Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(609,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.c (of order \(2\), degree \(1\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2702336256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.4 | ||
Root | \(-1.52274 + 1.63746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.609 |
Dual form | 1216.2.c.i.609.6 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.31342i | − 0.587381i | −0.955901 | − | 0.293691i | \(-0.905116\pi\) | ||||
0.955901 | − | 0.293691i | \(-0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.77753 | 1.80573 | 0.902867 | − | 0.429919i | \(-0.141458\pi\) | ||||
0.902867 | + | 0.429919i | \(0.141458\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.27492i | 0.685913i | 0.939351 | + | 0.342957i | \(0.111428\pi\) | ||||
−0.939351 | + | 0.342957i | \(0.888572\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.09095i | 1.68933i | 0.535299 | + | 0.844663i | \(0.320199\pi\) | ||||
−0.535299 | + | 0.844663i | \(0.679801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.27492 | −1.03682 | −0.518410 | − | 0.855132i | \(-0.673476\pi\) | ||||
−0.518410 | + | 0.855132i | \(0.673476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27492 | 0.654983 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.09095i | 1.13106i | 0.824727 | + | 0.565530i | \(0.191329\pi\) | ||||
−0.824727 | + | 0.565530i | \(0.808671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62685 | −0.471796 | −0.235898 | − | 0.971778i | \(-0.575803\pi\) | ||||
−0.235898 | + | 0.971778i | \(0.575803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 6.27492i | − 1.06065i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.837253i | 0.137644i | 0.997629 | + | 0.0688218i | \(0.0219240\pi\) | ||||
−0.997629 | + | 0.0688218i | \(0.978076\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5498 | −1.64761 | −0.823804 | − | 0.566875i | \(-0.808152\pi\) | ||||
−0.823804 | + | 0.566875i | \(0.808152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.2749i | − 1.56691i | −0.621448 | − | 0.783455i | \(-0.713455\pi\) | ||||
0.621448 | − | 0.783455i | \(-0.286545\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 3.94027i | − 0.587381i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.77753 | −0.696874 | −0.348437 | − | 0.937332i | \(-0.613287\pi\) | ||||
−0.348437 | + | 0.937332i | \(0.613287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.8248 | 2.26068 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923i | 1.42749i | 0.700404 | + | 0.713746i | \(0.253003\pi\) | ||||
−0.700404 | + | 0.713746i | \(0.746997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.98793 | 0.402893 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.54983i | − 1.11309i | −0.830816 | − | 0.556547i | \(-0.812126\pi\) | ||||
0.830816 | − | 0.556547i | \(-0.187874\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.31342i | − 0.168167i | −0.996459 | − | 0.0840834i | \(-0.973204\pi\) | ||||
0.996459 | − | 0.0840834i | \(-0.0267962\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.3326 | 1.80573 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.54983i | − 1.04453i | −0.852784 | − | 0.522264i | \(-0.825087\pi\) | ||||
0.852784 | − | 0.522264i | \(-0.174913\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.8087 | 1.75748 | 0.878738 | − | 0.477305i | \(-0.158386\pi\) | ||||
0.878738 | + | 0.477305i | \(0.158386\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.27492 | 0.500341 | 0.250171 | − | 0.968202i | \(-0.419513\pi\) | ||||
0.250171 | + | 0.968202i | \(0.419513\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8685i | 1.23858i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.30136 | 0.483940 | 0.241970 | − | 0.970284i | \(-0.422206\pi\) | ||||
0.241970 | + | 0.970284i | \(0.422206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0997i | 1.43788i | 0.695074 | + | 0.718938i | \(0.255371\pi\) | ||||
−0.695074 | + | 0.718938i | \(0.744629\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.61478i | 0.609008i | ||||||||
\(86\) | 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 | ||||||||
\(91\) | 29.0997i | 3.05047i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.31342 | −0.134754 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.45017 | 0.147242 | 0.0736210 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736210 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.82475i | 0.685913i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 13.8564i | − 1.37876i | −0.724398 | − | 0.689382i | \(-0.757882\pi\) | ||||
0.724398 | − | 0.689382i | \(-0.242118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.62685 | −0.258831 | −0.129416 | − | 0.991590i | \(-0.541310\pi\) | ||||
−0.129416 | + | 0.991590i | \(0.541310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 16.5498i | − 1.59993i | −0.600045 | − | 0.799966i | \(-0.704851\pi\) | ||||
0.600045 | − | 0.799966i | \(-0.295149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 3.46410i | − 0.331801i | −0.986143 | − | 0.165900i | \(-0.946947\pi\) | ||||
0.986143 | − | 0.165900i | \(-0.0530530\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.54983 | −0.239868 | −0.119934 | − | 0.992782i | \(-0.538268\pi\) | ||||
−0.119934 | + | 0.992782i | \(0.538268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.54983i | − 0.424274i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.2728i | 1.68933i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.4235 | −1.87222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.82475 | 0.529523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 10.8685i | − 0.972106i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4356 | 1.54716 | 0.773579 | − | 0.633699i | \(-0.218464\pi\) | ||||
0.773579 | + | 0.633699i | \(0.218464\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.27492i | 0.198760i | 0.995050 | + | 0.0993802i | \(0.0316860\pi\) | ||||
−0.995050 | + | 0.0993802i | \(0.968314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.77753i | − 0.414264i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.2749 | −1.73220 | −0.866102 | − | 0.499868i | \(-0.833382\pi\) | ||||
−0.866102 | + | 0.499868i | \(0.833382\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 10.2749i | − 0.871507i | −0.900066 | − | 0.435754i | \(-0.856482\pi\) | ||||
0.900066 | − | 0.435754i | \(-0.143518\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8564 | −1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.98793i | − 0.244781i | −0.992482 | − | 0.122390i | \(-0.960944\pi\) | ||||
0.992482 | − | 0.122390i | \(-0.0390560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.55505 | −0.777579 | −0.388790 | − | 0.921327i | \(-0.627107\pi\) | ||||
−0.388790 | + | 0.921327i | \(0.627107\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.8248 | −1.03682 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.45017i | 0.277124i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.25370i | − 0.419291i | −0.977778 | − | 0.209645i | \(-0.932769\pi\) | ||||
0.977778 | − | 0.209645i | \(-0.0672309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.5498 | 1.30431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.00000i | − 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.67451 | −0.129577 | −0.0647886 | − | 0.997899i | \(-0.520637\pi\) | ||||
−0.0647886 | + | 0.997899i | \(0.520637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24.0997 | −1.85382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.00000i | − 0.229416i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.71780i | 0.662802i | 0.943490 | + | 0.331401i | \(0.107521\pi\) | ||||
−0.943490 | + | 0.331401i | \(0.892479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.6460 | 1.18273 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 9.09967i | − 0.680141i | −0.940400 | − | 0.340071i | \(-0.889549\pi\) | ||||
0.940400 | − | 0.340071i | \(-0.110451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.46410i | 0.257485i | 0.991678 | + | 0.128742i | \(0.0410940\pi\) | ||||
−0.991678 | + | 0.128742i | \(0.958906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.09967 | 0.0808493 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 9.72508i | − 0.711168i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0312 | −0.725834 | −0.362917 | − | 0.931822i | \(-0.618219\pi\) | ||||
−0.362917 | + | 0.931822i | \(0.618219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0997 | −1.37482 | −0.687412 | − | 0.726268i | \(-0.741253\pi\) | ||||
−0.687412 | + | 0.726268i | \(0.741253\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12.1819i | − 0.867924i | −0.900931 | − | 0.433962i | \(-0.857115\pi\) | ||||
0.900931 | − | 0.433962i | \(-0.142885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.6339 | −1.32092 | −0.660462 | − | 0.750859i | \(-0.729640\pi\) | ||||
−0.660462 | + | 0.750859i | \(0.729640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.0997i | 2.04240i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.8564i | 0.967773i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3923 | 0.722315 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.27492 | 0.157359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4502i | 0.788262i | 0.919054 | + | 0.394131i | \(0.128954\pi\) | ||||
−0.919054 | + | 0.394131i | \(0.871046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.4953 | −0.920373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5498 | −0.851938 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 26.0383i | − 1.75153i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.4356 | −1.16757 | −0.583787 | − | 0.811907i | \(-0.698430\pi\) | ||||
−0.583787 | + | 0.811907i | \(0.698430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.82475 | 0.654983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4.00000i | − 0.265489i | −0.991150 | − | 0.132745i | \(-0.957621\pi\) | ||||
0.991150 | − | 0.132745i | \(-0.0423790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 22.0980i | − 1.46028i | −0.683298 | − | 0.730140i | \(-0.739455\pi\) | ||||
0.683298 | − | 0.730140i | \(-0.260545\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.3746 | 1.13825 | 0.569123 | − | 0.822252i | \(-0.307283\pi\) | ||||
0.569123 | + | 0.822252i | \(0.307283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.27492i | 0.409330i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.82518 | −0.247431 | −0.123715 | − | 0.992318i | \(-0.539481\pi\) | ||||
−0.123715 | + | 0.992318i | \(0.539481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.54983 | 0.164249 | 0.0821246 | − | 0.996622i | \(-0.473829\pi\) | ||||
0.0821246 | + | 0.996622i | \(0.473829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 20.7846i | − 1.32788i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.09095 | 0.387558 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.2749i | 1.15350i | 0.816920 | + | 0.576751i | \(0.195680\pi\) | ||||
−0.816920 | + | 0.576751i | \(0.804320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.88054i | 0.495446i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.5498 | 1.40662 | 0.703310 | − | 0.710883i | \(-0.251705\pi\) | ||||
0.703310 | + | 0.710883i | \(0.251705\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.2728i | 1.13106i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3326 | 0.883785 | 0.441892 | − | 0.897068i | \(-0.354307\pi\) | ||||
0.441892 | + | 0.897068i | \(0.354307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6495 | 0.838482 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 22.5742i | − 1.37637i | −0.725534 | − | 0.688187i | \(-0.758407\pi\) | ||||
0.725534 | − | 0.688187i | \(-0.241593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.04329 | 0.427849 | 0.213925 | − | 0.976850i | \(-0.431375\pi\) | ||||
0.213925 | + | 0.976850i | \(0.431375\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.45017i | 0.449262i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.98793i | 0.179527i | 0.995963 | + | 0.0897637i | \(0.0286112\pi\) | ||||
−0.995963 | + | 0.0897637i | \(0.971389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.88054 | −0.471796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.0997 | −1.13939 | −0.569695 | − | 0.821856i | \(-0.692939\pi\) | ||||
−0.569695 | + | 0.821856i | \(0.692939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.3746i | − 0.676149i | −0.941119 | − | 0.338074i | \(-0.890224\pi\) | ||||
0.941119 | − | 0.338074i | \(-0.109776\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −50.4021 | −2.97514 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27492 | 0.0749951 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 21.6219i | − 1.26316i | −0.775310 | − | 0.631581i | \(-0.782406\pi\) | ||||
0.775310 | − | 0.631581i | \(-0.217594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2296 | −0.653810 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.0997i | 1.22023i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 49.0887i | − 2.82942i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.72508 | −0.0987780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5498i | 0.944549i | 0.881452 | + | 0.472274i | \(0.156567\pi\) | ||||
−0.881452 | + | 0.472274i | \(0.843433\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.72987 | 0.324911 | 0.162455 | − | 0.986716i | \(-0.448059\pi\) | ||||
0.162455 | + | 0.986716i | \(0.448059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0997 | −0.853484 | −0.426742 | − | 0.904373i | \(-0.640339\pi\) | ||||
−0.426742 | + | 0.904373i | \(0.640339\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 18.8248i | − 1.06065i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.71780i | − 0.489640i | −0.969569 | − | 0.244820i | \(-0.921271\pi\) | ||||
0.969569 | − | 0.244820i | \(-0.0787289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8564 | −0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.27492i | 0.237863i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.9474i | 1.10648i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.8248 | −1.25837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 24.5498i | − 1.34938i | −0.738101 | − | 0.674690i | \(-0.764277\pi\) | ||||
0.738101 | − | 0.674690i | \(-0.235723\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.51176i | 0.137644i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.2296 | −0.613536 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6495 | −0.634589 | −0.317294 | − | 0.948327i | \(-0.602774\pi\) | ||||
−0.317294 | + | 0.948327i | \(0.602774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 5.97586i | − 0.323611i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 42.1605 | 2.27645 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.8248i | 0.795834i | 0.917421 | + | 0.397917i | \(0.130267\pi\) | ||||
−0.917421 | + | 0.397917i | \(0.869733\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.2323i | 1.88594i | 0.332877 | + | 0.942970i | \(0.391981\pi\) | ||||
−0.332877 | + | 0.942970i | \(0.608019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0000 | −0.532246 | −0.266123 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266123 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 19.4502i | − 1.03231i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.476171 | 0.0251313 | 0.0125657 | − | 0.999921i | \(-0.496000\pi\) | ||||
0.0125657 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 5.61478i | − 0.293891i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.78959 | −0.0934161 | −0.0467080 | − | 0.998909i | \(-0.514873\pi\) | ||||
−0.0467080 | + | 0.998909i | \(0.514873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.6495 | −1.64761 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 49.6495i | 2.57767i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2011i | 1.30486i | 0.757849 | + | 0.652431i | \(0.226251\pi\) | ||||
−0.757849 | + | 0.652431i | \(0.773749\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.0997 | −1.91073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6495i | 1.11206i | 0.831162 | + | 0.556030i | \(0.187676\pi\) | ||||
−0.831162 | + | 0.556030i | \(0.812324\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.97586 | −0.305352 | −0.152676 | − | 0.988276i | \(-0.548789\pi\) | ||||
−0.152676 | + | 0.988276i | \(0.548789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.2749 | 0.727517 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 30.8248i | − 1.56691i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.7967i | 0.902327i | 0.892441 | + | 0.451164i | \(0.148991\pi\) | ||||
−0.892441 | + | 0.451164i | \(0.851009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8087 | −0.748911 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 5.64950i | − 0.284257i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.0027i | 1.20466i | 0.798247 | + | 0.602331i | \(0.205761\pi\) | ||||
−0.798247 | + | 0.602331i | \(0.794239\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.90033 | 0.244711 | 0.122355 | − | 0.992486i | \(-0.460955\pi\) | ||||
0.122355 | + | 0.992486i | \(0.460955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 16.0000i | − 0.797017i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 11.8208i | − 0.587381i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.90468 | −0.0944116 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 40.8471i | − 2.00995i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2054 | 0.844581 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 12.0000i | − 0.586238i | −0.956076 | − | 0.293119i | \(-0.905307\pi\) | ||||
0.956076 | − | 0.293119i | \(-0.0946933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2487i | 1.18181i | 0.806741 | + | 0.590905i | \(0.201229\pi\) | ||||
−0.806741 | + | 0.590905i | \(0.798771\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.3326 | −0.696874 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.0000 | −0.679100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.27492i | − 0.303665i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.1101 | 0.920501 | 0.460251 | − | 0.887789i | \(-0.347760\pi\) | ||||
0.460251 | + | 0.887789i | \(0.347760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.6495 | 1.32875 | 0.664375 | − | 0.747399i | \(-0.268698\pi\) | ||||
0.664375 | + | 0.747399i | \(0.268698\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.46410i | − 0.165710i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.57919 | 0.170825 | 0.0854127 | − | 0.996346i | \(-0.472779\pi\) | ||||
0.0854127 | + | 0.996346i | \(0.472779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 47.4743 | 2.26068 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 27.3746i | − 1.30061i | −0.759675 | − | 0.650303i | \(-0.774642\pi\) | ||||
0.759675 | − | 0.650303i | \(-0.225358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1342i | 0.622623i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.45017 | −0.257209 | −0.128605 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128605 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 24.0000i | − 1.13012i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 38.2202 | 1.79179 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.72508 | −0.361364 | −0.180682 | − | 0.983542i | \(-0.557831\pi\) | ||||
−0.180682 | + | 0.983542i | \(0.557831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.2323i | 1.64093i | 0.571696 | + | 0.820465i | \(0.306286\pi\) | ||||
−0.571696 | + | 0.820465i | \(0.693714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.4427 | −1.55421 | −0.777107 | − | 0.629369i | \(-0.783313\pi\) | ||||
−0.777107 | + | 0.629369i | \(0.783313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.8248i | 1.42640i | 0.700961 | + | 0.713200i | \(0.252755\pi\) | ||||
−0.700961 | + | 0.713200i | \(0.747245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 40.8471i | − 1.88614i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.3746 | 1.07476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.27492i | − 0.150264i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.1769i | 1.42749i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3205 | −0.791394 | −0.395697 | − | 0.918381i | \(-0.629497\pi\) | ||||
−0.395697 | + | 0.918381i | \(0.629497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.09967 | −0.232525 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.90468i | − 0.0864872i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9041 | 0.584739 | 0.292370 | − | 0.956305i | \(-0.405556\pi\) | ||||
0.292370 | + | 0.956305i | \(0.405556\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12.0000i | − 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 26.0383i | − 1.17271i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.96379 | 0.402893 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 70.7492 | 3.17353 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.2749i | 1.53436i | 0.641434 | + | 0.767178i | \(0.278340\pi\) | ||||
−0.641434 | + | 0.767178i | \(0.721660\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.81312 | −0.303782 | −0.151891 | − | 0.988397i | \(-0.548536\pi\) | ||||
−0.151891 | + | 0.988397i | \(0.548536\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.1993 | −0.809860 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0192i | 0.577064i | 0.957470 | + | 0.288532i | \(0.0931671\pi\) | ||||
−0.957470 | + | 0.288532i | \(0.906833\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4235 | 0.903484 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.45017i | 0.152032i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 10.8685i | − 0.477995i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.09967 | 0.135799 | 0.0678995 | − | 0.997692i | \(-0.478370\pi\) | ||||
0.0678995 | + | 0.997692i | \(0.478370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.5498i | 0.898582i | 0.893386 | + | 0.449291i | \(0.148323\pi\) | ||||
−0.893386 | + | 0.449291i | \(0.851677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.2296 | 0.489167 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 25.6495i | − 1.11309i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 64.2585i | − 2.78335i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.7370 | −0.939770 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.0000i | 1.55063i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.28929i | 0.313391i | 0.987647 | + | 0.156695i | \(0.0500841\pi\) | ||||
−0.987647 | + | 0.156695i | \(0.949916\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.54983 | −0.194893 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 32.0000i | − 1.36822i | −0.729378 | − | 0.684111i | \(-0.760191\pi\) | ||||
0.729378 | − | 0.684111i | \(-0.239809\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 3.94027i | − 0.168167i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.09095 | 0.259483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.5498 | 0.873868 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.8443i | 0.713717i | 0.934158 | + | 0.356859i | \(0.116152\pi\) | ||||
−0.934158 | + | 0.356859i | \(0.883848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 62.5840 | 2.64702 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.0000i | 1.01148i | 0.862686 | + | 0.505740i | \(0.168780\pi\) | ||||
−0.862686 | + | 0.505740i | \(0.831220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.34901i | 0.140894i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.9977 | 1.80573 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.5498 | −1.44840 | −0.724202 | − | 0.689588i | \(-0.757792\pi\) | ||||
−0.724202 | + | 0.689588i | \(0.757792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 10.9003i | − 0.456165i | −0.973642 | − | 0.228082i | \(-0.926754\pi\) | ||||
0.973642 | − | 0.228082i | \(-0.0732455\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.3446 | 0.473104 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7251 | 0.654644 | 0.327322 | − | 0.944913i | \(-0.393854\pi\) | ||||
0.327322 | + | 0.944913i | \(0.393854\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.5840i | 2.59642i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.6416 | −0.979136 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.0000 | 0.992278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 29.7251i | − 1.22689i | −0.789739 | − | 0.613443i | \(-0.789784\pi\) | ||||
0.789739 | − | 0.613443i | \(-0.210216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.62685i | 0.108237i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0997 | −0.455809 | −0.227904 | − | 0.973684i | \(-0.573187\pi\) | ||||
−0.227904 | + | 0.973684i | \(0.573187\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.8248i | 1.09971i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.5934 | −1.45431 | −0.727153 | − | 0.686476i | \(-0.759157\pi\) | ||||
−0.727153 | + | 0.686476i | \(0.759157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0997 | −0.779092 | −0.389546 | − | 0.921007i | \(-0.627368\pi\) | ||||
−0.389546 | + | 0.921007i | \(0.627368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 25.6495i | − 1.04453i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 7.65037i | − 0.311032i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.8229 | 1.90048 | 0.950242 | − | 0.311513i | \(-0.100836\pi\) | ||||
0.950242 | + | 0.311513i | \(0.100836\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 29.0997i | − 1.17725i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8443i | 0.680336i | 0.940365 | + | 0.340168i | \(0.110484\pi\) | ||||
−0.940365 | + | 0.340168i | \(0.889516\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.2749 | 0.816237 | 0.408119 | − | 0.912929i | \(-0.366185\pi\) | ||||
0.408119 | + | 0.912929i | \(0.366185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −47.7753 | −1.91408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.09967 | 0.0839868 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 3.57919i | − 0.142712i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.07888 | 0.361425 | 0.180712 | − | 0.983536i | \(-0.442160\pi\) | ||||
0.180712 | + | 0.983536i | \(0.442160\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 22.9003i | − 0.908772i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 96.3878i | 3.81902i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 44.4262 | 1.75748 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.54983 | 0.100712 | 0.0503562 | − | 0.998731i | \(-0.483964\pi\) | ||||
0.0503562 | + | 0.998731i | \(0.483964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.92442i | 0.312509i | 0.987717 | + | 0.156254i | \(0.0499419\pi\) | ||||
−0.987717 | + | 0.156254i | \(0.950058\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.82518 | 0.150384 | 0.0751918 | − | 0.997169i | \(-0.476043\pi\) | ||||
0.0751918 | + | 0.997169i | \(0.476043\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.4502 | 0.763486 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.98793i | 0.116927i | 0.998290 | + | 0.0584634i | \(0.0186201\pi\) | ||||
−0.998290 | + | 0.0584634i | \(0.981380\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.98793 | 0.116748 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.8248 | 0.500341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 28.5498i | − 1.11214i | −0.831134 | − | 0.556072i | \(-0.812308\pi\) | ||||
0.831134 | − | 0.556072i | \(-0.187692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.837253i | 0.0325654i | 0.999867 | + | 0.0162827i | \(0.00518317\pi\) | ||||
−0.999867 | + | 0.0162827i | \(0.994817\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.27492 | −0.243331 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0997i | 0.816982i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.98793 | 0.115348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9003 | −0.651460 | −0.325730 | − | 0.945463i | \(-0.605610\pi\) | ||||
−0.325730 | + | 0.945463i | \(0.605610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.3112i | 1.70302i | 0.524342 | + | 0.851508i | \(0.324312\pi\) | ||||
−0.524342 | + | 0.851508i | \(0.675688\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.92820 | 0.265880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 38.1993i | − 1.46166i | −0.682561 | − | 0.730829i | \(-0.739134\pi\) | ||||
0.682561 | − | 0.730829i | \(-0.260866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.6296i | 1.01746i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −63.2990 | −2.41150 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 44.4743i | − 1.69188i | −0.533278 | − | 0.845940i | \(-0.679040\pi\) | ||||
0.533278 | − | 0.845940i | \(-0.320960\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 32.6054i | 1.23858i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.4953 | −0.511907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.0997 | 1.70827 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 48.7276i | − 1.84042i | −0.391430 | − | 0.920208i | \(-0.628019\pi\) | ||||
0.391430 | − | 0.920208i | \(-0.371981\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.837253 | 0.0315776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 66.1993i | − 2.48968i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 3.34901i | − 0.125775i | −0.998021 | − | 0.0628874i | \(-0.979969\pi\) | ||||
0.998021 | − | 0.0628874i | \(-0.0200309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.9041 | 0.483940 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.09967 | −0.340785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.1993i | 0.680617i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.4279 | 0.463482 | 0.231741 | − | 0.972777i | \(-0.425558\pi\) | ||||
0.231741 | + | 0.972777i | \(0.425558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5498 | −0.467380 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.9474i | 0.740826i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5863 | 0.726415 | 0.363207 | − | 0.931708i | \(-0.381682\pi\) | ||||
0.363207 | + | 0.931708i | \(0.381682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.9244i | 1.62460i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.67451i | 0.0618493i | 0.999522 | + | 0.0309247i | \(0.00984520\pi\) | ||||
−0.999522 | + | 0.0309247i | \(0.990155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.4502 | 0.716456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 14.8248i | − 0.545337i | −0.962108 | − | 0.272669i | \(-0.912094\pi\) | ||||
0.962108 | − | 0.272669i | \(-0.0879063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7605 | −0.981746 | −0.490873 | − | 0.871231i | \(-0.663322\pi\) | ||||
−0.490873 | + | 0.871231i | \(0.663322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.92442 | −0.143780 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.2990i | 1.43788i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 79.0673i | − 2.88905i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.7511 | −1.96141 | −0.980703 | − | 0.195503i | \(-0.937366\pi\) | ||||
−0.980703 | + | 0.195503i | \(0.937366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5498i | 0.456735i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.31342i | 0.0477372i | 0.999715 | + | 0.0238686i | \(0.00759833\pi\) | ||||
−0.999715 | + | 0.0238686i | \(0.992402\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.27492 | −0.154966 | −0.0774828 | − | 0.996994i | \(-0.524688\pi\) | ||||
−0.0774828 | + | 0.996994i | \(0.524688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 16.5498i | − 0.599144i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.8443i | 0.609008i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.0766 | 1.88038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.82475 | 0.318229 | 0.159114 | − | 0.987260i | \(-0.449136\pi\) | ||||
0.159114 | + | 0.987260i | \(0.449136\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.115088i | 0.00413942i | 0.999998 | + | 0.00206971i | \(0.000658809\pi\) | ||||
−0.999998 | + | 0.00206971i | \(0.999341\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.60271 | −0.309018 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.5498i | 0.377987i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.6887i | 1.20548i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.90033 | −0.246283 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.1993i | 1.64683i | 0.567441 | + | 0.823414i | \(0.307934\pi\) | ||||
−0.567441 | + | 0.823414i | \(0.692066\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.1819 | −0.433138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | 0.284088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 24.2487i | − 0.858933i | −0.903083 | − | 0.429467i | \(-0.858702\pi\) | ||||
0.903083 | − | 0.429467i | \(-0.141298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.4235 | 0.722532 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.72508i | 0.343191i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 21.7370i | − 0.766127i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.8248 | 0.591527 | 0.295763 | − | 0.955261i | \(-0.404426\pi\) | ||||
0.295763 | + | 0.955261i | \(0.404426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 43.2990i | − 1.52043i | −0.649669 | − | 0.760217i | \(-0.725093\pi\) | ||||
0.649669 | − | 0.760217i | \(-0.274907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.25370 | −0.184029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2749 | −0.359474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 87.2990i | 3.05047i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.3759i | 0.746023i | 0.927827 | + | 0.373011i | \(0.121675\pi\) | ||||
−0.927827 | + | 0.373011i | \(0.878325\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.9501 | 1.53200 | 0.766002 | − | 0.642839i | \(-0.222243\pi\) | ||||
0.766002 | + | 0.642839i | \(0.222243\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.35050i | 0.0817348i | 0.999165 | + | 0.0408674i | \(0.0130121\pi\) | ||||
−0.999165 | + | 0.0408674i | \(0.986988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 35.7084i | − 1.24021i | −0.784521 | − | 0.620103i | \(-0.787091\pi\) | ||||
0.784521 | − | 0.620103i | \(-0.212909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −67.6495 | −2.34392 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.19934i | 0.0761112i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.9424 | −1.34444 | −0.672220 | − | 0.740351i | \(-0.734659\pi\) | ||||
−0.672220 | + | 0.740351i | \(0.734659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.09967 | −0.279299 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.6531i | 1.08890i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.8279 | 0.956178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.90033i | 0.0994221i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 15.5309i | − 0.531768i | −0.964005 | − | 0.265884i | \(-0.914336\pi\) | ||||
0.964005 | − | 0.265884i | \(-0.0856639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.94027 | −0.134754 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.1993 | 1.50982 | 0.754910 | − | 0.655828i | \(-0.227680\pi\) | ||||
0.754910 | + | 0.655828i | \(0.227680\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 12.4743i | − 0.425616i | −0.977094 | − | 0.212808i | \(-0.931739\pi\) | ||||
0.977094 | − | 0.212808i | \(-0.0682609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.9430 | 0.951190 | 0.475595 | − | 0.879664i | \(-0.342233\pi\) | ||||
0.475595 | + | 0.879664i | \(0.342233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.4502 | 0.389317 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.78523i | 0.331941i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.0766 | 1.76455 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.35050 | 0.147242 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 51.9244i | − 1.75537i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 38.3353i | − 1.29449i | −0.762282 | − | 0.647245i | \(-0.775921\pi\) | ||||
0.762282 | − | 0.647245i | \(-0.224079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.8248 | −0.701604 | −0.350802 | − | 0.936450i | \(-0.614091\pi\) | ||||
−0.350802 | + | 0.936450i | \(0.614091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3746i | 1.72889i | 0.502725 | + | 0.864446i | \(0.332331\pi\) | ||||
−0.502725 | + | 0.864446i | \(0.667669\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.55505 | 0.320827 | 0.160414 | − | 0.987050i | \(-0.448717\pi\) | ||||
0.160414 | + | 0.987050i | \(0.448717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 83.2990 | 2.79376 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.4743i | 0.685913i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.77753i | 0.159874i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.9517 | −0.399502 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 16.0000i | − 0.533630i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 44.4262i | − 1.48005i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.54983 | 0.151242 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 21.6495i | − 0.718860i | −0.933172 | − | 0.359430i | \(-0.882971\pi\) | ||||
0.933172 | − | 0.359430i | \(-0.117029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 41.5692i | − 1.37876i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.4262 | −1.47191 | −0.735954 | − | 0.677032i | \(-0.763266\pi\) | ||||
−0.735954 | + | 0.677032i | \(0.763266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.8007 | −0.986258 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.8685i | 0.358909i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.7561 | −1.14650 | −0.573249 | − | 0.819381i | \(-0.694317\pi\) | ||||
−0.573249 | + | 0.819381i | \(0.694317\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 90.1993i | 2.96895i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.74194i | 0.0901543i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.88054 | −0.258831 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.0997 | 0.757876 | 0.378938 | − | 0.925422i | \(-0.376289\pi\) | ||||
0.378938 | + | 0.925422i | \(0.376289\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 15.8248i | − 0.518635i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.7732 | −0.417727 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.9244 | 1.23894 | 0.619468 | − | 0.785022i | \(-0.287348\pi\) | ||||
0.619468 | + | 0.785022i | \(0.287348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.1769i | 1.01634i | 0.861257 | + | 0.508169i | \(0.169678\pi\) | ||||
−0.861257 | + | 0.508169i | \(0.830322\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.5457 | −1.19009 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 30.1993i | − 0.981347i | −0.871344 | − | 0.490673i | \(-0.836751\pi\) | ||||
0.871344 | − | 0.490673i | \(-0.163249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.0383i | 0.845239i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.2990 | 1.46738 | 0.733689 | − | 0.679485i | \(-0.237797\pi\) | ||||
0.733689 | + | 0.679485i | \(0.237797\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.1752i | 0.426341i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −96.8639 | −3.12790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0997 | −0.777409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 49.6495i | − 1.59993i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.0860i | 0.807546i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.6695 | 0.664687 | 0.332344 | − | 0.943158i | \(-0.392161\pi\) | ||||
0.332344 | + | 0.943158i | \(0.392161\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 44.0000i | − 1.41203i | −0.708198 | − | 0.706014i | \(-0.750492\pi\) | ||||
0.708198 | − | 0.706014i | \(-0.249508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 49.0887i | − 1.57371i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.1993 | 1.03015 | 0.515074 | − | 0.857146i | \(-0.327764\pi\) | ||||
0.515074 | + | 0.857146i | \(0.327764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 22.7492i | − 0.727067i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 10.3923i | − 0.331801i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.6175 | 0.944651 | 0.472326 | − | 0.881424i | \(-0.343415\pi\) | ||||
0.472326 | + | 0.881424i | \(0.343415\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | −0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 35.5934i | − 1.13180i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.1249 | −1.27461 | −0.637305 | − | 0.770612i | \(-0.719951\pi\) | ||||
−0.637305 | + | 0.770612i | \(0.719951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.4743i | 0.775886i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.5906i | 0.367079i | 0.983012 | + | 0.183540i | \(0.0587556\pi\) | ||||
−0.983012 | + | 0.183540i | \(0.941244\pi\) | |||||||
\(998\) | 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 | 1216.2.c.i.609.4 | yes | 8 | |
4.3 | odd | 2 | inner | 1216.2.c.i.609.3 | ✓ | 8 | |
8.3 | odd | 2 | inner | 1216.2.c.i.609.5 | yes | 8 | |
8.5 | even | 2 | inner | 1216.2.c.i.609.6 | yes | 8 | |
16.3 | odd | 4 | 4864.2.a.bk.1.2 | 4 | |||
16.5 | even | 4 | 4864.2.a.bk.1.3 | 4 | |||
16.11 | odd | 4 | 4864.2.a.bj.1.3 | 4 | |||
16.13 | even | 4 | 4864.2.a.bj.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.c.i.609.3 | ✓ | 8 | 4.3 | odd | 2 | inner | |
1216.2.c.i.609.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1216.2.c.i.609.5 | yes | 8 | 8.3 | odd | 2 | inner | |
1216.2.c.i.609.6 | yes | 8 | 8.5 | even | 2 | inner | |
4864.2.a.bj.1.2 | 4 | 16.13 | even | 4 | |||
4864.2.a.bj.1.3 | 4 | 16.11 | odd | 4 | |||
4864.2.a.bk.1.2 | 4 | 16.3 | odd | 4 | |||
4864.2.a.bk.1.3 | 4 | 16.5 | even | 4 |