Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(361,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.do (of order \(6\), degree \(2\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.895644 + 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.361 |
Dual form | 819.2.do.d.667.1 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89564 | − | 1.09445i | −1.34042 | − | 0.773893i | −0.353553 | − | 0.935414i | \(-0.615027\pi\) |
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.39564 | + | 2.41733i | 0.697822 | + | 1.20866i | ||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 1.00000i | ||||||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.79129 | −1.19891 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 2.89564 | − | 5.01540i | 0.773893 | − | 1.34042i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.895644 | − | 1.55130i | 0.223911 | − | 0.387825i | ||||
\(17\) | 0.500000 | + | 0.866025i | 0.121268 | + | 0.210042i | 0.920268 | − | 0.391289i | \(-0.127971\pi\) |
−0.799000 | + | 0.601331i | \(0.794637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.29150i | 1.21395i | 0.794719 | + | 0.606977i | \(0.207618\pi\) | ||||
−0.794719 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(20\) | 4.18693 | + | 2.41733i | 0.936226 | + | 0.540531i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.79129 | − | 6.56670i | 0.808305 | − | 1.40003i | ||||
\(23\) | −4.29129 | + | 7.43273i | −0.894795 | + | 1.54983i | −0.0607377 | + | 0.998154i | \(0.519345\pi\) |
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | −1.89564 | + | 7.66115i | −0.371766 | + | 1.50248i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.39564 | + | 3.69253i | −1.20866 | + | 0.697822i | ||||
\(29\) | −3.50000 | − | 6.06218i | −0.649934 | − | 1.12572i | −0.983138 | − | 0.182864i | \(-0.941463\pi\) |
0.333205 | − | 0.942855i | \(-0.391870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.29129 | − | 3.05493i | −0.950343 | − | 0.548681i | −0.0571558 | − | 0.998365i | \(-0.518203\pi\) |
−0.893188 | + | 0.449684i | \(0.851537\pi\) | |||||||
\(32\) | −6.39564 | + | 3.69253i | −1.13060 | + | 0.652753i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.18890i | − | 0.375393i | ||||||
\(35\) | 2.29129 | + | 3.96863i | 0.387298 | + | 0.670820i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.08258 | − | 3.51178i | −0.999969 | − | 0.577333i | −0.0917301 | − | 0.995784i | \(-0.529240\pi\) |
−0.908239 | + | 0.418451i | \(0.862573\pi\) | |||||||
\(38\) | 5.79129 | − | 10.0308i | 0.939471 | − | 1.62721i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | 3.08258 | − | 1.77973i | 0.481417 | − | 0.277946i | −0.239590 | − | 0.970874i | \(-0.577013\pi\) |
0.721007 | + | 0.692928i | \(0.243680\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.29129 | + | 3.96863i | −0.349418 | + | 0.605210i | −0.986146 | − | 0.165878i | \(-0.946954\pi\) |
0.636728 | + | 0.771088i | \(0.280287\pi\) | |||||||
\(44\) | −8.37386 | + | 4.83465i | −1.26241 | + | 0.728851i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.2695 | − | 9.39320i | 2.39881 | − | 1.38495i | ||||
\(47\) | −0.708712 | + | 0.409175i | −0.103376 | + | 0.0596843i | −0.550797 | − | 0.834639i | \(-0.685676\pi\) |
0.447421 | + | 0.894324i | \(0.352343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 3.79129 | − | 2.18890i | 0.536169 | − | 0.309557i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.97822 | − | 7.25198i | 0.967705 | − | 1.00567i | ||||
\(53\) | −3.08258 | + | 5.33918i | −0.423424 | + | 0.733392i | −0.996272 | − | 0.0862695i | \(-0.972505\pi\) |
0.572848 | + | 0.819662i | \(0.305839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | + | 5.19615i | 0.404520 | + | 0.700649i | ||||
\(56\) | 4.58258 | 0.612372 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.3223i | 2.01192i | ||||||||
\(59\) | 3.70871 | − | 2.14123i | 0.482833 | − | 0.278764i | −0.238763 | − | 0.971078i | \(-0.576742\pi\) |
0.721596 | + | 0.692314i | \(0.243409\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.16515 | −0.661330 | −0.330665 | − | 0.943748i | \(-0.607273\pi\) | ||||
−0.330665 | + | 0.943748i | \(0.607273\pi\) | |||||||
\(62\) | 6.68693 | + | 11.5821i | 0.849241 | + | 1.47093i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.5826 | 1.57282 | ||||||||
\(65\) | −4.50000 | − | 4.33013i | −0.558156 | − | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0471i | 1.71613i | 0.513543 | + | 0.858064i | \(0.328333\pi\) | ||||
−0.513543 | + | 0.858064i | \(0.671667\pi\) | |||||||
\(68\) | −1.39564 | + | 2.41733i | −0.169247 | + | 0.293144i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 10.0308i | − | 1.19891i | ||||||
\(71\) | 3.87386 | + | 2.23658i | 0.459743 | + | 0.265433i | 0.711936 | − | 0.702244i | \(-0.247819\pi\) |
−0.252193 | + | 0.967677i | \(0.581152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.50000 | + | 4.33013i | 0.877809 | + | 0.506803i | 0.869935 | − | 0.493166i | \(-0.164160\pi\) |
0.00787336 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(74\) | 7.68693 | + | 13.3142i | 0.893588 | + | 1.54774i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.7913 | + | 7.38505i | −1.46726 | + | 0.847124i | ||||
\(77\) | −9.16515 | −1.04447 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.708712 | + | 1.22753i | 0.0797363 | + | 0.138107i | 0.903136 | − | 0.429354i | \(-0.141259\pi\) |
−0.823400 | + | 0.567462i | \(0.807925\pi\) | |||||||
\(80\) | − | 3.10260i | − | 0.346881i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.79129 | −0.860404 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | + | 0.866025i | 0.162698 | + | 0.0939336i | ||||
\(86\) | 8.68693 | − | 5.01540i | 0.936736 | − | 0.540825i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.00000 | 0.639602 | ||||||||
\(89\) | 13.5000 | + | 7.79423i | 1.43100 | + | 0.826187i | 0.997197 | − | 0.0748225i | \(-0.0238390\pi\) |
0.433800 | + | 0.901009i | \(0.357172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.16515 | − | 2.64575i | 0.960769 | − | 0.277350i | ||||
\(92\) | −23.9564 | −2.49763 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.79129 | 0.184757 | ||||||||
\(95\) | 4.58258 | + | 7.93725i | 0.470162 | + | 0.814345i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.08258 | + | 5.24383i | 0.922196 | + | 0.532430i | 0.884335 | − | 0.466853i | \(-0.154612\pi\) |
0.0378609 | + | 0.999283i | \(0.487946\pi\) | |||||||
\(98\) | 13.2695 | + | 7.66115i | 1.34042 | + | 0.773893i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.58258 | −0.558258 | ||||||||
\(101\) | −13.1652 | −1.30998 | −0.654991 | − | 0.755637i | \(-0.727327\pi\) | ||||
−0.654991 | + | 0.755637i | \(0.727327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.70871 | − | 2.95958i | −0.168364 | − | 0.291616i | 0.769481 | − | 0.638670i | \(-0.220515\pi\) |
−0.937845 | + | 0.347055i | \(0.887182\pi\) | |||||||
\(104\) | −6.00000 | + | 1.73205i | −0.588348 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.6869 | − | 6.74745i | 1.13514 | − | 0.655371i | ||||
\(107\) | −0.708712 | + | 1.22753i | −0.0685138 | + | 0.118669i | −0.898247 | − | 0.439490i | \(-0.855159\pi\) |
0.829733 | + | 0.558160i | \(0.188492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.6652 | + | 9.62163i | 1.59623 | + | 0.921585i | 0.992204 | + | 0.124622i | \(0.0397717\pi\) |
0.604028 | + | 0.796963i | \(0.293562\pi\) | |||||||
\(110\) | − | 13.1334i | − | 1.25222i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.10436 | + | 2.36965i | 0.387825 | + | 0.223911i | ||||
\(113\) | 6.08258 | − | 10.5353i | 0.572201 | − | 0.991080i | −0.424139 | − | 0.905597i | \(-0.639423\pi\) |
0.996340 | − | 0.0854834i | \(-0.0272435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.8655i | 1.38621i | ||||||||
\(116\) | 9.76951 | − | 16.9213i | 0.907076 | − | 1.57110i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.37386 | −0.862934 | ||||||||
\(119\) | −2.29129 | + | 1.32288i | −0.210042 | + | 0.121268i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 9.79129 | + | 5.65300i | 0.886462 | + | 0.511799i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 17.0544i | − | 1.53153i | ||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.29129 | − | 5.70068i | −0.292055 | − | 0.505853i | 0.682241 | − | 0.731128i | \(-0.261006\pi\) |
−0.974295 | + | 0.225274i | \(0.927672\pi\) | |||||||
\(128\) | −11.0608 | − | 6.38595i | −0.977645 | − | 0.564444i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.79129 | + | 13.1334i | 0.332518 | + | 1.15188i | ||||
\(131\) | 0.708712 | + | 1.22753i | 0.0619205 | + | 0.107249i | 0.895324 | − | 0.445416i | \(-0.146944\pi\) |
−0.833403 | + | 0.552665i | \(0.813611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.0000 | −1.21395 | ||||||||
\(134\) | 15.3739 | − | 26.6283i | 1.32810 | − | 2.30034i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.50000 | − | 0.866025i | 0.128624 | − | 0.0742611i | ||||
\(137\) | 7.50000 | − | 4.33013i | 0.640768 | − | 0.369948i | −0.144142 | − | 0.989557i | \(-0.546042\pi\) |
0.784910 | + | 0.619609i | \(0.212709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.29129 | − | 5.70068i | 0.279163 | − | 0.483525i | −0.692014 | − | 0.721884i | \(-0.743276\pi\) |
0.971177 | + | 0.238359i | \(0.0766096\pi\) | |||||||
\(140\) | −6.39564 | + | 11.0776i | −0.540531 | + | 0.936226i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.89564 | − | 8.47950i | −0.410833 | − | 0.711584i | ||||
\(143\) | 12.0000 | − | 3.46410i | 1.00349 | − | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.5000 | − | 6.06218i | −0.871978 | − | 0.503436i | ||||
\(146\) | −9.47822 | − | 16.4168i | −0.784423 | − | 1.35866i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 19.6048i | − | 1.61150i | ||||||
\(149\) | − | 3.65480i | − | 0.299413i | −0.988730 | − | 0.149707i | \(-0.952167\pi\) | ||
0.988730 | − | 0.149707i | \(-0.0478329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4564 | − | 8.34643i | −1.17645 | − | 0.679223i | −0.221258 | − | 0.975215i | \(-0.571016\pi\) |
−0.955190 | + | 0.295993i | \(0.904350\pi\) | |||||||
\(152\) | 9.16515 | 0.743392 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.3739 | + | 10.0308i | 1.40003 | + | 0.808305i | ||||
\(155\) | −10.5826 | −0.850013 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.08258 | + | 8.80328i | −0.405634 | + | 0.702578i | −0.994395 | − | 0.105729i | \(-0.966282\pi\) |
0.588761 | + | 0.808307i | \(0.299616\pi\) | |||||||
\(158\) | − | 3.10260i | − | 0.246830i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.39564 | + | 11.0776i | −0.505620 | + | 0.875760i | ||||
\(161\) | −19.6652 | − | 11.3537i | −1.54983 | − | 0.894795i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.46410i | 0.271329i | 0.990755 | + | 0.135665i | \(0.0433170\pi\) | ||||
−0.990755 | + | 0.135665i | \(0.956683\pi\) | |||||||
\(164\) | 8.60436 | + | 4.96773i | 0.671887 | + | 0.387914i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.79129 | + | 6.56670i | −0.294261 | + | 0.509675i | ||||
\(167\) | −3.87386 | + | 2.23658i | −0.299769 | + | 0.173071i | −0.642339 | − | 0.766421i | \(-0.722036\pi\) |
0.342570 | + | 0.939492i | \(0.388702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | −1.89564 | − | 3.28335i | −0.145389 | − | 0.251822i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.7913 | −0.975327 | ||||||||
\(173\) | −24.3303 | −1.84980 | −0.924899 | − | 0.380212i | \(-0.875851\pi\) | ||||
−0.924899 | + | 0.380212i | \(0.875851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.58258 | − | 2.64575i | −0.346410 | − | 0.200000i | ||||
\(176\) | 5.37386 | + | 3.10260i | 0.405070 | + | 0.233867i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.0608 | − | 29.5502i | −1.27876 | − | 2.21488i | ||||
\(179\) | −0.834849 | −0.0623995 | −0.0311998 | − | 0.999513i | \(-0.509933\pi\) | ||||
−0.0311998 | + | 0.999513i | \(0.509933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | −20.2695 | − | 5.01540i | −1.50248 | − | 0.371766i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.8739 | + | 7.43273i | 0.949074 | + | 0.547948i | ||||
\(185\) | −12.1652 | −0.894400 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00000 | + | 1.73205i | −0.219382 | + | 0.126660i | ||||
\(188\) | −1.97822 | − | 1.14213i | −0.144276 | − | 0.0832981i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 20.0616i | − | 1.45542i | ||||||
\(191\) | 14.3303 | 1.03690 | 0.518452 | − | 0.855107i | \(-0.326508\pi\) | ||||
0.518452 | + | 0.855107i | \(0.326508\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.65480i | 0.263078i | 0.991311 | + | 0.131539i | \(0.0419919\pi\) | ||||
−0.991311 | + | 0.131539i | \(0.958008\pi\) | |||||||
\(194\) | −11.4782 | − | 19.8809i | −0.824088 | − | 1.42736i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.76951 | − | 16.9213i | −0.697822 | − | 1.20866i | ||||
\(197\) | −15.2477 | + | 8.80328i | −1.08636 | + | 0.627208i | −0.932604 | − | 0.360902i | \(-0.882469\pi\) |
−0.153752 | + | 0.988110i | \(0.549136\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.29129 | − | 2.23658i | −0.0915370 | − | 0.158547i | 0.816621 | − | 0.577174i | \(-0.195845\pi\) |
−0.908158 | + | 0.418627i | \(0.862511\pi\) | |||||||
\(200\) | 3.00000 | + | 1.73205i | 0.212132 | + | 0.122474i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24.9564 | + | 14.4086i | 1.75593 | + | 1.01379i | ||||
\(203\) | 16.0390 | − | 9.26013i | 1.12572 | − | 0.649934i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.08258 | − | 5.33918i | 0.215296 | − | 0.372904i | ||||
\(206\) | 7.48040i | 0.521184i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.26951 | − | 1.55130i | −0.434712 | − | 0.107563i | ||||
\(209\) | −18.3303 | −1.26793 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.29129 | − | 5.70068i | −0.226582 | − | 0.392451i | 0.730211 | − | 0.683222i | \(-0.239422\pi\) |
−0.956793 | + | 0.290771i | \(0.906088\pi\) | |||||||
\(212\) | −17.2087 | −1.18190 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.68693 | − | 1.55130i | 0.183675 | − | 0.106045i | ||||
\(215\) | 7.93725i | 0.541316i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.08258 | − | 13.9994i | 0.548681 | − | 0.950343i | ||||
\(218\) | −21.0608 | − | 36.4784i | −1.42642 | − | 2.47063i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.37386 | + | 14.5040i | −0.564566 | + | 0.977857i | ||||
\(221\) | 2.50000 | − | 2.59808i | 0.168168 | − | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.29129 | + | 1.32288i | −0.153436 | + | 0.0885863i | −0.574752 | − | 0.818327i | \(-0.694902\pi\) |
0.421316 | + | 0.906914i | \(0.361568\pi\) | |||||||
\(224\) | −9.76951 | − | 16.9213i | −0.652753 | − | 1.13060i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.0608 | + | 13.3142i | −1.53398 | + | 0.885645i | ||||
\(227\) | 23.6216 | − | 13.6379i | 1.56782 | − | 0.905181i | 0.571397 | − | 0.820674i | \(-0.306402\pi\) |
0.996423 | − | 0.0845077i | \(-0.0269317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.08258 | − | 5.24383i | 0.600193 | − | 0.346522i | −0.168924 | − | 0.985629i | \(-0.554029\pi\) |
0.769118 | + | 0.639107i | \(0.220696\pi\) | |||||||
\(230\) | 16.2695 | − | 28.1796i | 1.07278 | − | 1.85811i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.5000 | + | 6.06218i | −0.689359 | + | 0.398001i | ||||
\(233\) | 10.0826 | + | 17.4635i | 0.660531 | + | 1.14407i | 0.980476 | + | 0.196638i | \(0.0630023\pi\) |
−0.319945 | + | 0.947436i | \(0.603664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.708712 | + | 1.22753i | −0.0462313 | + | 0.0800749i | ||||
\(236\) | 10.3521 | + | 5.97678i | 0.673863 | + | 0.389055i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.79129 | 0.375393 | ||||||||
\(239\) | 2.01810i | 0.130540i | 0.997868 | + | 0.0652701i | \(0.0207909\pi\) | ||||
−0.997868 | + | 0.0652701i | \(0.979209\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2477 | − | 7.07123i | 0.788945 | − | 0.455498i | −0.0506457 | − | 0.998717i | \(-0.516128\pi\) |
0.839591 | + | 0.543219i | \(0.182795\pi\) | |||||||
\(242\) | 1.89564 | + | 1.09445i | 0.121857 | + | 0.0703539i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.20871 | − | 12.4859i | −0.461491 | − | 0.799325i | ||||
\(245\) | −10.5000 | + | 6.06218i | −0.670820 | + | 0.387298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.3303 | − | 5.29150i | 1.16633 | − | 0.336690i | ||||
\(248\) | −5.29129 | + | 9.16478i | −0.335997 | + | 0.581964i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.2695 | − | 22.9835i | 0.839237 | − | 1.45360i | ||||
\(251\) | −10.2913 | + | 17.8250i | −0.649580 | + | 1.12511i | 0.333643 | + | 0.942700i | \(0.391722\pi\) |
−0.983223 | + | 0.182407i | \(0.941611\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.7477 | − | 14.8655i | −1.61875 | − | 0.934583i | ||||
\(254\) | 14.4086i | 0.904076i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.39564 | + | 2.41733i | 0.0872277 | + | 0.151083i | ||||
\(257\) | −4.66515 | + | 8.08028i | −0.291004 | + | 0.504034i | −0.974047 | − | 0.226344i | \(-0.927323\pi\) |
0.683043 | + | 0.730378i | \(0.260656\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.29129 | − | 16.0930i | 0.577333 | − | 0.999969i | ||||
\(260\) | 4.18693 | − | 16.9213i | 0.259662 | − | 1.04941i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 3.10260i | − | 0.191679i | ||||||
\(263\) | 4.83485 | 0.298130 | 0.149065 | − | 0.988827i | \(-0.452374\pi\) | ||||
0.149065 | + | 0.988827i | \(0.452374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6784i | 0.655966i | ||||||||
\(266\) | 26.5390 | + | 15.3223i | 1.62721 | + | 0.939471i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −33.9564 | + | 19.6048i | −2.07422 | + | 1.19755i | ||||
\(269\) | 8.08258 | + | 13.9994i | 0.492803 | + | 0.853560i | 0.999966 | − | 0.00829015i | \(-0.00263887\pi\) |
−0.507162 | + | 0.861851i | \(0.669306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0390 | − | 5.79603i | −0.609827 | − | 0.352084i | 0.163071 | − | 0.986614i | \(-0.447860\pi\) |
−0.772898 | + | 0.634531i | \(0.781193\pi\) | |||||||
\(272\) | 1.79129 | 0.108613 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.9564 | −1.14520 | ||||||||
\(275\) | −6.00000 | − | 3.46410i | −0.361814 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.66515 | − | 8.08028i | −0.280302 | − | 0.485497i | 0.691157 | − | 0.722704i | \(-0.257101\pi\) |
−0.971459 | + | 0.237208i | \(0.923768\pi\) | |||||||
\(278\) | −12.4782 | + | 7.20430i | −0.748394 | + | 0.432085i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.87386 | − | 3.96863i | 0.410792 | − | 0.237171i | ||||
\(281\) | 3.65480i | 0.218027i | 0.994040 | + | 0.109014i | \(0.0347692\pi\) | ||||
−0.994040 | + | 0.109014i | \(0.965231\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.3303 | −1.80295 | −0.901475 | − | 0.432832i | \(-0.857514\pi\) | ||||
−0.901475 | + | 0.432832i | \(0.857514\pi\) | |||||||
\(284\) | 12.4859i | 0.740899i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.5390 | − | 6.56670i | −1.56928 | − | 0.388297i | ||||
\(287\) | 4.70871 | + | 8.15573i | 0.277946 | + | 0.481417i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | 13.2695 | + | 22.9835i | 0.779212 | + | 1.34964i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 24.1733i | 1.41463i | ||||||||
\(293\) | −16.8303 | − | 9.71698i | −0.983237 | − | 0.567672i | −0.0799910 | − | 0.996796i | \(-0.525489\pi\) |
−0.903246 | + | 0.429124i | \(0.858822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.70871 | − | 6.42368i | 0.215930 | − | 0.374001i | ||||
\(296\) | −6.08258 | + | 10.5353i | −0.353543 | + | 0.612354i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.00000 | + | 6.92820i | −0.231714 | + | 0.401340i | ||||
\(299\) | 30.0390 | + | 7.43273i | 1.73720 | + | 0.429846i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.5000 | − | 6.06218i | −0.605210 | − | 0.349418i | ||||
\(302\) | 18.2695 | + | 31.6437i | 1.05129 | + | 1.82089i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.20871 | + | 4.73930i | 0.470802 | + | 0.271818i | ||||
\(305\) | −7.74773 | + | 4.47315i | −0.443634 | + | 0.256132i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9753i | 1.19712i | 0.801076 | + | 0.598562i | \(0.204261\pi\) | ||||
−0.801076 | + | 0.598562i | \(0.795739\pi\) | |||||||
\(308\) | −12.7913 | − | 22.1552i | −0.728851 | − | 1.26241i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.0608 | + | 11.5821i | 1.13938 | + | 0.657819i | ||||
\(311\) | −4.29129 | + | 7.43273i | −0.243337 | + | 0.421471i | −0.961663 | − | 0.274235i | \(-0.911575\pi\) |
0.718326 | + | 0.695707i | \(0.244909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.91742 | + | 11.9813i | 0.390996 | + | 0.677225i | 0.992581 | − | 0.121584i | \(-0.0387973\pi\) |
−0.601585 | + | 0.798809i | \(0.705464\pi\) | |||||||
\(314\) | 19.2695 | − | 11.1253i | 1.08744 | − | 0.627834i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.97822 | + | 3.42638i | −0.111284 | + | 0.192749i | ||||
\(317\) | −1.66515 | + | 0.961376i | −0.0935242 | + | 0.0539962i | −0.546033 | − | 0.837764i | \(-0.683863\pi\) |
0.452508 | + | 0.891760i | \(0.350529\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.0000 | − | 12.1244i | 1.17577 | − | 0.678834i | ||||
\(320\) | 18.8739 | − | 10.8968i | 1.05508 | − | 0.609151i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 24.8521 | + | 43.0451i | 1.38495 | + | 2.39881i | ||||
\(323\) | −4.58258 | + | 2.64575i | −0.254981 | + | 0.147214i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.00000 | + | 1.73205i | 0.388290 | + | 0.0960769i | ||||
\(326\) | 3.79129 | − | 6.56670i | 0.209980 | − | 0.363696i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.08258 | − | 5.33918i | −0.170207 | − | 0.294807i | ||||
\(329\) | −1.08258 | − | 1.87508i | −0.0596843 | − | 0.103376i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.0761i | − | 1.43327i | −0.697447 | − | 0.716636i | \(-0.745681\pi\) | ||
0.697447 | − | 0.716636i | \(-0.254319\pi\) | |||||||
\(332\) | 8.37386 | − | 4.83465i | 0.459575 | − | 0.265336i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.79129 | 0.535755 | ||||||||
\(335\) | 12.1652 | + | 21.0707i | 0.664653 | + | 1.15121i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.4955 | 1.27988 | 0.639939 | − | 0.768425i | \(-0.278959\pi\) | ||||
0.639939 | + | 0.768425i | \(0.278959\pi\) | |||||||
\(338\) | 28.4347 | − | 1.09445i | 1.54664 | − | 0.0595303i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.83465i | 0.262196i | ||||||||
\(341\) | 10.5826 | − | 18.3296i | 0.573079 | − | 0.992601i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5203i | − | 1.00000i | ||||||
\(344\) | 6.87386 | + | 3.96863i | 0.370614 | + | 0.213974i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 46.1216 | + | 26.6283i | 2.47951 | + | 1.43155i | ||||
\(347\) | −12.8739 | − | 22.2982i | −0.691105 | − | 1.19703i | −0.971476 | − | 0.237138i | \(-0.923791\pi\) |
0.280371 | − | 0.959892i | \(-0.409543\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.08258 | − | 5.24383i | 0.486179 | − | 0.280696i | −0.236809 | − | 0.971556i | \(-0.576102\pi\) |
0.722988 | + | 0.690861i | \(0.242768\pi\) | |||||||
\(350\) | 5.79129 | + | 10.0308i | 0.309557 | + | 0.536169i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.7913 | − | 22.1552i | −0.681778 | − | 1.18087i | ||||
\(353\) | − | 19.3386i | − | 1.02929i | −0.857403 | − | 0.514645i | \(-0.827924\pi\) | ||
0.857403 | − | 0.514645i | \(-0.172076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.74773 | 0.411207 | ||||||||
\(356\) | 43.5119i | 2.30612i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.58258 | + | 0.913701i | 0.0836417 | + | 0.0482906i | ||||
\(359\) | 16.0390 | − | 9.26013i | 0.846507 | − | 0.488731i | −0.0129639 | − | 0.999916i | \(-0.504127\pi\) |
0.859471 | + | 0.511185i | \(0.170793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | −41.7042 | − | 24.0779i | −2.19192 | − | 1.26551i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.1869 | + | 18.4626i | 1.00567 | + | 0.967705i | ||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1652 | 0.791614 | 0.395807 | − | 0.918334i | \(-0.370465\pi\) | ||||
0.395807 | + | 0.918334i | \(0.370465\pi\) | |||||||
\(368\) | 7.68693 | + | 13.3142i | 0.400709 | + | 0.694048i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 23.0608 | + | 13.3142i | 1.19887 | + | 0.692170i | ||||
\(371\) | −14.1261 | − | 8.15573i | −0.733392 | − | 0.423424i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.0000 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(374\) | 7.58258 | 0.392086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.708712 | + | 1.22753i | 0.0365490 | + | 0.0633048i | ||||
\(377\) | −17.5000 | + | 18.1865i | −0.901296 | + | 0.936654i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0390 | − | 9.26013i | 0.823869 | − | 0.475661i | −0.0278799 | − | 0.999611i | \(-0.508876\pi\) |
0.851749 | + | 0.523950i | \(0.175542\pi\) | |||||||
\(380\) | −12.7913 | + | 22.1552i | −0.656179 | + | 1.13654i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −27.1652 | − | 15.6838i | −1.38989 | − | 0.802453i | ||||
\(383\) | 17.7019i | 0.904525i | 0.891885 | + | 0.452263i | \(0.149383\pi\) | ||||
−0.891885 | + | 0.452263i | \(0.850617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.7477 | + | 7.93725i | −0.700649 | + | 0.404520i | ||||
\(386\) | 4.00000 | − | 6.92820i | 0.203595 | − | 0.352636i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 29.2741i | 1.48617i | ||||||||
\(389\) | 13.6652 | − | 23.6687i | 0.692851 | − | 1.20005i | −0.278049 | − | 0.960567i | \(-0.589688\pi\) |
0.970900 | − | 0.239486i | \(-0.0769788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.58258 | −0.434040 | ||||||||
\(392\) | 12.1244i | 0.612372i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 38.5390 | 1.94157 | ||||||||
\(395\) | 2.12614 | + | 1.22753i | 0.106978 | + | 0.0617635i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.8498i | 1.84944i | 0.380649 | + | 0.924720i | \(0.375701\pi\) | ||||
−0.380649 | + | 0.924720i | \(0.624299\pi\) | |||||||
\(398\) | 5.65300i | 0.283359i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.79129 | + | 3.10260i | 0.0895644 | + | 0.155130i | ||||
\(401\) | −30.0826 | − | 17.3682i | −1.50225 | − | 0.867326i | −0.999997 | − | 0.00260643i | \(-0.999170\pi\) |
−0.502256 | − | 0.864719i | \(-0.667496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.29129 | + | 21.3845i | −0.263578 | + | 1.06524i | ||||
\(404\) | −18.3739 | − | 31.8245i | −0.914134 | − | 1.58333i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −40.5390 | −2.01192 | ||||||||
\(407\) | 12.1652 | − | 21.0707i | 0.603004 | − | 1.04443i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.0826 | − | 15.6361i | 1.33915 | − | 0.773157i | 0.352466 | − | 0.935825i | \(-0.385343\pi\) |
0.986681 | + | 0.162668i | \(0.0520098\pi\) | |||||||
\(410\) | −11.6869 | + | 6.74745i | −0.577176 | + | 0.333233i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.76951 | − | 8.26103i | 0.234977 | − | 0.406992i | ||||
\(413\) | 5.66515 | + | 9.81233i | 0.278764 | + | 0.482833i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | − | 5.19615i | −0.147264 | − | 0.255069i | ||||
\(416\) | 19.1869 | + | 18.4626i | 0.940717 | + | 0.905205i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34.7477 | + | 20.0616i | 1.69957 | + | 0.981245i | ||||
\(419\) | 5.87386 | + | 10.1738i | 0.286957 | + | 0.497024i | 0.973082 | − | 0.230460i | \(-0.0740230\pi\) |
−0.686125 | + | 0.727484i | \(0.740690\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.5046i | 1.97407i | 0.160492 | + | 0.987037i | \(0.448692\pi\) | ||||
−0.160492 | + | 0.987037i | \(0.551308\pi\) | |||||||
\(422\) | 14.4086i | 0.701400i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.24773 | + | 5.33918i | 0.449109 | + | 0.259293i | ||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.6657i | − | 0.661330i | ||||||
\(428\) | −3.95644 | −0.191242 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.68693 | − | 15.0462i | 0.418921 | − | 0.725593i | ||||
\(431\) | − | 8.56490i | − | 0.412557i | −0.978493 | − | 0.206278i | \(-0.933865\pi\) | ||
0.978493 | − | 0.206278i | \(-0.0661353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.66515 | − | 13.2764i | 0.368364 | − | 0.638025i | −0.620946 | − | 0.783853i | \(-0.713251\pi\) |
0.989310 | + | 0.145829i | \(0.0465848\pi\) | |||||||
\(434\) | −30.6434 | + | 17.6920i | −1.47093 | + | 0.849241i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 53.7135i | 2.57241i | ||||||||
\(437\) | −39.3303 | − | 22.7074i | −1.88142 | − | 1.08624i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.29129 | − | 9.16478i | 0.252539 | − | 0.437411i | −0.711685 | − | 0.702499i | \(-0.752068\pi\) |
0.964224 | + | 0.265088i | \(0.0854009\pi\) | |||||||
\(440\) | 9.00000 | − | 5.19615i | 0.429058 | − | 0.247717i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.58258 | + | 2.18890i | −0.360666 | + | 0.104115i | ||||
\(443\) | −2.87386 | − | 4.97768i | −0.136541 | − | 0.236497i | 0.789644 | − | 0.613565i | \(-0.210265\pi\) |
−0.926185 | + | 0.377069i | \(0.876932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.0000 | 1.27992 | ||||||||
\(446\) | 5.79129 | 0.274225 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 33.2904i | 1.57282i | ||||||||
\(449\) | 10.6652 | + | 6.15753i | 0.503320 | + | 0.290592i | 0.730083 | − | 0.683358i | \(-0.239481\pi\) |
−0.226764 | + | 0.973950i | \(0.572815\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.16515 | + | 10.6784i | 0.290306 | + | 0.502824i | ||||
\(452\) | 33.9564 | 1.59718 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −59.7042 | −2.80206 | ||||||||
\(455\) | 11.4564 | − | 11.9059i | 0.537086 | − | 0.558156i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.24773 | − | 1.87508i | −0.151922 | − | 0.0877124i | 0.422112 | − | 0.906544i | \(-0.361289\pi\) |
−0.574034 | + | 0.818831i | \(0.694622\pi\) | |||||||
\(458\) | −22.9564 | −1.07268 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −35.9347 | + | 20.7469i | −1.67546 | + | 0.967328i | ||||
\(461\) | 27.4129 | + | 15.8268i | 1.27675 | + | 0.737129i | 0.976248 | − | 0.216654i | \(-0.0695143\pi\) |
0.300497 | + | 0.953783i | \(0.402848\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.4865i | 1.78862i | 0.447448 | + | 0.894310i | \(0.352333\pi\) | ||||
−0.447448 | + | 0.894310i | \(0.647667\pi\) | |||||||
\(464\) | −12.5390 | −0.582109 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 44.1395i | − | 2.04472i | ||||||
\(467\) | −14.4564 | − | 25.0393i | −0.668964 | − | 1.15868i | −0.978194 | − | 0.207693i | \(-0.933405\pi\) |
0.309230 | − | 0.950987i | \(-0.399929\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.1652 | −1.71613 | ||||||||
\(470\) | 2.68693 | − | 1.55130i | 0.123939 | − | 0.0715562i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.70871 | − | 6.42368i | −0.170707 | − | 0.295674i | ||||
\(473\) | −13.7477 | − | 7.93725i | −0.632121 | − | 0.364955i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.16515 | − | 5.29150i | −0.420526 | − | 0.242791i | ||||
\(476\) | −6.39564 | − | 3.69253i | −0.293144 | − | 0.169247i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.20871 | − | 3.82560i | 0.101024 | − | 0.174979i | ||||
\(479\) | 28.2849i | 1.29237i | 0.763181 | + | 0.646185i | \(0.223637\pi\) | ||||
−0.763181 | + | 0.646185i | \(0.776363\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.08258 | + | 24.5824i | −0.277342 | + | 1.12086i | ||||
\(482\) | −30.9564 | −1.41003 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.39564 | − | 2.41733i | −0.0634384 | − | 0.109878i | ||||
\(485\) | 18.1652 | 0.824837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.54356 | + | 5.50998i | −0.432460 | + | 0.249681i | −0.700394 | − | 0.713756i | \(-0.746992\pi\) |
0.267934 | + | 0.963437i | \(0.413659\pi\) | |||||||
\(488\) | 8.94630i | 0.404980i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.5390 | 1.19891 | ||||||||
\(491\) | 1.87386 | + | 3.24563i | 0.0845663 | + | 0.146473i | 0.905206 | − | 0.424972i | \(-0.139716\pi\) |
−0.820640 | + | 0.571445i | \(0.806383\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.50000 | − | 6.06218i | 0.157632 | − | 0.273027i | ||||
\(494\) | −40.5390 | − | 10.0308i | −1.82394 | − | 0.451307i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.47822 | + | 5.47225i | −0.425585 | + | 0.245711i | ||||
\(497\) | −5.91742 | + | 10.2493i | −0.265433 | + | 0.459743i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.7087 | − | 12.5335i | 0.971815 | − | 0.561078i | 0.0720262 | − | 0.997403i | \(-0.477053\pi\) |
0.899789 | + | 0.436325i | \(0.143720\pi\) | |||||||
\(500\) | −29.3085 | + | 16.9213i | −1.31072 | + | 0.756743i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 39.0172 | − | 22.5266i | 1.74142 | − | 1.00541i | ||||
\(503\) | 0.873864 | − | 1.51358i | 0.0389636 | − | 0.0674870i | −0.845886 | − | 0.533364i | \(-0.820928\pi\) |
0.884850 | + | 0.465877i | \(0.154261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.7477 | + | 11.4014i | −0.878762 | + | 0.507354i | ||||
\(506\) | 32.5390 | + | 56.3592i | 1.44654 | + | 2.50547i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.18693 | − | 15.9122i | 0.407604 | − | 0.705991i | ||||
\(509\) | 24.2477 | + | 13.9994i | 1.07476 | + | 0.620514i | 0.929479 | − | 0.368876i | \(-0.120257\pi\) |
0.145283 | + | 0.989390i | \(0.453591\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.4564 | + | 19.8431i | −0.506803 | + | 0.877809i | ||||
\(512\) | 19.4340i | 0.858868i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.6869 | − | 10.2116i | 0.780137 | − | 0.450412i | ||||
\(515\) | −5.12614 | − | 2.95958i | −0.225885 | − | 0.130415i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.41742 | − | 2.45505i | −0.0623382 | − | 0.107973i | ||||
\(518\) | −35.2259 | + | 20.3377i | −1.54774 | + | 0.893588i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.50000 | + | 7.79423i | −0.328897 | + | 0.341800i | ||||
\(521\) | 1.66515 | − | 2.88413i | 0.0729516 | − | 0.126356i | −0.827242 | − | 0.561846i | \(-0.810091\pi\) |
0.900194 | + | 0.435490i | \(0.143425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.87386 | − | 8.44178i | 0.213119 | − | 0.369133i | −0.739570 | − | 0.673080i | \(-0.764971\pi\) |
0.952689 | + | 0.303946i | \(0.0983044\pi\) | |||||||
\(524\) | −1.97822 | + | 3.42638i | −0.0864189 | + | 0.149682i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.16515 | − | 5.29150i | −0.399620 | − | 0.230720i | ||||
\(527\) | − | 6.10985i | − | 0.266149i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −25.3303 | − | 43.8734i | −1.10132 | − | 1.90754i | ||||
\(530\) | 11.6869 | − | 20.2424i | 0.507648 | − | 0.879272i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.5390 | − | 33.8426i | −0.847124 | − | 1.46726i | ||||
\(533\) | −9.24773 | − | 8.89863i | −0.400564 | − | 0.385442i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.45505i | 0.106141i | ||||||||
\(536\) | 24.3303 | 1.05091 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 35.3839i | − | 1.52551i | ||||||
\(539\) | − | 24.2487i | − | 1.04447i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.33485 | + | 4.23478i | −0.315350 | + | 0.182067i | −0.649318 | − | 0.760517i | \(-0.724946\pi\) |
0.333968 | + | 0.942584i | \(0.391612\pi\) | |||||||
\(542\) | 12.6869 | + | 21.9744i | 0.544950 | + | 0.943882i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.39564 | − | 3.69253i | −0.274211 | − | 0.158316i | ||||
\(545\) | 33.3303 | 1.42771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 20.9347 | + | 12.0866i | 0.894284 | + | 0.516315i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.58258 | + | 13.1334i | 0.323322 | + | 0.560010i | ||||
\(551\) | 32.0780 | − | 18.5203i | 1.36657 | − | 0.788990i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.24773 | + | 1.87508i | −0.138107 | + | 0.0797363i | ||||
\(554\) | 20.4231i | 0.867695i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.3739 | 0.779225 | ||||||||
\(557\) | − | 24.4394i | − | 1.03553i | −0.855523 | − | 0.517766i | \(-0.826764\pi\) | ||
0.855523 | − | 0.517766i | \(-0.173236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0390 | + | 3.96863i | 0.678378 | + | 0.167855i | ||||
\(560\) | 8.20871 | 0.346881 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.00000 | − | 6.92820i | 0.168730 | − | 0.292249i | ||||
\(563\) | 2.70871 | + | 4.69163i | 0.114159 | + | 0.197729i | 0.917443 | − | 0.397867i | \(-0.130249\pi\) |
−0.803284 | + | 0.595596i | \(0.796916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 21.0707i | − | 0.886449i | ||||||
\(566\) | 57.4955 | + | 33.1950i | 2.41671 | + | 1.39529i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.87386 | − | 6.70973i | 0.162544 | − | 0.281534i | ||||
\(569\) | −2.66515 | + | 4.61618i | −0.111729 | + | 0.193520i | −0.916467 | − | 0.400109i | \(-0.868972\pi\) |
0.804738 | + | 0.593629i | \(0.202306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.8739 | + | 41.3507i | −0.999090 | + | 1.73047i | −0.462609 | + | 0.886562i | \(0.653087\pi\) |
−0.536481 | + | 0.843913i | \(0.680247\pi\) | |||||||
\(572\) | 25.1216 | + | 24.1733i | 1.05039 | + | 1.01073i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 20.6138i | − | 0.860404i | ||||||
\(575\) | −8.58258 | − | 14.8655i | −0.357918 | − | 0.619932i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0826 | − | 6.97588i | −0.503004 | − | 0.290410i | 0.226949 | − | 0.973907i | \(-0.427125\pi\) |
−0.729953 | + | 0.683497i | \(0.760458\pi\) | |||||||
\(578\) | −30.3303 | + | 17.5112i | −1.26157 | + | 0.728370i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 33.8426i | − | 1.40524i | ||||||
\(581\) | 9.16515 | 0.380235 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.4955 | − | 10.6784i | −0.766003 | − | 0.442252i | ||||
\(584\) | 7.50000 | − | 12.9904i | 0.310352 | − | 0.537546i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.2695 | + | 36.8399i | 0.878635 | + | 1.52184i | ||||
\(587\) | 18.8739 | − | 10.8968i | 0.779008 | − | 0.449760i | −0.0570708 | − | 0.998370i | \(-0.518176\pi\) |
0.836079 | + | 0.548610i | \(0.184843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.1652 | − | 27.9989i | 0.666073 | − | 1.15367i | ||||
\(590\) | −14.0608 | + | 8.11800i | −0.578874 | + | 0.334213i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.8956 | + | 6.29060i | −0.447808 | + | 0.258542i | ||||
\(593\) | −15.2477 | + | 8.80328i | −0.626149 | + | 0.361507i | −0.779259 | − | 0.626702i | \(-0.784404\pi\) |
0.153110 | + | 0.988209i | \(0.451071\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.29129 | + | 3.96863i | −0.0939336 | + | 0.162698i | ||||
\(596\) | 8.83485 | − | 5.10080i | 0.361889 | − | 0.208937i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −48.8085 | − | 46.9660i | −1.99593 | − | 1.92058i | ||||
\(599\) | 4.12614 | − | 7.14668i | 0.168589 | − | 0.292005i | −0.769335 | − | 0.638846i | \(-0.779412\pi\) |
0.937924 | + | 0.346841i | \(0.112745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0826 | − | 22.6597i | −0.533649 | − | 0.924308i | −0.999227 | − | 0.0393010i | \(-0.987487\pi\) |
0.465578 | − | 0.885007i | \(-0.345846\pi\) | |||||||
\(602\) | 13.2695 | + | 22.9835i | 0.540825 | + | 0.936736i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 46.5946i | − | 1.89591i | ||||||
\(605\) | −1.50000 | + | 0.866025i | −0.0609837 | + | 0.0352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | −19.5390 | − | 33.8426i | −0.792412 | − | 1.37250i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.5826 | 0.792875 | ||||||||
\(611\) | 2.12614 | + | 2.04588i | 0.0860143 | + | 0.0827673i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.4394i | − | 0.987099i | −0.869718 | − | 0.493549i | \(-0.835699\pi\) | ||
0.869718 | − | 0.493549i | \(-0.164301\pi\) | |||||||
\(614\) | 22.9564 | − | 39.7617i | 0.926446 | − | 1.60465i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.8745i | 0.639602i | ||||||||
\(617\) | 18.2477 | + | 10.5353i | 0.734626 | + | 0.424136i | 0.820112 | − | 0.572203i | \(-0.193911\pi\) |
−0.0854862 | + | 0.996339i | \(0.527244\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.03901 | + | 0.599876i | 0.0417615 | + | 0.0241110i | 0.520735 | − | 0.853718i | \(-0.325658\pi\) |
−0.478974 | + | 0.877829i | \(0.658991\pi\) | |||||||
\(620\) | −14.7695 | − | 25.5815i | −0.593158 | − | 1.02738i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.2695 | − | 9.39320i | 0.652348 | − | 0.376633i | ||||
\(623\) | −20.6216 | + | 35.7176i | −0.826187 | + | 1.43100i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | − | 30.2831i | − | 1.21036i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.3739 | −1.13224 | ||||||||
\(629\) | − | 7.02355i | − | 0.280047i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.8739 | − | 17.8250i | −1.22907 | − | 0.709603i | −0.262234 | − | 0.965004i | \(-0.584459\pi\) |
−0.966835 | + | 0.255401i | \(0.917793\pi\) | |||||||
\(632\) | 2.12614 | − | 1.22753i | 0.0845732 | − | 0.0488283i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.20871 | 0.167149 | ||||||||
\(635\) | −9.87386 | − | 5.70068i | −0.391832 | − | 0.226224i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000 | + | 24.2487i | 0.277350 | + | 0.960769i | ||||
\(638\) | −53.0780 | −2.10138 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −22.1216 | −0.874433 | ||||||||
\(641\) | −8.24773 | − | 14.2855i | −0.325766 | − | 0.564243i | 0.655901 | − | 0.754847i | \(-0.272289\pi\) |
−0.981667 | + | 0.190604i | \(0.938955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.4564 | + | 17.0067i | 1.16165 | + | 0.670678i | 0.951699 | − | 0.307034i | \(-0.0993365\pi\) |
0.209950 | + | 0.977712i | \(0.432670\pi\) | |||||||
\(644\) | − | 63.3828i | − | 2.49763i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.5826 | 0.455710 | ||||||||
\(647\) | 38.3303 | 1.50692 | 0.753460 | − | 0.657494i | \(-0.228383\pi\) | ||||
0.753460 | + | 0.657494i | \(0.228383\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.41742 | + | 12.8474i | 0.291159 | + | 0.504303i | ||||
\(650\) | −11.3739 | − | 10.9445i | −0.446120 | − | 0.429279i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.37386 | + | 4.83465i | −0.327946 | + | 0.189340i | ||||
\(653\) | 13.2477 | − | 22.9457i | 0.518424 | − | 0.897936i | −0.481347 | − | 0.876530i | \(-0.659852\pi\) |
0.999771 | − | 0.0214061i | \(-0.00681428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.12614 | + | 1.22753i | 0.0830750 | + | 0.0479634i | ||||
\(656\) | − | 6.37600i | − | 0.248941i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.73930i | 0.184757i | ||||||||
\(659\) | 10.0390 | − | 17.3881i | 0.391064 | − | 0.677344i | −0.601526 | − | 0.798853i | \(-0.705440\pi\) |
0.992590 | + | 0.121510i | \(0.0387736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5.48220i | − | 0.213233i | −0.994300 | − | 0.106616i | \(-0.965998\pi\) | ||
0.994300 | − | 0.106616i | \(-0.0340017\pi\) | |||||||
\(662\) | −28.5390 | + | 49.4310i | −1.10920 | + | 1.92119i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | −21.0000 | + | 12.1244i | −0.814345 | + | 0.470162i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 60.0780 | 2.32623 | ||||||||
\(668\) | −10.8131 | − | 6.24293i | −0.418370 | − | 0.241546i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 53.2566i | − | 2.05748i | ||||||
\(671\) | − | 17.8926i | − | 0.690737i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6652 | + | 30.5969i | 0.680942 | + | 1.17943i | 0.974694 | + | 0.223544i | \(0.0717626\pi\) |
−0.293752 | + | 0.955882i | \(0.594904\pi\) | |||||||
\(674\) | −44.5390 | − | 25.7146i | −1.71558 | − | 0.990490i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −32.0998 | − | 16.9213i | −1.23461 | − | 0.650819i | ||||
\(677\) | 14.9174 | + | 25.8377i | 0.573323 | + | 0.993025i | 0.996222 | + | 0.0868478i | \(0.0276794\pi\) |
−0.422898 | + | 0.906177i | \(0.638987\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8739 | + | 24.0302i | −0.532430 | + | 0.922196i | ||||
\(680\) | 1.50000 | − | 2.59808i | 0.0575224 | − | 0.0996317i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −40.1216 | + | 23.1642i | −1.53634 | + | 0.887003i | ||||
\(683\) | −33.8739 | + | 19.5571i | −1.29615 | + | 0.748331i | −0.979736 | − | 0.200291i | \(-0.935811\pi\) |
−0.316411 | + | 0.948622i | \(0.602478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.50000 | − | 12.9904i | 0.286560 | − | 0.496337i | ||||
\(686\) | −20.2695 | + | 35.1078i | −0.773893 | + | 1.34042i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.10436 | + | 7.10895i | 0.156477 | + | 0.271026i | ||||
\(689\) | 21.5780 | + | 5.33918i | 0.822057 | + | 0.203406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.54356 | − | 3.77793i | −0.248929 | − | 0.143719i | 0.370345 | − | 0.928894i | \(-0.379240\pi\) |
−0.619274 | + | 0.785175i | \(0.712573\pi\) | |||||||
\(692\) | −33.9564 | − | 58.8143i | −1.29083 | − | 2.23578i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.3592i | 2.13937i | ||||||||
\(695\) | − | 11.4014i | − | 0.432478i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.08258 | + | 1.77973i | 0.116761 | + | 0.0674119i | ||||
\(698\) | −22.9564 | −0.868914 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 14.7701i | − | 0.558258i | ||||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5826 | − | 32.1860i | 0.700855 | − | 1.21392i | ||||
\(704\) | 43.5873i | 1.64276i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.1652 | + | 36.6591i | −0.796561 | + | 1.37968i | ||||
\(707\) | − | 34.8317i | − | 1.30998i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.5402i | 1.10941i | 0.832048 | + | 0.554703i | \(0.187168\pi\) | ||||
−0.832048 | + | 0.554703i | \(0.812832\pi\) | |||||||
\(710\) | −14.6869 | − | 8.47950i | −0.551191 | − | 0.318230i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.5000 | − | 23.3827i | 0.505934 | − | 0.876303i | ||||
\(713\) | 45.4129 | − | 26.2191i | 1.70073 | − | 0.981914i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0000 | − | 15.5885i | 0.560968 | − | 0.582975i | ||||
\(716\) | −1.16515 | − | 2.01810i | −0.0435438 | − | 0.0754200i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −40.5390 | −1.51290 | ||||||||
\(719\) | 34.3303 | 1.28030 | 0.640152 | − | 0.768248i | \(-0.278871\pi\) | ||||
0.640152 | + | 0.768248i | \(0.278871\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.83030 | − | 4.52083i | 0.291616 | − | 0.168364i | ||||
\(722\) | 17.0608 | + | 9.85005i | 0.634937 | + | 0.366581i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 30.7042 | + | 53.1812i | 1.14111 | + | 1.97646i | ||||
\(725\) | 14.0000 | 0.519947 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0000 | 1.03846 | 0.519231 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519231 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(728\) | −4.58258 | − | 15.8745i | −0.169842 | − | 0.588348i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28.4347 | − | 16.4168i | −1.05241 | − | 0.607611i | ||||
\(731\) | −4.58258 | −0.169493 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.8303 | − | 14.9131i | 0.954064 | − | 0.550829i | 0.0597230 | − | 0.998215i | \(-0.480978\pi\) |
0.894341 | + | 0.447386i | \(0.147645\pi\) | |||||||
\(734\) | −28.7477 | − | 16.5975i | −1.06110 | − | 0.612625i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 63.3828i | − | 2.33632i | ||||||
\(737\) | −48.6606 | −1.79244 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19.1479i | − | 0.704367i | −0.935931 | − | 0.352184i | \(-0.885439\pi\) | ||
0.935931 | − | 0.352184i | \(-0.114561\pi\) | |||||||
\(740\) | −16.9782 | − | 29.4071i | −0.624132 | − | 1.08103i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.8521 | + | 30.9207i | 0.655371 | + | 1.13514i | ||||
\(743\) | −6.70871 | + | 3.87328i | −0.246119 | + | 0.142097i | −0.617986 | − | 0.786189i | \(-0.712051\pi\) |
0.371867 | + | 0.928286i | \(0.378718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.16515 | − | 5.48220i | −0.115962 | − | 0.200852i | ||||
\(746\) | 49.2867 | + | 28.4557i | 1.80452 | + | 1.04184i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.37386 | − | 4.83465i | −0.306179 | − | 0.176772i | ||||
\(749\) | −3.24773 | − | 1.87508i | −0.118669 | − | 0.0685138i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.45644 | − | 11.1829i | 0.235599 | − | 0.408069i | −0.723848 | − | 0.689960i | \(-0.757628\pi\) |
0.959447 | + | 0.281891i | \(0.0909615\pi\) | |||||||
\(752\) | 1.46590i | 0.0534559i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 53.0780 | − | 15.3223i | 1.93299 | − | 0.558006i | ||||
\(755\) | −28.9129 | −1.05225 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.24773 | − | 3.89318i | −0.0816950 | − | 0.141500i | 0.822283 | − | 0.569079i | \(-0.192700\pi\) |
−0.903978 | + | 0.427579i | \(0.859367\pi\) | |||||||
\(758\) | −40.5390 | −1.47244 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.7477 | − | 7.93725i | 0.498682 | − | 0.287914i | ||||
\(761\) | 1.44600i | 0.0524175i | 0.999656 | + | 0.0262087i | \(0.00834345\pi\) | ||||
−0.999656 | + | 0.0262087i | \(0.991657\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.4564 | + | 44.0918i | −0.921585 | + | 1.59623i | ||||
\(764\) | 20.0000 | + | 34.6410i | 0.723575 | + | 1.25327i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.3739 | − | 33.5565i | 0.700006 | − | 1.21245i | ||||
\(767\) | −11.1261 | − | 10.7061i | −0.401742 | − | 0.386576i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.91742 | + | 1.68438i | −0.105205 | + | 0.0607401i | −0.551679 | − | 0.834056i | \(-0.686013\pi\) |
0.446474 | + | 0.894796i | \(0.352679\pi\) | |||||||
\(770\) | 34.7477 | 1.25222 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.83485 | + | 5.10080i | −0.317973 | + | 0.183582i | ||||
\(773\) | −21.2477 | + | 12.2674i | −0.764228 | + | 0.441227i | −0.830812 | − | 0.556554i | \(-0.812123\pi\) |
0.0665839 | + | 0.997781i | \(0.478790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.5826 | − | 6.10985i | 0.380137 | − | 0.219472i | ||||
\(776\) | 9.08258 | − | 15.7315i | 0.326045 | − | 0.564727i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −51.8085 | + | 29.9117i | −1.85743 | + | 1.07239i | ||||
\(779\) | 9.41742 | + | 16.3115i | 0.337414 | + | 0.584419i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.74773 | + | 13.4195i | −0.277235 | + | 0.480186i | ||||
\(782\) | 16.2695 | + | 9.39320i | 0.581796 | + | 0.335900i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.26951 | + | 10.8591i | −0.223911 | + | 0.387825i | ||||
\(785\) | 17.6066i | 0.628405i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.2913 | + | 15.1793i | −0.937183 | + | 0.541083i | −0.889076 | − | 0.457759i | \(-0.848652\pi\) |
−0.0481070 | + | 0.998842i | \(0.515319\pi\) | |||||||
\(788\) | −42.5608 | − | 24.5725i | −1.51617 | − | 0.875359i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.68693 | − | 4.65390i | −0.0955967 | − | 0.165578i | ||||
\(791\) | 27.8739 | + | 16.0930i | 0.991080 | + | 0.572201i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.16515 | + | 17.8926i | 0.183420 | + | 0.635385i | ||||
\(794\) | 40.3303 | − | 69.8541i | 1.43127 | − | 2.47903i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.60436 | − | 6.24293i | 0.127753 | − | 0.221275i | ||||
\(797\) | 12.0826 | − | 20.9276i | 0.427987 | − | 0.741295i | −0.568707 | − | 0.822540i | \(-0.692556\pi\) |
0.996694 | + | 0.0812451i | \(0.0258896\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.708712 | − | 0.409175i | −0.0250724 | − | 0.0144756i | ||||
\(800\) | − | 14.7701i | − | 0.522202i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38.0172 | + | 65.8478i | 1.34244 | + | 2.32517i | ||||
\(803\) | −15.0000 | + | 25.9808i | −0.529339 | + | 0.916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −39.3303 | −1.38621 | ||||||||
\(806\) | 33.4347 | − | 34.7463i | 1.17769 | − | 1.22389i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.8027i | 0.802197i | ||||||||
\(809\) | 33.1652 | 1.16602 | 0.583012 | − | 0.812463i | \(-0.301874\pi\) | ||||
0.583012 | + | 0.812463i | \(0.301874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.190700i | − | 0.00669640i | −0.999994 | − | 0.00334820i | \(-0.998934\pi\) | ||
0.999994 | − | 0.00334820i | \(-0.00106577\pi\) | |||||||
\(812\) | 44.7695 | + | 25.8477i | 1.57110 | + | 0.907076i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −46.1216 | + | 26.6283i | −1.61656 | + | 0.933322i | ||||
\(815\) | 3.00000 | + | 5.19615i | 0.105085 | + | 0.182013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.0000 | − | 12.1244i | −0.734697 | − | 0.424178i | ||||
\(818\) | −68.4519 | −2.39336 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.2087 | 0.600954 | ||||||||
\(821\) | −33.2477 | − | 19.1956i | −1.16035 | − | 0.669931i | −0.208965 | − | 0.977923i | \(-0.567009\pi\) |
−0.951389 | + | 0.307993i | \(0.900343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.2913 | − | 26.4853i | −0.533021 | − | 0.923219i | −0.999256 | − | 0.0385585i | \(-0.987723\pi\) |
0.466236 | − | 0.884661i | \(-0.345610\pi\) | |||||||
\(824\) | −5.12614 | + | 2.95958i | −0.178577 | + | 0.103102i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 24.8009i | − | 0.862934i | ||||||
\(827\) | 36.6591i | 1.27476i | 0.770549 | + | 0.637381i | \(0.219982\pi\) | ||||
−0.770549 | + | 0.637381i | \(0.780018\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.6606 | −1.62059 | −0.810295 | − | 0.586022i | \(-0.800693\pi\) | ||||
−0.810295 | + | 0.586022i | \(0.800693\pi\) | |||||||
\(830\) | 13.1334i | 0.455867i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.5826 | − | 43.5873i | −0.436222 | − | 1.51112i | ||||
\(833\) | −3.50000 | − | 6.06218i | −0.121268 | − | 0.210042i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.87386 | + | 6.70973i | −0.134061 | + | 0.232200i | ||||
\(836\) | −25.5826 | − | 44.3103i | −0.884792 | − | 1.53250i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 25.7146i | − | 0.888297i | ||||||
\(839\) | 23.1261 | + | 13.3519i | 0.798403 | + | 0.460958i | 0.842912 | − | 0.538051i | \(-0.180839\pi\) |
−0.0445095 | + | 0.999009i | \(0.514172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0000 | + | 17.3205i | −0.344828 | + | 0.597259i | ||||
\(842\) | 44.3303 | − | 76.7823i | 1.52772 | − | 2.64609i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.18693 | − | 15.9122i | 0.316227 | − | 0.547722i | ||||
\(845\) | −10.5000 | + | 19.9186i | −0.361211 | + | 0.685220i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.64575i | − | 0.0909091i | ||||||
\(848\) | 5.52178 | + | 9.56400i | 0.189619 | + | 0.328429i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.79129 | + | 2.18890i | 0.130040 | + | 0.0750787i | ||||
\(851\) | 52.2042 | − | 30.1401i | 1.78954 | − | 1.03319i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 30.9862i | − | 1.06095i | −0.847701 | − | 0.530474i | \(-0.822014\pi\) | ||
0.847701 | − | 0.530474i | \(-0.177986\pi\) | |||||||
\(854\) | −14.9564 | + | 25.9053i | −0.511799 | + | 0.886462i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.12614 | + | 1.22753i | 0.0726698 | + | 0.0419560i | ||||
\(857\) | 5.66515 | − | 9.81233i | 0.193518 | − | 0.335183i | −0.752896 | − | 0.658140i | \(-0.771344\pi\) |
0.946414 | + | 0.322957i | \(0.104677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.4564 | + | 40.6277i | 0.800323 | + | 1.38620i | 0.919403 | + | 0.393316i | \(0.128672\pi\) |
−0.119080 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(860\) | −19.1869 | + | 11.0776i | −0.654269 | + | 0.377742i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.37386 | + | 16.2360i | −0.319275 | + | 0.553001i | ||||
\(863\) | −17.4564 | + | 10.0785i | −0.594224 | + | 0.343075i | −0.766766 | − | 0.641927i | \(-0.778135\pi\) |
0.172542 | + | 0.985002i | \(0.444802\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.4955 | + | 21.0707i | −1.24088 | + | 0.716424i | ||||
\(866\) | −29.0608 | + | 16.7783i | −0.987526 | + | 0.570148i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 45.1216 | 1.53153 | ||||||||
\(869\) | −4.25227 | + | 2.45505i | −0.144248 | + | 0.0832819i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.6606 | − | 14.0471i | 1.64880 | − | 0.475968i | ||||
\(872\) | 16.6652 | − | 28.8649i | 0.564353 | − | 0.977488i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 49.7042 | + | 86.0901i | 1.68127 | + | 2.91204i | ||||
\(875\) | −32.0780 | −1.08444 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 16.0652i | − | 0.542484i | −0.962511 | − | 0.271242i | \(-0.912566\pi\) | ||
0.962511 | − | 0.271242i | \(-0.0874343\pi\) | |||||||
\(878\) | −20.0608 | + | 11.5821i | −0.677019 | + | 0.390877i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.7477 | 0.362306 | ||||||||
\(881\) | 9.24773 | + | 16.0175i | 0.311564 | + | 0.539644i | 0.978701 | − | 0.205290i | \(-0.0658139\pi\) |
−0.667137 | + | 0.744935i | \(0.732481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.3303 | 1.69375 | 0.846875 | − | 0.531792i | \(-0.178481\pi\) | ||||
0.846875 | + | 0.531792i | \(0.178481\pi\) | |||||||
\(884\) | 9.76951 | + | 2.41733i | 0.328584 | + | 0.0813035i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.5812i | 0.422674i | ||||||||
\(887\) | −18.7087 | + | 32.4044i | −0.628177 | + | 1.08803i | 0.359740 | + | 0.933053i | \(0.382865\pi\) |
−0.987917 | + | 0.154982i | \(0.950468\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.0826 | − | 8.70793i | 0.505853 | − | 0.292055i | ||||
\(890\) | −51.1824 | − | 29.5502i | −1.71564 | − | 0.990524i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.39564 | − | 3.69253i | −0.214142 | − | 0.123635i | ||||
\(893\) | −2.16515 | − | 3.75015i | −0.0724540 | − | 0.125494i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.25227 | + | 0.723000i | −0.0418589 | + | 0.0241672i | ||||
\(896\) | 16.8956 | − | 29.2641i | 0.564444 | − | 0.977645i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.4782 | − | 23.3450i | −0.449774 | − | 0.779031i | ||||
\(899\) | 42.7690i | 1.42643i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.16515 | −0.205391 | ||||||||
\(902\) | − | 26.9898i | − | 0.898662i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.2477 | − | 10.5353i | −0.606910 | − | 0.350400i | ||||
\(905\) | 33.0000 | − | 19.0526i | 1.09696 | − | 0.633328i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.83485 | 0.293356 | 0.146678 | − | 0.989184i | \(-0.453142\pi\) | ||||
0.146678 | + | 0.989184i | \(0.453142\pi\) | |||||||
\(908\) | 65.9347 | + | 38.0674i | 2.18812 | + | 1.26331i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −34.7477 | + | 10.0308i | −1.15188 | + | 0.332518i | ||||
\(911\) | −48.6606 | −1.61220 | −0.806099 | − | 0.591781i | \(-0.798425\pi\) | ||||
−0.806099 | + | 0.591781i | \(0.798425\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | 4.10436 | + | 7.10895i | 0.135760 | + | 0.235143i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.3521 | + | 14.6370i | 0.837656 | + | 0.483621i | ||||
\(917\) | −3.24773 | + | 1.87508i | −0.107249 | + | 0.0619205i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.83485 | −0.159487 | −0.0797435 | − | 0.996815i | \(-0.525410\pi\) | ||||
−0.0797435 | + | 0.996815i | \(0.525410\pi\) | |||||||
\(920\) | 25.7477 | 0.848877 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.6434 | − | 60.0041i | −1.14092 | − | 1.97613i | ||||
\(923\) | 3.87386 | − | 15.6560i | 0.127510 | − | 0.515325i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.1652 | − | 7.02355i | 0.399988 | − | 0.230933i | ||||
\(926\) | 42.1216 | − | 72.9567i | 1.38420 | − | 2.39751i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 44.7695 | + | 25.8477i | 1.46963 | + | 0.848492i | ||||
\(929\) | 42.3320i | 1.38887i | 0.719556 | + | 0.694434i | \(0.244345\pi\) | ||||
−0.719556 | + | 0.694434i | \(0.755655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 37.0405i | − | 1.21395i | ||||||
\(932\) | −28.1434 | + | 48.7457i | −0.921867 | + | 1.59672i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 63.2874i | 2.07083i | ||||||||
\(935\) | −3.00000 | + | 5.19615i | −0.0981105 | + | 0.169932i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.504546 | 0.0164828 | 0.00824140 | − | 0.999966i | \(-0.497377\pi\) | ||||
0.00824140 | + | 0.999966i | \(0.497377\pi\) | |||||||
\(938\) | 70.4519 | + | 40.6754i | 2.30034 | + | 1.32810i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.95644 | −0.129045 | ||||||||
\(941\) | −28.8303 | − | 16.6452i | −0.939841 | − | 0.542617i | −0.0499305 | − | 0.998753i | \(-0.515900\pi\) |
−0.889910 | + | 0.456135i | \(0.849233\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.5493i | 0.994821i | ||||||||
\(944\) | − | 7.67110i | − | 0.249673i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.3739 | + | 30.0924i | 0.564873 | + | 0.978389i | ||||
\(947\) | 13.0390 | + | 7.52808i | 0.423711 | + | 0.244630i | 0.696664 | − | 0.717398i | \(-0.254667\pi\) |
−0.272953 | + | 0.962027i | \(0.588000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.50000 | − | 30.3109i | 0.243460 | − | 0.983933i | ||||
\(950\) | 11.5826 | + | 20.0616i | 0.375788 | + | 0.650885i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.29129 | + | 3.96863i | 0.0742611 | + | 0.128624i | ||||
\(953\) | 23.6652 | − | 40.9892i | 0.766589 | − | 1.32777i | −0.172813 | − | 0.984955i | \(-0.555286\pi\) |
0.939402 | − | 0.342817i | \(-0.111381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4955 | − | 12.4104i | 0.695577 | − | 0.401591i | ||||
\(956\) | −4.87841 | + | 2.81655i | −0.157779 | + | 0.0910938i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.9564 | − | 53.6181i | 1.00016 | − | 1.73232i | ||||
\(959\) | 11.4564 | + | 19.8431i | 0.369948 | + | 0.640768i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.16515 | + | 5.48220i | 0.102102 | + | 0.176845i | ||||
\(962\) | 38.4347 | − | 39.9425i | 1.23918 | − | 1.28780i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34.1869 | + | 19.7378i | 1.10109 | + | 0.635713i | ||||
\(965\) | 3.16515 | + | 5.48220i | 0.101890 | + | 0.176478i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.29150i | 0.170163i | 0.996374 | + | 0.0850816i | \(0.0271151\pi\) | ||||
−0.996374 | + | 0.0850816i | \(0.972885\pi\) | |||||||
\(968\) | 1.73205i | 0.0556702i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34.4347 | − | 19.8809i | −1.10563 | − | 0.638336i | ||||
\(971\) | −50.3303 | −1.61518 | −0.807588 | − | 0.589747i | \(-0.799228\pi\) | ||||
−0.807588 | + | 0.589747i | \(0.799228\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0826 | + | 8.70793i | 0.483525 | + | 0.279163i | ||||
\(974\) | 24.1216 | 0.772906 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.62614 | + | 8.01270i | −0.148079 | + | 0.256480i | ||||
\(977\) | 3.65480i | 0.116927i | 0.998290 | + | 0.0584637i | \(0.0186202\pi\) | ||||
−0.998290 | + | 0.0584637i | \(0.981380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.0000 | + | 46.7654i | −0.862924 | + | 1.49463i | ||||
\(980\) | −29.3085 | − | 16.9213i | −0.936226 | − | 0.540531i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 8.20340i | − | 0.261781i | ||||||
\(983\) | 20.2913 | + | 11.7152i | 0.647192 | + | 0.373656i | 0.787379 | − | 0.616469i | \(-0.211437\pi\) |
−0.140188 | + | 0.990125i | \(0.544771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2477 | + | 26.4098i | −0.485833 | + | 0.841487i | ||||
\(986\) | −13.2695 | + | 7.66115i | −0.422587 | + | 0.243981i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.3739 | + | 36.9253i | 1.22084 | + | 1.17475i | ||||
\(989\) | −19.6652 | − | 34.0610i | −0.625315 | − | 1.08308i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.6606 | 1.03750 | 0.518749 | − | 0.854926i | \(-0.326398\pi\) | ||||
0.518749 | + | 0.854926i | \(0.326398\pi\) | |||||||
\(992\) | 45.1216 | 1.43261 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.4347 | − | 12.9527i | 0.711584 | − | 0.410833i | ||||
\(995\) | −3.87386 | − | 2.23658i | −0.122810 | − | 0.0709042i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.6652 | + | 40.9892i | 0.749483 | + | 1.29814i | 0.948071 | + | 0.318059i | \(0.103031\pi\) |
−0.198588 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(998\) | −54.8693 | −1.73686 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.do.d.361.1 | 4 | ||
3.2 | odd | 2 | 273.2.bl.b.88.2 | yes | 4 | ||
7.2 | even | 3 | 819.2.bm.d.478.2 | 4 | |||
13.4 | even | 6 | 819.2.bm.d.550.1 | 4 | |||
21.2 | odd | 6 | 273.2.t.b.205.1 | yes | 4 | ||
39.17 | odd | 6 | 273.2.t.b.4.2 | ✓ | 4 | ||
91.30 | even | 6 | inner | 819.2.do.d.667.1 | 4 | ||
273.212 | odd | 6 | 273.2.bl.b.121.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.b.4.2 | ✓ | 4 | 39.17 | odd | 6 | ||
273.2.t.b.205.1 | yes | 4 | 21.2 | odd | 6 | ||
273.2.bl.b.88.2 | yes | 4 | 3.2 | odd | 2 | ||
273.2.bl.b.121.2 | yes | 4 | 273.212 | odd | 6 | ||
819.2.bm.d.478.2 | 4 | 7.2 | even | 3 | |||
819.2.bm.d.550.1 | 4 | 13.4 | even | 6 | |||
819.2.do.d.361.1 | 4 | 1.1 | even | 1 | trivial | ||
819.2.do.d.667.1 | 4 | 91.30 | even | 6 | inner |