Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(15,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.h (of order \(8\), 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: | \(3.48774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 15.4 | ||
Character | \(\chi\) | \(=\) | 128.15 |
Dual form | 128.3.h.a.111.4 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 0.374985 | − | 0.155324i | 0.124995 | − | 0.0517746i | −0.319309 | − | 0.947651i | \(-0.603451\pi\) |
0.444304 | + | 0.895876i | \(0.353451\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.60625 | − | 3.15061i | −1.52125 | − | 0.630122i | −0.543408 | − | 0.839469i | \(-0.682866\pi\) |
−0.977842 | + | 0.209346i | \(0.932866\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.84161 | + | 6.84161i | −0.977372 | + | 0.977372i | −0.999750 | − | 0.0223772i | \(-0.992877\pi\) |
0.0223772 | + | 0.999750i | \(0.492877\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.24747 | + | 6.24747i | −0.694164 | + | 0.694164i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23818 | + | 0.927086i | 0.203471 | + | 0.0842806i | 0.482092 | − | 0.876121i | \(-0.339877\pi\) |
−0.278621 | + | 0.960401i | \(0.589877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.40964 | − | 0.583890i | 0.108433 | − | 0.0449146i | −0.327807 | − | 0.944745i | \(-0.606310\pi\) |
0.436241 | + | 0.899830i | \(0.356310\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.34159 | −0.222773 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.67812i | − | 0.157537i | −0.996893 | − | 0.0787683i | \(-0.974901\pi\) | ||
0.996893 | − | 0.0787683i | \(-0.0250987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.38908 | − | 13.0104i | −0.283636 | − | 0.684757i | 0.716279 | − | 0.697814i | \(-0.245844\pi\) |
−0.999915 | + | 0.0130566i | \(0.995844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50283 | + | 3.62816i | −0.0715635 | + | 0.172770i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.8388 | − | 18.8388i | −0.819076 | − | 0.819076i | 0.166898 | − | 0.985974i | \(-0.446625\pi\) |
−0.985974 | + | 0.166898i | \(0.946625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 30.2510 | + | 30.2510i | 1.21004 | + | 1.21004i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.77024 | + | 6.68795i | −0.102601 | + | 0.247702i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0298 | − | 24.2140i | −0.345855 | − | 0.834967i | −0.997100 | − | 0.0761000i | \(-0.975753\pi\) |
0.651245 | − | 0.758867i | \(-0.274247\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.5858i | 1.53503i | 0.641033 | + | 0.767513i | \(0.278506\pi\) | ||||
−0.641033 | + | 0.767513i | \(0.721494\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.983283 | 0.0297965 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 73.5942 | − | 30.4837i | 2.10269 | − | 0.870963i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −28.2682 | − | 11.7091i | −0.764006 | − | 0.316462i | −0.0335642 | − | 0.999437i | \(-0.510686\pi\) |
−0.730442 | + | 0.682975i | \(0.760686\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.437900 | − | 0.437900i | 0.0112282 | − | 0.0112282i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.93962 | − | 6.93962i | 0.169259 | − | 0.169259i | −0.617395 | − | 0.786654i | \(-0.711812\pi\) |
0.786654 | + | 0.617395i | \(0.211812\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.48982 | − | 3.51660i | −0.197438 | − | 0.0817814i | 0.281774 | − | 0.959481i | \(-0.409077\pi\) |
−0.479211 | + | 0.877700i | \(0.659077\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 67.2032 | − | 27.8365i | 1.49340 | − | 0.618588i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 67.0112 | 1.42577 | 0.712885 | − | 0.701281i | \(-0.247388\pi\) | ||||
0.712885 | + | 0.701281i | \(0.247388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 44.6152i | − | 0.910513i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.415976 | − | 1.00426i | −0.00815639 | − | 0.0196913i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5006 | + | 25.3507i | −0.198124 | + | 0.478315i | −0.991451 | − | 0.130482i | \(-0.958347\pi\) |
0.793326 | + | 0.608797i | \(0.208347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.1033 | − | 14.1033i | −0.256424 | − | 0.256424i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.04165 | − | 4.04165i | −0.0709061 | − | 0.0709061i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −27.9364 | + | 67.4445i | −0.473499 | + | 1.14313i | 0.489107 | + | 0.872224i | \(0.337323\pi\) |
−0.962606 | + | 0.270904i | \(0.912677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 31.5752 | + | 76.2294i | 0.517627 | + | 1.24966i | 0.939357 | + | 0.342941i | \(0.111423\pi\) |
−0.421730 | + | 0.906721i | \(0.638577\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 85.4855i | − | 1.35691i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.5616 | −0.193256 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −90.1903 | + | 37.3580i | −1.34612 | + | 0.557583i | −0.935211 | − | 0.354092i | \(-0.884790\pi\) |
−0.410913 | + | 0.911674i | \(0.634790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.99035 | − | 4.13814i | −0.144788 | − | 0.0599730i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.98379 | + | 1.98379i | −0.0279407 | + | 0.0279407i | −0.720939 | − | 0.692998i | \(-0.756289\pi\) |
0.692998 | + | 0.720939i | \(0.256289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55.5273 | + | 55.5273i | −0.760648 | + | 0.760648i | −0.976439 | − | 0.215792i | \(-0.930767\pi\) |
0.215792 | + | 0.976439i | \(0.430767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16.0424 | + | 6.64496i | 0.213898 | + | 0.0885995i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.6555 | + | 8.97002i | −0.281241 | + | 0.116494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9856 | −0.139058 | −0.0695292 | − | 0.997580i | \(-0.522150\pi\) | ||||
−0.0695292 | + | 0.997580i | \(0.522150\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 76.5792i | − | 0.945422i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −34.1779 | − | 82.5128i | −0.411782 | − | 0.994130i | −0.984659 | − | 0.174489i | \(-0.944173\pi\) |
0.572877 | − | 0.819641i | \(-0.305827\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.43772 | + | 20.3705i | −0.0992674 | + | 0.239653i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.52203 | − | 7.52203i | −0.0864602 | − | 0.0864602i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.1705 | − | 16.1705i | −0.181691 | − | 0.181691i | 0.610401 | − | 0.792093i | \(-0.291008\pi\) |
−0.792093 | + | 0.610401i | \(0.791008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.64942 | + | 13.6389i | −0.0620816 | + | 0.149878i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.39121 | + | 17.8440i | 0.0794754 | + | 0.191870i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 115.939i | 1.22041i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −62.6434 | −0.645808 | −0.322904 | − | 0.946432i | \(-0.604659\pi\) | ||||
−0.322904 | + | 0.946432i | \(0.604659\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19.7749 | + | 8.19105i | −0.199747 | + | 0.0827379i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 39.7340 | + | 16.4584i | 0.393406 | + | 0.162954i | 0.570612 | − | 0.821220i | \(-0.306706\pi\) |
−0.177206 | + | 0.984174i | \(0.556706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 36.3254 | − | 36.3254i | 0.352674 | − | 0.352674i | −0.508430 | − | 0.861104i | \(-0.669774\pi\) |
0.861104 | + | 0.508430i | \(0.169774\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.8619 | − | 22.8619i | 0.217732 | − | 0.217732i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −111.798 | − | 46.3084i | −1.04484 | − | 0.432789i | −0.206796 | − | 0.978384i | \(-0.566304\pi\) |
−0.838049 | + | 0.545596i | \(0.816304\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −55.7631 | + | 23.0978i | −0.511588 | + | 0.211907i | −0.623517 | − | 0.781809i | \(-0.714297\pi\) |
0.111929 | + | 0.993716i | \(0.464297\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.4189 | −0.111882 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 80.7753i | 0.714825i | 0.933947 | + | 0.357413i | \(0.116341\pi\) | ||||
−0.933947 | + | 0.357413i | \(0.883659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 83.9387 | + | 202.646i | 0.729901 | + | 1.76214i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.15882 | + | 12.4545i | −0.0440925 | + | 0.106449i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.3227 | + | 18.3227i | 0.153972 | + | 0.153972i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −81.4099 | − | 81.4099i | −0.672809 | − | 0.672809i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.52436 | − | 3.68014i | 0.0123932 | − | 0.0299198i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −56.0222 | − | 135.250i | −0.448178 | − | 1.08200i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 143.036i | − | 1.12627i | −0.826365 | − | 0.563135i | \(-0.809595\pi\) | ||
0.826365 | − | 0.563135i | \(-0.190405\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.72976 | −0.0289129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 56.1430 | − | 23.2552i | 0.428573 | − | 0.177521i | −0.157961 | − | 0.987445i | \(-0.550492\pi\) |
0.586534 | + | 0.809925i | \(0.300492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 125.882 | + | 52.1420i | 0.946481 | + | 0.392045i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 42.1423 | − | 42.1423i | 0.312165 | − | 0.312165i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 168.165 | − | 168.165i | 1.22748 | − | 1.22748i | 0.262563 | − | 0.964915i | \(-0.415432\pi\) |
0.964915 | − | 0.262563i | \(-0.0845679\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 97.5768 | + | 40.4176i | 0.701991 | + | 0.290774i | 0.704986 | − | 0.709221i | \(-0.250953\pi\) |
−0.00299484 | + | 0.999996i | \(0.500953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.1282 | − | 10.4084i | 0.178214 | − | 0.0738187i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.69634 | 0.0258485 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 215.778i | 1.48812i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.92979 | − | 16.7300i | −0.0471415 | − | 0.113810i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 44.3735 | − | 107.127i | 0.297809 | − | 0.718974i | −0.702167 | − | 0.712012i | \(-0.747784\pi\) |
0.999976 | − | 0.00696156i | \(-0.00221595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 128.078 | + | 128.078i | 0.848200 | + | 0.848200i | 0.989908 | − | 0.141708i | \(-0.0452594\pi\) |
−0.141708 | + | 0.989908i | \(0.545259\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.7315 | + | 16.7315i | 0.109356 | + | 0.109356i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 149.924 | − | 361.950i | 0.967254 | − | 2.33516i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1590 | + | 48.6682i | 0.128401 | + | 0.309988i | 0.974986 | − | 0.222265i | \(-0.0713452\pi\) |
−0.846585 | + | 0.532254i | \(0.821345\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.1371i | 0.0700447i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 257.775 | 1.60109 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −68.6749 | + | 28.4461i | −0.421319 | + | 0.174516i | −0.583262 | − | 0.812284i | \(-0.698224\pi\) |
0.161943 | + | 0.986800i | \(0.448224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.47910 | − | 3.09794i | −0.0453279 | − | 0.0187754i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −131.350 | + | 131.350i | −0.786527 | + | 0.786527i | −0.980923 | − | 0.194396i | \(-0.937725\pi\) |
0.194396 | + | 0.980923i | \(0.437725\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −117.855 | + | 117.855i | −0.697366 | + | 0.697366i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 114.950 | + | 47.6139i | 0.672223 | + | 0.278444i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −206.045 | + | 85.3465i | −1.19101 | + | 0.493333i | −0.888084 | − | 0.459681i | \(-0.847964\pi\) |
−0.302926 | + | 0.953014i | \(0.597964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −413.931 | −2.36532 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.6299i | 0.167400i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −80.2014 | − | 193.623i | −0.448053 | − | 1.08169i | −0.973051 | − | 0.230591i | \(-0.925934\pi\) |
0.524998 | − | 0.851104i | \(-0.324066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 93.4345 | − | 225.571i | 0.516213 | − | 1.24625i | −0.424000 | − | 0.905662i | \(-0.639374\pi\) |
0.940213 | − | 0.340586i | \(-0.110626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.6805 | + | 23.6805i | 0.129401 | + | 0.129401i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 178.124 | + | 178.124i | 0.962835 | + | 0.962835i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.48285 | − | 5.99413i | 0.0132773 | − | 0.0320542i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −26.8034 | − | 64.7092i | −0.141817 | − | 0.342377i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.1639i | − | 0.105570i | −0.998606 | − | 0.0527851i | \(-0.983190\pi\) | ||
0.998606 | − | 0.0527851i | \(-0.0168098\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 115.896 | 0.600497 | 0.300248 | − | 0.953861i | \(-0.402930\pi\) | ||||
0.300248 | + | 0.953861i | \(0.402930\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.71043 | + | 1.95112i | −0.0241560 | + | 0.0100058i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −177.705 | − | 73.6077i | −0.902055 | − | 0.373643i | −0.117045 | − | 0.993127i | \(-0.537342\pi\) |
−0.785010 | + | 0.619483i | \(0.787342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.1763 | − | 22.1763i | 0.111439 | − | 0.111439i | −0.649189 | − | 0.760627i | \(-0.724891\pi\) |
0.760627 | + | 0.649189i | \(0.224891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.0174 | + | 28.0174i | −0.139390 | + | 0.139390i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 234.283 | + | 97.0431i | 1.15410 | + | 0.478045i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −74.6485 | + | 30.9204i | −0.364139 | + | 0.150831i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 235.389 | 1.13715 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 34.1158i | − | 0.163233i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 116.936 | + | 282.308i | 0.554197 | + | 1.33795i | 0.914300 | + | 0.405038i | \(0.132742\pi\) |
−0.360103 | + | 0.932913i | \(0.617258\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.435761 | + | 1.05202i | −0.00204583 | + | 0.00493906i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 53.4962 | + | 53.4962i | 0.248820 | + | 0.248820i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −325.563 | − | 325.563i | −1.50029 | − | 1.50029i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.1972 | + | 29.4466i | −0.0556949 | + | 0.134459i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56373 | − | 3.77518i | −0.00707570 | − | 0.0170822i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1409i | 0.0544434i | 0.999629 | + | 0.0272217i | \(0.00866601\pi\) | ||||
−0.999629 | + | 0.0272217i | \(0.991334\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −377.985 | −1.67993 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −215.118 | + | 89.1048i | −0.947656 | + | 0.392532i | −0.802350 | − | 0.596854i | \(-0.796417\pi\) |
−0.145307 | + | 0.989387i | \(0.546417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 85.4872 | + | 35.4100i | 0.373307 | + | 0.154629i | 0.561445 | − | 0.827514i | \(-0.310245\pi\) |
−0.188139 | + | 0.982142i | \(0.560245\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.72724 | + | 6.72724i | −0.0291222 | + | 0.0291222i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 33.1162 | − | 33.1162i | 0.142129 | − | 0.142129i | −0.632462 | − | 0.774591i | \(-0.717956\pi\) |
0.774591 | + | 0.632462i | \(0.217956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −509.704 | − | 211.126i | −2.16895 | − | 0.898410i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.11944 | + | 1.70633i | −0.0173816 | + | 0.00719970i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −332.992 | −1.39327 | −0.696636 | − | 0.717425i | \(-0.745321\pi\) | ||||
−0.696636 | + | 0.717425i | \(0.745321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 218.867i | 0.908160i | 0.890961 | + | 0.454080i | \(0.150032\pi\) | ||||
−0.890961 | + | 0.454080i | \(0.849968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −36.8267 | − | 88.9076i | −0.151550 | − | 0.365875i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −140.565 | + | 339.354i | −0.573735 | + | 1.38512i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.1933 | − | 15.1933i | −0.0615112 | − | 0.0615112i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.6324 | − | 25.6324i | −0.102941 | − | 0.102941i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −92.6681 | + | 223.721i | −0.369196 | + | 0.891318i | 0.624687 | + | 0.780875i | \(0.285227\pi\) |
−0.993883 | + | 0.110442i | \(0.964773\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.6995 | − | 59.6298i | −0.0976263 | − | 0.235691i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.94919i | 0.0350949i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −138.514 | −0.538966 | −0.269483 | − | 0.963005i | \(-0.586853\pi\) | ||||
−0.269483 | + | 0.963005i | \(0.586853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 273.509 | − | 113.291i | 1.05602 | − | 0.437418i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 213.937 | + | 88.6158i | 0.819684 | + | 0.339524i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −91.6940 | + | 91.6940i | −0.348647 | + | 0.348647i | −0.859605 | − | 0.510959i | \(-0.829290\pi\) |
0.510959 | + | 0.859605i | \(0.329290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 159.740 | − | 159.740i | 0.602793 | − | 0.602793i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.57537 | − | 3.55204i | −0.0321175 | − | 0.0133035i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 179.504 | − | 74.3530i | 0.667301 | − | 0.276405i | −0.0232059 | − | 0.999731i | \(-0.507387\pi\) |
0.690507 | + | 0.723325i | \(0.257387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 454.375 | 1.67666 | 0.838331 | − | 0.545161i | \(-0.183532\pi\) | ||||
0.838331 | + | 0.545161i | \(0.183532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.99188i | 0.0219483i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 39.6620 | + | 95.7526i | 0.144226 | + | 0.348191i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.5345 | + | 30.2610i | −0.0452510 | + | 0.109246i | −0.944889 | − | 0.327391i | \(-0.893830\pi\) |
0.899638 | + | 0.436637i | \(0.143830\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −297.291 | − | 297.291i | −1.06556 | − | 1.06556i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 312.777 | + | 312.777i | 1.11308 | + | 1.11308i | 0.992731 | + | 0.120353i | \(0.0384027\pi\) |
0.120353 | + | 0.992731i | \(0.461597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 74.2838 | − | 179.337i | 0.262487 | − | 0.633700i | −0.736604 | − | 0.676324i | \(-0.763572\pi\) |
0.999091 | + | 0.0426244i | \(0.0135719\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.0081 | + | 43.4754i | 0.0631864 | + | 0.152545i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 94.9562i | 0.330858i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 281.828 | 0.975182 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.4903 | + | 9.73000i | −0.0807227 | + | 0.0334364i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −156.211 | − | 64.7046i | −0.533143 | − | 0.220835i | 0.0998364 | − | 0.995004i | \(-0.468168\pi\) |
−0.632979 | + | 0.774169i | \(0.718168\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 424.983 | − | 424.983i | 1.44062 | − | 1.44062i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.4006 | + | 12.4006i | −0.0417529 | + | 0.0417529i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.5555 | − | 15.5560i | −0.125604 | − | 0.0520268i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 82.1432 | − | 34.0248i | 0.272901 | − | 0.113039i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.4560 | 0.0576106 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 679.301i | − | 2.22722i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −111.488 | − | 269.157i | −0.363155 | − | 0.876733i | −0.994835 | − | 0.101504i | \(-0.967635\pi\) |
0.631681 | − | 0.775229i | \(-0.282365\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.97928 | − | 19.2637i | 0.0258229 | − | 0.0623420i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 74.0508 | + | 74.0508i | 0.238105 | + | 0.238105i | 0.816065 | − | 0.577960i | \(-0.196151\pi\) |
−0.577960 | + | 0.816065i | \(0.696151\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −119.709 | − | 119.709i | −0.382458 | − | 0.382458i | 0.489529 | − | 0.871987i | \(-0.337169\pi\) |
−0.871987 | + | 0.489529i | \(0.837169\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −269.332 | + | 650.224i | −0.855021 | + | 2.06420i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 154.558 | + | 373.135i | 0.487563 | + | 1.17708i | 0.955942 | + | 0.293554i | \(0.0948382\pi\) |
−0.468379 | + | 0.883528i | \(0.655162\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 63.4940i | − | 0.199041i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −49.1155 | −0.153008 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.8434 | + | 14.4326i | −0.107874 | + | 0.0446830i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 60.3061 | + | 24.9796i | 0.185557 | + | 0.0768604i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.3227 | + | 17.3227i | −0.0529745 | + | 0.0529745i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −458.464 | + | 458.464i | −1.39351 | + | 1.39351i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 376.019 | + | 155.752i | 1.13601 | + | 0.470551i | 0.869820 | − | 0.493370i | \(-0.164235\pi\) |
0.266190 | + | 0.963921i | \(0.414235\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 249.757 | − | 103.453i | 0.750021 | − | 0.310669i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 803.711 | 2.39914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 584.284i | − | 1.73378i | −0.498499 | − | 0.866890i | \(-0.666115\pi\) | ||
0.498499 | − | 0.866890i | \(-0.333885\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.5463 | + | 30.2895i | 0.0370098 | + | 0.0893495i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.1162 | + | 106.506i | −0.129373 | + | 0.312334i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −29.9994 | − | 29.9994i | −0.0874617 | − | 0.0874617i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 62.9514 | + | 62.9514i | 0.182468 | + | 0.182468i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0226 | − | 36.2679i | 0.0432929 | − | 0.104518i | −0.900754 | − | 0.434330i | \(-0.856985\pi\) |
0.944047 | + | 0.329812i | \(0.106985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 82.9090 | + | 200.160i | 0.237562 | + | 0.573525i | 0.997030 | − | 0.0770202i | \(-0.0245406\pi\) |
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.0451i | 0.0314675i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −213.926 | −0.606022 | −0.303011 | − | 0.952987i | \(-0.597992\pi\) | ||||
−0.303011 | + | 0.952987i | \(0.597992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.3394 | − | 8.83905i | 0.0601109 | − | 0.0248987i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.71666 | + | 4.02477i | 0.0272175 | + | 0.0112739i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −235.583 | + | 235.583i | −0.656219 | + | 0.656219i | −0.954483 | − | 0.298264i | \(-0.903592\pi\) |
0.298264 | + | 0.954483i | \(0.403592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 115.037 | − | 115.037i | 0.318663 | − | 0.318663i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −43.1724 | − | 17.8826i | −0.118932 | − | 0.0492633i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 597.299 | − | 247.410i | 1.63644 | − | 0.677834i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −266.252 | −0.725482 | −0.362741 | − | 0.931890i | \(-0.618159\pi\) | ||||
−0.362741 | + | 0.931890i | \(0.618159\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 86.7101i | 0.234987i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −101.598 | − | 245.280i | −0.273850 | − | 0.661133i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 133.648 | − | 322.655i | 0.358306 | − | 0.865028i | −0.637232 | − | 0.770672i | \(-0.719921\pi\) |
0.995539 | − | 0.0943560i | \(-0.0300792\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −42.0150 | − | 42.0150i | −0.112040 | − | 0.112040i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.2767 | − | 28.2767i | −0.0750045 | − | 0.0750045i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.26349 | + | 3.05034i | −0.00333376 | + | 0.00804840i | −0.925538 | − | 0.378656i | \(-0.876386\pi\) |
0.922204 | + | 0.386704i | \(0.126386\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.2169 | − | 53.6364i | −0.0583122 | − | 0.140778i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 310.584i | − | 0.810923i | −0.914112 | − | 0.405462i | \(-0.867111\pi\) | ||
0.914112 | − | 0.405462i | \(-0.132889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 192.978 | 0.501243 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 75.0098 | − | 31.0701i | 0.193824 | − | 0.0802844i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −677.246 | − | 280.524i | −1.74099 | − | 0.721142i | −0.998695 | − | 0.0510705i | \(-0.983737\pi\) |
−0.742296 | − | 0.670072i | \(-0.766263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50.4525 | + | 50.4525i | −0.129035 | + | 0.129035i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4407 | − | 17.4407i | 0.0443783 | − | 0.0443783i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 83.5594 | + | 34.6114i | 0.211543 | + | 0.0876239i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −467.679 | + | 193.719i | −1.17803 | + | 0.487957i | −0.883840 | − | 0.467789i | \(-0.845051\pi\) |
−0.294192 | + | 0.955746i | \(0.595051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 55.3027 | 0.138603 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 447.783i | 1.11667i | 0.829617 | + | 0.558333i | \(0.188559\pi\) | ||||
−0.829617 | + | 0.558333i | \(0.811441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.7849 | + | 67.0786i | 0.0689451 | + | 0.166448i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −241.271 | + | 582.480i | −0.595732 | + | 1.43822i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −52.4142 | − | 52.4142i | −0.128782 | − | 0.128782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 266.640 | + | 266.640i | 0.651931 | + | 0.651931i | 0.953458 | − | 0.301527i | \(-0.0974962\pi\) |
−0.301527 | + | 0.953458i | \(0.597496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.9392 | − | 89.1791i | 0.0898763 | − | 0.216981i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −270.299 | − | 652.559i | −0.654477 | − | 1.58005i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 735.294i | 1.77179i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 42.8676 | 0.102800 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 565.518 | − | 234.245i | 1.34969 | − | 0.559058i | 0.413481 | − | 0.910513i | \(-0.364313\pi\) |
0.936205 | + | 0.351455i | \(0.114313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −184.538 | − | 76.4382i | −0.438333 | − | 0.181564i | 0.152593 | − | 0.988289i | \(-0.451238\pi\) |
−0.590926 | + | 0.806726i | \(0.701238\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −418.651 | + | 418.651i | −0.989718 | + | 0.989718i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 81.0159 | − | 81.0159i | 0.190626 | − | 0.190626i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −737.557 | − | 305.506i | −1.72730 | − | 0.715471i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.38607 | − | 0.574129i | 0.00323093 | − | 0.00133830i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −329.019 | −0.763385 | −0.381692 | − | 0.924289i | \(-0.624659\pi\) | ||||
−0.381692 | + | 0.924289i | \(0.624659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 403.449i | 0.931753i | 0.884850 | + | 0.465877i | \(0.154261\pi\) | ||||
−0.884850 | + | 0.465877i | \(0.845739\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.5155 | + | 80.9135i | 0.0770470 | + | 0.186008i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −143.576 | + | 346.623i | −0.328549 | + | 0.793188i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −432.214 | − | 432.214i | −0.984542 | − | 0.984542i | 0.0153402 | − | 0.999882i | \(-0.495117\pi\) |
−0.999882 | + | 0.0153402i | \(0.995117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 278.732 | + | 278.732i | 0.632045 | + | 0.632045i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −138.144 | + | 333.509i | −0.311838 | + | 0.752843i | 0.687799 | + | 0.725901i | \(0.258577\pi\) |
−0.999637 | + | 0.0269419i | \(0.991423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 72.0501 | + | 173.944i | 0.161910 | + | 0.390886i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 47.0633i | − | 0.105287i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −320.009 | −0.712715 | −0.356358 | − | 0.934350i | \(-0.615981\pi\) | ||||
−0.356358 | + | 0.934350i | \(0.615981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.9658 | − | 9.09852i | 0.0487046 | − | 0.0201741i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 67.9210 | + | 28.1338i | 0.149936 | + | 0.0621055i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 85.9419 | − | 85.9419i | 0.188883 | − | 0.188883i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −148.390 | + | 148.390i | −0.324705 | + | 0.324705i | −0.850569 | − | 0.525864i | \(-0.823742\pi\) |
0.525864 | + | 0.850569i | \(0.323742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.9112 | + | 7.41904i | 0.0390221 | + | 0.0161635i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −224.303 | + | 92.9092i | −0.486557 | + | 0.201538i | −0.612456 | − | 0.790505i | \(-0.709818\pi\) |
0.125899 | + | 0.992043i | \(0.459818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −675.592 | −1.45916 | −0.729581 | − | 0.683894i | \(-0.760285\pi\) | ||||
−0.729581 | + | 0.683894i | \(0.760285\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 159.012i | − | 0.341962i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −190.920 | − | 460.923i | −0.408823 | − | 0.986987i | −0.985448 | − | 0.169977i | \(-0.945631\pi\) |
0.576625 | − | 0.817009i | \(-0.304369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 361.458 | − | 872.636i | 0.770698 | − | 1.86063i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.1187 | + | 15.1187i | 0.0320991 | + | 0.0320991i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.7416 | − | 15.7416i | −0.0332803 | − | 0.0332803i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 230.552 | − | 556.603i | 0.485373 | − | 1.17179i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −92.7755 | − | 223.980i | −0.194498 | − | 0.469559i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 775.709i | 1.61943i | 0.586821 | + | 0.809717i | \(0.300379\pi\) | ||||
−0.586821 | + | 0.809717i | \(0.699621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.6847 | −0.0970576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 96.6616 | − | 40.0385i | 0.200127 | − | 0.0828955i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 476.481 | + | 197.365i | 0.982435 | + | 0.406938i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 422.101 | − | 422.101i | 0.866738 | − | 0.866738i | −0.125372 | − | 0.992110i | \(-0.540012\pi\) |
0.992110 | + | 0.125372i | \(0.0400125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.3337 | + | 21.3337i | −0.0436272 | + | 0.0436272i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 277.565 | + | 114.971i | 0.565306 | + | 0.234157i | 0.646987 | − | 0.762501i | \(-0.276029\pi\) |
−0.0816809 | + | 0.996659i | \(0.526029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −64.8482 | + | 26.8610i | −0.131538 | + | 0.0544848i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 176.220 | 0.356000 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 27.1446i | − | 0.0546170i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 328.498 | + | 793.063i | 0.658312 | + | 1.58930i | 0.800410 | + | 0.599452i | \(0.204615\pi\) |
−0.142099 | + | 0.989852i | \(0.545385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.8525 | + | 69.6560i | −0.0575897 | + | 0.139034i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 115.459 | + | 115.459i | 0.229540 | + | 0.229540i | 0.812501 | − | 0.582960i | \(-0.198106\pi\) |
−0.582960 | + | 0.812501i | \(0.698106\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −250.373 | − | 250.373i | −0.495788 | − | 0.495788i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.8881 | + | 62.4995i | −0.0510614 | + | 0.123273i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −97.7110 | − | 235.895i | −0.191967 | − | 0.463449i | 0.798364 | − | 0.602175i | \(-0.205699\pi\) |
−0.990331 | + | 0.138727i | \(0.955699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 759.792i | − | 1.48687i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 101.942 | 0.198717 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −390.747 | + | 161.853i | −0.758733 | + | 0.314277i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 149.983 | + | 62.1252i | 0.290103 | + | 0.120165i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −64.0073 | + | 64.0073i | −0.123328 | + | 0.123328i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 229.899 | − | 229.899i | 0.441264 | − | 0.441264i | −0.451173 | − | 0.892437i | \(-0.648994\pi\) |
0.892437 | + | 0.451173i | \(0.148994\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 900.921 | + | 373.174i | 1.72260 | + | 0.713525i | 0.999746 | + | 0.0225265i | \(0.00717100\pi\) |
0.722856 | + | 0.690999i | \(0.242829\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −155.218 | + | 64.2933i | −0.295653 | + | 0.122463i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 127.441 | 0.241823 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 180.797i | 0.341772i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −246.826 | − | 595.890i | −0.464832 | − | 1.12220i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.73035 | − | 13.8343i | 0.0107511 | − | 0.0259555i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 704.466 | + | 704.466i | 1.31676 | + | 1.31676i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −60.1486 | − | 60.1486i | −0.112009 | − | 0.112009i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.3621 | − | 99.8569i | 0.0767386 | − | 0.185263i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 86.3781 | + | 208.535i | 0.159664 | + | 0.385462i | 0.983385 | − | 0.181533i | \(-0.0581058\pi\) |
−0.823721 | + | 0.566995i | \(0.808106\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 99.0983i | − | 0.182501i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 496.920 | 0.911780 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −497.491 | + | 206.067i | −0.909489 | + | 0.376723i | −0.787861 | − | 0.615853i | \(-0.788812\pi\) |
−0.121628 | + | 0.992576i | \(0.538812\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −673.507 | − | 278.976i | −1.22679 | − | 0.508152i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −260.983 | + | 260.983i | −0.473653 | + | 0.473653i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 75.1593 | − | 75.1593i | 0.135912 | − | 0.135912i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 94.4609 | + | 39.1270i | 0.170200 | + | 0.0704991i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −527.914 | + | 218.669i | −0.947782 | + | 0.392584i | −0.802397 | − | 0.596791i | \(-0.796442\pi\) |
−0.145385 | + | 0.989375i | \(0.546442\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.0209 | −0.0250820 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 2.63335i | − | 0.00469404i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 303.900 | + | 733.680i | 0.539788 | + | 1.30316i | 0.924871 | + | 0.380281i | \(0.124173\pi\) |
−0.385084 | + | 0.922882i | \(0.625827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 254.491 | − | 614.397i | 0.450427 | − | 1.08743i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 523.925 | + | 523.925i | 0.924029 | + | 0.924029i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −143.631 | − | 143.631i | −0.252426 | − | 0.252426i | 0.569538 | − | 0.821965i | \(-0.307122\pi\) |
−0.821965 | + | 0.569538i | \(0.807122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 371.018 | − | 895.717i | 0.649769 | − | 1.56868i | −0.163339 | − | 0.986570i | \(-0.552227\pi\) |
0.813109 | − | 0.582112i | \(-0.197773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.13194 | − | 7.56116i | −0.00546586 | − | 0.0131957i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1139.78i | − | 1.98223i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 706.702 | 1.22479 | 0.612393 | − | 0.790553i | \(-0.290207\pi\) | ||||
0.612393 | + | 0.790553i | \(0.290207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 43.4592 | − | 18.0014i | 0.0750590 | − | 0.0310905i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 798.352 | + | 330.688i | 1.37410 | + | 0.569171i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.0045 | + | 47.0045i | −0.0806253 | + | 0.0806253i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 78.4786 | − | 78.4786i | 0.134151 | − | 0.134151i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −293.599 | − | 121.613i | −0.500169 | − | 0.207177i | 0.118312 | − | 0.992976i | \(-0.462252\pi\) |
−0.618481 | + | 0.785800i | \(0.712252\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 619.110 | − | 256.444i | 1.05112 | − | 0.435389i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −78.0696 | −0.132097 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 674.627i | 1.13765i | 0.822458 | + | 0.568825i | \(0.192602\pi\) | ||||
−0.822458 | + | 0.568825i | \(0.807398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −81.6391 | − | 197.094i | −0.137209 | − | 0.331251i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.87127 | − | 11.7603i | 0.00815958 | − | 0.0196990i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −379.725 | − | 379.725i | −0.633932 | − | 0.633932i | 0.315120 | − | 0.949052i | \(-0.397955\pi\) |
−0.949052 | + | 0.315120i | \(0.897955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −548.542 | − | 548.542i | −0.912715 | − | 0.912715i | 0.0837700 | − | 0.996485i | \(-0.473304\pi\) |
−0.996485 | + | 0.0837700i | \(0.973304\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 330.068 | − | 796.855i | 0.547377 | − | 1.32148i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 362.733 | + | 875.715i | 0.599559 | + | 1.44746i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.05067i | − | 0.00173092i | −1.00000 | 0.000865460i | \(-0.999725\pi\) | |||
1.00000 | 0.000865460i | \(-0.000275484\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 102.926 | 0.169008 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 94.4614 | − | 39.1272i | 0.154601 | − | 0.0640379i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 625.826 | + | 259.226i | 1.02092 | + | 0.422881i | 0.829428 | − | 0.558613i | \(-0.188666\pi\) |
0.191495 | + | 0.981494i | \(0.438666\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.1894 | + | 23.1894i | −0.0377063 | + | 0.0377063i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 180.644 | − | 180.644i | 0.292779 | − | 0.292779i | −0.545398 | − | 0.838177i | \(-0.683622\pi\) |
0.838177 | + | 0.545398i | \(0.183622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −555.651 | − | 230.158i | −0.897658 | − | 0.371822i | −0.114339 | − | 0.993442i | \(-0.536475\pi\) |
−0.783319 | + | 0.621620i | \(0.786475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 178.181 | − | 73.8048i | 0.286925 | − | 0.118848i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 221.265 | 0.355160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 135.712i | 0.217139i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.29899 | − | 12.7929i | −0.00845135 | − | 0.0204034i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.3584 | + | 75.7058i | −0.0498543 | + | 0.120359i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 267.583 | + | 267.583i | 0.424062 | + | 0.424062i | 0.886600 | − | 0.462537i | \(-0.153061\pi\) |
−0.462537 | + | 0.886600i | \(0.653061\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 87.6981 | + | 87.6981i | 0.138544 | + | 0.138544i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −450.652 | + | 1087.97i | −0.709688 | + | 1.71334i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.0503 | − | 62.8911i | −0.0408954 | − | 0.0987301i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 24.7874i | − | 0.0387908i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −834.869 | −1.30245 | −0.651224 | − | 0.758886i | \(-0.725744\pi\) | ||||
−0.651224 | + | 0.758886i | \(0.725744\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1006.71 | + | 416.995i | −1.56565 | + | 0.648514i | −0.986060 | − | 0.166393i | \(-0.946788\pi\) |
−0.579592 | + | 0.814907i | \(0.696788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.3695 | + | 11.7510i | 0.0439837 | + | 0.0182187i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 857.194 | − | 857.194i | 1.32488 | − | 1.32488i | 0.415099 | − | 0.909776i | \(-0.363747\pi\) |
0.909776 | − | 0.415099i | \(-0.136253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −125.054 | + | 125.054i | −0.192687 | + | 0.192687i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −172.649 | − | 71.5136i | −0.265206 | − | 0.109852i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −105.248 | + | 43.5953i | −0.161177 | + | 0.0667616i | −0.461813 | − | 0.886977i | \(-0.652801\pi\) |
0.300636 | + | 0.953739i | \(0.402801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −500.306 | −0.763826 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 693.811i | − | 1.05603i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 222.875 | + | 538.067i | 0.338201 | + | 0.816490i | 0.997889 | + | 0.0649499i | \(0.0206888\pi\) |
−0.659687 | + | 0.751540i | \(0.729311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −396.971 | + | 958.372i | −0.600561 | + | 1.44988i | 0.272445 | + | 0.962171i | \(0.412168\pi\) |
−0.873005 | + | 0.487711i | \(0.837832\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.17275 | − | 1.17275i | −0.00176885 | − | 0.00176885i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −793.210 | − | 793.210i | −1.19280 | − | 1.19280i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −267.214 | + | 645.111i | −0.400620 | + | 0.967183i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.88577 | + | 4.55265i | 0.00281879 | + | 0.00680515i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 199.888i | 0.297896i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −908.805 | −1.35038 | −0.675190 | − | 0.737644i | \(-0.735938\pi\) | ||||
−0.675190 | + | 0.737644i | \(0.735938\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −286.120 | + | 118.515i | −0.423881 | + | 0.175577i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 963.142 | + | 398.947i | 1.42266 | + | 0.589286i | 0.955528 | − | 0.294900i | \(-0.0952865\pi\) |
0.467134 | + | 0.884186i | \(0.345287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 428.581 | − | 428.581i | 0.631195 | − | 0.631195i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −66.8259 | + | 66.8259i | −0.0981290 | + | 0.0981290i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −248.963 | − | 103.124i | −0.364515 | − | 0.150987i | 0.192906 | − | 0.981217i | \(-0.438209\pi\) |
−0.557420 | + | 0.830230i | \(0.688209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1808.92 | + | 749.280i | −2.64076 | + | 1.09384i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.5564 | 0.0546673 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.8664i | 0.0607640i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 222.756 | + | 537.780i | 0.322367 | + | 0.778263i | 0.999116 | + | 0.0420488i | \(0.0133885\pi\) |
−0.676748 | + | 0.736214i | \(0.736612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 79.2524 | − | 191.332i | 0.114361 | − | 0.276093i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −614.853 | − | 614.853i | −0.884681 | − | 0.884681i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5851 | − | 18.5851i | −0.0266645 | − | 0.0266645i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.27433 | − | 17.5618i | 0.0104068 | − | 0.0251242i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −236.347 | − | 570.592i | −0.337157 | − | 0.813969i | −0.997986 | − | 0.0634324i | \(-0.979795\pi\) |
0.660829 | − | 0.750536i | \(-0.270205\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 430.882i | 0.612919i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −223.924 | −0.317623 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −384.446 | + | 159.243i | −0.543771 | + | 0.225237i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −599.630 | − | 248.375i | −0.845740 | − | 0.350317i | −0.0826257 | − | 0.996581i | \(-0.526331\pi\) |
−0.763114 | + | 0.646264i | \(0.776331\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 68.6324 | − | 68.6324i | 0.0965293 | − | 0.0965293i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 896.458 | − | 896.458i | 1.25730 | − | 1.25730i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.1153 | − | 11.6457i | −0.0393221 | − | 0.0162877i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −124.867 | + | 51.7216i | −0.174152 | + | 0.0721361i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −96.4410 | −0.134132 | −0.0670661 | − | 0.997749i | \(-0.521364\pi\) | ||||
−0.0670661 | + | 0.997749i | \(0.521364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 497.048i | 0.689388i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33.9952 | + | 82.0716i | 0.0470196 | + | 0.113515i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 429.088 | − | 1035.91i | 0.591846 | − | 1.42884i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 708.402 | + | 708.402i | 0.974418 | + | 0.974418i | 0.999681 | − | 0.0252626i | \(-0.00804218\pi\) |
−0.0252626 | + | 0.999681i | \(0.508042\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 459.728 | + | 459.728i | 0.630628 | + | 0.630628i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.41788 | + | 22.7368i | −0.0128836 | + | 0.0311037i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −149.531 | − | 361.000i | −0.203999 | − | 0.492497i | 0.788458 | − | 0.615088i | \(-0.210880\pi\) |
−0.992457 | + | 0.122591i | \(0.960880\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 149.086i | 0.202838i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −236.497 | −0.320891 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 971.442 | − | 402.384i | 1.31454 | − | 0.544499i | 0.388331 | − | 0.921520i | \(-0.373052\pi\) |
0.926205 | + | 0.377021i | \(0.123052\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.05712 | − | 3.33737i | −0.0108733 | − | 0.00450387i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −117.181 | + | 117.181i | −0.157714 | + | 0.157714i | −0.781553 | − | 0.623839i | \(-0.785572\pi\) |
0.623839 | + | 0.781553i | \(0.285572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −675.032 | + | 675.032i | −0.906083 | + | 0.906083i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 729.022 | + | 301.971i | 0.975933 | + | 0.404245i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1081.70 | − | 448.056i | 1.44420 | − | 0.598206i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −604.910 | −0.805473 | −0.402736 | − | 0.915316i | \(-0.631941\pi\) | ||||
−0.402736 | + | 0.915316i | \(0.631941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 98.2854i | 0.130525i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −570.670 | − | 1377.72i | −0.755855 | − | 1.82479i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −459.899 | + | 1110.29i | −0.607528 | + | 1.46670i | 0.258152 | + | 0.966104i | \(0.416887\pi\) |
−0.865680 | + | 0.500598i | \(0.833113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.5238 | − | 18.5238i | −0.0244056 | − | 0.0244056i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 202.753 | + | 202.753i | 0.266430 | + | 0.266430i | 0.827660 | − | 0.561230i | \(-0.189672\pi\) |
−0.561230 | + | 0.827660i | \(0.689672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 223.483 | − | 539.535i | 0.292900 | − | 0.707124i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −74.5495 | − | 179.978i | −0.0974503 | − | 0.235266i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 111.384i | 0.145220i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 954.072 | 1.24067 | 0.620333 | − | 0.784338i | \(-0.286997\pi\) | ||||
0.620333 | + | 0.784338i | \(0.286997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −51.9407 | + | 21.5146i | −0.0673680 | + | 0.0279047i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 244.204 | + | 101.153i | 0.315918 | + | 0.130857i | 0.535007 | − | 0.844847i | \(-0.320309\pi\) |
−0.219090 | + | 0.975705i | \(0.570309\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1439.52 | + | 1439.52i | −1.85744 | + | 1.85744i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 84.9649 | − | 84.9649i | 0.109350 | − | 0.109350i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −127.685 | − | 52.8890i | −0.163909 | − | 0.0678934i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.27923 | + | 2.60094i | −0.00803999 | + | 0.00333027i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 189.727 | 0.242308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 433.696i | − | 0.552479i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.8368 | + | 47.8903i | 0.0252056 | + | 0.0608518i | 0.935981 | − | 0.352050i | \(-0.114515\pi\) |
−0.910776 | + | 0.412902i | \(0.864515\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.1416 | + | 48.6261i | −0.0255280 | + | 0.0616301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −552.633 | − | 552.633i | −0.698650 | − | 0.698650i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 89.0192 | + | 89.0192i | 0.112256 | + | 0.112256i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.0887 | − | 84.7116i | 0.0441367 | − | 0.106556i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 187.462 | + | 452.574i | 0.235210 | + | 0.567847i | 0.996775 | − | 0.0802411i | \(-0.0255690\pi\) |
−0.761566 | + | 0.648088i | \(0.775569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 179.464i | − | 0.224611i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 202.050 | 0.252247 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −175.759 | + | 72.8017i | −0.218878 | + | 0.0906622i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1960.70 | − | 812.148i | −2.43565 | − | 1.00888i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 55.7625 | − | 55.7625i | 0.0690985 | − | 0.0690985i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −772.357 | + | 772.357i | −0.954706 | + | 0.954706i | −0.999018 | − | 0.0443114i | \(-0.985891\pi\) |
0.0443114 | + | 0.999018i | \(0.485891\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −518.106 | − | 214.607i | −0.638849 | − | 0.264620i | 0.0396587 | − | 0.999213i | \(-0.487373\pi\) |
−0.678508 | + | 0.734593i | \(0.737373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 170.384 | − | 70.5753i | 0.209574 | − | 0.0868085i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 611.981 | 0.750897 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 129.407i | 0.158393i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −49.9141 | − | 120.503i | −0.0609452 | − | 0.147135i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 328.590 | − | 793.287i | 0.400232 | − | 0.966245i | −0.587378 | − | 0.809313i | \(-0.699840\pi\) |
0.987609 | − | 0.156932i | \(-0.0501604\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 370.318 | + | 370.318i | 0.449961 | + | 0.449961i | 0.895341 | − | 0.445381i | \(-0.146932\pi\) |
−0.445381 | + | 0.895341i | \(0.646932\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.7453 | + | 29.7453i | 0.0360549 | + | 0.0360549i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.6405 | − | 134.328i | 0.0672799 | − | 0.162428i | −0.886663 | − | 0.462416i | \(-0.846983\pi\) |
0.953943 | + | 0.299988i | \(0.0969827\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 492.586 | + | 1189.21i | 0.594193 | + | 1.43451i | 0.879419 | + | 0.476048i | \(0.157931\pi\) |
−0.285226 | + | 0.958460i | \(0.592069\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.2943i | 0.0159980i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −119.485 | −0.143439 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1412.91 | − | 585.248i | 1.69211 | − | 0.700896i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −318.252 | − | 131.824i | −0.380229 | − | 0.157496i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 215.217 | − | 215.217i | 0.256516 | − | 0.256516i | −0.567119 | − | 0.823636i | \(-0.691942\pi\) |
0.823636 | + | 0.567119i | \(0.191942\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 108.953 | − | 108.953i | 0.129552 | − | 0.129552i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 165.868 | + | 68.7048i | 0.196759 | + | 0.0815004i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1267.75 | − | 525.119i | 1.50029 | − | 0.621442i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1113.95 | 1.31517 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 78.7867i | − | 0.0927994i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 311.954 | + | 753.123i | 0.366573 | + | 0.884986i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −68.6449 | + | 165.723i | −0.0804747 | + | 0.194283i | −0.958996 | − | 0.283421i | \(-0.908531\pi\) |
0.878521 | + | 0.477704i | \(0.158531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −724.327 | − | 724.327i | −0.847166 | − | 0.847166i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 713.771 | + | 713.771i | 0.832871 | + | 0.832871i | 0.987909 | − | 0.155037i | \(-0.0495497\pi\) |
−0.155037 | + | 0.987909i | \(0.549550\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −343.845 | + | 830.116i | −0.400285 | + | 0.966375i | 0.587311 | + | 0.809361i | \(0.300187\pi\) |
−0.987596 | + | 0.157013i | \(0.949813\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.7490 | + | 35.6071i | 0.0171300 | + | 0.0413556i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1574.26i | − | 1.82417i | −0.410002 | − | 0.912085i | \(-0.634472\pi\) | ||
0.410002 | − | 0.912085i | \(-0.365528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1836.12 | 2.12268 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 105.681 | − | 43.7745i | 0.121893 | − | 0.0504897i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.5878 | − | 10.1846i | −0.0282944 | − | 0.0117199i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −105.322 | + | 105.322i | −0.120921 | + | 0.120921i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 391.363 | − | 391.363i | 0.448296 | − | 0.448296i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1308.61 | + | 542.043i | 1.49555 | + | 0.619477i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1227.56 | − | 508.470i | 1.39972 | − | 0.579784i | 0.450042 | − | 0.893007i | \(-0.351409\pi\) |
0.949679 | + | 0.313224i | \(0.101409\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −68.6268 | −0.0780738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1187.59i | − | 1.34800i | −0.738732 | − | 0.674000i | \(-0.764575\pi\) | ||
0.738732 | − | 0.674000i | \(-0.235425\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −544.271 | − | 1313.99i | −0.616389 | − | 1.48809i | −0.855869 | − | 0.517193i | \(-0.826977\pi\) |
0.239480 | − | 0.970901i | \(-0.423023\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 93.3522 | − | 225.372i | 0.105483 | − | 0.254658i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 95.1081 | + | 95.1081i | 0.107224 | + | 0.107224i | 0.758684 | − | 0.651459i | \(-0.225843\pi\) |
−0.651459 | + | 0.758684i | \(0.725843\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 978.598 | + | 978.598i | 1.10079 | + | 1.10079i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 70.9955 | − | 171.398i | 0.0796807 | − | 0.192366i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −361.129 | − | 871.842i | −0.404400 | − | 0.976307i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1725.43i | 1.92786i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.4990 | −0.0183935 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1152.25 | − | 477.276i | 1.28170 | − | 0.530896i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.8922 | + | 28.1219i | 0.0753521 | + | 0.0312119i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.5176 | − | 25.5176i | 0.0282587 | − | 0.0282587i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1421.37 | + | 1421.37i | −1.57058 | + | 1.57058i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −103.742 | − | 42.9713i | −0.114379 | − | 0.0473774i | 0.324760 | − | 0.945796i | \(-0.394716\pi\) |
−0.439139 | + | 0.898419i | \(0.644716\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −351.060 | + | 145.414i | −0.386205 | + | 0.159971i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −134.755 | −0.147920 | −0.0739598 | − | 0.997261i | \(-0.523564\pi\) | ||||
−0.0739598 | + | 0.997261i | \(0.523564\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 216.365i | − | 0.236982i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −105.512 | − | 254.728i | −0.115313 | − | 0.278391i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −225.005 | + | 543.211i | −0.245371 | + | 0.592379i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −847.025 | − | 847.025i | −0.921681 | − | 0.921681i | 0.0754671 | − | 0.997148i | \(-0.475955\pi\) |
−0.997148 | + | 0.0754671i | \(0.975955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −83.6129 | − | 83.6129i | −0.0907849 | − | 0.0907849i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.63811 | + | 3.95474i | −0.00177476 | + | 0.00428465i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −500.931 | − | 1209.35i | −0.541547 | − | 1.30741i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 453.884i | 0.489627i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1150.33 | −1.23824 | −0.619121 | − | 0.785295i | \(-0.712511\pi\) | ||||
−0.619121 | + | 0.785295i | \(0.712511\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −580.461 | + | 240.435i | −0.623481 | + | 0.258254i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.2698 | + | 16.2661i | 0.0420898 | + | 0.0174342i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −37.7704 | + | 37.7704i | −0.0403961 | + | 0.0403961i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1191.07 | − | 1191.07i | 1.27115 | − | 1.27115i | 0.325670 | − | 0.945484i | \(-0.394410\pi\) |
0.945484 | − | 0.325670i | \(-0.105590\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −63.4828 | − | 26.2954i | −0.0676068 | − | 0.0280037i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −741.098 | + | 306.973i | −0.787564 | + | 0.326220i | −0.739964 | − | 0.672647i | \(-0.765157\pi\) |
−0.0476005 | + | 0.998866i | \(0.515157\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −261.467 | −0.277272 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 576.642i | 0.610203i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 75.9383 | + | 183.331i | 0.0801883 | + | 0.193592i | 0.958889 | − | 0.283781i | \(-0.0915890\pi\) |
−0.878701 | + | 0.477373i | \(0.841589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.8514 | + | 110.695i | −0.0483155 | + | 0.116644i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 115.913 | + | 115.913i | 0.121886 | + | 0.121886i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −240.916 | − | 240.916i | −0.252798 | − | 0.252798i | 0.569319 | − | 0.822117i | \(-0.307207\pi\) |
−0.822117 | + | 0.569319i | \(0.807207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.5287 | + | 153.372i | −0.0665222 | + | 0.160599i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.86212 | − | 23.8093i | −0.0103052 | − | 0.0248791i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2301.03i | 2.39941i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1303.41 | −1.35631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 987.767 | − | 409.147i | 1.02572 | − | 0.424867i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −881.533 | − | 365.143i | −0.913506 | − | 0.378386i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −474.501 | + | 474.501i | −0.490694 | + | 0.490694i | −0.908525 | − | 0.417831i | \(-0.862791\pi\) |
0.417831 | + | 0.908525i | \(0.362791\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.8240 | + | 10.8240i | −0.0111703 | + | 0.0111703i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −486.579 | − | 201.548i | −0.501111 | − | 0.207567i | 0.117786 | − | 0.993039i | \(-0.462420\pi\) |
−0.618897 | + | 0.785472i | \(0.712420\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −944.103 | + | 391.060i | −0.970301 | + | 0.401912i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.4938 | 0.0271731 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 137.589i | − | 0.140828i | −0.997518 | − | 0.0704140i | \(-0.977568\pi\) | ||
0.997518 | − | 0.0704140i | \(-0.0224320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.2012 | − | 51.1841i | −0.0216559 | − | 0.0522821i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 204.075 | − | 492.681i | 0.208028 | − | 0.502224i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 602.812 | + | 602.812i | 0.613237 | + | 0.613237i | 0.943788 | − | 0.330551i | \(-0.107235\pi\) |
−0.330551 | + | 0.943788i | \(0.607235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1119.76 | + | 1119.76i | 1.13681 | + | 1.13681i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −100.707 | + | 243.128i | −0.102033 | + | 0.246330i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 93.6893 | + | 226.186i | 0.0947313 | + | 0.228702i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 82.2289i | − | 0.0829757i | −0.999139 | − | 0.0414879i | \(-0.986790\pi\) | ||
0.999139 | − | 0.0414879i | \(-0.0132098\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 165.193 | 0.166358 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −238.547 | + | 98.8096i | −0.239746 | + | 0.0993061i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1201.68 | + | 497.750i | 1.20529 | + | 0.499248i | 0.892705 | − | 0.450641i | \(-0.148805\pi\) |
0.312586 | + | 0.949889i | \(0.398805\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 156.620 | − | 156.620i | 0.156776 | − | 0.156776i |
(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 | 128.3.h.a.15.4 | 28 | ||
4.3 | odd | 2 | 32.3.h.a.27.7 | yes | 28 | ||
8.3 | odd | 2 | 256.3.h.b.31.4 | 28 | |||
8.5 | even | 2 | 256.3.h.a.31.4 | 28 | |||
12.11 | even | 2 | 288.3.u.a.91.1 | 28 | |||
32.3 | odd | 8 | 256.3.h.a.223.4 | 28 | |||
32.13 | even | 8 | 32.3.h.a.19.7 | ✓ | 28 | ||
32.19 | odd | 8 | inner | 128.3.h.a.111.4 | 28 | ||
32.29 | even | 8 | 256.3.h.b.223.4 | 28 | |||
96.77 | odd | 8 | 288.3.u.a.19.1 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.7 | ✓ | 28 | 32.13 | even | 8 | ||
32.3.h.a.27.7 | yes | 28 | 4.3 | odd | 2 | ||
128.3.h.a.15.4 | 28 | 1.1 | even | 1 | trivial | ||
128.3.h.a.111.4 | 28 | 32.19 | odd | 8 | inner | ||
256.3.h.a.31.4 | 28 | 8.5 | even | 2 | |||
256.3.h.a.223.4 | 28 | 32.3 | odd | 8 | |||
256.3.h.b.31.4 | 28 | 8.3 | odd | 2 | |||
256.3.h.b.223.4 | 28 | 32.29 | even | 8 | |||
288.3.u.a.19.1 | 28 | 96.77 | odd | 8 | |||
288.3.u.a.91.1 | 28 | 12.11 | even | 2 |