Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [125,2,Mod(24,125)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(125, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("125.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.e (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.998130025266\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.58140625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 74.1 | ||
Root | \(1.66637 + 0.917186i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 125.74 |
Dual form | 125.2.e.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.666375 | − | 0.917186i | −0.471198 | − | 0.648548i | 0.505586 | − | 0.862776i | \(-0.331276\pi\) |
−0.976784 | + | 0.214228i | \(0.931276\pi\) | |||||||
\(3\) | 2.47539 | + | 0.804303i | 1.42917 | + | 0.464365i | 0.918503 | − | 0.395415i | \(-0.129399\pi\) |
0.510665 | + | 0.859780i | \(0.329399\pi\) | |||||||
\(4\) | 0.220859 | − | 0.679734i | 0.110430 | − | 0.339867i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.911842 | − | 2.80636i | −0.372258 | − | 1.14569i | ||||
\(7\) | 0.407162i | 0.153893i | 0.997035 | + | 0.0769463i | \(0.0245170\pi\) | ||||
−0.997035 | + | 0.0769463i | \(0.975483\pi\) | |||||||
\(8\) | −2.92705 | + | 0.951057i | −1.03487 | + | 0.336249i | ||||
\(9\) | 3.05361 | + | 2.21858i | 1.01787 | + | 0.739525i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61803 | + | 1.17557i | −0.487856 | + | 0.354448i | −0.804359 | − | 0.594144i | \(-0.797491\pi\) |
0.316503 | + | 0.948591i | \(0.397491\pi\) | |||||||
\(12\) | 1.09343 | − | 1.50497i | 0.315645 | − | 0.434448i | ||||
\(13\) | 0.411842 | − | 0.566852i | 0.114224 | − | 0.157216i | −0.748077 | − | 0.663612i | \(-0.769023\pi\) |
0.862301 | + | 0.506396i | \(0.169023\pi\) | |||||||
\(14\) | 0.373443 | − | 0.271322i | 0.0998068 | − | 0.0725139i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.66637 | + | 1.21069i | 0.416594 | + | 0.302673i | ||||
\(17\) | −1.50527 | + | 0.489091i | −0.365081 | + | 0.118622i | −0.485812 | − | 0.874063i | \(-0.661476\pi\) |
0.120731 | + | 0.992685i | \(0.461476\pi\) | |||||||
\(18\) | − | 4.27913i | − | 1.00860i | ||||||
\(19\) | −1.52988 | − | 4.70847i | −0.350978 | − | 1.08020i | −0.958305 | − | 0.285747i | \(-0.907758\pi\) |
0.607328 | − | 0.794452i | \(-0.292242\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.327481 | + | 1.00788i | −0.0714623 | + | 0.219938i | ||||
\(22\) | 2.15643 | + | 0.700668i | 0.459753 | + | 0.149383i | ||||
\(23\) | 0.706192 | + | 0.971990i | 0.147251 | + | 0.202674i | 0.876271 | − | 0.481819i | \(-0.160024\pi\) |
−0.729020 | + | 0.684493i | \(0.760024\pi\) | |||||||
\(24\) | −8.01054 | −1.63514 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.794350 | −0.155785 | ||||||||
\(27\) | 1.18484 | + | 1.63079i | 0.228022 | + | 0.313846i | ||||
\(28\) | 0.276762 | + | 0.0899253i | 0.0523030 | + | 0.0169943i | ||||
\(29\) | −1.70239 | + | 5.23943i | −0.316127 | + | 0.972938i | 0.659161 | + | 0.752001i | \(0.270911\pi\) |
−0.975288 | + | 0.220937i | \(0.929089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53514 | + | 7.80237i | 0.455325 | + | 1.40135i | 0.870753 | + | 0.491721i | \(0.163632\pi\) |
−0.415428 | + | 0.909626i | \(0.636368\pi\) | |||||||
\(32\) | 3.82022i | 0.675325i | ||||||||
\(33\) | −4.95078 | + | 1.60861i | −0.861821 | + | 0.280023i | ||||
\(34\) | 1.45166 | + | 1.05469i | 0.248958 | + | 0.180878i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.18246 | − | 1.58565i | 0.363743 | − | 0.264275i | ||||
\(37\) | −3.01846 | + | 4.15456i | −0.496232 | + | 0.683005i | −0.981522 | − | 0.191348i | \(-0.938714\pi\) |
0.485290 | + | 0.874353i | \(0.338714\pi\) | |||||||
\(38\) | −3.29908 | + | 4.54079i | −0.535181 | + | 0.736613i | ||||
\(39\) | 1.47539 | − | 1.07193i | 0.236252 | − | 0.171647i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.83802 | − | 4.24157i | −0.911745 | − | 0.662422i | 0.0297106 | − | 0.999559i | \(-0.490541\pi\) |
−0.941456 | + | 0.337137i | \(0.890541\pi\) | |||||||
\(42\) | 1.14264 | − | 0.371267i | 0.176314 | − | 0.0572877i | ||||
\(43\) | − | 9.16531i | − | 1.39770i | −0.715270 | − | 0.698848i | \(-0.753696\pi\) | ||
0.715270 | − | 0.698848i | \(-0.246304\pi\) | |||||||
\(44\) | 0.441718 | + | 1.35947i | 0.0665915 | + | 0.204948i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.420907 | − | 1.29542i | 0.0620593 | − | 0.190999i | ||||
\(47\) | −1.21092 | − | 0.393451i | −0.176631 | − | 0.0573907i | 0.219367 | − | 0.975643i | \(-0.429601\pi\) |
−0.395997 | + | 0.918252i | \(0.629601\pi\) | |||||||
\(48\) | 3.15117 | + | 4.33721i | 0.454832 | + | 0.626022i | ||||
\(49\) | 6.83422 | 0.976317 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.11950 | −0.576846 | ||||||||
\(52\) | −0.294350 | − | 0.405138i | −0.0408190 | − | 0.0561825i | ||||
\(53\) | 4.83133 | + | 1.56979i | 0.663634 | + | 0.215628i | 0.621416 | − | 0.783481i | \(-0.286558\pi\) |
0.0422180 | + | 0.999108i | \(0.486558\pi\) | |||||||
\(54\) | 0.706192 | − | 2.17344i | 0.0961005 | − | 0.295767i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.387234 | − | 1.19178i | −0.0517463 | − | 0.159259i | ||||
\(57\) | − | 12.8858i | − | 1.70677i | ||||||
\(58\) | 5.93997 | − | 1.93001i | 0.779956 | − | 0.253423i | ||||
\(59\) | −5.25838 | − | 3.82044i | −0.684583 | − | 0.497379i | 0.190292 | − | 0.981728i | \(-0.439057\pi\) |
−0.874875 | + | 0.484349i | \(0.839057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.62101 | − | 5.53699i | 0.975770 | − | 0.708938i | 0.0190107 | − | 0.999819i | \(-0.493948\pi\) |
0.956759 | + | 0.290881i | \(0.0939483\pi\) | |||||||
\(62\) | 5.46687 | − | 7.52450i | 0.694293 | − | 0.955612i | ||||
\(63\) | −0.903319 | + | 1.24331i | −0.113807 | + | 0.156643i | ||||
\(64\) | 6.83660 | − | 4.96708i | 0.854575 | − | 0.620885i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.77447 | + | 3.46885i | 0.587696 | + | 0.426986i | ||||
\(67\) | 2.93090 | − | 0.952307i | 0.358066 | − | 0.116343i | −0.124459 | − | 0.992225i | \(-0.539720\pi\) |
0.482526 | + | 0.875882i | \(0.339720\pi\) | |||||||
\(68\) | 1.13120i | 0.137178i | ||||||||
\(69\) | 0.966327 | + | 2.97405i | 0.116332 | + | 0.358033i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.12183 | − | 6.53032i | 0.251815 | − | 0.775007i | −0.742625 | − | 0.669707i | \(-0.766420\pi\) |
0.994440 | − | 0.105300i | \(-0.0335803\pi\) | |||||||
\(72\) | −11.0481 | − | 3.58973i | −1.30203 | − | 0.423054i | ||||
\(73\) | 0.320429 | + | 0.441032i | 0.0375033 | + | 0.0516189i | 0.827357 | − | 0.561677i | \(-0.189843\pi\) |
−0.789854 | + | 0.613296i | \(0.789843\pi\) | |||||||
\(74\) | 5.82193 | 0.676786 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.53840 | −0.405882 | ||||||||
\(77\) | −0.478647 | − | 0.658801i | −0.0545469 | − | 0.0750774i | ||||
\(78\) | −1.96633 | − | 0.638898i | −0.222643 | − | 0.0723410i | ||||
\(79\) | −1.69390 | + | 5.21330i | −0.190579 | + | 0.586542i | −1.00000 | 0.000687140i | \(-0.999781\pi\) | |
0.809421 | + | 0.587229i | \(0.199781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.87783 | − | 5.77938i | −0.208648 | − | 0.642153i | ||||
\(82\) | 8.18102i | 0.903442i | ||||||||
\(83\) | 0.926457 | − | 0.301024i | 0.101692 | − | 0.0330417i | −0.257729 | − | 0.966217i | \(-0.582974\pi\) |
0.359421 | + | 0.933176i | \(0.382974\pi\) | |||||||
\(84\) | 0.612766 | + | 0.445201i | 0.0668583 | + | 0.0485754i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.40629 | + | 6.10753i | −0.906474 | + | 0.658592i | ||||
\(87\) | −8.42819 | + | 11.6004i | −0.903596 | + | 1.24369i | ||||
\(88\) | 3.61803 | − | 4.97980i | 0.385684 | − | 0.530848i | ||||
\(89\) | −1.83363 | + | 1.33221i | −0.194364 | + | 0.141214i | −0.680711 | − | 0.732552i | \(-0.738329\pi\) |
0.486347 | + | 0.873766i | \(0.338329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.230800 | + | 0.167686i | 0.0241945 | + | 0.0175783i | ||||
\(92\) | 0.816664 | − | 0.265350i | 0.0851431 | − | 0.0276647i | ||||
\(93\) | 21.3529i | 2.21420i | ||||||||
\(94\) | 0.446057 | + | 1.37282i | 0.0460073 | + | 0.141596i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.07261 | + | 9.45653i | −0.313597 | + | 0.965153i | ||||
\(97\) | 14.4736 | + | 4.70276i | 1.46957 | + | 0.477493i | 0.930979 | − | 0.365073i | \(-0.118956\pi\) |
0.538593 | + | 0.842566i | \(0.318956\pi\) | |||||||
\(98\) | −4.55415 | − | 6.26825i | −0.460039 | − | 0.633189i | ||||
\(99\) | −7.54893 | −0.758696 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.3965 | 1.83052 | 0.915261 | − | 0.402861i | \(-0.131984\pi\) | ||||
0.915261 | + | 0.402861i | \(0.131984\pi\) | |||||||
\(102\) | 2.74513 | + | 3.77835i | 0.271809 | + | 0.374113i | ||||
\(103\) | −11.3026 | − | 3.67243i | −1.11368 | − | 0.361856i | −0.306326 | − | 0.951927i | \(-0.599100\pi\) |
−0.807351 | + | 0.590071i | \(0.799100\pi\) | |||||||
\(104\) | −0.666375 | + | 2.05089i | −0.0653434 | + | 0.201106i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.77968 | − | 5.47730i | −0.172858 | − | 0.532002i | ||||
\(107\) | 0.754919i | 0.0729808i | 0.999334 | + | 0.0364904i | \(0.0116178\pi\) | ||||
−0.999334 | + | 0.0364904i | \(0.988382\pi\) | |||||||
\(108\) | 1.37019 | − | 0.445201i | 0.131846 | − | 0.0428395i | ||||
\(109\) | −7.40859 | − | 5.38265i | −0.709614 | − | 0.515565i | 0.173435 | − | 0.984845i | \(-0.444513\pi\) |
−0.883049 | + | 0.469281i | \(0.844513\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8134 | + | 7.85640i | −1.02636 | + | 0.745697i | ||||
\(112\) | −0.492947 | + | 0.678484i | −0.0465791 | + | 0.0641107i | ||||
\(113\) | 7.54710 | − | 10.3877i | 0.709971 | − | 0.977191i | −0.289827 | − | 0.957079i | \(-0.593598\pi\) |
0.999798 | − | 0.0201123i | \(-0.00640237\pi\) | |||||||
\(114\) | −11.8187 | + | 8.58677i | −1.10692 | + | 0.804225i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.18543 | + | 2.31435i | 0.295760 | + | 0.214882i | ||||
\(117\) | 2.51521 | − | 0.817241i | 0.232531 | − | 0.0755539i | ||||
\(118\) | 7.36876i | 0.678349i | ||||||||
\(119\) | −0.199139 | − | 0.612887i | −0.0182551 | − | 0.0561833i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.16312 | + | 6.65740i | −0.196647 | + | 0.605218i | ||||
\(122\) | −10.1569 | − | 3.30017i | −0.919562 | − | 0.298784i | ||||
\(123\) | −11.0399 | − | 15.1951i | −0.995432 | − | 1.37009i | ||||
\(124\) | 5.86345 | 0.526553 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.74230 | 0.155216 | ||||||||
\(127\) | −4.17632 | − | 5.74821i | −0.370588 | − | 0.510071i | 0.582472 | − | 0.812850i | \(-0.302085\pi\) |
−0.953061 | + | 0.302780i | \(0.902085\pi\) | |||||||
\(128\) | −1.84498 | − | 0.599472i | −0.163075 | − | 0.0529863i | ||||
\(129\) | 7.37169 | − | 22.6877i | 0.649041 | − | 1.99754i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.739865 | + | 2.27707i | 0.0646423 | + | 0.198949i | 0.978161 | − | 0.207848i | \(-0.0666459\pi\) |
−0.913519 | + | 0.406796i | \(0.866646\pi\) | |||||||
\(132\) | 3.72049i | 0.323827i | ||||||||
\(133\) | 1.91711 | − | 0.622907i | 0.166234 | − | 0.0540129i | ||||
\(134\) | −2.82652 | − | 2.05359i | −0.244174 | − | 0.177403i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.94084 | − | 2.86319i | 0.337924 | − | 0.245516i | ||||
\(137\) | 11.1793 | − | 15.3870i | 0.955111 | − | 1.31460i | 0.00589176 | − | 0.999983i | \(-0.498125\pi\) |
0.949219 | − | 0.314615i | \(-0.101875\pi\) | |||||||
\(138\) | 2.08382 | − | 2.86813i | 0.177386 | − | 0.244152i | ||||
\(139\) | −5.44849 | + | 3.95856i | −0.462135 | + | 0.335761i | −0.794368 | − | 0.607437i | \(-0.792198\pi\) |
0.332233 | + | 0.943197i | \(0.392198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.68104 | − | 1.94789i | −0.225784 | − | 0.164042i | ||||
\(142\) | −7.40346 | + | 2.40553i | −0.621284 | + | 0.201867i | ||||
\(143\) | 1.40134i | 0.117186i | ||||||||
\(144\) | 2.40244 | + | 7.39396i | 0.200204 | + | 0.616163i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.190983 | − | 0.587785i | 0.0158059 | − | 0.0486455i | ||||
\(147\) | 16.9174 | + | 5.49679i | 1.39532 | + | 0.453367i | ||||
\(148\) | 2.15734 | + | 2.96933i | 0.177332 | + | 0.244077i | ||||
\(149\) | 0.720492 | 0.0590250 | 0.0295125 | − | 0.999564i | \(-0.490605\pi\) | ||||
0.0295125 | + | 0.999564i | \(0.490605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5178 | −1.26282 | −0.631412 | − | 0.775447i | \(-0.717524\pi\) | ||||
−0.631412 | + | 0.775447i | \(0.717524\pi\) | |||||||
\(152\) | 8.95605 | + | 12.3269i | 0.726432 | + | 0.999847i | ||||
\(153\) | −5.68158 | − | 1.84606i | −0.459329 | − | 0.149245i | ||||
\(154\) | −0.285285 | + | 0.878017i | −0.0229889 | + | 0.0707526i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.402777 | − | 1.23962i | −0.0322480 | − | 0.0992491i | ||||
\(157\) | − | 2.78418i | − | 0.222202i | −0.993809 | − | 0.111101i | \(-0.964562\pi\) | ||
0.993809 | − | 0.111101i | \(-0.0354376\pi\) | |||||||
\(158\) | 5.91034 | − | 1.92039i | 0.470201 | − | 0.152778i | ||||
\(159\) | 10.6968 | + | 7.77171i | 0.848315 | + | 0.616337i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.395757 | + | 0.287534i | −0.0311900 | + | 0.0226609i | ||||
\(162\) | −4.04942 | + | 5.57355i | −0.318153 | + | 0.437900i | ||||
\(163\) | −14.2287 | + | 19.5842i | −1.11448 | + | 1.53395i | −0.299835 | + | 0.953991i | \(0.596932\pi\) |
−0.814645 | + | 0.579960i | \(0.803068\pi\) | |||||||
\(164\) | −4.17252 | + | 3.03151i | −0.325819 | + | 0.236721i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.893462 | − | 0.649138i | −0.0693461 | − | 0.0503829i | ||||
\(167\) | −18.1140 | + | 5.88559i | −1.40170 | + | 0.455441i | −0.909741 | − | 0.415176i | \(-0.863720\pi\) |
−0.491961 | + | 0.870617i | \(0.663720\pi\) | |||||||
\(168\) | − | 3.26158i | − | 0.251637i | ||||||
\(169\) | 3.86551 | + | 11.8968i | 0.297347 | + | 0.915141i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.77447 | − | 17.7720i | 0.441585 | − | 1.35906i | ||||
\(172\) | −6.22998 | − | 2.02424i | −0.475031 | − | 0.154347i | ||||
\(173\) | 7.78642 | + | 10.7171i | 0.591991 | + | 0.814805i | 0.994946 | − | 0.100415i | \(-0.0320169\pi\) |
−0.402955 | + | 0.915220i | \(0.632017\pi\) | |||||||
\(174\) | 16.2561 | 1.23237 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.11950 | −0.310519 | ||||||||
\(177\) | −9.94376 | − | 13.6864i | −0.747419 | − | 1.02873i | ||||
\(178\) | 2.44376 | + | 0.794027i | 0.183168 | + | 0.0595148i | ||||
\(179\) | 3.77772 | − | 11.6266i | 0.282360 | − | 0.869016i | −0.704817 | − | 0.709389i | \(-0.748971\pi\) |
0.987177 | − | 0.159627i | \(-0.0510290\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.37348 | + | 10.3825i | 0.250748 | + | 0.771724i | 0.994638 | + | 0.103421i | \(0.0329790\pi\) |
−0.743889 | + | 0.668303i | \(0.767021\pi\) | |||||||
\(182\) | − | 0.323429i | − | 0.0239741i | ||||||
\(183\) | 23.3184 | − | 7.57661i | 1.72375 | − | 0.560079i | ||||
\(184\) | −2.99148 | − | 2.17344i | −0.220535 | − | 0.160228i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 19.5846 | − | 14.2291i | 1.43601 | − | 1.04333i | ||||
\(187\) | 1.86061 | − | 2.56091i | 0.136062 | − | 0.187273i | ||||
\(188\) | −0.534884 | + | 0.736205i | −0.0390105 | + | 0.0536933i | ||||
\(189\) | −0.663995 | + | 0.482421i | −0.0482986 | + | 0.0350910i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.26824 | − | 0.921429i | −0.0917665 | − | 0.0666723i | 0.540956 | − | 0.841051i | \(-0.318063\pi\) |
−0.632722 | + | 0.774379i | \(0.718063\pi\) | |||||||
\(192\) | 20.9183 | − | 6.79677i | 1.50965 | − | 0.490514i | ||||
\(193\) | 1.65786i | 0.119335i | 0.998218 | + | 0.0596675i | \(0.0190040\pi\) | ||||
−0.998218 | + | 0.0596675i | \(0.980996\pi\) | |||||||
\(194\) | −5.33154 | − | 16.4088i | −0.382782 | − | 1.17808i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.50940 | − | 4.64545i | 0.107814 | − | 0.331818i | ||||
\(197\) | −12.6330 | − | 4.10470i | −0.900061 | − | 0.292448i | −0.177799 | − | 0.984067i | \(-0.556898\pi\) |
−0.722262 | + | 0.691619i | \(0.756898\pi\) | |||||||
\(198\) | 5.03042 | + | 6.92378i | 0.357496 | + | 0.492051i | ||||
\(199\) | −12.1025 | −0.857921 | −0.428960 | − | 0.903323i | \(-0.641120\pi\) | ||||
−0.428960 | + | 0.903323i | \(0.641120\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.02107 | 0.565763 | ||||||||
\(202\) | −12.2590 | − | 16.8730i | −0.862539 | − | 1.18718i | ||||
\(203\) | −2.13330 | − | 0.693150i | −0.149728 | − | 0.0486496i | ||||
\(204\) | −0.909830 | + | 2.80017i | −0.0637008 | + | 0.196051i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.16345 | + | 12.8138i | 0.290082 | + | 0.892779i | ||||
\(207\) | 4.53482i | 0.315192i | ||||||||
\(208\) | 1.37257 | − | 0.445974i | 0.0951704 | − | 0.0309227i | ||||
\(209\) | 8.01054 | + | 5.81999i | 0.554100 | + | 0.402577i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.42091 | − | 3.93852i | 0.373191 | − | 0.271139i | −0.385342 | − | 0.922774i | \(-0.625917\pi\) |
0.758533 | + | 0.651635i | \(0.225917\pi\) | |||||||
\(212\) | 2.13409 | − | 2.93732i | 0.146570 | − | 0.201736i | ||||
\(213\) | 10.5047 | − | 14.4585i | 0.719772 | − | 0.990681i | ||||
\(214\) | 0.692401 | − | 0.503059i | 0.0473316 | − | 0.0343884i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.01906 | − | 3.64656i | −0.341504 | − | 0.248117i | ||||
\(217\) | −3.17683 | + | 1.03221i | −0.215657 | + | 0.0700712i | ||||
\(218\) | 10.3819i | 0.703152i | ||||||||
\(219\) | 0.438463 | + | 1.34945i | 0.0296286 | + | 0.0911873i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.342690 | + | 1.05469i | −0.0230518 | + | 0.0709463i | ||||
\(222\) | 14.4116 | + | 4.68260i | 0.967241 | + | 0.314276i | ||||
\(223\) | 6.22564 | + | 8.56885i | 0.416900 | + | 0.573813i | 0.964884 | − | 0.262675i | \(-0.0846048\pi\) |
−0.547985 | + | 0.836488i | \(0.684605\pi\) | |||||||
\(224\) | −1.55545 | −0.103928 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.5566 | −0.968293 | ||||||||
\(227\) | 11.5272 | + | 15.8658i | 0.765087 | + | 1.05305i | 0.996774 | + | 0.0802612i | \(0.0255755\pi\) |
−0.231687 | + | 0.972790i | \(0.574425\pi\) | |||||||
\(228\) | −8.75892 | − | 2.84595i | −0.580074 | − | 0.188477i | ||||
\(229\) | −2.73139 | + | 8.40637i | −0.180496 | + | 0.555508i | −0.999842 | − | 0.0177908i | \(-0.994337\pi\) |
0.819346 | + | 0.573299i | \(0.194337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.654963 | − | 2.01577i | −0.0430934 | − | 0.132628i | ||||
\(232\) | − | 16.9552i | − | 1.11316i | ||||||
\(233\) | −10.5210 | + | 3.41848i | −0.689253 | + | 0.223952i | −0.632642 | − | 0.774445i | \(-0.718029\pi\) |
−0.0566109 | + | 0.998396i | \(0.518029\pi\) | |||||||
\(234\) | −2.42563 | − | 1.76233i | −0.158569 | − | 0.115207i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.75824 | + | 2.73052i | −0.244641 | + | 0.177742i | ||||
\(237\) | −8.38615 | + | 11.5425i | −0.544739 | + | 0.749769i | ||||
\(238\) | −0.429430 | + | 0.591060i | −0.0278358 | + | 0.0383127i | ||||
\(239\) | 13.0296 | − | 9.46655i | 0.842814 | − | 0.612340i | −0.0803411 | − | 0.996767i | \(-0.525601\pi\) |
0.923155 | + | 0.384427i | \(0.125601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.84498 | − | 3.52009i | −0.312093 | − | 0.226749i | 0.420701 | − | 0.907199i | \(-0.361784\pi\) |
−0.732794 | + | 0.680451i | \(0.761784\pi\) | |||||||
\(242\) | 7.54752 | − | 2.45234i | 0.485173 | − | 0.157642i | ||||
\(243\) | − | 21.8639i | − | 1.40257i | ||||||
\(244\) | −2.08051 | − | 6.40315i | −0.133191 | − | 0.409920i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.58002 | + | 20.2512i | −0.419527 | + | 1.29117i | ||||
\(247\) | −3.29908 | − | 1.07193i | −0.209915 | − | 0.0682056i | ||||
\(248\) | −14.8410 | − | 20.4269i | −0.942404 | − | 1.29711i | ||||
\(249\) | 2.53546 | 0.160678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.73176 | 0.235547 | 0.117773 | − | 0.993041i | \(-0.462424\pi\) | ||||
0.117773 | + | 0.993041i | \(0.462424\pi\) | |||||||
\(252\) | 0.645616 | + | 0.888614i | 0.0406700 | + | 0.0559774i | ||||
\(253\) | −2.28528 | − | 0.742534i | −0.143675 | − | 0.0466827i | ||||
\(254\) | −2.48918 | + | 7.66092i | −0.156185 | + | 0.480689i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.54307 | − | 13.9821i | −0.283942 | − | 0.873884i | ||||
\(257\) | 23.5935i | 1.47172i | 0.677132 | + | 0.735862i | \(0.263223\pi\) | ||||
−0.677132 | + | 0.735862i | \(0.736777\pi\) | |||||||
\(258\) | −25.7212 | + | 8.35731i | −1.60133 | + | 0.520304i | ||||
\(259\) | −1.69158 | − | 1.22900i | −0.105109 | − | 0.0763665i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.8225 | + | 12.2223i | −1.04129 | + | 0.756540i | ||||
\(262\) | 1.59547 | − | 2.19598i | 0.0985685 | − | 0.135668i | ||||
\(263\) | −3.90363 | + | 5.37289i | −0.240708 | + | 0.331307i | −0.912230 | − | 0.409678i | \(-0.865641\pi\) |
0.671522 | + | 0.740985i | \(0.265641\pi\) | |||||||
\(264\) | 12.9613 | − | 9.41695i | 0.797714 | − | 0.579573i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.84883 | − | 1.34326i | −0.113359 | − | 0.0823604i | ||||
\(267\) | −5.61044 | + | 1.82294i | −0.343353 | + | 0.111562i | ||||
\(268\) | − | 2.20256i | − | 0.134543i | ||||||
\(269\) | 4.03078 | + | 12.4055i | 0.245761 | + | 0.756375i | 0.995510 | + | 0.0946532i | \(0.0301742\pi\) |
−0.749749 | + | 0.661722i | \(0.769826\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.66147 | + | 11.2689i | −0.222419 | + | 0.684534i | 0.776125 | + | 0.630579i | \(0.217183\pi\) |
−0.998543 | + | 0.0539549i | \(0.982817\pi\) | |||||||
\(272\) | −3.10048 | − | 1.00741i | −0.187994 | − | 0.0610830i | ||||
\(273\) | 0.436451 | + | 0.600723i | 0.0264152 | + | 0.0363574i | ||||
\(274\) | −21.5623 | −1.30263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.23498 | 0.134530 | ||||||||
\(277\) | 9.96641 | + | 13.7176i | 0.598824 | + | 0.824210i | 0.995600 | − | 0.0937053i | \(-0.0298711\pi\) |
−0.396776 | + | 0.917915i | \(0.629871\pi\) | |||||||
\(278\) | 7.26147 | + | 2.35939i | 0.435514 | + | 0.141507i | ||||
\(279\) | −9.56882 | + | 29.4498i | −0.572870 | + | 1.76311i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.56826 | − | 4.82659i | −0.0935543 | − | 0.287930i | 0.893320 | − | 0.449421i | \(-0.148370\pi\) |
−0.986874 | + | 0.161491i | \(0.948370\pi\) | |||||||
\(282\) | 3.75704i | 0.223728i | ||||||||
\(283\) | −11.2461 | + | 3.65408i | −0.668511 | + | 0.217212i | −0.623558 | − | 0.781777i | \(-0.714314\pi\) |
−0.0449525 | + | 0.998989i | \(0.514314\pi\) | |||||||
\(284\) | −3.97026 | − | 2.88456i | −0.235592 | − | 0.171167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.28528 | − | 0.933814i | 0.0760005 | − | 0.0552176i | ||||
\(287\) | 1.72700 | − | 2.37702i | 0.101942 | − | 0.140311i | ||||
\(288\) | −8.47544 | + | 11.6654i | −0.499420 | + | 0.687393i | ||||
\(289\) | −11.7267 | + | 8.51992i | −0.689804 | + | 0.501172i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.0454 | + | 23.2823i | 1.87853 | + | 1.36484i | ||||
\(292\) | 0.370554 | − | 0.120400i | 0.0216851 | − | 0.00704590i | ||||
\(293\) | − | 19.4348i | − | 1.13540i | −0.823237 | − | 0.567698i | \(-0.807834\pi\) | ||
0.823237 | − | 0.567698i | \(-0.192166\pi\) | |||||||
\(294\) | −6.23173 | − | 19.1793i | −0.363442 | − | 1.11856i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.88398 | − | 15.0313i | 0.283875 | − | 0.873679i | ||||
\(297\) | −3.83422 | − | 1.24581i | −0.222484 | − | 0.0722894i | ||||
\(298\) | −0.480118 | − | 0.660825i | −0.0278125 | − | 0.0382806i | ||||
\(299\) | 0.841814 | 0.0486834 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.73176 | 0.215095 | ||||||||
\(302\) | 10.3407 | + | 14.2328i | 0.595040 | + | 0.819003i | ||||
\(303\) | 45.5386 | + | 14.7964i | 2.61612 | + | 0.850030i | ||||
\(304\) | 3.15117 | − | 9.69829i | 0.180732 | − | 0.556235i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.09288 | + | 6.44123i | 0.119642 | + | 0.368221i | ||||
\(307\) | − | 25.4169i | − | 1.45062i | −0.688423 | − | 0.725310i | \(-0.741697\pi\) | ||
0.688423 | − | 0.725310i | \(-0.258303\pi\) | |||||||
\(308\) | −0.553523 | + | 0.179851i | −0.0315399 | + | 0.0102479i | ||||
\(309\) | −25.0246 | − | 18.1814i | −1.42360 | − | 1.03431i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.8292 | + | 9.32097i | −0.727478 | + | 0.528544i | −0.888765 | − | 0.458364i | \(-0.848436\pi\) |
0.161287 | + | 0.986908i | \(0.448436\pi\) | |||||||
\(312\) | −3.29908 | + | 4.54079i | −0.186773 | + | 0.257072i | ||||
\(313\) | 4.12416 | − | 5.67642i | 0.233111 | − | 0.320850i | −0.676396 | − | 0.736538i | \(-0.736459\pi\) |
0.909507 | + | 0.415688i | \(0.136459\pi\) | |||||||
\(314\) | −2.55361 | + | 1.85530i | −0.144108 | + | 0.104701i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.16955 | + | 2.30281i | 0.178301 | + | 0.129543i | ||||
\(317\) | 12.3958 | − | 4.02763i | 0.696215 | − | 0.226214i | 0.0605344 | − | 0.998166i | \(-0.480720\pi\) |
0.635681 | + | 0.771952i | \(0.280720\pi\) | |||||||
\(318\) | − | 14.9899i | − | 0.840590i | ||||||
\(319\) | −3.40479 | − | 10.4789i | −0.190632 | − | 0.586704i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.607184 | + | 1.86872i | −0.0338897 | + | 0.104302i | ||||
\(322\) | 0.527445 | + | 0.171377i | 0.0293933 | + | 0.00955047i | ||||
\(323\) | 4.60575 | + | 6.33927i | 0.256271 | + | 0.352726i | ||||
\(324\) | −4.34318 | −0.241288 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.4440 | 1.51998 | ||||||||
\(327\) | −14.0099 | − | 19.2829i | −0.774747 | − | 1.06635i | ||||
\(328\) | 21.1221 | + | 6.86300i | 1.16628 | + | 0.378946i | ||||
\(329\) | 0.160198 | − | 0.493039i | 0.00883201 | − | 0.0271821i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.45225 | − | 16.7803i | −0.299683 | − | 0.922329i | −0.981608 | − | 0.190907i | \(-0.938857\pi\) |
0.681925 | − | 0.731422i | \(-0.261143\pi\) | |||||||
\(332\) | − | 0.696229i | − | 0.0382105i | ||||||
\(333\) | −18.4344 | + | 5.98970i | −1.01020 | + | 0.328234i | ||||
\(334\) | 17.4689 | + | 12.6919i | 0.955855 | + | 0.694469i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.76594 | + | 1.28303i | −0.0963401 | + | 0.0699952i | ||||
\(337\) | −14.6062 | + | 20.1037i | −0.795649 | + | 1.09512i | 0.197733 | + | 0.980256i | \(0.436642\pi\) |
−0.993382 | + | 0.114860i | \(0.963358\pi\) | |||||||
\(338\) | 8.33572 | − | 11.4731i | 0.453404 | − | 0.624056i | ||||
\(339\) | 27.0369 | − | 19.6434i | 1.46844 | − | 1.06689i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.2742 | − | 9.64426i | −0.718837 | − | 0.522266i | ||||
\(342\) | −20.1482 | + | 6.54654i | −1.08949 | + | 0.353996i | ||||
\(343\) | 5.63276i | 0.304141i | ||||||||
\(344\) | 8.71673 | + | 26.8273i | 0.469974 | + | 1.44643i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.64089 | − | 14.2832i | 0.249496 | − | 0.767869i | ||||
\(347\) | −12.6276 | − | 4.10297i | −0.677887 | − | 0.220259i | −0.0502171 | − | 0.998738i | \(-0.515991\pi\) |
−0.627670 | + | 0.778479i | \(0.715991\pi\) | |||||||
\(348\) | 6.02375 | + | 8.29098i | 0.322907 | + | 0.444443i | ||||
\(349\) | 18.1283 | 0.970385 | 0.485192 | − | 0.874407i | \(-0.338750\pi\) | ||||
0.485192 | + | 0.874407i | \(0.338750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41238 | 0.0753875 | ||||||||
\(352\) | −4.49094 | − | 6.18124i | −0.239368 | − | 0.329461i | ||||
\(353\) | −16.8377 | − | 5.47091i | −0.896182 | − | 0.291187i | −0.175522 | − | 0.984476i | \(-0.556161\pi\) |
−0.720660 | + | 0.693288i | \(0.756161\pi\) | |||||||
\(354\) | −5.92672 | + | 18.2406i | −0.315001 | + | 0.969475i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.500574 | + | 1.54061i | 0.0265304 | + | 0.0816521i | ||||
\(357\) | − | 1.67730i | − | 0.0887723i | ||||||
\(358\) | −13.1812 | + | 4.28282i | −0.696646 | + | 0.226354i | ||||
\(359\) | 26.3289 | + | 19.1291i | 1.38959 | + | 1.00959i | 0.995910 | + | 0.0903458i | \(0.0287972\pi\) |
0.393677 | + | 0.919249i | \(0.371203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.45789 | + | 3.23885i | −0.234626 | + | 0.170466i | ||||
\(362\) | 7.27467 | − | 10.0127i | 0.382348 | − | 0.526257i | ||||
\(363\) | −10.7091 | + | 14.7399i | −0.562084 | + | 0.773642i | ||||
\(364\) | 0.164956 | − | 0.119848i | 0.00864607 | − | 0.00628174i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −22.4879 | − | 16.3384i | −1.17546 | − | 0.854024i | ||||
\(367\) | 31.3355 | − | 10.1815i | 1.63570 | − | 0.531472i | 0.660129 | − | 0.751152i | \(-0.270501\pi\) |
0.975572 | + | 0.219680i | \(0.0705014\pi\) | |||||||
\(368\) | 2.47468i | 0.129002i | ||||||||
\(369\) | −8.41677 | − | 25.9042i | −0.438160 | − | 1.34852i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.639160 | + | 1.96713i | −0.0331835 | + | 0.102128i | ||||
\(372\) | 14.5143 | + | 4.71599i | 0.752533 | + | 0.244513i | ||||
\(373\) | −2.03754 | − | 2.80444i | −0.105500 | − | 0.145208i | 0.753003 | − | 0.658018i | \(-0.228605\pi\) |
−0.858503 | + | 0.512809i | \(0.828605\pi\) | |||||||
\(374\) | −3.58870 | −0.185567 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.91861 | 0.202087 | ||||||||
\(377\) | 2.26886 | + | 3.12282i | 0.116852 | + | 0.160834i | ||||
\(378\) | 0.884939 | + | 0.287534i | 0.0455164 | + | 0.0147892i | ||||
\(379\) | 0.595979 | − | 1.83424i | 0.0306134 | − | 0.0942183i | −0.934582 | − | 0.355747i | \(-0.884227\pi\) |
0.965196 | + | 0.261528i | \(0.0842265\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.71472 | − | 17.5881i | −0.292774 | − | 0.901065i | ||||
\(382\) | 1.77723i | 0.0909309i | ||||||||
\(383\) | 4.68874 | − | 1.52346i | 0.239583 | − | 0.0778454i | −0.186764 | − | 0.982405i | \(-0.559800\pi\) |
0.426348 | + | 0.904559i | \(0.359800\pi\) | |||||||
\(384\) | −4.08490 | − | 2.96786i | −0.208457 | − | 0.151453i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.52056 | − | 1.10475i | 0.0773945 | − | 0.0562304i | ||||
\(387\) | 20.3339 | − | 27.9873i | 1.03363 | − | 1.42267i | ||||
\(388\) | 6.39326 | − | 8.79956i | 0.324568 | − | 0.446730i | ||||
\(389\) | 10.8295 | − | 7.86809i | 0.549077 | − | 0.398928i | −0.278368 | − | 0.960475i | \(-0.589793\pi\) |
0.827445 | + | 0.561547i | \(0.189793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53840 | − | 1.11771i | −0.0778002 | − | 0.0565252i | ||||
\(392\) | −20.0041 | + | 6.49973i | −1.01036 | + | 0.328286i | ||||
\(393\) | 6.23172i | 0.314349i | ||||||||
\(394\) | 4.65351 | + | 14.3220i | 0.234441 | + | 0.721534i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.66725 | + | 5.13127i | −0.0837825 | + | 0.257856i | ||||
\(397\) | −2.03418 | − | 0.660946i | −0.102093 | − | 0.0331719i | 0.257525 | − | 0.966272i | \(-0.417093\pi\) |
−0.359618 | + | 0.933100i | \(0.617093\pi\) | |||||||
\(398\) | 8.06477 | + | 11.1002i | 0.404250 | + | 0.556403i | ||||
\(399\) | 5.24660 | 0.262659 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8213 | −1.33939 | −0.669696 | − | 0.742635i | \(-0.733576\pi\) | ||||
−0.669696 | + | 0.742635i | \(0.733576\pi\) | |||||||
\(402\) | −5.34504 | − | 7.35681i | −0.266586 | − | 0.366924i | ||||
\(403\) | 5.46687 | + | 1.77629i | 0.272324 | + | 0.0884835i | ||||
\(404\) | 4.06304 | − | 12.5048i | 0.202144 | − | 0.622135i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.785827 | + | 2.41853i | 0.0389999 | + | 0.120029i | ||||
\(407\) | − | 10.2706i | − | 0.509097i | ||||||
\(408\) | 12.0580 | − | 3.91788i | 0.596960 | − | 0.193964i | ||||
\(409\) | 11.3248 | + | 8.22796i | 0.559976 | + | 0.406847i | 0.831450 | − | 0.555599i | \(-0.187511\pi\) |
−0.271474 | + | 0.962446i | \(0.587511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 40.0489 | − | 29.0972i | 1.97547 | − | 1.43526i | ||||
\(412\) | −4.99256 | + | 6.87167i | −0.245966 | + | 0.338543i | ||||
\(413\) | 1.55554 | − | 2.14101i | 0.0765429 | − | 0.105352i | ||||
\(414\) | 4.15927 | − | 3.02189i | 0.204417 | − | 0.148518i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.16550 | + | 1.57333i | 0.106172 | + | 0.0771387i | ||||
\(417\) | −16.6710 | + | 5.41674i | −0.816384 | + | 0.265259i | ||||
\(418\) | − | 11.2254i | − | 0.549055i | ||||||
\(419\) | −9.54925 | − | 29.3896i | −0.466511 | − | 1.43577i | −0.857072 | − | 0.515197i | \(-0.827719\pi\) |
0.390560 | − | 0.920577i | \(-0.372281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.54622 | + | 7.83646i | −0.124095 | + | 0.381926i | −0.993735 | − | 0.111761i | \(-0.964351\pi\) |
0.869640 | + | 0.493687i | \(0.164351\pi\) | |||||||
\(422\) | −7.22471 | − | 2.34745i | −0.351693 | − | 0.114272i | ||||
\(423\) | −2.82477 | − | 3.88796i | −0.137345 | − | 0.189039i | ||||
\(424\) | −15.6345 | −0.759279 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −20.2612 | −0.981660 | ||||||||
\(427\) | 2.25445 | + | 3.10298i | 0.109100 | + | 0.150164i | ||||
\(428\) | 0.513144 | + | 0.166731i | 0.0248038 | + | 0.00805923i | ||||
\(429\) | −1.12710 | + | 3.46885i | −0.0544168 | + | 0.167478i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.38925 | + | 25.8194i | 0.404096 | + | 1.24368i | 0.921648 | + | 0.388027i | \(0.126843\pi\) |
−0.517552 | + | 0.855652i | \(0.673157\pi\) | |||||||
\(432\) | 4.15198i | 0.199762i | ||||||||
\(433\) | 20.4387 | − | 6.64093i | 0.982220 | − | 0.319143i | 0.226481 | − | 0.974016i | \(-0.427278\pi\) |
0.755739 | + | 0.654873i | \(0.227278\pi\) | |||||||
\(434\) | 3.06369 | + | 2.22590i | 0.147062 | + | 0.106847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.29503 | + | 3.84706i | −0.253586 | + | 0.184241i | ||||
\(437\) | 3.49620 | − | 4.81211i | 0.167246 | − | 0.230194i | ||||
\(438\) | 0.945515 | − | 1.30139i | 0.0451785 | − | 0.0621828i | ||||
\(439\) | −20.8691 | + | 15.1623i | −0.996027 | + | 0.723656i | −0.961233 | − | 0.275739i | \(-0.911078\pi\) |
−0.0347942 | + | 0.999394i | \(0.511078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.8690 | + | 15.1622i | 0.993763 | + | 0.722011i | ||||
\(442\) | 1.19571 | − | 0.388509i | 0.0568741 | − | 0.0184795i | ||||
\(443\) | − | 3.18479i | − | 0.151314i | −0.997134 | − | 0.0756570i | \(-0.975895\pi\) | ||
0.997134 | − | 0.0756570i | \(-0.0241054\pi\) | |||||||
\(444\) | 2.95203 | + | 9.08540i | 0.140097 | + | 0.431174i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.71063 | − | 11.4201i | 0.175703 | − | 0.540759i | ||||
\(447\) | 1.78350 | + | 0.579494i | 0.0843566 | + | 0.0274091i | ||||
\(448\) | 2.02240 | + | 2.78360i | 0.0955496 | + | 0.131513i | ||||
\(449\) | −36.0785 | −1.70265 | −0.851325 | − | 0.524639i | \(-0.824200\pi\) | ||||
−0.851325 | + | 0.524639i | \(0.824200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.4324 | 0.679594 | ||||||||
\(452\) | −5.39402 | − | 7.42424i | −0.253714 | − | 0.349207i | ||||
\(453\) | −38.4127 | − | 12.4811i | −1.80479 | − | 0.586411i | ||||
\(454\) | 6.87048 | − | 21.1452i | 0.322448 | − | 0.992392i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.2551 | + | 37.7174i | 0.573899 | + | 1.76628i | ||||
\(457\) | 25.5245i | 1.19399i | 0.802246 | + | 0.596994i | \(0.203638\pi\) | ||||
−0.802246 | + | 0.596994i | \(0.796362\pi\) | |||||||
\(458\) | 9.53033 | − | 3.09659i | 0.445323 | − | 0.144694i | ||||
\(459\) | −2.58111 | − | 1.87528i | −0.120476 | − | 0.0875307i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4614 | − | 9.78026i | 0.626959 | − | 0.455512i | −0.228387 | − | 0.973571i | \(-0.573345\pi\) |
0.855345 | + | 0.518058i | \(0.173345\pi\) | |||||||
\(462\) | −1.41238 | + | 1.94398i | −0.0657100 | + | 0.0904421i | ||||
\(463\) | −10.4730 | + | 14.4149i | −0.486723 | + | 0.669916i | −0.979779 | − | 0.200081i | \(-0.935880\pi\) |
0.493057 | + | 0.869997i | \(0.335880\pi\) | |||||||
\(464\) | −9.18017 | + | 6.66978i | −0.426178 | + | 0.309637i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.1463 | + | 7.37171i | 0.470018 | + | 0.341488i | ||||
\(467\) | 13.5507 | − | 4.40289i | 0.627051 | − | 0.203741i | 0.0217829 | − | 0.999763i | \(-0.493066\pi\) |
0.605269 | + | 0.796021i | \(0.293066\pi\) | |||||||
\(468\) | − | 1.89017i | − | 0.0873731i | ||||||
\(469\) | 0.387743 | + | 1.19335i | 0.0179043 | + | 0.0551038i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.23932 | − | 6.89193i | 0.103183 | − | 0.317563i | ||||
\(472\) | 19.0250 | + | 6.18160i | 0.875697 | + | 0.284531i | ||||
\(473\) | 10.7745 | + | 14.8298i | 0.495411 | + | 0.681874i | ||||
\(474\) | 16.1750 | 0.742941 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.460582 | −0.0211107 | ||||||||
\(477\) | 11.2703 | + | 15.5122i | 0.516031 | + | 0.710255i | ||||
\(478\) | −17.3652 | − | 5.64229i | −0.794265 | − | 0.258072i | ||||
\(479\) | −0.898820 | + | 2.76628i | −0.0410681 | + | 0.126395i | −0.969489 | − | 0.245137i | \(-0.921167\pi\) |
0.928420 | + | 0.371531i | \(0.121167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.11189 | + | 3.42205i | 0.0506978 | + | 0.156032i | ||||
\(482\) | 6.78945i | 0.309251i | ||||||||
\(483\) | −1.21092 | + | 0.393451i | −0.0550987 | + | 0.0179026i | ||||
\(484\) | 4.04752 | + | 2.94069i | 0.183978 | + | 0.133668i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −20.0532 | + | 14.5695i | −0.909633 | + | 0.660887i | ||||
\(487\) | −10.0307 | + | 13.8060i | −0.454533 | + | 0.625612i | −0.973364 | − | 0.229266i | \(-0.926368\pi\) |
0.518831 | + | 0.854877i | \(0.326368\pi\) | |||||||
\(488\) | −17.0411 | + | 23.4550i | −0.771414 | + | 1.06176i | ||||
\(489\) | −50.9733 | + | 37.0343i | −2.30509 | + | 1.67475i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8990 | − | 18.0902i | −1.12368 | − | 0.816398i | −0.138913 | − | 0.990305i | \(-0.544361\pi\) |
−0.984762 | + | 0.173906i | \(0.944361\pi\) | |||||||
\(492\) | −12.7669 | + | 4.14821i | −0.575575 | + | 0.187016i | ||||
\(493\) | − | 8.71937i | − | 0.392701i | ||||||
\(494\) | 1.21526 | + | 3.74018i | 0.0546770 | + | 0.168278i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.22177 | + | 16.0709i | −0.234464 | + | 0.721607i | ||||
\(497\) | 2.65890 | + | 0.863928i | 0.119268 | + | 0.0387525i | ||||
\(498\) | −1.68956 | − | 2.32549i | −0.0757112 | − | 0.104208i | ||||
\(499\) | 11.8824 | 0.531927 | 0.265964 | − | 0.963983i | \(-0.414310\pi\) | ||||
0.265964 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.5730 | −2.21476 | ||||||||
\(502\) | −2.48675 | − | 3.42272i | −0.110989 | − | 0.152763i | ||||
\(503\) | 2.83247 | + | 0.920324i | 0.126293 | + | 0.0410352i | 0.371482 | − | 0.928440i | \(-0.378850\pi\) |
−0.245188 | + | 0.969475i | \(0.578850\pi\) | |||||||
\(504\) | 1.46160 | − | 4.49834i | 0.0651049 | − | 0.200372i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.841814 | + | 2.59084i | 0.0374232 | + | 0.115177i | ||||
\(507\) | 32.5584i | 1.44597i | ||||||||
\(508\) | −4.82963 | + | 1.56924i | −0.214280 | + | 0.0696239i | ||||
\(509\) | −29.7038 | − | 21.5811i | −1.31660 | − | 0.956564i | −0.999968 | − | 0.00801464i | \(-0.997449\pi\) |
−0.316629 | − | 0.948549i | \(-0.602551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.179571 | + | 0.130466i | −0.00794377 | + | 0.00577149i | ||||
\(512\) | −12.0774 | + | 16.6231i | −0.533749 | + | 0.734642i | ||||
\(513\) | 5.86588 | − | 8.07369i | 0.258985 | − | 0.356462i | ||||
\(514\) | 21.6396 | − | 15.7221i | 0.954484 | − | 0.693473i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.7935 | − | 10.0216i | −0.607226 | − | 0.441176i | ||||
\(517\) | 2.42184 | − | 0.786902i | 0.106512 | − | 0.0346079i | ||||
\(518\) | 2.37047i | 0.104152i | ||||||||
\(519\) | 10.6546 | + | 32.7916i | 0.467687 | + | 1.43939i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.772662 | − | 2.37801i | 0.0338509 | − | 0.104182i | −0.932703 | − | 0.360644i | \(-0.882557\pi\) |
0.966554 | + | 0.256462i | \(0.0825568\pi\) | |||||||
\(522\) | 22.4202 | + | 7.28477i | 0.981306 | + | 0.318846i | ||||
\(523\) | −24.7609 | − | 34.0805i | −1.08272 | − | 1.49024i | −0.856491 | − | 0.516162i | \(-0.827360\pi\) |
−0.226229 | − | 0.974074i | \(-0.572640\pi\) | |||||||
\(524\) | 1.71121 | 0.0747545 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.52922 | 0.328290 | ||||||||
\(527\) | −7.63214 | − | 10.5047i | −0.332461 | − | 0.457594i | ||||
\(528\) | −10.1974 | − | 3.31333i | −0.443784 | − | 0.144194i | ||||
\(529\) | 6.66133 | − | 20.5015i | 0.289623 | − | 0.891369i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.58111 | − | 23.3322i | −0.328992 | − | 1.01253i | ||||
\(532\) | − | 1.44070i | − | 0.0624623i | ||||||
\(533\) | −4.80868 | + | 1.56244i | −0.208287 | + | 0.0676766i | ||||
\(534\) | 5.41063 | + | 3.93105i | 0.234141 | + | 0.170113i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.67320 | + | 5.57490i | −0.331432 | + | 0.240799i | ||||
\(537\) | 18.7027 | − | 25.7420i | 0.807080 | − | 1.11085i | ||||
\(538\) | 8.69212 | − | 11.9637i | 0.374744 | − | 0.515791i | ||||
\(539\) | −11.0580 | + | 8.03411i | −0.476302 | + | 0.346053i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.1259 | + | 16.0754i | 0.951268 | + | 0.691137i | 0.951107 | − | 0.308863i | \(-0.0999485\pi\) |
0.000161922 | 1.00000i | \(0.499948\pi\) | ||||||||
\(542\) | 12.7756 | − | 4.15103i | 0.548757 | − | 0.178302i | ||||
\(543\) | 28.4140i | 1.21936i | ||||||||
\(544\) | −1.86843 | − | 5.75045i | −0.0801085 | − | 0.246549i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.260135 | − | 0.800613i | 0.0111327 | − | 0.0342631i | ||||
\(547\) | −19.3437 | − | 6.28515i | −0.827077 | − | 0.268734i | −0.135263 | − | 0.990810i | \(-0.543188\pi\) |
−0.691814 | + | 0.722076i | \(0.743188\pi\) | |||||||
\(548\) | −7.99001 | − | 10.9973i | −0.341316 | − | 0.469781i | ||||
\(549\) | 35.5558 | 1.51748 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.2742 | 1.16192 | ||||||||
\(552\) | −5.65697 | − | 7.78616i | −0.240777 | − | 0.331401i | ||||
\(553\) | −2.12266 | − | 0.689692i | −0.0902645 | − | 0.0293287i | ||||
\(554\) | 5.94022 | − | 18.2821i | 0.252376 | − | 0.776732i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.48742 | + | 4.57781i | 0.0630807 | + | 0.194142i | ||||
\(557\) | − | 28.2605i | − | 1.19744i | −0.800960 | − | 0.598718i | \(-0.795677\pi\) | ||
0.800960 | − | 0.598718i | \(-0.204323\pi\) | |||||||
\(558\) | 33.3873 | − | 10.8482i | 1.41340 | − | 0.459241i | ||||
\(559\) | −5.19537 | − | 3.77466i | −0.219741 | − | 0.159651i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.66550 | − | 4.84277i | 0.281418 | − | 0.204462i | ||||
\(562\) | −3.38184 | + | 4.65470i | −0.142654 | + | 0.196347i | ||||
\(563\) | 7.59738 | − | 10.4569i | 0.320192 | − | 0.440706i | −0.618334 | − | 0.785915i | \(-0.712192\pi\) |
0.938526 | + | 0.345210i | \(0.112192\pi\) | |||||||
\(564\) | −1.91618 | + | 1.39219i | −0.0806858 | + | 0.0586216i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.8456 | + | 7.87977i | 0.455874 | + | 0.331212i | ||||
\(567\) | 2.35314 | − | 0.764582i | 0.0988226 | − | 0.0321094i | ||||
\(568\) | 21.1326i | 0.886703i | ||||||||
\(569\) | 0.953142 | + | 2.93347i | 0.0399578 | + | 0.122977i | 0.969046 | − | 0.246882i | \(-0.0794059\pi\) |
−0.929088 | + | 0.369859i | \(0.879406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.27552 | + | 3.92564i | −0.0533788 | + | 0.164283i | −0.974192 | − | 0.225721i | \(-0.927526\pi\) |
0.920813 | + | 0.390004i | \(0.127526\pi\) | |||||||
\(572\) | 0.952536 | + | 0.309498i | 0.0398275 | + | 0.0129407i | ||||
\(573\) | −2.39828 | − | 3.30095i | −0.100190 | − | 0.137899i | ||||
\(574\) | −3.33100 | −0.139033 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 31.8961 | 1.32901 | ||||||||
\(577\) | 3.73579 | + | 5.14187i | 0.155523 | + | 0.214059i | 0.879667 | − | 0.475589i | \(-0.157765\pi\) |
−0.724145 | + | 0.689648i | \(0.757765\pi\) | |||||||
\(578\) | 15.6287 | + | 5.07807i | 0.650068 | + | 0.211220i | ||||
\(579\) | −1.33342 | + | 4.10384i | −0.0554150 | + | 0.170550i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.122565 | + | 0.377218i | 0.00508487 | + | 0.0156496i | ||||
\(582\) | − | 44.9063i | − | 1.86143i | ||||||
\(583\) | −9.66266 | + | 3.13959i | −0.400187 | + | 0.130028i | ||||
\(584\) | −1.35736 | − | 0.986178i | −0.0561679 | − | 0.0408083i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.8254 | + | 12.9509i | −0.736359 | + | 0.534996i | ||||
\(587\) | 12.4046 | − | 17.0735i | 0.511992 | − | 0.704697i | −0.472261 | − | 0.881459i | \(-0.656562\pi\) |
0.984254 | + | 0.176761i | \(0.0565621\pi\) | |||||||
\(588\) | 7.47271 | − | 10.2853i | 0.308169 | − | 0.424159i | ||||
\(589\) | 32.8588 | − | 23.8733i | 1.35392 | − | 0.983683i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.9701 | − | 20.3215i | −1.15054 | − | 0.835913i | ||||
\(592\) | −10.0598 | + | 3.26862i | −0.413455 | + | 0.134340i | ||||
\(593\) | 21.6529i | 0.889177i | 0.895735 | + | 0.444589i | \(0.146650\pi\) | ||||
−0.895735 | + | 0.444589i | \(0.853350\pi\) | |||||||
\(594\) | 1.41238 | + | 4.34687i | 0.0579508 | + | 0.178354i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.159127 | − | 0.489743i | 0.00651810 | − | 0.0200607i | ||||
\(597\) | −29.9583 | − | 9.73405i | −1.22611 | − | 0.398388i | ||||
\(598\) | −0.560963 | − | 0.772100i | −0.0229395 | − | 0.0315735i | ||||
\(599\) | 3.38501 | 0.138308 | 0.0691539 | − | 0.997606i | \(-0.477970\pi\) | ||||
0.0691539 | + | 0.997606i | \(0.477970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8265 | 1.17586 | 0.587928 | − | 0.808913i | \(-0.299944\pi\) | ||||
0.587928 | + | 0.808913i | \(0.299944\pi\) | |||||||
\(602\) | −2.48675 | − | 3.42272i | −0.101352 | − | 0.139500i | ||||
\(603\) | 11.0626 | + | 3.59445i | 0.450503 | + | 0.146377i | ||||
\(604\) | −3.42726 | + | 10.5480i | −0.139453 | + | 0.429193i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.7747 | − | 51.6273i | −0.681427 | − | 2.09722i | ||||
\(607\) | 15.6708i | 0.636059i | 0.948081 | + | 0.318029i | \(0.103021\pi\) | ||||
−0.948081 | + | 0.318029i | \(0.896979\pi\) | |||||||
\(608\) | 17.9874 | − | 5.84446i | 0.729485 | − | 0.237024i | ||||
\(609\) | −4.72324 | − | 3.43163i | −0.191395 | − | 0.139057i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.721736 | + | 0.524372i | −0.0291983 | + | 0.0212138i | ||||
\(612\) | −2.50966 | + | 3.45425i | −0.101447 | + | 0.139630i | ||||
\(613\) | 22.4537 | − | 30.9048i | 0.906896 | − | 1.24823i | −0.0613201 | − | 0.998118i | \(-0.519531\pi\) |
0.968216 | − | 0.250117i | \(-0.0804690\pi\) | |||||||
\(614\) | −23.3120 | + | 16.9372i | −0.940797 | + | 0.683529i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.02758 | + | 1.47312i | 0.0816936 | + | 0.0593539i | ||||
\(617\) | −12.5842 | + | 4.08884i | −0.506619 | + | 0.164611i | −0.551164 | − | 0.834397i | \(-0.685816\pi\) |
0.0445449 | + | 0.999007i | \(0.485816\pi\) | |||||||
\(618\) | 35.0678i | 1.41064i | ||||||||
\(619\) | −1.86789 | − | 5.74878i | −0.0750770 | − | 0.231063i | 0.906475 | − | 0.422260i | \(-0.138763\pi\) |
−0.981552 | + | 0.191197i | \(0.938763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.748388 | + | 2.30330i | −0.0300318 | + | 0.0924284i | ||||
\(622\) | 17.0981 | + | 5.55552i | 0.685572 | + | 0.222756i | ||||
\(623\) | −0.542423 | − | 0.746582i | −0.0217317 | − | 0.0299112i | ||||
\(624\) | 3.75634 | 0.150374 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.95456 | −0.317928 | ||||||||
\(627\) | 15.1482 | + | 20.8497i | 0.604960 | + | 0.832655i | ||||
\(628\) | −1.89250 | − | 0.614911i | −0.0755190 | − | 0.0245376i | ||||
\(629\) | 2.51164 | − | 7.73003i | 0.100146 | − | 0.308216i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6763 | − | 35.9361i | −0.464828 | − | 1.43059i | −0.859199 | − | 0.511642i | \(-0.829037\pi\) |
0.394371 | − | 0.918952i | \(-0.370963\pi\) | |||||||
\(632\) | − | 16.8706i | − | 0.671076i | ||||||
\(633\) | 16.5866 | − | 5.38932i | 0.659259 | − | 0.214206i | ||||
\(634\) | −11.9543 | − | 8.68531i | −0.474766 | − | 0.344938i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.64520 | − | 5.55456i | 0.303152 | − | 0.220253i | ||||
\(637\) | 2.81462 | − | 3.87399i | 0.111519 | − | 0.153493i | ||||
\(638\) | −7.34220 | + | 10.1057i | −0.290681 | + | 0.400087i | ||||
\(639\) | 20.9673 | − | 15.2336i | 0.829452 | − | 0.602632i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.8737 | + | 12.2594i | 0.666470 | + | 0.484219i | 0.868842 | − | 0.495090i | \(-0.164865\pi\) |
−0.202372 | + | 0.979309i | \(0.564865\pi\) | |||||||
\(642\) | 2.11858 | − | 0.688367i | 0.0836135 | − | 0.0271677i | ||||
\(643\) | 37.5552i | 1.48103i | 0.672039 | + | 0.740516i | \(0.265419\pi\) | ||||
−0.672039 | + | 0.740516i | \(0.734581\pi\) | |||||||
\(644\) | 0.108040 | + | 0.332514i | 0.00425739 | + | 0.0131029i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.74513 | − | 8.44865i | 0.108006 | − | 0.332408i | ||||
\(647\) | −26.0592 | − | 8.46714i | −1.02449 | − | 0.332878i | −0.251882 | − | 0.967758i | \(-0.581049\pi\) |
−0.772611 | + | 0.634880i | \(0.781049\pi\) | |||||||
\(648\) | 10.9930 | + | 15.1306i | 0.431847 | + | 0.594387i | ||||
\(649\) | 12.9994 | 0.510272 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.69410 | −0.340749 | ||||||||
\(652\) | 10.1695 | + | 13.9971i | 0.398268 | + | 0.548169i | ||||
\(653\) | −21.9182 | − | 7.12164i | −0.857724 | − | 0.278691i | −0.153046 | − | 0.988219i | \(-0.548908\pi\) |
−0.704678 | + | 0.709528i | \(0.748908\pi\) | |||||||
\(654\) | −8.35021 | + | 25.6993i | −0.326519 | + | 1.00492i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.59309 | − | 14.1361i | −0.179330 | − | 0.551921i | ||||
\(657\) | 2.05763i | 0.0802760i | ||||||||
\(658\) | −0.558961 | + | 0.181617i | −0.0217906 | + | 0.00708018i | ||||
\(659\) | 16.5717 | + | 12.0400i | 0.645540 | + | 0.469012i | 0.861749 | − | 0.507335i | \(-0.169369\pi\) |
−0.216209 | + | 0.976347i | \(0.569369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.3181 | + | 8.22311i | −0.440224 | + | 0.319842i | −0.785724 | − | 0.618577i | \(-0.787709\pi\) |
0.345500 | + | 0.938419i | \(0.387709\pi\) | |||||||
\(662\) | −11.7574 | + | 16.1827i | −0.456965 | + | 0.628959i | ||||
\(663\) | −1.69659 | + | 2.33515i | −0.0658899 | + | 0.0906897i | ||||
\(664\) | −2.42550 | + | 1.76223i | −0.0941275 | + | 0.0683876i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.7779 | + | 12.9164i | 0.688880 | + | 0.500500i | ||||
\(667\) | −6.29489 | + | 2.04533i | −0.243739 | + | 0.0791957i | ||||
\(668\) | 13.6126i | 0.526687i | ||||||||
\(669\) | 8.51893 | + | 26.2186i | 0.329361 | + | 1.01367i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.82193 | + | 17.9181i | −0.224753 | + | 0.691719i | ||||
\(672\) | −3.85034 | − | 1.25105i | −0.148530 | − | 0.0482603i | ||||
\(673\) | 4.61160 | + | 6.34732i | 0.177764 | + | 0.244671i | 0.888596 | − | 0.458691i | \(-0.151681\pi\) |
−0.710832 | + | 0.703362i | \(0.751681\pi\) | |||||||
\(674\) | 28.1720 | 1.08514 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.94042 | 0.343862 | ||||||||
\(677\) | −8.46310 | − | 11.6485i | −0.325263 | − | 0.447687i | 0.614802 | − | 0.788682i | \(-0.289236\pi\) |
−0.940065 | + | 0.340995i | \(0.889236\pi\) | |||||||
\(678\) | −36.0334 | − | 11.7080i | −1.38385 | − | 0.449641i | ||||
\(679\) | −1.91478 | + | 5.89310i | −0.0734826 | + | 0.226156i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.7734 | + | 48.5455i | 0.604437 | + | 1.86027i | ||||
\(682\) | 18.6016i | 0.712291i | ||||||||
\(683\) | −12.0537 | + | 3.91647i | −0.461221 | + | 0.149860i | −0.530405 | − | 0.847744i | \(-0.677960\pi\) |
0.0691847 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(684\) | −10.8049 | − | 7.85021i | −0.413135 | − | 0.300160i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.16629 | − | 3.75353i | 0.197250 | − | 0.143310i | ||||
\(687\) | −13.5225 | + | 18.6122i | −0.515917 | + | 0.710099i | ||||
\(688\) | 11.0964 | − | 15.2728i | 0.423045 | − | 0.582271i | ||||
\(689\) | 2.87959 | − | 2.09214i | 0.109704 | − | 0.0797043i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.64805 | − | 3.37700i | −0.176820 | − | 0.128467i | 0.495855 | − | 0.868405i | \(-0.334855\pi\) |
−0.672675 | + | 0.739938i | \(0.734855\pi\) | |||||||
\(692\) | 9.00448 | − | 2.92573i | 0.342299 | − | 0.111220i | ||||
\(693\) | − | 3.07364i | − | 0.116758i | ||||||
\(694\) | 4.65155 | + | 14.3160i | 0.176571 | + | 0.543428i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 13.6371 | − | 41.9707i | 0.516913 | − | 1.59089i | ||||
\(697\) | 10.8623 | + | 3.52937i | 0.411439 | + | 0.133685i | ||||
\(698\) | −12.0802 | − | 16.6270i | −0.457243 | − | 0.629342i | ||||
\(699\) | −28.7931 | −1.08905 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.5834 | −1.15512 | −0.577560 | − | 0.816348i | \(-0.695995\pi\) | ||||
−0.577560 | + | 0.816348i | \(0.695995\pi\) | |||||||
\(702\) | −0.941177 | − | 1.29542i | −0.0355224 | − | 0.0488924i | ||||
\(703\) | 24.1795 | + | 7.85640i | 0.911948 | + | 0.296310i | ||||
\(704\) | −5.22270 | + | 16.0738i | −0.196838 | + | 0.605804i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.20239 | + | 19.0890i | 0.233430 | + | 0.718424i | ||||
\(707\) | 7.49036i | 0.281704i | ||||||||
\(708\) | −11.4993 | + | 3.73635i | −0.432170 | + | 0.140421i | ||||
\(709\) | −21.8998 | − | 15.9111i | −0.822464 | − | 0.597555i | 0.0949536 | − | 0.995482i | \(-0.469730\pi\) |
−0.917417 | + | 0.397927i | \(0.869730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.7386 | + | 12.1613i | −0.627747 | + | 0.456085i | ||||
\(712\) | 4.10011 | − | 5.64332i | 0.153658 | − | 0.211492i | ||||
\(713\) | −5.79353 | + | 7.97410i | −0.216969 | + | 0.298633i | ||||
\(714\) | −1.53840 | + | 1.11771i | −0.0575731 | + | 0.0418293i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.06868 | − | 5.13570i | −0.264169 | − | 0.191930i | ||||
\(717\) | 39.8673 | − | 12.9537i | 1.48887 | − | 0.483764i | ||||
\(718\) | − | 36.8957i | − | 1.37693i | ||||||
\(719\) | 5.16263 | + | 15.8889i | 0.192534 | + | 0.592557i | 0.999997 | + | 0.00263916i | \(0.000840071\pi\) |
−0.807463 | + | 0.589918i | \(0.799160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.49527 | − | 4.60198i | 0.0556869 | − | 0.171387i | ||||
\(722\) | 5.94125 | + | 1.93043i | 0.221110 | + | 0.0718431i | ||||
\(723\) | −9.16202 | − | 12.6104i | −0.340739 | − | 0.468987i | ||||
\(724\) | 7.80240 | 0.289974 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.6555 | 0.766597 | ||||||||
\(727\) | −6.87743 | − | 9.46598i | −0.255070 | − | 0.351074i | 0.662209 | − | 0.749319i | \(-0.269619\pi\) |
−0.917279 | + | 0.398246i | \(0.869619\pi\) | |||||||
\(728\) | −0.835044 | − | 0.271322i | −0.0309488 | − | 0.0100559i | ||||
\(729\) | 11.9517 | − | 36.7835i | 0.442655 | − | 1.36235i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.48267 | + | 13.7962i | 0.165798 | + | 0.510272i | ||||
\(732\) | − | 17.5237i | − | 0.647694i | ||||||
\(733\) | 32.4385 | − | 10.5399i | 1.19814 | − | 0.389300i | 0.359065 | − | 0.933312i | \(-0.383096\pi\) |
0.839077 | + | 0.544012i | \(0.183096\pi\) | |||||||
\(734\) | −30.2196 | − | 21.9558i | −1.11542 | − | 0.810403i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.71321 | + | 2.69781i | −0.136871 | + | 0.0994425i | ||||
\(737\) | −3.62279 | + | 4.98635i | −0.133447 | + | 0.183674i | ||||
\(738\) | −18.1502 | + | 24.9816i | −0.668119 | + | 0.919586i | ||||
\(739\) | 4.64794 | − | 3.37693i | 0.170977 | − | 0.124222i | −0.499006 | − | 0.866599i | \(-0.666301\pi\) |
0.669983 | + | 0.742376i | \(0.266301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.30434 | − | 5.30692i | −0.268332 | − | 0.194954i | ||||
\(742\) | 2.23015 | − | 0.724618i | 0.0818712 | − | 0.0266016i | ||||
\(743\) | − | 36.4348i | − | 1.33666i | −0.743863 | − | 0.668332i | \(-0.767009\pi\) | ||
0.743863 | − | 0.668332i | \(-0.232991\pi\) | |||||||
\(744\) | −20.3079 | − | 62.5012i | −0.744522 | − | 2.29140i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.21442 | + | 3.73761i | −0.0444632 | + | 0.136844i | ||||
\(747\) | 3.49688 | + | 1.13621i | 0.127944 | + | 0.0415716i | ||||
\(748\) | −1.32981 | − | 1.83032i | −0.0486226 | − | 0.0669233i | ||||
\(749\) | −0.307374 | −0.0112312 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.48912 | 0.0543387 | 0.0271693 | − | 0.999631i | \(-0.491351\pi\) | ||||
0.0271693 | + | 0.999631i | \(0.491351\pi\) | |||||||
\(752\) | −1.54149 | − | 2.12169i | −0.0562125 | − | 0.0773699i | ||||
\(753\) | 9.23757 | + | 3.00147i | 0.336636 | + | 0.109380i | ||||
\(754\) | 1.35230 | − | 4.16194i | 0.0492477 | − | 0.151569i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.181269 | + | 0.557888i | 0.00659268 | + | 0.0202902i | ||||
\(757\) | − | 5.53316i | − | 0.201106i | −0.994932 | − | 0.100553i | \(-0.967939\pi\) | ||
0.994932 | − | 0.100553i | \(-0.0320612\pi\) | |||||||
\(758\) | −2.07948 | + | 0.675664i | −0.0755301 | + | 0.0245412i | ||||
\(759\) | −5.05975 | − | 3.67613i | −0.183657 | − | 0.133435i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.1041 | − | 10.9738i | 0.547523 | − | 0.397799i | −0.279348 | − | 0.960190i | \(-0.590118\pi\) |
0.826871 | + | 0.562391i | \(0.190118\pi\) | |||||||
\(762\) | −12.3234 | + | 16.9617i | −0.446430 | + | 0.614458i | ||||
\(763\) | 2.19161 | − | 3.01649i | 0.0793416 | − | 0.109204i | ||||
\(764\) | −0.906429 | + | 0.658559i | −0.0327935 | + | 0.0238258i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.52176 | − | 3.28525i | −0.163378 | − | 0.118701i | ||||
\(767\) | −4.33125 | + | 1.40731i | −0.156392 | + | 0.0508149i | ||||
\(768\) | − | 38.2653i | − | 1.38078i | ||||||
\(769\) | 4.06150 | + | 12.5000i | 0.146462 | + | 0.450763i | 0.997196 | − | 0.0748333i | \(-0.0238425\pi\) |
−0.850734 | + | 0.525596i | \(0.823842\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9764 | + | 58.4032i | −0.683417 | + | 2.10334i | ||||
\(772\) | 1.12690 | + | 0.366152i | 0.0405581 | + | 0.0131781i | ||||
\(773\) | 16.4425 | + | 22.6311i | 0.591394 | + | 0.813984i | 0.994887 | − | 0.100999i | \(-0.0322039\pi\) |
−0.403493 | + | 0.914983i | \(0.632204\pi\) | |||||||
\(774\) | −39.2195 | −1.40972 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −46.8376 | −1.68137 | ||||||||
\(777\) | −3.19882 | − | 4.40280i | −0.114757 | − | 0.157950i | ||||
\(778\) | −14.4330 | − | 4.68957i | −0.517448 | − | 0.168129i | ||||
\(779\) | −11.0399 | + | 33.9772i | −0.395544 | + | 1.21736i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.24366 | + | 13.0606i | 0.151850 | + | 0.467347i | ||||
\(782\) | 2.15581i | 0.0770917i | ||||||||
\(783\) | −10.5615 | + | 3.43163i | −0.377437 | + | 0.122637i | ||||
\(784\) | 11.3884 | + | 8.27413i | 0.406727 | + | 0.295505i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.71564 | − | 4.15266i | 0.203870 | − | 0.148120i | ||||
\(787\) | 19.6126 | − | 26.9944i | 0.699114 | − | 0.962248i | −0.300849 | − | 0.953672i | \(-0.597270\pi\) |
0.999963 | − | 0.00857605i | \(-0.00272988\pi\) | |||||||
\(788\) | −5.58021 | + | 7.68050i | −0.198787 | + | 0.273606i | ||||
\(789\) | −13.9845 | + | 10.1603i | −0.497860 | + | 0.361716i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.22947 | + | 3.07289i | 0.150383 | + | 0.109259i | ||||
\(792\) | 22.0961 | − | 7.17946i | 0.785151 | − | 0.255111i | ||||
\(793\) | − | 6.60035i | − | 0.234385i | ||||||
\(794\) | 0.749317 | + | 2.30616i | 0.0265923 | + | 0.0818426i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.67294 | + | 8.22646i | −0.0947398 | + | 0.291579i | ||||
\(797\) | 35.5682 | + | 11.5568i | 1.25989 | + | 0.409363i | 0.861455 | − | 0.507833i | \(-0.169553\pi\) |
0.398435 | + | 0.917197i | \(0.369553\pi\) | |||||||
\(798\) | −3.49620 | − | 4.81211i | −0.123764 | − | 0.170347i | ||||
\(799\) | 2.01519 | 0.0712923 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.55478 | −0.302268 | ||||||||
\(802\) | 17.8730 | + | 24.6001i | 0.631119 | + | 0.868660i | ||||
\(803\) | −1.03693 | − | 0.336919i | −0.0365924 | − | 0.0118896i | ||||
\(804\) | 1.77153 | − | 5.45220i | 0.0624769 | − | 0.192284i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.01379 | − | 6.19781i | −0.0709328 | − | 0.218309i | ||||
\(807\) | 33.9504i | 1.19511i | ||||||||
\(808\) | −53.8476 | + | 17.4961i | −1.89435 | + | 0.615512i | ||||
\(809\) | 27.1844 | + | 19.7506i | 0.955751 | + | 0.694394i | 0.952160 | − | 0.305600i | \(-0.0988569\pi\) |
0.00359108 | + | 0.999994i | \(0.498857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.7471 | − | 22.3391i | 1.07968 | − | 0.784432i | 0.102051 | − | 0.994779i | \(-0.467459\pi\) |
0.977627 | + | 0.210347i | \(0.0674594\pi\) | |||||||
\(812\) | −0.942315 | + | 1.29699i | −0.0330688 | + | 0.0455153i | ||||
\(813\) | −18.1272 | + | 24.9499i | −0.635747 | + | 0.875031i | ||||
\(814\) | −9.42008 | + | 6.84409i | −0.330174 | + | 0.239885i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.86464 | − | 4.98745i | −0.240310 | − | 0.174596i | ||||
\(817\) | −43.1546 | + | 14.0218i | −1.50979 | + | 0.490560i | ||||
\(818\) | − | 15.8699i | − | 0.554877i | ||||||
\(819\) | 0.332749 | + | 1.02410i | 0.0116272 | + | 0.0357848i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.70479 | − | 23.7129i | 0.268899 | − | 0.827587i | −0.721870 | − | 0.692028i | \(-0.756717\pi\) |
0.990769 | − | 0.135558i | \(-0.0432827\pi\) | |||||||
\(822\) | −53.3751 | − | 17.3426i | −1.86167 | − | 0.604894i | ||||
\(823\) | −14.9653 | − | 20.5980i | −0.521659 | − | 0.718002i | 0.464172 | − | 0.885745i | \(-0.346352\pi\) |
−0.985831 | + | 0.167743i | \(0.946352\pi\) | |||||||
\(824\) | 36.5760 | 1.27418 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00027 | −0.104393 | ||||||||
\(827\) | 19.0082 | + | 26.1626i | 0.660980 | + | 0.909761i | 0.999513 | − | 0.0311933i | \(-0.00993074\pi\) |
−0.338533 | + | 0.940954i | \(0.609931\pi\) | |||||||
\(828\) | 3.08247 | + | 1.00156i | 0.107123 | + | 0.0348065i | ||||
\(829\) | −7.71962 | + | 23.7585i | −0.268113 | + | 0.825168i | 0.722846 | + | 0.691009i | \(0.242833\pi\) |
−0.990960 | + | 0.134159i | \(0.957167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.6377 | + | 41.9724i | 0.473085 | + | 1.45601i | ||||
\(832\) | − | 5.92099i | − | 0.205273i | ||||||
\(833\) | −10.2873 | + | 3.34256i | −0.356435 | + | 0.115813i | ||||
\(834\) | 16.0773 | + | 11.6808i | 0.556712 | + | 0.404475i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.72525 | − | 4.15964i | 0.198012 | − | 0.143864i | ||||
\(837\) | −9.72030 | + | 13.3788i | −0.335983 | + | 0.462440i | ||||
\(838\) | −20.5923 | + | 28.3429i | −0.711350 | + | 0.979089i | ||||
\(839\) | 15.6566 | − | 11.3752i | 0.540524 | − | 0.392714i | −0.283755 | − | 0.958897i | \(-0.591580\pi\) |
0.824280 | + | 0.566183i | \(0.191580\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.09201 | − | 0.793390i | −0.0376554 | − | 0.0273583i | ||||
\(842\) | 8.88423 | − | 2.88666i | 0.306171 | − | 0.0994809i | ||||
\(843\) | − | 13.2091i | − | 0.454944i | ||||||
\(844\) | −1.47989 | − | 4.55463i | −0.0509399 | − | 0.156777i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.68363 | + | 5.18167i | −0.0578843 | + | 0.178150i | ||||
\(847\) | −2.71064 | − | 0.880739i | −0.0931385 | − | 0.0302625i | ||||
\(848\) | 6.15027 | + | 8.46512i | 0.211201 | + | 0.290693i | ||||
\(849\) | −30.7775 | −1.05628 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.16980 | −0.211498 | ||||||||
\(852\) | −7.50789 | − | 10.3337i | −0.257216 | − | 0.354027i | ||||
\(853\) | 25.4765 | + | 8.27783i | 0.872300 | + | 0.283427i | 0.710756 | − | 0.703438i | \(-0.248353\pi\) |
0.161543 | + | 0.986866i | \(0.448353\pi\) | |||||||
\(854\) | 1.34370 | − | 4.13550i | 0.0459806 | − | 0.141514i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.717971 | − | 2.20969i | −0.0245397 | − | 0.0755255i | ||||
\(857\) | 47.5186i | 1.62320i | 0.584210 | + | 0.811602i | \(0.301404\pi\) | ||||
−0.584210 | + | 0.811602i | \(0.698596\pi\) | |||||||
\(858\) | 3.93265 | − | 1.27780i | 0.134259 | − | 0.0436233i | ||||
\(859\) | 9.32717 | + | 6.77658i | 0.318239 | + | 0.231214i | 0.735424 | − | 0.677608i | \(-0.236983\pi\) |
−0.417185 | + | 0.908822i | \(0.636983\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.18685 | − | 4.49501i | 0.210847 | − | 0.153190i | ||||
\(862\) | 18.0908 | − | 24.8999i | 0.616177 | − | 0.848095i | ||||
\(863\) | 10.5835 | − | 14.5669i | 0.360266 | − | 0.495864i | −0.589957 | − | 0.807435i | \(-0.700855\pi\) |
0.950223 | + | 0.311571i | \(0.100855\pi\) | |||||||
\(864\) | −6.22998 | + | 4.52634i | −0.211948 | + | 0.153989i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.7108 | − | 14.3207i | −0.669799 | − | 0.486638i | ||||
\(867\) | −35.8807 | + | 11.6583i | −1.21857 | + | 0.395938i | ||||
\(868\) | 2.38737i | 0.0810327i | ||||||||
\(869\) | −3.38781 | − | 10.4266i | −0.114924 | − | 0.353698i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.667251 | − | 2.05359i | 0.0226089 | − | 0.0695831i | ||||
\(872\) | 26.8045 | + | 8.70932i | 0.907716 | + | 0.294935i | ||||
\(873\) | 33.7633 | + | 46.4712i | 1.14271 | + | 1.57281i | ||||
\(874\) | −6.74338 | −0.228098 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.01411 | 0.0342635 | ||||||||
\(877\) | −10.0495 | − | 13.8320i | −0.339349 | − | 0.467074i | 0.604902 | − | 0.796300i | \(-0.293212\pi\) |
−0.944251 | + | 0.329226i | \(0.893212\pi\) | |||||||
\(878\) | 27.8132 | + | 9.03707i | 0.938652 | + | 0.304986i | ||||
\(879\) | 15.6315 | − | 48.1088i | 0.527238 | − | 1.62267i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7516 | − | 36.1678i | −0.395923 | − | 1.21853i | −0.928240 | − | 0.371981i | \(-0.878679\pi\) |
0.532318 | − | 0.846545i | \(-0.321321\pi\) | |||||||
\(882\) | − | 29.2445i | − | 0.984714i | ||||||
\(883\) | 35.0458 | − | 11.3871i | 1.17939 | − | 0.383206i | 0.347247 | − | 0.937774i | \(-0.387116\pi\) |
0.832138 | + | 0.554568i | \(0.187116\pi\) | |||||||
\(884\) | 0.641224 | + | 0.465877i | 0.0215667 | + | 0.0156691i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.92104 | + | 2.12226i | −0.0981344 | + | 0.0712988i | ||||
\(887\) | −17.5594 | + | 24.1684i | −0.589586 | + | 0.811495i | −0.994705 | − | 0.102769i | \(-0.967230\pi\) |
0.405120 | + | 0.914264i | \(0.367230\pi\) | |||||||
\(888\) | 24.1795 | − | 33.2802i | 0.811411 | − | 1.11681i | ||||
\(889\) | 2.34045 | − | 1.70044i | 0.0784961 | − | 0.0570308i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.83247 | + | 7.14371i | 0.329400 | + | 0.239323i | ||||
\(892\) | 7.19953 | − | 2.33927i | 0.241058 | − | 0.0783246i | ||||
\(893\) | 6.30351i | 0.210939i | ||||||||
\(894\) | −0.656975 | − | 2.02196i | −0.0219725 | − | 0.0676245i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.244082 | − | 0.751207i | 0.00815420 | − | 0.0250961i | ||||
\(897\) | 2.08382 | + | 0.677074i | 0.0695767 | + | 0.0226068i | ||||
\(898\) | 24.0418 | + | 33.0907i | 0.802285 | + | 1.10425i | ||||
\(899\) | −45.1958 | −1.50736 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.04022 | −0.267859 | ||||||||
\(902\) | −9.61736 | − | 13.2372i | −0.320223 | − | 0.440749i | ||||
\(903\) | 9.23757 | + | 3.00147i | 0.307407 | + | 0.0998826i | ||||
\(904\) | −12.2115 | + | 37.5830i | −0.406147 | + | 1.24999i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 14.1498 | + | 43.5487i | 0.470097 | + | 1.44681i | ||||
\(907\) | − | 43.4897i | − | 1.44405i | −0.691866 | − | 0.722026i | \(-0.743211\pi\) | ||
0.691866 | − | 0.722026i | \(-0.256789\pi\) | |||||||
\(908\) | 13.3304 | − | 4.33132i | 0.442386 | − | 0.143740i | ||||
\(909\) | 56.1758 | + | 40.8141i | 1.86323 | + | 1.35372i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7150 | − | 14.3238i | 0.653186 | − | 0.474568i | −0.211169 | − | 0.977450i | \(-0.567727\pi\) |
0.864355 | + | 0.502882i | \(0.167727\pi\) | |||||||
\(912\) | 15.6007 | − | 21.4726i | 0.516592 | − | 0.711028i | ||||
\(913\) | −1.14516 | + | 1.57618i | −0.0378994 | + | 0.0521640i | ||||
\(914\) | 23.4107 | − | 17.0089i | 0.774358 | − | 0.562604i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.11084 | + | 3.71325i | 0.168867 | + | 0.122689i | ||||
\(917\) | −0.927136 | + | 0.301245i | −0.0306167 | + | 0.00994797i | ||||
\(918\) | 3.61699i | 0.119379i | ||||||||
\(919\) | −14.0647 | − | 43.2867i | −0.463952 | − | 1.42790i | −0.860296 | − | 0.509795i | \(-0.829721\pi\) |
0.396344 | − | 0.918102i | \(-0.370279\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.4429 | − | 62.9168i | 0.673617 | − | 2.07318i | ||||
\(922\) | −17.9406 | − | 5.82926i | −0.590843 | − | 0.191977i | ||||
\(923\) | −2.82787 | − | 3.89223i | −0.0930804 | − | 0.128114i | ||||
\(924\) | −1.51484 | −0.0498346 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.2001 | 0.663816 | ||||||||
\(927\) | −26.3661 | − | 36.2898i | −0.865977 | − | 1.19191i | ||||
\(928\) | −20.0158 | − | 6.50352i | −0.657050 | − | 0.213488i | ||||
\(929\) | −2.79288 | + | 8.59560i | −0.0916314 | + | 0.282012i | −0.986361 | − | 0.164596i | \(-0.947368\pi\) |
0.894730 | + | 0.446608i | \(0.147368\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.4555 | − | 32.1787i | −0.342665 | − | 1.05462i | ||||
\(932\) | 7.90648i | 0.258985i | ||||||||
\(933\) | −39.2542 | + | 12.7545i | −1.28513 | + | 0.417562i | ||||
\(934\) | −13.0681 | − | 9.49453i | −0.427601 | − | 0.310671i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.58490 | + | 4.78421i | −0.215234 | + | 0.156377i | ||||
\(937\) | 19.5892 | − | 26.9623i | 0.639953 | − | 0.880819i | −0.358661 | − | 0.933468i | \(-0.616766\pi\) |
0.998613 | + | 0.0526490i | \(0.0167664\pi\) | |||||||
\(938\) | 0.836142 | − | 1.15085i | 0.0273010 | − | 0.0375766i | ||||
\(939\) | 14.7745 | − | 10.7343i | 0.482147 | − | 0.350300i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.7050 | + | 17.2227i | 0.772762 | + | 0.561444i | 0.902798 | − | 0.430065i | \(-0.141509\pi\) |
−0.130036 | + | 0.991509i | \(0.541509\pi\) | |||||||
\(942\) | −7.81341 | + | 2.53873i | −0.254575 | + | 0.0827163i | ||||
\(943\) | − | 8.66985i | − | 0.282329i | ||||||
\(944\) | −4.13706 | − | 12.7326i | −0.134650 | − | 0.414410i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.42184 | − | 19.7644i | 0.208792 | − | 0.642595i | ||||
\(947\) | 54.0634 | + | 17.5663i | 1.75682 | + | 0.570827i | 0.996863 | − | 0.0791426i | \(-0.0252182\pi\) |
0.759961 | + | 0.649969i | \(0.225218\pi\) | |||||||
\(948\) | 5.99371 | + | 8.24963i | 0.194667 | + | 0.267936i | ||||
\(949\) | 0.381966 | 0.0123991 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.9238 | 1.10005 | ||||||||
\(952\) | 1.16578 | + | 1.60456i | 0.0377832 | + | 0.0520041i | ||||
\(953\) | −18.1051 | − | 5.88270i | −0.586481 | − | 0.190559i | 0.000720915 | − | 1.00000i | \(-0.499771\pi\) |
−0.587202 | + | 0.809441i | \(0.699771\pi\) | |||||||
\(954\) | 6.71735 | − | 20.6739i | 0.217482 | − | 0.669342i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.55704 | − | 10.9474i | −0.115043 | − | 0.354065i | ||||
\(957\) | − | 28.6778i | − | 0.927021i | ||||||
\(958\) | 3.13615 | − | 1.01900i | 0.101324 | − | 0.0329223i | ||||
\(959\) | 6.26498 | + | 4.55178i | 0.202307 | + | 0.146985i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3705 | + | 21.3389i | −0.947435 | + | 0.688352i | ||||
\(962\) | 2.39772 | − | 3.30017i | 0.0773055 | − | 0.106402i | ||||
\(963\) | −1.67485 | + | 2.30523i | −0.0539711 | + | 0.0742849i | ||||
\(964\) | −3.46278 | + | 2.51586i | −0.111529 | + | 0.0810304i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.16779 | + | 0.848451i | 0.0375731 | + | 0.0272985i | ||||
\(967\) | 13.9905 | − | 4.54580i | 0.449906 | − | 0.146183i | −0.0752956 | − | 0.997161i | \(-0.523990\pi\) |
0.525201 | + | 0.850978i | \(0.323990\pi\) | |||||||
\(968\) | − | 21.5438i | − | 0.692443i | ||||||
\(969\) | 6.30233 | + | 19.3966i | 0.202460 | + | 0.623108i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0039 | + | 36.9441i | −0.385223 | + | 1.18559i | 0.551096 | + | 0.834442i | \(0.314210\pi\) |
−0.936319 | + | 0.351151i | \(0.885790\pi\) | |||||||
\(972\) | −14.8616 | − | 4.82884i | −0.476687 | − | 0.154885i | ||||
\(973\) | −1.61177 | − | 2.21842i | −0.0516711 | − | 0.0711191i | ||||
\(974\) | 19.3469 | 0.619914 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.4030 | 0.621076 | ||||||||
\(977\) | −34.3586 | − | 47.2906i | −1.09923 | − | 1.51296i | −0.836402 | − | 0.548116i | \(-0.815345\pi\) |
−0.262827 | − | 0.964843i | \(-0.584655\pi\) | |||||||
\(978\) | 67.9346 | + | 22.0733i | 2.17231 | + | 0.705826i | ||||
\(979\) | 1.40077 | − | 4.31111i | 0.0447687 | − | 0.137784i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.6811 | − | 32.8730i | −0.341021 | − | 1.04955i | ||||
\(982\) | 34.8918i | 1.11344i | ||||||||
\(983\) | −26.7812 | + | 8.70175i | −0.854189 | + | 0.277543i | −0.703199 | − | 0.710993i | \(-0.748246\pi\) |
−0.150989 | + | 0.988535i | \(0.548246\pi\) | |||||||
\(984\) | 46.7656 | + | 33.9772i | 1.49083 | + | 1.08315i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.99729 | + | 5.81037i | −0.254685 | + | 0.185040i | ||||
\(987\) | 0.793106 | − | 1.09162i | 0.0252449 | − | 0.0347466i | ||||
\(988\) | −1.45726 | + | 2.00575i | −0.0463617 | + | 0.0638114i | ||||
\(989\) | 8.90859 | − | 6.47247i | 0.283277 | − | 0.205812i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.8297 | − | 23.1256i | −1.01110 | − | 0.734610i | −0.0466640 | − | 0.998911i | \(-0.514859\pi\) |
−0.964440 | + | 0.264300i | \(0.914859\pi\) | |||||||
\(992\) | −29.8068 | + | 9.68480i | −0.946365 | + | 0.307493i | ||||
\(993\) | − | 45.9231i | − | 1.45733i | ||||||
\(994\) | −0.979439 | − | 3.01440i | −0.0310659 | − | 0.0956110i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.559979 | − | 1.72344i | 0.0177436 | − | 0.0546092i | ||||
\(997\) | −41.0074 | − | 13.3241i | −1.29872 | − | 0.421979i | −0.423583 | − | 0.905857i | \(-0.639228\pi\) |
−0.875136 | + | 0.483878i | \(0.839228\pi\) | |||||||
\(998\) | −7.91810 | − | 10.8983i | −0.250643 | − | 0.344980i | ||||
\(999\) | −10.3516 | −0.327511 |
(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 | 125.2.e.b.74.1 | 8 | ||
5.2 | odd | 4 | 125.2.d.b.51.3 | 16 | |||
5.3 | odd | 4 | 125.2.d.b.51.2 | 16 | |||
5.4 | even | 2 | 25.2.e.a.14.2 | yes | 8 | ||
15.14 | odd | 2 | 225.2.m.a.64.1 | 8 | |||
20.19 | odd | 2 | 400.2.y.c.289.2 | 8 | |||
25.2 | odd | 20 | 625.2.d.o.126.2 | 16 | |||
25.3 | odd | 20 | 625.2.a.f.1.6 | 8 | |||
25.4 | even | 10 | 625.2.b.c.624.3 | 8 | |||
25.6 | even | 5 | 625.2.e.i.124.2 | 8 | |||
25.8 | odd | 20 | 625.2.d.o.501.3 | 16 | |||
25.9 | even | 10 | inner | 125.2.e.b.49.1 | 8 | ||
25.11 | even | 5 | 625.2.e.a.499.1 | 8 | |||
25.12 | odd | 20 | 125.2.d.b.76.3 | 16 | |||
25.13 | odd | 20 | 125.2.d.b.76.2 | 16 | |||
25.14 | even | 10 | 625.2.e.i.499.2 | 8 | |||
25.16 | even | 5 | 25.2.e.a.9.2 | ✓ | 8 | ||
25.17 | odd | 20 | 625.2.d.o.501.2 | 16 | |||
25.19 | even | 10 | 625.2.e.a.124.1 | 8 | |||
25.21 | even | 5 | 625.2.b.c.624.6 | 8 | |||
25.22 | odd | 20 | 625.2.a.f.1.3 | 8 | |||
25.23 | odd | 20 | 625.2.d.o.126.3 | 16 | |||
75.41 | odd | 10 | 225.2.m.a.109.1 | 8 | |||
75.47 | even | 20 | 5625.2.a.x.1.6 | 8 | |||
75.53 | even | 20 | 5625.2.a.x.1.3 | 8 | |||
100.3 | even | 20 | 10000.2.a.bj.1.8 | 8 | |||
100.47 | even | 20 | 10000.2.a.bj.1.1 | 8 | |||
100.91 | odd | 10 | 400.2.y.c.209.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.9.2 | ✓ | 8 | 25.16 | even | 5 | ||
25.2.e.a.14.2 | yes | 8 | 5.4 | even | 2 | ||
125.2.d.b.51.2 | 16 | 5.3 | odd | 4 | |||
125.2.d.b.51.3 | 16 | 5.2 | odd | 4 | |||
125.2.d.b.76.2 | 16 | 25.13 | odd | 20 | |||
125.2.d.b.76.3 | 16 | 25.12 | odd | 20 | |||
125.2.e.b.49.1 | 8 | 25.9 | even | 10 | inner | ||
125.2.e.b.74.1 | 8 | 1.1 | even | 1 | trivial | ||
225.2.m.a.64.1 | 8 | 15.14 | odd | 2 | |||
225.2.m.a.109.1 | 8 | 75.41 | odd | 10 | |||
400.2.y.c.209.2 | 8 | 100.91 | odd | 10 | |||
400.2.y.c.289.2 | 8 | 20.19 | odd | 2 | |||
625.2.a.f.1.3 | 8 | 25.22 | odd | 20 | |||
625.2.a.f.1.6 | 8 | 25.3 | odd | 20 | |||
625.2.b.c.624.3 | 8 | 25.4 | even | 10 | |||
625.2.b.c.624.6 | 8 | 25.21 | even | 5 | |||
625.2.d.o.126.2 | 16 | 25.2 | odd | 20 | |||
625.2.d.o.126.3 | 16 | 25.23 | odd | 20 | |||
625.2.d.o.501.2 | 16 | 25.17 | odd | 20 | |||
625.2.d.o.501.3 | 16 | 25.8 | odd | 20 | |||
625.2.e.a.124.1 | 8 | 25.19 | even | 10 | |||
625.2.e.a.499.1 | 8 | 25.11 | even | 5 | |||
625.2.e.i.124.2 | 8 | 25.6 | even | 5 | |||
625.2.e.i.499.2 | 8 | 25.14 | even | 10 | |||
5625.2.a.x.1.3 | 8 | 75.53 | even | 20 | |||
5625.2.a.x.1.6 | 8 | 75.47 | even | 20 | |||
10000.2.a.bj.1.1 | 8 | 100.47 | even | 20 | |||
10000.2.a.bj.1.8 | 8 | 100.3 | even | 20 |