Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1889,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4032.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.i (of order \(2\), degree \(1\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.7 | ||
Character | \(\chi\) | \(=\) | 4032.1889 |
Dual form | 4032.2.i.c.1889.8 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.91870i | − | 1.75249i | −0.481862 | − | 0.876247i | \(-0.660039\pi\) | ||
0.481862 | − | 0.876247i | \(-0.339961\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.03709 | − | 1.68827i | 0.769948 | − | 0.638106i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62598 | 0.490252 | 0.245126 | − | 0.969491i | \(-0.421171\pi\) | ||||
0.245126 | + | 0.969491i | \(0.421171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.54668 | 0.706322 | 0.353161 | − | 0.935562i | \(-0.385107\pi\) | ||||
0.353161 | + | 0.935562i | \(0.385107\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.94004 | 0.713064 | 0.356532 | − | 0.934283i | \(-0.383959\pi\) | ||||
0.356532 | + | 0.934283i | \(0.383959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.72048 | 0.624122 | 0.312061 | − | 0.950062i | \(-0.398981\pi\) | ||||
0.312061 | + | 0.950062i | \(0.398981\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.57805i | − | 1.78865i | −0.447421 | − | 0.894324i | \(-0.647657\pi\) | ||
0.447421 | − | 0.894324i | \(-0.352343\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.3562 | −2.07124 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.21126 | 1.52479 | 0.762396 | − | 0.647111i | \(-0.224023\pi\) | ||||
0.762396 | + | 0.647111i | \(0.224023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.08855i | − | 1.45275i | −0.687300 | − | 0.726374i | \(-0.741204\pi\) | ||
0.687300 | − | 0.726374i | \(-0.258796\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.61582 | − | 7.98274i | −1.11828 | − | 1.34933i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.05701i | 1.32456i | 0.749254 | + | 0.662282i | \(0.230412\pi\) | ||||
−0.749254 | + | 0.662282i | \(0.769588\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.17811 | 1.43338 | 0.716690 | − | 0.697392i | \(-0.245656\pi\) | ||||
0.716690 | + | 0.697392i | \(0.245656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.05669i | 1.38113i | 0.723269 | + | 0.690566i | \(0.242639\pi\) | ||||
−0.723269 | + | 0.690566i | \(0.757361\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.17360 | 0.171187 | 0.0855934 | − | 0.996330i | \(-0.472721\pi\) | ||||
0.0855934 | + | 0.996330i | \(0.472721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.29949 | − | 6.87832i | 0.185641 | − | 0.982618i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | −0.336463 | −0.168232 | − | 0.985747i | \(-0.553806\pi\) | ||||
−0.168232 | + | 0.985747i | \(0.553806\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.37173i | − | 0.859164i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.45662i | 0.189635i | 0.995495 | + | 0.0948177i | \(0.0302268\pi\) | ||||
−0.995495 | + | 0.0948177i | \(0.969773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.74827 | 1.24814 | 0.624069 | − | 0.781369i | \(-0.285478\pi\) | ||||
0.624069 | + | 0.781369i | \(0.285478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.97967i | − | 1.23783i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.35618i | 0.898700i | 0.893356 | + | 0.449350i | \(0.148344\pi\) | ||||
−0.893356 | + | 0.449350i | \(0.851656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.71526i | 0.915633i | 0.889047 | + | 0.457817i | \(0.151368\pi\) | ||||
−0.889047 | + | 0.457817i | \(0.848632\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.0398i | 1.76027i | 0.474722 | + | 0.880136i | \(0.342549\pi\) | ||||
−0.474722 | + | 0.880136i | \(0.657451\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.31228 | − | 2.74510i | 0.377469 | − | 0.312833i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0913558 | −0.0102783 | −0.00513916 | − | 0.999987i | \(-0.501636\pi\) | ||||
−0.00513916 | + | 0.999987i | \(0.501636\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.03273i | − | 0.223121i | −0.993758 | − | 0.111561i | \(-0.964415\pi\) | ||
0.993758 | − | 0.111561i | \(-0.0355849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 11.5211i | − | 1.24964i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.48342 | 0.157242 | 0.0786211 | − | 0.996905i | \(-0.474948\pi\) | ||||
0.0786211 | + | 0.996905i | \(0.474948\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.18782 | − | 4.29949i | 0.543832 | − | 0.450709i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 10.6607i | − | 1.09377i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.53884i | − | 0.765453i | −0.923862 | − | 0.382727i | \(-0.874985\pi\) | ||
0.923862 | − | 0.382727i | \(-0.125015\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7561i | 1.16977i | 0.811115 | + | 0.584887i | \(0.198861\pi\) | ||||
−0.811115 | + | 0.584887i | \(0.801139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0789i | 1.38724i | 0.720342 | + | 0.693620i | \(0.243985\pi\) | ||||
−0.720342 | + | 0.693620i | \(0.756015\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.35369 | −0.807582 | −0.403791 | − | 0.914851i | \(-0.632308\pi\) | ||||
−0.403791 | + | 0.914851i | \(0.632308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.68427i | − | 0.448671i | −0.974512 | − | 0.224336i | \(-0.927979\pi\) | ||
0.974512 | − | 0.224336i | \(-0.0720212\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.73703i | − | 0.539694i | −0.962903 | − | 0.269847i | \(-0.913027\pi\) | ||
0.962903 | − | 0.269847i | \(-0.0869732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −33.6148 | −3.13459 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.98913 | − | 4.96358i | 0.549022 | − | 0.455010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.35618 | −0.759653 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.9892i | 1.87733i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.12881 | −0.100166 | −0.0500828 | − | 0.998745i | \(-0.515949\pi\) | ||||
−0.0500828 | + | 0.998745i | \(0.515949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 21.8456i | − | 1.90866i | −0.298761 | − | 0.954328i | \(-0.596573\pi\) | ||
0.298761 | − | 0.954328i | \(-0.403427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.54187 | − | 4.59291i | 0.480541 | − | 0.398256i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.9703i | − | 0.937260i | −0.883395 | − | 0.468630i | \(-0.844748\pi\) | ||
0.883395 | − | 0.468630i | \(-0.155252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.31568 | −0.705327 | −0.352663 | − | 0.935750i | \(-0.614724\pi\) | ||||
−0.352663 | + | 0.935750i | \(0.614724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.14086 | 0.346276 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 32.1774i | − | 2.67219i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.8438 | 1.13413 | 0.567065 | − | 0.823673i | \(-0.308079\pi\) | ||||
0.567065 | + | 0.823673i | \(0.308079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.1508 | −1.55847 | −0.779233 | − | 0.626734i | \(-0.784391\pi\) | ||||
−0.779233 | + | 0.626734i | \(0.784391\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.6966 | −2.54593 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4192 | −0.991162 | −0.495581 | − | 0.868562i | \(-0.665045\pi\) | ||||
−0.495581 | + | 0.868562i | \(0.665045\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.4821 | − | 17.4743i | −1.14135 | − | 1.37717i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3562i | 0.889485i | 0.895659 | + | 0.444742i | \(0.146705\pi\) | ||||
−0.895659 | + | 0.444742i | \(0.853295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.66379 | −0.515660 | −0.257830 | − | 0.966190i | \(-0.583007\pi\) | ||||
−0.257830 | + | 0.966190i | \(0.583007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.51441 | −0.501109 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.23315i | 0.701984i | 0.936379 | + | 0.350992i | \(0.114156\pi\) | ||||
−0.936379 | + | 0.350992i | \(0.885844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.0965 | + | 17.4840i | −1.59474 | + | 1.32167i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.3520 | −1.22221 | −0.611103 | − | 0.791551i | \(-0.709274\pi\) | ||||
−0.611103 | + | 0.791551i | \(0.709274\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6304 | −1.01314 | −0.506571 | − | 0.862198i | \(-0.669087\pi\) | ||||
−0.506571 | + | 0.862198i | \(0.669087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.5730 | 2.32129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.78045 | 0.349581 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4770i | 0.975164i | 0.873077 | + | 0.487582i | \(0.162121\pi\) | ||||
−0.873077 | + | 0.487582i | \(0.837879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.9552 | 0.860551 | 0.430275 | − | 0.902698i | \(-0.358416\pi\) | ||||
0.430275 | + | 0.902698i | \(0.358416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.90865 | −0.349727 | −0.174864 | − | 0.984593i | \(-0.555948\pi\) | ||||
−0.174864 | + | 0.984593i | \(0.555948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.36692i | − | 0.664004i | −0.943279 | − | 0.332002i | \(-0.892276\pi\) | ||
0.943279 | − | 0.332002i | \(-0.107724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.7271 | − | 13.8628i | 1.17401 | − | 0.972979i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 35.9662i | − | 2.51199i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.42346 | 0.305977 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.65567i | − | 0.664724i | −0.943152 | − | 0.332362i | \(-0.892155\pi\) | ||
0.943152 | − | 0.332362i | \(-0.107845\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35.4904 | 2.42043 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.6557 | − | 16.4771i | −0.927007 | − | 1.11854i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.48734 | 0.503653 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.70721i | 0.516113i | 0.966130 | + | 0.258056i | \(0.0830820\pi\) | ||||
−0.966130 | + | 0.258056i | \(0.916918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0314i | 0.997668i | 0.866698 | + | 0.498834i | \(0.166238\pi\) | ||||
−0.866698 | + | 0.498834i | \(0.833762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.87735 | 0.454468 | 0.227234 | − | 0.973840i | \(-0.427032\pi\) | ||||
0.227234 | + | 0.973840i | \(0.427032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.49461i | 0.490988i | 0.969398 | + | 0.245494i | \(0.0789502\pi\) | ||||
−0.969398 | + | 0.245494i | \(0.921050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.59897i | − | 0.300004i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.40464i | − | 0.349597i | −0.984604 | − | 0.174799i | \(-0.944073\pi\) | ||
0.984604 | − | 0.174799i | \(-0.0559275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.6588i | 0.751008i | 0.926821 | + | 0.375504i | \(0.122530\pi\) | ||||
−0.926821 | + | 0.375504i | \(0.877470\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26.9541 | − | 5.09229i | −1.72203 | − | 0.325335i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820 | 0.440831 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1840i | 0.705930i | 0.935637 | + | 0.352965i | \(0.114827\pi\) | ||||
−0.935637 | + | 0.352965i | \(0.885173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.9478i | − | 0.876888i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.39665 | −0.274256 | −0.137128 | − | 0.990553i | \(-0.543787\pi\) | ||||
−0.137128 | + | 0.990553i | \(0.543787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.6024 | + | 16.4129i | 0.845213 | + | 1.01985i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.6142i | − | 0.777828i | −0.921274 | − | 0.388914i | \(-0.872850\pi\) | ||
0.921274 | − | 0.388914i | \(-0.127150\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.59881i | 0.589650i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.4177i | 1.18392i | 0.805967 | + | 0.591960i | \(0.201646\pi\) | ||||
−0.805967 | + | 0.591960i | \(0.798354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 15.7387i | − | 0.956055i | −0.878345 | − | 0.478028i | \(-0.841352\pi\) | ||
0.878345 | − | 0.478028i | \(-0.158648\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.8390 | −1.01543 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.5977i | 1.59810i | 0.601265 | + | 0.799050i | \(0.294664\pi\) | ||||
−0.601265 | + | 0.799050i | \(0.705336\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.75568i | − | 0.224045i | −0.993706 | − | 0.112023i | \(-0.964267\pi\) | ||
0.993706 | − | 0.112023i | \(-0.0357329\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.3591 | −1.62633 | −0.813164 | − | 0.582035i | \(-0.802257\pi\) | ||||
−0.813164 | + | 0.582035i | \(0.802257\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.6966 | − | 15.4951i | 1.10363 | − | 0.914648i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.35618 | −0.491540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 24.9079i | − | 1.45514i | −0.686035 | − | 0.727569i | \(-0.740650\pi\) | ||
0.686035 | − | 0.727569i | \(-0.259350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.70804 | 0.332335 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 21.8456i | − | 1.26336i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.2901 | + | 18.4493i | 0.881309 | + | 1.06340i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 38.2005i | − | 2.18736i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5424 | −0.658762 | −0.329381 | − | 0.944197i | \(-0.606840\pi\) | ||||
−0.329381 | + | 0.944197i | \(0.606840\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.1322 | −1.36841 | −0.684207 | − | 0.729288i | \(-0.739852\pi\) | ||||
−0.684207 | + | 0.729288i | \(0.739852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.6314i | − | 0.940060i | −0.882650 | − | 0.470030i | \(-0.844243\pi\) | ||
0.882650 | − | 0.470030i | \(-0.155757\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0012 | 1.06721 | 0.533607 | − | 0.845733i | \(-0.320836\pi\) | ||||
0.533607 | + | 0.845733i | \(0.320836\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3514 | 0.747533 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.99832 | 0.445038 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.3739 | −1.46296 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.39073 | − | 1.98135i | 0.131805 | − | 0.109235i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.7691i | 1.30647i | 0.757157 | + | 0.653233i | \(0.226588\pi\) | ||||
−0.757157 | + | 0.653233i | \(0.773412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.8266 | 1.57497 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.19795 | −0.0652563 | −0.0326282 | − | 0.999468i | \(-0.510388\pi\) | ||||
−0.0326282 | + | 0.999468i | \(0.510388\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.1519i | − | 0.712213i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.96530 | − | 16.2057i | −0.484080 | − | 0.875024i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.62598 | 0.0872873 | 0.0436437 | − | 0.999047i | \(-0.486103\pi\) | ||||
0.0436437 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.2544 | 1.24478 | 0.622391 | − | 0.782707i | \(-0.286162\pi\) | ||||
0.622391 | + | 0.782707i | \(0.286162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.4476 | 1.62056 | 0.810280 | − | 0.586043i | \(-0.199315\pi\) | ||||
0.810280 | + | 0.586043i | \(0.199315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.2338 | 1.60464 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.71526i | 0.407196i | 0.979055 | + | 0.203598i | \(0.0652636\pi\) | ||||
−0.979055 | + | 0.203598i | \(0.934736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5990 | −0.610472 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 58.9363 | 3.08487 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 37.3905i | − | 1.95177i | −0.218292 | − | 0.975884i | \(-0.570048\pi\) | ||
0.218292 | − | 0.975884i | \(-0.429952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.98984 | + | 4.13540i | −0.259059 | + | 0.214699i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.5169i | 0.906991i | 0.891259 | + | 0.453495i | \(0.149823\pi\) | ||||
−0.891259 | + | 0.453495i | \(0.850177\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.9115 | 1.07699 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.6557i | 1.31784i | 0.752212 | + | 0.658922i | \(0.228987\pi\) | ||||
−0.752212 | + | 0.658922i | \(0.771013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.8376 | −1.93341 | −0.966706 | − | 0.255889i | \(-0.917632\pi\) | ||||
−0.966706 | + | 0.255889i | \(0.917632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.7572 | − | 12.9798i | −0.548238 | − | 0.661512i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.0374 | −1.16804 | −0.584021 | − | 0.811739i | \(-0.698521\pi\) | ||||
−0.584021 | + | 0.811739i | \(0.698521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.2198i | − | 1.27542i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.357996i | 0.0180127i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2753 | 0.917210 | 0.458605 | − | 0.888640i | \(-0.348349\pi\) | ||||
0.458605 | + | 0.888640i | \(0.348349\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.4743i | 0.872624i | 0.899795 | + | 0.436312i | \(0.143716\pi\) | ||||
−0.899795 | + | 0.436312i | \(0.856284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 20.5990i | − | 1.02611i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.1006i | 0.649371i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.9145i | 0.885814i | 0.896567 | + | 0.442907i | \(0.146053\pi\) | ||||
−0.896567 | + | 0.442907i | \(0.853947\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.45916 | + | 2.96726i | 0.121007 | + | 0.146009i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.96566 | −0.391019 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 26.0509i | − | 1.27267i | −0.771413 | − | 0.636335i | \(-0.780450\pi\) | ||
0.771413 | − | 0.636335i | \(-0.219550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.11513i | − | 0.0543480i | −0.999631 | − | 0.0271740i | \(-0.991349\pi\) | ||
0.999631 | − | 0.0271740i | \(-0.00865082\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.4476 | −1.47692 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.8581 | − | 16.4577i | 0.961002 | − | 0.796445i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 22.5414i | − | 1.08578i | −0.839803 | − | 0.542890i | \(-0.817330\pi\) | ||
0.839803 | − | 0.542890i | \(-0.182670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.9596i | 1.24754i | 0.781608 | + | 0.623770i | \(0.214400\pi\) | ||||
−0.781608 | + | 0.623770i | \(0.785600\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 23.3364i | − | 1.11633i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.0283i | 0.860442i | 0.902724 | + | 0.430221i | \(0.141564\pi\) | ||||
−0.902724 | + | 0.430221i | \(0.858436\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3350 | 0.491033 | 0.245516 | − | 0.969392i | \(-0.421043\pi\) | ||||
0.245516 | + | 0.969392i | \(0.421043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.81307i | − | 0.275566i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.7155i | 1.68552i | 0.538292 | + | 0.842758i | \(0.319070\pi\) | ||||
−0.538292 | + | 0.842758i | \(0.680930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.9234 | 0.702718 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.8484 | − | 20.3295i | −0.789864 | − | 0.953062i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.1979 | 0.617374 | 0.308687 | − | 0.951164i | \(-0.400110\pi\) | ||||
0.308687 | + | 0.951164i | \(0.400110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.57150i | − | 0.0731921i | −0.999330 | − | 0.0365960i | \(-0.988349\pi\) | ||
0.999330 | − | 0.0365960i | \(-0.0116515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.0274 | 1.76729 | 0.883643 | − | 0.468162i | \(-0.155084\pi\) | ||||
0.883643 | + | 0.468162i | \(0.155084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.9655i | 0.738795i | 0.929272 | + | 0.369397i | \(0.120436\pi\) | ||||
−0.929272 | + | 0.369397i | \(0.879564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4192 | + | 14.9852i | 0.573466 | + | 0.691953i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.7260i | 0.677103i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.1738 | −1.29270 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.8594 | −1.18154 | −0.590772 | − | 0.806838i | \(-0.701177\pi\) | ||||
−0.590772 | + | 0.806838i | \(0.701177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5186i | 0.935570i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.5424 | −1.34145 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.63386 | −0.0740370 | −0.0370185 | − | 0.999315i | \(-0.511786\pi\) | ||||
−0.0370185 | + | 0.999315i | \(0.511786\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.61687 | −0.388874 | −0.194437 | − | 0.980915i | \(-0.562288\pi\) | ||||
−0.194437 | + | 0.980915i | \(0.562288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.1414 | 1.08727 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.0255 | + | 15.7167i | 0.584271 | + | 0.704990i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.3680i | − | 0.732734i | −0.930471 | − | 0.366367i | \(-0.880602\pi\) | ||
0.930471 | − | 0.366367i | \(-0.119398\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.5232 | −1.45014 | −0.725068 | − | 0.688677i | \(-0.758192\pi\) | ||||
−0.725068 | + | 0.688677i | \(0.758192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 46.0685 | 2.05002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.775695i | 0.0343821i | 0.999852 | + | 0.0171910i | \(0.00547235\pi\) | ||||
−0.999852 | + | 0.0171910i | \(0.994528\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.3912 | + | 30.6374i | 1.12324 | + | 1.35532i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 55.1711 | 2.43113 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.90825 | 0.0839247 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.2749 | −1.23875 | −0.619374 | − | 0.785096i | \(-0.712614\pi\) | ||||
−0.619374 | + | 0.785096i | \(0.712614\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.5186 | 0.897218 | 0.448609 | − | 0.893728i | \(-0.351920\pi\) | ||||
0.448609 | + | 0.893728i | \(0.351920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 23.7807i | − | 1.03590i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −50.5830 | −2.19926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.3737 | 1.01243 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.7356i | 1.41528i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.11294 | − | 11.1840i | 0.0910109 | − | 0.481730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7038i | 0.503187i | 0.967833 | + | 0.251593i | \(0.0809546\pi\) | ||||
−0.967833 | + | 0.251593i | \(0.919045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.3562 | −0.786294 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.0685i | 1.79872i | 0.437208 | + | 0.899360i | \(0.355967\pi\) | ||||
−0.437208 | + | 0.899360i | \(0.644033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.3386 | 0.951655 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.186100 | + | 0.154233i | −0.00791378 | + | 0.00655867i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.9162 | −0.928620 | −0.464310 | − | 0.885673i | \(-0.653698\pi\) | ||||
−0.464310 | + | 0.885673i | \(0.653698\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.0645i | 0.975525i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.2690i | 1.10711i | 0.832814 | + | 0.553554i | \(0.186729\pi\) | ||||
−0.832814 | + | 0.553554i | \(0.813271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.4817 | −0.945811 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 40.4618i | − | 1.69625i | −0.529798 | − | 0.848124i | \(-0.677732\pi\) | ||
0.529798 | − | 0.848124i | \(-0.322268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.44074i | 0.269537i | 0.990877 | + | 0.134768i | \(0.0430290\pi\) | ||||
−0.990877 | + | 0.134768i | \(0.956971\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 88.8358i | 3.70471i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.1376i | 0.713450i | 0.934210 | + | 0.356725i | \(0.116107\pi\) | ||||
−0.934210 | + | 0.356725i | \(0.883893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.43180 | − | 4.14086i | −0.142375 | − | 0.171792i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.98283 | −0.164952 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.2367i | − | 0.793984i | −0.917822 | − | 0.396992i | \(-0.870054\pi\) | ||
0.917822 | − | 0.396992i | \(-0.129946\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 22.0048i | − | 0.906691i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.0268037 | −0.00110070 | −0.000550349 | − | 1.00000i | \(-0.500175\pi\) | ||||
−0.000550349 | 1.00000i | \(0.500175\pi\) | ||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.4508 | − | 23.4696i | −0.797403 | − | 0.962158i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 16.0460i | − | 0.655624i | −0.944743 | − | 0.327812i | \(-0.893689\pi\) | ||
0.944743 | − | 0.327812i | \(-0.106311\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.5786i | − | 0.921001i | −0.887660 | − | 0.460500i | \(-0.847670\pi\) | ||
0.887660 | − | 0.460500i | \(-0.152330\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.7453i | 1.33129i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.4523i | − | 1.11425i | −0.830427 | − | 0.557127i | \(-0.811904\pi\) | ||
0.830427 | − | 0.557127i | \(-0.188096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.98878 | 0.120913 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0391i | 0.567035i | 0.958967 | + | 0.283517i | \(0.0915013\pi\) | ||||
−0.958967 | + | 0.283517i | \(0.908499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.4556i | 0.783254i | 0.920124 | + | 0.391627i | \(0.128088\pi\) | ||||
−0.920124 | + | 0.391627i | \(0.871912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.05997 | 0.0827971 | 0.0413985 | − | 0.999143i | \(-0.486819\pi\) | ||||
0.0413985 | + | 0.999143i | \(0.486819\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.02186 | − | 2.50441i | 0.121068 | − | 0.100337i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.4696 | 1.21878 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.6879i | 0.944499i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.9182 | 1.74836 | 0.874178 | − | 0.485606i | \(-0.161401\pi\) | ||||
0.874178 | + | 0.485606i | \(0.161401\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.42346i | 0.175540i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.30938 | − | 17.5169i | 0.131122 | − | 0.694045i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.1986i | 1.58775i | 0.608081 | + | 0.793875i | \(0.291940\pi\) | ||||
−0.608081 | + | 0.793875i | \(0.708060\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.8705 | 1.57234 | 0.786169 | − | 0.618011i | \(-0.212061\pi\) | ||||
0.786169 | + | 0.618011i | \(0.212061\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.6879 | 0.931268 | 0.465634 | − | 0.884977i | \(-0.345826\pi\) | ||||
0.465634 | + | 0.884977i | \(0.345826\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.36843i | 0.0929692i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.44949 | 0.0958559 | 0.0479280 | − | 0.998851i | \(-0.484738\pi\) | ||||
0.0479280 | + | 0.998851i | \(0.484738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −85.6061 | −3.34491 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.8282 | −1.23985 | −0.619925 | − | 0.784661i | \(-0.712837\pi\) | ||||
−0.619925 | + | 0.784661i | \(0.712837\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.18031 | −0.240386 | −0.120193 | − | 0.992751i | \(-0.538351\pi\) | ||||
−0.120193 | + | 0.992751i | \(0.538351\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.9982 | − | 21.7169i | −0.697941 | − | 0.842146i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 70.4366i | − | 2.72731i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.8505 | 0.611903 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.55413 | −0.175549 | −0.0877744 | − | 0.996140i | \(-0.527975\pi\) | ||||
−0.0877744 | + | 0.996140i | \(0.527975\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 21.7649i | − | 0.836495i | −0.908333 | − | 0.418247i | \(-0.862645\pi\) | ||
0.908333 | − | 0.418247i | \(-0.137355\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.7276 | − | 15.3573i | −0.488440 | − | 0.589359i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.88749 | −0.378334 | −0.189167 | − | 0.981945i | \(-0.560579\pi\) | ||||
−0.189167 | + | 0.981945i | \(0.560579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.9895 | −1.64254 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.23807 | −0.237652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.1572 | −1.71786 | −0.858931 | − | 0.512092i | \(-0.828871\pi\) | ||||
−0.858931 | + | 0.512092i | \(0.828871\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.5866i | 1.23608i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.9840 | 1.02209 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.4490 | 0.772349 | 0.386175 | − | 0.922426i | \(-0.373796\pi\) | ||||
0.386175 | + | 0.922426i | \(0.373796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.9190i | 0.826689i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.8475 | + | 23.9482i | 0.746440 | + | 0.900666i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 11.4298i | − | 0.429254i | −0.976696 | − | 0.214627i | \(-0.931146\pi\) | ||
0.976696 | − | 0.214627i | \(-0.0688535\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −69.3840 | −2.59845 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 16.2268i | − | 0.606847i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.4926 | −1.28636 | −0.643178 | − | 0.765717i | \(-0.722384\pi\) | ||||
−0.643178 | + | 0.765717i | \(0.722384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7691 | + | 28.6801i | 0.885206 | + | 1.06810i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −85.0372 | −3.15820 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.4821i | − | 1.05634i | −0.849138 | − | 0.528172i | \(-0.822878\pi\) | ||
0.849138 | − | 0.528172i | \(-0.177122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.6270i | 0.984836i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.1574 | −0.818404 | −0.409202 | − | 0.912444i | \(-0.634193\pi\) | ||||
−0.409202 | + | 0.912444i | \(0.634193\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.9610i | 0.440590i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 26.1582i | − | 0.962246i | −0.876653 | − | 0.481123i | \(-0.840229\pi\) | ||
0.876653 | − | 0.481123i | \(-0.159771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.7619i | 1.78890i | 0.447168 | + | 0.894450i | \(0.352432\pi\) | ||||
−0.447168 | + | 0.894450i | \(0.647568\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 54.2497i | − | 1.98756i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.0172 | + | 14.1033i | −0.621796 | + | 0.515323i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.8931 | 0.616439 | 0.308220 | − | 0.951315i | \(-0.400267\pi\) | ||||
0.308220 | + | 0.951315i | \(0.400267\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 75.0460i | 2.73120i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.8802i | − | 0.540829i | −0.962744 | − | 0.270415i | \(-0.912839\pi\) | ||
0.962744 | − | 0.270415i | \(-0.0871608\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.78781 | 0.0648080 | 0.0324040 | − | 0.999475i | \(-0.489684\pi\) | ||||
0.0324040 | + | 0.999475i | \(0.489684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.90831 | − | 9.54228i | −0.286300 | − | 0.345454i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.70954i | 0.133944i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.6967i | 0.421793i | 0.977508 | + | 0.210897i | \(0.0676383\pi\) | ||||
−0.977508 | + | 0.210897i | \(0.932362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 32.5696i | − | 1.17145i | −0.810511 | − | 0.585723i | \(-0.800810\pi\) | ||
0.810511 | − | 0.585723i | \(-0.199190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 83.7665i | 3.00898i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.9689 | 0.894603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.5449i | 0.448891i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.6672i | 1.73701i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.7690 | 1.20374 | 0.601868 | − | 0.798596i | \(-0.294424\pi\) | ||||
0.601868 | + | 0.798596i | \(0.294424\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.68566 | − | 11.6869i | −0.344382 | − | 0.415537i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.8257 | 0.881588 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 14.2790i | − | 0.505789i | −0.967494 | − | 0.252894i | \(-0.918617\pi\) | ||
0.967494 | − | 0.252894i | \(-0.0813825\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.45042 | 0.122067 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.4544i | 0.862977i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −68.4764 | + | 56.7508i | −2.41348 | + | 2.00020i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15.9799i | − | 0.561823i | −0.959734 | − | 0.280911i | \(-0.909363\pi\) | ||
0.959734 | − | 0.280911i | \(-0.0906367\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3280 | 0.994732 | 0.497366 | − | 0.867541i | \(-0.334301\pi\) | ||||
0.497366 | + | 0.867541i | \(0.334301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.5014 | 1.55882 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.6386i | 0.861995i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.5883 | −1.17224 | −0.586120 | − | 0.810225i | \(-0.699345\pi\) | ||||
−0.586120 | + | 0.810225i | \(0.699345\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.45989 | 0.329751 | 0.164875 | − | 0.986314i | \(-0.447278\pi\) | ||||
0.164875 | + | 0.986314i | \(0.447278\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.8447 | 0.898709 | 0.449354 | − | 0.893354i | \(-0.351654\pi\) | ||||
0.449354 | + | 0.893354i | \(0.351654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9611 | 0.623815 | 0.311907 | − | 0.950113i | \(-0.399032\pi\) | ||||
0.311907 | + | 0.950113i | \(0.399032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.82054 | − | 20.2225i | 0.132374 | − | 0.700669i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.1134i | 0.903691i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3254 | −0.494569 | −0.247285 | − | 0.968943i | \(-0.579538\pi\) | ||||
−0.247285 | + | 0.968943i | \(0.579538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.4247 | 1.32499 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.5280i | 0.878190i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.0223 | + | 14.1075i | −0.584893 | + | 0.484739i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 69.1135 | 2.36918 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1418 | −1.03204 | −0.516018 | − | 0.856577i | \(-0.672586\pi\) | ||||
−0.516018 | + | 0.856577i | \(0.672586\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.7724 | −1.15364 | −0.576821 | − | 0.816870i | \(-0.695707\pi\) | ||||
−0.576821 | + | 0.816870i | \(0.695707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.4190 | −1.00376 | −0.501882 | − | 0.864936i | \(-0.667359\pi\) | ||||
−0.501882 | + | 0.864936i | \(0.667359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.8915i | 1.05156i | 0.850621 | + | 0.525780i | \(0.176226\pi\) | ||||
−0.850621 | + | 0.525780i | \(0.823774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.1819 | 1.23022 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.148543 | −0.00503897 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7338i | 0.634772i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.4355 | + | 42.7570i | 1.19794 | + | 1.44545i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 19.7472i | − | 0.666814i | −0.942783 | − | 0.333407i | \(-0.891802\pi\) | ||
0.942783 | − | 0.333407i | \(-0.108198\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.7188 | 1.13601 | 0.568007 | − | 0.823023i | \(-0.307714\pi\) | ||||
0.568007 | + | 0.823023i | \(0.307714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 25.2835i | − | 0.850856i | −0.904992 | − | 0.425428i | \(-0.860123\pi\) | ||
0.904992 | − | 0.425428i | \(-0.139877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.0134 | 1.27636 | 0.638182 | − | 0.769886i | \(-0.279687\pi\) | ||||
0.638182 | + | 0.769886i | \(0.279687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.29949 | + | 1.90573i | −0.0771223 | + | 0.0639163i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.19275 | 0.106841 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.0786i | 2.14191i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 66.4172i | − | 2.21514i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.20159 | −0.239920 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53.4135i | 1.77553i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9721i | 0.862391i | 0.902259 | + | 0.431195i | \(0.141908\pi\) | ||||
−0.902259 | + | 0.431195i | \(0.858092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 13.6256i | − | 0.451435i | −0.974193 | − | 0.225718i | \(-0.927527\pi\) | ||
0.974193 | − | 0.225718i | \(-0.0724727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.30519i | − | 0.109386i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.8812 | − | 44.5014i | −1.21793 | − | 1.46957i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.11164 | 0.168617 | 0.0843087 | − | 0.996440i | \(-0.473132\pi\) | ||||
0.0843087 | + | 0.996440i | \(0.473132\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.6483i | 0.646732i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 83.4399i | − | 2.74349i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.3276 | 1.19187 | 0.595935 | − | 0.803032i | \(-0.296781\pi\) | ||||
0.595935 | + | 0.803032i | \(0.296781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.53523 | − | 18.7124i | 0.115863 | − | 0.613273i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18.7331i | − | 0.612639i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.32103i | 0.0431562i | 0.999767 | + | 0.0215781i | \(0.00686906\pi\) | ||||
−0.999767 | + | 0.0215781i | \(0.993131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 11.1360i | − | 0.363024i | −0.983389 | − | 0.181512i | \(-0.941901\pi\) | ||
0.983389 | − | 0.181512i | \(-0.0580991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 78.7303i | − | 2.56381i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.5858 | −1.09139 | −0.545695 | − | 0.837984i | \(-0.683734\pi\) | ||||
−0.545695 | + | 0.837984i | \(0.683734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.3015i | 1.24332i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.3855i | 1.82651i | 0.407392 | + | 0.913253i | \(0.366438\pi\) | ||||
−0.407392 | + | 0.913253i | \(0.633562\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.8124 | 1.70897 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.5209 | − | 22.3476i | −0.598071 | − | 0.721642i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.4247 | −1.11047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 46.8486i | − | 1.50811i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1305 | 0.454405 | 0.227203 | − | 0.973847i | \(-0.427042\pi\) | ||||
0.227203 | + | 0.973847i | \(0.427042\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.3331i | 1.39063i | 0.718707 | + | 0.695313i | \(0.244734\pi\) | ||||
−0.718707 | + | 0.695313i | \(0.755266\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.9398 | + | 14.0391i | −0.543065 | + | 0.450073i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 44.2007i | − | 1.41411i | −0.707160 | − | 0.707053i | \(-0.750024\pi\) | ||
0.707160 | − | 0.707053i | \(-0.249976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.41202 | 0.0770884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.66379 | 0.212542 | 0.106271 | − | 0.994337i | \(-0.466109\pi\) | ||||
0.106271 | + | 0.994337i | \(0.466109\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.2355i | 0.612895i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 77.6888 | 2.47036 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.8862 | 0.790535 | 0.395267 | − | 0.918566i | \(-0.370652\pi\) | ||||
0.395267 | + | 0.918566i | \(0.370652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.7061 | −1.16366 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.85125 | −0.280322 | −0.140161 | − | 0.990129i | \(-0.544762\pi\) | ||||
−0.140161 | + | 0.990129i | \(0.544762\pi\) | |||||||
\(998\) | 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 | 4032.2.i.c.1889.7 | ✓ | 48 | |
3.2 | odd | 2 | inner | 4032.2.i.c.1889.32 | yes | 48 | |
4.3 | odd | 2 | inner | 4032.2.i.c.1889.35 | yes | 48 | |
7.6 | odd | 2 | inner | 4032.2.i.c.1889.14 | yes | 48 | |
8.3 | odd | 2 | inner | 4032.2.i.c.1889.18 | yes | 48 | |
8.5 | even | 2 | inner | 4032.2.i.c.1889.16 | yes | 48 | |
12.11 | even | 2 | inner | 4032.2.i.c.1889.34 | yes | 48 | |
21.20 | even | 2 | inner | 4032.2.i.c.1889.15 | yes | 48 | |
24.5 | odd | 2 | inner | 4032.2.i.c.1889.13 | yes | 48 | |
24.11 | even | 2 | inner | 4032.2.i.c.1889.41 | yes | 48 | |
28.27 | even | 2 | inner | 4032.2.i.c.1889.42 | yes | 48 | |
56.13 | odd | 2 | inner | 4032.2.i.c.1889.31 | yes | 48 | |
56.27 | even | 2 | inner | 4032.2.i.c.1889.33 | yes | 48 | |
84.83 | odd | 2 | inner | 4032.2.i.c.1889.17 | yes | 48 | |
168.83 | odd | 2 | inner | 4032.2.i.c.1889.36 | yes | 48 | |
168.125 | even | 2 | inner | 4032.2.i.c.1889.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.i.c.1889.7 | ✓ | 48 | 1.1 | even | 1 | trivial | |
4032.2.i.c.1889.8 | yes | 48 | 168.125 | even | 2 | inner | |
4032.2.i.c.1889.13 | yes | 48 | 24.5 | odd | 2 | inner | |
4032.2.i.c.1889.14 | yes | 48 | 7.6 | odd | 2 | inner | |
4032.2.i.c.1889.15 | yes | 48 | 21.20 | even | 2 | inner | |
4032.2.i.c.1889.16 | yes | 48 | 8.5 | even | 2 | inner | |
4032.2.i.c.1889.17 | yes | 48 | 84.83 | odd | 2 | inner | |
4032.2.i.c.1889.18 | yes | 48 | 8.3 | odd | 2 | inner | |
4032.2.i.c.1889.31 | yes | 48 | 56.13 | odd | 2 | inner | |
4032.2.i.c.1889.32 | yes | 48 | 3.2 | odd | 2 | inner | |
4032.2.i.c.1889.33 | yes | 48 | 56.27 | even | 2 | inner | |
4032.2.i.c.1889.34 | yes | 48 | 12.11 | even | 2 | inner | |
4032.2.i.c.1889.35 | yes | 48 | 4.3 | odd | 2 | inner | |
4032.2.i.c.1889.36 | yes | 48 | 168.83 | odd | 2 | inner | |
4032.2.i.c.1889.41 | yes | 48 | 24.11 | even | 2 | inner | |
4032.2.i.c.1889.42 | yes | 48 | 28.27 | even | 2 | inner |