Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(577,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.577 |
Dual form | 1728.2.i.j.1153.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.68614 | − | 2.92048i | 0.754065 | − | 1.30608i | −0.191773 | − | 0.981439i | \(-0.561424\pi\) |
0.945838 | − | 0.324640i | \(-0.105243\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.686141 | − | 1.18843i | −0.259337 | − | 0.449185i | 0.706728 | − | 0.707486i | \(-0.250171\pi\) |
−0.966064 | + | 0.258301i | \(0.916837\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.68614 | − | 4.65253i | 0.745001 | − | 1.29038i | −0.205193 | − | 0.978722i | \(-0.565782\pi\) |
0.950194 | − | 0.311659i | \(-0.100885\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.372281 | −0.0902915 | −0.0451457 | − | 0.998980i | \(-0.514375\pi\) | ||||
−0.0451457 | + | 0.998980i | \(0.514375\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.37228 | 1.46190 | 0.730951 | − | 0.682430i | \(-0.239077\pi\) | ||||
0.730951 | + | 0.682430i | \(0.239077\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.68614 | + | 4.65253i | −0.560099 | + | 0.970120i | 0.437388 | + | 0.899273i | \(0.355904\pi\) |
−0.997487 | + | 0.0708472i | \(0.977430\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.18614 | − | 5.51856i | −0.637228 | − | 1.10371i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.686141 | − | 1.18843i | −0.127413 | − | 0.220686i | 0.795261 | − | 0.606268i | \(-0.207334\pi\) |
−0.922674 | + | 0.385582i | \(0.874001\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.313859 | − | 0.543620i | 0.0563708 | − | 0.0976371i | −0.836463 | − | 0.548023i | \(-0.815380\pi\) |
0.892834 | + | 0.450386i | \(0.148714\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.62772 | −0.782227 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.74456 | 0.451203 | 0.225602 | − | 0.974220i | \(-0.427565\pi\) | ||||
0.225602 | + | 0.974220i | \(0.427565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.127719 | + | 0.221215i | −0.0199463 | + | 0.0345480i | −0.875826 | − | 0.482627i | \(-0.839683\pi\) |
0.855880 | + | 0.517175i | \(0.173016\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.87228 | − | 8.43904i | −0.743016 | − | 1.28694i | −0.951116 | − | 0.308834i | \(-0.900061\pi\) |
0.208100 | − | 0.978108i | \(-0.433272\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.686141 | + | 1.18843i | 0.100084 | + | 0.173350i | 0.911719 | − | 0.410814i | \(-0.134756\pi\) |
−0.811635 | + | 0.584165i | \(0.801422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.55842 | − | 4.43132i | 0.365489 | − | 0.633045i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7446 | −1.47588 | −0.737940 | − | 0.674867i | \(-0.764201\pi\) | ||||
−0.737940 | + | 0.674867i | \(0.764201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.37228 | 0.454718 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.50000 | − | 6.06218i | 0.455661 | − | 0.789228i | −0.543065 | − | 0.839691i | \(-0.682736\pi\) |
0.998726 | + | 0.0504625i | \(0.0160695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.68614 | − | 2.92048i | −0.215888 | − | 0.373929i | 0.737659 | − | 0.675174i | \(-0.235931\pi\) |
−0.953547 | + | 0.301244i | \(0.902598\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.05842 | − | 15.6896i | −1.12356 | − | 1.94606i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.87228 | + | 6.70699i | −0.473074 | + | 0.819389i | −0.999525 | − | 0.0308167i | \(-0.990189\pi\) |
0.526451 | + | 0.850206i | \(0.323523\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.11684 | 0.598881 | 0.299441 | − | 0.954115i | \(-0.403200\pi\) | ||||
0.299441 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.686141 | − | 1.18843i | 0.0781930 | − | 0.135434i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.313859 | − | 0.543620i | −0.0353119 | − | 0.0611621i | 0.847829 | − | 0.530269i | \(-0.177909\pi\) |
−0.883141 | + | 0.469107i | \(0.844576\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.68614 | + | 13.3128i | 0.843664 | + | 1.46127i | 0.886777 | + | 0.462198i | \(0.152939\pi\) |
−0.0431132 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.627719 | + | 1.08724i | −0.0680856 | + | 0.117928i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.37228 | −0.772825 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.7446 | − | 18.6101i | 1.10237 | − | 1.90936i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.87228 | + | 8.43904i | 0.494705 | + | 0.856855i | 0.999981 | − | 0.00610314i | \(-0.00194270\pi\) |
−0.505276 | + | 0.862958i | \(0.668609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.05842 | − | 8.76144i | −0.503332 | − | 0.871796i | −0.999993 | − | 0.00385151i | \(-0.998774\pi\) |
0.496661 | − | 0.867945i | \(-0.334559\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.31386 | + | 5.73977i | −0.326524 | + | 0.565557i | −0.981820 | − | 0.189816i | \(-0.939211\pi\) |
0.655295 | + | 0.755373i | \(0.272544\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.8614 | −1.53338 | −0.766690 | − | 0.642017i | \(-0.778098\pi\) | ||||
−0.766690 | + | 0.642017i | \(0.778098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.74456 | −0.646012 | −0.323006 | − | 0.946397i | \(-0.604693\pi\) | ||||
−0.323006 | + | 0.946397i | \(0.604693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.686141 | − | 1.18843i | 0.0645467 | − | 0.111798i | −0.831946 | − | 0.554856i | \(-0.812773\pi\) |
0.896493 | + | 0.443058i | \(0.146107\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.05842 | + | 15.6896i | 0.844702 | + | 1.46307i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.255437 | + | 0.442430i | 0.0234159 | + | 0.0405575i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.62772 | −0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.74456 | 0.421012 | 0.210506 | − | 0.977593i | \(-0.432489\pi\) | ||||
0.210506 | + | 0.977593i | \(0.432489\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.31386 | − | 10.9359i | 0.551644 | − | 0.955476i | −0.446512 | − | 0.894778i | \(-0.647334\pi\) |
0.998156 | − | 0.0606984i | \(-0.0193328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.37228 | − | 7.57301i | −0.379125 | − | 0.656664i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.12772 | + | 5.41737i | 0.267219 | + | 0.462837i | 0.968143 | − | 0.250399i | \(-0.0805619\pi\) |
−0.700924 | + | 0.713236i | \(0.747229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.87228 | − | 4.97494i | 0.243624 | − | 0.421969i | −0.718120 | − | 0.695919i | \(-0.754997\pi\) |
0.961744 | + | 0.273951i | \(0.0883305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.37228 | 0.449253 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.62772 | −0.384311 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.31386 | − | 2.27567i | 0.107636 | − | 0.186430i | −0.807176 | − | 0.590310i | \(-0.799005\pi\) |
0.914812 | + | 0.403880i | \(0.132339\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.68614 | − | 4.65253i | −0.218595 | − | 0.378618i | 0.735784 | − | 0.677217i | \(-0.236814\pi\) |
−0.954379 | + | 0.298599i | \(0.903481\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.05842 | − | 1.83324i | −0.0850145 | − | 0.147249i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.05842 | − | 12.2255i | 0.563323 | − | 0.975705i | −0.433880 | − | 0.900971i | \(-0.642856\pi\) |
0.997203 | − | 0.0747341i | \(-0.0238108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.37228 | 0.581017 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.941578 | − | 1.63086i | 0.0728615 | − | 0.126200i | −0.827293 | − | 0.561771i | \(-0.810120\pi\) |
0.900154 | + | 0.435571i | \(0.143454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.93070 | − | 13.7364i | −0.610054 | − | 1.05664i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.31386 | + | 9.20387i | 0.404005 | + | 0.699758i | 0.994205 | − | 0.107500i | \(-0.0342844\pi\) |
−0.590200 | + | 0.807257i | \(0.700951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.37228 | + | 7.57301i | −0.330513 | + | 0.572466i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783 | 1.71748 | 0.858738 | − | 0.512416i | \(-0.171249\pi\) | ||||
0.858738 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.4891 | 1.74593 | 0.872966 | − | 0.487780i | \(-0.162193\pi\) | ||||
0.872966 | + | 0.487780i | \(0.162193\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.62772 | − | 8.01544i | 0.340237 | − | 0.589307i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.186141 | − | 0.322405i | −0.0136120 | − | 0.0235766i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.43070 | + | 16.3345i | 0.682382 | + | 1.18192i | 0.974252 | + | 0.225462i | \(0.0723891\pi\) |
−0.291870 | + | 0.956458i | \(0.594278\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.87228 | − | 8.43904i | 0.350714 | − | 0.607455i | −0.635660 | − | 0.771969i | \(-0.719272\pi\) |
0.986375 | + | 0.164514i | \(0.0526054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.7446 | 1.90547 | 0.952736 | − | 0.303801i | \(-0.0982557\pi\) | ||||
0.952736 | + | 0.303801i | \(0.0982557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2337 | −1.29255 | −0.646276 | − | 0.763104i | \(-0.723674\pi\) | ||||
−0.646276 | + | 0.763104i | \(0.723674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.941578 | + | 1.63086i | −0.0660858 | + | 0.114464i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.430703 | + | 0.746000i | 0.0300816 | + | 0.0521029i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.18614 | + | 5.51856i | 0.220390 | + | 0.381727i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.68614 | − | 13.3128i | 0.529136 | − | 0.916490i | −0.470287 | − | 0.882514i | \(-0.655850\pi\) |
0.999423 | − | 0.0339764i | \(-0.0108171\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.8614 | −2.24113 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.861407 | −0.0584761 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00000 | + | 1.73205i | −0.0672673 | + | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8030 | + | 22.1754i | 0.857351 | + | 1.48498i | 0.874446 | + | 0.485122i | \(0.161225\pi\) |
−0.0170952 | + | 0.999854i | \(0.505442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.50000 | − | 12.9904i | −0.497792 | − | 0.862202i | 0.502204 | − | 0.864749i | \(-0.332523\pi\) |
−0.999997 | + | 0.00254715i | \(0.999189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.80298 | + | 15.2472i | −0.581718 | + | 1.00756i | 0.413558 | + | 0.910478i | \(0.364286\pi\) |
−0.995276 | + | 0.0970868i | \(0.969048\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.372281 | 0.0243890 | 0.0121945 | − | 0.999926i | \(-0.496118\pi\) | ||||
0.0121945 | + | 0.999926i | \(0.496118\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.62772 | 0.301879 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.43070 | + | 12.8704i | −0.480652 | + | 0.832514i | −0.999754 | − | 0.0221986i | \(-0.992933\pi\) |
0.519101 | + | 0.854713i | \(0.326267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.87228 | + | 4.97494i | 0.185020 | + | 0.320464i | 0.943583 | − | 0.331135i | \(-0.107432\pi\) |
−0.758563 | + | 0.651599i | \(0.774098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.62772 | − | 14.9436i | −0.551205 | − | 0.954715i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.1168 | − | 29.6472i | 1.08912 | − | 1.88641i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.1168 | −1.71160 | −0.855800 | − | 0.517307i | \(-0.826935\pi\) | ||||
−0.855800 | + | 0.517307i | \(0.826935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.37228 | −0.337752 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.24456 | + | 16.0121i | −0.576660 | + | 0.998804i | 0.419199 | + | 0.907894i | \(0.362311\pi\) |
−0.995859 | + | 0.0909101i | \(0.971022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.88316 | − | 3.26172i | −0.117014 | − | 0.202674i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.94158 | + | 3.36291i | 0.119723 | + | 0.207366i | 0.919658 | − | 0.392721i | \(-0.128466\pi\) |
−0.799935 | + | 0.600087i | \(0.795133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.1168 | + | 31.3793i | −1.11291 | + | 1.92761i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.25544 | −0.0765454 | −0.0382727 | − | 0.999267i | \(-0.512186\pi\) | ||||
−0.0382727 | + | 0.999267i | \(0.512186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.48913 | −0.0904579 | −0.0452290 | − | 0.998977i | \(-0.514402\pi\) | ||||
−0.0452290 | + | 0.998977i | \(0.514402\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.18614 | − | 5.51856i | 0.192132 | − | 0.332782i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.94158 | + | 10.2911i | 0.356995 | + | 0.618333i | 0.987457 | − | 0.157887i | \(-0.0504680\pi\) |
−0.630462 | + | 0.776220i | \(0.717135\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.43070 | + | 12.8704i | 0.443279 | + | 0.767781i | 0.997931 | − | 0.0643014i | \(-0.0204819\pi\) |
−0.554652 | + | 0.832082i | \(0.687149\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.43070 | − | 4.21010i | 0.144490 | − | 0.250265i | −0.784692 | − | 0.619885i | \(-0.787179\pi\) |
0.929183 | + | 0.369621i | \(0.120512\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.350532 | 0.0206912 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8614 | −0.991847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6861 | + | 21.9730i | −0.741132 | + | 1.28368i | 0.210848 | + | 0.977519i | \(0.432378\pi\) |
−0.951980 | + | 0.306160i | \(0.900956\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.8030 | − | 20.4434i | −0.687196 | − | 1.19026i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.4307 | + | 24.9947i | 0.834549 | + | 1.44548i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.68614 | + | 11.5807i | −0.385383 | + | 0.667502i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.3723 | −0.651175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6277 | 1.46265 | 0.731326 | − | 0.682029i | \(-0.238902\pi\) | ||||
0.731326 | + | 0.682029i | \(0.238902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0584 | − | 24.3499i | 0.797180 | − | 1.38076i | −0.124266 | − | 0.992249i | \(-0.539658\pi\) |
0.921446 | − | 0.388507i | \(-0.127009\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6168 | + | 20.1210i | 0.656623 | + | 1.13730i | 0.981484 | + | 0.191543i | \(0.0613490\pi\) |
−0.324861 | + | 0.945762i | \(0.605318\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.80298 | + | 8.31901i | 0.269762 | + | 0.467242i | 0.968800 | − | 0.247842i | \(-0.0797215\pi\) |
−0.699038 | + | 0.715085i | \(0.746388\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.686141 | − | 1.18843i | 0.0384165 | − | 0.0665393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.37228 | −0.131997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −34.2337 | −1.89894 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.941578 | − | 1.63086i | 0.0519109 | − | 0.0899123i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.56930 | + | 2.71810i | 0.0862563 | + | 0.149400i | 0.905926 | − | 0.423436i | \(-0.139176\pi\) |
−0.819670 | + | 0.572837i | \(0.805843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.0584 | + | 22.6179i | 0.713458 | + | 1.23575i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9891 | + | 22.4978i | −0.707563 | + | 1.22553i | 0.258196 | + | 0.966093i | \(0.416872\pi\) |
−0.965759 | + | 0.259442i | \(0.916461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.627719 | 0.0339929 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.6277 | −0.897812 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3614 | + | 24.8747i | −0.770961 | + | 1.33534i | 0.166076 | + | 0.986113i | \(0.446890\pi\) |
−0.937037 | + | 0.349230i | \(0.886443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0584 | + | 29.5461i | 0.913116 | + | 1.58156i | 0.809636 | + | 0.586933i | \(0.199665\pi\) |
0.103481 | + | 0.994631i | \(0.467002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9891 | + | 19.0337i | 0.584892 | + | 1.01306i | 0.994889 | + | 0.100976i | \(0.0321965\pi\) |
−0.409997 | + | 0.912087i | \(0.634470\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.74456 | + | 11.6819i | −0.357964 | + | 0.620012i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2337 | −0.751225 | −0.375613 | − | 0.926777i | \(-0.622568\pi\) | ||||
−0.375613 | + | 0.926777i | \(0.622568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.6060 | 1.13716 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.62772 | − | 14.9436i | 0.451595 | − | 0.782186i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6861 | + | 20.2410i | 0.610012 | + | 1.05657i | 0.991238 | + | 0.132089i | \(0.0421686\pi\) |
−0.381226 | + | 0.924482i | \(0.624498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.37228 | + | 12.7692i | 0.382750 | + | 0.662942i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.94158 | − | 3.36291i | 0.100531 | − | 0.174125i | −0.811372 | − | 0.584529i | \(-0.801279\pi\) |
0.911904 | + | 0.410404i | \(0.134612\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.37228 | −0.379692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.1168 | −1.18743 | −0.593716 | − | 0.804674i | \(-0.702340\pi\) | ||||
−0.593716 | + | 0.804674i | \(0.702340\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.1753 | − | 26.2843i | 0.775420 | − | 1.34307i | −0.159138 | − | 0.987256i | \(-0.550872\pi\) |
0.934558 | − | 0.355810i | \(-0.115795\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.31386 | − | 4.00772i | −0.117925 | − | 0.204252i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.8030 | + | 25.6395i | 0.750541 | + | 1.29998i | 0.947561 | + | 0.319576i | \(0.103540\pi\) |
−0.197020 | + | 0.980400i | \(0.563126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00000 | − | 1.73205i | 0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.11684 | −0.106510 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.2337 | −0.814745 | −0.407373 | − | 0.913262i | \(-0.633555\pi\) | ||||
−0.407373 | + | 0.913262i | \(0.633555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.61684 | − | 14.9248i | 0.430305 | − | 0.745310i | −0.566595 | − | 0.823997i | \(-0.691739\pi\) |
0.996899 | + | 0.0786871i | \(0.0250728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.68614 | − | 2.92048i | −0.0839926 | − | 0.145480i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.37228 | + | 2.37686i | 0.0680215 | + | 0.117817i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.87228 | − | 4.97494i | 0.142025 | − | 0.245995i | −0.786234 | − | 0.617929i | \(-0.787972\pi\) |
0.928259 | + | 0.371934i | \(0.121305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.60597 | −0.472679 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 51.8397 | 2.54471 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8030 | − | 23.9075i | 0.674320 | − | 1.16796i | −0.302347 | − | 0.953198i | \(-0.597770\pi\) |
0.976667 | − | 0.214759i | \(-0.0688964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.94158 | − | 15.4873i | −0.435786 | − | 0.754803i | 0.561574 | − | 0.827427i | \(-0.310196\pi\) |
−0.997359 | + | 0.0726236i | \(0.976863\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.18614 | + | 2.05446i | 0.0575363 | + | 0.0996557i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.31386 | + | 4.00772i | −0.111976 | + | 0.193947i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7446 | −0.613884 | −0.306942 | − | 0.951728i | \(-0.599306\pi\) | ||||
−0.306942 | + | 0.951728i | \(0.599306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8832 | 0.715239 | 0.357619 | − | 0.933867i | \(-0.383589\pi\) | ||||
0.357619 | + | 0.933867i | \(0.383589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.1168 | + | 29.6472i | −0.818810 | + | 1.41822i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.05842 | − | 8.76144i | −0.241425 | − | 0.418161i | 0.719695 | − | 0.694290i | \(-0.244282\pi\) |
−0.961121 | + | 0.276129i | \(0.910948\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.3614 | − | 23.1426i | −0.634820 | − | 1.09954i | −0.986553 | − | 0.163440i | \(-0.947741\pi\) |
0.351734 | − | 0.936100i | \(-0.385592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1168 | + | 17.5229i | −0.479584 | + | 0.830665i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1168 | 1.56288 | 0.781440 | − | 0.623980i | \(-0.214485\pi\) | ||||
0.781440 | + | 0.623980i | \(0.214485\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.255437 | −0.0120281 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.4307 | + | 21.5306i | −0.582760 | + | 1.00937i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.87228 | − | 6.70699i | −0.181138 | − | 0.313740i | 0.761131 | − | 0.648599i | \(-0.224645\pi\) |
−0.942268 | + | 0.334859i | \(0.891311\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0584 | + | 20.8858i | 0.561617 | + | 0.972749i | 0.997356 | + | 0.0726756i | \(0.0231538\pi\) |
−0.435739 | + | 0.900073i | \(0.643513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.17527 | + | 8.96382i | −0.240515 | + | 0.416584i | −0.960861 | − | 0.277031i | \(-0.910650\pi\) |
0.720346 | + | 0.693615i | \(0.243983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.62772 | −0.0753218 | −0.0376609 | − | 0.999291i | \(-0.511991\pi\) | ||||
−0.0376609 | + | 0.999291i | \(0.511991\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.6277 | 0.490742 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.87228 | − | 8.43904i | 0.224028 | − | 0.388027i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.3030 | − | 35.1658i | −0.931565 | − | 1.61352i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8030 | − | 25.6395i | −0.676366 | − | 1.17150i | −0.976068 | − | 0.217467i | \(-0.930221\pi\) |
0.299702 | − | 0.954033i | \(-0.403113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.37228 | − | 12.7692i | 0.336147 | − | 0.582224i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 32.8614 | 1.49216 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.74456 | 0.214997 | 0.107498 | − | 0.994205i | \(-0.465716\pi\) | ||||
0.107498 | + | 0.994205i | \(0.465716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.87228 | − | 10.1711i | 0.265012 | − | 0.459015i | −0.702555 | − | 0.711630i | \(-0.747957\pi\) |
0.967567 | + | 0.252615i | \(0.0812906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.255437 | + | 0.442430i | 0.0115043 | + | 0.0199261i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.74456 | + | 4.75372i | 0.123110 | + | 0.213234i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9891 | + | 22.4978i | −0.581473 | + | 1.00714i | 0.413832 | + | 0.910353i | \(0.364190\pi\) |
−0.995305 | + | 0.0967877i | \(0.969143\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.4891 | 1.31486 | 0.657428 | − | 0.753518i | \(-0.271645\pi\) | ||||
0.657428 | + | 0.753518i | \(0.271645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.1168 | −1.51818 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.94158 | − | 12.0232i | 0.307680 | − | 0.532917i | −0.670174 | − | 0.742204i | \(-0.733781\pi\) |
0.977854 | + | 0.209286i | \(0.0671140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.51087 | − | 6.08101i | −0.155312 | − | 0.269008i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.1753 | + | 19.3561i | 0.492441 | + | 0.852933i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.686141 | + | 1.18843i | −0.0301764 | + | 0.0522671i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.11684 | 0.224173 | 0.112087 | − | 0.993698i | \(-0.464247\pi\) | ||||
0.112087 | + | 0.993698i | \(0.464247\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.48913 | 0.414930 | 0.207465 | − | 0.978242i | \(-0.433479\pi\) | ||||
0.207465 | + | 0.978242i | \(0.433479\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.116844 | + | 0.202380i | −0.00508980 | + | 0.00881580i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.93070 | − | 5.07613i | −0.127422 | − | 0.220701i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.686141 | + | 1.18843i | 0.0297201 | + | 0.0514766i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.7446 | + | 46.3229i | −1.15627 | + | 2.00272i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.11684 | 0.220398 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.2337 | 1.38583 | 0.692917 | − | 0.721017i | \(-0.256325\pi\) | ||||
0.692917 | + | 0.721017i | \(0.256325\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.3723 | + | 19.6974i | −0.487135 | + | 0.843743i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8723 | + | 24.0275i | 0.593136 | + | 1.02734i | 0.993807 | + | 0.111120i | \(0.0354437\pi\) |
−0.400671 | + | 0.916222i | \(0.631223\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.37228 | − | 7.57301i | −0.186265 | − | 0.322621i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.430703 | + | 0.746000i | −0.0183154 | + | 0.0317231i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0000 | −0.593199 | −0.296600 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296600 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −52.3505 | −2.21419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.872281 | + | 1.51084i | −0.0367623 | + | 0.0636741i | −0.883821 | − | 0.467825i | \(-0.845038\pi\) |
0.847059 | + | 0.531499i | \(0.178371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.31386 | − | 4.00772i | −0.0973448 | − | 0.168606i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.61684 | − | 6.26456i | −0.151626 | − | 0.262624i | 0.780199 | − | 0.625531i | \(-0.215118\pi\) |
−0.931825 | + | 0.362907i | \(0.881784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.75544 | − | 3.04051i | 0.0734628 | − | 0.127241i | −0.826954 | − | 0.562270i | \(-0.809928\pi\) |
0.900417 | + | 0.435028i | \(0.143262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.2337 | 1.42764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.8614 | −0.577058 | −0.288529 | − | 0.957471i | \(-0.593166\pi\) | ||||
−0.288529 | + | 0.957471i | \(0.593166\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5475 | − | 18.2689i | 0.437586 | − | 0.757921i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.37228 | − | 9.30506i | −0.222497 | − | 0.385376i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.6168 | − | 21.8530i | −0.520753 | − | 0.901970i | −0.999709 | − | 0.0241315i | \(-0.992318\pi\) |
0.478956 | − | 0.877839i | \(-0.341015\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | − | 3.46410i | 0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.0000 | 1.06769 | 0.533846 | − | 0.845582i | \(-0.320746\pi\) | ||||
0.533846 | + | 0.845582i | \(0.320746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.72281 | 0.0706285 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.56930 | + | 9.64630i | −0.227555 | + | 0.394137i | −0.957083 | − | 0.289814i | \(-0.906407\pi\) |
0.729528 | + | 0.683951i | \(0.239740\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.9891 | + | 34.6222i | 0.815373 | + | 1.41227i | 0.909059 | + | 0.416666i | \(0.136802\pi\) |
−0.0936860 | + | 0.995602i | \(0.529865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.8614 | − | 29.2048i | −0.685514 | − | 1.18734i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.05842 | − | 5.29734i | 0.124138 | − | 0.215012i | −0.797258 | − | 0.603639i | \(-0.793717\pi\) |
0.921395 | + | 0.388626i | \(0.127050\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.37228 | 0.298251 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.25544 | 0.0507066 | 0.0253533 | − | 0.999679i | \(-0.491929\pi\) | ||||
0.0253533 | + | 0.999679i | \(0.491929\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.98913 | + | 6.90937i | −0.160596 | + | 0.278161i | −0.935083 | − | 0.354430i | \(-0.884675\pi\) |
0.774487 | + | 0.632590i | \(0.218008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.61684 | + | 11.4607i | 0.265953 | + | 0.460645i | 0.967813 | − | 0.251671i | \(-0.0809799\pi\) |
−0.701860 | + | 0.712315i | \(0.747647\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.11684 | + | 7.13058i | 0.164938 | + | 0.285681i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.12772 | − | 14.0776i | 0.325109 | − | 0.563105i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.02175 | −0.0407398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | − | 13.8564i | 0.317470 | − | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.7446 | − | 23.8063i | −0.544579 | − | 0.943239i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.6168 | − | 27.0492i | −0.616828 | − | 1.06838i | −0.990061 | − | 0.140640i | \(-0.955084\pi\) |
0.373233 | − | 0.927738i | \(-0.378249\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.50000 | + | 2.59808i | −0.0591542 | + | 0.102458i | −0.894086 | − | 0.447895i | \(-0.852174\pi\) |
0.834932 | + | 0.550353i | \(0.185507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.7228 | −0.932640 | −0.466320 | − | 0.884616i | \(-0.654420\pi\) | ||||
−0.466320 | + | 0.884616i | \(0.654420\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.00000 | 0.274774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.0584 | − | 34.7422i | 0.784947 | − | 1.35957i | −0.144084 | − | 0.989565i | \(-0.546024\pi\) |
0.929031 | − | 0.370002i | \(-0.120643\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.2921 | − | 36.8790i | −0.831952 | − | 1.44098i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.941578 | + | 1.63086i | 0.0366787 | + | 0.0635293i | 0.883782 | − | 0.467899i | \(-0.154989\pi\) |
−0.847103 | + | 0.531428i | \(0.821656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.54755 | − | 14.8048i | 0.332461 | − | 0.575839i | −0.650533 | − | 0.759478i | \(-0.725454\pi\) |
0.982994 | + | 0.183639i | \(0.0587877\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −29.4891 | −1.14354 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.37228 | 0.285456 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.68614 | − | 2.92048i | 0.0650927 | − | 0.112744i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.68614 | − | 4.65253i | −0.103543 | − | 0.179342i | 0.809599 | − | 0.586983i | \(-0.199685\pi\) |
−0.913142 | + | 0.407642i | \(0.866351\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.80298 | − | 16.9793i | −0.376759 | − | 0.652566i | 0.613829 | − | 0.789439i | \(-0.289628\pi\) |
−0.990589 | + | 0.136872i | \(0.956295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.68614 | − | 11.5807i | 0.256591 | − | 0.444428i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.62772 | 0.368394 | 0.184197 | − | 0.982889i | \(-0.441031\pi\) | ||||
0.184197 | + | 0.982889i | \(0.441031\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.0951 | 0.806002 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.8614 | + | 49.9894i | −1.09953 | + | 1.90445i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.05842 | + | 1.83324i | 0.0402643 | + | 0.0697398i | 0.885455 | − | 0.464725i | \(-0.153847\pi\) |
−0.845191 | + | 0.534464i | \(0.820513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.68614 | − | 16.7769i | −0.367416 | − | 0.636384i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0475473 | − | 0.0823543i | 0.00180098 | − | 0.00311939i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.5109 | −0.472529 | −0.236265 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236265 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.4891 | 0.659615 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.94158 | + | 12.0232i | −0.261065 | + | 0.452178i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.80298 | + | 10.0511i | 0.217936 | + | 0.377476i | 0.954177 | − | 0.299244i | \(-0.0967344\pi\) |
−0.736241 | + | 0.676719i | \(0.763401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.68614 | + | 2.92048i | 0.0631465 | + | 0.109373i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.05842 | − | 15.6896i | 0.338766 | − | 0.586760i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.5109 | 0.839514 | 0.419757 | − | 0.907637i | \(-0.362115\pi\) | ||||
0.419757 | + | 0.907637i | \(0.362115\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.09509 | 0.338719 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.37228 | + | 7.57301i | −0.162382 | + | 0.281255i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0584 | + | 24.3499i | 0.521398 | + | 0.903088i | 0.999690 | + | 0.0248871i | \(0.00792263\pi\) |
−0.478292 | + | 0.878201i | \(0.658744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.81386 | + | 3.14170i | 0.0670880 | + | 0.116200i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.56930 | + | 7.91425i | −0.168771 | + | 0.292320i | −0.937988 | − | 0.346668i | \(-0.887313\pi\) |
0.769217 | + | 0.638987i | \(0.220646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.74456 | −0.285275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8832 | 0.915342 | 0.457671 | − | 0.889122i | \(-0.348684\pi\) | ||||
0.457671 | + | 0.889122i | \(0.348684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.6861 | + | 35.8294i | −0.758901 | + | 1.31445i | 0.184511 | + | 0.982831i | \(0.440930\pi\) |
−0.943412 | + | 0.331624i | \(0.892403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.43070 | − | 7.67420i | −0.162328 | − | 0.281161i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.8832 | + | 18.8502i | 0.397662 | + | 0.688771i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6861 | + | 37.5615i | −0.791339 | + | 1.37064i | 0.133800 | + | 0.991008i | \(0.457282\pi\) |
−0.925138 | + | 0.379630i | \(0.876051\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.1168 | −0.659339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.4891 | −1.14449 | −0.572246 | − | 0.820082i | \(-0.693928\pi\) | ||||
−0.572246 | + | 0.820082i | \(0.693928\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.1753 | − | 28.0164i | 0.586353 | − | 1.01559i | −0.408352 | − | 0.912824i | \(-0.633897\pi\) |
0.994705 | − | 0.102769i | \(-0.0327701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.62772 | + | 8.01544i | 0.167535 | + | 0.290179i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.8030 | − | 32.5677i | −0.678936 | − | 1.17595i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.94158 | + | 13.7552i | −0.286381 | + | 0.496026i | −0.972943 | − | 0.231045i | \(-0.925786\pi\) |
0.686562 | + | 0.727071i | \(0.259119\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.9783 | −0.610665 | −0.305333 | − | 0.952246i | \(-0.598768\pi\) | ||||
−0.305333 | + | 0.952246i | \(0.598768\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.813859 | + | 1.40965i | −0.0291595 | + | 0.0505058i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | − | 3.46410i | −0.0715656 | − | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.8030 | − | 41.2280i | −0.849565 | − | 1.47149i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.9198 | − | 27.5740i | 0.567481 | − | 0.982905i | −0.429334 | − | 0.903146i | \(-0.641252\pi\) |
0.996814 | − | 0.0797592i | \(-0.0254151\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.88316 | −0.0669573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.1168 | −0.643348 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.8030 | + | 37.7639i | −0.772301 | + | 1.33767i | 0.163997 | + | 0.986461i | \(0.447561\pi\) |
−0.936299 | + | 0.351204i | \(0.885772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.255437 | − | 0.442430i | −0.00903672 | − | 0.0156521i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.55842 | + | 4.43132i | 0.0902848 | + | 0.156378i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.4307 | − | 21.5306i | 0.438125 | − | 0.758854i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.8614 | −1.47177 | −0.735884 | − | 0.677107i | \(-0.763233\pi\) | ||||
−0.735884 | + | 0.677107i | \(0.763233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.3505 | −1.45201 | −0.726007 | − | 0.687688i | \(-0.758626\pi\) | ||||
−0.726007 | + | 0.687688i | \(0.758626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.2337 | + | 35.0458i | −0.708755 | + | 1.22760i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.0475 | − | 53.7759i | −1.08622 | − | 1.88138i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.6861 | − | 21.9730i | −0.442749 | − | 0.766864i | 0.555143 | − | 0.831755i | \(-0.312664\pi\) |
−0.997892 | + | 0.0648905i | \(0.979330\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0584 | − | 36.4743i | 0.734050 | − | 1.27141i | −0.221088 | − | 0.975254i | \(-0.570961\pi\) |
0.955139 | − | 0.296159i | \(-0.0957058\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.9783 | 0.520845 | 0.260422 | − | 0.965495i | \(-0.416138\pi\) | ||||
0.260422 | + | 0.965495i | \(0.416138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.48913 | 0.260108 | 0.130054 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130054 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.952453 | + | 1.64970i | −0.0330005 | + | 0.0571586i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.17527 | − | 5.49972i | −0.109885 | − | 0.190326i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.5475 | + | 28.6612i | 0.571285 | + | 0.989494i | 0.996434 | + | 0.0843712i | \(0.0268881\pi\) |
−0.425150 | + | 0.905123i | \(0.639779\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5584 | − | 23.4839i | 0.467532 | − | 0.809789i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −53.4891 | −1.84008 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.7228 | −0.471521 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.37228 | + | 12.7692i | −0.252719 | + | 0.437721i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.94158 | + | 13.7552i | 0.271914 | + | 0.470970i | 0.969352 | − | 0.245676i | \(-0.0790099\pi\) |
−0.697438 | + | 0.716646i | \(0.745677\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.94158 | + | 17.2193i | 0.339598 | + | 0.588201i | 0.984357 | − | 0.176185i | \(-0.0563757\pi\) |
−0.644759 | + | 0.764386i | \(0.723042\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.2446 | + | 17.7441i | −0.349540 | + | 0.605421i | −0.986168 | − | 0.165750i | \(-0.946995\pi\) |
0.636628 | + | 0.771171i | \(0.280329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.9783 | 0.918350 | 0.459175 | − | 0.888346i | \(-0.348145\pi\) | ||||
0.459175 | + | 0.888346i | \(0.348145\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.8397 | 1.21858 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.313859 | − | 0.543620i | 0.0106469 | − | 0.0184411i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.8030 | + | 36.0318i | 0.704882 | + | 1.22089i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.17527 | + | 5.49972i | 0.107344 | + | 0.185925i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.430703 | + | 0.746000i | −0.0145438 | + | 0.0251906i | −0.873206 | − | 0.487352i | \(-0.837963\pi\) |
0.858662 | + | 0.512542i | \(0.171296\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.9783 | 0.706775 | 0.353388 | − | 0.935477i | \(-0.385030\pi\) | ||||
0.353388 | + | 0.935477i | \(0.385030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.8397 | −1.44167 | −0.720835 | − | 0.693107i | \(-0.756241\pi\) | ||||
−0.720835 | + | 0.693107i | \(0.756241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.43070 | − | 14.6024i | 0.283075 | − | 0.490301i | −0.689065 | − | 0.724699i | \(-0.741979\pi\) |
0.972141 | + | 0.234398i | \(0.0753120\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.25544 | − | 5.63858i | −0.109184 | − | 0.189112i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.37228 | + | 7.57301i | 0.146313 | + | 0.253421i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.7446 | − | 67.1076i | 1.29509 | − | 2.24316i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.861407 | −0.0287295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.6060 | − | 68.5996i | 1.31655 | − | 2.28033i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5000 | − | 32.0429i | −0.614282 | − | 1.06397i | −0.990510 | − | 0.137441i | \(-0.956112\pi\) |
0.376228 | − | 0.926527i | \(-0.377221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.05842 | + | 15.6896i | 0.300119 | + | 0.519821i | 0.976163 | − | 0.217040i | \(-0.0696403\pi\) |
−0.676044 | + | 0.736861i | \(0.736307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.68614 | + | 13.3128i | −0.254374 | + | 0.440589i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.3288 | −0.572247 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.76631 | −0.0582653 | −0.0291326 | − | 0.999576i | \(-0.509275\pi\) | ||||
−0.0291326 | + | 0.999576i | \(0.509275\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.7446 | + | 18.6101i | −0.353662 | + | 0.612560i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.74456 | − | 15.1460i | −0.287519 | − | 0.497998i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.2921 | − | 42.0752i | −0.796998 | − | 1.38044i | −0.921563 | − | 0.388230i | \(-0.873087\pi\) |
0.124564 | − | 0.992212i | \(-0.460247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3030 | − | 28.2376i | 0.534309 | − | 0.925450i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.25544 | −0.0410572 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.9198 | − | 41.4304i | 0.779764 | − | 1.35059i | −0.152313 | − | 0.988332i | \(-0.548672\pi\) |
0.932078 | − | 0.362259i | \(-0.117994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.686141 | − | 1.18843i | −0.0223438 | − | 0.0387006i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.1277 | − | 36.5943i | −0.686559 | − | 1.18915i | −0.972944 | − | 0.231040i | \(-0.925787\pi\) |
0.286386 | − | 0.958114i | \(-0.407546\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.7446 | − | 23.8063i | 0.446167 | − | 0.772785i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.1168 | 0.813614 | 0.406807 | − | 0.913514i | \(-0.366642\pi\) | ||||
0.406807 | + | 0.913514i | \(0.366642\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.6060 | 2.05824 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.29211 | − | 7.43415i | 0.138599 | − | 0.240061i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3030 | + | 26.5055i | 0.493645 | + | 0.855018i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.4307 | − | 28.4588i | −0.528923 | − | 0.916122i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.31386 | + | 2.27567i | −0.0422509 | + | 0.0731806i | −0.886378 | − | 0.462963i | \(-0.846786\pi\) |
0.844127 | + | 0.536144i | \(0.180120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.4891 | −0.561253 | −0.280626 | − | 0.959817i | \(-0.590542\pi\) | ||||
−0.280626 | + | 0.959817i | \(0.590542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.88316 | −0.252722 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.87228 | − | 10.1711i | 0.187871 | − | 0.325402i | −0.756669 | − | 0.653798i | \(-0.773175\pi\) |
0.944540 | + | 0.328396i | \(0.106508\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.00000 | − | 5.19615i | −0.0958804 | − | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9416 | − | 32.8078i | −0.604143 | − | 1.04641i | −0.992186 | − | 0.124765i | \(-0.960182\pi\) |
0.388044 | − | 0.921641i | \(-0.373151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.0951 | − | 78.1070i | 1.43685 | − | 2.48870i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.3505 | 1.66465 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.02175 | −0.159521 | −0.0797606 | − | 0.996814i | \(-0.525416\pi\) | ||||
−0.0797606 | + | 0.996814i | \(0.525416\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.7446 | + | 53.2511i | −0.974668 | + | 1.68817i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.17527 | − | 2.03562i | −0.0372210 | − | 0.0644687i | 0.846815 | − | 0.531888i | \(-0.178517\pi\) |
−0.884036 | + | 0.467419i | \(0.845184\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.i.j.577.2 | 4 | ||
3.2 | odd | 2 | 576.2.i.l.193.1 | 4 | |||
4.3 | odd | 2 | 1728.2.i.i.577.2 | 4 | |||
8.3 | odd | 2 | 216.2.i.b.145.1 | 4 | |||
8.5 | even | 2 | 432.2.i.d.145.1 | 4 | |||
9.2 | odd | 6 | 576.2.i.l.385.1 | 4 | |||
9.4 | even | 3 | 5184.2.a.bo.1.1 | 2 | |||
9.5 | odd | 6 | 5184.2.a.bs.1.2 | 2 | |||
9.7 | even | 3 | inner | 1728.2.i.j.1153.2 | 4 | ||
12.11 | even | 2 | 576.2.i.j.193.2 | 4 | |||
24.5 | odd | 2 | 144.2.i.d.49.2 | 4 | |||
24.11 | even | 2 | 72.2.i.b.49.1 | yes | 4 | ||
36.7 | odd | 6 | 1728.2.i.i.1153.2 | 4 | |||
36.11 | even | 6 | 576.2.i.j.385.2 | 4 | |||
36.23 | even | 6 | 5184.2.a.bt.1.2 | 2 | |||
36.31 | odd | 6 | 5184.2.a.bp.1.1 | 2 | |||
72.5 | odd | 6 | 1296.2.a.n.1.1 | 2 | |||
72.11 | even | 6 | 72.2.i.b.25.1 | ✓ | 4 | ||
72.13 | even | 6 | 1296.2.a.p.1.2 | 2 | |||
72.29 | odd | 6 | 144.2.i.d.97.2 | 4 | |||
72.43 | odd | 6 | 216.2.i.b.73.1 | 4 | |||
72.59 | even | 6 | 648.2.a.f.1.1 | 2 | |||
72.61 | even | 6 | 432.2.i.d.289.1 | 4 | |||
72.67 | odd | 6 | 648.2.a.g.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.i.b.25.1 | ✓ | 4 | 72.11 | even | 6 | ||
72.2.i.b.49.1 | yes | 4 | 24.11 | even | 2 | ||
144.2.i.d.49.2 | 4 | 24.5 | odd | 2 | |||
144.2.i.d.97.2 | 4 | 72.29 | odd | 6 | |||
216.2.i.b.73.1 | 4 | 72.43 | odd | 6 | |||
216.2.i.b.145.1 | 4 | 8.3 | odd | 2 | |||
432.2.i.d.145.1 | 4 | 8.5 | even | 2 | |||
432.2.i.d.289.1 | 4 | 72.61 | even | 6 | |||
576.2.i.j.193.2 | 4 | 12.11 | even | 2 | |||
576.2.i.j.385.2 | 4 | 36.11 | even | 6 | |||
576.2.i.l.193.1 | 4 | 3.2 | odd | 2 | |||
576.2.i.l.385.1 | 4 | 9.2 | odd | 6 | |||
648.2.a.f.1.1 | 2 | 72.59 | even | 6 | |||
648.2.a.g.1.2 | 2 | 72.67 | odd | 6 | |||
1296.2.a.n.1.1 | 2 | 72.5 | odd | 6 | |||
1296.2.a.p.1.2 | 2 | 72.13 | even | 6 | |||
1728.2.i.i.577.2 | 4 | 4.3 | odd | 2 | |||
1728.2.i.i.1153.2 | 4 | 36.7 | odd | 6 | |||
1728.2.i.j.577.2 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.i.j.1153.2 | 4 | 9.7 | even | 3 | inner | ||
5184.2.a.bo.1.1 | 2 | 9.4 | even | 3 | |||
5184.2.a.bp.1.1 | 2 | 36.31 | odd | 6 | |||
5184.2.a.bs.1.2 | 2 | 9.5 | odd | 6 | |||
5184.2.a.bt.1.2 | 2 | 36.23 | even | 6 |