Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,2,Mod(721,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.721");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.2476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 721.3 | ||
Root | \(1.71903 + 0.211943i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.721 |
Dual form | 2160.2.q.k.1441.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.04307 | − | 3.53869i | 0.772206 | − | 1.33750i | −0.164145 | − | 0.986436i | \(-0.552487\pi\) |
0.936351 | − | 0.351064i | \(-0.114180\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.675970 | − | 1.17081i | 0.203813 | − | 0.353014i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
0.949754 | + | 0.312998i | \(0.101333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.324030 | − | 0.561237i | −0.0898699 | − | 0.155659i | 0.817586 | − | 0.575806i | \(-0.195312\pi\) |
−0.907456 | + | 0.420147i | \(0.861978\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.35194 | 0.327893 | 0.163947 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163947 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.648061 | −0.148675 | −0.0743377 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743377 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.39500 | − | 4.14827i | −0.499393 | − | 0.864974i | 0.500607 | − | 0.865675i | \(-0.333110\pi\) |
−1.00000 | 0.000700856i | \(0.999777\pi\) | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.93807 | − | 3.35683i | 0.359890 | − | 0.623349i | −0.628052 | − | 0.778172i | \(-0.716147\pi\) |
0.987942 | + | 0.154823i | \(0.0494807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.84823 | − | 6.66533i | −0.691163 | − | 1.19713i | −0.971457 | − | 0.237215i | \(-0.923766\pi\) |
0.280295 | − | 0.959914i | \(-0.409568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.08613 | 0.690682 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.52420 | 1.23697 | 0.618485 | − | 0.785796i | \(-0.287747\pi\) | ||||
0.618485 | + | 0.785796i | \(0.287747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0898394 | − | 0.155606i | −0.0140306 | − | 0.0243016i | 0.858925 | − | 0.512102i | \(-0.171133\pi\) |
−0.872955 | + | 0.487800i | \(0.837800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.410161 | + | 0.710419i | −0.0625489 | + | 0.108338i | −0.895604 | − | 0.444852i | \(-0.853256\pi\) |
0.833055 | + | 0.553190i | \(0.186590\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.45323 | + | 9.44526i | −0.795435 | + | 1.37773i | 0.127128 | + | 0.991886i | \(0.459424\pi\) |
−0.922563 | + | 0.385847i | \(0.873909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.84823 | − | 8.39738i | −0.692604 | − | 1.19963i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.17226 | −0.573104 | −0.286552 | − | 0.958065i | \(-0.592509\pi\) | ||||
−0.286552 | + | 0.958065i | \(0.592509\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.35194 | 0.182295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.08613 | − | 3.61328i | −0.271591 | − | 0.470409i | 0.697678 | − | 0.716411i | \(-0.254216\pi\) |
−0.969269 | + | 0.246002i | \(0.920883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.91016 | − | 3.30850i | 0.244571 | − | 0.423609i | −0.717440 | − | 0.696620i | \(-0.754686\pi\) |
0.962011 | + | 0.273011i | \(0.0880195\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.324030 | − | 0.561237i | 0.0401910 | − | 0.0696129i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.07097 | + | 7.05113i | 0.497349 | + | 0.861433i | 0.999995 | − | 0.00305885i | \(-0.000973664\pi\) |
−0.502647 | + | 0.864492i | \(0.667640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.11644 | −0.725888 | −0.362944 | − | 0.931811i | \(-0.618228\pi\) | ||||
−0.362944 | + | 0.931811i | \(0.618228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3445 | −1.44482 | −0.722408 | − | 0.691467i | \(-0.756965\pi\) | ||||
−0.722408 | + | 0.691467i | \(0.756965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.76210 | − | 4.78410i | −0.314770 | − | 0.545198i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.17226 | − | 8.95862i | 0.581925 | − | 1.00792i | −0.413326 | − | 0.910583i | \(-0.635633\pi\) |
0.995251 | − | 0.0973403i | \(-0.0310335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.12920 | − | 10.6161i | 0.672767 | − | 1.16527i | −0.304350 | − | 0.952560i | \(-0.598439\pi\) |
0.977116 | − | 0.212706i | \(-0.0682275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.675970 | + | 1.17081i | 0.0733192 | + | 0.126993i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.64806 | −0.277592 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.324030 | − | 0.561237i | −0.0332448 | − | 0.0575817i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.79001 | − | 11.7606i | 0.689421 | − | 1.19411i | −0.282605 | − | 0.959237i | \(-0.591198\pi\) |
0.972025 | − | 0.234876i | \(-0.0754683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.734191 | + | 1.27166i | −0.0730547 | + | 0.126535i | −0.900239 | − | 0.435397i | \(-0.856608\pi\) |
0.827184 | + | 0.561931i | \(0.189941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.76210 | + | 6.51615i | 0.370691 | + | 0.642055i | 0.989672 | − | 0.143351i | \(-0.0457877\pi\) |
−0.618981 | + | 0.785406i | \(0.712454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.20999 | 0.116974 | 0.0584871 | − | 0.998288i | \(-0.481372\pi\) | ||||
0.0584871 | + | 0.998288i | \(0.481372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1042 | 1.35094 | 0.675469 | − | 0.737388i | \(-0.263941\pi\) | ||||
0.675469 | + | 0.737388i | \(0.263941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.96227 | − | 10.3270i | −0.560883 | − | 0.971478i | −0.997420 | − | 0.0717915i | \(-0.977128\pi\) |
0.436537 | − | 0.899687i | \(-0.356205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.39500 | − | 4.14827i | 0.223335 | − | 0.386828i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.76210 | − | 4.78410i | 0.253201 | − | 0.438557i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.58613 | + | 7.94341i | 0.416921 | + | 0.722128i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.07871 | 0.628134 | 0.314067 | − | 0.949401i | \(-0.398308\pi\) | ||||
0.314067 | + | 0.949401i | \(0.398308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.32403 | + | 2.29329i | −0.114808 | + | 0.198853i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.73419 | + | 6.46781i | −0.319033 | + | 0.552582i | −0.980287 | − | 0.197581i | \(-0.936692\pi\) |
0.661253 | + | 0.750163i | \(0.270025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | + | 6.92820i | 0.339276 | + | 0.587643i | 0.984297 | − | 0.176522i | \(-0.0564848\pi\) |
−0.645021 | + | 0.764165i | \(0.723151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.876139 | −0.0732664 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.87614 | 0.321896 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.29241 | − | 9.16673i | −0.433571 | − | 0.750968i | 0.563607 | − | 0.826043i | \(-0.309413\pi\) |
−0.997178 | + | 0.0750759i | \(0.976080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.84823 | − | 15.3256i | 0.720059 | − | 1.24718i | −0.240917 | − | 0.970546i | \(-0.577448\pi\) |
0.960976 | − | 0.276633i | \(-0.0892185\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.84823 | − | 6.66533i | 0.309097 | − | 0.535372i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.26581 | + | 2.19245i | 0.101023 | + | 0.174976i | 0.912106 | − | 0.409954i | \(-0.134455\pi\) |
−0.811084 | + | 0.584930i | \(0.801122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.5726 | −1.54254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.47580 | −0.663876 | −0.331938 | − | 0.943301i | \(-0.607702\pi\) | ||||
−0.331938 | + | 0.943301i | \(0.607702\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.36710 | − | 11.0281i | −0.492701 | − | 0.853383i | 0.507264 | − | 0.861791i | \(-0.330657\pi\) |
−0.999965 | + | 0.00840816i | \(0.997324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.29001 | − | 10.8946i | 0.483847 | − | 0.838047i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5242 | − | 19.9605i | 0.876169 | − | 1.51757i | 0.0206561 | − | 0.999787i | \(-0.493424\pi\) |
0.855513 | − | 0.517782i | \(-0.173242\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.04307 | + | 3.53869i | 0.154441 | + | 0.267500i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.22808 | 0.166534 | 0.0832672 | − | 0.996527i | \(-0.473465\pi\) | ||||
0.0832672 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.468382 | 0.0348146 | 0.0174073 | − | 0.999848i | \(-0.494459\pi\) | ||||
0.0174073 | + | 0.999848i | \(0.494459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.76210 | + | 6.51615i | 0.276595 | + | 0.479077i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.913870 | − | 1.58287i | 0.0668288 | − | 0.115751i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1140 | − | 17.5180i | 0.731826 | − | 1.26756i | −0.224276 | − | 0.974526i | \(-0.572002\pi\) |
0.956102 | − | 0.293034i | \(-0.0946650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.96467 | + | 17.2593i | 0.717273 | + | 1.24235i | 0.962076 | + | 0.272780i | \(0.0879432\pi\) |
−0.244804 | + | 0.969573i | \(0.578723\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5800 | 1.11003 | 0.555015 | − | 0.831840i | \(-0.312712\pi\) | ||||
0.555015 | + | 0.831840i | \(0.312712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.58482 | −0.254121 | −0.127061 | − | 0.991895i | \(-0.540554\pi\) | ||||
−0.127061 | + | 0.991895i | \(0.540554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.91920 | − | 13.7165i | −0.555819 | − | 0.962707i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0898394 | − | 0.155606i | 0.00627466 | − | 0.0108680i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.438069 | + | 0.758758i | −0.0303019 | + | 0.0524844i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.49629 | + | 12.9840i | 0.516066 | + | 0.893852i | 0.999826 | + | 0.0186518i | \(0.00593739\pi\) |
−0.483760 | + | 0.875201i | \(0.660729\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.820321 | −0.0559454 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.4487 | −2.13488 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.438069 | − | 0.758758i | −0.0294677 | − | 0.0510396i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4155 | + | 23.2363i | −0.898368 | + | 1.55602i | −0.0687878 | + | 0.997631i | \(0.521913\pi\) |
−0.829580 | + | 0.558388i | \(0.811420\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.675970 | + | 1.17081i | −0.0448657 | + | 0.0777096i | −0.887586 | − | 0.460642i | \(-0.847619\pi\) |
0.842721 | + | 0.538351i | \(0.180953\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.11775 | + | 7.13215i | 0.272108 | + | 0.471306i | 0.969402 | − | 0.245480i | \(-0.0789457\pi\) |
−0.697293 | + | 0.716786i | \(0.745612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.58744 | −0.562582 | −0.281291 | − | 0.959623i | \(-0.590763\pi\) | ||||
−0.281291 | + | 0.959623i | \(0.590763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9065 | −0.711458 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.9623 | + | 20.7193i | 0.773775 | + | 1.34022i | 0.935480 | + | 0.353378i | \(0.114967\pi\) |
−0.161706 | + | 0.986839i | \(0.551700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.12015 | − | 5.40426i | 0.200987 | − | 0.348119i | −0.747860 | − | 0.663857i | \(-0.768919\pi\) |
0.948847 | + | 0.315737i | \(0.102252\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.84823 | − | 8.39738i | 0.309742 | − | 0.536489i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.209991 | + | 0.363716i | 0.0133614 | + | 0.0231427i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.5726 | −1.80349 | −0.901743 | − | 0.432272i | \(-0.857712\pi\) | ||||
−0.901743 | + | 0.432272i | \(0.857712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.47580 | −0.407130 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.3724 | − | 26.6258i | 0.955196 | − | 1.65445i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.9344 | + | 27.5991i | −0.982555 | + | 1.70183i | −0.330220 | + | 0.943904i | \(0.607123\pi\) |
−0.652335 | + | 0.757931i | \(0.726211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.08613 | − | 3.61328i | −0.128150 | − | 0.221962i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.4971 | 1.92041 | 0.960207 | − | 0.279289i | \(-0.0900987\pi\) | ||||
0.960207 | + | 0.279289i | \(0.0900987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.24030 | 0.196834 | 0.0984172 | − | 0.995145i | \(-0.468622\pi\) | ||||
0.0984172 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.675970 | + | 1.17081i | 0.0407625 | + | 0.0706027i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.79241 | − | 4.83660i | 0.167780 | − | 0.290603i | −0.769859 | − | 0.638214i | \(-0.779674\pi\) |
0.937639 | + | 0.347611i | \(0.113007\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0521 | + | 20.8749i | −0.718969 | + | 1.24529i | 0.242440 | + | 0.970166i | \(0.422052\pi\) |
−0.961409 | + | 0.275124i | \(0.911281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.27114 | − | 9.12989i | −0.313337 | − | 0.542715i | 0.665746 | − | 0.746179i | \(-0.268114\pi\) |
−0.979083 | + | 0.203463i | \(0.934780\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.734191 | −0.0433379 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1723 | −0.892486 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.49629 | + | 16.4481i | 0.554779 | + | 0.960906i | 0.997921 | + | 0.0644541i | \(0.0205306\pi\) |
−0.443141 | + | 0.896452i | \(0.646136\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.08613 | − | 3.61328i | 0.121459 | − | 0.210373i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.55211 | + | 2.68833i | −0.0897607 | + | 0.155470i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.67597 | + | 2.90286i | 0.0966013 | + | 0.167318i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.82032 | 0.218751 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.4791 | −1.68246 | −0.841229 | − | 0.540679i | \(-0.818167\pi\) | ||||
−0.841229 | + | 0.540679i | \(0.818167\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.70628 | + | 8.15152i | 0.266869 | + | 0.462230i | 0.968052 | − | 0.250751i | \(-0.0806776\pi\) |
−0.701183 | + | 0.712982i | \(0.747344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.81050 | + | 10.0641i | −0.328429 | + | 0.568855i | −0.982200 | − | 0.187837i | \(-0.939852\pi\) |
0.653771 | + | 0.756692i | \(0.273186\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.58984 | + | 7.94984i | −0.257791 | + | 0.446507i | −0.965650 | − | 0.259847i | \(-0.916328\pi\) |
0.707859 | + | 0.706354i | \(0.249661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.62015 | − | 4.53824i | −0.146700 | − | 0.254092i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.876139 | −0.0487497 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.648061 | 0.0359479 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.2826 | + | 38.5946i | 1.22848 | + | 2.12779i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.61033 | + | 6.25327i | −0.198442 | + | 0.343711i | −0.948023 | − | 0.318201i | \(-0.896921\pi\) |
0.749582 | + | 0.661912i | \(0.230255\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.07097 | + | 7.05113i | −0.222421 | + | 0.385245i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.14195 | − | 1.97791i | −0.0622059 | − | 0.107744i | 0.833245 | − | 0.552904i | \(-0.186480\pi\) |
−0.895451 | + | 0.445160i | \(0.853147\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.4051 | −0.563470 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0181 | −0.594921 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.354343 | + | 0.613740i | 0.0190221 | + | 0.0329473i | 0.875380 | − | 0.483436i | \(-0.160611\pi\) |
−0.856358 | + | 0.516383i | \(0.827278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6723 | − | 18.4849i | 0.571273 | − | 0.989474i | −0.425163 | − | 0.905117i | \(-0.639783\pi\) |
0.996436 | − | 0.0843569i | \(-0.0268836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.04840 | + | 8.74408i | −0.268699 | + | 0.465401i | −0.968526 | − | 0.248912i | \(-0.919927\pi\) |
0.699827 | + | 0.714312i | \(0.253260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.05822 | − | 5.29699i | −0.162314 | − | 0.281135i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.5578 | 1.61278 | 0.806388 | − | 0.591386i | \(-0.201419\pi\) | ||||
0.806388 | + | 0.591386i | \(0.201419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5800 | −0.977896 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.17226 | − | 10.6907i | −0.323071 | − | 0.559575i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.58984 | + | 6.21778i | −0.187388 | + | 0.324566i | −0.944379 | − | 0.328860i | \(-0.893336\pi\) |
0.756991 | + | 0.653426i | \(0.226669\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.52420 | + | 14.7643i | −0.442554 | + | 0.766527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9623 | + | 18.9872i | 0.567605 | + | 0.983120i | 0.996802 | + | 0.0799096i | \(0.0254632\pi\) |
−0.429197 | + | 0.903211i | \(0.641204\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.51197 | −0.129373 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3929 | 0.893414 | 0.446707 | − | 0.894680i | \(-0.352597\pi\) | ||||
0.446707 | + | 0.894680i | \(0.352597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.237900 | − | 0.412055i | −0.0121561 | − | 0.0210550i | 0.859883 | − | 0.510491i | \(-0.170536\pi\) |
−0.872039 | + | 0.489436i | \(0.837203\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.76210 | − | 4.78410i | 0.140770 | − | 0.243820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.79372 | + | 4.83886i | −0.141647 | + | 0.245340i | −0.928117 | − | 0.372289i | \(-0.878573\pi\) |
0.786470 | + | 0.617629i | \(0.211906\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.23790 | − | 5.60821i | −0.163748 | − | 0.283619i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.3445 | 0.520489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.75228 | 0.188321 | 0.0941607 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941607 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7826 | + | 20.4080i | 0.588394 | + | 1.01913i | 0.994443 | + | 0.105278i | \(0.0335731\pi\) |
−0.406048 | + | 0.913852i | \(0.633094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.49389 | + | 4.31954i | −0.124229 | + | 0.215172i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.08613 | − | 8.80944i | 0.252110 | − | 0.436668i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.524200 | − | 0.907940i | −0.0259200 | − | 0.0448948i | 0.852774 | − | 0.522279i | \(-0.174918\pi\) |
−0.878694 | + | 0.477385i | \(0.841585\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.0484 | −0.838897 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.2584 | 0.601741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.9599 | + | 22.4471i | 0.633131 | + | 1.09661i | 0.986908 | + | 0.161285i | \(0.0515638\pi\) |
−0.353777 | + | 0.935330i | \(0.615103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.82032 | + | 6.61699i | −0.186191 | + | 0.322492i | −0.943977 | − | 0.330011i | \(-0.892948\pi\) |
0.757786 | + | 0.652503i | \(0.226281\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.675970 | + | 1.17081i | −0.0327893 | + | 0.0567928i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.80516 | − | 13.5189i | −0.377718 | − | 0.654227i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.98516 | 0.384632 | 0.192316 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192316 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5120 | −0.601287 | −0.300644 | − | 0.953737i | \(-0.597201\pi\) | ||||
−0.300644 | + | 0.953737i | \(0.597201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.55211 | + | 2.68833i | 0.0742474 | + | 0.128600i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.38225 | + | 7.59028i | −0.209153 | + | 0.362264i | −0.951448 | − | 0.307809i | \(-0.900404\pi\) |
0.742295 | + | 0.670074i | \(0.233737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.83548 | + | 3.17914i | −0.0872062 | + | 0.151046i | −0.906329 | − | 0.422572i | \(-0.861127\pi\) |
0.819123 | + | 0.573618i | \(0.194461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.50000 | + | 2.59808i | 0.0711068 | + | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.1723 | −1.32953 | −0.664766 | − | 0.747052i | \(-0.731469\pi\) | ||||
−0.664766 | + | 0.747052i | \(0.731469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.242915 | −0.0114384 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.32403 | − | 2.29329i | −0.0620715 | − | 0.107511i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6308 | + | 30.5375i | −0.824735 | + | 1.42848i | 0.0773867 | + | 0.997001i | \(0.475342\pi\) |
−0.902122 | + | 0.431482i | \(0.857991\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3384 | − | 30.0310i | 0.807530 | − | 1.39868i | −0.107039 | − | 0.994255i | \(-0.534137\pi\) |
0.914570 | − | 0.404428i | \(-0.132530\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.72437 | + | 6.45080i | 0.173086 | + | 0.299794i | 0.939497 | − | 0.342556i | \(-0.111293\pi\) |
−0.766411 | + | 0.642350i | \(0.777959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.9655 | 1.38664 | 0.693319 | − | 0.720630i | \(-0.256148\pi\) | ||||
0.693319 | + | 0.720630i | \(0.256148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.2691 | 1.53622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.554512 | + | 0.960443i | 0.0254965 | + | 0.0441612i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.324030 | − | 0.561237i | 0.0148675 | − | 0.0257513i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.99258 | − | 6.91535i | 0.182426 | − | 0.315971i | −0.760280 | − | 0.649595i | \(-0.774938\pi\) |
0.942706 | + | 0.333625i | \(0.108272\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.43807 | − | 4.22286i | −0.111166 | − | 0.192546i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.5800 | 0.616637 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9442 | 0.541243 | 0.270621 | − | 0.962686i | \(-0.412771\pi\) | ||||
0.270621 | + | 0.962686i | \(0.412771\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.61033 | + | 7.98533i | 0.208061 | + | 0.360373i | 0.951104 | − | 0.308872i | \(-0.0999513\pi\) |
−0.743042 | + | 0.669244i | \(0.766618\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.62015 | − | 4.53824i | 0.118006 | − | 0.204392i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.4963 | + | 21.6442i | −0.560535 | + | 0.970876i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0861 | + | 26.1299i | 0.675348 | + | 1.16974i | 0.976367 | + | 0.216119i | \(0.0693399\pi\) |
−0.301019 | + | 0.953618i | \(0.597327\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5981 | −0.472546 | −0.236273 | − | 0.971687i | \(-0.575926\pi\) | ||||
−0.236273 | + | 0.971687i | \(0.575926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.46838 | −0.0653421 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3761 | + | 24.9002i | 0.637211 | + | 1.10368i | 0.986042 | + | 0.166496i | \(0.0532454\pi\) |
−0.348831 | + | 0.937186i | \(0.613421\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.2207 | + | 43.6835i | −1.11570 | + | 1.93244i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.76210 | + | 6.51615i | −0.165778 | + | 0.287136i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.37243 | + | 12.7694i | 0.324239 | + | 0.561599i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0942 | 1.58132 | 0.790658 | − | 0.612259i | \(-0.209739\pi\) | ||||
0.790658 | + | 0.612259i | \(0.209739\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.1297 | −0.486669 | −0.243334 | − | 0.969942i | \(-0.578241\pi\) | ||||
−0.243334 | + | 0.969942i | \(0.578241\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.20257 | − | 9.01112i | −0.226628 | − | 0.392531i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0279088 | − | 0.0483395i | 0.00121343 | − | 0.00210172i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0582214 | + | 0.100842i | −0.00252185 | + | 0.00436797i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.604996 | + | 1.04788i | 0.0261562 | + | 0.0453039i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.1090 | −0.564646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.7374 | −1.49348 | −0.746740 | − | 0.665116i | \(-0.768382\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.05211 | + | 12.2146i | 0.302079 | + | 0.523216i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.35727 | + | 2.35087i | −0.0580328 | + | 0.100516i | −0.893582 | − | 0.448899i | \(-0.851816\pi\) |
0.835549 | + | 0.549415i | \(0.185149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.25599 | + | 2.17543i | −0.0535068 | + | 0.0926766i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.1345 | − | 36.6061i | −0.898732 | − | 1.55665i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.93676 | 0.378663 | 0.189331 | − | 0.981913i | \(-0.439368\pi\) | ||||
0.189331 | + | 0.981913i | \(0.439368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.531618 | 0.0224850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.68130 | + | 8.10826i | 0.197293 | + | 0.341722i | 0.947650 | − | 0.319311i | \(-0.103451\pi\) |
−0.750357 | + | 0.661033i | \(0.770118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.96227 | − | 10.3270i | 0.250835 | − | 0.434458i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.9368 | − | 31.0674i | 0.751948 | − | 1.30241i | −0.194929 | − | 0.980817i | \(-0.562448\pi\) |
0.946877 | − | 0.321595i | \(-0.104219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | + | 17.3205i | 0.418487 | + | 0.724841i | 0.995788 | − | 0.0916910i | \(-0.0292272\pi\) |
−0.577301 | + | 0.816532i | \(0.695894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.79001 | 0.199757 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.35675 | 0.0564821 | 0.0282411 | − | 0.999601i | \(-0.491009\pi\) | ||||
0.0282411 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.0447 | − | 43.3787i | −1.03903 | − | 1.79965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.82032 | + | 4.88494i | −0.116806 | + | 0.202314i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.3950 | + | 24.9329i | −0.594145 | + | 1.02909i | 0.399521 | + | 0.916724i | \(0.369176\pi\) |
−0.993667 | + | 0.112366i | \(0.964157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.49389 | + | 4.31954i | 0.102759 | + | 0.177984i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.9171 | −1.26961 | −0.634807 | − | 0.772671i | \(-0.718920\pi\) | ||||
−0.634807 | + | 0.772671i | \(0.718920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.52420 | 0.226470 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.696460 | − | 1.20630i | −0.0284566 | − | 0.0492882i | 0.851446 | − | 0.524442i | \(-0.175726\pi\) |
−0.879903 | + | 0.475153i | \(0.842393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.41256 | + | 7.64279i | −0.179992 | + | 0.311756i | −0.941878 | − | 0.335956i | \(-0.890941\pi\) |
0.761885 | + | 0.647712i | \(0.224274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.58613 | + | 7.94341i | −0.186453 | + | 0.322946i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.07839 | − | 1.86783i | −0.0437706 | − | 0.0758129i | 0.843310 | − | 0.537427i | \(-0.180604\pi\) |
−0.887081 | + | 0.461614i | \(0.847270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.06804 | 0.285942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.57521 | −0.386739 | −0.193370 | − | 0.981126i | \(-0.561942\pi\) | ||||
−0.193370 | + | 0.981126i | \(0.561942\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.8384 | − | 32.6291i | −0.758406 | − | 1.31360i | −0.943663 | − | 0.330907i | \(-0.892645\pi\) |
0.185258 | − | 0.982690i | \(-0.440688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.55211 | − | 14.8127i | 0.343738 | − | 0.595372i | −0.641385 | − | 0.767219i | \(-0.721640\pi\) |
0.985124 | + | 0.171847i | \(0.0549734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.12920 | − | 10.6161i | 0.245561 | − | 0.425324i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1723 | 0.405595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.1090 | −1.31805 | −0.659025 | − | 0.752121i | \(-0.729031\pi\) | ||||
−0.659025 | + | 0.752121i | \(0.729031\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.53936 | + | 6.13034i | 0.140455 | + | 0.243275i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.14195 | + | 5.44201i | −0.124489 | + | 0.215620i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5763 | + | 20.0508i | −0.457237 | + | 0.791957i | −0.998814 | − | 0.0486939i | \(-0.984494\pi\) |
0.541577 | + | 0.840651i | \(0.317827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5319 | + | 37.2944i | 0.849137 | + | 1.47075i | 0.881980 | + | 0.471287i | \(0.156211\pi\) |
−0.0328430 | + | 0.999461i | \(0.510456\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.6439 | −0.811595 | −0.405798 | − | 0.913963i | \(-0.633006\pi\) | ||||
−0.405798 | + | 0.913963i | \(0.633006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.64064 | −0.221415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.41758 | + | 5.91942i | 0.133740 | + | 0.231645i | 0.925116 | − | 0.379686i | \(-0.123968\pi\) |
−0.791375 | + | 0.611331i | \(0.790635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | + | 5.19615i | −0.117220 | + | 0.203030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4307 | − | 23.2626i | 0.523184 | − | 0.906181i | −0.476452 | − | 0.879200i | \(-0.658077\pi\) |
0.999636 | − | 0.0269806i | \(-0.00858924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.06063 | + | 1.83706i | 0.0412535 | + | 0.0714532i | 0.885915 | − | 0.463848i | \(-0.153532\pi\) |
−0.844661 | + | 0.535301i | \(0.820198\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.64806 | −0.102687 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.5667 | −0.718907 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.58242 | − | 4.47288i | −0.0996933 | − | 0.172674i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.4102 | + | 30.1553i | −0.671112 | + | 1.16240i | 0.306477 | + | 0.951878i | \(0.400850\pi\) |
−0.977589 | + | 0.210523i | \(0.932483\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.3421 | + | 21.3772i | −0.474346 | + | 0.821592i | −0.999569 | − | 0.0293735i | \(-0.990649\pi\) |
0.525222 | + | 0.850965i | \(0.323982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.7449 | − | 48.0555i | −1.06475 | − | 1.84420i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.4610 | −1.47167 | −0.735834 | − | 0.677162i | \(-0.763210\pi\) | ||||
−0.735834 | + | 0.677162i | \(0.763210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.46838 | −0.285352 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.35194 | + | 2.34163i | 0.0515048 | + | 0.0892089i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.240304 | − | 0.416219i | 0.00914159 | − | 0.0158337i | −0.861418 | − | 0.507896i | \(-0.830423\pi\) |
0.870560 | + | 0.492062i | \(0.163757\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.00000 | + | 6.92820i | −0.151729 | + | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.121457 | − | 0.210370i | −0.00460053 | − | 0.00796835i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1797 | 0.686637 | 0.343318 | − | 0.939219i | \(-0.388449\pi\) | ||||
0.343318 | + | 0.939219i | \(0.388449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.87614 | −0.183907 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.00000 | + | 5.19615i | 0.112827 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.59355 | + | 6.22421i | −0.134959 | + | 0.233755i | −0.925582 | − | 0.378548i | \(-0.876423\pi\) |
0.790623 | + | 0.612303i | \(0.209757\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.4331 | + | 31.9270i | −0.690323 | + | 1.19568i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.438069 | − | 0.758758i | −0.0163829 | − | 0.0283760i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.5168 | 0.466797 | 0.233399 | − | 0.972381i | \(-0.425015\pi\) | ||||
0.233399 | + | 0.972381i | \(0.425015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.7449 | 1.14500 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.93807 | + | 3.35683i | 0.0719781 | + | 0.124670i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.21292 | − | 7.29699i | 0.156249 | − | 0.270631i | −0.777264 | − | 0.629174i | \(-0.783393\pi\) |
0.933513 | + | 0.358544i | \(0.116727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.554512 | + | 0.960443i | −0.0205094 | + | 0.0355233i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0000 | + | 19.0526i | 0.406294 | + | 0.703722i | 0.994471 | − | 0.105010i | \(-0.0334875\pi\) |
−0.588177 | + | 0.808732i | \(0.700154\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0074 | 0.405463 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.81290 | 0.0666887 | 0.0333444 | − | 0.999444i | \(-0.489384\pi\) | ||||
0.0333444 | + | 0.999444i | \(0.489384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.0686 | − | 17.4393i | −0.369380 | − | 0.639785i | 0.620089 | − | 0.784532i | \(-0.287097\pi\) |
−0.989469 | + | 0.144747i | \(0.953763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.29241 | − | 9.16673i | 0.193899 | − | 0.335843i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.47209 | − | 4.28179i | 0.0903282 | − | 0.156453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.10662 | + | 10.5770i | 0.222834 | + | 0.385959i | 0.955667 | − | 0.294449i | \(-0.0951360\pi\) |
−0.732834 | + | 0.680408i | \(0.761803\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.6965 | 0.644040 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.9533 | 1.92462 | 0.962310 | − | 0.271955i | \(-0.0876701\pi\) | ||||
0.962310 | + | 0.271955i | \(0.0876701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.22677 | − | 15.9812i | −0.334470 | − | 0.579319i | 0.648913 | − | 0.760863i | \(-0.275224\pi\) |
−0.983383 | + | 0.181543i | \(0.941891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.8158 | − | 49.9105i | 1.04320 | − | 1.80688i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.35194 | + | 2.34163i | −0.0488157 | + | 0.0845513i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.22677 | + | 3.85688i | 0.0802995 | + | 0.139083i | 0.903379 | − | 0.428844i | \(-0.141079\pi\) |
−0.823079 | + | 0.567927i | \(0.807746\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.9368 | −1.40046 | −0.700229 | − | 0.713918i | \(-0.746919\pi\) | ||||
−0.700229 | + | 0.713918i | \(0.746919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.69646 | 0.276465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0582214 | + | 0.100842i | 0.00208600 | + | 0.00361305i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.13453 | + | 7.16121i | −0.147945 | + | 0.256248i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.26581 | + | 2.19245i | −0.0451787 | + | 0.0782517i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.1140 | + | 29.6424i | 0.610050 | + | 1.05664i | 0.991231 | + | 0.132137i | \(0.0421838\pi\) |
−0.381182 | + | 0.924500i | \(0.624483\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.7252 | −1.73247 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.47580 | −0.0879183 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.9828 | + | 20.7547i | 0.424451 | + | 0.735171i | 0.996369 | − | 0.0851400i | \(-0.0271337\pi\) |
−0.571918 | + | 0.820311i | \(0.693800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.37243 | + | 12.7694i | −0.260818 | + | 0.451750i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.34452 | + | 14.4531i | −0.294472 | + | 0.510040i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.78630 | − | 16.9504i | −0.344922 | − | 0.597422i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.283896 | 0.00998124 | 0.00499062 | − | 0.999988i | \(-0.498411\pi\) | ||||
0.00499062 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.4413 | −1.13917 | −0.569584 | − | 0.821933i | \(-0.692896\pi\) | ||||
−0.569584 | + | 0.821933i | \(0.692896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.23790 | − | 7.34026i | −0.148447 | − | 0.257118i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.265809 | − | 0.460395i | 0.00929948 | − | 0.0161072i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.8347 | − | 36.0868i | 0.727136 | − | 1.25944i | −0.230953 | − | 0.972965i | \(-0.574184\pi\) |
0.958089 | − | 0.286472i | \(-0.0924824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.68130 | − | 16.7685i | −0.337469 | − | 0.584514i | 0.646487 | − | 0.762925i | \(-0.276237\pi\) |
−0.983956 | + | 0.178412i | \(0.942904\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.8097 | 0.654076 | 0.327038 | − | 0.945011i | \(-0.393950\pi\) | ||||
0.327038 | + | 0.945011i | \(0.393950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.1016 | −1.14967 | −0.574833 | − | 0.818271i | \(-0.694933\pi\) | ||||
−0.574833 | + | 0.818271i | \(0.694933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.55451 | − | 11.3527i | −0.227100 | − | 0.393349i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.36710 | − | 11.0281i | 0.220342 | − | 0.381644i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.8482 | − | 34.3781i | 0.685237 | − | 1.18687i | −0.288125 | − | 0.957593i | \(-0.593032\pi\) |
0.973362 | − | 0.229273i | \(-0.0736347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.98777 | + | 12.1032i | 0.240958 | + | 0.417351i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.5800 | 0.432766 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.4791 | 1.28780 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.0205 | − | 31.2124i | −0.617734 | − | 1.06995i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.05822 | − | 3.56494i | 0.0704722 | − | 0.122061i | −0.828636 | − | 0.559788i | \(-0.810883\pi\) |
0.899108 | + | 0.437726i | \(0.144216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.37243 | − | 12.7694i | 0.251837 | − | 0.436195i | −0.712194 | − | 0.701982i | \(-0.752299\pi\) |
0.964032 | + | 0.265787i | \(0.0856319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.9269 | − | 32.7824i | −0.645779 | − | 1.11852i | −0.984121 | − | 0.177499i | \(-0.943199\pi\) |
0.338342 | − | 0.941023i | \(-0.390134\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7704 | 0.911274 | 0.455637 | − | 0.890166i | \(-0.349412\pi\) | ||||
0.455637 | + | 0.890166i | \(0.349412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.0484 | 0.783669 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.99258 | − | 12.1115i | −0.237207 | − | 0.410855i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.63824 | − | 4.56956i | 0.0893933 | − | 0.154834i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.04307 | + | 3.53869i | −0.0690682 | + | 0.119630i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4841 | + | 40.6756i | 0.793001 | + | 1.37352i | 0.924101 | + | 0.382148i | \(0.124816\pi\) |
−0.131101 | + | 0.991369i | \(0.541851\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8055 | 0.667264 | 0.333632 | − | 0.942703i | \(-0.391726\pi\) | ||||
0.333632 | + | 0.942703i | \(0.391726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.20257 | 0.208733 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.71370 | − | 11.6285i | −0.225424 | − | 0.390446i | 0.731023 | − | 0.682353i | \(-0.239043\pi\) |
−0.956447 | + | 0.291907i | \(0.905710\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.4623 | − | 25.0494i | 0.485049 | − | 0.840129i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.53402 | − | 6.12111i | 0.118262 | − | 0.204835i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.11404 | + | 1.92957i | 0.0372382 | + | 0.0644985i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.8325 | −0.994971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64064 | −0.187917 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.234191 | + | 0.405631i | 0.00778477 | + | 0.0134836i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.336783 | − | 0.583325i | 0.0111827 | − | 0.0193690i | −0.860380 | − | 0.509653i | \(-0.829774\pi\) |
0.871563 | + | 0.490284i | \(0.163107\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.95485 | − | 6.85000i | 0.131030 | − | 0.226951i | −0.793044 | − | 0.609165i | \(-0.791505\pi\) |
0.924074 | + | 0.382214i | \(0.124838\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.28630 | − | 14.3523i | −0.274236 | − | 0.474992i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.5168 | 0.809615 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.58263 | 0.283115 | 0.141557 | − | 0.989930i | \(-0.454789\pi\) | ||||
0.141557 | + | 0.989930i | \(0.454789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.98191 | + | 3.43277i | 0.0652355 | + | 0.112991i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.76210 | + | 6.51615i | −0.123697 | + | 0.214250i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.8081 | − | 25.6484i | 0.485838 | − | 0.841496i | −0.514030 | − | 0.857772i | \(-0.671848\pi\) |
0.999868 | + | 0.0162766i | \(0.00518122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.14195 | + | 5.44201i | 0.102973 | + | 0.178355i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.82774 | 0.0597735 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2058 | −0.496753 | −0.248376 | − | 0.968664i | \(-0.579897\pi\) | ||||
−0.248376 | + | 0.968664i | \(0.579897\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.82643 | + | 4.89553i | 0.0921391 | + | 0.159590i | 0.908411 | − | 0.418078i | \(-0.137296\pi\) |
−0.816272 | + | 0.577668i | \(0.803963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.430332 | + | 0.745356i | −0.0140135 | + | 0.0242721i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.1981 | − | 34.9841i | 0.656350 | − | 1.13683i | −0.325204 | − | 0.945644i | \(-0.605433\pi\) |
0.981554 | − | 0.191187i | \(-0.0612337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | + | 6.92820i | 0.129845 | + | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9320 | 0.742839 | 0.371419 | − | 0.928465i | \(-0.378871\pi\) | ||||
0.371419 | + | 0.928465i | \(0.378871\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.2281 | 0.654565 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.2584 | + | 26.4283i | 0.492719 | + | 0.853415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1177 | + | 24.4527i | −0.455411 | + | 0.788795i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.96467 | + | 17.2593i | −0.320774 | + | 0.555597i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.18501 | + | 8.98071i | 0.166739 | + | 0.288800i | 0.937271 | − | 0.348601i | \(-0.113343\pi\) |
−0.770533 | + | 0.637401i | \(0.780010\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.0410 | 1.54171 | 0.770854 | − | 0.637012i | \(-0.219830\pi\) | ||||
0.770854 | + | 0.637012i | \(0.219830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.6890 | 1.04796 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.5266 | + | 23.4288i | 0.432754 | + | 0.749553i | 0.997109 | − | 0.0759796i | \(-0.0242084\pi\) |
−0.564355 | + | 0.825532i | \(0.690875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.02791 | − | 3.51244i | 0.0648122 | − | 0.112258i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2408 | − | 19.4697i | 0.358527 | − | 0.620987i | −0.629188 | − | 0.777253i | \(-0.716612\pi\) |
0.987715 | + | 0.156266i | \(0.0499458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.79001 | + | 13.4927i | 0.248210 | + | 0.429913i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.92935 | 0.124946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.5316 | 0.842805 | 0.421402 | − | 0.906874i | \(-0.361538\pi\) | ||||
0.421402 | + | 0.906874i | \(0.361538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.79241 | − | 3.10455i | −0.0568233 | − | 0.0984208i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.1829 | − | 24.5656i | 0.449178 | − | 0.777999i | −0.549155 | − | 0.835721i | \(-0.685050\pi\) |
0.998333 | + | 0.0577217i | \(0.0183836\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))