Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [858,2,Mod(133,858)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(858, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("858.133");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 858 = 2 \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 858.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.85116449343\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 858.529 |
Dual form | 858.2.i.g.133.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/858\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 1.00000 | + | 1.73205i | 0.377964 | + | 0.654654i | 0.990766 | − | 0.135583i | \(-0.0432908\pi\) |
−0.612801 | + | 0.790237i | \(0.709957\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.50000 | − | 4.33013i | −0.573539 | − | 0.993399i | −0.996199 | − | 0.0871106i | \(-0.972237\pi\) |
0.422659 | − | 0.906289i | \(-0.361097\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 4.00000 | − | 6.92820i | 0.834058 | − | 1.44463i | −0.0607377 | − | 0.998154i | \(-0.519345\pi\) |
0.894795 | − | 0.446476i | \(-0.147321\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −3.50000 | − | 0.866025i | −0.686406 | − | 0.169842i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | − | 1.73205i | 0.188982 | − | 0.327327i | ||||
\(29\) | 1.00000 | − | 1.73205i | 0.185695 | − | 0.321634i | −0.758115 | − | 0.652121i | \(-0.773880\pi\) |
0.943811 | + | 0.330487i | \(0.107213\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | −1.00000 | − | 1.73205i | −0.169031 | − | 0.292770i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −5.00000 | + | 8.66025i | −0.821995 | + | 1.42374i | 0.0821995 | + | 0.996616i | \(0.473806\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | −3.50000 | − | 0.866025i | −0.560449 | − | 0.138675i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 1.00000 | − | 1.73205i | 0.156174 | − | 0.270501i | −0.777312 | − | 0.629115i | \(-0.783417\pi\) |
0.933486 | + | 0.358614i | \(0.116751\pi\) | |||||||
\(42\) | 1.00000 | − | 1.73205i | 0.154303 | − | 0.267261i | ||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −4.00000 | − | 6.92820i | −0.589768 | − | 1.02151i | ||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | −2.50000 | + | 2.59808i | −0.346688 | + | 0.360288i | ||||
\(53\) | −1.00000 | −0.137361 | −0.0686803 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686803 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −0.500000 | + | 0.866025i | −0.0674200 | + | 0.116775i | ||||
\(56\) | −1.00000 | − | 1.73205i | −0.133631 | − | 0.231455i | ||||
\(57\) | −5.00000 | −0.662266 | ||||||||
\(58\) | −1.00000 | − | 1.73205i | −0.131306 | − | 0.227429i | ||||
\(59\) | 0.500000 | + | 0.866025i | 0.0650945 | + | 0.112747i | 0.896736 | − | 0.442566i | \(-0.145932\pi\) |
−0.831641 | + | 0.555313i | \(0.812598\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 5.50000 | + | 9.52628i | 0.704203 | + | 1.21972i | 0.966978 | + | 0.254858i | \(0.0820288\pi\) |
−0.262776 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(62\) | 1.50000 | − | 2.59808i | 0.190500 | − | 0.329956i | ||||
\(63\) | 1.00000 | − | 1.73205i | 0.125988 | − | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | + | 3.46410i | 0.124035 | + | 0.429669i | ||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | −2.50000 | + | 4.33013i | −0.303170 | + | 0.525105i | ||||
\(69\) | −4.00000 | − | 6.92820i | −0.481543 | − | 0.834058i | ||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 8.00000 | 0.936329 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(74\) | 5.00000 | + | 8.66025i | 0.581238 | + | 1.00673i | ||||
\(75\) | −2.00000 | + | 3.46410i | −0.230940 | + | 0.400000i | ||||
\(76\) | −2.50000 | + | 4.33013i | −0.286770 | + | 0.496700i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | −2.50000 | + | 2.59808i | −0.283069 | + | 0.294174i | ||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.00000 | − | 1.73205i | −0.110432 | − | 0.191273i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | −1.00000 | − | 1.73205i | −0.109109 | − | 0.188982i | ||||
\(85\) | 2.50000 | + | 4.33013i | 0.271163 | + | 0.469668i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | −1.00000 | − | 1.73205i | −0.107211 | − | 0.185695i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −1.00000 | + | 1.73205i | −0.106000 | + | 0.183597i | −0.914146 | − | 0.405385i | \(-0.867138\pi\) |
0.808146 | + | 0.588982i | \(0.200471\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 5.00000 | − | 5.19615i | 0.524142 | − | 0.544705i | ||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | 1.50000 | − | 2.59808i | 0.155543 | − | 0.269408i | ||||
\(94\) | 1.00000 | − | 1.73205i | 0.103142 | − | 0.178647i | ||||
\(95\) | 2.50000 | + | 4.33013i | 0.256495 | + | 0.444262i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −2.50000 | − | 4.33013i | −0.253837 | − | 0.439658i | 0.710742 | − | 0.703452i | \(-0.248359\pi\) |
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | −1.50000 | − | 2.59808i | −0.151523 | − | 0.262445i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | 6.00000 | − | 10.3923i | 0.597022 | − | 1.03407i | −0.396236 | − | 0.918149i | \(-0.629684\pi\) |
0.993258 | − | 0.115924i | \(-0.0369830\pi\) | |||||||
\(102\) | −2.50000 | + | 4.33013i | −0.247537 | + | 0.428746i | ||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 1.00000 | + | 3.46410i | 0.0980581 | + | 0.339683i | ||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | −0.500000 | + | 0.866025i | −0.0485643 | + | 0.0841158i | ||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 19.0000 | 1.81987 | 0.909935 | − | 0.414751i | \(-0.136131\pi\) | ||||
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0.500000 | + | 0.866025i | 0.0476731 | + | 0.0825723i | ||||
\(111\) | 5.00000 | + | 8.66025i | 0.474579 | + | 0.821995i | ||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | −2.00000 | − | 3.46410i | −0.188144 | − | 0.325875i | 0.756487 | − | 0.654008i | \(-0.226914\pi\) |
−0.944632 | + | 0.328133i | \(0.893581\pi\) | |||||||
\(114\) | −2.50000 | + | 4.33013i | −0.234146 | + | 0.405554i | ||||
\(115\) | −4.00000 | + | 6.92820i | −0.373002 | + | 0.646058i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | −2.50000 | + | 2.59808i | −0.231125 | + | 0.240192i | ||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 5.00000 | − | 8.66025i | 0.458349 | − | 0.793884i | ||||
\(120\) | 0.500000 | − | 0.866025i | 0.0456435 | − | 0.0790569i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 11.0000 | 0.995893 | ||||||||
\(123\) | −1.00000 | − | 1.73205i | −0.0901670 | − | 0.156174i | ||||
\(124\) | −1.50000 | − | 2.59808i | −0.134704 | − | 0.233314i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | −1.00000 | − | 1.73205i | −0.0890871 | − | 0.154303i | ||||
\(127\) | −8.00000 | + | 13.8564i | −0.709885 | + | 1.22956i | 0.255014 | + | 0.966937i | \(0.417920\pi\) |
−0.964899 | + | 0.262620i | \(0.915413\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 3.50000 | + | 0.866025i | 0.306970 | + | 0.0759555i | ||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | −0.500000 | + | 0.866025i | −0.0435194 | + | 0.0753778i | ||||
\(133\) | 5.00000 | − | 8.66025i | 0.433555 | − | 0.750939i | ||||
\(134\) | 1.00000 | + | 1.73205i | 0.0863868 | + | 0.149626i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 2.50000 | + | 4.33013i | 0.214373 | + | 0.371305i | ||||
\(137\) | −5.00000 | − | 8.66025i | −0.427179 | − | 0.739895i | 0.569442 | − | 0.822031i | \(-0.307159\pi\) |
−0.996621 | + | 0.0821359i | \(0.973826\pi\) | |||||||
\(138\) | −8.00000 | −0.681005 | ||||||||
\(139\) | −4.50000 | − | 7.79423i | −0.381685 | − | 0.661098i | 0.609618 | − | 0.792695i | \(-0.291323\pi\) |
−0.991303 | + | 0.131597i | \(0.957989\pi\) | |||||||
\(140\) | −1.00000 | + | 1.73205i | −0.0845154 | + | 0.146385i | ||||
\(141\) | 1.00000 | − | 1.73205i | 0.0842152 | − | 0.145865i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.50000 | − | 0.866025i | −0.292685 | − | 0.0724207i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.00000 | + | 1.73205i | −0.0830455 | + | 0.143839i | ||||
\(146\) | 4.00000 | − | 6.92820i | 0.331042 | − | 0.573382i | ||||
\(147\) | −1.50000 | − | 2.59808i | −0.123718 | − | 0.214286i | ||||
\(148\) | 10.0000 | 0.821995 | ||||||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | 2.00000 | + | 3.46410i | 0.163299 | + | 0.282843i | ||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | 2.50000 | + | 4.33013i | 0.202777 | + | 0.351220i | ||||
\(153\) | −2.50000 | + | 4.33013i | −0.202113 | + | 0.350070i | ||||
\(154\) | 1.00000 | − | 1.73205i | 0.0805823 | − | 0.139573i | ||||
\(155\) | −3.00000 | −0.240966 | ||||||||
\(156\) | 1.00000 | + | 3.46410i | 0.0800641 | + | 0.277350i | ||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | −2.00000 | + | 3.46410i | −0.159111 | + | 0.275589i | ||||
\(159\) | −0.500000 | + | 0.866025i | −0.0396526 | + | 0.0686803i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 11.0000 | + | 19.0526i | 0.861586 | + | 1.49231i | 0.870397 | + | 0.492350i | \(0.163862\pi\) |
−0.00881059 | + | 0.999961i | \(0.502805\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0.500000 | + | 0.866025i | 0.0389249 | + | 0.0674200i | ||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | 5.50000 | − | 9.52628i | 0.425603 | − | 0.737166i | −0.570874 | − | 0.821038i | \(-0.693395\pi\) |
0.996477 | + | 0.0838722i | \(0.0267288\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 5.00000 | 0.383482 | ||||||||
\(171\) | −2.50000 | + | 4.33013i | −0.191180 | + | 0.331133i | ||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | 4.00000 | + | 6.92820i | 0.304114 | + | 0.526742i | 0.977064 | − | 0.212947i | \(-0.0683062\pi\) |
−0.672949 | + | 0.739689i | \(0.734973\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | −4.00000 | − | 6.92820i | −0.302372 | − | 0.523723i | ||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 1.00000 | + | 1.73205i | 0.0749532 | + | 0.129823i | ||||
\(179\) | −7.50000 | + | 12.9904i | −0.560576 | + | 0.970947i | 0.436870 | + | 0.899525i | \(0.356087\pi\) |
−0.997446 | + | 0.0714220i | \(0.977246\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | −2.00000 | − | 6.92820i | −0.148250 | − | 0.513553i | ||||
\(183\) | 11.0000 | 0.813143 | ||||||||
\(184\) | −4.00000 | + | 6.92820i | −0.294884 | + | 0.510754i | ||||
\(185\) | 5.00000 | − | 8.66025i | 0.367607 | − | 0.636715i | ||||
\(186\) | −1.50000 | − | 2.59808i | −0.109985 | − | 0.190500i | ||||
\(187\) | −5.00000 | −0.365636 | ||||||||
\(188\) | −1.00000 | − | 1.73205i | −0.0729325 | − | 0.126323i | ||||
\(189\) | −1.00000 | − | 1.73205i | −0.0727393 | − | 0.125988i | ||||
\(190\) | 5.00000 | 0.362738 | ||||||||
\(191\) | −9.00000 | − | 15.5885i | −0.651217 | − | 1.12794i | −0.982828 | − | 0.184525i | \(-0.940925\pi\) |
0.331611 | − | 0.943416i | \(-0.392408\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −9.00000 | + | 15.5885i | −0.647834 | + | 1.12208i | 0.335805 | + | 0.941932i | \(0.390992\pi\) |
−0.983639 | + | 0.180150i | \(0.942342\pi\) | |||||||
\(194\) | −5.00000 | −0.358979 | ||||||||
\(195\) | 3.50000 | + | 0.866025i | 0.250640 | + | 0.0620174i | ||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 11.0000 | − | 19.0526i | 0.783718 | − | 1.35744i | −0.146045 | − | 0.989278i | \(-0.546654\pi\) |
0.929762 | − | 0.368161i | \(-0.120012\pi\) | |||||||
\(198\) | −0.500000 | + | 0.866025i | −0.0355335 | + | 0.0615457i | ||||
\(199\) | −8.50000 | − | 14.7224i | −0.602549 | − | 1.04365i | −0.992434 | − | 0.122782i | \(-0.960818\pi\) |
0.389885 | − | 0.920864i | \(-0.372515\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | 1.00000 | + | 1.73205i | 0.0705346 | + | 0.122169i | ||||
\(202\) | −6.00000 | − | 10.3923i | −0.422159 | − | 0.731200i | ||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 2.50000 | + | 4.33013i | 0.175035 | + | 0.303170i | ||||
\(205\) | −1.00000 | + | 1.73205i | −0.0698430 | + | 0.120972i | ||||
\(206\) | −2.00000 | + | 3.46410i | −0.139347 | + | 0.241355i | ||||
\(207\) | −8.00000 | −0.556038 | ||||||||
\(208\) | 3.50000 | + | 0.866025i | 0.242681 | + | 0.0600481i | ||||
\(209\) | −5.00000 | −0.345857 | ||||||||
\(210\) | −1.00000 | + | 1.73205i | −0.0690066 | + | 0.119523i | ||||
\(211\) | −1.50000 | + | 2.59808i | −0.103264 | + | 0.178859i | −0.913028 | − | 0.407898i | \(-0.866262\pi\) |
0.809763 | + | 0.586756i | \(0.199595\pi\) | |||||||
\(212\) | 0.500000 | + | 0.866025i | 0.0343401 | + | 0.0594789i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.00000 | − | 3.46410i | −0.136717 | − | 0.236801i | ||||
\(215\) | −2.00000 | − | 3.46410i | −0.136399 | − | 0.236250i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.00000 | + | 5.19615i | 0.203653 | + | 0.352738i | ||||
\(218\) | 9.50000 | − | 16.4545i | 0.643421 | − | 1.11444i | ||||
\(219\) | 4.00000 | − | 6.92820i | 0.270295 | − | 0.468165i | ||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −12.5000 | + | 12.9904i | −0.840841 | + | 0.873828i | ||||
\(222\) | 10.0000 | 0.671156 | ||||||||
\(223\) | −2.50000 | + | 4.33013i | −0.167412 | + | 0.289967i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | −1.00000 | + | 1.73205i | −0.0668153 | + | 0.115728i | ||||
\(225\) | 2.00000 | + | 3.46410i | 0.133333 | + | 0.230940i | ||||
\(226\) | −4.00000 | −0.266076 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 2.50000 | + | 4.33013i | 0.165567 | + | 0.286770i | ||||
\(229\) | 24.0000 | 1.58596 | 0.792982 | − | 0.609245i | \(-0.208527\pi\) | ||||
0.792982 | + | 0.609245i | \(0.208527\pi\) | |||||||
\(230\) | 4.00000 | + | 6.92820i | 0.263752 | + | 0.456832i | ||||
\(231\) | 1.00000 | − | 1.73205i | 0.0657952 | − | 0.113961i | ||||
\(232\) | −1.00000 | + | 1.73205i | −0.0656532 | + | 0.113715i | ||||
\(233\) | 29.0000 | 1.89985 | 0.949927 | − | 0.312473i | \(-0.101157\pi\) | ||||
0.949927 | + | 0.312473i | \(0.101157\pi\) | |||||||
\(234\) | 1.00000 | + | 3.46410i | 0.0653720 | + | 0.226455i | ||||
\(235\) | −2.00000 | −0.130466 | ||||||||
\(236\) | 0.500000 | − | 0.866025i | 0.0325472 | − | 0.0563735i | ||||
\(237\) | −2.00000 | + | 3.46410i | −0.129914 | + | 0.225018i | ||||
\(238\) | −5.00000 | − | 8.66025i | −0.324102 | − | 0.561361i | ||||
\(239\) | 15.0000 | 0.970269 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(240\) | −0.500000 | − | 0.866025i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | 14.0000 | + | 24.2487i | 0.901819 | + | 1.56200i | 0.825131 | + | 0.564942i | \(0.191101\pi\) |
0.0766885 | + | 0.997055i | \(0.475565\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 5.50000 | − | 9.52628i | 0.352101 | − | 0.609858i | ||||
\(245\) | −1.50000 | + | 2.59808i | −0.0958315 | + | 0.165985i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | −12.5000 | + | 12.9904i | −0.795356 | + | 0.826558i | ||||
\(248\) | −3.00000 | −0.190500 | ||||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 4.50000 | − | 7.79423i | 0.284605 | − | 0.492950i | ||||
\(251\) | 12.0000 | + | 20.7846i | 0.757433 | + | 1.31191i | 0.944156 | + | 0.329500i | \(0.106880\pi\) |
−0.186722 | + | 0.982413i | \(0.559786\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | −4.00000 | − | 6.92820i | −0.251478 | − | 0.435572i | ||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | 5.00000 | 0.313112 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 2.00000 | − | 3.46410i | 0.124515 | − | 0.215666i | ||||
\(259\) | −20.0000 | −1.24274 | ||||||||
\(260\) | 2.50000 | − | 2.59808i | 0.155043 | − | 0.161126i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 3.00000 | − | 5.19615i | 0.185341 | − | 0.321019i | ||||
\(263\) | 10.5000 | − | 18.1865i | 0.647458 | − | 1.12143i | −0.336270 | − | 0.941766i | \(-0.609166\pi\) |
0.983728 | − | 0.179664i | \(-0.0575011\pi\) | |||||||
\(264\) | 0.500000 | + | 0.866025i | 0.0307729 | + | 0.0533002i | ||||
\(265\) | 1.00000 | 0.0614295 | ||||||||
\(266\) | −5.00000 | − | 8.66025i | −0.306570 | − | 0.530994i | ||||
\(267\) | 1.00000 | + | 1.73205i | 0.0611990 | + | 0.106000i | ||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | 10.5000 | + | 18.1865i | 0.640196 | + | 1.10885i | 0.985389 | + | 0.170321i | \(0.0544803\pi\) |
−0.345192 | + | 0.938532i | \(0.612186\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 10.0000 | − | 17.3205i | 0.607457 | − | 1.05215i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.991658 | − | 0.128897i | \(-0.0411435\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | −2.00000 | − | 6.92820i | −0.121046 | − | 0.419314i | ||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | −2.00000 | + | 3.46410i | −0.120605 | + | 0.208893i | ||||
\(276\) | −4.00000 | + | 6.92820i | −0.240772 | + | 0.417029i | ||||
\(277\) | −8.50000 | − | 14.7224i | −0.510716 | − | 0.884585i | −0.999923 | − | 0.0124177i | \(-0.996047\pi\) |
0.489207 | − | 0.872167i | \(-0.337286\pi\) | |||||||
\(278\) | −9.00000 | −0.539784 | ||||||||
\(279\) | −1.50000 | − | 2.59808i | −0.0898027 | − | 0.155543i | ||||
\(280\) | 1.00000 | + | 1.73205i | 0.0597614 | + | 0.103510i | ||||
\(281\) | −3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | \(-0.528521\pi\) | ||||
−0.0894825 | + | 0.995988i | \(0.528521\pi\) | |||||||
\(282\) | −1.00000 | − | 1.73205i | −0.0595491 | − | 0.103142i | ||||
\(283\) | 4.50000 | − | 7.79423i | 0.267497 | − | 0.463319i | −0.700718 | − | 0.713439i | \(-0.747137\pi\) |
0.968215 | + | 0.250120i | \(0.0804700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.00000 | 0.296174 | ||||||||
\(286\) | −2.50000 | + | 2.59808i | −0.147828 | + | 0.153627i | ||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 1.00000 | + | 1.73205i | 0.0587220 | + | 0.101710i | ||||
\(291\) | −5.00000 | −0.293105 | ||||||||
\(292\) | −4.00000 | − | 6.92820i | −0.234082 | − | 0.405442i | ||||
\(293\) | 11.0000 | + | 19.0526i | 0.642627 | + | 1.11306i | 0.984844 | + | 0.173442i | \(0.0554888\pi\) |
−0.342217 | + | 0.939621i | \(0.611178\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | −0.500000 | − | 0.866025i | −0.0291111 | − | 0.0504219i | ||||
\(296\) | 5.00000 | − | 8.66025i | 0.290619 | − | 0.503367i | ||||
\(297\) | −0.500000 | + | 0.866025i | −0.0290129 | + | 0.0502519i | ||||
\(298\) | 4.00000 | 0.231714 | ||||||||
\(299\) | −28.0000 | − | 6.92820i | −1.61928 | − | 0.400668i | ||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | −4.00000 | + | 6.92820i | −0.230556 | + | 0.399335i | ||||
\(302\) | −10.0000 | + | 17.3205i | −0.575435 | + | 0.996683i | ||||
\(303\) | −6.00000 | − | 10.3923i | −0.344691 | − | 0.597022i | ||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | −5.50000 | − | 9.52628i | −0.314929 | − | 0.545473i | ||||
\(306\) | 2.50000 | + | 4.33013i | 0.142915 | + | 0.247537i | ||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −1.00000 | − | 1.73205i | −0.0569803 | − | 0.0986928i | ||||
\(309\) | −2.00000 | + | 3.46410i | −0.113776 | + | 0.197066i | ||||
\(310\) | −1.50000 | + | 2.59808i | −0.0851943 | + | 0.147561i | ||||
\(311\) | −22.0000 | −1.24751 | −0.623753 | − | 0.781622i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781622i | \(0.714393\pi\) | |||||||
\(312\) | 3.50000 | + | 0.866025i | 0.198148 | + | 0.0490290i | ||||
\(313\) | −15.0000 | −0.847850 | −0.423925 | − | 0.905697i | \(-0.639348\pi\) | ||||
−0.423925 | + | 0.905697i | \(0.639348\pi\) | |||||||
\(314\) | 7.00000 | − | 12.1244i | 0.395033 | − | 0.684217i | ||||
\(315\) | −1.00000 | + | 1.73205i | −0.0563436 | + | 0.0975900i | ||||
\(316\) | 2.00000 | + | 3.46410i | 0.112509 | + | 0.194871i | ||||
\(317\) | 2.00000 | 0.112331 | 0.0561656 | − | 0.998421i | \(-0.482113\pi\) | ||||
0.0561656 | + | 0.998421i | \(0.482113\pi\) | |||||||
\(318\) | 0.500000 | + | 0.866025i | 0.0280386 | + | 0.0485643i | ||||
\(319\) | −1.00000 | − | 1.73205i | −0.0559893 | − | 0.0969762i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −2.00000 | − | 3.46410i | −0.111629 | − | 0.193347i | ||||
\(322\) | 8.00000 | − | 13.8564i | 0.445823 | − | 0.772187i | ||||
\(323\) | −12.5000 | + | 21.6506i | −0.695519 | + | 1.20467i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.00000 | + | 13.8564i | 0.221880 | + | 0.768615i | ||||
\(326\) | 22.0000 | 1.21847 | ||||||||
\(327\) | 9.50000 | − | 16.4545i | 0.525351 | − | 0.909935i | ||||
\(328\) | −1.00000 | + | 1.73205i | −0.0552158 | + | 0.0956365i | ||||
\(329\) | 2.00000 | + | 3.46410i | 0.110264 | + | 0.190982i | ||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 7.00000 | + | 12.1244i | 0.384755 | + | 0.666415i | 0.991735 | − | 0.128302i | \(-0.0409527\pi\) |
−0.606980 | + | 0.794717i | \(0.707619\pi\) | |||||||
\(332\) | −3.00000 | − | 5.19615i | −0.164646 | − | 0.285176i | ||||
\(333\) | 10.0000 | 0.547997 | ||||||||
\(334\) | −5.50000 | − | 9.52628i | −0.300947 | − | 0.521255i | ||||
\(335\) | 1.00000 | − | 1.73205i | 0.0546358 | − | 0.0946320i | ||||
\(336\) | −1.00000 | + | 1.73205i | −0.0545545 | + | 0.0944911i | ||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0.500000 | + | 12.9904i | 0.0271964 | + | 0.706584i | ||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | 2.50000 | − | 4.33013i | 0.135582 | − | 0.234834i | ||||
\(341\) | 1.50000 | − | 2.59808i | 0.0812296 | − | 0.140694i | ||||
\(342\) | 2.50000 | + | 4.33013i | 0.135185 | + | 0.234146i | ||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −2.00000 | − | 3.46410i | −0.107833 | − | 0.186772i | ||||
\(345\) | 4.00000 | + | 6.92820i | 0.215353 | + | 0.373002i | ||||
\(346\) | 8.00000 | 0.430083 | ||||||||
\(347\) | −3.00000 | − | 5.19615i | −0.161048 | − | 0.278944i | 0.774197 | − | 0.632945i | \(-0.218154\pi\) |
−0.935245 | + | 0.354001i | \(0.884821\pi\) | |||||||
\(348\) | −1.00000 | + | 1.73205i | −0.0536056 | + | 0.0928477i | ||||
\(349\) | 14.5000 | − | 25.1147i | 0.776167 | − | 1.34436i | −0.157969 | − | 0.987444i | \(-0.550495\pi\) |
0.934136 | − | 0.356917i | \(-0.116172\pi\) | |||||||
\(350\) | −8.00000 | −0.427618 | ||||||||
\(351\) | 1.00000 | + | 3.46410i | 0.0533761 | + | 0.184900i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −12.0000 | + | 20.7846i | −0.638696 | + | 1.10625i | 0.347024 | + | 0.937856i | \(0.387192\pi\) |
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(354\) | 0.500000 | − | 0.866025i | 0.0265747 | − | 0.0460287i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | −5.00000 | − | 8.66025i | −0.264628 | − | 0.458349i | ||||
\(358\) | 7.50000 | + | 12.9904i | 0.396387 | + | 0.686563i | ||||
\(359\) | −23.0000 | −1.21389 | −0.606947 | − | 0.794742i | \(-0.707606\pi\) | ||||
−0.606947 | + | 0.794742i | \(0.707606\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | −1.00000 | + | 1.73205i | −0.0525588 | + | 0.0910346i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −7.00000 | − | 1.73205i | −0.366900 | − | 0.0907841i | ||||
\(365\) | −8.00000 | −0.418739 | ||||||||
\(366\) | 5.50000 | − | 9.52628i | 0.287490 | − | 0.497947i | ||||
\(367\) | 4.50000 | − | 7.79423i | 0.234898 | − | 0.406855i | −0.724345 | − | 0.689438i | \(-0.757858\pi\) |
0.959243 | + | 0.282582i | \(0.0911910\pi\) | |||||||
\(368\) | 4.00000 | + | 6.92820i | 0.208514 | + | 0.361158i | ||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | −5.00000 | − | 8.66025i | −0.259938 | − | 0.450225i | ||||
\(371\) | −1.00000 | − | 1.73205i | −0.0519174 | − | 0.0899236i | ||||
\(372\) | −3.00000 | −0.155543 | ||||||||
\(373\) | −11.5000 | − | 19.9186i | −0.595447 | − | 1.03135i | −0.993484 | − | 0.113975i | \(-0.963641\pi\) |
0.398036 | − | 0.917370i | \(-0.369692\pi\) | |||||||
\(374\) | −2.50000 | + | 4.33013i | −0.129272 | + | 0.223906i | ||||
\(375\) | 4.50000 | − | 7.79423i | 0.232379 | − | 0.402492i | ||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | −7.00000 | − | 1.73205i | −0.360518 | − | 0.0892052i | ||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 1.00000 | − | 1.73205i | 0.0513665 | − | 0.0889695i | −0.839199 | − | 0.543825i | \(-0.816976\pi\) |
0.890565 | + | 0.454855i | \(0.150309\pi\) | |||||||
\(380\) | 2.50000 | − | 4.33013i | 0.128247 | − | 0.222131i | ||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | −18.0000 | −0.920960 | ||||||||
\(383\) | 2.00000 | + | 3.46410i | 0.102195 | + | 0.177007i | 0.912589 | − | 0.408879i | \(-0.134080\pi\) |
−0.810394 | + | 0.585886i | \(0.800747\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −2.00000 | −0.101929 | ||||||||
\(386\) | 9.00000 | + | 15.5885i | 0.458088 | + | 0.793432i | ||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | −2.50000 | + | 4.33013i | −0.126918 | + | 0.219829i | ||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 2.50000 | − | 2.59808i | 0.126592 | − | 0.131559i | ||||
\(391\) | −40.0000 | −2.02289 | ||||||||
\(392\) | −1.50000 | + | 2.59808i | −0.0757614 | + | 0.131223i | ||||
\(393\) | 3.00000 | − | 5.19615i | 0.151330 | − | 0.262111i | ||||
\(394\) | −11.0000 | − | 19.0526i | −0.554172 | − | 0.959854i | ||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | 9.00000 | + | 15.5885i | 0.451697 | + | 0.782362i | 0.998492 | − | 0.0549046i | \(-0.0174855\pi\) |
−0.546795 | + | 0.837267i | \(0.684152\pi\) | |||||||
\(398\) | −17.0000 | −0.852133 | ||||||||
\(399\) | −5.00000 | − | 8.66025i | −0.250313 | − | 0.433555i | ||||
\(400\) | 2.00000 | − | 3.46410i | 0.100000 | − | 0.173205i | ||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 2.00000 | 0.0997509 | ||||||||
\(403\) | −3.00000 | − | 10.3923i | −0.149441 | − | 0.517678i | ||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 2.00000 | − | 3.46410i | 0.0992583 | − | 0.171920i | ||||
\(407\) | 5.00000 | + | 8.66025i | 0.247841 | + | 0.429273i | ||||
\(408\) | 5.00000 | 0.247537 | ||||||||
\(409\) | −15.0000 | − | 25.9808i | −0.741702 | − | 1.28467i | −0.951720 | − | 0.306968i | \(-0.900685\pi\) |
0.210017 | − | 0.977698i | \(-0.432648\pi\) | |||||||
\(410\) | 1.00000 | + | 1.73205i | 0.0493865 | + | 0.0855399i | ||||
\(411\) | −10.0000 | −0.493264 | ||||||||
\(412\) | 2.00000 | + | 3.46410i | 0.0985329 | + | 0.170664i | ||||
\(413\) | −1.00000 | + | 1.73205i | −0.0492068 | + | 0.0852286i | ||||
\(414\) | −4.00000 | + | 6.92820i | −0.196589 | + | 0.340503i | ||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 2.50000 | − | 2.59808i | 0.122573 | − | 0.127381i | ||||
\(417\) | −9.00000 | −0.440732 | ||||||||
\(418\) | −2.50000 | + | 4.33013i | −0.122279 | + | 0.211793i | ||||
\(419\) | 2.00000 | − | 3.46410i | 0.0977064 | − | 0.169232i | −0.813029 | − | 0.582224i | \(-0.802183\pi\) |
0.910735 | + | 0.412991i | \(0.135516\pi\) | |||||||
\(420\) | 1.00000 | + | 1.73205i | 0.0487950 | + | 0.0845154i | ||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | 1.50000 | + | 2.59808i | 0.0730189 | + | 0.126472i | ||||
\(423\) | −1.00000 | − | 1.73205i | −0.0486217 | − | 0.0842152i | ||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | 10.0000 | + | 17.3205i | 0.485071 | + | 0.840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.0000 | + | 19.0526i | −0.532327 | + | 0.922018i | ||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | −2.50000 | + | 2.59808i | −0.120701 | + | 0.125436i | ||||
\(430\) | −4.00000 | −0.192897 | ||||||||
\(431\) | 18.5000 | − | 32.0429i | 0.891114 | − | 1.54345i | 0.0525716 | − | 0.998617i | \(-0.483258\pi\) |
0.838542 | − | 0.544837i | \(-0.183408\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 10.5000 | + | 18.1865i | 0.504598 | + | 0.873989i | 0.999986 | + | 0.00531724i | \(0.00169254\pi\) |
−0.495388 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(434\) | 6.00000 | 0.288009 | ||||||||
\(435\) | 1.00000 | + | 1.73205i | 0.0479463 | + | 0.0830455i | ||||
\(436\) | −9.50000 | − | 16.4545i | −0.454967 | − | 0.788027i | ||||
\(437\) | −40.0000 | −1.91346 | ||||||||
\(438\) | −4.00000 | − | 6.92820i | −0.191127 | − | 0.331042i | ||||
\(439\) | −12.0000 | + | 20.7846i | −0.572729 | + | 0.991995i | 0.423556 | + | 0.905870i | \(0.360782\pi\) |
−0.996284 | + | 0.0861252i | \(0.972552\pi\) | |||||||
\(440\) | 0.500000 | − | 0.866025i | 0.0238366 | − | 0.0412861i | ||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 5.00000 | + | 17.3205i | 0.237826 | + | 0.823853i | ||||
\(443\) | −29.0000 | −1.37783 | −0.688916 | − | 0.724841i | \(-0.741913\pi\) | ||||
−0.688916 | + | 0.724841i | \(0.741913\pi\) | |||||||
\(444\) | 5.00000 | − | 8.66025i | 0.237289 | − | 0.410997i | ||||
\(445\) | 1.00000 | − | 1.73205i | 0.0474045 | − | 0.0821071i | ||||
\(446\) | 2.50000 | + | 4.33013i | 0.118378 | + | 0.205037i | ||||
\(447\) | 4.00000 | 0.189194 | ||||||||
\(448\) | 1.00000 | + | 1.73205i | 0.0472456 | + | 0.0818317i | ||||
\(449\) | −6.00000 | − | 10.3923i | −0.283158 | − | 0.490443i | 0.689003 | − | 0.724758i | \(-0.258049\pi\) |
−0.972161 | + | 0.234315i | \(0.924715\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | −1.00000 | − | 1.73205i | −0.0470882 | − | 0.0815591i | ||||
\(452\) | −2.00000 | + | 3.46410i | −0.0940721 | + | 0.162938i | ||||
\(453\) | −10.0000 | + | 17.3205i | −0.469841 | + | 0.813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.00000 | + | 5.19615i | −0.234404 | + | 0.243599i | ||||
\(456\) | 5.00000 | 0.234146 | ||||||||
\(457\) | 2.00000 | − | 3.46410i | 0.0935561 | − | 0.162044i | −0.815449 | − | 0.578829i | \(-0.803510\pi\) |
0.909005 | + | 0.416785i | \(0.136843\pi\) | |||||||
\(458\) | 12.0000 | − | 20.7846i | 0.560723 | − | 0.971201i | ||||
\(459\) | 2.50000 | + | 4.33013i | 0.116690 | + | 0.202113i | ||||
\(460\) | 8.00000 | 0.373002 | ||||||||
\(461\) | −5.00000 | − | 8.66025i | −0.232873 | − | 0.403348i | 0.725779 | − | 0.687928i | \(-0.241479\pi\) |
−0.958652 | + | 0.284579i | \(0.908146\pi\) | |||||||
\(462\) | −1.00000 | − | 1.73205i | −0.0465242 | − | 0.0805823i | ||||
\(463\) | −21.0000 | −0.975953 | −0.487976 | − | 0.872857i | \(-0.662265\pi\) | ||||
−0.487976 | + | 0.872857i | \(0.662265\pi\) | |||||||
\(464\) | 1.00000 | + | 1.73205i | 0.0464238 | + | 0.0804084i | ||||
\(465\) | −1.50000 | + | 2.59808i | −0.0695608 | + | 0.120483i | ||||
\(466\) | 14.5000 | − | 25.1147i | 0.671700 | − | 1.16342i | ||||
\(467\) | −29.0000 | −1.34196 | −0.670980 | − | 0.741475i | \(-0.734126\pi\) | ||||
−0.670980 | + | 0.741475i | \(0.734126\pi\) | |||||||
\(468\) | 3.50000 | + | 0.866025i | 0.161788 | + | 0.0400320i | ||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | −1.00000 | + | 1.73205i | −0.0461266 | + | 0.0798935i | ||||
\(471\) | 7.00000 | − | 12.1244i | 0.322543 | − | 0.558661i | ||||
\(472\) | −0.500000 | − | 0.866025i | −0.0230144 | − | 0.0398621i | ||||
\(473\) | 4.00000 | 0.183920 | ||||||||
\(474\) | 2.00000 | + | 3.46410i | 0.0918630 | + | 0.159111i | ||||
\(475\) | 10.0000 | + | 17.3205i | 0.458831 | + | 0.794719i | ||||
\(476\) | −10.0000 | −0.458349 | ||||||||
\(477\) | 0.500000 | + | 0.866025i | 0.0228934 | + | 0.0396526i | ||||
\(478\) | 7.50000 | − | 12.9904i | 0.343042 | − | 0.594166i | ||||
\(479\) | 1.50000 | − | 2.59808i | 0.0685367 | − | 0.118709i | −0.829721 | − | 0.558179i | \(-0.811500\pi\) |
0.898257 | + | 0.439470i | \(0.144834\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 35.0000 | + | 8.66025i | 1.59586 | + | 0.394874i | ||||
\(482\) | 28.0000 | 1.27537 | ||||||||
\(483\) | 8.00000 | − | 13.8564i | 0.364013 | − | 0.630488i | ||||
\(484\) | −0.500000 | + | 0.866025i | −0.0227273 | + | 0.0393648i | ||||
\(485\) | 2.50000 | + | 4.33013i | 0.113519 | + | 0.196621i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −8.00000 | − | 13.8564i | −0.362515 | − | 0.627894i | 0.625859 | − | 0.779936i | \(-0.284748\pi\) |
−0.988374 | + | 0.152042i | \(0.951415\pi\) | |||||||
\(488\) | −5.50000 | − | 9.52628i | −0.248973 | − | 0.431234i | ||||
\(489\) | 22.0000 | 0.994874 | ||||||||
\(490\) | 1.50000 | + | 2.59808i | 0.0677631 | + | 0.117369i | ||||
\(491\) | 15.0000 | − | 25.9808i | 0.676941 | − | 1.17250i | −0.298957 | − | 0.954267i | \(-0.596639\pi\) |
0.975898 | − | 0.218229i | \(-0.0700279\pi\) | |||||||
\(492\) | −1.00000 | + | 1.73205i | −0.0450835 | + | 0.0780869i | ||||
\(493\) | −10.0000 | −0.450377 | ||||||||
\(494\) | 5.00000 | + | 17.3205i | 0.224961 | + | 0.779287i | ||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | −1.50000 | + | 2.59808i | −0.0673520 | + | 0.116657i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | −14.0000 | −0.626726 | −0.313363 | − | 0.949633i | \(-0.601456\pi\) | ||||
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(500\) | −4.50000 | − | 7.79423i | −0.201246 | − | 0.348569i | ||||
\(501\) | −5.50000 | − | 9.52628i | −0.245722 | − | 0.425603i | ||||
\(502\) | 24.0000 | 1.07117 | ||||||||
\(503\) | −10.5000 | − | 18.1865i | −0.468172 | − | 0.810897i | 0.531167 | − | 0.847267i | \(-0.321754\pi\) |
−0.999338 | + | 0.0363700i | \(0.988421\pi\) | |||||||
\(504\) | −1.00000 | + | 1.73205i | −0.0445435 | + | 0.0771517i | ||||
\(505\) | −6.00000 | + | 10.3923i | −0.266996 | + | 0.462451i | ||||
\(506\) | −8.00000 | −0.355643 | ||||||||
\(507\) | 0.500000 | + | 12.9904i | 0.0222058 | + | 0.576923i | ||||
\(508\) | 16.0000 | 0.709885 | ||||||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 2.50000 | − | 4.33013i | 0.110702 | − | 0.191741i | ||||
\(511\) | 8.00000 | + | 13.8564i | 0.353899 | + | 0.612971i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.50000 | + | 4.33013i | 0.110378 | + | 0.191180i | ||||
\(514\) | 9.00000 | + | 15.5885i | 0.396973 | + | 0.687577i | ||||
\(515\) | 4.00000 | 0.176261 | ||||||||
\(516\) | −2.00000 | − | 3.46410i | −0.0880451 | − | 0.152499i | ||||
\(517\) | 1.00000 | − | 1.73205i | 0.0439799 | − | 0.0761755i | ||||
\(518\) | −10.0000 | + | 17.3205i | −0.439375 | + | 0.761019i | ||||
\(519\) | 8.00000 | 0.351161 | ||||||||
\(520\) | −1.00000 | − | 3.46410i | −0.0438529 | − | 0.151911i | ||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | −1.00000 | + | 1.73205i | −0.0437688 | + | 0.0758098i | ||||
\(523\) | −12.5000 | + | 21.6506i | −0.546587 | + | 0.946716i | 0.451918 | + | 0.892059i | \(0.350740\pi\) |
−0.998505 | + | 0.0546569i | \(0.982594\pi\) | |||||||
\(524\) | −3.00000 | − | 5.19615i | −0.131056 | − | 0.226995i | ||||
\(525\) | −8.00000 | −0.349149 | ||||||||
\(526\) | −10.5000 | − | 18.1865i | −0.457822 | − | 0.792971i | ||||
\(527\) | −7.50000 | − | 12.9904i | −0.326705 | − | 0.565870i | ||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −20.5000 | − | 35.5070i | −0.891304 | − | 1.54378i | ||||
\(530\) | 0.500000 | − | 0.866025i | 0.0217186 | − | 0.0376177i | ||||
\(531\) | 0.500000 | − | 0.866025i | 0.0216982 | − | 0.0375823i | ||||
\(532\) | −10.0000 | −0.433555 | ||||||||
\(533\) | −7.00000 | − | 1.73205i | −0.303204 | − | 0.0750234i | ||||
\(534\) | 2.00000 | 0.0865485 | ||||||||
\(535\) | −2.00000 | + | 3.46410i | −0.0864675 | + | 0.149766i | ||||
\(536\) | 1.00000 | − | 1.73205i | 0.0431934 | − | 0.0748132i | ||||
\(537\) | 7.50000 | + | 12.9904i | 0.323649 | + | 0.560576i | ||||
\(538\) | 21.0000 | 0.905374 | ||||||||
\(539\) | −1.50000 | − | 2.59808i | −0.0646096 | − | 0.111907i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | 42.0000 | 1.80572 | 0.902861 | − | 0.429934i | \(-0.141463\pi\) | ||||
0.902861 | + | 0.429934i | \(0.141463\pi\) | |||||||
\(542\) | −10.0000 | − | 17.3205i | −0.429537 | − | 0.743980i | ||||
\(543\) | −1.00000 | + | 1.73205i | −0.0429141 | + | 0.0743294i | ||||
\(544\) | 2.50000 | − | 4.33013i | 0.107187 | − | 0.185653i | ||||
\(545\) | −19.0000 | −0.813871 | ||||||||
\(546\) | −7.00000 | − | 1.73205i | −0.299572 | − | 0.0741249i | ||||
\(547\) | −19.0000 | −0.812381 | −0.406191 | − | 0.913788i | \(-0.633143\pi\) | ||||
−0.406191 | + | 0.913788i | \(0.633143\pi\) | |||||||
\(548\) | −5.00000 | + | 8.66025i | −0.213589 | + | 0.369948i | ||||
\(549\) | 5.50000 | − | 9.52628i | 0.234734 | − | 0.406572i | ||||
\(550\) | 2.00000 | + | 3.46410i | 0.0852803 | + | 0.147710i | ||||
\(551\) | −10.0000 | −0.426014 | ||||||||
\(552\) | 4.00000 | + | 6.92820i | 0.170251 | + | 0.294884i | ||||
\(553\) | −4.00000 | − | 6.92820i | −0.170097 | − | 0.294617i | ||||
\(554\) | −17.0000 | −0.722261 | ||||||||
\(555\) | −5.00000 | − | 8.66025i | −0.212238 | − | 0.367607i | ||||
\(556\) | −4.50000 | + | 7.79423i | −0.190843 | + | 0.330549i | ||||
\(557\) | −6.00000 | + | 10.3923i | −0.254228 | + | 0.440336i | −0.964686 | − | 0.263404i | \(-0.915155\pi\) |
0.710457 | + | 0.703740i | \(0.248488\pi\) | |||||||
\(558\) | −3.00000 | −0.127000 | ||||||||
\(559\) | 10.0000 | − | 10.3923i | 0.422955 | − | 0.439548i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | −2.50000 | + | 4.33013i | −0.105550 | + | 0.182818i | ||||
\(562\) | −1.50000 | + | 2.59808i | −0.0632737 | + | 0.109593i | ||||
\(563\) | 15.0000 | + | 25.9808i | 0.632175 | + | 1.09496i | 0.987106 | + | 0.160066i | \(0.0511708\pi\) |
−0.354932 | + | 0.934892i | \(0.615496\pi\) | |||||||
\(564\) | −2.00000 | −0.0842152 | ||||||||
\(565\) | 2.00000 | + | 3.46410i | 0.0841406 | + | 0.145736i | ||||
\(566\) | −4.50000 | − | 7.79423i | −0.189149 | − | 0.327616i | ||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.50000 | + | 11.2583i | −0.272494 | + | 0.471974i | −0.969500 | − | 0.245092i | \(-0.921182\pi\) |
0.697006 | + | 0.717066i | \(0.254515\pi\) | |||||||
\(570\) | 2.50000 | − | 4.33013i | 0.104713 | − | 0.181369i | ||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 1.00000 | + | 3.46410i | 0.0418121 | + | 0.144841i | ||||
\(573\) | −18.0000 | −0.751961 | ||||||||
\(574\) | 2.00000 | − | 3.46410i | 0.0834784 | − | 0.144589i | ||||
\(575\) | −16.0000 | + | 27.7128i | −0.667246 | + | 1.15570i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 34.0000 | 1.41544 | 0.707719 | − | 0.706494i | \(-0.249724\pi\) | ||||
0.707719 | + | 0.706494i | \(0.249724\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | 9.00000 | + | 15.5885i | 0.374027 | + | 0.647834i | ||||
\(580\) | 2.00000 | 0.0830455 | ||||||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | −2.50000 | + | 4.33013i | −0.103628 | + | 0.179490i | ||||
\(583\) | −0.500000 | + | 0.866025i | −0.0207079 | + | 0.0358671i | ||||
\(584\) | −8.00000 | −0.331042 | ||||||||
\(585\) | 2.50000 | − | 2.59808i | 0.103362 | − | 0.107417i | ||||
\(586\) | 22.0000 | 0.908812 | ||||||||
\(587\) | −1.50000 | + | 2.59808i | −0.0619116 | + | 0.107234i | −0.895320 | − | 0.445424i | \(-0.853053\pi\) |
0.833408 | + | 0.552658i | \(0.186386\pi\) | |||||||
\(588\) | −1.50000 | + | 2.59808i | −0.0618590 | + | 0.107143i | ||||
\(589\) | −7.50000 | − | 12.9904i | −0.309032 | − | 0.535259i | ||||
\(590\) | −1.00000 | −0.0411693 | ||||||||
\(591\) | −11.0000 | − | 19.0526i | −0.452480 | − | 0.783718i | ||||
\(592\) | −5.00000 | − | 8.66025i | −0.205499 | − | 0.355934i | ||||
\(593\) | −39.0000 | −1.60154 | −0.800769 | − | 0.598973i | \(-0.795576\pi\) | ||||
−0.800769 | + | 0.598973i | \(0.795576\pi\) | |||||||
\(594\) | 0.500000 | + | 0.866025i | 0.0205152 | + | 0.0355335i | ||||
\(595\) | −5.00000 | + | 8.66025i | −0.204980 | + | 0.355036i | ||||
\(596\) | 2.00000 | − | 3.46410i | 0.0819232 | − | 0.141895i | ||||
\(597\) | −17.0000 | −0.695764 | ||||||||
\(598\) | −20.0000 | + | 20.7846i | −0.817861 | + | 0.849946i | ||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 2.00000 | − | 3.46410i | 0.0816497 | − | 0.141421i | ||||
\(601\) | 5.00000 | − | 8.66025i | 0.203954 | − | 0.353259i | −0.745845 | − | 0.666120i | \(-0.767954\pi\) |
0.949799 | + | 0.312861i | \(0.101287\pi\) | |||||||
\(602\) | 4.00000 | + | 6.92820i | 0.163028 | + | 0.282372i | ||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 10.0000 | + | 17.3205i | 0.406894 | + | 0.704761i | ||||
\(605\) | 0.500000 | + | 0.866025i | 0.0203279 | + | 0.0352089i | ||||
\(606\) | −12.0000 | −0.487467 | ||||||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | 2.50000 | − | 4.33013i | 0.101388 | − | 0.175610i | ||||
\(609\) | 2.00000 | − | 3.46410i | 0.0810441 | − | 0.140372i | ||||
\(610\) | −11.0000 | −0.445377 | ||||||||
\(611\) | −2.00000 | − | 6.92820i | −0.0809113 | − | 0.280285i | ||||
\(612\) | 5.00000 | 0.202113 | ||||||||
\(613\) | −6.50000 | + | 11.2583i | −0.262533 | + | 0.454720i | −0.966914 | − | 0.255102i | \(-0.917891\pi\) |
0.704382 | + | 0.709821i | \(0.251224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.00000 | + | 1.73205i | 0.0403239 | + | 0.0698430i | ||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | −3.00000 | − | 5.19615i | −0.120775 | − | 0.209189i | 0.799298 | − | 0.600935i | \(-0.205205\pi\) |
−0.920074 | + | 0.391745i | \(0.871871\pi\) | |||||||
\(618\) | 2.00000 | + | 3.46410i | 0.0804518 | + | 0.139347i | ||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 1.50000 | + | 2.59808i | 0.0602414 | + | 0.104341i | ||||
\(621\) | −4.00000 | + | 6.92820i | −0.160514 | + | 0.278019i | ||||
\(622\) | −11.0000 | + | 19.0526i | −0.441060 | + | 0.763938i | ||||
\(623\) | −4.00000 | −0.160257 | ||||||||
\(624\) | 2.50000 | − | 2.59808i | 0.100080 | − | 0.104006i | ||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −7.50000 | + | 12.9904i | −0.299760 | + | 0.519200i | ||||
\(627\) | −2.50000 | + | 4.33013i | −0.0998404 | + | 0.172929i | ||||
\(628\) | −7.00000 | − | 12.1244i | −0.279330 | − | 0.483814i | ||||
\(629\) | 50.0000 | 1.99363 | ||||||||
\(630\) | 1.00000 | + | 1.73205i | 0.0398410 | + | 0.0690066i | ||||
\(631\) | 4.50000 | + | 7.79423i | 0.179142 | + | 0.310283i | 0.941587 | − | 0.336770i | \(-0.109334\pi\) |
−0.762445 | + | 0.647053i | \(0.776001\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | 1.50000 | + | 2.59808i | 0.0596196 | + | 0.103264i | ||||
\(634\) | 1.00000 | − | 1.73205i | 0.0397151 | − | 0.0687885i | ||||
\(635\) | 8.00000 | − | 13.8564i | 0.317470 | − | 0.549875i | ||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | −10.5000 | − | 2.59808i | −0.416025 | − | 0.102940i | ||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 15.0000 | + | 25.9808i | 0.592464 | + | 1.02618i | 0.993899 | + | 0.110291i | \(0.0351782\pi\) |
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(642\) | −4.00000 | −0.157867 | ||||||||
\(643\) | −4.00000 | − | 6.92820i | −0.157745 | − | 0.273222i | 0.776310 | − | 0.630351i | \(-0.217089\pi\) |
−0.934055 | + | 0.357129i | \(0.883756\pi\) | |||||||
\(644\) | −8.00000 | − | 13.8564i | −0.315244 | − | 0.546019i | ||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | 12.5000 | + | 21.6506i | 0.491806 | + | 0.851833i | ||||
\(647\) | 21.0000 | − | 36.3731i | 0.825595 | − | 1.42997i | −0.0758684 | − | 0.997118i | \(-0.524173\pi\) |
0.901464 | − | 0.432855i | \(-0.142494\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 1.00000 | 0.0392534 | ||||||||
\(650\) | 14.0000 | + | 3.46410i | 0.549125 | + | 0.135873i | ||||
\(651\) | 6.00000 | 0.235159 | ||||||||
\(652\) | 11.0000 | − | 19.0526i | 0.430793 | − | 0.746156i | ||||
\(653\) | −20.5000 | + | 35.5070i | −0.802227 | + | 1.38950i | 0.115920 | + | 0.993259i | \(0.463018\pi\) |
−0.918147 | + | 0.396239i | \(0.870315\pi\) | |||||||
\(654\) | −9.50000 | − | 16.4545i | −0.371479 | − | 0.643421i | ||||
\(655\) | −6.00000 | −0.234439 | ||||||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | −4.00000 | − | 6.92820i | −0.156055 | − | 0.270295i | ||||
\(658\) | 4.00000 | 0.155936 | ||||||||
\(659\) | −5.00000 | − | 8.66025i | −0.194772 | − | 0.337356i | 0.752054 | − | 0.659102i | \(-0.229063\pi\) |
−0.946826 | + | 0.321746i | \(0.895730\pi\) | |||||||
\(660\) | 0.500000 | − | 0.866025i | 0.0194625 | − | 0.0337100i | ||||
\(661\) | 19.0000 | − | 32.9090i | 0.739014 | − | 1.28001i | −0.213925 | − | 0.976850i | \(-0.568625\pi\) |
0.952940 | − | 0.303160i | \(-0.0980418\pi\) | |||||||
\(662\) | 14.0000 | 0.544125 | ||||||||
\(663\) | 5.00000 | + | 17.3205i | 0.194184 | + | 0.672673i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | −5.00000 | + | 8.66025i | −0.193892 | + | 0.335830i | ||||
\(666\) | 5.00000 | − | 8.66025i | 0.193746 | − | 0.335578i | ||||
\(667\) | −8.00000 | − | 13.8564i | −0.309761 | − | 0.536522i | ||||
\(668\) | −11.0000 | −0.425603 | ||||||||
\(669\) | 2.50000 | + | 4.33013i | 0.0966556 | + | 0.167412i | ||||
\(670\) | −1.00000 | − | 1.73205i | −0.0386334 | − | 0.0669150i | ||||
\(671\) | 11.0000 | 0.424650 | ||||||||
\(672\) | 1.00000 | + | 1.73205i | 0.0385758 | + | 0.0668153i | ||||
\(673\) | 10.0000 | − | 17.3205i | 0.385472 | − | 0.667657i | −0.606363 | − | 0.795188i | \(-0.707372\pi\) |
0.991835 | + | 0.127532i | \(0.0407054\pi\) | |||||||
\(674\) | −1.00000 | + | 1.73205i | −0.0385186 | + | 0.0667161i | ||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 11.5000 | + | 6.06218i | 0.442308 | + | 0.233161i | ||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | −2.00000 | + | 3.46410i | −0.0768095 | + | 0.133038i | ||||
\(679\) | 5.00000 | − | 8.66025i | 0.191882 | − | 0.332350i | ||||
\(680\) | −2.50000 | − | 4.33013i | −0.0958706 | − | 0.166053i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.50000 | − | 2.59808i | −0.0574380 | − | 0.0994855i | ||||
\(683\) | −22.0000 | − | 38.1051i | −0.841807 | − | 1.45805i | −0.888366 | − | 0.459136i | \(-0.848159\pi\) |
0.0465592 | − | 0.998916i | \(-0.485174\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 5.00000 | + | 8.66025i | 0.191040 | + | 0.330891i | ||||
\(686\) | 10.0000 | − | 17.3205i | 0.381802 | − | 0.661300i | ||||
\(687\) | 12.0000 | − | 20.7846i | 0.457829 | − | 0.792982i | ||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | 1.00000 | + | 3.46410i | 0.0380970 | + | 0.131972i | ||||
\(690\) | 8.00000 | 0.304555 | ||||||||
\(691\) | 15.0000 | − | 25.9808i | 0.570627 | − | 0.988355i | −0.425875 | − | 0.904782i | \(-0.640034\pi\) |
0.996502 | − | 0.0835727i | \(-0.0266331\pi\) | |||||||
\(692\) | 4.00000 | − | 6.92820i | 0.152057 | − | 0.263371i | ||||
\(693\) | −1.00000 | − | 1.73205i | −0.0379869 | − | 0.0657952i | ||||
\(694\) | −6.00000 | −0.227757 | ||||||||
\(695\) | 4.50000 | + | 7.79423i | 0.170695 | + | 0.295652i | ||||
\(696\) | 1.00000 | + | 1.73205i | 0.0379049 | + | 0.0656532i | ||||
\(697\) | −10.0000 | −0.378777 | ||||||||
\(698\) | −14.5000 | − | 25.1147i | −0.548833 | − | 0.950607i | ||||
\(699\) | 14.5000 | − | 25.1147i | 0.548440 | − | 0.949927i | ||||
\(700\) | −4.00000 | + | 6.92820i | −0.151186 | + | 0.261861i | ||||
\(701\) | −22.0000 | −0.830929 | −0.415464 | − | 0.909610i | \(-0.636381\pi\) | ||||
−0.415464 | + | 0.909610i | \(0.636381\pi\) | |||||||
\(702\) | 3.50000 | + | 0.866025i | 0.132099 | + | 0.0326860i | ||||
\(703\) | 50.0000 | 1.88579 | ||||||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | −1.00000 | + | 1.73205i | −0.0376622 | + | 0.0652328i | ||||
\(706\) | 12.0000 | + | 20.7846i | 0.451626 | + | 0.782239i | ||||
\(707\) | 24.0000 | 0.902613 | ||||||||
\(708\) | −0.500000 | − | 0.866025i | −0.0187912 | − | 0.0325472i | ||||
\(709\) | 25.0000 | + | 43.3013i | 0.938895 | + | 1.62621i | 0.767537 | + | 0.641004i | \(0.221482\pi\) |
0.171358 | + | 0.985209i | \(0.445185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | + | 3.46410i | 0.0750059 | + | 0.129914i | ||||
\(712\) | 1.00000 | − | 1.73205i | 0.0374766 | − | 0.0649113i | ||||
\(713\) | 12.0000 | − | 20.7846i | 0.449404 | − | 0.778390i | ||||
\(714\) | −10.0000 | −0.374241 | ||||||||
\(715\) | 3.50000 | + | 0.866025i | 0.130893 | + | 0.0323875i | ||||
\(716\) | 15.0000 | 0.560576 | ||||||||
\(717\) | 7.50000 | − | 12.9904i | 0.280093 | − | 0.485135i | ||||
\(718\) | −11.5000 | + | 19.9186i | −0.429176 | + | 0.743355i | ||||
\(719\) | 16.0000 | + | 27.7128i | 0.596699 | + | 1.03351i | 0.993305 | + | 0.115524i | \(0.0368548\pi\) |
−0.396605 | + | 0.917989i | \(0.629812\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −4.00000 | − | 6.92820i | −0.148968 | − | 0.258020i | ||||
\(722\) | 3.00000 | + | 5.19615i | 0.111648 | + | 0.193381i | ||||
\(723\) | 28.0000 | 1.04133 | ||||||||
\(724\) | 1.00000 | + | 1.73205i | 0.0371647 | + | 0.0643712i | ||||
\(725\) | −4.00000 | + | 6.92820i | −0.148556 | + | 0.257307i | ||||
\(726\) | −0.500000 | + | 0.866025i | −0.0185567 | + | 0.0321412i | ||||
\(727\) | 16.0000 | 0.593407 | 0.296704 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296704 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(728\) | −5.00000 | + | 5.19615i | −0.185312 | + | 0.192582i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.00000 | + | 6.92820i | −0.148047 | + | 0.256424i | ||||
\(731\) | 10.0000 | − | 17.3205i | 0.369863 | − | 0.640622i | ||||
\(732\) | −5.50000 | − | 9.52628i | −0.203286 | − | 0.352101i | ||||
\(733\) | −1.00000 | −0.0369358 | −0.0184679 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184679 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(734\) | −4.50000 | − | 7.79423i | −0.166098 | − | 0.287690i | ||||
\(735\) | 1.50000 | + | 2.59808i | 0.0553283 | + | 0.0958315i | ||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | 1.00000 | + | 1.73205i | 0.0368355 | + | 0.0638009i | ||||
\(738\) | −1.00000 | + | 1.73205i | −0.0368105 | + | 0.0637577i | ||||
\(739\) | −8.00000 | + | 13.8564i | −0.294285 | + | 0.509716i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | −10.0000 | −0.367607 | ||||||||
\(741\) | 5.00000 | + | 17.3205i | 0.183680 | + | 0.636285i | ||||
\(742\) | −2.00000 | −0.0734223 | ||||||||
\(743\) | −4.50000 | + | 7.79423i | −0.165089 | + | 0.285943i | −0.936687 | − | 0.350168i | \(-0.886124\pi\) |
0.771598 | + | 0.636111i | \(0.219458\pi\) | |||||||
\(744\) | −1.50000 | + | 2.59808i | −0.0549927 | + | 0.0952501i | ||||
\(745\) | −2.00000 | − | 3.46410i | −0.0732743 | − | 0.126915i | ||||
\(746\) | −23.0000 | −0.842090 | ||||||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | 2.50000 | + | 4.33013i | 0.0914091 | + | 0.158325i | ||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | −4.50000 | − | 7.79423i | −0.164317 | − | 0.284605i | ||||
\(751\) | 4.50000 | − | 7.79423i | 0.164207 | − | 0.284415i | −0.772166 | − | 0.635421i | \(-0.780827\pi\) |
0.936374 | + | 0.351005i | \(0.114160\pi\) | |||||||
\(752\) | −1.00000 | + | 1.73205i | −0.0364662 | + | 0.0631614i | ||||
\(753\) | 24.0000 | 0.874609 | ||||||||
\(754\) | −5.00000 | + | 5.19615i | −0.182089 | + | 0.189233i | ||||
\(755\) | 20.0000 | 0.727875 | ||||||||
\(756\) | −1.00000 | + | 1.73205i | −0.0363696 | + | 0.0629941i | ||||
\(757\) | −12.0000 | + | 20.7846i | −0.436147 | + | 0.755429i | −0.997389 | − | 0.0722229i | \(-0.976991\pi\) |
0.561241 | + | 0.827652i | \(0.310324\pi\) | |||||||
\(758\) | −1.00000 | − | 1.73205i | −0.0363216 | − | 0.0629109i | ||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | −2.50000 | − | 4.33013i | −0.0906845 | − | 0.157070i | ||||
\(761\) | 21.5000 | + | 37.2391i | 0.779374 | + | 1.34992i | 0.932303 | + | 0.361679i | \(0.117796\pi\) |
−0.152928 | + | 0.988237i | \(0.548870\pi\) | |||||||
\(762\) | 16.0000 | 0.579619 | ||||||||
\(763\) | 19.0000 | + | 32.9090i | 0.687846 | + | 1.19138i | ||||
\(764\) | −9.00000 | + | 15.5885i | −0.325609 | + | 0.563971i | ||||
\(765\) | 2.50000 | − | 4.33013i | 0.0903877 | − | 0.156556i | ||||
\(766\) | 4.00000 | 0.144526 | ||||||||
\(767\) | 2.50000 | − | 2.59808i | 0.0902698 | − | 0.0938111i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 3.00000 | − | 5.19615i | 0.108183 | − | 0.187378i | −0.806851 | − | 0.590755i | \(-0.798830\pi\) |
0.915034 | + | 0.403376i | \(0.132163\pi\) | |||||||
\(770\) | −1.00000 | + | 1.73205i | −0.0360375 | + | 0.0624188i | ||||
\(771\) | 9.00000 | + | 15.5885i | 0.324127 | + | 0.561405i | ||||
\(772\) | 18.0000 | 0.647834 | ||||||||
\(773\) | 22.5000 | + | 38.9711i | 0.809269 | + | 1.40169i | 0.913371 | + | 0.407128i | \(0.133470\pi\) |
−0.104102 | + | 0.994567i | \(0.533197\pi\) | |||||||
\(774\) | −2.00000 | − | 3.46410i | −0.0718885 | − | 0.124515i | ||||
\(775\) | −12.0000 | −0.431053 | ||||||||
\(776\) | 2.50000 | + | 4.33013i | 0.0897448 | + | 0.155443i | ||||
\(777\) | −10.0000 | + | 17.3205i | −0.358748 | + | 0.621370i | ||||
\(778\) | −15.0000 | + | 25.9808i | −0.537776 | + | 0.931455i | ||||
\(779\) | −10.0000 | −0.358287 | ||||||||
\(780\) | −1.00000 | − | 3.46410i | −0.0358057 | − | 0.124035i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −20.0000 | + | 34.6410i | −0.715199 | + | 1.23876i | ||||
\(783\) | −1.00000 | + | 1.73205i | −0.0357371 | + | 0.0618984i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | −3.00000 | − | 5.19615i | −0.107006 | − | 0.185341i | ||||
\(787\) | 12.0000 | + | 20.7846i | 0.427754 | + | 0.740891i | 0.996673 | − | 0.0815020i | \(-0.0259717\pi\) |
−0.568919 | + | 0.822393i | \(0.692638\pi\) | |||||||
\(788\) | −22.0000 | −0.783718 | ||||||||
\(789\) | −10.5000 | − | 18.1865i | −0.373810 | − | 0.647458i | ||||
\(790\) | 2.00000 | − | 3.46410i | 0.0711568 | − | 0.123247i | ||||
\(791\) | 4.00000 | − | 6.92820i | 0.142224 | − | 0.246339i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 27.5000 | − | 28.5788i | 0.976554 | − | 1.01486i | ||||
\(794\) | 18.0000 | 0.638796 | ||||||||
\(795\) | 0.500000 | − | 0.866025i | 0.0177332 | − | 0.0307148i | ||||
\(796\) | −8.50000 | + | 14.7224i | −0.301275 | + | 0.521823i | ||||
\(797\) | −23.5000 | − | 40.7032i | −0.832413 | − | 1.44178i | −0.896120 | − | 0.443812i | \(-0.853626\pi\) |
0.0637070 | − | 0.997969i | \(-0.479708\pi\) | |||||||
\(798\) | −10.0000 | −0.353996 | ||||||||
\(799\) | −5.00000 | − | 8.66025i | −0.176887 | − | 0.306378i | ||||
\(800\) | −2.00000 | − | 3.46410i | −0.0707107 | − | 0.122474i | ||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | −3.00000 | − | 5.19615i | −0.105934 | − | 0.183483i | ||||
\(803\) | 4.00000 | − | 6.92820i | 0.141157 | − | 0.244491i | ||||
\(804\) | 1.00000 | − | 1.73205i | 0.0352673 | − | 0.0610847i | ||||
\(805\) | −16.0000 | −0.563926 | ||||||||
\(806\) | −10.5000 | − | 2.59808i | −0.369847 | − | 0.0915133i | ||||
\(807\) | 21.0000 | 0.739235 | ||||||||
\(808\) | −6.00000 | + | 10.3923i | −0.211079 | + | 0.365600i | ||||
\(809\) | 25.5000 | − | 44.1673i | 0.896532 | − | 1.55284i | 0.0646355 | − | 0.997909i | \(-0.479412\pi\) |
0.831897 | − | 0.554930i | \(-0.187255\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 27.0000 | 0.948098 | 0.474049 | − | 0.880498i | \(-0.342792\pi\) | ||||
0.474049 | + | 0.880498i | \(0.342792\pi\) | |||||||
\(812\) | −2.00000 | − | 3.46410i | −0.0701862 | − | 0.121566i | ||||
\(813\) | −10.0000 | − | 17.3205i | −0.350715 | − | 0.607457i | ||||
\(814\) | 10.0000 | 0.350500 | ||||||||
\(815\) | −11.0000 | − | 19.0526i | −0.385313 | − | 0.667382i | ||||
\(816\) | 2.50000 | − | 4.33013i | 0.0875175 | − | 0.151585i | ||||
\(817\) | 10.0000 | − | 17.3205i | 0.349856 | − | 0.605968i | ||||
\(818\) | −30.0000 | −1.04893 | ||||||||
\(819\) | −7.00000 | − | 1.73205i | −0.244600 | − | 0.0605228i | ||||
\(820\) | 2.00000 | 0.0698430 | ||||||||
\(821\) | 15.0000 | − | 25.9808i | 0.523504 | − | 0.906735i | −0.476122 | − | 0.879379i | \(-0.657958\pi\) |
0.999626 | − | 0.0273557i | \(-0.00870868\pi\) | |||||||
\(822\) | −5.00000 | + | 8.66025i | −0.174395 | + | 0.302061i | ||||
\(823\) | 11.5000 | + | 19.9186i | 0.400865 | + | 0.694318i | 0.993831 | − | 0.110910i | \(-0.0353764\pi\) |
−0.592966 | + | 0.805228i | \(0.702043\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | 2.00000 | + | 3.46410i | 0.0696311 | + | 0.120605i | ||||
\(826\) | 1.00000 | + | 1.73205i | 0.0347945 | + | 0.0602658i | ||||
\(827\) | −22.0000 | −0.765015 | −0.382507 | − | 0.923952i | \(-0.624939\pi\) | ||||
−0.382507 | + | 0.923952i | \(0.624939\pi\) | |||||||
\(828\) | 4.00000 | + | 6.92820i | 0.139010 | + | 0.240772i | ||||
\(829\) | 14.0000 | − | 24.2487i | 0.486240 | − | 0.842193i | −0.513635 | − | 0.858009i | \(-0.671701\pi\) |
0.999875 | + | 0.0158163i | \(0.00503471\pi\) | |||||||
\(830\) | −3.00000 | + | 5.19615i | −0.104132 | + | 0.180361i | ||||
\(831\) | −17.0000 | −0.589723 | ||||||||
\(832\) | −1.00000 | − | 3.46410i | −0.0346688 | − | 0.120096i | ||||
\(833\) | −15.0000 | −0.519719 | ||||||||
\(834\) | −4.50000 | + | 7.79423i | −0.155822 | + | 0.269892i | ||||
\(835\) | −5.50000 | + | 9.52628i | −0.190335 | + | 0.329670i | ||||
\(836\) | 2.50000 | + | 4.33013i | 0.0864643 | + | 0.149761i | ||||
\(837\) | −3.00000 | −0.103695 | ||||||||
\(838\) | −2.00000 | − | 3.46410i | −0.0690889 | − | 0.119665i | ||||
\(839\) | 20.0000 | + | 34.6410i | 0.690477 | + | 1.19594i | 0.971682 | + | 0.236293i | \(0.0759325\pi\) |
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(840\) | 2.00000 | 0.0690066 | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | 13.0000 | − | 22.5167i | 0.448010 | − | 0.775975i | ||||
\(843\) | −1.50000 | + | 2.59808i | −0.0516627 | + | 0.0894825i | ||||
\(844\) | 3.00000 | 0.103264 | ||||||||
\(845\) | 11.0000 | − | 6.92820i | 0.378412 | − | 0.238337i | ||||
\(846\) | −2.00000 | −0.0687614 | ||||||||
\(847\) | 1.00000 | − | 1.73205i | 0.0343604 | − | 0.0595140i | ||||
\(848\) | 0.500000 | − | 0.866025i | 0.0171701 | − | 0.0297394i | ||||
\(849\) | −4.50000 | − | 7.79423i | −0.154440 | − | 0.267497i | ||||
\(850\) | 20.0000 | 0.685994 | ||||||||
\(851\) | 40.0000 | + | 69.2820i | 1.37118 | + | 2.37496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.0000 | 1.67773 | 0.838864 | − | 0.544341i | \(-0.183220\pi\) | ||||
0.838864 | + | 0.544341i | \(0.183220\pi\) | |||||||
\(854\) | 11.0000 | + | 19.0526i | 0.376412 | + | 0.651965i | ||||
\(855\) | 2.50000 | − | 4.33013i | 0.0854982 | − | 0.148087i | ||||
\(856\) | −2.00000 | + | 3.46410i | −0.0683586 | + | 0.118401i | ||||
\(857\) | −11.0000 | −0.375753 | −0.187876 | − | 0.982193i | \(-0.560160\pi\) | ||||
−0.187876 | + | 0.982193i | \(0.560160\pi\) | |||||||
\(858\) | 1.00000 | + | 3.46410i | 0.0341394 | + | 0.118262i | ||||
\(859\) | −50.0000 | −1.70598 | −0.852989 | − | 0.521929i | \(-0.825213\pi\) | ||||
−0.852989 | + | 0.521929i | \(0.825213\pi\) | |||||||
\(860\) | −2.00000 | + | 3.46410i | −0.0681994 | + | 0.118125i | ||||
\(861\) | 2.00000 | − | 3.46410i | 0.0681598 | − | 0.118056i | ||||
\(862\) | −18.5000 | − | 32.0429i | −0.630113 | − | 1.09139i | ||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −4.00000 | − | 6.92820i | −0.136004 | − | 0.235566i | ||||
\(866\) | 21.0000 | 0.713609 | ||||||||
\(867\) | 4.00000 | + | 6.92820i | 0.135847 | + | 0.235294i | ||||
\(868\) | 3.00000 | − | 5.19615i | 0.101827 | − | 0.176369i | ||||
\(869\) | −2.00000 | + | 3.46410i | −0.0678454 | + | 0.117512i | ||||
\(870\) | 2.00000 | 0.0678064 | ||||||||
\(871\) | 7.00000 | + | 1.73205i | 0.237186 | + | 0.0586883i | ||||
\(872\) | −19.0000 | −0.643421 | ||||||||
\(873\) | −2.50000 | + | 4.33013i | −0.0846122 | + | 0.146553i | ||||
\(874\) | −20.0000 | + | 34.6410i | −0.676510 | + | 1.17175i | ||||
\(875\) | 9.00000 | + | 15.5885i | 0.304256 | + | 0.526986i | ||||
\(876\) | −8.00000 | −0.270295 | ||||||||
\(877\) | −1.00000 | − | 1.73205i | −0.0337676 | − | 0.0584872i | 0.848648 | − | 0.528958i | \(-0.177417\pi\) |
−0.882415 | + | 0.470471i | \(0.844084\pi\) | |||||||
\(878\) | 12.0000 | + | 20.7846i | 0.404980 | + | 0.701447i | ||||
\(879\) | 22.0000 | 0.742042 | ||||||||
\(880\) | −0.500000 | − | 0.866025i | −0.0168550 | − | 0.0291937i | ||||
\(881\) | 9.00000 | − | 15.5885i | 0.303218 | − | 0.525188i | −0.673645 | − | 0.739055i | \(-0.735272\pi\) |
0.976863 | + | 0.213866i | \(0.0686057\pi\) | |||||||
\(882\) | −1.50000 | + | 2.59808i | −0.0505076 | + | 0.0874818i | ||||
\(883\) | −8.00000 | −0.269221 | −0.134611 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134611 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(884\) | 17.5000 | + | 4.33013i | 0.588589 | + | 0.145638i | ||||
\(885\) | −1.00000 | −0.0336146 | ||||||||
\(886\) | −14.5000 | + | 25.1147i | −0.487137 | + | 0.843746i | ||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | −5.00000 | − | 8.66025i | −0.167789 | − | 0.290619i | ||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | −1.00000 | − | 1.73205i | −0.0335201 | − | 0.0580585i | ||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 5.00000 | 0.167412 | ||||||||
\(893\) | −5.00000 | − | 8.66025i | −0.167319 | − | 0.289804i | ||||
\(894\) | 2.00000 | − | 3.46410i | 0.0668900 | − | 0.115857i | ||||
\(895\) | 7.50000 | − | 12.9904i | 0.250697 | − | 0.434221i | ||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | −20.0000 | + | 20.7846i | −0.667781 | + | 0.693978i | ||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 2.00000 | − | 3.46410i | 0.0666667 | − | 0.115470i | ||||
\(901\) | 2.50000 | + | 4.33013i | 0.0832871 | + | 0.144257i | ||||
\(902\) | −2.00000 | −0.0665927 | ||||||||
\(903\) | 4.00000 | + | 6.92820i | 0.133112 | + | 0.230556i | ||||
\(904\) | 2.00000 | + | 3.46410i | 0.0665190 | + | 0.115214i | ||||
\(905\) | 2.00000 | 0.0664822 | ||||||||
\(906\) | 10.0000 | + | 17.3205i | 0.332228 | + | 0.575435i | ||||
\(907\) | 1.00000 | − | 1.73205i | 0.0332045 | − | 0.0575118i | −0.848946 | − | 0.528480i | \(-0.822762\pi\) |
0.882150 | + | 0.470968i | \(0.156095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 2.00000 | + | 6.92820i | 0.0662994 | + | 0.229668i | ||||
\(911\) | 10.0000 | 0.331315 | 0.165657 | − | 0.986183i | \(-0.447025\pi\) | ||||
0.165657 | + | 0.986183i | \(0.447025\pi\) | |||||||
\(912\) | 2.50000 | − | 4.33013i | 0.0827833 | − | 0.143385i | ||||
\(913\) | 3.00000 | − | 5.19615i | 0.0992855 | − | 0.171968i | ||||
\(914\) | −2.00000 | − | 3.46410i | −0.0661541 | − | 0.114582i | ||||
\(915\) | −11.0000 | −0.363649 | ||||||||
\(916\) | −12.0000 | − | 20.7846i | −0.396491 | − | 0.686743i | ||||
\(917\) | 6.00000 | + | 10.3923i | 0.198137 | + | 0.343184i | ||||
\(918\) | 5.00000 | 0.165025 | ||||||||
\(919\) | 22.0000 | + | 38.1051i | 0.725713 | + | 1.25697i | 0.958680 | + | 0.284487i | \(0.0918233\pi\) |
−0.232967 | + | 0.972485i | \(0.574843\pi\) | |||||||
\(920\) | 4.00000 | − | 6.92820i | 0.131876 | − | 0.228416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.0000 | −0.329332 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 20.0000 | − | 34.6410i | 0.657596 | − | 1.13899i | ||||
\(926\) | −10.5000 | + | 18.1865i | −0.345051 | + | 0.597647i | ||||
\(927\) | 2.00000 | + | 3.46410i | 0.0656886 | + | 0.113776i | ||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 1.50000 | + | 2.59808i | 0.0491869 | + | 0.0851943i | ||||
\(931\) | −15.0000 | −0.491605 | ||||||||
\(932\) | −14.5000 | − | 25.1147i | −0.474963 | − | 0.822661i | ||||
\(933\) | −11.0000 | + | 19.0526i | −0.360124 | + | 0.623753i | ||||
\(934\) | −14.5000 | + | 25.1147i | −0.474454 | + | 0.821779i | ||||
\(935\) | 5.00000 | 0.163517 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | 6.00000 | 0.196011 | 0.0980057 | − | 0.995186i | \(-0.468754\pi\) | ||||
0.0980057 | + | 0.995186i | \(0.468754\pi\) | |||||||
\(938\) | −2.00000 | + | 3.46410i | −0.0653023 | + | 0.113107i | ||||
\(939\) | −7.50000 | + | 12.9904i | −0.244753 | + | 0.423925i | ||||
\(940\) | 1.00000 | + | 1.73205i | 0.0326164 | + | 0.0564933i | ||||
\(941\) | 48.0000 | 1.56476 | 0.782378 | − | 0.622804i | \(-0.214007\pi\) | ||||
0.782378 | + | 0.622804i | \(0.214007\pi\) | |||||||
\(942\) | −7.00000 | − | 12.1244i | −0.228072 | − | 0.395033i | ||||
\(943\) | −8.00000 | − | 13.8564i | −0.260516 | − | 0.451227i | ||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 1.00000 | + | 1.73205i | 0.0325300 | + | 0.0563436i | ||||
\(946\) | 2.00000 | − | 3.46410i | 0.0650256 | − | 0.112628i | ||||
\(947\) | −28.5000 | + | 49.3634i | −0.926126 | + | 1.60410i | −0.136385 | + | 0.990656i | \(0.543548\pi\) |
−0.789741 | + | 0.613441i | \(0.789785\pi\) | |||||||
\(948\) | 4.00000 | 0.129914 | ||||||||
\(949\) | −8.00000 | − | 27.7128i | −0.259691 | − | 0.899596i | ||||
\(950\) | 20.0000 | 0.648886 | ||||||||
\(951\) | 1.00000 | − | 1.73205i | 0.0324272 | − | 0.0561656i | ||||
\(952\) | −5.00000 | + | 8.66025i | −0.162051 | + | 0.280680i | ||||
\(953\) | 15.0000 | + | 25.9808i | 0.485898 | + | 0.841599i | 0.999869 | − | 0.0162081i | \(-0.00515944\pi\) |
−0.513971 | + | 0.857808i | \(0.671826\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | −2.00000 | −0.0646508 | ||||||||
\(958\) | −1.50000 | − | 2.59808i | −0.0484628 | − | 0.0839400i | ||||
\(959\) | 10.0000 | − | 17.3205i | 0.322917 | − | 0.559308i | ||||
\(960\) | −0.500000 | + | 0.866025i | −0.0161374 | + | 0.0279508i | ||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 25.0000 | − | 25.9808i | 0.806032 | − | 0.837653i | ||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | 14.0000 | − | 24.2487i | 0.450910 | − | 0.780998i | ||||
\(965\) | 9.00000 | − | 15.5885i | 0.289720 | − | 0.501810i | ||||
\(966\) | −8.00000 | − | 13.8564i | −0.257396 | − | 0.445823i | ||||
\(967\) | −50.0000 | −1.60789 | −0.803946 | − | 0.594703i | \(-0.797270\pi\) | ||||
−0.803946 | + | 0.594703i | \(0.797270\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 12.5000 | + | 21.6506i | 0.401558 | + | 0.695519i | ||||
\(970\) | 5.00000 | 0.160540 | ||||||||
\(971\) | 21.5000 | + | 37.2391i | 0.689968 | + | 1.19506i | 0.971848 | + | 0.235610i | \(0.0757087\pi\) |
−0.281880 | + | 0.959450i | \(0.590958\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 9.00000 | − | 15.5885i | 0.288527 | − | 0.499743i | ||||
\(974\) | −16.0000 | −0.512673 | ||||||||
\(975\) | 14.0000 | + | 3.46410i | 0.448359 | + | 0.110940i | ||||
\(976\) | −11.0000 | −0.352101 | ||||||||
\(977\) | −21.0000 | + | 36.3731i | −0.671850 | + | 1.16368i | 0.305530 | + | 0.952183i | \(0.401167\pi\) |
−0.977379 | + | 0.211495i | \(0.932167\pi\) | |||||||
\(978\) | 11.0000 | − | 19.0526i | 0.351741 | − | 0.609234i | ||||
\(979\) | 1.00000 | + | 1.73205i | 0.0319601 | + | 0.0553566i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | −9.50000 | − | 16.4545i | −0.303312 | − | 0.525351i | ||||
\(982\) | −15.0000 | − | 25.9808i | −0.478669 | − | 0.829079i | ||||
\(983\) | −10.0000 | −0.318950 | −0.159475 | − | 0.987202i | \(-0.550980\pi\) | ||||
−0.159475 | + | 0.987202i | \(0.550980\pi\) | |||||||
\(984\) | 1.00000 | + | 1.73205i | 0.0318788 | + | 0.0552158i | ||||
\(985\) | −11.0000 | + | 19.0526i | −0.350489 | + | 0.607065i | ||||
\(986\) | −5.00000 | + | 8.66025i | −0.159232 | + | 0.275799i | ||||
\(987\) | 4.00000 | 0.127321 | ||||||||
\(988\) | 17.5000 | + | 4.33013i | 0.556749 | + | 0.137760i | ||||
\(989\) | 32.0000 | 1.01754 | ||||||||
\(990\) | 0.500000 | − | 0.866025i | 0.0158910 | − | 0.0275241i | ||||
\(991\) | 26.0000 | − | 45.0333i | 0.825917 | − | 1.43053i | −0.0752991 | − | 0.997161i | \(-0.523991\pi\) |
0.901216 | − | 0.433370i | \(-0.142676\pi\) | |||||||
\(992\) | 1.50000 | + | 2.59808i | 0.0476250 | + | 0.0824890i | ||||
\(993\) | 14.0000 | 0.444277 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.50000 | + | 14.7224i | 0.269468 | + | 0.466732i | ||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | 4.50000 | + | 7.79423i | 0.142516 | + | 0.246846i | 0.928444 | − | 0.371473i | \(-0.121147\pi\) |
−0.785927 | + | 0.618319i | \(0.787814\pi\) | |||||||
\(998\) | −7.00000 | + | 12.1244i | −0.221581 | + | 0.383790i | ||||
\(999\) | 5.00000 | − | 8.66025i | 0.158193 | − | 0.273998i |
(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 | 858.2.i.g.529.1 | yes | 2 | |
13.3 | even | 3 | inner | 858.2.i.g.133.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
858.2.i.g.133.1 | ✓ | 2 | 13.3 | even | 3 | inner | |
858.2.i.g.529.1 | yes | 2 | 1.1 | even | 1 | trivial |