Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(257,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.cc (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(0.939693 - 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.257 |
Dual form | 912.2.cc.b.401.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.11334 | − | 1.32683i | −0.642788 | − | 0.766044i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64543 | − | 4.58202i | 0.999878 | − | 1.73184i | 0.486436 | − | 0.873716i | \(-0.338297\pi\) |
0.513442 | − | 0.858124i | \(-0.328370\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.520945 | + | 2.95442i | −0.173648 | + | 0.984808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.74510 | − | 4.46324i | 1.03870 | − | 1.23788i | 0.0679785 | − | 0.997687i | \(-0.478345\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | + | 2.59808i | −0.802955 | + | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.02481 | + | 1.59132i | −1.96938 | + | 0.347254i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.83022 | + | 3.21394i | 0.766044 | + | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.50000 | − | 2.59808i | 0.866025 | − | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.84864 | + | 1.06731i | 0.332026 | + | 0.191695i | 0.656740 | − | 0.754117i | \(-0.271935\pi\) |
−0.324714 | + | 0.945812i | \(0.605268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.0511i | − | 1.81680i | −0.418105 | − | 0.908399i | \(-0.637306\pi\) | ||
0.418105 | − | 0.908399i | \(-0.362694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.0915 | −1.61594 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.31180 | − | 3.02525i | −1.26754 | − | 0.461346i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
−0.886292 | + | 0.463127i | \(0.846727\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.4966 | − | 18.1806i | −1.49951 | − | 2.59723i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.34389 | + | 1.75135i | 0.972722 | + | 0.231972i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.5890 | + | 5.30996i | −1.86793 | + | 0.679871i | −0.896258 | + | 0.443533i | \(0.853725\pi\) |
−0.971671 | + | 0.236338i | \(0.924053\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.1591 | + | 10.2027i | 1.53190 | + | 1.28542i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.51501 | − | 1.32510i | −0.918105 | − | 0.161887i | −0.305424 | − | 0.952217i | \(-0.598798\pi\) |
−0.612682 | + | 0.790330i | \(0.709909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.56805 | − | 2.99395i | 0.417608 | − | 0.350415i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.827252 | + | 0.561830i | \(0.189903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 1.00000i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.87598 | + | 8.19448i | 0.773608 | + | 0.921951i | 0.998626 | − | 0.0524041i | \(-0.0166884\pi\) |
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.45723 | − | 3.07818i | −0.939693 | − | 0.342020i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.5432 | − | 28.9673i | −1.10523 | − | 3.03660i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.642026 | − | 3.64111i | −0.0665750 | − | 0.377566i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.7631 | − | 3.30844i | 1.90510 | − | 0.335921i | 0.908474 | − | 0.417941i | \(-0.137248\pi\) |
0.996631 | + | 0.0820195i | \(0.0261370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.10488 | − | 1.79261i | 0.305933 | − | 0.176631i | −0.339172 | − | 0.940724i | \(-0.610147\pi\) |
0.645105 | + | 0.764094i | \(0.276813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.14677 | + | 11.3932i | −0.397189 | + | 1.09127i | 0.566458 | + | 0.824090i | \(0.308313\pi\) |
−0.963647 | + | 0.267177i | \(0.913909\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.6630 | + | 12.3037i | −1.39175 | + | 1.16781i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.2353 | + | 13.3897i | 1.03870 | + | 1.23788i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.4734 | − | 17.2488i | 1.28431 | − | 1.53058i | 0.608167 | − | 0.793809i | \(-0.291905\pi\) |
0.676142 | − | 0.736771i | \(-0.263650\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.23989 | + | 14.3965i | 0.461346 | + | 1.26754i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64543 | + | 22.9101i | 0.229388 | + | 1.98656i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0556 | + | 13.4722i | 1.36181 | + | 1.14270i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
0.386398 | + | 0.922332i | \(0.373719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.4363 | + | 34.1684i | −1.02573 | + | 2.81816i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.66025i | 0.704761i | 0.935857 | + | 0.352381i | \(0.114628\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.47653 | − | 0.901383i | −0.197649 | − | 0.0719382i | 0.241299 | − | 0.970451i | \(-0.422426\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.388003 | − | 0.672042i | −0.0303908 | − | 0.0526384i | 0.850430 | − | 0.526088i | \(-0.176342\pi\) |
−0.880821 | + | 0.473450i | \(0.843009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.63728 | − | 20.6280i | −0.279791 | − | 1.58677i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.85251 | − | 11.6939i | −0.447553 | − | 0.894258i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.8589 | − | 9.04790i | 1.87916 | − | 0.683957i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.5861 | + | 4.51151i | 1.90180 | + | 0.335338i | 0.996073 | − | 0.0885316i | \(-0.0282174\pi\) |
0.905723 | + | 0.423870i | \(0.139329\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.2879 | + | 13.4453i | 1.72149 | + | 0.993904i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 27.4921i | − | 1.99976i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.35932 | − | 5.19523i | −0.313791 | − | 0.373961i | 0.585979 | − | 0.810326i | \(-0.300710\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.251907 | − | 1.42864i | 0.0178572 | − | 0.101273i | −0.974576 | − | 0.224055i | \(-0.928070\pi\) |
0.992434 | + | 0.122782i | \(0.0391815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.60859 | + | 11.4464i | 0.466134 | + | 0.807368i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.6643 | − | 3.46735i | 1.35375 | − | 0.238702i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
0.803005 | + | 0.595973i | \(0.203233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.78090 | − | 5.64700i | 0.663971 | − | 0.383344i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.94491 | − | 1.40090i | −0.536867 | − | 0.0946642i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.87851 | + | 24.3935i | −0.594549 | + | 1.63351i | 0.167412 | + | 0.985887i | \(0.446459\pi\) |
−0.761961 | + | 0.647623i | \(0.775763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4907 | + | 9.64181i | −0.766044 | + | 0.642788i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.2891 | 1.60507 | 0.802535 | − | 0.596606i | \(-0.203484\pi\) | ||||
0.802535 | + | 0.596606i | \(0.203484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.21735 | − | 18.2465i | 0.208989 | − | 1.18524i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.86143 | + | 9.36889i | −0.506399 | + | 0.603503i | −0.957309 | − | 0.289066i | \(-0.906655\pi\) |
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.33157 | + | 14.6484i | 0.342020 | + | 0.939693i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.51202 | + | 25.3514i | −0.0962076 | + | 1.61307i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −50.6366 | − | 29.2350i | −3.14640 | − | 1.81658i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.2511 | + | 9.91858i | 1.65539 | + | 0.602511i | 0.989628 | − | 0.143657i | \(-0.0458861\pi\) |
0.665758 | + | 0.746168i | \(0.268108\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.6964 | + | 46.2395i | −1.61574 | + | 2.79854i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5000 | − | 26.8468i | −0.931305 | − | 1.61307i | −0.781094 | − | 0.624413i | \(-0.785338\pi\) |
−0.150210 | − | 0.988654i | \(-0.547995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.11633 | + | 4.90566i | −0.246438 | + | 0.293694i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.34120 | + | 24.6202i | 0.258058 | + | 1.46352i | 0.788100 | + | 0.615547i | \(0.211065\pi\) |
−0.530042 | + | 0.847971i | \(0.677824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9748 | + | 5.81434i | −0.939693 | + | 0.342020i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.2795 | − | 21.2120i | −1.48191 | − | 1.24347i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.8500 | + | 30.0818i | −2.06636 | + | 1.73388i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.11334 | + | 1.32683i | 0.0635417 | + | 0.0757261i | 0.796879 | − | 0.604139i | \(-0.206483\pi\) |
−0.733337 | + | 0.679865i | \(0.762038\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.83527 | − | 2.12387i | −0.331957 | − | 0.120823i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.07769 | + | 34.4683i | −0.343531 | + | 1.94826i | −0.0271446 | + | 0.999632i | \(0.508641\pi\) |
−0.316387 | + | 0.948630i | \(0.602470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.6891 | − | 5.05867i | 1.59139 | − | 0.280604i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.7335 | − | 7.18242i | 1.09127 | − | 0.397189i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.6871 | − | 14.2531i | 1.35692 | − | 0.783420i | 0.367716 | − | 0.929938i | \(-0.380140\pi\) |
0.989208 | + | 0.146518i | \(0.0468065\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.6498 | + | 5.75703i | 1.78920 | + | 0.315484i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.43061 | − | 23.1629i | 0.459244 | − | 1.26176i | −0.466805 | − | 0.884361i | \(-0.654595\pi\) |
0.926049 | − | 0.377403i | \(-0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −74.0360 | −3.99757 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8418 | − | 27.4389i | 0.847994 | − | 1.46877i | −0.0350017 | − | 0.999387i | \(-0.511144\pi\) |
0.882996 | − | 0.469381i | \(-0.155523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.25712 | − | 29.8146i | 0.280604 | − | 1.59139i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.7631 | − | 3.30844i | 0.984808 | − | 0.173648i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.2147 | − | 23.6749i | −1.47279 | − | 1.23582i | −0.913493 | − | 0.406855i | \(-0.866625\pi\) |
−0.559301 | − | 0.828965i | \(-0.688930\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | + | 3.46410i | 0.310668 | + | 0.179364i | 0.647225 | − | 0.762299i | \(-0.275929\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 38.5433i | − | 1.97983i | −0.141648 | − | 0.989917i | \(-0.545240\pi\) | ||
0.141648 | − | 0.989917i | \(-0.454760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.0000 | −1.99803 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.2679 | − | 22.9806i | 0.674443 | − | 1.16817i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.31356 | + | 24.4634i | 0.216491 | + | 1.22778i | 0.878300 | + | 0.478110i | \(0.158678\pi\) |
−0.661809 | + | 0.749673i | \(0.730211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.4525 | − | 29.0168i | 1.37434 | − | 1.45266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.6870 | − | 4.25373i | 0.582172 | − | 0.211893i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6459 | + | 2.40614i | 0.674746 | + | 0.118976i | 0.500514 | − | 0.865729i | \(-0.333144\pi\) |
0.174232 | + | 0.984705i | \(0.444256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 36.3021i | − | 1.77772i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.11334 | − | 1.32683i | −0.0542609 | − | 0.0646656i | 0.738231 | − | 0.674548i | \(-0.235661\pi\) |
−0.792492 | + | 0.609882i | \(0.791217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.2638 | + | 80.8942i | −0.690275 | + | 3.91474i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.4516 | − | 28.7154i | −0.502270 | − | 1.37997i | −0.889053 | − | 0.457804i | \(-0.848636\pi\) |
0.386784 | − | 0.922170i | \(-0.373586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.4206 | − | 3.42437i | 0.926893 | − | 0.163436i | 0.310228 | − | 0.950662i | \(-0.399595\pi\) |
0.616665 | + | 0.787226i | \(0.288483\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 59.1814 | − | 21.5403i | 2.81816 | − | 1.02573i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.4907 | − | 9.64181i | 0.539879 | − | 0.453012i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.3806 | −1.60826 | −0.804129 | − | 0.594455i | \(-0.797368\pi\) | ||||
−0.804129 | + | 0.594455i | \(0.797368\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.9133 | + | 27.5626i | −0.739553 | + | 1.28094i | 0.213144 | + | 0.977021i | \(0.431630\pi\) |
−0.952697 | + | 0.303923i | \(0.901704\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.9521 | + | 30.9285i | −1.19836 | + | 1.42814i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.56124 | + | 4.28947i | 0.0719382 | + | 0.197649i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.7558 | − | 1.29757i | −0.998226 | − | 0.0595368i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.3239 | − | 41.3877i | −2.24898 | − | 1.88711i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.5000 | + | 18.1865i | 1.42740 | + | 0.824110i | 0.996915 | − | 0.0784867i | \(-0.0250088\pi\) |
0.430486 | + | 0.902597i | \(0.358342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.459704 | + | 1.26302i | −0.0207885 | + | 0.0571160i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.2366 | + | 6.63760i | 0.816384 | + | 0.297140i | 0.716258 | − | 0.697835i | \(-0.245853\pi\) |
0.100126 | + | 0.994975i | \(0.468075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.3203 | + | 27.7921i | −1.03569 | + | 1.23429i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.27930 | − | 24.2691i | −0.189305 | − | 1.07360i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.00000 | + | 20.7846i | −0.397360 | + | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4599 | + | 2.72600i | 0.676015 | + | 0.119200i | 0.501107 | − | 0.865385i | \(-0.332926\pi\) |
0.174908 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −39.6814 | − | 22.9101i | −1.73184 | − | 0.999878i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6190 | − | 14.7841i | 0.766044 | − | 0.642788i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.89234 | + | 39.0884i | −0.296325 | + | 1.68054i | 0.365444 | + | 0.930834i | \(0.380917\pi\) |
−0.661768 | + | 0.749708i | \(0.730194\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.5000 | − | 38.9711i | −0.965567 | − | 1.67241i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1471 | − | 41.6163i | −0.647642 | − | 1.77938i | −0.626264 | − | 0.779611i | \(-0.715417\pi\) |
−0.0213785 | − | 0.999771i | \(-0.506805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.08781 | − | 45.8683i | −0.345179 | − | 1.95761i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.7372 | − | 9.82797i | 2.37019 | − | 0.417928i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.6309 | + | 25.7677i | −1.88769 | + | 1.08986i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −36.4773 | + | 30.6081i | −1.53190 | + | 1.28542i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 47.1275 | 1.97223 | 0.986113 | − | 0.166076i | \(-0.0531097\pi\) | ||||
0.986113 | + | 0.166076i | \(0.0531097\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.50000 | − | 9.52628i | 0.228968 | − | 0.396584i | −0.728535 | − | 0.685009i | \(-0.759798\pi\) |
0.957503 | + | 0.288425i | \(0.0931316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.03977 | + | 11.5681i | −0.0847701 | + | 0.480755i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.24320 | + | 1.06731i | −0.380860 | + | 0.0439779i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.17601 | + | 1.25632i | −0.0890583 | + | 0.0514178i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.5301 | + | 23.9774i | 1.69405 | + | 0.978059i | 0.951188 | + | 0.308611i | \(0.0998642\pi\) |
0.742859 | + | 0.669448i | \(0.233469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.82981 | − | 21.5122i | 0.318855 | − | 0.876046i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 47.3533i | − | 1.92201i | −0.276531 | − | 0.961005i | \(-0.589185\pi\) | ||
0.276531 | − | 0.961005i | \(-0.410815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.1656 | + | 16.0749i | 1.78383 | + | 0.649261i | 0.999585 | + | 0.0288097i | \(0.00917168\pi\) |
0.784245 | + | 0.620451i | \(0.213051\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.00996231 | − | 0.0172552i | −0.000400419 | − | 0.000693546i | 0.865825 | − | 0.500347i | \(-0.166794\pi\) |
−0.866226 | + | 0.499653i | \(0.833461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2604 | − | 5.55434i | 0.607508 | − | 0.221115i | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) |
0.627412 | + | 0.778687i | \(0.284114\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.4937 | − | 22.2308i | −1.05303 | − | 0.883596i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −120.455 | − | 21.2395i | −4.77261 | − | 0.841540i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.12133 | − | 6.81460i | 0.320274 | − | 0.268742i | −0.468449 | − | 0.883491i | \(-0.655187\pi\) |
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.3821 | − | 6.69053i | −0.720450 | − | 0.262222i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.98663 | + | 12.1012i | 0.272575 | + | 0.472113i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8479 | + | 32.5519i | 0.460831 | + | 1.26612i | 0.924862 | + | 0.380303i | \(0.124180\pi\) |
−0.464031 | + | 0.885819i | \(0.653597\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.2508 | − | 15.3780i | 1.63351 | − | 0.594549i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.0261 | + | 21.3770i | −1.42725 | + | 0.824023i | −0.996903 | − | 0.0786409i | \(-0.974942\pi\) |
−0.430346 | + | 0.902664i | \(0.641609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.5861 | + | 4.51151i | 0.984808 | + | 0.173648i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.4771 | − | 94.7252i | 1.32311 | − | 3.63522i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.0421 | − | 32.2275i | −1.03172 | − | 1.22955i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.5000 | + | 42.4352i | −0.932024 | + | 1.61431i | −0.152167 | + | 0.988355i | \(0.548625\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.7117 | + | 38.6790i | 1.08288 | + | 1.45881i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.5431 | + | 23.9505i | 1.07196 | + | 0.899479i | 0.995228 | − | 0.0975728i | \(-0.0311079\pi\) |
0.0767291 | + | 0.997052i | \(0.475552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.7920 | + | 16.0457i | −1.04228 | + | 0.601760i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.9689i | − | 0.706437i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.1834 | 0.787818 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.8730 | − | 17.7883i | −1.81260 | − | 0.659733i | −0.996666 | − | 0.0815889i | \(-0.974001\pi\) |
−0.815935 | − | 0.578144i | \(-0.803777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.50000 | + | 6.06218i | 0.129275 | + | 0.223912i | 0.923396 | − | 0.383849i | \(-0.125402\pi\) |
−0.794121 | + | 0.607760i | \(0.792068\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.67153 | + | 20.8223i | 0.135060 | + | 0.765961i | 0.974818 | + | 0.223001i | \(0.0715853\pi\) |
−0.839759 | + | 0.542960i | \(0.817304\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.3203 | − | 26.2185i | 1.29752 | − | 0.963162i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.5435 | − | 5.91463i | −1.22402 | − | 0.215828i | −0.475965 | − | 0.879464i | \(-0.657901\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.0453 | + | 33.6020i | −1.45547 | + | 1.22129i | −0.527011 | + | 0.849858i | \(0.676688\pi\) |
−0.928461 | + | 0.371429i | \(0.878868\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.2337 | + | 49.1404i | 1.49276 | + | 1.77900i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.96544 | + | 16.8179i | −0.106937 | + | 0.606467i | 0.883493 | + | 0.468445i | \(0.155186\pi\) |
−0.990429 | + | 0.138022i | \(0.955925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.65043 | + | 10.0295i | 0.131127 | + | 0.360269i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.5859 | + | 99.7346i | 0.630890 | + | 3.57796i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4062 | + | 11.2042i | −0.691755 | + | 0.399385i | −0.804269 | − | 0.594265i | \(-0.797443\pi\) |
0.112514 | + | 0.993650i | \(0.464110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.9376 | + | 85.0004i | −1.09863 | + | 3.01845i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.8335 | + | 33.1707i | −0.977367 | + | 1.16478i | 0.00895645 | + | 0.999960i | \(0.497149\pi\) |
−0.986324 | + | 0.164821i | \(0.947295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.1795 | − | 47.2003i | −0.602511 | − | 1.65539i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.9511 | − | 11.0063i | 1.29276 | − | 0.385063i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 91.0741 | − | 16.0588i | 3.18239 | − | 0.561141i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.83022 | + | 3.21394i | 0.133513 | + | 0.112031i | 0.707099 | − | 0.707115i | \(-0.250004\pi\) |
−0.573586 | + | 0.819146i | \(0.694448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.62551 | + | 1.51584i | 0.0911876 | + | 0.0526472i | 0.544900 | − | 0.838501i | \(-0.316567\pi\) |
−0.453713 | + | 0.891148i | \(0.649901\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.3643 | + | 50.4555i | −0.637050 | + | 1.75028i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.0918 | 0.383390 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.2511 | + | 9.91858i | 0.939693 | + | 0.342020i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.0997 | + | 50.4022i | 0.999878 | + | 1.73184i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.8335 | − | 33.1707i | 0.955244 | − | 1.13842i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.93371 | − | 16.6379i | −0.100448 | − | 0.569670i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) |
0.892493 | − | 0.451061i | \(-0.148954\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.8494 | + | 10.8643i | −1.01845 | + | 0.370685i | −0.796672 | − | 0.604412i | \(-0.793408\pi\) |
−0.221777 | + | 0.975097i | \(0.571186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.5000 | + | 14.7224i | 0.866025 | + | 0.500000i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.0587 | + | 28.5787i | −1.15404 | + | 0.968351i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 57.1577i | 1.93449i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.83234 | + | 11.7177i | 0.332014 | + | 0.395679i | 0.906064 | − | 0.423141i | \(-0.139073\pi\) |
−0.574049 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.50903 | + | 31.2433i | −0.185394 | + | 1.05142i | 0.740055 | + | 0.672546i | \(0.234799\pi\) |
−0.925449 | + | 0.378873i | \(0.876312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.7457 | − | 111.948i | −1.36657 | − | 3.75461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 79.8266 | + | 14.0756i | 2.65646 | + | 0.468406i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.14677 | − | 11.3932i | 0.137691 | − | 0.378304i | −0.851613 | − | 0.524171i | \(-0.824375\pi\) |
0.989304 | + | 0.145868i | \(0.0465973\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8665 | − | 34.4098i | 0.655335 | − | 1.13507i | −0.326475 | − | 0.945206i | \(-0.605861\pi\) |
0.981810 | − | 0.189867i | \(-0.0608058\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.520945 | − | 2.95442i | 0.0171657 | − | 0.0973516i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.5177 | − | 42.3284i | 1.16781 | − | 1.39175i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.67864 | + | 10.1070i | 0.120823 | + | 0.331957i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 83.9728 | + | 36.3613i | 2.75210 | + | 1.19169i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.5492 | + | 35.7030i | 1.39002 | + | 1.16637i | 0.965331 | + | 0.261029i | \(0.0840619\pi\) |
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.5000 | − | 30.3109i | 1.71327 | − | 0.989158i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 27.1377i | − | 0.880926i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2217 | − | 22.9006i | −0.426506 | − | 0.738730i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.46766 | − | 53.6938i | −0.304460 | − | 1.72668i | −0.626038 | − | 0.779793i | \(-0.715324\pi\) |
0.321578 | − | 0.946883i | \(-0.395787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 104.204 | − | 37.9271i | 3.34062 | − | 1.21589i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38.6528 | − | 32.4335i | −1.23788 | − | 1.03870i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.5000 | − | 18.1865i | −1.00572 | − | 0.580651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.8744 | + | 43.9452i | 1.17135 | + | 1.39596i | 0.901342 | + | 0.433108i | \(0.142583\pi\) |
0.270011 | + | 0.962857i | \(0.412973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −46.3965 | − | 16.8870i | −1.47235 | − | 0.535891i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3616 | + | 58.7635i | −0.328155 | + | 1.86106i | 0.158352 | + | 0.987383i | \(0.449382\pi\) |
−0.486507 | + | 0.873677i | \(0.661729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.7117 | − | 49.7302i | −0.908399 | − | 1.57339i |
(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 | 912.2.cc.b.257.1 | 6 | ||
3.2 | odd | 2 | CM | 912.2.cc.b.257.1 | 6 | ||
4.3 | odd | 2 | 228.2.t.a.29.1 | ✓ | 6 | ||
12.11 | even | 2 | 228.2.t.a.29.1 | ✓ | 6 | ||
19.2 | odd | 18 | inner | 912.2.cc.b.401.1 | 6 | ||
57.2 | even | 18 | inner | 912.2.cc.b.401.1 | 6 | ||
76.59 | even | 18 | 228.2.t.a.173.1 | yes | 6 | ||
228.59 | odd | 18 | 228.2.t.a.173.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.t.a.29.1 | ✓ | 6 | 4.3 | odd | 2 | ||
228.2.t.a.29.1 | ✓ | 6 | 12.11 | even | 2 | ||
228.2.t.a.173.1 | yes | 6 | 76.59 | even | 18 | ||
228.2.t.a.173.1 | yes | 6 | 228.59 | odd | 18 | ||
912.2.cc.b.257.1 | 6 | 1.1 | even | 1 | trivial | ||
912.2.cc.b.257.1 | 6 | 3.2 | odd | 2 | CM | ||
912.2.cc.b.401.1 | 6 | 19.2 | odd | 18 | inner | ||
912.2.cc.b.401.1 | 6 | 57.2 | even | 18 | inner |