Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.2.j.a.149.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 1.73205 | + | 1.00000i | 1.00000 | + | 0.577350i | 0.908248 | − | 0.418432i | \(-0.137420\pi\) |
0.0917517 | + | 0.995782i | \(0.470753\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 1.73205 | − | 1.00000i | 0.500000 | − | 0.288675i | ||||
\(13\) | 5.00000i | 1.38675i | 0.720577 | + | 0.693375i | \(0.243877\pi\) | ||||
−0.720577 | + | 0.693375i | \(0.756123\pi\) | |||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 5.19615 | + | 3.00000i | 1.26025 | + | 0.727607i | 0.973123 | − | 0.230285i | \(-0.0739659\pi\) |
0.287129 | + | 0.957892i | \(0.407299\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.00000 | + | 1.73205i | −1.09109 | + | 0.377964i | ||||
\(22\) | − | 3.00000i | − | 0.639602i | ||||||
\(23\) | 2.59808 | − | 1.50000i | 0.541736 | − | 0.312772i | −0.204046 | − | 0.978961i | \(-0.565409\pi\) |
0.745782 | + | 0.666190i | \(0.232076\pi\) | |||||||
\(24\) | −1.00000 | + | 1.73205i | −0.204124 | + | 0.353553i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.50000 | − | 4.33013i | −0.490290 | − | 0.849208i | ||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 0.866025 | + | 2.50000i | 0.163663 | + | 0.472456i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −5.19615 | + | 3.00000i | −0.904534 | + | 0.522233i | ||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.52628 | + | 5.50000i | −1.56611 | + | 0.904194i | −0.569495 | + | 0.821995i | \(0.692861\pi\) |
−0.996616 | + | 0.0821995i | \(0.973806\pi\) | |||||||
\(38\) | 0.866025 | + | 0.500000i | 0.140488 | + | 0.0811107i | ||||
\(39\) | −5.00000 | + | 8.66025i | −0.800641 | + | 1.38675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 3.46410 | − | 4.00000i | 0.534522 | − | 0.617213i | ||||
\(43\) | − | 10.0000i | − | 1.52499i | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||
0.646997 | − | 0.762493i | \(-0.276025\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | −2.59808 | + | 1.50000i | −0.378968 | + | 0.218797i | −0.677369 | − | 0.735643i | \(-0.736880\pi\) |
0.298401 | + | 0.954441i | \(0.403547\pi\) | |||||||
\(48\) | − | 2.00000i | − | 0.288675i | ||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | + | 10.3923i | 0.840168 | + | 1.45521i | ||||
\(52\) | 4.33013 | + | 2.50000i | 0.600481 | + | 0.346688i | ||||
\(53\) | −2.59808 | − | 1.50000i | −0.356873 | − | 0.206041i | 0.310835 | − | 0.950464i | \(-0.399391\pi\) |
−0.667708 | + | 0.744423i | \(0.732725\pi\) | |||||||
\(54\) | 2.00000 | + | 3.46410i | 0.272166 | + | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | −5.19615 | + | 3.00000i | −0.682288 | + | 0.393919i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | 4.00000i | 0.508001i | ||||||||
\(63\) | −2.59808 | − | 0.500000i | −0.327327 | − | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | ||||
\(67\) | −3.46410 | − | 2.00000i | −0.423207 | − | 0.244339i | 0.273241 | − | 0.961946i | \(-0.411904\pi\) |
−0.696449 | + | 0.717607i | \(0.745238\pi\) | |||||||
\(68\) | 5.19615 | − | 3.00000i | 0.630126 | − | 0.363803i | ||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 3.46410 | + | 2.00000i | 0.405442 | + | 0.234082i | 0.688830 | − | 0.724923i | \(-0.258125\pi\) |
−0.283387 | + | 0.959006i | \(0.591458\pi\) | |||||||
\(74\) | 5.50000 | − | 9.52628i | 0.639362 | − | 1.10741i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −2.59808 | − | 7.50000i | −0.296078 | − | 0.854704i | ||||
\(78\) | − | 10.0000i | − | 1.13228i | ||||||
\(79\) | −5.00000 | − | 8.66025i | −0.562544 | − | 0.974355i | −0.997274 | − | 0.0737937i | \(-0.976489\pi\) |
0.434730 | − | 0.900561i | \(-0.356844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | −2.59808 | + | 1.50000i | −0.286910 | + | 0.165647i | ||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | −1.00000 | + | 5.19615i | −0.109109 | + | 0.566947i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.00000 | + | 8.66025i | 0.539164 | + | 0.933859i | ||||
\(87\) | 10.3923 | + | 6.00000i | 1.11417 | + | 0.643268i | ||||
\(88\) | −2.59808 | − | 1.50000i | −0.276956 | − | 0.159901i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 8.66025i | −1.04828 | − | 0.907841i | ||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | 6.92820 | − | 4.00000i | 0.718421 | − | 0.414781i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | + | 1.73205i | 0.102062 | + | 0.176777i | ||||
\(97\) | − | 14.0000i | − | 1.42148i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) | ||
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | 4.33013 | + | 5.50000i | 0.437409 | + | 0.555584i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | − | 10.3923i | 0.597022 | − | 1.03407i | −0.396236 | − | 0.918149i | \(-0.629684\pi\) |
0.993258 | − | 0.115924i | \(-0.0369830\pi\) | |||||||
\(102\) | −10.3923 | − | 6.00000i | −1.02899 | − | 0.594089i | ||||
\(103\) | −3.46410 | + | 2.00000i | −0.341328 | + | 0.197066i | −0.660859 | − | 0.750510i | \(-0.729808\pi\) |
0.319531 | + | 0.947576i | \(0.396475\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 10.3923 | − | 6.00000i | 1.00466 | − | 0.580042i | 0.0950377 | − | 0.995474i | \(-0.469703\pi\) |
0.909624 | + | 0.415432i | \(0.136370\pi\) | |||||||
\(108\) | −3.46410 | − | 2.00000i | −0.333333 | − | 0.192450i | ||||
\(109\) | −2.00000 | + | 3.46410i | −0.191565 | + | 0.331801i | −0.945769 | − | 0.324840i | \(-0.894690\pi\) |
0.754204 | + | 0.656640i | \(0.228023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.0000 | −2.08815 | ||||||||
\(112\) | 2.59808 | + | 0.500000i | 0.245495 | + | 0.0472456i | ||||
\(113\) | 12.0000i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(114\) | 1.00000 | + | 1.73205i | 0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | −4.33013 | + | 2.50000i | −0.400320 | + | 0.231125i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.0000 | + | 5.19615i | −1.37505 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −3.46410 | − | 2.00000i | −0.313625 | − | 0.181071i | ||||
\(123\) | 5.19615 | + | 3.00000i | 0.468521 | + | 0.270501i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.50000 | − | 0.866025i | 0.222718 | − | 0.0771517i | ||||
\(127\) | 19.0000i | 1.68598i | 0.537931 | + | 0.842989i | \(0.319206\pi\) | ||||
−0.537931 | + | 0.842989i | \(0.680794\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 10.0000 | − | 17.3205i | 0.880451 | − | 1.52499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | \(-0.208503\pi\) |
−0.924084 | + | 0.382190i | \(0.875170\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | 2.59808 | + | 0.500000i | 0.225282 | + | 0.0433555i | ||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | 10.3923 | + | 6.00000i | 0.887875 | + | 0.512615i | 0.873247 | − | 0.487278i | \(-0.162010\pi\) |
0.0146279 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(138\) | −5.19615 | + | 3.00000i | −0.442326 | + | 0.255377i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | −10.3923 | + | 6.00000i | −0.872103 | + | 0.503509i | ||||
\(143\) | −12.9904 | − | 7.50000i | −1.08631 | − | 0.627182i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 5.19615 | − | 13.0000i | 0.428571 | − | 1.07222i | ||||
\(148\) | 11.0000i | 0.904194i | ||||||||
\(149\) | 9.00000 | + | 15.5885i | 0.737309 | + | 1.27706i | 0.953703 | + | 0.300750i | \(0.0972370\pi\) |
−0.216394 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.00000 | + | 12.1244i | −0.569652 | + | 0.986666i | 0.426948 | + | 0.904276i | \(0.359589\pi\) |
−0.996600 | + | 0.0823900i | \(0.973745\pi\) | |||||||
\(152\) | 0.866025 | − | 0.500000i | 0.0702439 | − | 0.0405554i | ||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | 6.00000 | + | 5.19615i | 0.483494 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.00000 | + | 8.66025i | 0.400320 | + | 0.693375i | ||||
\(157\) | 4.33013 | + | 2.50000i | 0.345582 | + | 0.199522i | 0.662738 | − | 0.748852i | \(-0.269394\pi\) |
−0.317156 | + | 0.948373i | \(0.602728\pi\) | |||||||
\(158\) | 8.66025 | + | 5.00000i | 0.688973 | + | 0.397779i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50000 | + | 7.79423i | −0.118217 | + | 0.614271i | ||||
\(162\) | 11.0000i | 0.864242i | ||||||||
\(163\) | −3.46410 | + | 2.00000i | −0.271329 | + | 0.156652i | −0.629492 | − | 0.777007i | \(-0.716737\pi\) |
0.358162 | + | 0.933659i | \(0.383403\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | − | 9.00000i | − | 0.696441i | −0.937413 | − | 0.348220i | \(-0.886786\pi\) | ||
0.937413 | − | 0.348220i | \(-0.113214\pi\) | |||||||
\(168\) | −1.73205 | − | 5.00000i | −0.133631 | − | 0.385758i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | − | 0.866025i | 0.0382360 | − | 0.0662266i | ||||
\(172\) | −8.66025 | − | 5.00000i | −0.660338 | − | 0.381246i | ||||
\(173\) | 2.59808 | − | 1.50000i | 0.197528 | − | 0.114043i | −0.397974 | − | 0.917397i | \(-0.630287\pi\) |
0.595502 | + | 0.803354i | \(0.296953\pi\) | |||||||
\(174\) | −12.0000 | −0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.19615 | − | 3.00000i | −0.389468 | − | 0.224860i | ||||
\(179\) | −1.50000 | + | 2.59808i | −0.112115 | + | 0.194189i | −0.916623 | − | 0.399753i | \(-0.869096\pi\) |
0.804508 | + | 0.593942i | \(0.202429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 12.9904 | + | 2.50000i | 0.962911 | + | 0.185312i | ||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.00000 | + | 6.92820i | −0.293294 | + | 0.508001i | ||||
\(187\) | −15.5885 | + | 9.00000i | −1.13994 | + | 0.658145i | ||||
\(188\) | 3.00000i | 0.218797i | ||||||||
\(189\) | 8.00000 | + | 6.92820i | 0.581914 | + | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | −1.73205 | − | 1.00000i | −0.125000 | − | 0.0721688i | ||||
\(193\) | 3.46410 | + | 2.00000i | 0.249351 | + | 0.143963i | 0.619467 | − | 0.785022i | \(-0.287349\pi\) |
−0.370116 | + | 0.928986i | \(0.620682\pi\) | |||||||
\(194\) | 7.00000 | + | 12.1244i | 0.502571 | + | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 3.00000i | 0.213741i | 0.994273 | + | 0.106871i | \(0.0340831\pi\) | ||||
−0.994273 | + | 0.106871i | \(0.965917\pi\) | |||||||
\(198\) | 2.59808 | − | 1.50000i | 0.184637 | − | 0.106600i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | − | 6.92820i | −0.282138 | − | 0.488678i | ||||
\(202\) | 12.0000i | 0.844317i | ||||||||
\(203\) | −10.3923 | + | 12.0000i | −0.729397 | + | 0.842235i | ||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.00000 | − | 3.46410i | 0.139347 | − | 0.241355i | ||||
\(207\) | 2.59808 | + | 1.50000i | 0.180579 | + | 0.104257i | ||||
\(208\) | 4.33013 | − | 2.50000i | 0.300240 | − | 0.173344i | ||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | −0.0688428 | −0.0344214 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344214 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(212\) | −2.59808 | + | 1.50000i | −0.178437 | + | 0.103020i | ||||
\(213\) | 20.7846 | + | 12.0000i | 1.42414 | + | 0.822226i | ||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 3.46410 | + | 10.0000i | 0.235159 | + | 0.678844i | ||||
\(218\) | − | 4.00000i | − | 0.270914i | ||||||
\(219\) | 4.00000 | + | 6.92820i | 0.270295 | + | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | + | 25.9808i | −1.00901 | + | 1.74766i | ||||
\(222\) | 19.0526 | − | 11.0000i | 1.27872 | − | 0.738272i | ||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | −2.50000 | + | 0.866025i | −0.167038 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | − | 10.3923i | −0.399114 | − | 0.691286i | ||||
\(227\) | −20.7846 | − | 12.0000i | −1.37952 | − | 0.796468i | −0.387421 | − | 0.921903i | \(-0.626634\pi\) |
−0.992102 | + | 0.125435i | \(0.959967\pi\) | |||||||
\(228\) | −1.73205 | − | 1.00000i | −0.114708 | − | 0.0662266i | ||||
\(229\) | −14.0000 | − | 24.2487i | −0.925146 | − | 1.60240i | −0.791326 | − | 0.611394i | \(-0.790609\pi\) |
−0.133820 | − | 0.991006i | \(-0.542724\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00000 | − | 15.5885i | 0.197386 | − | 1.02565i | ||||
\(232\) | 6.00000i | 0.393919i | ||||||||
\(233\) | −5.19615 | + | 3.00000i | −0.340411 | + | 0.196537i | −0.660454 | − | 0.750867i | \(-0.729636\pi\) |
0.320043 | + | 0.947403i | \(0.396303\pi\) | |||||||
\(234\) | 2.50000 | − | 4.33013i | 0.163430 | − | 0.283069i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 20.0000i | − | 1.29914i | ||||||
\(238\) | 10.3923 | − | 12.0000i | 0.673633 | − | 0.777844i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | − | 21.6506i | 0.805196 | − | 1.39464i | −0.110963 | − | 0.993825i | \(-0.535394\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(242\) | −1.73205 | − | 1.00000i | −0.111340 | − | 0.0642824i | ||||
\(243\) | 8.66025 | − | 5.00000i | 0.555556 | − | 0.320750i | ||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 4.33013 | − | 2.50000i | 0.275519 | − | 0.159071i | ||||
\(248\) | 3.46410 | + | 2.00000i | 0.219971 | + | 0.127000i | ||||
\(249\) | 12.0000 | − | 20.7846i | 0.760469 | − | 1.31717i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | −1.73205 | + | 2.00000i | −0.109109 | + | 0.125988i | ||||
\(253\) | 9.00000i | 0.565825i | ||||||||
\(254\) | −9.50000 | − | 16.4545i | −0.596083 | − | 1.03245i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.3923 | − | 6.00000i | 0.648254 | − | 0.374270i | −0.139533 | − | 0.990217i | \(-0.544560\pi\) |
0.787787 | + | 0.615948i | \(0.211227\pi\) | |||||||
\(258\) | 20.0000i | 1.24515i | ||||||||
\(259\) | 5.50000 | − | 28.5788i | 0.341753 | − | 1.77580i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | 2.59808 | + | 1.50000i | 0.160510 | + | 0.0926703i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.50000 | + | 0.866025i | −0.153285 | + | 0.0530994i | ||||
\(267\) | 12.0000i | 0.734388i | ||||||||
\(268\) | −3.46410 | + | 2.00000i | −0.211604 | + | 0.122169i | ||||
\(269\) | −6.00000 | + | 10.3923i | −0.365826 | + | 0.633630i | −0.988908 | − | 0.148527i | \(-0.952547\pi\) |
0.623082 | + | 0.782157i | \(0.285880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | − | 6.00000i | − | 0.363803i | ||||||
\(273\) | −8.66025 | − | 25.0000i | −0.524142 | − | 1.51307i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | − | 5.19615i | 0.180579 | − | 0.312772i | ||||
\(277\) | 1.73205 | + | 1.00000i | 0.104069 | + | 0.0600842i | 0.551131 | − | 0.834419i | \(-0.314196\pi\) |
−0.447062 | + | 0.894503i | \(0.647530\pi\) | |||||||
\(278\) | −3.46410 | + | 2.00000i | −0.207763 | + | 0.119952i | ||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | \(-0.528521\pi\) | ||||
−0.0894825 | + | 0.995988i | \(0.528521\pi\) | |||||||
\(282\) | 5.19615 | − | 3.00000i | 0.309426 | − | 0.178647i | ||||
\(283\) | −22.5167 | − | 13.0000i | −1.33848 | − | 0.772770i | −0.351895 | − | 0.936039i | \(-0.614463\pi\) |
−0.986581 | + | 0.163270i | \(0.947796\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0000 | 0.886969 | ||||||||
\(287\) | −5.19615 | + | 6.00000i | −0.306719 | + | 0.354169i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 9.50000 | + | 16.4545i | 0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0000 | − | 24.2487i | 0.820695 | − | 1.42148i | ||||
\(292\) | 3.46410 | − | 2.00000i | 0.202721 | − | 0.117041i | ||||
\(293\) | − | 27.0000i | − | 1.57736i | −0.614806 | − | 0.788678i | \(-0.710766\pi\) | ||
0.614806 | − | 0.788678i | \(-0.289234\pi\) | |||||||
\(294\) | 2.00000 | + | 13.8564i | 0.116642 | + | 0.808122i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.50000 | − | 9.52628i | −0.319681 | − | 0.553704i | ||||
\(297\) | 10.3923 | + | 6.00000i | 0.603023 | + | 0.348155i | ||||
\(298\) | −15.5885 | − | 9.00000i | −0.903015 | − | 0.521356i | ||||
\(299\) | 7.50000 | + | 12.9904i | 0.433736 | + | 0.751253i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | + | 17.3205i | 1.15278 | + | 0.998337i | ||||
\(302\) | − | 14.0000i | − | 0.805609i | ||||||
\(303\) | 20.7846 | − | 12.0000i | 1.19404 | − | 0.689382i | ||||
\(304\) | −0.500000 | + | 0.866025i | −0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.00000 | − | 5.19615i | −0.171499 | − | 0.297044i | ||||
\(307\) | − | 2.00000i | − | 0.114146i | −0.998370 | − | 0.0570730i | \(-0.981823\pi\) | ||
0.998370 | − | 0.0570730i | \(-0.0181768\pi\) | |||||||
\(308\) | −7.79423 | − | 1.50000i | −0.444117 | − | 0.0854704i | ||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | −8.66025 | − | 5.00000i | −0.490290 | − | 0.283069i | ||||
\(313\) | 6.92820 | − | 4.00000i | 0.391605 | − | 0.226093i | −0.291250 | − | 0.956647i | \(-0.594071\pi\) |
0.682855 | + | 0.730554i | \(0.260738\pi\) | |||||||
\(314\) | −5.00000 | −0.282166 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −15.5885 | + | 9.00000i | −0.875535 | + | 0.505490i | −0.869184 | − | 0.494489i | \(-0.835355\pi\) |
−0.00635137 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(318\) | 5.19615 | + | 3.00000i | 0.291386 | + | 0.168232i | ||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | −2.59808 | − | 7.50000i | −0.144785 | − | 0.417959i | ||||
\(323\) | − | 6.00000i | − | 0.333849i | ||||||
\(324\) | −5.50000 | − | 9.52628i | −0.305556 | − | 0.529238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | ||||
\(327\) | −6.92820 | + | 4.00000i | −0.383131 | + | 0.221201i | ||||
\(328\) | 3.00000i | 0.165647i | ||||||||
\(329\) | 1.50000 | − | 7.79423i | 0.0826977 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | −10.3923 | − | 6.00000i | −0.570352 | − | 0.329293i | ||||
\(333\) | −9.52628 | − | 5.50000i | −0.522037 | − | 0.301398i | ||||
\(334\) | 4.50000 | + | 7.79423i | 0.246229 | + | 0.426481i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.00000 | + | 3.46410i | 0.218218 | + | 0.188982i | ||||
\(337\) | − | 14.0000i | − | 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | 10.3923 | − | 6.00000i | 0.565267 | − | 0.326357i | ||||
\(339\) | −12.0000 | + | 20.7846i | −0.651751 | + | 1.12887i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | ||||
\(342\) | 1.00000i | 0.0540738i | ||||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.50000 | + | 2.59808i | −0.0806405 | + | 0.139673i | ||||
\(347\) | 20.7846 | + | 12.0000i | 1.11578 | + | 0.644194i | 0.940319 | − | 0.340293i | \(-0.110526\pi\) |
0.175457 | + | 0.984487i | \(0.443860\pi\) | |||||||
\(348\) | 10.3923 | − | 6.00000i | 0.557086 | − | 0.321634i | ||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | −2.59808 | + | 1.50000i | −0.138478 | + | 0.0799503i | ||||
\(353\) | −10.3923 | − | 6.00000i | −0.553127 | − | 0.319348i | 0.197256 | − | 0.980352i | \(-0.436797\pi\) |
−0.750382 | + | 0.661004i | \(0.770130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −31.1769 | − | 6.00000i | −1.65006 | − | 0.317554i | ||||
\(358\) | − | 3.00000i | − | 0.158555i | ||||||
\(359\) | 3.00000 | + | 5.19615i | 0.158334 | + | 0.274242i | 0.934268 | − | 0.356572i | \(-0.116054\pi\) |
−0.775934 | + | 0.630814i | \(0.782721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | −1.73205 | + | 1.00000i | −0.0910346 | + | 0.0525588i | ||||
\(363\) | 4.00000i | 0.209946i | ||||||||
\(364\) | −12.5000 | + | 4.33013i | −0.655178 | + | 0.226960i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.00000 | − | 6.92820i | −0.209083 | − | 0.362143i | ||||
\(367\) | −0.866025 | − | 0.500000i | −0.0452062 | − | 0.0260998i | 0.477227 | − | 0.878780i | \(-0.341642\pi\) |
−0.522433 | + | 0.852680i | \(0.674975\pi\) | |||||||
\(368\) | −2.59808 | − | 1.50000i | −0.135434 | − | 0.0781929i | ||||
\(369\) | 1.50000 | + | 2.59808i | 0.0780869 | + | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.50000 | − | 2.59808i | 0.389381 | − | 0.134885i | ||||
\(372\) | − | 8.00000i | − | 0.414781i | ||||||
\(373\) | −29.4449 | + | 17.0000i | −1.52460 | + | 0.880227i | −0.525022 | + | 0.851089i | \(0.675943\pi\) |
−0.999575 | + | 0.0291379i | \(0.990724\pi\) | |||||||
\(374\) | 9.00000 | − | 15.5885i | 0.465379 | − | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | − | 2.59808i | −0.0773566 | − | 0.133986i | ||||
\(377\) | 30.0000i | 1.54508i | ||||||||
\(378\) | −10.3923 | − | 2.00000i | −0.534522 | − | 0.102869i | ||||
\(379\) | 25.0000 | 1.28416 | 0.642082 | − | 0.766636i | \(-0.278071\pi\) | ||||
0.642082 | + | 0.766636i | \(0.278071\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.0000 | + | 32.9090i | −0.973399 | + | 1.68598i | ||||
\(382\) | 10.3923 | + | 6.00000i | 0.531717 | + | 0.306987i | ||||
\(383\) | 12.9904 | − | 7.50000i | 0.663777 | − | 0.383232i | −0.129937 | − | 0.991522i | \(-0.541478\pi\) |
0.793715 | + | 0.608290i | \(0.208144\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | 8.66025 | − | 5.00000i | 0.440225 | − | 0.254164i | ||||
\(388\) | −12.1244 | − | 7.00000i | −0.615521 | − | 0.355371i | ||||
\(389\) | −12.0000 | + | 20.7846i | −0.608424 | + | 1.05382i | 0.383076 | + | 0.923717i | \(0.374865\pi\) |
−0.991500 | + | 0.130105i | \(0.958469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 6.92820 | − | 1.00000i | 0.349927 | − | 0.0505076i | ||||
\(393\) | − | 6.00000i | − | 0.302660i | ||||||
\(394\) | −1.50000 | − | 2.59808i | −0.0755689 | − | 0.130889i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | + | 2.59808i | −0.0753778 | + | 0.130558i | ||||
\(397\) | −1.73205 | + | 1.00000i | −0.0869291 | + | 0.0501886i | −0.542834 | − | 0.839840i | \(-0.682649\pi\) |
0.455905 | + | 0.890028i | \(0.349316\pi\) | |||||||
\(398\) | − | 4.00000i | − | 0.200502i | ||||||
\(399\) | 4.00000 | + | 3.46410i | 0.200250 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5000 | − | 18.1865i | −0.524345 | − | 0.908192i | −0.999598 | − | 0.0283431i | \(-0.990977\pi\) |
0.475253 | − | 0.879849i | \(-0.342356\pi\) | |||||||
\(402\) | 6.92820 | + | 4.00000i | 0.345547 | + | 0.199502i | ||||
\(403\) | 17.3205 | + | 10.0000i | 0.862796 | + | 0.498135i | ||||
\(404\) | −6.00000 | − | 10.3923i | −0.298511 | − | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | − | 15.5885i | 0.148888 | − | 0.773642i | ||||
\(407\) | − | 33.0000i | − | 1.63575i | ||||||
\(408\) | −10.3923 | + | 6.00000i | −0.514496 | + | 0.297044i | ||||
\(409\) | −11.0000 | + | 19.0526i | −0.543915 | + | 0.942088i | 0.454759 | + | 0.890614i | \(0.349725\pi\) |
−0.998674 | + | 0.0514740i | \(0.983608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | + | 20.7846i | 0.591916 | + | 1.02523i | ||||
\(412\) | 4.00000i | 0.197066i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.00000 | −0.147442 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | + | 4.33013i | −0.122573 | + | 0.212302i | ||||
\(417\) | 6.92820 | + | 4.00000i | 0.339276 | + | 0.195881i | ||||
\(418\) | −2.59808 | + | 1.50000i | −0.127076 | + | 0.0733674i | ||||
\(419\) | −15.0000 | −0.732798 | −0.366399 | − | 0.930458i | \(-0.619409\pi\) | ||||
−0.366399 | + | 0.930458i | \(0.619409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 0.866025 | − | 0.500000i | 0.0421575 | − | 0.0243396i | ||||
\(423\) | −2.59808 | − | 1.50000i | −0.126323 | − | 0.0729325i | ||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −24.0000 | −1.16280 | ||||||||
\(427\) | −10.3923 | − | 2.00000i | −0.502919 | − | 0.0967868i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | −15.0000 | − | 25.9808i | −0.724207 | − | 1.25436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | −3.46410 | + | 2.00000i | −0.166667 | + | 0.0962250i | ||||
\(433\) | − | 16.0000i | − | 0.768911i | −0.923144 | − | 0.384455i | \(-0.874389\pi\) | ||
0.923144 | − | 0.384455i | \(-0.125611\pi\) | |||||||
\(434\) | −8.00000 | − | 6.92820i | −0.384012 | − | 0.332564i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | −2.59808 | − | 1.50000i | −0.124283 | − | 0.0717547i | ||||
\(438\) | −6.92820 | − | 4.00000i | −0.331042 | − | 0.191127i | ||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | − | 30.0000i | − | 1.42695i | ||||||
\(443\) | −20.7846 | + | 12.0000i | −0.987507 | + | 0.570137i | −0.904528 | − | 0.426414i | \(-0.859777\pi\) |
−0.0829786 | + | 0.996551i | \(0.526443\pi\) | |||||||
\(444\) | −11.0000 | + | 19.0526i | −0.522037 | + | 0.904194i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.00000 | − | 6.92820i | −0.189405 | − | 0.328060i | ||||
\(447\) | 36.0000i | 1.70274i | ||||||||
\(448\) | 1.73205 | − | 2.00000i | 0.0818317 | − | 0.0944911i | ||||
\(449\) | 3.00000 | 0.141579 | 0.0707894 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707894 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | ||||
\(452\) | 10.3923 | + | 6.00000i | 0.488813 | + | 0.282216i | ||||
\(453\) | −24.2487 | + | 14.0000i | −1.13930 | + | 0.657777i | ||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 19.0526 | − | 11.0000i | 0.891241 | − | 0.514558i | 0.0168929 | − | 0.999857i | \(-0.494623\pi\) |
0.874348 | + | 0.485299i | \(0.161289\pi\) | |||||||
\(458\) | 24.2487 | + | 14.0000i | 1.13307 | + | 0.654177i | ||||
\(459\) | 12.0000 | − | 20.7846i | 0.560112 | − | 0.970143i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 5.19615 | + | 15.0000i | 0.241747 | + | 0.697863i | ||||
\(463\) | − | 19.0000i | − | 0.883005i | −0.897260 | − | 0.441502i | \(-0.854446\pi\) | ||
0.897260 | − | 0.441502i | \(-0.145554\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | − | 5.19615i | 0.138972 | − | 0.240707i | ||||
\(467\) | 15.5885 | − | 9.00000i | 0.721348 | − | 0.416470i | −0.0939008 | − | 0.995582i | \(-0.529934\pi\) |
0.815249 | + | 0.579111i | \(0.196600\pi\) | |||||||
\(468\) | 5.00000i | 0.231125i | ||||||||
\(469\) | 10.0000 | − | 3.46410i | 0.461757 | − | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.9808 | + | 15.0000i | 1.19460 | + | 0.689701i | ||||
\(474\) | 10.0000 | + | 17.3205i | 0.459315 | + | 0.795557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.00000 | + | 15.5885i | −0.137505 | + | 0.714496i | ||||
\(477\) | − | 3.00000i | − | 0.137361i | ||||||
\(478\) | 5.19615 | − | 3.00000i | 0.237666 | − | 0.137217i | ||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.5000 | − | 47.6314i | −1.25389 | − | 2.17180i | ||||
\(482\) | 25.0000i | 1.13872i | ||||||||
\(483\) | −10.3923 | + | 12.0000i | −0.472866 | + | 0.546019i | ||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.00000 | + | 8.66025i | −0.226805 | + | 0.392837i | ||||
\(487\) | −13.8564 | − | 8.00000i | −0.627894 | − | 0.362515i | 0.152042 | − | 0.988374i | \(-0.451415\pi\) |
−0.779936 | + | 0.625859i | \(0.784748\pi\) | |||||||
\(488\) | −3.46410 | + | 2.00000i | −0.156813 | + | 0.0905357i | ||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 5.19615 | − | 3.00000i | 0.234261 | − | 0.135250i | ||||
\(493\) | 31.1769 | + | 18.0000i | 1.40414 | + | 0.810679i | ||||
\(494\) | −2.50000 | + | 4.33013i | −0.112480 | + | 0.194822i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −20.7846 | + | 24.0000i | −0.932317 | + | 1.07655i | ||||
\(498\) | 24.0000i | 1.07547i | ||||||||
\(499\) | −14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) |
0.361478 | − | 0.932381i | \(-0.382272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.00000 | − | 15.5885i | 0.402090 | − | 0.696441i | ||||
\(502\) | 12.9904 | − | 7.50000i | 0.579789 | − | 0.334741i | ||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 0.500000 | − | 2.59808i | 0.0222718 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.50000 | − | 7.79423i | −0.200049 | − | 0.346496i | ||||
\(507\) | −20.7846 | − | 12.0000i | −0.923077 | − | 0.532939i | ||||
\(508\) | 16.4545 | + | 9.50000i | 0.730050 | + | 0.421494i | ||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | + | 3.46410i | −0.442374 | + | 0.153243i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.46410 | + | 2.00000i | −0.152944 | + | 0.0883022i | ||||
\(514\) | −6.00000 | + | 10.3923i | −0.264649 | + | 0.458385i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10.0000 | − | 17.3205i | −0.440225 | − | 0.762493i | ||||
\(517\) | − | 9.00000i | − | 0.395820i | ||||||
\(518\) | 9.52628 | + | 27.5000i | 0.418561 | + | 1.20828i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.5000 | + | 28.5788i | −0.722878 | + | 1.25206i | 0.236963 | + | 0.971519i | \(0.423848\pi\) |
−0.959841 | + | 0.280543i | \(0.909485\pi\) | |||||||
\(522\) | −5.19615 | − | 3.00000i | −0.227429 | − | 0.131306i | ||||
\(523\) | 17.3205 | − | 10.0000i | 0.757373 | − | 0.437269i | −0.0709788 | − | 0.997478i | \(-0.522612\pi\) |
0.828352 | + | 0.560208i | \(0.189279\pi\) | |||||||
\(524\) | −3.00000 | −0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.7846 | − | 12.0000i | 0.905392 | − | 0.522728i | ||||
\(528\) | 5.19615 | + | 3.00000i | 0.226134 | + | 0.130558i | ||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.73205 | − | 2.00000i | 0.0750939 | − | 0.0867110i | ||||
\(533\) | 15.0000i | 0.649722i | ||||||||
\(534\) | −6.00000 | − | 10.3923i | −0.259645 | − | 0.449719i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.00000 | − | 3.46410i | 0.0863868 | − | 0.149626i | ||||
\(537\) | −5.19615 | + | 3.00000i | −0.224231 | + | 0.129460i | ||||
\(538\) | − | 12.0000i | − | 0.517357i | ||||||
\(539\) | 19.5000 | + | 7.79423i | 0.839924 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | − | 6.92820i | −0.171973 | − | 0.297867i | 0.767136 | − | 0.641484i | \(-0.221681\pi\) |
−0.939110 | + | 0.343617i | \(0.888348\pi\) | |||||||
\(542\) | −13.8564 | − | 8.00000i | −0.595184 | − | 0.343629i | ||||
\(543\) | 3.46410 | + | 2.00000i | 0.148659 | + | 0.0858282i | ||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 20.0000 | + | 17.3205i | 0.855921 | + | 0.741249i | ||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | 10.3923 | − | 6.00000i | 0.443937 | − | 0.256307i | ||||
\(549\) | −2.00000 | + | 3.46410i | −0.0853579 | + | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00000 | − | 5.19615i | −0.127804 | − | 0.221364i | ||||
\(552\) | 6.00000i | 0.255377i | ||||||||
\(553\) | 25.9808 | + | 5.00000i | 1.10481 | + | 0.212622i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | −23.3827 | − | 13.5000i | −0.990756 | − | 0.572013i | −0.0852559 | − | 0.996359i | \(-0.527171\pi\) |
−0.905500 | + | 0.424346i | \(0.860504\pi\) | |||||||
\(558\) | −3.46410 | + | 2.00000i | −0.146647 | + | 0.0846668i | ||||
\(559\) | 50.0000 | 2.11477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.0000 | −1.51992 | ||||||||
\(562\) | 2.59808 | − | 1.50000i | 0.109593 | − | 0.0632737i | ||||
\(563\) | 15.5885 | + | 9.00000i | 0.656975 | + | 0.379305i | 0.791123 | − | 0.611656i | \(-0.209497\pi\) |
−0.134148 | + | 0.990961i | \(0.542830\pi\) | |||||||
\(564\) | −3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.0000 | 1.09286 | ||||||||
\(567\) | 9.52628 | + | 27.5000i | 0.400066 | + | 1.15489i | ||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | −1.50000 | − | 2.59808i | −0.0628833 | − | 0.108917i | 0.832870 | − | 0.553469i | \(-0.186696\pi\) |
−0.895753 | + | 0.444552i | \(0.853363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | −12.9904 | + | 7.50000i | −0.543155 | + | 0.313591i | ||||
\(573\) | − | 24.0000i | − | 1.00261i | ||||||
\(574\) | 1.50000 | − | 7.79423i | 0.0626088 | − | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 17.3205 | + | 10.0000i | 0.721062 | + | 0.416305i | 0.815144 | − | 0.579259i | \(-0.196658\pi\) |
−0.0940813 | + | 0.995565i | \(0.529991\pi\) | |||||||
\(578\) | −16.4545 | − | 9.50000i | −0.684416 | − | 0.395148i | ||||
\(579\) | 4.00000 | + | 6.92820i | 0.166234 | + | 0.287926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | ||||
\(582\) | 28.0000i | 1.16064i | ||||||||
\(583\) | 7.79423 | − | 4.50000i | 0.322804 | − | 0.186371i | ||||
\(584\) | −2.00000 | + | 3.46410i | −0.0827606 | + | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.5000 | + | 23.3827i | 0.557680 | + | 0.965930i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | −8.66025 | − | 11.0000i | −0.357143 | − | 0.453632i | ||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.00000 | + | 5.19615i | −0.123404 | + | 0.213741i | ||||
\(592\) | 9.52628 | + | 5.50000i | 0.391528 | + | 0.226049i | ||||
\(593\) | −31.1769 | + | 18.0000i | −1.28028 | + | 0.739171i | −0.976900 | − | 0.213697i | \(-0.931449\pi\) |
−0.303383 | + | 0.952869i | \(0.598116\pi\) | |||||||
\(594\) | −12.0000 | −0.492366 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | −6.92820 | + | 4.00000i | −0.283552 | + | 0.163709i | ||||
\(598\) | −12.9904 | − | 7.50000i | −0.531216 | − | 0.306698i | ||||
\(599\) | 21.0000 | − | 36.3731i | 0.858037 | − | 1.48616i | −0.0157622 | − | 0.999876i | \(-0.505017\pi\) |
0.873799 | − | 0.486287i | \(-0.161649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | −25.9808 | − | 5.00000i | −1.05890 | − | 0.203785i | ||||
\(603\) | − | 4.00000i | − | 0.162893i | ||||||
\(604\) | 7.00000 | + | 12.1244i | 0.284826 | + | 0.493333i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.0000 | + | 20.7846i | −0.487467 | + | 0.844317i | ||||
\(607\) | 16.4545 | − | 9.50000i | 0.667867 | − | 0.385593i | −0.127401 | − | 0.991851i | \(-0.540664\pi\) |
0.795268 | + | 0.606258i | \(0.207330\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | −30.0000 | + | 10.3923i | −1.21566 | + | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.50000 | − | 12.9904i | −0.303418 | − | 0.525535i | ||||
\(612\) | 5.19615 | + | 3.00000i | 0.210042 | + | 0.121268i | ||||
\(613\) | −40.7032 | − | 23.5000i | −1.64399 | − | 0.949156i | −0.979396 | − | 0.201948i | \(-0.935273\pi\) |
−0.664590 | − | 0.747208i | \(-0.731394\pi\) | |||||||
\(614\) | 1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.50000 | − | 2.59808i | 0.302184 | − | 0.104679i | ||||
\(617\) | 6.00000i | 0.241551i | 0.992680 | + | 0.120775i | \(0.0385381\pi\) | ||||
−0.992680 | + | 0.120775i | \(0.961462\pi\) | |||||||
\(618\) | 6.92820 | − | 4.00000i | 0.278693 | − | 0.160904i | ||||
\(619\) | −0.500000 | + | 0.866025i | −0.0200967 | + | 0.0348085i | −0.875899 | − | 0.482495i | \(-0.839731\pi\) |
0.855802 | + | 0.517303i | \(0.173064\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.00000 | − | 10.3923i | −0.240772 | − | 0.417029i | ||||
\(622\) | − | 12.0000i | − | 0.481156i | ||||||
\(623\) | −15.5885 | − | 3.00000i | −0.624538 | − | 0.120192i | ||||
\(624\) | 10.0000 | 0.400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.00000 | + | 6.92820i | −0.159872 | + | 0.276907i | ||||
\(627\) | 5.19615 | + | 3.00000i | 0.207514 | + | 0.119808i | ||||
\(628\) | 4.33013 | − | 2.50000i | 0.172791 | − | 0.0997609i | ||||
\(629\) | −66.0000 | −2.63159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 8.66025 | − | 5.00000i | 0.344486 | − | 0.198889i | ||||
\(633\) | −1.73205 | − | 1.00000i | −0.0688428 | − | 0.0397464i | ||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 34.6410 | − | 5.00000i | 1.37253 | − | 0.198107i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 6.00000 | + | 10.3923i | 0.237356 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.5000 | − | 38.9711i | 0.888697 | − | 1.53927i | 0.0472793 | − | 0.998882i | \(-0.484945\pi\) |
0.841417 | − | 0.540386i | \(-0.181722\pi\) | |||||||
\(642\) | −20.7846 | + | 12.0000i | −0.820303 | + | 0.473602i | ||||
\(643\) | 38.0000i | 1.49857i | 0.662246 | + | 0.749287i | \(0.269604\pi\) | ||||
−0.662246 | + | 0.749287i | \(0.730396\pi\) | |||||||
\(644\) | 6.00000 | + | 5.19615i | 0.236433 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.00000 | + | 5.19615i | 0.118033 | + | 0.204440i | ||||
\(647\) | −18.1865 | − | 10.5000i | −0.714986 | − | 0.412798i | 0.0979182 | − | 0.995194i | \(-0.468782\pi\) |
−0.812905 | + | 0.582397i | \(0.802115\pi\) | |||||||
\(648\) | 9.52628 | + | 5.50000i | 0.374228 | + | 0.216060i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | + | 20.7846i | −0.156772 | + | 0.814613i | ||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | 18.1865 | − | 10.5000i | 0.711694 | − | 0.410897i | −0.0999939 | − | 0.994988i | \(-0.531882\pi\) |
0.811688 | + | 0.584091i | \(0.198549\pi\) | |||||||
\(654\) | 4.00000 | − | 6.92820i | 0.156412 | − | 0.270914i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | 2.59808 | + | 7.50000i | 0.101284 | + | 0.292380i | ||||
\(659\) | −24.0000 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0000 | + | 38.1051i | −0.855701 | + | 1.48212i | 0.0202925 | + | 0.999794i | \(0.493540\pi\) |
−0.875993 | + | 0.482323i | \(0.839793\pi\) | |||||||
\(662\) | −6.06218 | − | 3.50000i | −0.235613 | − | 0.136031i | ||||
\(663\) | −51.9615 | + | 30.0000i | −2.01802 | + | 1.16510i | ||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.0000 | 0.426241 | ||||||||
\(667\) | 15.5885 | − | 9.00000i | 0.603587 | − | 0.348481i | ||||
\(668\) | −7.79423 | − | 4.50000i | −0.301568 | − | 0.174110i | ||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | −5.19615 | − | 1.00000i | −0.200446 | − | 0.0385758i | ||||
\(673\) | − | 34.0000i | − | 1.31060i | −0.755367 | − | 0.655302i | \(-0.772541\pi\) | ||
0.755367 | − | 0.655302i | \(-0.227459\pi\) | |||||||
\(674\) | 7.00000 | + | 12.1244i | 0.269630 | + | 0.467013i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | 2.59808 | − | 1.50000i | 0.0998522 | − | 0.0576497i | −0.449242 | − | 0.893410i | \(-0.648306\pi\) |
0.549095 | + | 0.835760i | \(0.314973\pi\) | |||||||
\(678\) | − | 24.0000i | − | 0.921714i | ||||||
\(679\) | 28.0000 | + | 24.2487i | 1.07454 | + | 0.930580i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.0000 | − | 41.5692i | −0.919682 | − | 1.59294i | ||||
\(682\) | −10.3923 | − | 6.00000i | −0.397942 | − | 0.229752i | ||||
\(683\) | 10.3923 | + | 6.00000i | 0.397650 | + | 0.229584i | 0.685470 | − | 0.728101i | \(-0.259597\pi\) |
−0.287819 | + | 0.957685i | \(0.592930\pi\) | |||||||
\(684\) | −0.500000 | − | 0.866025i | −0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | − | 56.0000i | − | 2.13653i | ||||||
\(688\) | −8.66025 | + | 5.00000i | −0.330169 | + | 0.190623i | ||||
\(689\) | 7.50000 | − | 12.9904i | 0.285727 | − | 0.494894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0000 | − | 27.7128i | −0.608669 | − | 1.05425i | −0.991460 | − | 0.130410i | \(-0.958371\pi\) |
0.382791 | − | 0.923835i | \(-0.374963\pi\) | |||||||
\(692\) | − | 3.00000i | − | 0.114043i | ||||||
\(693\) | 5.19615 | − | 6.00000i | 0.197386 | − | 0.227921i | ||||
\(694\) | −24.0000 | −0.911028 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | + | 10.3923i | −0.227429 | + | 0.393919i | ||||
\(697\) | 15.5885 | + | 9.00000i | 0.590455 | + | 0.340899i | ||||
\(698\) | −8.66025 | + | 5.00000i | −0.327795 | + | 0.189253i | ||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | −17.3205 | + | 10.0000i | −0.653720 | + | 0.377426i | ||||
\(703\) | 9.52628 | + | 5.50000i | 0.359290 | + | 0.207436i | ||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | 10.3923 | + | 30.0000i | 0.390843 | + | 1.12827i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.00000 | + | 12.1244i | 0.262891 | + | 0.455340i | 0.967009 | − | 0.254743i | \(-0.0819909\pi\) |
−0.704118 | + | 0.710083i | \(0.748658\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | ||||
\(712\) | −5.19615 | + | 3.00000i | −0.194734 | + | 0.112430i | ||||
\(713\) | − | 12.0000i | − | 0.449404i | ||||||
\(714\) | 30.0000 | − | 10.3923i | 1.12272 | − | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | −10.3923 | − | 6.00000i | −0.388108 | − | 0.224074i | ||||
\(718\) | −5.19615 | − | 3.00000i | −0.193919 | − | 0.111959i | ||||
\(719\) | −18.0000 | − | 31.1769i | −0.671287 | − | 1.16270i | −0.977539 | − | 0.210752i | \(-0.932409\pi\) |
0.306253 | − | 0.951950i | \(-0.400925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | − | 10.3923i | 0.0744839 | − | 0.387030i | ||||
\(722\) | 18.0000i | 0.669891i | ||||||||
\(723\) | 43.3013 | − | 25.0000i | 1.61039 | − | 0.929760i | ||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.00000 | − | 3.46410i | −0.0742270 | − | 0.128565i | ||||
\(727\) | − | 29.0000i | − | 1.07555i | −0.843088 | − | 0.537775i | \(-0.819265\pi\) | ||
0.843088 | − | 0.537775i | \(-0.180735\pi\) | |||||||
\(728\) | 8.66025 | − | 10.0000i | 0.320970 | − | 0.370625i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.0000 | − | 51.9615i | 1.10959 | − | 1.92187i | ||||
\(732\) | 6.92820 | + | 4.00000i | 0.256074 | + | 0.147844i | ||||
\(733\) | 40.7032 | − | 23.5000i | 1.50341 | − | 0.867992i | 0.503415 | − | 0.864045i | \(-0.332077\pi\) |
0.999992 | − | 0.00394730i | \(-0.00125647\pi\) | |||||||
\(734\) | 1.00000 | 0.0369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | 0.110581 | ||||||||
\(737\) | 10.3923 | − | 6.00000i | 0.382805 | − | 0.221013i | ||||
\(738\) | −2.59808 | − | 1.50000i | −0.0956365 | − | 0.0552158i | ||||
\(739\) | −18.5000 | + | 32.0429i | −0.680534 | + | 1.17872i | 0.294285 | + | 0.955718i | \(0.404919\pi\) |
−0.974818 | + | 0.223001i | \(0.928415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.0000 | 0.367359 | ||||||||
\(742\) | −5.19615 | + | 6.00000i | −0.190757 | + | 0.220267i | ||||
\(743\) | 9.00000i | 0.330178i | 0.986279 | + | 0.165089i | \(0.0527911\pi\) | ||||
−0.986279 | + | 0.165089i | \(0.947209\pi\) | |||||||
\(744\) | 4.00000 | + | 6.92820i | 0.146647 | + | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.0000 | − | 29.4449i | 0.622414 | − | 1.07805i | ||||
\(747\) | 10.3923 | − | 6.00000i | 0.380235 | − | 0.219529i | ||||
\(748\) | 18.0000i | 0.658145i | ||||||||
\(749\) | −6.00000 | + | 31.1769i | −0.219235 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | − | 22.5167i | −0.474377 | − | 0.821645i | 0.525193 | − | 0.850983i | \(-0.323993\pi\) |
−0.999570 | + | 0.0293387i | \(0.990660\pi\) | |||||||
\(752\) | 2.59808 | + | 1.50000i | 0.0947421 | + | 0.0546994i | ||||
\(753\) | −25.9808 | − | 15.0000i | −0.946792 | − | 0.546630i | ||||
\(754\) | −15.0000 | − | 25.9808i | −0.546268 | − | 0.946164i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.0000 | − | 3.46410i | 0.363696 | − | 0.125988i | ||||
\(757\) | − | 26.0000i | − | 0.944986i | −0.881334 | − | 0.472493i | \(-0.843354\pi\) | ||
0.881334 | − | 0.472493i | \(-0.156646\pi\) | |||||||
\(758\) | −21.6506 | + | 12.5000i | −0.786386 | + | 0.454020i | ||||
\(759\) | −9.00000 | + | 15.5885i | −0.326679 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.5000 | + | 44.1673i | 0.924374 | + | 1.60106i | 0.792564 | + | 0.609788i | \(0.208745\pi\) |
0.131810 | + | 0.991275i | \(0.457921\pi\) | |||||||
\(762\) | − | 38.0000i | − | 1.37659i | ||||||
\(763\) | −3.46410 | − | 10.0000i | −0.125409 | − | 0.362024i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.50000 | + | 12.9904i | −0.270986 | + | 0.469362i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.73205 | + | 1.00000i | −0.0625000 | + | 0.0360844i | ||||
\(769\) | 49.0000 | 1.76699 | 0.883493 | − | 0.468445i | \(-0.155186\pi\) | ||||
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0000 | 0.864339 | ||||||||
\(772\) | 3.46410 | − | 2.00000i | 0.124676 | − | 0.0719816i | ||||
\(773\) | −33.7750 | − | 19.5000i | −1.21480 | − | 0.701366i | −0.251000 | − | 0.967987i | \(-0.580760\pi\) |
−0.963802 | + | 0.266621i | \(0.914093\pi\) | |||||||
\(774\) | −5.00000 | + | 8.66025i | −0.179721 | + | 0.311286i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | 38.1051 | − | 44.0000i | 1.36701 | − | 1.57849i | ||||
\(778\) | − | 24.0000i | − | 0.860442i | ||||||
\(779\) | −1.50000 | − | 2.59808i | −0.0537431 | − | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | + | 31.1769i | −0.644091 | + | 1.11560i | ||||
\(782\) | −15.5885 | + | 9.00000i | −0.557442 | + | 0.321839i | ||||
\(783\) | − | 24.0000i | − | 0.857690i | ||||||
\(784\) | −5.50000 | + | 4.33013i | −0.196429 | + | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.00000 | + | 5.19615i | 0.107006 | + | 0.185341i | ||||
\(787\) | −29.4449 | − | 17.0000i | −1.04960 | − | 0.605985i | −0.127060 | − | 0.991895i | \(-0.540554\pi\) |
−0.922536 | + | 0.385911i | \(0.873887\pi\) | |||||||
\(788\) | 2.59808 | + | 1.50000i | 0.0925526 | + | 0.0534353i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0000 | − | 20.7846i | −0.853342 | − | 0.739016i | ||||
\(792\) | − | 3.00000i | − | 0.106600i | ||||||
\(793\) | −17.3205 | + | 10.0000i | −0.615069 | + | 0.355110i | ||||
\(794\) | 1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 30.0000i | 1.06265i | 0.847167 | + | 0.531327i | \(0.178307\pi\) | ||||
−0.847167 | + | 0.531327i | \(0.821693\pi\) | |||||||
\(798\) | −5.19615 | − | 1.00000i | −0.183942 | − | 0.0353996i | ||||
\(799\) | −18.0000 | −0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | 18.1865 | + | 10.5000i | 0.642189 | + | 0.370768i | ||||
\(803\) | −10.3923 | + | 6.00000i | −0.366736 | + | 0.211735i | ||||
\(804\) | −8.00000 | −0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | −20.7846 | + | 12.0000i | −0.731653 | + | 0.422420i | ||||
\(808\) | 10.3923 | + | 6.00000i | 0.365600 | + | 0.211079i | ||||
\(809\) | 19.5000 | − | 33.7750i | 0.685583 | − | 1.18747i | −0.287670 | − | 0.957730i | \(-0.592880\pi\) |
0.973253 | − | 0.229736i | \(-0.0737862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.0000 | 1.65039 | 0.825197 | − | 0.564846i | \(-0.191064\pi\) | ||||
0.825197 | + | 0.564846i | \(0.191064\pi\) | |||||||
\(812\) | 5.19615 | + | 15.0000i | 0.182349 | + | 0.526397i | ||||
\(813\) | 32.0000i | 1.12229i | ||||||||
\(814\) | 16.5000 | + | 28.5788i | 0.578325 | + | 1.00169i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.00000 | − | 10.3923i | 0.210042 | − | 0.363803i | ||||
\(817\) | −8.66025 | + | 5.00000i | −0.302984 | + | 0.174928i | ||||
\(818\) | − | 22.0000i | − | 0.769212i | ||||||
\(819\) | 2.50000 | − | 12.9904i | 0.0873571 | − | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | −20.7846 | − | 12.0000i | −0.724947 | − | 0.418548i | ||||
\(823\) | −38.1051 | − | 22.0000i | −1.32826 | − | 0.766872i | −0.343230 | − | 0.939251i | \(-0.611521\pi\) |
−0.985031 | + | 0.172379i | \(0.944854\pi\) | |||||||
\(824\) | −2.00000 | − | 3.46410i | −0.0696733 | − | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0000i | 1.87776i | 0.344239 | + | 0.938882i | \(0.388137\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(828\) | 2.59808 | − | 1.50000i | 0.0902894 | − | 0.0521286i | ||||
\(829\) | 7.00000 | − | 12.1244i | 0.243120 | − | 0.421096i | −0.718481 | − | 0.695546i | \(-0.755162\pi\) |
0.961601 | + | 0.274450i | \(0.0884958\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | + | 3.46410i | 0.0693792 | + | 0.120168i | ||||
\(832\) | − | 5.00000i | − | 0.173344i | ||||||
\(833\) | 15.5885 | − | 39.0000i | 0.540108 | − | 1.35127i | ||||
\(834\) | −8.00000 | −0.277017 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.50000 | − | 2.59808i | 0.0518786 | − | 0.0898563i | ||||
\(837\) | −13.8564 | − | 8.00000i | −0.478947 | − | 0.276520i | ||||
\(838\) | 12.9904 | − | 7.50000i | 0.448745 | − | 0.259083i | ||||
\(839\) | 6.00000 | 0.207143 | 0.103572 | − | 0.994622i | \(-0.466973\pi\) | ||||
0.103572 | + | 0.994622i | \(0.466973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 29.4449 | − | 17.0000i | 1.01474 | − | 0.585859i | ||||
\(843\) | −5.19615 | − | 3.00000i | −0.178965 | − | 0.103325i | ||||
\(844\) | −0.500000 | + | 0.866025i | −0.0172107 | + | 0.0298098i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | −5.19615 | − | 1.00000i | −0.178542 | − | 0.0343604i | ||||
\(848\) | 3.00000i | 0.103020i | ||||||||
\(849\) | −26.0000 | − | 45.0333i | −0.892318 | − | 1.54554i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.5000 | + | 28.5788i | −0.565613 | + | 0.979670i | ||||
\(852\) | 20.7846 | − | 12.0000i | 0.712069 | − | 0.411113i | ||||
\(853\) | − | 1.00000i | − | 0.0342393i | −0.999853 | − | 0.0171197i | \(-0.994550\pi\) | ||
0.999853 | − | 0.0171197i | \(-0.00544963\pi\) | |||||||
\(854\) | 10.0000 | − | 3.46410i | 0.342193 | − | 0.118539i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | + | 10.3923i | 0.205076 | + | 0.355202i | ||||
\(857\) | −15.5885 | − | 9.00000i | −0.532492 | − | 0.307434i | 0.209539 | − | 0.977800i | \(-0.432804\pi\) |
−0.742030 | + | 0.670366i | \(0.766137\pi\) | |||||||
\(858\) | 25.9808 | + | 15.0000i | 0.886969 | + | 0.512092i | ||||
\(859\) | 16.0000 | + | 27.7128i | 0.545913 | + | 0.945549i | 0.998549 | + | 0.0538535i | \(0.0171504\pi\) |
−0.452636 | + | 0.891695i | \(0.649516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0000 | + | 5.19615i | −0.511199 | + | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.7750 | − | 19.5000i | 1.14971 | − | 0.663788i | 0.200897 | − | 0.979612i | \(-0.435615\pi\) |
0.948818 | + | 0.315825i | \(0.102281\pi\) | |||||||
\(864\) | 2.00000 | − | 3.46410i | 0.0680414 | − | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.00000 | + | 13.8564i | 0.271851 | + | 0.470860i | ||||
\(867\) | 38.0000i | 1.29055i | ||||||||
\(868\) | 10.3923 | + | 2.00000i | 0.352738 | + | 0.0678844i | ||||
\(869\) | 30.0000 | 1.01768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | − | 17.3205i | 0.338837 | − | 0.586883i | ||||
\(872\) | −3.46410 | − | 2.00000i | −0.117309 | − | 0.0677285i | ||||
\(873\) | 12.1244 | − | 7.00000i | 0.410347 | − | 0.236914i | ||||
\(874\) | 3.00000 | 0.101477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.00000 | 0.270295 | ||||||||
\(877\) | 6.06218 | − | 3.50000i | 0.204705 | − | 0.118187i | −0.394143 | − | 0.919049i | \(-0.628959\pi\) |
0.598848 | + | 0.800862i | \(0.295625\pi\) | |||||||
\(878\) | 8.66025 | + | 5.00000i | 0.292269 | + | 0.168742i | ||||
\(879\) | 27.0000 | − | 46.7654i | 0.910687 | − | 1.57736i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | −2.59808 | + | 6.50000i | −0.0874818 | + | 0.218866i | ||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 15.0000 | + | 25.9808i | 0.504505 | + | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | − | 20.7846i | 0.403148 | − | 0.698273i | ||||
\(887\) | −20.7846 | + | 12.0000i | −0.697879 | + | 0.402921i | −0.806557 | − | 0.591156i | \(-0.798672\pi\) |
0.108678 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(888\) | − | 22.0000i | − | 0.738272i | ||||||
\(889\) | −38.0000 | − | 32.9090i | −1.27448 | − | 1.10373i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.5000 | + | 28.5788i | 0.552771 | + | 0.957427i | ||||
\(892\) | 6.92820 | + | 4.00000i | 0.231973 | + | 0.133930i | ||||
\(893\) | 2.59808 | + | 1.50000i | 0.0869413 | + | 0.0501956i | ||||
\(894\) | −18.0000 | − | 31.1769i | −0.602010 | − | 1.04271i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 30.0000i | 1.00167i | ||||||||
\(898\) | −2.59808 | + | 1.50000i | −0.0866989 | + | 0.0500556i | ||||
\(899\) | 12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | − | 15.5885i | −0.299833 | − | 0.519327i | ||||
\(902\) | − | 9.00000i | − | 0.299667i | ||||||
\(903\) | 17.3205 | + | 50.0000i | 0.576390 | + | 1.66390i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 14.0000 | − | 24.2487i | 0.465119 | − | 0.805609i | ||||
\(907\) | −8.66025 | − | 5.00000i | −0.287559 | − | 0.166022i | 0.349281 | − | 0.937018i | \(-0.386426\pi\) |
−0.636841 | + | 0.770996i | \(0.719759\pi\) | |||||||
\(908\) | −20.7846 | + | 12.0000i | −0.689761 | + | 0.398234i | ||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | −1.73205 | + | 1.00000i | −0.0573539 | + | 0.0331133i | ||||
\(913\) | 31.1769 | + | 18.0000i | 1.03181 | + | 0.595713i | ||||
\(914\) | −11.0000 | + | 19.0526i | −0.363848 | + | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.0000 | −0.925146 | ||||||||
\(917\) | 7.79423 | + | 1.50000i | 0.257388 | + | 0.0495344i | ||||
\(918\) | 24.0000i | 0.792118i | ||||||||
\(919\) | 19.0000 | + | 32.9090i | 0.626752 | + | 1.08557i | 0.988199 | + | 0.153174i | \(0.0489495\pi\) |
−0.361447 | + | 0.932393i | \(0.617717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | − | 3.46410i | 0.0659022 | − | 0.114146i | ||||
\(922\) | −5.19615 | + | 3.00000i | −0.171126 | + | 0.0987997i | ||||
\(923\) | 60.0000i | 1.97492i | ||||||||
\(924\) | −12.0000 | − | 10.3923i | −0.394771 | − | 0.341882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.50000 | + | 16.4545i | 0.312189 | + | 0.540728i | ||||
\(927\) | −3.46410 | − | 2.00000i | −0.113776 | − | 0.0656886i | ||||
\(928\) | 5.19615 | + | 3.00000i | 0.170572 | + | 0.0984798i | ||||
\(929\) | 16.5000 | + | 28.5788i | 0.541347 | + | 0.937641i | 0.998827 | + | 0.0484211i | \(0.0154190\pi\) |
−0.457480 | + | 0.889220i | \(0.651248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.50000 | + | 4.33013i | −0.180255 | + | 0.141914i | ||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | −20.7846 | + | 12.0000i | −0.680458 | + | 0.392862i | ||||
\(934\) | −9.00000 | + | 15.5885i | −0.294489 | + | 0.510070i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.50000 | − | 4.33013i | −0.0817151 | − | 0.141535i | ||||
\(937\) | − | 2.00000i | − | 0.0653372i | −0.999466 | − | 0.0326686i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326686i | \(-0.0104006\pi\) | |||||||
\(938\) | −6.92820 | + | 8.00000i | −0.226214 | + | 0.261209i | ||||
\(939\) | 16.0000 | 0.522140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | −8.66025 | − | 5.00000i | −0.282166 | − | 0.162909i | ||||
\(943\) | 7.79423 | − | 4.50000i | 0.253815 | − | 0.146540i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.0000 | −0.975384 | ||||||||
\(947\) | −25.9808 | + | 15.0000i | −0.844261 | + | 0.487435i | −0.858710 | − | 0.512461i | \(-0.828734\pi\) |
0.0144491 | + | 0.999896i | \(0.495401\pi\) | |||||||
\(948\) | −17.3205 | − | 10.0000i | −0.562544 | − | 0.324785i | ||||
\(949\) | −10.0000 | + | 17.3205i | −0.324614 | + | 0.562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.0000 | −1.16738 | ||||||||
\(952\) | −5.19615 | − | 15.0000i | −0.168408 | − | 0.486153i | ||||
\(953\) | − | 12.0000i | − | 0.388718i | −0.980930 | − | 0.194359i | \(-0.937737\pi\) | ||
0.980930 | − | 0.194359i | \(-0.0622627\pi\) | |||||||
\(954\) | 1.50000 | + | 2.59808i | 0.0485643 | + | 0.0841158i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.00000 | + | 5.19615i | −0.0970269 | + | 0.168056i | ||||
\(957\) | −31.1769 | + | 18.0000i | −1.00781 | + | 0.581857i | ||||
\(958\) | 24.0000i | 0.775405i | ||||||||
\(959\) | −30.0000 | + | 10.3923i | −0.968751 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 47.6314 | + | 27.5000i | 1.53570 | + | 0.886636i | ||||
\(963\) | 10.3923 | + | 6.00000i | 0.334887 | + | 0.193347i | ||||
\(964\) | −12.5000 | − | 21.6506i | −0.402598 | − | 0.697320i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.00000 | − | 15.5885i | 0.0965234 | − | 0.501550i | ||||
\(967\) | − | 32.0000i | − | 1.02905i | −0.857475 | − | 0.514525i | \(-0.827968\pi\) | ||
0.857475 | − | 0.514525i | \(-0.172032\pi\) | |||||||
\(968\) | −1.73205 | + | 1.00000i | −0.0556702 | + | 0.0321412i | ||||
\(969\) | 6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.5000 | − | 23.3827i | −0.433236 | − | 0.750386i | 0.563914 | − | 0.825833i | \(-0.309295\pi\) |
−0.997150 | + | 0.0754473i | \(0.975962\pi\) | |||||||
\(972\) | − | 10.0000i | − | 0.320750i | ||||||
\(973\) | −6.92820 | + | 8.00000i | −0.222108 | + | 0.256468i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | − | 3.46410i | 0.0640184 | − | 0.110883i | ||||
\(977\) | −25.9808 | − | 15.0000i | −0.831198 | − | 0.479893i | 0.0230645 | − | 0.999734i | \(-0.492658\pi\) |
−0.854263 | + | 0.519841i | \(0.825991\pi\) | |||||||
\(978\) | 6.92820 | − | 4.00000i | 0.221540 | − | 0.127906i | ||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 10.3923 | − | 6.00000i | 0.331632 | − | 0.191468i | ||||
\(983\) | −49.3634 | − | 28.5000i | −1.57445 | − | 0.909009i | −0.995613 | − | 0.0935651i | \(-0.970174\pi\) |
−0.578836 | − | 0.815444i | \(-0.696493\pi\) | |||||||
\(984\) | −3.00000 | + | 5.19615i | −0.0956365 | + | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −36.0000 | −1.14647 | ||||||||
\(987\) | 10.3923 | − | 12.0000i | 0.330791 | − | 0.381964i | ||||
\(988\) | − | 5.00000i | − | 0.159071i | ||||||
\(989\) | −15.0000 | − | 25.9808i | −0.476972 | − | 0.826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0000 | + | 17.3205i | −0.317660 | + | 0.550204i | −0.979999 | − | 0.199000i | \(-0.936231\pi\) |
0.662339 | + | 0.749204i | \(0.269564\pi\) | |||||||
\(992\) | 3.46410 | − | 2.00000i | 0.109985 | − | 0.0635001i | ||||
\(993\) | 14.0000i | 0.444277i | ||||||||
\(994\) | 6.00000 | − | 31.1769i | 0.190308 | − | 0.988872i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.0000 | − | 20.7846i | −0.380235 | − | 0.658586i | ||||
\(997\) | 12.1244 | + | 7.00000i | 0.383982 | + | 0.221692i | 0.679549 | − | 0.733630i | \(-0.262175\pi\) |
−0.295567 | + | 0.955322i | \(0.595509\pi\) | |||||||
\(998\) | 24.2487 | + | 14.0000i | 0.767580 | + | 0.443162i | ||||
\(999\) | 22.0000 | + | 38.1051i | 0.696049 | + | 1.20559i |
(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 | 350.2.j.a.249.1 | 4 | ||
5.2 | odd | 4 | 70.2.e.b.11.1 | ✓ | 2 | ||
5.3 | odd | 4 | 350.2.e.h.151.1 | 2 | |||
5.4 | even | 2 | inner | 350.2.j.a.249.2 | 4 | ||
7.2 | even | 3 | inner | 350.2.j.a.149.2 | 4 | ||
7.3 | odd | 6 | 2450.2.c.p.99.1 | 2 | |||
7.4 | even | 3 | 2450.2.c.f.99.1 | 2 | |||
15.2 | even | 4 | 630.2.k.e.361.1 | 2 | |||
20.7 | even | 4 | 560.2.q.d.81.1 | 2 | |||
35.2 | odd | 12 | 70.2.e.b.51.1 | yes | 2 | ||
35.3 | even | 12 | 2450.2.a.f.1.1 | 1 | |||
35.4 | even | 6 | 2450.2.c.f.99.2 | 2 | |||
35.9 | even | 6 | inner | 350.2.j.a.149.1 | 4 | ||
35.12 | even | 12 | 490.2.e.a.471.1 | 2 | |||
35.17 | even | 12 | 490.2.a.j.1.1 | 1 | |||
35.18 | odd | 12 | 2450.2.a.p.1.1 | 1 | |||
35.23 | odd | 12 | 350.2.e.h.51.1 | 2 | |||
35.24 | odd | 6 | 2450.2.c.p.99.2 | 2 | |||
35.27 | even | 4 | 490.2.e.a.361.1 | 2 | |||
35.32 | odd | 12 | 490.2.a.g.1.1 | 1 | |||
105.2 | even | 12 | 630.2.k.e.541.1 | 2 | |||
105.17 | odd | 12 | 4410.2.a.c.1.1 | 1 | |||
105.32 | even | 12 | 4410.2.a.m.1.1 | 1 | |||
140.67 | even | 12 | 3920.2.a.be.1.1 | 1 | |||
140.87 | odd | 12 | 3920.2.a.g.1.1 | 1 | |||
140.107 | even | 12 | 560.2.q.d.401.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.b.11.1 | ✓ | 2 | 5.2 | odd | 4 | ||
70.2.e.b.51.1 | yes | 2 | 35.2 | odd | 12 | ||
350.2.e.h.51.1 | 2 | 35.23 | odd | 12 | |||
350.2.e.h.151.1 | 2 | 5.3 | odd | 4 | |||
350.2.j.a.149.1 | 4 | 35.9 | even | 6 | inner | ||
350.2.j.a.149.2 | 4 | 7.2 | even | 3 | inner | ||
350.2.j.a.249.1 | 4 | 1.1 | even | 1 | trivial | ||
350.2.j.a.249.2 | 4 | 5.4 | even | 2 | inner | ||
490.2.a.g.1.1 | 1 | 35.32 | odd | 12 | |||
490.2.a.j.1.1 | 1 | 35.17 | even | 12 | |||
490.2.e.a.361.1 | 2 | 35.27 | even | 4 | |||
490.2.e.a.471.1 | 2 | 35.12 | even | 12 | |||
560.2.q.d.81.1 | 2 | 20.7 | even | 4 | |||
560.2.q.d.401.1 | 2 | 140.107 | even | 12 | |||
630.2.k.e.361.1 | 2 | 15.2 | even | 4 | |||
630.2.k.e.541.1 | 2 | 105.2 | even | 12 | |||
2450.2.a.f.1.1 | 1 | 35.3 | even | 12 | |||
2450.2.a.p.1.1 | 1 | 35.18 | odd | 12 | |||
2450.2.c.f.99.1 | 2 | 7.4 | even | 3 | |||
2450.2.c.f.99.2 | 2 | 35.4 | even | 6 | |||
2450.2.c.p.99.1 | 2 | 7.3 | odd | 6 | |||
2450.2.c.p.99.2 | 2 | 35.24 | odd | 6 | |||
3920.2.a.g.1.1 | 1 | 140.87 | odd | 12 | |||
3920.2.a.be.1.1 | 1 | 140.67 | even | 12 | |||
4410.2.a.c.1.1 | 1 | 105.17 | odd | 12 | |||
4410.2.a.m.1.1 | 1 | 105.32 | even | 12 |