Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(641,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.641");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.d (of order \(2\), degree \(1\), 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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.641 |
Dual form | 1280.2.d.m.641.3 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.23607i | − 0.713644i | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
0.934172 | − | 0.356822i | \(-0.116140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.47214 | 0.490712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.00000i | − 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214i | 1.24035i | 0.784465 | + | 0.620174i | \(0.212938\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.23607 | −0.319151 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.47214i | 1.02598i | 0.858395 | + | 0.512989i | \(0.171462\pi\) | ||||
−0.858395 | + | 0.512989i | \(0.828538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 4.00000i | − 0.872872i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.76393 | 0.993348 | 0.496674 | − | 0.867937i | \(-0.334554\pi\) | ||||
0.496674 | + | 0.867937i | \(0.334554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.52786i | − 1.06384i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47214 | 1.16243 | 0.581215 | − | 0.813750i | \(-0.302578\pi\) | ||||
0.581215 | + | 0.813750i | \(0.302578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.47214 | −0.430344 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.23607i | − 0.546995i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.94427i | 1.14163i | 0.821078 | + | 0.570816i | \(0.193373\pi\) | ||||
−0.821078 | + | 0.570816i | \(0.806627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.52786 | 0.885167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4721 | −1.94782 | −0.973910 | − | 0.226934i | \(-0.927130\pi\) | ||||
−0.973910 | + | 0.226934i | \(0.927130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.70820i | − 1.17549i | −0.809046 | − | 0.587745i | \(-0.800016\pi\) | ||||
0.809046 | − | 0.587745i | \(-0.199984\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.47214i | − 0.219453i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.23607 | −1.05549 | −0.527744 | − | 0.849403i | \(-0.676962\pi\) | ||||
−0.527744 | + | 0.849403i | \(0.676962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 5.52786i | − 0.774056i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.472136i | 0.0648529i | 0.999474 | + | 0.0324264i | \(0.0103235\pi\) | ||||
−0.999474 | + | 0.0324264i | \(0.989677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.52786 | 0.732183 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.47214i | − 1.10298i | −0.834182 | − | 0.551489i | \(-0.814060\pi\) | ||||
0.834182 | − | 0.551489i | \(-0.185940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000i | 0.768221i | 0.923287 | + | 0.384111i | \(0.125492\pi\) | ||||
−0.923287 | + | 0.384111i | \(0.874508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.76393 | 0.600199 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.47214 | 0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.70820i | − 0.941707i | −0.882211 | − | 0.470853i | \(-0.843946\pi\) | ||||
0.882211 | − | 0.470853i | \(-0.156054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 5.88854i | − 0.708897i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.47214 | 0.293389 | 0.146694 | − | 0.989182i | \(-0.453137\pi\) | ||||
0.146694 | + | 0.989182i | \(0.453137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.47214 | −0.523424 | −0.261712 | − | 0.965146i | \(-0.584287\pi\) | ||||
−0.261712 | + | 0.965146i | \(0.584287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.23607i | 0.142729i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 6.47214i | − 0.737568i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9443 | 1.45634 | 0.728172 | − | 0.685394i | \(-0.240370\pi\) | ||||
0.728172 | + | 0.685394i | \(0.240370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.70820i | 0.407028i | 0.979072 | + | 0.203514i | \(0.0652363\pi\) | ||||
−0.979072 | + | 0.203514i | \(0.934764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.47214i | − 0.485071i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.47214 | 0.265041 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.9443 | 1.58409 | 0.792045 | − | 0.610463i | \(-0.209017\pi\) | ||||
0.792045 | + | 0.610463i | \(0.209017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4721i | 1.51709i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 8.00000i | − 0.829561i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.47214 | 0.458831 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4721 | −1.67249 | −0.836246 | − | 0.548354i | \(-0.815254\pi\) | ||||
−0.836246 | + | 0.548354i | \(0.815254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 2.94427i | − 0.295910i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.0000i | − 0.995037i | −0.867453 | − | 0.497519i | \(-0.834245\pi\) | ||||
0.867453 | − | 0.497519i | \(-0.165755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.23607 | −0.318859 | −0.159430 | − | 0.987209i | \(-0.550966\pi\) | ||||
−0.159430 | + | 0.987209i | \(0.550966\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 17.2361i | − 1.66627i | −0.553067 | − | 0.833137i | \(-0.686543\pi\) | ||||
0.553067 | − | 0.833137i | \(-0.313457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 14.9443i | − 1.43140i | −0.698407 | − | 0.715701i | \(-0.746107\pi\) | ||||
0.698407 | − | 0.715701i | \(-0.253893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.58359 | 0.814719 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.94427 | −0.276974 | −0.138487 | − | 0.990364i | \(-0.544224\pi\) | ||||
−0.138487 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.76393i | − 0.444239i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.58359i | 0.608653i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.4721 | 1.32666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.4164i | 1.39005i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.1803 | −1.79072 | −0.895358 | − | 0.445348i | \(-0.853080\pi\) | ||||
−0.895358 | + | 0.445348i | \(0.853080\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.52786 | −0.838882 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 14.9443i | − 1.30569i | −0.757493 | − | 0.652844i | \(-0.773576\pi\) | ||||
0.757493 | − | 0.652844i | \(-0.226424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4721i | 1.25489i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.52786 | −0.475763 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.4721i | 1.73642i | 0.496194 | + | 0.868212i | \(0.334731\pi\) | ||||
−0.496194 | + | 0.868212i | \(0.665269\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.94427i | 0.753244i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.94427 | 0.747958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 4.29180i | − 0.353981i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.94427i | 0.568897i | 0.958691 | + | 0.284448i | \(0.0918105\pi\) | ||||
−0.958691 | + | 0.284448i | \(0.908190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.4164 | −1.90560 | −0.952800 | − | 0.303598i | \(-0.901812\pi\) | ||||
−0.952800 | + | 0.303598i | \(0.901812\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.58359 | 0.532252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.47214i | − 0.519854i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.05573i | − 0.403491i | −0.979438 | − | 0.201746i | \(-0.935339\pi\) | ||||
0.979438 | − | 0.201746i | \(-0.0646614\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.583592 | 0.0462819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.4164 | 1.21498 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7082i | 0.917057i | 0.888680 | + | 0.458529i | \(0.151623\pi\) | ||||
−0.888680 | + | 0.458529i | \(0.848377\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.47214i | 0.192456i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.6525 | −1.13384 | −0.566921 | − | 0.823772i | \(-0.691866\pi\) | ||||
−0.566921 | + | 0.823772i | \(0.691866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.58359i | 0.503460i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9443i | 0.832078i | 0.909347 | + | 0.416039i | \(0.136582\pi\) | ||||
−0.909347 | + | 0.416039i | \(0.863418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.23607 | −0.244624 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.4721 | −0.787134 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.4721i | 1.53016i | 0.643936 | + | 0.765080i | \(0.277300\pi\) | ||||
−0.643936 | + | 0.765080i | \(0.722700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9443i | 0.813481i | 0.913544 | + | 0.406741i | \(0.133335\pi\) | ||||
−0.913544 | + | 0.406741i | \(0.866665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.41641 | 0.548237 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.94427 | 0.510553 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.94427i | − 0.654070i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 17.8885i | − 1.30120i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4164 | 0.826062 | 0.413031 | − | 0.910717i | \(-0.364470\pi\) | ||||
0.413031 | + | 0.910717i | \(0.364470\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5279 | −0.829794 | −0.414897 | − | 0.909868i | \(-0.636182\pi\) | ||||
−0.414897 | + | 0.909868i | \(0.636182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 5.52786i | − 0.395859i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.472136i | 0.0336383i | 0.999859 | + | 0.0168191i | \(0.00535395\pi\) | ||||
−0.999859 | + | 0.0168191i | \(0.994646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.944272 | 0.0669377 | 0.0334688 | − | 0.999440i | \(-0.489345\pi\) | ||||
0.0334688 | + | 0.999440i | \(0.489345\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.52786 | −0.672044 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.47214i | 0.454255i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.4721i | 0.871092i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.01316 | 0.487448 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.94427 | 0.618688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.05573i | 0.0726793i | 0.999339 | + | 0.0363397i | \(0.0115698\pi\) | ||||
−0.999339 | + | 0.0363397i | \(0.988430\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.05573i | − 0.209375i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.70820 | −0.525695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.9443 | 1.42179 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.52786i | 0.373538i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0000i | 1.34535i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.76393 | −0.586876 | −0.293438 | − | 0.955978i | \(-0.594799\pi\) | ||||
−0.293438 | + | 0.955978i | \(0.594799\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.47214 | −0.0981424 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.1803i | 0.675693i | 0.941201 | + | 0.337846i | \(0.109698\pi\) | ||||
−0.941201 | + | 0.337846i | \(0.890302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.94427i | 0.194563i | 0.995257 | + | 0.0972815i | \(0.0310147\pi\) | ||||
−0.995257 | + | 0.0972815i | \(0.968985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5279 | −1.01726 | −0.508632 | − | 0.860984i | \(-0.669849\pi\) | ||||
−0.508632 | + | 0.860984i | \(0.669849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.23607i | 0.472029i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 16.0000i | − 1.03931i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9443 | −0.837295 | −0.418648 | − | 0.908149i | \(-0.637496\pi\) | ||||
−0.418648 | + | 0.908149i | \(0.637496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.3607 | 1.69804 | 0.849020 | − | 0.528360i | \(-0.177193\pi\) | ||||
0.849020 | + | 0.528360i | \(0.177193\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 13.5967i | − 0.872232i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.47214i | − 0.221827i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.0000 | −1.27257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.58359 | 0.290473 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.00000i | − 0.126239i | −0.998006 | − | 0.0631194i | \(-0.979895\pi\) | ||||
0.998006 | − | 0.0631194i | \(-0.0201049\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.52786i | − 0.599012i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.52786 | −0.346168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.94427 | −0.183659 | −0.0918293 | − | 0.995775i | \(-0.529271\pi\) | ||||
−0.0918293 | + | 0.995775i | \(0.529271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.4721i | 1.39635i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.94427i | 0.182246i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.7082 | 1.09193 | 0.545967 | − | 0.837806i | \(-0.316162\pi\) | ||||
0.545967 | + | 0.837806i | \(0.316162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.472136 | 0.0290031 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 18.4721i | − 1.13048i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.8885i | 1.45651i | 0.685306 | + | 0.728255i | \(0.259668\pi\) | ||||
−0.685306 | + | 0.728255i | \(0.740332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.3607 | −1.47981 | −0.739903 | − | 0.672714i | \(-0.765129\pi\) | ||||
−0.739903 | + | 0.672714i | \(0.765129\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.8885 | 1.08266 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000i | 0.120605i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 10.9443i | − 0.657578i | −0.944403 | − | 0.328789i | \(-0.893360\pi\) | ||||
0.944403 | − | 0.328789i | \(-0.106640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.52786 | 0.570418 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.52786 | −0.210455 | −0.105227 | − | 0.994448i | \(-0.533557\pi\) | ||||
−0.105227 | + | 0.994448i | \(0.533557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.29180i | 0.492896i | 0.969156 | + | 0.246448i | \(0.0792635\pi\) | ||||
−0.969156 | + | 0.246448i | \(0.920737\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 5.52786i | − 0.327442i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.3607 | −2.38242 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.3607i | 1.19356i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 23.8885i | − 1.39558i | −0.716301 | − | 0.697792i | \(-0.754166\pi\) | ||||
0.716301 | − | 0.697792i | \(-0.245834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.47214 | −0.493267 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.0557 | −0.641518 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.3050i | 1.23210i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 24.9443i | − 1.43776i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.3607 | −0.710102 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.291796i | 0.0166537i | 0.999965 | + | 0.00832684i | \(0.00265055\pi\) | ||||
−0.999965 | + | 0.00832684i | \(0.997349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000i | 0.227552i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4164 | 0.874184 | 0.437092 | − | 0.899417i | \(-0.356008\pi\) | ||||
0.437092 | + | 0.899417i | \(0.356008\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.8328 | 1.62973 | 0.814864 | − | 0.579653i | \(-0.196812\pi\) | ||||
0.814864 | + | 0.579653i | \(0.196812\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 4.76393i | − 0.268417i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.4721i | 1.14983i | 0.818213 | + | 0.574915i | \(0.194965\pi\) | ||||
−0.818213 | + | 0.574915i | \(0.805035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.3050 | −1.18913 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.0000i | 1.11283i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.47214i | − 0.248069i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.4721 | −1.02151 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.4164 | −1.29099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8885i | 0.873313i | 0.899628 | + | 0.436657i | \(0.143838\pi\) | ||||
−0.899628 | + | 0.436657i | \(0.856162\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2229i | 0.560212i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.70820 | −0.421144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.05573 | 0.275403 | 0.137702 | − | 0.990474i | \(-0.456029\pi\) | ||||
0.137702 | + | 0.990474i | \(0.456029\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.63932i | 0.197661i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 12.9443i | − 0.700972i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.88854 | −0.317029 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 17.2361i | − 0.925281i | −0.886546 | − | 0.462640i | \(-0.846902\pi\) | ||||
0.886546 | − | 0.462640i | \(-0.153098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9443i | 0.799949i | 0.916526 | + | 0.399974i | \(0.130981\pi\) | ||||
−0.916526 | + | 0.399974i | \(0.869019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.7214 | 1.31953 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.05573 | 0.269089 | 0.134545 | − | 0.990908i | \(-0.457043\pi\) | ||||
0.134545 | + | 0.990908i | \(0.457043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.47214i | − 0.131207i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 17.8885i | − 0.946762i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0557 | 0.794611 | 0.397305 | − | 0.917686i | \(-0.369945\pi\) | ||||
0.397305 | + | 0.917686i | \(0.369945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8.65248i | − 0.454137i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.47214i | 0.234082i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.2918 | −0.954824 | −0.477412 | − | 0.878680i | \(-0.658425\pi\) | ||||
−0.477412 | + | 0.878680i | \(0.658425\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.3607 | −0.955819 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52786i | 0.0793227i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.05573i | 0.261776i | 0.991397 | + | 0.130888i | \(0.0417828\pi\) | ||||
−0.991397 | + | 0.130888i | \(0.958217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.23607 | 0.0638303 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5279i | 0.797613i | 0.917035 | + | 0.398806i | \(0.130575\pi\) | ||||
−0.917035 | + | 0.398806i | \(0.869425\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.9443i | 1.27793i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2918 | 0.525886 | 0.262943 | − | 0.964811i | \(-0.415307\pi\) | ||||
0.262943 | + | 0.964811i | \(0.415307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.47214 | −0.329851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 11.3475i | − 0.576827i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8885i | 0.602773i | 0.953502 | + | 0.301387i | \(0.0974495\pi\) | ||||
−0.953502 | + | 0.301387i | \(0.902551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.3050 | 1.07744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.4721 | −0.931796 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 12.9443i | − 0.651297i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.4721i | 0.625959i | 0.949760 | + | 0.312979i | \(0.101327\pi\) | ||||
−0.949760 | + | 0.312979i | \(0.898673\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.8885 | 0.895547 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.00000 | −0.0998752 | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9443i | 1.44182i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.41641i | 0.120072i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.8885 | 0.688430 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4164 | −0.861186 | −0.430593 | − | 0.902546i | \(-0.641696\pi\) | ||||
−0.430593 | + | 0.902546i | \(0.641696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47214i | 0.121941i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 27.4164i | − 1.34907i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.70820 | 0.182029 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.3050 | 1.23919 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.47214i | 0.218478i | 0.994016 | + | 0.109239i | \(0.0348414\pi\) | ||||
−0.994016 | + | 0.109239i | \(0.965159\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 28.8328i | − 1.40523i | −0.711572 | − | 0.702613i | \(-0.752017\pi\) | ||||
0.711572 | − | 0.702613i | \(-0.247983\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.6525 | −0.517941 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47214 | −0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.4164i | 0.939626i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 11.0557i | − 0.533776i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.3607 | −1.17341 | −0.586706 | − | 0.809800i | \(-0.699576\pi\) | ||||
−0.586706 | + | 0.809800i | \(0.699576\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.472136 | −0.0226894 | −0.0113447 | − | 0.999936i | \(-0.503611\pi\) | ||||
−0.0113447 | + | 0.999936i | \(0.503611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.47214i | − 0.118530i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.3050i | 1.01915i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.0557 | −0.718571 | −0.359285 | − | 0.933228i | \(-0.616980\pi\) | ||||
−0.359285 | + | 0.933228i | \(0.616980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.11146 | 0.243403 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.65248i | − 0.221046i | −0.993874 | − | 0.110523i | \(-0.964747\pi\) | ||||
0.993874 | − | 0.110523i | \(-0.0352526\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 14.9443i | − 0.708426i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.58359 | 0.405990 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.41641 | −0.0668444 | −0.0334222 | − | 0.999441i | \(-0.510641\pi\) | ||||
−0.0334222 | + | 0.999441i | \(0.510641\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.9443i | 1.17458i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.9443i | 1.35992i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.4721 | 0.678464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.88854 | −0.181898 | −0.0909492 | − | 0.995856i | \(-0.528990\pi\) | ||||
−0.0909492 | + | 0.995856i | \(0.528990\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 24.7214i | − 1.15389i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 41.7771i | − 1.94575i | −0.231325 | − | 0.972876i | \(-0.574306\pi\) | ||||
0.231325 | − | 0.972876i | \(-0.425694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.12461 | 0.0522651 | 0.0261326 | − | 0.999658i | \(-0.491681\pi\) | ||||
0.0261326 | + | 0.999658i | \(0.491681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.00000 | −0.370991 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 41.5967i | − 1.92487i | −0.271516 | − | 0.962434i | \(-0.587525\pi\) | ||||
0.271516 | − | 0.962434i | \(-0.412475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 24.9443i | − 1.15182i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.24922 | −0.287949 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.4164 | −0.708847 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.47214i | − 0.205196i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.695048i | 0.0318241i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.9443 | 0.591439 | 0.295719 | − | 0.955275i | \(-0.404441\pi\) | ||||
0.295719 | + | 0.955275i | \(0.404441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.0557 | −1.41602 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 19.0557i | − 0.867066i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.4721i | 0.747961i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7639 | −0.578389 | −0.289194 | − | 0.957270i | \(-0.593387\pi\) | ||||
−0.289194 | + | 0.957270i | \(0.593387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.4721 | 0.654453 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 21.0557i | − 0.950232i | −0.879923 | − | 0.475116i | \(-0.842406\pi\) | ||||
0.879923 | − | 0.475116i | \(-0.157594\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.94427i | 0.402830i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.94427 | −0.132335 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 14.5836i | − 0.652851i | −0.945223 | − | 0.326426i | \(-0.894156\pi\) | ||||
0.945223 | − | 0.326426i | \(-0.105844\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.1115i | 0.809160i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.12461 | −0.228495 | −0.114248 | − | 0.993452i | \(-0.536446\pi\) | ||||
−0.114248 | + | 0.993452i | \(0.536446\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.65248i | 0.384270i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8328i | 0.746101i | 0.927811 | + | 0.373051i | \(0.121688\pi\) | ||||
−0.927811 | + | 0.373051i | \(0.878312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.4721 | −0.640210 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.7214 | 1.09147 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.23607i | 0.142598i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4721i | 0.636484i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.5279 | 0.593807 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8885 | 0.696090 | 0.348045 | − | 0.937478i | \(-0.386846\pi\) | ||||
0.348045 | + | 0.937478i | \(0.386846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0689i | 0.877551i | 0.898597 | + | 0.438776i | \(0.144588\pi\) | ||||
−0.898597 | + | 0.438776i | \(0.855412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000i | 0.174574i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.9443 | 1.26083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.304952 | −0.0132588 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 12.4721i | − 0.541245i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 55.7771i | − 2.41597i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.2361 | −0.745180 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.3050 | 1.09199 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 6.94427i | − 0.299111i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 23.8885i | − 1.02705i | −0.858075 | − | 0.513524i | \(-0.828340\pi\) | ||||
0.858075 | − | 0.513524i | \(-0.171660\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5279 | 0.580536 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.9443 | −0.640142 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.6525i | − 0.883036i | −0.897252 | − | 0.441518i | \(-0.854440\pi\) | ||||
0.897252 | − | 0.441518i | \(-0.145560\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.83282i | 0.376975i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.94427 | −0.381039 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 41.8885 | 1.78128 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 8.58359i | − 0.364353i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 13.0557i | − 0.553189i | −0.960987 | − | 0.276594i | \(-0.910794\pi\) | ||||
0.960987 | − | 0.276594i | \(-0.0892059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.4721 | 1.45802 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0557 | −0.466773 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4.29180i | − 0.180878i | −0.995902 | − | 0.0904388i | \(-0.971173\pi\) | ||||
0.995902 | − | 0.0904388i | \(-0.0288270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.94427i | 0.123866i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.81966 | −0.328395 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.3607 | 1.44047 | 0.720237 | − | 0.693728i | \(-0.244033\pi\) | ||||
0.720237 | + | 0.693728i | \(0.244033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 16.8328i | − 0.704431i | −0.935919 | − | 0.352216i | \(-0.885428\pi\) | ||||
0.935919 | − | 0.352216i | \(-0.114572\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 14.1115i | − 0.589515i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.76393 | −0.198670 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8885 | 0.827971 | 0.413985 | − | 0.910283i | \(-0.364136\pi\) | ||||
0.413985 | + | 0.910283i | \(0.364136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.2492i | 0.592178i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000i | 0.497844i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.944272 | 0.0391077 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.58359 | 0.272198 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.65248i | 0.357126i | 0.983928 | + | 0.178563i | \(0.0571448\pi\) | ||||
−0.983928 | + | 0.178563i | \(0.942855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.9443i | 1.19263i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.583592 | 0.0240058 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0000 | −0.574911 | −0.287456 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287456 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 14.4721i | − 0.593300i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.16718i | − 0.0477697i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.8885 | 0.894342 | 0.447171 | − | 0.894449i | \(-0.352432\pi\) | ||||
0.447171 | + | 0.894449i | \(0.352432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3607 | 0.912111 | 0.456056 | − | 0.889951i | \(-0.349262\pi\) | ||||
0.456056 | + | 0.889951i | \(0.349262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 11.3475i | − 0.462107i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 7.00000i | − 0.284590i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.87539 | 0.279063 | 0.139532 | − | 0.990218i | \(-0.455440\pi\) | ||||
0.139532 | + | 0.990218i | \(0.455440\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 32.3607i | − 1.30917i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5279i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.4164 | 0.621650 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4164 | −1.02323 | −0.511613 | − | 0.859216i | \(-0.670952\pi\) | ||||
−0.511613 | + | 0.859216i | \(0.670952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4721i | 0.822845i | 0.911445 | + | 0.411422i | \(0.134968\pi\) | ||||
−0.911445 | + | 0.411422i | \(0.865032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 26.3344i | − 1.05676i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 48.3607 | 1.93753 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 11.0557i | − 0.441523i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.0557i | 1.23827i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.4721 | 1.37231 | 0.686157 | − | 0.727453i | \(-0.259296\pi\) | ||||
0.686157 | + | 0.727453i | \(0.259296\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.30495 | 0.0518672 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.1803i | 0.800832i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5279i | 0.615236i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.63932 | 0.143969 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.472136 | 0.0186482 | 0.00932412 | − | 0.999957i | \(-0.497032\pi\) | ||||
0.00932412 | + | 0.999957i | \(0.497032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 22.1803i | − 0.874707i | −0.899290 | − | 0.437354i | \(-0.855916\pi\) | ||||
0.899290 | − | 0.437354i | \(-0.144084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.52786i | 0.375159i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.7639 | −0.501802 | −0.250901 | − | 0.968013i | \(-0.580727\pi\) | ||||
−0.250901 | + | 0.968013i | \(0.580727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.9443 | −0.665121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 25.8885i | − 1.01465i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 49.4164i | 1.93381i | 0.255130 | + | 0.966907i | \(0.417882\pi\) | ||||
−0.255130 | + | 0.966907i | \(0.582118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9443 | −0.583921 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.58359 | −0.256850 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 21.4164i | − 0.834265i | −0.908846 | − | 0.417132i | \(-0.863035\pi\) | ||||
0.908846 | − | 0.417132i | \(-0.136965\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.8885i | 1.39590i | 0.716145 | + | 0.697951i | \(0.245905\pi\) | ||||
−0.716145 | + | 0.697951i | \(0.754095\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.7214 | 0.960098 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.4721 | 0.561205 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.52786i | 0.368920i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8328i | 0.418821i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.3050 | −0.898340 | −0.449170 | − | 0.893446i | \(-0.648280\pi\) | ||||
−0.449170 | + | 0.893446i | \(0.648280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.52786i | 0.212768i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 30.3607i | − 1.16686i | −0.812165 | − | 0.583428i | \(-0.801711\pi\) | ||||
0.812165 | − | 0.583428i | \(-0.198289\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −53.3050 | −2.04566 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.5836 | 0.482204 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.2918i | 0.929500i | 0.885442 | + | 0.464750i | \(0.153856\pi\) | ||||
−0.885442 | + | 0.464750i | \(0.846144\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000i | 0.0764161i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.63932 | 0.138849 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.11146 | −0.0804401 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0000i | 1.14125i | 0.821209 | + | 0.570627i | \(0.193300\pi\) | ||||
−0.821209 | + | 0.570627i | \(0.806700\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 9.52786i | − 0.361934i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.4721 | 0.776552 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.7771 | −2.11271 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.1935i | 0.725965i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.05573i | 0.342030i | 0.985268 | + | 0.171015i | \(0.0547047\pi\) | ||||
−0.985268 | + | 0.171015i | \(0.945295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.0557 | −1.17129 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.94427 | 0.336861 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 32.3607i | − 1.21705i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 18.0000i | − 0.676004i | −0.941145 | − | 0.338002i | \(-0.890249\pi\) | ||||
0.941145 | − | 0.338002i | \(-0.109751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.0557 | 0.714646 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.8328 | 1.15470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 8.94427i | − 0.334497i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000i | 0.597531i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.8328 | 0.851520 | 0.425760 | − | 0.904836i | \(-0.360007\pi\) | ||||
0.425760 | + | 0.904836i | \(0.360007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4721 | −0.390003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 32.5836i | − 1.21180i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.00000i | − 0.0742781i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.70820 | −0.0633538 | −0.0316769 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316769 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.0557 | −0.890953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 34.4721i | − 1.27500i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 51.8885i | − 1.91655i | −0.285853 | − | 0.958274i | \(-0.592277\pi\) | ||||
0.285853 | − | 0.958274i | \(-0.407723\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.29180 | −0.158305 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.4164 | −0.567871 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 49.1935i | − 1.80961i | −0.425824 | − | 0.904806i | \(-0.640016\pi\) | ||||
0.425824 | − | 0.904806i | \(-0.359984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.7214i | 0.908162i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.6525 | 1.12453 | 0.562265 | − | 0.826957i | \(-0.309930\pi\) | ||||
0.562265 | + | 0.826957i | \(0.309930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.94427 | 0.254418 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.45898i | 0.199734i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 55.7771i | − 2.03805i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.3607 | 0.597010 | 0.298505 | − | 0.954408i | \(-0.403512\pi\) | ||||
0.298505 | + | 0.954408i | \(0.403512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.47214 | −0.0900896 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.4164i | 0.852210i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.8885i | 0.722861i | 0.932399 | + | 0.361431i | \(0.117712\pi\) | ||||
−0.932399 | + | 0.361431i | \(0.882288\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.7771 | −0.427481 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.88854 | −0.140960 | −0.0704798 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704798 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 48.3607i | − 1.75077i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6.58359i | − 0.238030i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.8885 | 1.36808 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9443 | −0.538904 | −0.269452 | − | 0.963014i | \(-0.586843\pi\) | ||||
−0.269452 | + | 0.963014i | \(0.586843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.63932i | 0.131067i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.3607i | 0.660388i | 0.943913 | + | 0.330194i | \(0.107114\pi\) | ||||
−0.943913 | + | 0.330194i | \(0.892886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.47214 | −0.232486 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.7771 | 0.996497 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 55.7771i | − 1.99842i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 4.94427i | − 0.176920i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.0557 | 0.395099 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.05573 | −0.180447 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.0689i | 1.57089i | 0.618934 | + | 0.785443i | \(0.287565\pi\) | ||||
−0.618934 | + | 0.785443i | \(0.712435\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 21.8885i | − 0.779253i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.52786 | −0.338772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.8328 | −0.952861 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 0.583592i | − 0.0206979i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.4164i | 0.900295i | 0.892954 | + | 0.450148i | \(0.148629\pi\) | ||||
−0.892954 | + | 0.450148i | \(0.851371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.3607 | −1.14484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.0000 | 0.777332 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.94427i | 0.315637i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 15.4164i | − 0.543357i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.5279 | 1.03943 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.1115 | 0.425816 | 0.212908 | − | 0.977072i | \(-0.431707\pi\) | ||||
0.212908 | + | 0.977072i | \(0.431707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 2.00000i | − 0.0702295i | −0.999383 | − | 0.0351147i | \(-0.988820\pi\) | ||||
0.999383 | − | 0.0351147i | \(-0.0111797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.1115i | 1.05605i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.7082 | 0.410120 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.4721 | 1.20603 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.3050i | 0.744455i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0557i | 0.734850i | 0.930053 | + | 0.367425i | \(0.119761\pi\) | ||||
−0.930053 | + | 0.367425i | \(0.880239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.70820 | 0.0595442 | 0.0297721 | − | 0.999557i | \(-0.490522\pi\) | ||||
0.0297721 | + | 0.999557i | \(0.490522\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.47214 | 0.0860687 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.18034i | − 0.214911i | −0.994210 | − | 0.107456i | \(-0.965730\pi\) | ||||
0.994210 | − | 0.107456i | \(-0.0342704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000i | 1.31979i | 0.751356 | + | 0.659897i | \(0.229400\pi\) | ||||
−0.751356 | + | 0.659897i | \(0.770600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.5279 | −0.469276 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.5279 | 0.538009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.6525i | 0.507070i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 35.7771i | − 1.23664i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.00000 | −0.138095 | −0.0690477 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690477 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.36068i | 0.150190i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.00000i | 0.240807i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.6525 | 0.778348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.2492 | 0.351752 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.0820i | 1.13404i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.52786i | − 0.257749i | −0.991661 | − | 0.128875i | \(-0.958864\pi\) | ||||
0.991661 | − | 0.128875i | \(-0.0411365\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.58359 | 0.225154 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.8328 | −0.848273 | −0.424136 | − | 0.905598i | \(-0.639422\pi\) | ||||
−0.424136 | + | 0.905598i | \(0.639422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.4164i | 1.68607i | 0.537862 | + | 0.843033i | \(0.319232\pi\) | ||||
−0.537862 | + | 0.843033i | \(0.680768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.8885i | 1.70020i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2918 | 0.622660 | 0.311330 | − | 0.950302i | \(-0.399226\pi\) | ||||
0.311330 | + | 0.950302i | \(0.399226\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.9443 | 0.372116 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3.70820i | − 0.125937i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 25.8885i | − 0.878209i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.4721 | 1.16804 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.2492 | −0.820712 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.23607i | 0.109399i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 51.8885i | − 1.75215i | −0.482173 | − | 0.876076i | \(-0.660152\pi\) | ||||
0.482173 | − | 0.876076i | \(-0.339848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.5279 | −0.995950 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4721 | −0.824487 | −0.412244 | − | 0.911074i | \(-0.635255\pi\) | ||||
−0.412244 | + | 0.911074i | \(0.635255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.7082i | 0.932455i | 0.884665 | + | 0.466228i | \(0.154387\pi\) | ||||
−0.884665 | + | 0.466228i | \(0.845613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.4721i | 0.352017i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.5967 | −0.389381 | −0.194690 | − | 0.980865i | \(-0.562370\pi\) | ||||
−0.194690 | + | 0.980865i | \(0.562370\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −65.3050 | −2.19026 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.83282i | 0.161905i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 32.3607i | − 1.08291i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.4721 | 0.684308 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26.3344 | 0.879279 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.9443i | 0.431716i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.11146i | 0.0703428i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.8328 | −1.02605 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9443 | 0.363800 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 9.23607i | − 0.306679i | −0.988174 | − | 0.153339i | \(-0.950997\pi\) | ||||
0.988174 | − | 0.153339i | \(-0.0490027\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 14.7214i | − 0.488277i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.3050 | −1.76607 | −0.883036 | − | 0.469305i | \(-0.844504\pi\) | ||||
−0.883036 | + | 0.469305i | \(0.844504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.41641 | 0.245447 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 7.41641i | − 0.245179i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 48.3607i | − 1.59701i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.88854 | 0.194245 | 0.0971226 | − | 0.995272i | \(-0.469036\pi\) | ||||
0.0971226 | + | 0.995272i | \(0.469036\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.360680 | 0.0118848 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.0557i | 0.363904i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.94427i | − 0.228326i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.76393 | −0.156468 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.4721 | 0.802905 | 0.401452 | − | 0.915880i | \(-0.368506\pi\) | ||||
0.401452 | + | 0.915880i | \(0.368506\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5279i | 0.508905i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 19.0557i | − 0.623857i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.94427 | −0.292509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.52786 | 0.115250 | 0.0576251 | − | 0.998338i | \(-0.481647\pi\) | ||||
0.0576251 | + | 0.998338i | \(0.481647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 35.6393i | − 1.16305i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 44.8328i | − 1.46151i | −0.682641 | − | 0.730754i | \(-0.739169\pi\) | ||||
0.682641 | − | 0.730754i | \(-0.260831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59.4164 | −1.93486 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.8885 | −0.581914 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 21.8197i | − 0.709044i | −0.935048 | − | 0.354522i | \(-0.884644\pi\) | ||||
0.935048 | − | 0.354522i | \(-0.115356\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 20.0000i | − 0.649227i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.3050 | 0.820569 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.7771 | −1.48287 | −0.741433 | − | 0.671027i | \(-0.765853\pi\) | ||||
−0.741433 | + | 0.671027i | \(0.765853\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 11.4164i | − 0.369426i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 4.94427i | − 0.159826i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.47214 | −0.208996 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 25.3738i | − 0.817660i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5279i | 0.371095i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.34752 | 0.0433335 | 0.0216667 | − | 0.999765i | \(-0.493103\pi\) | ||||
0.0216667 | + | 0.999765i | \(0.493103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.7214 | 0.794164 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8885i | 0.766620i | 0.923620 | + | 0.383310i | \(0.125216\pi\) | ||||
−0.923620 | + | 0.383310i | \(0.874784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 66.2492i | 2.12385i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.52786 | −0.177033 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.3050 | −1.25748 | −0.628738 | − | 0.777617i | \(-0.716428\pi\) | ||||
−0.628738 | + | 0.777617i | \(0.716428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 29.8885i | − 0.955242i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 22.0000i | − 0.702406i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.0132 | −1.24433 | −0.622163 | − | 0.782888i | \(-0.713746\pi\) | ||||
−0.622163 | + | 0.782888i | \(0.713746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.472136 | 0.0150435 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.9443i | 0.921306i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 36.7214i | − 1.16767i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5279 | −0.556791 | −0.278395 | − | 0.960467i | \(-0.589803\pi\) | ||||
−0.278395 | + | 0.960467i | \(0.589803\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.6393 | 0.623235 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 0.944272i | − 0.0299354i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 34.5836i | − 1.09527i | −0.836716 | − | 0.547637i | \(-0.815528\pi\) | ||||
0.836716 | − | 0.547637i | \(-0.184472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.3870 | 1.21451 |
(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 | 1280.2.d.m.641.2 | 4 | ||
4.3 | odd | 2 | 1280.2.d.k.641.3 | 4 | |||
8.3 | odd | 2 | 1280.2.d.k.641.2 | 4 | |||
8.5 | even | 2 | inner | 1280.2.d.m.641.3 | 4 | ||
16.3 | odd | 4 | 640.2.a.k.1.1 | yes | 2 | ||
16.5 | even | 4 | 640.2.a.l.1.1 | yes | 2 | ||
16.11 | odd | 4 | 640.2.a.j.1.2 | yes | 2 | ||
16.13 | even | 4 | 640.2.a.i.1.2 | ✓ | 2 | ||
48.5 | odd | 4 | 5760.2.a.bw.1.1 | 2 | |||
48.11 | even | 4 | 5760.2.a.cd.1.2 | 2 | |||
48.29 | odd | 4 | 5760.2.a.ch.1.1 | 2 | |||
48.35 | even | 4 | 5760.2.a.ci.1.2 | 2 | |||
80.3 | even | 4 | 3200.2.c.w.2049.2 | 4 | |||
80.13 | odd | 4 | 3200.2.c.u.2049.3 | 4 | |||
80.19 | odd | 4 | 3200.2.a.be.1.2 | 2 | |||
80.27 | even | 4 | 3200.2.c.v.2049.2 | 4 | |||
80.29 | even | 4 | 3200.2.a.bl.1.1 | 2 | |||
80.37 | odd | 4 | 3200.2.c.x.2049.3 | 4 | |||
80.43 | even | 4 | 3200.2.c.v.2049.3 | 4 | |||
80.53 | odd | 4 | 3200.2.c.x.2049.2 | 4 | |||
80.59 | odd | 4 | 3200.2.a.bk.1.1 | 2 | |||
80.67 | even | 4 | 3200.2.c.w.2049.3 | 4 | |||
80.69 | even | 4 | 3200.2.a.bf.1.2 | 2 | |||
80.77 | odd | 4 | 3200.2.c.u.2049.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.a.i.1.2 | ✓ | 2 | 16.13 | even | 4 | ||
640.2.a.j.1.2 | yes | 2 | 16.11 | odd | 4 | ||
640.2.a.k.1.1 | yes | 2 | 16.3 | odd | 4 | ||
640.2.a.l.1.1 | yes | 2 | 16.5 | even | 4 | ||
1280.2.d.k.641.2 | 4 | 8.3 | odd | 2 | |||
1280.2.d.k.641.3 | 4 | 4.3 | odd | 2 | |||
1280.2.d.m.641.2 | 4 | 1.1 | even | 1 | trivial | ||
1280.2.d.m.641.3 | 4 | 8.5 | even | 2 | inner | ||
3200.2.a.be.1.2 | 2 | 80.19 | odd | 4 | |||
3200.2.a.bf.1.2 | 2 | 80.69 | even | 4 | |||
3200.2.a.bk.1.1 | 2 | 80.59 | odd | 4 | |||
3200.2.a.bl.1.1 | 2 | 80.29 | even | 4 | |||
3200.2.c.u.2049.2 | 4 | 80.77 | odd | 4 | |||
3200.2.c.u.2049.3 | 4 | 80.13 | odd | 4 | |||
3200.2.c.v.2049.2 | 4 | 80.27 | even | 4 | |||
3200.2.c.v.2049.3 | 4 | 80.43 | even | 4 | |||
3200.2.c.w.2049.2 | 4 | 80.3 | even | 4 | |||
3200.2.c.w.2049.3 | 4 | 80.67 | even | 4 | |||
3200.2.c.x.2049.2 | 4 | 80.53 | odd | 4 | |||
3200.2.c.x.2049.3 | 4 | 80.37 | odd | 4 | |||
5760.2.a.bw.1.1 | 2 | 48.5 | odd | 4 | |||
5760.2.a.cd.1.2 | 2 | 48.11 | even | 4 | |||
5760.2.a.ch.1.1 | 2 | 48.29 | odd | 4 | |||
5760.2.a.ci.1.2 | 2 | 48.35 | even | 4 |