Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,4,Mod(5,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.j (of order \(22\), degree \(10\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.8593839112\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(-0.786053 + 0.618159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.161 |
Dual form | 201.4.j.a.5.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{17}{22}\right)\) |
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 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(3\) | 4.72659 | + | 2.15856i | 0.909632 | + | 0.415415i | ||||
\(4\) | 1.13852 | − | 7.91857i | 0.142315 | − | 0.989821i | ||||
\(5\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.6079 | − | 10.0583i | 0.626769 | − | 0.543099i | −0.282521 | − | 0.959261i | \(-0.591171\pi\) |
0.909290 | + | 0.416162i | \(0.136625\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 17.6812 | + | 20.4052i | 0.654861 | + | 0.755750i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(12\) | 22.4740 | − | 34.9703i | 0.540641 | − | 0.841254i | ||||
\(13\) | 6.52521 | − | 10.1534i | 0.139213 | − | 0.216619i | −0.764646 | − | 0.644451i | \(-0.777086\pi\) |
0.903858 | + | 0.427832i | \(0.140722\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −61.4076 | − | 18.0309i | −0.959493 | − | 0.281733i | ||||
\(17\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 108.092 | − | 124.745i | 1.30516 | − | 1.50623i | 0.589534 | − | 0.807743i | \(-0.299311\pi\) |
0.715622 | − | 0.698487i | \(-0.246143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 76.5774 | − | 22.4851i | 0.795741 | − | 0.233651i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −105.157 | − | 67.5801i | −0.841254 | − | 0.540641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 39.5260 | + | 134.613i | 0.281733 | + | 0.959493i | ||||
\(28\) | −66.4317 | − | 103.370i | −0.448372 | − | 0.697681i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 127.777 | + | 198.825i | 0.740305 | + | 1.15194i | 0.983315 | + | 0.181913i | \(0.0582288\pi\) |
−0.243010 | + | 0.970024i | \(0.578135\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 181.711 | − | 116.778i | 0.841254 | − | 0.540641i | ||||
\(37\) | 143.439 | 0.637332 | 0.318666 | − | 0.947867i | \(-0.396765\pi\) | ||||
0.318666 | + | 0.947867i | \(0.396765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 52.7587 | − | 33.9060i | 0.216619 | − | 0.139213i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 96.5466 | − | 13.8813i | 0.342400 | − | 0.0492297i | 0.0310302 | − | 0.999518i | \(-0.490121\pi\) |
0.311370 | + | 0.950289i | \(0.399212\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(48\) | −251.327 | − | 217.776i | −0.755750 | − | 0.654861i | ||||
\(49\) | −15.2399 | + | 105.996i | −0.0444313 | + | 0.309026i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −72.9715 | − | 63.2302i | −0.194603 | − | 0.168624i | ||||
\(53\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 780.174 | − | 356.294i | 1.81292 | − | 0.827934i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −156.106 | − | 531.649i | −0.327662 | − | 1.11591i | −0.944415 | − | 0.328756i | \(-0.893371\pi\) |
0.616753 | − | 0.787157i | \(-0.288448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 410.485 | + | 59.0189i | 0.820893 | + | 0.118027i | ||||
\(64\) | −212.692 | + | 465.732i | −0.415415 | + | 0.909632i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 193.169 | + | 513.273i | 0.352228 | + | 0.935914i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1196.68 | + | 351.377i | −1.91864 | + | 0.563363i | −0.953966 | + | 0.299916i | \(0.903041\pi\) |
−0.964674 | + | 0.263447i | \(0.915141\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −351.157 | − | 546.410i | −0.540641 | − | 0.841254i | ||||
\(76\) | −864.735 | − | 997.957i | −1.30516 | − | 1.50623i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −754.678 | + | 1174.30i | −1.07478 | + | 1.67240i | −0.445304 | + | 0.895379i | \(0.646904\pi\) |
−0.629480 | + | 0.777017i | \(0.716732\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −103.748 | + | 721.580i | −0.142315 | + | 0.989821i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(84\) | −90.8655 | − | 631.983i | −0.118027 | − | 0.820893i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.3823 | − | 183.493i | −0.0303914 | − | 0.211377i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 174.774 | + | 1215.58i | 0.194873 | + | 1.35537i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1779.67i | 1.86287i | 0.363911 | + | 0.931434i | \(0.381441\pi\) | ||||
−0.363911 | + | 0.931434i | \(0.618559\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −654.861 | + | 755.750i | −0.654861 | + | 0.755750i | ||||
\(101\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 348.533 | − | 223.989i | 0.333418 | − | 0.214275i | −0.363210 | − | 0.931707i | \(-0.618319\pi\) |
0.696628 | + | 0.717433i | \(0.254683\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(108\) | 1110.94 | − | 159.730i | 0.989821 | − | 0.142315i | ||||
\(109\) | −1033.70 | + | 1608.46i | −0.908350 | + | 1.41342i | 0.00218975 | + | 0.999998i | \(0.499303\pi\) |
−0.910539 | + | 0.413422i | \(0.864333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 677.978 | + | 309.622i | 0.579737 | + | 0.264757i | ||||
\(112\) | −894.175 | + | 408.356i | −0.754389 | + | 0.344518i | ||||
\(113\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 322.557 | − | 46.3767i | 0.254875 | − | 0.0366455i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1119.71 | − | 719.593i | −0.841254 | − | 0.540641i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1719.89 | − | 785.446i | 1.24557 | − | 0.568832i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −795.116 | − | 917.612i | −0.555552 | − | 0.641141i | 0.406616 | − | 0.913599i | \(-0.366709\pi\) |
−0.962168 | + | 0.272458i | \(0.912163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 486.299 | + | 142.790i | 0.331909 | + | 0.0974573i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2535.25i | − | 1.65289i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 422.986 | − | 1440.56i | 0.258109 | − | 0.879040i | −0.723852 | − | 0.689956i | \(-0.757630\pi\) |
0.981961 | − | 0.189084i | \(-0.0605518\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −717.837 | − | 1571.84i | −0.415415 | − | 0.909632i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −300.832 | + | 468.103i | −0.168790 | + | 0.262643i | ||||
\(148\) | 163.308 | − | 1135.83i | 0.0907018 | − | 0.630845i | ||||
\(149\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 107.436 | + | 747.237i | 0.0579010 | + | 0.402710i | 0.998075 | + | 0.0620161i | \(0.0197530\pi\) |
−0.940174 | + | 0.340694i | \(0.889338\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −208.420 | − | 456.376i | −0.106968 | − | 0.234227i | ||||
\(157\) | 792.863 | − | 1736.13i | 0.403040 | − | 0.882535i | −0.593913 | − | 0.804529i | \(-0.702418\pi\) |
0.996953 | − | 0.0780055i | \(-0.0248552\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2860.06 | 1.37434 | 0.687169 | − | 0.726498i | \(-0.258853\pi\) | ||||
0.687169 | + | 0.726498i | \(0.258853\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 852.153 | + | 1865.96i | 0.387871 | + | 0.849320i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4456.64 | 1.99303 | ||||||||
\(172\) | − | 780.315i | − | 0.345921i | ||||||
\(173\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1900.39 | + | 273.235i | −0.820893 | + | 0.118027i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −699.161 | + | 1530.95i | −0.287117 | + | 0.628699i | −0.997148 | − | 0.0754717i | \(-0.975954\pi\) |
0.710031 | + | 0.704171i | \(0.248681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 409.747 | − | 2849.85i | 0.165516 | − | 1.15119i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1812.80 | + | 1165.01i | 0.697681 | + | 0.448372i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(192\) | −2010.62 | + | 1742.21i | −0.755750 | + | 0.654861i | ||||
\(193\) | 3963.56 | − | 2547.23i | 1.47826 | − | 0.950018i | 0.480944 | − | 0.876751i | \(-0.340294\pi\) |
0.997312 | − | 0.0732663i | \(-0.0233423\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 821.986 | + | 241.357i | 0.299558 | + | 0.0879581i | ||||
\(197\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −825.591 | − | 952.783i | −0.294093 | − | 0.339402i | 0.589404 | − | 0.807839i | \(-0.299363\pi\) |
−0.883497 | + | 0.468437i | \(0.844817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −194.901 | + | 2842.99i | −0.0683944 | + | 0.997658i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −583.772 | + | 505.842i | −0.194603 | + | 0.168624i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2276.57 | + | 4985.00i | 0.742776 | + | 1.62645i | 0.778934 | + | 0.627106i | \(0.215761\pi\) |
−0.0361575 | + | 0.999346i | \(0.511512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3483.07 | + | 1022.72i | 1.08962 | + | 0.319940i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6414.67 | − | 922.291i | −1.97929 | − | 0.284578i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2758.72 | − | 6040.74i | −0.828418 | − | 1.81398i | −0.483469 | − | 0.875362i | \(-0.660623\pi\) |
−0.344949 | − | 0.938621i | \(-0.612104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −480.313 | − | 3340.65i | −0.142315 | − | 0.989821i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(228\) | −1933.09 | − | 6583.51i | −0.561501 | − | 1.91230i | ||||
\(229\) | 3715.94 | + | 5782.11i | 1.07230 | + | 1.66853i | 0.644370 | + | 0.764714i | \(0.277120\pi\) |
0.427927 | + | 0.903813i | \(0.359244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6101.85 | + | 3921.42i | −1.67240 | + | 1.07478i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5308.44 | − | 1558.70i | 1.41887 | − | 0.416617i | 0.519747 | − | 0.854320i | \(-0.326026\pi\) |
0.899119 | + | 0.437704i | \(0.144208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2047.94 | + | 3186.66i | −0.540641 | + | 0.841254i | ||||
\(244\) | −4387.63 | + | 630.846i | −1.15119 | + | 0.165516i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −561.263 | − | 1911.49i | −0.144584 | − | 0.492409i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(252\) | 934.690 | − | 3183.26i | 0.233651 | − | 0.795741i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3445.77 | + | 2214.46i | 0.841254 | + | 0.540641i | ||||
\(257\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1665.03 | − | 1442.76i | 0.399460 | − | 0.346134i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4284.31 | − | 945.249i | 0.976515 | − | 0.215449i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5851.10 | − | 2672.11i | −1.31155 | − | 0.598963i | −0.367883 | − | 0.929872i | \(-0.619917\pi\) |
−0.943663 | + | 0.330909i | \(0.892645\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 271.382 | − | 924.243i | 0.0601641 | − | 0.204900i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4999.94 | − | 5770.24i | −1.08454 | − | 1.25162i | −0.965963 | − | 0.258680i | \(-0.916713\pi\) |
−0.118576 | − | 0.992945i | \(-0.537833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1797.81 | + | 6122.80i | −0.385779 | + | 1.31384i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2097.93 | − | 2421.14i | 0.440667 | − | 0.508557i | −0.491354 | − | 0.870960i | \(-0.663498\pi\) |
0.932022 | + | 0.362403i | \(0.118043\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4713.99 | + | 1384.15i | −0.959493 | + | 0.281733i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3841.52 | + | 8411.77i | −0.773863 | + | 1.69452i | ||||
\(292\) | 1419.96 | + | 9876.04i | 0.284578 | + | 1.97929i | ||||
\(293\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4726.59 | + | 2158.56i | −0.909632 | + | 0.415415i | ||||
\(301\) | 981.083 | − | 1132.23i | 0.187869 | − | 0.216813i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8886.91 | + | 5711.27i | −1.67664 | + | 1.07751i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2597.85 | + | 1669.54i | −0.482955 | + | 0.310376i | −0.759366 | − | 0.650663i | \(-0.774491\pi\) |
0.276412 | + | 0.961039i | \(0.410855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2130.87 | − | 306.372i | 0.392300 | − | 0.0564043i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4058.54 | − | 1853.47i | 0.732915 | − | 0.334711i | −0.0137555 | − | 0.999905i | \(-0.504379\pi\) |
0.746670 | + | 0.665194i | \(0.231651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8439.58 | + | 7312.94i | 1.50242 | + | 1.30185i | ||||
\(317\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5595.76 | + | 1643.06i | 0.959493 | + | 0.281733i | ||||
\(325\) | −1372.34 | + | 626.726i | −0.234227 | + | 0.106968i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8357.82 | + | 5371.24i | −1.41342 | + | 0.908350i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4042.35 | − | 581.202i | −0.671262 | − | 0.0965129i | −0.201747 | − | 0.979438i | \(-0.564662\pi\) |
−0.469515 | + | 0.882925i | \(0.655571\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2536.18 | + | 2926.91i | 0.417364 | + | 0.481663i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5107.86 | −0.829335 | ||||||||
\(337\) | 5200.71 | − | 4506.44i | 0.840654 | − | 0.728431i | −0.123906 | − | 0.992294i | \(-0.539542\pi\) |
0.964560 | + | 0.263863i | \(0.0849967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3737.50 | + | 5815.66i | 0.588356 | + | 0.915499i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1680.39 | − | 11687.4i | 0.257734 | − | 1.79258i | −0.291148 | − | 0.956678i | \(-0.594037\pi\) |
0.548881 | − | 0.835900i | \(-0.315054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1624.70 | + | 477.055i | 0.247066 | + | 0.0725450i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2901.24 | − | 20178.6i | −0.422983 | − | 2.94191i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3739.11 | − | 5818.18i | −0.540641 | − | 0.841254i | ||||
\(364\) | −1483.04 | −0.213550 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10561.2 | + | 4823.13i | −1.50215 | + | 0.686010i | −0.985420 | − | 0.170138i | \(-0.945579\pi\) |
−0.516731 | + | 0.856148i | \(0.672851\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9824.63 | 1.36931 | ||||||||
\(373\) | 4474.37i | 0.621110i | 0.950555 | + | 0.310555i | \(0.100515\pi\) | ||||
−0.950555 | + | 0.310555i | \(0.899485\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1248.94 | + | 570.370i | 0.169271 | + | 0.0773033i | 0.498248 | − | 0.867034i | \(-0.333977\pi\) |
−0.328978 | + | 0.944338i | \(0.606704\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1777.46 | − | 6053.48i | −0.239008 | − | 0.813987i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1990.31 | + | 1724.62i | 0.261430 | + | 0.226530i | ||||
\(388\) | 14092.4 | + | 2026.19i | 1.84391 | + | 0.265114i | ||||
\(389\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15144.9 | − | 4446.95i | −1.91461 | − | 0.562182i | −0.976312 | − | 0.216366i | \(-0.930580\pi\) |
−0.938302 | − | 0.345816i | \(-0.887602\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5472.49 | − | 11983.1i | 0.686634 | − | 1.50352i | ||||
\(400\) | 5238.89 | + | 6046.00i | 0.654861 | + | 0.755750i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2852.53 | 0.352592 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8643.73 | − | 7489.83i | 1.04500 | − | 0.905497i | 0.0493597 | − | 0.998781i | \(-0.484282\pi\) |
0.995640 | + | 0.0932841i | \(0.0297365\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1376.86 | − | 3014.90i | −0.164643 | − | 0.360518i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5108.81 | − | 5895.88i | 0.599951 | − | 0.692380i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10214.1 | − | 11787.6i | 1.18243 | − | 1.36460i | 0.266211 | − | 0.963915i | \(-0.414228\pi\) |
0.916218 | − | 0.400680i | \(-0.131226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7159.57 | − | 4601.18i | −0.811419 | − | 0.521467i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | − | 8978.95i | − | 1.00000i | ||||||
\(433\) | 8867.86 | + | 13798.7i | 0.984208 | + | 1.53146i | 0.840481 | + | 0.541840i | \(0.182272\pi\) |
0.143727 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11559.8 | + | 10016.7i | 1.26976 | + | 1.10025i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12770.5 | 1.38838 | 0.694192 | − | 0.719790i | \(-0.255762\pi\) | ||||
0.694192 | + | 0.719790i | \(0.255762\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2432.34 | + | 1563.17i | −0.262643 | + | 0.168790i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(444\) | 3223.66 | − | 5016.11i | 0.344568 | − | 0.536158i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2215.56 | + | 7545.51i | 0.233651 | + | 0.795741i | ||||
\(449\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1105.15 | + | 3763.79i | −0.114623 | + | 0.390371i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2433.08 | + | 1563.64i | 0.249047 | + | 0.160053i | 0.659209 | − | 0.751960i | \(-0.270891\pi\) |
−0.410162 | + | 0.912013i | \(0.634528\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3768.64 | − | 12834.8i | −0.378280 | − | 1.28830i | −0.900263 | − | 0.435347i | \(-0.856626\pi\) |
0.521983 | − | 0.852956i | \(-0.325192\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(468\) | − | 2606.99i | − | 0.257496i | ||||||
\(469\) | 7404.95 | + | 4015.08i | 0.729060 | + | 0.395307i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7495.07 | − | 6494.51i | 0.733237 | − | 0.635353i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19796.8 | + | 5812.88i | −1.91230 | + | 0.561501i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 935.971 | − | 1456.40i | 0.0887248 | − | 0.138058i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6972.96 | + | 8047.22i | −0.654861 | + | 0.755750i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21183.8 | − | 3045.77i | −1.97111 | − | 0.283402i | −0.998755 | − | 0.0498761i | \(-0.984117\pi\) |
−0.972351 | − | 0.233526i | \(-0.924974\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13518.3 | + | 6173.61i | 1.25014 | + | 0.570920i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4261.49 | − | 14513.3i | −0.385779 | − | 1.31384i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21952.7i | 1.96941i | 0.174223 | + | 0.984706i | \(0.444259\pi\) | ||||
−0.174223 | + | 0.984706i | \(0.555741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10659.0i | 0.933696i | ||||||||
\(508\) | −8171.43 | + | 5251.46i | −0.713679 | + | 0.458653i | ||||
\(509\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10356.7 | + | 16115.3i | −0.896582 | + | 1.39511i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21064.7 | + | 9619.93i | 1.81292 | + | 0.827934i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1684.36 | − | 3688.23i | 0.143701 | − | 0.314661i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19774.6 | − | 12708.4i | −1.65331 | − | 1.06252i | −0.926935 | − | 0.375222i | \(-0.877566\pi\) |
−0.726377 | − | 0.687297i | \(-0.758797\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9572.17 | − | 2810.64i | −0.795741 | − | 0.233651i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7967.69 | − | 9195.21i | −0.654861 | − | 0.755750i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20075.6 | − | 2886.43i | −1.63606 | − | 0.235230i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5886.59 | − | 20047.9i | 0.467808 | − | 1.59321i | −0.300931 | − | 0.953646i | \(-0.597297\pi\) |
0.768739 | − | 0.639562i | \(-0.220884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6609.29 | + | 5726.98i | −0.522342 | + | 0.452612i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −566.436 | + | 1929.10i | −0.0442761 | + | 0.150791i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) |
0.934388 | + | 0.356257i | \(0.115947\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8088.27 | − | 12585.6i | 0.628778 | − | 0.978398i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3051.27 | + | 21222.0i | 0.234635 | + | 1.63192i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10925.6 | − | 4989.55i | −0.833359 | − | 0.380582i | ||||
\(557\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 489.044 | − | 1070.86i | 0.0370024 | − | 0.0810240i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6053.59 | + | 9419.57i | 0.448372 | + | 0.697681i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1337.40 | − | 2928.49i | −0.0980182 | − | 0.214630i | 0.854270 | − | 0.519829i | \(-0.174004\pi\) |
−0.952289 | + | 0.305199i | \(0.901277\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13264.0 | + | 3894.67i | −0.959493 | + | 0.281733i | ||||
\(577\) | −15314.2 | + | 2201.85i | −1.10492 | + | 0.158864i | −0.670546 | − | 0.741868i | \(-0.733940\pi\) |
−0.434376 | + | 0.900732i | \(0.643031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24232.5 | − | 3484.10i | 1.73932 | − | 0.250077i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(588\) | 3364.21 | + | 2915.10i | 0.235948 | + | 0.204450i | ||||
\(589\) | 38614.0 | + | 5551.86i | 2.70130 | + | 0.388388i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8808.26 | − | 2586.34i | −0.611515 | − | 0.179557i | ||||
\(593\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1845.59 | − | 6285.50i | −0.126524 | − | 0.430902i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18986.7 | + | 21911.8i | 1.28866 | + | 1.48719i | 0.779331 | + | 0.626612i | \(0.215559\pi\) |
0.509324 | + | 0.860575i | \(0.329896\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7057.99 | + | 13017.0i | −0.476656 | + | 0.879090i | ||||
\(604\) | 6039.37 | 0.406852 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3651.25 | + | 25395.0i | −0.244151 | + | 1.69811i | 0.386701 | + | 0.922205i | \(0.373615\pi\) |
−0.630852 | + | 0.775903i | \(0.717294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11258.1 | − | 24651.8i | −0.741777 | − | 1.62427i | −0.780609 | − | 0.625020i | \(-0.785091\pi\) |
0.0388314 | − | 0.999246i | \(-0.487636\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20368.5 | − | 5980.73i | −1.32258 | − | 0.388345i | −0.457158 | − | 0.889385i | \(-0.651133\pi\) |
−0.865424 | + | 0.501040i | \(0.832951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3851.14 | + | 1130.80i | −0.247066 | + | 0.0725450i | ||||
\(625\) | 6490.86 | + | 14213.0i | 0.415415 | + | 0.909632i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12845.0 | − | 8254.95i | −0.816193 | − | 0.524536i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8037.52 | − | 12506.6i | −0.507082 | − | 0.789035i | 0.489469 | − | 0.872021i | \(-0.337191\pi\) |
−0.996551 | + | 0.0829861i | \(0.973554\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28476.1i | 1.78803i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 976.779 | + | 846.384i | 0.0607557 | + | 0.0526451i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30133.3 | + | 8847.95i | −1.84812 | + | 0.542658i | −0.848207 | + | 0.529665i | \(0.822318\pi\) |
−0.999916 | + | 0.0129929i | \(0.995864\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14255.4 | + | 12352.4i | 0.858241 | + | 0.743670i | ||||
\(652\) | 3256.23 | − | 22647.6i | 0.195589 | − | 1.36035i | ||||
\(653\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28328.7 | − | 18205.7i | −1.68220 | − | 1.08109i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12404.4 | + | 10748.5i | −0.729918 | + | 0.632477i | −0.938401 | − | 0.345549i | \(-0.887693\pi\) |
0.208483 | + | 0.978026i | \(0.433147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 34507.0i | − | 1.99419i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28258.5 | + | 12905.2i | 1.61855 | + | 0.739168i | 0.998953 | − | 0.0457511i | \(-0.0145681\pi\) |
0.619599 | + | 0.784919i | \(0.287295\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4940.75 | − | 16826.6i | 0.281733 | − | 0.959493i | ||||
\(676\) | 15745.9 | − | 4623.41i | 0.895875 | − | 0.263053i | ||||
\(677\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17900.5 | + | 20658.3i | 1.01172 | + | 1.16759i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(684\) | 5073.97 | − | 35290.2i | 0.283638 | − | 1.97274i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5082.67 | + | 35350.7i | 0.282265 | + | 1.96319i | ||||
\(688\) | −6178.98 | − | 888.403i | −0.342400 | − | 0.0492297i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29873.5 | + | 8771.64i | −1.64463 | + | 0.482907i | −0.967482 | − | 0.252939i | \(-0.918603\pi\) |
−0.677149 | + | 0.735846i | \(0.736785\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15359.5i | 0.829335i | ||||||||
\(701\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15504.6 | − | 17893.3i | 0.831818 | − | 0.959969i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4281.78 | + | 2751.73i | −0.226806 | + | 0.145759i | −0.649109 | − | 0.760695i | \(-0.724858\pi\) |
0.422303 | + | 0.906455i | \(0.361222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37305.6 | + | 5363.73i | −1.96775 | + | 0.282919i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1792.80 | − | 6105.71i | 0.0926037 | − | 0.315379i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28455.4 | + | 4091.26i | 1.46371 | + | 0.210450i | ||||
\(724\) | 11326.9 | + | 7279.37i | 0.581439 | + | 0.373668i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4826.52 | − | 2204.20i | 0.246225 | − | 0.112447i | −0.288480 | − | 0.957486i | \(-0.593150\pi\) |
0.534705 | + | 0.845039i | \(0.320423\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16558.4 | + | 10641.4i | −0.841254 | + | 0.540641i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −22100.2 | − | 6489.22i | −1.11591 | − | 0.327662i | ||||
\(733\) | 35064.1 | + | 5041.46i | 1.76688 | + | 0.254039i | 0.947624 | − | 0.319388i | \(-0.103477\pi\) |
0.819257 | + | 0.573427i | \(0.194386\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20771.7 | − | 17998.8i | 1.03396 | − | 0.895935i | 0.0393130 | − | 0.999227i | \(-0.487483\pi\) |
0.994651 | + | 0.103292i | \(0.0329376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1473.20 | − | 10246.3i | 0.0730356 | − | 0.507973i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4290.09 | − | 29838.2i | 0.208452 | − | 1.44982i | −0.569757 | − | 0.821813i | \(-0.692963\pi\) |
0.778210 | − | 0.628005i | \(-0.216128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11289.2 | − | 13028.4i | 0.543099 | − | 0.626769i | ||||
\(757\) | 7199.08 | + | 3287.71i | 0.345647 | + | 0.157852i | 0.580672 | − | 0.814137i | \(-0.302790\pi\) |
−0.235025 | + | 0.971989i | \(0.575517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4179.37 | + | 29068.2i | 0.198301 | + | 1.37921i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 11506.7 | + | 17904.8i | 0.540641 | + | 0.841254i | ||||
\(769\) | 30181.1 | − | 13783.2i | 1.41529 | − | 0.646342i | 0.446627 | − | 0.894720i | \(-0.352625\pi\) |
0.968663 | + | 0.248378i | \(0.0798977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15657.8 | − | 34285.8i | −0.729970 | − | 1.59841i | ||||
\(773\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 29543.0i | − | 1.36931i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10984.2 | − | 3225.25i | 0.507151 | − | 0.148913i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2847.05 | − | 6234.17i | 0.129694 | − | 0.283991i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30000.7 | − | 4313.45i | 1.35884 | − | 0.195372i | 0.575929 | − | 0.817500i | \(-0.304641\pi\) |
0.782916 | + | 0.622128i | \(0.213731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6416.68 | − | 1884.11i | −0.287343 | − | 0.0843716i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8484.63 | + | 5452.74i | −0.377801 | + | 0.242798i | ||||
\(797\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 22290.6 | + | 4780.14i | 0.977770 | + | 0.209680i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31447.0 | + | 27249.0i | −1.36160 | + | 1.17983i | −0.396470 | + | 0.918048i | \(0.629765\pi\) |
−0.965127 | + | 0.261783i | \(0.915690\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21887.8 | − | 25259.9i | −0.944206 | − | 1.08967i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8704.28 | − | 13544.1i | 0.372735 | − | 0.579987i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3277.74 | − | 3782.72i | 0.139846 | − | 0.161391i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27814.2 | − | 32099.3i | 1.17806 | − | 1.35955i | 0.258786 | − | 0.965935i | \(-0.416677\pi\) |
0.919274 | − | 0.393619i | \(-0.128777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39167.0 | + | 25171.1i | 1.64093 | + | 1.05456i | 0.939915 | + | 0.341408i | \(0.110904\pi\) |
0.701010 | + | 0.713151i | \(0.252733\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11177.2 | − | 38066.2i | −0.466588 | − | 1.58905i | ||||
\(832\) | 3340.91 | + | 5198.55i | 0.139213 | + | 0.216619i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21713.9 | + | 25059.2i | −0.896707 | + | 1.03486i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24389.0 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 42066.0 | − | 12351.7i | 1.71561 | − | 0.503747i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20235.4 | + | 2909.41i | −0.820893 | + | 0.118027i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15142.2 | − | 6915.21i | 0.612107 | − | 0.279540i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4251.34 | − | 29568.7i | 0.170648 | − | 1.18688i | −0.706871 | − | 0.707343i | \(-0.749894\pi\) |
0.877519 | − | 0.479542i | \(-0.159197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40091.5 | + | 25765.2i | 1.59244 | + | 1.02340i | 0.970738 | + | 0.240141i | \(0.0771936\pi\) |
0.621699 | + | 0.783256i | \(0.286443\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25268.9 | − | 3633.11i | −0.989821 | − | 0.142315i | ||||
\(868\) | 12064.1 | − | 26416.6i | 0.471752 | − | 1.03299i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6471.94 | + | 1387.89i | 0.251772 | + | 0.0539917i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36314.6 | + | 31466.8i | −1.40786 | + | 1.21992i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14606.5 | + | 49745.0i | −0.563363 | + | 1.91864i | ||||
\(877\) | −41322.6 | + | 12133.4i | −1.59107 | + | 0.467179i | −0.953043 | − | 0.302836i | \(-0.902066\pi\) |
−0.638025 | + | 0.770016i | \(0.720248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 662.048 | − | 1030.17i | 0.0252318 | − | 0.0392615i | −0.828409 | − | 0.560124i | \(-0.810753\pi\) |
0.853640 | + | 0.520863i | \(0.174390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18459.3 | − | 2654.05i | −0.696406 | − | 0.100128i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −50974.9 | + | 14967.6i | −1.91342 | + | 0.561829i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −27000.0 | −1.00000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7081.16 | − | 3233.86i | 0.260959 | − | 0.119176i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28797.2 | + | 18506.9i | −1.05424 | + | 0.677519i | −0.948469 | − | 0.316871i | \(-0.897368\pi\) |
−0.105772 | + | 0.994390i | \(0.533731\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(912\) | −54332.9 | + | 7811.89i | −1.97274 | + | 0.283638i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 50016.7 | − | 22841.9i | 1.80415 | − | 0.823927i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40941.2 | − | 35475.8i | −1.46956 | − | 1.27338i | −0.887971 | − | 0.459899i | \(-0.847886\pi\) |
−0.581590 | − | 0.813482i | \(-0.697569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15882.7 | + | 2283.59i | −0.568246 | + | 0.0817014i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15083.6 | − | 9693.64i | −0.536158 | − | 0.344568i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10733.0 | + | 3151.51i | 0.380280 | + | 0.111660i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11575.1 | + | 13358.4i | 0.407475 | + | 0.470252i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52886.2i | 1.84388i | 0.387329 | + | 0.921942i | \(0.373398\pi\) | ||||
−0.387329 | + | 0.921942i | \(0.626602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23183.9 | 0.805727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(948\) | 24105.0 | + | 52782.6i | 0.825837 | + | 1.80833i | ||||
\(949\) | −4240.90 | + | 14443.2i | −0.145064 | + | 0.494042i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10828.8 | + | 23711.7i | −0.363492 | + | 0.795936i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6298.91 | − | 43809.9i | −0.210450 | − | 1.46371i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9593.99 | −0.319050 | −0.159525 | − | 0.987194i | \(-0.550996\pi\) | ||||
−0.159525 | + | 0.987194i | \(0.550996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(972\) | 22902.2 | + | 19844.9i | 0.755750 | + | 0.654861i | ||||
\(973\) | −9579.61 | − | 20976.4i | −0.315630 | − | 0.691134i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7839.30 | −0.257496 | ||||||||
\(976\) | 35462.0i | 1.16302i | ||||||||
\(977\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51098.1 | + | 7346.80i | −1.66303 | + | 0.239108i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15775.3 | + | 2268.14i | −0.507973 | + | 0.0730356i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27693.0 | + | 3981.65i | 0.887686 | + | 0.127630i | 0.571048 | − | 0.820917i | \(-0.306537\pi\) |
0.316638 | + | 0.948547i | \(0.397446\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17852.0 | − | 11472.8i | −0.570508 | − | 0.366643i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52903.6 | + | 33999.1i | −1.68052 | + | 1.08000i | −0.813958 | + | 0.580923i | \(0.802692\pi\) |
−0.866557 | + | 0.499078i | \(0.833672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5669.58 | + | 19308.8i | 0.179557 | + | 0.611515i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 201.4.j.a.161.2 | yes | 20 | |
3.2 | odd | 2 | CM | 201.4.j.a.161.2 | yes | 20 | |
67.5 | odd | 22 | inner | 201.4.j.a.5.2 | ✓ | 20 | |
201.5 | even | 22 | inner | 201.4.j.a.5.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.4.j.a.5.2 | ✓ | 20 | 67.5 | odd | 22 | inner | |
201.4.j.a.5.2 | ✓ | 20 | 201.5 | even | 22 | inner | |
201.4.j.a.161.2 | yes | 20 | 1.1 | even | 1 | trivial | |
201.4.j.a.161.2 | yes | 20 | 3.2 | odd | 2 | CM |