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.s.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 | ||||||||
\(11\) | −3.00000 | + | 5.19615i | −0.904534 | + | 1.56670i | −0.0829925 | + | 0.996550i | \(0.526448\pi\) |
−0.821541 | + | 0.570149i | \(0.806886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | + | 3.46410i | 0.458831 | + | 0.794719i | 0.998899 | − | 0.0469020i | \(-0.0149348\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | − | 1.73205i | −0.208514 | − | 0.361158i | 0.742732 | − | 0.669588i | \(-0.233529\pi\) |
−0.951247 | + | 0.308431i | \(0.900196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 5.19615i | 0.493197 | + | 0.854242i | 0.999969 | − | 0.00783774i | \(-0.00249486\pi\) |
−0.506772 | + | 0.862080i | \(0.669162\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 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 | 0.682489 | − | 0.730896i | \(-0.260898\pi\) |
−0.974219 | + | 0.225605i | \(0.927564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | − | 3.46410i | 0.274721 | − | 0.475831i | −0.695344 | − | 0.718677i | \(-0.744748\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | −1.61808 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | − | 1.73205i | −0.128037 | − | 0.221766i | 0.794879 | − | 0.606768i | \(-0.207534\pi\) |
−0.922916 | + | 0.385002i | \(0.874201\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | + | 10.3923i | −0.733017 | + | 1.26962i | 0.222571 | + | 0.974916i | \(0.428555\pi\) |
−0.955588 | + | 0.294706i | \(0.904778\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 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 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.00000 | − | 12.1244i | −0.741999 | − | 1.28518i | −0.951584 | − | 0.307389i | \(-0.900545\pi\) |
0.209585 | − | 0.977790i | \(-0.432789\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | + | 15.5885i | −0.895533 | + | 1.55111i | −0.0623905 | + | 0.998052i | \(0.519872\pi\) |
−0.833143 | + | 0.553058i | \(0.813461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | − | 10.3923i | −0.591198 | − | 1.02398i | −0.994071 | − | 0.108729i | \(-0.965322\pi\) |
0.402874 | − | 0.915255i | \(-0.368011\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | + | 15.5885i | 0.870063 | + | 1.50699i | 0.861931 | + | 0.507026i | \(0.169255\pi\) |
0.00813215 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | − | 12.1244i | 0.670478 | − | 1.16130i | −0.307290 | − | 0.951616i | \(-0.599422\pi\) |
0.977769 | − | 0.209687i | \(-0.0672444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | − | 3.46410i | 0.186501 | − | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 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 | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 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 | ||||||||
\(137\) | −10.0000 | + | 17.3205i | −0.854358 | + | 1.47979i | 0.0228820 | + | 0.999738i | \(0.492716\pi\) |
−0.877240 | + | 0.480053i | \(0.840618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.0000 | + | 31.1769i | −1.50524 | + | 2.60714i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | + | 13.8564i | 0.664364 | + | 1.15071i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00000 | − | 3.46410i | −0.163846 | − | 0.283790i | 0.772399 | − | 0.635138i | \(-0.219057\pi\) |
−0.936245 | + | 0.351348i | \(0.885723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | + | 15.5885i | −0.718278 | + | 1.24409i | 0.243403 | + | 0.969925i | \(0.421736\pi\) |
−0.961681 | + | 0.274169i | \(0.911597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.00000 | − | 8.66025i | −0.380143 | − | 0.658427i | 0.610939 | − | 0.791677i | \(-0.290792\pi\) |
−0.991082 | + | 0.133250i | \(0.957459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.00000 | + | 1.73205i | −0.0747435 | + | 0.129460i | −0.900975 | − | 0.433872i | \(-0.857147\pi\) |
0.826231 | + | 0.563331i | \(0.190480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | + | 10.3923i | −0.441129 | + | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | − | 10.3923i | −0.438763 | − | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00000 | + | 1.73205i | 0.0723575 | + | 0.125327i | 0.899934 | − | 0.436026i | \(-0.143614\pi\) |
−0.827577 | + | 0.561353i | \(0.810281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00000 | + | 5.19615i | −0.215945 | + | 0.374027i | −0.953564 | − | 0.301189i | \(-0.902616\pi\) |
0.737620 | + | 0.675216i | \(0.235950\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0000 | − | 17.3205i | −0.698430 | − | 1.20972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.0000 | −1.92760 | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | 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 | ||||||||
\(227\) | 10.0000 | − | 17.3205i | 0.663723 | − | 1.14960i | −0.315906 | − | 0.948790i | \(-0.602309\pi\) |
0.979630 | − | 0.200812i | \(-0.0643581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.73205i | 0.0660819 | + | 0.114457i | 0.897173 | − | 0.441679i | \(-0.145617\pi\) |
−0.831092 | + | 0.556136i | \(0.812283\pi\) | |||||||
\(230\) | 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 | ||||||||
\(239\) | 26.0000 | 1.68180 | 0.840900 | − | 0.541190i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541190i | \(0.182026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | − | 19.0526i | 0.708572 | − | 1.22728i | −0.256814 | − | 0.966461i | \(-0.582673\pi\) |
0.965387 | − | 0.260822i | \(-0.0839937\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 20.7846i | 0.763542 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.00000 | + | 15.5885i | 0.561405 | + | 0.972381i | 0.997374 | + | 0.0724199i | \(0.0230722\pi\) |
−0.435970 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000 | − | 5.19615i | 0.184988 | − | 0.320408i | −0.758585 | − | 0.651575i | \(-0.774109\pi\) |
0.943572 | + | 0.331166i | \(0.107442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00000 | 0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00000 | + | 5.19615i | −0.182913 | + | 0.316815i | −0.942871 | − | 0.333157i | \(-0.891886\pi\) |
0.759958 | + | 0.649972i | \(0.225219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00000 | − | 3.46410i | −0.121491 | − | 0.210429i | 0.798865 | − | 0.601511i | \(-0.205434\pi\) |
−0.920356 | + | 0.391082i | \(0.872101\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 5.19615i | 0.180907 | + | 0.313340i | ||||
\(276\) | 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 | ||||||||
\(283\) | 10.0000 | − | 17.3205i | 0.594438 | − | 1.02960i | −0.399188 | − | 0.916869i | \(-0.630708\pi\) |
0.993626 | − | 0.112728i | \(-0.0359589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 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 | ||||||||
\(305\) | 2.00000 | − | 3.46410i | 0.114520 | − | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | − | 10.3923i | 0.340229 | − | 0.589294i | −0.644246 | − | 0.764818i | \(-0.722829\pi\) |
0.984475 | + | 0.175525i | \(0.0561621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.00000 | + | 1.73205i | 0.0565233 | + | 0.0979013i | 0.892903 | − | 0.450250i | \(-0.148665\pi\) |
−0.836379 | + | 0.548151i | \(0.815332\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.0000 | + | 41.5692i | −1.34374 | + | 2.32743i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 5.19615i | 0.166410 | − | 0.288231i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | + | 24.2487i | 0.769510 | + | 1.33283i | 0.937829 | + | 0.347097i | \(0.112833\pi\) |
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.0000 | −1.31126 | ||||||||
\(336\) | 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 | ||||||||
\(341\) | 12.0000 | + | 20.7846i | 0.649836 | + | 1.12555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | + | 15.5885i | −0.483145 | + | 0.836832i | −0.999813 | − | 0.0193540i | \(-0.993839\pi\) |
0.516667 | + | 0.856186i | \(0.327172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | + | 15.5885i | −0.479022 | + | 0.829690i | −0.999711 | − | 0.0240566i | \(-0.992342\pi\) |
0.520689 | + | 0.853746i | \(0.325675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0000 | − | 25.9808i | −0.791670 | − | 1.37121i | −0.924932 | − | 0.380131i | \(-0.875879\pi\) |
0.133263 | − | 0.991081i | \(-0.457455\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | −8.00000 | + | 13.8564i | −0.417597 | + | 0.723299i | −0.995697 | − | 0.0926670i | \(-0.970461\pi\) |
0.578101 | + | 0.815966i | \(0.303794\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 48.0000 | 2.47213 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 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 | ||||||||
\(389\) | −8.00000 | + | 13.8564i | −0.405616 | + | 0.702548i | −0.994393 | − | 0.105748i | \(-0.966276\pi\) |
0.588777 | + | 0.808296i | \(0.299610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | + | 13.8564i | −0.402524 | + | 0.697191i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00000 | − | 1.73205i | −0.0501886 | − | 0.0869291i | 0.839840 | − | 0.542834i | \(-0.182649\pi\) |
−0.890028 | + | 0.455905i | \(0.849316\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 12.0000 | − | 20.7846i | 0.597763 | − | 1.03536i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.0000 | −1.78445 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.00000 | + | 15.5885i | −0.445021 | + | 0.770800i | −0.998054 | − | 0.0623602i | \(-0.980137\pi\) |
0.553032 | + | 0.833160i | \(0.313471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.0000 | 1.36789 | 0.683945 | − | 0.729534i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729534i | \(0.260263\pi\) | |||||||
\(420\) | 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 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.00000 | − | 15.5885i | 0.433515 | − | 0.750870i | −0.563658 | − | 0.826008i | \(-0.690607\pi\) |
0.997173 | + | 0.0751385i | \(0.0239399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.0000 | 1.82616 | 0.913082 | − | 0.407777i | \(-0.133696\pi\) | ||||
0.913082 | + | 0.407777i | \(0.133696\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | − | 6.92820i | 0.191346 | − | 0.331421i | ||||
\(438\) | 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 | ||||||||
\(443\) | 11.0000 | + | 19.0526i | 0.522626 | + | 0.905214i | 0.999653 | + | 0.0263261i | \(0.00838082\pi\) |
−0.477028 | + | 0.878888i | \(0.658286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0000 | − | 24.2487i | 0.663664 | − | 1.14950i | ||||
\(446\) | 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 | ||||||||
\(451\) | 30.0000 | − | 51.9615i | 1.41264 | − | 2.44677i | ||||
\(452\) | 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 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0000 | − | 20.7846i | 0.551761 | − | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.00000 | − | 3.46410i | 0.0913823 | − | 0.158279i | −0.816711 | − | 0.577047i | \(-0.804205\pi\) |
0.908093 | + | 0.418769i | \(0.137538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | + | 31.1769i | 0.820729 | + | 1.42154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | + | 3.46410i | 0.0908153 | + | 0.157297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.0000 | + | 34.6410i | −0.906287 | + | 1.56973i | −0.0871056 | + | 0.996199i | \(0.527762\pi\) |
−0.819181 | + | 0.573535i | \(0.805572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.0000 | 0.812329 | 0.406164 | − | 0.913800i | \(-0.366866\pi\) | ||||
0.406164 | + | 0.913800i | \(0.366866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | + | 13.8564i | −0.360302 | + | 0.624061i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) |
0.361478 | − | 0.932381i | \(-0.382272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.0000 | 1.42681 | 0.713405 | − | 0.700752i | \(-0.247152\pi\) | ||||
0.713405 | + | 0.700752i | \(0.247152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.0000 | − | 20.7846i | 0.528783 | − | 0.915879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000 | 1.05552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0000 | − | 25.9808i | 0.657162 | − | 1.13824i | −0.324185 | − | 0.945994i | \(-0.605090\pi\) |
0.981347 | − | 0.192244i | \(-0.0615766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | − | 13.8564i | −0.349816 | − | 0.605898i | 0.636401 | − | 0.771358i | \(-0.280422\pi\) |
−0.986216 | + | 0.165460i | \(0.947089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000 | + | 6.92820i | 0.174243 | + | 0.301797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.0000 | −2.59889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 31.1769i | −0.778208 | + | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0000 | − | 19.0526i | −0.472927 | − | 0.819133i | 0.526593 | − | 0.850118i | \(-0.323469\pi\) |
−0.999520 | + | 0.0309841i | \(0.990136\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.0000 | 1.19939 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0000 | + | 27.7128i | 0.681623 | + | 1.18061i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0000 | − | 17.3205i | 0.423714 | − | 0.733893i | −0.572586 | − | 0.819845i | \(-0.694060\pi\) |
0.996299 | + | 0.0859514i | \(0.0273930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.0000 | − | 24.2487i | 0.590030 | − | 1.02196i | −0.404198 | − | 0.914671i | \(-0.632449\pi\) |
0.994228 | − | 0.107290i | \(-0.0342173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | − | 10.3923i | −0.251533 | − | 0.435668i | 0.712415 | − | 0.701758i | \(-0.247601\pi\) |
−0.963948 | + | 0.266090i | \(0.914268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0000 | − | 24.2487i | 0.585882 | − | 1.01478i | −0.408883 | − | 0.912587i | \(-0.634082\pi\) |
0.994765 | − | 0.102190i | \(-0.0325850\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0000 | + | 25.9808i | −0.624458 | + | 1.08159i | 0.364187 | + | 0.931326i | \(0.381347\pi\) |
−0.988645 | + | 0.150268i | \(0.951987\pi\) | |||||||
\(578\) | 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 | ||||||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.00000 | − | 15.5885i | −0.369586 | − | 0.640141i | 0.619915 | − | 0.784669i | \(-0.287167\pi\) |
−0.989501 | + | 0.144528i | \(0.953834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.0000 | − | 22.5167i | 0.531166 | − | 0.920006i | −0.468173 | − | 0.883637i | \(-0.655088\pi\) |
0.999338 | − | 0.0363689i | \(-0.0115791\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.0000 | − | 43.3013i | 1.01639 | − | 1.76045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | − | 20.7846i | −0.485468 | − | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0000 | + | 19.0526i | −0.444286 | + | 0.769526i | −0.998002 | − | 0.0631797i | \(-0.979876\pi\) |
0.553716 | + | 0.832705i | \(0.313209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000 | 0.483102 | 0.241551 | − | 0.970388i | \(-0.422344\pi\) | ||||
0.241551 | + | 0.970388i | \(0.422344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | − | 20.7846i | 0.482321 | − | 0.835404i | −0.517473 | − | 0.855699i | \(-0.673127\pi\) |
0.999794 | + | 0.0202954i | \(0.00646066\pi\) | |||||||
\(620\) | 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 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 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 | ||||||||
\(641\) | 10.0000 | − | 17.3205i | 0.394976 | − | 0.684119i | −0.598122 | − | 0.801405i | \(-0.704086\pi\) |
0.993098 | + | 0.117286i | \(0.0374195\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.0000 | −1.10421 | −0.552106 | − | 0.833774i | \(-0.686176\pi\) | ||||
−0.552106 | + | 0.833774i | \(0.686176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0000 | − | 31.1769i | 0.707653 | − | 1.22569i | −0.258073 | − | 0.966126i | \(-0.583087\pi\) |
0.965726 | − | 0.259565i | \(-0.0835793\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | − | 62.3538i | −1.41312 | − | 2.44760i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.00000 | − | 6.92820i | −0.156532 | − | 0.271122i | 0.777084 | − | 0.629397i | \(-0.216698\pi\) |
−0.933616 | + | 0.358276i | \(0.883365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | + | 13.8564i | −0.312586 | + | 0.541415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.0000 | −1.32445 | −0.662226 | − | 0.749304i | \(-0.730388\pi\) | ||||
−0.662226 | + | 0.749304i | \(0.730388\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | − | 12.1244i | 0.272268 | − | 0.471583i | −0.697174 | − | 0.716902i | \(-0.745559\pi\) |
0.969442 | + | 0.245319i | \(0.0788928\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | − | 13.8564i | −0.309761 | − | 0.536522i | ||||
\(668\) | 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 | ||||||||
\(677\) | −9.00000 | − | 15.5885i | −0.345898 | − | 0.599113i | 0.639618 | − | 0.768693i | \(-0.279092\pi\) |
−0.985517 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.00000 | − | 5.19615i | 0.114792 | − | 0.198825i | −0.802905 | − | 0.596107i | \(-0.796713\pi\) |
0.917697 | + | 0.397282i | \(0.130047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.0000 | −1.52832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0000 | − | 17.3205i | 0.378777 | − | 0.656061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.0000 | 1.51078 | 0.755390 | − | 0.655276i | \(-0.227448\pi\) | ||||
0.755390 | + | 0.655276i | \(0.227448\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | + | 20.7846i | −0.452589 | + | 0.783906i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.00000 | − | 8.66025i | −0.187779 | − | 0.325243i | 0.756730 | − | 0.653727i | \(-0.226796\pi\) |
−0.944509 | + | 0.328484i | \(0.893462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −72.0000 | −2.69265 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | + | 41.5692i | 0.895049 | + | 1.55027i | 0.833744 | + | 0.552151i | \(0.186193\pi\) |
0.0613050 | + | 0.998119i | \(0.480474\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | − | 6.92820i | 0.148556 | − | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.0000 | −0.741759 | −0.370879 | − | 0.928681i | \(-0.620944\pi\) | ||||
−0.370879 | + | 0.928681i | \(0.620944\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | − | 6.92820i | 0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0000 | + | 29.4449i | 0.627909 | + | 1.08757i | 0.987971 | + | 0.154642i | \(0.0494225\pi\) |
−0.360061 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.0000 | − | 62.3538i | −1.32608 | − | 2.29683i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.00000 | + | 3.46410i | −0.0735712 | + | 0.127429i | −0.900464 | − | 0.434930i | \(-0.856773\pi\) |
0.826893 | + | 0.562360i | \(0.190106\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.0000 | −0.366864 | −0.183432 | − | 0.983032i | \(-0.558721\pi\) | ||||
−0.183432 | + | 0.983032i | \(0.558721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | − | 6.92820i | 0.146549 | − | 0.253830i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | − | 6.92820i | −0.145962 | − | 0.252814i | 0.783769 | − | 0.621052i | \(-0.213294\pi\) |
−0.929731 | + | 0.368238i | \(0.879961\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | + | 36.3731i | 0.761249 | + | 1.31852i | 0.942207 | + | 0.335032i | \(0.108747\pi\) |
−0.180957 | + | 0.983491i | \(0.557920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.0000 | + | 62.3538i | −1.29988 | + | 2.25147i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0000 | − | 19.0526i | 0.395643 | − | 0.685273i | −0.597540 | − | 0.801839i | \(-0.703855\pi\) |
0.993183 | + | 0.116566i | \(0.0371886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | − | 3.46410i | −0.0718421 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.0000 | − | 34.6410i | −0.716574 | − | 1.24114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | + | 31.1769i | −0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.00000 | − | 13.8564i | 0.285169 | − | 0.493928i | −0.687481 | − | 0.726202i | \(-0.741284\pi\) |
0.972650 | + | 0.232275i | \(0.0746169\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.00000 | − | 10.3923i | −0.211735 | − | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.0000 | 1.68551 | 0.842754 | − | 0.538299i | \(-0.180933\pi\) | ||||
0.842754 | + | 0.538299i | \(0.180933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | − | 6.92820i | 0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | − | 13.8564i | −0.279885 | − | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | + | 10.3923i | 0.209401 | + | 0.362694i | 0.951526 | − | 0.307568i | \(-0.0995151\pi\) |
−0.742125 | + | 0.670262i | \(0.766182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.0000 | −0.625921 | −0.312961 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312961 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0000 | − | 22.5167i | 0.451509 | − | 0.782036i | −0.546971 | − | 0.837151i | \(-0.684219\pi\) |
0.998480 | + | 0.0551154i | \(0.0175527\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | − | 20.7846i | −0.415277 | − | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.0000 | + | 39.8372i | 0.791224 | + | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | − | 10.3923i | 0.205677 | − | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000 | 0.0684787 | 0.0342393 | − | 0.999414i | \(-0.489099\pi\) | ||||
0.0342393 | + | 0.999414i | \(0.489099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | + | 3.46410i | 0.0682391 | + | 0.118194i | 0.898126 | − | 0.439738i | \(-0.144929\pi\) |
−0.829887 | + | 0.557931i | \(0.811595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.0000 | − | 22.5167i | −0.442525 | − | 0.766476i | 0.555351 | − | 0.831616i | \(-0.312584\pi\) |
−0.997876 | + | 0.0651400i | \(0.979251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0000 | − | 17.3205i | 0.340010 | − | 0.588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.0000 | −1.62829 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.0000 | + | 62.3538i | −1.21981 | + | 2.11278i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0000 | + | 29.4449i | 0.574049 | + | 0.994282i | 0.996144 | + | 0.0877308i | \(0.0279615\pi\) |
−0.422095 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 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 | ||||||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | −4.00000 | −0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.0000 | − | 27.7128i | 0.533630 | − | 0.924274i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | + | 6.92820i | 0.133259 | + | 0.230812i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.0000 | + | 38.1051i | 0.731305 | + | 1.26666i | ||||
\(906\) | 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 | ||||||||
\(911\) | −2.00000 | −0.0662630 | −0.0331315 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331315 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 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 | \(0.0103130\pi\) |
−0.471684 | + | 0.881768i | \(0.656354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0000 | 1.18495 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.00000 | + | 8.66025i | 0.164045 | + | 0.284134i | 0.936316 | − | 0.351160i | \(-0.114213\pi\) |
−0.772271 | + | 0.635293i | \(0.780879\pi\) | |||||||
\(930\) | 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 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 10.0000 | + | 17.3205i | 0.325645 | + | 0.564033i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.0000 | − | 19.0526i | −0.357452 | − | 0.619125i | 0.630082 | − | 0.776528i | \(-0.283021\pi\) |
−0.987534 | + | 0.157403i | \(0.949688\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | + | 10.3923i | −0.194768 | + | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0000 | 1.29573 | 0.647864 | − | 0.761756i | \(-0.275663\pi\) | ||||
0.647864 | + | 0.761756i | \(0.275663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.00000 | + | 3.46410i | −0.0647185 | + | 0.112096i | ||||
\(956\) | 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 | ||||||||
\(965\) | −12.0000 | −0.386294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.00000 | + | 13.8564i | 0.256732 | + | 0.444673i | 0.965365 | − | 0.260905i | \(-0.0840208\pi\) |
−0.708632 | + | 0.705578i | \(0.750687\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000 | − | 31.1769i | 0.575871 | − | 0.997438i | −0.420075 | − | 0.907489i | \(-0.637996\pi\) |
0.995946 | − | 0.0899487i | \(-0.0286703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 84.0000 | 2.68465 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0000 | − | 20.7846i | 0.382741 | − | 0.662926i | −0.608712 | − | 0.793391i | \(-0.708314\pi\) |
0.991453 | + | 0.130465i | \(0.0416470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | + | 20.7846i | 0.382352 | + | 0.662253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | + | 6.92820i | 0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.0000 | − | 20.7846i | 0.381193 | − | 0.660245i | −0.610040 | − | 0.792370i | \(-0.708847\pi\) |
0.991233 | + | 0.132125i | \(0.0421802\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.0000 | −1.01447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0000 | − | 39.8372i | 0.728417 | − | 1.26166i | −0.229135 | − | 0.973395i | \(-0.573590\pi\) |
0.957552 | − | 0.288261i | \(-0.0930771\pi\) | |||||||
\(998\) | 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.s.361.1 | 2 | ||
3.2 | odd | 2 | 3528.2.s.k.361.1 | 2 | |||
7.2 | even | 3 | inner | 3528.2.s.s.3313.1 | 2 | ||
7.3 | odd | 6 | 504.2.a.g.1.1 | yes | 1 | ||
7.4 | even | 3 | 3528.2.a.g.1.1 | 1 | |||
7.5 | odd | 6 | 3528.2.s.c.3313.1 | 2 | |||
7.6 | odd | 2 | 3528.2.s.c.361.1 | 2 | |||
21.2 | odd | 6 | 3528.2.s.k.3313.1 | 2 | |||
21.5 | even | 6 | 3528.2.s.z.3313.1 | 2 | |||
21.11 | odd | 6 | 3528.2.a.t.1.1 | 1 | |||
21.17 | even | 6 | 504.2.a.d.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 3528.2.s.z.361.1 | 2 | |||
28.3 | even | 6 | 1008.2.a.i.1.1 | 1 | |||
28.11 | odd | 6 | 7056.2.a.j.1.1 | 1 | |||
56.3 | even | 6 | 4032.2.a.i.1.1 | 1 | |||
56.45 | odd | 6 | 4032.2.a.j.1.1 | 1 | |||
84.11 | even | 6 | 7056.2.a.bv.1.1 | 1 | |||
84.59 | odd | 6 | 1008.2.a.c.1.1 | 1 | |||
168.59 | odd | 6 | 4032.2.a.ba.1.1 | 1 | |||
168.101 | even | 6 | 4032.2.a.bl.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.a.d.1.1 | ✓ | 1 | 21.17 | even | 6 | ||
504.2.a.g.1.1 | yes | 1 | 7.3 | odd | 6 | ||
1008.2.a.c.1.1 | 1 | 84.59 | odd | 6 | |||
1008.2.a.i.1.1 | 1 | 28.3 | even | 6 | |||
3528.2.a.g.1.1 | 1 | 7.4 | even | 3 | |||
3528.2.a.t.1.1 | 1 | 21.11 | odd | 6 | |||
3528.2.s.c.361.1 | 2 | 7.6 | odd | 2 | |||
3528.2.s.c.3313.1 | 2 | 7.5 | odd | 6 | |||
3528.2.s.k.361.1 | 2 | 3.2 | odd | 2 | |||
3528.2.s.k.3313.1 | 2 | 21.2 | odd | 6 | |||
3528.2.s.s.361.1 | 2 | 1.1 | even | 1 | trivial | ||
3528.2.s.s.3313.1 | 2 | 7.2 | even | 3 | inner | ||
3528.2.s.z.361.1 | 2 | 21.20 | even | 2 | |||
3528.2.s.z.3313.1 | 2 | 21.5 | even | 6 | |||
4032.2.a.i.1.1 | 1 | 56.3 | even | 6 | |||
4032.2.a.j.1.1 | 1 | 56.45 | odd | 6 | |||
4032.2.a.ba.1.1 | 1 | 168.59 | odd | 6 | |||
4032.2.a.bl.1.1 | 1 | 168.101 | even | 6 | |||
7056.2.a.j.1.1 | 1 | 28.11 | odd | 6 | |||
7056.2.a.bv.1.1 | 1 | 84.11 | even | 6 |