Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,3,Mod(129,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.129");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.s (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: | \(21.3624527258\) |
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 | 129.2 | ||
Root | \(-1.60021 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.129 |
Dual form | 784.3.s.f.705.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0.262512 | − | 0.964929i | \(-0.415449\pi\) |
−0.704397 | + | 0.709806i | \(0.748782\pi\) | |||||||
\(4\) | 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 | −0.996265 | − | 0.0863508i | \(-0.972479\pi\) |
0.572914 | + | 0.819615i | \(0.305813\pi\) | |||||||
\(12\) | 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 | −0.951823 | − | 0.306648i | \(-0.900793\pi\) |
−0.210347 | + | 0.977627i | \(0.567459\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.31371 | + | 14.3998i | 0.361466 | + | 0.626077i | 0.988202 | − | 0.153154i | \(-0.0489432\pi\) |
−0.626737 | + | 0.779231i | \(0.715610\pi\) | |||||||
\(24\) | 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 | 0.374147 | − | 0.927369i | \(-0.377935\pi\) |
−0.616052 | + | 0.787706i | \(0.711269\pi\) | |||||||
\(32\) | 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 | \(-0.320355\pi\) | ||||
0.534884 | + | 0.844926i | \(0.320355\pi\) | |||||||
\(44\) | 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 | \(-0.297624\pi\) |
0.993714 | − | 0.111948i | \(-0.0357090\pi\) | |||||||
\(48\) | 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 | 0.861712 | − | 0.507397i | \(-0.169392\pi\) |
−0.00856255 | + | 0.999963i | \(0.502726\pi\) | |||||||
\(60\) | 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 | −0.932671 | − | 0.360728i | \(-0.882528\pi\) |
0.778735 | + | 0.627353i | \(0.215862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 25.4521i | − | 0.368872i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 78.9706 | 1.11226 | 0.556131 | − | 0.831095i | \(-0.312285\pi\) | ||||
0.556131 | + | 0.831095i | \(0.312285\pi\) | |||||||
\(72\) | 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 | \(-0.973060\pi\) |
0.425001 | − | 0.905193i | \(-0.360274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.6127 | + | 20.1138i | −0.143367 | + | 0.248318i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 71.8544i | 0.865715i | 0.901462 | + | 0.432858i | \(0.142495\pi\) | ||||
−0.901462 | + | 0.432858i | \(0.857505\pi\) | |||||||
\(84\) | 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 | −0.583224 | − | 0.812312i | \(-0.698209\pi\) |
0.411871 | + | 0.911242i | \(0.364876\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.05887 | + | 12.2263i | 0.0659708 | + | 0.114265i | 0.897124 | − | 0.441778i | \(-0.145652\pi\) |
−0.831153 | + | 0.556043i | \(0.812319\pi\) | |||||||
\(108\) | 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 | \(-0.746754\pi\) | ||||
−0.699860 | + | 0.714280i | \(0.746754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −60.9801 | − | 35.2069i | −0.472714 | − | 0.272922i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 97.5265 | − | 56.3069i | 0.744477 | − | 0.429824i | −0.0792180 | − | 0.996857i | \(-0.525242\pi\) |
0.823695 | + | 0.567033i | \(0.191909\pi\) | |||||||
\(132\) | 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 | \(-0.782776\pi\) | ||
0.776043 | − | 0.630679i | \(-0.217224\pi\) | |||||||
\(140\) | 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 | −0.653275 | − | 0.757121i | \(-0.726605\pi\) |
0.982323 | + | 0.187192i | \(0.0599388\pi\) | |||||||
\(152\) | 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 | \(0.00860138\pi\) |
−0.476419 | + | 0.879219i | \(0.658065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −63.5980 | + | 110.155i | −0.385442 | + | 0.667606i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 94.9055i | 0.568296i | 0.958780 | + | 0.284148i | \(0.0917108\pi\) | ||||
−0.958780 | + | 0.284148i | \(0.908289\pi\) | |||||||
\(168\) | 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 | \(0.359722\pi\) |
−0.996565 | + | 0.0828083i | \(0.973611\pi\) | |||||||
\(180\) | 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 | 0.878315 | − | 0.478083i | \(-0.158668\pi\) |
−0.853189 | + | 0.521602i | \(0.825335\pi\) | |||||||
\(192\) | 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 | 0.926722 | − | 0.375748i | \(-0.122614\pi\) |
0.137954 | + | 0.990439i | \(0.455947\pi\) | |||||||
\(200\) | 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 | \(-0.763764\pi\) | ||||
−0.737013 | + | 0.675879i | \(0.763764\pi\) | |||||||
\(212\) | 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 | \(0.0838671\pi\) | ||||
−0.965490 | + | 0.260438i | \(0.916133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −363.451 | −1.61534 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −51.2456 | − | 29.5867i | −0.225752 | − | 0.130338i | 0.382859 | − | 0.923807i | \(-0.374940\pi\) |
−0.608611 | + | 0.793469i | \(0.708273\pi\) | |||||||
\(228\) | 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 | \(-0.495247\pi\) | ||||
0.0149311 | + | 0.999889i | \(0.495247\pi\) | |||||||
\(240\) | 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 | \(-0.885305\pi\) | ||
0.935782 | − | 0.352579i | \(-0.114695\pi\) | |||||||
\(252\) | 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 | −0.783326 | − | 0.621611i | \(-0.786479\pi\) |
0.929994 | + | 0.367575i | \(0.119812\pi\) | |||||||
\(264\) | 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 | −0.139389 | − | 0.990238i | \(-0.544514\pi\) |
0.787876 | + | 0.615833i | \(0.211181\pi\) | |||||||
\(272\) | 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 | −0.00160358 | − | 0.999999i | \(-0.500510\pi\) |
−0.866826 | + | 0.498611i | \(0.833844\pi\) | |||||||
\(284\) | 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 | \(0.0880689\pi\) | ||||
−0.961969 | + | 0.273160i | \(0.911931\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.1960 | 0.100958 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −246.039 | − | 142.051i | −0.791121 | − | 0.456754i | 0.0492358 | − | 0.998787i | \(-0.484321\pi\) |
−0.840357 | + | 0.542033i | \(0.817655\pi\) | |||||||
\(312\) | 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 | 0.974648 | − | 0.223746i | \(-0.0718285\pi\) |
−0.681093 | + | 0.732197i | \(0.738495\pi\) | |||||||
\(332\) | 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 | −0.958285 | − | 0.285813i | \(-0.907736\pi\) |
0.726664 | + | 0.686993i | \(0.241070\pi\) | |||||||
\(348\) | 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 | \(-0.924883\pi\) |
0.283662 | − | 0.958924i | \(-0.408451\pi\) | |||||||
\(360\) | 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 | \(0.102192\pi\) |
0.747735 | + | 0.663997i | \(0.231141\pi\) | |||||||
\(368\) | 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 | \(-0.640867\pi\) | ||||
−0.428242 | + | 0.903664i | \(0.640867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 235.654 | + | 136.055i | 0.618515 | + | 0.357100i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 338.835 | − | 195.626i | 0.884686 | − | 0.510773i | 0.0124851 | − | 0.999922i | \(-0.496026\pi\) |
0.872200 | + | 0.489149i | \(0.162692\pi\) | |||||||
\(384\) | 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 | \(0.00410443\pi\) | ||||
−0.999917 | + | 0.0128941i | \(0.995896\pi\) | |||||||
\(420\) | 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 | \(-0.461060\pi\) |
0.798539 | − | 0.601943i | \(-0.205606\pi\) | |||||||
\(432\) | 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 | \(-0.261258\pi\) |
0.974474 | − | 0.224500i | \(-0.0720749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 387.108 | + | 670.490i | 0.873832 | + | 1.51352i | 0.858002 | + | 0.513647i | \(0.171706\pi\) |
0.0158306 | + | 0.999875i | \(0.494961\pi\) | |||||||
\(444\) | 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 | \(-0.558068\pi\) | ||||
−0.181415 | + | 0.983407i | \(0.558068\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −102.413 | − | 59.1283i | −0.220243 | − | 0.127158i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −315.389 | + | 182.090i | −0.675350 | + | 0.389914i | −0.798101 | − | 0.602524i | \(-0.794162\pi\) |
0.122750 | + | 0.992438i | \(0.460829\pi\) | |||||||
\(468\) | 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 | 0.370955 | − | 0.928651i | \(-0.379031\pi\) |
−0.618758 | + | 0.785582i | \(0.712364\pi\) | |||||||
\(480\) | 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 | \(-0.639388\pi\) |
0.996330 | − | 0.0855930i | \(-0.0272785\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 261.095i | − | 0.533937i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 537.647 | 1.09500 | 0.547502 | − | 0.836805i | \(-0.315579\pi\) | ||||
0.547502 | + | 0.836805i | \(0.315579\pi\) | |||||||
\(492\) | 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 | \(-0.947564\pi\) |
0.351212 | − | 0.936296i | \(-0.385770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 72.6375 | − | 125.812i | 0.144985 | − | 0.251122i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 91.1385i | 0.181190i | 0.995888 | + | 0.0905949i | \(0.0288769\pi\) | ||||
−0.995888 | + | 0.0905949i | \(0.971123\pi\) | |||||||
\(504\) | 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 | −0.935525 | − | 0.353260i | \(-0.885073\pi\) |
−0.161830 | + | 0.986819i | \(0.551740\pi\) | |||||||
\(524\) | 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 | \(-0.424013\pi\) | ||||
0.236459 | + | 0.971641i | \(0.424013\pi\) | |||||||
\(548\) | 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 | 0.436796 | − | 0.899561i | \(-0.356113\pi\) |
−0.560644 | + | 0.828057i | \(0.689447\pi\) | |||||||
\(564\) | 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 | \(-0.657945\pi\) |
0.999625 | − | 0.0273980i | \(-0.00872213\pi\) | |||||||
\(572\) | 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 | \(-0.796551\pi\) | ||
0.802601 | − | 0.596516i | \(-0.203449\pi\) | |||||||
\(588\) | 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 | −0.757323 | − | 0.653041i | \(-0.773493\pi\) |
0.944211 | + | 0.329340i | \(0.106826\pi\) | |||||||
\(600\) | 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 | −0.253633 | − | 0.967301i | \(-0.581625\pi\) |
0.710891 | + | 0.703303i | \(0.248292\pi\) | |||||||
\(608\) | 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 | 0.0940632 | − | 0.995566i | \(-0.470014\pi\) |
−0.815154 | + | 0.579244i | \(0.803348\pi\) | |||||||
\(620\) | 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 | \(-0.399321\pi\) | ||||
0.311045 | + | 0.950395i | \(0.399321\pi\) | |||||||
\(632\) | 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 | \(-0.751063\pi\) | ||
0.709463 | − | 0.704742i | \(-0.248937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 628.215 | 0.973977 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −99.0082 | − | 57.1624i | −0.153027 | − | 0.0883499i | 0.421531 | − | 0.906814i | \(-0.361493\pi\) |
−0.574558 | + | 0.818464i | \(0.694826\pi\) | |||||||
\(648\) | 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 | \(-0.664282\pi\) | ||||
−0.493498 | + | 0.869747i | \(0.664282\pi\) | |||||||
\(660\) | 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 | −0.958040 | − | 0.286635i | \(-0.907463\pi\) |
0.727253 | + | 0.686369i | \(0.240797\pi\) | |||||||
\(684\) | 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 | −0.275190 | − | 0.961390i | \(-0.588741\pi\) |
0.694993 | + | 0.719016i | \(0.255407\pi\) | |||||||
\(692\) | 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 | −0.954021 | − | 0.299741i | \(-0.903100\pi\) |
−0.217427 | + | 0.976077i | \(0.569766\pi\) | |||||||
\(720\) | 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 | \(0.150134\pi\) | ||||
−0.890816 | + | 0.454365i | \(0.849866\pi\) | |||||||
\(728\) | 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 | −0.956490 | − | 0.291765i | \(-0.905757\pi\) |
0.730921 | + | 0.682462i | \(0.239091\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.2504i | 0.0138332i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 610.118 | 0.821154 | 0.410577 | − | 0.911826i | \(-0.365327\pi\) | ||||
0.410577 | + | 0.911826i | \(0.365327\pi\) | |||||||
\(744\) | 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 | 0.859931 | − | 0.510410i | \(-0.170506\pi\) |
−0.871994 | + | 0.489517i | \(0.837173\pi\) | |||||||
\(752\) | 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 | 0.0184477 | − | 0.999830i | \(-0.494128\pi\) |
−0.856654 | + | 0.515891i | \(0.827461\pi\) | |||||||
\(788\) | 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 | \(-0.824027\pi\) | ||
0.851039 | − | 0.525103i | \(-0.175973\pi\) | |||||||
\(812\) | 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 | \(0.585168\pi\) |
−0.703019 | + | 0.711171i | \(0.748165\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 778.393i | − | 0.943507i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1182.45 | −1.42981 | −0.714904 | − | 0.699223i | \(-0.753530\pi\) | ||||
−0.714904 | + | 0.699223i | \(0.753530\pi\) | |||||||
\(828\) | 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 | \(0.113476\pi\) | ||||
−0.937125 | + | 0.348993i | \(0.886524\pi\) | |||||||
\(840\) | 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 | −0.621083 | − | 0.783745i | \(-0.713307\pi\) |
0.368201 | + | 0.929746i | \(0.379974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 748.563 | + | 1296.55i | 0.867397 | + | 1.50238i | 0.864647 | + | 0.502379i | \(0.167542\pi\) |
0.00274946 | + | 0.999996i | \(0.499125\pi\) | |||||||
\(864\) | 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 | \(-0.212742\pi\) | ||||
0.784845 | + | 0.619692i | \(0.212742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 687.429 | + | 396.887i | 0.776756 | + | 0.448460i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −262.921 | + | 151.798i | −0.296416 | + | 0.171136i | −0.640832 | − | 0.767681i | \(-0.721410\pi\) |
0.344416 | + | 0.938817i | \(0.388077\pi\) | |||||||
\(888\) | 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 | \(-0.577996\pi\) |
0.961450 | − | 0.274978i | \(-0.0886707\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 622.431i | 0.684742i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 466.118 | 0.511655 | 0.255828 | − | 0.966722i | \(-0.417652\pi\) | ||||
0.255828 | + | 0.966722i | \(0.417652\pi\) | |||||||
\(912\) | 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 | \(-0.945145\pi\) |
0.344088 | − | 0.938937i | \(-0.388188\pi\) | |||||||
\(920\) | 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 | 0.898830 | − | 0.438297i | \(-0.144418\pi\) |
−0.828992 | + | 0.559261i | \(0.811085\pi\) | |||||||
\(948\) | 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 | \(-0.416935\pi\) | ||||
0.258004 | + | 0.966144i | \(0.416935\pi\) | |||||||
\(968\) | 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 | \(0.710528\pi\) |
−0.990521 | + | 0.137359i | \(0.956138\pi\) | |||||||
\(972\) | 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 | 0.949175 | − | 0.314747i | \(-0.101920\pi\) |
0.202008 | + | 0.979384i | \(0.435253\pi\) | |||||||
\(984\) | 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 | \(-0.658635\pi\) |
0.999682 | − | 0.0252284i | \(-0.00803130\pi\) | |||||||
\(992\) | 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 | 784.3.s.f.129.2 | 8 | ||
4.3 | odd | 2 | 392.3.o.b.129.3 | 8 | |||
7.2 | even | 3 | inner | 784.3.s.f.705.3 | 8 | ||
7.3 | odd | 6 | 112.3.c.c.97.2 | 4 | |||
7.4 | even | 3 | 112.3.c.c.97.3 | 4 | |||
7.5 | odd | 6 | inner | 784.3.s.f.705.2 | 8 | ||
7.6 | odd | 2 | inner | 784.3.s.f.129.3 | 8 | ||
21.11 | odd | 6 | 1008.3.f.h.433.4 | 4 | |||
21.17 | even | 6 | 1008.3.f.h.433.1 | 4 | |||
28.3 | even | 6 | 56.3.c.a.41.3 | yes | 4 | ||
28.11 | odd | 6 | 56.3.c.a.41.2 | ✓ | 4 | ||
28.19 | even | 6 | 392.3.o.b.313.3 | 8 | |||
28.23 | odd | 6 | 392.3.o.b.313.2 | 8 | |||
28.27 | even | 2 | 392.3.o.b.129.2 | 8 | |||
56.3 | even | 6 | 448.3.c.f.321.2 | 4 | |||
56.11 | odd | 6 | 448.3.c.f.321.3 | 4 | |||
56.45 | odd | 6 | 448.3.c.e.321.3 | 4 | |||
56.53 | even | 6 | 448.3.c.e.321.2 | 4 | |||
84.11 | even | 6 | 504.3.f.a.433.4 | 4 | |||
84.59 | odd | 6 | 504.3.f.a.433.1 | 4 | |||
140.3 | odd | 12 | 1400.3.p.a.1049.3 | 8 | |||
140.39 | odd | 6 | 1400.3.f.a.601.3 | 4 | |||
140.59 | even | 6 | 1400.3.f.a.601.2 | 4 | |||
140.67 | even | 12 | 1400.3.p.a.1049.4 | 8 | |||
140.87 | odd | 12 | 1400.3.p.a.1049.6 | 8 | |||
140.123 | even | 12 | 1400.3.p.a.1049.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.c.a.41.2 | ✓ | 4 | 28.11 | odd | 6 | ||
56.3.c.a.41.3 | yes | 4 | 28.3 | even | 6 | ||
112.3.c.c.97.2 | 4 | 7.3 | odd | 6 | |||
112.3.c.c.97.3 | 4 | 7.4 | even | 3 | |||
392.3.o.b.129.2 | 8 | 28.27 | even | 2 | |||
392.3.o.b.129.3 | 8 | 4.3 | odd | 2 | |||
392.3.o.b.313.2 | 8 | 28.23 | odd | 6 | |||
392.3.o.b.313.3 | 8 | 28.19 | even | 6 | |||
448.3.c.e.321.2 | 4 | 56.53 | even | 6 | |||
448.3.c.e.321.3 | 4 | 56.45 | odd | 6 | |||
448.3.c.f.321.2 | 4 | 56.3 | even | 6 | |||
448.3.c.f.321.3 | 4 | 56.11 | odd | 6 | |||
504.3.f.a.433.1 | 4 | 84.59 | odd | 6 | |||
504.3.f.a.433.4 | 4 | 84.11 | even | 6 | |||
784.3.s.f.129.2 | 8 | 1.1 | even | 1 | trivial | ||
784.3.s.f.129.3 | 8 | 7.6 | odd | 2 | inner | ||
784.3.s.f.705.2 | 8 | 7.5 | odd | 6 | inner | ||
784.3.s.f.705.3 | 8 | 7.2 | even | 3 | inner | ||
1008.3.f.h.433.1 | 4 | 21.17 | even | 6 | |||
1008.3.f.h.433.4 | 4 | 21.11 | odd | 6 | |||
1400.3.f.a.601.2 | 4 | 140.59 | even | 6 | |||
1400.3.f.a.601.3 | 4 | 140.39 | odd | 6 | |||
1400.3.p.a.1049.3 | 8 | 140.3 | odd | 12 | |||
1400.3.p.a.1049.4 | 8 | 140.67 | even | 12 | |||
1400.3.p.a.1049.5 | 8 | 140.123 | even | 12 | |||
1400.3.p.a.1049.6 | 8 | 140.87 | odd | 12 |