 0.665206i | 0.0254721 | − | 0.0254721i | ||||
\(683\) | −1.82278 | + | 1.82278i | −0.0697468 | + | 0.0697468i | −0.741120 | − | 0.671373i | \(-0.765705\pi\) |
0.671373 | + | 0.741120i | \(0.265705\pi\) | |||||||
\(684\) | 3.24257 | − | 17.0723i | 0.123983 | − | 0.652774i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 21.5744 | + | 26.0578i | 0.823115 | + | 0.994166i | ||||
\(688\) | −0.397015 | − | 0.397015i | −0.0151360 | − | 0.0151360i | ||||
\(689\) | 59.3025 | 2.25924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.8515 | −1.02148 | −0.510740 | − | 0.859735i | \(-0.670629\pi\) | ||||
−0.510740 | + | 0.859735i | \(0.670629\pi\) | |||||||
\(692\) | 8.48843 | + | 8.48843i | 0.322682 | + | 0.322682i | ||||
\(693\) | 1.93582 | − | 1.31784i | 0.0735355 | − | 0.0500607i | ||||
\(694\) | 17.1084i | 0.649425i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.541553 | − | 5.75357i | 0.0205275 | − | 0.218088i | ||||
\(697\) | −1.21933 | + | 1.21933i | −0.0461853 | + | 0.0461853i | ||||
\(698\) | 0.0807296 | − | 0.0807296i | 0.00305566 | − | 0.00305566i | ||||
\(699\) | −0.672470 | + | 7.14447i | −0.0254352 | + | 0.270229i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 40.3766i | − | 1.52500i | −0.646987 | − | 0.762501i | \(-0.723971\pi\) | ||
0.646987 | − | 0.762501i | \(-0.276029\pi\) | |||||||
\(702\) | 24.7946 | − | 13.6697i | 0.935811 | − | 0.515929i | ||||
\(703\) | −36.4214 | − | 36.4214i | −1.37366 | − | 1.37366i | ||||
\(704\) | 0.780604 | 0.0294201 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.7399 | −0.931097 | ||||||||
\(707\) | 6.02735 | + | 6.02735i | 0.226682 | + | 0.226682i | ||||
\(708\) | −14.0010 | − | 16.9105i | −0.526188 | − | 0.635535i | ||||
\(709\) | − | 14.0214i | − | 0.526584i | −0.964716 | − | 0.263292i | \(-0.915192\pi\) | ||
0.964716 | − | 0.263292i | \(-0.0848082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.9981 | + | 7.02713i | 1.38754 | + | 0.263538i | ||||
\(712\) | 13.1414 | − | 13.1414i | 0.492494 | − | 0.492494i | ||||
\(713\) | −2.10514 | + | 2.10514i | −0.0788380 | + | 0.0788380i | ||||
\(714\) | −7.25104 | − | 0.682501i | −0.271363 | − | 0.0255420i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 2.37051i | − | 0.0885902i | ||||||
\(717\) | −16.0552 | + | 13.2929i | −0.599594 | + | 0.496431i | ||||
\(718\) | 18.0130 | + | 18.0130i | 0.672240 | + | 0.672240i | ||||
\(719\) | 15.3457 | 0.572299 | 0.286149 | − | 0.958185i | \(-0.407625\pi\) | ||||
0.286149 | + | 0.958185i | \(0.407625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8692 | −0.404791 | ||||||||
\(722\) | 10.2905 | + | 10.2905i | 0.382972 | + | 0.382972i | ||||
\(723\) | −7.71088 | + | 6.38419i | −0.286771 | + | 0.237430i | ||||
\(724\) | − | 6.15369i | − | 0.228700i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.9179 | + | 1.68652i | 0.664997 | + | 0.0625927i | ||||
\(727\) | −37.3012 | + | 37.3012i | −1.38342 | + | 1.38342i | −0.544965 | + | 0.838459i | \(0.683457\pi\) |
−0.838459 | + | 0.544965i | \(0.816543\pi\) | |||||||
\(728\) | 3.85292 | − | 3.85292i | 0.142799 | − | 0.142799i | ||||
\(729\) | −14.4126 | + | 22.8315i | −0.533801 | + | 0.845610i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.36089i | − | 0.0873209i | ||||||
\(732\) | −10.0653 | − | 12.1570i | −0.372024 | − | 0.449334i | ||||
\(733\) | −0.763659 | − | 0.763659i | −0.0282064 | − | 0.0282064i | 0.692863 | − | 0.721069i | \(-0.256349\pi\) |
−0.721069 | + | 0.692863i | \(0.756349\pi\) | |||||||
\(734\) | −33.8832 | −1.25065 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.47033 | −0.0910576 | ||||||||
\(737\) | −3.87163 | − | 3.87163i | −0.142613 | − | 0.142613i | ||||
\(738\) | 0.692329 | + | 1.01698i | 0.0254850 | + | 0.0374356i | ||||
\(739\) | 5.91073i | 0.217430i | 0.994073 | + | 0.108715i | \(0.0346736\pi\) | ||||
−0.994073 | + | 0.108715i | \(0.965326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.12294 | + | 54.4272i | −0.188196 | + | 1.99943i | ||||
\(742\) | −7.69577 | + | 7.69577i | −0.282521 | + | 0.282521i | ||||
\(743\) | 29.0001 | − | 29.0001i | 1.06391 | − | 1.06391i | 0.0660966 | − | 0.997813i | \(-0.478945\pi\) |
0.997813 | − | 0.0660966i | \(-0.0210546\pi\) | |||||||
\(744\) | −0.195609 | + | 2.07819i | −0.00717138 | + | 0.0761902i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.86152i | 0.214605i | ||||||||
\(747\) | −8.60942 | − | 12.6466i | −0.315002 | − | 0.462716i | ||||
\(748\) | 2.32098 | + | 2.32098i | 0.0848633 | + | 0.0848633i | ||||
\(749\) | −12.0686 | −0.440977 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.1470 | 0.990609 | 0.495304 | − | 0.868720i | \(-0.335057\pi\) | ||||
0.495304 | + | 0.868720i | \(0.335057\pi\) | |||||||
\(752\) | −4.50070 | − | 4.50070i | −0.164124 | − | 0.164124i | ||||
\(753\) | 1.66420 | + | 2.01004i | 0.0606468 | + | 0.0732498i | ||||
\(754\) | 18.1802i | 0.662082i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.44370 | + | 4.99157i | −0.0525068 | + | 0.181542i | ||||
\(757\) | 21.7239 | − | 21.7239i | 0.789567 | − | 0.789567i | −0.191856 | − | 0.981423i | \(-0.561451\pi\) |
0.981423 | + | 0.191856i | \(0.0614507\pi\) | |||||||
\(758\) | −9.60165 | + | 9.60165i | −0.348748 | + | 0.348748i | ||||
\(759\) | 3.32531 | + | 0.312993i | 0.120701 | + | 0.0113609i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.8482i | 1.00950i | 0.863267 | + | 0.504748i | \(0.168415\pi\) | ||||
−0.863267 | + | 0.504748i | \(0.831585\pi\) | |||||||
\(762\) | −23.6391 | + | 19.5718i | −0.856353 | + | 0.709013i | ||||
\(763\) | −2.60052 | − | 2.60052i | −0.0941451 | − | 0.0941451i | ||||
\(764\) | −9.64185 | −0.348830 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.6523 | 0.565541 | ||||||||
\(767\) | 48.8371 | + | 48.8371i | 1.76340 | + | 1.76340i | ||||
\(768\) | −1.33413 | + | 1.10458i | −0.0481412 | + | 0.0398582i | ||||
\(769\) | 28.9571i | 1.04422i | 0.852878 | + | 0.522110i | \(0.174855\pi\) | ||||
−0.852878 | + | 0.522110i | \(0.825145\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.41213 | + | 0.791789i | 0.302955 | + | 0.0285156i | ||||
\(772\) | −6.77716 | + | 6.77716i | −0.243915 | + | 0.243915i | ||||
\(773\) | −26.3889 | + | 26.3889i | −0.949144 | + | 0.949144i | −0.998768 | − | 0.0496237i | \(-0.984198\pi\) |
0.0496237 | + | 0.998768i | \(0.484198\pi\) | |||||||
\(774\) | −1.65481 | − | 0.314301i | −0.0594808 | − | 0.0112973i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 12.4734i | − | 0.447768i | ||||||
\(777\) | 9.82213 | + | 11.8633i | 0.352367 | + | 0.425592i | ||||
\(778\) | −20.6295 | − | 20.6295i | −0.739605 | − | 0.739605i | ||||
\(779\) | −2.37545 | −0.0851093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.47217 | −0.0526783 | ||||||||
\(782\) | −7.34506 | − | 7.34506i | −0.262659 | − | 0.262659i | ||||
\(783\) | −8.37037 | − | 15.1825i | −0.299133 | − | 0.542578i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.92945 | − | 20.4989i | 0.0688212 | − | 0.731171i | ||||
\(787\) | 15.9989 | − | 15.9989i | 0.570300 | − | 0.570300i | −0.361912 | − | 0.932212i | \(-0.617876\pi\) |
0.932212 | + | 0.361912i | \(0.117876\pi\) | |||||||
\(788\) | 2.34224 | − | 2.34224i | 0.0834390 | − | 0.0834390i | ||||
\(789\) | 2.26192 | − | 24.0311i | 0.0805264 | − | 0.855530i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 16.7465i | − | 0.595439i | ||||||
\(792\) | 1.93582 | − | 1.31784i | 0.0687862 | − | 0.0468275i | ||||
\(793\) | 35.1090 | + | 35.1090i | 1.24676 | + | 1.24676i | ||||
\(794\) | −14.7097 | −0.522028 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.94617 | −0.352533 | ||||||||
\(797\) | 20.6511 | + | 20.6511i | 0.731499 | + | 0.731499i | 0.970917 | − | 0.239418i | \(-0.0769565\pi\) |
−0.239418 | + | 0.970917i | \(0.576957\pi\) | |||||||
\(798\) | −6.39829 | − | 7.72791i | −0.226497 | − | 0.273565i | ||||
\(799\) | − | 26.7639i | − | 0.946840i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.4035 | − | 54.7749i | 0.367590 | − | 1.93538i | ||||
\(802\) | 2.18135 | − | 2.18135i | 0.0770260 | − | 0.0770260i | ||||
\(803\) | −6.62348 | + | 6.62348i | −0.233737 | + | 0.233737i | ||||
\(804\) | 12.0955 | + | 1.13848i | 0.426575 | + | 0.0401512i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.56668i | − | 0.231301i | ||||||
\(807\) | 12.2457 | − | 10.1388i | 0.431069 | − | 0.356902i | ||||
\(808\) | 6.02735 | + | 6.02735i | 0.212041 | + | 0.212041i | ||||
\(809\) | −15.4725 | −0.543983 | −0.271992 | − | 0.962300i | \(-0.587682\pi\) | ||||
−0.271992 | + | 0.962300i | \(0.587682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4390 | 0.823054 | 0.411527 | − | 0.911398i | \(-0.364996\pi\) | ||||
0.411527 | + | 0.911398i | \(0.364996\pi\) | |||||||
\(812\) | −2.35927 | − | 2.35927i | −0.0827940 | − | 0.0827940i | ||||
\(813\) | 10.4829 | − | 8.67929i | 0.367652 | − | 0.304396i | ||||
\(814\) | − | 6.94125i | − | 0.243291i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.25104 | − | 0.682501i | −0.253837 | − | 0.0238923i | ||||
\(817\) | 2.29970 | − | 2.29970i | 0.0804565 | − | 0.0804565i | ||||
\(818\) | −1.74916 | + | 1.74916i | −0.0611579 | + | 0.0611579i | ||||
\(819\) | 3.05021 | − | 16.0595i | 0.106583 | − | 0.561163i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.9077i | 0.939087i | 0.882909 | + | 0.469543i | \(0.155581\pi\) | ||||
−0.882909 | + | 0.469543i | \(0.844419\pi\) | |||||||
\(822\) | −6.79101 | − | 8.20224i | −0.236864 | − | 0.286086i | ||||
\(823\) | −29.5001 | − | 29.5001i | −1.02831 | − | 1.02831i | −0.999587 | − | 0.0287224i | \(-0.990856\pi\) |
−0.0287224 | − | 0.999587i | \(-0.509144\pi\) | |||||||
\(824\) | −10.8692 | −0.378647 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.6753 | −0.441031 | ||||||||
\(827\) | 14.8938 | + | 14.8938i | 0.517909 | + | 0.517909i | 0.916938 | − | 0.399030i | \(-0.130653\pi\) |
−0.399030 | + | 0.916938i | \(0.630653\pi\) | |||||||
\(828\) | −6.12616 | + | 4.17050i | −0.212899 | + | 0.144935i | ||||
\(829\) | 34.3997i | 1.19475i | 0.801962 | + | 0.597375i | \(0.203790\pi\) | ||||
−0.801962 | + | 0.597375i | \(0.796210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.649347 | − | 6.89880i | 0.0225256 | − | 0.239317i | ||||
\(832\) | 3.85292 | − | 3.85292i | 0.133576 | − | 0.133576i | ||||
\(833\) | −2.97331 | + | 2.97331i | −0.103019 | + | 0.103019i | ||||
\(834\) | 1.88922 | − | 20.0715i | 0.0654184 | − | 0.695019i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.52164i | 0.156384i | ||||||||
\(837\) | 3.02338 | + | 5.48393i | 0.104503 | + | 0.189552i | ||||
\(838\) | 16.6982 | + | 16.6982i | 0.576828 | + | 0.576828i | ||||
\(839\) | −19.6850 | −0.679602 | −0.339801 | − | 0.940497i | \(-0.610360\pi\) | ||||
−0.339801 | + | 0.940497i | \(0.610360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8677 | −0.616128 | ||||||||
\(842\) | 13.8882 | + | 13.8882i | 0.478620 | + | 0.478620i | ||||
\(843\) | −1.09435 | − | 1.32176i | −0.0376914 | − | 0.0455240i | ||||
\(844\) | − | 14.9895i | − | 0.515960i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.7595 | − | 3.56303i | −0.644964 | − | 0.122499i | ||||
\(847\) | 7.34730 | − | 7.34730i | 0.252456 | − | 0.252456i | ||||
\(848\) | −7.69577 | + | 7.69577i | −0.264274 | + | 0.264274i | ||||
\(849\) | −39.0802 | − | 3.67841i | −1.34123 | − | 0.126243i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.9666i | 0.753004i | ||||||||
\(852\) | 2.51607 | − | 2.08317i | 0.0861993 | − | 0.0713683i | ||||
\(853\) | −0.519079 | − | 0.519079i | −0.0177729 | − | 0.0177729i | 0.698164 | − | 0.715937i | \(-0.254000\pi\) |
−0.715937 | + | 0.698164i | \(0.754000\pi\) | |||||||
\(854\) | −9.11230 | −0.311816 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0686 | −0.412496 | ||||||||
\(857\) | −3.46899 | − | 3.46899i | −0.118498 | − | 0.118498i | 0.645371 | − | 0.763869i | \(-0.276703\pi\) |
−0.763869 | + | 0.645371i | \(0.776703\pi\) | |||||||
\(858\) | −5.67458 | + | 4.69824i | −0.193727 | + | 0.160395i | ||||
\(859\) | 30.0887i | 1.02661i | 0.858205 | + | 0.513307i | \(0.171580\pi\) | ||||
−0.858205 | + | 0.513307i | \(0.828420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.707173 | + | 0.0665624i | 0.0241004 | + | 0.00226844i | ||||
\(862\) | −20.4613 | + | 20.4613i | −0.696915 | + | 0.696915i | ||||
\(863\) | 10.2849 | − | 10.2849i | 0.350102 | − | 0.350102i | −0.510046 | − | 0.860147i | \(-0.670372\pi\) |
0.860147 | + | 0.510046i | \(0.170372\pi\) | |||||||
\(864\) | −1.44370 | + | 4.99157i | −0.0491156 | + | 0.169817i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.5704i | 0.868918i | ||||||||
\(867\) | −0.752356 | − | 0.908703i | −0.0255514 | − | 0.0308612i | ||||
\(868\) | 0.852168 | + | 0.852168i | 0.0289245 | + | 0.0289245i | ||||
\(869\) | −9.79907 | −0.332411 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.2194 | −1.29501 | ||||||||
\(872\) | −2.60052 | − | 2.60052i | −0.0880647 | − | 0.0880647i | ||||
\(873\) | −21.0580 | − | 30.9326i | −0.712704 | − | 1.04691i | ||||
\(874\) | − | 14.3094i | − | 0.484022i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.94769 | − | 20.6926i | 0.0658062 | − | 0.699139i | ||||
\(877\) | −25.3250 | + | 25.3250i | −0.855164 | + | 0.855164i | −0.990764 | − | 0.135600i | \(-0.956704\pi\) |
0.135600 | + | 0.990764i | \(0.456704\pi\) | |||||||
\(878\) | −8.83119 | + | 8.83119i | −0.298038 | + | 0.298038i | ||||
\(879\) | 0.0753109 | − | 0.800119i | 0.00254017 | − | 0.0269873i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9.27692i | − | 0.312547i | −0.987714 | − | 0.156274i | \(-0.950052\pi\) | ||
0.987714 | − | 0.156274i | \(-0.0499482\pi\) | |||||||
\(882\) | 1.68823 | + | 2.47989i | 0.0568458 | + | 0.0835023i | ||||
\(883\) | −13.4381 | − | 13.4381i | −0.452228 | − | 0.452228i | 0.443866 | − | 0.896093i | \(-0.353607\pi\) |
−0.896093 | + | 0.443866i | \(0.853607\pi\) | |||||||
\(884\) | 22.9119 | 0.770609 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.8079 | 0.934224 | ||||||||
\(887\) | 39.1904 | + | 39.1904i | 1.31589 | + | 1.31589i | 0.917001 | + | 0.398885i | \(0.130603\pi\) |
0.398885 | + | 0.917001i | \(0.369397\pi\) | |||||||
\(888\) | 9.82213 | + | 11.8633i | 0.329609 | + | 0.398105i | ||||
\(889\) | 17.7188i | 0.594268i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.57579 | − | 6.53621i | 0.0862923 | − | 0.218971i | ||||
\(892\) | 7.97398 | − | 7.97398i | 0.266989 | − | 0.266989i | ||||
\(893\) | 26.0703 | − | 26.0703i | 0.872408 | − | 0.872408i | ||||
\(894\) | −9.98313 | − | 0.939659i | −0.333886 | − | 0.0314269i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 17.9580 | − | 14.8682i | 0.599600 | − | 0.496436i | ||||
\(898\) | 26.0240 | + | 26.0240i | 0.868431 | + | 0.868431i | ||||
\(899\) | −4.02098 | −0.134107 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.7638 | −1.52461 | ||||||||
\(902\) | −0.226358 | − | 0.226358i | −0.00753691 | − | 0.00753691i | ||||
\(903\) | −0.749064 | + | 0.620184i | −0.0249273 | + | 0.0206384i | ||||
\(904\) | − | 16.7465i | − | 0.556982i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.563776 | + | 0.0530653i | 0.0187302 | + | 0.00176297i | ||||
\(907\) | 23.8197 | − | 23.8197i | 0.790921 | − | 0.790921i | −0.190723 | − | 0.981644i | \(-0.561083\pi\) |
0.981644 | + | 0.190723i | \(0.0610831\pi\) | |||||||
\(908\) | −20.3950 | + | 20.3950i | −0.676831 | + | 0.676831i | ||||
\(909\) | 25.1227 | + | 4.77161i | 0.833269 | + | 0.158264i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.6041i | 1.44467i | 0.691544 | + | 0.722335i | \(0.256931\pi\) | ||||
−0.691544 | + | 0.722335i | \(0.743069\pi\) | |||||||
\(912\) | −6.39829 | − | 7.72791i | −0.211869 | − | 0.255897i | ||||
\(913\) | 2.81487 | + | 2.81487i | 0.0931585 | + | 0.0931585i | ||||
\(914\) | 0.798284 | 0.0264049 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.5317 | 0.645346 | ||||||||
\(917\) | −8.40562 | − | 8.40562i | −0.277578 | − | 0.277578i | ||||
\(918\) | −19.1340 | + | 10.5489i | −0.631517 | + | 0.348166i | ||||
\(919\) | 1.67169i | 0.0551439i | 0.999620 | + | 0.0275720i | \(0.00877754\pi\) | ||||
−0.999620 | + | 0.0275720i | \(0.991222\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.21520 | + | 12.9106i | −0.0400423 | + | 0.425418i | ||||
\(922\) | −0.949307 | + | 0.949307i | −0.0312638 | + | 0.0312638i | ||||
\(923\) | −7.26636 | + | 7.26636i | −0.239175 | + | 0.239175i | ||||
\(924\) | 0.126701 | − | 1.34610i | 0.00416815 | − | 0.0442833i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 38.5908i | − | 1.26817i | ||||||
\(927\) | −26.9545 | + | 18.3498i | −0.885302 | + | 0.602686i | ||||
\(928\) | −2.35927 | − | 2.35927i | −0.0774467 | − | 0.0774467i | ||||
\(929\) | 35.1462 | 1.15311 | 0.576554 | − | 0.817059i | \(-0.304397\pi\) | ||||
0.576554 | + | 0.817059i | \(0.304397\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.79249 | −0.189841 | ||||||||
\(932\) | 2.92961 | + | 2.92961i | 0.0959625 | + | 0.0959625i | ||||
\(933\) | −13.4086 | − | 16.1950i | −0.438976 | − | 0.530200i | ||||
\(934\) | 26.7646i | 0.875765i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.05021 | − | 16.0595i | 0.0996992 | − | 0.524920i | ||||
\(937\) | −15.8397 | + | 15.8397i | −0.517459 | + | 0.517459i | −0.916802 | − | 0.399342i | \(-0.869238\pi\) |
0.399342 | + | 0.916802i | \(0.369238\pi\) | |||||||
\(938\) | 4.95979 | − | 4.95979i | 0.161943 | − | 0.161943i | ||||
\(939\) | 29.8023 | + | 2.80513i | 0.972562 | + | 0.0915421i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.3284i | 0.467093i | 0.972346 | + | 0.233546i | \(0.0750331\pi\) | ||||
−0.972346 | + | 0.233546i | \(0.924967\pi\) | |||||||
\(942\) | −29.6981 | + | 24.5884i | −0.967615 | + | 0.801133i | ||||
\(943\) | 0.716343 | + | 0.716343i | 0.0233273 | + | 0.0233273i | ||||
\(944\) | −12.6753 | −0.412547 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.438281 | 0.0142497 | ||||||||
\(947\) | −19.8875 | − | 19.8875i | −0.646255 | − | 0.646255i | 0.305831 | − | 0.952086i | \(-0.401066\pi\) |
−0.952086 | + | 0.305831i | \(0.901066\pi\) | |||||||
\(948\) | 16.7475 | − | 13.8660i | 0.543935 | − | 0.450348i | ||||
\(949\) | 65.3846i | 2.12247i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.87173 | + | 0.552675i | 0.190404 | + | 0.0179217i | ||||
\(952\) | −2.97331 | + | 2.97331i | −0.0963655 | + | 0.0963655i | ||||
\(953\) | −0.913118 | + | 0.913118i | −0.0295788 | + | 0.0295788i | −0.721742 | − | 0.692163i | \(-0.756658\pi\) |
0.692163 | + | 0.721742i | \(0.256658\pi\) | |||||||
\(954\) | −6.09244 | + | 32.0770i | −0.197250 | + | 1.03853i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.0343i | 0.389216i | ||||||||
\(957\) | 2.87688 | + | 3.47472i | 0.0929963 | + | 0.112322i | ||||
\(958\) | −11.1242 | − | 11.1242i | −0.359408 | − | 0.359408i | ||||
\(959\) | −6.14802 | −0.198530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5476 | −0.953149 | ||||||||
\(962\) | −34.2608 | − | 34.2608i | −1.10461 | − | 1.10461i | ||||
\(963\) | −29.9288 | + | 20.3746i | −0.964444 | + | 0.656563i | ||||
\(964\) | 5.77972i | 0.186152i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.400963 | + | 4.25991i | −0.0129008 | + | 0.137060i | ||||
\(967\) | 8.20069 | − | 8.20069i | 0.263716 | − | 0.263716i | −0.562846 | − | 0.826562i | \(-0.690293\pi\) |
0.826562 | + | 0.562846i | \(0.190293\pi\) | |||||||
\(968\) | 7.34730 | − | 7.34730i | 0.236151 | − | 0.236151i | ||||
\(969\) | 3.95338 | − | 42.0016i | 0.127001 | − | 1.34928i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.9665i | − | 0.801214i | −0.916250 | − | 0.400607i | \(-0.868799\pi\) | ||
0.916250 | − | 0.400607i | \(-0.131201\pi\) | |||||||
\(972\) | 4.84671 | + | 14.8158i | 0.155458 | + | 0.475219i | ||||
\(973\) | −8.23037 | − | 8.23037i | −0.263854 | − | 0.263854i | ||||
\(974\) | 2.39187 | 0.0766404 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.11230 | −0.291678 | ||||||||
\(977\) | −5.79833 | − | 5.79833i | −0.185505 | − | 0.185505i | 0.608245 | − | 0.793750i | \(-0.291874\pi\) |
−0.793750 | + | 0.608245i | \(0.791874\pi\) | |||||||
\(978\) | −0.408567 | − | 0.493471i | −0.0130645 | − | 0.0157795i | ||||
\(979\) | 14.5073i | 0.463656i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.8393 | − | 2.05873i | −0.346072 | − | 0.0657301i | ||||
\(982\) | −5.83675 | + | 5.83675i | −0.186258 | + | 0.186258i | ||||
\(983\) | −6.34808 | + | 6.34808i | −0.202472 | + | 0.202472i | −0.801058 | − | 0.598586i | \(-0.795729\pi\) |
0.598586 | + | 0.801058i | \(0.295729\pi\) | |||||||
\(984\) | 0.707173 | + | 0.0665624i | 0.0225439 | + | 0.00212193i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 14.0297i | − | 0.446795i | ||||||
\(987\) | −8.49165 | + | 7.03062i | −0.270292 | + | 0.223787i | ||||
\(988\) | 22.3180 | + | 22.3180i | 0.710031 | + | 0.710031i | ||||
\(989\) | −1.38700 | −0.0441041 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.4308 | −1.95141 | −0.975707 | − | 0.219080i | \(-0.929694\pi\) | ||||
−0.975707 | + | 0.219080i | \(0.929694\pi\) | |||||||
\(992\) | 0.852168 | + | 0.852168i | 0.0270564 | + | 0.0270564i | ||||
\(993\) | 20.3841 | − | 16.8769i | 0.646871 | − | 0.535574i | ||||
\(994\) | − | 1.88593i | − | 0.0598182i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.79401 | − | 0.827733i | −0.278649 | − | 0.0262277i | ||||
\(997\) | 16.8640 | − | 16.8640i | 0.534088 | − | 0.534088i | −0.387698 | − | 0.921786i | \(-0.626730\pi\) |
0.921786 | + | 0.387698i | \(0.126730\pi\) | |||||||
\(998\) | −13.0443 | + | 13.0443i | −0.412912 | + | 0.412912i | ||||
\(999\) | 44.3858 | + | 12.8376i | 1.40430 | + | 0.406163i |
(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 | 1050.2.j.c.743.1 | 12 | ||
3.2 | odd | 2 | 1050.2.j.d.743.6 | 12 | |||
5.2 | odd | 4 | 1050.2.j.d.407.6 | 12 | |||
5.3 | odd | 4 | 210.2.j.b.197.1 | yes | 12 | ||
5.4 | even | 2 | 210.2.j.a.113.6 | ✓ | 12 | ||
15.2 | even | 4 | inner | 1050.2.j.c.407.1 | 12 | ||
15.8 | even | 4 | 210.2.j.a.197.6 | yes | 12 | ||
15.14 | odd | 2 | 210.2.j.b.113.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.j.a.113.6 | ✓ | 12 | 5.4 | even | 2 | ||
210.2.j.a.197.6 | yes | 12 | 15.8 | even | 4 | ||
210.2.j.b.113.1 | yes | 12 | 15.14 | odd | 2 | ||
210.2.j.b.197.1 | yes | 12 | 5.3 | odd | 4 | ||
1050.2.j.c.407.1 | 12 | 15.2 | even | 4 | inner | ||
1050.2.j.c.743.1 | 12 | 1.1 | even | 1 | trivial | ||
1050.2.j.d.407.6 | 12 | 5.2 | odd | 4 | |||
1050.2.j.d.743.6 | 12 | 3.2 | odd | 2 |