Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(961,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1537.2 | ||
Root | \(-0.309017 + 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1537 |
Dual form | 1568.2.i.n.961.2 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.618034 | − | 1.07047i | 0.356822 | − | 0.618034i | −0.630606 | − | 0.776103i | \(-0.717194\pi\) |
0.987428 | + | 0.158069i | \(0.0505269\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.61803 | + | 2.80252i | 0.723607 | + | 1.25332i | 0.959545 | + | 0.281556i | \(0.0908504\pi\) |
−0.235938 | + | 0.971768i | \(0.575816\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.736068 | + | 1.27491i | 0.245356 | + | 0.424969i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | − | 5.60503i | 0.975711 | − | 1.68998i | 0.298143 | − | 0.954521i | \(-0.403633\pi\) |
0.677568 | − | 0.735460i | \(-0.263034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.763932 | −0.211877 | −0.105938 | − | 0.994373i | \(-0.533785\pi\) | ||||
−0.105938 | + | 0.994373i | \(0.533785\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607 | − | 3.87298i | 0.542326 | − | 0.939336i | −0.456444 | − | 0.889752i | \(-0.650877\pi\) |
0.998770 | − | 0.0495842i | \(-0.0157896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.618034 | − | 1.07047i | −0.141787 | − | 0.245582i | 0.786383 | − | 0.617740i | \(-0.211951\pi\) |
−0.928170 | + | 0.372158i | \(0.878618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.73607 | + | 4.73901i | −0.547214 | + | 0.947802i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.52786 | 1.06384 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.23607 | + | 2.14093i | −0.222004 | + | 0.384523i | −0.955417 | − | 0.295261i | \(-0.904593\pi\) |
0.733412 | + | 0.679784i | \(0.237927\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | − | 6.92820i | −0.696311 | − | 1.20605i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.23607 | + | 3.87298i | 0.367607 | + | 0.636715i | 0.989191 | − | 0.146633i | \(-0.0468437\pi\) |
−0.621584 | + | 0.783348i | \(0.713510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.472136 | + | 0.817763i | −0.0756023 | + | 0.130947i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.47214 | 1.32313 | 0.661563 | − | 0.749890i | \(-0.269894\pi\) | ||||
0.661563 | + | 0.749890i | \(0.269894\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.47214 | 0.986991 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.38197 | + | 4.12569i | −0.355083 | + | 0.615021i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.23607 | + | 9.06914i | 0.763759 | + | 1.32287i | 0.940900 | + | 0.338684i | \(0.109982\pi\) |
−0.177141 | + | 0.984185i | \(0.556685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.76393 | − | 4.78727i | −0.387028 | − | 0.670352i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00000 | − | 8.66025i | 0.686803 | − | 1.18958i | −0.286064 | − | 0.958211i | \(-0.592347\pi\) |
0.972867 | − | 0.231367i | \(-0.0743197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.9443 | 2.82413 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.52786 | −0.202371 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.61803 | + | 7.99867i | −0.601217 | + | 1.04134i | 0.391420 | + | 0.920212i | \(0.371984\pi\) |
−0.992637 | + | 0.121126i | \(0.961349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.61803 | + | 9.73072i | 0.719316 | + | 1.24589i | 0.961271 | + | 0.275604i | \(0.0888778\pi\) |
−0.241956 | + | 0.970287i | \(0.577789\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23607 | − | 2.14093i | −0.153315 | − | 0.265550i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | + | 3.46410i | −0.244339 | + | 0.423207i | −0.961946 | − | 0.273241i | \(-0.911904\pi\) |
0.717607 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.94427 | −0.595220 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.94427 | −0.586777 | −0.293389 | − | 0.955993i | \(-0.594783\pi\) | ||||
−0.293389 | + | 0.955993i | \(0.594783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.47214 | + | 2.54981i | −0.172300 | + | 0.298433i | −0.939224 | − | 0.343306i | \(-0.888453\pi\) |
0.766923 | + | 0.641739i | \(0.221787\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.38197 | + | 5.85774i | 0.390516 | + | 0.676393i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.47214 | − | 11.2101i | −0.728172 | − | 1.26123i | −0.957655 | − | 0.287918i | \(-0.907037\pi\) |
0.229483 | − | 0.973313i | \(-0.426297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.20820 | − | 2.09267i | 0.134245 | − | 0.232519i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.23607 | 1.01379 | 0.506895 | − | 0.862008i | \(-0.330793\pi\) | ||||
0.506895 | + | 0.862008i | \(0.330793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4721 | 1.56972 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.76393 | + | 4.78727i | −0.296325 | + | 0.513249i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.52786 | + | 2.64634i | 0.158432 | + | 0.274412i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | − | 3.46410i | 0.205196 | − | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4721 | −1.26635 | −0.633177 | − | 0.774007i | \(-0.718249\pi\) | ||||
−0.633177 | + | 0.774007i | \(0.718249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.52786 | 0.957586 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.854102 | + | 1.47935i | −0.0849863 | + | 0.147201i | −0.905385 | − | 0.424591i | \(-0.860418\pi\) |
0.820399 | + | 0.571791i | \(0.193751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.76393 | − | 4.78727i | −0.272338 | − | 0.471704i | 0.697122 | − | 0.716953i | \(-0.254464\pi\) |
−0.969460 | + | 0.245249i | \(0.921130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.47214 | − | 7.74597i | −0.432338 | − | 0.748831i | 0.564736 | − | 0.825271i | \(-0.308978\pi\) |
−0.997074 | + | 0.0764405i | \(0.975644\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.23607 | + | 7.33708i | −0.405742 | + | 0.702765i | −0.994407 | − | 0.105611i | \(-0.966320\pi\) |
0.588666 | + | 0.808377i | \(0.299653\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.52786 | 0.524682 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.4721 | −1.17328 | −0.586640 | − | 0.809848i | \(-0.699550\pi\) | ||||
−0.586640 | + | 0.809848i | \(0.699550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.47214 | − | 11.2101i | 0.603530 | − | 1.04534i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.562306 | − | 0.973942i | −0.0519852 | − | 0.0900410i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.4443 | − | 26.7503i | −1.40402 | − | 2.43184i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.23607 | − | 9.06914i | 0.472120 | − | 0.817736i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.94427 | 0.793676 | 0.396838 | − | 0.917889i | \(-0.370108\pi\) | ||||
0.396838 | + | 0.917889i | \(0.370108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | − | 6.92820i | 0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.85410 | + | 10.1396i | 0.511475 | + | 0.885901i | 0.999912 | + | 0.0133016i | \(0.00423415\pi\) |
−0.488436 | + | 0.872600i | \(0.662433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.94427 | + | 15.4919i | 0.769800 | + | 1.33333i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.47214 | + | 12.9421i | −0.638388 | + | 1.10572i | 0.347399 | + | 0.937717i | \(0.387065\pi\) |
−0.985787 | + | 0.168002i | \(0.946268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.23607 | −0.104842 | −0.0524210 | − | 0.998625i | \(-0.516694\pi\) | ||||
−0.0524210 | + | 0.998625i | \(0.516694\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9443 | 1.09010 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.47214 | + | 4.28187i | −0.206730 | + | 0.358068i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.23607 | − | 12.5332i | −0.600923 | − | 1.04083i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.47214 | − | 2.54981i | −0.120602 | − | 0.208889i | 0.799403 | − | 0.600795i | \(-0.205149\pi\) |
−0.920005 | + | 0.391906i | \(0.871816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.47214 | − | 7.74597i | 0.363937 | − | 0.630358i | −0.624668 | − | 0.780891i | \(-0.714766\pi\) |
0.988605 | + | 0.150533i | \(0.0480989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.58359 | 0.532252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.381966 | − | 0.661585i | 0.0304842 | − | 0.0528002i | −0.850381 | − | 0.526168i | \(-0.823628\pi\) |
0.880865 | + | 0.473368i | \(0.156962\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.18034 | − | 10.7047i | −0.490133 | − | 0.848935i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.70820 | + | 2.95870i | 0.133797 | + | 0.231743i | 0.925137 | − | 0.379633i | \(-0.123950\pi\) |
−0.791340 | + | 0.611376i | \(0.790616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.9443 | − | 22.4201i | 1.00771 | − | 1.74541i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.4164 | −1.81202 | −0.906008 | − | 0.423261i | \(-0.860886\pi\) | ||||
−0.906008 | + | 0.423261i | \(0.860886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4164 | −0.955108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.909830 | − | 1.57587i | 0.0695764 | − | 0.120510i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.85410 | + | 4.94345i | 0.216993 | + | 0.375844i | 0.953887 | − | 0.300165i | \(-0.0970417\pi\) |
−0.736894 | + | 0.676008i | \(0.763708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.70820 | + | 9.88690i | 0.429055 | + | 0.743145i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.52786 | − | 6.11044i | 0.263685 | − | 0.456716i | −0.703533 | − | 0.710662i | \(-0.748395\pi\) |
0.967218 | + | 0.253947i | \(0.0817287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1803 | 0.905358 | 0.452679 | − | 0.891674i | \(-0.350468\pi\) | ||||
0.452679 | + | 0.891674i | \(0.350468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.8885 | 1.02667 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.23607 | + | 12.5332i | −0.532006 | + | 0.921462i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.4721 | − | 25.0665i | −1.05831 | − | 1.83304i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.47214 | − | 4.28187i | −0.178877 | − | 0.309825i | 0.762619 | − | 0.646848i | \(-0.223913\pi\) |
−0.941496 | + | 0.337023i | \(0.890580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.236068 | + | 0.408882i | −0.0169925 | + | 0.0294320i | −0.874397 | − | 0.485212i | \(-0.838742\pi\) |
0.857404 | + | 0.514644i | \(0.172076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.05573 | −0.218825 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9443 | 0.779747 | 0.389874 | − | 0.920868i | \(-0.372519\pi\) | ||||
0.389874 | + | 0.920868i | \(0.372519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.70820 | − | 13.3510i | 0.546420 | − | 0.946427i | −0.452096 | − | 0.891969i | \(-0.649324\pi\) |
0.998516 | − | 0.0544581i | \(-0.0173431\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.47214 | + | 4.28187i | 0.174371 | + | 0.302019i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7082 | + | 23.7433i | 0.957422 | + | 1.65830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.94427 | − | 5.09963i | 0.204641 | − | 0.354449i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.05573 | + | 5.29268i | −0.209375 | + | 0.362648i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.4721 | + | 18.1383i | 0.714194 | + | 1.23702i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.81966 | + | 3.15174i | 0.122961 | + | 0.212975i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.70820 | + | 2.95870i | −0.114906 | + | 0.199023i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9443 | −0.866813 | −0.433406 | − | 0.901199i | \(-0.642688\pi\) | ||||
−0.433406 | + | 0.901199i | \(0.642688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.05573 | −0.537049 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.61803 | + | 14.9269i | −0.571999 | + | 0.990731i | 0.424362 | + | 0.905493i | \(0.360499\pi\) |
−0.996361 | + | 0.0852385i | \(0.972835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.7984 | + | 20.4354i | 0.779658 | + | 1.35041i | 0.932139 | + | 0.362102i | \(0.117941\pi\) |
−0.152480 | + | 0.988307i | \(0.548726\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.94427 | + | 13.7599i | 0.520447 | + | 0.901440i | 0.999717 | + | 0.0237728i | \(0.00756784\pi\) |
−0.479271 | + | 0.877667i | \(0.659099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.9443 | + | 29.3483i | −1.10532 | + | 1.91447i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8885 | −0.898375 | −0.449188 | − | 0.893437i | \(-0.648287\pi\) | ||||
−0.449188 | + | 0.893437i | \(0.648287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.23607 | − | 10.8012i | 0.401700 | − | 0.695766i | −0.592231 | − | 0.805768i | \(-0.701753\pi\) |
0.993931 | + | 0.110003i | \(0.0350860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.79837 | + | 11.7751i | 0.436116 | + | 0.755375i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.472136 | + | 0.817763i | 0.0300413 | + | 0.0520330i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.70820 | − | 9.88690i | 0.361743 | − | 0.626557i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.29180 | −0.270896 | −0.135448 | − | 0.990784i | \(-0.543247\pi\) | ||||
−0.135448 | + | 0.990784i | \(0.543247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.8885 | −1.62760 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.94427 | − | 15.4919i | 0.560112 | − | 0.970143i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.00000 | − | 12.1244i | −0.436648 | − | 0.756297i | 0.560781 | − | 0.827964i | \(-0.310501\pi\) |
−0.997429 | + | 0.0716680i | \(0.977168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.29180 | − | 5.70156i | −0.203757 | − | 0.352918i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.52786 | + | 9.57454i | −0.340863 | + | 0.590392i | −0.984593 | − | 0.174861i | \(-0.944052\pi\) |
0.643730 | + | 0.765252i | \(0.277386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.3607 | 1.98790 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.41641 | −0.453877 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.09017 | + | 3.62028i | −0.127440 | + | 0.220732i | −0.922684 | − | 0.385557i | \(-0.874009\pi\) |
0.795244 | + | 0.606289i | \(0.207343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | − | 20.7846i | −0.728948 | − | 1.26258i | −0.957328 | − | 0.289003i | \(-0.906676\pi\) |
0.228380 | − | 0.973572i | \(-0.426657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.7082 | + | 30.6715i | 1.06784 | + | 1.84956i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.94427 | + | 6.83168i | −0.236988 | + | 0.410476i | −0.959849 | − | 0.280518i | \(-0.909494\pi\) |
0.722860 | + | 0.690994i | \(0.242827\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.63932 | −0.217880 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.09017 | + | 5.35233i | −0.183692 | + | 0.318163i | −0.943135 | − | 0.332410i | \(-0.892138\pi\) |
0.759443 | + | 0.650574i | \(0.225471\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.47214 | − | 4.28187i | −0.146437 | − | 0.253636i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.50000 | − | 2.59808i | −0.0882353 | − | 0.152828i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.70820 | + | 13.3510i | −0.451863 | + | 0.782650i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.7639 | 0.745677 | 0.372838 | − | 0.927896i | \(-0.378385\pi\) | ||||
0.372838 | + | 0.927896i | \(0.378385\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.8885 | −1.74018 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.8885 | − | 30.9839i | 1.03800 | − | 1.79787i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.52786 | + | 2.64634i | 0.0883587 | + | 0.153042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.05573 | + | 1.82857i | 0.0606500 | + | 0.105049i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.1803 | + | 31.4893i | −1.04100 | + | 1.80307i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.81966 | −0.103853 | −0.0519267 | − | 0.998651i | \(-0.516536\pi\) | ||||
−0.0519267 | + | 0.998651i | \(0.516536\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.83282 | −0.388705 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | − | 6.92820i | 0.226819 | − | 0.392862i | −0.730044 | − | 0.683400i | \(-0.760501\pi\) |
0.956864 | + | 0.290537i | \(0.0938340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.23607 | − | 7.33708i | −0.239437 | − | 0.414717i | 0.721116 | − | 0.692814i | \(-0.243629\pi\) |
−0.960553 | + | 0.278098i | \(0.910296\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.52786 | − | 7.84249i | −0.254310 | − | 0.440478i | 0.710398 | − | 0.703800i | \(-0.248515\pi\) |
−0.964708 | + | 0.263322i | \(0.915182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.4721 | + | 25.0665i | −0.810284 | + | 1.40345i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0557 | −0.617071 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.52786 | −0.307579 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.09017 | − | 3.62028i | 0.115942 | − | 0.200817i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.23607 | + | 9.06914i | 0.289555 | + | 0.501524i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.2361 | − | 19.4614i | −0.617590 | − | 1.06970i | −0.989924 | − | 0.141599i | \(-0.954776\pi\) |
0.372334 | − | 0.928099i | \(-0.378558\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.29180 | + | 5.70156i | −0.180389 | + | 0.312443i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.9443 | −0.707221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3607 | 0.564382 | 0.282191 | − | 0.959358i | \(-0.408939\pi\) | ||||
0.282191 | + | 0.959358i | \(0.408939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.70820 | + | 13.3510i | −0.418652 | + | 0.725127i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | + | 13.8564i | 0.433224 | + | 0.750366i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | − | 13.8564i | −0.430706 | − | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.23607 | + | 5.60503i | −0.173721 | + | 0.300894i | −0.939718 | − | 0.341950i | \(-0.888913\pi\) |
0.765997 | + | 0.642844i | \(0.222246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.6525 | −1.42667 | −0.713337 | − | 0.700821i | \(-0.752817\pi\) | ||||
−0.713337 | + | 0.700821i | \(0.752817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.22291 | −0.225402 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.94427 | + | 13.7599i | −0.422831 | + | 0.732365i | −0.996215 | − | 0.0869220i | \(-0.972297\pi\) |
0.573384 | + | 0.819287i | \(0.305630\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | − | 13.8564i | −0.424596 | − | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.47214 | + | 14.6742i | 0.447142 | + | 0.774473i | 0.998199 | − | 0.0599949i | \(-0.0191084\pi\) |
−0.551056 | + | 0.834468i | \(0.685775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.73607 | − | 15.1313i | 0.459793 | − | 0.796385i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −38.1803 | −2.00395 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.52786 | −0.498711 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.4164 | + | 19.7738i | −0.595932 | + | 1.03218i | 0.397483 | + | 0.917610i | \(0.369884\pi\) |
−0.993415 | + | 0.114574i | \(0.963450\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.23607 | + | 10.8012i | 0.324637 | + | 0.562287i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.47214 | − | 2.54981i | −0.0762243 | − | 0.132024i | 0.825394 | − | 0.564558i | \(-0.190953\pi\) |
−0.901618 | + | 0.432533i | \(0.857620\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.944272 | + | 1.63553i | −0.0487620 | + | 0.0844582i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.41641 | 0.175954 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.58359 | −0.235443 | −0.117722 | − | 0.993047i | \(-0.537559\pi\) | ||||
−0.117722 | + | 0.993047i | \(0.537559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.52786 | − | 9.57454i | 0.283201 | − | 0.490519i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.70820 | − | 13.3510i | −0.393871 | − | 0.682204i | 0.599086 | − | 0.800685i | \(-0.295531\pi\) |
−0.992956 | + | 0.118481i | \(0.962198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.76393 | + | 8.25137i | 0.242164 | + | 0.419441i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.23607 | − | 3.87298i | 0.113373 | − | 0.196368i | −0.803755 | − | 0.594960i | \(-0.797168\pi\) |
0.917128 | + | 0.398592i | \(0.130501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8885 | −0.904663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.4721 | 0.730023 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.9443 | − | 36.2765i | 1.05382 | − | 1.82527i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.61803 | − | 13.1948i | −0.382338 | − | 0.662229i | 0.609058 | − | 0.793126i | \(-0.291548\pi\) |
−0.991396 | + | 0.130897i | \(0.958214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7639 | + | 20.3757i | 0.587463 | + | 1.01752i | 0.994563 | + | 0.104132i | \(0.0332065\pi\) |
−0.407101 | + | 0.913383i | \(0.633460\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.944272 | − | 1.63553i | 0.0470375 | − | 0.0814714i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.81966 | 0.388562 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.9443 | 1.43471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7082 | + | 18.5472i | −0.529487 | + | 0.917098i | 0.469922 | + | 0.882708i | \(0.344282\pi\) |
−0.999408 | + | 0.0343897i | \(0.989051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.23607 | + | 15.9973i | 0.455582 | + | 0.789091i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.9443 | + | 25.8842i | 0.733585 | + | 1.27061i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.763932 | + | 1.32317i | −0.0374099 | + | 0.0647959i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.1803 | −1.08358 | −0.541790 | − | 0.840514i | \(-0.682253\pi\) | ||||
−0.541790 | + | 0.840514i | \(0.682253\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.70820 | + | 13.3510i | −0.374786 | + | 0.649148i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.2361 | + | 21.1935i | 0.593536 | + | 1.02804i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.05573 | + | 5.29268i | 0.147532 | + | 0.255533i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0000 | − | 24.2487i | 0.674356 | − | 1.16802i | −0.302300 | − | 0.953213i | \(-0.597755\pi\) |
0.976657 | − | 0.214807i | \(-0.0689121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.41641 | −0.452524 | −0.226262 | − | 0.974067i | \(-0.572651\pi\) | ||||
−0.226262 | + | 0.974067i | \(0.572651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.8885 | −0.857690 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.47214 | + | 4.28187i | −0.118258 | + | 0.204829i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.94427 | + | 12.0278i | 0.329932 | + | 0.571460i | 0.982498 | − | 0.186273i | \(-0.0596407\pi\) |
−0.652566 | + | 0.757732i | \(0.726307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.70820 | − | 16.8151i | 0.460213 | − | 0.797112i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.63932 | −0.172134 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.88854 | −0.372283 | −0.186142 | − | 0.982523i | \(-0.559598\pi\) | ||||
−0.186142 | + | 0.982523i | \(0.559598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.4164 | − | 47.4866i | 1.29099 | − | 2.23606i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.52786 | − | 9.57454i | −0.259722 | − | 0.449851i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.76393 | + | 6.51932i | 0.176069 | + | 0.304961i | 0.940531 | − | 0.339708i | \(-0.110328\pi\) |
−0.764462 | + | 0.644669i | \(0.776995\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.3607 | − | 21.4093i | 0.576947 | − | 0.999302i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.7082 | −1.01105 | −0.505526 | − | 0.862811i | \(-0.668702\pi\) | ||||
−0.505526 | + | 0.862811i | \(0.668702\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.7771 | −1.66270 | −0.831351 | − | 0.555748i | \(-0.812432\pi\) | ||||
−0.831351 | + | 0.555748i | \(0.812432\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.94427 | + | 8.56373i | −0.229285 | + | 0.397133i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.0344 | − | 27.7725i | −0.741985 | − | 1.28516i | −0.951590 | − | 0.307370i | \(-0.900551\pi\) |
0.209605 | − | 0.977786i | \(-0.432782\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.472136 | − | 0.817763i | −0.0217549 | − | 0.0376806i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.9443 | − | 36.2765i | 0.963019 | − | 1.66800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.76393 | 0.310350 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.7214 | 0.674045 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.29180 | + | 7.43361i | −0.196097 | + | 0.339650i | −0.947260 | − | 0.320467i | \(-0.896160\pi\) |
0.751162 | + | 0.660117i | \(0.229493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70820 | − | 2.95870i | −0.0778874 | − | 0.134905i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.1803 | − | 34.9534i | −0.916342 | − | 1.58715i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0000 | + | 17.3205i | −0.453143 | + | 0.784867i | −0.998579 | − | 0.0532853i | \(-0.983031\pi\) |
0.545436 | + | 0.838152i | \(0.316364\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.22291 | 0.190967 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.8885 | 1.70989 | 0.854943 | − | 0.518722i | \(-0.173592\pi\) | ||||
0.854943 | + | 0.518722i | \(0.173592\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | + | 17.3205i | −0.450377 | + | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.4164 | + | 26.7020i | 0.692916 | + | 1.20017i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.9443 | − | 18.9560i | −0.489933 | − | 0.848589i | 0.510000 | − | 0.860174i | \(-0.329645\pi\) |
−0.999933 | + | 0.0115857i | \(0.996312\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.4721 | + | 25.0665i | −0.646567 | + | 1.11989i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.94427 | 0.220454 | 0.110227 | − | 0.993906i | \(-0.464842\pi\) | ||||
0.110227 | + | 0.993906i | \(0.464842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.52786 | −0.245987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.67376 | + | 13.2913i | −0.340804 | + | 0.590289i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.5623 | − | 35.6150i | −0.911408 | − | 1.57861i | −0.812077 | − | 0.583551i | \(-0.801663\pi\) |
−0.0993316 | − | 0.995054i | \(-0.531670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.41641 | − | 5.91739i | −0.150838 | − | 0.261259i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.94427 | − | 15.4919i | 0.394132 | − | 0.682656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 67.7771 | 2.98083 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.05573 | 0.309712 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.29180 | + | 5.70156i | −0.144216 | + | 0.249790i | −0.929080 | − | 0.369878i | \(-0.879399\pi\) |
0.784864 | + | 0.619668i | \(0.212733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.14590 | − | 3.71680i | −0.0938336 | − | 0.162525i | 0.815288 | − | 0.579056i | \(-0.196579\pi\) |
−0.909121 | + | 0.416532i | \(0.863245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.52786 | + | 9.57454i | 0.240798 | + | 0.417074i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.5967 | −0.590049 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.47214 | −0.280339 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.4721 | − | 25.0665i | 0.625685 | − | 1.08372i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.36068 | − | 7.55292i | −0.188177 | − | 0.325933i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.52786 | + | 4.37839i | 0.108681 | + | 0.188242i | 0.915236 | − | 0.402917i | \(-0.132004\pi\) |
−0.806555 | + | 0.591159i | \(0.798671\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.52786 | − | 13.0386i | 0.323052 | − | 0.559542i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.4164 | −1.17439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.58359 | −0.195980 | −0.0979901 | − | 0.995187i | \(-0.531241\pi\) | ||||
−0.0979901 | + | 0.995187i | \(0.531241\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.27051 | + | 14.3249i | −0.352977 | + | 0.611374i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.76393 | + | 4.78727i | 0.117747 | + | 0.203945i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.94427 | + | 15.4919i | 0.379663 | + | 0.657596i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.52786 | + | 7.84249i | −0.191852 | + | 0.332297i | −0.945864 | − | 0.324563i | \(-0.894783\pi\) |
0.754012 | + | 0.656860i | \(0.228116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.94427 | −0.209120 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.7771 | −1.51051 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.90983 | + | 15.4323i | −0.375505 | + | 0.650393i | −0.990402 | − | 0.138214i | \(-0.955864\pi\) |
0.614898 | + | 0.788607i | \(0.289197\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1803 | − | 34.9534i | −0.848993 | − | 1.47050i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.1803 | − | 22.8290i | −0.552549 | − | 0.957042i | −0.998090 | − | 0.0617808i | \(-0.980322\pi\) |
0.445541 | − | 0.895261i | \(-0.353011\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.23607 | − | 12.5332i | 0.302820 | − | 0.524500i | −0.673954 | − | 0.738774i | \(-0.735405\pi\) |
0.976774 | + | 0.214274i | \(0.0687386\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.11146 | −0.255310 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.8885 | 0.912815 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00000 | + | 5.19615i | −0.124892 | + | 0.216319i | −0.921691 | − | 0.387926i | \(-0.873192\pi\) |
0.796799 | + | 0.604245i | \(0.206525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.291796 | + | 0.505406i | 0.0121266 | + | 0.0210039i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.3607 | − | 56.0503i | −1.34024 | − | 2.32137i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.81966 | − | 3.15174i | 0.0752337 | − | 0.130309i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.70820 | 0.153054 | 0.0765270 | − | 0.997068i | \(-0.475617\pi\) | ||||
0.0765270 | + | 0.997068i | \(0.475617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.05573 | 0.125909 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.76393 | − | 11.7155i | 0.278231 | − | 0.481910i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4164 | + | 28.4341i | 0.674141 | + | 1.16765i | 0.976719 | + | 0.214522i | \(0.0688194\pi\) |
−0.302578 | + | 0.953125i | \(0.597847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.52786 | − | 16.5027i | −0.389950 | − | 0.675412i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.94427 | + | 15.4919i | −0.365453 | + | 0.632983i | −0.988849 | − | 0.148923i | \(-0.952419\pi\) |
0.623396 | + | 0.781907i | \(0.285753\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.7771 | −1.21463 | −0.607316 | − | 0.794460i | \(-0.707754\pi\) | ||||
−0.607316 | + | 0.794460i | \(0.707754\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.88854 | −0.239800 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 49.9787 | − | 86.5657i | 2.03192 | − | 3.51940i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.94427 | + | 8.56373i | 0.200682 | + | 0.347591i | 0.948748 | − | 0.316033i | \(-0.102351\pi\) |
−0.748066 | + | 0.663624i | \(0.769018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | − | 6.92820i | −0.161823 | − | 0.280285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.7082 | + | 25.4754i | −0.594059 | + | 1.02894i | 0.399620 | + | 0.916681i | \(0.369142\pi\) |
−0.993679 | + | 0.112259i | \(0.964191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 33.8885 | 1.36652 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.3607 | 1.38331 | 0.691654 | − | 0.722229i | \(-0.256882\pi\) | ||||
0.691654 | + | 0.722229i | \(0.256882\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.0344 | + | 41.6289i | −0.966026 | + | 1.67321i | −0.259192 | + | 0.965826i | \(0.583456\pi\) |
−0.706833 | + | 0.707380i | \(0.749877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.0557 | − | 19.1491i | −0.443651 | − | 0.768426i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.2082 | + | 19.4132i | 0.448328 | + | 0.776527i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.94427 | + | 8.56373i | −0.197455 | + | 0.342002i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.9443 | −1.78920 | −0.894602 | − | 0.446865i | \(-0.852541\pi\) | ||||
−0.894602 | + | 0.446865i | \(0.852541\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.41641 | + | 12.8456i | −0.294776 | + | 0.510567i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.4721 | + | 25.0665i | 0.574309 | + | 0.994733i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.63932 | − | 6.30349i | −0.143969 | − | 0.249362i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.29180 | + | 12.6298i | −0.288009 | + | 0.498846i | −0.973334 | − | 0.229391i | \(-0.926327\pi\) |
0.685326 | + | 0.728237i | \(0.259660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.7082 | 1.72368 | 0.861842 | − | 0.507177i | \(-0.169311\pi\) | ||||
0.861842 | + | 0.507177i | \(0.169311\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.8885 | 1.01936 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.1803 | + | 17.6329i | −0.400230 | + | 0.693219i | −0.993753 | − | 0.111598i | \(-0.964403\pi\) |
0.593523 | + | 0.804817i | \(0.297737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.8885 | + | 51.7685i | 1.17323 | + | 2.03209i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.70820 | + | 8.15485i | 0.184246 | + | 0.319124i | 0.943322 | − | 0.331878i | \(-0.107682\pi\) |
−0.759076 | + | 0.651002i | \(0.774349\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9443 | + | 32.8124i | −0.740214 | + | 1.28209i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.33437 | −0.169100 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.3050 | 1.45319 | 0.726597 | − | 0.687064i | \(-0.241101\pi\) | ||||
0.726597 | + | 0.687064i | \(0.241101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.3262 | + | 19.6176i | −0.440540 | + | 0.763037i | −0.997730 | − | 0.0673481i | \(-0.978546\pi\) |
0.557190 | + | 0.830385i | \(0.311880\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.11146 | + | 3.65715i | 0.0820022 | + | 0.142032i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.94427 | + | 15.4919i | 0.346324 | + | 0.599850i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 72.7214 | 2.80738 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.94427 | −0.113493 | −0.0567467 | − | 0.998389i | \(-0.518073\pi\) | ||||
−0.0567467 | + | 0.998389i | \(0.518073\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.1246 | + | 26.1966i | −0.582147 | + | 1.00831i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.90983 | + | 17.1643i | 0.380866 | + | 0.659679i | 0.991186 | − | 0.132476i | \(-0.0422927\pi\) |
−0.610321 | + | 0.792155i | \(0.708959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.6525 | + | 18.4506i | 0.408204 | + | 0.707030i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.8885 | + | 20.5916i | −0.454902 | + | 0.787914i | −0.998683 | − | 0.0513135i | \(-0.983659\pi\) |
0.543780 | + | 0.839228i | \(0.316993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48.3607 | −1.84777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.1672 | 1.11280 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.81966 | + | 6.61585i | −0.145517 | + | 0.252044i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.09017 | − | 12.2805i | −0.269723 | − | 0.467174i | 0.699067 | − | 0.715056i | \(-0.253599\pi\) |
−0.968790 | + | 0.247882i | \(0.920265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.00000 | − | 3.46410i | −0.0758643 | − | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.9443 | − | 32.8124i | 0.717565 | − | 1.24286i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.6393 | 0.742827 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.4164 | −1.56428 | −0.782138 | − | 0.623105i | \(-0.785871\pi\) | ||||
−0.782138 | + | 0.623105i | \(0.785871\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.76393 | − | 4.78727i | 0.104244 | − | 0.180555i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.9443 | + | 36.2765i | 0.788807 | + | 1.36625i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.819660 | − | 1.41969i | −0.0307830 | − | 0.0533177i | 0.850223 | − | 0.526422i | \(-0.176467\pi\) |
−0.881006 | + | 0.473104i | \(0.843133\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.52786 | − | 16.5027i | 0.357323 | − | 0.618901i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.88854 | 0.370329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | −0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.58359 | + | 14.8672i | −0.320560 | + | 0.555226i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.5967 | + | 44.3349i | 0.954598 | + | 1.65341i | 0.735286 | + | 0.677757i | \(0.237048\pi\) |
0.219311 | + | 0.975655i | \(0.429619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.70820 | − | 13.3510i | −0.286671 | − | 0.496529i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.2361 | − | 21.1935i | 0.454436 | − | 0.787107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.3607 | −0.458432 | −0.229216 | − | 0.973376i | \(-0.573616\pi\) | ||||
−0.229216 | + | 0.973376i | \(0.573616\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0557 | 0.890953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.4721 | − | 25.0665i | 0.535271 | − | 0.927117i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.38197 | − | 4.12569i | −0.0879799 | − | 0.152386i | 0.818677 | − | 0.574254i | \(-0.194708\pi\) |
−0.906657 | + | 0.421868i | \(0.861374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9443 | + | 22.4201i | 0.476808 | + | 0.825856i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.70820 | − | 2.95870i | 0.0628373 | − | 0.108837i | −0.832895 | − | 0.553431i | \(-0.813318\pi\) |
0.895733 | + | 0.444593i | \(0.146652\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.16718 | 0.0428776 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.9443 | 0.915117 | 0.457558 | − | 0.889180i | \(-0.348724\pi\) | ||||
0.457558 | + | 0.889180i | \(0.348724\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.76393 | − | 8.25137i | 0.174537 | − | 0.302307i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.79837 | + | 11.7751i | 0.248739 | + | 0.430829i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0000 | − | 31.1769i | −0.656829 | − | 1.13766i | −0.981432 | − | 0.191811i | \(-0.938564\pi\) |
0.324603 | − | 0.945851i | \(-0.394769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.65248 | + | 4.59422i | −0.0966616 | + | 0.167423i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.9443 | 1.05339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3050 | 1.42856 | 0.714281 | − | 0.699859i | \(-0.246754\pi\) | ||||
0.714281 | + | 0.699859i | \(0.246754\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.0000 | + | 27.7128i | −0.580763 | + | 1.00591i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.76393 | − | 3.05522i | −0.0639425 | − | 0.110752i | 0.832282 | − | 0.554353i | \(-0.187034\pi\) |
−0.896224 | + | 0.443601i | \(0.853701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.6525 | + | 18.4506i | 0.385141 | + | 0.667084i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.52786 | − | 6.11044i | 0.127384 | − | 0.220635i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3607 | 0.662103 | 0.331052 | − | 0.943613i | \(-0.392597\pi\) | ||||
0.331052 | + | 0.943613i | \(0.392597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.3050 | −0.623223 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.0902 | − | 34.7972i | 0.722593 | − | 1.25157i | −0.237364 | − | 0.971421i | \(-0.576283\pi\) |
0.959957 | − | 0.280147i | \(-0.0903833\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.76393 | − | 11.7155i | −0.242968 | − | 0.420832i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.23607 | − | 9.06914i | −0.187602 | − | 0.324936i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0000 | + | 27.7128i | −0.572525 | + | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.7214 | −0.883469 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.47214 | 0.0882343 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.14590 | + | 10.6450i | −0.219078 | + | 0.379454i | −0.954526 | − | 0.298127i | \(-0.903638\pi\) |
0.735449 | + | 0.677580i | \(0.236971\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.83282 | + | 11.8348i | 0.243255 | + | 0.421329i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.29180 | − | 7.43361i | −0.152406 | − | 0.263975i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.0000 | − | 34.6410i | 0.709327 | − | 1.22859i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.1803 | 1.84832 | 0.924161 | − | 0.382003i | \(-0.124765\pi\) | ||||
0.924161 | + | 0.382003i | \(0.124765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.8328 | 1.65683 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.41641 | − | 7.64944i | 0.156046 | − | 0.270280i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.52786 | + | 16.5027i | 0.336231 | + | 0.582369i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.58359 | + | 4.47491i | 0.0909468 | + | 0.157524i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.70820 | − | 15.0831i | 0.306164 | − | 0.530292i | −0.671356 | − | 0.741135i | \(-0.734288\pi\) |
0.977520 | + | 0.210843i | \(0.0676210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.0132 | 1.86154 | 0.930772 | − | 0.365601i | \(-0.119136\pi\) | ||||
0.930772 | + | 0.365601i | \(0.119136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.6656 | −1.04042 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.52786 | + | 9.57454i | −0.193633 | + | 0.335382i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00000 | − | 6.92820i | −0.139942 | − | 0.242387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.05573 | − | 3.56063i | −0.0717454 | − | 0.124267i | 0.827921 | − | 0.560845i | \(-0.189524\pi\) |
−0.899666 | + | 0.436578i | \(0.856190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.88854 | − | 17.1275i | 0.344693 | − | 0.597026i | −0.640605 | − | 0.767871i | \(-0.721316\pi\) |
0.985298 | + | 0.170845i | \(0.0546497\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 43.7771 | 1.52412 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.0557 | 0.523539 | 0.261769 | − | 0.965130i | \(-0.415694\pi\) | ||||
0.261769 | + | 0.965130i | \(0.415694\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.61803 | − | 9.73072i | 0.195122 | − | 0.337962i | −0.751818 | − | 0.659370i | \(-0.770823\pi\) |
0.946941 | + | 0.321409i | \(0.104156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.87539 | + | 8.44442i | 0.169125 | + | 0.292934i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.8885 | − | 65.6249i | −1.31119 | − | 2.27104i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.83282 | + | 11.8348i | −0.236177 | + | 0.409070i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.5279 | 0.743224 | 0.371612 | − | 0.928388i | \(-0.378805\pi\) | ||||
0.371612 | + | 0.928388i | \(0.378805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.0689 | − | 27.8321i | 0.553442 | − | 0.958589i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.0902 | − | 34.7972i | −0.691123 | − | 1.19706i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.81966 | + | 6.61585i | 0.131090 | + | 0.227055i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.94427 | − | 15.4919i | 0.306606 | − | 0.531057i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.7082 | −0.469360 | −0.234680 | − | 0.972073i | \(-0.575404\pi\) | ||||
−0.234680 | + | 0.972073i | \(0.575404\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.88854 | 0.201384 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.7639 | + | 23.8398i | −0.470167 | + | 0.814353i | −0.999418 | − | 0.0341122i | \(-0.989140\pi\) |
0.529251 | + | 0.848465i | \(0.322473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9098 | − | 29.2887i | −0.576956 | − | 0.999317i | −0.995826 | − | 0.0912709i | \(-0.970907\pi\) |
0.418870 | − | 0.908046i | \(-0.362426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.4721 | + | 18.1383i | 0.356476 | + | 0.617434i | 0.987369 | − | 0.158435i | \(-0.0506449\pi\) |
−0.630894 | + | 0.775869i | \(0.717312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.23607 | + | 15.9973i | −0.314036 | + | 0.543926i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.70820 | −0.125937 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −83.7771 | −2.84194 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.52786 | − | 2.64634i | 0.0517697 | − | 0.0896677i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.18034 | − | 15.9008i | −0.310707 | − | 0.538161i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.70820 | − | 11.6190i | −0.226520 | − | 0.392344i | 0.730254 | − | 0.683175i | \(-0.239402\pi\) |
−0.956774 | + | 0.290831i | \(0.906068\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.88854 | − | 13.6634i | 0.266074 | − | 0.460854i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.8328 | −0.836639 | −0.418319 | − | 0.908300i | \(-0.637381\pi\) | ||||
−0.418319 | + | 0.908300i | \(0.637381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0557 | 0.775887 | 0.387944 | − | 0.921683i | \(-0.373186\pi\) | ||||
0.387944 | + | 0.921683i | \(0.373186\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.4721 | + | 31.9947i | −0.620934 | + | 1.07549i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.6525 | − | 28.8429i | −0.559135 | − | 0.968451i | −0.997569 | − | 0.0696873i | \(-0.977800\pi\) |
0.438433 | − | 0.898764i | \(-0.355533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.81966 | − | 13.5440i | −0.261968 | − | 0.453743i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.47214 | − | 11.2101i | 0.216582 | − | 0.375131i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.8328 | 0.763217 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.77709 | 0.126113 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.52786 | − | 9.57454i | 0.184365 | − | 0.319329i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.3607 | − | 38.7298i | −0.744942 | − | 1.29028i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.7082 | + | 34.1356i | 0.655123 | + | 1.13471i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.472136 | + | 0.817763i | −0.0156770 | + | 0.0271534i | −0.873757 | − | 0.486362i | \(-0.838324\pi\) |
0.858080 | + | 0.513515i | \(0.171657\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.51471 | −0.0834076 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.8328 | −1.15406 | −0.577031 | − | 0.816722i | \(-0.695789\pi\) | ||||
−0.577031 | + | 0.816722i | \(0.695789\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.8885 | − | 51.7685i | 0.989166 | − | 1.71329i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.4721 | + | 38.9229i | 0.742906 | + | 1.28675i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.8885 | + | 30.9839i | 0.590089 | + | 1.02206i | 0.994220 | + | 0.107362i | \(0.0342405\pi\) |
−0.404131 | + | 0.914701i | \(0.632426\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.12461 | + | 1.94788i | −0.0370572 | + | 0.0641850i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.77709 | 0.124324 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.4721 | −0.804639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.06888 | − | 7.04751i | 0.133640 | − | 0.231471i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.6525 | − | 40.9673i | −0.776013 | − | 1.34409i | −0.934224 | − | 0.356688i | \(-0.883906\pi\) |
0.158211 | − | 0.987405i | \(-0.449427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.94427 | − | 8.56373i | −0.161868 | − | 0.280364i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.8328 | − | 81.1168i | 1.53160 | − | 2.65280i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.05573 | 0.295838 | 0.147919 | − | 0.988999i | \(-0.452743\pi\) | ||||
0.147919 | + | 0.988999i | \(0.452743\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.4721 | −0.341745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.7984 | + | 30.8277i | −0.580210 | + | 1.00495i | 0.415244 | + | 0.909710i | \(0.363696\pi\) |
−0.995454 | + | 0.0952436i | \(0.969637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.9443 | − | 29.3483i | −0.551781 | − | 0.955713i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.29180 | + | 3.96951i | 0.0744734 | + | 0.128992i | 0.900857 | − | 0.434116i | \(-0.142939\pi\) |
−0.826384 | + | 0.563107i | \(0.809606\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.12461 | − | 1.94788i | 0.0365064 | − | 0.0632310i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.1935 | −0.362974 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.8885 | 1.68083 | 0.840417 | − | 0.541940i | \(-0.182310\pi\) | ||||
0.840417 | + | 0.541940i | \(0.182310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | − | 13.8564i | 0.258874 | − | 0.448383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.8885 | + | 30.9839i | 0.578254 | + | 1.00157i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.4443 | + | 21.5541i | 0.401428 | + | 0.695294i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.58359 | − | 11.4031i | 0.212153 | − | 0.367460i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.52786 | −0.0491837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8885 | 0.961151 | 0.480575 | − | 0.876953i | \(-0.340428\pi\) | ||||
0.480575 | + | 0.876953i | \(0.340428\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.41641 | + | 5.91739i | −0.109751 | + | 0.190094i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3820 | + | 19.7141i | 0.365265 | + | 0.632657i | 0.988819 | − | 0.149123i | \(-0.0476452\pi\) |
−0.623554 | + | 0.781780i | \(0.714312\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.58359 | − | 4.47491i | −0.0827412 | − | 0.143312i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.41641 | − | 11.1135i | 0.205279 | − | 0.355554i | −0.744943 | − | 0.667129i | \(-0.767523\pi\) |
0.950222 | + | 0.311575i | \(0.100856\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.8328 | −1.24110 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.4721 | −0.398205 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.76393 | + | 4.78727i | −0.0881557 | + | 0.152690i | −0.906732 | − | 0.421708i | \(-0.861431\pi\) |
0.818576 | + | 0.574398i | \(0.194764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.7082 | + | 30.6715i | 0.564230 | + | 0.977276i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.9443 | − | 22.4201i | −0.411604 | − | 0.712919i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.0000 | − | 20.7846i | 0.381193 | − | 0.660245i | −0.610040 | − | 0.792370i | \(-0.708847\pi\) |
0.991233 | + | 0.132125i | \(0.0421802\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.7771 | −0.881479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.8885 | 1.58157 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.03444 | − | 15.6481i | 0.286124 | − | 0.495581i | −0.686757 | − | 0.726887i | \(-0.740967\pi\) |
0.972881 | + | 0.231306i | \(0.0742999\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.3607 | + | 21.4093i | 0.391075 | + | 0.677361i |
(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 | 1568.2.i.n.1537.2 | 4 | ||
4.3 | odd | 2 | 1568.2.i.w.1537.1 | 4 | |||
7.2 | even | 3 | inner | 1568.2.i.n.961.2 | 4 | ||
7.3 | odd | 6 | 224.2.a.c.1.2 | ✓ | 2 | ||
7.4 | even | 3 | 1568.2.a.v.1.1 | 2 | |||
7.5 | odd | 6 | 1568.2.i.v.961.1 | 4 | |||
7.6 | odd | 2 | 1568.2.i.v.1537.1 | 4 | |||
21.17 | even | 6 | 2016.2.a.r.1.1 | 2 | |||
28.3 | even | 6 | 224.2.a.d.1.1 | yes | 2 | ||
28.11 | odd | 6 | 1568.2.a.k.1.2 | 2 | |||
28.19 | even | 6 | 1568.2.i.m.961.2 | 4 | |||
28.23 | odd | 6 | 1568.2.i.w.961.1 | 4 | |||
28.27 | even | 2 | 1568.2.i.m.1537.2 | 4 | |||
35.24 | odd | 6 | 5600.2.a.bk.1.1 | 2 | |||
56.3 | even | 6 | 448.2.a.i.1.2 | 2 | |||
56.11 | odd | 6 | 3136.2.a.by.1.1 | 2 | |||
56.45 | odd | 6 | 448.2.a.j.1.1 | 2 | |||
56.53 | even | 6 | 3136.2.a.bf.1.2 | 2 | |||
84.59 | odd | 6 | 2016.2.a.o.1.1 | 2 | |||
112.3 | even | 12 | 1792.2.b.m.897.2 | 4 | |||
112.45 | odd | 12 | 1792.2.b.k.897.3 | 4 | |||
112.59 | even | 12 | 1792.2.b.m.897.3 | 4 | |||
112.101 | odd | 12 | 1792.2.b.k.897.2 | 4 | |||
140.59 | even | 6 | 5600.2.a.z.1.2 | 2 | |||
168.59 | odd | 6 | 4032.2.a.bv.1.2 | 2 | |||
168.101 | even | 6 | 4032.2.a.bw.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.a.c.1.2 | ✓ | 2 | 7.3 | odd | 6 | ||
224.2.a.d.1.1 | yes | 2 | 28.3 | even | 6 | ||
448.2.a.i.1.2 | 2 | 56.3 | even | 6 | |||
448.2.a.j.1.1 | 2 | 56.45 | odd | 6 | |||
1568.2.a.k.1.2 | 2 | 28.11 | odd | 6 | |||
1568.2.a.v.1.1 | 2 | 7.4 | even | 3 | |||
1568.2.i.m.961.2 | 4 | 28.19 | even | 6 | |||
1568.2.i.m.1537.2 | 4 | 28.27 | even | 2 | |||
1568.2.i.n.961.2 | 4 | 7.2 | even | 3 | inner | ||
1568.2.i.n.1537.2 | 4 | 1.1 | even | 1 | trivial | ||
1568.2.i.v.961.1 | 4 | 7.5 | odd | 6 | |||
1568.2.i.v.1537.1 | 4 | 7.6 | odd | 2 | |||
1568.2.i.w.961.1 | 4 | 28.23 | odd | 6 | |||
1568.2.i.w.1537.1 | 4 | 4.3 | odd | 2 | |||
1792.2.b.k.897.2 | 4 | 112.101 | odd | 12 | |||
1792.2.b.k.897.3 | 4 | 112.45 | odd | 12 | |||
1792.2.b.m.897.2 | 4 | 112.3 | even | 12 | |||
1792.2.b.m.897.3 | 4 | 112.59 | even | 12 | |||
2016.2.a.o.1.1 | 2 | 84.59 | odd | 6 | |||
2016.2.a.r.1.1 | 2 | 21.17 | even | 6 | |||
3136.2.a.bf.1.2 | 2 | 56.53 | even | 6 | |||
3136.2.a.by.1.1 | 2 | 56.11 | odd | 6 | |||
4032.2.a.bv.1.2 | 2 | 168.59 | odd | 6 | |||
4032.2.a.bw.1.2 | 2 | 168.101 | even | 6 | |||
5600.2.a.z.1.2 | 2 | 140.59 | even | 6 | |||
5600.2.a.bk.1.1 | 2 | 35.24 | odd | 6 |