Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
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.bc (of order \(12\), degree \(4\), 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: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 607.4 | ||
Root | \(-1.09227 + 0.838128i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.607 |
Dual form | 1050.2.bc.h.493.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | 0.258819 | − | 0.965926i | 0.149429 | − | 0.557678i | ||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 2.64131 | − | 0.153213i | 0.998322 | − | 0.0579090i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.27722 | + | 3.94427i | 0.686609 | + | 1.18924i | 0.972928 | + | 0.231107i | \(0.0742348\pi\) |
−0.286319 | + | 0.958134i | \(0.592432\pi\) | |||||||
\(12\) | −0.258819 | − | 0.965926i | −0.0747146 | − | 0.278839i | ||||
\(13\) | 1.77772 | + | 1.77772i | 0.493051 | + | 0.493051i | 0.909266 | − | 0.416215i | \(-0.136644\pi\) |
−0.416215 | + | 0.909266i | \(0.636644\pi\) | |||||||
\(14\) | 2.51166 | − | 0.831614i | 0.671268 | − | 0.222258i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 3.98386 | + | 1.06747i | 0.966228 | + | 0.258900i | 0.707234 | − | 0.706979i | \(-0.249943\pi\) |
0.258993 | + | 0.965879i | \(0.416609\pi\) | |||||||
\(18\) | −0.965926 | − | 0.258819i | −0.227671 | − | 0.0610042i | ||||
\(19\) | −1.88956 | + | 3.27281i | −0.433494 | + | 0.750834i | −0.997171 | − | 0.0751610i | \(-0.976053\pi\) |
0.563677 | + | 0.825995i | \(0.309386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.535629 | − | 2.59097i | 0.116884 | − | 0.565395i | ||||
\(22\) | 3.22048 | + | 3.22048i | 0.686609 | + | 0.686609i | ||||
\(23\) | −2.08426 | − | 7.77857i | −0.434599 | − | 1.62194i | −0.742025 | − | 0.670372i | \(-0.766134\pi\) |
0.307426 | − | 0.951572i | \(-0.400532\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.17725 | + | 1.25704i | 0.426995 | + | 0.246525i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.21084 | − | 1.45334i | 0.417809 | − | 0.274656i | ||||
\(29\) | 1.55563i | 0.288873i | 0.989514 | + | 0.144436i | \(0.0461369\pi\) | ||||
−0.989514 | + | 0.144436i | \(0.953863\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.37208 | − | 1.94687i | 0.605643 | − | 0.349668i | −0.165615 | − | 0.986190i | \(-0.552961\pi\) |
0.771258 | + | 0.636522i | \(0.219628\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | 4.39926 | − | 1.17878i | 0.765813 | − | 0.205199i | ||||
\(34\) | 4.12440 | 0.707328 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −11.0461 | + | 2.95980i | −1.81597 | + | 0.486589i | −0.996277 | − | 0.0862078i | \(-0.972525\pi\) |
−0.819697 | + | 0.572797i | \(0.805858\pi\) | |||||||
\(38\) | −0.978107 | + | 3.65035i | −0.158670 | + | 0.592164i | ||||
\(39\) | 2.17725 | − | 1.25704i | 0.348640 | − | 0.201287i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.3796i | − | 1.77720i | −0.458682 | − | 0.888600i | \(-0.651678\pi\) | ||
0.458682 | − | 0.888600i | \(-0.348322\pi\) | |||||||
\(42\) | −0.153213 | − | 2.64131i | −0.0236412 | − | 0.407563i | ||||
\(43\) | −0.367260 | + | 0.367260i | −0.0560066 | + | 0.0560066i | −0.734555 | − | 0.678549i | \(-0.762609\pi\) |
0.678549 | + | 0.734555i | \(0.262609\pi\) | |||||||
\(44\) | 3.94427 | + | 2.27722i | 0.594621 | + | 0.343304i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.02648 | − | 6.97408i | −0.593673 | − | 1.02827i | ||||
\(47\) | −1.30713 | − | 4.87829i | −0.190665 | − | 0.711572i | −0.993347 | − | 0.115164i | \(-0.963261\pi\) |
0.802681 | − | 0.596408i | \(-0.203406\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 6.95305 | − | 0.809365i | 0.993293 | − | 0.115624i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.06220 | − | 3.57183i | 0.288765 | − | 0.500156i | ||||
\(52\) | 2.42841 | + | 0.650691i | 0.336760 | + | 0.0902346i | ||||
\(53\) | −8.14732 | − | 2.18307i | −1.11912 | − | 0.299868i | −0.348593 | − | 0.937274i | \(-0.613341\pi\) |
−0.770528 | + | 0.637407i | \(0.780007\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.75935 | − | 1.97603i | 0.235103 | − | 0.264058i | ||||
\(57\) | 2.67224 | + | 2.67224i | 0.353947 | + | 0.353947i | ||||
\(58\) | 0.402626 | + | 1.50262i | 0.0528674 | + | 0.197304i | ||||
\(59\) | 0.221511 | + | 0.383668i | 0.0288383 | + | 0.0499493i | 0.880084 | − | 0.474817i | \(-0.157486\pi\) |
−0.851246 | + | 0.524767i | \(0.824153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.09442 | + | 4.09597i | 0.908348 | + | 0.524435i | 0.879899 | − | 0.475160i | \(-0.157610\pi\) |
0.0284488 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(62\) | 2.75329 | − | 2.75329i | 0.349668 | − | 0.349668i | ||||
\(63\) | −2.36405 | − | 1.18797i | −0.297842 | − | 0.149670i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.94427 | − | 2.27722i | 0.485506 | − | 0.280307i | ||||
\(67\) | −2.41103 | + | 8.99808i | −0.294554 | + | 1.09929i | 0.647017 | + | 0.762476i | \(0.276016\pi\) |
−0.941571 | + | 0.336815i | \(0.890650\pi\) | |||||||
\(68\) | 3.98386 | − | 1.06747i | 0.483114 | − | 0.129450i | ||||
\(69\) | −8.05297 | −0.969464 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.68403 | −0.793248 | −0.396624 | − | 0.917981i | \(-0.629818\pi\) | ||||
−0.396624 | + | 0.917981i | \(0.629818\pi\) | |||||||
\(72\) | −0.965926 | + | 0.258819i | −0.113835 | + | 0.0305021i | ||||
\(73\) | 1.12560 | − | 4.20080i | 0.131742 | − | 0.491666i | −0.868249 | − | 0.496130i | \(-0.834754\pi\) |
0.999990 | + | 0.00446349i | \(0.00142078\pi\) | |||||||
\(74\) | −9.90370 | + | 5.71790i | −1.15128 | + | 0.664693i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.77912i | 0.433494i | ||||||||
\(77\) | 6.61917 | + | 10.0691i | 0.754324 | + | 1.14748i | ||||
\(78\) | 1.77772 | − | 1.77772i | 0.201287 | − | 0.201287i | ||||
\(79\) | 4.08283 | + | 2.35722i | 0.459354 | + | 0.265208i | 0.711773 | − | 0.702410i | \(-0.247893\pi\) |
−0.252418 | + | 0.967618i | \(0.581226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.94527 | − | 10.9919i | −0.325250 | − | 1.21385i | ||||
\(83\) | −3.21718 | − | 3.21718i | −0.353131 | − | 0.353131i | 0.508142 | − | 0.861273i | \(-0.330332\pi\) |
−0.861273 | + | 0.508142i | \(0.830332\pi\) | |||||||
\(84\) | −0.831614 | − | 2.51166i | −0.0907365 | − | 0.274044i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.259692 | + | 0.449799i | −0.0280033 | + | 0.0485031i | ||||
\(87\) | 1.50262 | + | 0.402626i | 0.161098 | + | 0.0431660i | ||||
\(88\) | 4.39926 | + | 1.17878i | 0.468963 | + | 0.125658i | ||||
\(89\) | −3.02425 | + | 5.23816i | −0.320570 | + | 0.555244i | −0.980606 | − | 0.195990i | \(-0.937208\pi\) |
0.660035 | + | 0.751234i | \(0.270541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.96788 | + | 4.42314i | 0.520775 | + | 0.463671i | ||||
\(92\) | −5.69431 | − | 5.69431i | −0.593673 | − | 0.593673i | ||||
\(93\) | −1.00777 | − | 3.76106i | −0.104501 | − | 0.390004i | ||||
\(94\) | −2.52519 | − | 4.37376i | −0.260453 | − | 0.451118i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.866025 | − | 0.500000i | −0.0883883 | − | 0.0510310i | ||||
\(97\) | 0.462652 | − | 0.462652i | 0.0469752 | − | 0.0469752i | −0.683229 | − | 0.730204i | \(-0.739425\pi\) |
0.730204 | + | 0.683229i | \(0.239425\pi\) | |||||||
\(98\) | 6.50665 | − | 2.58137i | 0.657271 | − | 0.260758i | ||||
\(99\) | − | 4.55445i | − | 0.457739i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.85151 | + | 2.80102i | −0.482743 | + | 0.278712i | −0.721559 | − | 0.692353i | \(-0.756574\pi\) |
0.238816 | + | 0.971065i | \(0.423241\pi\) | |||||||
\(102\) | 1.06747 | − | 3.98386i | 0.105695 | − | 0.394461i | ||||
\(103\) | 5.36863 | − | 1.43852i | 0.528987 | − | 0.141742i | 0.0155666 | − | 0.999879i | \(-0.495045\pi\) |
0.513420 | + | 0.858137i | \(0.328378\pi\) | |||||||
\(104\) | 2.51408 | 0.246525 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.43473 | −0.819253 | ||||||||
\(107\) | 7.23514 | − | 1.93865i | 0.699447 | − | 0.187416i | 0.108464 | − | 0.994100i | \(-0.465407\pi\) |
0.590983 | + | 0.806684i | \(0.298740\pi\) | |||||||
\(108\) | −0.258819 | + | 0.965926i | −0.0249049 | + | 0.0929463i | ||||
\(109\) | −1.27034 | + | 0.733433i | −0.121677 | + | 0.0702501i | −0.559603 | − | 0.828761i | \(-0.689046\pi\) |
0.437926 | + | 0.899011i | \(0.355713\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.4358i | 1.08544i | ||||||||
\(112\) | 1.18797 | − | 2.36405i | 0.112253 | − | 0.223382i | ||||
\(113\) | −7.08834 | + | 7.08834i | −0.666815 | + | 0.666815i | −0.956977 | − | 0.290163i | \(-0.906291\pi\) |
0.290163 | + | 0.956977i | \(0.406291\pi\) | |||||||
\(114\) | 3.27281 | + | 1.88956i | 0.306527 | + | 0.176973i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.777814 | + | 1.34721i | 0.0722182 | + | 0.125086i | ||||
\(117\) | −0.650691 | − | 2.42841i | −0.0601564 | − | 0.224507i | ||||
\(118\) | 0.313264 | + | 0.313264i | 0.0288383 | + | 0.0288383i | ||||
\(119\) | 10.6862 | + | 2.20915i | 0.979599 | + | 0.202512i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.87150 | + | 8.43768i | −0.442863 | + | 0.767062i | ||||
\(122\) | 7.91280 | + | 2.12023i | 0.716391 | + | 0.191957i | ||||
\(123\) | −10.9919 | − | 2.94527i | −0.991105 | − | 0.265566i | ||||
\(124\) | 1.94687 | − | 3.37208i | 0.174834 | − | 0.302821i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.59097 | − | 0.535629i | −0.230822 | − | 0.0477177i | ||||
\(127\) | −12.9176 | − | 12.9176i | −1.14625 | − | 1.14625i | −0.987283 | − | 0.158971i | \(-0.949182\pi\) |
−0.158971 | − | 0.987283i | \(-0.550818\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | 0.259692 | + | 0.449799i | 0.0228646 | + | 0.0396026i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.323655 | + | 0.186862i | 0.0282779 | + | 0.0163262i | 0.514072 | − | 0.857747i | \(-0.328136\pi\) |
−0.485794 | + | 0.874073i | \(0.661470\pi\) | |||||||
\(132\) | 3.22048 | − | 3.22048i | 0.280307 | − | 0.280307i | ||||
\(133\) | −4.48947 | + | 8.93402i | −0.389287 | + | 0.774677i | ||||
\(134\) | 9.31550i | 0.804737i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.57183 | − | 2.06220i | 0.306282 | − | 0.176832i | ||||
\(137\) | 0.688094 | − | 2.56800i | 0.0587878 | − | 0.219399i | −0.930282 | − | 0.366844i | \(-0.880438\pi\) |
0.989070 | + | 0.147445i | \(0.0471049\pi\) | |||||||
\(138\) | −7.77857 | + | 2.08426i | −0.662156 | + | 0.177424i | ||||
\(139\) | −4.58070 | −0.388530 | −0.194265 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194265 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.05038 | −0.425319 | ||||||||
\(142\) | −6.45627 | + | 1.72995i | −0.541798 | + | 0.145174i | ||||
\(143\) | −2.96354 | + | 11.0601i | −0.247823 | + | 0.924889i | ||||
\(144\) | −0.866025 | + | 0.500000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 4.34898i | − | 0.359925i | ||||||
\(147\) | 1.01780 | − | 6.92561i | 0.0839463 | − | 0.571215i | ||||
\(148\) | −8.08634 | + | 8.08634i | −0.664693 | + | 0.664693i | ||||
\(149\) | −14.9338 | − | 8.62203i | −1.22342 | − | 0.706344i | −0.257778 | − | 0.966204i | \(-0.582990\pi\) |
−0.965646 | + | 0.259860i | \(0.916324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.78385 | + | 4.82177i | 0.226546 | + | 0.392390i | 0.956782 | − | 0.290805i | \(-0.0939231\pi\) |
−0.730236 | + | 0.683195i | \(0.760590\pi\) | |||||||
\(152\) | 0.978107 | + | 3.65035i | 0.0793350 | + | 0.296082i | ||||
\(153\) | −2.91639 | − | 2.91639i | −0.235776 | − | 0.235776i | ||||
\(154\) | 8.99971 | + | 8.01287i | 0.725217 | + | 0.645696i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.25704 | − | 2.17725i | 0.100644 | − | 0.174320i | ||||
\(157\) | 3.99014 | + | 1.06916i | 0.318448 | + | 0.0853279i | 0.414503 | − | 0.910048i | \(-0.363956\pi\) |
−0.0960544 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(158\) | 4.55381 | + | 1.22019i | 0.362281 | + | 0.0970730i | ||||
\(159\) | −4.21737 | + | 7.30469i | −0.334459 | + | 0.579300i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.69696 | − | 20.2263i | −0.527795 | − | 1.59406i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 5.62644 | + | 20.9982i | 0.440697 | + | 1.64470i | 0.727054 | + | 0.686580i | \(0.240889\pi\) |
−0.286357 | + | 0.958123i | \(0.592444\pi\) | |||||||
\(164\) | −5.68982 | − | 9.85506i | −0.444300 | − | 0.769551i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.94022 | − | 2.27489i | −0.305821 | − | 0.176566i | ||||
\(167\) | −17.4949 | + | 17.4949i | −1.35380 | + | 1.35380i | −0.472425 | + | 0.881371i | \(0.656621\pi\) |
−0.881371 | + | 0.472425i | \(0.843379\pi\) | |||||||
\(168\) | −1.45334 | − | 2.21084i | −0.112128 | − | 0.170570i | ||||
\(169\) | − | 6.67942i | − | 0.513802i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.27281 | − | 1.88956i | 0.250278 | − | 0.144498i | ||||
\(172\) | −0.134426 | + | 0.501686i | −0.0102499 | + | 0.0382532i | ||||
\(173\) | 16.0017 | − | 4.28763i | 1.21658 | − | 0.325982i | 0.407241 | − | 0.913321i | \(-0.366491\pi\) |
0.809342 | + | 0.587338i | \(0.199824\pi\) | |||||||
\(174\) | 1.55563 | 0.117932 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.55445 | 0.343304 | ||||||||
\(177\) | 0.427926 | − | 0.114663i | 0.0321649 | − | 0.00861856i | ||||
\(178\) | −1.56547 | + | 5.84241i | −0.117337 | + | 0.437907i | ||||
\(179\) | 11.0222 | − | 6.36367i | 0.823837 | − | 0.475643i | −0.0279007 | − | 0.999611i | \(-0.508882\pi\) |
0.851738 | + | 0.523968i | \(0.175549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.09951i | 0.676361i | 0.941081 | + | 0.338180i | \(0.109811\pi\) | ||||
−0.941081 | + | 0.338180i | \(0.890189\pi\) | |||||||
\(182\) | 5.94340 | + | 2.98665i | 0.440554 | + | 0.221385i | ||||
\(183\) | 5.79257 | − | 5.79257i | 0.428199 | − | 0.428199i | ||||
\(184\) | −6.97408 | − | 4.02648i | −0.514136 | − | 0.296836i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.94687 | − | 3.37208i | −0.142751 | − | 0.247253i | ||||
\(187\) | 4.86175 | + | 18.1443i | 0.355526 | + | 1.32684i | ||||
\(188\) | −3.57116 | − | 3.57116i | −0.260453 | − | 0.260453i | ||||
\(189\) | −1.75935 | + | 1.97603i | −0.127974 | + | 0.143735i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.10308 | + | 15.7670i | −0.658676 | + | 1.14086i | 0.322283 | + | 0.946643i | \(0.395550\pi\) |
−0.980959 | + | 0.194216i | \(0.937784\pi\) | |||||||
\(192\) | −0.965926 | − | 0.258819i | −0.0697097 | − | 0.0186787i | ||||
\(193\) | −9.72810 | − | 2.60664i | −0.700244 | − | 0.187630i | −0.108904 | − | 0.994052i | \(-0.534734\pi\) |
−0.591340 | + | 0.806422i | \(0.701401\pi\) | |||||||
\(194\) | 0.327144 | − | 0.566631i | 0.0234876 | − | 0.0406817i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.61684 | − | 4.17746i | 0.401203 | − | 0.298390i | ||||
\(197\) | −16.2439 | − | 16.2439i | −1.15733 | − | 1.15733i | −0.985048 | − | 0.172283i | \(-0.944886\pi\) |
−0.172283 | − | 0.985048i | \(-0.555114\pi\) | |||||||
\(198\) | −1.17878 | − | 4.39926i | −0.0837721 | − | 0.312642i | ||||
\(199\) | 12.6984 | + | 21.9943i | 0.900168 | + | 1.55914i | 0.827275 | + | 0.561797i | \(0.189890\pi\) |
0.0728933 | + | 0.997340i | \(0.476777\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.06746 | + | 4.65775i | 0.569035 | + | 0.328532i | ||||
\(202\) | −3.96124 | + | 3.96124i | −0.278712 | + | 0.278712i | ||||
\(203\) | 0.238342 | + | 4.10890i | 0.0167283 | + | 0.288388i | ||||
\(204\) | − | 4.12440i | − | 0.288765i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.81338 | − | 2.77901i | 0.335364 | − | 0.193623i | ||||
\(207\) | −2.08426 | + | 7.77857i | −0.144866 | + | 0.540648i | ||||
\(208\) | 2.42841 | − | 0.650691i | 0.168380 | − | 0.0451173i | ||||
\(209\) | −17.2118 | −1.19056 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6182 | −0.937517 | −0.468759 | − | 0.883326i | \(-0.655299\pi\) | ||||
−0.468759 | + | 0.883326i | \(0.655299\pi\) | |||||||
\(212\) | −8.14732 | + | 2.18307i | −0.559560 | + | 0.149934i | ||||
\(213\) | −1.72995 | + | 6.45627i | −0.118534 | + | 0.442377i | ||||
\(214\) | 6.48684 | − | 3.74518i | 0.443432 | − | 0.256015i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 8.60842 | − | 5.65893i | 0.584378 | − | 0.384153i | ||||
\(218\) | −1.03723 | + | 1.03723i | −0.0702501 | + | 0.0702501i | ||||
\(219\) | −3.76633 | − | 2.17449i | −0.254505 | − | 0.146939i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.18452 | + | 8.97985i | 0.348749 | + | 0.604050i | ||||
\(222\) | 2.95980 | + | 11.0461i | 0.198649 | + | 0.741369i | ||||
\(223\) | 15.8412 | + | 15.8412i | 1.06081 | + | 1.06081i | 0.998027 | + | 0.0627803i | \(0.0199968\pi\) |
0.0627803 | + | 0.998027i | \(0.480003\pi\) | |||||||
\(224\) | 0.535629 | − | 2.59097i | 0.0357883 | − | 0.173116i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.01221 | + | 8.68141i | −0.333407 | + | 0.577479i | ||||
\(227\) | 10.5795 | + | 2.83476i | 0.702184 | + | 0.188150i | 0.592209 | − | 0.805785i | \(-0.298256\pi\) |
0.109976 | + | 0.993934i | \(0.464923\pi\) | |||||||
\(228\) | 3.65035 | + | 0.978107i | 0.241750 | + | 0.0647767i | ||||
\(229\) | 14.4722 | − | 25.0665i | 0.956347 | − | 1.65644i | 0.225092 | − | 0.974338i | \(-0.427732\pi\) |
0.731255 | − | 0.682104i | \(-0.238935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.4392 | − | 3.78754i | 0.752645 | − | 0.249202i | ||||
\(232\) | 1.09999 | + | 1.09999i | 0.0722182 | + | 0.0722182i | ||||
\(233\) | −0.365476 | − | 1.36397i | −0.0239431 | − | 0.0893569i | 0.952920 | − | 0.303220i | \(-0.0980619\pi\) |
−0.976864 | + | 0.213864i | \(0.931395\pi\) | |||||||
\(234\) | −1.25704 | − | 2.17725i | −0.0821751 | − | 0.142332i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.383668 | + | 0.221511i | 0.0249747 | + | 0.0144191i | ||||
\(237\) | 3.33362 | − | 3.33362i | 0.216542 | − | 0.216542i | ||||
\(238\) | 10.8938 | − | 0.631910i | 0.706141 | − | 0.0409606i | ||||
\(239\) | 4.36430i | 0.282303i | 0.989988 | + | 0.141152i | \(0.0450805\pi\) | ||||
−0.989988 | + | 0.141152i | \(0.954920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.65862 | + | 1.53496i | −0.171257 | + | 0.0988752i | −0.583178 | − | 0.812344i | \(-0.698191\pi\) |
0.411922 | + | 0.911219i | \(0.364858\pi\) | |||||||
\(242\) | −2.52167 | + | 9.41101i | −0.162099 | + | 0.604963i | ||||
\(243\) | 0.965926 | − | 0.258819i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | 8.19194 | 0.524435 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.3796 | −0.725539 | ||||||||
\(247\) | −9.17725 | + | 2.45904i | −0.583934 | + | 0.156465i | ||||
\(248\) | 1.00777 | − | 3.76106i | 0.0639937 | − | 0.238828i | ||||
\(249\) | −3.94022 | + | 2.27489i | −0.249701 | + | 0.144165i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.25355i | − | 0.0791234i | −0.999217 | − | 0.0395617i | \(-0.987404\pi\) | ||
0.999217 | − | 0.0395617i | \(-0.0125962\pi\) | |||||||
\(252\) | −2.64131 | + | 0.153213i | −0.166387 | + | 0.00965150i | ||||
\(253\) | 25.9344 | − | 25.9344i | 1.63048 | − | 1.63048i | ||||
\(254\) | −15.8208 | − | 9.13414i | −0.992685 | − | 0.573127i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.82683 | − | 6.81783i | −0.113955 | − | 0.425285i | 0.885252 | − | 0.465112i | \(-0.153986\pi\) |
−0.999207 | + | 0.0398273i | \(0.987319\pi\) | |||||||
\(258\) | 0.367260 | + | 0.367260i | 0.0228646 | + | 0.0228646i | ||||
\(259\) | −28.7228 | + | 9.51018i | −1.78475 | + | 0.590934i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.777814 | − | 1.34721i | 0.0481455 | − | 0.0833904i | ||||
\(262\) | 0.360990 | + | 0.0967271i | 0.0223021 | + | 0.00597582i | ||||
\(263\) | −5.49409 | − | 1.47214i | −0.338780 | − | 0.0907758i | 0.0854182 | − | 0.996345i | \(-0.472777\pi\) |
−0.424198 | + | 0.905569i | \(0.639444\pi\) | |||||||
\(264\) | 2.27722 | − | 3.94427i | 0.140153 | − | 0.242753i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.02421 | + | 9.79156i | −0.124112 | + | 0.600359i | ||||
\(267\) | 4.27694 | + | 4.27694i | 0.261745 | + | 0.261745i | ||||
\(268\) | 2.41103 | + | 8.99808i | 0.147277 | + | 0.549645i | ||||
\(269\) | −3.85391 | − | 6.67517i | −0.234977 | − | 0.406992i | 0.724289 | − | 0.689496i | \(-0.242168\pi\) |
−0.959266 | + | 0.282504i | \(0.908835\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4900 | − | 8.94316i | −0.940951 | − | 0.543258i | −0.0506925 | − | 0.998714i | \(-0.516143\pi\) |
−0.890258 | + | 0.455456i | \(0.849476\pi\) | |||||||
\(272\) | 2.91639 | − | 2.91639i | 0.176832 | − | 0.176832i | ||||
\(273\) | 5.55821 | − | 3.65381i | 0.336398 | − | 0.221139i | ||||
\(274\) | − | 2.65859i | − | 0.160611i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.97408 | + | 4.02648i | −0.419790 | + | 0.242366i | ||||
\(277\) | −3.81664 | + | 14.2439i | −0.229319 | + | 0.855832i | 0.751308 | + | 0.659951i | \(0.229423\pi\) |
−0.980628 | + | 0.195881i | \(0.937244\pi\) | |||||||
\(278\) | −4.42461 | + | 1.18557i | −0.265371 | + | 0.0711059i | ||||
\(279\) | −3.89374 | −0.233112 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.587402 | 0.0350415 | 0.0175207 | − | 0.999847i | \(-0.494423\pi\) | ||||
0.0175207 | + | 0.999847i | \(0.494423\pi\) | |||||||
\(282\) | −4.87829 | + | 1.30713i | −0.290498 | + | 0.0778387i | ||||
\(283\) | −4.81795 | + | 17.9809i | −0.286398 | + | 1.06885i | 0.661414 | + | 0.750021i | \(0.269957\pi\) |
−0.947812 | + | 0.318830i | \(0.896710\pi\) | |||||||
\(284\) | −5.78854 | + | 3.34201i | −0.343486 | + | 0.198312i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.4502i | 0.677066i | ||||||||
\(287\) | −1.74351 | − | 30.0572i | −0.102916 | − | 1.77422i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 0.00921092 | + | 0.00531793i | 0.000541819 | + | 0.000312819i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.327144 | − | 0.566631i | −0.0191775 | − | 0.0332165i | ||||
\(292\) | −1.12560 | − | 4.20080i | −0.0658708 | − | 0.245833i | ||||
\(293\) | −20.6736 | − | 20.6736i | −1.20777 | − | 1.20777i | −0.971749 | − | 0.236018i | \(-0.924158\pi\) |
−0.236018 | − | 0.971749i | \(-0.575842\pi\) | |||||||
\(294\) | −0.809365 | − | 6.95305i | −0.0472031 | − | 0.405510i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.71790 | + | 9.90370i | −0.332346 | + | 0.575641i | ||||
\(297\) | −4.39926 | − | 1.17878i | −0.255271 | − | 0.0683996i | ||||
\(298\) | −16.6565 | − | 4.46309i | −0.964884 | − | 0.258540i | ||||
\(299\) | 10.1229 | − | 17.5334i | 0.585422 | − | 1.01398i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.913778 | + | 1.02632i | −0.0526693 | + | 0.0591559i | ||||
\(302\) | 3.93696 | + | 3.93696i | 0.226546 | + | 0.226546i | ||||
\(303\) | 1.44991 | + | 5.41115i | 0.0832954 | + | 0.310863i | ||||
\(304\) | 1.88956 | + | 3.27281i | 0.108374 | + | 0.187709i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.57183 | − | 2.06220i | −0.204188 | − | 0.117888i | ||||
\(307\) | −1.63464 | + | 1.63464i | −0.0932937 | + | 0.0932937i | −0.752213 | − | 0.658920i | \(-0.771014\pi\) |
0.658920 | + | 0.752213i | \(0.271014\pi\) | |||||||
\(308\) | 10.7669 | + | 5.41055i | 0.613503 | + | 0.308294i | ||||
\(309\) | − | 5.55802i | − | 0.316185i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0239 | − | 6.94197i | 0.681810 | − | 0.393643i | −0.118727 | − | 0.992927i | \(-0.537881\pi\) |
0.800537 | + | 0.599284i | \(0.204548\pi\) | |||||||
\(312\) | 0.650691 | − | 2.42841i | 0.0368381 | − | 0.137482i | ||||
\(313\) | −13.0307 | + | 3.49157i | −0.736540 | + | 0.197355i | −0.607540 | − | 0.794289i | \(-0.707843\pi\) |
−0.129000 | + | 0.991645i | \(0.541177\pi\) | |||||||
\(314\) | 4.13090 | 0.233120 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.71445 | 0.265208 | ||||||||
\(317\) | 13.2497 | − | 3.55024i | 0.744175 | − | 0.199401i | 0.133242 | − | 0.991083i | \(-0.457461\pi\) |
0.610933 | + | 0.791682i | \(0.290794\pi\) | |||||||
\(318\) | −2.18307 | + | 8.14732i | −0.122420 | + | 0.456879i | ||||
\(319\) | −6.13581 | + | 3.54251i | −0.343539 | + | 0.198343i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 7.49036i | − | 0.418071i | ||||||
\(322\) | −11.7037 | − | 17.8038i | −0.652223 | − | 0.992167i | ||||
\(323\) | −11.0214 | + | 11.0214i | −0.613245 | + | 0.613245i | ||||
\(324\) | 0.866025 | + | 0.500000i | 0.0481125 | + | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.8694 | + | 18.8264i | 0.602003 | + | 1.04270i | ||||
\(327\) | 0.379653 | + | 1.41688i | 0.0209948 | + | 0.0783538i | ||||
\(328\) | −8.04662 | − | 8.04662i | −0.444300 | − | 0.444300i | ||||
\(329\) | −4.19996 | − | 12.6848i | −0.231552 | − | 0.699336i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6194 | + | 28.7856i | −0.913483 | + | 1.58220i | −0.104375 | + | 0.994538i | \(0.533284\pi\) |
−0.809108 | + | 0.587660i | \(0.800049\pi\) | |||||||
\(332\) | −4.39475 | − | 1.17757i | −0.241193 | − | 0.0646275i | ||||
\(333\) | 11.0461 | + | 2.95980i | 0.605325 | + | 0.162196i | ||||
\(334\) | −12.3708 | + | 21.4268i | −0.676898 | + | 1.17242i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.97603 | − | 1.75935i | −0.107801 | − | 0.0959805i | ||||
\(337\) | 17.0329 | + | 17.0329i | 0.927842 | + | 0.927842i | 0.997566 | − | 0.0697246i | \(-0.0222121\pi\) |
−0.0697246 | + | 0.997566i | \(0.522212\pi\) | |||||||
\(338\) | −1.72876 | − | 6.45183i | −0.0940323 | − | 0.350933i | ||||
\(339\) | 5.01221 | + | 8.68141i | 0.272226 | + | 0.471509i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.3579 | + | 8.86691i | 0.831679 | + | 0.480170i | ||||
\(342\) | 2.67224 | − | 2.67224i | 0.144498 | − | 0.144498i | ||||
\(343\) | 18.2412 | − | 3.20308i | 0.984931 | − | 0.172950i | ||||
\(344\) | 0.519384i | 0.0280033i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.3467 | − | 8.28306i | 0.771283 | − | 0.445300i | ||||
\(347\) | −0.532414 | + | 1.98700i | −0.0285815 | + | 0.106668i | −0.978743 | − | 0.205090i | \(-0.934251\pi\) |
0.950162 | + | 0.311758i | \(0.100918\pi\) | |||||||
\(348\) | 1.50262 | − | 0.402626i | 0.0805489 | − | 0.0215830i | ||||
\(349\) | 11.7250 | 0.627627 | 0.313814 | − | 0.949485i | \(-0.398393\pi\) | ||||
0.313814 | + | 0.949485i | \(0.398393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.51408 | −0.134191 | ||||||||
\(352\) | 4.39926 | − | 1.17878i | 0.234481 | − | 0.0628291i | ||||
\(353\) | 2.95640 | − | 11.0334i | 0.157353 | − | 0.587250i | −0.841539 | − | 0.540196i | \(-0.818350\pi\) |
0.998892 | − | 0.0470542i | \(-0.0149833\pi\) | |||||||
\(354\) | 0.383668 | − | 0.221511i | 0.0203917 | − | 0.0117732i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.04851i | 0.320570i | ||||||||
\(357\) | 4.89966 | − | 9.75027i | 0.259317 | − | 0.516039i | ||||
\(358\) | 8.99958 | − | 8.99958i | 0.475643 | − | 0.475643i | ||||
\(359\) | −2.08846 | − | 1.20577i | −0.110225 | − | 0.0636383i | 0.443874 | − | 0.896089i | \(-0.353604\pi\) |
−0.554099 | + | 0.832451i | \(0.686937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.35914 | + | 4.08615i | 0.124165 | + | 0.215061i | ||||
\(362\) | 2.35513 | + | 8.78945i | 0.123783 | + | 0.461963i | ||||
\(363\) | 6.88934 | + | 6.88934i | 0.361596 | + | 0.361596i | ||||
\(364\) | 6.51388 | + | 1.34661i | 0.341420 | + | 0.0705817i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.09597 | − | 7.09442i | 0.214100 | − | 0.370832i | ||||
\(367\) | −5.03135 | − | 1.34815i | −0.262635 | − | 0.0703727i | 0.125099 | − | 0.992144i | \(-0.460075\pi\) |
−0.387733 | + | 0.921772i | \(0.626742\pi\) | |||||||
\(368\) | −7.77857 | − | 2.08426i | −0.405486 | − | 0.108650i | ||||
\(369\) | −5.68982 | + | 9.85506i | −0.296200 | + | 0.513034i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.8541 | − | 4.51789i | −1.13461 | − | 0.234557i | ||||
\(372\) | −2.75329 | − | 2.75329i | −0.142751 | − | 0.142751i | ||||
\(373\) | 0.0379573 | + | 0.141659i | 0.00196535 | + | 0.00733480i | 0.966902 | − | 0.255150i | \(-0.0821248\pi\) |
−0.964936 | + | 0.262485i | \(0.915458\pi\) | |||||||
\(374\) | 9.39217 | + | 16.2677i | 0.485658 | + | 0.841184i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.37376 | − | 2.52519i | −0.225559 | − | 0.130227i | ||||
\(377\) | −2.76547 | + | 2.76547i | −0.142429 | + | 0.142429i | ||||
\(378\) | −1.18797 | + | 2.36405i | −0.0611026 | + | 0.121594i | ||||
\(379\) | − | 18.5438i | − | 0.952530i | −0.879302 | − | 0.476265i | \(-0.841990\pi\) | ||
0.879302 | − | 0.476265i | \(-0.158010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8208 | + | 9.13414i | −0.810524 | + | 0.467956i | ||||
\(382\) | −4.71210 | + | 17.5858i | −0.241092 | + | 0.899768i | ||||
\(383\) | 3.71843 | − | 0.996351i | 0.190003 | − | 0.0509112i | −0.162563 | − | 0.986698i | \(-0.551976\pi\) |
0.352566 | + | 0.935787i | \(0.385309\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0713 | −0.512614 | ||||||||
\(387\) | 0.501686 | − | 0.134426i | 0.0255021 | − | 0.00683328i | ||||
\(388\) | 0.169342 | − | 0.631994i | 0.00859706 | − | 0.0320847i | ||||
\(389\) | 15.4340 | − | 8.91085i | 0.782537 | − | 0.451798i | −0.0547917 | − | 0.998498i | \(-0.517449\pi\) |
0.837329 | + | 0.546700i | \(0.184116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 33.2136i | − | 1.67969i | ||||||
\(392\) | 4.34424 | − | 5.48886i | 0.219417 | − | 0.277229i | ||||
\(393\) | 0.264263 | − | 0.264263i | 0.0133303 | − | 0.0133303i | ||||
\(394\) | −19.8946 | − | 11.4862i | −1.00228 | − | 0.578665i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.27722 | − | 3.94427i | −0.114435 | − | 0.198207i | ||||
\(397\) | −6.63778 | − | 24.7725i | −0.333141 | − | 1.24330i | −0.905871 | − | 0.423554i | \(-0.860782\pi\) |
0.572730 | − | 0.819744i | \(-0.305884\pi\) | |||||||
\(398\) | 17.9583 | + | 17.9583i | 0.900168 | + | 0.900168i | ||||
\(399\) | 7.46764 | + | 6.64879i | 0.373849 | + | 0.332856i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.63060 | − | 4.55632i | 0.131366 | − | 0.227532i | −0.792838 | − | 0.609433i | \(-0.791397\pi\) |
0.924203 | + | 0.381901i | \(0.124730\pi\) | |||||||
\(402\) | 8.99808 | + | 2.41103i | 0.448784 | + | 0.120251i | ||||
\(403\) | 9.45560 | + | 2.53362i | 0.471017 | + | 0.126209i | ||||
\(404\) | −2.80102 | + | 4.85151i | −0.139356 | + | 0.241371i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.29368 | + | 3.90720i | 0.0642043 | + | 0.193911i | ||||
\(407\) | −36.8288 | − | 36.8288i | −1.82554 | − | 1.82554i | ||||
\(408\) | −1.06747 | − | 3.98386i | −0.0528477 | − | 0.197230i | ||||
\(409\) | 4.18773 | + | 7.25336i | 0.207070 | + | 0.358655i | 0.950790 | − | 0.309835i | \(-0.100274\pi\) |
−0.743720 | + | 0.668491i | \(0.766941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.30241 | − | 1.32929i | −0.113569 | − | 0.0655693i | ||||
\(412\) | 3.93011 | − | 3.93011i | 0.193623 | − | 0.193623i | ||||
\(413\) | 0.643862 | + | 0.979449i | 0.0316824 | + | 0.0481955i | ||||
\(414\) | 8.05297i | 0.395782i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.17725 | − | 1.25704i | 0.106749 | − | 0.0616313i | ||||
\(417\) | −1.18557 | + | 4.42461i | −0.0580577 | + | 0.216674i | ||||
\(418\) | −16.6253 | + | 4.45474i | −0.813170 | + | 0.217888i | ||||
\(419\) | 9.53078 | 0.465609 | 0.232805 | − | 0.972524i | \(-0.425210\pi\) | ||||
0.232805 | + | 0.972524i | \(0.425210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8461 | 0.821027 | 0.410514 | − | 0.911854i | \(-0.365349\pi\) | ||||
0.410514 | + | 0.911854i | \(0.365349\pi\) | |||||||
\(422\) | −13.1542 | + | 3.52466i | −0.640336 | + | 0.171578i | ||||
\(423\) | −1.30713 | + | 4.87829i | −0.0635550 | + | 0.237191i | ||||
\(424\) | −7.30469 | + | 4.21737i | −0.354747 | + | 0.204813i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.68403i | 0.323842i | ||||||||
\(427\) | 19.3661 | + | 9.73177i | 0.937193 | + | 0.470953i | ||||
\(428\) | 5.29649 | − | 5.29649i | 0.256015 | − | 0.256015i | ||||
\(429\) | 9.91619 | + | 5.72511i | 0.478758 | + | 0.276411i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7791 | − | 18.6699i | −0.519209 | − | 0.899297i | −0.999751 | − | 0.0223251i | \(-0.992893\pi\) |
0.480541 | − | 0.876972i | \(-0.340440\pi\) | |||||||
\(432\) | 0.258819 | + | 0.965926i | 0.0124524 | + | 0.0464731i | ||||
\(433\) | −25.8823 | − | 25.8823i | −1.24382 | − | 1.24382i | −0.958402 | − | 0.285422i | \(-0.907866\pi\) |
−0.285422 | − | 0.958402i | \(-0.592134\pi\) | |||||||
\(434\) | 6.85045 | − | 7.69413i | 0.328832 | − | 0.369330i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.733433 | + | 1.27034i | −0.0351251 | + | 0.0608384i | ||||
\(437\) | 29.3961 | + | 7.87667i | 1.40621 | + | 0.376792i | ||||
\(438\) | −4.20080 | − | 1.12560i | −0.200722 | − | 0.0537832i | ||||
\(439\) | 10.5899 | − | 18.3422i | 0.505426 | − | 0.875424i | −0.494554 | − | 0.869147i | \(-0.664669\pi\) |
0.999980 | − | 0.00627716i | \(-0.00199809\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.42620 | − | 2.77559i | −0.306010 | − | 0.132171i | ||||
\(442\) | 7.33202 | + | 7.33202i | 0.348749 | + | 0.348749i | ||||
\(443\) | 1.07420 | + | 4.00895i | 0.0510366 | + | 0.190471i | 0.986738 | − | 0.162322i | \(-0.0518985\pi\) |
−0.935701 | + | 0.352794i | \(0.885232\pi\) | |||||||
\(444\) | 5.71790 | + | 9.90370i | 0.271360 | + | 0.470009i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.4015 | + | 11.2014i | 0.918686 | + | 0.530404i | ||||
\(447\) | −12.1934 | + | 12.1934i | −0.576728 | + | 0.576728i | ||||
\(448\) | −0.153213 | − | 2.64131i | −0.00723862 | − | 0.124790i | ||||
\(449\) | − | 29.3795i | − | 1.38651i | −0.720694 | − | 0.693253i | \(-0.756177\pi\) | ||
0.720694 | − | 0.693253i | \(-0.243823\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.8843 | − | 25.9140i | 2.11352 | − | 1.22024i | ||||
\(452\) | −2.59451 | + | 9.68285i | −0.122036 | + | 0.455443i | ||||
\(453\) | 5.37799 | − | 1.44103i | 0.252680 | − | 0.0677053i | ||||
\(454\) | 10.9527 | 0.514035 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.77912 | 0.176973 | ||||||||
\(457\) | −0.455291 | + | 0.121995i | −0.0212976 | + | 0.00570668i | −0.269452 | − | 0.963014i | \(-0.586843\pi\) |
0.248155 | + | 0.968720i | \(0.420176\pi\) | |||||||
\(458\) | 7.49134 | − | 27.9581i | 0.350047 | − | 1.30639i | ||||
\(459\) | −3.57183 | + | 2.06220i | −0.166719 | + | 0.0962551i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 26.3199i | − | 1.22584i | −0.790145 | − | 0.612920i | \(-0.789995\pi\) | ||
0.790145 | − | 0.612920i | \(-0.210005\pi\) | |||||||
\(462\) | 10.0691 | − | 6.61917i | 0.468459 | − | 0.307952i | ||||
\(463\) | 1.02619 | − | 1.02619i | 0.0476909 | − | 0.0476909i | −0.682859 | − | 0.730550i | \(-0.739264\pi\) |
0.730550 | + | 0.682859i | \(0.239264\pi\) | |||||||
\(464\) | 1.34721 | + | 0.777814i | 0.0625428 | + | 0.0361091i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.706045 | − | 1.22291i | −0.0327069 | − | 0.0566500i | ||||
\(467\) | 8.02693 | + | 29.9569i | 0.371442 | + | 1.38624i | 0.858475 | + | 0.512856i | \(0.171413\pi\) |
−0.487033 | + | 0.873384i | \(0.661921\pi\) | |||||||
\(468\) | −1.77772 | − | 1.77772i | −0.0821751 | − | 0.0821751i | ||||
\(469\) | −4.98966 | + | 24.1361i | −0.230401 | + | 1.11450i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.06545 | − | 3.57747i | 0.0951709 | − | 0.164841i | ||||
\(472\) | 0.427926 | + | 0.114663i | 0.0196969 | + | 0.00527777i | ||||
\(473\) | −2.28490 | − | 0.612238i | −0.105060 | − | 0.0281507i | ||||
\(474\) | 2.35722 | − | 4.08283i | 0.108271 | − | 0.187531i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.3591 | − | 3.42990i | 0.474807 | − | 0.157209i | ||||
\(477\) | 5.96425 | + | 5.96425i | 0.273084 | + | 0.273084i | ||||
\(478\) | 1.12956 | + | 4.21559i | 0.0516650 | + | 0.192817i | ||||
\(479\) | 16.6760 | + | 28.8837i | 0.761945 | + | 1.31973i | 0.941847 | + | 0.336043i | \(0.109089\pi\) |
−0.179901 | + | 0.983685i | \(0.557578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.8987 | − | 14.3752i | −1.13528 | − | 0.655455i | ||||
\(482\) | −2.17075 | + | 2.17075i | −0.0988752 | + | 0.0988752i | ||||
\(483\) | −21.2704 | + | 1.23382i | −0.967837 | + | 0.0561407i | ||||
\(484\) | 9.74299i | 0.442863i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.866025 | − | 0.500000i | 0.0392837 | − | 0.0226805i | ||||
\(487\) | 0.855056 | − | 3.19111i | 0.0387463 | − | 0.144603i | −0.943843 | − | 0.330395i | \(-0.892818\pi\) |
0.982589 | + | 0.185791i | \(0.0594849\pi\) | |||||||
\(488\) | 7.91280 | − | 2.12023i | 0.358196 | − | 0.0959783i | ||||
\(489\) | 21.7389 | 0.983067 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.61649 | 0.163210 | 0.0816051 | − | 0.996665i | \(-0.473995\pi\) | ||||
0.0816051 | + | 0.996665i | \(0.473995\pi\) | |||||||
\(492\) | −10.9919 | + | 2.94527i | −0.495552 | + | 0.132783i | ||||
\(493\) | −1.66059 | + | 6.19740i | −0.0747891 | + | 0.279117i | ||||
\(494\) | −8.22809 | + | 4.75049i | −0.370199 | + | 0.213735i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.89374i | − | 0.174834i | ||||||
\(497\) | −17.6546 | + | 1.02408i | −0.791917 | + | 0.0459362i | ||||
\(498\) | −3.21718 | + | 3.21718i | −0.144165 | + | 0.144165i | ||||
\(499\) | −0.561004 | − | 0.323896i | −0.0251140 | − | 0.0144996i | 0.487390 | − | 0.873184i | \(-0.337949\pi\) |
−0.512504 | + | 0.858685i | \(0.671282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.3708 | + | 21.4268i | 0.552685 | + | 0.957278i | ||||
\(502\) | −0.324443 | − | 1.21084i | −0.0144806 | − | 0.0540423i | ||||
\(503\) | 12.9189 | + | 12.9189i | 0.576027 | + | 0.576027i | 0.933806 | − | 0.357779i | \(-0.116466\pi\) |
−0.357779 | + | 0.933806i | \(0.616466\pi\) | |||||||
\(504\) | −2.51166 | + | 0.831614i | −0.111878 | + | 0.0370430i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 18.3384 | − | 31.7631i | 0.815242 | − | 1.41204i | ||||
\(507\) | −6.45183 | − | 1.72876i | −0.286536 | − | 0.0767770i | ||||
\(508\) | −17.6458 | − | 4.72818i | −0.782906 | − | 0.209779i | ||||
\(509\) | −10.1554 | + | 17.5896i | −0.450128 | + | 0.779645i | −0.998394 | − | 0.0566595i | \(-0.981955\pi\) |
0.548265 | + | 0.836304i | \(0.315288\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.32944 | − | 11.2681i | 0.103049 | − | 0.498470i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −0.978107 | − | 3.65035i | −0.0431845 | − | 0.161167i | ||||
\(514\) | −3.52917 | − | 6.11270i | −0.155665 | − | 0.269620i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.449799 | + | 0.259692i | 0.0198013 | + | 0.0114323i | ||||
\(517\) | 16.2646 | − | 16.2646i | 0.715318 | − | 0.715318i | ||||
\(518\) | −25.2827 | + | 16.6201i | −1.11086 | + | 0.730247i | ||||
\(519\) | − | 16.5661i | − | 0.727172i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.07875 | − | 0.622814i | 0.0472607 | − | 0.0272860i | −0.476183 | − | 0.879346i | \(-0.657980\pi\) |
0.523444 | + | 0.852060i | \(0.324647\pi\) | |||||||
\(522\) | 0.402626 | − | 1.50262i | 0.0176225 | − | 0.0657679i | ||||
\(523\) | −19.6016 | + | 5.25224i | −0.857119 | + | 0.229664i | −0.660509 | − | 0.750818i | \(-0.729660\pi\) |
−0.196609 | + | 0.980482i | \(0.562993\pi\) | |||||||
\(524\) | 0.373725 | 0.0163262 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.68790 | −0.248004 | ||||||||
\(527\) | 15.5121 | − | 4.15646i | 0.675718 | − | 0.181058i | ||||
\(528\) | 1.17878 | − | 4.39926i | 0.0512997 | − | 0.191453i | ||||
\(529\) | −36.2434 | + | 20.9252i | −1.57580 | + | 0.909790i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.443022i | − | 0.0192255i | ||||||
\(532\) | 0.579009 | + | 9.98182i | 0.0251032 | + | 0.432767i | ||||
\(533\) | 20.2298 | − | 20.2298i | 0.876250 | − | 0.876250i | ||||
\(534\) | 5.23816 | + | 3.02425i | 0.226677 | + | 0.130872i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.65775 | + | 8.06746i | 0.201184 | + | 0.348461i | ||||
\(537\) | −3.29408 | − | 12.2937i | −0.142150 | − | 0.530510i | ||||
\(538\) | −5.45025 | − | 5.45025i | −0.234977 | − | 0.234977i | ||||
\(539\) | 19.0260 | + | 25.5816i | 0.819508 | + | 1.10188i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0068 | − | 29.4566i | 0.731178 | − | 1.26644i | −0.225202 | − | 0.974312i | \(-0.572304\pi\) |
0.956380 | − | 0.292126i | \(-0.0943625\pi\) | |||||||
\(542\) | −17.2769 | − | 4.62932i | −0.742104 | − | 0.198846i | ||||
\(543\) | 8.78945 | + | 2.35513i | 0.377191 | + | 0.101068i | ||||
\(544\) | 2.06220 | − | 3.57183i | 0.0884160 | − | 0.153141i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.42314 | − | 4.96788i | 0.189293 | − | 0.212606i | ||||
\(547\) | −27.8171 | − | 27.8171i | −1.18937 | − | 1.18937i | −0.977241 | − | 0.212132i | \(-0.931959\pi\) |
−0.212132 | − | 0.977241i | \(-0.568041\pi\) | |||||||
\(548\) | −0.688094 | − | 2.56800i | −0.0293939 | − | 0.109700i | ||||
\(549\) | −4.09597 | − | 7.09442i | −0.174812 | − | 0.302783i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.09127 | − | 2.93945i | −0.216896 | − | 0.125225i | ||||
\(552\) | −5.69431 | + | 5.69431i | −0.242366 | + | 0.242366i | ||||
\(553\) | 11.1452 | + | 5.60062i | 0.473941 | + | 0.238163i | ||||
\(554\) | 14.7464i | 0.626512i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.96700 | + | 2.29035i | −0.168238 | + | 0.0971324i | ||||
\(557\) | −0.365782 | + | 1.36512i | −0.0154987 | + | 0.0578419i | −0.973242 | − | 0.229782i | \(-0.926199\pi\) |
0.957743 | + | 0.287624i | \(0.0928653\pi\) | |||||||
\(558\) | −3.76106 | + | 1.00777i | −0.159218 | + | 0.0426625i | ||||
\(559\) | −1.30577 | −0.0552282 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.7843 | 0.793076 | ||||||||
\(562\) | 0.567387 | − | 0.152031i | 0.0239338 | − | 0.00641303i | ||||
\(563\) | −9.90152 | + | 36.9530i | −0.417299 | + | 1.55738i | 0.362886 | + | 0.931834i | \(0.381791\pi\) |
−0.780185 | + | 0.625548i | \(0.784875\pi\) | |||||||
\(564\) | −4.37376 | + | 2.52519i | −0.184168 | + | 0.106330i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.6151i | 0.782453i | ||||||||
\(567\) | 1.45334 | + | 2.21084i | 0.0610346 | + | 0.0928464i | ||||
\(568\) | −4.72632 | + | 4.72632i | −0.198312 | + | 0.198312i | ||||
\(569\) | 31.1820 | + | 18.0029i | 1.30722 | + | 0.754723i | 0.981631 | − | 0.190789i | \(-0.0611047\pi\) |
0.325587 | + | 0.945512i | \(0.394438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.1990 | + | 29.7895i | 0.719756 | + | 1.24665i | 0.961096 | + | 0.276213i | \(0.0890795\pi\) |
−0.241341 | + | 0.970440i | \(0.577587\pi\) | |||||||
\(572\) | 2.96354 | + | 11.0601i | 0.123912 | + | 0.462445i | ||||
\(573\) | 12.8737 | + | 12.8737i | 0.537806 | + | 0.537806i | ||||
\(574\) | −9.46346 | − | 28.5817i | −0.394997 | − | 1.19298i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 43.1900 | + | 11.5727i | 1.79802 | + | 0.481779i | 0.993666 | − | 0.112370i | \(-0.0358442\pi\) |
0.804355 | + | 0.594148i | \(0.202511\pi\) | |||||||
\(578\) | 0.0102734 | + | 0.00275276i | 0.000427319 | + | 0.000114500i | ||||
\(579\) | −5.03564 | + | 8.72198i | −0.209274 | + | 0.362473i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.99048 | − | 8.00466i | −0.372988 | − | 0.332089i | ||||
\(582\) | −0.462652 | − | 0.462652i | −0.0191775 | − | 0.0191775i | ||||
\(583\) | −9.94267 | − | 37.1066i | −0.411783 | − | 1.53680i | ||||
\(584\) | −2.17449 | − | 3.76633i | −0.0899811 | − | 0.155852i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.3199 | − | 14.6185i | −1.04596 | − | 0.603883i | ||||
\(587\) | 19.7182 | − | 19.7182i | 0.813859 | − | 0.813859i | −0.171351 | − | 0.985210i | \(-0.554813\pi\) |
0.985210 | + | 0.171351i | \(0.0548132\pi\) | |||||||
\(588\) | −2.58137 | − | 6.50665i | −0.106454 | − | 0.268330i | ||||
\(589\) | 14.7149i | 0.606316i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.8946 | + | 11.4862i | −0.818356 | + | 0.472478i | ||||
\(592\) | −2.95980 | + | 11.0461i | −0.121647 | + | 0.453994i | ||||
\(593\) | 9.62724 | − | 2.57961i | 0.395343 | − | 0.105932i | −0.0556699 | − | 0.998449i | \(-0.517729\pi\) |
0.451013 | + | 0.892517i | \(0.351063\pi\) | |||||||
\(594\) | −4.55445 | −0.186871 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.2441 | −0.706344 | ||||||||
\(597\) | 24.5315 | − | 6.57319i | 1.00401 | − | 0.269023i | ||||
\(598\) | 5.23999 | − | 19.5559i | 0.214279 | − | 0.799701i | ||||
\(599\) | −14.2556 | + | 8.23048i | −0.582469 | + | 0.336288i | −0.762114 | − | 0.647443i | \(-0.775838\pi\) |
0.179645 | + | 0.983731i | \(0.442505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0216i | 1.38777i | 0.720086 | + | 0.693885i | \(0.244102\pi\) | ||||
−0.720086 | + | 0.693885i | \(0.755898\pi\) | |||||||
\(602\) | −0.617012 | + | 1.22785i | −0.0251475 | + | 0.0500434i | ||||
\(603\) | 6.58705 | − | 6.58705i | 0.268246 | − | 0.268246i | ||||
\(604\) | 4.82177 | + | 2.78385i | 0.196195 | + | 0.113273i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.80102 | + | 4.85151i | 0.113784 | + | 0.197079i | ||||
\(607\) | −9.31678 | − | 34.7707i | −0.378156 | − | 1.41130i | −0.848678 | − | 0.528910i | \(-0.822601\pi\) |
0.470521 | − | 0.882389i | \(-0.344066\pi\) | |||||||
\(608\) | 2.67224 | + | 2.67224i | 0.108374 | + | 0.108374i | ||||
\(609\) | 4.03058 | + | 0.833240i | 0.163327 | + | 0.0337646i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.34852 | − | 10.9960i | 0.256833 | − | 0.444849i | ||||
\(612\) | −3.98386 | − | 1.06747i | −0.161038 | − | 0.0431500i | ||||
\(613\) | −31.8017 | − | 8.52125i | −1.28446 | − | 0.344170i | −0.448906 | − | 0.893579i | \(-0.648186\pi\) |
−0.835554 | + | 0.549409i | \(0.814853\pi\) | |||||||
\(614\) | −1.15586 | + | 2.00201i | −0.0466469 | + | 0.0807947i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.8004 | + | 2.43950i | 0.475452 | + | 0.0982901i | ||||
\(617\) | 10.3705 | + | 10.3705i | 0.417499 | + | 0.417499i | 0.884341 | − | 0.466842i | \(-0.154608\pi\) |
−0.466842 | + | 0.884341i | \(0.654608\pi\) | |||||||
\(618\) | −1.43852 | − | 5.36863i | −0.0578658 | − | 0.215958i | ||||
\(619\) | 2.58828 | + | 4.48304i | 0.104032 | + | 0.180188i | 0.913342 | − | 0.407193i | \(-0.133492\pi\) |
−0.809310 | + | 0.587381i | \(0.800159\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.97408 | + | 4.02648i | 0.279860 | + | 0.161577i | ||||
\(622\) | 9.81743 | − | 9.81743i | 0.393643 | − | 0.393643i | ||||
\(623\) | −7.18544 | + | 14.2990i | −0.287879 | + | 0.572876i | ||||
\(624\) | − | 2.51408i | − | 0.100644i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.6830 | + | 6.74520i | −0.466948 | + | 0.269592i | ||||
\(627\) | −4.45474 | + | 16.6253i | −0.177905 | + | 0.663951i | ||||
\(628\) | 3.99014 | − | 1.06916i | 0.159224 | − | 0.0426640i | ||||
\(629\) | −47.1658 | −1.88062 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.5385 | 0.578769 | 0.289384 | − | 0.957213i | \(-0.406549\pi\) | ||||
0.289384 | + | 0.957213i | \(0.406549\pi\) | |||||||
\(632\) | 4.55381 | − | 1.22019i | 0.181141 | − | 0.0485365i | ||||
\(633\) | −3.52466 | + | 13.1542i | −0.140093 | + | 0.522832i | ||||
\(634\) | 11.8793 | − | 6.85853i | 0.471788 | − | 0.272387i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.43473i | 0.334459i | ||||||||
\(637\) | 13.7994 | + | 10.9218i | 0.546752 | + | 0.432736i | ||||
\(638\) | −5.00987 | + | 5.00987i | −0.198343 | + | 0.198343i | ||||
\(639\) | 5.78854 | + | 3.34201i | 0.228991 | + | 0.132208i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.8743 | − | 36.1553i | −0.824484 | − | 1.42805i | −0.902313 | − | 0.431082i | \(-0.858132\pi\) |
0.0778281 | − | 0.996967i | \(-0.475201\pi\) | |||||||
\(642\) | −1.93865 | − | 7.23514i | −0.0765124 | − | 0.285548i | ||||
\(643\) | −15.5128 | − | 15.5128i | −0.611766 | − | 0.611766i | 0.331640 | − | 0.943406i | \(-0.392398\pi\) |
−0.943406 | + | 0.331640i | \(0.892398\pi\) | |||||||
\(644\) | −15.9129 | − | 14.1680i | −0.627056 | − | 0.558298i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.79328 | + | 13.4984i | −0.306623 | + | 0.531086i | ||||
\(647\) | 13.8141 | + | 3.70148i | 0.543089 | + | 0.145520i | 0.519926 | − | 0.854211i | \(-0.325960\pi\) |
0.0231633 | + | 0.999732i | \(0.492626\pi\) | |||||||
\(648\) | 0.965926 | + | 0.258819i | 0.0379452 | + | 0.0101674i | ||||
\(649\) | −1.00886 | + | 1.74740i | −0.0396012 | + | 0.0685913i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.23809 | − | 9.77973i | −0.126911 | − | 0.383298i | ||||
\(652\) | 15.3717 | + | 15.3717i | 0.602003 | + | 0.602003i | ||||
\(653\) | −3.95094 | − | 14.7451i | −0.154612 | − | 0.577021i | −0.999138 | − | 0.0415062i | \(-0.986784\pi\) |
0.844526 | − | 0.535515i | \(-0.179882\pi\) | |||||||
\(654\) | 0.733433 | + | 1.27034i | 0.0286795 | + | 0.0496743i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.85506 | − | 5.68982i | −0.384775 | − | 0.222150i | ||||
\(657\) | −3.07520 | + | 3.07520i | −0.119975 | + | 0.119975i | ||||
\(658\) | −7.33993 | − | 11.1656i | −0.286140 | − | 0.435279i | ||||
\(659\) | − | 18.9116i | − | 0.736690i | −0.929689 | − | 0.368345i | \(-0.879924\pi\) | ||
0.929689 | − | 0.368345i | \(-0.120076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5815 | − | 11.3054i | 0.761632 | − | 0.439728i | −0.0682495 | − | 0.997668i | \(-0.521741\pi\) |
0.829881 | + | 0.557940i | \(0.188408\pi\) | |||||||
\(662\) | −8.60281 | + | 32.1061i | −0.334358 | + | 1.24784i | ||||
\(663\) | 10.0157 | − | 2.68371i | 0.388979 | − | 0.104226i | ||||
\(664\) | −4.54978 | −0.176566 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.4358 | 0.443129 | ||||||||
\(667\) | 12.1006 | − | 3.24233i | 0.468535 | − | 0.125544i | ||||
\(668\) | −6.40358 | + | 23.8985i | −0.247762 | + | 0.924660i | ||||
\(669\) | 19.4015 | − | 11.2014i | 0.750104 | − | 0.433073i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.3097i | 1.44033i | ||||||||
\(672\) | −2.36405 | − | 1.18797i | −0.0911952 | − | 0.0458269i | ||||
\(673\) | 24.2623 | − | 24.2623i | 0.935243 | − | 0.935243i | −0.0627838 | − | 0.998027i | \(-0.519998\pi\) |
0.998027 | + | 0.0627838i | \(0.0199978\pi\) | |||||||
\(674\) | 20.8610 | + | 12.0441i | 0.803534 | + | 0.463921i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.33971 | − | 5.78455i | −0.128450 | − | 0.222483i | ||||
\(677\) | −2.30402 | − | 8.59870i | −0.0885505 | − | 0.330475i | 0.907412 | − | 0.420241i | \(-0.138055\pi\) |
−0.995963 | + | 0.0897664i | \(0.971388\pi\) | |||||||
\(678\) | 7.08834 | + | 7.08834i | 0.272226 | + | 0.272226i | ||||
\(679\) | 1.15112 | − | 1.29289i | 0.0441761 | − | 0.0496166i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.47634 | − | 9.48530i | 0.209854 | − | 0.363477i | ||||
\(682\) | 17.1296 | + | 4.58985i | 0.655925 | + | 0.175755i | ||||
\(683\) | 46.2697 | + | 12.3979i | 1.77046 | + | 0.474394i | 0.988792 | − | 0.149299i | \(-0.0477018\pi\) |
0.781669 | + | 0.623693i | \(0.214368\pi\) | |||||||
\(684\) | 1.88956 | − | 3.27281i | 0.0722491 | − | 0.125139i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.7906 | − | 7.81510i | 0.641068 | − | 0.298382i | ||||
\(687\) | −20.4667 | − | 20.4667i | −0.780854 | − | 0.780854i | ||||
\(688\) | 0.134426 | + | 0.501686i | 0.00512496 | + | 0.0191266i | ||||
\(689\) | −10.6028 | − | 18.3645i | −0.403934 | − | 0.699633i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.3848 | − | 12.9239i | −0.851559 | − | 0.491648i | 0.00961738 | − | 0.999954i | \(-0.496939\pi\) |
−0.861177 | + | 0.508306i | \(0.830272\pi\) | |||||||
\(692\) | 11.7140 | − | 11.7140i | 0.445300 | − | 0.445300i | ||||
\(693\) | −0.697800 | − | 12.0297i | −0.0265072 | − | 0.456971i | ||||
\(694\) | 2.05709i | 0.0780861i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.34721 | − | 0.777814i | 0.0510660 | − | 0.0294829i | ||||
\(697\) | 12.1474 | − | 45.3349i | 0.460117 | − | 1.71718i | ||||
\(698\) | 11.3255 | − | 3.03467i | 0.428677 | − | 0.114864i | ||||
\(699\) | −1.41209 | −0.0534102 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.95788 | 0.149487 | 0.0747435 | − | 0.997203i | \(-0.476186\pi\) | ||||
0.0747435 | + | 0.997203i | \(0.476186\pi\) | |||||||
\(702\) | −2.42841 | + | 0.650691i | −0.0916544 | + | 0.0245587i | ||||
\(703\) | 11.1854 | − | 41.7447i | 0.421867 | − | 1.57443i | ||||
\(704\) | 3.94427 | − | 2.27722i | 0.148655 | − | 0.0858261i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 11.4227i | − | 0.429897i | ||||||
\(707\) | −12.3852 | + | 8.14167i | −0.465793 | + | 0.306199i | ||||
\(708\) | 0.313264 | − | 0.313264i | 0.0117732 | − | 0.0117732i | ||||
\(709\) | 25.1665 | + | 14.5299i | 0.945148 | + | 0.545682i | 0.891570 | − | 0.452882i | \(-0.149604\pi\) |
0.0535778 | + | 0.998564i | \(0.482937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.35722 | − | 4.08283i | −0.0884028 | − | 0.153118i | ||||
\(712\) | 1.56547 | + | 5.84241i | 0.0586684 | + | 0.218954i | ||||
\(713\) | −22.1722 | − | 22.1722i | −0.830354 | − | 0.830354i | ||||
\(714\) | 2.20915 | − | 10.6862i | 0.0826753 | − | 0.399920i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.36367 | − | 11.0222i | 0.237821 | − | 0.411919i | ||||
\(717\) | 4.21559 | + | 1.12956i | 0.157434 | + | 0.0421843i | ||||
\(718\) | −2.32938 | − | 0.624155i | −0.0869316 | − | 0.0232932i | ||||
\(719\) | 10.1319 | − | 17.5490i | 0.377857 | − | 0.654467i | −0.612893 | − | 0.790166i | \(-0.709995\pi\) |
0.990750 | + | 0.135699i | \(0.0433279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.9598 | − | 4.62212i | 0.519891 | − | 0.172137i | ||||
\(722\) | 3.33633 | + | 3.33633i | 0.124165 | + | 0.124165i | ||||
\(723\) | 0.794551 | + | 2.96531i | 0.0295497 | + | 0.110281i | ||||
\(724\) | 4.54975 | + | 7.88040i | 0.169090 | + | 0.292873i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.43768 | + | 4.87150i | 0.313152 | + | 0.180798i | ||||
\(727\) | −2.80940 | + | 2.80940i | −0.104195 | + | 0.104195i | −0.757282 | − | 0.653088i | \(-0.773473\pi\) |
0.653088 | + | 0.757282i | \(0.273473\pi\) | |||||||
\(728\) | 6.64046 | − | 0.385189i | 0.246112 | − | 0.0142760i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.85515 | + | 1.07107i | −0.0686152 | + | 0.0396150i | ||||
\(732\) | 2.12023 | − | 7.91280i | 0.0783659 | − | 0.292466i | ||||
\(733\) | 1.68418 | − | 0.451275i | 0.0622066 | − | 0.0166682i | −0.227582 | − | 0.973759i | \(-0.573082\pi\) |
0.289788 | + | 0.957091i | \(0.406415\pi\) | |||||||
\(734\) | −5.20884 | −0.192262 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.05297 | −0.296836 | ||||||||
\(737\) | −40.9813 | + | 10.9809i | −1.50957 | + | 0.404487i | ||||
\(738\) | −2.94527 | + | 10.9919i | −0.108417 | + | 0.404617i | ||||
\(739\) | 20.2692 | − | 11.7024i | 0.745615 | − | 0.430481i | −0.0784926 | − | 0.996915i | \(-0.525011\pi\) |
0.824107 | + | 0.566434i | \(0.191677\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.50098i | 0.349027i | ||||||||
\(742\) | −22.2787 | + | 1.29231i | −0.817879 | + | 0.0474421i | ||||
\(743\) | −1.84057 | + | 1.84057i | −0.0675240 | + | 0.0675240i | −0.740062 | − | 0.672538i | \(-0.765204\pi\) |
0.672538 | + | 0.740062i | \(0.265204\pi\) | |||||||
\(744\) | −3.37208 | − | 1.94687i | −0.123626 | − | 0.0713757i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.0733279 | + | 0.127008i | 0.00268472 | + | 0.00465008i | ||||
\(747\) | 1.17757 | + | 4.39475i | 0.0430850 | + | 0.160795i | ||||
\(748\) | 13.2825 | + | 13.2825i | 0.485658 | + | 0.485658i | ||||
\(749\) | 18.8132 | − | 6.22909i | 0.687420 | − | 0.227606i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.1862 | + | 36.6956i | −0.773096 | + | 1.33904i | 0.162762 | + | 0.986665i | \(0.447960\pi\) |
−0.935858 | + | 0.352376i | \(0.885374\pi\) | |||||||
\(752\) | −4.87829 | − | 1.30713i | −0.177893 | − | 0.0476663i | ||||
\(753\) | −1.21084 | − | 0.324443i | −0.0441254 | − | 0.0118234i | ||||
\(754\) | −1.95548 | + | 3.38699i | −0.0712145 | + | 0.123347i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.535629 | + | 2.59097i | −0.0194807 | + | 0.0942325i | ||||
\(757\) | −10.2470 | − | 10.2470i | −0.372434 | − | 0.372434i | 0.495929 | − | 0.868363i | \(-0.334828\pi\) |
−0.868363 | + | 0.495929i | \(0.834828\pi\) | |||||||
\(758\) | −4.79948 | − | 17.9119i | −0.174325 | − | 0.650590i | ||||
\(759\) | −18.3384 | − | 31.7631i | −0.665642 | − | 1.15293i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.4082 | + | 7.74124i | 0.486048 | + | 0.280620i | 0.722933 | − | 0.690918i | \(-0.242793\pi\) |
−0.236886 | + | 0.971538i | \(0.576127\pi\) | |||||||
\(762\) | −12.9176 | + | 12.9176i | −0.467956 | + | 0.467956i | ||||
\(763\) | −3.24300 | + | 2.13186i | −0.117404 | + | 0.0771784i | ||||
\(764\) | 18.2062i | 0.658676i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.33386 | − | 1.92480i | 0.120457 | − | 0.0695460i | ||||
\(767\) | −0.288270 | + | 1.07584i | −0.0104088 | + | 0.0388463i | ||||
\(768\) | −0.965926 | + | 0.258819i | −0.0348548 | + | 0.00933933i | ||||
\(769\) | −15.9644 | −0.575691 | −0.287846 | − | 0.957677i | \(-0.592939\pi\) | ||||
−0.287846 | + | 0.957677i | \(0.592939\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.05834 | −0.254200 | ||||||||
\(772\) | −9.72810 | + | 2.60664i | −0.350122 | + | 0.0938149i | ||||
\(773\) | −5.99662 | + | 22.3797i | −0.215683 | + | 0.804941i | 0.770241 | + | 0.637752i | \(0.220136\pi\) |
−0.985925 | + | 0.167189i | \(0.946531\pi\) | |||||||
\(774\) | 0.449799 | − | 0.259692i | 0.0161677 | − | 0.00933443i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 0.654289i | − | 0.0234876i | ||||||
\(777\) | 1.75211 | + | 30.2055i | 0.0628567 | + | 1.08362i | ||||
\(778\) | 12.6018 | − | 12.6018i | 0.451798 | − | 0.451798i | ||||
\(779\) | 37.2434 | + | 21.5025i | 1.33438 | + | 0.770406i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.2210 | − | 26.3636i | −0.544651 | − | 0.943363i | ||||
\(782\) | −8.59632 | − | 32.0819i | −0.307404 | − | 1.14725i | ||||
\(783\) | −1.09999 | − | 1.09999i | −0.0393106 | − | 0.0393106i | ||||
\(784\) | 2.77559 | − | 6.42620i | 0.0991284 | − | 0.229507i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.186862 | − | 0.323655i | 0.00666516 | − | 0.0115444i | ||||
\(787\) | 2.03363 | + | 0.544910i | 0.0724912 | + | 0.0194239i | 0.294882 | − | 0.955534i | \(-0.404720\pi\) |
−0.222391 | + | 0.974958i | \(0.571386\pi\) | |||||||
\(788\) | −22.1896 | − | 5.94568i | −0.790471 | − | 0.211806i | ||||
\(789\) | −2.84395 | + | 4.92586i | −0.101247 | + | 0.175365i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.6365 | + | 19.8085i | −0.627081 | + | 0.704310i | ||||
\(792\) | −3.22048 | − | 3.22048i | −0.114435 | − | 0.114435i | ||||
\(793\) | 5.33042 | + | 19.8934i | 0.189289 | + | 0.706435i | ||||
\(794\) | −12.8232 | − | 22.2105i | −0.455079 | − | 0.788219i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.9943 | + | 12.6984i | 0.779569 | + | 0.450084i | ||||
\(797\) | −23.6759 | + | 23.6759i | −0.838642 | + | 0.838642i | −0.988680 | − | 0.150038i | \(-0.952060\pi\) |
0.150038 | + | 0.988680i | \(0.452060\pi\) | |||||||
\(798\) | 8.93402 | + | 4.48947i | 0.316261 | + | 0.158926i | ||||
\(799\) | − | 20.8298i | − | 0.736904i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.23816 | − | 3.02425i | 0.185081 | − | 0.106857i | ||||
\(802\) | 1.36170 | − | 5.08192i | 0.0480832 | − | 0.179449i | ||||
\(803\) | 19.1323 | − | 5.12649i | 0.675164 | − | 0.180910i | ||||
\(804\) | 9.31550 | 0.328532 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.78915 | 0.344808 | ||||||||
\(807\) | −7.44518 | + | 1.99493i | −0.262083 | + | 0.0702249i | ||||
\(808\) | −1.44991 | + | 5.41115i | −0.0510078 | + | 0.190364i | ||||
\(809\) | −1.15441 | + | 0.666500i | −0.0405869 | + | 0.0234329i | −0.520156 | − | 0.854071i | \(-0.674126\pi\) |
0.479569 | + | 0.877504i | \(0.340793\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.6705i | − | 1.46325i | −0.681708 | − | 0.731624i | \(-0.738763\pi\) | ||
0.681708 | − | 0.731624i | \(-0.261237\pi\) | |||||||
\(812\) | 2.26086 | + | 3.43924i | 0.0793406 | + | 0.120694i | ||||
\(813\) | −12.6475 | + | 12.6475i | −0.443568 | + | 0.443568i | ||||
\(814\) | −45.1059 | − | 26.0419i | −1.58096 | − | 0.912768i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.06220 | − | 3.57183i | −0.0721914 | − | 0.125039i | ||||
\(817\) | −0.508013 | − | 1.89593i | −0.0177731 | − | 0.0663302i | ||||
\(818\) | 5.92234 | + | 5.92234i | 0.207070 | + | 0.207070i | ||||
\(819\) | −2.09074 | − | 6.31449i | −0.0730564 | − | 0.220646i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.0833 | − | 27.8571i | 0.561312 | − | 0.972221i | −0.436070 | − | 0.899913i | \(-0.643630\pi\) |
0.997382 | − | 0.0723083i | \(-0.0230366\pi\) | |||||||
\(822\) | −2.56800 | − | 0.688094i | −0.0895693 | − | 0.0240000i | ||||
\(823\) | 14.2933 | + | 3.82988i | 0.498233 | + | 0.133501i | 0.499180 | − | 0.866498i | \(-0.333635\pi\) |
−0.000946758 | 1.00000i | \(0.500301\pi\) | ||||||||
\(824\) | 2.77901 | − | 4.81338i | 0.0968113 | − | 0.167682i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.875423 | + | 0.779431i | 0.0304599 | + | 0.0271199i | ||||
\(827\) | 34.2632 | + | 34.2632i | 1.19145 | + | 1.19145i | 0.976661 | + | 0.214788i | \(0.0689062\pi\) |
0.214788 | + | 0.976661i | \(0.431094\pi\) | |||||||
\(828\) | 2.08426 | + | 7.77857i | 0.0724331 | + | 0.270324i | ||||
\(829\) | −25.2456 | − | 43.7267i | −0.876817 | − | 1.51869i | −0.854814 | − | 0.518934i | \(-0.826329\pi\) |
−0.0220025 | − | 0.999758i | \(-0.507004\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.7707 | + | 7.37318i | 0.443011 | + | 0.255773i | ||||
\(832\) | 1.77772 | − | 1.77772i | 0.0616313 | − | 0.0616313i | ||||
\(833\) | 28.5640 | + | 4.19779i | 0.989682 | + | 0.145445i | ||||
\(834\) | 4.58070i | 0.158617i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −14.9058 | + | 8.60589i | −0.515529 | + | 0.297641i | ||||
\(837\) | −1.00777 | + | 3.76106i | −0.0348338 | + | 0.130001i | ||||
\(838\) | 9.20603 | − | 2.46675i | 0.318017 | − | 0.0852124i | ||||
\(839\) | 22.4313 | 0.774414 | 0.387207 | − | 0.921993i | \(-0.373440\pi\) | ||||
0.387207 | + | 0.921993i | \(0.373440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.5800 | 0.916553 | ||||||||
\(842\) | 16.2721 | − | 4.36008i | 0.560772 | − | 0.150258i | ||||
\(843\) | 0.152031 | − | 0.567387i | 0.00523622 | − | 0.0195418i | ||||
\(844\) | −11.7937 | + | 6.80911i | −0.405957 | + | 0.234379i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.05038i | 0.173636i | ||||||||
\(847\) | −11.5744 | + | 23.0329i | −0.397700 | + | 0.791420i | ||||
\(848\) | −5.96425 | + | 5.96425i | −0.204813 | + | 0.204813i | ||||
\(849\) | 16.1212 | + | 9.30757i | 0.553278 | + | 0.319435i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.0461 | + | 79.7542i | 1.57844 | + | 2.73394i | ||||
\(852\) | 1.72995 | + | 6.45627i | 0.0592672 | + | 0.221188i | ||||
\(853\) | 24.4497 | + | 24.4497i | 0.837140 | + | 0.837140i | 0.988482 | − | 0.151341i | \(-0.0483592\pi\) |
−0.151341 | + | 0.988482i | \(0.548359\pi\) | |||||||
\(854\) | 21.2250 | + | 4.38784i | 0.726305 | + | 0.150149i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.74518 | − | 6.48684i | 0.128008 | − | 0.221716i | ||||
\(857\) | −14.0196 | − | 3.75655i | −0.478901 | − | 0.128321i | 0.0112896 | − | 0.999936i | \(-0.496406\pi\) |
−0.490191 | + | 0.871615i | \(0.663073\pi\) | |||||||
\(858\) | 11.0601 | + | 2.96354i | 0.377585 | + | 0.101173i | ||||
\(859\) | −8.65502 | + | 14.9909i | −0.295306 | + | 0.511484i | −0.975056 | − | 0.221959i | \(-0.928755\pi\) |
0.679750 | + | 0.733444i | \(0.262088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.4842 | − | 6.09527i | −1.00482 | − | 0.207726i | ||||
\(862\) | −15.2439 | − | 15.2439i | −0.519209 | − | 0.519209i | ||||
\(863\) | 2.42352 | + | 9.04469i | 0.0824975 | + | 0.307885i | 0.994829 | − | 0.101568i | \(-0.0323861\pi\) |
−0.912331 | + | 0.409453i | \(0.865719\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −31.6992 | − | 18.3016i | −1.07718 | − | 0.621912i | ||||
\(867\) | 0.00752068 | − | 0.00752068i | 0.000255416 | − | 0.000255416i | ||||
\(868\) | 4.62564 | − | 9.20499i | 0.157005 | − | 0.312438i | ||||
\(869\) | 21.4717i | 0.728378i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.2822 | + | 11.7099i | −0.687236 | + | 0.396776i | ||||
\(872\) | −0.379653 | + | 1.41688i | −0.0128567 | + | 0.0479817i | ||||
\(873\) | −0.631994 | + | 0.169342i | −0.0213898 | + | 0.00573137i | ||||
\(874\) | 30.4331 | 1.02942 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.34898 | −0.146939 | ||||||||
\(877\) | −36.1496 | + | 9.68626i | −1.22069 | + | 0.327082i | −0.810946 | − | 0.585120i | \(-0.801047\pi\) |
−0.409740 | + | 0.912202i | \(0.634381\pi\) | |||||||
\(878\) | 5.48171 | − | 20.4580i | 0.184999 | − | 0.690425i | ||||
\(879\) | −25.3199 | + | 14.6185i | −0.854020 | + | 0.493069i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.1425i | 1.65565i | 0.560984 | + | 0.827827i | \(0.310423\pi\) | ||||
−0.560984 | + | 0.827827i | \(0.689577\pi\) | |||||||
\(882\) | −6.92561 | − | 1.01780i | −0.233197 | − | 0.0342709i | ||||
\(883\) | −22.9167 | + | 22.9167i | −0.771207 | + | 0.771207i | −0.978318 | − | 0.207110i | \(-0.933594\pi\) |
0.207110 | + | 0.978318i | \(0.433594\pi\) | |||||||
\(884\) | 8.97985 | + | 5.18452i | 0.302025 | + | 0.174374i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.07519 | + | 3.59433i | 0.0697173 | + | 0.120754i | ||||
\(887\) | 6.78961 | + | 25.3392i | 0.227973 | + | 0.850806i | 0.981192 | + | 0.193036i | \(0.0618334\pi\) |
−0.753219 | + | 0.657770i | \(0.771500\pi\) | |||||||
\(888\) | 8.08634 | + | 8.08634i | 0.271360 | + | 0.271360i | ||||
\(889\) | −36.0986 | − | 32.1403i | −1.21071 | − | 1.07795i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.27722 | + | 3.94427i | −0.0762899 | + | 0.132138i | ||||
\(892\) | 21.6395 | + | 5.79830i | 0.724545 | + | 0.194141i | ||||
\(893\) | 18.4356 | + | 4.93981i | 0.616925 | + | 0.165304i | ||||
\(894\) | −8.62203 | + | 14.9338i | −0.288364 | + | 0.499461i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.831614 | − | 2.51166i | −0.0277823 | − | 0.0839086i | ||||
\(897\) | −14.3159 | − | 14.3159i | −0.477995 | − | 0.477995i | ||||
\(898\) | −7.60399 | − | 28.3785i | −0.253748 | − | 0.947002i | ||||
\(899\) | 3.02860 | + | 5.24569i | 0.101010 | + | 0.174954i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.1274 | − | 17.3941i | −1.00369 | − | 0.579481i | ||||
\(902\) | 36.6479 | − | 36.6479i | 1.22024 | − | 1.22024i | ||||
\(903\) | 0.754842 | + | 1.14827i | 0.0251196 | + | 0.0382121i | ||||
\(904\) | 10.0244i | 0.333407i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.82177 | − | 2.78385i | 0.160193 | − | 0.0924872i | ||||
\(907\) | −0.327416 | + | 1.22193i | −0.0108717 | + | 0.0405736i | −0.971149 | − | 0.238475i | \(-0.923352\pi\) |
0.960277 | + | 0.279049i | \(0.0900191\pi\) | |||||||
\(908\) | 10.5795 | − | 2.83476i | 0.351092 | − | 0.0940749i | ||||
\(909\) | 5.60204 | 0.185808 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.7996 | −1.64993 | −0.824967 | − | 0.565182i | \(-0.808806\pi\) | ||||
−0.824967 | + | 0.565182i | \(0.808806\pi\) | |||||||
\(912\) | 3.65035 | − | 0.978107i | 0.120875 | − | 0.0323884i | ||||
\(913\) | 5.36318 | − | 20.0156i | 0.177495 | − | 0.662421i | ||||
\(914\) | −0.408203 | + | 0.235676i | −0.0135021 | + | 0.00779547i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 28.9443i | − | 0.956347i | ||||||
\(917\) | 0.883504 | + | 0.443974i | 0.0291759 | + | 0.0146613i | ||||
\(918\) | −2.91639 | + | 2.91639i | −0.0962551 | + | 0.0962551i | ||||
\(919\) | −43.6221 | − | 25.1852i | −1.43896 | − | 0.830784i | −0.441182 | − | 0.897418i | \(-0.645441\pi\) |
−0.997777 | + | 0.0666338i | \(0.978774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.15586 | + | 2.00201i | 0.0380870 | + | 0.0659686i | ||||
\(922\) | −6.81209 | − | 25.4231i | −0.224344 | − | 0.837264i | ||||
\(923\) | −11.8823 | − | 11.8823i | −0.391112 | − | 0.391112i | ||||
\(924\) | 8.01287 | − | 8.99971i | 0.263604 | − | 0.296069i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.725623 | − | 1.25682i | 0.0238455 | − | 0.0413015i | ||||
\(927\) | −5.36863 | − | 1.43852i | −0.176329 | − | 0.0472472i | ||||
\(928\) | 1.50262 | + | 0.402626i | 0.0493259 | + | 0.0132168i | ||||
\(929\) | −11.4115 | + | 19.7652i | −0.374398 | + | 0.648476i | −0.990237 | − | 0.139396i | \(-0.955484\pi\) |
0.615839 | + | 0.787872i | \(0.288817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.4893 | + | 24.2854i | −0.343773 | + | 0.795921i | ||||
\(932\) | −0.998499 | − | 0.998499i | −0.0327069 | − | 0.0327069i | ||||
\(933\) | −3.59343 | − | 13.4109i | −0.117644 | − | 0.439052i | ||||
\(934\) | 15.5068 | + | 26.8586i | 0.507399 | + | 0.878841i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.17725 | − | 1.25704i | −0.0711658 | − | 0.0410876i | ||||
\(937\) | −24.9461 | + | 24.9461i | −0.814954 | + | 0.814954i | −0.985372 | − | 0.170418i | \(-0.945488\pi\) |
0.170418 | + | 0.985372i | \(0.445488\pi\) | |||||||
\(938\) | 1.42725 | + | 24.6051i | 0.0466015 | + | 0.803386i | ||||
\(939\) | 13.4904i | 0.440242i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.1409 | + | 9.31896i | −0.526179 | + | 0.303789i | −0.739459 | − | 0.673202i | \(-0.764919\pi\) |
0.213280 | + | 0.976991i | \(0.431585\pi\) | |||||||
\(942\) | 1.06916 | − | 3.99014i | 0.0348350 | − | 0.130006i | ||||
\(943\) | −88.5173 | + | 23.7181i | −2.88252 | + | 0.772369i | ||||
\(944\) | 0.443022 | 0.0144191 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.36551 | −0.0769092 | ||||||||
\(947\) | 2.45198 | − | 0.657006i | 0.0796786 | − | 0.0213498i | −0.218760 | − | 0.975779i | \(-0.570201\pi\) |
0.298438 | + | 0.954429i | \(0.403534\pi\) | |||||||
\(948\) | 1.22019 | − | 4.55381i | 0.0396299 | − | 0.147901i | ||||
\(949\) | 9.46884 | − | 5.46684i | 0.307372 | − | 0.177461i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 13.7171i | − | 0.444806i | ||||||
\(952\) | 9.11836 | − | 5.99416i | 0.295528 | − | 0.194272i | ||||
\(953\) | −31.1031 | + | 31.1031i | −1.00753 | + | 1.00753i | −0.00755624 | + | 0.999971i | \(0.502405\pi\) |
−0.999971 | + | 0.00755624i | \(0.997595\pi\) | |||||||
\(954\) | 7.30469 | + | 4.21737i | 0.236498 | + | 0.136542i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.18215 | + | 3.77959i | 0.0705758 | + | 0.122241i | ||||
\(957\) | 1.83374 | + | 6.84361i | 0.0592764 | + | 0.221222i | ||||
\(958\) | 23.5834 | + | 23.5834i | 0.761945 | + | 0.761945i | ||||
\(959\) | 1.42402 | − | 6.88831i | 0.0459840 | − | 0.222435i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.91940 | + | 13.7168i | −0.255465 | + | 0.442477i | ||||
\(962\) | −27.7708 | − | 7.44117i | −0.895368 | − | 0.239913i | ||||
\(963\) | −7.23514 | − | 1.93865i | −0.233149 | − | 0.0624721i | ||||
\(964\) | −1.53496 | + | 2.65862i | −0.0494376 | + | 0.0856284i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −20.2263 | + | 6.69696i | −0.650770 | + | 0.215471i | ||||
\(967\) | 14.7707 | + | 14.7707i | 0.474993 | + | 0.474993i | 0.903526 | − | 0.428533i | \(-0.140969\pi\) |
−0.428533 | + | 0.903526i | \(0.640969\pi\) | |||||||
\(968\) | 2.52167 | + | 9.41101i | 0.0810496 | + | 0.302481i | ||||
\(969\) | 7.79328 | + | 13.4984i | 0.250356 | + | 0.433630i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.39194 | + | 5.42244i | 0.301402 | + | 0.174014i | 0.643072 | − | 0.765805i | \(-0.277659\pi\) |
−0.341671 | + | 0.939820i | \(0.610993\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −12.0990 | + | 0.701821i | −0.387878 | + | 0.0224994i | ||||
\(974\) | − | 3.30368i | − | 0.105857i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.09442 | − | 4.09597i | 0.227087 | − | 0.131109i | ||||
\(977\) | −4.43616 | + | 16.5560i | −0.141925 | + | 0.529673i | 0.857948 | + | 0.513737i | \(0.171739\pi\) |
−0.999873 | + | 0.0159356i | \(0.994927\pi\) | |||||||
\(978\) | 20.9982 | − | 5.62644i | 0.671447 | − | 0.179914i | ||||
\(979\) | −27.5476 | −0.880426 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.46687 | 0.0468334 | ||||||||
\(982\) | 3.49327 | − | 0.936018i | 0.111475 | − | 0.0298695i | ||||
\(983\) | 0.434966 | − | 1.62331i | 0.0138732 | − | 0.0517757i | −0.958642 | − | 0.284614i | \(-0.908135\pi\) |
0.972515 | + | 0.232838i | \(0.0748013\pi\) | |||||||
\(984\) | −9.85506 | + | 5.68982i | −0.314168 | + | 0.181385i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.41602i | 0.204328i | ||||||||
\(987\) | −13.3396 | + | 0.773782i | −0.424605 | + | 0.0246298i | ||||
\(988\) | −6.71821 | + | 6.71821i | −0.213735 | + | 0.213735i | ||||
\(989\) | 3.62222 | + | 2.09129i | 0.115180 | + | 0.0664992i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.40392 | + | 14.5560i | 0.266959 | + | 0.462387i | 0.968075 | − | 0.250660i | \(-0.0806478\pi\) |
−0.701116 | + | 0.713047i | \(0.747314\pi\) | |||||||
\(992\) | −1.00777 | − | 3.76106i | −0.0319968 | − | 0.119414i | ||||
\(993\) | 23.5033 | + | 23.5033i | 0.745855 | + | 0.745855i | ||||
\(994\) | −16.7880 | + | 5.55853i | −0.532482 | + | 0.176306i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.27489 | + | 3.94022i | −0.0720826 | + | 0.124851i | ||||
\(997\) | −16.8680 | − | 4.51978i | −0.534216 | − | 0.143143i | −0.0183818 | − | 0.999831i | \(-0.505851\pi\) |
−0.515835 | + | 0.856688i | \(0.672518\pi\) | |||||||
\(998\) | −0.625718 | − | 0.167661i | −0.0198068 | − | 0.00530721i | ||||
\(999\) | 5.71790 | − | 9.90370i | 0.180906 | − | 0.313339i |
(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.bc.h.607.4 | 16 | ||
5.2 | odd | 4 | 210.2.u.b.103.4 | yes | 16 | ||
5.3 | odd | 4 | 1050.2.bc.g.943.1 | 16 | |||
5.4 | even | 2 | 210.2.u.a.187.2 | yes | 16 | ||
7.3 | odd | 6 | 1050.2.bc.g.157.1 | 16 | |||
15.2 | even | 4 | 630.2.bv.b.523.1 | 16 | |||
15.14 | odd | 2 | 630.2.bv.a.397.3 | 16 | |||
35.2 | odd | 12 | 1470.2.m.e.1273.5 | 16 | |||
35.3 | even | 12 | inner | 1050.2.bc.h.493.4 | 16 | ||
35.9 | even | 6 | 1470.2.m.d.97.8 | 16 | |||
35.12 | even | 12 | 1470.2.m.d.1273.8 | 16 | |||
35.17 | even | 12 | 210.2.u.a.73.2 | ✓ | 16 | ||
35.19 | odd | 6 | 1470.2.m.e.97.5 | 16 | |||
35.24 | odd | 6 | 210.2.u.b.157.4 | yes | 16 | ||
105.17 | odd | 12 | 630.2.bv.a.73.3 | 16 | |||
105.59 | even | 6 | 630.2.bv.b.577.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.73.2 | ✓ | 16 | 35.17 | even | 12 | ||
210.2.u.a.187.2 | yes | 16 | 5.4 | even | 2 | ||
210.2.u.b.103.4 | yes | 16 | 5.2 | odd | 4 | ||
210.2.u.b.157.4 | yes | 16 | 35.24 | odd | 6 | ||
630.2.bv.a.73.3 | 16 | 105.17 | odd | 12 | |||
630.2.bv.a.397.3 | 16 | 15.14 | odd | 2 | |||
630.2.bv.b.523.1 | 16 | 15.2 | even | 4 | |||
630.2.bv.b.577.1 | 16 | 105.59 | even | 6 | |||
1050.2.bc.g.157.1 | 16 | 7.3 | odd | 6 | |||
1050.2.bc.g.943.1 | 16 | 5.3 | odd | 4 | |||
1050.2.bc.h.493.4 | 16 | 35.3 | even | 12 | inner | ||
1050.2.bc.h.607.4 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.d.97.8 | 16 | 35.9 | even | 6 | |||
1470.2.m.d.1273.8 | 16 | 35.12 | even | 12 | |||
1470.2.m.e.97.5 | 16 | 35.19 | odd | 6 | |||
1470.2.m.e.1273.5 | 16 | 35.2 | odd | 12 |