Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (of order \(6\), degree \(2\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.31726512.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 10x^{4} + 3x^{3} + 84x^{2} - 27x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 304) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 559.1 | ||
Root | \(-1.35887 + 2.35363i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.559 |
Dual form | 2736.2.bm.l.1855.1 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.85887 | + | 3.21966i | −0.831312 | + | 1.43987i | 0.0656858 | + | 0.997840i | \(0.479076\pi\) |
−0.896998 | + | 0.442035i | \(0.854257\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.36936i | 0.895535i | 0.894150 | + | 0.447768i | \(0.147781\pi\) | ||||
−0.894150 | + | 0.447768i | \(0.852219\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.10141i | − | 1.23662i | −0.785933 | − | 0.618311i | \(-0.787817\pi\) | ||
0.785933 | − | 0.618311i | \(-0.212183\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 1.73205i | 0.832050 | − | 0.480384i | −0.0225039 | − | 0.999747i | \(-0.507164\pi\) |
0.854554 | + | 0.519362i | \(0.173830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.91080 | − | 6.77370i | 0.948508 | − | 1.64286i | 0.199938 | − | 0.979808i | \(-0.435926\pi\) |
0.748570 | − | 0.663056i | \(-0.230741\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.35887 | − | 0.0157306i | −0.999993 | − | 0.00360885i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.05193 | − | 1.18468i | 0.427857 | − | 0.247023i | −0.270576 | − | 0.962699i | \(-0.587214\pi\) |
0.698433 | + | 0.715675i | \(0.253881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41080 | − | 7.63973i | −0.882160 | − | 1.52795i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.57661 | + | 1.48761i | −0.478465 | + | 0.276242i | −0.719776 | − | 0.694206i | \(-0.755756\pi\) |
0.241312 | + | 0.970448i | \(0.422422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.33162 | 0.239167 | 0.119583 | − | 0.992824i | \(-0.461844\pi\) | ||||
0.119583 | + | 0.992824i | \(0.461844\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.62854 | − | 4.40434i | −1.28946 | − | 0.744469i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.97521i | − | 0.489122i | −0.969634 | − | 0.244561i | \(-0.921356\pi\) | ||
0.969634 | − | 0.244561i | \(-0.0786439\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.07918 | − | 1.20041i | −0.324713 | − | 0.187473i | 0.328779 | − | 0.944407i | \(-0.393363\pi\) |
−0.653491 | + | 0.756934i | \(0.726696\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | − | 1.73205i | −0.457496 | − | 0.264135i | 0.253495 | − | 0.967337i | \(-0.418420\pi\) |
−0.710991 | + | 0.703201i | \(0.751753\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.05193 | + | 2.91673i | −0.736900 | + | 0.425449i | −0.820941 | − | 0.571013i | \(-0.806551\pi\) |
0.0840414 | + | 0.996462i | \(0.473217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.38612 | 0.198017 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 3.46410i | 0.824163 | − | 0.475831i | −0.0276867 | − | 0.999617i | \(-0.508814\pi\) |
0.851850 | + | 0.523786i | \(0.175481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.2052 | + | 7.62400i | 1.78058 | + | 1.02802i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.44807 | − | 4.24018i | 0.318712 | − | 0.552025i | −0.661508 | − | 0.749938i | \(-0.730083\pi\) |
0.980220 | + | 0.197913i | \(0.0634165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.141129 | − | 0.244443i | −0.0180698 | − | 0.0312978i | 0.856849 | − | 0.515567i | \(-0.172419\pi\) |
−0.874919 | + | 0.484269i | \(0.839085\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.8786i | 1.59740i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.26967 | − | 5.66323i | −0.399454 | − | 0.691874i | 0.594205 | − | 0.804314i | \(-0.297467\pi\) |
−0.993659 | + | 0.112440i | \(0.964134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.306942 | + | 0.531638i | −0.0359248 | + | 0.0622236i | −0.883429 | − | 0.468565i | \(-0.844771\pi\) |
0.847504 | + | 0.530789i | \(0.178104\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.71774 | 1.10744 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.71774 | − | 9.90342i | 0.643296 | − | 1.11422i | −0.341396 | − | 0.939920i | \(-0.610900\pi\) |
0.984692 | − | 0.174302i | \(-0.0557669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0314612i | 0.00345332i | 0.999999 | + | 0.00172666i | \(0.000549613\pi\) | ||||
−0.999999 | + | 0.00172666i | \(0.999450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.5393 | + | 25.1829i | 1.57701 | + | 2.73147i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7324 | − | 8.50575i | 1.56163 | − | 0.901608i | 0.564539 | − | 0.825407i | \(-0.309054\pi\) |
0.997092 | − | 0.0762015i | \(-0.0242792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.10386 | + | 7.10809i | 0.430201 | + | 0.745130i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.15322 | − | 14.0048i | 0.836503 | − | 1.43687i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6532 | + | 7.30534i | 1.28474 | + | 0.741745i | 0.977711 | − | 0.209955i | \(-0.0673318\pi\) |
0.307029 | + | 0.951700i | \(0.400665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.19049 | + | 8.99020i | 0.516474 | + | 0.894558i | 0.999817 | + | 0.0191276i | \(0.00608889\pi\) |
−0.483344 | + | 0.875431i | \(0.660578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6432 | −1.34430 | −0.672152 | − | 0.740413i | \(-0.734630\pi\) | ||||
−0.672152 | + | 0.740413i | \(0.734630\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.20772 | −0.793470 | −0.396735 | − | 0.917933i | \(-0.629857\pi\) | ||||
−0.396735 | + | 0.917933i | \(0.629857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.1532 | + | 6.43932i | 1.06829 | + | 0.616775i | 0.927712 | − | 0.373296i | \(-0.121772\pi\) |
0.140573 | + | 0.990070i | \(0.455106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.73205i | − | 0.162938i | −0.996676 | − | 0.0814688i | \(-0.974039\pi\) | ||
0.996676 | − | 0.0814688i | \(-0.0259611\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.80868i | 0.821414i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.0494 | + | 9.26611i | 1.47124 | + | 0.849422i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.82160 | −0.529236 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.2077 | 1.27078 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.82160 | − | 6.61920i | −0.339112 | − | 0.587359i | 0.645154 | − | 0.764053i | \(-0.276793\pi\) |
−0.984266 | + | 0.176693i | \(0.943460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.18047 | + | 2.99095i | 0.452620 | + | 0.261320i | 0.708936 | − | 0.705273i | \(-0.249176\pi\) |
−0.256316 | + | 0.966593i | \(0.582509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0372715 | − | 10.3277i | 0.00323185 | − | 0.895529i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.21774 | + | 14.2335i | 0.702089 | + | 1.21605i | 0.967732 | + | 0.251982i | \(0.0810825\pi\) |
−0.265643 | + | 0.964072i | \(0.585584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.44807 | − | 1.41339i | 0.207643 | − | 0.119883i | −0.392573 | − | 0.919721i | \(-0.628415\pi\) |
0.600215 | + | 0.799838i | \(0.295082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.10386 | − | 12.3042i | −0.594054 | − | 1.02893i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 11.0611i | − | 0.918573i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.24499 | − | 3.88843i | 0.183917 | − | 0.318553i | −0.759294 | − | 0.650747i | \(-0.774456\pi\) |
0.943211 | + | 0.332195i | \(0.107789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.1825 | 1.88657 | 0.943284 | − | 0.331987i | \(-0.107719\pi\) | ||||
0.943284 | + | 0.331987i | \(0.107719\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47532 | + | 4.28738i | −0.198822 | + | 0.344370i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.38612 | − | 2.40082i | 0.110624 | − | 0.191607i | −0.805398 | − | 0.592734i | \(-0.798048\pi\) |
0.916022 | + | 0.401128i | \(0.131382\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.80694 | + | 4.86177i | 0.221218 | + | 0.383161i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.6336i | − | 1.77280i | −0.462918 | − | 0.886401i | \(-0.653198\pi\) | ||
0.462918 | − | 0.886401i | \(-0.346802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0494 | + | 17.4060i | 0.777643 | + | 1.34692i | 0.933297 | + | 0.359106i | \(0.116918\pi\) |
−0.155654 | + | 0.987812i | \(0.549748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.0000 | − | 8.66025i | −1.14043 | − | 0.658427i | −0.193892 | − | 0.981023i | \(-0.562111\pi\) |
−0.946537 | + | 0.322596i | \(0.895445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.1013 | − | 10.4508i | 1.36833 | − | 0.790005i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.9455 | −0.892849 | −0.446425 | − | 0.894821i | \(-0.647303\pi\) | ||||
−0.446425 | + | 0.894821i | \(0.647303\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.7350 | + | 7.35253i | −0.946582 | + | 0.546510i | −0.892018 | − | 0.452001i | \(-0.850710\pi\) |
−0.0545647 | + | 0.998510i | \(0.517377\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.57918 | + | 5.53054i | 0.704275 | + | 0.406613i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.7818 | − | 16.0398i | −2.03160 | − | 1.17295i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.54925i | 0.184457i | 0.995738 | + | 0.0922287i | \(0.0293991\pi\) | ||||
−0.995738 | + | 0.0922287i | \(0.970601\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.73240 | − | 1.57755i | −0.196682 | − | 0.113555i | 0.398425 | − | 0.917201i | \(-0.369557\pi\) |
−0.595107 | + | 0.803646i | \(0.702890\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.92546 | −0.422171 | −0.211086 | − | 0.977468i | \(-0.567700\pi\) | ||||
−0.211086 | + | 0.977468i | \(0.567700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.3064 | + | 12.8786i | −1.58126 | + | 0.912942i | −0.586586 | + | 0.809887i | \(0.699529\pi\) |
−0.994676 | + | 0.103055i | \(0.967138\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.52468 | − | 6.10493i | −0.247384 | − | 0.428482i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.72984 | − | 4.46282i | 0.539875 | − | 0.311697i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0645178 | + | 17.8775i | −0.00446279 | + | 1.23661i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.24242 | + | 16.0083i | −0.636275 | + | 1.10206i | 0.349969 | + | 0.936761i | \(0.386192\pi\) |
−0.986244 | + | 0.165299i | \(0.947141\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.1532 | − | 6.43932i | 0.760644 | − | 0.439158i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.15510i | 0.214182i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.0948i | − | 1.82259i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8735 | − | 20.5656i | 0.795110 | − | 1.37717i | −0.127659 | − | 0.991818i | \(-0.540746\pi\) |
0.922769 | − | 0.385353i | \(-0.125920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.15322 | 0.142914 | 0.0714572 | − | 0.997444i | \(-0.477235\pi\) | ||||
0.0714572 | + | 0.997444i | \(0.477235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.43548 | −0.359187 | −0.179593 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179593 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.74242 | − | 15.1423i | 0.572735 | − | 0.992007i | −0.423548 | − | 0.905873i | \(-0.639216\pi\) |
0.996284 | − | 0.0861330i | \(-0.0274510\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 21.6873i | − | 1.41472i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.0815i | − | 1.36365i | −0.731517 | − | 0.681823i | \(-0.761187\pi\) | ||
0.731517 | − | 0.681823i | \(-0.238813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.07405 | + | 3.50685i | −0.391264 | + | 0.225896i | −0.682708 | − | 0.730692i | \(-0.739198\pi\) |
0.291444 | + | 0.956588i | \(0.405864\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.57661 | + | 4.46282i | −0.164614 | + | 0.285119i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1039 | + | 7.50259i | −0.833779 | + | 0.477379i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.28433 | − | 5.36031i | 0.586022 | − | 0.338340i | −0.177501 | − | 0.984121i | \(-0.556801\pi\) |
0.763523 | + | 0.645781i | \(0.223468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.85887 | − | 8.41581i | −0.305475 | − | 0.529097i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.2324 | − | 9.37178i | 1.01255 | − | 0.584596i | 0.100612 | − | 0.994926i | \(-0.467920\pi\) |
0.911937 | + | 0.410330i | \(0.134587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.04937 | 0.438026 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.94294 | + | 2.85381i | 0.304795 | + | 0.175973i | 0.644595 | − | 0.764524i | \(-0.277026\pi\) |
−0.339800 | + | 0.940498i | \(0.610359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.7573i | 1.58226i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4648 | − | 8.35125i | −0.881934 | − | 0.509185i | −0.0106386 | − | 0.999943i | \(-0.503386\pi\) |
−0.871296 | + | 0.490758i | \(0.836720\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9974 | − | 6.34937i | −0.668047 | − | 0.385697i | 0.127289 | − | 0.991866i | \(-0.459372\pi\) |
−0.795336 | + | 0.606169i | \(0.792706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −31.3337 | + | 18.0905i | −1.88949 | + | 1.09090i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.82673 | 0.350094 | 0.175047 | − | 0.984560i | \(-0.443992\pi\) | ||||
0.175047 | + | 0.984560i | \(0.443992\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.76760 | − | 1.02053i | 0.105446 | − | 0.0608794i | −0.446349 | − | 0.894859i | \(-0.647276\pi\) |
0.551796 | + | 0.833979i | \(0.313943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.92339 | + | 4.57457i | 0.470997 | + | 0.271930i | 0.716657 | − | 0.697426i | \(-0.245671\pi\) |
−0.245660 | + | 0.969356i | \(0.579005\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.84421 | − | 4.92632i | 0.167889 | − | 0.290792i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.0887 | − | 38.2588i | −1.29934 | − | 2.25052i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2410i | 0.656704i | 0.944555 | + | 0.328352i | \(0.106493\pi\) | ||||
−0.944555 | + | 0.328352i | \(0.893507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.10129 | + | 15.7639i | 0.529898 | + | 0.917810i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.10386 | − | 7.10809i | 0.237332 | − | 0.411071i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.10386 | − | 7.10809i | 0.236542 | − | 0.409704i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.04937 | 0.0600865 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.93805 | + | 13.7491i | −0.453048 | + | 0.784702i | −0.998574 | − | 0.0533918i | \(-0.982997\pi\) |
0.545525 | + | 0.838094i | \(0.316330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.81124i | − | 0.386230i | −0.981176 | − | 0.193115i | \(-0.938141\pi\) | ||
0.981176 | − | 0.193115i | \(-0.0618590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.30694 | + | 3.99574i | 0.130396 | + | 0.225853i | 0.923829 | − | 0.382805i | \(-0.125042\pi\) |
−0.793433 | + | 0.608657i | \(0.791708\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.15835 | − | 0.668774i | 0.0650594 | − | 0.0375621i | −0.467117 | − | 0.884195i | \(-0.654707\pi\) |
0.532177 | + | 0.846633i | \(0.321374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.10129 | + | 10.5678i | 0.341607 | + | 0.591681i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1532 | + | 29.4642i | −0.954431 | + | 1.63943i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.4648 | − | 15.2795i | −1.46800 | − | 0.847552i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.91080 | − | 11.9699i | −0.381005 | − | 0.659920i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.619010 | 0.0340239 | 0.0170119 | − | 0.999855i | \(-0.494585\pi\) | ||||
0.0170119 | + | 0.999855i | \(0.494585\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.3116 | 1.32828 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.65835 | + | 3.26685i | 0.308230 | + | 0.177957i | 0.646134 | − | 0.763224i | \(-0.276385\pi\) |
−0.337904 | + | 0.941181i | \(0.609718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.46154i | − | 0.295759i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8698i | 1.07287i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.0661 | − | 11.0078i | −1.02352 | − | 0.590930i | −0.108399 | − | 0.994107i | \(-0.534573\pi\) |
−0.915122 | + | 0.403177i | \(0.867906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3064 | 0.658749 | 0.329374 | − | 0.944199i | \(-0.393162\pi\) | ||||
0.329374 | + | 0.944199i | \(0.393162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.77223 | −0.520124 | −0.260062 | − | 0.965592i | \(-0.583743\pi\) | ||||
−0.260062 | + | 0.965592i | \(0.583743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.1532 | + | 19.3179i | 0.591952 | + | 1.02529i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.79485 | + | 2.76831i | 0.253062 | + | 0.146106i | 0.621166 | − | 0.783679i | \(-0.286659\pi\) |
−0.368103 | + | 0.929785i | \(0.619993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9995 | + | 0.137135i | 0.999974 | + | 0.00721765i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.14113 | − | 1.97649i | −0.0597294 | − | 0.103454i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4622 | + | 7.77242i | −0.702723 | + | 0.405717i | −0.808361 | − | 0.588687i | \(-0.799645\pi\) |
0.105638 | + | 0.994405i | \(0.466312\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.20772 | + | 14.2162i | 0.426123 | + | 0.738067i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.6803i | − | 0.915450i | −0.889094 | − | 0.457725i | \(-0.848664\pi\) | ||
0.889094 | − | 0.457725i | \(-0.151336\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.15322 | + | 8.92564i | −0.265405 | + | 0.459694i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.3861 | −0.841698 | −0.420849 | − | 0.907131i | \(-0.638268\pi\) | ||||
−0.420849 | + | 0.907131i | \(0.638268\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.05193 | + | 13.9464i | −0.411434 | + | 0.712625i | −0.995047 | − | 0.0994071i | \(-0.968305\pi\) |
0.583612 | + | 0.812032i | \(0.301639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.0640 | + | 31.2878i | −0.920628 | + | 1.59457i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.82160 | + | 8.35125i | 0.244465 | + | 0.423425i | 0.961981 | − | 0.273116i | \(-0.0880544\pi\) |
−0.717516 | + | 0.696542i | \(0.754721\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.5322i | − | 0.937214i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.2571 | + | 36.8183i | 1.06956 | + | 1.85253i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.80438 | − | 11.7855i | 0.341502 | − | 0.591499i | −0.643210 | − | 0.765690i | \(-0.722398\pi\) |
0.984712 | + | 0.174191i | \(0.0557311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9648 | + | 10.9493i | 0.947057 | + | 0.546783i | 0.892165 | − | 0.451709i | \(-0.149185\pi\) |
0.0548914 | + | 0.998492i | \(0.482519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.99487 | − | 2.30644i | 0.198999 | − | 0.114892i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.2026 | −0.604860 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.3856 | − | 12.3470i | 1.05745 | − | 0.610520i | 0.132725 | − | 0.991153i | \(-0.457627\pi\) |
0.924726 | + | 0.380633i | \(0.124294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.0465 | + | 5.80037i | 0.494358 | + | 0.285418i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.101294 | − | 0.0584824i | −0.00497235 | − | 0.00287079i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.69803i | − | 0.180661i | −0.995912 | − | 0.0903303i | \(-0.971208\pi\) | ||
0.995912 | − | 0.0903303i | \(-0.0287923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.5715 | − | 12.4543i | −1.05133 | − | 0.606986i | −0.128308 | − | 0.991734i | \(-0.540955\pi\) |
−0.923021 | + | 0.384749i | \(0.874288\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −68.9990 | −3.34694 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.579175 | − | 0.334387i | 0.0280283 | − | 0.0161821i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.2077 | − | 19.4123i | −0.539857 | − | 0.935059i | −0.998911 | − | 0.0466511i | \(-0.985145\pi\) |
0.459055 | − | 0.888408i | \(-0.348188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8805 | − | 17.2515i | 1.43596 | − | 0.829055i | 0.438399 | − | 0.898781i | \(-0.355546\pi\) |
0.997566 | + | 0.0697258i | \(0.0222124\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.96273 | + | 5.13160i | −0.428745 | + | 0.245478i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.38355 | + | 5.86049i | −0.161488 | + | 0.279706i | −0.935403 | − | 0.353584i | \(-0.884963\pi\) |
0.773914 | + | 0.633290i | \(0.218296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.1753 | + | 15.6897i | −1.29114 | + | 0.745440i | −0.978856 | − | 0.204549i | \(-0.934427\pi\) |
−0.312283 | + | 0.949989i | \(0.601094\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 63.2444i | 2.99807i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10.4778i | − | 0.494478i | −0.968954 | − | 0.247239i | \(-0.920477\pi\) | ||
0.968954 | − | 0.247239i | \(-0.0795233\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.92339 | + | 8.52756i | −0.231833 | + | 0.401547i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −30.5142 | −1.43053 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.46480 | −0.208854 | −0.104427 | − | 0.994533i | \(-0.533301\pi\) | ||||
−0.104427 | + | 0.994533i | \(0.533301\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.97482 | − | 17.2769i | 0.464574 | − | 0.804665i | −0.534608 | − | 0.845100i | \(-0.679541\pi\) |
0.999182 | + | 0.0404345i | \(0.0128742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 42.1000i | − | 1.95655i | −0.207304 | − | 0.978276i | \(-0.566469\pi\) | ||
0.207304 | − | 0.978276i | \(-0.433531\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 13.5159i | − | 0.625443i | −0.949845 | − | 0.312722i | \(-0.898759\pi\) | ||
0.949845 | − | 0.312722i | \(-0.101241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4183 | − | 7.74704i | 0.619598 | − | 0.357725i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.10386 | + | 12.3042i | −0.326636 | + | 0.565750i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.1059 | + | 33.3700i | 0.876640 | + | 1.53112i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.10386 | − | 2.36936i | 0.187510 | − | 0.108259i | −0.403306 | − | 0.915065i | \(-0.632139\pi\) |
0.590816 | + | 0.806806i | \(0.298806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.15322 | − | 8.92564i | −0.234967 | − | 0.406974i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −47.0414 | + | 27.1594i | −2.13604 | + | 1.23324i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.8458 | 1.17118 | 0.585592 | − | 0.810606i | \(-0.300862\pi\) | ||||
0.585592 | + | 0.810606i | \(0.300862\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.2622 | + | 15.1625i | 1.18520 | + | 0.684274i | 0.957211 | − | 0.289391i | \(-0.0934527\pi\) |
0.227986 | + | 0.973664i | \(0.426786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.2709i | 1.04807i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.3116 | + | 7.10809i | 0.552250 | + | 0.318841i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.5908 | + | 16.5069i | 1.27990 | + | 0.738950i | 0.976830 | − | 0.214019i | \(-0.0686553\pi\) |
0.303069 | + | 0.952969i | \(0.401989\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.5219 | − | 15.8897i | 1.22714 | − | 0.708489i | 0.260708 | − | 0.965418i | \(-0.416044\pi\) |
0.966430 | + | 0.256929i | \(0.0827106\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.5938 | −1.71740 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.3116 | + | 8.84014i | −0.678674 | + | 0.391832i | −0.799355 | − | 0.600859i | \(-0.794825\pi\) |
0.120682 | + | 0.992691i | \(0.461492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.25964 | − | 0.727256i | −0.0557234 | − | 0.0321719i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.3609 | − | 43.9264i | 1.11754 | − | 1.93563i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.9627 | + | 20.7201i | 0.526120 | + | 0.911267i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.68248i | − | 0.336576i | −0.985738 | − | 0.168288i | \(-0.946176\pi\) | ||
0.985738 | − | 0.168288i | \(-0.0538238\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5938 | + | 21.8132i | 0.550690 | + | 0.953823i | 0.998225 | + | 0.0595564i | \(0.0189686\pi\) |
−0.447535 | + | 0.894266i | \(0.647698\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.20772 | − | 9.02003i | 0.226852 | − | 0.392919i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.69306 | + | 15.0568i | −0.377959 | + | 0.654644i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.31670 | −0.360236 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2571 | − | 26.4260i | 0.659621 | − | 1.14250i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.68504i | − | 0.244872i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3861 | − | 19.7213i | −0.489527 | − | 0.847886i | 0.510400 | − | 0.859937i | \(-0.329497\pi\) |
−0.999927 | + | 0.0120508i | \(0.996164\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.4648 | + | 23.9397i | −1.77616 | + | 1.02546i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.9255 | + | 34.5119i | 0.851951 | + | 1.47562i | 0.879445 | + | 0.476000i | \(0.157914\pi\) |
−0.0274940 | + | 0.999622i | \(0.508753\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.2545 | − | 6.44376i | 0.479459 | − | 0.274513i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.4648 | + | 13.5474i | 0.997825 | + | 0.576094i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8710 | + | 25.7573i | 0.630103 | + | 1.09137i | 0.987530 | + | 0.157429i | \(0.0503207\pi\) |
−0.357427 | + | 0.933941i | \(0.616346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.0545 | −1.01378 | −0.506888 | − | 0.862012i | \(-0.669204\pi\) | ||||
−0.506888 | + | 0.862012i | \(0.669204\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.57661 | + | 3.21966i | 0.234610 | + | 0.135452i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14.6962i | − | 0.616096i | −0.951371 | − | 0.308048i | \(-0.900324\pi\) | ||
0.951371 | − | 0.308048i | \(-0.0996758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 34.1174i | − | 1.42777i | −0.700264 | − | 0.713884i | \(-0.746934\pi\) | ||
0.700264 | − | 0.713884i | \(-0.253066\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.1013 | − | 10.4508i | −0.754876 | − | 0.435828i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5645 | −0.647959 | −0.323980 | − | 0.946064i | \(-0.605021\pi\) | ||||
−0.323980 | + | 0.946064i | \(0.605021\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0745431 | −0.00309257 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.2077 | − | 24.6085i | −0.588423 | − | 1.01918i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.25708 | − | 3.61253i | −0.258257 | − | 0.149105i | 0.365282 | − | 0.930897i | \(-0.380973\pi\) |
−0.623539 | + | 0.781792i | \(0.714306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.80438 | − | 0.0209473i | −0.239165 | − | 0.000863117i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.8463 | − | 37.8389i | −0.897119 | − | 1.55386i | −0.831160 | − | 0.556034i | \(-0.812322\pi\) |
−0.0659596 | − | 0.997822i | \(-0.521011\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −59.6674 | + | 34.4490i | −2.44612 | + | 1.41227i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.3090 | + | 24.7839i | 0.584650 | + | 1.01264i | 0.994919 | + | 0.100679i | \(0.0321016\pi\) |
−0.410269 | + | 0.911965i | \(0.634565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1307i | 0.576402i | 0.957570 | + | 0.288201i | \(0.0930572\pi\) | ||||
−0.957570 | + | 0.288201i | \(0.906943\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.8216 | − | 18.7436i | 0.439961 | − | 0.762034i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.876091 | −0.0355595 | −0.0177797 | − | 0.999842i | \(-0.505660\pi\) | ||||
−0.0177797 | + | 0.999842i | \(0.505660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.1039 | + | 17.5004i | −0.408758 | + | 0.707990i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.33162 | − | 2.30644i | 0.0537838 | − | 0.0931563i | −0.837880 | − | 0.545854i | \(-0.816205\pi\) |
0.891664 | + | 0.452698i | \(0.149538\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0645178 | + | 0.111748i | 0.00259739 | + | 0.00449881i | 0.867321 | − | 0.497749i | \(-0.165840\pi\) |
−0.864724 | + | 0.502248i | \(0.832507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.1304i | − | 1.29143i | −0.763579 | − | 0.645715i | \(-0.776560\pi\) | ||
0.763579 | − | 0.645715i | \(-0.223440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.1532 | + | 34.9064i | 0.807422 | + | 1.39850i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.35631 | + | 7.54535i | −0.174252 | + | 0.301814i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.1532 | − | 11.6355i | −0.803562 | − | 0.463937i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.05706 | − | 4.07439i | 0.280937 | − | 0.162199i | −0.352911 | − | 0.935657i | \(-0.614808\pi\) |
0.633848 | + | 0.773458i | \(0.281475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.4154 | 1.12763 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.15835 | − | 2.40082i | 0.164760 | − | 0.0951241i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.6972 | − | 14.2589i | −0.975481 | − | 0.563194i | −0.0745779 | − | 0.997215i | \(-0.523761\pi\) |
−0.900903 | + | 0.434021i | \(0.857094\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.2350 | + | 13.4147i | 0.916297 | + | 0.529025i | 0.882452 | − | 0.470402i | \(-0.155891\pi\) |
0.0338455 | + | 0.999427i | \(0.489225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 5.03558i | − | 0.197969i | −0.995089 | − | 0.0989845i | \(-0.968441\pi\) | ||
0.995089 | − | 0.0989845i | \(-0.0315594\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.3907 | − | 10.0406i | −0.682647 | − | 0.394126i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.1774 | −0.985268 | −0.492634 | − | 0.870237i | \(-0.663966\pi\) | ||||
−0.492634 | + | 0.870237i | \(0.663966\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.2596 | + | 11.1196i | −0.752537 | + | 0.434477i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0987 | − | 24.4197i | −0.549209 | − | 0.951257i | −0.998329 | − | 0.0577859i | \(-0.981596\pi\) |
0.449120 | − | 0.893471i | \(-0.351737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.1998 | − | 19.1679i | 1.29132 | − | 0.745545i | 0.312433 | − | 0.949940i | \(-0.398856\pi\) |
0.978888 | + | 0.204395i | \(0.0655228\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.1825 | + | 19.3179i | 1.28676 | + | 0.749118i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.52468 | + | 6.10493i | −0.136476 | + | 0.236384i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.00256 | + | 0.578830i | −0.0387035 | + | 0.0223455i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.8183i | − | 1.41924i | −0.704583 | − | 0.709621i | \(-0.748866\pi\) | ||
0.704583 | − | 0.709621i | \(-0.251134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.24352i | 0.355258i | 0.984098 | + | 0.177629i | \(0.0568426\pi\) | ||||
−0.984098 | + | 0.177629i | \(0.943157\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.3090 | + | 29.9801i | −0.664259 | + | 1.15053i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.58457 | −0.290215 | −0.145108 | − | 0.989416i | \(-0.546353\pi\) | ||||
−0.145108 | + | 0.989416i | \(0.546353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −61.1029 | −2.33462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 36.1496i | − | 1.37519i | −0.726092 | − | 0.687597i | \(-0.758666\pi\) | ||
0.726092 | − | 0.687597i | \(-0.241334\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.5093i | 0.398639i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.2625 | + | 9.38914i | −0.615985 | + | 0.355639i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.8044 | − | 18.7137i | 0.408076 | − | 0.706808i | −0.586598 | − | 0.809878i | \(-0.699533\pi\) |
0.994674 | + | 0.103070i | \(0.0328666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0468020 | + | 12.9686i | −0.00176517 | + | 0.489119i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.3011 | + | 12.2982i | −0.801109 | + | 0.462520i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.34885 | + | 12.7286i | 0.275992 | + | 0.478032i | 0.970385 | − | 0.241564i | \(-0.0776604\pi\) |
−0.694393 | + | 0.719596i | \(0.744327\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.73240 | − | 1.57755i | 0.102329 | − | 0.0590798i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 52.8206 | 1.97538 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.6674 | − | 11.9323i | −0.770763 | − | 0.445000i | 0.0623834 | − | 0.998052i | \(-0.480130\pi\) |
−0.833147 | + | 0.553052i | \(0.813463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 32.3257i | − | 1.20387i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.7298 | + | 13.1231i | 0.844165 | + | 0.487379i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8416 | + | 11.4556i | 0.735886 | + | 0.424864i | 0.820572 | − | 0.571544i | \(-0.193655\pi\) |
−0.0846856 | + | 0.996408i | \(0.526989\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.4648 | + | 13.5474i | −0.867877 | + | 0.501069i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.3106 | −1.52584 | −0.762921 | − | 0.646492i | \(-0.776235\pi\) | ||||
−0.762921 | + | 0.646492i | \(0.776235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.2273 | + | 13.4103i | −0.855588 | + | 0.493974i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.6013 | − | 11.3168i | −0.721045 | − | 0.416296i | 0.0940920 | − | 0.995564i | \(-0.470005\pi\) |
−0.815137 | + | 0.579268i | \(0.803339\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.2545 | + | 29.8857i | −0.633007 | + | 1.09640i | 0.353927 | + | 0.935273i | \(0.384846\pi\) |
−0.986934 | + | 0.161127i | \(0.948487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.34628 | + | 14.4562i | 0.305784 | + | 0.529634i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.4471i | − | 0.710580i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.28226 | − | 16.0773i | −0.338714 | − | 0.586671i | 0.645477 | − | 0.763780i | \(-0.276659\pi\) |
−0.984191 | + | 0.177109i | \(0.943325\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.0933 | + | 74.6399i | −1.56833 | + | 2.71642i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.51003 | − | 16.4718i | 0.345648 | − | 0.598679i | −0.639823 | − | 0.768522i | \(-0.720993\pi\) |
0.985471 | + | 0.169842i | \(0.0543259\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6632 | −0.567792 | −0.283896 | − | 0.958855i | \(-0.591627\pi\) | ||||
−0.283896 | + | 0.958855i | \(0.591627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.2571 | + | 26.4260i | −0.552343 | + | 0.956687i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 16.9607i | − | 0.612417i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.91080 | + | 13.7019i | 0.285271 | + | 0.494103i | 0.972675 | − | 0.232172i | \(-0.0745832\pi\) |
−0.687404 | + | 0.726275i | \(0.741250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.1895 | − | 22.0487i | 1.37358 | − | 0.793037i | 0.382204 | − | 0.924078i | \(-0.375165\pi\) |
0.991377 | + | 0.131041i | \(0.0418318\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.87353 | − | 10.1732i | −0.210983 | − | 0.365434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.04397 | + | 5.26515i | 0.324034 | + | 0.188644i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.3116 | − | 12.3042i | −0.762588 | − | 0.440280i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.15322 | + | 8.92564i | 0.183926 | + | 0.318570i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.60876 | −0.0929921 | −0.0464961 | − | 0.998918i | \(-0.514805\pi\) | ||||
−0.0464961 | + | 0.998918i | \(0.514805\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.10386 | 0.145916 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.846777 | − | 0.488887i | −0.0300699 | − | 0.0173609i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.7059i | 1.76067i | 0.474351 | + | 0.880336i | \(0.342683\pi\) | ||||
−0.474351 | + | 0.880336i | \(0.657317\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.6270i | 1.61417i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.18047 | + | 1.25889i | 0.0769471 | + | 0.0444254i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.8710 | −0.735605 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −51.1280 | −1.79757 | −0.898783 | − | 0.438393i | \(-0.855548\pi\) | ||||
−0.898783 | + | 0.438393i | \(0.855548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.72287 | + | 2.98410i | 0.0604981 | + | 0.104786i | 0.894688 | − | 0.446691i | \(-0.147398\pi\) |
−0.834190 | + | 0.551477i | \(0.814064\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 72.8725 | + | 42.0730i | 2.55261 | + | 1.47375i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.0494 | + | 7.59698i | 0.456540 | + | 0.265785i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.59383 | + | 4.49265i | 0.0905254 | + | 0.156795i | 0.907732 | − | 0.419550i | \(-0.137812\pi\) |
−0.817207 | + | 0.576344i | \(0.804479\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.3661 | − | 12.3357i | 0.744774 | − | 0.429996i | −0.0790284 | − | 0.996872i | \(-0.525182\pi\) |
0.823803 | + | 0.566877i | \(0.191848\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.12598 | + | 8.87845i | 0.178248 | + | 0.308734i | 0.941280 | − | 0.337626i | \(-0.109624\pi\) |
−0.763033 | + | 0.646360i | \(0.776291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.7973i | 1.52114i | 0.649254 | + | 0.760572i | \(0.275081\pi\) | ||||
−0.649254 | + | 0.760572i | \(0.724919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.42082 | − | 9.38914i | 0.187820 | − | 0.325315i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −74.7219 | −2.58586 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.25964 | − | 12.5741i | 0.250631 | − | 0.434105i | −0.713069 | − | 0.701094i | \(-0.752695\pi\) |
0.963700 | + | 0.266989i | \(0.0860287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0740 | + | 17.4488i | −0.347381 | + | 0.601681i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.85887 | − | 3.21966i | −0.0639471 | − | 0.110760i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.7935i | − | 0.473950i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.52468 | − | 6.10493i | −0.120825 | − | 0.209274i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.3861 | − | 19.7213i | 0.389853 | − | 0.675246i | −0.602576 | − | 0.798061i | \(-0.705859\pi\) |
0.992429 | + | 0.122816i | \(0.0391924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.80645 | − | 1.62030i | −0.0958664 | − | 0.0553485i | 0.451300 | − | 0.892372i | \(-0.350960\pi\) |
−0.547167 | + | 0.837024i | \(0.684294\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.4869 | + | 8.94138i | −0.528407 | + | 0.305076i | −0.740367 | − | 0.672202i | \(-0.765348\pi\) |
0.211961 | + | 0.977278i | \(0.432015\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.9949 | 0.952957 | 0.476478 | − | 0.879186i | \(-0.341913\pi\) | ||||
0.476478 | + | 0.879186i | \(0.341913\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.7661 | − | 32.1966i | 1.89610 | − | 1.09472i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.6180 | − | 23.4508i | −1.37787 | − | 0.795515i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.6180 | − | 11.3265i | −0.664731 | − | 0.383783i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.6632i | 1.13803i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.1946 | − | 21.4743i | −1.25597 | − | 0.725137i | −0.283684 | − | 0.958918i | \(-0.591557\pi\) |
−0.972289 | + | 0.233781i | \(0.924890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.9707 | −0.369612 | −0.184806 | − | 0.982775i | \(-0.559166\pi\) | ||||
−0.184806 | + | 0.982775i | \(0.559166\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.2792 | + | 14.5950i | −0.850713 | + | 0.491159i | −0.860891 | − | 0.508789i | \(-0.830093\pi\) |
0.0101785 | + | 0.999948i | \(0.496760\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.0494 | + | 22.6022i | 0.438155 | + | 0.758906i | 0.997547 | − | 0.0699966i | \(-0.0222988\pi\) |
−0.559392 | + | 0.828903i | \(0.688966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.6833 | − | 9.05476i | 0.526001 | − | 0.303687i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.0666 | − | 12.6342i | 0.738430 | − | 0.422787i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.2052 | − | 38.4605i | 0.742236 | − | 1.28559i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.43108 | + | 1.98093i | −0.114433 | + | 0.0660679i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 54.1896i | − | 1.80532i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 54.6696i | − | 1.81728i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.8836 | − | 18.8509i | 0.361382 | − | 0.625933i | −0.626806 | − | 0.779175i | \(-0.715638\pi\) |
0.988189 | + | 0.153242i | \(0.0489715\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.3116 | −1.40184 | −0.700922 | − | 0.713237i | \(-0.747228\pi\) | ||||
−0.700922 | + | 0.713237i | \(0.747228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.129036 | 0.00427045 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.08664 | + | 12.2744i | −0.234021 | + | 0.405337i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.3694i | 0.935821i | 0.883776 | + | 0.467911i | \(0.154993\pi\) | ||||
−0.883776 | + | 0.467911i | \(0.845007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 20.7846i | − | 0.684134i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.7298 | + | 13.1231i | −0.747352 | + | 0.431484i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.4255 | − | 38.8420i | 0.735755 | − | 1.27437i | −0.218636 | − | 0.975807i | \(-0.570161\pi\) |
0.954391 | − | 0.298559i | \(-0.0965060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.04190 | − | 0.0218045i | −0.198015 | − | 0.000714613i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 103.285 | − | 59.6319i | 3.37779 | − | 1.95017i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.3856 | − | 17.9884i | −0.339283 | − | 0.587656i | 0.645015 | − | 0.764170i | \(-0.276851\pi\) |
−0.984298 | + | 0.176514i | \(0.943518\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.31157 | − | 1.91194i | 0.107954 | − | 0.0623274i | −0.445051 | − | 0.895505i | \(-0.646814\pi\) |
0.553005 | + | 0.833178i | \(0.313481\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.68843 | −0.185241 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.2571 | + | 17.4689i | 0.983223 | + | 0.567664i | 0.903242 | − | 0.429132i | \(-0.141181\pi\) |
0.0799814 | + | 0.996796i | \(0.474514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.12655i | 0.0690309i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.2324 | + | 5.90768i | 0.331460 | + | 0.191368i | 0.656489 | − | 0.754336i | \(-0.272041\pi\) |
−0.325029 | + | 0.945704i | \(0.605374\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.20772 | − | 4.73873i | −0.265595 | − | 0.153342i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.7244 | + | 19.4708i | −1.08902 | + | 0.628745i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2268 | −0.942799 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.1584 | − | 5.86493i | 0.327009 | − | 0.188799i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.2520 | + | 14.5792i | 0.812048 | + | 0.468836i | 0.847667 | − | 0.530529i | \(-0.178007\pi\) |
−0.0356185 | + | 0.999365i | \(0.511340\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.49744 | + | 16.4500i | −0.304787 | + | 0.527907i | −0.977214 | − | 0.212257i | \(-0.931919\pi\) |
0.672427 | + | 0.740164i | \(0.265252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.34885 | + | 5.80037i | 0.107359 | + | 0.185951i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.1518i | 0.836669i | 0.908293 | + | 0.418335i | \(0.137386\pi\) | ||||
−0.908293 | + | 0.418335i | \(0.862614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.8856 | − | 60.4237i | −1.11495 | − | 1.93115i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.3116 | + | 36.9127i | −0.679734 | + | 1.17733i | 0.295327 | + | 0.955396i | \(0.404571\pi\) |
−0.975061 | + | 0.221937i | \(0.928762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.0147 | − | 19.0779i | 0.350956 | − | 0.607874i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.20772 | −0.260990 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.46066 | + | 14.6543i | −0.268762 | + | 0.465509i | −0.968542 | − | 0.248849i | \(-0.919948\pi\) |
0.699781 | + | 0.714358i | \(0.253281\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 95.7588i | − | 3.03576i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.85374 | + | 6.67488i | 0.122049 | + | 0.211396i | 0.920576 | − | 0.390564i | \(-0.127720\pi\) |
−0.798526 | + | 0.601960i | \(0.794387\pi\) | |||||||
\(998\) | 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 | 2736.2.bm.l.559.1 | 6 | ||
3.2 | odd | 2 | 304.2.n.d.255.3 | yes | 6 | ||
4.3 | odd | 2 | 2736.2.bm.m.559.1 | 6 | |||
12.11 | even | 2 | 304.2.n.e.255.1 | yes | 6 | ||
19.12 | odd | 6 | 2736.2.bm.m.1855.1 | 6 | |||
24.5 | odd | 2 | 1216.2.n.e.255.1 | 6 | |||
24.11 | even | 2 | 1216.2.n.d.255.3 | 6 | |||
57.50 | even | 6 | 304.2.n.e.31.1 | yes | 6 | ||
76.31 | even | 6 | inner | 2736.2.bm.l.1855.1 | 6 | ||
228.107 | odd | 6 | 304.2.n.d.31.3 | ✓ | 6 | ||
456.107 | odd | 6 | 1216.2.n.e.639.1 | 6 | |||
456.221 | even | 6 | 1216.2.n.d.639.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.n.d.31.3 | ✓ | 6 | 228.107 | odd | 6 | ||
304.2.n.d.255.3 | yes | 6 | 3.2 | odd | 2 | ||
304.2.n.e.31.1 | yes | 6 | 57.50 | even | 6 | ||
304.2.n.e.255.1 | yes | 6 | 12.11 | even | 2 | ||
1216.2.n.d.255.3 | 6 | 24.11 | even | 2 | |||
1216.2.n.d.639.3 | 6 | 456.221 | even | 6 | |||
1216.2.n.e.255.1 | 6 | 24.5 | odd | 2 | |||
1216.2.n.e.639.1 | 6 | 456.107 | odd | 6 | |||
2736.2.bm.l.559.1 | 6 | 1.1 | even | 1 | trivial | ||
2736.2.bm.l.1855.1 | 6 | 76.31 | even | 6 | inner | ||
2736.2.bm.m.559.1 | 6 | 4.3 | odd | 2 | |||
2736.2.bm.m.1855.1 | 6 | 19.12 | odd | 6 |