Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [513,2,Mod(235,513)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(513, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("513.235");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 513 = 3^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 513.h (of order \(3\), 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: | \(4.09632562369\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 171) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 235.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 513.235 |
Dual form | 513.2.h.b.334.1 |
$q$-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 \(\left(\mathbb{Z}/513\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.50000 | − | 2.59808i | 0.474342 | − | 0.821584i | ||||
\(11\) | 2.50000 | − | 4.33013i | 0.753778 | − | 1.30558i | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −0.500000 | + | 0.866025i | −0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.50000 | − | 4.33013i | 0.533002 | − | 0.923186i | ||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | −0.500000 | − | 0.866025i | −0.0928477 | − | 0.160817i | 0.815861 | − | 0.578249i | \(-0.196264\pi\) |
−0.908708 | + | 0.417432i | \(0.862930\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.50000 | − | 4.33013i | −0.428746 | − | 0.742611i | ||||
\(35\) | 1.50000 | + | 2.59808i | 0.253546 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | −4.00000 | − | 1.73205i | −0.648886 | − | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.50000 | + | 7.79423i | −0.711512 | + | 1.23238i | ||||
\(41\) | −4.50000 | + | 7.79423i | −0.702782 | + | 1.21725i | 0.264704 | + | 0.964330i | \(0.414726\pi\) |
−0.967486 | + | 0.252924i | \(0.918608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | −2.50000 | + | 4.33013i | −0.376889 | + | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 1.50000 | + | 2.59808i | 0.218797 | + | 0.378968i | 0.954441 | − | 0.298401i | \(-0.0964533\pi\) |
−0.735643 | + | 0.677369i | \(0.763120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | + | 5.19615i | 0.428571 | + | 0.742307i | ||||
\(50\) | −2.00000 | − | 3.46410i | −0.282843 | − | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | −0.500000 | + | 0.866025i | −0.0686803 | + | 0.118958i | −0.898321 | − | 0.439340i | \(-0.855212\pi\) |
0.829640 | + | 0.558298i | \(0.188546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.50000 | − | 12.9904i | −1.01130 | − | 1.75162i | ||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.500000 | − | 0.866025i | −0.0656532 | − | 0.113715i | ||||
\(59\) | 2.50000 | − | 4.33013i | 0.325472 | − | 0.563735i | −0.656136 | − | 0.754643i | \(-0.727810\pi\) |
0.981608 | + | 0.190909i | \(0.0611434\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | −1.50000 | − | 2.59808i | −0.190500 | − | 0.329956i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 2.50000 | + | 4.33013i | 0.303170 | + | 0.525105i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.50000 | + | 2.59808i | 0.179284 | + | 0.310530i | ||||
\(71\) | 1.50000 | + | 2.59808i | 0.178017 | + | 0.308335i | 0.941201 | − | 0.337846i | \(-0.109698\pi\) |
−0.763184 | + | 0.646181i | \(0.776365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | \(-0.0721453\pi\) |
−0.681822 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | + | 1.73205i | 0.458831 | + | 0.198680i | ||||
\(77\) | 2.50000 | + | 4.33013i | 0.284901 | + | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −1.50000 | + | 2.59808i | −0.167705 | + | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.50000 | + | 7.79423i | −0.496942 | + | 0.860729i | ||||
\(83\) | 4.50000 | − | 7.79423i | 0.493939 | − | 0.855528i | −0.506036 | − | 0.862512i | \(-0.668890\pi\) |
0.999976 | + | 0.00698436i | \(0.00222321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.0000 | −1.62698 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.50000 | + | 12.9904i | −0.799503 | + | 1.38478i | ||||
\(89\) | −4.50000 | + | 7.79423i | −0.476999 | + | 0.826187i | −0.999653 | − | 0.0263586i | \(-0.991609\pi\) |
0.522654 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | + | 1.73205i | −0.104828 | + | 0.181568i | ||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | −10.5000 | + | 7.79423i | −1.07728 | + | 0.799671i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 3.00000 | + | 5.19615i | 0.303046 | + | 0.524891i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | 3.50000 | + | 6.06218i | 0.348263 | + | 0.603209i | 0.985941 | − | 0.167094i | \(-0.0534383\pi\) |
−0.637678 | + | 0.770303i | \(0.720105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50000 | + | 4.33013i | 0.246332 | + | 0.426660i | 0.962505 | − | 0.271263i | \(-0.0874412\pi\) |
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.500000 | + | 0.866025i | −0.0485643 | + | 0.0841158i | ||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.50000 | + | 4.33013i | 0.239457 | + | 0.414751i | 0.960558 | − | 0.278078i | \(-0.0896974\pi\) |
−0.721102 | + | 0.692829i | \(0.756364\pi\) | |||||||
\(110\) | −7.50000 | − | 12.9904i | −0.715097 | − | 1.23858i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | −8.50000 | − | 14.7224i | −0.799613 | − | 1.38497i | −0.919868 | − | 0.392227i | \(-0.871705\pi\) |
0.120256 | − | 0.992743i | \(-0.461629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | − | 20.7846i | 1.11901 | − | 1.93817i | ||||
\(116\) | 0.500000 | + | 0.866025i | 0.0464238 | + | 0.0804084i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.50000 | − | 4.33013i | 0.230144 | − | 0.398621i | ||||
\(119\) | 5.00000 | 0.458349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 6.50000 | + | 11.2583i | 0.588482 | + | 1.01928i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.50000 | + | 2.59808i | 0.134704 | + | 0.233314i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.50000 | + | 11.2583i | −0.576782 | + | 0.999015i | 0.419064 | + | 0.907957i | \(0.362358\pi\) |
−0.995846 | + | 0.0910585i | \(0.970975\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.00000 | − | 5.19615i | 0.263117 | − | 0.455733i | ||||
\(131\) | −3.50000 | + | 6.06218i | −0.305796 | + | 0.529655i | −0.977438 | − | 0.211221i | \(-0.932256\pi\) |
0.671642 | + | 0.740876i | \(0.265589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50000 | − | 2.59808i | 0.303488 | − | 0.225282i | ||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.50000 | + | 12.9904i | 0.643120 | + | 1.11392i | ||||
\(137\) | 1.50000 | + | 2.59808i | 0.128154 | + | 0.221969i | 0.922961 | − | 0.384893i | \(-0.125762\pi\) |
−0.794808 | + | 0.606861i | \(0.792428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | −1.50000 | − | 2.59808i | −0.126773 | − | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.50000 | + | 2.59808i | 0.125877 | + | 0.218026i | ||||
\(143\) | 5.00000 | − | 8.66025i | 0.418121 | − | 0.724207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | 2.50000 | + | 4.33013i | 0.206901 | + | 0.358364i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | 7.50000 | − | 12.9904i | 0.614424 | − | 1.06421i | −0.376061 | − | 0.926595i | \(-0.622722\pi\) |
0.990485 | − | 0.137619i | \(-0.0439449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.50000 | − | 12.9904i | 0.610341 | − | 1.05714i | −0.380841 | − | 0.924640i | \(-0.624366\pi\) |
0.991183 | − | 0.132502i | \(-0.0423010\pi\) | |||||||
\(152\) | 12.0000 | + | 5.19615i | 0.973329 | + | 0.421464i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.50000 | + | 4.33013i | 0.201456 | + | 0.348932i | ||||
\(155\) | −9.00000 | −0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50000 | + | 2.59808i | −0.119713 | + | 0.207349i | −0.919654 | − | 0.392730i | \(-0.871531\pi\) |
0.799941 | + | 0.600079i | \(0.204864\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.50000 | − | 12.9904i | 0.592927 | − | 1.02698i | ||||
\(161\) | −4.00000 | + | 6.92820i | −0.315244 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 4.50000 | − | 7.79423i | 0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50000 | − | 7.79423i | 0.349268 | − | 0.604949i | ||||
\(167\) | 4.00000 | 0.309529 | 0.154765 | − | 0.987951i | \(-0.450538\pi\) | ||||
0.154765 | + | 0.987951i | \(0.450538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −15.0000 | −1.15045 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | −2.50000 | + | 4.33013i | −0.188445 | + | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.50000 | + | 7.79423i | −0.337289 | + | 0.584202i | ||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.50000 | + | 6.06218i | −0.260153 | + | 0.450598i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) |
0.706129 | + | 0.708083i | \(0.250440\pi\) | |||||||
\(182\) | −1.00000 | + | 1.73205i | −0.0741249 | + | 0.128388i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −24.0000 | −1.76930 | ||||||||
\(185\) | −9.00000 | + | 15.5885i | −0.661693 | + | 1.14609i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.0000 | −1.82818 | ||||||||
\(188\) | −1.50000 | − | 2.59808i | −0.109399 | − | 0.189484i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.5000 | + | 7.79423i | −0.761750 | + | 0.565453i | ||||
\(191\) | −1.50000 | + | 2.59808i | −0.108536 | + | 0.187990i | −0.915177 | − | 0.403051i | \(-0.867950\pi\) |
0.806641 | + | 0.591041i | \(0.201283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.50000 | − | 14.7224i | 0.611843 | − | 1.05974i | −0.379086 | − | 0.925361i | \(-0.623762\pi\) |
0.990930 | − | 0.134382i | \(-0.0429051\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | − | 5.19615i | −0.214286 | − | 0.371154i | ||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | − | 2.59808i | 0.106332 | − | 0.184173i | −0.807950 | − | 0.589252i | \(-0.799423\pi\) |
0.914282 | + | 0.405079i | \(0.132756\pi\) | |||||||
\(200\) | 6.00000 | + | 10.3923i | 0.424264 | + | 0.734847i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.50000 | + | 6.06218i | 0.246259 | + | 0.426533i | ||||
\(203\) | 1.00000 | 0.0701862 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5000 | + | 23.3827i | 0.942881 | + | 1.63312i | ||||
\(206\) | 2.50000 | + | 4.33013i | 0.174183 | + | 0.301694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | −17.5000 | + | 12.9904i | −1.21050 | + | 0.898563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.50000 | − | 12.9904i | 0.516321 | − | 0.894295i | −0.483499 | − | 0.875345i | \(-0.660634\pi\) |
0.999820 | − | 0.0189499i | \(-0.00603229\pi\) | |||||||
\(212\) | 0.500000 | − | 0.866025i | 0.0343401 | − | 0.0594789i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 12.0000 | − | 20.7846i | 0.818393 | − | 1.41750i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.00000 | 0.203653 | ||||||||
\(218\) | 2.50000 | + | 4.33013i | 0.169321 | + | 0.293273i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.50000 | + | 12.9904i | 0.505650 | + | 0.875811i | ||||
\(221\) | −5.00000 | − | 8.66025i | −0.336336 | − | 0.582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | −2.50000 | + | 4.33013i | −0.167038 | + | 0.289319i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.50000 | − | 14.7224i | −0.565412 | − | 0.979322i | ||||
\(227\) | 10.5000 | − | 18.1865i | 0.696909 | − | 1.20708i | −0.272623 | − | 0.962121i | \(-0.587891\pi\) |
0.969533 | − | 0.244962i | \(-0.0787754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.50000 | + | 14.7224i | 0.561696 | + | 0.972886i | 0.997349 | + | 0.0727709i | \(0.0231842\pi\) |
−0.435653 | + | 0.900115i | \(0.643482\pi\) | |||||||
\(230\) | 12.0000 | − | 20.7846i | 0.791257 | − | 1.37050i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50000 | + | 2.59808i | 0.0984798 | + | 0.170572i | ||||
\(233\) | −4.50000 | − | 7.79423i | −0.294805 | − | 0.510617i | 0.680135 | − | 0.733087i | \(-0.261921\pi\) |
−0.974939 | + | 0.222470i | \(0.928588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | 0.587095 | ||||||||
\(236\) | −2.50000 | + | 4.33013i | −0.162736 | + | 0.281867i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.00000 | 0.324102 | ||||||||
\(239\) | 7.50000 | + | 12.9904i | 0.485135 | + | 0.840278i | 0.999854 | − | 0.0170808i | \(-0.00543724\pi\) |
−0.514719 | + | 0.857359i | \(0.672104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | −7.00000 | − | 12.1244i | −0.449977 | − | 0.779383i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.50000 | − | 11.2583i | −0.416120 | − | 0.720741i | ||||
\(245\) | 18.0000 | 1.14998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.00000 | − | 3.46410i | −0.509028 | − | 0.220416i | ||||
\(248\) | 4.50000 | + | 7.79423i | 0.285750 | + | 0.494934i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.00000 | 0.189737 | ||||||||
\(251\) | 2.50000 | − | 4.33013i | 0.157799 | − | 0.273315i | −0.776276 | − | 0.630393i | \(-0.782894\pi\) |
0.934075 | + | 0.357078i | \(0.116227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.0000 | − | 34.6410i | 1.25739 | − | 2.17786i | ||||
\(254\) | −6.50000 | + | 11.2583i | −0.407846 | + | 0.706410i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 10.0000 | 0.623783 | 0.311891 | − | 0.950118i | \(-0.399037\pi\) | ||||
0.311891 | + | 0.950118i | \(0.399037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00000 | − | 5.19615i | 0.186411 | − | 0.322873i | ||||
\(260\) | −3.00000 | + | 5.19615i | −0.186052 | + | 0.322252i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.50000 | + | 6.06218i | −0.216231 | + | 0.374523i | ||||
\(263\) | 8.00000 | 0.493301 | 0.246651 | − | 0.969104i | \(-0.420670\pi\) | ||||
0.246651 | + | 0.969104i | \(0.420670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.50000 | + | 2.59808i | 0.0921443 | + | 0.159599i | ||||
\(266\) | 3.50000 | − | 2.59808i | 0.214599 | − | 0.159298i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | −12.5000 | − | 21.6506i | −0.762138 | − | 1.32006i | −0.941746 | − | 0.336324i | \(-0.890816\pi\) |
0.179608 | − | 0.983738i | \(-0.442517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.5000 | − | 23.3827i | −0.820067 | − | 1.42040i | −0.905632 | − | 0.424064i | \(-0.860603\pi\) |
0.0855654 | − | 0.996333i | \(-0.472730\pi\) | |||||||
\(272\) | 2.50000 | + | 4.33013i | 0.151585 | + | 0.262553i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.50000 | + | 2.59808i | 0.0906183 | + | 0.156956i | ||||
\(275\) | −20.0000 | −1.20605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.50000 | + | 6.06218i | −0.210295 | + | 0.364241i | −0.951807 | − | 0.306699i | \(-0.900776\pi\) |
0.741512 | + | 0.670940i | \(0.234109\pi\) | |||||||
\(278\) | 20.0000 | 1.19952 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.50000 | − | 7.79423i | −0.268926 | − | 0.465794i | ||||
\(281\) | 5.50000 | + | 9.52628i | 0.328102 | + | 0.568290i | 0.982135 | − | 0.188176i | \(-0.0602575\pi\) |
−0.654033 | + | 0.756466i | \(0.726924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5000 | + | 25.1147i | −0.861936 | + | 1.49292i | 0.00812260 | + | 0.999967i | \(0.497414\pi\) |
−0.870058 | + | 0.492949i | \(0.835919\pi\) | |||||||
\(284\) | −1.50000 | − | 2.59808i | −0.0890086 | − | 0.154167i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.00000 | − | 8.66025i | 0.295656 | − | 0.512092i | ||||
\(287\) | −4.50000 | − | 7.79423i | −0.265627 | − | 0.460079i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | −3.00000 | −0.176166 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.50000 | − | 4.33013i | −0.146301 | − | 0.253402i | ||||
\(293\) | −2.50000 | − | 4.33013i | −0.146052 | − | 0.252969i | 0.783713 | − | 0.621123i | \(-0.213323\pi\) |
−0.929765 | + | 0.368154i | \(0.879990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.50000 | − | 12.9904i | −0.436667 | − | 0.756329i | ||||
\(296\) | 18.0000 | 1.04623 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.50000 | − | 12.9904i | 0.434463 | − | 0.752513i | ||||
\(299\) | 16.0000 | 0.925304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | + | 6.92820i | −0.230556 | + | 0.399335i | ||||
\(302\) | 7.50000 | − | 12.9904i | 0.431577 | − | 0.747512i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000 | + | 1.73205i | 0.229416 | + | 0.0993399i | ||||
\(305\) | 39.0000 | 2.23313 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5000 | + | 28.5788i | 0.941705 | + | 1.63108i | 0.762218 | + | 0.647320i | \(0.224110\pi\) |
0.179486 | + | 0.983760i | \(0.442556\pi\) | |||||||
\(308\) | −2.50000 | − | 4.33013i | −0.142451 | − | 0.246732i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.00000 | −0.511166 | ||||||||
\(311\) | −10.5000 | − | 18.1865i | −0.595400 | − | 1.03126i | −0.993490 | − | 0.113917i | \(-0.963660\pi\) |
0.398090 | − | 0.917346i | \(-0.369673\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | −1.50000 | + | 2.59808i | −0.0846499 | + | 0.146618i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | −8.50000 | − | 14.7224i | −0.477408 | − | 0.826894i | 0.522257 | − | 0.852788i | \(-0.325090\pi\) |
−0.999665 | + | 0.0258939i | \(0.991757\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.00000 | −0.279946 | ||||||||
\(320\) | 10.5000 | − | 18.1865i | 0.586968 | − | 1.01666i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.00000 | + | 6.92820i | −0.222911 | + | 0.386094i | ||||
\(323\) | 2.50000 | + | 21.6506i | 0.139104 | + | 1.20467i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | − | 6.92820i | −0.221880 | − | 0.384308i | ||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.5000 | − | 23.3827i | 0.745413 | − | 1.29109i | ||||
\(329\) | −3.00000 | −0.165395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | − | 16.4545i | 0.522167 | − | 0.904420i | −0.477500 | − | 0.878632i | \(-0.658457\pi\) |
0.999667 | − | 0.0257885i | \(-0.00820965\pi\) | |||||||
\(332\) | −4.50000 | + | 7.79423i | −0.246970 | + | 0.427764i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.00000 | 0.218870 | ||||||||
\(335\) | −6.00000 | + | 10.3923i | −0.327815 | + | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.50000 | − | 4.33013i | 0.136184 | − | 0.235877i | −0.789865 | − | 0.613280i | \(-0.789850\pi\) |
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.0000 | 0.813489 | ||||||||
\(341\) | −15.0000 | −0.812296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −24.0000 | −1.29399 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | 0.500000 | − | 0.866025i | 0.0268414 | − | 0.0464907i | −0.852293 | − | 0.523065i | \(-0.824788\pi\) |
0.879134 | + | 0.476575i | \(0.158122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.50000 | + | 12.9904i | −0.401466 | + | 0.695359i | −0.993903 | − | 0.110257i | \(-0.964832\pi\) |
0.592437 | + | 0.805617i | \(0.298166\pi\) | |||||||
\(350\) | 4.00000 | 0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.5000 | − | 21.6506i | 0.666252 | − | 1.15398i | ||||
\(353\) | −18.5000 | + | 32.0429i | −0.984656 | + | 1.70547i | −0.341199 | + | 0.939991i | \(0.610833\pi\) |
−0.643457 | + | 0.765482i | \(0.722500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.00000 | 0.477670 | ||||||||
\(356\) | 4.50000 | − | 7.79423i | 0.238500 | − | 0.413093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | −6.50000 | − | 11.2583i | −0.343057 | − | 0.594192i | 0.641942 | − | 0.766753i | \(-0.278129\pi\) |
−0.984999 | + | 0.172561i | \(0.944796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | −3.50000 | + | 6.06218i | −0.183956 | + | 0.318621i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | − | 1.73205i | 0.0524142 | − | 0.0907841i | ||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.50000 | + | 4.33013i | 0.130499 | + | 0.226031i | 0.923869 | − | 0.382709i | \(-0.125009\pi\) |
−0.793370 | + | 0.608740i | \(0.791675\pi\) | |||||||
\(368\) | −8.00000 | −0.417029 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.00000 | + | 15.5885i | −0.467888 | + | 0.810405i | ||||
\(371\) | −0.500000 | − | 0.866025i | −0.0259587 | − | 0.0449618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.50000 | + | 4.33013i | 0.129445 | + | 0.224205i | 0.923462 | − | 0.383691i | \(-0.125347\pi\) |
−0.794017 | + | 0.607896i | \(0.792014\pi\) | |||||||
\(374\) | −25.0000 | −1.29272 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.50000 | − | 7.79423i | −0.232070 | − | 0.401957i | ||||
\(377\) | −1.00000 | − | 1.73205i | −0.0515026 | − | 0.0892052i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 10.5000 | − | 7.79423i | 0.538639 | − | 0.399835i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.50000 | + | 2.59808i | −0.0767467 | + | 0.132929i | ||||
\(383\) | −11.5000 | + | 19.9186i | −0.587623 | + | 1.01779i | 0.406920 | + | 0.913464i | \(0.366603\pi\) |
−0.994543 | + | 0.104328i | \(0.966731\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.0000 | 0.764471 | ||||||||
\(386\) | 8.50000 | − | 14.7224i | 0.432639 | − | 0.749352i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.0000 | 0.507673 | ||||||||
\(389\) | 1.50000 | + | 2.59808i | 0.0760530 | + | 0.131728i | 0.901544 | − | 0.432688i | \(-0.142435\pi\) |
−0.825491 | + | 0.564416i | \(0.809102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.0000 | − | 34.6410i | −1.01144 | − | 1.75187i | ||||
\(392\) | −9.00000 | − | 15.5885i | −0.454569 | − | 0.787336i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.00000 | −0.100759 | ||||||||
\(395\) | 6.00000 | − | 10.3923i | 0.301893 | − | 0.522894i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.50000 | − | 6.06218i | −0.175660 | − | 0.304252i | 0.764730 | − | 0.644351i | \(-0.222873\pi\) |
−0.940389 | + | 0.340099i | \(0.889539\pi\) | |||||||
\(398\) | 1.50000 | − | 2.59808i | 0.0751882 | − | 0.130230i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | + | 3.46410i | 0.100000 | + | 0.173205i | ||||
\(401\) | −16.5000 | + | 28.5788i | −0.823971 | + | 1.42716i | 0.0787327 | + | 0.996896i | \(0.474913\pi\) |
−0.902703 | + | 0.430263i | \(0.858421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | − | 5.19615i | −0.149441 | − | 0.258839i | ||||
\(404\) | −3.50000 | − | 6.06218i | −0.174132 | − | 0.301605i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.00000 | 0.0496292 | ||||||||
\(407\) | −15.0000 | + | 25.9808i | −0.743522 | + | 1.28782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 13.5000 | + | 23.3827i | 0.666717 | + | 1.15479i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.50000 | − | 4.33013i | −0.123166 | − | 0.213330i | ||||
\(413\) | 2.50000 | + | 4.33013i | 0.123017 | + | 0.213072i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5000 | − | 23.3827i | −0.662689 | − | 1.14781i | ||||
\(416\) | 10.0000 | 0.490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.5000 | + | 12.9904i | −0.855953 | + | 0.635380i | ||||
\(419\) | −0.500000 | − | 0.866025i | −0.0244266 | − | 0.0423081i | 0.853554 | − | 0.521005i | \(-0.174443\pi\) |
−0.877980 | + | 0.478697i | \(0.841109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | 7.50000 | − | 12.9904i | 0.365094 | − | 0.632362i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | −10.0000 | + | 17.3205i | −0.485071 | + | 0.840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.0000 | −0.629114 | ||||||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | − | 20.7846i | 0.578691 | − | 1.00232i | ||||
\(431\) | 0.500000 | − | 0.866025i | 0.0240842 | − | 0.0417150i | −0.853732 | − | 0.520712i | \(-0.825666\pi\) |
0.877816 | + | 0.478997i | \(0.159000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5000 | + | 23.3827i | −0.648769 | + | 1.12370i | 0.334649 | + | 0.942343i | \(0.391382\pi\) |
−0.983417 | + | 0.181357i | \(0.941951\pi\) | |||||||
\(434\) | 3.00000 | 0.144005 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.50000 | − | 4.33013i | −0.119728 | − | 0.207375i | ||||
\(437\) | −32.0000 | − | 13.8564i | −1.53077 | − | 0.662842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | −0.763638 | −0.381819 | − | 0.924237i | \(-0.624702\pi\) | ||||
−0.381819 | + | 0.924237i | \(0.624702\pi\) | |||||||
\(440\) | 22.5000 | + | 38.9711i | 1.07265 | + | 1.85788i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.00000 | − | 8.66025i | −0.237826 | − | 0.411926i | ||||
\(443\) | −12.5000 | − | 21.6506i | −0.593893 | − | 1.02865i | −0.993702 | − | 0.112054i | \(-0.964257\pi\) |
0.399809 | − | 0.916598i | \(-0.369076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5000 | + | 23.3827i | 0.639961 | + | 1.10845i | ||||
\(446\) | −24.0000 | −1.13643 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.50000 | + | 6.06218i | −0.165359 | + | 0.286411i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5000 | + | 38.9711i | 1.05948 | + | 1.83508i | ||||
\(452\) | 8.50000 | + | 14.7224i | 0.399806 | + | 0.692485i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.5000 | − | 18.1865i | 0.492789 | − | 0.853536i | ||||
\(455\) | 3.00000 | + | 5.19615i | 0.140642 | + | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.50000 | + | 16.4545i | −0.444391 | + | 0.769708i | −0.998010 | − | 0.0630623i | \(-0.979913\pi\) |
0.553618 | + | 0.832771i | \(0.313247\pi\) | |||||||
\(458\) | 8.50000 | + | 14.7224i | 0.397179 | + | 0.687934i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | + | 20.7846i | −0.559503 | + | 0.969087i | ||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.500000 | + | 0.866025i | 0.0232370 | + | 0.0402476i | 0.877410 | − | 0.479741i | \(-0.159269\pi\) |
−0.854173 | + | 0.519989i | \(0.825936\pi\) | |||||||
\(464\) | 0.500000 | + | 0.866025i | 0.0232119 | + | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.50000 | − | 7.79423i | −0.208458 | − | 0.361061i | ||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | − | 3.46410i | 0.0923514 | − | 0.159957i | ||||
\(470\) | 9.00000 | 0.415139 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.50000 | + | 12.9904i | −0.345215 | + | 0.597931i | ||||
\(473\) | 20.0000 | − | 34.6410i | 0.919601 | − | 1.59280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | + | 17.3205i | 0.0917663 | + | 0.794719i | ||||
\(476\) | −5.00000 | −0.229175 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.50000 | + | 12.9904i | 0.343042 | + | 0.594166i | ||||
\(479\) | −2.50000 | − | 4.33013i | −0.114228 | − | 0.197849i | 0.803243 | − | 0.595652i | \(-0.203106\pi\) |
−0.917471 | + | 0.397803i | \(0.869773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 0.500000 | + | 0.866025i | 0.0227744 | + | 0.0394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | + | 12.1244i | 0.318182 | + | 0.551107i | ||||
\(485\) | −15.0000 | + | 25.9808i | −0.681115 | + | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0000 | 1.45006 | 0.725029 | − | 0.688718i | \(-0.241826\pi\) | ||||
0.725029 | + | 0.688718i | \(0.241826\pi\) | |||||||
\(488\) | −19.5000 | − | 33.7750i | −0.882724 | − | 1.52892i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.0000 | 0.813157 | ||||||||
\(491\) | −13.5000 | + | 23.3827i | −0.609246 | + | 1.05525i | 0.382118 | + | 0.924113i | \(0.375195\pi\) |
−0.991365 | + | 0.131132i | \(0.958139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.50000 | + | 4.33013i | −0.112594 | + | 0.195019i | ||||
\(494\) | −8.00000 | − | 3.46410i | −0.359937 | − | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50000 | + | 2.59808i | 0.0673520 | + | 0.116657i | ||||
\(497\) | −3.00000 | −0.134568 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5000 | + | 25.1147i | −0.649109 | + | 1.12429i | 0.334227 | + | 0.942493i | \(0.391525\pi\) |
−0.983336 | + | 0.181797i | \(0.941809\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.50000 | − | 4.33013i | 0.111580 | − | 0.193263i | ||||
\(503\) | 14.5000 | − | 25.1147i | 0.646523 | − | 1.11981i | −0.337424 | − | 0.941353i | \(-0.609556\pi\) |
0.983948 | − | 0.178458i | \(-0.0571109\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.0000 | 0.934488 | ||||||||
\(506\) | 20.0000 | − | 34.6410i | 0.889108 | − | 1.53998i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.50000 | − | 11.2583i | 0.288391 | − | 0.499508i | ||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.00000 | −0.221187 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.0000 | 0.441081 | ||||||||
\(515\) | 15.0000 | 0.660979 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.0000 | 0.659699 | ||||||||
\(518\) | 3.00000 | − | 5.19615i | 0.131812 | − | 0.228306i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.00000 | + | 15.5885i | −0.394676 | + | 0.683599i | ||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.5000 | + | 25.1147i | −0.634041 | + | 1.09819i | 0.352677 | + | 0.935745i | \(0.385272\pi\) |
−0.986718 | + | 0.162446i | \(0.948062\pi\) | |||||||
\(524\) | 3.50000 | − | 6.06218i | 0.152898 | − | 0.264827i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.00000 | 0.348817 | ||||||||
\(527\) | −7.50000 | + | 12.9904i | −0.326705 | + | 0.565870i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 1.50000 | + | 2.59808i | 0.0651558 | + | 0.112853i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.50000 | + | 2.59808i | −0.151744 | + | 0.112641i | ||||
\(533\) | −9.00000 | + | 15.5885i | −0.389833 | + | 0.675211i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 31.1769i | −0.778208 | + | 1.34790i | ||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.5000 | − | 21.6506i | −0.538913 | − | 0.933425i | ||||
\(539\) | 30.0000 | 1.29219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.50000 | + | 2.59808i | −0.0644900 | + | 0.111700i | −0.896468 | − | 0.443109i | \(-0.853875\pi\) |
0.831978 | + | 0.554809i | \(0.187209\pi\) | |||||||
\(542\) | −13.5000 | − | 23.3827i | −0.579875 | − | 1.00437i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.5000 | − | 21.6506i | −0.535933 | − | 0.928263i | ||||
\(545\) | 15.0000 | 0.642529 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.50000 | + | 4.33013i | 0.106892 | + | 0.185143i | 0.914510 | − | 0.404564i | \(-0.132577\pi\) |
−0.807617 | + | 0.589707i | \(0.799243\pi\) | |||||||
\(548\) | −1.50000 | − | 2.59808i | −0.0640768 | − | 0.110984i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.0000 | −0.852803 | ||||||||
\(551\) | 0.500000 | + | 4.33013i | 0.0213007 | + | 0.184470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | + | 3.46410i | −0.0850487 | + | 0.147309i | ||||
\(554\) | −3.50000 | + | 6.06218i | −0.148701 | + | 0.257557i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0000 | −0.848189 | ||||||||
\(557\) | −6.50000 | + | 11.2583i | −0.275414 | + | 0.477031i | −0.970239 | − | 0.242147i | \(-0.922148\pi\) |
0.694826 | + | 0.719178i | \(0.255482\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | −1.50000 | − | 2.59808i | −0.0633866 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.50000 | + | 9.52628i | 0.232003 | + | 0.401842i | ||||
\(563\) | 13.5000 | + | 23.3827i | 0.568957 | + | 0.985463i | 0.996669 | + | 0.0815478i | \(0.0259863\pi\) |
−0.427712 | + | 0.903915i | \(0.640680\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −51.0000 | −2.14559 | ||||||||
\(566\) | −14.5000 | + | 25.1147i | −0.609480 | + | 1.05565i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.50000 | − | 7.79423i | −0.188816 | − | 0.327039i | ||||
\(569\) | −4.50000 | + | 7.79423i | −0.188650 | + | 0.326751i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5000 | + | 18.1865i | 0.439411 | + | 0.761083i | 0.997644 | − | 0.0686016i | \(-0.0218537\pi\) |
−0.558233 | + | 0.829684i | \(0.688520\pi\) | |||||||
\(572\) | −5.00000 | + | 8.66025i | −0.209061 | + | 0.362103i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.50000 | − | 7.79423i | −0.187826 | − | 0.325325i | ||||
\(575\) | −16.0000 | − | 27.7128i | −0.667246 | − | 1.15570i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.0000 | −1.74848 | −0.874241 | − | 0.485491i | \(-0.838641\pi\) | ||||
−0.874241 | + | 0.485491i | \(0.838641\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.00000 | 0.124568 | ||||||||
\(581\) | 4.50000 | + | 7.79423i | 0.186691 | + | 0.323359i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.50000 | + | 4.33013i | 0.103539 | + | 0.179336i | ||||
\(584\) | −7.50000 | − | 12.9904i | −0.310352 | − | 0.537546i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.50000 | − | 4.33013i | −0.103274 | − | 0.178876i | ||||
\(587\) | 4.00000 | 0.165098 | 0.0825488 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825488 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50000 | + | 12.9904i | 0.0618064 | + | 0.535259i | ||||
\(590\) | −7.50000 | − | 12.9904i | −0.308770 | − | 0.534806i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | −4.50000 | + | 7.79423i | −0.184793 | + | 0.320071i | −0.943507 | − | 0.331353i | \(-0.892495\pi\) |
0.758714 | + | 0.651424i | \(0.225828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.50000 | − | 12.9904i | 0.307470 | − | 0.532554i | ||||
\(596\) | −7.50000 | + | 12.9904i | −0.307212 | + | 0.532107i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.0000 | 0.654289 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.50000 | + | 2.59808i | −0.0611863 | + | 0.105978i | −0.894996 | − | 0.446074i | \(-0.852822\pi\) |
0.833810 | + | 0.552052i | \(0.186155\pi\) | |||||||
\(602\) | −4.00000 | + | 6.92820i | −0.163028 | + | 0.282372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.50000 | + | 12.9904i | −0.305171 | + | 0.528571i | ||||
\(605\) | −42.0000 | −1.70754 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5000 | − | 19.9186i | −0.466771 | − | 0.808470i | 0.532509 | − | 0.846424i | \(-0.321249\pi\) |
−0.999279 | + | 0.0379540i | \(0.987916\pi\) | |||||||
\(608\) | −20.0000 | − | 8.66025i | −0.811107 | − | 0.351220i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.0000 | 1.57906 | ||||||||
\(611\) | 3.00000 | + | 5.19615i | 0.121367 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.50000 | + | 7.79423i | 0.181753 | + | 0.314806i | 0.942478 | − | 0.334269i | \(-0.108489\pi\) |
−0.760724 | + | 0.649075i | \(0.775156\pi\) | |||||||
\(614\) | 16.5000 | + | 28.5788i | 0.665886 | + | 1.15335i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.50000 | − | 12.9904i | −0.302184 | − | 0.523397i | ||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50000 | − | 9.52628i | 0.221064 | − | 0.382893i | −0.734068 | − | 0.679076i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957138\pi\) | |||||||
\(620\) | 9.00000 | 0.361449 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.5000 | − | 18.1865i | −0.421012 | − | 0.729214i | ||||
\(623\) | −4.50000 | − | 7.79423i | −0.180289 | − | 0.312269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 8.50000 | + | 14.7224i | 0.339728 | + | 0.588427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.50000 | − | 2.59808i | 0.0598565 | − | 0.103675i | ||||
\(629\) | 15.0000 | + | 25.9808i | 0.598089 | + | 1.03592i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5000 | − | 33.7750i | 0.776283 | − | 1.34456i | −0.157788 | − | 0.987473i | \(-0.550436\pi\) |
0.934071 | − | 0.357088i | \(-0.116230\pi\) | |||||||
\(632\) | −12.0000 | −0.477334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.50000 | − | 14.7224i | −0.337578 | − | 0.584702i | ||||
\(635\) | 19.5000 | + | 33.7750i | 0.773834 | + | 1.34032i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000 | + | 10.3923i | 0.237729 | + | 0.411758i | ||||
\(638\) | −5.00000 | −0.197952 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.50000 | + | 7.79423i | −0.177878 | + | 0.308094i | ||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.50000 | − | 6.06218i | 0.138027 | − | 0.239069i | −0.788723 | − | 0.614749i | \(-0.789257\pi\) |
0.926750 | + | 0.375680i | \(0.122591\pi\) | |||||||
\(644\) | 4.00000 | − | 6.92820i | 0.157622 | − | 0.273009i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.50000 | + | 21.6506i | 0.0983612 | + | 0.851833i | ||||
\(647\) | −48.0000 | −1.88707 | −0.943537 | − | 0.331266i | \(-0.892524\pi\) | ||||
−0.943537 | + | 0.331266i | \(0.892524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.5000 | − | 21.6506i | −0.490668 | − | 0.849862i | ||||
\(650\) | −4.00000 | − | 6.92820i | −0.156893 | − | 0.271746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | −4.50000 | − | 7.79423i | −0.176099 | − | 0.305012i | 0.764442 | − | 0.644692i | \(-0.223014\pi\) |
−0.940541 | + | 0.339680i | \(0.889681\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.5000 | + | 18.1865i | 0.410269 | + | 0.710607i | ||||
\(656\) | 4.50000 | − | 7.79423i | 0.175695 | − | 0.304314i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.00000 | −0.116952 | ||||||||
\(659\) | 11.5000 | + | 19.9186i | 0.447976 | + | 0.775918i | 0.998254 | − | 0.0590638i | \(-0.0188115\pi\) |
−0.550278 | + | 0.834982i | \(0.685478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | −1.16686 | −0.583432 | − | 0.812162i | \(-0.698291\pi\) | ||||
−0.583432 | + | 0.812162i | \(0.698291\pi\) | |||||||
\(662\) | 9.50000 | − | 16.4545i | 0.369228 | − | 0.639522i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.5000 | + | 23.3827i | −0.523902 | + | 0.907424i | ||||
\(665\) | −1.50000 | − | 12.9904i | −0.0581675 | − | 0.503745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | − | 6.92820i | −0.154881 | − | 0.268261i | ||||
\(668\) | −4.00000 | −0.154765 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.00000 | + | 10.3923i | −0.231800 | + | 0.401490i | ||||
\(671\) | 65.0000 | 2.50930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.50000 | − | 7.79423i | 0.173462 | − | 0.300445i | −0.766166 | − | 0.642643i | \(-0.777838\pi\) |
0.939628 | + | 0.342198i | \(0.111171\pi\) | |||||||
\(674\) | 2.50000 | − | 4.33013i | 0.0962964 | − | 0.166790i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | −18.5000 | + | 32.0429i | −0.711013 | + | 1.23151i | 0.253465 | + | 0.967345i | \(0.418430\pi\) |
−0.964477 | + | 0.264166i | \(0.914903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00000 | − | 8.66025i | 0.191882 | − | 0.332350i | ||||
\(680\) | 45.0000 | 1.72567 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.0000 | −0.574380 | ||||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | 0.343872 | ||||||||
\(686\) | −13.0000 | −0.496342 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | −1.00000 | + | 1.73205i | −0.0380970 | + | 0.0659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.50000 | − | 16.4545i | 0.361397 | − | 0.625958i | −0.626794 | − | 0.779185i | \(-0.715633\pi\) |
0.988191 | + | 0.153227i | \(0.0489666\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.500000 | − | 0.866025i | 0.0189797 | − | 0.0328739i | ||||
\(695\) | 30.0000 | − | 51.9615i | 1.13796 | − | 1.97101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.0000 | 1.70450 | ||||||||
\(698\) | −7.50000 | + | 12.9904i | −0.283879 | + | 0.491693i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.00000 | −0.151186 | ||||||||
\(701\) | 9.50000 | + | 16.4545i | 0.358810 | + | 0.621477i | 0.987762 | − | 0.155967i | \(-0.0498493\pi\) |
−0.628952 | + | 0.777444i | \(0.716516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | + | 10.3923i | 0.905177 | + | 0.391953i | ||||
\(704\) | 17.5000 | − | 30.3109i | 0.659556 | − | 1.14238i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.5000 | + | 32.0429i | −0.696257 | + | 1.20595i | ||||
\(707\) | −7.00000 | −0.263262 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5000 | − | 33.7750i | −0.732338 | − | 1.26845i | −0.955882 | − | 0.293752i | \(-0.905096\pi\) |
0.223544 | − | 0.974694i | \(-0.428237\pi\) | |||||||
\(710\) | 9.00000 | 0.337764 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.5000 | − | 23.3827i | 0.505934 | − | 0.876303i | ||||
\(713\) | −12.0000 | − | 20.7846i | −0.449404 | − | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0000 | − | 25.9808i | −0.560968 | − | 0.971625i | ||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.50000 | − | 11.2583i | −0.242578 | − | 0.420157i | ||||
\(719\) | 1.50000 | + | 2.59808i | 0.0559406 | + | 0.0968919i | 0.892640 | − | 0.450771i | \(-0.148851\pi\) |
−0.836699 | + | 0.547663i | \(0.815518\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.00000 | −0.186210 | ||||||||
\(722\) | 13.0000 | + | 13.8564i | 0.483810 | + | 0.515682i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.50000 | − | 6.06218i | 0.130076 | − | 0.225299i | ||||
\(725\) | −2.00000 | + | 3.46410i | −0.0742781 | + | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 3.00000 | − | 5.19615i | 0.111187 | − | 0.192582i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.0000 | 0.555175 | ||||||||
\(731\) | −20.0000 | − | 34.6410i | −0.739727 | − | 1.28124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.50000 | − | 16.4545i | −0.350891 | − | 0.607760i | 0.635515 | − | 0.772088i | \(-0.280788\pi\) |
−0.986406 | + | 0.164328i | \(0.947454\pi\) | |||||||
\(734\) | 2.50000 | + | 4.33013i | 0.0922767 | + | 0.159828i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 40.0000 | 1.47442 | ||||||||
\(737\) | −10.0000 | + | 17.3205i | −0.368355 | + | 0.638009i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.50000 | − | 16.4545i | −0.349463 | − | 0.605288i | 0.636691 | − | 0.771119i | \(-0.280303\pi\) |
−0.986154 | + | 0.165831i | \(0.946969\pi\) | |||||||
\(740\) | 9.00000 | − | 15.5885i | 0.330847 | − | 0.573043i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.500000 | − | 0.866025i | −0.0183556 | − | 0.0317928i | ||||
\(743\) | 20.5000 | − | 35.5070i | 0.752072 | − | 1.30263i | −0.194745 | − | 0.980854i | \(-0.562388\pi\) |
0.946817 | − | 0.321773i | \(-0.104279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.5000 | − | 38.9711i | −0.824336 | − | 1.42779i | ||||
\(746\) | 2.50000 | + | 4.33013i | 0.0915315 | + | 0.158537i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 25.0000 | 0.914091 | ||||||||
\(749\) | 6.00000 | − | 10.3923i | 0.219235 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | 0.875772 | 0.437886 | − | 0.899030i | \(-0.355727\pi\) | ||||
0.437886 | + | 0.899030i | \(0.355727\pi\) | |||||||
\(752\) | −1.50000 | − | 2.59808i | −0.0546994 | − | 0.0947421i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.00000 | − | 1.73205i | −0.0364179 | − | 0.0630776i | ||||
\(755\) | −22.5000 | − | 38.9711i | −0.818859 | − | 1.41831i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.5000 | − | 26.8468i | −0.563357 | − | 0.975763i | −0.997200 | − | 0.0747748i | \(-0.976176\pi\) |
0.433843 | − | 0.900988i | \(-0.357157\pi\) | |||||||
\(758\) | −20.0000 | −0.726433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 31.5000 | − | 23.3827i | 1.14263 | − | 0.848179i | ||||
\(761\) | −4.50000 | − | 7.79423i | −0.163125 | − | 0.282541i | 0.772863 | − | 0.634573i | \(-0.218824\pi\) |
−0.935988 | + | 0.352032i | \(0.885491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | −0.181012 | ||||||||
\(764\) | 1.50000 | − | 2.59808i | 0.0542681 | − | 0.0939951i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.5000 | + | 19.9186i | −0.415512 | + | 0.719688i | ||||
\(767\) | 5.00000 | − | 8.66025i | 0.180540 | − | 0.312704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 15.0000 | 0.540562 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.50000 | + | 14.7224i | −0.305922 | + | 0.529872i | ||||
\(773\) | −8.50000 | + | 14.7224i | −0.305724 | + | 0.529529i | −0.977422 | − | 0.211296i | \(-0.932232\pi\) |
0.671698 | + | 0.740825i | \(0.265565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | + | 10.3923i | −0.215526 | + | 0.373303i | ||||
\(776\) | 30.0000 | 1.07694 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.50000 | + | 2.59808i | 0.0537776 | + | 0.0931455i | ||||
\(779\) | 31.5000 | − | 23.3827i | 1.12860 | − | 0.837772i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0000 | 0.536742 | ||||||||
\(782\) | −20.0000 | − | 34.6410i | −0.715199 | − | 1.23876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | − | 5.19615i | −0.107143 | − | 0.185577i | ||||
\(785\) | 4.50000 | + | 7.79423i | 0.160612 | + | 0.278188i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.50000 | − | 6.06218i | −0.124762 | − | 0.216093i | 0.796878 | − | 0.604140i | \(-0.206483\pi\) |
−0.921640 | + | 0.388047i | \(0.873150\pi\) | |||||||
\(788\) | 2.00000 | 0.0712470 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.00000 | − | 10.3923i | 0.213470 | − | 0.369742i | ||||
\(791\) | 17.0000 | 0.604450 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.0000 | + | 22.5167i | 0.461644 | + | 0.799590i | ||||
\(794\) | −3.50000 | − | 6.06218i | −0.124210 | − | 0.215139i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.50000 | + | 2.59808i | −0.0531661 | + | 0.0920864i | ||||
\(797\) | 5.50000 | + | 9.52628i | 0.194820 | + | 0.337438i | 0.946841 | − | 0.321700i | \(-0.104254\pi\) |
−0.752022 | + | 0.659139i | \(0.770921\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.50000 | − | 12.9904i | 0.265331 | − | 0.459567i | ||||
\(800\) | −10.0000 | − | 17.3205i | −0.353553 | − | 0.612372i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.5000 | + | 28.5788i | −0.582635 | + | 1.00915i | ||||
\(803\) | 25.0000 | 0.882231 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | + | 20.7846i | 0.422944 | + | 0.732561i | ||||
\(806\) | −3.00000 | − | 5.19615i | −0.105670 | − | 0.183027i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.5000 | − | 18.1865i | −0.369389 | − | 0.639800i | ||||
\(809\) | 2.00000 | 0.0703163 | 0.0351581 | − | 0.999382i | \(-0.488807\pi\) | ||||
0.0351581 | + | 0.999382i | \(0.488807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.5000 | + | 21.6506i | −0.438934 | + | 0.760257i | −0.997608 | − | 0.0691313i | \(-0.977977\pi\) |
0.558673 | + | 0.829388i | \(0.311311\pi\) | |||||||
\(812\) | −1.00000 | −0.0350931 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.0000 | + | 25.9808i | −0.525750 | + | 0.910625i | ||||
\(815\) | 18.0000 | − | 31.1769i | 0.630512 | − | 1.09208i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | − | 13.8564i | −1.11954 | − | 0.484774i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.5000 | − | 23.3827i | −0.471440 | − | 0.816559i | ||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.0000 | 1.39431 | 0.697156 | − | 0.716919i | \(-0.254448\pi\) | ||||
0.697156 | + | 0.716919i | \(0.254448\pi\) | |||||||
\(824\) | −7.50000 | − | 12.9904i | −0.261275 | − | 0.452541i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.50000 | + | 4.33013i | 0.0869861 | + | 0.150664i | ||||
\(827\) | 4.50000 | − | 7.79423i | 0.156480 | − | 0.271032i | −0.777117 | − | 0.629356i | \(-0.783319\pi\) |
0.933597 | + | 0.358325i | \(0.116652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | −13.5000 | − | 23.3827i | −0.468592 | − | 0.811625i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.0000 | 0.485363 | ||||||||
\(833\) | 15.0000 | − | 25.9808i | 0.519719 | − | 0.900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | − | 10.3923i | 0.207639 | − | 0.359641i | ||||
\(836\) | 17.5000 | − | 12.9904i | 0.605250 | − | 0.449282i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.500000 | − | 0.866025i | −0.0172722 | − | 0.0299164i | ||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | 26.0000 | 0.896019 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.50000 | + | 12.9904i | −0.258161 | + | 0.447147i | ||||
\(845\) | −13.5000 | + | 23.3827i | −0.464414 | + | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0000 | 0.481046 | ||||||||
\(848\) | 0.500000 | − | 0.866025i | 0.0171701 | − | 0.0297394i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.0000 | + | 17.3205i | −0.342997 | + | 0.594089i | ||||
\(851\) | −48.0000 | −1.64542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.0000 | −1.30110 | −0.650548 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(854\) | −13.0000 | −0.444851 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.0000 | 1.23045 | ||||||||
\(857\) | −14.0000 | −0.478231 | −0.239115 | − | 0.970991i | \(-0.576857\pi\) | ||||
−0.239115 | + | 0.970991i | \(0.576857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0000 | −0.409435 | −0.204717 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204717 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(860\) | −12.0000 | + | 20.7846i | −0.409197 | + | 0.708749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.500000 | − | 0.866025i | 0.0170301 | − | 0.0294969i | ||||
\(863\) | 16.0000 | 0.544646 | 0.272323 | − | 0.962206i | \(-0.412208\pi\) | ||||
0.272323 | + | 0.962206i | \(0.412208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | − | 15.5885i | 0.306009 | − | 0.530023i | ||||
\(866\) | −13.5000 | + | 23.3827i | −0.458749 | + | 0.794576i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.00000 | −0.101827 | ||||||||
\(869\) | 10.0000 | − | 17.3205i | 0.339227 | − | 0.587558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | −7.50000 | − | 12.9904i | −0.253982 | − | 0.439910i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.0000 | − | 13.8564i | −1.08242 | − | 0.468700i | ||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5000 | + | 33.7750i | −0.658468 | + | 1.14050i | 0.322544 | + | 0.946554i | \(0.395462\pi\) |
−0.981012 | + | 0.193946i | \(0.937871\pi\) | |||||||
\(878\) | −16.0000 | −0.539974 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.50000 | + | 12.9904i | 0.252825 | + | 0.437906i | ||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.5000 | + | 25.1147i | −0.487964 | + | 0.845178i | −0.999904 | − | 0.0138428i | \(-0.995594\pi\) |
0.511940 | + | 0.859021i | \(0.328927\pi\) | |||||||
\(884\) | 5.00000 | + | 8.66025i | 0.168168 | + | 0.291276i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.5000 | − | 21.6506i | −0.419946 | − | 0.727367i | ||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.50000 | − | 11.2583i | −0.218003 | − | 0.377592i | ||||
\(890\) | 13.5000 | + | 23.3827i | 0.452521 | + | 0.783789i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.0000 | 0.803579 | ||||||||
\(893\) | −1.50000 | − | 12.9904i | −0.0501956 | − | 0.434707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | − | 31.1769i | 0.601674 | − | 1.04213i | ||||
\(896\) | 1.50000 | − | 2.59808i | 0.0501115 | − | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.0000 | −1.00111 | ||||||||
\(899\) | −1.50000 | + | 2.59808i | −0.0500278 | + | 0.0866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.00000 | 0.166574 | ||||||||
\(902\) | 22.5000 | + | 38.9711i | 0.749168 | + | 1.29760i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.5000 | + | 44.1673i | 0.848117 | + | 1.46898i | ||||
\(905\) | 10.5000 | + | 18.1865i | 0.349032 | + | 0.604541i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0000 | 0.531271 | 0.265636 | − | 0.964073i | \(-0.414418\pi\) | ||||
0.265636 | + | 0.964073i | \(0.414418\pi\) | |||||||
\(908\) | −10.5000 | + | 18.1865i | −0.348455 | + | 0.603541i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.00000 | + | 5.19615i | 0.0994490 | + | 0.172251i | ||||
\(911\) | 22.5000 | − | 38.9711i | 0.745458 | − | 1.29117i | −0.204522 | − | 0.978862i | \(-0.565564\pi\) |
0.949980 | − | 0.312310i | \(-0.101103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.5000 | − | 38.9711i | −0.744641 | − | 1.28976i | ||||
\(914\) | −9.50000 | + | 16.4545i | −0.314232 | + | 0.544266i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.50000 | − | 14.7224i | −0.280848 | − | 0.486443i | ||||
\(917\) | −3.50000 | − | 6.06218i | −0.115580 | − | 0.200191i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | −36.0000 | + | 62.3538i | −1.18688 | + | 2.05574i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.0000 | 0.987997 | ||||||||
\(923\) | 3.00000 | + | 5.19615i | 0.0987462 | + | 0.171033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.0000 | + | 20.7846i | 0.394558 | + | 0.683394i | ||||
\(926\) | 0.500000 | + | 0.866025i | 0.0164310 | + | 0.0284594i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.50000 | − | 4.33013i | −0.0820665 | − | 0.142143i | ||||
\(929\) | −50.0000 | −1.64045 | −0.820223 | − | 0.572043i | \(-0.806151\pi\) | ||||
−0.820223 | + | 0.572043i | \(0.806151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | − | 25.9808i | −0.0983210 | − | 0.851485i | ||||
\(932\) | 4.50000 | + | 7.79423i | 0.147402 | + | 0.255308i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.00000 | −0.261768 | ||||||||
\(935\) | −37.5000 | + | 64.9519i | −1.22638 | + | 2.12415i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.50000 | − | 7.79423i | 0.147009 | − | 0.254626i | −0.783112 | − | 0.621881i | \(-0.786369\pi\) |
0.930121 | + | 0.367254i | \(0.119702\pi\) | |||||||
\(938\) | 2.00000 | − | 3.46410i | 0.0653023 | − | 0.113107i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.00000 | −0.293548 | ||||||||
\(941\) | −18.0000 | −0.586783 | −0.293392 | − | 0.955992i | \(-0.594784\pi\) | ||||
−0.293392 | + | 0.955992i | \(0.594784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0000 | + | 62.3538i | −1.17232 | + | 2.03052i | ||||
\(944\) | −2.50000 | + | 4.33013i | −0.0813681 | + | 0.140934i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.0000 | − | 34.6410i | 0.650256 | − | 1.12628i | ||||
\(947\) | −28.0000 | −0.909878 | −0.454939 | − | 0.890523i | \(-0.650339\pi\) | ||||
−0.454939 | + | 0.890523i | \(0.650339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.00000 | + | 8.66025i | 0.162307 | + | 0.281124i | ||||
\(950\) | 2.00000 | + | 17.3205i | 0.0648886 | + | 0.561951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.0000 | −0.486153 | ||||||||
\(953\) | 11.5000 | + | 19.9186i | 0.372522 | + | 0.645226i | 0.989953 | − | 0.141399i | \(-0.0451599\pi\) |
−0.617431 | + | 0.786625i | \(0.711827\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.50000 | + | 7.79423i | 0.145617 | + | 0.252215i | ||||
\(956\) | −7.50000 | − | 12.9904i | −0.242567 | − | 0.420139i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.50000 | − | 4.33013i | −0.0807713 | − | 0.139900i | ||||
\(959\) | −3.00000 | −0.0968751 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | −12.0000 | −0.386896 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.500000 | − | 0.866025i | −0.0161039 | − | 0.0278928i | ||||
\(965\) | −25.5000 | − | 44.1673i | −0.820874 | − | 1.42180i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.5000 | + | 32.0429i | −0.594920 | + | 1.03043i | 0.398638 | + | 0.917108i | \(0.369483\pi\) |
−0.993558 | + | 0.113323i | \(0.963850\pi\) | |||||||
\(968\) | 21.0000 | + | 36.3731i | 0.674966 | + | 1.16907i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.0000 | + | 25.9808i | −0.481621 | + | 0.834192i | ||||
\(971\) | −10.5000 | − | 18.1865i | −0.336961 | − | 0.583634i | 0.646899 | − | 0.762576i | \(-0.276066\pi\) |
−0.983860 | + | 0.178942i | \(0.942732\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0000 | + | 17.3205i | −0.320585 | + | 0.555270i | ||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.50000 | − | 11.2583i | −0.208060 | − | 0.360370i | ||||
\(977\) | −10.5000 | − | 18.1865i | −0.335925 | − | 0.581839i | 0.647737 | − | 0.761864i | \(-0.275715\pi\) |
−0.983662 | + | 0.180025i | \(0.942382\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.5000 | + | 38.9711i | 0.719103 | + | 1.24552i | ||||
\(980\) | −18.0000 | −0.574989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.5000 | + | 23.3827i | −0.430802 | + | 0.746171i | ||||
\(983\) | −8.00000 | −0.255160 | −0.127580 | − | 0.991828i | \(-0.540721\pi\) | ||||
−0.127580 | + | 0.991828i | \(0.540721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.00000 | + | 5.19615i | −0.0955879 | + | 0.165563i | ||||
\(986\) | −2.50000 | + | 4.33013i | −0.0796162 | + | 0.137899i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.00000 | + | 3.46410i | 0.254514 | + | 0.110208i | ||||
\(989\) | 64.0000 | 2.03508 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5000 | − | 19.9186i | −0.365310 | − | 0.632735i | 0.623516 | − | 0.781810i | \(-0.285704\pi\) |
−0.988826 | + | 0.149076i | \(0.952370\pi\) | |||||||
\(992\) | −7.50000 | − | 12.9904i | −0.238125 | − | 0.412445i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.00000 | −0.0951542 | ||||||||
\(995\) | −4.50000 | − | 7.79423i | −0.142660 | − | 0.247094i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.50000 | + | 4.33013i | 0.0791758 | + | 0.137136i | 0.902895 | − | 0.429862i | \(-0.141438\pi\) |
−0.823719 | + | 0.566999i | \(0.808104\pi\) | |||||||
\(998\) | −14.5000 | + | 25.1147i | −0.458989 | + | 0.794993i | ||||
\(999\) | 0 | 0 |
(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 | 513.2.h.b.235.1 | 2 | ||
3.2 | odd | 2 | 171.2.h.a.7.1 | yes | 2 | ||
9.4 | even | 3 | 513.2.g.a.64.1 | 2 | |||
9.5 | odd | 6 | 171.2.g.a.121.1 | yes | 2 | ||
19.11 | even | 3 | 513.2.g.a.505.1 | 2 | |||
57.11 | odd | 6 | 171.2.g.a.106.1 | ✓ | 2 | ||
171.49 | even | 3 | inner | 513.2.h.b.334.1 | 2 | ||
171.68 | odd | 6 | 171.2.h.a.49.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.a.106.1 | ✓ | 2 | 57.11 | odd | 6 | ||
171.2.g.a.121.1 | yes | 2 | 9.5 | odd | 6 | ||
171.2.h.a.7.1 | yes | 2 | 3.2 | odd | 2 | ||
171.2.h.a.49.1 | yes | 2 | 171.68 | odd | 6 | ||
513.2.g.a.64.1 | 2 | 9.4 | even | 3 | |||
513.2.g.a.505.1 | 2 | 19.11 | even | 3 | |||
513.2.h.b.235.1 | 2 | 1.1 | even | 1 | trivial | ||
513.2.h.b.334.1 | 2 | 171.49 | even | 3 | inner |