Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,4,Mod(177,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.177");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.1287487223\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.361 |
Dual form | 392.4.i.b.177.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.00000 | + | 3.46410i | −0.384900 | + | 0.666667i | −0.991755 | − | 0.128146i | \(-0.959097\pi\) |
0.606855 | + | 0.794812i | \(0.292431\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.0894427 | − | 0.154919i | 0.817833 | − | 0.575456i | \(-0.195175\pi\) |
−0.907276 | + | 0.420536i | \(0.861842\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.50000 | + | 9.52628i | 0.203704 | + | 0.352825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.0000 | − | 38.1051i | 0.603023 | − | 1.04447i | −0.389338 | − | 0.921095i | \(-0.627296\pi\) |
0.992361 | − | 0.123371i | \(-0.0393705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.0000 | −0.469362 | −0.234681 | − | 0.972072i | \(-0.575405\pi\) | ||||
−0.234681 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.00000 | 0.137706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.0000 | − | 43.3013i | 0.356670 | − | 0.617771i | −0.630732 | − | 0.776001i | \(-0.717245\pi\) |
0.987402 | + | 0.158230i | \(0.0505787\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.0000 | + | 38.1051i | 0.265639 | + | 0.460101i | 0.967731 | − | 0.251986i | \(-0.0810837\pi\) |
−0.702092 | + | 0.712087i | \(0.747750\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 28.0000 | + | 48.4974i | 0.253844 | + | 0.439670i | 0.964581 | − | 0.263788i | \(-0.0849718\pi\) |
−0.710737 | + | 0.703458i | \(0.751638\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.5000 | − | 104.789i | 0.484000 | − | 0.838313i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −152.000 | −1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 198.000 | 1.26785 | 0.633925 | − | 0.773394i | \(-0.281443\pi\) | ||||
0.633925 | + | 0.773394i | \(0.281443\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −80.0000 | + | 138.564i | −0.463498 | + | 0.802801i | −0.999132 | − | 0.0416484i | \(-0.986739\pi\) |
0.535635 | + | 0.844450i | \(0.320072\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 88.0000 | + | 152.420i | 0.464207 | + | 0.804030i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 81.0000 | + | 140.296i | 0.359900 | + | 0.623366i | 0.987944 | − | 0.154812i | \(-0.0494773\pi\) |
−0.628043 | + | 0.778178i | \(0.716144\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44.0000 | − | 76.2102i | 0.180657 | − | 0.312908i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 198.000 | 0.754205 | 0.377102 | − | 0.926172i | \(-0.376920\pi\) | ||||
0.377102 | + | 0.926172i | \(0.376920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.0000 | 0.184417 | 0.0922084 | − | 0.995740i | \(-0.470607\pi\) | ||||
0.0922084 | + | 0.995740i | \(0.470607\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.0000 | − | 19.0526i | 0.0364396 | − | 0.0631153i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 264.000 | + | 457.261i | 0.819327 | + | 1.41912i | 0.906179 | + | 0.422894i | \(0.138986\pi\) |
−0.0868522 | + | 0.996221i | \(0.527681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 100.000 | + | 173.205i | 0.274565 | + | 0.475560i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 121.000 | − | 209.578i | 0.313597 | − | 0.543166i | −0.665541 | − | 0.746361i | \(-0.731799\pi\) |
0.979138 | + | 0.203195i | \(0.0651327\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −88.0000 | −0.215744 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −176.000 | −0.408978 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −334.000 | + | 578.505i | −0.737002 | + | 1.27652i | 0.216838 | + | 0.976208i | \(0.430426\pi\) |
−0.953840 | + | 0.300317i | \(0.902908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 275.000 | + | 476.314i | 0.577215 | + | 0.999766i | 0.995797 | + | 0.0915873i | \(0.0291941\pi\) |
−0.418582 | + | 0.908179i | \(0.637473\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.0000 | + | 38.1051i | 0.0419810 | + | 0.0727132i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −94.0000 | + | 162.813i | −0.171402 | + | 0.296877i | −0.938910 | − | 0.344162i | \(-0.888163\pi\) |
0.767508 | + | 0.641039i | \(0.221496\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −224.000 | −0.390818 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 728.000 | 1.21687 | 0.608435 | − | 0.793604i | \(-0.291798\pi\) | ||||
0.608435 | + | 0.793604i | \(0.291798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77.0000 | − | 133.368i | 0.123454 | − | 0.213829i | −0.797673 | − | 0.603090i | \(-0.793936\pi\) |
0.921128 | + | 0.389261i | \(0.127269\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 242.000 | + | 419.156i | 0.372583 | + | 0.645333i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 328.000 | + | 568.113i | 0.467125 | + | 0.809084i | 0.999295 | − | 0.0375534i | \(-0.0119564\pi\) |
−0.532170 | + | 0.846638i | \(0.678623\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 155.500 | − | 269.334i | 0.213306 | − | 0.369457i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −236.000 | −0.312101 | −0.156050 | − | 0.987749i | \(-0.549876\pi\) | ||||
−0.156050 | + | 0.987749i | \(0.549876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −100.000 | −0.127606 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −396.000 | + | 685.892i | −0.487996 | + | 0.845234i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 357.000 | + | 618.342i | 0.425190 | + | 0.736451i | 0.996438 | − | 0.0843265i | \(-0.0268739\pi\) |
−0.571248 | + | 0.820778i | \(0.693541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −320.000 | − | 554.256i | −0.356801 | − | 0.617997i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 44.0000 | − | 76.2102i | 0.0475190 | − | 0.0823053i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 478.000 | 0.500346 | 0.250173 | − | 0.968201i | \(-0.419513\pi\) | ||||
0.250173 | + | 0.968201i | \(0.419513\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 484.000 | 0.491352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 783.000 | − | 1356.20i | 0.771400 | − | 1.33610i | −0.165396 | − | 0.986227i | \(-0.552890\pi\) |
0.936796 | − | 0.349877i | \(-0.113777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −484.000 | − | 838.313i | −0.463009 | − | 0.801955i | 0.536100 | − | 0.844154i | \(-0.319897\pi\) |
−0.999109 | + | 0.0421991i | \(0.986564\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 390.000 | + | 675.500i | 0.352362 | + | 0.610309i | 0.986663 | − | 0.162778i | \(-0.0520453\pi\) |
−0.634301 | + | 0.773086i | \(0.718712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 997.000 | − | 1726.85i | 0.876103 | − | 1.51746i | 0.0205209 | − | 0.999789i | \(-0.493468\pi\) |
0.855583 | − | 0.517666i | \(-0.173199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −648.000 | −0.554103 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −942.000 | −0.784212 | −0.392106 | − | 0.919920i | \(-0.628253\pi\) | ||||
−0.392106 | + | 0.919920i | \(0.628253\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 56.0000 | − | 96.9948i | 0.0454089 | − | 0.0786506i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −121.000 | − | 209.578i | −0.0956107 | − | 0.165603i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −302.500 | − | 523.945i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −396.000 | + | 685.892i | −0.290294 | + | 0.502803i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −492.000 | −0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1408.00 | 0.983778 | 0.491889 | − | 0.870658i | \(-0.336307\pi\) | ||||
0.491889 | + | 0.870658i | \(0.336307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −104.000 | + | 180.133i | −0.0709821 | + | 0.122945i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1346.00 | − | 2331.34i | −0.897714 | − | 1.55489i | −0.830409 | − | 0.557154i | \(-0.811893\pi\) |
−0.0673052 | − | 0.997732i | \(-0.521440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 152.000 | + | 263.272i | 0.0969043 | + | 0.167843i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −813.000 | + | 1408.16i | −0.507002 | + | 0.878153i | 0.492965 | + | 0.870049i | \(0.335913\pi\) |
−0.999967 | + | 0.00810420i | \(0.997420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 684.000 | 0.417382 | 0.208691 | − | 0.977982i | \(-0.433080\pi\) | ||||
0.208691 | + | 0.977982i | \(0.433080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2112.00 | −1.26144 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −484.000 | + | 838.313i | −0.283036 | + | 0.490232i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −198.000 | − | 342.946i | −0.113400 | − | 0.196415i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −151.000 | − | 261.540i | −0.0830228 | − | 0.143800i | 0.821524 | − | 0.570174i | \(-0.193124\pi\) |
−0.904547 | + | 0.426374i | \(0.859791\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −676.000 | + | 1170.87i | −0.364319 | + | 0.631018i | −0.988667 | − | 0.150128i | \(-0.952031\pi\) |
0.624348 | + | 0.781146i | \(0.285365\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 550.000 | 0.290620 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 320.000 | 0.165826 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1571.00 | − | 2721.05i | 0.798595 | − | 1.38321i | −0.121936 | − | 0.992538i | \(-0.538910\pi\) |
0.920531 | − | 0.390670i | \(-0.127756\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 484.000 | + | 838.313i | 0.241407 | + | 0.418129i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1518.00 | − | 2629.25i | −0.729441 | − | 1.26343i | −0.957120 | − | 0.289693i | \(-0.906447\pi\) |
0.227678 | − | 0.973736i | \(-0.426887\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 176.000 | − | 304.841i | 0.0830399 | − | 0.143829i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 264.000 | 0.122329 | 0.0611645 | − | 0.998128i | \(-0.480519\pi\) | ||||
0.0611645 | + | 0.998128i | \(0.480519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1713.00 | −0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −242.000 | + | 419.156i | −0.108223 | + | 0.187448i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1413.00 | − | 2447.39i | −0.620973 | − | 1.07556i | −0.989305 | − | 0.145863i | \(-0.953404\pi\) |
0.368331 | − | 0.929695i | \(-0.379929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1336.00 | − | 2314.02i | −0.567344 | − | 0.982669i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1542.00 | + | 2670.82i | −0.643880 | + | 1.11523i | 0.340679 | + | 0.940180i | \(0.389343\pi\) |
−0.984559 | + | 0.175053i | \(0.943990\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2418.00 | 0.992975 | 0.496488 | − | 0.868044i | \(-0.334623\pi\) | ||||
0.496488 | + | 0.868044i | \(0.334623\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2200.00 | −0.888681 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 162.000 | − | 280.592i | 0.0643810 | − | 0.111511i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1100.00 | − | 1905.26i | −0.430160 | − | 0.745059i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 480.000 | + | 831.384i | 0.181841 | + | 0.314957i | 0.942507 | − | 0.334185i | \(-0.108461\pi\) |
−0.760667 | + | 0.649143i | \(0.775128\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1441.00 | + | 2495.89i | −0.537438 | + | 0.930869i | 0.461604 | + | 0.887086i | \(0.347274\pi\) |
−0.999041 | + | 0.0437828i | \(0.986059\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −176.000 | −0.0646340 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1086.00 | 0.392763 | 0.196381 | − | 0.980528i | \(-0.437081\pi\) | ||||
0.196381 | + | 0.980528i | \(0.437081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 44.0000 | − | 76.2102i | 0.0156738 | − | 0.0271477i | −0.858082 | − | 0.513512i | \(-0.828344\pi\) |
0.873756 | + | 0.486365i | \(0.161677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −376.000 | − | 651.251i | −0.131945 | − | 0.228536i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −198.000 | − | 342.946i | −0.0674581 | − | 0.116841i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −308.000 | + | 533.472i | −0.103418 | + | 0.179125i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1936.00 | 0.640746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3476.00 | −1.13411 | −0.567056 | − | 0.823679i | \(-0.691918\pi\) | ||||
−0.567056 | + | 0.823679i | \(0.691918\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1456.00 | + | 2521.87i | −0.468373 | + | 0.811246i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −52.0000 | − | 90.0666i | −0.0164947 | − | 0.0285697i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 308.000 | + | 533.472i | 0.0950352 | + | 0.164606i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −550.000 | + | 952.628i | −0.167407 | + | 0.289958i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −928.000 | −0.278670 | −0.139335 | − | 0.990245i | \(-0.544497\pi\) | ||||
−0.139335 | + | 0.990245i | \(0.544497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1331.00 | 0.394370 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 78.0000 | − | 135.100i | 0.0228064 | − | 0.0395018i | −0.854397 | − | 0.519621i | \(-0.826073\pi\) |
0.877203 | + | 0.480119i | \(0.159407\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −817.000 | − | 1415.09i | −0.235759 | − | 0.408347i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
−0.959493 | + | 0.281732i | \(0.909091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 451.000 | + | 781.155i | 0.126807 | + | 0.219636i | 0.922438 | − | 0.386146i | \(-0.126194\pi\) |
−0.795631 | + | 0.605782i | \(0.792860\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 528.000 | − | 914.523i | 0.146566 | − | 0.253859i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2624.00 | −0.719186 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1616.00 | 0.437365 | 0.218683 | − | 0.975796i | \(-0.429824\pi\) | ||||
0.218683 | + | 0.975796i | \(0.429824\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2409.00 | − | 4172.51i | 0.643889 | − | 1.11525i | −0.340667 | − | 0.940184i | \(-0.610653\pi\) |
0.984557 | − | 0.175065i | \(-0.0560136\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1430.00 | − | 2476.83i | −0.377508 | − | 0.653864i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −484.000 | − | 838.313i | −0.124681 | − | 0.215954i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 472.000 | − | 817.528i | 0.120128 | − | 0.208067i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2140.00 | 0.538150 | 0.269075 | − | 0.963119i | \(-0.413282\pi\) | ||||
0.269075 | + | 0.963119i | \(0.413282\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2464.00 | 0.612294 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 200.000 | − | 346.410i | 0.0491156 | − | 0.0850708i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 385.000 | + | 666.840i | 0.0934461 | + | 0.161853i | 0.908959 | − | 0.416886i | \(-0.136878\pi\) |
−0.815513 | + | 0.578739i | \(0.803545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1089.00 | + | 1886.20i | 0.258266 | + | 0.447330i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3700.00 | − | 6408.59i | 0.867497 | − | 1.50255i | 0.00295121 | − | 0.999996i | \(-0.499061\pi\) |
0.864546 | − | 0.502554i | \(-0.167606\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −484.000 | −0.112196 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2856.00 | −0.654623 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1397.00 | + | 2419.67i | −0.316642 | + | 0.548439i | −0.979785 | − | 0.200053i | \(-0.935889\pi\) |
0.663143 | + | 0.748492i | \(0.269222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4312.00 | + | 7468.60i | 0.966551 | + | 1.67412i | 0.705389 | + | 0.708821i | \(0.250772\pi\) |
0.261162 | + | 0.965295i | \(0.415894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2662.00 | − | 4610.72i | −0.583726 | − | 1.01104i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 937.000 | − | 1622.93i | 0.203245 | − | 0.352031i | −0.746327 | − | 0.665579i | \(-0.768185\pi\) |
0.949572 | + | 0.313549i | \(0.101518\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1760.00 | −0.377665 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3338.00 | 0.708642 | 0.354321 | − | 0.935124i | \(-0.384712\pi\) | ||||
0.354321 | + | 0.935124i | \(0.384712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3586.00 | − | 6211.13i | 0.753235 | − | 1.30464i | −0.193012 | − | 0.981196i | \(-0.561826\pi\) |
0.946247 | − | 0.323445i | \(-0.104841\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 176.000 | + | 304.841i | 0.0365801 | + | 0.0633587i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1206.50 | + | 2089.72i | 0.245573 | + | 0.425345i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −956.000 | + | 1655.84i | −0.192583 | + | 0.333564i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5214.00 | −1.03961 | −0.519804 | − | 0.854286i | \(-0.673995\pi\) | ||||
−0.519804 | + | 0.854286i | \(0.673995\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1336.00 | 0.263678 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3344.00 | + | 5791.98i | −0.653328 | + | 1.13160i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −616.000 | − | 1066.94i | −0.119144 | − | 0.206364i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3132.00 | + | 5424.78i | 0.593824 | + | 1.02853i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 550.000 | − | 952.628i | 0.103255 | − | 0.178844i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −396.000 | −0.0736186 | −0.0368093 | − | 0.999322i | \(-0.511719\pi\) | ||||
−0.0368093 | + | 0.999322i | \(0.511719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3872.00 | 0.712849 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2028.00 | + | 3512.60i | −0.369766 | + | 0.640454i | −0.989529 | − | 0.144335i | \(-0.953896\pi\) |
0.619762 | + | 0.784789i | \(0.287229\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1077.00 | + | 1865.42i | 0.194491 | + | 0.336868i | 0.946733 | − | 0.322018i | \(-0.104361\pi\) |
−0.752243 | + | 0.658886i | \(0.771028\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3693.00 | + | 6396.46i | 0.654320 | + | 1.13332i | 0.982064 | + | 0.188549i | \(0.0603785\pi\) |
−0.327743 | + | 0.944767i | \(0.606288\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4356.00 | − | 7544.81i | 0.764543 | − | 1.32423i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3120.00 | −0.542497 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2200.00 | 0.378982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1331.00 | + | 2305.36i | −0.227171 | + | 0.393472i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3988.00 | + | 6907.42i | 0.674425 | + | 1.16814i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 566.000 | + | 980.341i | 0.0939884 | + | 0.162793i | 0.909186 | − | 0.416390i | \(-0.136705\pi\) |
−0.815198 | + | 0.579183i | \(0.803372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −891.000 | + | 1543.26i | −0.146626 | + | 0.253964i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 376.000 | 0.0613226 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3342.00 | −0.540209 | −0.270104 | − | 0.962831i | \(-0.587058\pi\) | ||||
−0.270104 | + | 0.962831i | \(0.587058\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1884.00 | − | 3263.18i | 0.301843 | − | 0.522808i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3520.00 | + | 6096.82i | 0.558999 | + | 0.968215i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 224.000 | + | 387.979i | 0.0349558 | + | 0.0605452i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1122.00 | + | 1943.36i | −0.173580 | + | 0.300649i | −0.939669 | − | 0.342086i | \(-0.888867\pi\) |
0.766089 | + | 0.642734i | \(0.222200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6522.00 | 1.00033 | 0.500164 | − | 0.865931i | \(-0.333273\pi\) | ||||
0.500164 | + | 0.865931i | \(0.333273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3344.00 | 0.508517 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5615.00 | + | 9725.47i | −0.846618 | + | 1.46639i | 0.0375899 | + | 0.999293i | \(0.488032\pi\) |
−0.884208 | + | 0.467093i | \(0.845301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −728.000 | − | 1260.93i | −0.108840 | − | 0.188517i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −924.000 | − | 1600.41i | −0.135841 | − | 0.235283i | 0.790078 | − | 0.613007i | \(-0.210040\pi\) |
−0.925918 | + | 0.377724i | \(0.876707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2461.50 | − | 4263.44i | 0.358872 | − | 0.621584i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2420.00 | 0.349909 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −308.000 | −0.0441684 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3560.00 | − | 6166.10i | 0.506350 | − | 0.877024i | −0.493623 | − | 0.869676i | \(-0.664328\pi\) |
0.999973 | − | 0.00734805i | \(-0.00233898\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1089.00 | + | 1886.20i | 0.153634 | + | 0.266103i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3175.00 | − | 5499.26i | −0.440738 | − | 0.763381i | 0.557006 | − | 0.830508i | \(-0.311950\pi\) |
−0.997744 | + | 0.0671276i | \(0.978617\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 984.000 | − | 1704.34i | 0.135503 | − | 0.234698i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4356.00 | −0.595081 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7900.00 | −1.07070 | −0.535351 | − | 0.844630i | \(-0.679821\pi\) | ||||
−0.535351 | + | 0.844630i | \(0.679821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2816.00 | + | 4877.46i | −0.378656 | + | 0.655852i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5184.00 | + | 8978.95i | 0.691619 | + | 1.19792i | 0.971307 | + | 0.237828i | \(0.0764355\pi\) |
−0.279688 | + | 0.960091i | \(0.590231\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 286.000 | + | 495.367i | 0.0375664 | + | 0.0650669i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4415.00 | + | 7647.00i | −0.575448 | + | 0.996706i | 0.420544 | + | 0.907272i | \(0.361839\pi\) |
−0.995993 | + | 0.0894338i | \(0.971494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2800.00 | 0.362154 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10768.0 | 1.38212 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 656.000 | − | 1136.23i | 0.0835619 | − | 0.144733i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4939.00 | + | 8554.60i | 0.624386 | + | 1.08147i | 0.988659 | + | 0.150176i | \(0.0479842\pi\) |
−0.364273 | + | 0.931292i | \(0.618683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6567.00 | + | 11374.4i | 0.817806 | + | 1.41648i | 0.907295 | + | 0.420494i | \(0.138143\pi\) |
−0.0894889 | + | 0.995988i | \(0.528523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1760.00 | − | 3048.41i | 0.217548 | − | 0.376804i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −622.000 | −0.0763146 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7128.00 | 0.868113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 453.000 | − | 784.619i | 0.0547663 | − | 0.0948580i | −0.837343 | − | 0.546679i | \(-0.815892\pi\) |
0.892109 | + | 0.451821i | \(0.149225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3252.00 | − | 5632.63i | −0.390290 | − | 0.676003i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 236.000 | + | 408.764i | 0.0279151 | + | 0.0483504i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1368.00 | + | 2369.45i | −0.160650 | + | 0.278255i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5412.00 | 0.631011 | 0.315505 | − | 0.948924i | \(-0.397826\pi\) | ||||
0.315505 | + | 0.948924i | \(0.397826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4642.00 | −0.537381 | −0.268690 | − | 0.963227i | \(-0.586591\pi\) | ||||
−0.268690 | + | 0.963227i | \(0.586591\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2904.00 | + | 5029.88i | −0.333800 | + | 0.578158i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3025.00 | − | 5239.45i | −0.345257 | − | 0.598002i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1936.00 | − | 3353.25i | −0.217881 | − | 0.377381i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −328.000 | + | 568.113i | −0.0366571 | + | 0.0634919i | −0.883772 | − | 0.467918i | \(-0.845004\pi\) |
0.847115 | + | 0.531410i | \(0.178338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9490.00 | −1.05326 | −0.526629 | − | 0.850096i | \(-0.676544\pi\) | ||||
−0.526629 | + | 0.850096i | \(0.676544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1584.00 | 0.174591 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1232.00 | + | 2133.89i | −0.134862 | + | 0.233587i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2772.00 | + | 4801.24i | 0.301368 | + | 0.521984i | 0.976446 | − | 0.215762i | \(-0.0692236\pi\) |
−0.675078 | + | 0.737746i | \(0.735890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3826.00 | − | 6626.83i | −0.410336 | − | 0.710722i | 0.584591 | − | 0.811328i | \(-0.301255\pi\) |
−0.994926 | + | 0.100606i | \(0.967922\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 714.000 | − | 1236.68i | 0.0760603 | − | 0.131740i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1208.00 | 0.127822 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −446.000 | −0.0468776 | −0.0234388 | − | 0.999725i | \(-0.507461\pi\) | ||||
−0.0234388 | + | 0.999725i | \(0.507461\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4356.00 | − | 7544.81i | 0.454803 | − | 0.787741i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2704.00 | − | 4683.47i | −0.280453 | − | 0.485758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −781.000 | − | 1352.73i | −0.0799423 | − | 0.138464i | 0.823283 | − | 0.567632i | \(-0.192140\pi\) |
−0.903225 | + | 0.429168i | \(0.858807\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3800.00 | + | 6581.79i | −0.386424 | + | 0.669307i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10582.0 | −1.06910 | −0.534548 | − | 0.845138i | \(-0.679518\pi\) | ||||
−0.534548 | + | 0.845138i | \(0.679518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10768.0 | −1.08085 | −0.540423 | − | 0.841394i | \(-0.681736\pi\) | ||||
−0.540423 | + | 0.841394i | \(0.681736\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −640.000 | + | 1108.51i | −0.0638264 | + | 0.110551i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4938.00 | − | 8552.87i | −0.489301 | − | 0.847494i | 0.510624 | − | 0.859804i | \(-0.329415\pi\) |
−0.999924 | + | 0.0123108i | \(0.996081\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6284.00 | + | 10884.2i | 0.614759 | + | 1.06479i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1144.00 | − | 1981.47i | 0.111208 | − | 0.192617i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5324.00 | 0.514278 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2662.00 | 0.255523 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −176.000 | + | 304.841i | −0.0167884 | + | 0.0290784i | −0.874298 | − | 0.485390i | \(-0.838677\pi\) |
0.857509 | + | 0.514469i | \(0.172011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1782.00 | − | 3086.51i | −0.168924 | − | 0.292584i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −478.000 | − | 827.920i | −0.0447523 | − | 0.0775132i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7588.00 | − | 13142.8i | 0.706047 | − | 1.22291i | −0.260265 | − | 0.965537i | \(-0.583810\pi\) |
0.966312 | − | 0.257373i | \(-0.0828568\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12144.0 | 1.12305 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8844.00 | −0.812880 | −0.406440 | − | 0.913677i | \(-0.633230\pi\) | ||||
−0.406440 | + | 0.913677i | \(0.633230\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4950.00 | − | 8573.65i | 0.452204 | − | 0.783241i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −484.000 | − | 838.313i | −0.0439478 | − | 0.0761199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9702.00 | − | 16804.4i | −0.870383 | − | 1.50755i | −0.861601 | − | 0.507586i | \(-0.830538\pi\) |
−0.00878220 | − | 0.999961i | \(-0.502795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −528.000 | + | 914.523i | −0.0470844 | + | 0.0815526i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16488.0 | −1.46156 | −0.730779 | − | 0.682614i | \(-0.760843\pi\) | ||||
−0.730779 | + | 0.682614i | \(0.760843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3132.00 | −0.275984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3426.00 | − | 5934.01i | 0.300107 | − | 0.519800i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6477.00 | − | 11218.5i | −0.564024 | − | 0.976917i | −0.997140 | − | 0.0755793i | \(-0.975919\pi\) |
0.433116 | − | 0.901338i | \(-0.357414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3344.00 | − | 5791.98i | −0.287800 | − | 0.498484i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −968.000 | + | 1676.63i | −0.0828256 | + | 0.143458i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23232.0 | 1.97629 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11304.0 | 0.956051 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5485.00 | − | 9500.30i | 0.461233 | − | 0.798878i | −0.537790 | − | 0.843079i | \(-0.680741\pi\) |
0.999023 | + | 0.0442004i | \(0.0140740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8470.00 | − | 14670.5i | −0.708159 | − | 1.22657i | −0.965539 | − | 0.260257i | \(-0.916193\pi\) |
0.257380 | − | 0.966310i | \(-0.417141\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4000.00 | + | 6928.20i | 0.330631 | + | 0.572670i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4515.50 | − | 7821.08i | 0.371127 | − | 0.642811i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7348.00 | −0.600520 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4356.00 | −0.353995 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 780.000 | − | 1351.00i | 0.0630324 | − | 0.109175i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6168.00 | − | 10683.3i | −0.495659 | − | 0.858506i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −99.0000 | − | 171.473i | −0.00786755 | − | 0.0136270i | 0.862065 | − | 0.506798i | \(-0.169171\pi\) |
−0.869932 | + | 0.493171i | \(0.835838\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4836.00 | + | 8376.20i | −0.382196 | + | 0.661984i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3988.00 | −0.313444 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15268.0 | −1.19344 | −0.596721 | − | 0.802449i | \(-0.703530\pi\) | ||||
−0.596721 | + | 0.802449i | \(0.703530\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3025.00 | + | 5239.45i | −0.235162 | + | 0.407312i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4356.00 | + | 7544.81i | 0.336791 | + | 0.583339i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 648.000 | + | 1122.37i | 0.0495605 | + | 0.0858413i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10427.0 | + | 18060.1i | −0.793189 | + | 1.37384i | 0.130794 | + | 0.991410i | \(0.458247\pi\) |
−0.923983 | + | 0.382434i | \(0.875086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1144.00 | −0.0865582 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8800.00 | 0.662275 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9658.00 | + | 16728.1i | −0.722977 | + | 1.25223i | 0.236824 | + | 0.971553i | \(0.423894\pi\) |
−0.959801 | + | 0.280681i | \(0.909440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 942.000 | + | 1631.59i | 0.0701420 | + | 0.121490i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3509.00 | − | 6077.77i | −0.258532 | − | 0.447791i | 0.707317 | − | 0.706897i | \(-0.249906\pi\) |
−0.965849 | + | 0.259106i | \(0.916572\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12210.0 | + | 21148.3i | −0.894873 | + | 1.54997i | −0.0609117 | + | 0.998143i | \(0.519401\pi\) |
−0.833961 | + | 0.551823i | \(0.813933\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3840.00 | −0.279962 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6776.00 | 0.491441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11617.0 | − | 20121.2i | 0.838166 | − | 1.45175i | −0.0532596 | − | 0.998581i | \(-0.516961\pi\) |
0.891426 | − | 0.453166i | \(-0.149706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5764.00 | − | 9983.54i | −0.413720 | − | 0.716583i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5324.00 | − | 9221.44i | −0.378212 | − | 0.655082i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −242.000 | + | 419.156i | −0.0171034 | + | 0.0296239i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10604.0 | 0.745611 | 0.372806 | − | 0.927909i | \(-0.378396\pi\) | ||||
0.372806 | + | 0.927909i | \(0.378396\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7040.00 | −0.492493 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2172.00 | + | 3762.01i | −0.151175 | + | 0.261842i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6919.00 | − | 11984.1i | −0.479139 | − | 0.829893i | 0.520575 | − | 0.853816i | \(-0.325718\pi\) |
−0.999714 | + | 0.0239233i | \(0.992384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 176.000 | + | 304.841i | 0.0120657 | + | 0.0208983i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1980.00 | − | 3429.46i | 0.135059 | − | 0.233930i | −0.790561 | − | 0.612384i | \(-0.790211\pi\) |
0.925620 | + | 0.378454i | \(0.123544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5942.00 | 0.403293 | 0.201647 | − | 0.979458i | \(-0.435371\pi\) | ||||
0.201647 | + | 0.979458i | \(0.435371\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2068.00 | −0.139661 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −605.000 | + | 1047.89i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1520.00 | − | 2632.72i | −0.101639 | − | 0.176044i | 0.810721 | − | 0.585433i | \(-0.199075\pi\) |
−0.912360 | + | 0.409389i | \(0.865742\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5808.00 | − | 10059.8i | −0.384561 | − | 0.666079i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1265.00 | − | 2191.04i | 0.0833489 | − | 0.144365i | −0.821338 | − | 0.570442i | \(-0.806772\pi\) |
0.904686 | + | 0.426078i | \(0.140105\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1584.00 | 0.103859 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19206.0 | −1.25317 | −0.626584 | − | 0.779354i | \(-0.715547\pi\) | ||||
−0.626584 | + | 0.779354i | \(0.715547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5498.00 | − | 9522.82i | 0.357000 | − | 0.618343i | −0.630458 | − | 0.776224i | \(-0.717133\pi\) |
0.987458 | + | 0.157881i | \(0.0504661\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4256.00 | − | 7371.61i | −0.275020 | − | 0.476349i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7070.50 | − | 12246.5i | −0.452512 | − | 0.783774i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3872.00 | + | 6706.50i | −0.246623 | + | 0.427164i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8100.00 | 0.513463 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6680.00 | −0.421437 | −0.210718 | − | 0.977547i | \(-0.567580\pi\) | ||||
−0.210718 | + | 0.977547i | \(0.567580\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6952.00 | − | 12041.2i | 0.436520 | − | 0.756075i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1408.00 | − | 2438.73i | −0.0879918 | − | 0.152406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4004.00 | + | 6935.13i | 0.247881 | + | 0.429342i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3137.00 | + | 5433.44i | −0.193298 | + | 0.334802i | −0.946341 | − | 0.323169i | \(-0.895252\pi\) |
0.753043 | + | 0.657971i | \(0.228585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9084.00 | −0.557135 | −0.278568 | − | 0.960417i | \(-0.589860\pi\) | ||||
−0.278568 | + | 0.960417i | \(0.589860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 416.000 | 0.0253953 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11828.0 | + | 20486.7i | −0.718712 | + | 1.24485i | 0.242798 | + | 0.970077i | \(0.421935\pi\) |
−0.961510 | + | 0.274769i | \(0.911399\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14696.0 | + | 25454.2i | 0.888857 | + | 1.53955i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3381.00 | + | 5856.06i | 0.202617 | + | 0.350943i | 0.949371 | − | 0.314158i | \(-0.101722\pi\) |
−0.746754 | + | 0.665100i | \(0.768389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2692.00 | + | 4662.68i | −0.160588 | + | 0.278147i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1694.00 | 0.100592 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15276.0 | 0.902987 | 0.451494 | − | 0.892274i | \(-0.350891\pi\) | ||||
0.451494 | + | 0.892274i | \(0.350891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5527.00 | − | 9573.04i | 0.325228 | − | 0.563311i | −0.656331 | − | 0.754473i | \(-0.727892\pi\) |
0.981558 | + | 0.191163i | \(0.0612258\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2200.00 | − | 3810.51i | −0.128870 | − | 0.223210i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5544.00 | + | 9602.49i | 0.321836 | + | 0.557436i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1856.00 | − | 3214.69i | 0.107260 | − | 0.185780i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24200.0 | 1.39230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21278.0 | −1.21873 | −0.609366 | − | 0.792889i | \(-0.708576\pi\) | ||||
−0.609366 | + | 0.792889i | \(0.708576\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9196.00 | + | 15927.9i | −0.524377 | + | 0.908247i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4463.00 | + | 7730.14i | 0.253363 | + | 0.438838i | 0.964450 | − | 0.264266i | \(-0.0851298\pi\) |
−0.711086 | + | 0.703105i | \(0.751796\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 312.000 | + | 540.400i | 0.0175563 | + | 0.0304085i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4058.00 | + | 7028.66i | −0.227343 | + | 0.393769i | −0.957020 | − | 0.290023i | \(-0.906337\pi\) |
0.729677 | + | 0.683792i | \(0.239670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3252.00 | 0.181391 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6536.00 | 0.362975 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2662.00 | + | 4610.72i | −0.147190 | + | 0.254941i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5882.00 | − | 10187.9i | −0.323823 | − | 0.560878i | 0.657450 | − | 0.753498i | \(-0.271635\pi\) |
−0.981273 | + | 0.192620i | \(0.938302\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −684.000 | − | 1184.72i | −0.0373318 | − | 0.0646606i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4950.00 | − | 8573.65i | 0.269002 | − | 0.465926i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3608.00 | −0.195232 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4698.00 | −0.253126 | −0.126563 | − | 0.991959i | \(-0.540395\pi\) | ||||
−0.126563 | + | 0.991959i | \(0.540395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3564.00 | + | 6173.03i | −0.191207 | + | 0.331181i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2112.00 | + | 3658.09i | 0.112826 | + | 0.195421i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12319.0 | − | 21337.1i | −0.652538 | − | 1.13023i | −0.982505 | − | 0.186237i | \(-0.940371\pi\) |
0.329966 | − | 0.943993i | \(-0.392963\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3608.00 | + | 6249.24i | −0.190310 | + | 0.329627i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8960.00 | −0.470624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1936.00 | 0.101262 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3232.00 | + | 5597.99i | −0.168342 | + | 0.291577i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8312.00 | + | 14396.8i | 0.431134 | + | 0.746746i | 0.996971 | − | 0.0777710i | \(-0.0247803\pi\) |
−0.565837 | + | 0.824517i | \(0.691447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9636.00 | + | 16690.0i | 0.495666 | + | 0.858519i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11979.0 | − | 20748.2i | 0.613640 | − | 1.06286i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30216.0 | −1.54147 | −0.770735 | − | 0.637155i | \(-0.780111\pi\) | ||||
−0.770735 | + | 0.637155i | \(0.780111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1300.00 | − | 2251.67i | 0.0657760 | − | 0.113927i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1661.00 | − | 2876.94i | −0.0836977 | − | 0.144969i | 0.821138 | − | 0.570730i | \(-0.193340\pi\) |
−0.904836 | + | 0.425761i | \(0.860006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4136.00 | + | 7163.76i | 0.206718 | + | 0.358047i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7346.00 | − | 12723.6i | 0.365666 | − | 0.633352i | −0.623217 | − | 0.782049i | \(-0.714175\pi\) |
0.988883 | + | 0.148697i | \(0.0475080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3872.00 | 0.191959 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28600.0 | 1.41216 | 0.706078 | − | 0.708134i | \(-0.250463\pi\) | ||||
0.706078 | + | 0.708134i | \(0.250463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −302.000 | + | 523.079i | −0.0148516 | + | 0.0257237i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1298.00 | − | 2248.20i | −0.0635761 | − | 0.110117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14808.0 | + | 25648.2i | 0.719509 | + | 1.24623i | 0.961194 | + | 0.275872i | \(0.0889666\pi\) |
−0.241685 | + | 0.970355i | \(0.577700\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4280.00 | + | 7413.18i | −0.207134 | + | 0.358767i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2704.00 | 0.130343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2894.00 | 0.138949 | 0.0694744 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694744 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4928.00 | + | 8535.55i | −0.235672 | + | 0.408196i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7381.00 | + | 12784.3i | 0.351591 | + | 0.608974i | 0.986528 | − | 0.163590i | \(-0.0523073\pi\) |
−0.634937 | + | 0.772564i | \(0.718974\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −550.000 | − | 952.628i | −0.0259938 | − | 0.0450227i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7348.00 | − | 12727.1i | 0.345920 | − | 0.599152i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7678.00 | 0.360047 | 0.180023 | − | 0.983662i | \(-0.442383\pi\) | ||||
0.180023 | + | 0.983662i | \(0.442383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3080.00 | −0.143870 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13695.0 | − | 23720.4i | 0.637225 | − | 1.10371i | −0.348814 | − | 0.937192i | \(-0.613416\pi\) |
0.986039 | − | 0.166514i | \(-0.0532511\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9680.00 | + | 16766.3i | 0.448666 | + | 0.777112i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4356.00 | + | 7544.81i | 0.200346 | + | 0.347010i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16016.0 | − | 27740.5i | 0.733800 | − | 1.27098i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30096.0 | −1.37362 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6284.00 | −0.285714 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9878.00 | − | 17109.2i | 0.447411 | − | 0.774939i | −0.550805 | − | 0.834634i | \(-0.685679\pi\) |
0.998217 | + | 0.0596946i | \(0.0190127\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14800.0 | + | 25634.4i | 0.667800 | + | 1.15666i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6050.00 | − | 10478.9i | −0.270923 | − | 0.469252i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 968.000 | − | 1676.63i | 0.0431842 | − | 0.0747972i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38854.0 | −1.72682 | −0.863412 | − | 0.504499i | \(-0.831677\pi\) | ||||
−0.863412 | + | 0.504499i | \(0.831677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26400.0 | 1.16892 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3927.00 | + | 6801.76i | −0.173226 | + | 0.300036i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3388.00 | − | 5868.19i | −0.148892 | − | 0.257888i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5588.00 | − | 9678.70i | −0.243751 | − | 0.422189i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7139.00 | − | 12365.1i | 0.310252 | − | 0.537372i | −0.668165 | − | 0.744013i | \(-0.732920\pi\) |
0.978417 | + | 0.206641i | \(0.0662532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 716.000 | 0.0310014 | 0.0155007 | − | 0.999880i | \(-0.495066\pi\) | ||||
0.0155007 | + | 0.999880i | \(0.495066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34496.0 | −1.48810 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3036.00 | + | 5258.51i | −0.130486 | + | 0.226009i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1144.00 | + | 1981.47i | 0.0489884 | + | 0.0848503i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11769.0 | + | 20384.5i | 0.500293 | + | 0.866534i | 1.00000 | 0.000338894i | \(0.000107873\pi\) | |
−0.499706 | + | 0.866195i | \(0.666559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3308.00 | − | 5729.62i | 0.140109 | − | 0.242676i | −0.787429 | − | 0.616406i | \(-0.788588\pi\) |
0.927537 | + | 0.373730i | \(0.121921\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21296.0 | 0.898705 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27236.0 | 1.14521 | 0.572605 | − | 0.819831i | \(-0.305933\pi\) | ||||
0.572605 | + | 0.819831i | \(0.305933\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6035.00 | − | 10452.9i | 0.252840 | − | 0.437931i | −0.711467 | − | 0.702720i | \(-0.751969\pi\) |
0.964307 | + | 0.264788i | \(0.0853021\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3748.00 | + | 6491.73i | 0.156458 | + | 0.270993i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −264.000 | − | 457.261i | −0.0109414 | − | 0.0189511i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12160.0 | − | 21061.7i | 0.502164 | − | 0.869773i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42024.0 | 1.72924 | 0.864618 | − | 0.502429i | \(-0.167560\pi\) | ||||
0.864618 | + | 0.502429i | \(0.167560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14815.0 | 0.607446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6676.00 | + | 11563.2i | −0.272756 | + | 0.472428i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1713.00 | + | 2967.00i | 0.0697385 | + | 0.120791i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14344.0 | + | 24844.5i | 0.579841 | + | 1.00431i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4536.00 | + | 7856.58i | −0.182717 | + | 0.316475i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2414.00 | −0.0968978 | −0.0484489 | − | 0.998826i | \(-0.515428\pi\) | ||||
−0.0484489 | + | 0.998826i | \(0.515428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 968.000 | 0.0387192 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18843.0 | + | 32637.0i | −0.751067 | + | 1.30089i | 0.196239 | + | 0.980556i | \(0.437127\pi\) |
−0.947306 | + | 0.320330i | \(0.896206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20322.0 | + | 35198.7i | 0.807192 | + | 1.39810i | 0.914801 | + | 0.403904i | \(0.132347\pi\) |
−0.107610 | + | 0.994193i | \(0.534320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9328.00 | + | 16156.6i | 0.367936 | + | 0.637284i | 0.989243 | − | 0.146284i | \(-0.0467312\pi\) |
−0.621307 | + | 0.783568i | \(0.713398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2826.00 | + | 4894.78i | −0.111083 | + | 0.192402i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9652.00 | −0.378084 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28864.0 | 1.12675 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2068.00 | − | 3581.88i | 0.0804495 | − | 0.139343i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2629.00 | + | 4553.56i | 0.101922 | + | 0.176535i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6501.00 | + | 11260.1i | 0.250311 | + | 0.433552i | 0.963612 | − | 0.267307i | \(-0.0861336\pi\) |
−0.713300 | + | 0.700859i | \(0.752800\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10428.0 | − | 18061.8i | 0.400145 | − | 0.693072i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49490.0 | −1.89258 | −0.946289 | − | 0.323323i | \(-0.895200\pi\) | ||||
−0.946289 | + | 0.323323i | \(0.895200\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1100.00 | 0.0419229 | 0.0209615 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209615 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2672.00 | + | 4628.04i | −0.101490 | + | 0.175785i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7052.00 | − | 12214.4i | −0.266948 | − | 0.462368i | 0.701124 | − | 0.713039i | \(-0.252682\pi\) |
−0.968072 | + | 0.250672i | \(0.919349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6842.00 | − | 11850.7i | −0.257257 | − | 0.445581i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11616.0 | + | 20119.5i | −0.435291 | + | 0.753946i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6168.00 | 0.230361 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4928.00 | 0.183435 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15840.0 | + | 27435.7i | −0.587646 | + | 1.01783i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6050.00 | − | 10478.9i | −0.223701 | − | 0.387462i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2418.00 | − | 4188.10i | −0.0888144 | − | 0.153831i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6358.00 | − | 11012.4i | 0.232761 | − | 0.403153i | −0.725859 | − | 0.687844i | \(-0.758557\pi\) |
0.958620 | + | 0.284690i | \(0.0918908\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17226.0 | 0.628548 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39632.0 | −1.44135 | −0.720673 | − | 0.693275i | \(-0.756167\pi\) | ||||
−0.720673 | + | 0.693275i | \(0.756167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5192.00 | + | 8992.81i | −0.188204 | + | 0.325979i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2200.00 | + | 3810.51i | 0.0794861 | + | 0.137674i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2852.00 | − | 4939.81i | −0.102371 | − | 0.177311i | 0.810290 | − | 0.586029i | \(-0.199310\pi\) |
−0.912661 | + | 0.408717i | \(0.865976\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 792.000 | − | 1371.78i | 0.0283358 | − | 0.0490791i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16016.0 | −0.571152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19602.0 | 0.696767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5324.00 | − | 9221.44i | 0.188633 | − | 0.326723i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4081.00 | + | 7068.50i | 0.144126 | + | 0.249634i | 0.929047 | − | 0.369963i | \(-0.120630\pi\) |
−0.784920 | + | 0.619597i | \(0.787296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8112.00 | − | 14050.4i | −0.284646 | − | 0.493022i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2200.00 | + | 3810.51i | −0.0769494 | + | 0.133280i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55110.0 | 1.92141 | 0.960707 | − | 0.277564i | \(-0.0895270\pi\) | ||||
0.960707 | + | 0.277564i | \(0.0895270\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8616.00 | −0.299438 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8187.00 | − | 14180.3i | 0.283622 | − | 0.491248i | −0.688652 | − | 0.725092i | \(-0.741797\pi\) |
0.972274 | + | 0.233844i | \(0.0751305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5544.00 | + | 9602.49i | 0.191450 | + | 0.331601i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4230.00 | − | 7326.57i | −0.145149 | − | 0.251406i | 0.784279 | − | 0.620408i | \(-0.213033\pi\) |
−0.929429 | + | 0.369002i | \(0.879700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1694.00 | + | 2934.09i | −0.0579447 | + | 0.100363i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29544.0 | −1.00739 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20502.0 | −0.696878 | −0.348439 | − | 0.937331i | \(-0.613288\pi\) | ||||
−0.348439 | + | 0.937331i | \(0.613288\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 960.000 | − | 1662.77i | 0.0325287 | − | 0.0563413i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17424.0 | + | 30179.3i | 0.588545 | + | 1.01939i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2095.50 | + | 3629.51i | 0.0703400 | + | 0.121833i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4290.00 | + | 7430.50i | −0.143555 | + | 0.248644i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5764.00 | 0.192280 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36520.0 | −1.21448 | −0.607241 | − | 0.794518i | \(-0.707724\pi\) | ||||
−0.607241 | + | 0.794518i | \(0.707724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4400.00 | + | 7621.02i | −0.145870 | + | 0.252655i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10122.0 | + | 17531.8i | 0.334532 | + | 0.579426i | 0.983395 | − | 0.181479i | \(-0.0580885\pi\) |
−0.648863 | + | 0.760905i | \(0.724755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5324.00 | − | 9221.44i | −0.174876 | − | 0.302895i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25017.0 | + | 43330.7i | −0.819206 | + | 1.41891i | 0.0870612 | + | 0.996203i | \(0.472252\pi\) |
−0.906268 | + | 0.422704i | \(0.861081\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31416.0 | 1.02560 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21934.0 | 0.713862 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18564.0 | − | 32153.8i | 0.602339 | − | 1.04328i | −0.390126 | − | 0.920761i | \(-0.627569\pi\) |
0.992466 | − | 0.122521i | \(-0.0390979\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1086.00 | − | 1881.01i | −0.0351298 | − | 0.0608466i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1456.00 | + | 2521.87i | 0.0468131 | + | 0.0810826i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13904.0 | + | 24082.4i | −0.445686 | + | 0.771951i | −0.998100 | − | 0.0616190i | \(-0.980374\pi\) |
0.552413 | + | 0.833570i | \(0.313707\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4528.00 | −0.144705 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −176.000 | −0.00560761 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14257.0 | + | 24693.8i | −0.452882 | + | 0.784415i | −0.998564 | − | 0.0535775i | \(-0.982938\pi\) |
0.545681 | + | 0.837993i | \(0.316271\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12312.0 | − | 21325.0i | −0.389924 | − | 0.675369i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))