Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4368,2,Mod(337,4368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4368.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4368.h (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: | \(34.8786556029\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.6 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4368.337 |
Dual form | 4368.2.h.o.337.1 |
$q$-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 \(\left(\mathbb{Z}/4368\mathbb{Z}\right)^\times\).
\(n\) | \(1093\) | \(1249\) | \(1457\) | \(2017\) | \(3823\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.15633i | 1.85877i | 0.369118 | + | 0.929383i | \(0.379660\pi\) | ||||
−0.369118 | + | 0.929383i | \(0.620340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.19394i | − | 0.963008i | −0.876444 | − | 0.481504i | \(-0.840091\pi\) | ||
0.876444 | − | 0.481504i | \(-0.159909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.48119 | − | 3.28726i | 0.410809 | − | 0.911721i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.15633i | − | 1.07316i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.35026 | 0.812558 | 0.406279 | − | 0.913749i | \(-0.366826\pi\) | ||||
0.406279 | + | 0.913749i | \(0.366826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.38787i | 0.547816i | 0.961756 | + | 0.273908i | \(0.0883163\pi\) | ||||
−0.961756 | + | 0.273908i | \(0.911684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.387873 | −0.0808771 | −0.0404386 | − | 0.999182i | \(-0.512876\pi\) | ||||
−0.0404386 | + | 0.999182i | \(0.512876\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.2750 | −2.45501 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.92478 | −1.47159 | −0.735797 | − | 0.677202i | \(-0.763192\pi\) | ||||
−0.735797 | + | 0.677202i | \(0.763192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.7005i | 1.92187i | 0.276773 | + | 0.960935i | \(0.410735\pi\) | ||||
−0.276773 | + | 0.960935i | \(0.589265\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.19394i | 0.555993i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.15633 | 0.702547 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.61213i | 0.265032i | 0.991181 | + | 0.132516i | \(0.0423056\pi\) | ||||
−0.991181 | + | 0.132516i | \(0.957694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.48119 | + | 3.28726i | −0.237181 | + | 0.526383i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.45580i | − | 0.227358i | −0.993518 | − | 0.113679i | \(-0.963736\pi\) | ||
0.993518 | − | 0.113679i | \(-0.0362635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.92478 | −0.293526 | −0.146763 | − | 0.989172i | \(-0.546885\pi\) | ||||
−0.146763 | + | 0.989172i | \(0.546885\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.15633i | 0.619588i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.76845i | − | 0.549685i | −0.961489 | − | 0.274843i | \(-0.911374\pi\) | ||
0.961489 | − | 0.274843i | \(-0.0886258\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.35026 | −0.469130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.2750 | 1.79001 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.38787i | − | 0.316282i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.15633i | − | 0.801485i | −0.916191 | − | 0.400743i | \(-0.868752\pi\) | ||
0.916191 | − | 0.400743i | \(-0.131248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4387 | 1.84868 | 0.924340 | − | 0.381569i | \(-0.124616\pi\) | ||||
0.924340 | + | 0.381569i | \(0.124616\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.6629 | + | 6.15633i | 1.69468 | + | 0.763598i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.61213i | 0.685630i | 0.939403 | + | 0.342815i | \(0.111380\pi\) | ||||
−0.939403 | + | 0.342815i | \(0.888620\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.387873 | 0.0466944 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8192i | 1.40269i | 0.712824 | + | 0.701343i | \(0.247416\pi\) | ||||
−0.712824 | + | 0.701343i | \(0.752584\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6629i | 1.83321i | 0.399800 | + | 0.916603i | \(0.369080\pi\) | ||||
−0.399800 | + | 0.916603i | \(0.630920\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.2750 | 1.41740 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.19394 | −0.363983 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.96239 | 1.00835 | 0.504174 | − | 0.863602i | \(-0.331797\pi\) | ||||
0.504174 | + | 0.863602i | \(0.331797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.99271i | 0.767549i | 0.923427 | + | 0.383775i | \(0.125376\pi\) | ||||
−0.923427 | + | 0.383775i | \(0.874624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.9248i | 1.51035i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.92478 | 0.849625 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 0.932071i | − | 0.0987994i | −0.998779 | − | 0.0493997i | \(-0.984269\pi\) | ||
0.998779 | − | 0.0493997i | \(-0.0157308\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.28726 | − | 1.48119i | −0.344598 | − | 0.155271i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 10.7005i | − | 1.10959i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.92478 | −1.01826 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.35026i | 0.340168i | 0.985430 | + | 0.170084i | \(0.0544038\pi\) | ||||
−0.985430 | + | 0.170084i | \(0.945596\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.19394i | − | 0.321003i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.0508 | −1.39811 | −0.699053 | − | 0.715070i | \(-0.746395\pi\) | ||||
−0.699053 | + | 0.715070i | \(0.746395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.42548 | −0.140457 | −0.0702286 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702286 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.15633 | −0.405616 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.53690 | −0.921967 | −0.460984 | − | 0.887409i | \(-0.652503\pi\) | ||||
−0.460984 | + | 0.887409i | \(0.652503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.23743i | 0.597437i | 0.954341 | + | 0.298719i | \(0.0965592\pi\) | ||||
−0.954341 | + | 0.298719i | \(0.903441\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.61213i | − | 0.153016i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.92478 | −0.369212 | −0.184606 | − | 0.982813i | \(-0.559101\pi\) | ||||
−0.184606 | + | 0.982813i | \(0.559101\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.61213i | − | 0.150332i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.48119 | − | 3.28726i | 0.136936 | − | 0.303907i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.35026i | − | 0.307118i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.798769 | 0.0726154 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.45580i | 0.131265i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 30.2374i | − | 2.70452i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.962389 | 0.0853982 | 0.0426991 | − | 0.999088i | \(-0.486404\pi\) | ||||
0.0426991 | + | 0.999088i | \(0.486404\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.92478 | 0.169467 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.1490 | −1.49832 | −0.749159 | − | 0.662390i | \(-0.769542\pi\) | ||||
−0.749159 | + | 0.662390i | \(0.769542\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.38787 | 0.207055 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 4.15633i | − | 0.357720i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4.85685i | − | 0.414949i | −0.978240 | − | 0.207474i | \(-0.933476\pi\) | ||
0.978240 | − | 0.207474i | \(-0.0665243\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.57452 | −0.218368 | −0.109184 | − | 0.994022i | \(-0.534824\pi\) | ||||
−0.109184 | + | 0.994022i | \(0.534824\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.76845i | 0.317361i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.4993 | − | 4.73084i | −0.877995 | − | 0.395613i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 32.9380i | − | 2.73535i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3806i | 1.09618i | 0.836419 | + | 0.548090i | \(0.184645\pi\) | ||||
−0.836419 | + | 0.548090i | \(0.815355\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8496i | 1.28982i | 0.764259 | + | 0.644909i | \(0.223105\pi\) | ||||
−0.764259 | + | 0.644909i | \(0.776895\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.35026 | 0.270853 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −44.4749 | −3.57231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7005 | −1.01361 | −0.506806 | − | 0.862060i | \(-0.669174\pi\) | ||||
−0.506806 | + | 0.862060i | \(0.669174\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.387873i | 0.0305687i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.61213i | − | 0.752880i | −0.926441 | − | 0.376440i | \(-0.877148\pi\) | ||
0.926441 | − | 0.376440i | \(-0.122852\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.2750 | −1.03346 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0811i | 0.934864i | 0.884029 | + | 0.467432i | \(0.154821\pi\) | ||||
−0.884029 | + | 0.467432i | \(0.845179\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.61213 | − | 9.73813i | −0.662471 | − | 0.749087i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.38787i | 0.182605i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.27504 | −0.705168 | −0.352584 | − | 0.935780i | \(-0.614697\pi\) | ||||
−0.352584 | + | 0.935780i | \(0.614697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2750i | 0.927906i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.15633i | 0.462738i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.01317 | 0.374702 | 0.187351 | − | 0.982293i | \(-0.440010\pi\) | ||||
0.187351 | + | 0.982293i | \(0.440010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8496 | −1.02943 | −0.514715 | − | 0.857362i | \(-0.672102\pi\) | ||||
−0.514715 | + | 0.857362i | \(0.672102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.4387 | −1.06734 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.70052 | −0.492632 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.7005i | − | 0.782500i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.5647 | 1.34329 | 0.671646 | − | 0.740872i | \(-0.265588\pi\) | ||||
0.671646 | + | 0.740872i | \(0.265588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0884i | 0.942123i | 0.882100 | + | 0.471062i | \(0.156129\pi\) | ||||
−0.882100 | + | 0.471062i | \(0.843871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.6629 | − | 6.15633i | −0.978421 | − | 0.440864i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.24472i | 0.516165i | 0.966123 | + | 0.258083i | \(0.0830906\pi\) | ||||
−0.966123 | + | 0.258083i | \(0.916909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.62530 | −0.611431 | −0.305716 | − | 0.952123i | \(-0.598896\pi\) | ||||
−0.305716 | + | 0.952123i | \(0.598896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.61213i | − | 0.395849i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.92478i | 0.556210i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.05079 | 0.422605 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.387873 | −0.0269590 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.62672 | 0.527551 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8872 | −1.30025 | −0.650123 | − | 0.759829i | \(-0.725283\pi\) | ||||
−0.650123 | + | 0.759829i | \(0.725283\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 11.8192i | − | 0.809841i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.00000i | − | 0.545595i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.7005 | 0.726399 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 15.6629i | − | 1.05840i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.96239 | − | 11.0132i | 0.333806 | − | 0.740826i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.1622i | − | 1.08230i | −0.840926 | − | 0.541151i | \(-0.817989\pi\) | ||
0.840926 | − | 0.541151i | \(-0.182011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.2750 | −0.818336 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 27.2447i | − | 1.80830i | −0.427220 | − | 0.904148i | \(-0.640507\pi\) | ||
0.427220 | − | 0.904148i | \(-0.359493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5125i | 1.28942i | 0.764427 | + | 0.644710i | \(0.223022\pi\) | ||||
−0.764427 | + | 0.644710i | \(0.776978\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.19394 | 0.210146 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.8496 | −1.43141 | −0.715706 | − | 0.698402i | \(-0.753895\pi\) | ||||
−0.715706 | + | 0.698402i | \(0.753895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.6629 | 1.02174 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.96239 | −0.582170 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.49341i | 0.549393i | 0.961531 | + | 0.274697i | \(0.0885774\pi\) | ||||
−0.961531 | + | 0.274697i | \(0.911423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.48612i | 0.353392i | 0.984265 | + | 0.176696i | \(0.0565409\pi\) | ||||
−0.984265 | + | 0.176696i | \(0.943459\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 4.15633i | − | 0.265538i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.84955 | + | 3.53690i | 0.499455 | + | 0.225048i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.99271i | − | 0.443145i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.44851 | −0.407026 | −0.203513 | − | 0.979072i | \(-0.565236\pi\) | ||||
−0.203513 | + | 0.979072i | \(0.565236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.23884i | 0.0778853i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 13.9248i | − | 0.872003i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.90034 | 0.617566 | 0.308783 | − | 0.951132i | \(-0.400078\pi\) | ||||
0.308783 | + | 0.951132i | \(0.400078\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.61213 | 0.100173 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.92478 | −0.490531 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.46168 | −0.213456 | −0.106728 | − | 0.994288i | \(-0.534037\pi\) | ||||
−0.106728 | + | 0.994288i | \(0.534037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 24.9380i | − | 1.53193i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.932071i | 0.0570418i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.7513 | 1.02135 | 0.510673 | − | 0.859775i | \(-0.329396\pi\) | ||||
0.510673 | + | 0.859775i | \(0.329396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.38787i | 0.388036i | 0.980998 | + | 0.194018i | \(0.0621520\pi\) | ||||
−0.980998 | + | 0.194018i | \(0.937848\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.28726 | + | 1.48119i | 0.198954 | + | 0.0896460i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 39.2057i | 2.36419i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.1768 | 0.731633 | 0.365816 | − | 0.930687i | \(-0.380790\pi\) | ||||
0.365816 | + | 0.930687i | \(0.380790\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.7005i | 0.640624i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.3054i | − | 1.62890i | −0.580233 | − | 0.814450i | \(-0.697039\pi\) | ||
0.580233 | − | 0.814450i | \(-0.302961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.0738 | −1.60937 | −0.804685 | − | 0.593701i | \(-0.797666\pi\) | ||||
−0.804685 | + | 0.593701i | \(0.797666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.92478 | 0.587893 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.45580 | −0.0859333 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.77575 | −0.339750 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3.35026i | − | 0.196396i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.7816i | 0.980393i | 0.871612 | + | 0.490197i | \(0.163075\pi\) | ||||
−0.871612 | + | 0.490197i | \(0.836925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.5877 | 1.48977 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.19394i | 0.185331i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.574515 | + | 1.27504i | −0.0332251 | + | 0.0737374i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.92478i | 0.110942i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.0508 | 0.807197 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 60.0118i | 3.43626i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.2995i | − | 0.987333i | −0.869651 | − | 0.493667i | \(-0.835656\pi\) | ||
0.869651 | − | 0.493667i | \(-0.164344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.42548 | 0.0810930 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.1490 | −0.972432 | −0.486216 | − | 0.873839i | \(-0.661623\pi\) | ||||
−0.486216 | + | 0.873839i | \(0.661623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.8119 | −0.611127 | −0.305564 | − | 0.952172i | \(-0.598845\pi\) | ||||
−0.305564 | + | 0.952172i | \(0.598845\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.15633 | 0.234182 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 14.1563i | − | 0.795098i | −0.917581 | − | 0.397549i | \(-0.869861\pi\) | ||
0.917581 | − | 0.397549i | \(-0.130139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.3112i | 1.41716i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.53690 | 0.532298 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000i | 0.445132i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.1817 | + | 40.3512i | −1.00854 | + | 2.23828i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.23743i | − | 0.344931i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.76845 | −0.207761 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.2506i | − | 0.948179i | −0.880477 | − | 0.474089i | \(-0.842777\pi\) | ||
0.880477 | − | 0.474089i | \(-0.157223\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.61213i | 0.0883440i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.3258 | −1.27443 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.97556 | −0.325510 | −0.162755 | − | 0.986667i | \(-0.552038\pi\) | ||||
−0.162755 | + | 0.986667i | \(0.552038\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.92478 | 0.213165 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.1768 | 1.85078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.61213i | 0.0867940i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.7889 | −1.38442 | −0.692211 | − | 0.721695i | \(-0.743363\pi\) | ||||
−0.692211 | + | 0.721695i | \(0.743363\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9624i | 0.693861i | 0.937891 | + | 0.346930i | \(0.112776\pi\) | ||||
−0.937891 | + | 0.346930i | \(0.887224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.48119 | + | 3.28726i | −0.0790603 | + | 0.175461i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 3.78304i | − | 0.201351i | −0.994919 | − | 0.100675i | \(-0.967900\pi\) | ||
0.994919 | − | 0.100675i | \(-0.0321004\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −49.1246 | −2.60726 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.35026i | 0.177315i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10.6702i | − | 0.563152i | −0.959539 | − | 0.281576i | \(-0.909143\pi\) | ||
0.959539 | − | 0.281576i | \(-0.0908571\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.2981 | 0.699898 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.798769 | −0.0419245 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −65.1002 | −3.40750 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.82653 | −0.356342 | −0.178171 | − | 0.984000i | \(-0.557018\pi\) | ||||
−0.178171 | + | 0.984000i | \(0.557018\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.45580i | − | 0.0757860i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000i | 0.311504i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5745 | 0.858196 | 0.429098 | − | 0.903258i | \(-0.358832\pi\) | ||||
0.429098 | + | 0.903258i | \(0.358832\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.2374i | 1.56145i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7381 | + | 26.0508i | −0.604545 | + | 1.34168i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0738i | 0.979756i | 0.871791 | + | 0.489878i | \(0.162959\pi\) | ||||
−0.871791 | + | 0.489878i | \(0.837041\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.962389 | −0.0493047 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8.29218i | − | 0.423711i | −0.977301 | − | 0.211855i | \(-0.932049\pi\) | ||
0.977301 | − | 0.211855i | \(-0.0679506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 13.2750i | − | 0.676559i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.92478 | −0.0978419 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.700523 | 0.0355180 | 0.0177590 | − | 0.999842i | \(-0.494347\pi\) | ||||
0.0177590 | + | 0.999842i | \(0.494347\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.29948 | −0.0657174 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.1490 | 0.865054 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.2506i | 1.87428i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.4993i | − | 0.627322i | −0.949535 | − | 0.313661i | \(-0.898445\pi\) | ||
0.949535 | − | 0.313661i | \(-0.101555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.38787 | −0.119543 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.7064i | 1.43353i | 0.697315 | + | 0.716765i | \(0.254378\pi\) | ||||
−0.697315 | + | 0.716765i | \(0.745622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.1754 | + | 15.8496i | 1.75221 | + | 0.789523i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.15633i | 0.206529i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.14903 | 0.255228 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.4518i | − | 1.15962i | −0.814752 | − | 0.579809i | \(-0.803127\pi\) | ||
0.814752 | − | 0.579809i | \(-0.196873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.85685i | 0.239571i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.15633 | −0.302933 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.0640 | −1.42669 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.57452 | 0.126075 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.1768 | 1.66965 | 0.834823 | − | 0.550519i | \(-0.185570\pi\) | ||||
0.834823 | + | 0.550519i | \(0.185570\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.55149i | 0.270563i | 0.990807 | + | 0.135282i | \(0.0431939\pi\) | ||||
−0.990807 | + | 0.135282i | \(0.956806\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.76845i | − | 0.183228i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.1246 | −1.99484 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 14.4387i | − | 0.698736i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.4993 | + | 4.73084i | 0.506911 | + | 0.228407i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.43136i | 0.261620i | 0.991407 | + | 0.130810i | \(0.0417577\pi\) | ||||
−0.991407 | + | 0.130810i | \(0.958242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.2130 | 1.93251 | 0.966256 | − | 0.257582i | \(-0.0829257\pi\) | ||||
0.966256 | + | 0.257582i | \(0.0829257\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 32.9380i | 1.57925i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.926192i | − | 0.0443058i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5745 | 1.07742 | 0.538711 | − | 0.842490i | \(-0.318911\pi\) | ||||
0.538711 | + | 0.842490i | \(0.318911\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.23743 | 0.391372 | 0.195686 | − | 0.980667i | \(-0.437307\pi\) | ||||
0.195686 | + | 0.980667i | \(0.437307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.87399 | 0.183645 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 13.3806i | − | 0.632880i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.40834i | 0.113657i | 0.998384 | + | 0.0568283i | \(0.0180988\pi\) | ||||
−0.998384 | + | 0.0568283i | \(0.981901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.64974 | −0.218948 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 15.8496i | − | 0.744677i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.15633 | − | 13.6629i | 0.288613 | − | 0.640527i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.5633i | 1.38291i | 0.722419 | + | 0.691455i | \(0.243030\pi\) | ||||
−0.722419 | + | 0.691455i | \(0.756970\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.35026 | −0.156377 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.7196i | − | 1.57048i | −0.619193 | − | 0.785239i | \(-0.712540\pi\) | ||
0.619193 | − | 0.785239i | \(-0.287460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.8364i | − | 0.782453i | −0.920294 | − | 0.391226i | \(-0.872051\pi\) | ||
0.920294 | − | 0.391226i | \(-0.127949\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 44.4749 | 2.06247 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.7005 | 1.05045 | 0.525227 | − | 0.850962i | \(-0.323980\pi\) | ||||
0.525227 | + | 0.850962i | \(0.323980\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.61213 | 0.259144 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.7005 | 0.585209 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.14762i | 0.282668i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 29.3112i | − | 1.34489i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0957i | 0.461284i | 0.973039 | + | 0.230642i | \(0.0740826\pi\) | ||||
−0.973039 | + | 0.230642i | \(0.925917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.29948 | + | 2.38787i | 0.241635 | + | 0.108878i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.387873i | − | 0.0176488i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.9248 | −0.632292 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.40105i | − | 0.426002i | −0.977052 | − | 0.213001i | \(-0.931676\pi\) | ||
0.977052 | − | 0.213001i | \(-0.0683238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.61213i | 0.434675i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.7612 | −0.936938 | −0.468469 | − | 0.883480i | \(-0.655194\pi\) | ||||
−0.468469 | + | 0.883480i | \(0.655194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.5501 | −1.19576 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.2750 | 0.596669 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.8192 | 0.530165 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.9525i | 1.02750i | 0.857941 | + | 0.513748i | \(0.171744\pi\) | ||||
−0.857941 | + | 0.513748i | \(0.828256\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 12.0811i | − | 0.539744i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.9234 | 1.55716 | 0.778578 | − | 0.627548i | \(-0.215941\pi\) | ||||
0.778578 | + | 0.627548i | \(0.215941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 58.3996i | − | 2.59875i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.61213 | + | 9.73813i | 0.382478 | + | 0.432486i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.2301i | 0.852361i | 0.904638 | + | 0.426180i | \(0.140141\pi\) | ||||
−0.904638 | + | 0.426180i | \(0.859859\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.6629 | 0.692886 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.38787i | − | 0.105427i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.92478i | − | 0.261077i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0362 | −0.529351 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.27504 | 0.407129 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5271 | 0.943117 | 0.471559 | − | 0.881835i | \(-0.343692\pi\) | ||||
0.471559 | + | 0.881835i | \(0.343692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.6747 | −1.73485 | −0.867426 | − | 0.497566i | \(-0.834227\pi\) | ||||
−0.867426 | + | 0.497566i | \(0.834227\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 12.2750i | − | 0.535727i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.8496i | 1.56163i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8496 | −0.993459 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.15633i | − | 0.267162i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.78560 | − | 2.15633i | −0.207287 | − | 0.0934008i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 39.6385i | − | 1.71372i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.01317 | −0.216334 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.19394i | 0.137573i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.0263i | − | 0.431066i | −0.976497 | − | 0.215533i | \(-0.930851\pi\) | ||
0.976497 | − | 0.215533i | \(-0.0691489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8496 | 0.594341 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.9248 | −1.11050 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4485 | 1.13086 | 0.565428 | − | 0.824797i | \(-0.308711\pi\) | ||||
0.565428 | + | 0.824797i | \(0.308711\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4387 | 0.616227 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.9234i | − | 0.806162i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.96239i | − | 0.381120i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.70052 | 0.284421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.84367i | 0.247604i | 0.992307 | + | 0.123802i | \(0.0395088\pi\) | ||||
−0.992307 | + | 0.123802i | \(0.960491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.85097 | + | 6.32724i | −0.120583 | + | 0.267614i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.7005i | 0.451776i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.25060 | −0.0527066 | −0.0263533 | − | 0.999653i | \(-0.508389\pi\) | ||||
−0.0263533 | + | 0.999653i | \(0.508389\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 16.3127i | − | 0.686278i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.2228 | −1.60238 | −0.801192 | − | 0.598407i | \(-0.795801\pi\) | ||||
−0.801192 | + | 0.598407i | \(0.795801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.73813 | 0.407528 | 0.203764 | − | 0.979020i | \(-0.434682\pi\) | ||||
0.203764 | + | 0.979020i | \(0.434682\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.5647 | −0.775550 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.76116 | 0.198554 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.87399i | − | 0.161276i | −0.996743 | − | 0.0806382i | \(-0.974304\pi\) | ||
0.996743 | − | 0.0806382i | \(-0.0256958\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 13.0884i | − | 0.543935i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.99271 | 0.290106 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.1636i | 0.793676i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.6629 | + | 6.15633i | 0.564892 | + | 0.254533i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.2447i | 0.464119i | 0.972702 | + | 0.232060i | \(0.0745465\pi\) | ||||
−0.972702 | + | 0.232060i | \(0.925454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.5515 | −1.05283 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 7.24472i | − | 0.298008i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.7210i | 1.17943i | 0.807612 | + | 0.589715i | \(0.200760\pi\) | ||||
−0.807612 | + | 0.589715i | \(0.799240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.9248 | 0.570860 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.62530 | 0.353010 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.1344 | 0.863530 | 0.431765 | − | 0.901986i | \(-0.357891\pi\) | ||||
0.431765 | + | 0.901986i | \(0.357891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9135 | 0.771498 | 0.385749 | − | 0.922604i | \(-0.373943\pi\) | ||||
0.385749 | + | 0.922604i | \(0.373943\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.61213i | 0.228543i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.31994i | 0.134975i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.1246 | 1.66920 | 0.834598 | − | 0.550860i | \(-0.185700\pi\) | ||||
0.834598 | + | 0.550860i | \(0.185700\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 7.92478i | − | 0.321128i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.3879 | − | 5.58181i | −0.501160 | − | 0.225816i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.3258i | − | 0.942121i | −0.882101 | − | 0.471061i | \(-0.843871\pi\) | ||
0.882101 | − | 0.471061i | \(-0.156129\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.05079 | −0.243991 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.7830i | 0.715918i | 0.933737 | + | 0.357959i | \(0.116527\pi\) | ||||
−0.933737 | + | 0.357959i | \(0.883473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.93795i | 0.359247i | 0.983735 | + | 0.179623i | \(0.0574879\pi\) | ||||
−0.983735 | + | 0.179623i | \(0.942512\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.387873 | 0.0155648 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.932071 | −0.0373427 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 64.3014 | 2.57206 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.62672 | −0.304582 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.40105i | 0.215354i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 32.2638i | − | 1.28440i | −0.766537 | − | 0.642200i | \(-0.778022\pi\) | ||
0.766537 | − | 0.642200i | \(-0.221978\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.8872 | 0.750697 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000i | 0.158735i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.48119 | + | 3.28726i | −0.0586871 | + | 0.130246i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.8192i | 0.467562i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −49.4274 | −1.95226 | −0.976132 | − | 0.217176i | \(-0.930315\pi\) | ||||
−0.976132 | + | 0.217176i | \(0.930315\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.07522i | 0.239583i | 0.992799 | + | 0.119792i | \(0.0382227\pi\) | ||||
−0.992799 | + | 0.119792i | \(0.961777\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000i | 0.315000i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.9986 | 0.511027 | 0.255514 | − | 0.966805i | \(-0.417755\pi\) | ||||
0.255514 | + | 0.966805i | \(0.417755\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.6629 | −0.771837 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.7005 | −0.419387 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.4010 | 0.602690 | 0.301345 | − | 0.953515i | \(-0.402564\pi\) | ||||
0.301345 | + | 0.953515i | \(0.402564\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 71.2769i | − | 2.78502i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.6629i | 0.611068i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.76116 | −0.341286 | −0.170643 | − | 0.985333i | \(-0.554585\pi\) | ||||
−0.170643 | + | 0.985333i | \(0.554585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.4372i | 1.30056i | 0.759695 | + | 0.650279i | \(0.225348\pi\) | ||||
−0.759695 | + | 0.650279i | \(0.774652\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.96239 | + | 11.0132i | −0.192723 | + | 0.427716i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.92478i | 0.384866i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.07381 | 0.119018 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.1622i | 0.624867i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 46.1162i | − | 1.78029i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.176793 | −0.00681488 | −0.00340744 | − | 0.999994i | \(-0.501085\pi\) | ||||
−0.00340744 | + | 0.999994i | \(0.501085\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.2750 | 0.472466 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.67750 | −0.218204 | −0.109102 | − | 0.994031i | \(-0.534798\pi\) | ||||
−0.109102 | + | 0.994031i | \(0.534798\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.35026 | 0.128571 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2447i | 1.04402i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.4299i | 1.92965i | 0.262896 | + | 0.964824i | \(0.415322\pi\) | ||||
−0.262896 | + | 0.964824i | \(0.584678\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.1866 | 0.771292 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 19.5125i | − | 0.744447i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.88717 | + | 19.7235i | −0.338574 | + | 0.751407i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.5633i | 1.58114i | 0.612371 | + | 0.790570i | \(0.290216\pi\) | ||||
−0.612371 | + | 0.790570i | \(0.709784\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.19394 | −0.121328 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10.7005i | − | 0.405894i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.87732i | − | 0.184742i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.8496 | 0.826426 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.47486 | −0.0934740 | −0.0467370 | − | 0.998907i | \(-0.514882\pi\) | ||||
−0.0467370 | + | 0.998907i | \(0.514882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.84955 | −0.145189 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.6629 | −0.589899 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0508i | 0.528434i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.91019i | 0.297073i | 0.988907 | + | 0.148537i | \(0.0474563\pi\) | ||||
−0.988907 | + | 0.148537i | \(0.952544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.96239 | 0.336116 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.15045i | − | 0.155435i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.6629 | − | 43.6385i | 0.735351 | − | 1.63199i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 8.49341i | − | 0.317192i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.5501 | −0.990151 | −0.495075 | − | 0.868850i | \(-0.664860\pi\) | ||||
−0.495075 | + | 0.868850i | \(0.664860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42548i | 0.0530878i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 5.48612i | − | 0.204031i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 97.2769 | 3.61278 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.44851 | 0.239162 | 0.119581 | − | 0.992824i | \(-0.461845\pi\) | ||||
0.119581 | + | 0.992824i | \(0.461845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.44851 | −0.238507 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 28.8119i | − | 1.06419i | −0.846684 | − | 0.532097i | \(-0.821404\pi\) | ||
0.846684 | − | 0.532097i | \(-0.178596\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.15633i | 0.153308i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.9248 | 0.660268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.6121i | 1.08930i | 0.838664 | + | 0.544650i | \(0.183337\pi\) | ||||
−0.838664 | + | 0.544650i | \(0.816663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.84955 | − | 3.53690i | −0.288361 | − | 0.129931i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.77830i | − | 0.138612i | −0.997595 | − | 0.0693062i | \(-0.977921\pi\) | ||
0.997595 | − | 0.0693062i | \(-0.0220786\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −55.6140 | −2.03754 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.99271i | 0.255850i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.53690i | 0.348471i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0752 | 0.367650 | 0.183825 | − | 0.982959i | \(-0.441152\pi\) | ||||
0.183825 | + | 0.982959i | \(0.441152\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.44851 | 0.234997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −65.8759 | −2.39747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.4979 | 1.43557 | 0.717787 | − | 0.696262i | \(-0.245155\pi\) | ||||
0.717787 | + | 0.696262i | \(0.245155\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.23884i | − | 0.0449671i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.7685i | − | 0.934106i | −0.884229 | − | 0.467053i | \(-0.845316\pi\) | ||
0.884229 | − | 0.467053i | \(-0.154684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.23743 | 0.225810 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.9248i | 0.503451i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.2374 | − | 9.11871i | −0.730731 | − | 0.329258i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.4372i | − | 1.78275i | −0.453264 | − | 0.891376i | \(-0.649741\pi\) | ||
0.453264 | − | 0.891376i | \(-0.350259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.90034 | −0.356552 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.2184i | 0.547367i | 0.961820 | + | 0.273683i | \(0.0882421\pi\) | ||||
−0.961820 | + | 0.273683i | \(0.911758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 131.349i | − | 4.71821i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.61213 | −0.0578347 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.47627 | 0.124550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.7499 | 1.35080 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.92478 | 0.283208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 52.7875i | − | 1.88407i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.6107i | 0.948569i | 0.880372 | + | 0.474285i | \(0.157293\pi\) | ||||
−0.880372 | + | 0.474285i | \(0.842707\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.46168 | 0.123239 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.92478i | 0.139549i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.3865 | − | 47.4636i | 0.759455 | − | 1.68548i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.9380i | 0.884458i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.2473 | 0.433821 | 0.216910 | − | 0.976192i | \(-0.430402\pi\) | ||||
0.216910 | + | 0.976192i | \(0.430402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.6253i | − | 0.446651i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 0.932071i | − | 0.0329331i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.0263 | 1.76539 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.61213 | −0.0568200 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.7513 | −0.589674 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.9234 | −1.01689 | −0.508446 | − | 0.861094i | \(-0.669780\pi\) | ||||
−0.508446 | + | 0.861094i | \(0.669780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.1002i | 1.16230i | 0.813795 | + | 0.581152i | \(0.197398\pi\) | ||||
−0.813795 | + | 0.581152i | \(0.802602\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 6.38787i | − | 0.224032i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.9511 | 1.39943 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.59612i | − | 0.160798i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.28726 | − | 1.48119i | −0.114866 | − | 0.0517571i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.46898i | − | 0.225769i | −0.993608 | − | 0.112884i | \(-0.963991\pi\) | ||
0.993608 | − | 0.112884i | \(-0.0360090\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.55149 | −0.332944 | −0.166472 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166472 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 39.2057i | − | 1.36497i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.3430i | − | 1.26377i | −0.775063 | − | 0.631884i | \(-0.782282\pi\) | ||
0.775063 | − | 0.631884i | \(-0.217718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.7645 | −0.755912 | −0.377956 | − | 0.925824i | \(-0.623373\pi\) | ||||
−0.377956 | + | 0.925824i | \(0.623373\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.1768 | −0.422408 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.35026 | −0.116080 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50.2130 | −1.73769 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 10.7005i | − | 0.369864i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.0693432i | 0.00239399i | 0.999999 | + | 0.00119700i | \(0.000381016\pi\) | ||||
−0.999999 | + | 0.00119700i | \(0.999619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8021 | 1.16559 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.3054i | 0.940446i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.4749 | − | 35.7948i | 1.39238 | − | 1.23138i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.798769i | − | 0.0274460i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.0738 | 0.929171 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.625301i | − | 0.0214350i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.17347i | − | 0.177136i | −0.996070 | − | 0.0885681i | \(-0.971771\pi\) | ||
0.996070 | − | 0.0885681i | \(-0.0282291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.92478 | −0.339420 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.2750 | 1.40993 | 0.704964 | − | 0.709243i | \(-0.250963\pi\) | ||||
0.704964 | + | 0.709243i | \(0.250963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.1768 | 0.483706 | 0.241853 | − | 0.970313i | \(-0.422245\pi\) | ||||
0.241853 | + | 0.970313i | \(0.422245\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.45580 | 0.0496136 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.62786i | 0.259655i | 0.991537 | + | 0.129828i | \(0.0414424\pi\) | ||||
−0.991537 | + | 0.129828i | \(0.958558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 38.5501i | − | 1.31074i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.77575 | 0.196155 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 28.6253i | − | 0.971047i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.4485 | + | 8.31265i | 0.625104 | + | 0.281663i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.35026i | 0.113389i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.2374 | −1.02221 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.1754i | 1.45793i | 0.684552 | + | 0.728964i | \(0.259998\pi\) | ||||
−0.684552 | + | 0.728964i | \(0.740002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 16.7816i | − | 0.566030i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.9003 | −1.00737 | −0.503684 | − | 0.863888i | \(-0.668022\pi\) | ||||
−0.503684 | + | 0.863888i | \(0.668022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.83971 | 0.331132 | 0.165566 | − | 0.986199i | \(-0.447055\pi\) | ||||
0.165566 | + | 0.986199i | \(0.447055\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −25.5877 | −0.860121 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.0249 | 1.44464 | 0.722318 | − | 0.691561i | \(-0.243077\pi\) | ||||
0.722318 | + | 0.691561i | \(0.243077\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.962389i | − | 0.0322775i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.19394i | − | 0.107001i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.99859 | 0.301126 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.8364i | 0.696483i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.574515 | − | 1.27504i | 0.0191825 | − | 0.0425723i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 84.7993i | − | 2.82821i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.1016 | −0.669680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.92478i | − | 0.0640526i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 57.5633i | − | 1.91347i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.2605 | 0.373897 | 0.186949 | − | 0.982370i | \(-0.440140\pi\) | ||||
0.186949 | + | 0.982370i | \(0.440140\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.0508 | −0.466035 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.5633 | −0.780685 | −0.390343 | − | 0.920670i | \(-0.627643\pi\) | ||||
−0.390343 | + | 0.920670i | \(0.627643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.3343 | 0.739156 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 60.0118i | − | 1.98393i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.1490i | 0.566311i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8411 | −0.423589 | −0.211795 | − | 0.977314i | \(-0.567931\pi\) | ||||
−0.211795 | + | 0.977314i | \(0.567931\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.2995i | 0.570037i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.8529 | + | 17.5066i | 1.27886 | + | 0.576236i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 19.7889i | − | 0.650656i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.42548 | −0.0468191 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.6194i | 0.807737i | 0.914817 | + | 0.403869i | \(0.132335\pi\) | ||||
−0.914817 | + | 0.403869i | \(0.867665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.38787i | − | 0.0782594i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.1490 | 0.561434 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 44.4749 | 1.45448 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.4847 | 1.45325 | 0.726626 | − | 0.687033i | \(-0.241087\pi\) | ||||
0.726626 | + | 0.687033i | \(0.241087\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.8119 | 0.352834 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.69464i | 0.0878429i | 0.999035 | + | 0.0439214i | \(0.0139851\pi\) | ||||
−0.999035 | + | 0.0439214i | \(0.986015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.564666i | 0.0183881i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.15633 | −0.135205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.09237i | 0.100488i | 0.998737 | + | 0.0502442i | \(0.0160000\pi\) | ||||
−0.998737 | + | 0.0502442i | \(0.984000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51.4880 | + | 23.1998i | 1.67137 | + | 0.753098i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.1563i | 0.459050i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.57925 | 0.277909 | 0.138955 | − | 0.990299i | \(-0.455626\pi\) | ||||
0.138955 | + | 0.990299i | \(0.455626\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 77.1608i | 2.49686i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 25.3112i | − | 0.818196i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.85685 | −0.156836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −83.5012 | −2.69359 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.53690 | −0.307322 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54.3996 | −1.75119 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.43533i | − | 0.239104i | −0.992828 | − | 0.119552i | \(-0.961854\pi\) | ||
0.992828 | − | 0.119552i | \(-0.0381459\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.00000i | − | 0.256997i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.3244 | −1.67917 | −0.839585 | − | 0.543228i | \(-0.817202\pi\) | ||||
−0.839585 | + | 0.543228i | \(0.817202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.57452i | 0.0825352i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.1817 | − | 40.3512i | 0.582281 | − | 1.29227i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 12.0811i | − | 0.386509i | −0.981149 | − | 0.193254i | \(-0.938096\pi\) | ||
0.981149 | − | 0.193254i | \(-0.0619043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.97698 | −0.0951446 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.23743i | 0.199146i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 16.7553i | − | 0.534410i | −0.963640 | − | 0.267205i | \(-0.913900\pi\) | ||
0.963640 | − | 0.267205i | \(-0.0861001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.1114 | −0.959430 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.76845 | 0.119951 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.746569 | 0.0237395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.77433 | 0.0563635 | 0.0281818 | − | 0.999603i | \(-0.491028\pi\) | ||||
0.0281818 | + | 0.999603i | \(0.491028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2506i | 0.547431i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 35.8496i | − | 1.13651i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5501 | 0.777509 | 0.388754 | − | 0.921341i | \(-0.372905\pi\) | ||||
0.388754 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.61213i | − | 0.0510054i |
(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 | 4368.2.h.o.337.6 | 6 | ||
4.3 | odd | 2 | 273.2.c.b.64.2 | ✓ | 6 | ||
12.11 | even | 2 | 819.2.c.c.64.5 | 6 | |||
13.12 | even | 2 | inner | 4368.2.h.o.337.1 | 6 | ||
28.27 | even | 2 | 1911.2.c.h.883.2 | 6 | |||
52.31 | even | 4 | 3549.2.a.q.1.1 | 3 | |||
52.47 | even | 4 | 3549.2.a.k.1.3 | 3 | |||
52.51 | odd | 2 | 273.2.c.b.64.5 | yes | 6 | ||
156.155 | even | 2 | 819.2.c.c.64.2 | 6 | |||
364.363 | even | 2 | 1911.2.c.h.883.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.c.b.64.2 | ✓ | 6 | 4.3 | odd | 2 | ||
273.2.c.b.64.5 | yes | 6 | 52.51 | odd | 2 | ||
819.2.c.c.64.2 | 6 | 156.155 | even | 2 | |||
819.2.c.c.64.5 | 6 | 12.11 | even | 2 | |||
1911.2.c.h.883.2 | 6 | 28.27 | even | 2 | |||
1911.2.c.h.883.5 | 6 | 364.363 | even | 2 | |||
3549.2.a.k.1.3 | 3 | 52.47 | even | 4 | |||
3549.2.a.q.1.1 | 3 | 52.31 | even | 4 | |||
4368.2.h.o.337.1 | 6 | 13.12 | even | 2 | inner | ||
4368.2.h.o.337.6 | 6 | 1.1 | even | 1 | trivial |