Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.c (of order \(2\), degree \(1\), 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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.5 | ||
Root | \(-1.41833i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.i.151.10 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41833i | − | 0.709164i | −0.935025 | − | 0.354582i | \(-0.884623\pi\) | ||
0.935025 | − | 0.354582i | \(-0.115377\pi\) | |||||||
\(3\) | − | 1.48141i | − | 0.493802i | −0.969041 | − | 0.246901i | \(-0.920588\pi\) | ||
0.969041 | − | 0.246901i | \(-0.0794123\pi\) | |||||||
\(4\) | 1.98835 | 0.497087 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.10112 | −0.350187 | ||||||||
\(7\) | −2.50491 | −0.357844 | −0.178922 | − | 0.983863i | \(-0.557261\pi\) | ||||
−0.178922 | + | 0.983863i | \(0.557261\pi\) | |||||||
\(8\) | − | 8.49344i | − | 1.06168i | ||||||
\(9\) | 6.80543 | 0.756159 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.7700 | 1.52454 | 0.762272 | − | 0.647257i | \(-0.224084\pi\) | ||||
0.762272 | + | 0.647257i | \(0.224084\pi\) | |||||||
\(12\) | − | 2.94555i | − | 0.245463i | ||||||
\(13\) | 12.8905i | 0.991576i | 0.868444 | + | 0.495788i | \(0.165121\pi\) | ||||
−0.868444 | + | 0.495788i | \(0.834879\pi\) | |||||||
\(14\) | 3.55278i | 0.253770i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.09308 | −0.255818 | ||||||||
\(17\) | 10.1212 | 0.595366 | 0.297683 | − | 0.954665i | \(-0.403786\pi\) | ||||
0.297683 | + | 0.954665i | \(0.403786\pi\) | |||||||
\(18\) | − | 9.65233i | − | 0.536241i | ||||||
\(19\) | 2.53793 | − | 18.8297i | 0.133575 | − | 0.991039i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.71079i | 0.176704i | ||||||||
\(22\) | − | 23.7853i | − | 1.08115i | ||||||
\(23\) | −18.7736 | −0.816244 | −0.408122 | − | 0.912927i | \(-0.633816\pi\) | ||||
−0.408122 | + | 0.912927i | \(0.633816\pi\) | |||||||
\(24\) | −12.5822 | −0.524260 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 18.2829 | 0.703190 | ||||||||
\(27\) | − | 23.4143i | − | 0.867196i | ||||||
\(28\) | −4.98063 | −0.177880 | ||||||||
\(29\) | − | 30.4098i | − | 1.04861i | −0.851529 | − | 0.524307i | \(-0.824324\pi\) | ||
0.851529 | − | 0.524307i | \(-0.175676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 56.8943i | 1.83530i | 0.397389 | + | 0.917650i | \(0.369916\pi\) | ||||
−0.397389 | + | 0.917650i | \(0.630084\pi\) | |||||||
\(32\) | − | 28.1684i | − | 0.880263i | ||||||
\(33\) | − | 24.8432i | − | 0.752824i | ||||||
\(34\) | − | 14.3552i | − | 0.422212i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 13.5316 | 0.375877 | ||||||||
\(37\) | − | 19.1200i | − | 0.516758i | −0.966044 | − | 0.258379i | \(-0.916812\pi\) | ||
0.966044 | − | 0.258379i | \(-0.0831883\pi\) | |||||||
\(38\) | −26.7067 | − | 3.59961i | −0.702809 | − | 0.0947267i | ||||
\(39\) | 19.0961 | 0.489643 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 15.2087i | − | 0.370943i | −0.982650 | − | 0.185471i | \(-0.940619\pi\) | ||
0.982650 | − | 0.185471i | \(-0.0593812\pi\) | |||||||
\(42\) | 5.26311 | 0.125312 | ||||||||
\(43\) | 68.0964 | 1.58364 | 0.791819 | − | 0.610756i | \(-0.209135\pi\) | ||||
0.791819 | + | 0.610756i | \(0.209135\pi\) | |||||||
\(44\) | 33.3446 | 0.757831 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 26.6271i | 0.578850i | ||||||||
\(47\) | −33.9534 | −0.722412 | −0.361206 | − | 0.932486i | \(-0.617635\pi\) | ||||
−0.361206 | + | 0.932486i | \(0.617635\pi\) | |||||||
\(48\) | 6.06352i | 0.126323i | ||||||||
\(49\) | −42.7254 | −0.871948 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 14.9937i | − | 0.293993i | ||||||
\(52\) | 25.6308i | 0.492900i | ||||||||
\(53\) | 2.77237i | 0.0523089i | 0.999658 | + | 0.0261544i | \(0.00832617\pi\) | ||||
−0.999658 | + | 0.0261544i | \(0.991674\pi\) | |||||||
\(54\) | −33.2091 | −0.614984 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 21.2753i | 0.379916i | ||||||||
\(57\) | −27.8945 | − | 3.75971i | −0.489377 | − | 0.0659598i | ||||
\(58\) | −43.1311 | −0.743639 | ||||||||
\(59\) | − | 41.0403i | − | 0.695599i | −0.937569 | − | 0.347799i | \(-0.886929\pi\) | ||
0.937569 | − | 0.347799i | \(-0.113071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −80.3350 | −1.31697 | −0.658484 | − | 0.752595i | \(-0.728802\pi\) | ||||
−0.658484 | + | 0.752595i | \(0.728802\pi\) | |||||||
\(62\) | 80.6948 | 1.30153 | ||||||||
\(63\) | −17.0470 | −0.270587 | ||||||||
\(64\) | −56.3244 | −0.880068 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −35.2358 | −0.533875 | ||||||||
\(67\) | − | 73.7575i | − | 1.10086i | −0.834882 | − | 0.550429i | \(-0.814464\pi\) | ||
0.834882 | − | 0.550429i | \(-0.185536\pi\) | |||||||
\(68\) | 20.1245 | 0.295949 | ||||||||
\(69\) | 27.8113i | 0.403063i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 119.192i | 1.67876i | 0.543543 | + | 0.839381i | \(0.317083\pi\) | ||||
−0.543543 | + | 0.839381i | \(0.682917\pi\) | |||||||
\(72\) | − | 57.8015i | − | 0.802799i | ||||||
\(73\) | −66.3948 | −0.909517 | −0.454759 | − | 0.890615i | \(-0.650275\pi\) | ||||
−0.454759 | + | 0.890615i | \(0.650275\pi\) | |||||||
\(74\) | −27.1185 | −0.366466 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.04629 | − | 37.4401i | 0.0663985 | − | 0.492632i | ||||
\(77\) | −42.0073 | −0.545549 | ||||||||
\(78\) | − | 27.0845i | − | 0.347237i | ||||||
\(79\) | − | 56.0205i | − | 0.709120i | −0.935033 | − | 0.354560i | \(-0.884631\pi\) | ||
0.935033 | − | 0.354560i | \(-0.115369\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 26.5628 | 0.327936 | ||||||||
\(82\) | −21.5709 | −0.263059 | ||||||||
\(83\) | 124.244 | 1.49692 | 0.748460 | − | 0.663180i | \(-0.230793\pi\) | ||||
0.748460 | + | 0.663180i | \(0.230793\pi\) | |||||||
\(84\) | 7.37834i | 0.0878374i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 96.5830i | − | 1.12306i | ||||||
\(87\) | −45.0493 | −0.517808 | ||||||||
\(88\) | − | 142.435i | − | 1.61858i | ||||||
\(89\) | 9.31740i | 0.104690i | 0.998629 | + | 0.0523450i | \(0.0166695\pi\) | ||||
−0.998629 | + | 0.0523450i | \(0.983330\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 32.2895i | − | 0.354830i | ||||||
\(92\) | −37.3285 | −0.405744 | ||||||||
\(93\) | 84.2836 | 0.906276 | ||||||||
\(94\) | 48.1570i | 0.512308i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −41.7289 | −0.434676 | ||||||||
\(97\) | − | 7.61982i | − | 0.0785548i | −0.999228 | − | 0.0392774i | \(-0.987494\pi\) | ||
0.999228 | − | 0.0392774i | \(-0.0125056\pi\) | |||||||
\(98\) | 60.5986i | 0.618353i | ||||||||
\(99\) | 114.127 | 1.15280 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −32.1518 | −0.318335 | −0.159168 | − | 0.987252i | \(-0.550881\pi\) | ||||
−0.159168 | + | 0.987252i | \(0.550881\pi\) | |||||||
\(102\) | −21.2659 | −0.208489 | ||||||||
\(103\) | 43.2792i | 0.420186i | 0.977681 | + | 0.210093i | \(0.0673767\pi\) | ||||
−0.977681 | + | 0.210093i | \(0.932623\pi\) | |||||||
\(104\) | 109.485 | 1.05274 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.93213 | 0.0370956 | ||||||||
\(107\) | 157.913i | 1.47582i | 0.674899 | + | 0.737910i | \(0.264187\pi\) | ||||
−0.674899 | + | 0.737910i | \(0.735813\pi\) | |||||||
\(108\) | − | 46.5557i | − | 0.431072i | ||||||
\(109\) | 58.7451i | 0.538946i | 0.963008 | + | 0.269473i | \(0.0868494\pi\) | ||||
−0.963008 | + | 0.269473i | \(0.913151\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −28.3246 | −0.255176 | ||||||||
\(112\) | 10.2528 | 0.0915428 | ||||||||
\(113\) | 149.248i | 1.32078i | 0.750924 | + | 0.660389i | \(0.229609\pi\) | ||||
−0.750924 | + | 0.660389i | \(0.770391\pi\) | |||||||
\(114\) | −5.33249 | + | 39.5635i | −0.0467763 | + | 0.347049i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 60.4653i | − | 0.521253i | ||||||
\(117\) | 87.7254i | 0.749790i | ||||||||
\(118\) | −58.2086 | −0.493293 | ||||||||
\(119\) | −25.3527 | −0.213048 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 160.233 | 1.32424 | ||||||||
\(122\) | 113.941i | 0.933946i | ||||||||
\(123\) | −22.5302 | −0.183172 | ||||||||
\(124\) | 113.126i | 0.912304i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 24.1782i | 0.191891i | ||||||||
\(127\) | 97.3189i | 0.766290i | 0.923688 | + | 0.383145i | \(0.125159\pi\) | ||||
−0.923688 | + | 0.383145i | \(0.874841\pi\) | |||||||
\(128\) | − | 32.7873i | − | 0.256151i | ||||||
\(129\) | − | 100.878i | − | 0.782004i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.432007 | 0.00329777 | 0.00164888 | − | 0.999999i | \(-0.499475\pi\) | ||||
0.00164888 | + | 0.999999i | \(0.499475\pi\) | |||||||
\(132\) | − | 49.3969i | − | 0.374219i | ||||||
\(133\) | −6.35728 | + | 47.1668i | −0.0477991 | + | 0.354637i | ||||
\(134\) | −104.612 | −0.780689 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 85.9640i | − | 0.632088i | ||||||
\(137\) | 134.070 | 0.978612 | 0.489306 | − | 0.872112i | \(-0.337250\pi\) | ||||
0.489306 | + | 0.872112i | \(0.337250\pi\) | |||||||
\(138\) | 39.4456 | 0.285838 | ||||||||
\(139\) | 16.0211 | 0.115260 | 0.0576300 | − | 0.998338i | \(-0.481646\pi\) | ||||
0.0576300 | + | 0.998338i | \(0.481646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 50.2987i | 0.356729i | ||||||||
\(142\) | 169.053 | 1.19052 | ||||||||
\(143\) | 216.173i | 1.51170i | ||||||||
\(144\) | −27.8552 | −0.193439 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 94.1695i | 0.644997i | ||||||||
\(147\) | 63.2937i | 0.430570i | ||||||||
\(148\) | − | 38.0173i | − | 0.256874i | ||||||
\(149\) | 87.2737 | 0.585729 | 0.292865 | − | 0.956154i | \(-0.405391\pi\) | ||||
0.292865 | + | 0.956154i | \(0.405391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 125.657i | − | 0.832167i | −0.909326 | − | 0.416084i | \(-0.863402\pi\) | ||
0.909326 | − | 0.416084i | \(-0.136598\pi\) | |||||||
\(152\) | −159.929 | − | 21.5557i | −1.05217 | − | 0.141814i | ||||
\(153\) | 68.8793 | 0.450192 | ||||||||
\(154\) | 59.5801i | 0.386884i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 37.9696 | 0.243395 | ||||||||
\(157\) | 76.4512 | 0.486950 | 0.243475 | − | 0.969907i | \(-0.421713\pi\) | ||||
0.243475 | + | 0.969907i | \(0.421713\pi\) | |||||||
\(158\) | −79.4554 | −0.502882 | ||||||||
\(159\) | 4.10701 | 0.0258303 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 47.0262 | 0.292088 | ||||||||
\(162\) | − | 37.6748i | − | 0.232560i | ||||||
\(163\) | −252.353 | −1.54818 | −0.774088 | − | 0.633078i | \(-0.781791\pi\) | ||||
−0.774088 | + | 0.633078i | \(0.781791\pi\) | |||||||
\(164\) | − | 30.2401i | − | 0.184391i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 176.219i | − | 1.06156i | ||||||
\(167\) | 305.922i | 1.83187i | 0.401328 | + | 0.915935i | \(0.368549\pi\) | ||||
−0.401328 | + | 0.915935i | \(0.631451\pi\) | |||||||
\(168\) | 31.5174 | 0.187603 | ||||||||
\(169\) | 2.83522 | 0.0167765 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.2717 | − | 128.145i | 0.101004 | − | 0.749383i | ||||
\(172\) | 135.399 | 0.787205 | ||||||||
\(173\) | 104.461i | 0.603822i | 0.953336 | + | 0.301911i | \(0.0976245\pi\) | ||||
−0.953336 | + | 0.301911i | \(0.902376\pi\) | |||||||
\(174\) | 63.8947i | 0.367211i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −68.6409 | −0.390005 | ||||||||
\(177\) | −60.7974 | −0.343488 | ||||||||
\(178\) | 13.2151 | 0.0742423 | ||||||||
\(179\) | 200.911i | 1.12241i | 0.827678 | + | 0.561203i | \(0.189661\pi\) | ||||
−0.827678 | + | 0.561203i | \(0.810339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1515i | 0.100284i | 0.998742 | + | 0.0501421i | \(0.0159674\pi\) | ||||
−0.998742 | + | 0.0501421i | \(0.984033\pi\) | |||||||
\(182\) | −45.7971 | −0.251632 | ||||||||
\(183\) | 119.009i | 0.650322i | ||||||||
\(184\) | 159.452i | 0.866589i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 119.542i | − | 0.642698i | ||||||
\(187\) | 169.733 | 0.907662 | ||||||||
\(188\) | −67.5111 | −0.359101 | ||||||||
\(189\) | 58.6506i | 0.310321i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 237.592 | 1.24394 | 0.621969 | − | 0.783042i | \(-0.286333\pi\) | ||||
0.621969 | + | 0.783042i | \(0.286333\pi\) | |||||||
\(192\) | 83.4393i | 0.434580i | ||||||||
\(193\) | − | 243.676i | − | 1.26257i | −0.775551 | − | 0.631285i | \(-0.782528\pi\) | ||
0.775551 | − | 0.631285i | \(-0.217472\pi\) | |||||||
\(194\) | −10.8074 | −0.0557082 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −84.9530 | −0.433434 | ||||||||
\(197\) | 102.247 | 0.519020 | 0.259510 | − | 0.965740i | \(-0.416439\pi\) | ||||
0.259510 | + | 0.965740i | \(0.416439\pi\) | |||||||
\(198\) | − | 161.869i | − | 0.817523i | ||||||
\(199\) | −93.7720 | −0.471216 | −0.235608 | − | 0.971848i | \(-0.575708\pi\) | ||||
−0.235608 | + | 0.971848i | \(0.575708\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −109.265 | −0.543607 | ||||||||
\(202\) | 45.6018i | 0.225752i | ||||||||
\(203\) | 76.1739i | 0.375241i | ||||||||
\(204\) | − | 29.8126i | − | 0.146140i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 61.3840 | 0.297981 | ||||||||
\(207\) | −127.763 | −0.617210 | ||||||||
\(208\) | − | 52.7618i | − | 0.253663i | ||||||
\(209\) | 42.5610 | − | 315.774i | 0.203641 | − | 1.51088i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 66.2032i | − | 0.313759i | −0.987618 | − | 0.156880i | \(-0.949856\pi\) | ||
0.987618 | − | 0.156880i | \(-0.0501435\pi\) | |||||||
\(212\) | 5.51244i | 0.0260021i | ||||||||
\(213\) | 176.572 | 0.828977 | ||||||||
\(214\) | 223.972 | 1.04660 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −198.868 | −0.920684 | ||||||||
\(217\) | − | 142.515i | − | 0.656752i | ||||||
\(218\) | 83.3197 | 0.382201 | ||||||||
\(219\) | 98.3577i | 0.449122i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 130.468i | 0.590351i | ||||||||
\(222\) | 40.1735i | 0.180962i | ||||||||
\(223\) | 226.345i | 1.01500i | 0.861652 | + | 0.507500i | \(0.169430\pi\) | ||||
−0.861652 | + | 0.507500i | \(0.830570\pi\) | |||||||
\(224\) | 70.5593i | 0.314997i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 211.682 | 0.936648 | ||||||||
\(227\) | − | 88.6093i | − | 0.390349i | −0.980768 | − | 0.195175i | \(-0.937473\pi\) | ||
0.980768 | − | 0.195175i | \(-0.0625274\pi\) | |||||||
\(228\) | −55.4640 | − | 7.47560i | −0.243263 | − | 0.0327877i | ||||
\(229\) | −359.123 | −1.56822 | −0.784112 | − | 0.620619i | \(-0.786881\pi\) | ||||
−0.784112 | + | 0.620619i | \(0.786881\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 62.2299i | 0.269394i | ||||||||
\(232\) | −258.284 | −1.11329 | ||||||||
\(233\) | −242.528 | −1.04089 | −0.520446 | − | 0.853895i | \(-0.674234\pi\) | ||||
−0.520446 | + | 0.853895i | \(0.674234\pi\) | |||||||
\(234\) | 124.423 | 0.531724 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 81.6024i | − | 0.345773i | ||||||
\(237\) | −82.9892 | −0.350165 | ||||||||
\(238\) | 35.9585i | 0.151086i | ||||||||
\(239\) | 143.682 | 0.601182 | 0.300591 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300591 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 401.898i | 1.66763i | 0.552046 | + | 0.833813i | \(0.313847\pi\) | ||||
−0.552046 | + | 0.833813i | \(0.686153\pi\) | |||||||
\(242\) | − | 227.262i | − | 0.939100i | ||||||
\(243\) | − | 250.079i | − | 1.02913i | ||||||
\(244\) | −159.734 | −0.654647 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 31.9552i | 0.129899i | ||||||||
\(247\) | 242.725 | + | 32.7152i | 0.982690 | + | 0.132450i | ||||
\(248\) | 483.228 | 1.94850 | ||||||||
\(249\) | − | 184.057i | − | 0.739183i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −45.3071 | −0.180506 | −0.0902531 | − | 0.995919i | \(-0.528768\pi\) | ||||
−0.0902531 | + | 0.995919i | \(0.528768\pi\) | |||||||
\(252\) | −33.8954 | −0.134505 | ||||||||
\(253\) | −314.833 | −1.24440 | ||||||||
\(254\) | 138.030 | 0.543425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −271.801 | −1.06172 | ||||||||
\(257\) | − | 47.2850i | − | 0.183988i | −0.995760 | − | 0.0919941i | \(-0.970676\pi\) | ||
0.995760 | − | 0.0919941i | \(-0.0293241\pi\) | |||||||
\(258\) | −143.079 | −0.554569 | ||||||||
\(259\) | 47.8940i | 0.184919i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 206.952i | − | 0.792920i | ||||||
\(262\) | − | 0.612728i | − | 0.00233866i | ||||||
\(263\) | 326.709 | 1.24224 | 0.621119 | − | 0.783716i | \(-0.286678\pi\) | ||||
0.621119 | + | 0.783716i | \(0.286678\pi\) | |||||||
\(264\) | −211.004 | −0.799257 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 66.8979 | + | 9.01671i | 0.251496 | + | 0.0338974i | ||||
\(267\) | 13.8029 | 0.0516961 | ||||||||
\(268\) | − | 146.656i | − | 0.547223i | ||||||
\(269\) | − | 415.031i | − | 1.54287i | −0.636311 | − | 0.771433i | \(-0.719540\pi\) | ||
0.636311 | − | 0.771433i | \(-0.280460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −363.836 | −1.34257 | −0.671285 | − | 0.741200i | \(-0.734257\pi\) | ||||
−0.671285 | + | 0.741200i | \(0.734257\pi\) | |||||||
\(272\) | −41.4270 | −0.152305 | ||||||||
\(273\) | −47.8339 | −0.175216 | ||||||||
\(274\) | − | 190.155i | − | 0.693996i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 55.2986i | 0.200357i | ||||||||
\(277\) | −332.903 | −1.20182 | −0.600909 | − | 0.799318i | \(-0.705194\pi\) | ||||
−0.600909 | + | 0.799318i | \(0.705194\pi\) | |||||||
\(278\) | − | 22.7232i | − | 0.0817382i | ||||||
\(279\) | 387.190i | 1.38778i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 258.538i | 0.920063i | 0.887903 | + | 0.460032i | \(0.152162\pi\) | ||||
−0.887903 | + | 0.460032i | \(0.847838\pi\) | |||||||
\(282\) | 71.3401 | 0.252979 | ||||||||
\(283\) | 191.340 | 0.676114 | 0.338057 | − | 0.941126i | \(-0.390230\pi\) | ||||
0.338057 | + | 0.941126i | \(0.390230\pi\) | |||||||
\(284\) | 236.995i | 0.834491i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 306.605 | 1.07204 | ||||||||
\(287\) | 38.0963i | 0.132740i | ||||||||
\(288\) | − | 191.698i | − | 0.665619i | ||||||
\(289\) | −186.561 | −0.645539 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.2881 | −0.0387906 | ||||||||
\(292\) | −132.016 | −0.452109 | ||||||||
\(293\) | 479.052i | 1.63499i | 0.575935 | + | 0.817495i | \(0.304638\pi\) | ||||
−0.575935 | + | 0.817495i | \(0.695362\pi\) | |||||||
\(294\) | 89.7712 | 0.305344 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −162.395 | −0.548631 | ||||||||
\(297\) | − | 392.657i | − | 1.32208i | ||||||
\(298\) | − | 123.783i | − | 0.415378i | ||||||
\(299\) | − | 242.001i | − | 0.809368i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −170.575 | −0.566695 | ||||||||
\(302\) | −178.223 | −0.590143 | ||||||||
\(303\) | 47.6300i | 0.157195i | ||||||||
\(304\) | −10.3880 | + | 77.0716i | −0.0341709 | + | 0.253525i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 97.6934i | − | 0.319260i | ||||||
\(307\) | 270.388i | 0.880742i | 0.897816 | + | 0.440371i | \(0.145153\pi\) | ||||
−0.897816 | + | 0.440371i | \(0.854847\pi\) | |||||||
\(308\) | −83.5251 | −0.271185 | ||||||||
\(309\) | 64.1140 | 0.207489 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7303 | 0.0666569 | 0.0333285 | − | 0.999444i | \(-0.489389\pi\) | ||||
0.0333285 | + | 0.999444i | \(0.489389\pi\) | |||||||
\(312\) | − | 162.191i | − | 0.519844i | ||||||
\(313\) | 337.610 | 1.07863 | 0.539313 | − | 0.842106i | \(-0.318684\pi\) | ||||
0.539313 | + | 0.842106i | \(0.318684\pi\) | |||||||
\(314\) | − | 108.433i | − | 0.345327i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 111.388i | − | 0.352494i | ||||||
\(317\) | − | 392.652i | − | 1.23865i | −0.785135 | − | 0.619324i | \(-0.787407\pi\) | ||
0.785135 | − | 0.619324i | \(-0.212593\pi\) | |||||||
\(318\) | − | 5.82508i | − | 0.0183179i | ||||||
\(319\) | − | 509.972i | − | 1.59866i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 233.933 | 0.728763 | ||||||||
\(322\) | − | 66.6985i | − | 0.207138i | ||||||
\(323\) | 25.6870 | − | 190.580i | 0.0795262 | − | 0.590031i | ||||
\(324\) | 52.8161 | 0.163013 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 357.919i | 1.09791i | ||||||||
\(327\) | 87.0254 | 0.266133 | ||||||||
\(328\) | −129.174 | −0.393822 | ||||||||
\(329\) | 85.0501 | 0.258511 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 101.930i | − | 0.307946i | −0.988075 | − | 0.153973i | \(-0.950793\pi\) | ||
0.988075 | − | 0.153973i | \(-0.0492069\pi\) | |||||||
\(332\) | 247.041 | 0.744100 | ||||||||
\(333\) | − | 130.120i | − | 0.390751i | ||||||
\(334\) | 433.898 | 1.29909 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 15.1886i | − | 0.0452041i | ||||||
\(337\) | − | 356.299i | − | 1.05727i | −0.848850 | − | 0.528633i | \(-0.822705\pi\) | ||
0.848850 | − | 0.528633i | \(-0.177295\pi\) | |||||||
\(338\) | − | 4.02127i | − | 0.0118973i | ||||||
\(339\) | 221.097 | 0.652203 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 954.117i | 2.79800i | ||||||||
\(342\) | −181.751 | − | 24.4969i | −0.531435 | − | 0.0716285i | ||||
\(343\) | 229.764 | 0.669866 | ||||||||
\(344\) | − | 578.372i | − | 1.68132i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 148.160 | 0.428208 | ||||||||
\(347\) | −457.590 | −1.31870 | −0.659352 | − | 0.751835i | \(-0.729169\pi\) | ||||
−0.659352 | + | 0.751835i | \(0.729169\pi\) | |||||||
\(348\) | −89.5737 | −0.257396 | ||||||||
\(349\) | −292.657 | −0.838559 | −0.419280 | − | 0.907857i | \(-0.637717\pi\) | ||||
−0.419280 | + | 0.907857i | \(0.637717\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 301.822 | 0.859891 | ||||||||
\(352\) | − | 472.384i | − | 1.34200i | ||||||
\(353\) | −643.379 | −1.82260 | −0.911302 | − | 0.411739i | \(-0.864922\pi\) | ||||
−0.911302 | + | 0.411739i | \(0.864922\pi\) | |||||||
\(354\) | 86.2306i | 0.243589i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.5262i | 0.0520400i | ||||||||
\(357\) | 37.5577i | 0.105204i | ||||||||
\(358\) | 284.957 | 0.795970 | ||||||||
\(359\) | −512.837 | −1.42851 | −0.714257 | − | 0.699883i | \(-0.753235\pi\) | ||||
−0.714257 | + | 0.699883i | \(0.753235\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −348.118 | − | 95.5771i | −0.964315 | − | 0.264756i | ||||
\(362\) | 25.7447 | 0.0711180 | ||||||||
\(363\) | − | 237.370i | − | 0.653911i | ||||||
\(364\) | − | 64.2028i | − | 0.176381i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 168.794 | 0.461185 | ||||||||
\(367\) | −374.320 | −1.01994 | −0.509972 | − | 0.860191i | \(-0.670344\pi\) | ||||
−0.509972 | + | 0.860191i | \(0.670344\pi\) | |||||||
\(368\) | 76.8419 | 0.208809 | ||||||||
\(369\) | − | 103.501i | − | 0.280492i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6.94454i | − | 0.0187184i | ||||||
\(372\) | 167.585 | 0.450498 | ||||||||
\(373\) | − | 338.585i | − | 0.907736i | −0.891069 | − | 0.453868i | \(-0.850044\pi\) | ||
0.891069 | − | 0.453868i | \(-0.149956\pi\) | |||||||
\(374\) | − | 240.737i | − | 0.643681i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 288.381i | 0.766970i | ||||||||
\(377\) | 391.998 | 1.03978 | ||||||||
\(378\) | 83.1858 | 0.220068 | ||||||||
\(379\) | 511.061i | 1.34845i | 0.738527 | + | 0.674224i | \(0.235522\pi\) | ||||
−0.738527 | + | 0.674224i | \(0.764478\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 144.169 | 0.378396 | ||||||||
\(382\) | − | 336.984i | − | 0.882156i | ||||||
\(383\) | 196.052i | 0.511886i | 0.966692 | + | 0.255943i | \(0.0823859\pi\) | ||||
−0.966692 | + | 0.255943i | \(0.917614\pi\) | |||||||
\(384\) | −48.5713 | −0.126488 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −345.612 | −0.895369 | ||||||||
\(387\) | 463.426 | 1.19748 | ||||||||
\(388\) | − | 15.1509i | − | 0.0390486i | ||||||
\(389\) | −271.187 | −0.697140 | −0.348570 | − | 0.937283i | \(-0.613333\pi\) | ||||
−0.348570 | + | 0.937283i | \(0.613333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −190.012 | −0.485964 | ||||||||
\(392\) | 362.886i | 0.925729i | ||||||||
\(393\) | − | 0.639979i | − | 0.00162844i | ||||||
\(394\) | − | 145.020i | − | 0.368070i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 226.924 | 0.573041 | ||||||||
\(397\) | 538.992 | 1.35766 | 0.678831 | − | 0.734294i | \(-0.262487\pi\) | ||||
0.678831 | + | 0.734294i | \(0.262487\pi\) | |||||||
\(398\) | 132.999i | 0.334169i | ||||||||
\(399\) | 69.8732 | + | 9.41772i | 0.175121 | + | 0.0236033i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 247.355i | − | 0.616846i | −0.951249 | − | 0.308423i | \(-0.900199\pi\) | ||
0.951249 | − | 0.308423i | \(-0.0998013\pi\) | |||||||
\(402\) | 154.973i | 0.385506i | ||||||||
\(403\) | −733.396 | −1.81984 | ||||||||
\(404\) | −63.9290 | −0.158240 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 108.039 | 0.266107 | ||||||||
\(407\) | − | 320.643i | − | 0.787820i | ||||||
\(408\) | −127.348 | −0.312127 | ||||||||
\(409\) | 705.490i | 1.72491i | 0.506130 | + | 0.862457i | \(0.331075\pi\) | ||||
−0.506130 | + | 0.862457i | \(0.668925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 198.612i | − | 0.483241i | ||||||
\(412\) | 86.0540i | 0.208869i | ||||||||
\(413\) | 102.802i | 0.248916i | ||||||||
\(414\) | 181.209i | 0.437703i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 363.105 | 0.872848 | ||||||||
\(417\) | − | 23.7338i | − | 0.0569157i | ||||||
\(418\) | −447.871 | − | 60.3655i | −1.07146 | − | 0.144415i | ||||
\(419\) | −53.2615 | −0.127116 | −0.0635578 | − | 0.997978i | \(-0.520245\pi\) | ||||
−0.0635578 | + | 0.997978i | \(0.520245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 632.760i | − | 1.50299i | −0.659738 | − | 0.751496i | \(-0.729333\pi\) | ||
0.659738 | − | 0.751496i | \(-0.270667\pi\) | |||||||
\(422\) | −93.8979 | −0.222507 | ||||||||
\(423\) | −231.067 | −0.546258 | ||||||||
\(424\) | 23.5470 | 0.0555353 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 250.437i | − | 0.587880i | ||||||
\(427\) | 201.232 | 0.471269 | ||||||||
\(428\) | 313.985i | 0.733611i | ||||||||
\(429\) | 320.241 | 0.746482 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 114.829i | − | 0.266425i | −0.991088 | − | 0.133212i | \(-0.957471\pi\) | ||
0.991088 | − | 0.133212i | \(-0.0425293\pi\) | |||||||
\(432\) | 95.8366i | 0.221844i | ||||||||
\(433\) | − | 757.439i | − | 1.74928i | −0.484772 | − | 0.874641i | \(-0.661097\pi\) | ||
0.484772 | − | 0.874641i | \(-0.338903\pi\) | |||||||
\(434\) | −202.133 | −0.465744 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 116.806i | 0.267903i | ||||||||
\(437\) | −47.6461 | + | 353.502i | −0.109030 | + | 0.808929i | ||||
\(438\) | 139.503 | 0.318501 | ||||||||
\(439\) | 290.888i | 0.662614i | 0.943523 | + | 0.331307i | \(0.107490\pi\) | ||||
−0.943523 | + | 0.331307i | \(0.892510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −290.765 | −0.659331 | ||||||||
\(442\) | 185.046 | 0.418655 | ||||||||
\(443\) | −251.148 | −0.566926 | −0.283463 | − | 0.958983i | \(-0.591483\pi\) | ||||
−0.283463 | + | 0.958983i | \(0.591483\pi\) | |||||||
\(444\) | −56.3191 | −0.126845 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 321.031 | 0.719801 | ||||||||
\(447\) | − | 129.288i | − | 0.289235i | ||||||
\(448\) | 141.087 | 0.314927 | ||||||||
\(449\) | − | 569.985i | − | 1.26945i | −0.772736 | − | 0.634727i | \(-0.781112\pi\) | ||
0.772736 | − | 0.634727i | \(-0.218888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 255.049i | − | 0.565519i | ||||||
\(452\) | 296.757i | 0.656541i | ||||||||
\(453\) | −186.149 | −0.410926 | ||||||||
\(454\) | −125.677 | −0.276822 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −31.9328 | + | 236.920i | −0.0700281 | + | 0.519562i | ||||
\(457\) | −97.0937 | −0.212459 | −0.106229 | − | 0.994342i | \(-0.533878\pi\) | ||||
−0.106229 | + | 0.994342i | \(0.533878\pi\) | |||||||
\(458\) | 509.355i | 1.11213i | ||||||||
\(459\) | − | 236.981i | − | 0.516299i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 242.929 | 0.526961 | 0.263480 | − | 0.964665i | \(-0.415130\pi\) | ||||
0.263480 | + | 0.964665i | \(0.415130\pi\) | |||||||
\(462\) | 88.2624 | 0.191044 | ||||||||
\(463\) | 666.435 | 1.43938 | 0.719692 | − | 0.694293i | \(-0.244283\pi\) | ||||
0.719692 | + | 0.694293i | \(0.244283\pi\) | |||||||
\(464\) | 124.470i | 0.268254i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 343.984i | 0.738162i | ||||||||
\(467\) | −453.552 | −0.971204 | −0.485602 | − | 0.874180i | \(-0.661399\pi\) | ||||
−0.485602 | + | 0.874180i | \(0.661399\pi\) | |||||||
\(468\) | 174.429i | 0.372711i | ||||||||
\(469\) | 184.756i | 0.393936i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 113.255i | − | 0.240457i | ||||||
\(472\) | −348.573 | −0.738503 | ||||||||
\(473\) | 1141.98 | 2.41433 | ||||||||
\(474\) | 117.706i | 0.248324i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −50.4101 | −0.105904 | ||||||||
\(477\) | 18.8672i | 0.0395539i | ||||||||
\(478\) | − | 203.789i | − | 0.426336i | ||||||
\(479\) | 922.912 | 1.92675 | 0.963373 | − | 0.268163i | \(-0.0864167\pi\) | ||||
0.963373 | + | 0.268163i | \(0.0864167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 246.467 | 0.512405 | ||||||||
\(482\) | 570.023 | 1.18262 | ||||||||
\(483\) | − | 69.6649i | − | 0.144234i | ||||||
\(484\) | 318.598 | 0.658260 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −354.694 | −0.729822 | ||||||||
\(487\) | 345.986i | 0.710444i | 0.934782 | + | 0.355222i | \(0.115595\pi\) | ||||
−0.934782 | + | 0.355222i | \(0.884405\pi\) | |||||||
\(488\) | 682.321i | 1.39820i | ||||||||
\(489\) | 373.837i | 0.764493i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 237.336 | 0.483372 | 0.241686 | − | 0.970354i | \(-0.422300\pi\) | ||||
0.241686 | + | 0.970354i | \(0.422300\pi\) | |||||||
\(492\) | −44.7979 | −0.0910526 | ||||||||
\(493\) | − | 307.785i | − | 0.624310i | ||||||
\(494\) | 46.4008 | − | 344.263i | 0.0939287 | − | 0.696888i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 232.873i | − | 0.469502i | ||||||
\(497\) | − | 298.566i | − | 0.600736i | ||||||
\(498\) | −261.052 | −0.524202 | ||||||||
\(499\) | 352.497 | 0.706407 | 0.353204 | − | 0.935547i | \(-0.385092\pi\) | ||||
0.353204 | + | 0.935547i | \(0.385092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 453.195 | 0.904581 | ||||||||
\(502\) | 64.2602i | 0.128008i | ||||||||
\(503\) | −191.562 | −0.380839 | −0.190420 | − | 0.981703i | \(-0.560985\pi\) | ||||
−0.190420 | + | 0.981703i | \(0.560985\pi\) | |||||||
\(504\) | 144.788i | 0.287277i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 446.536i | 0.882483i | ||||||||
\(507\) | − | 4.20012i | − | 0.00828425i | ||||||
\(508\) | 193.504i | 0.380913i | ||||||||
\(509\) | − | 372.483i | − | 0.731794i | −0.930655 | − | 0.365897i | \(-0.880762\pi\) | ||
0.930655 | − | 0.365897i | \(-0.119238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 166.313 | 0.325466 | ||||||||
\(512\) | 254.353i | 0.496783i | ||||||||
\(513\) | −440.885 | − | 59.4238i | −0.859424 | − | 0.115836i | ||||
\(514\) | −67.0656 | −0.130478 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 200.581i | − | 0.388724i | ||||||
\(517\) | −569.397 | −1.10135 | ||||||||
\(518\) | 67.9293 | 0.131138 | ||||||||
\(519\) | 154.749 | 0.298169 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 304.679i | 0.584797i | 0.956297 | + | 0.292399i | \(0.0944534\pi\) | ||||
−0.956297 | + | 0.292399i | \(0.905547\pi\) | |||||||
\(522\) | −293.526 | −0.562310 | ||||||||
\(523\) | 721.855i | 1.38022i | 0.723705 | + | 0.690110i | \(0.242438\pi\) | ||||
−0.723705 | + | 0.690110i | \(0.757562\pi\) | |||||||
\(524\) | 0.858981 | 0.00163928 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 463.380i | − | 0.880950i | ||||||
\(527\) | 575.840i | 1.09268i | ||||||||
\(528\) | 101.685i | 0.192586i | ||||||||
\(529\) | −176.552 | −0.333746 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 279.297i | − | 0.525983i | ||||||
\(532\) | −12.6405 | + | 93.7840i | −0.0237603 | + | 0.176286i | ||||
\(533\) | 196.047 | 0.367818 | ||||||||
\(534\) | − | 19.5770i | − | 0.0366610i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −626.455 | −1.16876 | ||||||||
\(537\) | 297.631 | 0.554247 | ||||||||
\(538\) | −588.650 | −1.09414 | ||||||||
\(539\) | −716.505 | −1.32932 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −652.655 | −1.20639 | −0.603193 | − | 0.797595i | \(-0.706105\pi\) | ||||
−0.603193 | + | 0.797595i | \(0.706105\pi\) | |||||||
\(542\) | 516.039i | 0.952101i | ||||||||
\(543\) | 26.8897 | 0.0495206 | ||||||||
\(544\) | − | 285.099i | − | 0.524079i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 67.8441i | 0.124257i | ||||||||
\(547\) | 1019.58i | 1.86394i | 0.362531 | + | 0.931972i | \(0.381913\pi\) | ||||
−0.362531 | + | 0.931972i | \(0.618087\pi\) | |||||||
\(548\) | 266.578 | 0.486455 | ||||||||
\(549\) | −546.715 | −0.995837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −572.609 | − | 77.1780i | −1.03922 | − | 0.140069i | ||||
\(552\) | 236.214 | 0.427924 | ||||||||
\(553\) | 140.326i | 0.253755i | ||||||||
\(554\) | 472.166i | 0.852285i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.8556 | 0.0572943 | ||||||||
\(557\) | 209.280 | 0.375727 | 0.187863 | − | 0.982195i | \(-0.439844\pi\) | ||||
0.187863 | + | 0.982195i | \(0.439844\pi\) | |||||||
\(558\) | 549.163 | 0.984163 | ||||||||
\(559\) | 877.796i | 1.57030i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 251.443i | − | 0.448206i | ||||||
\(562\) | 366.691 | 0.652475 | ||||||||
\(563\) | 9.61456i | 0.0170774i | 0.999964 | + | 0.00853868i | \(0.00271798\pi\) | ||||
−0.999964 | + | 0.00853868i | \(0.997282\pi\) | |||||||
\(564\) | 100.011i | 0.177325i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 271.383i | − | 0.479476i | ||||||
\(567\) | −66.5375 | −0.117350 | ||||||||
\(568\) | 1012.35 | 1.78231 | ||||||||
\(569\) | 734.454i | 1.29078i | 0.763853 | + | 0.645390i | \(0.223305\pi\) | ||||
−0.763853 | + | 0.645390i | \(0.776695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.9034 | 0.0471163 | 0.0235581 | − | 0.999722i | \(-0.492501\pi\) | ||||
0.0235581 | + | 0.999722i | \(0.492501\pi\) | |||||||
\(572\) | 429.828i | 0.751447i | ||||||||
\(573\) | − | 351.971i | − | 0.614260i | ||||||
\(574\) | 54.0330 | 0.0941342 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −383.312 | −0.665472 | ||||||||
\(577\) | −722.739 | −1.25258 | −0.626290 | − | 0.779590i | \(-0.715428\pi\) | ||||
−0.626290 | + | 0.779590i | \(0.715428\pi\) | |||||||
\(578\) | 264.604i | 0.457793i | ||||||||
\(579\) | −360.983 | −0.623460 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −311.221 | −0.535664 | ||||||||
\(582\) | 16.0102i | 0.0275089i | ||||||||
\(583\) | 46.4926i | 0.0797472i | ||||||||
\(584\) | 563.920i | 0.965616i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 679.453 | 1.15948 | ||||||||
\(587\) | 539.053 | 0.918318 | 0.459159 | − | 0.888354i | \(-0.348151\pi\) | ||||
0.459159 | + | 0.888354i | \(0.348151\pi\) | |||||||
\(588\) | 125.850i | 0.214031i | ||||||||
\(589\) | 1071.30 | + | 144.394i | 1.81885 | + | 0.245151i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 151.469i | − | 0.256293i | ||||||
\(592\) | 78.2599i | 0.132196i | ||||||||
\(593\) | −349.866 | −0.589994 | −0.294997 | − | 0.955498i | \(-0.595319\pi\) | ||||
−0.294997 | + | 0.955498i | \(0.595319\pi\) | |||||||
\(594\) | −556.916 | −0.937570 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 173.530 | 0.291158 | ||||||||
\(597\) | 138.914i | 0.232688i | ||||||||
\(598\) | −343.237 | −0.573974 | ||||||||
\(599\) | − | 432.796i | − | 0.722530i | −0.932463 | − | 0.361265i | \(-0.882345\pi\) | ||
0.932463 | − | 0.361265i | \(-0.117655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 548.198i | − | 0.912143i | −0.889943 | − | 0.456072i | \(-0.849256\pi\) | ||
0.889943 | − | 0.456072i | \(-0.150744\pi\) | |||||||
\(602\) | 241.932i | 0.401880i | ||||||||
\(603\) | − | 501.952i | − | 0.832425i | ||||||
\(604\) | − | 249.850i | − | 0.413659i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 67.5549 | 0.111477 | ||||||||
\(607\) | − | 145.705i | − | 0.240040i | −0.992771 | − | 0.120020i | \(-0.961704\pi\) | ||
0.992771 | − | 0.120020i | \(-0.0382959\pi\) | |||||||
\(608\) | −530.404 | − | 71.4895i | −0.872375 | − | 0.117581i | ||||
\(609\) | 112.844 | 0.185295 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 437.675i | − | 0.716326i | ||||||
\(612\) | 136.956 | 0.223784 | ||||||||
\(613\) | 572.788 | 0.934401 | 0.467201 | − | 0.884151i | \(-0.345263\pi\) | ||||
0.467201 | + | 0.884151i | \(0.345263\pi\) | |||||||
\(614\) | 383.498 | 0.624590 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 356.786i | 0.579199i | ||||||||
\(617\) | −548.520 | −0.889012 | −0.444506 | − | 0.895776i | \(-0.646621\pi\) | ||||
−0.444506 | + | 0.895776i | \(0.646621\pi\) | |||||||
\(618\) | − | 90.9347i | − | 0.147144i | ||||||
\(619\) | 317.700 | 0.513248 | 0.256624 | − | 0.966511i | \(-0.417390\pi\) | ||||
0.256624 | + | 0.966511i | \(0.417390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 439.570i | 0.707843i | ||||||||
\(622\) | − | 29.4024i | − | 0.0472707i | ||||||
\(623\) | − | 23.3392i | − | 0.0374627i | ||||||
\(624\) | −78.1618 | −0.125259 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 478.841i | − | 0.764922i | ||||||
\(627\) | −467.790 | − | 63.0502i | −0.746077 | − | 0.100559i | ||||
\(628\) | 152.011 | 0.242057 | ||||||||
\(629\) | − | 193.518i | − | 0.307660i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −320.013 | −0.507152 | −0.253576 | − | 0.967315i | \(-0.581607\pi\) | ||||
−0.253576 | + | 0.967315i | \(0.581607\pi\) | |||||||
\(632\) | −475.807 | −0.752859 | ||||||||
\(633\) | −98.0739 | −0.154935 | ||||||||
\(634\) | −556.908 | −0.878405 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.16616 | 0.0128399 | ||||||||
\(637\) | − | 550.752i | − | 0.864603i | ||||||
\(638\) | −723.308 | −1.13371 | ||||||||
\(639\) | 811.154i | 1.26941i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 529.676i | 0.826328i | 0.910657 | + | 0.413164i | \(0.135576\pi\) | ||||
−0.910657 | + | 0.413164i | \(0.864424\pi\) | |||||||
\(642\) | − | 331.794i | − | 0.516812i | ||||||
\(643\) | 876.680 | 1.36342 | 0.681710 | − | 0.731622i | \(-0.261236\pi\) | ||||
0.681710 | + | 0.731622i | \(0.261236\pi\) | |||||||
\(644\) | 93.5044 | 0.145193 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −270.305 | − | 36.4325i | −0.418428 | − | 0.0563971i | ||||
\(647\) | 664.468 | 1.02700 | 0.513499 | − | 0.858090i | \(-0.328349\pi\) | ||||
0.513499 | + | 0.858090i | \(0.328349\pi\) | |||||||
\(648\) | − | 225.610i | − | 0.348163i | ||||||
\(649\) | − | 688.246i | − | 1.06047i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −211.123 | −0.324305 | ||||||||
\(652\) | −501.765 | −0.769578 | ||||||||
\(653\) | 502.217 | 0.769091 | 0.384546 | − | 0.923106i | \(-0.374358\pi\) | ||||
0.384546 | + | 0.923106i | \(0.374358\pi\) | |||||||
\(654\) | − | 123.430i | − | 0.188732i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 62.2503i | 0.0948937i | ||||||||
\(657\) | −451.845 | −0.687740 | ||||||||
\(658\) | − | 120.629i | − | 0.183327i | ||||||
\(659\) | 760.007i | 1.15327i | 0.817001 | + | 0.576636i | \(0.195635\pi\) | ||||
−0.817001 | + | 0.576636i | \(0.804365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 855.497i | − | 1.29425i | −0.762385 | − | 0.647123i | \(-0.775972\pi\) | ||
0.762385 | − | 0.647123i | \(-0.224028\pi\) | |||||||
\(662\) | −144.570 | −0.218384 | ||||||||
\(663\) | 193.276 | 0.291517 | ||||||||
\(664\) | − | 1055.26i | − | 1.58925i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −184.553 | −0.277107 | ||||||||
\(667\) | 570.902i | 0.855925i | ||||||||
\(668\) | 608.280i | 0.910598i | ||||||||
\(669\) | 335.309 | 0.501209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1347.22 | −2.00778 | ||||||||
\(672\) | 104.527 | 0.155546 | ||||||||
\(673\) | − | 413.053i | − | 0.613749i | −0.951750 | − | 0.306875i | \(-0.900717\pi\) | ||
0.951750 | − | 0.306875i | \(-0.0992832\pi\) | |||||||
\(674\) | −505.348 | −0.749775 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.63740 | 0.00833936 | ||||||||
\(677\) | − | 184.789i | − | 0.272952i | −0.990643 | − | 0.136476i | \(-0.956422\pi\) | ||
0.990643 | − | 0.136476i | \(-0.0435777\pi\) | |||||||
\(678\) | − | 313.588i | − | 0.462519i | ||||||
\(679\) | 19.0870i | 0.0281104i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −131.266 | −0.192755 | ||||||||
\(682\) | 1353.25 | 1.98424 | ||||||||
\(683\) | 1166.19i | 1.70745i | 0.520723 | + | 0.853726i | \(0.325663\pi\) | ||||
−0.520723 | + | 0.853726i | \(0.674337\pi\) | |||||||
\(684\) | 34.3422 | − | 254.796i | 0.0502078 | − | 0.372509i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 325.880i | − | 0.475044i | ||||||
\(687\) | 532.008i | 0.774393i | ||||||||
\(688\) | −278.724 | −0.405122 | ||||||||
\(689\) | −35.7372 | −0.0518683 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1210.49 | 1.75180 | 0.875898 | − | 0.482496i | \(-0.160270\pi\) | ||||
0.875898 | + | 0.482496i | \(0.160270\pi\) | |||||||
\(692\) | 207.705i | 0.300152i | ||||||||
\(693\) | −285.878 | −0.412522 | ||||||||
\(694\) | 649.012i | 0.935176i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 382.624i | 0.549747i | ||||||||
\(697\) | − | 153.930i | − | 0.220847i | ||||||
\(698\) | 415.084i | 0.594676i | ||||||||
\(699\) | 359.282i | 0.513995i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 799.506 | 1.14052 | 0.570261 | − | 0.821464i | \(-0.306842\pi\) | ||||
0.570261 | + | 0.821464i | \(0.306842\pi\) | |||||||
\(702\) | − | 428.082i | − | 0.609803i | ||||||
\(703\) | −360.025 | − | 48.5253i | −0.512127 | − | 0.0690261i | ||||
\(704\) | −944.559 | −1.34170 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 912.522i | 1.29252i | ||||||||
\(707\) | 80.5375 | 0.113914 | ||||||||
\(708\) | −120.886 | −0.170743 | ||||||||
\(709\) | 688.559 | 0.971169 | 0.485584 | − | 0.874190i | \(-0.338607\pi\) | ||||
0.485584 | + | 0.874190i | \(0.338607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 381.244i | − | 0.536208i | ||||||
\(712\) | 79.1368 | 0.111147 | ||||||||
\(713\) | − | 1068.11i | − | 1.49805i | ||||||
\(714\) | 53.2692 | 0.0746067 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 399.480i | 0.557934i | ||||||||
\(717\) | − | 212.852i | − | 0.296865i | ||||||
\(718\) | 727.370i | 1.01305i | ||||||||
\(719\) | −828.034 | −1.15165 | −0.575823 | − | 0.817574i | \(-0.695318\pi\) | ||||
−0.575823 | + | 0.817574i | \(0.695318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 108.410i | − | 0.150361i | ||||||
\(722\) | −135.560 | + | 493.745i | −0.187756 | + | 0.683857i | ||||
\(723\) | 595.375 | 0.823478 | ||||||||
\(724\) | 36.0914i | 0.0498500i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −336.668 | −0.463730 | ||||||||
\(727\) | 11.4411 | 0.0157374 | 0.00786868 | − | 0.999969i | \(-0.497495\pi\) | ||||
0.00786868 | + | 0.999969i | \(0.497495\pi\) | |||||||
\(728\) | −274.249 | −0.376716 | ||||||||
\(729\) | −131.403 | −0.180251 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 689.219 | 0.942844 | ||||||||
\(732\) | 236.631i | 0.323266i | ||||||||
\(733\) | −1402.01 | −1.91270 | −0.956352 | − | 0.292216i | \(-0.905607\pi\) | ||||
−0.956352 | + | 0.292216i | \(0.905607\pi\) | |||||||
\(734\) | 530.908i | 0.723307i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 528.823i | 0.718509i | ||||||||
\(737\) | − | 1236.91i | − | 1.67831i | ||||||
\(738\) | −146.799 | −0.198915 | ||||||||
\(739\) | 57.5237 | 0.0778400 | 0.0389200 | − | 0.999242i | \(-0.487608\pi\) | ||||
0.0389200 | + | 0.999242i | \(0.487608\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 48.4645 | − | 359.574i | 0.0654041 | − | 0.485255i | ||||
\(742\) | −9.84963 | −0.0132744 | ||||||||
\(743\) | − | 1315.28i | − | 1.77023i | −0.465373 | − | 0.885115i | \(-0.654080\pi\) | ||
0.465373 | − | 0.885115i | \(-0.345920\pi\) | |||||||
\(744\) | − | 715.858i | − | 0.962174i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −480.225 | −0.643733 | ||||||||
\(747\) | 845.537 | 1.13191 | ||||||||
\(748\) | 337.488 | 0.451187 | ||||||||
\(749\) | − | 395.557i | − | 0.528114i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 494.439i | − | 0.658374i | −0.944265 | − | 0.329187i | \(-0.893225\pi\) | ||
0.944265 | − | 0.329187i | \(-0.106775\pi\) | |||||||
\(752\) | 138.974 | 0.184806 | ||||||||
\(753\) | 67.1182i | 0.0891344i | ||||||||
\(754\) | − | 555.981i | − | 0.737375i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 116.618i | 0.154256i | ||||||||
\(757\) | −582.272 | −0.769183 | −0.384591 | − | 0.923087i | \(-0.625658\pi\) | ||||
−0.384591 | + | 0.923087i | \(0.625658\pi\) | |||||||
\(758\) | 724.852 | 0.956270 | ||||||||
\(759\) | 466.396i | 0.614487i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 879.724 | 1.15601 | 0.578006 | − | 0.816033i | \(-0.303831\pi\) | ||||
0.578006 | + | 0.816033i | \(0.303831\pi\) | |||||||
\(762\) | − | 204.479i | − | 0.268345i | ||||||
\(763\) | − | 147.151i | − | 0.192859i | ||||||
\(764\) | 472.416 | 0.618346 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 278.066 | 0.363011 | ||||||||
\(767\) | 529.030 | 0.689739 | ||||||||
\(768\) | 402.647i | 0.524280i | ||||||||
\(769\) | 664.542 | 0.864164 | 0.432082 | − | 0.901834i | \(-0.357779\pi\) | ||||
0.432082 | + | 0.901834i | \(0.357779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −70.0483 | −0.0908538 | ||||||||
\(772\) | − | 484.513i | − | 0.627607i | ||||||
\(773\) | − | 246.948i | − | 0.319467i | −0.987160 | − | 0.159733i | \(-0.948937\pi\) | ||
0.987160 | − | 0.159733i | \(-0.0510635\pi\) | |||||||
\(774\) | − | 657.289i | − | 0.849211i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −64.7185 | −0.0834001 | ||||||||
\(777\) | 70.9505 | 0.0913133 | ||||||||
\(778\) | 384.633i | 0.494386i | ||||||||
\(779\) | −286.375 | − | 38.5985i | −0.367619 | − | 0.0495488i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1998.85i | 2.55935i | ||||||||
\(782\) | 269.499i | 0.344628i | ||||||||
\(783\) | −712.024 | −0.909354 | ||||||||
\(784\) | 174.879 | 0.223060 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.907699 | −0.00115483 | ||||||||
\(787\) | 423.704i | 0.538379i | 0.963087 | + | 0.269189i | \(0.0867558\pi\) | ||||
−0.963087 | + | 0.269189i | \(0.913244\pi\) | |||||||
\(788\) | 203.303 | 0.257998 | ||||||||
\(789\) | − | 483.988i | − | 0.613420i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 373.852i | − | 0.472633i | ||||||
\(792\) | − | 969.331i | − | 1.22390i | ||||||
\(793\) | − | 1035.56i | − | 1.30587i | ||||||
\(794\) | − | 764.467i | − | 0.962805i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −186.451 | −0.234235 | ||||||||
\(797\) | − | 1487.62i | − | 1.86653i | −0.359190 | − | 0.933264i | \(-0.616947\pi\) | ||
0.359190 | − | 0.933264i | \(-0.383053\pi\) | |||||||
\(798\) | 13.3574 | − | 99.1031i | 0.0167386 | − | 0.124189i | ||||
\(799\) | −343.650 | −0.430100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 63.4090i | 0.0791622i | ||||||||
\(802\) | −350.831 | −0.437445 | ||||||||
\(803\) | −1113.44 | −1.38660 | ||||||||
\(804\) | −217.257 | −0.270220 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1040.20i | 1.29056i | ||||||||
\(807\) | −614.830 | −0.761871 | ||||||||
\(808\) | 273.080i | 0.337970i | ||||||||
\(809\) | 775.380 | 0.958443 | 0.479221 | − | 0.877694i | \(-0.340919\pi\) | ||||
0.479221 | + | 0.877694i | \(0.340919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 315.542i | − | 0.389078i | −0.980895 | − | 0.194539i | \(-0.937679\pi\) | ||
0.980895 | − | 0.194539i | \(-0.0623211\pi\) | |||||||
\(812\) | 151.460i | 0.186527i | ||||||||
\(813\) | 538.990i | 0.662964i | ||||||||
\(814\) | −454.777 | −0.558694 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 61.3702i | 0.0752086i | ||||||||
\(817\) | 172.824 | − | 1282.24i | 0.211535 | − | 1.56945i | ||||
\(818\) | 1000.62 | 1.22325 | ||||||||
\(819\) | − | 219.744i | − | 0.268308i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 878.348 | 1.06985 | 0.534926 | − | 0.844899i | \(-0.320340\pi\) | ||||
0.534926 | + | 0.844899i | \(0.320340\pi\) | |||||||
\(822\) | −281.697 | −0.342697 | ||||||||
\(823\) | −1178.55 | −1.43202 | −0.716009 | − | 0.698091i | \(-0.754033\pi\) | ||||
−0.716009 | + | 0.698091i | \(0.754033\pi\) | |||||||
\(824\) | 367.589 | 0.446103 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 145.807 | 0.176522 | ||||||||
\(827\) | 14.2277i | 0.0172040i | 0.999963 | + | 0.00860201i | \(0.00273814\pi\) | ||||
−0.999963 | + | 0.00860201i | \(0.997262\pi\) | |||||||
\(828\) | −254.036 | −0.306807 | ||||||||
\(829\) | − | 839.046i | − | 1.01212i | −0.862499 | − | 0.506059i | \(-0.831102\pi\) | ||
0.862499 | − | 0.506059i | \(-0.168898\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 493.165i | 0.593460i | ||||||||
\(832\) | − | 726.049i | − | 0.872655i | ||||||
\(833\) | −432.434 | −0.519128 | ||||||||
\(834\) | −33.6624 | −0.0403625 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 84.6262 | − | 627.869i | 0.101227 | − | 0.751040i | ||||
\(837\) | 1332.14 | 1.59156 | ||||||||
\(838\) | 75.5422i | 0.0901458i | ||||||||
\(839\) | 809.554i | 0.964903i | 0.875923 | + | 0.482452i | \(0.160254\pi\) | ||||
−0.875923 | + | 0.482452i | \(0.839746\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −83.7574 | −0.0995927 | ||||||||
\(842\) | −897.460 | −1.06587 | ||||||||
\(843\) | 383.000 | 0.454329 | ||||||||
\(844\) | − | 131.635i | − | 0.155966i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 327.729i | 0.387387i | ||||||||
\(847\) | −401.368 | −0.473870 | ||||||||
\(848\) | − | 11.3475i | − | 0.0133815i | ||||||
\(849\) | − | 283.453i | − | 0.333867i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 358.952i | 0.421800i | ||||||||
\(852\) | 351.087 | 0.412074 | ||||||||
\(853\) | 1263.87 | 1.48168 | 0.740840 | − | 0.671681i | \(-0.234428\pi\) | ||||
0.740840 | + | 0.671681i | \(0.234428\pi\) | |||||||
\(854\) | − | 285.413i | − | 0.334207i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1341.22 | 1.56685 | ||||||||
\(857\) | − | 226.840i | − | 0.264691i | −0.991204 | − | 0.132346i | \(-0.957749\pi\) | ||
0.991204 | − | 0.132346i | \(-0.0422508\pi\) | |||||||
\(858\) | − | 454.206i | − | 0.529378i | ||||||
\(859\) | −263.283 | −0.306499 | −0.153249 | − | 0.988188i | \(-0.548974\pi\) | ||||
−0.153249 | + | 0.988188i | \(0.548974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 56.4361 | 0.0655472 | ||||||||
\(862\) | −162.865 | −0.188939 | ||||||||
\(863\) | − | 430.419i | − | 0.498747i | −0.968407 | − | 0.249373i | \(-0.919775\pi\) | ||
0.968407 | − | 0.249373i | \(-0.0802247\pi\) | |||||||
\(864\) | −659.543 | −0.763360 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1074.30 | −1.24053 | ||||||||
\(867\) | 276.373i | 0.318769i | ||||||||
\(868\) | − | 283.370i | − | 0.326463i | ||||||
\(869\) | − | 939.463i | − | 1.08109i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 950.771 | 1.09159 | ||||||||
\(872\) | 498.948 | 0.572188 | ||||||||
\(873\) | − | 51.8562i | − | 0.0594000i | ||||||
\(874\) | 501.381 | + | 67.5777i | 0.573663 | + | 0.0773201i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 195.569i | 0.223253i | ||||||||
\(877\) | − | 825.399i | − | 0.941162i | −0.882357 | − | 0.470581i | \(-0.844044\pi\) | ||
0.882357 | − | 0.470581i | \(-0.155956\pi\) | |||||||
\(878\) | 412.574 | 0.469902 | ||||||||
\(879\) | 709.671 | 0.807362 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −340.053 | −0.385985 | −0.192992 | − | 0.981200i | \(-0.561819\pi\) | ||||
−0.192992 | + | 0.981200i | \(0.561819\pi\) | |||||||
\(882\) | 412.400i | 0.467574i | ||||||||
\(883\) | 1129.39 | 1.27904 | 0.639518 | − | 0.768776i | \(-0.279134\pi\) | ||||
0.639518 | + | 0.768776i | \(0.279134\pi\) | |||||||
\(884\) | 259.415i | 0.293456i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 356.211i | 0.402044i | ||||||||
\(887\) | 240.033i | 0.270612i | 0.990804 | + | 0.135306i | \(0.0432018\pi\) | ||||
−0.990804 | + | 0.135306i | \(0.956798\pi\) | |||||||
\(888\) | 240.573i | 0.270915i | ||||||||
\(889\) | − | 243.775i | − | 0.274213i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 445.458 | 0.499953 | ||||||||
\(892\) | 450.052i | 0.504543i | ||||||||
\(893\) | −86.1712 | + | 639.333i | −0.0964963 | + | 0.715938i | ||||
\(894\) | −183.372 | −0.205115 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 82.1292i | 0.0916621i | ||||||||
\(897\) | −358.502 | −0.399668 | ||||||||
\(898\) | −808.425 | −0.900251 | ||||||||
\(899\) | 1730.15 | 1.92452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.0598i | 0.0311429i | ||||||||
\(902\) | −361.743 | −0.401045 | ||||||||
\(903\) | 252.691i | 0.279835i | ||||||||
\(904\) | 1267.63 | 1.40224 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 264.021i | 0.291414i | ||||||||
\(907\) | 162.059i | 0.178676i | 0.996001 | + | 0.0893379i | \(0.0284751\pi\) | ||||
−0.996001 | + | 0.0893379i | \(0.971525\pi\) | |||||||
\(908\) | − | 176.186i | − | 0.194038i | ||||||
\(909\) | −218.807 | −0.240712 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1545.15i | − | 1.69611i | −0.529911 | − | 0.848054i | \(-0.677775\pi\) | ||
0.529911 | − | 0.848054i | \(-0.322225\pi\) | |||||||
\(912\) | 114.174 | + | 15.3888i | 0.125191 | + | 0.0168737i | ||||
\(913\) | 2083.58 | 2.28212 | ||||||||
\(914\) | 137.711i | 0.150668i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −714.062 | −0.779544 | ||||||||
\(917\) | −1.08214 | −0.00118009 | ||||||||
\(918\) | −336.117 | −0.366140 | ||||||||
\(919\) | −607.021 | −0.660524 | −0.330262 | − | 0.943889i | \(-0.607137\pi\) | ||||
−0.330262 | + | 0.943889i | \(0.607137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 400.554 | 0.434912 | ||||||||
\(922\) | − | 344.553i | − | 0.373702i | ||||||
\(923\) | −1536.45 | −1.66462 | ||||||||
\(924\) | 123.735i | 0.133912i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 945.223i | − | 1.02076i | ||||||
\(927\) | 294.533i | 0.317728i | ||||||||
\(928\) | −856.597 | −0.923057 | ||||||||
\(929\) | −696.933 | −0.750197 | −0.375099 | − | 0.926985i | \(-0.622391\pi\) | ||||
−0.375099 | + | 0.926985i | \(0.622391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −108.434 | + | 804.508i | −0.116471 | + | 0.864134i | ||||
\(932\) | −482.229 | −0.517414 | ||||||||
\(933\) | − | 30.7100i | − | 0.0329153i | ||||||
\(934\) | 643.285i | 0.688742i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 745.090 | 0.796036 | ||||||||
\(937\) | −896.631 | −0.956916 | −0.478458 | − | 0.878110i | \(-0.658804\pi\) | ||||
−0.478458 | + | 0.878110i | \(0.658804\pi\) | |||||||
\(938\) | 262.044 | 0.279365 | ||||||||
\(939\) | − | 500.137i | − | 0.532628i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1627.92i | 1.72999i | 0.501782 | + | 0.864994i | \(0.332678\pi\) | ||||
−0.501782 | + | 0.864994i | \(0.667322\pi\) | |||||||
\(942\) | −160.633 | −0.170523 | ||||||||
\(943\) | 285.521i | 0.302780i | ||||||||
\(944\) | 167.981i | 0.177946i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 1619.70i | − | 1.71215i | ||||||
\(947\) | 373.464 | 0.394365 | 0.197182 | − | 0.980367i | \(-0.436821\pi\) | ||||
0.197182 | + | 0.980367i | \(0.436821\pi\) | |||||||
\(948\) | −165.011 | −0.174063 | ||||||||
\(949\) | − | 855.861i | − | 0.901856i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −581.677 | −0.611648 | ||||||||
\(952\) | 215.332i | 0.226189i | ||||||||
\(953\) | − | 17.8029i | − | 0.0186809i | −0.999956 | − | 0.00934043i | \(-0.997027\pi\) | ||
0.999956 | − | 0.00934043i | \(-0.00297319\pi\) | |||||||
\(954\) | 26.7598 | 0.0280502 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 285.691 | 0.298840 | ||||||||
\(957\) | −755.477 | −0.789422 | ||||||||
\(958\) | − | 1308.99i | − | 1.36638i | ||||||
\(959\) | −335.833 | −0.350191 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2275.96 | −2.36833 | ||||||||
\(962\) | − | 349.571i | − | 0.363379i | ||||||
\(963\) | 1074.66i | 1.11596i | ||||||||
\(964\) | 799.113i | 0.828955i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −98.8076 | −0.102285 | ||||||||
\(967\) | −446.545 | −0.461784 | −0.230892 | − | 0.972979i | \(-0.574164\pi\) | ||||
−0.230892 | + | 0.972979i | \(0.574164\pi\) | |||||||
\(968\) | − | 1360.92i | − | 1.40591i | ||||||
\(969\) | −282.326 | − | 38.0528i | −0.291359 | − | 0.0392702i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 928.748i | 0.956486i | 0.878228 | + | 0.478243i | \(0.158726\pi\) | ||||
−0.878228 | + | 0.478243i | \(0.841274\pi\) | |||||||
\(972\) | − | 497.244i | − | 0.511568i | ||||||
\(973\) | −40.1315 | −0.0412451 | ||||||||
\(974\) | 490.722 | 0.503821 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 328.818 | 0.336904 | ||||||||
\(977\) | − | 1334.75i | − | 1.36617i | −0.730338 | − | 0.683086i | \(-0.760637\pi\) | ||
0.730338 | − | 0.683086i | \(-0.239363\pi\) | |||||||
\(978\) | 530.223 | 0.542151 | ||||||||
\(979\) | 156.253i | 0.159604i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 399.786i | 0.407529i | ||||||||
\(982\) | − | 336.620i | − | 0.342790i | ||||||
\(983\) | − | 715.994i | − | 0.728376i | −0.931325 | − | 0.364188i | \(-0.881346\pi\) | ||
0.931325 | − | 0.364188i | \(-0.118654\pi\) | |||||||
\(984\) | 191.359i | 0.194470i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −436.539 | −0.442738 | ||||||||
\(987\) | − | 125.994i | − | 0.127653i | ||||||
\(988\) | 482.621 | + | 65.0491i | 0.488483 | + | 0.0658392i | ||||
\(989\) | −1278.41 | −1.29263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 246.568i | − | 0.248807i | −0.992232 | − | 0.124404i | \(-0.960298\pi\) | ||
0.992232 | − | 0.124404i | \(-0.0397018\pi\) | |||||||
\(992\) | 1602.62 | 1.61555 | ||||||||
\(993\) | −151.000 | −0.152064 | ||||||||
\(994\) | −423.464 | −0.426020 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 365.968i | − | 0.367438i | ||||||
\(997\) | 1358.93 | 1.36301 | 0.681507 | − | 0.731812i | \(-0.261325\pi\) | ||||
0.681507 | + | 0.731812i | \(0.261325\pi\) | |||||||
\(998\) | − | 499.956i | − | 0.500958i | ||||||
\(999\) | −447.682 | −0.448130 |
(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 | 475.3.c.i.151.5 | yes | 14 | |
5.2 | odd | 4 | 475.3.d.d.474.19 | 28 | |||
5.3 | odd | 4 | 475.3.d.d.474.10 | 28 | |||
5.4 | even | 2 | 475.3.c.h.151.10 | yes | 14 | ||
19.18 | odd | 2 | inner | 475.3.c.i.151.10 | yes | 14 | |
95.18 | even | 4 | 475.3.d.d.474.20 | 28 | |||
95.37 | even | 4 | 475.3.d.d.474.9 | 28 | |||
95.94 | odd | 2 | 475.3.c.h.151.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.3.c.h.151.5 | ✓ | 14 | 95.94 | odd | 2 | ||
475.3.c.h.151.10 | yes | 14 | 5.4 | even | 2 | ||
475.3.c.i.151.5 | yes | 14 | 1.1 | even | 1 | trivial | |
475.3.c.i.151.10 | yes | 14 | 19.18 | odd | 2 | inner | |
475.3.d.d.474.9 | 28 | 95.37 | even | 4 | |||
475.3.d.d.474.10 | 28 | 5.3 | odd | 4 | |||
475.3.d.d.474.19 | 28 | 5.2 | odd | 4 | |||
475.3.d.d.474.20 | 28 | 95.18 | even | 4 |