Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3528,2,Mod(361,3528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3528.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.s (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.1712218331\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3528.361 |
Dual form | 3528.2.s.u.3313.1 |
$q$-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 \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(1765\) | \(2647\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | − | 8.66025i | −0.821995 | − | 1.42374i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) |
0.0821995 | − | 0.996616i | \(-0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.00000 | + | 3.46410i | 0.291730 | + | 0.505291i | 0.974219 | − | 0.225605i | \(-0.0724358\pi\) |
−0.682489 | + | 0.730896i | \(0.739102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | − | 10.3923i | 0.781133 | − | 1.35296i | −0.150148 | − | 0.988663i | \(-0.547975\pi\) |
0.931282 | − | 0.364299i | \(-0.118692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 5.19615i | 0.384111 | + | 0.665299i | 0.991645 | − | 0.128994i | \(-0.0411748\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | − | 3.46410i | −0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000 | 1.75623 | 0.878114 | − | 0.478451i | \(-0.158802\pi\) | ||||
0.878114 | + | 0.478451i | \(0.158802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | − | 6.92820i | 0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.0000 | 1.82762 | 0.913812 | − | 0.406138i | \(-0.133125\pi\) | ||||
0.913812 | + | 0.406138i | \(0.133125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.00000 | − | 12.1244i | 0.696526 | − | 1.20642i | −0.273138 | − | 0.961975i | \(-0.588061\pi\) |
0.969664 | − | 0.244443i | \(-0.0786053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | − | 3.46410i | −0.197066 | − | 0.341328i | 0.750510 | − | 0.660859i | \(-0.229808\pi\) |
−0.947576 | + | 0.319531i | \(0.896475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0000 | −1.50515 | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | − | 10.3923i | 0.559503 | − | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | + | 6.92820i | 0.349482 | + | 0.605320i | 0.986157 | − | 0.165812i | \(-0.0530244\pi\) |
−0.636676 | + | 0.771132i | \(0.719691\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | − | 10.3923i | 0.512615 | − | 0.887875i | −0.487278 | − | 0.873247i | \(-0.662010\pi\) |
0.999893 | − | 0.0146279i | \(-0.00465636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | − | 3.46410i | 0.167248 | − | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | + | 20.7846i | −0.976546 | + | 1.69143i | −0.301811 | + | 0.953368i | \(0.597591\pi\) |
−0.674735 | + | 0.738060i | \(0.735742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | − | 5.19615i | 0.239426 | − | 0.414698i | −0.721124 | − | 0.692806i | \(-0.756374\pi\) |
0.960550 | + | 0.278108i | \(0.0897074\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | + | 10.3923i | 0.469956 | + | 0.813988i | 0.999410 | − | 0.0343508i | \(-0.0109363\pi\) |
−0.529454 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.00000 | −0.309529 | −0.154765 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154765 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.00000 | − | 8.66025i | 0.373718 | − | 0.647298i | −0.616417 | − | 0.787420i | \(-0.711416\pi\) |
0.990134 | + | 0.140122i | \(0.0447496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0000 | − | 17.3205i | 0.735215 | − | 1.27343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | + | 10.3923i | 0.438763 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0000 | − | 22.5167i | −0.940647 | − | 1.62925i | −0.764241 | − | 0.644931i | \(-0.776886\pi\) |
−0.176406 | − | 0.984317i | \(-0.556447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0000 | − | 22.5167i | 0.935760 | − | 1.62078i | 0.162488 | − | 0.986710i | \(-0.448048\pi\) |
0.773272 | − | 0.634074i | \(-0.218619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | − | 3.46410i | −0.139686 | − | 0.241943i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | − | 6.92820i | −0.272798 | − | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.0000 | − | 24.2487i | 0.929213 | − | 1.60944i | 0.144571 | − | 0.989494i | \(-0.453820\pi\) |
0.784642 | − | 0.619949i | \(-0.212847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.00000 | + | 3.46410i | 0.131024 | + | 0.226941i | 0.924072 | − | 0.382219i | \(-0.124840\pi\) |
−0.793047 | + | 0.609160i | \(0.791507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 6.92820i | −0.260931 | + | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0000 | 0.905585 | 0.452792 | − | 0.891616i | \(-0.350428\pi\) | ||||
0.452792 | + | 0.891616i | \(0.350428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | + | 6.92820i | 0.254514 | + | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.0000 | + | 22.5167i | 0.810918 | + | 1.40455i | 0.912222 | + | 0.409695i | \(0.134365\pi\) |
−0.101305 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | − | 15.5885i | 0.554964 | − | 0.961225i | −0.442943 | − | 0.896550i | \(-0.646065\pi\) |
0.997906 | − | 0.0646755i | \(-0.0206012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0000 | 1.47431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.00000 | − | 8.66025i | 0.304855 | − | 0.528025i | −0.672374 | − | 0.740212i | \(-0.734725\pi\) |
0.977229 | + | 0.212187i | \(0.0680585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.00000 | − | 10.3923i | −0.364474 | − | 0.631288i | 0.624218 | − | 0.781251i | \(-0.285418\pi\) |
−0.988692 | + | 0.149963i | \(0.952085\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | + | 1.73205i | 0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0000 | − | 24.2487i | 0.832214 | − | 1.44144i | −0.0640654 | − | 0.997946i | \(-0.520407\pi\) |
0.896279 | − | 0.443491i | \(-0.146260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | + | 10.3923i | 0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | + | 10.3923i | −0.343559 | + | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0000 | − | 17.3205i | 0.567048 | − | 0.982156i | −0.429808 | − | 0.902920i | \(-0.641419\pi\) |
0.996856 | − | 0.0792356i | \(-0.0252479\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | − | 12.1244i | −0.395663 | − | 0.685309i | 0.597522 | − | 0.801852i | \(-0.296152\pi\) |
−0.993186 | + | 0.116543i | \(0.962819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | − | 10.3923i | −0.336994 | − | 0.583690i | 0.646872 | − | 0.762598i | \(-0.276077\pi\) |
−0.983866 | + | 0.178908i | \(0.942743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | + | 1.73205i | −0.0554700 | + | 0.0960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | − | 17.3205i | −0.549650 | − | 0.952021i | −0.998298 | − | 0.0583130i | \(-0.981428\pi\) |
0.448649 | − | 0.893708i | \(-0.351905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | − | 6.92820i | −0.216612 | − | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.00000 | + | 5.19615i | −0.161048 | + | 0.278944i | −0.935245 | − | 0.354001i | \(-0.884821\pi\) |
0.774197 | + | 0.632945i | \(0.218154\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0000 | + | 22.5167i | −0.691920 | + | 1.19844i | 0.279288 | + | 0.960207i | \(0.409902\pi\) |
−0.971208 | + | 0.238233i | \(0.923432\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.0000 | − | 24.2487i | −0.743043 | − | 1.28699i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.00000 | + | 5.19615i | 0.158334 | + | 0.274242i | 0.934268 | − | 0.356572i | \(-0.116054\pi\) |
−0.775934 | + | 0.630814i | \(0.782721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0000 | − | 20.7846i | −0.613171 | − | 1.06204i | −0.990702 | − | 0.136047i | \(-0.956560\pi\) |
0.377531 | − | 0.925997i | \(-0.376773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.00000 | − | 6.92820i | 0.202808 | − | 0.351274i | −0.746624 | − | 0.665246i | \(-0.768327\pi\) |
0.949432 | + | 0.313972i | \(0.101660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | + | 13.8564i | −0.402524 | + | 0.697191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0000 | + | 19.0526i | 0.552074 | + | 0.956221i | 0.998125 | + | 0.0612128i | \(0.0194968\pi\) |
−0.446051 | + | 0.895008i | \(0.647170\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | − | 10.3923i | −0.299626 | − | 0.518967i | 0.676425 | − | 0.736512i | \(-0.263528\pi\) |
−0.976050 | + | 0.217545i | \(0.930195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.0000 | 0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | + | 1.73205i | −0.0494468 | + | 0.0856444i | −0.889689 | − | 0.456566i | \(-0.849079\pi\) |
0.840243 | + | 0.542211i | \(0.182412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.0000 | + | 27.7128i | 0.785409 | + | 1.36037i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.00000 | 0.195413 | 0.0977064 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977064 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | − | 5.19615i | −0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.00000 | + | 8.66025i | −0.240842 | + | 0.417150i | −0.960954 | − | 0.276707i | \(-0.910757\pi\) |
0.720113 | + | 0.693857i | \(0.244090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | + | 20.7846i | −0.574038 | + | 0.994263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.00000 | + | 15.5885i | 0.427603 | + | 0.740630i | 0.996660 | − | 0.0816684i | \(-0.0260248\pi\) |
−0.569057 | + | 0.822298i | \(0.692691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.00000 | −0.377543 | −0.188772 | − | 0.982021i | \(-0.560451\pi\) | ||||
−0.188772 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | − | 3.46410i | 0.0941763 | − | 0.163118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | − | 19.0526i | −0.514558 | − | 0.891241i | −0.999857 | − | 0.0168929i | \(-0.994623\pi\) |
0.485299 | − | 0.874348i | \(-0.338711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0000 | 0.838344 | 0.419172 | − | 0.907907i | \(-0.362320\pi\) | ||||
0.419172 | + | 0.907907i | \(0.362320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.00000 | + | 3.46410i | 0.0925490 | + | 0.160300i | 0.908583 | − | 0.417704i | \(-0.137165\pi\) |
−0.816034 | + | 0.578004i | \(0.803832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0000 | + | 31.1769i | −0.822441 | + | 1.42451i | 0.0814184 | + | 0.996680i | \(0.474055\pi\) |
−0.903859 | + | 0.427830i | \(0.859278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0000 | + | 17.3205i | 0.455961 | + | 0.789747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.0000 | + | 31.1769i | 0.817338 | + | 1.41567i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | + | 6.92820i | −0.181257 | + | 0.313947i | −0.942309 | − | 0.334744i | \(-0.891350\pi\) |
0.761052 | + | 0.648691i | \(0.224683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | + | 3.46410i | 0.0895323 | + | 0.155074i | 0.907314 | − | 0.420455i | \(-0.138129\pi\) |
−0.817781 | + | 0.575529i | \(0.804796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.0000 | 1.24598 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.00000 | − | 12.1244i | −0.310270 | − | 0.537403i | 0.668151 | − | 0.744026i | \(-0.267086\pi\) |
−0.978421 | + | 0.206623i | \(0.933753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.00000 | − | 6.92820i | 0.176261 | − | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.00000 | −0.351840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | − | 5.19615i | 0.131432 | − | 0.227648i | −0.792797 | − | 0.609486i | \(-0.791376\pi\) |
0.924229 | + | 0.381839i | \(0.124709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000 | + | 13.8564i | 0.349816 | + | 0.605898i | 0.986216 | − | 0.165460i | \(-0.0529109\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | + | 20.7846i | 0.522728 | + | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | 0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | + | 10.3923i | −0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.0000 | −1.53925 | −0.769624 | − | 0.638497i | \(-0.779557\pi\) | ||||
−0.769624 | + | 0.638497i | \(0.779557\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0000 | + | 17.3205i | −0.423714 | + | 0.733893i | −0.996299 | − | 0.0859514i | \(-0.972607\pi\) |
0.572586 | + | 0.819845i | \(0.305940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.0000 | + | 24.2487i | −0.590030 | + | 1.02196i | 0.404198 | + | 0.914671i | \(0.367551\pi\) |
−0.994228 | + | 0.107290i | \(0.965783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0000 | − | 27.7128i | −0.673125 | − | 1.16589i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.00000 | + | 3.46410i | 0.0838444 | + | 0.145223i | 0.904898 | − | 0.425628i | \(-0.139947\pi\) |
−0.821054 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0000 | − | 29.4449i | 0.707719 | − | 1.22581i | −0.257982 | − | 0.966150i | \(-0.583058\pi\) |
0.965701 | − | 0.259656i | \(-0.0836092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | + | 20.7846i | 0.496989 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0000 | − | 22.5167i | −0.533846 | − | 0.924648i | −0.999218 | − | 0.0395334i | \(-0.987413\pi\) |
0.465372 | − | 0.885115i | \(-0.345920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.00000 | + | 15.5885i | −0.367730 | + | 0.636927i | −0.989210 | − | 0.146503i | \(-0.953198\pi\) |
0.621480 | + | 0.783430i | \(0.286532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | + | 12.1244i | −0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0000 | − | 34.6410i | −0.811775 | − | 1.40604i | −0.911621 | − | 0.411033i | \(-0.865168\pi\) |
0.0998457 | − | 0.995003i | \(-0.468165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | − | 6.92820i | −0.161823 | − | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.00000 | + | 5.19615i | −0.121169 | + | 0.209871i | −0.920229 | − | 0.391381i | \(-0.871998\pi\) |
0.799060 | + | 0.601251i | \(0.205331\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.0000 | 1.12724 | 0.563619 | − | 0.826035i | \(-0.309409\pi\) | ||||
0.563619 | + | 0.826035i | \(0.309409\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0000 | − | 34.6410i | 0.803868 | − | 1.39234i | −0.113185 | − | 0.993574i | \(-0.536105\pi\) |
0.917053 | − | 0.398766i | \(-0.130561\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −60.0000 | −2.39236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | − | 13.8564i | −0.317470 | − | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.00000 | + | 10.3923i | −0.236986 | + | 0.410471i | −0.959848 | − | 0.280521i | \(-0.909493\pi\) |
0.722862 | + | 0.690992i | \(0.242826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.0000 | 1.73519 | 0.867595 | − | 0.497271i | \(-0.165665\pi\) | ||||
0.867595 | + | 0.497271i | \(0.165665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.0000 | + | 17.3205i | −0.393141 | + | 0.680939i | −0.992862 | − | 0.119269i | \(-0.961945\pi\) |
0.599721 | + | 0.800209i | \(0.295278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.0000 | + | 20.7846i | 0.471041 | + | 0.815867i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.0000 | + | 27.7128i | 0.626128 | + | 1.08449i | 0.988322 | + | 0.152383i | \(0.0486948\pi\) |
−0.362193 | + | 0.932103i | \(0.617972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | + | 13.8564i | −0.312586 | + | 0.541415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.0000 | 1.63609 | 0.818044 | − | 0.575156i | \(-0.195059\pi\) | ||||
0.818044 | + | 0.575156i | \(0.195059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00000 | + | 8.66025i | −0.194477 | + | 0.336845i | −0.946729 | − | 0.322031i | \(-0.895634\pi\) |
0.752252 | + | 0.658876i | \(0.228968\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00000 | −0.0770943 | −0.0385472 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385472 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.0000 | + | 25.9808i | 0.576497 | + | 0.998522i | 0.995877 | + | 0.0907112i | \(0.0289140\pi\) |
−0.419380 | + | 0.907811i | \(0.637753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0000 | + | 25.9808i | −0.573959 | + | 0.994126i | 0.422195 | + | 0.906505i | \(0.361260\pi\) |
−0.996154 | + | 0.0876211i | \(0.972074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | 0.916993 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | + | 20.7846i | −0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | + | 34.6410i | 0.760836 | + | 1.31781i | 0.942420 | + | 0.334431i | \(0.108544\pi\) |
−0.181584 | + | 0.983375i | \(0.558123\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0000 | − | 27.7128i | −0.606915 | − | 1.05121i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | + | 10.3923i | −0.227266 | + | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.0000 | 1.81293 | 0.906467 | − | 0.422276i | \(-0.138769\pi\) | ||||
0.906467 | + | 0.422276i | \(0.138769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | + | 34.6410i | −0.754314 | + | 1.30651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.00000 | + | 5.19615i | 0.112667 | + | 0.195146i | 0.916845 | − | 0.399244i | \(-0.130727\pi\) |
−0.804178 | + | 0.594389i | \(0.797394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | 0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0000 | + | 27.7128i | 0.596699 | + | 1.03351i | 0.993305 | + | 0.115524i | \(0.0368548\pi\) |
−0.396605 | + | 0.917989i | \(0.629812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0000 | + | 22.5167i | 0.480166 | + | 0.831672i | 0.999741 | − | 0.0227529i | \(-0.00724310\pi\) |
−0.519575 | + | 0.854425i | \(0.673910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.00000 | + | 6.92820i | 0.147342 | + | 0.255204i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.0000 | − | 38.1051i | 0.809283 | − | 1.40172i | −0.104078 | − | 0.994569i | \(-0.533189\pi\) |
0.913361 | − | 0.407150i | \(-0.133477\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.00000 | 0.0733729 | 0.0366864 | − | 0.999327i | \(-0.488320\pi\) | ||||
0.0366864 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000 | − | 20.7846i | 0.439646 | − | 0.761489i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | + | 6.92820i | 0.145962 | + | 0.252814i | 0.929731 | − | 0.368238i | \(-0.120039\pi\) |
−0.783769 | + | 0.621052i | \(0.786706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −48.0000 | −1.74690 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | − | 25.9808i | −0.543750 | − | 0.941802i | −0.998684 | − | 0.0512772i | \(-0.983671\pi\) |
0.454935 | − | 0.890525i | \(-0.349663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | + | 20.7846i | −0.433295 | + | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.0000 | −0.937584 | −0.468792 | − | 0.883309i | \(-0.655311\pi\) | ||||
−0.468792 | + | 0.883309i | \(0.655311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.00000 | + | 8.66025i | −0.179838 | + | 0.311488i | −0.941825 | − | 0.336104i | \(-0.890891\pi\) |
0.761987 | + | 0.647592i | \(0.224224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | + | 3.46410i | 0.0718421 | + | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.00000 | + | 6.92820i | 0.143315 | + | 0.248229i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0000 | − | 24.2487i | 0.500959 | − | 0.867687i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.0000 | 0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0000 | − | 27.7128i | 0.570338 | − | 0.987855i | −0.426193 | − | 0.904632i | \(-0.640145\pi\) |
0.996531 | − | 0.0832226i | \(-0.0265213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.00000 | − | 10.3923i | −0.213066 | − | 0.369042i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00000 | − | 3.46410i | −0.0705785 | − | 0.122245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.0000 | + | 27.7128i | −0.562530 | + | 0.974331i | 0.434745 | + | 0.900554i | \(0.356839\pi\) |
−0.997275 | + | 0.0737769i | \(0.976495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | + | 20.7846i | −0.420342 | + | 0.728053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.0000 | − | 38.1051i | −0.767805 | − | 1.32988i | −0.938751 | − | 0.344597i | \(-0.888015\pi\) |
0.170945 | − | 0.985281i | \(-0.445318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.0000 | + | 41.5692i | −0.836587 | + | 1.44901i | 0.0561440 | + | 0.998423i | \(0.482119\pi\) |
−0.892731 | + | 0.450589i | \(0.851214\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0000 | 0.904109 | 0.452054 | − | 0.891990i | \(-0.350691\pi\) | ||||
0.452054 | + | 0.891990i | \(0.350691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0000 | + | 39.8372i | −0.798823 | + | 1.38360i | 0.121560 | + | 0.992584i | \(0.461210\pi\) |
−0.920383 | + | 0.391018i | \(0.872123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | − | 6.92820i | −0.138426 | − | 0.239760i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.0000 | 1.24286 | 0.621429 | − | 0.783470i | \(-0.286552\pi\) | ||||
0.621429 | + | 0.783470i | \(0.286552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | − | 15.5885i | −0.309609 | − | 0.536259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.0000 | + | 51.9615i | −1.02839 | + | 1.78122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.0000 | + | 25.9808i | −0.512390 | + | 0.887486i | 0.487507 | + | 0.873119i | \(0.337907\pi\) |
−0.999897 | + | 0.0143666i | \(0.995427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00000 | − | 3.46410i | −0.0682391 | − | 0.118194i | 0.829887 | − | 0.557931i | \(-0.188405\pi\) |
−0.898126 | + | 0.439738i | \(0.855071\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.0000 | + | 43.3013i | 0.851010 | + | 1.47399i | 0.880298 | + | 0.474421i | \(0.157343\pi\) |
−0.0292880 | + | 0.999571i | \(0.509324\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | + | 10.3923i | −0.204006 | + | 0.353349i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.00000 | + | 6.92820i | −0.135535 | + | 0.234753i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.00000 | + | 15.5885i | 0.303908 | + | 0.526385i | 0.977018 | − | 0.213158i | \(-0.0683750\pi\) |
−0.673109 | + | 0.739543i | \(0.735042\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.0000 | −1.81931 | −0.909653 | − | 0.415369i | \(-0.863653\pi\) | ||||
−0.909653 | + | 0.415369i | \(0.863653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.0000 | + | 17.3205i | 0.335767 | + | 0.581566i | 0.983632 | − | 0.180190i | \(-0.0576711\pi\) |
−0.647865 | + | 0.761755i | \(0.724338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000 | − | 13.8564i | 0.267710 | − | 0.463687i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | 0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | − | 62.3538i | −1.19933 | − | 2.07731i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.0000 | + | 24.2487i | 0.465376 | + | 0.806054i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.0000 | + | 27.7128i | −0.529523 | + | 0.917160i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | − | 27.7128i | −0.527791 | − | 0.914161i | −0.999475 | − | 0.0323936i | \(-0.989687\pi\) |
0.471684 | − | 0.881768i | \(-0.343646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.0000 | 0.921631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.0000 | + | 29.4449i | 0.557752 | + | 0.966055i | 0.997684 | + | 0.0680235i | \(0.0216693\pi\) |
−0.439932 | + | 0.898031i | \(0.644997\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | + | 20.7846i | −0.392442 | + | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.00000 | + | 5.19615i | −0.0977972 | + | 0.169390i | −0.910773 | − | 0.412908i | \(-0.864513\pi\) |
0.812975 | + | 0.582298i | \(0.197846\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | + | 10.3923i | 0.195387 | + | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.00000 | + | 12.1244i | 0.227469 | + | 0.393989i | 0.957057 | − | 0.289898i | \(-0.0936215\pi\) |
−0.729588 | + | 0.683887i | \(0.760288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.00000 | − | 3.46410i | 0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.0000 | − | 45.0333i | 0.841340 | − | 1.45724i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52.0000 | 1.67394 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0000 | − | 41.5692i | −0.770197 | − | 1.33402i | −0.937455 | − | 0.348107i | \(-0.886825\pi\) |
0.167258 | − | 0.985913i | \(-0.446509\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.0000 | − | 45.0333i | 0.831814 | − | 1.44074i | −0.0647848 | − | 0.997899i | \(-0.520636\pi\) |
0.896599 | − | 0.442844i | \(-0.146031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.0000 | + | 20.7846i | −0.382741 | + | 0.662926i | −0.991453 | − | 0.130465i | \(-0.958353\pi\) |
0.608712 | + | 0.793391i | \(0.291686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | − | 20.7846i | −0.382352 | − | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | + | 20.7846i | 0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | + | 6.92820i | −0.127064 | + | 0.220082i | −0.922538 | − | 0.385906i | \(-0.873889\pi\) |
0.795474 | + | 0.605988i | \(0.207222\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0000 | − | 19.0526i | 0.348373 | − | 0.603401i | −0.637587 | − | 0.770378i | \(-0.720067\pi\) |
0.985961 | + | 0.166978i | \(0.0534008\pi\) | |||||||
\(998\) | 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 | 3528.2.s.u.361.1 | 2 | ||
3.2 | odd | 2 | 3528.2.s.i.361.1 | 2 | |||
7.2 | even | 3 | inner | 3528.2.s.u.3313.1 | 2 | ||
7.3 | odd | 6 | 504.2.a.f.1.1 | yes | 1 | ||
7.4 | even | 3 | 3528.2.a.e.1.1 | 1 | |||
7.5 | odd | 6 | 3528.2.s.f.3313.1 | 2 | |||
7.6 | odd | 2 | 3528.2.s.f.361.1 | 2 | |||
21.2 | odd | 6 | 3528.2.s.i.3313.1 | 2 | |||
21.5 | even | 6 | 3528.2.s.x.3313.1 | 2 | |||
21.11 | odd | 6 | 3528.2.a.u.1.1 | 1 | |||
21.17 | even | 6 | 504.2.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 3528.2.s.x.361.1 | 2 | |||
28.3 | even | 6 | 1008.2.a.k.1.1 | 1 | |||
28.11 | odd | 6 | 7056.2.a.l.1.1 | 1 | |||
56.3 | even | 6 | 4032.2.a.l.1.1 | 1 | |||
56.45 | odd | 6 | 4032.2.a.g.1.1 | 1 | |||
84.11 | even | 6 | 7056.2.a.bt.1.1 | 1 | |||
84.59 | odd | 6 | 1008.2.a.f.1.1 | 1 | |||
168.59 | odd | 6 | 4032.2.a.bg.1.1 | 1 | |||
168.101 | even | 6 | 4032.2.a.bf.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.a.a.1.1 | ✓ | 1 | 21.17 | even | 6 | ||
504.2.a.f.1.1 | yes | 1 | 7.3 | odd | 6 | ||
1008.2.a.f.1.1 | 1 | 84.59 | odd | 6 | |||
1008.2.a.k.1.1 | 1 | 28.3 | even | 6 | |||
3528.2.a.e.1.1 | 1 | 7.4 | even | 3 | |||
3528.2.a.u.1.1 | 1 | 21.11 | odd | 6 | |||
3528.2.s.f.361.1 | 2 | 7.6 | odd | 2 | |||
3528.2.s.f.3313.1 | 2 | 7.5 | odd | 6 | |||
3528.2.s.i.361.1 | 2 | 3.2 | odd | 2 | |||
3528.2.s.i.3313.1 | 2 | 21.2 | odd | 6 | |||
3528.2.s.u.361.1 | 2 | 1.1 | even | 1 | trivial | ||
3528.2.s.u.3313.1 | 2 | 7.2 | even | 3 | inner | ||
3528.2.s.x.361.1 | 2 | 21.20 | even | 2 | |||
3528.2.s.x.3313.1 | 2 | 21.5 | even | 6 | |||
4032.2.a.g.1.1 | 1 | 56.45 | odd | 6 | |||
4032.2.a.l.1.1 | 1 | 56.3 | even | 6 | |||
4032.2.a.bf.1.1 | 1 | 168.101 | even | 6 | |||
4032.2.a.bg.1.1 | 1 | 168.59 | odd | 6 | |||
7056.2.a.l.1.1 | 1 | 28.11 | odd | 6 | |||
7056.2.a.bt.1.1 | 1 | 84.11 | even | 6 |