Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2816,2,Mod(1407,2816)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2816, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2816.1407");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2816 = 2^{8} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2816.g (of order \(2\), degree \(1\), 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: | \(22.4858732092\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 352) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1407.1 | ||
Root | \(-0.892524 - 1.09700i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2816.1407 |
Dual form | 2816.2.g.d.1407.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2816\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(1541\) | \(2047\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.81361 | −1.62444 | −0.812218 | − | 0.583354i | \(-0.801740\pi\) | ||||
−0.812218 | + | 0.583354i | \(0.801740\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.289169i | − | 0.129320i | −0.997907 | − | 0.0646601i | \(-0.979404\pi\) | ||
0.997907 | − | 0.0646601i | \(-0.0205963\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.38799 | −1.65850 | −0.829252 | − | 0.558876i | \(-0.811233\pi\) | ||||
−0.829252 | + | 0.558876i | \(0.811233\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.91638 | 1.63879 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.10278 | − | 2.56483i | 0.634011 | − | 0.773324i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55956 | −0.432544 | −0.216272 | − | 0.976333i | \(-0.569390\pi\) | ||||
−0.216272 | + | 0.976333i | \(0.569390\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.813607i | 0.210072i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.57009i | − | 0.865875i | −0.901424 | − | 0.432938i | \(-0.857477\pi\) | ||
0.901424 | − | 0.432938i | \(-0.142523\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.39852i | − | 1.46792i | −0.679192 | − | 0.733961i | \(-0.737670\pi\) | ||
0.679192 | − | 0.733961i | \(-0.262330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.3461 | 2.69413 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.39194i | 0.707269i | 0.935384 | + | 0.353635i | \(0.115054\pi\) | ||||
−0.935384 | + | 0.353635i | \(0.884946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.91638 | 0.983276 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.39194 | −1.03768 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.64632 | 0.677104 | 0.338552 | − | 0.940948i | \(-0.390063\pi\) | ||||
0.338552 | + | 0.940948i | \(0.390063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.01916i | 1.61989i | 0.586507 | + | 0.809944i | \(0.300503\pi\) | ||||
−0.586507 | + | 0.809944i | \(0.699497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.91638 | + | 7.21641i | −1.02991 | + | 1.25622i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26887i | 0.214478i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.289169i | − | 0.0475390i | −0.999717 | − | 0.0237695i | \(-0.992433\pi\) | ||
0.999717 | − | 0.0237695i | \(-0.00756678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.38799 | 0.702640 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.68921i | 1.04468i | 0.852737 | + | 0.522340i | \(0.174941\pi\) | ||||
−0.852737 | + | 0.522340i | \(0.825059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.12965i | − | 0.782265i | −0.920334 | − | 0.391132i | \(-0.872083\pi\) | ||
0.920334 | − | 0.391132i | \(-0.127917\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.42166i | − | 0.211929i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.04888i | − | 1.02818i | −0.857735 | − | 0.514092i | \(-0.828129\pi\) | ||
0.857735 | − | 0.514092i | \(-0.171871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.2544 | 1.75063 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0448i | 1.40656i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.25443i | − | 1.27119i | −0.772021 | − | 0.635597i | \(-0.780754\pi\) | ||
0.772021 | − | 0.635597i | \(-0.219246\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.741667 | − | 0.608056i | −0.100006 | − | 0.0819903i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.0029i | 2.38455i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.440820 | −0.0573898 | −0.0286949 | − | 0.999588i | \(-0.509135\pi\) | ||||
−0.0286949 | + | 0.999588i | \(0.509135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7865 | 1.38107 | 0.690535 | − | 0.723299i | \(-0.257375\pi\) | ||||
0.690535 | + | 0.723299i | \(0.257375\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21.5730 | −2.71794 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.450976i | 0.0559366i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.97028 | −0.485047 | −0.242523 | − | 0.970146i | \(-0.577975\pi\) | ||||
−0.242523 | + | 0.970146i | \(0.577975\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 9.54359i | − | 1.14891i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.76473i | − | 0.684148i | −0.939673 | − | 0.342074i | \(-0.888871\pi\) | ||
0.939673 | − | 0.342074i | \(-0.111129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.68921i | − | 0.782913i | −0.920197 | − | 0.391457i | \(-0.871971\pi\) | ||
0.920197 | − | 0.391457i | \(-0.128029\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.8328 | −1.59727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.22695 | + | 11.2544i | −1.05151 | + | 1.28256i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.421663 | 0.0468514 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.9056i | − | 1.52634i | −0.646197 | − | 0.763170i | \(-0.723642\pi\) | ||
0.646197 | − | 0.763170i | \(-0.276358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.03236 | −0.111975 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.2593 | −1.09991 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.5925 | −1.33480 | −0.667400 | − | 0.744700i | \(-0.732593\pi\) | ||||
−0.667400 | + | 0.744700i | \(0.732593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.84333 | 0.717375 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 25.3764i | − | 2.63141i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.85025 | −0.189832 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.75971 | −0.889414 | −0.444707 | − | 0.895676i | \(-0.646692\pi\) | ||||
−0.444707 | + | 0.895676i | \(0.646692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3380 | − | 12.6097i | 1.03901 | − | 1.26732i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.8733 | −1.28094 | −0.640469 | − | 0.767984i | \(-0.721260\pi\) | ||||
−0.640469 | + | 0.767984i | \(0.721260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2056i | 1.59678i | 0.602140 | + | 0.798390i | \(0.294315\pi\) | ||||
−0.602140 | + | 0.798390i | \(0.705685\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 3.57009i | − | 0.348406i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6912i | 1.32357i | 0.749692 | + | 0.661787i | \(0.230202\pi\) | ||||
−0.749692 | + | 0.661787i | \(0.769798\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.527200 | −0.0504966 | −0.0252483 | − | 0.999681i | \(-0.508038\pi\) | ||||
−0.0252483 | + | 0.999681i | \(0.508038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.813607i | 0.0772241i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.49472 | 0.234683 | 0.117342 | − | 0.993092i | \(-0.462563\pi\) | ||||
0.117342 | + | 0.993092i | \(0.462563\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.980843 | 0.0914641 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.66739 | −0.708850 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.6655i | 1.43606i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.15667 | − | 10.7865i | −0.196061 | − | 0.980592i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 18.8208i | − | 1.69702i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.86751i | − | 0.256478i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.90465 | 0.257746 | 0.128873 | − | 0.991661i | \(-0.458864\pi\) | ||||
0.128873 | + | 0.991661i | \(0.458864\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.4328i | 1.27074i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.39852i | − | 0.559041i | −0.960140 | − | 0.279521i | \(-0.909824\pi\) | ||
0.960140 | − | 0.279521i | \(-0.0901756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.0766i | 2.43455i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.55918i | 0.134193i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.33804 | −0.114317 | −0.0571584 | − | 0.998365i | \(-0.518204\pi\) | ||||
−0.0571584 | + | 0.998365i | \(0.518204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.37745i | 0.201653i | 0.994904 | + | 0.100826i | \(0.0321487\pi\) | ||||
−0.994904 | + | 0.100826i | \(0.967851\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.8328i | 1.67022i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.27940 | + | 4.00000i | −0.274237 | + | 0.334497i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.05440i | − | 0.0875632i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −34.4791 | −2.84379 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.55956 | −0.127764 | −0.0638820 | − | 0.997957i | \(-0.520348\pi\) | ||||
−0.0638820 | + | 0.997957i | \(0.520348\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.72157 | −0.628373 | −0.314186 | − | 0.949361i | \(-0.601732\pi\) | ||||
−0.314186 | + | 0.949361i | \(0.601732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 17.5519i | − | 1.41899i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.60806 | 0.209484 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.12193i | − | 0.328966i | −0.986380 | − | 0.164483i | \(-0.947404\pi\) | ||
0.986380 | − | 0.164483i | \(-0.0525956\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.0383i | 2.06497i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 14.8838i | − | 1.17301i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.7144 | −1.46583 | −0.732913 | − | 0.680323i | \(-0.761840\pi\) | ||||
−0.732913 | + | 0.680323i | \(0.761840\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.08676 | + | 1.71083i | 0.162454 | + | 0.133188i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.92572 | −0.535928 | −0.267964 | − | 0.963429i | \(-0.586351\pi\) | ||||
−0.267964 | + | 0.963429i | \(0.586351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5678 | −0.812906 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 31.4576i | − | 2.40562i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0791 | −1.37453 | −0.687266 | − | 0.726406i | \(-0.741189\pi\) | ||||
−0.687266 | + | 0.726406i | \(0.741189\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.5730 | −1.63077 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.24029 | 0.0932261 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6952 | 0.874144 | 0.437072 | − | 0.899427i | \(-0.356016\pi\) | ||||
0.437072 | + | 0.899427i | \(0.356016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.96526i | 0.220406i | 0.993909 | + | 0.110203i | \(0.0351501\pi\) | ||||
−0.993909 | + | 0.110203i | \(0.964850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.3490 | −2.24346 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0836184 | −0.00614775 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.15667 | − | 7.50711i | −0.669602 | − | 0.548974i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23.6598 | 1.72100 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.98084i | − | 0.505116i | −0.967582 | − | 0.252558i | \(-0.918728\pi\) | ||
0.967582 | − | 0.252558i | \(-0.0812719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.17352i | − | 0.300417i | −0.988654 | − | 0.150208i | \(-0.952006\pi\) | ||
0.988654 | − | 0.150208i | \(-0.0479944\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1.26887i | − | 0.0908655i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.9056 | −0.990735 | −0.495367 | − | 0.868684i | \(-0.664967\pi\) | ||||
−0.495367 | + | 0.868684i | \(0.664967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.4600i | − | 1.09593i | −0.836502 | − | 0.547964i | \(-0.815403\pi\) | ||
0.836502 | − | 0.547964i | \(-0.184597\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.1708 | 0.787928 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0000 | −1.12298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.93431 | 0.135098 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.6761i | 1.15907i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.4111 | − | 13.4547i | −1.13518 | − | 0.930678i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.18405i | 0.425728i | 0.977082 | + | 0.212864i | \(0.0682791\pi\) | ||||
−0.977082 | + | 0.212864i | \(0.931721\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.2197i | 1.11135i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.48333 | −0.101163 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 39.5759i | − | 2.68659i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.8208i | 1.27179i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.56777i | 0.374529i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.98084i | − | 0.467472i | −0.972300 | − | 0.233736i | \(-0.924905\pi\) | ||
0.972300 | − | 0.233736i | \(-0.0750951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 24.1708 | 1.61139 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6912i | 0.908714i | 0.890820 | + | 0.454357i | \(0.150131\pi\) | ||||
−0.890820 | + | 0.454357i | \(0.849869\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2786i | 1.40613i | 0.711126 | + | 0.703065i | \(0.248186\pi\) | ||||
−0.711126 | + | 0.703065i | \(0.751814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 25.9610 | − | 31.6655i | 1.70811 | − | 2.08344i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 27.8113i | − | 1.82198i | −0.412433 | − | 0.910988i | \(-0.635321\pi\) | ||
0.412433 | − | 0.910988i | \(-0.364679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.03831 | −0.132965 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31.8323 | −2.06773 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.50440 | 0.356050 | 0.178025 | − | 0.984026i | \(-0.443029\pi\) | ||||
0.178025 | + | 0.984026i | \(0.443029\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4118i | 0.670680i | 0.942097 | + | 0.335340i | \(0.108851\pi\) | ||||
−0.942097 | + | 0.335340i | \(0.891149\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.9894 | 0.961573 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.54359i | − | 0.226392i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.97887i | 0.634941i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 39.1250i | 2.47944i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2841 | −0.964727 | −0.482363 | − | 0.875971i | \(-0.660222\pi\) | ||||
−0.482363 | + | 0.875971i | \(0.660222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.69975 | + | 7.13249i | 0.546948 | + | 0.448416i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.90465 | 0.181896 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.5678 | −0.721578 | −0.360789 | − | 0.932647i | \(-0.617493\pi\) | ||||
−0.360789 | + | 0.932647i | \(0.617493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.26887i | 0.0788436i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.9267 | 1.10963 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.4443 | 1.69229 | 0.846145 | − | 0.532952i | \(-0.178918\pi\) | ||||
0.846145 | + | 0.532952i | \(0.178918\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.67609 | −0.164391 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.4303 | 2.16830 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.25443i | 0.0764837i | 0.999269 | + | 0.0382419i | \(0.0121757\pi\) | ||||
−0.999269 | + | 0.0382419i | \(0.987824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.9610 | −1.57702 | −0.788509 | − | 0.615023i | \(-0.789147\pi\) | ||||
−0.788509 | + | 0.615023i | \(0.789147\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −19.2544 | −1.16533 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3380 | − | 12.6097i | 0.623408 | − | 0.760392i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.527200 | −0.0316764 | −0.0158382 | − | 0.999875i | \(-0.505042\pi\) | ||||
−0.0158382 | + | 0.999875i | \(0.505042\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 44.3416i | 2.65466i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2593i | 0.612019i | 0.952028 | + | 0.306009i | \(0.0989939\pi\) | ||||
−0.952028 | + | 0.306009i | \(0.901006\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.59192i | − | 0.154074i | −0.997028 | − | 0.0770368i | \(-0.975454\pi\) | ||
0.997028 | − | 0.0770368i | \(-0.0245459\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.20588 | 0.308370 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 29.3522i | − | 1.73260i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.25443 | 0.250260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.6464 | 1.44480 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.73308 | −0.334930 | −0.167465 | − | 0.985878i | \(-0.553558\pi\) | ||||
−0.167465 | + | 0.985878i | \(0.553558\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.127471i | 0.00742166i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.3380 | + | 13.8294i | −0.657900 | + | 0.802463i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 5.28994i | − | 0.305925i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.5089i | 1.29739i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.2203 | 2.08080 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.11912i | − | 0.178600i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.1745i | − | 0.866054i | −0.901381 | − | 0.433027i | \(-0.857445\pi\) | ||
0.901381 | − | 0.433027i | \(-0.142555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 45.5960i | − | 2.59387i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.1466i | − | 0.745477i | −0.927936 | − | 0.372738i | \(-0.878419\pi\) | ||
0.927936 | − | 0.372738i | \(-0.121581\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.6030 | 0.881936 | 0.440968 | − | 0.897523i | \(-0.354635\pi\) | ||||
0.440968 | + | 0.897523i | \(0.354635\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.23824i | 0.351485i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.44584i | 0.0812066i | 0.999175 | + | 0.0406033i | \(0.0129280\pi\) | ||||
−0.999175 | + | 0.0406033i | \(0.987072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.66739 | − | 9.35218i | 0.429291 | − | 0.523621i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 38.5215i | − | 2.15006i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.8433 | −1.27104 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.66739 | −0.425310 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.48333 | 0.0820286 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.9304i | 1.70525i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0680 | 0.773249 | 0.386624 | − | 0.922237i | \(-0.373641\pi\) | ||||
0.386624 | + | 0.922237i | \(0.373641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.42166i | − | 0.0779066i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.14808i | 0.0627263i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.66814i | − | 0.145343i | −0.997356 | − | 0.0726715i | \(-0.976848\pi\) | ||
0.997356 | − | 0.0726715i | \(-0.0231525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.01916 | −0.381228 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.1326 | + | 18.9653i | 1.25270 | + | 1.02703i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23.0564 | −1.24493 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.75971 | −0.148578 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.9294i | 1.06987i | 0.844894 | + | 0.534933i | \(0.179663\pi\) | ||||
−0.844894 | + | 0.534933i | \(0.820337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.60170 | −0.513967 | −0.256984 | − | 0.966416i | \(-0.582729\pi\) | ||||
−0.256984 | + | 0.966416i | \(0.582729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.40906 | 0.448842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.24029 | 0.385362 | 0.192681 | − | 0.981261i | \(-0.438282\pi\) | ||||
0.192681 | + | 0.981261i | \(0.438282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.66698 | −0.0884740 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 44.0766i | − | 2.33278i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.35466 | 0.388164 | 0.194082 | − | 0.980985i | \(-0.437827\pi\) | ||||
0.194082 | + | 0.980985i | \(0.437827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.9411 | −1.15479 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.06803 | + | 30.3490i | 0.318489 | + | 1.59291i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.93431 | −0.101246 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5280i | 0.810555i | 0.914194 | + | 0.405278i | \(0.132825\pi\) | ||||
−0.914194 | + | 0.405278i | \(0.867175\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.8867i | 1.71201i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.6083i | 2.10828i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.3919 | −1.72897 | −0.864483 | − | 0.502662i | \(-0.832354\pi\) | ||||
−0.864483 | + | 0.502662i | \(0.832354\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.06803i | 0.416631i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.68665 | −0.292877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.1275 | −0.725679 | −0.362840 | − | 0.931852i | \(-0.618193\pi\) | ||||
−0.362840 | + | 0.931852i | \(0.618193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.17255 | −0.418692 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 38.3713i | 1.96068i | 0.197307 | + | 0.980342i | \(0.436781\pi\) | ||||
−0.197307 | + | 0.980342i | \(0.563219\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.25443 | + | 2.66814i | 0.165861 | + | 0.135981i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 25.2193i | − | 1.28197i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 28.3658i | − | 1.43820i | −0.694905 | − | 0.719101i | \(-0.744554\pi\) | ||
0.694905 | − | 0.719101i | \(-0.255446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.1096 | 0.612407 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0029i | 0.908127i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.27157i | − | 0.164610i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 21.2544i | − | 1.06673i | −0.845885 | − | 0.533365i | \(-0.820927\pi\) | ||
0.845885 | − | 0.533365i | \(-0.179073\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 78.9966i | − | 3.95478i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0766 | −0.902704 | −0.451352 | − | 0.892346i | \(-0.649058\pi\) | ||||
−0.451352 | + | 0.892346i | \(0.649058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 14.0659i | − | 0.700673i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.121932i | − | 0.00605883i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.741667 | − | 0.608056i | −0.0367631 | − | 0.0301402i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4328i | 0.713657i | 0.934170 | + | 0.356829i | \(0.116142\pi\) | ||||
−0.934170 | + | 0.356829i | \(0.883858\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.76473 | 0.185700 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.93431 | 0.0951812 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.02107 | −0.197387 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.68921i | − | 0.327572i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.61665 | 0.225538 | 0.112769 | − | 0.993621i | \(-0.464028\pi\) | ||||
0.112769 | + | 0.993621i | \(0.464028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.2544i | 0.645981i | 0.946402 | + | 0.322991i | \(0.104688\pi\) | ||||
−0.946402 | + | 0.322991i | \(0.895312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 34.6550i | − | 1.68498i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 17.5519i | − | 0.851394i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −47.3311 | −2.29051 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.22695 | − | 11.2544i | 0.445481 | − | 0.543369i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.33359 | 0.160573 | 0.0802866 | − | 0.996772i | \(-0.474416\pi\) | ||||
0.0802866 | + | 0.996772i | \(0.474416\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.759707 | −0.0365092 | −0.0182546 | − | 0.999833i | \(-0.505811\pi\) | ||||
−0.0182546 | + | 0.999833i | \(0.505811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.96667i | 0.142241i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.7034 | 1.03822 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2593 | −0.489650 | −0.244825 | − | 0.969567i | \(-0.578731\pi\) | ||||
−0.244825 | + | 0.969567i | \(0.578731\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 60.2474 | 2.86893 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.7336 | 1.41268 | 0.706342 | − | 0.707871i | \(-0.250344\pi\) | ||||
0.706342 | + | 0.707871i | \(0.250344\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.64135i | 0.172616i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.38799 | 0.207545 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0036 | 0.802448 | 0.401224 | − | 0.915980i | \(-0.368585\pi\) | ||||
0.401224 | + | 0.915980i | \(0.368585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.1567 | + | 14.0659i | 0.807876 | + | 0.662338i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.7255 | 1.02075 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.97887i | − | 0.0927711i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3348i | 0.717331i | 0.933466 | + | 0.358665i | \(0.116768\pi\) | ||||
−0.933466 | + | 0.358665i | \(0.883232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.2497i | 0.898501i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.2841 | −1.27075 | −0.635373 | − | 0.772206i | \(-0.719153\pi\) | ||||
−0.635373 | + | 0.772206i | \(0.719153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8625i | 0.737192i | 0.929590 | + | 0.368596i | \(0.120161\pi\) | ||||
−0.929590 | + | 0.368596i | \(0.879839\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.33804 | −0.340294 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.32246 | −0.0611961 | −0.0305980 | − | 0.999532i | \(-0.509741\pi\) | ||||
−0.0305980 | + | 0.999532i | \(0.509741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.4215 | 0.804452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.5975i | 0.534384i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.1567 | − | 10.7865i | −0.604945 | − | 0.495964i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 31.4576i | − | 1.44337i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 45.4983i | − | 2.08322i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.2747 | −1.70313 | −0.851563 | − | 0.524253i | \(-0.824345\pi\) | ||||
−0.851563 | + | 0.524253i | \(0.824345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.450976i | 0.0205627i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 41.8772i | 1.90548i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.53303i | 0.115019i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.43026i | − | 0.246068i | −0.992402 | − | 0.123034i | \(-0.960738\pi\) | ||
0.992402 | − | 0.123034i | \(-0.0392625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 52.6550 | 2.38114 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.374751i | 0.0169123i | 0.999964 | + | 0.00845613i | \(0.00269170\pi\) | ||||
−0.999964 | + | 0.00845613i | \(0.997308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 13.0177i | − | 0.586288i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.64632 | − | 2.98944i | −0.163890 | − | 0.134365i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.2956i | 1.13466i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.61665 | 0.206670 | 0.103335 | − | 0.994647i | \(-0.467049\pi\) | ||||
0.103335 | + | 0.994647i | \(0.467049\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.4863 | 0.870582 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.48333 | 0.0661386 | 0.0330693 | − | 0.999453i | \(-0.489472\pi\) | ||||
0.0330693 | + | 0.999453i | \(0.489472\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.72254i | 0.165651i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.7336 | 1.32051 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4458i | 0.773273i | 0.922232 | + | 0.386637i | \(0.126363\pi\) | ||||
−0.922232 | + | 0.386637i | \(0.873637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.3522i | 1.29846i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 34.5005i | 1.52323i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.68614 | 0.206496 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0791 | − | 14.8222i | −0.795120 | − | 0.651880i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 50.8676 | 2.23284 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.3663 | 1.46180 | 0.730902 | − | 0.682482i | \(-0.239099\pi\) | ||||
0.730902 | + | 0.682482i | \(0.239099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.9838i | − | 0.917557i | −0.888551 | − | 0.458779i | \(-0.848287\pi\) | ||
0.888551 | − | 0.458779i | \(-0.151713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 60.6980 | 2.64908 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.1992 | 1.40262 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4947 | 0.499770 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.16724 | −0.0940501 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.4322i | − | 0.451870i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.95905 | 0.171165 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −32.9058 | −1.41999 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.7683 | − | 31.4305i | 1.10992 | − | 1.35381i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.2850 | −1.00110 | −0.500551 | − | 0.865707i | \(-0.666869\pi\) | ||||
−0.500551 | + | 0.865707i | \(0.666869\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.34307i | − | 0.358035i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.152450i | 0.00653023i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 22.6816i | − | 0.969795i | −0.874571 | − | 0.484898i | \(-0.838857\pi\) | ||
0.874571 | − | 0.484898i | \(-0.161143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 53.0306 | 2.26329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.3311i | − | 0.993936i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.6444 | −2.11109 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.235269 | 0.00998663 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.6845 | 1.72386 | 0.861929 | − | 0.507029i | \(-0.169256\pi\) | ||||
0.861929 | + | 0.507029i | \(0.169256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000i | 0.338364i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.7633 | + | 21.1220i | 1.08773 | + | 0.891773i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.0895i | 0.804525i | 0.915524 | + | 0.402262i | \(0.131776\pi\) | ||||
−0.915524 | + | 0.402262i | \(0.868224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.721394i | − | 0.0303493i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.85025 | −0.0777032 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.6485i | 1.11716i | 0.829450 | + | 0.558581i | \(0.188654\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.6605i | 0.780919i | 0.920620 | + | 0.390459i | \(0.127684\pi\) | ||||
−0.920620 | + | 0.390459i | \(0.872316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.6413i | 0.820529i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.6761i | 0.695441i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5230 | −0.771122 | −0.385561 | − | 0.922682i | \(-0.625992\pi\) | ||||
−0.385561 | + | 0.922682i | \(0.625992\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7426i | 0.488008i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 61.0177i | 2.53144i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.7360 | − | 19.4600i | −0.983045 | − | 0.805950i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.21717i | 0.0916686i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3622 | 0.551518 | 0.275759 | − | 0.961227i | \(-0.411071\pi\) | ||||
0.275759 | + | 0.961227i | \(0.411071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.7093 | 2.37787 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.1250 | 1.60939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9.24899i | − | 0.379811i | −0.981802 | − | 0.189905i | \(-0.939182\pi\) | ||
0.981802 | − | 0.189905i | \(-0.0608181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.52998 | 0.185711 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 43.4983i | 1.78027i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 33.7733i | − | 1.37994i | −0.723838 | − | 0.689970i | \(-0.757624\pi\) | ||
0.723838 | − | 0.689970i | \(-0.242376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 33.4901i | − | 1.36609i | −0.730375 | − | 0.683046i | \(-0.760655\pi\) | ||
0.730375 | − | 0.683046i | \(-0.239345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.5194 | −0.794892 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.11912 | + | 0.623642i | −0.126810 | + | 0.0253547i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.5519 | −0.712412 | −0.356206 | − | 0.934408i | \(-0.615930\pi\) | ||||
−0.356206 | + | 0.934408i | \(0.615930\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 45.0177 | 1.82421 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.9931i | 0.444735i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.3262 | −1.42681 | −0.713406 | − | 0.700751i | \(-0.752848\pi\) | ||||
−0.713406 | + | 0.700751i | \(0.752848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.44239 | −0.219458 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.2544 | 1.01670 | 0.508352 | − | 0.861149i | \(-0.330255\pi\) | ||||
0.508352 | + | 0.861149i | \(0.330255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.7547 | 0.794008 | 0.397004 | − | 0.917817i | \(-0.370050\pi\) | ||||
0.397004 | + | 0.917817i | \(0.370050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 18.2892i | − | 0.733919i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.2556 | 2.21377 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.7527 | 0.950109 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 46.1744 | + | 37.8561i | 1.84403 | + | 1.51183i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.03236 | −0.0411628 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0575i | 0.758666i | 0.925260 | + | 0.379333i | \(0.123846\pi\) | ||||
−0.925260 | + | 0.379333i | \(0.876154\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 17.3995i | − | 0.691568i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 0.839934i | − | 0.0333318i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.1115 | −0.757225 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 28.3416i | − | 1.12118i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.3275 | −0.881883 | −0.440941 | − | 0.897536i | \(-0.645355\pi\) | ||||
−0.440941 | + | 0.897536i | \(0.645355\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.9703 | −0.472062 | −0.236031 | − | 0.971746i | \(-0.575847\pi\) | ||||
−0.236031 | + | 0.971746i | \(0.575847\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.17352 | 0.164332 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.2353i | 0.402390i | 0.979551 | + | 0.201195i | \(0.0644825\pi\) | ||||
−0.979551 | + | 0.201195i | \(0.935518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.926944 | + | 1.13063i | −0.0363857 | + | 0.0443809i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 111.351i | 4.36419i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.1325i | 0.592180i | 0.955160 | + | 0.296090i | \(0.0956829\pi\) | ||||
−0.955160 | + | 0.296090i | \(0.904317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.85025 | −0.0722953 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 32.8867i | − | 1.28303i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.374751i | 0.0145982i | 0.999973 | + | 0.00729911i | \(0.00232340\pi\) | ||||
−0.999973 | + | 0.00729911i | \(0.997677\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 47.6202i | − | 1.85221i | −0.377263 | − | 0.926106i | \(-0.623135\pi\) | ||
0.377263 | − | 0.926106i | \(-0.376865\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 15.6655i | − | 0.608399i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.11888 | 0.314837 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.3681i | 0.478895i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.6413i | 0.759378i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.6816 | − | 27.6655i | 0.875613 | − | 1.06802i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.8745i | 1.53705i | 0.639821 | + | 0.768524i | \(0.279008\pi\) | ||||
−0.639821 | + | 0.768524i | \(0.720992\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.5089 | −1.02033 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.9380 | −0.574113 | −0.287057 | − | 0.957914i | \(-0.592677\pi\) | ||||
−0.287057 | + | 0.957914i | \(0.592677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.4375 | 1.47510 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 38.5215i | − | 1.47615i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2056 | 0.467032 | 0.233516 | − | 0.972353i | \(-0.424977\pi\) | ||||
0.233516 | + | 0.972353i | \(0.424977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.386920i | 0.0147835i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 59.8696i | − | 2.28417i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.4328i | 0.549847i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.1658 | −1.22364 | −0.611822 | − | 0.790995i | \(-0.709563\pi\) | ||||
−0.611822 | + | 0.790995i | \(0.709563\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −45.3632 | + | 55.3311i | −1.72321 | + | 2.10185i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.687484 | 0.0260778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.8811 | 0.904562 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 78.2499i | 2.95968i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.657608 | −0.0248375 | −0.0124188 | − | 0.999923i | \(-0.503953\pi\) | ||||
−0.0124188 | + | 0.999923i | \(0.503953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.85025 | −0.0697835 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.73501 | 0.215993 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.4877 | 2.12444 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 33.2302i | − | 1.24799i | −0.781429 | − | 0.623994i | \(-0.785509\pi\) | ||
0.781429 | − | 0.623994i | \(-0.214491\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 55.6225 | 2.08601 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.5925 | −1.14570 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.15667 | + | 0.948300i | 0.0432572 | + | 0.0354644i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.4872 | −0.578381 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 18.1164i | − | 0.675627i | −0.941213 | − | 0.337814i | \(-0.890313\pi\) | ||
0.941213 | − | 0.337814i | \(-0.109687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 71.1097i | − | 2.64826i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 29.2946i | − | 1.08948i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.9267 | 0.665781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.3708i | 0.792600i | 0.918121 | + | 0.396300i | \(0.129706\pi\) | ||||
−0.918121 | + | 0.396300i | \(0.870294\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.4394 | −1.60887 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.3133 | −0.677344 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.4683 | −1.27312 | −0.636558 | − | 0.771229i | \(-0.719643\pi\) | ||||
−0.636558 | + | 0.771229i | \(0.719643\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.97028i | 0.367759i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.34861 | + | 10.1831i | −0.307525 | + | 0.375099i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.15072i | 0.336615i | 0.985735 | + | 0.168307i | \(0.0538301\pi\) | ||||
−0.985735 | + | 0.168307i | \(0.946170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 28.0766i | − | 1.03142i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.98774 | 0.256355 | 0.128178 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128178 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.450976i | 0.0165225i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 68.3654i | − | 2.50136i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 60.0766i | − | 2.19515i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 40.5285i | − | 1.47891i | −0.673208 | − | 0.739453i | \(-0.735084\pi\) | ||
0.673208 | − | 0.739453i | \(-0.264916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 43.0036 | 1.56714 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.23284i | 0.0812612i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.74557i | 0.245172i | 0.992458 | + | 0.122586i | \(0.0391187\pi\) | ||||
−0.992458 | + | 0.122586i | \(0.960881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.4777 | − | 20.0680i | −0.888483 | − | 0.728423i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.0363i | − | 0.545064i | −0.962147 | − | 0.272532i | \(-0.912139\pi\) | ||
0.962147 | − | 0.272532i | \(-0.0878610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.31335 | 0.0837488 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.07547 | −0.183504 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.687484 | 0.0248236 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.66814i | − | 0.0962157i | −0.998842 | − | 0.0481079i | \(-0.984681\pi\) | ||
0.998842 | − | 0.0481079i | \(-0.0153191\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.5472 | 1.17216 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.3311i | 1.48657i | 0.668972 | + | 0.743287i | \(0.266734\pi\) | ||||
−0.668972 | + | 0.743287i | \(0.733266\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.3416i | 1.59280i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 3.57009i | − | 0.128076i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 42.8011 | 1.53351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.7855 | − | 12.1219i | −0.529068 | − | 0.433757i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.6607 | −0.702618 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.19193 | −0.0425419 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 14.3346i | − | 0.510972i | −0.966813 | − | 0.255486i | \(-0.917765\pi\) | ||
0.966813 | − | 0.255486i | \(-0.0822355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −77.2176 | −2.74902 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9468 | −0.389223 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.8222 | −0.597374 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.52946 | 0.267042 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.0313i | 1.27629i | 0.769914 | + | 0.638147i | \(0.220299\pi\) | ||||
−0.769914 | + | 0.638147i | \(0.779701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.1652 | −0.890279 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −61.9094 | −2.18746 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.1567 | − | 14.0659i | −0.605446 | − | 0.496375i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.30393 | −0.151694 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3.52946i | − | 0.124243i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 47.7705i | − | 1.67952i | −0.542956 | − | 0.839761i | \(-0.682695\pi\) | ||
0.542956 | − | 0.839761i | \(-0.317305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.9620i | − | 1.29791i | −0.760827 | − | 0.648955i | \(-0.775206\pi\) | ||
0.760827 | − | 0.648955i | \(-0.224794\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 73.0440 | 2.56177 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.41162i | 0.189561i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.8222 | −1.14830 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.6444 | 1.17563 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.8076 | −0.516788 | −0.258394 | − | 0.966040i | \(-0.583193\pi\) | ||||
−0.258394 | + | 0.966040i | \(0.583193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.4096i | 1.12973i | 0.825184 | + | 0.564865i | \(0.191072\pi\) | ||||
−0.825184 | + | 0.564865i | \(0.808928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.0872 | + | 35.4786i | −1.01269 | + | 1.23521i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9573i | 0.450570i | 0.974293 | + | 0.225285i | \(0.0723314\pi\) | ||||
−0.974293 | + | 0.225285i | \(0.927669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 14.5542i | − | 0.505487i | −0.967533 | − | 0.252743i | \(-0.918667\pi\) | ||
0.967533 | − | 0.252743i | \(-0.0813328\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.48333 | 0.0514563 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 43.7495i | − | 1.51583i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00270i | 0.0693063i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 48.6308i | − | 1.68093i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 39.7436i | − | 1.37210i | −0.727554 | − | 0.686051i | \(-0.759343\pi\) | ||
0.727554 | − | 0.686051i | \(-0.240657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.7044 | −0.541530 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 28.8657i | − | 0.994186i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.05587i | 0.105125i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.46346 | + | 47.3311i | 0.325168 | + | 1.62631i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.29264i | 0.250283i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.980843 | 0.0336229 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.7429 | −0.436307 | −0.218154 | − | 0.975914i | \(-0.570003\pi\) | ||||
−0.218154 | + | 0.975914i | \(0.570003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.09654 | −0.311095 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.1613i | 0.381261i | 0.981662 | + | 0.190631i | \(0.0610533\pi\) | ||||
−0.981662 | + | 0.190631i | \(0.938947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.6152 | −1.86345 | −0.931723 | − | 0.363169i | \(-0.881695\pi\) | ||||
−0.931723 | + | 0.363169i | \(0.881695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 82.5855i | 2.81451i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.9688i | 1.29247i | 0.763137 | + | 0.646237i | \(0.223658\pi\) | ||||
−0.763137 | + | 0.646237i | \(0.776342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.22792i | 0.177755i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9703 | −0.406532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.7902 | − | 29.0177i | 0.807027 | − | 0.984358i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.19189 | 0.209804 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −43.0661 | −1.45757 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.5826i | 0.425369i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.3919 | −1.12756 | −0.563782 | − | 0.825924i | \(-0.690654\pi\) | ||||
−0.563782 | + | 0.825924i | \(0.690654\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.1306 | 0.544073 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.4358 | 1.46339 | 0.731695 | − | 0.681633i | \(-0.238730\pi\) | ||||
0.731695 | + | 0.681633i | \(0.238730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.7733 | 0.463509 | 0.231755 | − | 0.972774i | \(-0.425553\pi\) | ||||
0.231755 | + | 0.972774i | \(0.425553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 0.358654i | − | 0.0120560i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.6627 | 1.39890 | 0.699448 | − | 0.714683i | \(-0.253429\pi\) | ||||
0.699448 | + | 0.714683i | \(0.253429\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7456 | −0.427473 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.886662 | − | 1.08149i | 0.0297043 | − | 0.0362314i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.1024 | −1.50929 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.38190i | − | 0.113044i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8838i | 0.496956i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.8867i | 1.09683i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.0392 | −1.10069 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 63.3311i | − | 2.10753i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.857459 | 0.0285029 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2056 | 0.405279 | 0.202639 | − | 0.979253i | \(-0.435048\pi\) | ||||
0.202639 | + | 0.979253i | \(0.435048\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −63.2899 | −2.09919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 9.36222i | − | 0.310184i | −0.987900 | − | 0.155092i | \(-0.950433\pi\) | ||
0.987900 | − | 0.155092i | \(-0.0495675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.6655 | − | 29.2404i | −1.18036 | − | 0.967716i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.77597i | 0.290125i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.0766i | 0.927172i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.8113 | −0.917409 | −0.458704 | − | 0.888589i | \(-0.651686\pi\) | ||||
−0.458704 | + | 0.888589i | \(0.651686\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.6951i | 1.40685i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.99044i | 0.295924i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.42166i | − | 0.0467440i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 79.6727i | 2.61679i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.76328 | −0.254705 | −0.127352 | − | 0.991858i | \(-0.540648\pi\) | ||||
−0.127352 | + | 0.991858i | \(0.540648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 78.4102i | − | 2.56979i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.9894i | 1.21098i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.17082 | + | 2.64782i | −0.0709934 | + | 0.0865930i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.4882i | 1.35536i | 0.735357 | + | 0.677680i | \(0.237015\pi\) | ||||
−0.735357 | + | 0.677680i | \(0.762985\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.9008 | −1.43265 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.1439 | −0.656671 | −0.328336 | − | 0.944561i | \(-0.606488\pi\) | ||||
−0.328336 | + | 0.944561i | \(0.606488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.6894 | −0.738870 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 6.84166i | − | 0.222559i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.3225 | −1.34280 | −0.671400 | − | 0.741095i | \(-0.734307\pi\) | ||||
−0.671400 | + | 0.741095i | \(0.734307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4322i | 0.338644i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.06803i | − | 0.131915i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 28.1098i | − | 0.910565i | −0.890347 | − | 0.455283i | \(-0.849538\pi\) | ||
0.890347 | − | 0.455283i | \(-0.150462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.01864 | −0.0653217 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.5730 | + | 26.3133i | −0.697357 | + | 0.850590i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.87132 | 0.189595 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −50.3452 | −1.62404 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 67.3110i | 2.16907i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.20685 | −0.0388499 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.5730 | −0.693741 | −0.346871 | − | 0.937913i | \(-0.612756\pi\) | ||||
−0.346871 | + | 0.937913i | \(0.612756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 64.2721 | 2.06472 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.9320 | −0.575464 | −0.287732 | − | 0.957711i | \(-0.592901\pi\) | ||||
−0.287732 | + | 0.957711i | \(0.592901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.4322i | − | 0.334442i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.5730 | 0.690889 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.8953 | −1.40433 | −0.702167 | − | 0.712012i | \(-0.747784\pi\) | ||||
−0.702167 | + | 0.712012i | \(0.747784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.4791 | + | 32.2975i | −0.846277 | + | 1.03223i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.59192 | −0.0827536 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.7053i | 0.692291i | 0.938181 | + | 0.346146i | \(0.112510\pi\) | ||||
−0.938181 | + | 0.346146i | \(0.887490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.02107i | 0.128122i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 87.0259i | − | 2.77006i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.3995 | 0.553272 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 54.3799i | − | 1.72744i | −0.503976 | − | 0.863718i | \(-0.668130\pi\) | ||
0.503976 | − | 0.863718i | \(-0.331870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.5819 | −1.25609 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.47054 | −0.141726 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.1384 | 1.87293 | 0.936466 | − | 0.350758i | \(-0.114076\pi\) | ||||
0.936466 | + | 0.350758i | \(0.114076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.55918i | 0.0493303i |
(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 | 2816.2.g.d.1407.1 | 12 | ||
4.3 | odd | 2 | 2816.2.g.i.1407.10 | 12 | |||
8.3 | odd | 2 | inner | 2816.2.g.d.1407.4 | 12 | ||
8.5 | even | 2 | 2816.2.g.i.1407.11 | 12 | |||
11.10 | odd | 2 | inner | 2816.2.g.d.1407.2 | 12 | ||
16.3 | odd | 4 | 704.2.e.d.703.11 | 12 | |||
16.5 | even | 4 | 352.2.e.a.351.12 | yes | 12 | ||
16.11 | odd | 4 | 352.2.e.a.351.1 | ✓ | 12 | ||
16.13 | even | 4 | 704.2.e.d.703.2 | 12 | |||
44.43 | even | 2 | 2816.2.g.i.1407.9 | 12 | |||
48.5 | odd | 4 | 3168.2.o.e.703.7 | 12 | |||
48.11 | even | 4 | 3168.2.o.e.703.6 | 12 | |||
88.21 | odd | 2 | 2816.2.g.i.1407.12 | 12 | |||
88.43 | even | 2 | inner | 2816.2.g.d.1407.3 | 12 | ||
176.21 | odd | 4 | 352.2.e.a.351.11 | yes | 12 | ||
176.43 | even | 4 | 352.2.e.a.351.2 | yes | 12 | ||
176.109 | odd | 4 | 704.2.e.d.703.1 | 12 | |||
176.131 | even | 4 | 704.2.e.d.703.12 | 12 | |||
528.197 | even | 4 | 3168.2.o.e.703.5 | 12 | |||
528.395 | odd | 4 | 3168.2.o.e.703.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.e.a.351.1 | ✓ | 12 | 16.11 | odd | 4 | ||
352.2.e.a.351.2 | yes | 12 | 176.43 | even | 4 | ||
352.2.e.a.351.11 | yes | 12 | 176.21 | odd | 4 | ||
352.2.e.a.351.12 | yes | 12 | 16.5 | even | 4 | ||
704.2.e.d.703.1 | 12 | 176.109 | odd | 4 | |||
704.2.e.d.703.2 | 12 | 16.13 | even | 4 | |||
704.2.e.d.703.11 | 12 | 16.3 | odd | 4 | |||
704.2.e.d.703.12 | 12 | 176.131 | even | 4 | |||
2816.2.g.d.1407.1 | 12 | 1.1 | even | 1 | trivial | ||
2816.2.g.d.1407.2 | 12 | 11.10 | odd | 2 | inner | ||
2816.2.g.d.1407.3 | 12 | 88.43 | even | 2 | inner | ||
2816.2.g.d.1407.4 | 12 | 8.3 | odd | 2 | inner | ||
2816.2.g.i.1407.9 | 12 | 44.43 | even | 2 | |||
2816.2.g.i.1407.10 | 12 | 4.3 | odd | 2 | |||
2816.2.g.i.1407.11 | 12 | 8.5 | even | 2 | |||
2816.2.g.i.1407.12 | 12 | 88.21 | odd | 2 | |||
3168.2.o.e.703.5 | 12 | 528.197 | even | 4 | |||
3168.2.o.e.703.6 | 12 | 48.11 | even | 4 | |||
3168.2.o.e.703.7 | 12 | 48.5 | odd | 4 | |||
3168.2.o.e.703.8 | 12 | 528.395 | odd | 4 |