Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (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: | \(15.5708283941\) |
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 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1699.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1699 |
Dual form | 1950.2.z.k.1849.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −1.73205 | + | 1.00000i | −0.654654 | + | 0.377964i | −0.790237 | − | 0.612801i | \(-0.790043\pi\) |
0.135583 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(8\) | − | 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 | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 3.46410 | + | 1.00000i | 0.960769 | + | 0.277350i | ||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −5.19615 | + | 3.00000i | −1.26025 | + | 0.727607i | −0.973123 | − | 0.230285i | \(-0.926034\pi\) |
−0.287129 | + | 0.957892i | \(0.592701\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | −2.59808 | + | 1.50000i | −0.553912 | + | 0.319801i | ||||
\(23\) | −2.59808 | − | 1.50000i | −0.541736 | − | 0.312772i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.50000 | − | 2.59808i | −0.490290 | − | 0.509525i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.73205 | − | 1.00000i | −0.327327 | − | 0.188982i | ||||
\(29\) | 1.50000 | − | 2.59808i | 0.278543 | − | 0.482451i | −0.692480 | − | 0.721437i | \(-0.743482\pi\) |
0.971023 | + | 0.238987i | \(0.0768152\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | 0.898027 | 0.449013 | − | 0.893525i | \(-0.351776\pi\) | ||||
0.449013 | + | 0.893525i | \(0.351776\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −2.59808 | + | 1.50000i | −0.452267 | + | 0.261116i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −6.06218 | − | 3.50000i | −0.996616 | − | 0.575396i | −0.0893706 | − | 0.995998i | \(-0.528486\pi\) |
−0.907245 | + | 0.420602i | \(0.861819\pi\) | |||||||
\(38\) | − | 2.00000i | − | 0.324443i | ||||||
\(39\) | −2.50000 | − | 2.59808i | −0.400320 | − | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | −1.73205 | − | 1.00000i | −0.267261 | − | 0.154303i | ||||
\(43\) | −0.866025 | + | 0.500000i | −0.132068 | + | 0.0762493i | −0.564578 | − | 0.825380i | \(-0.690961\pi\) |
0.432511 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | 3.00000i | 0.437595i | 0.975770 | + | 0.218797i | \(0.0702134\pi\) | ||||
−0.975770 | + | 0.218797i | \(0.929787\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | −1.50000 | + | 2.59808i | −0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 0.866025 | + | 3.50000i | 0.120096 | + | 0.485363i | ||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | + | 1.73205i | 0.133631 | + | 0.231455i | ||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | −2.59808 | + | 1.50000i | −0.341144 | + | 0.196960i | ||||
\(59\) | −4.50000 | − | 7.79423i | −0.585850 | − | 1.01472i | −0.994769 | − | 0.102151i | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | −4.33013 | − | 2.50000i | −0.549927 | − | 0.317500i | ||||
\(63\) | −1.73205 | − | 1.00000i | −0.218218 | − | 0.125988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00000 | 0.369274 | ||||||||
\(67\) | 6.92820 | + | 4.00000i | 0.846415 | + | 0.488678i | 0.859440 | − | 0.511237i | \(-0.170813\pi\) |
−0.0130248 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(68\) | −5.19615 | − | 3.00000i | −0.630126 | − | 0.363803i | ||||
\(69\) | 1.50000 | + | 2.59808i | 0.180579 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | + | 10.3923i | 0.712069 | + | 1.23334i | 0.964079 | + | 0.265615i | \(0.0855750\pi\) |
−0.252010 | + | 0.967725i | \(0.581092\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | 14.0000i | 1.63858i | 0.573382 | + | 0.819288i | \(0.305631\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | 3.50000 | + | 6.06218i | 0.406867 | + | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | 6.00000i | 0.683763i | ||||||||
\(78\) | 0.866025 | + | 3.50000i | 0.0980581 | + | 0.396297i | ||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.19615 | − | 3.00000i | 0.573819 | − | 0.331295i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 1.00000 | + | 1.73205i | 0.109109 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | −2.59808 | + | 1.50000i | −0.278543 | + | 0.160817i | ||||
\(88\) | −2.59808 | − | 1.50000i | −0.276956 | − | 0.159901i | ||||
\(89\) | −9.00000 | + | 15.5885i | −0.953998 | + | 1.65237i | −0.217354 | + | 0.976093i | \(0.569742\pi\) |
−0.736644 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.00000 | + | 1.73205i | −0.733799 | + | 0.181568i | ||||
\(92\) | − | 3.00000i | − | 0.312772i | ||||||
\(93\) | −4.33013 | − | 2.50000i | −0.449013 | − | 0.259238i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.1244 | + | 7.00000i | −1.23104 | + | 0.710742i | −0.967247 | − | 0.253837i | \(-0.918307\pi\) |
−0.263795 | + | 0.964579i | \(0.584974\pi\) | |||||||
\(98\) | 2.59808 | − | 1.50000i | 0.262445 | − | 0.151523i | ||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | + | 5.19615i | −0.298511 | + | 0.517036i | −0.975796 | − | 0.218685i | \(-0.929823\pi\) |
0.677284 | + | 0.735721i | \(0.263157\pi\) | |||||||
\(102\) | −5.19615 | − | 3.00000i | −0.514496 | − | 0.297044i | ||||
\(103\) | 14.0000i | 1.37946i | 0.724066 | + | 0.689730i | \(0.242271\pi\) | ||||
−0.724066 | + | 0.689730i | \(0.757729\pi\) | |||||||
\(104\) | 1.00000 | − | 3.46410i | 0.0980581 | − | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | + | 5.19615i | −0.291386 | + | 0.504695i | ||||
\(107\) | −5.19615 | − | 3.00000i | −0.502331 | − | 0.290021i | 0.227345 | − | 0.973814i | \(-0.426996\pi\) |
−0.729676 | + | 0.683793i | \(0.760329\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50000 | + | 6.06218i | 0.332205 | + | 0.575396i | ||||
\(112\) | − | 2.00000i | − | 0.188982i | ||||||
\(113\) | 12.9904 | − | 7.50000i | 1.22203 | − | 0.705541i | 0.256681 | − | 0.966496i | \(-0.417371\pi\) |
0.965351 | + | 0.260955i | \(0.0840376\pi\) | |||||||
\(114\) | −1.00000 | + | 1.73205i | −0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0.866025 | + | 3.50000i | 0.0800641 | + | 0.323575i | ||||
\(118\) | 9.00000i | 0.828517i | ||||||||
\(119\) | 6.00000 | − | 10.3923i | 0.550019 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | 5.19615 | − | 3.00000i | 0.468521 | − | 0.270501i | ||||
\(124\) | 2.50000 | + | 4.33013i | 0.224507 | + | 0.388857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | + | 1.73205i | 0.0890871 | + | 0.154303i | ||||
\(127\) | 12.1244 | + | 7.00000i | 1.07586 | + | 0.621150i | 0.929777 | − | 0.368122i | \(-0.119999\pi\) |
0.146085 | + | 0.989272i | \(0.453333\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | 0.786334 | 0.393167 | − | 0.919467i | \(-0.371379\pi\) | ||||
0.393167 | + | 0.919467i | \(0.371379\pi\) | |||||||
\(132\) | −2.59808 | − | 1.50000i | −0.226134 | − | 0.130558i | ||||
\(133\) | −3.46410 | − | 2.00000i | −0.300376 | − | 0.173422i | ||||
\(134\) | −4.00000 | − | 6.92820i | −0.345547 | − | 0.598506i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | + | 5.19615i | 0.257248 | + | 0.445566i | ||||
\(137\) | −7.79423 | + | 4.50000i | −0.665906 | + | 0.384461i | −0.794524 | − | 0.607233i | \(-0.792279\pi\) |
0.128618 | + | 0.991694i | \(0.458946\pi\) | |||||||
\(138\) | − | 3.00000i | − | 0.255377i | ||||||
\(139\) | 7.00000 | + | 12.1244i | 0.593732 | + | 1.02837i | 0.993724 | + | 0.111856i | \(0.0356795\pi\) |
−0.399992 | + | 0.916519i | \(0.630987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.50000 | − | 2.59808i | 0.126323 | − | 0.218797i | ||||
\(142\) | − | 12.0000i | − | 1.00702i | ||||||
\(143\) | 7.79423 | − | 7.50000i | 0.651786 | − | 0.627182i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.00000 | − | 12.1244i | 0.579324 | − | 1.00342i | ||||
\(147\) | 2.59808 | − | 1.50000i | 0.214286 | − | 0.123718i | ||||
\(148\) | − | 7.00000i | − | 0.575396i | ||||||
\(149\) | −4.50000 | − | 7.79423i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 1.73205 | − | 1.00000i | 0.140488 | − | 0.0811107i | ||||
\(153\) | −5.19615 | − | 3.00000i | −0.420084 | − | 0.242536i | ||||
\(154\) | 3.00000 | − | 5.19615i | 0.241747 | − | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00000 | − | 3.46410i | 0.0800641 | − | 0.277350i | ||||
\(157\) | 13.0000i | 1.03751i | 0.854922 | + | 0.518756i | \(0.173605\pi\) | ||||
−0.854922 | + | 0.518756i | \(0.826395\pi\) | |||||||
\(158\) | 4.33013 | + | 2.50000i | 0.344486 | + | 0.198889i | ||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | −11.2583 | + | 6.50000i | −0.881820 | + | 0.509119i | −0.871258 | − | 0.490825i | \(-0.836695\pi\) |
−0.0105623 | + | 0.999944i | \(0.503362\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | −7.79423 | − | 4.50000i | −0.603136 | − | 0.348220i | 0.167139 | − | 0.985933i | \(-0.446547\pi\) |
−0.770274 | + | 0.637713i | \(0.779881\pi\) | |||||||
\(168\) | − | 2.00000i | − | 0.154303i | ||||||
\(169\) | 11.0000 | + | 6.92820i | 0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | + | 1.73205i | −0.0764719 | + | 0.132453i | ||||
\(172\) | −0.866025 | − | 0.500000i | −0.0660338 | − | 0.0381246i | ||||
\(173\) | 10.3923 | − | 6.00000i | 0.790112 | − | 0.456172i | −0.0498898 | − | 0.998755i | \(-0.515887\pi\) |
0.840002 | + | 0.542583i | \(0.182554\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.50000 | + | 2.59808i | 0.113067 | + | 0.195837i | ||||
\(177\) | 9.00000i | 0.676481i | ||||||||
\(178\) | 15.5885 | − | 9.00000i | 1.16840 | − | 0.674579i | ||||
\(179\) | −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 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 6.92820 | + | 2.00000i | 0.513553 | + | 0.148250i | ||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | −1.50000 | + | 2.59808i | −0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.50000 | + | 4.33013i | 0.183309 | + | 0.317500i | ||||
\(187\) | 18.0000i | 1.31629i | ||||||||
\(188\) | −2.59808 | + | 1.50000i | −0.189484 | + | 0.109399i | ||||
\(189\) | 1.00000 | + | 1.73205i | 0.0727393 | + | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | + | 10.3923i | 0.434145 | + | 0.751961i | 0.997225 | − | 0.0744412i | \(-0.0237173\pi\) |
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 3.46410 | + | 2.00000i | 0.249351 | + | 0.143963i | 0.619467 | − | 0.785022i | \(-0.287349\pi\) |
−0.370116 | + | 0.928986i | \(0.620682\pi\) | |||||||
\(194\) | 14.0000 | 1.00514 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 20.7846 | + | 12.0000i | 1.48084 | + | 0.854965i | 0.999764 | − | 0.0217133i | \(-0.00691209\pi\) |
0.481078 | + | 0.876678i | \(0.340245\pi\) | |||||||
\(198\) | −2.59808 | − | 1.50000i | −0.184637 | − | 0.106600i | ||||
\(199\) | 4.00000 | + | 6.92820i | 0.283552 | + | 0.491127i | 0.972257 | − | 0.233915i | \(-0.0751537\pi\) |
−0.688705 | + | 0.725042i | \(0.741820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | − | 6.92820i | −0.282138 | − | 0.488678i | ||||
\(202\) | 5.19615 | − | 3.00000i | 0.365600 | − | 0.211079i | ||||
\(203\) | 6.00000i | 0.421117i | ||||||||
\(204\) | 3.00000 | + | 5.19615i | 0.210042 | + | 0.363803i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.00000 | − | 12.1244i | 0.487713 | − | 0.844744i | ||||
\(207\) | − | 3.00000i | − | 0.208514i | ||||||
\(208\) | −2.59808 | + | 2.50000i | −0.180144 | + | 0.173344i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | + | 17.3205i | −0.688428 | + | 1.19239i | 0.283918 | + | 0.958849i | \(0.408366\pi\) |
−0.972346 | + | 0.233544i | \(0.924968\pi\) | |||||||
\(212\) | 5.19615 | − | 3.00000i | 0.356873 | − | 0.206041i | ||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −8.66025 | + | 5.00000i | −0.587896 | + | 0.339422i | ||||
\(218\) | 12.1244 | + | 7.00000i | 0.821165 | + | 0.474100i | ||||
\(219\) | 7.00000 | − | 12.1244i | 0.473016 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.0000 | + | 5.19615i | −1.41261 | + | 0.349531i | ||||
\(222\) | − | 7.00000i | − | 0.469809i | ||||||
\(223\) | 8.66025 | + | 5.00000i | 0.579934 | + | 0.334825i | 0.761107 | − | 0.648626i | \(-0.224656\pi\) |
−0.181173 | + | 0.983451i | \(0.557990\pi\) | |||||||
\(224\) | −1.00000 | + | 1.73205i | −0.0668153 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 1.73205 | − | 1.00000i | 0.114708 | − | 0.0662266i | ||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00000 | − | 5.19615i | 0.197386 | − | 0.341882i | ||||
\(232\) | −2.59808 | − | 1.50000i | −0.170572 | − | 0.0984798i | ||||
\(233\) | 21.0000i | 1.37576i | 0.725826 | + | 0.687878i | \(0.241458\pi\) | ||||
−0.725826 | + | 0.687878i | \(0.758542\pi\) | |||||||
\(234\) | 1.00000 | − | 3.46410i | 0.0653720 | − | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.50000 | − | 7.79423i | 0.292925 | − | 0.507361i | ||||
\(237\) | 4.33013 | + | 2.50000i | 0.281272 | + | 0.162392i | ||||
\(238\) | −10.3923 | + | 6.00000i | −0.673633 | + | 0.388922i | ||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | − | 14.7224i | −0.547533 | − | 0.948355i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 1.00000 | − | 1.73205i | 0.0640184 | − | 0.110883i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 1.73205 | + | 7.00000i | 0.110208 | + | 0.445399i | ||||
\(248\) | − | 5.00000i | − | 0.317500i | ||||||
\(249\) | −3.00000 | + | 5.19615i | −0.190117 | + | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.50000 | − | 12.9904i | −0.473396 | − | 0.819946i | 0.526140 | − | 0.850398i | \(-0.323639\pi\) |
−0.999536 | + | 0.0304521i | \(0.990305\pi\) | |||||||
\(252\) | − | 2.00000i | − | 0.125988i | ||||||
\(253\) | −7.79423 | + | 4.50000i | −0.490019 | + | 0.282913i | ||||
\(254\) | −7.00000 | − | 12.1244i | −0.439219 | − | 0.760750i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −18.1865 | − | 10.5000i | −1.13444 | − | 0.654972i | −0.189396 | − | 0.981901i | \(-0.560653\pi\) |
−0.945049 | + | 0.326929i | \(0.893986\pi\) | |||||||
\(258\) | −0.866025 | − | 0.500000i | −0.0539164 | − | 0.0311286i | ||||
\(259\) | 14.0000 | 0.869918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | −7.79423 | − | 4.50000i | −0.481529 | − | 0.278011i | ||||
\(263\) | 12.9904 | + | 7.50000i | 0.801021 | + | 0.462470i | 0.843828 | − | 0.536614i | \(-0.180297\pi\) |
−0.0428069 | + | 0.999083i | \(0.513630\pi\) | |||||||
\(264\) | 1.50000 | + | 2.59808i | 0.0923186 | + | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.00000 | + | 3.46410i | 0.122628 | + | 0.212398i | ||||
\(267\) | 15.5885 | − | 9.00000i | 0.953998 | − | 0.550791i | ||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50000 | + | 9.52628i | −0.334101 | + | 0.578680i | −0.983312 | − | 0.181928i | \(-0.941766\pi\) |
0.649211 | + | 0.760609i | \(0.275099\pi\) | |||||||
\(272\) | − | 6.00000i | − | 0.363803i | ||||||
\(273\) | 6.92820 | + | 2.00000i | 0.419314 | + | 0.121046i | ||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | + | 2.59808i | −0.0902894 | + | 0.156386i | ||||
\(277\) | 0.866025 | − | 0.500000i | 0.0520344 | − | 0.0300421i | −0.473757 | − | 0.880656i | \(-0.657103\pi\) |
0.525792 | + | 0.850613i | \(0.323769\pi\) | |||||||
\(278\) | − | 14.0000i | − | 0.839664i | ||||||
\(279\) | 2.50000 | + | 4.33013i | 0.149671 | + | 0.259238i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | −2.59808 | + | 1.50000i | −0.154713 | + | 0.0893237i | ||||
\(283\) | 26.8468 | + | 15.5000i | 1.59588 | + | 0.921379i | 0.992270 | + | 0.124096i | \(0.0396032\pi\) |
0.603606 | + | 0.797283i | \(0.293730\pi\) | |||||||
\(284\) | −6.00000 | + | 10.3923i | −0.356034 | + | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.5000 | + | 2.59808i | −0.620878 | + | 0.153627i | ||||
\(287\) | − | 12.0000i | − | 0.708338i | ||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | 9.50000 | − | 16.4545i | 0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0000 | 0.820695 | ||||||||
\(292\) | −12.1244 | + | 7.00000i | −0.709524 | + | 0.409644i | ||||
\(293\) | −25.9808 | + | 15.0000i | −1.51781 | + | 0.876309i | −0.518032 | + | 0.855361i | \(0.673335\pi\) |
−0.999781 | + | 0.0209480i | \(0.993332\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.50000 | + | 6.06218i | −0.203433 | + | 0.352357i | ||||
\(297\) | −2.59808 | − | 1.50000i | −0.150756 | − | 0.0870388i | ||||
\(298\) | 9.00000i | 0.521356i | ||||||||
\(299\) | −7.50000 | − | 7.79423i | −0.433736 | − | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | − | 1.73205i | 0.0576390 | − | 0.0998337i | ||||
\(302\) | −6.92820 | − | 4.00000i | −0.398673 | − | 0.230174i | ||||
\(303\) | 5.19615 | − | 3.00000i | 0.298511 | − | 0.172345i | ||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.00000 | + | 5.19615i | 0.171499 | + | 0.297044i | ||||
\(307\) | − | 8.00000i | − | 0.456584i | −0.973593 | − | 0.228292i | \(-0.926686\pi\) | ||
0.973593 | − | 0.228292i | \(-0.0733141\pi\) | |||||||
\(308\) | −5.19615 | + | 3.00000i | −0.296078 | + | 0.170941i | ||||
\(309\) | 7.00000 | − | 12.1244i | 0.398216 | − | 0.689730i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | −2.59808 | + | 2.50000i | −0.147087 | + | 0.141535i | ||||
\(313\) | 8.00000i | 0.452187i | 0.974106 | + | 0.226093i | \(0.0725954\pi\) | ||||
−0.974106 | + | 0.226093i | \(0.927405\pi\) | |||||||
\(314\) | 6.50000 | − | 11.2583i | 0.366816 | − | 0.635344i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.50000 | − | 4.33013i | −0.140636 | − | 0.243589i | ||||
\(317\) | − | 12.0000i | − | 0.673987i | −0.941507 | − | 0.336994i | \(-0.890590\pi\) | ||
0.941507 | − | 0.336994i | \(-0.109410\pi\) | |||||||
\(318\) | 5.19615 | − | 3.00000i | 0.291386 | − | 0.168232i | ||||
\(319\) | −4.50000 | − | 7.79423i | −0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.00000 | + | 5.19615i | 0.167444 | + | 0.290021i | ||||
\(322\) | −5.19615 | − | 3.00000i | −0.289570 | − | 0.167183i | ||||
\(323\) | −10.3923 | − | 6.00000i | −0.578243 | − | 0.333849i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.0000 | 0.720003 | ||||||||
\(327\) | 12.1244 | + | 7.00000i | 0.670478 | + | 0.387101i | ||||
\(328\) | 5.19615 | + | 3.00000i | 0.286910 | + | 0.165647i | ||||
\(329\) | −3.00000 | − | 5.19615i | −0.165395 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | − | 27.7128i | −0.879440 | − | 1.52323i | −0.851957 | − | 0.523612i | \(-0.824584\pi\) |
−0.0274825 | − | 0.999622i | \(-0.508749\pi\) | |||||||
\(332\) | 5.19615 | − | 3.00000i | 0.285176 | − | 0.164646i | ||||
\(333\) | − | 7.00000i | − | 0.383598i | ||||||
\(334\) | 4.50000 | + | 7.79423i | 0.246229 | + | 0.426481i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.00000 | + | 1.73205i | −0.0545545 | + | 0.0944911i | ||||
\(337\) | − | 14.0000i | − | 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | −6.06218 | − | 11.5000i | −0.329739 | − | 0.625518i | ||||
\(339\) | −15.0000 | −0.814688 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.50000 | − | 12.9904i | 0.406148 | − | 0.703469i | ||||
\(342\) | 1.73205 | − | 1.00000i | 0.0936586 | − | 0.0540738i | ||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 0.500000 | + | 0.866025i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | −0.645124 | ||||||||
\(347\) | 25.9808 | − | 15.0000i | 1.39472 | − | 0.805242i | 0.400887 | − | 0.916127i | \(-0.368702\pi\) |
0.993833 | + | 0.110885i | \(0.0353686\pi\) | |||||||
\(348\) | −2.59808 | − | 1.50000i | −0.139272 | − | 0.0804084i | ||||
\(349\) | 4.00000 | − | 6.92820i | 0.214115 | − | 0.370858i | −0.738883 | − | 0.673833i | \(-0.764647\pi\) |
0.952998 | + | 0.302975i | \(0.0979799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | − | 3.46410i | 0.0533761 | − | 0.184900i | ||||
\(352\) | − | 3.00000i | − | 0.159901i | ||||||
\(353\) | −25.9808 | − | 15.0000i | −1.38282 | − | 0.798369i | −0.390324 | − | 0.920677i | \(-0.627637\pi\) |
−0.992492 | + | 0.122308i | \(0.960970\pi\) | |||||||
\(354\) | 4.50000 | − | 7.79423i | 0.239172 | − | 0.414259i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.0000 | −0.953998 | ||||||||
\(357\) | −10.3923 | + | 6.00000i | −0.550019 | + | 0.317554i | ||||
\(358\) | 2.59808 | − | 1.50000i | 0.137313 | − | 0.0792775i | ||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 13.8564 | + | 8.00000i | 0.728277 | + | 0.420471i | ||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | −5.00000 | − | 5.19615i | −0.262071 | − | 0.272352i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.00000 | − | 1.73205i | 0.0522708 | − | 0.0905357i | ||||
\(367\) | 17.3205 | + | 10.0000i | 0.904123 | + | 0.521996i | 0.878536 | − | 0.477677i | \(-0.158521\pi\) |
0.0255875 | + | 0.999673i | \(0.491854\pi\) | |||||||
\(368\) | 2.59808 | − | 1.50000i | 0.135434 | − | 0.0781929i | ||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 10.3923i | 0.311504 | + | 0.539542i | ||||
\(372\) | − | 5.00000i | − | 0.259238i | ||||||
\(373\) | −21.6506 | + | 12.5000i | −1.12103 | + | 0.647225i | −0.941663 | − | 0.336557i | \(-0.890737\pi\) |
−0.179364 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(374\) | 9.00000 | − | 15.5885i | 0.465379 | − | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 7.79423 | − | 7.50000i | 0.401423 | − | 0.386270i | ||||
\(378\) | − | 2.00000i | − | 0.102869i | ||||||
\(379\) | 19.0000 | − | 32.9090i | 0.975964 | − | 1.69042i | 0.299249 | − | 0.954175i | \(-0.403264\pi\) |
0.676715 | − | 0.736245i | \(-0.263403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.00000 | − | 12.1244i | −0.358621 | − | 0.621150i | ||||
\(382\) | − | 12.0000i | − | 0.613973i | ||||||
\(383\) | −18.1865 | + | 10.5000i | −0.929288 | + | 0.536525i | −0.886586 | − | 0.462563i | \(-0.846930\pi\) |
−0.0427020 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | − | 3.46410i | −0.101797 | − | 0.176318i | ||||
\(387\) | −0.866025 | − | 0.500000i | −0.0440225 | − | 0.0254164i | ||||
\(388\) | −12.1244 | − | 7.00000i | −0.615521 | − | 0.355371i | ||||
\(389\) | −3.00000 | −0.152106 | −0.0760530 | − | 0.997104i | \(-0.524232\pi\) | ||||
−0.0760530 | + | 0.997104i | \(0.524232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 2.59808 | + | 1.50000i | 0.131223 | + | 0.0757614i | ||||
\(393\) | −7.79423 | − | 4.50000i | −0.393167 | − | 0.226995i | ||||
\(394\) | −12.0000 | − | 20.7846i | −0.604551 | − | 1.04711i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | 26.8468 | − | 15.5000i | 1.34740 | − | 0.777923i | 0.359521 | − | 0.933137i | \(-0.382940\pi\) |
0.987881 | + | 0.155214i | \(0.0496068\pi\) | |||||||
\(398\) | − | 8.00000i | − | 0.401004i | ||||||
\(399\) | 2.00000 | + | 3.46410i | 0.100125 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | − | 10.3923i | 0.299626 | − | 0.518967i | −0.676425 | − | 0.736512i | \(-0.736472\pi\) |
0.976050 | + | 0.217545i | \(0.0698049\pi\) | |||||||
\(402\) | 8.00000i | 0.399004i | ||||||||
\(403\) | 17.3205 | + | 5.00000i | 0.862796 | + | 0.249068i | ||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | − | 5.19615i | 0.148888 | − | 0.257881i | ||||
\(407\) | −18.1865 | + | 10.5000i | −0.901473 | + | 0.520466i | ||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | −5.00000 | − | 8.66025i | −0.247234 | − | 0.428222i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.962757 | + | 0.270367i | \(0.912855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000 | 0.443937 | ||||||||
\(412\) | −12.1244 | + | 7.00000i | −0.597324 | + | 0.344865i | ||||
\(413\) | 15.5885 | + | 9.00000i | 0.767058 | + | 0.442861i | ||||
\(414\) | −1.50000 | + | 2.59808i | −0.0737210 | + | 0.127688i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.50000 | − | 0.866025i | 0.171602 | − | 0.0424604i | ||||
\(417\) | − | 14.0000i | − | 0.685583i | ||||||
\(418\) | −5.19615 | − | 3.00000i | −0.254152 | − | 0.146735i | ||||
\(419\) | −6.00000 | + | 10.3923i | −0.293119 | + | 0.507697i | −0.974546 | − | 0.224189i | \(-0.928027\pi\) |
0.681426 | + | 0.731887i | \(0.261360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | −0.779792 | −0.389896 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389896 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(422\) | 17.3205 | − | 10.0000i | 0.843149 | − | 0.486792i | ||||
\(423\) | −2.59808 | + | 1.50000i | −0.126323 | + | 0.0729325i | ||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.00000 | + | 10.3923i | −0.290701 | + | 0.503509i | ||||
\(427\) | 3.46410 | + | 2.00000i | 0.167640 | + | 0.0967868i | ||||
\(428\) | − | 6.00000i | − | 0.290021i | ||||||
\(429\) | −10.5000 | + | 2.59808i | −0.506945 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | −34.6410 | + | 20.0000i | −1.66474 | + | 0.961139i | −0.694337 | + | 0.719650i | \(0.744302\pi\) |
−0.970404 | + | 0.241489i | \(0.922364\pi\) | |||||||
\(434\) | 10.0000 | 0.480015 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | − | 6.00000i | − | 0.287019i | ||||||
\(438\) | −12.1244 | + | 7.00000i | −0.579324 | + | 0.334473i | ||||
\(439\) | −2.00000 | + | 3.46410i | −0.0954548 | + | 0.165333i | −0.909798 | − | 0.415051i | \(-0.863764\pi\) |
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 20.7846 | + | 6.00000i | 0.988623 | + | 0.285391i | ||||
\(443\) | − | 36.0000i | − | 1.71041i | −0.518289 | − | 0.855206i | \(-0.673431\pi\) | ||
0.518289 | − | 0.855206i | \(-0.326569\pi\) | |||||||
\(444\) | −3.50000 | + | 6.06218i | −0.166103 | + | 0.287698i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.00000 | − | 8.66025i | −0.236757 | − | 0.410075i | ||||
\(447\) | 9.00000i | 0.425685i | ||||||||
\(448\) | 1.73205 | − | 1.00000i | 0.0818317 | − | 0.0472456i | ||||
\(449\) | 18.0000 | + | 31.1769i | 0.849473 | + | 1.47133i | 0.881680 | + | 0.471848i | \(0.156413\pi\) |
−0.0322072 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 15.5885i | 0.423793 | + | 0.734032i | ||||
\(452\) | 12.9904 | + | 7.50000i | 0.611016 | + | 0.352770i | ||||
\(453\) | −6.92820 | − | 4.00000i | −0.325515 | − | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 1.73205 | + | 1.00000i | 0.0810219 | + | 0.0467780i | 0.539964 | − | 0.841688i | \(-0.318438\pi\) |
−0.458942 | + | 0.888466i | \(0.651771\pi\) | |||||||
\(458\) | 12.1244 | + | 7.00000i | 0.566534 | + | 0.327089i | ||||
\(459\) | 3.00000 | + | 5.19615i | 0.140028 | + | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.50000 | − | 12.9904i | −0.349310 | − | 0.605022i | 0.636817 | − | 0.771015i | \(-0.280251\pi\) |
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(462\) | −5.19615 | + | 3.00000i | −0.241747 | + | 0.139573i | ||||
\(463\) | − | 34.0000i | − | 1.58011i | −0.613033 | − | 0.790057i | \(-0.710051\pi\) | ||
0.613033 | − | 0.790057i | \(-0.289949\pi\) | |||||||
\(464\) | 1.50000 | + | 2.59808i | 0.0696358 | + | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5000 | − | 18.1865i | 0.486403 | − | 0.842475i | ||||
\(467\) | − | 18.0000i | − | 0.832941i | −0.909149 | − | 0.416470i | \(-0.863267\pi\) | ||
0.909149 | − | 0.416470i | \(-0.136733\pi\) | |||||||
\(468\) | −2.59808 | + | 2.50000i | −0.120096 | + | 0.115563i | ||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | − | 11.2583i | 0.299504 | − | 0.518756i | ||||
\(472\) | −7.79423 | + | 4.50000i | −0.358758 | + | 0.207129i | ||||
\(473\) | 3.00000i | 0.137940i | ||||||||
\(474\) | −2.50000 | − | 4.33013i | −0.114829 | − | 0.198889i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | 5.19615 | − | 3.00000i | 0.237915 | − | 0.137361i | ||||
\(478\) | 20.7846 | + | 12.0000i | 0.950666 | + | 0.548867i | ||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5000 | − | 18.1865i | −0.797931 | − | 0.829235i | ||||
\(482\) | 17.0000i | 0.774329i | ||||||||
\(483\) | −5.19615 | − | 3.00000i | −0.236433 | − | 0.136505i | ||||
\(484\) | −1.00000 | + | 1.73205i | −0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −1.73205 | + | 1.00000i | −0.0784867 | + | 0.0453143i | −0.538730 | − | 0.842479i | \(-0.681096\pi\) |
0.460243 | + | 0.887793i | \(0.347762\pi\) | |||||||
\(488\) | −1.73205 | + | 1.00000i | −0.0784063 | + | 0.0452679i | ||||
\(489\) | 13.0000 | 0.587880 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 5.19615 | + | 3.00000i | 0.234261 | + | 0.135250i | ||||
\(493\) | 18.0000i | 0.810679i | ||||||||
\(494\) | 2.00000 | − | 6.92820i | 0.0899843 | − | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.50000 | + | 4.33013i | −0.112253 | + | 0.194428i | ||||
\(497\) | −20.7846 | − | 12.0000i | −0.932317 | − | 0.538274i | ||||
\(498\) | 5.19615 | − | 3.00000i | 0.232845 | − | 0.134433i | ||||
\(499\) | −32.0000 | −1.43252 | −0.716258 | − | 0.697835i | \(-0.754147\pi\) | ||||
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.50000 | + | 7.79423i | 0.201045 | + | 0.348220i | ||||
\(502\) | 15.0000i | 0.669483i | ||||||||
\(503\) | 20.7846 | − | 12.0000i | 0.926740 | − | 0.535054i | 0.0409609 | − | 0.999161i | \(-0.486958\pi\) |
0.885779 | + | 0.464107i | \(0.153625\pi\) | |||||||
\(504\) | −1.00000 | + | 1.73205i | −0.0445435 | + | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | 0.400099 | ||||||||
\(507\) | −6.06218 | − | 11.5000i | −0.269231 | − | 0.510733i | ||||
\(508\) | 14.0000i | 0.621150i | ||||||||
\(509\) | 1.50000 | − | 2.59808i | 0.0664863 | − | 0.115158i | −0.830866 | − | 0.556473i | \(-0.812154\pi\) |
0.897352 | + | 0.441315i | \(0.145488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | − | 24.2487i | −0.619324 | − | 1.07270i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.73205 | − | 1.00000i | 0.0764719 | − | 0.0441511i | ||||
\(514\) | 10.5000 | + | 18.1865i | 0.463135 | + | 0.802174i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.500000 | + | 0.866025i | 0.0220113 | + | 0.0381246i | ||||
\(517\) | 7.79423 | + | 4.50000i | 0.342790 | + | 0.197910i | ||||
\(518\) | −12.1244 | − | 7.00000i | −0.532714 | − | 0.307562i | ||||
\(519\) | −12.0000 | −0.526742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | −2.59808 | − | 1.50000i | −0.113715 | − | 0.0656532i | ||||
\(523\) | −9.52628 | − | 5.50000i | −0.416555 | − | 0.240498i | 0.277047 | − | 0.960856i | \(-0.410644\pi\) |
−0.693602 | + | 0.720358i | \(0.743977\pi\) | |||||||
\(524\) | 4.50000 | + | 7.79423i | 0.196583 | + | 0.340492i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.50000 | − | 12.9904i | −0.327016 | − | 0.566408i | ||||
\(527\) | −25.9808 | + | 15.0000i | −1.13174 | + | 0.653410i | ||||
\(528\) | − | 3.00000i | − | 0.130558i | ||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.50000 | − | 7.79423i | 0.195283 | − | 0.338241i | ||||
\(532\) | − | 4.00000i | − | 0.173422i | ||||||
\(533\) | −15.5885 | + | 15.0000i | −0.675211 | + | 0.649722i | ||||
\(534\) | −18.0000 | −0.778936 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.00000 | − | 6.92820i | 0.172774 | − | 0.299253i | ||||
\(537\) | 2.59808 | − | 1.50000i | 0.112115 | − | 0.0647298i | ||||
\(538\) | − | 18.0000i | − | 0.776035i | ||||||
\(539\) | 4.50000 | + | 7.79423i | 0.193829 | + | 0.335721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | 9.52628 | − | 5.50000i | 0.409189 | − | 0.236245i | ||||
\(543\) | 13.8564 | + | 8.00000i | 0.594635 | + | 0.343313i | ||||
\(544\) | −3.00000 | + | 5.19615i | −0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.00000 | − | 5.19615i | −0.213980 | − | 0.222375i | ||||
\(547\) | − | 20.0000i | − | 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | −7.79423 | − | 4.50000i | −0.332953 | − | 0.192230i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 2.59808 | − | 1.50000i | 0.110581 | − | 0.0638442i | ||||
\(553\) | 8.66025 | − | 5.00000i | 0.368271 | − | 0.212622i | ||||
\(554\) | −1.00000 | −0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.00000 | + | 12.1244i | −0.296866 | + | 0.514187i | ||||
\(557\) | −5.19615 | − | 3.00000i | −0.220168 | − | 0.127114i | 0.385860 | − | 0.922557i | \(-0.373905\pi\) |
−0.606028 | + | 0.795443i | \(0.707238\pi\) | |||||||
\(558\) | − | 5.00000i | − | 0.211667i | ||||||
\(559\) | −3.50000 | + | 0.866025i | −0.148034 | + | 0.0366290i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | − | 15.5885i | 0.379980 | − | 0.658145i | ||||
\(562\) | −15.5885 | − | 9.00000i | −0.657559 | − | 0.379642i | ||||
\(563\) | 31.1769 | − | 18.0000i | 1.31395 | − | 0.758610i | 0.331202 | − | 0.943560i | \(-0.392546\pi\) |
0.982748 | + | 0.184950i | \(0.0592124\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.5000 | − | 26.8468i | −0.651514 | − | 1.12845i | ||||
\(567\) | − | 2.00000i | − | 0.0839921i | ||||||
\(568\) | 10.3923 | − | 6.00000i | 0.436051 | − | 0.251754i | ||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | 10.3923 | + | 3.00000i | 0.434524 | + | 0.125436i | ||||
\(573\) | − | 12.0000i | − | 0.501307i | ||||||
\(574\) | −6.00000 | + | 10.3923i | −0.250435 | + | 0.433766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 2.00000i | − | 0.0832611i | −0.999133 | − | 0.0416305i | \(-0.986745\pi\) | ||
0.999133 | − | 0.0416305i | \(-0.0132552\pi\) | |||||||
\(578\) | −16.4545 | + | 9.50000i | −0.684416 | + | 0.395148i | ||||
\(579\) | −2.00000 | − | 3.46410i | −0.0831172 | − | 0.143963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | −12.1244 | − | 7.00000i | −0.502571 | − | 0.290159i | ||||
\(583\) | −15.5885 | − | 9.00000i | −0.645608 | − | 0.372742i | ||||
\(584\) | 14.0000 | 0.579324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0000 | 1.23929 | ||||||||
\(587\) | 15.5885 | + | 9.00000i | 0.643404 | + | 0.371470i | 0.785925 | − | 0.618322i | \(-0.212187\pi\) |
−0.142520 | + | 0.989792i | \(0.545521\pi\) | |||||||
\(588\) | 2.59808 | + | 1.50000i | 0.107143 | + | 0.0618590i | ||||
\(589\) | 5.00000 | + | 8.66025i | 0.206021 | + | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | − | 20.7846i | −0.493614 | − | 0.854965i | ||||
\(592\) | 6.06218 | − | 3.50000i | 0.249154 | − | 0.143849i | ||||
\(593\) | 27.0000i | 1.10876i | 0.832265 | + | 0.554379i | \(0.187044\pi\) | ||||
−0.832265 | + | 0.554379i | \(0.812956\pi\) | |||||||
\(594\) | 1.50000 | + | 2.59808i | 0.0615457 | + | 0.106600i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.50000 | − | 7.79423i | 0.184327 | − | 0.319264i | ||||
\(597\) | − | 8.00000i | − | 0.327418i | ||||||
\(598\) | 2.59808 | + | 10.5000i | 0.106243 | + | 0.429377i | ||||
\(599\) | −6.00000 | −0.245153 | −0.122577 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122577 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.50000 | − | 16.4545i | 0.387513 | − | 0.671192i | −0.604601 | − | 0.796528i | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | −1.73205 | + | 1.00000i | −0.0705931 | + | 0.0407570i | ||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 4.00000 | + | 6.92820i | 0.162758 | + | 0.281905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.00000 | −0.243733 | ||||||||
\(607\) | 19.0526 | − | 11.0000i | 0.773320 | − | 0.446476i | −0.0607380 | − | 0.998154i | \(-0.519345\pi\) |
0.834058 | + | 0.551678i | \(0.186012\pi\) | |||||||
\(608\) | 1.73205 | + | 1.00000i | 0.0702439 | + | 0.0405554i | ||||
\(609\) | 3.00000 | − | 5.19615i | 0.121566 | − | 0.210559i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | + | 10.3923i | −0.121367 | + | 0.420428i | ||||
\(612\) | − | 6.00000i | − | 0.242536i | ||||||
\(613\) | 26.8468 | + | 15.5000i | 1.08433 | + | 0.626039i | 0.932062 | − | 0.362300i | \(-0.118008\pi\) |
0.152270 | + | 0.988339i | \(0.451342\pi\) | |||||||
\(614\) | −4.00000 | + | 6.92820i | −0.161427 | + | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.00000 | 0.241747 | ||||||||
\(617\) | −18.1865 | + | 10.5000i | −0.732162 | + | 0.422714i | −0.819213 | − | 0.573490i | \(-0.805589\pi\) |
0.0870504 | + | 0.996204i | \(0.472256\pi\) | |||||||
\(618\) | −12.1244 | + | 7.00000i | −0.487713 | + | 0.281581i | ||||
\(619\) | 46.0000 | 1.84890 | 0.924448 | − | 0.381308i | \(-0.124526\pi\) | ||||
0.924448 | + | 0.381308i | \(0.124526\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50000 | + | 2.59808i | −0.0601929 | + | 0.104257i | ||||
\(622\) | 10.3923 | + | 6.00000i | 0.416693 | + | 0.240578i | ||||
\(623\) | − | 36.0000i | − | 1.44231i | ||||||
\(624\) | 3.50000 | − | 0.866025i | 0.140112 | − | 0.0346688i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.00000 | − | 6.92820i | 0.159872 | − | 0.276907i | ||||
\(627\) | −5.19615 | − | 3.00000i | −0.207514 | − | 0.119808i | ||||
\(628\) | −11.2583 | + | 6.50000i | −0.449256 | + | 0.259378i | ||||
\(629\) | 42.0000 | 1.67465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | + | 13.8564i | 0.318475 | + | 0.551615i | 0.980170 | − | 0.198158i | \(-0.0634960\pi\) |
−0.661695 | + | 0.749773i | \(0.730163\pi\) | |||||||
\(632\) | 5.00000i | 0.198889i | ||||||||
\(633\) | 17.3205 | − | 10.0000i | 0.688428 | − | 0.397464i | ||||
\(634\) | −6.00000 | + | 10.3923i | −0.238290 | + | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | −7.79423 | + | 7.50000i | −0.308819 | + | 0.297161i | ||||
\(638\) | 9.00000i | 0.356313i | ||||||||
\(639\) | −6.00000 | + | 10.3923i | −0.237356 | + | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.00000 | − | 5.19615i | −0.118493 | − | 0.205236i | 0.800678 | − | 0.599095i | \(-0.204473\pi\) |
−0.919171 | + | 0.393860i | \(0.871140\pi\) | |||||||
\(642\) | − | 6.00000i | − | 0.236801i | ||||||
\(643\) | −13.8564 | + | 8.00000i | −0.546443 | + | 0.315489i | −0.747686 | − | 0.664052i | \(-0.768835\pi\) |
0.201243 | + | 0.979541i | \(0.435502\pi\) | |||||||
\(644\) | 3.00000 | + | 5.19615i | 0.118217 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | 20.7846 | + | 12.0000i | 0.817127 | + | 0.471769i | 0.849425 | − | 0.527710i | \(-0.176949\pi\) |
−0.0322975 | + | 0.999478i | \(0.510282\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −27.0000 | −1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0000 | 0.391931 | ||||||||
\(652\) | −11.2583 | − | 6.50000i | −0.440910 | − | 0.254560i | ||||
\(653\) | −5.19615 | − | 3.00000i | −0.203341 | − | 0.117399i | 0.394872 | − | 0.918736i | \(-0.370789\pi\) |
−0.598213 | + | 0.801337i | \(0.704122\pi\) | |||||||
\(654\) | −7.00000 | − | 12.1244i | −0.273722 | − | 0.474100i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | −12.1244 | + | 7.00000i | −0.473016 | + | 0.273096i | ||||
\(658\) | 6.00000i | 0.233904i | ||||||||
\(659\) | 7.50000 | + | 12.9904i | 0.292159 | + | 0.506033i | 0.974320 | − | 0.225168i | \(-0.0722932\pi\) |
−0.682161 | + | 0.731202i | \(0.738960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | 32.0000i | 1.24372i | ||||||||
\(663\) | 20.7846 | + | 6.00000i | 0.807207 | + | 0.233021i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.50000 | + | 6.06218i | −0.135622 | + | 0.234905i | ||||
\(667\) | −7.79423 | + | 4.50000i | −0.301794 | + | 0.174241i | ||||
\(668\) | − | 9.00000i | − | 0.348220i | ||||||
\(669\) | −5.00000 | − | 8.66025i | −0.193311 | − | 0.334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | −0.231627 | ||||||||
\(672\) | 1.73205 | − | 1.00000i | 0.0668153 | − | 0.0385758i | ||||
\(673\) | 3.46410 | + | 2.00000i | 0.133531 | + | 0.0770943i | 0.565278 | − | 0.824901i | \(-0.308769\pi\) |
−0.431746 | + | 0.901995i | \(0.642102\pi\) | |||||||
\(674\) | −7.00000 | + | 12.1244i | −0.269630 | + | 0.467013i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.500000 | + | 12.9904i | −0.0192308 | + | 0.499630i | ||||
\(677\) | 36.0000i | 1.38359i | 0.722093 | + | 0.691796i | \(0.243180\pi\) | ||||
−0.722093 | + | 0.691796i | \(0.756820\pi\) | |||||||
\(678\) | 12.9904 | + | 7.50000i | 0.498893 | + | 0.288036i | ||||
\(679\) | 14.0000 | − | 24.2487i | 0.537271 | − | 0.930580i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.9904 | + | 7.50000i | −0.497427 | + | 0.287190i | ||||
\(683\) | −10.3923 | + | 6.00000i | −0.397650 | + | 0.229584i | −0.685470 | − | 0.728101i | \(-0.740403\pi\) |
0.287819 | + | 0.957685i | \(0.407070\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.0000 | + | 17.3205i | −0.381802 | + | 0.661300i | ||||
\(687\) | 12.1244 | + | 7.00000i | 0.462573 | + | 0.267067i | ||||
\(688\) | − | 1.00000i | − | 0.0381246i | ||||||
\(689\) | 6.00000 | − | 20.7846i | 0.228582 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.0000 | − | 39.8372i | 0.874961 | − | 1.51548i | 0.0181572 | − | 0.999835i | \(-0.494220\pi\) |
0.856804 | − | 0.515642i | \(-0.172447\pi\) | |||||||
\(692\) | 10.3923 | + | 6.00000i | 0.395056 | + | 0.228086i | ||||
\(693\) | −5.19615 | + | 3.00000i | −0.197386 | + | 0.113961i | ||||
\(694\) | −30.0000 | −1.13878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.50000 | + | 2.59808i | 0.0568574 | + | 0.0984798i | ||||
\(697\) | − | 36.0000i | − | 1.36360i | ||||||
\(698\) | −6.92820 | + | 4.00000i | −0.262236 | + | 0.151402i | ||||
\(699\) | 10.5000 | − | 18.1865i | 0.397146 | − | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.0000 | −0.793159 | −0.396580 | − | 0.918000i | \(-0.629803\pi\) | ||||
−0.396580 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(702\) | −2.59808 | + | 2.50000i | −0.0980581 | + | 0.0943564i | ||||
\(703\) | − | 14.0000i | − | 0.528020i | ||||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | + | 25.9808i | 0.564532 | + | 0.977799i | ||||
\(707\) | − | 12.0000i | − | 0.451306i | ||||||
\(708\) | −7.79423 | + | 4.50000i | −0.292925 | + | 0.169120i | ||||
\(709\) | 16.0000 | + | 27.7128i | 0.600893 | + | 1.04078i | 0.992686 | + | 0.120723i | \(0.0385214\pi\) |
−0.391794 | + | 0.920053i | \(0.628145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | − | 4.33013i | −0.0937573 | − | 0.162392i | ||||
\(712\) | 15.5885 | + | 9.00000i | 0.584202 | + | 0.337289i | ||||
\(713\) | −12.9904 | − | 7.50000i | −0.486494 | − | 0.280877i | ||||
\(714\) | 12.0000 | 0.449089 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.00000 | −0.112115 | ||||||||
\(717\) | 20.7846 | + | 12.0000i | 0.776215 | + | 0.448148i | ||||
\(718\) | 20.7846 | + | 12.0000i | 0.775675 | + | 0.447836i | ||||
\(719\) | 18.0000 | + | 31.1769i | 0.671287 | + | 1.16270i | 0.977539 | + | 0.210752i | \(0.0675914\pi\) |
−0.306253 | + | 0.951950i | \(0.599075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | − | 24.2487i | −0.521387 | − | 0.903069i | ||||
\(722\) | −12.9904 | + | 7.50000i | −0.483452 | + | 0.279121i | ||||
\(723\) | 17.0000i | 0.632237i | ||||||||
\(724\) | −8.00000 | − | 13.8564i | −0.297318 | − | 0.514969i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00000 | + | 1.73205i | −0.0371135 | + | 0.0642824i | ||||
\(727\) | 4.00000i | 0.148352i | 0.997245 | + | 0.0741759i | \(0.0236326\pi\) | ||||
−0.997245 | + | 0.0741759i | \(0.976367\pi\) | |||||||
\(728\) | 1.73205 | + | 7.00000i | 0.0641941 | + | 0.259437i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00000 | − | 5.19615i | 0.110959 | − | 0.192187i | ||||
\(732\) | −1.73205 | + | 1.00000i | −0.0640184 | + | 0.0369611i | ||||
\(733\) | − | 22.0000i | − | 0.812589i | −0.913742 | − | 0.406294i | \(-0.866821\pi\) | ||
0.913742 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(734\) | −10.0000 | − | 17.3205i | −0.369107 | − | 0.639312i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 20.7846 | − | 12.0000i | 0.765611 | − | 0.442026i | ||||
\(738\) | 5.19615 | + | 3.00000i | 0.191273 | + | 0.110432i | ||||
\(739\) | −8.00000 | + | 13.8564i | −0.294285 | + | 0.509716i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00000 | − | 6.92820i | 0.0734718 | − | 0.254514i | ||||
\(742\) | − | 12.0000i | − | 0.440534i | ||||||
\(743\) | 7.79423 | + | 4.50000i | 0.285943 | + | 0.165089i | 0.636111 | − | 0.771598i | \(-0.280542\pi\) |
−0.350168 | + | 0.936687i | \(0.613876\pi\) | |||||||
\(744\) | −2.50000 | + | 4.33013i | −0.0916544 | + | 0.158750i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.0000 | 0.915315 | ||||||||
\(747\) | 5.19615 | − | 3.00000i | 0.190117 | − | 0.109764i | ||||
\(748\) | −15.5885 | + | 9.00000i | −0.569970 | + | 0.329073i | ||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5000 | + | 35.5070i | −0.748056 | + | 1.29567i | 0.200698 | + | 0.979653i | \(0.435679\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | −2.59808 | − | 1.50000i | −0.0947421 | − | 0.0546994i | ||||
\(753\) | 15.0000i | 0.546630i | ||||||||
\(754\) | −10.5000 | + | 2.59808i | −0.382387 | + | 0.0946164i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.00000 | + | 1.73205i | −0.0363696 | + | 0.0629941i | ||||
\(757\) | 32.9090 | + | 19.0000i | 1.19610 | + | 0.690567i | 0.959683 | − | 0.281086i | \(-0.0906945\pi\) |
0.236414 | + | 0.971652i | \(0.424028\pi\) | |||||||
\(758\) | −32.9090 | + | 19.0000i | −1.19531 | + | 0.690111i | ||||
\(759\) | 9.00000 | 0.326679 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | + | 10.3923i | 0.217500 | + | 0.376721i | 0.954043 | − | 0.299670i | \(-0.0968765\pi\) |
−0.736543 | + | 0.676391i | \(0.763543\pi\) | |||||||
\(762\) | 14.0000i | 0.507166i | ||||||||
\(763\) | 24.2487 | − | 14.0000i | 0.877862 | − | 0.506834i | ||||
\(764\) | −6.00000 | + | 10.3923i | −0.217072 | + | 0.375980i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.0000 | 0.758761 | ||||||||
\(767\) | −7.79423 | − | 31.5000i | −0.281433 | − | 1.13740i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −6.50000 | + | 11.2583i | −0.234396 | + | 0.405986i | −0.959097 | − | 0.283078i | \(-0.908645\pi\) |
0.724701 | + | 0.689063i | \(0.241978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5000 | + | 18.1865i | 0.378148 | + | 0.654972i | ||||
\(772\) | 4.00000i | 0.143963i | ||||||||
\(773\) | −41.5692 | + | 24.0000i | −1.49514 | + | 0.863220i | −0.999984 | − | 0.00558380i | \(-0.998223\pi\) |
−0.495156 | + | 0.868804i | \(0.664889\pi\) | |||||||
\(774\) | 0.500000 | + | 0.866025i | 0.0179721 | + | 0.0311286i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.00000 | + | 12.1244i | 0.251285 | + | 0.435239i | ||||
\(777\) | −12.1244 | − | 7.00000i | −0.434959 | − | 0.251124i | ||||
\(778\) | 2.59808 | + | 1.50000i | 0.0931455 | + | 0.0537776i | ||||
\(779\) | −12.0000 | −0.429945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | −15.5885 | − | 9.00000i | −0.557442 | − | 0.321839i | ||||
\(783\) | −2.59808 | − | 1.50000i | −0.0928477 | − | 0.0536056i | ||||
\(784\) | −1.50000 | − | 2.59808i | −0.0535714 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.50000 | + | 7.79423i | 0.160510 | + | 0.278011i | ||||
\(787\) | −30.3109 | + | 17.5000i | −1.08047 | + | 0.623808i | −0.931022 | − | 0.364963i | \(-0.881082\pi\) |
−0.149444 | + | 0.988770i | \(0.547748\pi\) | |||||||
\(788\) | 24.0000i | 0.854965i | ||||||||
\(789\) | −7.50000 | − | 12.9904i | −0.267007 | − | 0.462470i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.0000 | + | 25.9808i | −0.533339 | + | 0.923770i | ||||
\(792\) | − | 3.00000i | − | 0.106600i | ||||||
\(793\) | −1.73205 | − | 7.00000i | −0.0615069 | − | 0.248577i | ||||
\(794\) | −31.0000 | −1.10015 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00000 | + | 6.92820i | −0.141776 | + | 0.245564i | ||||
\(797\) | 20.7846 | − | 12.0000i | 0.736229 | − | 0.425062i | −0.0844678 | − | 0.996426i | \(-0.526919\pi\) |
0.820696 | + | 0.571364i | \(0.193586\pi\) | |||||||
\(798\) | − | 4.00000i | − | 0.141598i | ||||||
\(799\) | −9.00000 | − | 15.5885i | −0.318397 | − | 0.551480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | −10.3923 | + | 6.00000i | −0.366965 | + | 0.211867i | ||||
\(803\) | 36.3731 | + | 21.0000i | 1.28358 | + | 0.741074i | ||||
\(804\) | 4.00000 | − | 6.92820i | 0.141069 | − | 0.244339i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.5000 | − | 12.9904i | −0.440294 | − | 0.457567i | ||||
\(807\) | − | 18.0000i | − | 0.633630i | ||||||
\(808\) | 5.19615 | + | 3.00000i | 0.182800 | + | 0.105540i | ||||
\(809\) | 15.0000 | − | 25.9808i | 0.527372 | − | 0.913435i | −0.472119 | − | 0.881535i | \(-0.656511\pi\) |
0.999491 | − | 0.0319002i | \(-0.0101559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.0000 | 1.12367 | 0.561836 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(812\) | −5.19615 | + | 3.00000i | −0.182349 | + | 0.105279i | ||||
\(813\) | 9.52628 | − | 5.50000i | 0.334101 | − | 0.192893i | ||||
\(814\) | 21.0000 | 0.736050 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | −1.73205 | − | 1.00000i | −0.0605968 | − | 0.0349856i | ||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | −5.00000 | − | 5.19615i | −0.174714 | − | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5000 | + | 23.3827i | −0.471153 | + | 0.816061i | −0.999456 | − | 0.0329950i | \(-0.989495\pi\) |
0.528302 | + | 0.849056i | \(0.322829\pi\) | |||||||
\(822\) | −7.79423 | − | 4.50000i | −0.271855 | − | 0.156956i | ||||
\(823\) | 12.1244 | − | 7.00000i | 0.422628 | − | 0.244005i | −0.273573 | − | 0.961851i | \(-0.588205\pi\) |
0.696201 | + | 0.717847i | \(0.254872\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.00000 | − | 15.5885i | −0.313150 | − | 0.542392i | ||||
\(827\) | − | 6.00000i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332667\pi\) | |||||||
\(828\) | 2.59808 | − | 1.50000i | 0.0902894 | − | 0.0521286i | ||||
\(829\) | 13.0000 | − | 22.5167i | 0.451509 | − | 0.782036i | −0.546971 | − | 0.837151i | \(-0.684219\pi\) |
0.998480 | + | 0.0551154i | \(0.0175527\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00000 | −0.0346896 | ||||||||
\(832\) | −3.46410 | − | 1.00000i | −0.120096 | − | 0.0346688i | ||||
\(833\) | − | 18.0000i | − | 0.623663i | ||||||
\(834\) | −7.00000 | + | 12.1244i | −0.242390 | + | 0.419832i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.00000 | + | 5.19615i | 0.103757 | + | 0.179713i | ||||
\(837\) | − | 5.00000i | − | 0.172825i | ||||||
\(838\) | 10.3923 | − | 6.00000i | 0.358996 | − | 0.207267i | ||||
\(839\) | 21.0000 | + | 36.3731i | 0.725001 | + | 1.25574i | 0.958974 | + | 0.283495i | \(0.0914938\pi\) |
−0.233973 | + | 0.972243i | \(0.575173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 13.8564 | + | 8.00000i | 0.477523 | + | 0.275698i | ||||
\(843\) | −15.5885 | − | 9.00000i | −0.536895 | − | 0.309976i | ||||
\(844\) | −20.0000 | −0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | −3.46410 | − | 2.00000i | −0.119028 | − | 0.0687208i | ||||
\(848\) | 5.19615 | + | 3.00000i | 0.178437 | + | 0.103020i | ||||
\(849\) | −15.5000 | − | 26.8468i | −0.531959 | − | 0.921379i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5000 | + | 18.1865i | 0.359935 | + | 0.623426i | ||||
\(852\) | 10.3923 | − | 6.00000i | 0.356034 | − | 0.205557i | ||||
\(853\) | − | 19.0000i | − | 0.650548i | −0.945620 | − | 0.325274i | \(-0.894544\pi\) | ||
0.945620 | − | 0.325274i | \(-0.105456\pi\) | |||||||
\(854\) | −2.00000 | − | 3.46410i | −0.0684386 | − | 0.118539i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | + | 5.19615i | −0.102538 | + | 0.177601i | ||||
\(857\) | − | 3.00000i | − | 0.102478i | −0.998686 | − | 0.0512390i | \(-0.983683\pi\) | ||
0.998686 | − | 0.0512390i | \(-0.0163170\pi\) | |||||||
\(858\) | 10.3923 | + | 3.00000i | 0.354787 | + | 0.102418i | ||||
\(859\) | 46.0000 | 1.56950 | 0.784750 | − | 0.619813i | \(-0.212791\pi\) | ||||
0.784750 | + | 0.619813i | \(0.212791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | + | 10.3923i | −0.204479 | + | 0.354169i | ||||
\(862\) | 10.3923 | − | 6.00000i | 0.353963 | − | 0.204361i | ||||
\(863\) | − | 45.0000i | − | 1.53182i | −0.642949 | − | 0.765909i | \(-0.722289\pi\) | ||
0.642949 | − | 0.765909i | \(-0.277711\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 40.0000 | 1.35926 | ||||||||
\(867\) | −16.4545 | + | 9.50000i | −0.558824 | + | 0.322637i | ||||
\(868\) | −8.66025 | − | 5.00000i | −0.293948 | − | 0.169711i | ||||
\(869\) | −7.50000 | + | 12.9904i | −0.254420 | + | 0.440668i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | + | 20.7846i | 0.677674 | + | 0.704260i | ||||
\(872\) | 14.0000i | 0.474100i | ||||||||
\(873\) | −12.1244 | − | 7.00000i | −0.410347 | − | 0.236914i | ||||
\(874\) | −3.00000 | + | 5.19615i | −0.101477 | + | 0.175762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.0000 | 0.473016 | ||||||||
\(877\) | −19.9186 | + | 11.5000i | −0.672603 | + | 0.388327i | −0.797062 | − | 0.603897i | \(-0.793614\pi\) |
0.124459 | + | 0.992225i | \(0.460280\pi\) | |||||||
\(878\) | 3.46410 | − | 2.00000i | 0.116908 | − | 0.0674967i | ||||
\(879\) | 30.0000 | 1.01187 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00000 | + | 5.19615i | −0.101073 | + | 0.175063i | −0.912127 | − | 0.409908i | \(-0.865561\pi\) |
0.811054 | + | 0.584971i | \(0.198894\pi\) | |||||||
\(882\) | 2.59808 | + | 1.50000i | 0.0874818 | + | 0.0505076i | ||||
\(883\) | − | 19.0000i | − | 0.639401i | −0.947519 | − | 0.319700i | \(-0.896418\pi\) | ||
0.947519 | − | 0.319700i | \(-0.103582\pi\) | |||||||
\(884\) | −15.0000 | − | 15.5885i | −0.504505 | − | 0.524297i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0000 | + | 31.1769i | −0.604722 | + | 1.04741i | ||||
\(887\) | −49.3634 | − | 28.5000i | −1.65746 | − | 0.956936i | −0.973880 | − | 0.227063i | \(-0.927088\pi\) |
−0.683582 | − | 0.729873i | \(-0.739579\pi\) | |||||||
\(888\) | 6.06218 | − | 3.50000i | 0.203433 | − | 0.117452i | ||||
\(889\) | −28.0000 | −0.939090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | + | 2.59808i | 0.0502519 | + | 0.0870388i | ||||
\(892\) | 10.0000i | 0.334825i | ||||||||
\(893\) | −5.19615 | + | 3.00000i | −0.173883 | + | 0.100391i | ||||
\(894\) | 4.50000 | − | 7.79423i | 0.150503 | − | 0.260678i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 2.59808 | + | 10.5000i | 0.0867472 | + | 0.350585i | ||||
\(898\) | − | 36.0000i | − | 1.20134i | ||||||
\(899\) | 7.50000 | − | 12.9904i | 0.250139 | − | 0.433253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | + | 31.1769i | 0.599667 | + | 1.03865i | ||||
\(902\) | − | 18.0000i | − | 0.599334i | ||||||
\(903\) | −1.73205 | + | 1.00000i | −0.0576390 | + | 0.0332779i | ||||
\(904\) | −7.50000 | − | 12.9904i | −0.249446 | − | 0.432054i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | 14.7224 | + | 8.50000i | 0.488850 | + | 0.282238i | 0.724097 | − | 0.689698i | \(-0.242257\pi\) |
−0.235247 | + | 0.971936i | \(0.575590\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 1.73205 | + | 1.00000i | 0.0573539 | + | 0.0331133i | ||||
\(913\) | −15.5885 | − | 9.00000i | −0.515903 | − | 0.297857i | ||||
\(914\) | −1.00000 | − | 1.73205i | −0.0330771 | − | 0.0572911i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00000 | − | 12.1244i | −0.231287 | − | 0.400600i | ||||
\(917\) | −15.5885 | + | 9.00000i | −0.514776 | + | 0.297206i | ||||
\(918\) | − | 6.00000i | − | 0.198030i | ||||||
\(919\) | −8.00000 | − | 13.8564i | −0.263896 | − | 0.457081i | 0.703378 | − | 0.710816i | \(-0.251674\pi\) |
−0.967274 | + | 0.253735i | \(0.918341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.00000 | + | 6.92820i | −0.131804 | + | 0.228292i | ||||
\(922\) | 15.0000i | 0.493999i | ||||||||
\(923\) | 10.3923 | + | 42.0000i | 0.342067 | + | 1.38245i | ||||
\(924\) | 6.00000 | 0.197386 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.0000 | + | 29.4449i | −0.558655 | + | 0.967618i | ||||
\(927\) | −12.1244 | + | 7.00000i | −0.398216 | + | 0.229910i | ||||
\(928\) | − | 3.00000i | − | 0.0984798i | ||||||
\(929\) | −6.00000 | − | 10.3923i | −0.196854 | − | 0.340960i | 0.750653 | − | 0.660697i | \(-0.229739\pi\) |
−0.947507 | + | 0.319736i | \(0.896406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | −18.1865 | + | 10.5000i | −0.595720 | + | 0.343939i | ||||
\(933\) | 10.3923 | + | 6.00000i | 0.340229 | + | 0.196431i | ||||
\(934\) | −9.00000 | + | 15.5885i | −0.294489 | + | 0.510070i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.50000 | − | 0.866025i | 0.114401 | − | 0.0283069i | ||||
\(937\) | − | 2.00000i | − | 0.0653372i | −0.999466 | − | 0.0326686i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326686i | \(-0.0104006\pi\) | |||||||
\(938\) | 13.8564 | + | 8.00000i | 0.452428 | + | 0.261209i | ||||
\(939\) | 4.00000 | − | 6.92820i | 0.130535 | − | 0.226093i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0000 | 1.36916 | 0.684580 | − | 0.728937i | \(-0.259985\pi\) | ||||
0.684580 | + | 0.728937i | \(0.259985\pi\) | |||||||
\(942\) | −11.2583 | + | 6.50000i | −0.366816 | + | 0.211781i | ||||
\(943\) | 15.5885 | − | 9.00000i | 0.507630 | − | 0.293080i | ||||
\(944\) | 9.00000 | 0.292925 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.50000 | − | 2.59808i | 0.0487692 | − | 0.0844707i | ||||
\(947\) | −10.3923 | − | 6.00000i | −0.337705 | − | 0.194974i | 0.321552 | − | 0.946892i | \(-0.395796\pi\) |
−0.659256 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(948\) | 5.00000i | 0.162392i | ||||||||
\(949\) | −14.0000 | + | 48.4974i | −0.454459 | + | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | + | 10.3923i | −0.194563 | + | 0.336994i | ||||
\(952\) | −10.3923 | − | 6.00000i | −0.336817 | − | 0.194461i | ||||
\(953\) | 7.79423 | − | 4.50000i | 0.252480 | − | 0.145769i | −0.368419 | − | 0.929660i | \(-0.620101\pi\) |
0.620899 | + | 0.783890i | \(0.286768\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 9.00000i | 0.290929i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000 | − | 15.5885i | 0.290625 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 6.06218 | + | 24.5000i | 0.195452 | + | 0.789912i | ||||
\(963\) | − | 6.00000i | − | 0.193347i | ||||||
\(964\) | 8.50000 | − | 14.7224i | 0.273767 | − | 0.474178i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.00000 | + | 5.19615i | 0.0965234 | + | 0.167183i | ||||
\(967\) | − | 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 | ||||||||
\(971\) | 24.0000 | + | 41.5692i | 0.770197 | + | 1.33402i | 0.937455 | + | 0.348107i | \(0.113175\pi\) |
−0.167258 | + | 0.985913i | \(0.553491\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | −24.2487 | − | 14.0000i | −0.777378 | − | 0.448819i | ||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −49.3634 | − | 28.5000i | −1.57928 | − | 0.911796i | −0.994960 | − | 0.100270i | \(-0.968029\pi\) |
−0.584316 | − | 0.811526i | \(-0.698637\pi\) | |||||||
\(978\) | −11.2583 | − | 6.50000i | −0.360002 | − | 0.207847i | ||||
\(979\) | 27.0000 | + | 46.7654i | 0.862924 | + | 1.49463i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.00000 | − | 12.1244i | −0.223493 | − | 0.387101i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.00000i | 0.287055i | 0.989646 | + | 0.143528i | \(0.0458446\pi\) | ||||
−0.989646 | + | 0.143528i | \(0.954155\pi\) | |||||||
\(984\) | −3.00000 | − | 5.19615i | −0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | − | 15.5885i | 0.286618 | − | 0.496438i | ||||
\(987\) | 6.00000i | 0.190982i | ||||||||
\(988\) | −5.19615 | + | 5.00000i | −0.165312 | + | 0.159071i | ||||
\(989\) | 3.00000 | 0.0953945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5000 | − | 21.6506i | 0.397076 | − | 0.687755i | −0.596288 | − | 0.802771i | \(-0.703358\pi\) |
0.993364 | + | 0.115015i | \(0.0366917\pi\) | |||||||
\(992\) | 4.33013 | − | 2.50000i | 0.137482 | − | 0.0793751i | ||||
\(993\) | 32.0000i | 1.01549i | ||||||||
\(994\) | 12.0000 | + | 20.7846i | 0.380617 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | −0.190117 | ||||||||
\(997\) | 19.0526 | − | 11.0000i | 0.603401 | − | 0.348373i | −0.166978 | − | 0.985961i | \(-0.553401\pi\) |
0.770378 | + | 0.637587i | \(0.220067\pi\) | |||||||
\(998\) | 27.7128 | + | 16.0000i | 0.877234 | + | 0.506471i | ||||
\(999\) | −3.50000 | + | 6.06218i | −0.110735 | + | 0.191799i |
(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 | 1950.2.z.k.1699.1 | 4 | ||
5.2 | odd | 4 | 390.2.i.c.61.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1950.2.i.n.451.1 | 2 | |||
5.4 | even | 2 | inner | 1950.2.z.k.1699.2 | 4 | ||
13.3 | even | 3 | inner | 1950.2.z.k.1849.2 | 4 | ||
15.2 | even | 4 | 1170.2.i.d.451.1 | 2 | |||
65.3 | odd | 12 | 1950.2.i.n.601.1 | 2 | |||
65.7 | even | 12 | 5070.2.b.j.1351.1 | 2 | |||
65.17 | odd | 12 | 5070.2.a.v.1.1 | 1 | |||
65.22 | odd | 12 | 5070.2.a.j.1.1 | 1 | |||
65.29 | even | 6 | inner | 1950.2.z.k.1849.1 | 4 | ||
65.32 | even | 12 | 5070.2.b.j.1351.2 | 2 | |||
65.42 | odd | 12 | 390.2.i.c.211.1 | yes | 2 | ||
195.107 | even | 12 | 1170.2.i.d.991.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.c.61.1 | ✓ | 2 | 5.2 | odd | 4 | ||
390.2.i.c.211.1 | yes | 2 | 65.42 | odd | 12 | ||
1170.2.i.d.451.1 | 2 | 15.2 | even | 4 | |||
1170.2.i.d.991.1 | 2 | 195.107 | even | 12 | |||
1950.2.i.n.451.1 | 2 | 5.3 | odd | 4 | |||
1950.2.i.n.601.1 | 2 | 65.3 | odd | 12 | |||
1950.2.z.k.1699.1 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.z.k.1699.2 | 4 | 5.4 | even | 2 | inner | ||
1950.2.z.k.1849.1 | 4 | 65.29 | even | 6 | inner | ||
1950.2.z.k.1849.2 | 4 | 13.3 | even | 3 | inner | ||
5070.2.a.j.1.1 | 1 | 65.22 | odd | 12 | |||
5070.2.a.v.1.1 | 1 | 65.17 | odd | 12 | |||
5070.2.b.j.1351.1 | 2 | 65.7 | even | 12 | |||
5070.2.b.j.1351.2 | 2 | 65.32 | even | 12 |