Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (of order \(3\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 793.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.793 |
Dual form | 1386.2.k.j.991.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | −3.00000 | −0.670820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 2.50000 | − | 4.33013i | 0.521286 | − | 0.902894i | −0.478407 | − | 0.878138i | \(-0.658786\pi\) |
0.999694 | − | 0.0247559i | \(-0.00788087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | −3.00000 | + | 5.19615i | −0.588348 | + | 1.01905i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | −1.50000 | + | 7.79423i | −0.253546 | + | 1.31747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | −3.00000 | − | 5.19615i | −0.486664 | − | 0.842927i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | −5.00000 | −0.780869 | −0.390434 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390434 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.50000 | + | 4.33013i | 0.368605 | + | 0.638442i | ||||
\(47\) | 4.50000 | − | 7.79423i | 0.656392 | − | 1.13691i | −0.325150 | − | 0.945662i | \(-0.605415\pi\) |
0.981543 | − | 0.191243i | \(-0.0612518\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | − | 5.19615i | −0.416025 | − | 0.720577i | ||||
\(53\) | 1.00000 | + | 1.73205i | 0.137361 | + | 0.237915i | 0.926497 | − | 0.376303i | \(-0.122805\pi\) |
−0.789136 | + | 0.614218i | \(0.789471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | −2.50000 | + | 0.866025i | −0.334077 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | + | 5.19615i | −0.393919 | + | 0.682288i | ||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50000 | − | 4.33013i | 0.320092 | − | 0.554416i | −0.660415 | − | 0.750901i | \(-0.729619\pi\) |
0.980507 | + | 0.196485i | \(0.0629528\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.00000 | − | 15.5885i | 1.11631 | − | 1.93351i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | − | 4.33013i | −0.305424 | − | 0.529009i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −2.50000 | + | 4.33013i | −0.303170 | + | 0.525105i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | − | 5.19615i | −0.717137 | − | 0.621059i | ||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | − | 10.3923i | −0.702247 | − | 1.21633i | −0.967676 | − | 0.252197i | \(-0.918847\pi\) |
0.265429 | − | 0.964130i | \(-0.414486\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 2.00000 | + | 1.73205i | 0.227921 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 1.50000 | + | 2.59808i | 0.167705 | + | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.50000 | − | 4.33013i | 0.276079 | − | 0.478183i | ||||
\(83\) | −1.00000 | −0.109764 | −0.0548821 | − | 0.998493i | \(-0.517478\pi\) | ||||
−0.0548821 | + | 0.998493i | \(0.517478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.0000 | −1.62698 | ||||||||
\(86\) | 5.00000 | − | 8.66025i | 0.539164 | − | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.0000 | + | 5.19615i | −1.57243 | + | 0.544705i | ||||
\(92\) | −5.00000 | −0.521286 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.50000 | + | 7.79423i | 0.464140 | + | 0.803913i | ||||
\(95\) | 9.00000 | + | 15.5885i | 0.923381 | + | 1.59934i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.00000 | 0.913812 | 0.456906 | − | 0.889515i | \(-0.348958\pi\) | ||||
0.456906 | + | 0.889515i | \(0.348958\pi\) | |||||||
\(98\) | 1.00000 | + | 6.92820i | 0.101015 | + | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | −4.00000 | − | 6.92820i | −0.398015 | − | 0.689382i | 0.595466 | − | 0.803380i | \(-0.296967\pi\) |
−0.993481 | + | 0.113998i | \(0.963634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | − | 1.73205i | 0.0985329 | − | 0.170664i | −0.812545 | − | 0.582899i | \(-0.801918\pi\) |
0.911078 | + | 0.412235i | \(0.135252\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −6.50000 | + | 11.2583i | −0.628379 | + | 1.08838i | 0.359498 | + | 0.933146i | \(0.382948\pi\) |
−0.987877 | + | 0.155238i | \(0.950386\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.50000 | + | 9.52628i | 0.526804 | + | 0.912452i | 0.999512 | + | 0.0312328i | \(0.00994332\pi\) |
−0.472708 | + | 0.881219i | \(0.656723\pi\) | |||||||
\(110\) | 1.50000 | − | 2.59808i | 0.143019 | − | 0.247717i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.50000 | − | 12.9904i | −0.699379 | − | 1.21136i | ||||
\(116\) | −3.00000 | − | 5.19615i | −0.278543 | − | 0.482451i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 10.0000 | + | 8.66025i | 0.916698 | + | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 2.50000 | + | 4.33013i | 0.226339 | + | 0.392031i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.00000 | + | 3.46410i | −0.179605 | + | 0.311086i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.00000 | + | 15.5885i | 0.789352 | + | 1.36720i | ||||
\(131\) | −2.00000 | + | 3.46410i | −0.174741 | + | 0.302660i | −0.940072 | − | 0.340977i | \(-0.889242\pi\) |
0.765331 | + | 0.643637i | \(0.222575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | − | 15.5885i | 0.260133 | − | 1.35169i | ||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | −1.00000 | − | 1.73205i | −0.0854358 | − | 0.147979i | 0.820141 | − | 0.572161i | \(-0.193895\pi\) |
−0.905577 | + | 0.424182i | \(0.860562\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.0000 | 1.86602 | 0.933008 | − | 0.359856i | \(-0.117174\pi\) | ||||
0.933008 | + | 0.359856i | \(0.117174\pi\) | |||||||
\(140\) | 7.50000 | − | 2.59808i | 0.633866 | − | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | − | 3.46410i | 0.167836 | − | 0.290701i | ||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | − | 15.5885i | 0.747409 | − | 1.29455i | ||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50000 | − | 7.79423i | −0.366205 | − | 0.634285i | 0.622764 | − | 0.782410i | \(-0.286010\pi\) |
−0.988969 | + | 0.148124i | \(0.952676\pi\) | |||||||
\(152\) | −3.00000 | + | 5.19615i | −0.243332 | + | 0.421464i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.50000 | + | 0.866025i | −0.201456 | + | 0.0697863i | ||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0000 | + | 20.7846i | 0.957704 | + | 1.65879i | 0.728055 | + | 0.685519i | \(0.240425\pi\) |
0.229650 | + | 0.973273i | \(0.426242\pi\) | |||||||
\(158\) | 0.500000 | + | 0.866025i | 0.0397779 | + | 0.0688973i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.00000 | −0.237171 | ||||||||
\(161\) | −2.50000 | + | 12.9904i | −0.197028 | + | 1.02379i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.500000 | − | 0.866025i | 0.0391630 | − | 0.0678323i | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | 2.50000 | + | 4.33013i | 0.195217 | + | 0.338126i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.500000 | − | 0.866025i | 0.0388075 | − | 0.0672166i | ||||
\(167\) | 24.0000 | 1.85718 | 0.928588 | − | 0.371113i | \(-0.121024\pi\) | ||||
0.928588 | + | 0.371113i | \(0.121024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 7.50000 | − | 12.9904i | 0.575224 | − | 0.996317i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | −6.00000 | + | 10.3923i | −0.456172 | + | 0.790112i | −0.998755 | − | 0.0498898i | \(-0.984113\pi\) |
0.542583 | + | 0.840002i | \(0.317446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | + | 6.92820i | 0.604743 | + | 0.523723i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | + | 5.19615i | 0.224860 | + | 0.389468i | ||||
\(179\) | −4.00000 | − | 6.92820i | −0.298974 | − | 0.517838i | 0.676927 | − | 0.736050i | \(-0.263311\pi\) |
−0.975901 | + | 0.218212i | \(0.929978\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 3.00000 | − | 15.5885i | 0.222375 | − | 1.15549i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.50000 | − | 4.33013i | 0.184302 | − | 0.319221i | ||||
\(185\) | −3.00000 | − | 5.19615i | −0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.50000 | + | 4.33013i | −0.182818 | + | 0.316650i | ||||
\(188\) | −9.00000 | −0.656392 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | −1.30586 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00000 | − | 5.19615i | −0.215945 | − | 0.374027i | 0.737620 | − | 0.675216i | \(-0.235950\pi\) |
−0.953564 | + | 0.301189i | \(0.902616\pi\) | |||||||
\(194\) | −4.50000 | + | 7.79423i | −0.323081 | + | 0.559593i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 24.0000 | 1.70993 | 0.854965 | − | 0.518686i | \(-0.173579\pi\) | ||||
0.854965 | + | 0.518686i | \(0.173579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00000 | − | 8.66025i | −0.354441 | − | 0.613909i | 0.632581 | − | 0.774494i | \(-0.281995\pi\) |
−0.987022 | + | 0.160585i | \(0.948662\pi\) | |||||||
\(200\) | −2.00000 | − | 3.46410i | −0.141421 | − | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.00000 | 0.562878 | ||||||||
\(203\) | −15.0000 | + | 5.19615i | −1.05279 | + | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.50000 | + | 12.9904i | −0.523823 | + | 0.907288i | ||||
\(206\) | 1.00000 | + | 1.73205i | 0.0696733 | + | 0.120678i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | + | 5.19615i | −0.208013 | + | 0.360288i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | 1.00000 | − | 1.73205i | 0.0686803 | − | 0.118958i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.50000 | − | 11.2583i | −0.444331 | − | 0.769604i | ||||
\(215\) | −15.0000 | + | 25.9808i | −1.02299 | + | 1.77187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | + | 6.92820i | 0.543075 | + | 0.470317i | ||||
\(218\) | −11.0000 | −0.745014 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.50000 | + | 2.59808i | 0.101130 | + | 0.175162i | ||||
\(221\) | −15.0000 | − | 25.9808i | −1.00901 | − | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.00000 | − | 8.66025i | 0.332595 | − | 0.576072i | ||||
\(227\) | 1.50000 | + | 2.59808i | 0.0995585 | + | 0.172440i | 0.911502 | − | 0.411296i | \(-0.134924\pi\) |
−0.811943 | + | 0.583736i | \(0.801590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0000 | + | 22.5167i | −0.859064 | + | 1.48794i | 0.0137585 | + | 0.999905i | \(0.495620\pi\) |
−0.872823 | + | 0.488037i | \(0.837713\pi\) | |||||||
\(230\) | 15.0000 | 0.989071 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | −14.5000 | + | 25.1147i | −0.949927 | + | 1.64532i | −0.204354 | + | 0.978897i | \(0.565509\pi\) |
−0.745573 | + | 0.666424i | \(0.767824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.5000 | − | 23.3827i | −0.880643 | − | 1.52532i | ||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.5000 | + | 4.33013i | −0.810255 | + | 0.280680i | ||||
\(239\) | −26.0000 | −1.68180 | −0.840900 | − | 0.541190i | \(-0.817974\pi\) | ||||
−0.840900 | + | 0.541190i | \(0.817974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | + | 22.5167i | 0.837404 | + | 1.45043i | 0.892058 | + | 0.451920i | \(0.149261\pi\) |
−0.0546547 | + | 0.998505i | \(0.517406\pi\) | |||||||
\(242\) | −0.500000 | − | 0.866025i | −0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.00000 | −0.320092 | ||||||||
\(245\) | −3.00000 | − | 20.7846i | −0.191663 | − | 1.32788i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.0000 | + | 31.1769i | −1.14531 | + | 1.98374i | ||||
\(248\) | −2.00000 | − | 3.46410i | −0.127000 | − | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.50000 | + | 2.59808i | −0.0948683 | + | 0.164317i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | −2.50000 | + | 4.33013i | −0.156864 | + | 0.271696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −7.00000 | + | 12.1244i | −0.436648 | + | 0.756297i | −0.997429 | − | 0.0716680i | \(-0.977168\pi\) |
0.560781 | + | 0.827964i | \(0.310501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | + | 5.19615i | −0.0621370 | + | 0.322873i | ||||
\(260\) | −18.0000 | −1.11631 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.00000 | − | 3.46410i | −0.123560 | − | 0.214013i | ||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 12.0000 | + | 10.3923i | 0.735767 | + | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.50000 | + | 4.33013i | −0.152712 | + | 0.264505i | ||||
\(269\) | −4.50000 | − | 7.79423i | −0.274370 | − | 0.475223i | 0.695606 | − | 0.718423i | \(-0.255136\pi\) |
−0.969976 | + | 0.243201i | \(0.921803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | −2.00000 | + | 3.46410i | −0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | − | 15.5885i | −0.540758 | − | 0.936620i | −0.998861 | − | 0.0477206i | \(-0.984804\pi\) |
0.458103 | − | 0.888899i | \(-0.348529\pi\) | |||||||
\(278\) | −11.0000 | + | 19.0526i | −0.659736 | + | 1.14270i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.50000 | + | 7.79423i | −0.0896421 | + | 0.465794i | ||||
\(281\) | −11.0000 | −0.656205 | −0.328102 | − | 0.944642i | \(-0.606409\pi\) | ||||
−0.328102 | + | 0.944642i | \(0.606409\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.00000 | + | 5.19615i | 0.178331 | + | 0.308879i | 0.941309 | − | 0.337546i | \(-0.109597\pi\) |
−0.762978 | + | 0.646425i | \(0.776263\pi\) | |||||||
\(284\) | 2.00000 | + | 3.46410i | 0.118678 | + | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | 12.5000 | − | 4.33013i | 0.737852 | − | 0.255599i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 9.00000 | + | 15.5885i | 0.528498 | + | 0.915386i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | + | 10.3923i | −0.351123 | + | 0.608164i | ||||
\(293\) | −8.00000 | −0.467365 | −0.233682 | − | 0.972313i | \(-0.575078\pi\) | ||||
−0.233682 | + | 0.972313i | \(0.575078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.0000 | −2.09600 | ||||||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.00000 | + | 15.5885i | 0.521356 | + | 0.903015i | ||||
\(299\) | 15.0000 | − | 25.9808i | 0.867472 | − | 1.50251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.0000 | − | 8.66025i | 1.44098 | − | 0.499169i | ||||
\(302\) | 9.00000 | 0.517892 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | −7.50000 | − | 12.9904i | −0.429449 | − | 0.743827i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000 | 1.02731 | 0.513657 | − | 0.857996i | \(-0.328290\pi\) | ||||
0.513657 | + | 0.857996i | \(0.328290\pi\) | |||||||
\(308\) | 0.500000 | − | 2.59808i | 0.0284901 | − | 0.148039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.00000 | − | 10.3923i | 0.340777 | − | 0.590243i | ||||
\(311\) | −10.5000 | − | 18.1865i | −0.595400 | − | 1.03126i | −0.993490 | − | 0.113917i | \(-0.963660\pi\) |
0.398090 | − | 0.917346i | \(-0.369673\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | − | 5.19615i | 0.169570 | − | 0.293704i | −0.768699 | − | 0.639611i | \(-0.779095\pi\) |
0.938269 | + | 0.345907i | \(0.112429\pi\) | |||||||
\(314\) | −24.0000 | −1.35440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | 4.50000 | − | 7.79423i | 0.252745 | − | 0.437767i | −0.711535 | − | 0.702650i | \(-0.752000\pi\) |
0.964281 | + | 0.264883i | \(0.0853332\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | − | 5.19615i | −0.167968 | − | 0.290929i | ||||
\(320\) | 1.50000 | − | 2.59808i | 0.0838525 | − | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.0000 | − | 8.66025i | −0.557278 | − | 0.482617i | ||||
\(323\) | 30.0000 | 1.66924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | − | 20.7846i | −0.665640 | − | 1.15292i | ||||
\(326\) | 0.500000 | + | 0.866025i | 0.0276924 | + | 0.0479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.00000 | −0.276079 | ||||||||
\(329\) | −4.50000 | + | 23.3827i | −0.248093 | + | 1.28913i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.5000 | + | 30.3109i | −0.961887 | + | 1.66604i | −0.244131 | + | 0.969742i | \(0.578503\pi\) |
−0.717756 | + | 0.696295i | \(0.754831\pi\) | |||||||
\(332\) | 0.500000 | + | 0.866025i | 0.0274411 | + | 0.0475293i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0000 | + | 20.7846i | −0.656611 | + | 1.13728i | ||||
\(335\) | −15.0000 | −0.819538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | −11.5000 | + | 19.9186i | −0.625518 | + | 1.08343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.50000 | + | 12.9904i | 0.406745 | + | 0.704502i | ||||
\(341\) | −2.00000 | + | 3.46410i | −0.108306 | + | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −10.0000 | −0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.00000 | − | 10.3923i | −0.322562 | − | 0.558694i | ||||
\(347\) | 3.50000 | + | 6.06218i | 0.187890 | + | 0.325435i | 0.944547 | − | 0.328378i | \(-0.106502\pi\) |
−0.756657 | + | 0.653812i | \(0.773169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0000 | −1.01705 | −0.508523 | − | 0.861048i | \(-0.669808\pi\) | ||||
−0.508523 | + | 0.861048i | \(0.669808\pi\) | |||||||
\(350\) | −10.0000 | + | 3.46410i | −0.534522 | + | 0.185164i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 12.0000 | + | 20.7846i | 0.638696 | + | 1.10625i | 0.985719 | + | 0.168397i | \(0.0538590\pi\) |
−0.347024 | + | 0.937856i | \(0.612808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.00000 | 0.422813 | ||||||||
\(359\) | −5.00000 | + | 8.66025i | −0.263890 | + | 0.457071i | −0.967272 | − | 0.253741i | \(-0.918339\pi\) |
0.703382 | + | 0.710812i | \(0.251672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 11.0000 | − | 19.0526i | 0.578147 | − | 1.00138i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0000 | + | 10.3923i | 0.628971 | + | 0.544705i | ||||
\(365\) | −36.0000 | −1.88433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00000 | + | 12.1244i | 0.365397 | + | 0.632886i | 0.988840 | − | 0.148983i | \(-0.0475999\pi\) |
−0.623443 | + | 0.781869i | \(0.714267\pi\) | |||||||
\(368\) | 2.50000 | + | 4.33013i | 0.130322 | + | 0.225723i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | −4.00000 | − | 3.46410i | −0.207670 | − | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50000 | − | 6.06218i | 0.181223 | − | 0.313888i | −0.761074 | − | 0.648665i | \(-0.775328\pi\) |
0.942297 | + | 0.334777i | \(0.108661\pi\) | |||||||
\(374\) | −2.50000 | − | 4.33013i | −0.129272 | − | 0.223906i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.50000 | − | 7.79423i | 0.232070 | − | 0.401957i | ||||
\(377\) | 36.0000 | 1.85409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0000 | 0.667765 | 0.333883 | − | 0.942615i | \(-0.391641\pi\) | ||||
0.333883 | + | 0.942615i | \(0.391641\pi\) | |||||||
\(380\) | 9.00000 | − | 15.5885i | 0.461690 | − | 0.799671i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00000 | − | 6.92820i | 0.204390 | − | 0.354015i | −0.745548 | − | 0.666452i | \(-0.767812\pi\) |
0.949938 | + | 0.312437i | \(0.101145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.50000 | − | 2.59808i | 0.382235 | − | 0.132410i | ||||
\(386\) | 6.00000 | 0.305392 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.50000 | − | 7.79423i | −0.228453 | − | 0.395692i | ||||
\(389\) | −10.5000 | − | 18.1865i | −0.532371 | − | 0.922094i | −0.999286 | − | 0.0377914i | \(-0.987968\pi\) |
0.466915 | − | 0.884302i | \(-0.345366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.0000 | −1.26430 | ||||||||
\(392\) | 5.50000 | − | 4.33013i | 0.277792 | − | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.0000 | + | 20.7846i | −0.604551 | + | 1.04711i | ||||
\(395\) | −1.50000 | − | 2.59808i | −0.0754732 | − | 0.130723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | + | 22.5167i | −0.652451 | + | 1.13008i | 0.330075 | + | 0.943955i | \(0.392926\pi\) |
−0.982526 | + | 0.186124i | \(0.940407\pi\) | |||||||
\(398\) | 10.0000 | 0.501255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | − | 20.7846i | −0.597763 | − | 1.03536i | ||||
\(404\) | −4.00000 | + | 6.92820i | −0.199007 | + | 0.344691i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | − | 15.5885i | 0.148888 | − | 0.773642i | ||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | − | 8.66025i | −0.247234 | − | 0.428222i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.962757 | + | 0.270367i | \(0.912855\pi\) | |||||||
\(410\) | −7.50000 | − | 12.9904i | −0.370399 | − | 0.641549i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.00000 | −0.0985329 | ||||||||
\(413\) | 24.0000 | + | 20.7846i | 1.18096 | + | 1.02274i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.50000 | + | 2.59808i | −0.0736321 | + | 0.127535i | ||||
\(416\) | −3.00000 | − | 5.19615i | −0.147087 | − | 0.254762i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.00000 | + | 5.19615i | −0.146735 | + | 0.254152i | ||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | −7.00000 | + | 12.1244i | −0.340755 | + | 0.590204i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.00000 | + | 1.73205i | 0.0485643 | + | 0.0841158i | ||||
\(425\) | −10.0000 | + | 17.3205i | −0.485071 | + | 0.840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.50000 | + | 12.9904i | −0.120983 | + | 0.628649i | ||||
\(428\) | 13.0000 | 0.628379 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.0000 | − | 25.9808i | −0.723364 | − | 1.25290i | ||||
\(431\) | 11.0000 | + | 19.0526i | 0.529851 | + | 0.917729i | 0.999394 | + | 0.0348195i | \(0.0110856\pi\) |
−0.469542 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0000 | 0.528626 | 0.264313 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264313 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(434\) | −10.0000 | + | 3.46410i | −0.480015 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.50000 | − | 9.52628i | 0.263402 | − | 0.456226i | ||||
\(437\) | 15.0000 | + | 25.9808i | 0.717547 | + | 1.24283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.50000 | − | 4.33013i | 0.119318 | − | 0.206666i | −0.800179 | − | 0.599761i | \(-0.795262\pi\) |
0.919498 | + | 0.393095i | \(0.128596\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0000 | 1.42695 | ||||||||
\(443\) | 1.00000 | − | 1.73205i | 0.0475114 | − | 0.0822922i | −0.841292 | − | 0.540581i | \(-0.818204\pi\) |
0.888803 | + | 0.458289i | \(0.151538\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | −8.00000 | + | 13.8564i | −0.378811 | + | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.50000 | + | 4.33013i | 0.117720 | + | 0.203898i | ||||
\(452\) | 5.00000 | + | 8.66025i | 0.235180 | + | 0.407344i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.00000 | −0.140797 | ||||||||
\(455\) | −9.00000 | + | 46.7654i | −0.421927 | + | 2.19239i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | − | 22.5167i | 0.608114 | − | 1.05328i | −0.383437 | − | 0.923567i | \(-0.625260\pi\) |
0.991551 | − | 0.129718i | \(-0.0414071\pi\) | |||||||
\(458\) | −13.0000 | − | 22.5167i | −0.607450 | − | 1.05213i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.50000 | + | 12.9904i | −0.349689 | + | 0.605680i | ||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0000 | 1.30127 | 0.650635 | − | 0.759390i | \(-0.274503\pi\) | ||||
0.650635 | + | 0.759390i | \(0.274503\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.5000 | − | 25.1147i | −0.671700 | − | 1.16342i | ||||
\(467\) | 8.00000 | − | 13.8564i | 0.370196 | − | 0.641198i | −0.619400 | − | 0.785076i | \(-0.712624\pi\) |
0.989595 | + | 0.143878i | \(0.0459572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | + | 8.66025i | 0.461757 | + | 0.399893i | ||||
\(470\) | 27.0000 | 1.24542 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.00000 | − | 10.3923i | −0.276172 | − | 0.478345i | ||||
\(473\) | 5.00000 | + | 8.66025i | 0.229900 | + | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0000 | 1.10120 | ||||||||
\(476\) | 2.50000 | − | 12.9904i | 0.114587 | − | 0.595413i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.0000 | − | 22.5167i | 0.594606 | − | 1.02989i | ||||
\(479\) | 6.00000 | + | 10.3923i | 0.274147 | + | 0.474837i | 0.969920 | − | 0.243426i | \(-0.0782712\pi\) |
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | −26.0000 | −1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 13.5000 | − | 23.3827i | 0.613003 | − | 1.06175i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | + | 3.46410i | 0.0906287 | + | 0.156973i | 0.907776 | − | 0.419456i | \(-0.137779\pi\) |
−0.817147 | + | 0.576429i | \(0.804446\pi\) | |||||||
\(488\) | 2.50000 | − | 4.33013i | 0.113170 | − | 0.196016i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 19.5000 | + | 7.79423i | 0.880920 | + | 0.352107i | ||||
\(491\) | 3.00000 | 0.135388 | 0.0676941 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676941 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.0000 | − | 25.9808i | −0.675566 | − | 1.17011i | ||||
\(494\) | −18.0000 | − | 31.1769i | −0.809858 | − | 1.40272i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 10.0000 | − | 3.46410i | 0.448561 | − | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.00000 | + | 10.3923i | −0.268597 | + | 0.465223i | −0.968500 | − | 0.249015i | \(-0.919893\pi\) |
0.699903 | + | 0.714238i | \(0.253227\pi\) | |||||||
\(500\) | −1.50000 | − | 2.59808i | −0.0670820 | − | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | − | 10.3923i | 0.267793 | − | 0.463831i | ||||
\(503\) | 42.0000 | 1.87269 | 0.936344 | − | 0.351085i | \(-0.114187\pi\) | ||||
0.936344 | + | 0.351085i | \(0.114187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.0000 | −1.06799 | ||||||||
\(506\) | 2.50000 | − | 4.33013i | 0.111139 | − | 0.192498i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.50000 | − | 4.33013i | −0.110920 | − | 0.192118i | ||||
\(509\) | 1.00000 | − | 1.73205i | 0.0443242 | − | 0.0767718i | −0.843012 | − | 0.537895i | \(-0.819220\pi\) |
0.887336 | + | 0.461123i | \(0.152553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000 | + | 20.7846i | 1.06170 | + | 0.919457i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.00000 | − | 12.1244i | −0.308757 | − | 0.534782i | ||||
\(515\) | −3.00000 | − | 5.19615i | −0.132196 | − | 0.228970i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.00000 | −0.395820 | ||||||||
\(518\) | −4.00000 | − | 3.46410i | −0.175750 | − | 0.152204i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | − | 15.5885i | 0.394676 | − | 0.683599i | ||||
\(521\) | 1.00000 | + | 1.73205i | 0.0438108 | + | 0.0758825i | 0.887099 | − | 0.461579i | \(-0.152717\pi\) |
−0.843288 | + | 0.537461i | \(0.819383\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | + | 5.19615i | −0.131181 | + | 0.227212i | −0.924132 | − | 0.382073i | \(-0.875210\pi\) |
0.792951 | + | 0.609285i | \(0.208544\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | −10.0000 | + | 17.3205i | −0.435607 | + | 0.754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | − | 1.73205i | −0.0434783 | − | 0.0753066i | ||||
\(530\) | −3.00000 | + | 5.19615i | −0.130312 | + | 0.225706i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.0000 | + | 5.19615i | −0.650332 | + | 0.225282i | ||||
\(533\) | −30.0000 | −1.29944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.5000 | + | 33.7750i | 0.843059 | + | 1.46022i | ||||
\(536\) | −2.50000 | − | 4.33013i | −0.107984 | − | 0.187033i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.00000 | 0.388018 | ||||||||
\(539\) | −6.50000 | − | 2.59808i | −0.279975 | − | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5000 | − | 33.7750i | 0.838370 | − | 1.45210i | −0.0528859 | − | 0.998601i | \(-0.516842\pi\) |
0.891256 | − | 0.453500i | \(-0.149825\pi\) | |||||||
\(542\) | 12.0000 | + | 20.7846i | 0.515444 | + | 0.892775i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.50000 | + | 4.33013i | −0.107187 | + | 0.185653i | ||||
\(545\) | 33.0000 | 1.41356 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.0000 | −1.79579 | −0.897895 | − | 0.440209i | \(-0.854904\pi\) | ||||
−0.897895 | + | 0.440209i | \(0.854904\pi\) | |||||||
\(548\) | −1.00000 | + | 1.73205i | −0.0427179 | + | 0.0739895i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | − | 3.46410i | −0.0852803 | − | 0.147710i | ||||
\(551\) | −18.0000 | + | 31.1769i | −0.766826 | + | 1.32818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 2.59808i | −0.0212622 | + | 0.110481i | ||||
\(554\) | 18.0000 | 0.764747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.0000 | − | 19.0526i | −0.466504 | − | 0.808008i | ||||
\(557\) | −16.0000 | − | 27.7128i | −0.677942 | − | 1.17423i | −0.975600 | − | 0.219557i | \(-0.929539\pi\) |
0.297658 | − | 0.954673i | \(-0.403795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −60.0000 | −2.53773 | ||||||||
\(560\) | −6.00000 | − | 5.19615i | −0.253546 | − | 0.219578i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.50000 | − | 9.52628i | 0.232003 | − | 0.401842i | ||||
\(563\) | −8.00000 | − | 13.8564i | −0.337160 | − | 0.583978i | 0.646737 | − | 0.762713i | \(-0.276133\pi\) |
−0.983897 | + | 0.178735i | \(0.942800\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.0000 | + | 25.9808i | −0.631055 | + | 1.09302i | ||||
\(566\) | −6.00000 | −0.252199 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0000 | + | 29.4449i | 0.711428 | + | 1.23223i | 0.964321 | + | 0.264735i | \(0.0852845\pi\) |
−0.252893 | + | 0.967494i | \(0.581382\pi\) | |||||||
\(572\) | −3.00000 | + | 5.19615i | −0.125436 | + | 0.217262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.50000 | + | 12.9904i | −0.104348 | + | 0.542208i | ||||
\(575\) | −20.0000 | −0.834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.50000 | + | 6.06218i | 0.145707 | + | 0.252372i | 0.929636 | − | 0.368478i | \(-0.120121\pi\) |
−0.783930 | + | 0.620850i | \(0.786788\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18.0000 | −0.747409 | ||||||||
\(581\) | 2.50000 | − | 0.866025i | 0.103717 | − | 0.0359288i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00000 | − | 1.73205i | 0.0414158 | − | 0.0717342i | ||||
\(584\) | −6.00000 | − | 10.3923i | −0.248282 | − | 0.430037i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.00000 | − | 6.92820i | 0.165238 | − | 0.286201i | ||||
\(587\) | 24.0000 | 0.990586 | 0.495293 | − | 0.868726i | \(-0.335061\pi\) | ||||
0.495293 | + | 0.868726i | \(0.335061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | 0.988903 | ||||||||
\(590\) | 18.0000 | − | 31.1769i | 0.741048 | − | 1.28353i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | + | 1.73205i | 0.0410997 | + | 0.0711868i | ||||
\(593\) | 7.00000 | − | 12.1244i | 0.287456 | − | 0.497888i | −0.685746 | − | 0.727841i | \(-0.740524\pi\) |
0.973202 | + | 0.229953i | \(0.0738573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.5000 | − | 12.9904i | 1.53735 | − | 0.532554i | ||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.0000 | + | 25.9808i | 0.613396 | + | 1.06243i | ||||
\(599\) | −1.50000 | − | 2.59808i | −0.0612883 | − | 0.106155i | 0.833753 | − | 0.552137i | \(-0.186188\pi\) |
−0.895042 | + | 0.445983i | \(0.852854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.0000 | −1.79480 | −0.897399 | − | 0.441221i | \(-0.854546\pi\) | ||||
−0.897399 | + | 0.441221i | \(0.854546\pi\) | |||||||
\(602\) | −5.00000 | + | 25.9808i | −0.203785 | + | 1.05890i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.50000 | + | 7.79423i | −0.183102 | + | 0.317143i | ||||
\(605\) | 1.50000 | + | 2.59808i | 0.0609837 | + | 0.105627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.5000 | + | 28.5788i | −0.669714 | + | 1.15998i | 0.308270 | + | 0.951299i | \(0.400250\pi\) |
−0.977984 | + | 0.208680i | \(0.933083\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0000 | 0.607332 | ||||||||
\(611\) | 27.0000 | − | 46.7654i | 1.09230 | − | 1.89192i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5000 | + | 35.5070i | 0.827987 | + | 1.43412i | 0.899615 | + | 0.436684i | \(0.143847\pi\) |
−0.0716275 | + | 0.997431i | \(0.522819\pi\) | |||||||
\(614\) | −9.00000 | + | 15.5885i | −0.363210 | + | 0.629099i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | + | 1.73205i | 0.0805823 | + | 0.0697863i | ||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.5000 | + | 25.1147i | 0.582804 | + | 1.00945i | 0.995145 | + | 0.0984169i | \(0.0313779\pi\) |
−0.412341 | + | 0.911030i | \(0.635289\pi\) | |||||||
\(620\) | 6.00000 | + | 10.3923i | 0.240966 | + | 0.417365i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.0000 | 0.842023 | ||||||||
\(623\) | −3.00000 | + | 15.5885i | −0.120192 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 3.00000 | + | 5.19615i | 0.119904 | + | 0.207680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.0000 | − | 20.7846i | 0.478852 | − | 0.829396i | ||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0000 | 1.11466 | 0.557331 | − | 0.830290i | \(-0.311825\pi\) | ||||
0.557331 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(632\) | 0.500000 | − | 0.866025i | 0.0198889 | − | 0.0344486i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.50000 | + | 7.79423i | 0.178718 | + | 0.309548i | ||||
\(635\) | 7.50000 | − | 12.9904i | 0.297628 | − | 0.515508i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.0000 | − | 25.9808i | 1.30751 | − | 1.02940i | ||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | −20.0000 | − | 34.6410i | −0.789953 | − | 1.36824i | −0.925995 | − | 0.377535i | \(-0.876772\pi\) |
0.136043 | − | 0.990703i | \(-0.456562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.0000 | 1.41970 | 0.709851 | − | 0.704352i | \(-0.248762\pi\) | ||||
0.709851 | + | 0.704352i | \(0.248762\pi\) | |||||||
\(644\) | 12.5000 | − | 4.33013i | 0.492569 | − | 0.170631i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.0000 | + | 25.9808i | −0.590167 | + | 1.02220i | ||||
\(647\) | 8.50000 | + | 14.7224i | 0.334169 | + | 0.578799i | 0.983325 | − | 0.181857i | \(-0.0582109\pi\) |
−0.649155 | + | 0.760656i | \(0.724878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | 24.0000 | 0.941357 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | −0.0391630 | ||||||||
\(653\) | −13.5000 | + | 23.3827i | −0.528296 | + | 0.915035i | 0.471160 | + | 0.882048i | \(0.343835\pi\) |
−0.999456 | + | 0.0329874i | \(0.989498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | + | 10.3923i | 0.234439 | + | 0.406061i | ||||
\(656\) | 2.50000 | − | 4.33013i | 0.0976086 | − | 0.169063i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.0000 | − | 15.5885i | −0.701713 | − | 0.607701i | ||||
\(659\) | −31.0000 | −1.20759 | −0.603794 | − | 0.797140i | \(-0.706345\pi\) | ||||
−0.603794 | + | 0.797140i | \(0.706345\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00000 | − | 3.46410i | −0.0777910 | − | 0.134738i | 0.824506 | − | 0.565854i | \(-0.191453\pi\) |
−0.902297 | + | 0.431116i | \(0.858120\pi\) | |||||||
\(662\) | −17.5000 | − | 30.3109i | −0.680157 | − | 1.17807i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.00000 | −0.0388075 | ||||||||
\(665\) | −36.0000 | − | 31.1769i | −1.39602 | − | 1.20899i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0000 | − | 25.9808i | 0.580802 | − | 1.00598i | ||||
\(668\) | −12.0000 | − | 20.7846i | −0.464294 | − | 0.804181i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.50000 | − | 12.9904i | 0.289750 | − | 0.501862i | ||||
\(671\) | −5.00000 | −0.193023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 1.00000 | − | 1.73205i | 0.0385186 | − | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5000 | − | 19.9186i | −0.442308 | − | 0.766099i | ||||
\(677\) | −9.00000 | + | 15.5885i | −0.345898 | + | 0.599113i | −0.985517 | − | 0.169580i | \(-0.945759\pi\) |
0.639618 | + | 0.768693i | \(0.279092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.5000 | + | 7.79423i | −0.863471 | + | 0.299115i | ||||
\(680\) | −15.0000 | −0.575224 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | −6.00000 | − | 10.3923i | −0.229584 | − | 0.397650i | 0.728101 | − | 0.685470i | \(-0.240403\pi\) |
−0.957685 | + | 0.287819i | \(0.907070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.00000 | − | 8.66025i | 0.190623 | − | 0.330169i | ||||
\(689\) | 6.00000 | + | 10.3923i | 0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5000 | − | 23.3827i | 0.513564 | − | 0.889519i | −0.486312 | − | 0.873785i | \(-0.661658\pi\) |
0.999876 | − | 0.0157341i | \(-0.00500851\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.00000 | −0.265716 | ||||||||
\(695\) | 33.0000 | − | 57.1577i | 1.25176 | − | 2.16811i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5000 | + | 21.6506i | 0.473471 | + | 0.820076i | ||||
\(698\) | 9.50000 | − | 16.4545i | 0.359580 | − | 0.622811i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000 | − | 10.3923i | 0.0755929 | − | 0.392792i | ||||
\(701\) | 10.0000 | 0.377695 | 0.188847 | − | 0.982006i | \(-0.439525\pi\) | ||||
0.188847 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.00000 | + | 10.3923i | 0.226294 | + | 0.391953i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 16.0000 | + | 13.8564i | 0.601742 | + | 0.521124i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | + | 17.3205i | −0.375558 | + | 0.650485i | −0.990410 | − | 0.138157i | \(-0.955882\pi\) |
0.614852 | + | 0.788642i | \(0.289216\pi\) | |||||||
\(710\) | −6.00000 | − | 10.3923i | −0.225176 | − | 0.390016i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | −20.0000 | −0.749006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | −4.00000 | + | 6.92820i | −0.149487 | + | 0.258919i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.00000 | − | 8.66025i | −0.186598 | − | 0.323198i | ||||
\(719\) | 18.5000 | − | 32.0429i | 0.689934 | − | 1.19500i | −0.281925 | − | 0.959436i | \(-0.590973\pi\) |
0.971859 | − | 0.235564i | \(-0.0756936\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.00000 | + | 5.19615i | −0.0372419 | + | 0.193515i | ||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0000 | + | 19.0526i | 0.408812 | + | 0.708083i | ||||
\(725\) | −12.0000 | − | 20.7846i | −0.445669 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0000 | 0.815935 | 0.407967 | − | 0.912996i | \(-0.366238\pi\) | ||||
0.407967 | + | 0.912996i | \(0.366238\pi\) | |||||||
\(728\) | −15.0000 | + | 5.19615i | −0.555937 | + | 0.192582i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.0000 | − | 31.1769i | 0.666210 | − | 1.15391i | ||||
\(731\) | 25.0000 | + | 43.3013i | 0.924658 | + | 1.60156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.50000 | − | 12.9904i | 0.277019 | − | 0.479811i | −0.693624 | − | 0.720338i | \(-0.743987\pi\) |
0.970642 | + | 0.240527i | \(0.0773202\pi\) | |||||||
\(734\) | −14.0000 | −0.516749 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.00000 | −0.184302 | ||||||||
\(737\) | −2.50000 | + | 4.33013i | −0.0920887 | + | 0.159502i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00000 | + | 8.66025i | 0.183928 | + | 0.318573i | 0.943215 | − | 0.332184i | \(-0.107785\pi\) |
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(740\) | −3.00000 | + | 5.19615i | −0.110282 | + | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.00000 | − | 1.73205i | 0.183556 | − | 0.0635856i | ||||
\(743\) | −22.0000 | −0.807102 | −0.403551 | − | 0.914957i | \(-0.632224\pi\) | ||||
−0.403551 | + | 0.914957i | \(0.632224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.0000 | − | 46.7654i | −0.989203 | − | 1.71335i | ||||
\(746\) | 3.50000 | + | 6.06218i | 0.128144 | + | 0.221952i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.00000 | 0.182818 | ||||||||
\(749\) | 6.50000 | − | 33.7750i | 0.237505 | − | 1.23411i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | − | 1.73205i | 0.0364905 | − | 0.0632034i | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | 4.50000 | + | 7.79423i | 0.164098 | + | 0.284226i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.0000 | + | 31.1769i | −0.655521 | + | 1.13540i | ||||
\(755\) | −27.0000 | −0.982631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | −6.50000 | + | 11.2583i | −0.236091 | + | 0.408921i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.00000 | + | 15.5885i | 0.326464 | + | 0.565453i | ||||
\(761\) | 23.5000 | − | 40.7032i | 0.851874 | − | 1.47549i | −0.0276404 | − | 0.999618i | \(-0.508799\pi\) |
0.879515 | − | 0.475872i | \(-0.157867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.0000 | − | 19.0526i | −0.796453 | − | 0.689749i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.00000 | + | 6.92820i | 0.144526 | + | 0.250326i | ||||
\(767\) | −36.0000 | − | 62.3538i | −1.29988 | − | 2.25147i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.0000 | 1.65880 | 0.829401 | − | 0.558653i | \(-0.188682\pi\) | ||||
0.829401 | + | 0.558653i | \(0.188682\pi\) | |||||||
\(770\) | −1.50000 | + | 7.79423i | −0.0540562 | + | 0.280885i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.00000 | + | 5.19615i | −0.107972 | + | 0.187014i | ||||
\(773\) | 5.50000 | + | 9.52628i | 0.197821 | + | 0.342636i | 0.947822 | − | 0.318801i | \(-0.103280\pi\) |
−0.750000 | + | 0.661437i | \(0.769947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | + | 13.8564i | −0.287368 | + | 0.497737i | ||||
\(776\) | 9.00000 | 0.323081 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.0000 | 0.752886 | ||||||||
\(779\) | 15.0000 | − | 25.9808i | 0.537431 | − | 0.930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 12.5000 | − | 21.6506i | 0.446999 | − | 0.774225i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 72.0000 | 2.56979 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0000 | + | 43.3013i | 0.891154 | + | 1.54352i | 0.838494 | + | 0.544911i | \(0.183437\pi\) |
0.0526599 | + | 0.998613i | \(0.483230\pi\) | |||||||
\(788\) | −12.0000 | − | 20.7846i | −0.427482 | − | 0.740421i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.00000 | 0.106735 | ||||||||
\(791\) | 25.0000 | − | 8.66025i | 0.888898 | − | 0.307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.0000 | − | 25.9808i | 0.532666 | − | 0.922604i | ||||
\(794\) | −13.0000 | − | 22.5167i | −0.461353 | − | 0.799086i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.00000 | + | 8.66025i | −0.177220 | + | 0.306955i | ||||
\(797\) | 53.0000 | 1.87736 | 0.938678 | − | 0.344795i | \(-0.112051\pi\) | ||||
0.938678 | + | 0.344795i | \(0.112051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.0000 | −1.59199 | ||||||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.00000 | − | 5.19615i | −0.105934 | − | 0.183483i | ||||
\(803\) | −6.00000 | + | 10.3923i | −0.211735 | + | 0.366736i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.0000 | + | 25.9808i | 1.05736 | + | 0.915702i | ||||
\(806\) | 24.0000 | 0.845364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.00000 | − | 6.92820i | −0.140720 | − | 0.243733i | ||||
\(809\) | 7.50000 | + | 12.9904i | 0.263686 | + | 0.456717i | 0.967219 | − | 0.253946i | \(-0.0817284\pi\) |
−0.703533 | + | 0.710663i | \(0.748395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.0000 | 1.47482 | 0.737410 | − | 0.675446i | \(-0.236049\pi\) | ||||
0.737410 | + | 0.675446i | \(0.236049\pi\) | |||||||
\(812\) | 12.0000 | + | 10.3923i | 0.421117 | + | 0.364698i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.00000 | − | 1.73205i | 0.0350500 | − | 0.0607083i | ||||
\(815\) | −1.50000 | − | 2.59808i | −0.0525427 | − | 0.0910066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | − | 51.9615i | 1.04957 | − | 1.81790i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.0000 | 0.523823 | ||||||||
\(821\) | −4.00000 | + | 6.92820i | −0.139601 | + | 0.241796i | −0.927346 | − | 0.374206i | \(-0.877915\pi\) |
0.787745 | + | 0.616002i | \(0.211249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.00000 | − | 8.66025i | −0.174289 | − | 0.301877i | 0.765626 | − | 0.643286i | \(-0.222429\pi\) |
−0.939915 | + | 0.341409i | \(0.889096\pi\) | |||||||
\(824\) | 1.00000 | − | 1.73205i | 0.0348367 | − | 0.0603388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.0000 | + | 10.3923i | −1.04383 | + | 0.361595i | ||||
\(827\) | 15.0000 | 0.521601 | 0.260801 | − | 0.965393i | \(-0.416014\pi\) | ||||
0.260801 | + | 0.965393i | \(0.416014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0000 | + | 46.7654i | 0.937749 | + | 1.62423i | 0.769657 | + | 0.638457i | \(0.220427\pi\) |
0.168091 | + | 0.985771i | \(0.446240\pi\) | |||||||
\(830\) | −1.50000 | − | 2.59808i | −0.0520658 | − | 0.0901805i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | −32.5000 | − | 12.9904i | −1.12606 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.0000 | − | 62.3538i | 1.24583 | − | 2.15784i | ||||
\(836\) | −3.00000 | − | 5.19615i | −0.103757 | − | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.0000 | + | 17.3205i | −0.345444 | + | 0.598327i | ||||
\(839\) | 9.00000 | 0.310715 | 0.155357 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155357 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −4.00000 | + | 6.92820i | −0.137849 | + | 0.238762i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.00000 | − | 12.1244i | −0.240950 | − | 0.417338i | ||||
\(845\) | 34.5000 | − | 59.7558i | 1.18684 | − | 2.05566i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.500000 | − | 2.59808i | 0.0171802 | − | 0.0892710i | ||||
\(848\) | −2.00000 | −0.0686803 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.0000 | − | 17.3205i | −0.342997 | − | 0.594089i | ||||
\(851\) | −5.00000 | − | 8.66025i | −0.171398 | − | 0.296870i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0000 | 0.513590 | 0.256795 | − | 0.966466i | \(-0.417333\pi\) | ||||
0.256795 | + | 0.966466i | \(0.417333\pi\) | |||||||
\(854\) | −10.0000 | − | 8.66025i | −0.342193 | − | 0.296348i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.50000 | + | 11.2583i | −0.222165 | + | 0.384802i | ||||
\(857\) | 1.50000 | + | 2.59808i | 0.0512390 | + | 0.0887486i | 0.890507 | − | 0.454969i | \(-0.150350\pi\) |
−0.839268 | + | 0.543718i | \(0.817016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.5000 | − | 38.9711i | 0.767690 | − | 1.32968i | −0.171122 | − | 0.985250i | \(-0.554739\pi\) |
0.938813 | − | 0.344428i | \(-0.111927\pi\) | |||||||
\(860\) | 30.0000 | 1.02299 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.0000 | −0.749323 | ||||||||
\(863\) | −19.5000 | + | 33.7750i | −0.663788 | + | 1.14971i | 0.315825 | + | 0.948818i | \(0.397719\pi\) |
−0.979612 | + | 0.200897i | \(0.935615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0000 | + | 31.1769i | 0.612018 | + | 1.06005i | ||||
\(866\) | −5.50000 | + | 9.52628i | −0.186898 | + | 0.323716i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.00000 | − | 10.3923i | 0.0678844 | − | 0.352738i | ||||
\(869\) | −1.00000 | −0.0339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0000 | − | 25.9808i | −0.508256 | − | 0.880325i | ||||
\(872\) | 5.50000 | + | 9.52628i | 0.186254 | + | 0.322601i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −30.0000 | −1.01477 | ||||||||
\(875\) | −7.50000 | + | 2.59808i | −0.253546 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.50000 | − | 2.59808i | 0.0506514 | − | 0.0877308i | −0.839588 | − | 0.543224i | \(-0.817204\pi\) |
0.890239 | + | 0.455493i | \(0.150537\pi\) | |||||||
\(878\) | 2.50000 | + | 4.33013i | 0.0843709 | + | 0.146135i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | 26.0000 | 0.875962 | 0.437981 | − | 0.898984i | \(-0.355694\pi\) | ||||
0.437981 | + | 0.898984i | \(0.355694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0000 | −0.437485 | −0.218742 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218742 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(884\) | −15.0000 | + | 25.9808i | −0.504505 | + | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.00000 | + | 1.73205i | 0.0335957 | + | 0.0581894i | ||||
\(887\) | −12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | \(-0.965338\pi\) |
0.591156 | + | 0.806557i | \(0.298672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5000 | + | 4.33013i | −0.419237 | + | 0.145228i | ||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.00000 | − | 13.8564i | −0.267860 | − | 0.463947i | ||||
\(893\) | 27.0000 | + | 46.7654i | 0.903521 | + | 1.56494i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0000 | −0.802232 | ||||||||
\(896\) | 0.500000 | − | 2.59808i | 0.0167038 | − | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.00000 | − | 1.73205i | 0.0333704 | − | 0.0577993i | ||||
\(899\) | −12.0000 | − | 20.7846i | −0.400222 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.00000 | − | 8.66025i | 0.166574 | − | 0.288515i | ||||
\(902\) | −5.00000 | −0.166482 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | −33.0000 | + | 57.1577i | −1.09696 | + | 1.89999i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.5000 | − | 19.9186i | −0.381851 | − | 0.661386i | 0.609476 | − | 0.792805i | \(-0.291380\pi\) |
−0.991327 | + | 0.131419i | \(0.958047\pi\) | |||||||
\(908\) | 1.50000 | − | 2.59808i | 0.0497792 | − | 0.0862202i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −36.0000 | − | 31.1769i | −1.19339 | − | 1.03350i | ||||
\(911\) | −51.0000 | −1.68971 | −0.844853 | − | 0.534999i | \(-0.820312\pi\) | ||||
−0.844853 | + | 0.534999i | \(0.820312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.500000 | + | 0.866025i | 0.0165476 | + | 0.0286613i | ||||
\(914\) | 13.0000 | + | 22.5167i | 0.430002 | + | 0.744785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 2.00000 | − | 10.3923i | 0.0660458 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.50000 | − | 14.7224i | 0.280389 | − | 0.485648i | −0.691091 | − | 0.722767i | \(-0.742870\pi\) |
0.971481 | + | 0.237119i | \(0.0762032\pi\) | |||||||
\(920\) | −7.50000 | − | 12.9904i | −0.247268 | − | 0.428280i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.00000 | + | 8.66025i | −0.164666 | + | 0.285210i | ||||
\(923\) | −24.0000 | −0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | −14.0000 | + | 24.2487i | −0.460069 | + | 0.796862i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.00000 | − | 5.19615i | −0.0984798 | − | 0.170572i | ||||
\(929\) | −13.0000 | + | 22.5167i | −0.426516 | + | 0.738748i | −0.996561 | − | 0.0828661i | \(-0.973593\pi\) |
0.570045 | + | 0.821614i | \(0.306926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | + | 41.5692i | 0.196642 | + | 1.36238i | ||||
\(932\) | 29.0000 | 0.949927 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.00000 | + | 13.8564i | 0.261768 | + | 0.453395i | ||||
\(935\) | 7.50000 | + | 12.9904i | 0.245276 | + | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | −12.5000 | + | 4.33013i | −0.408139 | + | 0.141384i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.5000 | + | 23.3827i | −0.440321 | + | 0.762659i | ||||
\(941\) | 3.00000 | + | 5.19615i | 0.0977972 | + | 0.169390i | 0.910773 | − | 0.412908i | \(-0.135487\pi\) |
−0.812975 | + | 0.582298i | \(0.802154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.5000 | + | 21.6506i | −0.407056 | + | 0.705042i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0000 | −0.325128 | ||||||||
\(947\) | −15.0000 | + | 25.9808i | −0.487435 | + | 0.844261i | −0.999896 | − | 0.0144491i | \(-0.995401\pi\) |
0.512461 | + | 0.858710i | \(0.328734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36.0000 | − | 62.3538i | −1.16861 | − | 2.02409i | ||||
\(950\) | −12.0000 | + | 20.7846i | −0.389331 | + | 0.674342i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.0000 | + | 8.66025i | 0.324102 | + | 0.280680i | ||||
\(953\) | 21.0000 | 0.680257 | 0.340128 | − | 0.940379i | \(-0.389529\pi\) | ||||
0.340128 | + | 0.940379i | \(0.389529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.0000 | + | 22.5167i | 0.420450 | + | 0.728241i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.0000 | −0.387702 | ||||||||
\(959\) | 4.00000 | + | 3.46410i | 0.129167 | + | 0.111862i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 6.00000 | + | 10.3923i | 0.193448 | + | 0.335061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.0000 | − | 22.5167i | 0.418702 | − | 0.725213i | ||||
\(965\) | −18.0000 | −0.579441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0000 | −0.675314 | −0.337657 | − | 0.941269i | \(-0.609634\pi\) | ||||
−0.337657 | + | 0.941269i | \(0.609634\pi\) | |||||||
\(968\) | −0.500000 | + | 0.866025i | −0.0160706 | + | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.5000 | + | 23.3827i | 0.433459 | + | 0.750773i | ||||
\(971\) | −17.0000 | + | 29.4449i | −0.545556 | + | 0.944931i | 0.453016 | + | 0.891503i | \(0.350348\pi\) |
−0.998572 | + | 0.0534281i | \(0.982985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −55.0000 | + | 19.0526i | −1.76322 | + | 0.610797i | ||||
\(974\) | −4.00000 | −0.128168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.50000 | + | 4.33013i | 0.0800230 | + | 0.138604i | ||||
\(977\) | −14.0000 | − | 24.2487i | −0.447900 | − | 0.775785i | 0.550349 | − | 0.834934i | \(-0.314494\pi\) |
−0.998249 | + | 0.0591494i | \(0.981161\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | −16.5000 | + | 12.9904i | −0.527073 | + | 0.414963i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.50000 | + | 2.59808i | −0.0478669 | + | 0.0829079i | ||||
\(983\) | −29.5000 | − | 51.0955i | −0.940904 | − | 1.62969i | −0.763752 | − | 0.645510i | \(-0.776645\pi\) |
−0.177152 | − | 0.984184i | \(-0.556688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | − | 62.3538i | 1.14706 | − | 1.98676i | ||||
\(986\) | 30.0000 | 0.955395 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 36.0000 | 1.14531 | ||||||||
\(989\) | −25.0000 | + | 43.3013i | −0.794954 | + | 1.37690i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0000 | − | 19.0526i | −0.349427 | − | 0.605224i | 0.636721 | − | 0.771094i | \(-0.280290\pi\) |
−0.986148 | + | 0.165870i | \(0.946957\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.00000 | + | 10.3923i | −0.0634361 | + | 0.329624i | ||||
\(995\) | −30.0000 | −0.951064 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.00000 | − | 12.1244i | −0.221692 | − | 0.383982i | 0.733630 | − | 0.679549i | \(-0.237825\pi\) |
−0.955322 | + | 0.295567i | \(0.904491\pi\) | |||||||
\(998\) | −6.00000 | − | 10.3923i | −0.189927 | − | 0.328963i | ||||
\(999\) | 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 | 1386.2.k.j.793.1 | 2 | ||
3.2 | odd | 2 | 462.2.i.a.331.1 | yes | 2 | ||
7.2 | even | 3 | 9702.2.a.be.1.1 | 1 | |||
7.4 | even | 3 | inner | 1386.2.k.j.991.1 | 2 | ||
7.5 | odd | 6 | 9702.2.a.ce.1.1 | 1 | |||
21.2 | odd | 6 | 3234.2.a.o.1.1 | 1 | |||
21.5 | even | 6 | 3234.2.a.a.1.1 | 1 | |||
21.11 | odd | 6 | 462.2.i.a.67.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.a.67.1 | ✓ | 2 | 21.11 | odd | 6 | ||
462.2.i.a.331.1 | yes | 2 | 3.2 | odd | 2 | ||
1386.2.k.j.793.1 | 2 | 1.1 | even | 1 | trivial | ||
1386.2.k.j.991.1 | 2 | 7.4 | even | 3 | inner | ||
3234.2.a.a.1.1 | 1 | 21.5 | even | 6 | |||
3234.2.a.o.1.1 | 1 | 21.2 | odd | 6 | |||
9702.2.a.be.1.1 | 1 | 7.2 | even | 3 | |||
9702.2.a.ce.1.1 | 1 | 7.5 | odd | 6 |