Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3456,2,Mod(1153,3456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3456.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3456.i (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: | \(27.5962989386\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3456.2305 |
Dual form | 3456.2.i.d.1153.1 |
$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(2431\) | \(2945\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 1.73205i | 0.447214 | − | 0.774597i | −0.550990 | − | 0.834512i | \(-0.685750\pi\) |
0.998203 | + | 0.0599153i | \(0.0190830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.73205i | 0.377964 | + | 0.654654i | 0.990766 | − | 0.135583i | \(-0.0432908\pi\) |
−0.612801 | + | 0.790237i | \(0.709957\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | 1.64399 | 0.821995 | − | 0.569495i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50000 | + | 7.79423i | 0.686244 | + | 1.18861i | 0.973044 | + | 0.230618i | \(0.0740749\pi\) |
−0.286801 | + | 0.957990i | \(0.592592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000 | + | 6.92820i | 0.583460 | + | 1.01058i | 0.995066 | + | 0.0992202i | \(0.0316348\pi\) |
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.0000 | −1.64833 | −0.824163 | − | 0.566352i | \(-0.808354\pi\) | ||||
−0.824163 | + | 0.566352i | \(0.808354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0000 | 1.34840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.50000 | − | 6.06218i | 0.455661 | − | 0.789228i | −0.543065 | − | 0.839691i | \(-0.682736\pi\) |
0.998726 | + | 0.0504625i | \(0.0160695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.00000 | − | 6.92820i | −0.496139 | − | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0000 | −1.52153 | −0.760767 | − | 0.649025i | \(-0.775177\pi\) | ||||
−0.760767 | + | 0.649025i | \(0.775177\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.00000 | + | 8.66025i | −0.569803 | + | 0.986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | − | 1.73205i | −0.112509 | − | 0.194871i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.916781 | + | 0.399390i | \(0.869222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | + | 10.3923i | 0.658586 | + | 1.14070i | 0.980982 | + | 0.194099i | \(0.0621783\pi\) |
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | + | 1.73205i | −0.108465 | + | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00000 | + | 8.66025i | −0.512989 | + | 0.888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.50000 | − | 11.2583i | −0.659975 | − | 1.14311i | −0.980622 | − | 0.195911i | \(-0.937234\pi\) |
0.320647 | − | 0.947199i | \(-0.396100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | − | 6.92820i | 0.394132 | − | 0.682656i | −0.598858 | − | 0.800855i | \(-0.704379\pi\) |
0.992990 | + | 0.118199i | \(0.0377120\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0000 | −1.06341 | −0.531705 | − | 0.846930i | \(-0.678449\pi\) | ||||
−0.531705 | + | 0.846930i | \(0.678449\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0000 | 1.14939 | 0.574696 | − | 0.818367i | \(-0.305120\pi\) | ||||
0.574696 | + | 0.818367i | \(0.305120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.00000 | − | 12.1244i | 0.658505 | − | 1.14056i | −0.322498 | − | 0.946570i | \(-0.604523\pi\) |
0.981003 | − | 0.193993i | \(-0.0621440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | + | 6.92820i | 0.373002 | + | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | − | 1.73205i | −0.0916698 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | − | 8.66025i | −0.433555 | − | 0.750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.500000 | + | 0.866025i | 0.0427179 | + | 0.0739895i | 0.886594 | − | 0.462549i | \(-0.153065\pi\) |
−0.843876 | + | 0.536538i | \(0.819732\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.500000 | + | 0.866025i | −0.0424094 | + | 0.0734553i | −0.886451 | − | 0.462822i | \(-0.846837\pi\) |
0.844042 | + | 0.536278i | \(0.180170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.0000 | 1.67248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | + | 20.7846i | −0.957704 | + | 1.65879i | −0.229650 | + | 0.973273i | \(0.573758\pi\) |
−0.728055 | + | 0.685519i | \(0.759575\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | − | 1.73205i | 0.0773823 | − | 0.134030i | −0.824737 | − | 0.565516i | \(-0.808677\pi\) |
0.902120 | + | 0.431486i | \(0.142010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | + | 15.5885i | 0.684257 | + | 1.18517i | 0.973670 | + | 0.227964i | \(0.0732068\pi\) |
−0.289412 | + | 0.957205i | \(0.593460\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 1.73205i | −0.0755929 | + | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0000 | − | 17.3205i | 0.735215 | − | 1.27343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.50000 | − | 4.33013i | −0.182818 | − | 0.316650i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.00000 | − | 1.73205i | −0.0723575 | − | 0.125327i | 0.827577 | − | 0.561353i | \(-0.189719\pi\) |
−0.899934 | + | 0.436026i | \(0.856386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | + | 0.866025i | −0.0359908 | + | 0.0623379i | −0.883460 | − | 0.468507i | \(-0.844792\pi\) |
0.847469 | + | 0.530845i | \(0.178125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.0000 | 1.42494 | 0.712470 | − | 0.701702i | \(-0.247576\pi\) | ||||
0.712470 | + | 0.701702i | \(0.247576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | + | 10.3923i | −0.421117 | + | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.5000 | − | 21.6506i | −0.864643 | − | 1.49761i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | − | 17.3205i | 0.688428 | − | 1.19239i | −0.283918 | − | 0.958849i | \(-0.591634\pi\) |
0.972346 | − | 0.233544i | \(-0.0750324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0000 | 1.22759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | + | 3.46410i | −0.134535 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.0000 | − | 20.7846i | −0.803579 | − | 1.39184i | −0.917246 | − | 0.398321i | \(-0.869593\pi\) |
0.113666 | − | 0.993519i | \(-0.463740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | − | 12.1244i | 0.462573 | − | 0.801200i | −0.536515 | − | 0.843891i | \(-0.680260\pi\) |
0.999088 | + | 0.0426906i | \(0.0135930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.00000 | 0.589610 | 0.294805 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294805 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000 | 1.04372 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | + | 10.3923i | −0.388108 | + | 0.672222i | −0.992195 | − | 0.124696i | \(-0.960204\pi\) |
0.604087 | + | 0.796918i | \(0.293538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5000 | − | 21.6506i | −0.805196 | − | 1.39464i | −0.916159 | − | 0.400815i | \(-0.868727\pi\) |
0.110963 | − | 0.993825i | \(-0.464606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | − | 5.19615i | −0.191663 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0000 | + | 17.3205i | −0.636285 | + | 1.10208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.00000 | 0.189358 | 0.0946792 | − | 0.995508i | \(-0.469817\pi\) | ||||
0.0946792 | + | 0.995508i | \(0.469817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.50000 | − | 2.59808i | 0.0935674 | − | 0.162064i | −0.815442 | − | 0.578838i | \(-0.803506\pi\) |
0.909010 | + | 0.416775i | \(0.136840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0000 | + | 17.3205i | 0.621370 | + | 1.07624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | + | 15.5885i | 0.554964 | + | 0.961225i | 0.997906 | + | 0.0646755i | \(0.0206012\pi\) |
−0.442943 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | + | 20.7846i | −0.737154 | + | 1.27679i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.50000 | + | 4.33013i | −0.150756 | + | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0000 | + | 25.9808i | 0.894825 | + | 1.54988i | 0.834021 | + | 0.551733i | \(0.186033\pi\) |
0.0608039 | + | 0.998150i | \(0.480634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000 | − | 20.7846i | 0.713326 | − | 1.23552i | −0.250276 | − | 0.968175i | \(-0.580521\pi\) |
0.963602 | − | 0.267342i | \(-0.0861454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | −0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.00000 | − | 8.66025i | 0.292103 | − | 0.505937i | −0.682204 | − | 0.731162i | \(-0.738978\pi\) |
0.974307 | + | 0.225225i | \(0.0723116\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.00000 | − | 12.1244i | −0.407556 | − | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00000 | + | 13.8564i | 0.462652 | + | 0.801337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.00000 | + | 15.5885i | −0.518751 | + | 0.898504i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.00000 | −0.171219 | −0.0856095 | − | 0.996329i | \(-0.527284\pi\) | ||||
−0.0856095 | + | 0.996329i | \(0.527284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.00000 | − | 8.66025i | 0.283524 | − | 0.491078i | −0.688726 | − | 0.725022i | \(-0.741830\pi\) |
0.972250 | + | 0.233944i | \(0.0751631\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.5000 | − | 21.6506i | −0.706542 | − | 1.22377i | −0.966132 | − | 0.258047i | \(-0.916921\pi\) |
0.259590 | − | 0.965719i | \(-0.416412\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0000 | + | 25.9808i | −0.839839 | + | 1.45464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.00000 | 0.278207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | + | 13.8564i | −0.441054 | + | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | + | 17.3205i | 0.549650 | + | 0.952021i | 0.998298 | + | 0.0583130i | \(0.0185721\pi\) |
−0.448649 | + | 0.893708i | \(0.648095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.00000 | − | 12.1244i | −0.382451 | − | 0.662424i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.50000 | + | 16.4545i | −0.517498 | + | 0.896333i | 0.482295 | + | 0.876009i | \(0.339803\pi\) |
−0.999793 | + | 0.0203242i | \(0.993530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.50000 | + | 2.59808i | −0.0805242 | + | 0.139472i | −0.903475 | − | 0.428640i | \(-0.858993\pi\) |
0.822951 | + | 0.568112i | \(0.192326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.00000 | − | 13.8564i | −0.428230 | − | 0.741716i | 0.568486 | − | 0.822693i | \(-0.307529\pi\) |
−0.996716 | + | 0.0809766i | \(0.974196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50000 | − | 7.79423i | −0.239511 | − | 0.414845i | 0.721063 | − | 0.692869i | \(-0.243654\pi\) |
−0.960574 | + | 0.278024i | \(0.910320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.0000 | −1.79445 | −0.897226 | − | 0.441572i | \(-0.854421\pi\) | ||||
−0.897226 | + | 0.441572i | \(0.854421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0000 | + | 22.5167i | −0.680451 | + | 1.17858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | + | 19.0526i | 0.574195 | + | 0.994535i | 0.996129 | + | 0.0879086i | \(0.0280183\pi\) |
−0.421933 | + | 0.906627i | \(0.638648\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.623009 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0000 | − | 27.7128i | 0.828449 | − | 1.43492i | −0.0708063 | − | 0.997490i | \(-0.522557\pi\) |
0.899255 | − | 0.437425i | \(-0.144109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.0000 | −1.28416 | −0.642082 | − | 0.766636i | \(-0.721929\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.00000 | − | 5.19615i | 0.153293 | − | 0.265511i | −0.779143 | − | 0.626846i | \(-0.784346\pi\) |
0.932436 | + | 0.361335i | \(0.117679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0000 | + | 17.3205i | 0.509647 | + | 0.882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.0000 | − | 32.9090i | −0.963338 | − | 1.66855i | −0.714015 | − | 0.700130i | \(-0.753125\pi\) |
−0.249323 | − | 0.968420i | \(-0.580208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | − | 3.46410i | 0.101144 | − | 0.175187i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0000 | + | 43.3013i | 1.23920 | + | 2.14636i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | + | 21.6506i | −0.618085 | + | 1.07056i | 0.371750 | + | 0.928333i | \(0.378758\pi\) |
−0.989835 | + | 0.142222i | \(0.954575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.0000 | 0.688895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000 | 1.17811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0000 | + | 17.3205i | −0.488532 | + | 0.846162i | −0.999913 | − | 0.0131919i | \(-0.995801\pi\) |
0.511381 | + | 0.859354i | \(0.329134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.00000 | + | 1.73205i | 0.0487370 | + | 0.0844150i | 0.889365 | − | 0.457198i | \(-0.151147\pi\) |
−0.840628 | + | 0.541613i | \(0.817814\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.500000 | − | 0.866025i | −0.0242536 | − | 0.0420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | + | 6.92820i | −0.193574 | + | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0000 | 0.481683 | 0.240842 | − | 0.970564i | \(-0.422577\pi\) | ||||
0.240842 | + | 0.970564i | \(0.422577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.0000 | 1.58588 | 0.792939 | − | 0.609301i | \(-0.208550\pi\) | ||||
0.792939 | + | 0.609301i | \(0.208550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0000 | − | 17.3205i | 0.478365 | − | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | − | 20.7846i | −0.572729 | − | 0.991995i | −0.996284 | − | 0.0861252i | \(-0.972552\pi\) |
0.423556 | − | 0.905870i | \(-0.360782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.50000 | + | 12.9904i | 0.356336 | + | 0.617192i | 0.987346 | − | 0.158583i | \(-0.0506926\pi\) |
−0.631010 | + | 0.775775i | \(0.717359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | + | 17.3205i | −0.474045 | + | 0.821071i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0000 | −0.802280 | −0.401140 | − | 0.916017i | \(-0.631386\pi\) | ||||
−0.401140 | + | 0.916017i | \(0.631386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0000 | −0.706322 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.00000 | − | 13.8564i | 0.375046 | − | 0.649598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.50000 | + | 2.59808i | 0.0701670 | + | 0.121533i | 0.898974 | − | 0.438001i | \(-0.144313\pi\) |
−0.828807 | + | 0.559534i | \(0.810980\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0000 | − | 17.3205i | −0.465746 | − | 0.806696i | 0.533488 | − | 0.845807i | \(-0.320881\pi\) |
−0.999235 | + | 0.0391109i | \(0.987547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | + | 1.73205i | −0.0464739 | + | 0.0804952i | −0.888327 | − | 0.459212i | \(-0.848132\pi\) |
0.841853 | + | 0.539707i | \(0.181465\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.0000 | −1.34196 | −0.670980 | − | 0.741475i | \(-0.734126\pi\) | ||||
−0.670980 | + | 0.741475i | \(0.734126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0000 | 0.646460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.5000 | + | 38.9711i | −1.03455 | + | 1.79190i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.50000 | − | 4.33013i | −0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.00000 | − | 15.5885i | −0.411220 | − | 0.712255i | 0.583803 | − | 0.811895i | \(-0.301564\pi\) |
−0.995023 | + | 0.0996406i | \(0.968231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | − | 34.6410i | 0.911922 | − | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.0000 | −1.18060 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0000 | −0.453143 | −0.226572 | − | 0.973995i | \(-0.572752\pi\) | ||||
−0.226572 | + | 0.973995i | \(0.572752\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5000 | − | 21.6506i | 0.564117 | − | 0.977079i | −0.433014 | − | 0.901387i | \(-0.642550\pi\) |
0.997131 | − | 0.0756923i | \(-0.0241167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.00000 | − | 5.19615i | −0.135113 | − | 0.234023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | − | 10.3923i | −0.269137 | − | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | − | 4.33013i | 0.111915 | − | 0.193843i | −0.804627 | − | 0.593780i | \(-0.797635\pi\) |
0.916542 | + | 0.399937i | \(0.130968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.00000 | −0.178351 | −0.0891756 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891756 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | − | 24.2487i | 0.620539 | − | 1.07481i | −0.368846 | − | 0.929490i | \(-0.620247\pi\) |
0.989385 | − | 0.145315i | \(-0.0464195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0000 | − | 22.5167i | −0.575086 | − | 0.996078i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | − | 13.8564i | −0.352522 | − | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.0000 | + | 34.6410i | −0.879599 | + | 1.52351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.00000 | 0.306676 | 0.153338 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153338 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −44.0000 | −1.92399 | −0.961993 | − | 0.273075i | \(-0.911959\pi\) | ||||
−0.961993 | + | 0.273075i | \(0.911959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | + | 10.3923i | 0.259889 | + | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.0000 | + | 19.0526i | −0.475571 | + | 0.823714i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.0000 | 0.646096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | − | 20.7846i | 0.514024 | − | 0.890315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.500000 | + | 0.866025i | 0.0213785 | + | 0.0370286i | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | − | 25.9808i | −0.639021 | − | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000 | − | 3.46410i | 0.0850487 | − | 0.147309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.0000 | −1.10166 | −0.550828 | − | 0.834619i | \(-0.685688\pi\) | ||||
−0.550828 | + | 0.834619i | \(0.685688\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5000 | − | 28.5788i | 0.695392 | − | 1.20445i | −0.274656 | − | 0.961542i | \(-0.588564\pi\) |
0.970048 | − | 0.242912i | \(-0.0781026\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | − | 24.2487i | −0.588984 | − | 1.02015i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.50000 | − | 16.4545i | −0.398261 | − | 0.689808i | 0.595251 | − | 0.803540i | \(-0.297053\pi\) |
−0.993511 | + | 0.113732i | \(0.963719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.50000 | + | 16.4545i | −0.397563 | + | 0.688599i | −0.993425 | − | 0.114488i | \(-0.963477\pi\) |
0.595862 | + | 0.803087i | \(0.296811\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.0000 | 0.957503 | 0.478751 | − | 0.877951i | \(-0.341090\pi\) | ||||
0.478751 | + | 0.877951i | \(0.341090\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | + | 20.7846i | −0.497844 | + | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.0000 | − | 51.9615i | −1.24247 | − | 2.15203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.50000 | − | 4.33013i | −0.103186 | − | 0.178723i | 0.809810 | − | 0.586693i | \(-0.199570\pi\) |
−0.912996 | + | 0.407969i | \(0.866237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | −0.163984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0000 | − | 36.3731i | 0.858037 | − | 1.48616i | −0.0157622 | − | 0.999876i | \(-0.505017\pi\) |
0.873799 | − | 0.486287i | \(-0.161649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.50000 | + | 7.79423i | 0.183559 | + | 0.317933i | 0.943090 | − | 0.332538i | \(-0.107905\pi\) |
−0.759531 | + | 0.650471i | \(0.774572\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.0000 | + | 24.2487i | 0.569181 | + | 0.985850i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.50000 | + | 14.7224i | −0.342197 | + | 0.592703i | −0.984840 | − | 0.173463i | \(-0.944504\pi\) |
0.642643 | + | 0.766165i | \(0.277838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.5000 | − | 30.3109i | −0.703384 | − | 1.21830i | −0.967271 | − | 0.253744i | \(-0.918338\pi\) |
0.263887 | − | 0.964554i | \(-0.414995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.0000 | − | 17.3205i | −0.400642 | − | 0.693932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0000 | −0.875806 | −0.437903 | − | 0.899022i | \(-0.644279\pi\) | ||||
−0.437903 | + | 0.899022i | \(0.644279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.0000 | − | 34.6410i | 0.793676 | − | 1.37469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | − | 10.3923i | −0.237729 | − | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5000 | − | 18.1865i | 0.414080 | − | 0.717207i | −0.581252 | − | 0.813724i | \(-0.697437\pi\) |
0.995331 | + | 0.0965169i | \(0.0307702\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.0000 | −1.65119 | −0.825595 | − | 0.564263i | \(-0.809160\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.0000 | 1.37387 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | + | 20.7846i | 0.468879 | + | 0.812122i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | − | 20.7846i | −0.467454 | − | 0.809653i | 0.531855 | − | 0.846836i | \(-0.321495\pi\) |
−0.999309 | + | 0.0371821i | \(0.988162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00000 | − | 1.73205i | 0.0388955 | − | 0.0673690i | −0.845922 | − | 0.533306i | \(-0.820949\pi\) |
0.884818 | + | 0.465937i | \(0.154283\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.0000 | −0.775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0000 | + | 17.3205i | −0.386046 | + | 0.668651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | − | 8.66025i | −0.192736 | − | 0.333828i | 0.753420 | − | 0.657539i | \(-0.228403\pi\) |
−0.946156 | + | 0.323711i | \(0.895069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.0000 | − | 24.2487i | −0.538064 | − | 0.931954i | −0.999008 | − | 0.0445248i | \(-0.985823\pi\) |
0.460945 | − | 0.887429i | \(-0.347511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.0000 | − | 22.5167i | 0.498894 | − | 0.864110i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0000 | −0.573959 | −0.286980 | − | 0.957937i | \(-0.592651\pi\) | ||||
−0.286980 | + | 0.957937i | \(0.592651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.0000 | + | 41.5692i | −0.914327 | + | 1.58366i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.00000 | + | 10.3923i | 0.228251 | + | 0.395342i | 0.957290 | − | 0.289130i | \(-0.0933661\pi\) |
−0.729039 | + | 0.684472i | \(0.760033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.00000 | + | 1.73205i | 0.0379322 | + | 0.0657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50000 | − | 2.59808i | 0.0568166 | − | 0.0984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.0000 | −1.88579 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.00000 | + | 10.3923i | −0.225653 | + | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | − | 17.3205i | −0.375558 | − | 0.650485i | 0.614852 | − | 0.788642i | \(-0.289216\pi\) |
−0.990410 | + | 0.138157i | \(0.955882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.0000 | − | 34.6410i | 0.747958 | − | 1.29550i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0000 | + | 41.5692i | 0.890111 | + | 1.54172i | 0.839742 | + | 0.542986i | \(0.182706\pi\) |
0.0503692 | + | 0.998731i | \(0.483960\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.50000 | − | 7.79423i | −0.166439 | − | 0.288280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00000 | + | 15.5885i | −0.332423 | + | 0.575773i | −0.982986 | − | 0.183679i | \(-0.941199\pi\) |
0.650564 | + | 0.759452i | \(0.274533\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.0000 | 1.28924 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0000 | −0.772497 | −0.386249 | − | 0.922395i | \(-0.626229\pi\) | ||||
−0.386249 | + | 0.922395i | \(0.626229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.0000 | + | 32.9090i | −0.697042 | + | 1.20731i | 0.272445 | + | 0.962171i | \(0.412168\pi\) |
−0.969487 | + | 0.245141i | \(0.921166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0000 | − | 19.0526i | −0.401931 | − | 0.696165i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | − | 1.73205i | 0.0364905 | − | 0.0632034i | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.0000 | 1.16460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0000 | 0.508839 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.00000 | − | 8.66025i | 0.181250 | − | 0.313934i | −0.761057 | − | 0.648686i | \(-0.775319\pi\) |
0.942306 | + | 0.334752i | \(0.108652\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0000 | + | 20.7846i | 0.434429 | + | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.0000 | − | 24.2487i | −0.505511 | − | 0.875570i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00000 | + | 1.73205i | −0.0360609 | + | 0.0624593i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0000 | 0.863220 | 0.431610 | − | 0.902060i | \(-0.357946\pi\) | ||||
0.431610 | + | 0.902060i | \(0.357946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.50000 | − | 12.9904i | 0.268715 | − | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.0000 | − | 25.9808i | −0.536742 | − | 0.929665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.0000 | + | 41.5692i | 0.856597 | + | 1.48367i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | + | 24.2487i | −0.499046 | + | 0.864373i | −0.999999 | − | 0.00110111i | \(-0.999650\pi\) |
0.500953 | + | 0.865474i | \(0.332983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.0000 | 0.995565 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.0000 | − | 25.9808i | 0.531327 | − | 0.920286i | −0.468004 | − | 0.883726i | \(-0.655027\pi\) |
0.999331 | − | 0.0365596i | \(-0.0116399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.00000 | − | 6.92820i | −0.141510 | − | 0.245102i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.5000 | − | 56.2917i | −1.14690 | − | 1.98649i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | + | 13.8564i | −0.281963 | + | 0.488374i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.00000 | 0.105474 | 0.0527372 | − | 0.998608i | \(-0.483205\pi\) | ||||
0.0527372 | + | 0.998608i | \(0.483205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.00000 | 0.316033 | 0.158016 | − | 0.987436i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987436i | \(0.449490\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.5000 | − | 38.9711i | −0.787175 | − | 1.36343i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.00000 | − | 12.1244i | −0.244302 | − | 0.423143i | 0.717633 | − | 0.696421i | \(-0.245225\pi\) |
−0.961935 | + | 0.273278i | \(0.911892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.0000 | + | 29.4449i | −0.592583 | + | 1.02638i | 0.401300 | + | 0.915947i | \(0.368558\pi\) |
−0.993883 | + | 0.110437i | \(0.964775\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.0000 | −1.53003 | −0.765015 | − | 0.644013i | \(-0.777268\pi\) | ||||
−0.765015 | + | 0.644013i | \(0.777268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00000 | −0.0694629 | −0.0347314 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347314 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.50000 | + | 2.59808i | −0.0519719 | + | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00000 | − | 3.46410i | −0.0692129 | − | 0.119880i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | − | 41.5692i | −0.828572 | − | 1.43513i | −0.899158 | − | 0.437623i | \(-0.855820\pi\) |
0.0705865 | − | 0.997506i | \(-0.477513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | −0.206406 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.0000 | −0.962091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.0000 | + | 34.6410i | −0.685591 | + | 1.18748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.00000 | − | 6.92820i | −0.136957 | − | 0.237217i | 0.789386 | − | 0.613897i | \(-0.210399\pi\) |
−0.926343 | + | 0.376680i | \(0.877066\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.50000 | − | 11.2583i | 0.221777 | − | 0.384129i | −0.733571 | − | 0.679613i | \(-0.762148\pi\) |
0.955348 | + | 0.295484i | \(0.0954809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.0000 | 0.748889 | 0.374444 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374444 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0000 | 1.22404 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.00000 | − | 8.66025i | 0.169613 | − | 0.293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.0000 | − | 24.2487i | −0.474372 | − | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0000 | + | 20.7846i | 0.405674 | + | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.00000 | − | 13.8564i | 0.270141 | − | 0.467898i | −0.698757 | − | 0.715359i | \(-0.746263\pi\) |
0.968898 | + | 0.247462i | \(0.0795964\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00000 | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0000 | − | 25.9808i | 0.503651 | − | 0.872349i | −0.496340 | − | 0.868128i | \(-0.665323\pi\) |
0.999991 | − | 0.00422062i | \(-0.00134347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 34.6410i | 0.670778 | + | 1.16182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.0000 | − | 34.6410i | −0.669274 | − | 1.15922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | − | 20.7846i | 0.401116 | − | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0000 | − | 34.6410i | 0.664822 | − | 1.15151i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.50000 | + | 9.52628i | 0.182625 | + | 0.316315i | 0.942773 | − | 0.333434i | \(-0.108207\pi\) |
−0.760149 | + | 0.649749i | \(0.774874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | − | 10.3923i | −0.198789 | − | 0.344312i | 0.749347 | − | 0.662177i | \(-0.230367\pi\) |
−0.948136 | + | 0.317865i | \(0.897034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.0000 | + | 51.9615i | −0.992855 | + | 1.71968i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.0000 | −0.792550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.0000 | 1.18753 | 0.593765 | − | 0.804638i | \(-0.297641\pi\) | ||||
0.593765 | + | 0.804638i | \(0.297641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0000 | + | 20.7846i | −0.394985 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00000 | + | 8.66025i | 0.164399 | + | 0.284747i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.00000 | − | 5.19615i | −0.0984268 | − | 0.170480i | 0.812607 | − | 0.582812i | \(-0.198048\pi\) |
−0.911034 | + | 0.412332i | \(0.864714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.50000 | + | 12.9904i | −0.245803 | + | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.0000 | −0.327035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0000 | −0.849383 | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||||
−0.424691 | + | 0.905338i | \(0.639617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | − | 24.2487i | 0.456387 | − | 0.790485i | −0.542380 | − | 0.840133i | \(-0.682477\pi\) |
0.998767 | + | 0.0496480i | \(0.0158099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | − | 10.3923i | −0.195387 | − | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.5000 | + | 19.9186i | 0.373700 | + | 0.647267i | 0.990132 | − | 0.140141i | \(-0.0447557\pi\) |
−0.616432 | + | 0.787408i | \(0.711422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.0000 | + | 45.0333i | −0.843996 | + | 1.46184i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.00000 | −0.0323932 | −0.0161966 | − | 0.999869i | \(-0.505156\pi\) | ||||
−0.0161966 | + | 0.999869i | \(0.505156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | −0.129437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.00000 | + | 1.73205i | −0.0322917 | + | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00000 | + | 1.73205i | 0.0321911 | + | 0.0557567i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.00000 | + | 12.1244i | −0.225105 | + | 0.389893i | −0.956351 | − | 0.292221i | \(-0.905606\pi\) |
0.731246 | + | 0.682114i | \(0.238939\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.0000 | −0.898563 | −0.449281 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449281 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.00000 | −0.0641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.5000 | − | 49.3634i | 0.911796 | − | 1.57928i | 0.100270 | − | 0.994960i | \(-0.468029\pi\) |
0.811526 | − | 0.584316i | \(-0.198637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.0000 | − | 43.3013i | −0.799003 | − | 1.38391i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.0000 | + | 39.8372i | 0.733586 | + | 1.27061i | 0.955341 | + | 0.295506i | \(0.0954882\pi\) |
−0.221755 | + | 0.975102i | \(0.571178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | − | 34.6410i | 0.637253 | − | 1.10375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.0000 | −1.14473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.00000 | + | 3.46410i | −0.0634043 | + | 0.109819i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3456.2.i.d.2305.1 | 2 | ||
3.2 | odd | 2 | 1152.2.i.a.769.1 | yes | 2 | ||
4.3 | odd | 2 | 3456.2.i.c.2305.1 | 2 | |||
8.3 | odd | 2 | 3456.2.i.a.2305.1 | 2 | |||
8.5 | even | 2 | 3456.2.i.b.2305.1 | 2 | |||
9.2 | odd | 6 | 1152.2.i.a.385.1 | ✓ | 2 | ||
9.7 | even | 3 | inner | 3456.2.i.d.1153.1 | 2 | ||
12.11 | even | 2 | 1152.2.i.c.769.1 | yes | 2 | ||
24.5 | odd | 2 | 1152.2.i.d.769.1 | yes | 2 | ||
24.11 | even | 2 | 1152.2.i.b.769.1 | yes | 2 | ||
36.7 | odd | 6 | 3456.2.i.c.1153.1 | 2 | |||
36.11 | even | 6 | 1152.2.i.c.385.1 | yes | 2 | ||
72.11 | even | 6 | 1152.2.i.b.385.1 | yes | 2 | ||
72.29 | odd | 6 | 1152.2.i.d.385.1 | yes | 2 | ||
72.43 | odd | 6 | 3456.2.i.a.1153.1 | 2 | |||
72.61 | even | 6 | 3456.2.i.b.1153.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.a.385.1 | ✓ | 2 | 9.2 | odd | 6 | ||
1152.2.i.a.769.1 | yes | 2 | 3.2 | odd | 2 | ||
1152.2.i.b.385.1 | yes | 2 | 72.11 | even | 6 | ||
1152.2.i.b.769.1 | yes | 2 | 24.11 | even | 2 | ||
1152.2.i.c.385.1 | yes | 2 | 36.11 | even | 6 | ||
1152.2.i.c.769.1 | yes | 2 | 12.11 | even | 2 | ||
1152.2.i.d.385.1 | yes | 2 | 72.29 | odd | 6 | ||
1152.2.i.d.769.1 | yes | 2 | 24.5 | odd | 2 | ||
3456.2.i.a.1153.1 | 2 | 72.43 | odd | 6 | |||
3456.2.i.a.2305.1 | 2 | 8.3 | odd | 2 | |||
3456.2.i.b.1153.1 | 2 | 72.61 | even | 6 | |||
3456.2.i.b.2305.1 | 2 | 8.5 | even | 2 | |||
3456.2.i.c.1153.1 | 2 | 36.7 | odd | 6 | |||
3456.2.i.c.2305.1 | 2 | 4.3 | odd | 2 | |||
3456.2.i.d.1153.1 | 2 | 9.7 | even | 3 | inner | ||
3456.2.i.d.2305.1 | 2 | 1.1 | even | 1 | trivial |