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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1153.1 | ||
Root | \(-1.02187 + 0.977642i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1153 |
Dual form | 1728.2.i.n.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.18614 | − | 2.05446i | −0.530458 | − | 0.918781i | −0.999368 | − | 0.0355348i | \(-0.988687\pi\) |
0.468910 | − | 0.883246i | \(-0.344647\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.10489 | + | 1.91373i | −0.417610 | + | 0.723322i | −0.995699 | − | 0.0926519i | \(-0.970466\pi\) |
0.578088 | + | 0.815974i | \(0.303799\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.96790 | − | 5.14055i | 0.894855 | − | 1.54993i | 0.0608712 | − | 0.998146i | \(-0.480612\pi\) |
0.833984 | − | 0.551789i | \(-0.186055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.18614 | + | 3.78651i | 0.606326 | + | 1.05019i | 0.991840 | + | 0.127486i | \(0.0406908\pi\) |
−0.385514 | + | 0.922702i | \(0.625976\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.37228 | −0.817898 | −0.408949 | − | 0.912557i | \(-0.634105\pi\) | ||||
−0.408949 | + | 0.912557i | \(0.634105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.72601 | 0.854805 | 0.427403 | − | 0.904061i | \(-0.359429\pi\) | ||||
0.427403 | + | 0.904061i | \(0.359429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.10489 | + | 1.91373i | 0.230386 | + | 0.399041i | 0.957922 | − | 0.287029i | \(-0.0926677\pi\) |
−0.727536 | + | 0.686070i | \(0.759334\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.313859 | + | 0.543620i | −0.0627719 | + | 0.108724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.186141 | + | 0.322405i | −0.0345655 | + | 0.0598691i | −0.882791 | − | 0.469767i | \(-0.844338\pi\) |
0.848225 | + | 0.529636i | \(0.177671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.83090 | − | 8.36737i | −0.867656 | − | 1.50282i | −0.864386 | − | 0.502830i | \(-0.832292\pi\) |
−0.00327038 | − | 0.999995i | \(-0.501041\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.24224 | 0.886099 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.500000 | + | 0.866025i | 0.0780869 | + | 0.135250i | 0.902424 | − | 0.430848i | \(-0.141786\pi\) |
−0.824338 | + | 0.566099i | \(0.808452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96790 | − | 5.14055i | 0.452600 | − | 0.783927i | −0.545946 | − | 0.837820i | \(-0.683830\pi\) |
0.998547 | + | 0.0538934i | \(0.0171631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.10489 | − | 1.91373i | 0.161165 | − | 0.279146i | −0.774122 | − | 0.633037i | \(-0.781808\pi\) |
0.935287 | + | 0.353891i | \(0.115141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.05842 | + | 1.83324i | 0.151203 | + | 0.261892i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.0814 | −1.89873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.17769 | − | 8.96801i | −0.674077 | − | 1.16754i | −0.976738 | − | 0.214437i | \(-0.931208\pi\) |
0.302661 | − | 0.953098i | \(-0.402125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.55842 | − | 13.0916i | 0.967757 | − | 1.67620i | 0.265738 | − | 0.964045i | \(-0.414384\pi\) |
0.702019 | − | 0.712159i | \(-0.252282\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.18614 | − | 8.98266i | 0.643262 | − | 1.11416i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.17769 | − | 8.96801i | −0.632555 | − | 1.09562i | −0.987028 | − | 0.160551i | \(-0.948673\pi\) |
0.354473 | − | 0.935066i | \(-0.384660\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.41957 | −0.524507 | −0.262253 | − | 0.964999i | \(-0.584466\pi\) | ||||
−0.262253 | + | 0.964999i | \(0.584466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.62772 | 0.541634 | 0.270817 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270817 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.55842 | + | 11.3595i | 0.747402 | + | 1.29454i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.83090 | − | 8.36737i | 0.543519 | − | 0.941403i | −0.455179 | − | 0.890400i | \(-0.650425\pi\) |
0.998698 | − | 0.0510030i | \(-0.0162418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.04069 | − | 12.1948i | 0.772816 | − | 1.33856i | −0.163198 | − | 0.986593i | \(-0.552181\pi\) |
0.936014 | − | 0.351963i | \(-0.114486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | + | 6.92820i | 0.433861 | + | 0.751469i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.25544 | −0.133076 | −0.0665380 | − | 0.997784i | \(-0.521195\pi\) | ||||
−0.0665380 | + | 0.997784i | \(0.521195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.66181 | −1.01283 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.41957 | − | 7.65492i | −0.453439 | − | 0.785379i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.50000 | + | 7.79423i | −0.456906 | + | 0.791384i | −0.998796 | − | 0.0490655i | \(-0.984376\pi\) |
0.541890 | + | 0.840450i | \(0.317709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.55842 | − | 13.0916i | 0.752091 | − | 1.30266i | −0.194716 | − | 0.980860i | \(-0.562379\pi\) |
0.946808 | − | 0.321800i | \(-0.104288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.10489 | + | 1.91373i | 0.108868 | + | 0.188566i | 0.915312 | − | 0.402745i | \(-0.131944\pi\) |
−0.806444 | + | 0.591311i | \(0.798611\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.72601 | −0.360207 | −0.180104 | − | 0.983648i | \(-0.557643\pi\) | ||||
−0.180104 | + | 0.983648i | \(0.557643\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.4891 | −1.67515 | −0.837577 | − | 0.546319i | \(-0.816029\pi\) | ||||
−0.837577 | + | 0.546319i | \(0.816029\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.81386 | + | 10.0699i | 0.546922 | + | 0.947296i | 0.998483 | + | 0.0550564i | \(0.0175339\pi\) |
−0.451561 | + | 0.892240i | \(0.649133\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.62112 | − | 4.53991i | 0.244420 | − | 0.423349i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.72601 | − | 6.45364i | 0.341563 | − | 0.591604i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.1168 | − | 20.9870i | −1.10153 | − | 1.90791i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3723 | −0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.45202 | 0.661260 | 0.330630 | − | 0.943760i | \(-0.392739\pi\) | ||||
0.330630 | + | 0.943760i | \(0.392739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.83090 | + | 8.36737i | 0.422078 | + | 0.731061i | 0.996143 | − | 0.0877494i | \(-0.0279675\pi\) |
−0.574065 | + | 0.818810i | \(0.694634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.11684 | + | 7.13058i | −0.356976 | + | 0.618300i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.24456 | + | 10.8159i | −0.533509 | + | 0.924065i | 0.465725 | + | 0.884930i | \(0.345794\pi\) |
−0.999234 | + | 0.0391351i | \(0.987540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.45167 | + | 2.51437i | 0.123129 | + | 0.213266i | 0.921000 | − | 0.389562i | \(-0.127374\pi\) |
−0.797871 | + | 0.602829i | \(0.794040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.9530 | 2.17030 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.883156 | 0.0733421 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.81386 | + | 10.0699i | 0.476290 | + | 0.824958i | 0.999631 | − | 0.0271650i | \(-0.00864795\pi\) |
−0.523341 | + | 0.852123i | \(0.675315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.10489 | − | 1.91373i | 0.0899149 | − | 0.155737i | −0.817560 | − | 0.575843i | \(-0.804674\pi\) |
0.907475 | + | 0.420106i | \(0.138007\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4603 | + | 19.8498i | −0.920510 | + | 1.59437i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.55842 | − | 2.69927i | −0.124376 | − | 0.215425i | 0.797113 | − | 0.603830i | \(-0.206359\pi\) |
−0.921489 | + | 0.388405i | \(0.873026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.88316 | −0.384847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.83915 | −0.692335 | −0.346168 | − | 0.938173i | \(-0.612517\pi\) | ||||
−0.346168 | + | 0.938173i | \(0.612517\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.83090 | − | 8.36737i | −0.373827 | − | 0.647487i | 0.616324 | − | 0.787493i | \(-0.288621\pi\) |
−0.990151 | + | 0.140006i | \(0.955288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05842 | + | 5.29734i | −0.235263 | + | 0.407488i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.186141 | − | 0.322405i | 0.0141520 | − | 0.0245120i | −0.858863 | − | 0.512206i | \(-0.828828\pi\) |
0.873015 | + | 0.487694i | \(0.162162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.693562 | − | 1.20128i | −0.0524284 | − | 0.0908086i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.83915 | 0.660669 | 0.330334 | − | 0.943864i | \(-0.392838\pi\) | ||||
0.330334 | + | 0.943864i | \(0.392838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.23369 | 0.612005 | 0.306003 | − | 0.952031i | \(-0.401008\pi\) | ||||
0.306003 | + | 0.952031i | \(0.401008\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.74456 | + | 8.21782i | 0.348827 | + | 0.604186i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0086 | + | 17.3354i | −0.731901 | + | 1.26769i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.55691 | − | 14.8210i | 0.619157 | − | 1.07241i | −0.370483 | − | 0.928839i | \(-0.620808\pi\) |
0.989640 | − | 0.143572i | \(-0.0458587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | − | 0.866025i | −0.0359908 | − | 0.0623379i | 0.847469 | − | 0.530845i | \(-0.178125\pi\) |
−0.883460 | + | 0.468507i | \(0.844792\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.744563 | 0.0530479 | 0.0265239 | − | 0.999648i | \(-0.491556\pi\) | ||||
0.0265239 | + | 0.999648i | \(0.491556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7107 | 1.46815 | 0.734073 | − | 0.679071i | \(-0.237617\pi\) | ||||
0.734073 | + | 0.679071i | \(0.237617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.411331 | − | 0.712446i | −0.0288698 | − | 0.0500039i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.18614 | − | 2.05446i | 0.0828437 | − | 0.143489i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.0584 | − | 19.1537i | 0.764927 | − | 1.32489i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.62112 | − | 4.53991i | −0.180445 | − | 0.312540i | 0.761587 | − | 0.648063i | \(-0.224421\pi\) |
−0.942032 | + | 0.335522i | \(0.891087\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0814 | −0.960342 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.3505 | 1.44937 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.37228 | − | 12.7692i | −0.495913 | − | 0.858947i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.10489 | + | 1.91373i | −0.0739891 | + | 0.128153i | −0.900646 | − | 0.434553i | \(-0.856906\pi\) |
0.826657 | + | 0.562706i | \(0.190240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.48412 | + | 7.76673i | −0.297622 | + | 0.515496i | −0.975591 | − | 0.219594i | \(-0.929527\pi\) |
0.677970 | + | 0.735090i | \(0.262860\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.18614 | − | 3.78651i | −0.144464 | − | 0.250219i | 0.784709 | − | 0.619865i | \(-0.212813\pi\) |
−0.929173 | + | 0.369645i | \(0.879479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.86141 | −0.187457 | −0.0937285 | − | 0.995598i | \(-0.529879\pi\) | ||||
−0.0937285 | + | 0.995598i | \(0.529879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.24224 | −0.341966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.55691 | + | 14.8210i | 0.553501 | + | 0.958692i | 0.998018 | + | 0.0629214i | \(0.0200418\pi\) |
−0.444518 | + | 0.895770i | \(0.646625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.127719 | + | 0.221215i | −0.00822708 | + | 0.0142497i | −0.870110 | − | 0.492858i | \(-0.835952\pi\) |
0.861883 | + | 0.507108i | \(0.169285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.51087 | − | 4.34896i | 0.160414 | − | 0.277845i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.14558 | + | 14.1086i | 0.518291 | + | 0.897706i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.1780 | −0.705551 | −0.352776 | − | 0.935708i | \(-0.614762\pi\) | ||||
−0.352776 | + | 0.935708i | \(0.614762\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.1168 | 0.824649 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.24456 | − | 5.61975i | −0.202390 | − | 0.350550i | 0.746908 | − | 0.664928i | \(-0.231538\pi\) |
−0.949298 | + | 0.314377i | \(0.898204\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.41957 | − | 7.65492i | 0.274619 | − | 0.475654i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.55691 | + | 14.8210i | −0.527642 | + | 0.913903i | 0.471839 | + | 0.881685i | \(0.343590\pi\) |
−0.999481 | + | 0.0322179i | \(0.989743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.74456 | + | 8.21782i | 0.291456 | + | 0.504817i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.48913 | 0.578562 | 0.289281 | − | 0.957244i | \(-0.406584\pi\) | ||||
0.289281 | + | 0.957244i | \(0.406584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9040 | 0.905356 | 0.452678 | − | 0.891674i | \(-0.350469\pi\) | ||||
0.452678 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.86301 | + | 3.22682i | 0.112343 | + | 0.194585i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.55842 | − | 11.3595i | 0.394057 | − | 0.682527i | −0.598923 | − | 0.800807i | \(-0.704404\pi\) |
0.992980 | + | 0.118279i | \(0.0377378\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9307 | − | 22.3966i | 0.771381 | − | 1.33607i | −0.165425 | − | 0.986222i | \(-0.552900\pi\) |
0.936806 | − | 0.349849i | \(-0.113767\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.62112 | + | 4.53991i | 0.155809 | + | 0.269870i | 0.933353 | − | 0.358959i | \(-0.116868\pi\) |
−0.777544 | + | 0.628828i | \(0.783535\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.20979 | −0.130440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.62772 | −0.331042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1861 | + | 17.6429i | 0.595081 | + | 1.03071i | 0.993535 | + | 0.113522i | \(0.0362132\pi\) |
−0.398455 | + | 0.917188i | \(0.630453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2829 | + | 21.2747i | −0.715140 | + | 1.23866i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.83090 | + | 8.36737i | −0.279378 | + | 0.483898i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.55842 | + | 11.3595i | 0.378021 | + | 0.654752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −35.8614 | −2.05342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.8563 | 1.64692 | 0.823459 | − | 0.567376i | \(-0.192041\pi\) | ||||
0.823459 | + | 0.567376i | \(0.192041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.34713 | − | 10.9935i | −0.359913 | − | 0.623387i | 0.628033 | − | 0.778186i | \(-0.283860\pi\) |
−0.987946 | + | 0.154800i | \(0.950527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.61684 | + | 16.6569i | −0.543576 | + | 0.941502i | 0.455119 | + | 0.890431i | \(0.349597\pi\) |
−0.998695 | + | 0.0510708i | \(0.983737\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.18614 | + | 7.25061i | −0.235117 | + | 0.407235i | −0.959307 | − | 0.282366i | \(-0.908881\pi\) |
0.724190 | + | 0.689601i | \(0.242214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.10489 | + | 1.91373i | 0.0618621 | + | 0.107148i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.5652 | −0.699144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.74456 | −0.152241 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.44158 | + | 4.22894i | 0.134609 | + | 0.233149i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.7025 | + | 28.9296i | −0.918052 | + | 1.59011i | −0.115682 | + | 0.993286i | \(0.536905\pi\) |
−0.802370 | + | 0.596827i | \(0.796428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.2829 | + | 21.2747i | −0.671088 | + | 1.16236i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | + | 7.79423i | 0.245131 | + | 0.424579i | 0.962168 | − | 0.272456i | \(-0.0878358\pi\) |
−0.717038 | + | 0.697034i | \(0.754502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −57.3505 | −3.10571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1463 | −1.08780 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.17769 | + | 8.96801i | 0.277953 | + | 0.481428i | 0.970876 | − | 0.239583i | \(-0.0770108\pi\) |
−0.692923 | + | 0.721011i | \(0.743677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5584 | + | 20.0198i | −0.618708 | + | 1.07163i | 0.371014 | + | 0.928627i | \(0.379010\pi\) |
−0.989722 | + | 0.143007i | \(0.954323\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.61684 | + | 16.6569i | −0.511853 | + | 0.886555i | 0.488053 | + | 0.872814i | \(0.337707\pi\) |
−0.999906 | + | 0.0137411i | \(0.995626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.24224 | + | 9.07982i | 0.278229 | + | 0.481907i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3561 | −1.17991 | −0.589954 | − | 0.807437i | \(-0.700854\pi\) | ||||
−0.589954 | + | 0.807437i | \(0.700854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.11684 | −0.269308 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.48913 | − | 9.50744i | −0.287314 | − | 0.497642i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.6700 | − | 23.6772i | 0.713571 | − | 1.23594i | −0.249937 | − | 0.968262i | \(-0.580410\pi\) |
0.963508 | − | 0.267679i | \(-0.0862566\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.41957 | − | 7.65492i | 0.229453 | − | 0.397424i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.55842 | − | 14.8236i | −0.443138 | − | 0.767538i | 0.554782 | − | 0.831996i | \(-0.312802\pi\) |
−0.997920 | + | 0.0644576i | \(0.979468\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.62772 | −0.0838318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.14558 | 0.418411 | 0.209205 | − | 0.977872i | \(-0.432912\pi\) | ||||
0.209205 | + | 0.977872i | \(0.432912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4603 | + | 19.8498i | 0.585592 | + | 1.01428i | 0.994801 | + | 0.101835i | \(0.0324713\pi\) |
−0.409209 | + | 0.912441i | \(0.634195\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.5584 | − | 26.9480i | 0.792931 | − | 1.37340i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.67527 | − | 16.7581i | 0.490555 | − | 0.849667i | −0.509385 | − | 0.860538i | \(-0.670127\pi\) |
0.999941 | + | 0.0108715i | \(0.00346057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.72601 | − | 6.45364i | −0.188432 | − | 0.326375i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.9205 | −1.15326 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | 0.200754 | 0.100377 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100377 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.9891 | + | 24.2299i | 0.698584 | + | 1.20998i | 0.968958 | + | 0.247227i | \(0.0795193\pi\) |
−0.270374 | + | 0.962755i | \(0.587147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.1221 | − | 36.5845i | 1.05217 | − | 1.82240i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8716 | + | 20.5622i | −0.588453 | + | 1.01923i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.12772 | + | 15.8097i | 0.451337 | + | 0.781738i | 0.998469 | − | 0.0553079i | \(-0.0176140\pi\) |
−0.547133 | + | 0.837046i | \(0.684281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.8832 | 1.12601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.4050 | −1.63979 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.62112 | + | 4.53991i | 0.128050 | + | 0.221789i | 0.922921 | − | 0.384989i | \(-0.125795\pi\) |
−0.794871 | + | 0.606778i | \(0.792462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.1861 | + | 19.3750i | −0.545179 | + | 0.944278i | 0.453416 | + | 0.891299i | \(0.350205\pi\) |
−0.998596 | + | 0.0529792i | \(0.983128\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.05842 | − | 1.83324i | 0.0513410 | − | 0.0889252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.7025 | + | 28.9296i | 0.808291 | + | 1.40000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.45202 | −0.358951 | −0.179476 | − | 0.983762i | \(-0.557440\pi\) | ||||
−0.179476 | + | 0.983762i | \(0.557440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1168 | −0.870640 | −0.435320 | − | 0.900276i | \(-0.643365\pi\) | ||||
−0.435320 | + | 0.900276i | \(0.643365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.11684 | + | 7.13058i | 0.196935 | + | 0.341102i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.4603 | + | 19.8498i | −0.546969 | + | 0.947377i | 0.451512 | + | 0.892265i | \(0.350885\pi\) |
−0.998480 | + | 0.0551120i | \(0.982448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.48412 | − | 7.76673i | 0.213047 | − | 0.369008i | −0.739620 | − | 0.673025i | \(-0.764995\pi\) |
0.952667 | + | 0.304017i | \(0.0983279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.48913 | + | 2.57924i | 0.0705913 | + | 0.122268i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1168 | 0.854987 | 0.427493 | − | 0.904018i | \(-0.359397\pi\) | ||||
0.427493 | + | 0.904018i | \(0.359397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.93580 | 0.279506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.4603 | + | 19.8498i | 0.537265 | + | 0.930571i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.9891 | − | 22.4978i | 0.607606 | − | 1.05240i | −0.384028 | − | 0.923321i | \(-0.625463\pi\) |
0.991634 | − | 0.129083i | \(-0.0412032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5584 | − | 25.2159i | 0.678053 | − | 1.17442i | −0.297513 | − | 0.954718i | \(-0.596157\pi\) |
0.975566 | − | 0.219705i | \(-0.0705095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.9123 | + | 32.7570i | 0.878928 | + | 1.52235i | 0.852518 | + | 0.522697i | \(0.175074\pi\) |
0.0264102 | + | 0.999651i | \(0.491592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.3083 | 1.68015 | 0.840075 | − | 0.542470i | \(-0.182511\pi\) | ||||
0.840075 | + | 0.542470i | \(0.182511\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.8832 | 1.05665 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.6168 | − | 30.5133i | −0.810023 | − | 1.40300i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.16944 | + | 2.02554i | −0.0536577 | + | 0.0929379i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.10489 | + | 1.91373i | −0.0504839 | + | 0.0874406i | −0.890163 | − | 0.455642i | \(-0.849410\pi\) |
0.839679 | + | 0.543083i | \(0.182743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.74456 | − | 15.1460i | −0.398718 | − | 0.690599i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.3505 | 0.969478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.45202 | 0.337683 | 0.168842 | − | 0.985643i | \(-0.445997\pi\) | ||||
0.168842 | + | 0.985643i | \(0.445997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0645501 | − | 0.111804i | −0.00291310 | − | 0.00504564i | 0.864565 | − | 0.502521i | \(-0.167594\pi\) |
−0.867478 | + | 0.497475i | \(0.834261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.627719 | − | 1.08724i | 0.0282710 | − | 0.0489669i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.88316 | − | 8.45787i | 0.219039 | − | 0.379388i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6297 | + | 21.8753i | 0.565383 | + | 0.979273i | 0.997014 | + | 0.0772222i | \(0.0246051\pi\) |
−0.431631 | + | 0.902050i | \(0.642062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.4845 | −0.467479 | −0.233740 | − | 0.972299i | \(-0.575096\pi\) | ||||
−0.233740 | + | 0.972299i | \(0.575096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.8614 | −1.59581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.67527 | + | 11.5619i | 0.295876 | + | 0.512472i | 0.975188 | − | 0.221377i | \(-0.0710552\pi\) |
−0.679312 | + | 0.733849i | \(0.737722\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.11313 | + | 8.85621i | −0.226192 | + | 0.391776i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.62112 | − | 4.53991i | 0.115500 | − | 0.200052i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.55842 | − | 11.3595i | −0.288439 | − | 0.499591i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3505 | 0.716330 | 0.358165 | − | 0.933658i | \(-0.383403\pi\) | ||||
0.358165 | + | 0.933658i | \(0.383403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.3236 | 0.844963 | 0.422481 | − | 0.906372i | \(-0.361159\pi\) | ||||
0.422481 | + | 0.906372i | \(0.361159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.2912 | + | 28.2171i | 0.709654 | + | 1.22916i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.05842 | − | 15.6896i | 0.393844 | − | 0.682159i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.18614 | + | 3.78651i | −0.0946923 | + | 0.164012i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.41957 | + | 7.65492i | 0.191075 | + | 0.330951i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.5652 | 0.541220 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.74456 | −0.375958 | −0.187979 | − | 0.982173i | \(-0.560194\pi\) | ||||
−0.187979 | + | 0.982173i | \(0.560194\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.7446 | + | 35.9306i | 0.888599 | + | 1.53910i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.758112 | − | 1.31309i | 0.0324145 | − | 0.0561436i | −0.849363 | − | 0.527809i | \(-0.823014\pi\) |
0.881778 | + | 0.471665i | \(0.156347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.693562 | + | 1.20128i | −0.0295467 | + | 0.0511765i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6753 | + | 18.4901i | 0.453958 | + | 0.786279i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.7446 | −0.794233 | −0.397116 | − | 0.917768i | \(-0.629989\pi\) | ||||
−0.397116 | + | 0.917768i | \(0.629989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.9530 | 1.09769 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.1135 | − | 19.2491i | −0.468377 | − | 0.811254i | 0.530969 | − | 0.847391i | \(-0.321828\pi\) |
−0.999347 | + | 0.0361375i | \(0.988495\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7921 | − | 23.8886i | 0.580238 | − | 1.00500i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.8723 | + | 34.4198i | −0.833089 | + | 1.44295i | 0.0624872 | + | 0.998046i | \(0.480097\pi\) |
−0.895577 | + | 0.444907i | \(0.853237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0645501 | − | 0.111804i | −0.00270134 | − | 0.00467885i | 0.864672 | − | 0.502338i | \(-0.167527\pi\) |
−0.867373 | + | 0.497659i | \(0.834193\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.38712 | −0.0578471 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1168 | 0.754214 | 0.377107 | − | 0.926170i | \(-0.376919\pi\) | ||||
0.377107 | + | 0.926170i | \(0.376919\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.5584 | + | 26.9480i | 0.645472 | + | 1.11799i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.8716 | + | 20.5622i | −0.491671 | + | 0.851599i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.87125 | − | 10.1693i | 0.242332 | − | 0.419732i | −0.719046 | − | 0.694963i | \(-0.755421\pi\) |
0.961378 | + | 0.275231i | \(0.0887542\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.0000 | − | 31.1769i | −0.741677 | − | 1.28462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.7228 | 0.727789 | 0.363894 | − | 0.931440i | \(-0.381447\pi\) | ||||
0.363894 | + | 0.931440i | \(0.381447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.6783 | −0.724739 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.6700 | − | 23.6772i | −0.558543 | − | 0.967425i | −0.997618 | − | 0.0689747i | \(-0.978027\pi\) |
0.439075 | − | 0.898450i | \(-0.355306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.38316 | − | 2.39570i | 0.0564201 | − | 0.0977225i | −0.836436 | − | 0.548065i | \(-0.815365\pi\) |
0.892856 | + | 0.450342i | \(0.148698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.7446 | + | 49.7870i | −1.16863 | + | 2.02413i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.9123 | − | 32.7570i | −0.767626 | − | 1.32957i | −0.938847 | − | 0.344335i | \(-0.888105\pi\) |
0.171221 | − | 0.985233i | \(-0.445229\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.66181 | 0.390875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.4674 | −1.47290 | −0.736452 | − | 0.676490i | \(-0.763500\pi\) | ||||
−0.736452 | + | 0.676490i | \(0.763500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.8723 | − | 32.6878i | −0.759769 | − | 1.31596i | −0.942968 | − | 0.332883i | \(-0.891978\pi\) |
0.183199 | − | 0.983076i | \(-0.441355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.758112 | − | 1.31309i | 0.0304711 | − | 0.0527775i | −0.850388 | − | 0.526157i | \(-0.823633\pi\) |
0.880859 | + | 0.473379i | \(0.156966\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.38712 | − | 2.40257i | 0.0555740 | − | 0.0962569i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8723 | + | 24.0275i | 0.554891 | + | 0.961100i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4891 | 0.537847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.83915 | − | 15.3098i | −0.350771 | − | 0.607553i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.62772 | + | 8.01544i | −0.183357 | + | 0.317583i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.87228 | − | 11.9031i | 0.271439 | − | 0.470146i | −0.697792 | − | 0.716301i | \(-0.745834\pi\) |
0.969230 | + | 0.246155i | \(0.0791672\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.90370 | − | 15.4217i | −0.351127 | − | 0.608171i | 0.635320 | − | 0.772249i | \(-0.280868\pi\) |
−0.986447 | + | 0.164079i | \(0.947535\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.0344 | 1.57391 | 0.786956 | − | 0.617009i | \(-0.211656\pi\) | ||||
0.786956 | + | 0.617009i | \(0.211656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −61.4674 | −2.41281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.5584 | − | 35.6082i | −0.804513 | − | 1.39346i | −0.916619 | − | 0.399762i | \(-0.869093\pi\) |
0.112106 | − | 0.993696i | \(-0.464240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.4603 | − | 19.8498i | 0.447790 | − | 0.775594i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.8798 | + | 27.5047i | −0.618591 | + | 1.07143i | 0.371153 | + | 0.928572i | \(0.378963\pi\) |
−0.989743 | + | 0.142858i | \(0.954371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.55842 | − | 2.69927i | −0.0606156 | − | 0.104989i | 0.834125 | − | 0.551575i | \(-0.185973\pi\) |
−0.894741 | + | 0.446586i | \(0.852640\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.5326 | 0.757443 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.822662 | −0.0318536 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.8653 | − | 77.7089i | −1.73200 | − | 2.99992i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6753 | + | 20.2222i | −0.450048 | + | 0.779507i | −0.998388 | − | 0.0567487i | \(-0.981927\pi\) |
0.548340 | + | 0.836255i | \(0.315260\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.675266 | + | 1.16959i | −0.0259526 | + | 0.0449512i | −0.878710 | − | 0.477356i | \(-0.841595\pi\) |
0.852757 | + | 0.522307i | \(0.174929\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.94404 | − | 17.2236i | −0.381617 | − | 0.660980i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.3083 | −1.38930 | −0.694650 | − | 0.719348i | \(-0.744441\pi\) | ||||
−0.694650 | + | 0.719348i | \(0.744441\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.6277 | 1.13202 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.74456 | − | 15.1460i | −0.333141 | − | 0.577018i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.3319 | + | 40.4120i | −0.887586 | + | 1.53734i | −0.0448646 | + | 0.998993i | \(0.514286\pi\) |
−0.842721 | + | 0.538350i | \(0.819048\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.44378 | − | 5.96480i | 0.130630 | − | 0.226258i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.68614 | − | 2.92048i | −0.0638671 | − | 0.110621i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.7446 | 1.31228 | 0.656142 | − | 0.754637i | \(-0.272187\pi\) | ||||
0.656142 | + | 0.754637i | \(0.272187\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9040 | −0.562117 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.7025 | + | 28.9296i | 0.628162 | + | 1.08801i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.30298 | + | 10.9171i | −0.236714 | + | 0.410000i | −0.959769 | − | 0.280790i | \(-0.909404\pi\) |
0.723056 | + | 0.690790i | \(0.242737\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.6753 | − | 18.4901i | 0.399792 | − | 0.692460i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.7839 | − | 53.3192i | −1.15125 | − | 1.99403i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5823 | 1.21512 | 0.607558 | − | 0.794275i | \(-0.292149\pi\) | ||||
0.607558 | + | 0.794275i | \(0.292149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.88316 | −0.181858 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.116844 | − | 0.202380i | −0.00433948 | − | 0.00751619i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3961 | − | 30.1309i | 0.645184 | − | 1.11749i | −0.339075 | − | 0.940759i | \(-0.610114\pi\) |
0.984259 | − | 0.176732i | \(-0.0565527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0086 | + | 17.3354i | −0.370181 | + | 0.641172i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4416 | + | 19.8174i | 0.422604 | + | 0.731972i | 0.996193 | − | 0.0871711i | \(-0.0277827\pi\) |
−0.573589 | + | 0.819143i | \(0.694449\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −61.4674 | −2.26418 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5976 | −0.573767 | −0.286884 | − | 0.957965i | \(-0.592619\pi\) | ||||
−0.286884 | + | 0.957965i | \(0.592619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.7991 | + | 23.9008i | 0.506242 | + | 0.876836i | 0.999974 | + | 0.00722236i | \(0.00229897\pi\) |
−0.493732 | + | 0.869614i | \(0.664368\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.7921 | − | 23.8886i | 0.505304 | − | 0.875212i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.11684 | − | 7.13058i | 0.150426 | − | 0.260546i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4603 | − | 19.8498i | −0.418191 | − | 0.724328i | 0.577567 | − | 0.816344i | \(-0.304002\pi\) |
−0.995758 | + | 0.0920156i | \(0.970669\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.24224 | −0.190784 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4674 | 1.25274 | 0.626369 | − | 0.779527i | \(-0.284540\pi\) | ||||
0.626369 | + | 0.779527i | \(0.284540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.1861 | + | 17.6429i | 0.369247 | + | 0.639555i | 0.989448 | − | 0.144888i | \(-0.0462822\pi\) |
−0.620201 | + | 0.784443i | \(0.712949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3236 | − | 33.4695i | 0.699562 | − | 1.21168i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.6383 | − | 39.2107i | 0.817421 | − | 1.41582i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.44158 | + | 12.8892i | 0.268350 | + | 0.464796i | 0.968436 | − | 0.249263i | \(-0.0801882\pi\) |
−0.700086 | + | 0.714059i | \(0.746855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7446 | −0.674195 | −0.337098 | − | 0.941470i | \(-0.609445\pi\) | ||||
−0.337098 | + | 0.941470i | \(0.609445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.06490 | 0.217858 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.86301 | + | 3.22682i | 0.0667491 | + | 0.115613i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1168 | + | 22.7190i | −0.469358 | + | 0.812951i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.69702 | + | 6.40342i | −0.131952 | + | 0.228548i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.1221 | − | 36.5845i | −0.752921 | − | 1.30410i | −0.946402 | − | 0.322993i | \(-0.895311\pi\) |
0.193481 | − | 0.981104i | \(-0.438022\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.6948 | −0.913601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.0951 | 2.34711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0475 | − | 39.9195i | −0.816386 | − | 1.41402i | −0.908328 | − | 0.418258i | \(-0.862641\pi\) |
0.0919424 | − | 0.995764i | \(-0.470692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.72601 | + | 6.45364i | −0.131817 | + | 0.228313i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.7346 | − | 23.7890i | 0.484683 | − | 0.839496i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.79211 | + | 10.0322i | 0.204145 | + | 0.353590i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.6277 | 0.443967 | 0.221983 | − | 0.975050i | \(-0.428747\pi\) | ||||
0.221983 | + | 0.975050i | \(0.428747\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.5341 | −1.17754 | −0.588771 | − | 0.808300i | \(-0.700388\pi\) | ||||
−0.588771 | + | 0.808300i | \(0.700388\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.4845 | + | 18.1596i | 0.367255 | + | 0.636104i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0584 | − | 19.1537i | 0.386885 | − | 0.670105i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.18614 | + | 7.25061i | −0.146097 | + | 0.253048i | −0.929782 | − | 0.368111i | \(-0.880005\pi\) |
0.783684 | + | 0.621159i | \(0.213338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4603 | + | 19.8498i | 0.399480 | + | 0.691919i | 0.993662 | − | 0.112411i | \(-0.0358575\pi\) |
−0.594182 | + | 0.804331i | \(0.702524\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.83915 | 0.307367 | 0.153684 | − | 0.988120i | \(-0.450886\pi\) | ||||
0.153684 | + | 0.988120i | \(0.450886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.23369 | 0.285968 | 0.142984 | − | 0.989725i | \(-0.454330\pi\) | ||||
0.142984 | + | 0.989725i | \(0.454330\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.56930 | − | 6.18220i | −0.123669 | − | 0.214201i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.4603 | + | 19.8498i | −0.396599 | + | 0.686929i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.83090 | − | 8.36737i | 0.166781 | − | 0.288874i | −0.770505 | − | 0.637434i | \(-0.779996\pi\) |
0.937286 | + | 0.348560i | \(0.113329\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4307 | + | 24.9947i | 0.497610 | + | 0.861887i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5109 | 0.499189 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 53.5513 | 1.84004 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.41957 | − | 7.65492i | −0.151501 | − | 0.262407i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5584 | + | 18.2877i | −0.361513 | + | 0.626160i | −0.988210 | − | 0.153104i | \(-0.951073\pi\) |
0.626697 | + | 0.779263i | \(0.284407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.0475 | + | 38.1875i | −0.753130 | + | 1.30446i | 0.193169 | + | 0.981166i | \(0.438123\pi\) |
−0.946299 | + | 0.323294i | \(0.895210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.90370 | − | 15.4217i | −0.303790 | − | 0.526180i | 0.673201 | − | 0.739459i | \(-0.264919\pi\) |
−0.976991 | + | 0.213279i | \(0.931586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.6783 | −0.601776 | −0.300888 | − | 0.953659i | \(-0.597283\pi\) | ||||
−0.300888 | + | 0.953659i | \(0.597283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.883156 | −0.0300282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.6753 | − | 49.6670i | −0.972742 | − | 1.68484i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.6383 | − | 39.2107i | 0.767069 | − | 1.32860i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.4603 | − | 19.8498i | 0.387428 | − | 0.671044i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.67527 | − | 11.5619i | −0.225408 | − | 0.390418i | 0.731034 | − | 0.682341i | \(-0.239038\pi\) |
−0.956442 | + | 0.291923i | \(0.905705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.23369 | −0.142637 | −0.0713183 | − | 0.997454i | \(-0.522721\pi\) | ||||
−0.0713183 | + | 0.997454i | \(0.522721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.4043 | −0.720312 | −0.360156 | − | 0.932892i | \(-0.617277\pi\) | ||||
−0.360156 | + | 0.932892i | \(0.617277\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.4603 | − | 19.8498i | −0.384798 | − | 0.666490i | 0.606943 | − | 0.794745i | \(-0.292396\pi\) |
−0.991741 | + | 0.128256i | \(0.959062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.23369 | + | 14.2612i | −0.276149 | + | 0.478304i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.11684 | − | 7.13058i | 0.137765 | − | 0.238616i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.4845 | − | 18.1596i | −0.350457 | − | 0.607010i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.59691 | 0.119964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.4891 | 0.449388 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.76631 | − | 16.9157i | −0.324643 | − | 0.562299i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.1459 | − | 24.5015i | 0.469708 | − | 0.813558i | −0.529692 | − | 0.848190i | \(-0.677693\pi\) |
0.999400 | + | 0.0346319i | \(0.0110259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3643 | − | 45.6643i | 0.873488 | − | 1.51293i | 0.0151242 | − | 0.999886i | \(-0.495186\pi\) |
0.858364 | − | 0.513041i | \(-0.171481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.7921 | − | 72.3861i | −1.38312 | − | 2.39563i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.3505 | −0.705057 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.1303 | −0.828973 | −0.414486 | − | 0.910056i | \(-0.636039\pi\) | ||||
−0.414486 | + | 0.910056i | \(0.636039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.66181 | − | 16.7347i | −0.318022 | − | 0.550831i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.25544 | − | 2.17448i | 0.0412785 | − | 0.0714965i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.1861 | − | 31.4993i | 0.596668 | − | 1.03346i | −0.396641 | − | 0.917974i | \(-0.629824\pi\) |
0.993309 | − | 0.115485i | \(-0.0368424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.94369 | + | 6.83067i | 0.129249 | + | 0.223866i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 47.4864 | 1.55297 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.2337 | 0.399657 | 0.199829 | − | 0.979831i | \(-0.435961\pi\) | ||||
0.199829 | + | 0.979831i | \(0.435961\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0475 | + | 39.9195i | 0.751329 | + | 1.30134i | 0.947179 | + | 0.320705i | \(0.103920\pi\) |
−0.195850 | + | 0.980634i | \(0.562747\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.10489 | + | 1.91373i | −0.0359803 | + | 0.0623197i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.0493 | + | 29.5302i | −0.554027 | + | 0.959603i | 0.443951 | + | 0.896051i | \(0.353576\pi\) |
−0.997979 | + | 0.0635523i | \(0.979757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.1168 | + | 17.5229i | 0.328407 | + | 0.568817i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.6060 | 1.02382 | 0.511909 | − | 0.859040i | \(-0.328939\pi\) | ||||
0.511909 | + | 0.859040i | \(0.328939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.5988 | −1.31375 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.7991 | − | 23.9008i | −0.445598 | − | 0.771798i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.1753 | + | 53.9971i | −1.00565 | + | 1.74184i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.18614 | + | 2.05446i | −0.0381832 | + | 0.0661353i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.7991 | + | 23.9008i | 0.443751 | + | 0.768599i | 0.997964 | − | 0.0637757i | \(-0.0203142\pi\) |
−0.554214 | + | 0.832375i | \(0.686981\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.1317 | 1.57671 | 0.788356 | − | 0.615220i | \(-0.210933\pi\) | ||||
0.788356 | + | 0.615220i | \(0.210933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.41578 | −0.205680 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.38316 | + | 9.32390i | 0.172222 | + | 0.298298i | 0.939197 | − | 0.343380i | \(-0.111572\pi\) |
−0.766974 | + | 0.641678i | \(0.778239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.72601 | + | 6.45364i | −0.119084 | + | 0.206259i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.2994 | − | 35.1596i | 0.647451 | − | 1.12142i | −0.336279 | − | 0.941762i | \(-0.609169\pi\) |
0.983730 | − | 0.179655i | \(-0.0574981\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.883156 | − | 1.52967i | −0.0281397 | − | 0.0487394i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.1168 | 0.417091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.4864 | −1.50845 | −0.754227 | − | 0.656613i | \(-0.771988\pi\) | ||||
−0.754227 | + | 0.656613i | \(0.771988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.5659 | − | 42.5493i | −0.778790 | − | 1.34890i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.6753 | − | 35.8106i | 0.654792 | − | 1.13413i | −0.327154 | − | 0.944971i | \(-0.606089\pi\) |
0.981946 | − | 0.189162i | \(-0.0605772\pi\) | |||||||
\(998\) | 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.n.1153.1 | 8 | ||
3.2 | odd | 2 | 576.2.i.n.385.4 | 8 | |||
4.3 | odd | 2 | inner | 1728.2.i.n.1153.2 | 8 | ||
8.3 | odd | 2 | 864.2.i.f.289.4 | 8 | |||
8.5 | even | 2 | 864.2.i.f.289.3 | 8 | |||
9.2 | odd | 6 | 5184.2.a.cf.1.2 | 4 | |||
9.4 | even | 3 | inner | 1728.2.i.n.577.1 | 8 | ||
9.5 | odd | 6 | 576.2.i.n.193.4 | 8 | |||
9.7 | even | 3 | 5184.2.a.cc.1.4 | 4 | |||
12.11 | even | 2 | 576.2.i.n.385.1 | 8 | |||
24.5 | odd | 2 | 288.2.i.f.97.1 | ✓ | 8 | ||
24.11 | even | 2 | 288.2.i.f.97.4 | yes | 8 | ||
36.7 | odd | 6 | 5184.2.a.cc.1.3 | 4 | |||
36.11 | even | 6 | 5184.2.a.cf.1.1 | 4 | |||
36.23 | even | 6 | 576.2.i.n.193.1 | 8 | |||
36.31 | odd | 6 | inner | 1728.2.i.n.577.2 | 8 | ||
72.5 | odd | 6 | 288.2.i.f.193.1 | yes | 8 | ||
72.11 | even | 6 | 2592.2.a.u.1.3 | 4 | |||
72.13 | even | 6 | 864.2.i.f.577.3 | 8 | |||
72.29 | odd | 6 | 2592.2.a.u.1.4 | 4 | |||
72.43 | odd | 6 | 2592.2.a.x.1.1 | 4 | |||
72.59 | even | 6 | 288.2.i.f.193.4 | yes | 8 | ||
72.61 | even | 6 | 2592.2.a.x.1.2 | 4 | |||
72.67 | odd | 6 | 864.2.i.f.577.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.f.97.1 | ✓ | 8 | 24.5 | odd | 2 | ||
288.2.i.f.97.4 | yes | 8 | 24.11 | even | 2 | ||
288.2.i.f.193.1 | yes | 8 | 72.5 | odd | 6 | ||
288.2.i.f.193.4 | yes | 8 | 72.59 | even | 6 | ||
576.2.i.n.193.1 | 8 | 36.23 | even | 6 | |||
576.2.i.n.193.4 | 8 | 9.5 | odd | 6 | |||
576.2.i.n.385.1 | 8 | 12.11 | even | 2 | |||
576.2.i.n.385.4 | 8 | 3.2 | odd | 2 | |||
864.2.i.f.289.3 | 8 | 8.5 | even | 2 | |||
864.2.i.f.289.4 | 8 | 8.3 | odd | 2 | |||
864.2.i.f.577.3 | 8 | 72.13 | even | 6 | |||
864.2.i.f.577.4 | 8 | 72.67 | odd | 6 | |||
1728.2.i.n.577.1 | 8 | 9.4 | even | 3 | inner | ||
1728.2.i.n.577.2 | 8 | 36.31 | odd | 6 | inner | ||
1728.2.i.n.1153.1 | 8 | 1.1 | even | 1 | trivial | ||
1728.2.i.n.1153.2 | 8 | 4.3 | odd | 2 | inner | ||
2592.2.a.u.1.3 | 4 | 72.11 | even | 6 | |||
2592.2.a.u.1.4 | 4 | 72.29 | odd | 6 | |||
2592.2.a.x.1.1 | 4 | 72.43 | odd | 6 | |||
2592.2.a.x.1.2 | 4 | 72.61 | even | 6 | |||
5184.2.a.cc.1.3 | 4 | 36.7 | odd | 6 | |||
5184.2.a.cc.1.4 | 4 | 9.7 | even | 3 | |||
5184.2.a.cf.1.1 | 4 | 36.11 | even | 6 | |||
5184.2.a.cf.1.2 | 4 | 9.2 | odd | 6 |