Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(129,392)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.129");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.o (of order \(6\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 129.3 | ||
Root | \(1.60021 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.129 |
Dual form | 392.3.o.b.313.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 1.32565 | + | 0.765367i | 0.441885 | + | 0.255122i | 0.704397 | − | 0.709806i | \(-0.251218\pi\) |
−0.262512 | + | 0.964929i | \(0.584551\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.72648 | + | 4.46088i | −1.54530 | + | 0.892177i | −0.546805 | + | 0.837260i | \(0.684156\pi\) |
−0.998491 | + | 0.0549170i | \(0.982511\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.32843 | − | 5.76500i | −0.369825 | − | 0.640556i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.65685 | − | 8.06591i | 0.423350 | − | 0.733264i | −0.572914 | − | 0.819615i | \(-0.694187\pi\) |
0.996265 | + | 0.0863508i | \(0.0275206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.262632i | 0.0202025i | 0.999949 | + | 0.0101012i | \(0.00321538\pi\) | ||||
−0.999949 | + | 0.0101012i | \(0.996785\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.6569 | −0.910457 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.8017 | − | 7.39104i | −0.753038 | − | 0.434767i | 0.0737524 | − | 0.997277i | \(-0.476503\pi\) |
−0.826791 | + | 0.562510i | \(0.809836\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22.0812 | − | 12.7486i | 1.16217 | − | 0.670979i | 0.210347 | − | 0.977627i | \(-0.432541\pi\) |
0.951823 | + | 0.306648i | \(0.0992073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.31371 | − | 14.3998i | −0.361466 | − | 0.626077i | 0.626737 | − | 0.779231i | \(-0.284390\pi\) |
−0.988202 | + | 0.153154i | \(0.951057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 27.2990 | − | 47.2832i | 1.09196 | − | 1.89133i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 23.9665i | − | 0.887647i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.6863 | 0.506424 | 0.253212 | − | 0.967411i | \(-0.418513\pi\) | ||||
0.253212 | + | 0.967411i | \(0.418513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.49903 | + | 4.32957i | 0.241904 | + | 0.139664i | 0.616052 | − | 0.787706i | \(-0.288731\pi\) |
−0.374147 | + | 0.927369i | \(0.622065\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.3468 | − | 7.12840i | 0.374144 | − | 0.216012i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −21.9706 | − | 38.0541i | −0.593799 | − | 1.02849i | −0.993715 | − | 0.111938i | \(-0.964294\pi\) |
0.399916 | − | 0.916552i | \(-0.369039\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.201010 | + | 0.348160i | −0.00515411 | + | 0.00892717i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.9159i | 0.558925i | 0.960157 | + | 0.279463i | \(0.0901563\pi\) | ||||
−0.960157 | + | 0.279463i | \(0.909844\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −46.0000 | −1.06977 | −0.534884 | − | 0.844926i | \(-0.679645\pi\) | ||||
−0.534884 | + | 0.844926i | \(0.679645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 51.4340 | + | 29.6955i | 1.14298 | + | 0.659899i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −74.6135 | + | 43.0781i | −1.58752 | + | 0.916556i | −0.593807 | + | 0.804608i | \(0.702376\pi\) |
−0.993714 | + | 0.111948i | \(0.964291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.3137 | − | 19.5959i | −0.221837 | − | 0.384234i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30.3137 | − | 52.5049i | 0.571957 | − | 0.990658i | −0.424408 | − | 0.905471i | \(-0.639518\pi\) |
0.996365 | − | 0.0851872i | \(-0.0271488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 83.0948i | 1.51081i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 39.0294 | 0.684727 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −50.3358 | − | 29.0614i | −0.853150 | − | 0.492566i | 0.00856255 | − | 0.999963i | \(-0.497274\pi\) |
−0.861712 | + | 0.507397i | \(0.830608\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.63626 | − | 4.98615i | 0.141578 | − | 0.0817402i | −0.427538 | − | 0.903997i | \(-0.640619\pi\) |
0.569116 | + | 0.822257i | \(0.307286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.17157 | − | 2.02922i | −0.0180242 | − | 0.0312188i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3137 | − | 17.8639i | 0.153936 | − | 0.266625i | −0.778735 | − | 0.627353i | \(-0.784138\pi\) |
0.932671 | + | 0.360728i | \(0.117472\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 25.4521i | − | 0.368872i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −78.9706 | −1.11226 | −0.556131 | − | 0.831095i | \(-0.687715\pi\) | ||||
−0.556131 | + | 0.831095i | \(0.687715\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18.5592 | − | 10.7151i | −0.254235 | − | 0.146783i | 0.367467 | − | 0.930037i | \(-0.380225\pi\) |
−0.621702 | + | 0.783254i | \(0.713558\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 72.3780 | − | 41.7875i | 0.965041 | − | 0.557166i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 45.1421 | + | 78.1885i | 0.571419 | + | 0.989727i | 0.996421 | + | 0.0845347i | \(0.0269404\pi\) |
−0.425001 | + | 0.905193i | \(0.639726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.6127 | + | 20.1138i | −0.143367 | + | 0.248318i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 71.8544i | − | 0.865715i | −0.901462 | − | 0.432858i | \(-0.857505\pi\) | ||
0.901462 | − | 0.432858i | \(-0.142495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 131.882 | 1.55156 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.4689 | + | 11.2404i | 0.223781 | + | 0.129200i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.74152 | + | 1.00547i | −0.0195677 | + | 0.0112974i | −0.509752 | − | 0.860321i | \(-0.670263\pi\) |
0.490184 | + | 0.871619i | \(0.336929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.62742 | + | 11.4790i | 0.0712625 | + | 0.123430i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −113.740 | + | 197.004i | −1.19726 | + | 2.07372i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 158.581i | − | 1.63485i | −0.576032 | − | 0.817427i | \(-0.695399\pi\) | ||
0.576032 | − | 0.817427i | \(-0.304601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −62.0000 | −0.626263 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −80.9753 | − | 46.7511i | −0.801736 | − | 0.462882i | 0.0423421 | − | 0.999103i | \(-0.486518\pi\) |
−0.844078 | + | 0.536221i | \(0.819851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.6494 | − | 10.1899i | 0.171353 | − | 0.0989308i | −0.411871 | − | 0.911242i | \(-0.635124\pi\) |
0.583224 | + | 0.812312i | \(0.301791\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.05887 | − | 12.2263i | −0.0659708 | − | 0.114265i | 0.831153 | − | 0.556043i | \(-0.187681\pi\) |
−0.897124 | + | 0.441778i | \(0.854348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.6274 | + | 20.1393i | −0.106674 | + | 0.184764i | −0.914421 | − | 0.404765i | \(-0.867353\pi\) |
0.807747 | + | 0.589529i | \(0.200687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 67.2622i | − | 0.605965i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.7157 | 0.121378 | 0.0606891 | − | 0.998157i | \(-0.480670\pi\) | ||||
0.0606891 | + | 0.998157i | \(0.480670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 128.471 | + | 74.1730i | 1.11714 | + | 0.644983i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.51408 | − | 0.874153i | 0.0129408 | − | 0.00747139i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.1274 | + | 29.6656i | 0.141549 | + | 0.245170i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.5391 | + | 30.3786i | −0.142594 | + | 0.246981i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 264.066i | 2.11253i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 177.765 | 1.39972 | 0.699860 | − | 0.714280i | \(-0.253246\pi\) | ||||
0.699860 | + | 0.714280i | \(0.253246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −60.9801 | − | 35.2069i | −0.472714 | − | 0.272922i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −97.5265 | + | 56.3069i | −0.744477 | + | 0.429824i | −0.823695 | − | 0.567033i | \(-0.808091\pi\) |
0.0792180 | + | 0.996857i | \(0.474758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 106.912 | + | 185.176i | 0.791938 | + | 1.37168i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −60.8823 | + | 105.451i | −0.444396 | + | 0.769716i | −0.998010 | − | 0.0630570i | \(-0.979915\pi\) |
0.553614 | + | 0.832773i | \(0.313248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 175.329i | 1.26136i | 0.776043 | + | 0.630679i | \(0.217224\pi\) | ||||
−0.776043 | + | 0.630679i | \(0.782776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −131.882 | −0.935335 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.11837 | + | 1.22304i | 0.0148138 | + | 0.00855273i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −113.473 | + | 65.5139i | −0.782575 | + | 0.451820i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 118.882 | + | 205.910i | 0.797867 | + | 1.38195i | 0.921002 | + | 0.389557i | \(0.127372\pi\) |
−0.123135 | + | 0.992390i | \(0.539295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −49.6863 | + | 86.0592i | −0.329048 | + | 0.569928i | −0.982323 | − | 0.187192i | \(-0.940061\pi\) |
0.653275 | + | 0.757121i | \(0.273395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 98.4021i | 0.643151i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −77.2548 | −0.498418 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 83.7046 | + | 48.3269i | 0.533151 | + | 0.307815i | 0.742298 | − | 0.670069i | \(-0.233736\pi\) |
−0.209148 | + | 0.977884i | \(0.567069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 80.3710 | − | 46.4022i | 0.505478 | − | 0.291838i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −85.2843 | − | 147.717i | −0.523216 | − | 0.906237i | −0.999635 | − | 0.0270188i | \(-0.991399\pi\) |
0.476419 | − | 0.879219i | \(-0.341935\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −63.5980 | + | 110.155i | −0.385442 | + | 0.667606i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 94.9055i | − | 0.568296i | −0.958780 | − | 0.284148i | \(-0.908289\pi\) | ||
0.958780 | − | 0.284148i | \(-0.0917108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.931 | 0.999592 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −146.992 | − | 84.8656i | −0.859600 | − | 0.496290i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 158.240 | − | 91.3600i | 0.914683 | − | 0.528092i | 0.0327478 | − | 0.999464i | \(-0.489574\pi\) |
0.881935 | + | 0.471371i | \(0.156241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −44.4853 | − | 77.0508i | −0.251329 | − | 0.435315i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 102.029 | − | 176.720i | 0.569997 | − | 0.987264i | −0.426569 | − | 0.904455i | \(-0.640278\pi\) |
0.996565 | − | 0.0828083i | \(-0.0263889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 229.167i | − | 1.26612i | −0.774104 | − | 0.633059i | \(-0.781799\pi\) | ||
0.774104 | − | 0.633059i | \(-0.218201\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.2649 | 0.0834149 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 339.510 | + | 196.016i | 1.83519 | + | 1.05955i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −119.231 | + | 68.8380i | −0.637598 | + | 0.368117i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.79899 | − | 8.31209i | −0.0251256 | − | 0.0435188i | 0.853189 | − | 0.521602i | \(-0.174665\pi\) |
−0.878315 | + | 0.478083i | \(0.841332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.71068 | − | 2.96298i | 0.00886362 | − | 0.0153522i | −0.861560 | − | 0.507656i | \(-0.830512\pi\) |
0.870423 | + | 0.492304i | \(0.163845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.58673i | − | 0.0183935i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −146.451 | −0.743405 | −0.371703 | − | 0.928352i | \(-0.621226\pi\) | ||||
−0.371703 | + | 0.928352i | \(0.621226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −211.871 | − | 122.324i | −1.06468 | − | 0.614691i | −0.137954 | − | 0.990439i | \(-0.544053\pi\) |
−0.926722 | + | 0.375748i | \(0.877386\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.3448 | − | 15.7875i | 0.136044 | − | 0.0785450i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −102.225 | − | 177.060i | −0.498660 | − | 0.863705i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −55.3431 | + | 95.8571i | −0.267358 | + | 0.463078i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 237.474i | − | 1.13624i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 311.019 | 1.47403 | 0.737013 | − | 0.675879i | \(-0.236236\pi\) | ||||
0.737013 | + | 0.675879i | \(0.236236\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −104.688 | − | 60.4415i | −0.491491 | − | 0.283763i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 355.418 | − | 205.201i | 1.65311 | − | 0.954422i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.4020 | − | 28.4091i | −0.0748951 | − | 0.129722i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.94113 | − | 3.36213i | 0.00878337 | − | 0.0152132i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 116.156i | − | 0.520877i | −0.965490 | − | 0.260438i | \(-0.916133\pi\) | ||
0.965490 | − | 0.260438i | \(-0.0838671\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −363.451 | −1.61534 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 51.2456 | + | 29.5867i | 0.225752 | + | 0.130338i | 0.608611 | − | 0.793469i | \(-0.291727\pi\) |
−0.382859 | + | 0.923807i | \(0.625060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −111.426 | + | 64.3320i | −0.486578 | + | 0.280926i | −0.723154 | − | 0.690687i | \(-0.757308\pi\) |
0.236576 | + | 0.971613i | \(0.423975\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 44.4903 | + | 77.0595i | 0.190946 | + | 0.330728i | 0.945564 | − | 0.325437i | \(-0.105511\pi\) |
−0.754618 | + | 0.656164i | \(0.772178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 384.333 | − | 665.684i | 1.63546 | − | 2.83270i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 138.201i | 0.583127i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.13708 | −0.0298623 | −0.0149311 | − | 0.999889i | \(-0.504753\pi\) | ||||
−0.0149311 | + | 0.999889i | \(0.504753\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −318.222 | − | 183.725i | −1.32042 | − | 0.762346i | −0.336626 | − | 0.941638i | \(-0.609286\pi\) |
−0.983796 | + | 0.179292i | \(0.942619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −217.589 | + | 125.625i | −0.895428 | + | 0.516976i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.34820 | + | 5.79925i | 0.0135555 | + | 0.0234787i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 54.9949 | − | 95.2540i | 0.220863 | − | 0.382546i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 176.995i | 0.705159i | 0.935782 | + | 0.352579i | \(0.114695\pi\) | ||||
−0.935782 | + | 0.352579i | \(0.885305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −154.863 | −0.612106 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 174.830 | + | 100.938i | 0.685609 | + | 0.395836i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.7837 | + | 13.7315i | −0.0925437 | + | 0.0534301i | −0.545558 | − | 0.838073i | \(-0.683682\pi\) |
0.453014 | + | 0.891503i | \(0.350349\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −48.8823 | − | 84.6665i | −0.187288 | − | 0.324393i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −38.5736 | + | 66.8114i | −0.146668 | + | 0.254036i | −0.929994 | − | 0.367575i | \(-0.880188\pi\) |
0.783326 | + | 0.621611i | \(0.213521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 540.904i | 2.04115i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.07821 | −0.0115289 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.7687 | + | 17.1870i | 0.110664 | + | 0.0638920i | 0.554311 | − | 0.832310i | \(-0.312982\pi\) |
−0.443646 | + | 0.896202i | \(0.646315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −175.740 | + | 101.464i | −0.648487 | + | 0.374404i | −0.787876 | − | 0.615833i | \(-0.788819\pi\) |
0.139389 | + | 0.990238i | \(0.455486\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −254.255 | − | 440.382i | −0.924563 | − | 1.60139i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 127.049 | − | 220.055i | 0.458660 | − | 0.794422i | −0.540231 | − | 0.841517i | \(-0.681663\pi\) |
0.998890 | + | 0.0470949i | \(0.0149963\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 57.6426i | − | 0.206604i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −221.529 | −0.788359 | −0.394180 | − | 0.919033i | \(-0.628971\pi\) | ||||
−0.394180 | + | 0.919033i | \(0.628971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 245.766 | + | 141.893i | 0.868430 | + | 0.501388i | 0.866826 | − | 0.498611i | \(-0.166156\pi\) |
0.00160358 | + | 0.999999i | \(0.499490\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −301.560 | + | 174.106i | −1.05811 | + | 0.610898i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −35.2452 | − | 61.0464i | −0.121956 | − | 0.211233i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 121.373 | − | 210.223i | 0.417088 | − | 0.722417i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 398.073i | − | 1.35861i | −0.733855 | − | 0.679306i | \(-0.762281\pi\) | ||
0.733855 | − | 0.679306i | \(-0.237719\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 518.558 | 1.75783 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −193.311 | − | 111.608i | −0.650880 | − | 0.375786i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.78184 | − | 2.18345i | 0.0126483 | − | 0.00730251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −71.5635 | − | 123.952i | −0.236183 | − | 0.409081i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −44.4853 | + | 77.0508i | −0.145853 | + | 0.252625i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 167.720i | − | 0.546320i | −0.961969 | − | 0.273160i | \(-0.911931\pi\) | ||
0.961969 | − | 0.273160i | \(-0.0880689\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.1960 | 0.100958 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 246.039 | + | 142.051i | 0.791121 | + | 0.456754i | 0.840357 | − | 0.542033i | \(-0.182345\pi\) |
−0.0492358 | + | 0.998787i | \(0.515679\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 445.406 | − | 257.156i | 1.42302 | − | 0.821583i | 0.426468 | − | 0.904503i | \(-0.359758\pi\) |
0.996556 | + | 0.0829197i | \(0.0264245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.28427 | − | 16.0808i | −0.0292879 | − | 0.0507282i | 0.851010 | − | 0.525150i | \(-0.175991\pi\) |
−0.880298 | + | 0.474421i | \(0.842657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 68.3919 | − | 118.458i | 0.214395 | − | 0.371343i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 21.6105i | − | 0.0673225i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −376.902 | −1.16688 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.4181 | + | 7.16960i | 0.0382096 | + | 0.0220603i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −30.8279 | + | 17.7985i | −0.0942748 | + | 0.0544296i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −97.1665 | − | 168.297i | −0.293554 | − | 0.508451i | 0.681093 | − | 0.732197i | \(-0.261505\pi\) |
−0.974648 | + | 0.223746i | \(0.928172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −146.255 | + | 253.321i | −0.439204 | + | 0.760723i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 184.033i | 0.549352i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −125.265 | −0.371706 | −0.185853 | − | 0.982578i | \(-0.559505\pi\) | ||||
−0.185853 | + | 0.982578i | \(0.559505\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.1823 | + | 10.4976i | 0.0536351 | + | 0.0309663i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 69.8438 | − | 40.3243i | 0.204821 | − | 0.118253i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 113.539 | + | 196.655i | 0.329099 | + | 0.570016i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 80.3726 | − | 139.209i | 0.231621 | − | 0.401180i | −0.726664 | − | 0.686993i | \(-0.758930\pi\) |
0.958285 | + | 0.285813i | \(0.0922637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 93.0671i | − | 0.266668i | −0.991071 | − | 0.133334i | \(-0.957432\pi\) | ||
0.991071 | − | 0.133334i | \(-0.0425683\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.29437 | 0.0179327 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 164.225 | + | 94.8154i | 0.465227 | + | 0.268599i | 0.714239 | − | 0.699901i | \(-0.246773\pi\) |
−0.249013 | + | 0.968500i | \(0.580106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 610.164 | − | 352.279i | 1.71877 | − | 0.992334i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 247.215 | + | 428.189i | 0.688622 | + | 1.19273i | 0.972284 | + | 0.233804i | \(0.0751174\pi\) |
−0.283662 | + | 0.958924i | \(0.591549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 144.554 | − | 250.375i | 0.400426 | − | 0.693558i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 52.4350i | 0.144449i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 191.196 | 0.523825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −622.667 | − | 359.497i | −1.69664 | − | 0.979556i | −0.948906 | − | 0.315559i | \(-0.897808\pi\) |
−0.747735 | − | 0.663997i | \(-0.768859\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 132.111 | − | 76.2741i | 0.358023 | − | 0.206705i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −66.4214 | − | 115.045i | −0.178073 | − | 0.308432i | 0.763147 | − | 0.646225i | \(-0.223653\pi\) |
−0.941221 | + | 0.337793i | \(0.890320\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −202.108 | + | 350.061i | −0.538954 | + | 0.933495i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.85710i | 0.0102310i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 324.607 | 0.856483 | 0.428242 | − | 0.903664i | \(-0.359133\pi\) | ||||
0.428242 | + | 0.903664i | \(0.359133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 235.654 | + | 136.055i | 0.618515 | + | 0.357100i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −338.835 | + | 195.626i | −0.884686 | + | 0.510773i | −0.872200 | − | 0.489149i | \(-0.837308\pi\) |
−0.0124851 | + | 0.999922i | \(0.503974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 153.108 | + | 265.190i | 0.395627 | + | 0.685246i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −111.676 | + | 193.429i | −0.287085 | + | 0.497246i | −0.973113 | − | 0.230329i | \(-0.926020\pi\) |
0.686027 | + | 0.727576i | \(0.259353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 245.788i | 0.628613i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −172.382 | −0.438631 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −697.580 | − | 402.748i | −1.76602 | − | 1.01961i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 193.162 | − | 111.522i | 0.486554 | − | 0.280912i | −0.236590 | − | 0.971610i | \(-0.576030\pi\) |
0.723144 | + | 0.690698i | \(0.242696\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −68.1127 | − | 117.975i | −0.169857 | − | 0.294201i | 0.768512 | − | 0.639835i | \(-0.220997\pi\) |
−0.938369 | + | 0.345634i | \(0.887664\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.13708 | + | 1.96949i | −0.00282155 | + | 0.00488707i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 207.212i | − | 0.511634i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −409.255 | −1.00554 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 581.611 | + | 335.793i | 1.42203 | + | 0.821010i | 0.996472 | − | 0.0839200i | \(-0.0267440\pi\) |
0.425559 | + | 0.904931i | \(0.360077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −161.418 | + | 93.1945i | −0.392744 | + | 0.226751i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 320.534 | + | 555.181i | 0.772371 | + | 1.33779i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −134.191 | + | 232.425i | −0.321801 | + | 0.557375i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10.8053i | − | 0.0257882i | −0.999917 | − | 0.0128941i | \(-0.995896\pi\) | ||
0.999917 | − | 0.0128941i | \(-0.00410443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 421.647 | 1.00154 | 0.500768 | − | 0.865581i | \(-0.333051\pi\) | ||||
0.500768 | + | 0.865581i | \(0.333051\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 496.691 | + | 286.765i | 1.17421 | + | 0.677931i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −698.944 | + | 403.536i | −1.64457 | + | 0.949496i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.87215 | + | 3.24266i | 0.00436399 | + | 0.00755864i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −396.765 | + | 687.216i | −0.920567 | + | 1.59447i | −0.122028 | + | 0.992527i | \(0.538940\pi\) |
−0.798539 | + | 0.601943i | \(0.794394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 254.627i | 0.588053i | 0.955797 | + | 0.294027i | \(0.0949954\pi\) | ||||
−0.955797 | + | 0.294027i | \(0.905005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −200.569 | −0.461077 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −367.154 | − | 211.976i | −0.840169 | − | 0.485072i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −727.043 | + | 419.758i | −1.65613 | + | 0.956169i | −0.681660 | + | 0.731669i | \(0.738742\pi\) |
−0.974474 | + | 0.224500i | \(0.927925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −387.108 | − | 670.490i | −0.873832 | − | 1.51352i | −0.858002 | − | 0.513647i | \(-0.828294\pi\) |
−0.0158306 | − | 0.999875i | \(-0.505039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.97056 | − | 15.5375i | 0.0201586 | − | 0.0349157i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 363.954i | 0.814215i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 751.921 | 1.67466 | 0.837328 | − | 0.546700i | \(-0.184116\pi\) | ||||
0.837328 | + | 0.546700i | \(0.184116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 184.838 | + | 106.716i | 0.409840 | + | 0.236621i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −131.734 | + | 76.0565i | −0.290803 | + | 0.167895i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 125.995 | + | 218.230i | 0.275700 | + | 0.477527i | 0.970312 | − | 0.241859i | \(-0.0777570\pi\) |
−0.694611 | + | 0.719385i | \(0.744424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −177.137 | + | 306.810i | −0.385920 | + | 0.668432i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 93.4121i | 0.202629i | 0.994854 | + | 0.101315i | \(0.0323049\pi\) | ||||
−0.994854 | + | 0.101315i | \(0.967695\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 167.990 | 0.362829 | 0.181415 | − | 0.983407i | \(-0.441932\pi\) | ||||
0.181415 | + | 0.983407i | \(0.441932\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −102.413 | − | 59.1283i | −0.220243 | − | 0.127158i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 315.389 | − | 182.090i | 0.675350 | − | 0.389914i | −0.122750 | − | 0.992438i | \(-0.539171\pi\) |
0.798101 | + | 0.602524i | \(0.205838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 73.9756 | + | 128.130i | 0.157061 | + | 0.272037i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −214.215 | + | 371.032i | −0.452886 | + | 0.784422i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1392.10i | − | 2.93073i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −403.588 | −0.846096 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 118.698 | + | 68.5303i | 0.247804 | + | 0.143069i | 0.618758 | − | 0.785582i | \(-0.287636\pi\) |
−0.370955 | + | 0.928651i | \(0.620969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.99425 | − | 5.77018i | 0.0207781 | − | 0.0119962i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 707.411 | + | 1225.27i | 1.45858 | + | 2.52633i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −278.706 | + | 482.732i | −0.572291 | + | 0.991237i | 0.424039 | + | 0.905644i | \(0.360612\pi\) |
−0.996330 | + | 0.0855930i | \(0.972722\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 261.095i | − | 0.533937i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −537.647 | −1.09500 | −0.547502 | − | 0.836805i | \(-0.684421\pi\) | ||||
−0.547502 | + | 0.836805i | \(0.684421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −188.009 | − | 108.547i | −0.381357 | − | 0.220176i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 479.042 | − | 276.575i | 0.967761 | − | 0.558737i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 316.990 | + | 549.043i | 0.635250 | + | 1.10029i | 0.986462 | + | 0.163990i | \(0.0524364\pi\) |
−0.351212 | + | 0.936296i | \(0.614230\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 72.6375 | − | 125.812i | 0.144985 | − | 0.251122i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 91.1385i | − | 0.181190i | −0.995888 | − | 0.0905949i | \(-0.971123\pi\) | ||
0.995888 | − | 0.0905949i | \(-0.0288769\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 834.205 | 1.65189 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 223.944 | + | 129.294i | 0.441704 | + | 0.255018i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 306.024 | − | 176.683i | 0.601227 | − | 0.347118i | −0.168297 | − | 0.985736i | \(-0.553827\pi\) |
0.769524 | + | 0.638618i | \(0.220494\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −305.539 | − | 529.209i | −0.595593 | − | 1.03160i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −90.9117 | + | 157.464i | −0.176528 | + | 0.305755i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 802.434i | 1.55210i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 279.696 | 0.538912 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −821.892 | − | 474.520i | −1.57753 | − | 0.910786i | −0.995203 | − | 0.0978305i | \(-0.968810\pi\) |
−0.582325 | − | 0.812956i | \(-0.697857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 573.917 | − | 331.351i | 1.09736 | − | 0.633558i | 0.161830 | − | 0.986819i | \(-0.448260\pi\) |
0.935525 | + | 0.353260i | \(0.114927\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −64.0000 | − | 110.851i | −0.121442 | − | 0.210344i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 126.265 | − | 218.697i | 0.238685 | − | 0.413415i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 386.915i | 0.728654i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.01847 | −0.0112917 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 109.080 | + | 62.9777i | 0.203889 | + | 0.117715i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 270.512 | − | 156.180i | 0.503746 | − | 0.290838i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −513.451 | − | 889.323i | −0.949077 | − | 1.64385i | −0.747374 | − | 0.664403i | \(-0.768686\pi\) |
−0.201703 | − | 0.979447i | \(-0.564648\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 175.397 | − | 303.796i | 0.323015 | − | 0.559478i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 207.474i | − | 0.380687i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −258.686 | −0.472918 | −0.236459 | − | 0.971641i | \(-0.575987\pi\) | ||||
−0.236459 | + | 0.971641i | \(0.575987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −57.4904 | − | 33.1921i | −0.104718 | − | 0.0604591i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 324.291 | − | 187.230i | 0.588551 | − | 0.339800i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 300.049 | + | 519.700i | 0.540628 | + | 0.936396i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 370.765 | − | 642.183i | 0.665645 | − | 1.15293i | −0.313464 | − | 0.949600i | \(-0.601490\pi\) |
0.979110 | − | 0.203332i | \(-0.0651770\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.0811i | − | 0.0216120i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −210.745 | −0.375660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 69.7267 | + | 40.2568i | 0.123849 | + | 0.0715040i | 0.560644 | − | 0.828057i | \(-0.310553\pi\) |
−0.436796 | + | 0.899561i | \(0.643887\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −105.974 | + | 61.1843i | −0.187565 | + | 0.108291i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 371.485 | + | 643.431i | 0.652874 | + | 1.13081i | 0.982422 | + | 0.186672i | \(0.0597702\pi\) |
−0.329548 | + | 0.944139i | \(0.606896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −298.941 | + | 517.781i | −0.523540 | + | 0.906797i | 0.476085 | + | 0.879399i | \(0.342055\pi\) |
−0.999625 | + | 0.0273980i | \(0.991278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 14.6920i | − | 0.0256404i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −907.823 | −1.57882 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 719.466 | + | 415.384i | 1.24691 | + | 0.719902i | 0.970491 | − | 0.241136i | \(-0.0775199\pi\) |
0.276416 | + | 0.961038i | \(0.410853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.53554 | − | 2.61859i | 0.00783339 | − | 0.00452261i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −282.333 | − | 489.015i | −0.484276 | − | 0.838791i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.79899 | + | 13.5082i | −0.0133316 | + | 0.0230910i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 700.310i | 1.19303i | 0.802601 | + | 0.596516i | \(0.203449\pi\) | ||||
−0.802601 | + | 0.596516i | \(0.796551\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 220.784 | 0.374845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −194.143 | − | 112.089i | −0.328499 | − | 0.189659i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −361.176 | + | 208.525i | −0.609065 | + | 0.351644i | −0.772599 | − | 0.634894i | \(-0.781044\pi\) |
0.163534 | + | 0.986538i | \(0.447711\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −187.245 | − | 324.317i | −0.313643 | − | 0.543245i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −111.946 | + | 193.896i | −0.186888 | + | 0.323700i | −0.944211 | − | 0.329340i | \(-0.893174\pi\) |
0.757323 | + | 0.653041i | \(0.226507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 721.185i | − | 1.19998i | −0.800009 | − | 0.599988i | \(-0.795172\pi\) | ||
0.800009 | − | 0.599988i | \(-0.204828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −137.314 | −0.227718 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −264.669 | − | 152.807i | −0.437470 | − | 0.252573i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −277.556 | + | 160.247i | −0.457258 | + | 0.263998i | −0.710891 | − | 0.703303i | \(-0.751708\pi\) |
0.253633 | + | 0.967301i | \(0.418375\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.3137 | − | 19.5959i | −0.0185167 | − | 0.0320719i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −97.6863 | + | 169.198i | −0.159358 | + | 0.276016i | −0.934637 | − | 0.355603i | \(-0.884276\pi\) |
0.775280 | + | 0.631618i | \(0.217609\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 312.960i | − | 0.508878i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 838.284 | 1.35865 | 0.679323 | − | 0.733840i | \(-0.262274\pi\) | ||||
0.679323 | + | 0.733840i | \(0.262274\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 446.355 | + | 257.703i | 0.721091 | + | 0.416322i | 0.815154 | − | 0.579244i | \(-0.196652\pi\) |
−0.0940632 | + | 0.995566i | \(0.529986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −345.112 | + | 199.250i | −0.555735 | + | 0.320854i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −495.495 | − | 858.222i | −0.792792 | − | 1.37316i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 181.754 | − | 314.808i | 0.289879 | − | 0.502086i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 649.541i | 1.03266i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −392.538 | −0.622089 | −0.311045 | − | 0.950395i | \(-0.600679\pi\) | ||||
−0.311045 | + | 0.950395i | \(0.600679\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 412.304 | + | 238.044i | 0.651349 | + | 0.376057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1373.49 | + | 792.987i | −2.16298 | + | 1.24880i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 262.848 | + | 455.266i | 0.411342 | + | 0.712466i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 406.730 | − | 704.477i | 0.634524 | − | 1.09903i | −0.352092 | − | 0.935966i | \(-0.614529\pi\) |
0.986616 | − | 0.163063i | \(-0.0521372\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 906.299i | 1.40948i | 0.709463 | + | 0.704742i | \(0.248937\pi\) | ||||
−0.709463 | + | 0.704742i | \(0.751063\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 628.215 | 0.973977 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 99.0082 | + | 57.1624i | 0.153027 | + | 0.0883499i | 0.574558 | − | 0.818464i | \(-0.305174\pi\) |
−0.421531 | + | 0.906814i | \(0.638507\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −468.813 | + | 270.670i | −0.722363 | + | 0.417056i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −207.843 | − | 359.994i | −0.318289 | − | 0.551293i | 0.661842 | − | 0.749643i | \(-0.269775\pi\) |
−0.980131 | + | 0.198351i | \(0.936442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 502.357 | − | 870.109i | 0.766958 | − | 1.32841i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 142.658i | 0.217136i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 650.431 | 0.986996 | 0.493498 | − | 0.869747i | \(-0.335718\pi\) | ||||
0.493498 | + | 0.869747i | \(0.335718\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 886.648 | + | 511.906i | 1.34137 | + | 0.774442i | 0.987009 | − | 0.160666i | \(-0.0513640\pi\) |
0.354364 | + | 0.935108i | \(0.384697\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.14652 | − | 2.97135i | 0.00776248 | − | 0.00448167i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −122.098 | − | 211.479i | −0.183055 | − | 0.317060i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 88.9016 | − | 153.982i | 0.132887 | − | 0.230168i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 92.8791i | − | 0.138419i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1187.21 | −1.76406 | −0.882032 | − | 0.471190i | \(-0.843824\pi\) | ||||
−0.882032 | + | 0.471190i | \(0.843824\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1133.21 | − | 654.261i | −1.67883 | − | 0.969275i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 784.468 | − | 452.913i | 1.15874 | − | 0.669000i | 0.207740 | − | 0.978184i | \(-0.433389\pi\) |
0.951002 | + | 0.309184i | \(0.100056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.2893 | + | 78.4434i | 0.0665041 | + | 0.115189i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 157.627 | − | 273.019i | 0.230787 | − | 0.399735i | −0.727253 | − | 0.686369i | \(-0.759203\pi\) |
0.958040 | + | 0.286635i | \(0.0925367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1086.35i | − | 1.58592i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −196.950 | −0.286682 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.7895 | + | 7.96136i | 0.0200138 | + | 0.0115550i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −290.084 | + | 167.480i | −0.419803 | + | 0.242374i | −0.694993 | − | 0.719016i | \(-0.744593\pi\) |
0.275190 | + | 0.961390i | \(0.411259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −782.122 | − | 1354.67i | −1.12536 | − | 1.94917i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 169.373 | − | 293.362i | 0.243002 | − | 0.420892i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 136.206i | 0.194858i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −362.353 | −0.516909 | −0.258455 | − | 0.966023i | \(-0.583213\pi\) | ||||
−0.258455 | + | 0.966023i | \(0.583213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −970.274 | − | 560.188i | −1.38019 | − | 0.796854i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1018.99 | − | 588.312i | 1.44537 | − | 0.834484i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 558.980 | + | 968.181i | 0.788406 | + | 1.36556i | 0.926943 | + | 0.375202i | \(0.122427\pi\) |
−0.138537 | + | 0.990357i | \(0.544240\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 300.505 | − | 520.489i | 0.422651 | − | 0.732052i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 143.979i | − | 0.201934i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.8234 | −0.0305222 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.46131 | − | 5.46249i | −0.0131957 | − | 0.00761853i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 842.271 | − | 486.285i | 1.17145 | − | 0.676336i | 0.217427 | − | 0.976077i | \(-0.430234\pi\) |
0.954021 | + | 0.299741i | \(0.0969002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −281.235 | − | 487.113i | −0.388983 | − | 0.673738i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 400.921 | − | 694.415i | 0.552994 | − | 0.957814i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 660.646i | − | 0.908729i | −0.890816 | − | 0.454365i | \(-0.849866\pi\) | ||
0.890816 | − | 0.454365i | \(-0.150134\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −175.569 | −0.240835 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 588.876 | + | 339.988i | 0.805576 | + | 0.465099i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 223.626 | − | 129.111i | 0.305084 | − | 0.176140i | −0.339641 | − | 0.940555i | \(-0.610305\pi\) |
0.644724 | + | 0.764415i | \(0.276972\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −96.0589 | − | 166.379i | −0.130338 | − | 0.225751i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 166.696 | − | 288.725i | 0.225569 | − | 0.390697i | −0.730921 | − | 0.682462i | \(-0.760909\pi\) |
0.956490 | + | 0.291765i | \(0.0942425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.2504i | 0.0138332i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −610.118 | −0.821154 | −0.410577 | − | 0.911826i | \(-0.634673\pi\) | ||||
−0.410577 | + | 0.911826i | \(0.634673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1837.08 | − | 1060.64i | −2.46588 | − | 1.42368i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −414.241 | + | 239.162i | −0.554539 | + | 0.320163i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.05887 | + | 15.6904i | 0.0120624 | + | 0.0208927i | 0.871994 | − | 0.489517i | \(-0.162827\pi\) |
−0.859931 | + | 0.510410i | \(0.829494\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −135.466 | + | 234.634i | −0.179902 | + | 0.311599i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 886.579i | − | 1.17428i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 107.137 | 0.141529 | 0.0707643 | − | 0.997493i | \(-0.477456\pi\) | ||||
0.0707643 | + | 0.997493i | \(0.477456\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −205.295 | − | 118.527i | −0.270480 | − | 0.156162i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 777.937 | − | 449.142i | 1.02226 | − | 0.590200i | 0.107500 | − | 0.994205i | \(-0.465716\pi\) |
0.914757 | + | 0.404005i | \(0.132382\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −438.960 | − | 760.302i | −0.573805 | − | 0.993859i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.63247 | − | 13.2198i | 0.00995107 | − | 0.0172358i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 929.350i | 1.20852i | 0.796788 | + | 0.604259i | \(0.206531\pi\) | ||||
−0.796788 | + | 0.604259i | \(0.793469\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.0387 | −0.0545249 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 791.889 | + | 457.198i | 1.02444 | + | 0.591459i | 0.915386 | − | 0.402577i | \(-0.131886\pi\) |
0.109051 | + | 0.994036i | \(0.465219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 409.432 | − | 236.386i | 0.528299 | − | 0.305014i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 292.146 | + | 506.012i | 0.375027 | + | 0.649566i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −367.754 | + | 636.969i | −0.470876 | + | 0.815582i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 351.979i | − | 0.449526i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −862.323 | −1.09850 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 659.669 | + | 380.860i | 0.838207 | + | 0.483939i | 0.856654 | − | 0.515891i | \(-0.172539\pi\) |
−0.0184477 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −102.270 | + | 59.0459i | −0.129620 | + | 0.0748364i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.30952 | + | 2.26816i | 0.00165135 | + | 0.00286023i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −413.990 | + | 717.052i | −0.520742 | + | 0.901952i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 395.267i | − | 0.495943i | −0.968767 | − | 0.247972i | \(-0.920236\pi\) | ||
0.968767 | − | 0.247972i | \(-0.0797639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1273.57 | 1.59395 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.5931 | + | 6.69326i | 0.0144732 | + | 0.00835613i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −172.855 | + | 99.7977i | −0.215261 | + | 0.124281i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.3087 | + | 45.5679i | 0.0326006 | + | 0.0564658i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 438.897 | − | 760.191i | 0.542517 | − | 0.939668i | −0.456241 | − | 0.889856i | \(-0.650805\pi\) |
0.998759 | − | 0.0498115i | \(-0.0158621\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 851.717i | 1.05021i | 0.851039 | + | 0.525103i | \(0.175973\pi\) | ||||
−0.851039 | + | 0.525103i | \(0.824027\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −310.627 | −0.382076 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1317.89 | + | 760.887i | 1.61705 | + | 0.933603i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1015.74 | + | 586.436i | −1.24325 | + | 0.717792i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −218.519 | − | 378.486i | −0.266162 | − | 0.461006i | 0.701705 | − | 0.712467i | \(-0.252422\pi\) |
−0.967867 | + | 0.251461i | \(0.919089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 796.172 | − | 1379.01i | 0.967402 | − | 1.67559i | 0.264383 | − | 0.964418i | \(-0.414832\pi\) |
0.703019 | − | 0.711171i | \(-0.251835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 778.393i | − | 0.943507i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1182.45 | 1.42981 | 0.714904 | − | 0.699223i | \(-0.246470\pi\) | ||||
0.714904 | + | 0.699223i | \(0.246470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −907.637 | − | 524.025i | −1.09486 | − | 0.632117i | −0.159992 | − | 0.987118i | \(-0.551147\pi\) |
−0.934866 | + | 0.355002i | \(0.884480\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 336.846 | − | 194.478i | 0.405350 | − | 0.234029i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 423.362 | + | 733.285i | 0.507021 | + | 0.878186i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 103.765 | − | 179.725i | 0.123972 | − | 0.214726i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 585.611i | − | 0.697986i | −0.937125 | − | 0.348993i | \(-0.886524\pi\) | ||
0.937125 | − | 0.348993i | \(-0.113476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −625.313 | −0.743535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −293.671 | − | 169.551i | −0.348364 | − | 0.201128i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1305.24 | + | 753.582i | −1.54467 | + | 0.891813i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 217.200 | + | 376.202i | 0.255831 | + | 0.443112i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −365.314 | + | 632.742i | −0.429276 | + | 0.743528i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 901.189i | 1.05649i | 0.849091 | + | 0.528247i | \(0.177150\pi\) | ||||
−0.849091 | + | 0.528247i | \(0.822850\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1514.30 | 1.77111 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 836.578 | + | 482.999i | 0.976171 | + | 0.563592i | 0.901112 | − | 0.433587i | \(-0.142752\pi\) |
0.0750587 | + | 0.997179i | \(0.476086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 217.226 | − | 125.415i | 0.252882 | − | 0.146001i | −0.368201 | − | 0.929746i | \(-0.620026\pi\) |
0.621083 | + | 0.783745i | \(0.286693\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −748.563 | − | 1296.55i | −0.867397 | − | 1.50238i | −0.864647 | − | 0.502379i | \(-0.832458\pi\) |
−0.00274946 | − | 0.999996i | \(-0.500875\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −815.092 | + | 1411.78i | −0.942303 | + | 1.63212i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 107.902i | − | 0.124454i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 840.881 | 0.967643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.69163 | + | 2.70871i | 0.00538649 | + | 0.00310989i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −914.220 | + | 527.825i | −1.04722 | + | 0.604611i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −70.6771 | − | 122.416i | −0.0805896 | − | 0.139585i | 0.822914 | − | 0.568166i | \(-0.192347\pi\) |
−0.903503 | + | 0.428581i | \(0.859014\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 304.672 | − | 527.707i | 0.346612 | − | 0.600350i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1413.83i | 1.60480i | 0.596788 | + | 0.802399i | \(0.296443\pi\) | ||||
−0.596788 | + | 0.802399i | \(0.703557\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1386.04 | −1.56969 | −0.784845 | − | 0.619692i | \(-0.787258\pi\) | ||||
−0.784845 | + | 0.619692i | \(0.787258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 687.429 | + | 396.887i | 0.776756 | + | 0.448460i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 262.921 | − | 151.798i | 0.296416 | − | 0.171136i | −0.344416 | − | 0.938817i | \(-0.611923\pi\) |
0.640832 | + | 0.767681i | \(0.278590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 108.157 | + | 187.334i | 0.121389 | + | 0.210251i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1098.37 | + | 1902.44i | −1.22998 | + | 2.13039i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1820.57i | 2.03415i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.68456 | 0.00745213 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 110.133 | + | 63.5853i | 0.122506 | + | 0.0707289i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −776.131 | + | 448.099i | −0.861411 | + | 0.497336i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1022.29 | + | 1770.66i | 1.12960 | + | 1.95653i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −652.009 | + | 1129.31i | −0.718864 | + | 1.24511i | 0.242587 | + | 0.970130i | \(0.422004\pi\) |
−0.961450 | + | 0.274978i | \(0.911329\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 622.431i | 0.684742i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −466.118 | −0.511655 | −0.255828 | − | 0.966722i | \(-0.582348\pi\) | ||||
−0.255828 | + | 0.966722i | \(0.582348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −579.571 | − | 334.615i | −0.634798 | − | 0.366501i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −117.944 | + | 68.0951i | −0.128901 | + | 0.0744209i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 589.171 | + | 1020.47i | 0.641100 | + | 1.11042i | 0.985188 | + | 0.171480i | \(0.0548549\pi\) |
−0.344088 | + | 0.938937i | \(0.611812\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 128.368 | − | 222.339i | 0.139378 | − | 0.241411i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 20.7402i | − | 0.0224705i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2399.10 | −2.59362 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −117.489 | − | 67.8325i | −0.126741 | − | 0.0731742i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 789.089 | − | 455.581i | 0.849396 | − | 0.490399i | −0.0110511 | − | 0.999939i | \(-0.503518\pi\) |
0.860447 | + | 0.509540i | \(0.170184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 217.442 | + | 376.620i | 0.233056 | + | 0.403665i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 614.156 | − | 1063.75i | 0.656852 | − | 1.13770i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1035.35i | − | 1.10496i | −0.833527 | − | 0.552479i | \(-0.813682\pi\) | ||
0.833527 | − | 0.552479i | \(-0.186318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 787.273 | 0.838417 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.8135 | + | 32.2239i | 0.0593130 | + | 0.0342443i | 0.529363 | − | 0.848395i | \(-0.322431\pi\) |
−0.470050 | + | 0.882640i | \(0.655764\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 329.984 | − | 190.516i | 0.349930 | − | 0.202032i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −66.1371 | − | 114.553i | −0.0698385 | − | 0.120964i | 0.828992 | − | 0.559261i | \(-0.188915\pi\) |
−0.898830 | + | 0.438297i | \(0.855582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.81414 | − | 4.87424i | 0.00296538 | − | 0.00513618i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 28.4235i | − | 0.0298880i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1346.86 | 1.41329 | 0.706643 | − | 0.707570i | \(-0.250209\pi\) | ||||
0.706643 | + | 0.707570i | \(0.250209\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74.1586 | + | 42.8155i | 0.0776530 | + | 0.0448330i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 181.328 | − | 104.690i | 0.189476 | − | 0.109394i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −443.010 | − | 767.315i | −0.460988 | − | 0.798455i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −46.9899 | + | 81.3889i | −0.0487953 | + | 0.0845160i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.5246i | 0.0316317i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −498.979 | −0.516007 | −0.258004 | − | 0.966144i | \(-0.583065\pi\) | ||||
−0.258004 | + | 0.966144i | \(0.583065\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −499.641 | − | 288.468i | −0.515626 | − | 0.297697i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1558.20 | − | 899.628i | 1.60474 | − | 0.926496i | 0.614217 | − | 0.789137i | \(-0.289472\pi\) |
0.990521 | − | 0.137359i | \(-0.0438615\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.9747 | + | 19.0088i | 0.0112562 | + | 0.0194962i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −690.803 | + | 1196.51i | −0.707066 | + | 1.22467i | 0.258875 | + | 0.965911i | \(0.416648\pi\) |
−0.965941 | + | 0.258763i | \(0.916685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.7293i | 0.0191310i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 154.804 | 0.157802 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1131.61 | − | 653.337i | −1.15118 | − | 0.664636i | −0.202008 | − | 0.979384i | \(-0.564747\pi\) |
−0.949175 | + | 0.314747i | \(0.898080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1131.55 | − | 653.300i | 1.14878 | − | 0.663249i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 382.431 | + | 662.389i | 0.386684 | + | 0.669757i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −516.994 | + | 895.460i | −0.521689 | + | 0.903592i | 0.477992 | + | 0.878364i | \(0.341365\pi\) |
−0.999682 | + | 0.0252284i | \(0.991969\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 297.472i | − | 0.299569i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2182.68 | 2.19365 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −339.049 | − | 195.750i | −0.340069 | − | 0.196339i | 0.320234 | − | 0.947339i | \(-0.396239\pi\) |
−0.660302 | + | 0.751000i | \(0.729572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −912.023 | + | 526.557i | −0.912936 | + | 0.527084i |
(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 | 392.3.o.b.129.3 | 8 | ||
4.3 | odd | 2 | 784.3.s.f.129.2 | 8 | |||
7.2 | even | 3 | inner | 392.3.o.b.313.2 | 8 | ||
7.3 | odd | 6 | 56.3.c.a.41.3 | yes | 4 | ||
7.4 | even | 3 | 56.3.c.a.41.2 | ✓ | 4 | ||
7.5 | odd | 6 | inner | 392.3.o.b.313.3 | 8 | ||
7.6 | odd | 2 | inner | 392.3.o.b.129.2 | 8 | ||
21.11 | odd | 6 | 504.3.f.a.433.4 | 4 | |||
21.17 | even | 6 | 504.3.f.a.433.1 | 4 | |||
28.3 | even | 6 | 112.3.c.c.97.2 | 4 | |||
28.11 | odd | 6 | 112.3.c.c.97.3 | 4 | |||
28.19 | even | 6 | 784.3.s.f.705.2 | 8 | |||
28.23 | odd | 6 | 784.3.s.f.705.3 | 8 | |||
28.27 | even | 2 | 784.3.s.f.129.3 | 8 | |||
35.3 | even | 12 | 1400.3.p.a.1049.3 | 8 | |||
35.4 | even | 6 | 1400.3.f.a.601.3 | 4 | |||
35.17 | even | 12 | 1400.3.p.a.1049.6 | 8 | |||
35.18 | odd | 12 | 1400.3.p.a.1049.5 | 8 | |||
35.24 | odd | 6 | 1400.3.f.a.601.2 | 4 | |||
35.32 | odd | 12 | 1400.3.p.a.1049.4 | 8 | |||
56.3 | even | 6 | 448.3.c.e.321.3 | 4 | |||
56.11 | odd | 6 | 448.3.c.e.321.2 | 4 | |||
56.45 | odd | 6 | 448.3.c.f.321.2 | 4 | |||
56.53 | even | 6 | 448.3.c.f.321.3 | 4 | |||
84.11 | even | 6 | 1008.3.f.h.433.4 | 4 | |||
84.59 | odd | 6 | 1008.3.f.h.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.c.a.41.2 | ✓ | 4 | 7.4 | even | 3 | ||
56.3.c.a.41.3 | yes | 4 | 7.3 | odd | 6 | ||
112.3.c.c.97.2 | 4 | 28.3 | even | 6 | |||
112.3.c.c.97.3 | 4 | 28.11 | odd | 6 | |||
392.3.o.b.129.2 | 8 | 7.6 | odd | 2 | inner | ||
392.3.o.b.129.3 | 8 | 1.1 | even | 1 | trivial | ||
392.3.o.b.313.2 | 8 | 7.2 | even | 3 | inner | ||
392.3.o.b.313.3 | 8 | 7.5 | odd | 6 | inner | ||
448.3.c.e.321.2 | 4 | 56.11 | odd | 6 | |||
448.3.c.e.321.3 | 4 | 56.3 | even | 6 | |||
448.3.c.f.321.2 | 4 | 56.45 | odd | 6 | |||
448.3.c.f.321.3 | 4 | 56.53 | even | 6 | |||
504.3.f.a.433.1 | 4 | 21.17 | even | 6 | |||
504.3.f.a.433.4 | 4 | 21.11 | odd | 6 | |||
784.3.s.f.129.2 | 8 | 4.3 | odd | 2 | |||
784.3.s.f.129.3 | 8 | 28.27 | even | 2 | |||
784.3.s.f.705.2 | 8 | 28.19 | even | 6 | |||
784.3.s.f.705.3 | 8 | 28.23 | odd | 6 | |||
1008.3.f.h.433.1 | 4 | 84.59 | odd | 6 | |||
1008.3.f.h.433.4 | 4 | 84.11 | even | 6 | |||
1400.3.f.a.601.2 | 4 | 35.24 | odd | 6 | |||
1400.3.f.a.601.3 | 4 | 35.4 | even | 6 | |||
1400.3.p.a.1049.3 | 8 | 35.3 | even | 12 | |||
1400.3.p.a.1049.4 | 8 | 35.32 | odd | 12 | |||
1400.3.p.a.1049.5 | 8 | 35.18 | odd | 12 | |||
1400.3.p.a.1049.6 | 8 | 35.17 | even | 12 |