Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(161,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.h (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 13x^{10} + 129x^{8} - 512x^{6} + 1548x^{4} - 160x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.5 | ||
Root | \(-2.47317 + 1.42789i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.161 |
Dual form | 1728.3.h.j.161.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −0.519033 | −0.103807 | −0.0519033 | − | 0.998652i | \(-0.516529\pi\) | ||||
−0.0519033 | + | 0.998652i | \(0.516529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.4117 | −1.48739 | −0.743694 | − | 0.668520i | \(-0.766928\pi\) | ||||
−0.743694 | + | 0.668520i | \(0.766928\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.1346 | −1.28497 | −0.642483 | − | 0.766300i | \(-0.722096\pi\) | ||||
−0.642483 | + | 0.766300i | \(0.722096\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.39052i | − 0.414655i | −0.978272 | − | 0.207328i | \(-0.933523\pi\) | ||||
0.978272 | − | 0.207328i | \(-0.0664766\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 24.9326i | − 1.46662i | −0.679892 | − | 0.733312i | \(-0.737973\pi\) | ||||
0.679892 | − | 0.733312i | \(-0.262027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.3367i | 0.701929i | 0.936389 | + | 0.350964i | \(0.114146\pi\) | ||||
−0.936389 | + | 0.350964i | \(0.885854\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 41.1084i | 1.78732i | 0.448742 | + | 0.893662i | \(0.351872\pi\) | ||||
−0.448742 | + | 0.893662i | \(0.648128\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.7306 | −0.989224 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.85538 | −0.270875 | −0.135438 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135438 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.1945 | 0.844985 | 0.422493 | − | 0.906366i | \(-0.361155\pi\) | ||||
0.422493 | + | 0.906366i | \(0.361155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.40403 | 0.154401 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.53769i | − 0.0415591i | −0.999784 | − | 0.0207795i | \(-0.993385\pi\) | ||||
0.999784 | − | 0.0207795i | \(-0.00661481\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 21.3367i | − 0.520406i | −0.965554 | − | 0.260203i | \(-0.916210\pi\) | ||||
0.965554 | − | 0.260203i | \(-0.0837895\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 64.1345i | − 1.49150i | −0.666226 | − | 0.745750i | \(-0.732091\pi\) | ||||
0.666226 | − | 0.745750i | \(-0.267909\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 19.8630i | − 0.422618i | −0.977419 | − | 0.211309i | \(-0.932227\pi\) | ||||
0.977419 | − | 0.211309i | \(-0.0677726\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 59.4039 | 1.21232 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 68.6521 | 1.29532 | 0.647661 | − | 0.761928i | \(-0.275747\pi\) | ||||
0.647661 | + | 0.761928i | \(0.275747\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.33635 | 0.133388 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 67.8652 | 1.15026 | 0.575129 | − | 0.818063i | \(-0.304952\pi\) | ||||
0.575129 | + | 0.818063i | \(0.304952\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 58.6563i | 0.961579i | 0.876836 | + | 0.480789i | \(0.159650\pi\) | ||||
−0.876836 | + | 0.480789i | \(0.840350\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.79786i | 0.0430440i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 56.1345i | 0.837828i | 0.908026 | + | 0.418914i | \(0.137589\pi\) | ||||
−0.908026 | + | 0.418914i | \(0.862411\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 107.615i | 1.51570i | 0.652430 | + | 0.757849i | \(0.273750\pi\) | ||||
−0.652430 | + | 0.757849i | \(0.726250\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.73060 | 0.105899 | 0.0529493 | − | 0.998597i | \(-0.483138\pi\) | ||||
0.0529493 | + | 0.998597i | \(0.483138\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 147.166 | 1.91124 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64.3579 | −0.814657 | −0.407329 | − | 0.913282i | \(-0.633540\pi\) | ||||
−0.407329 | + | 0.913282i | \(0.633540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 125.192 | 1.50834 | 0.754168 | − | 0.656682i | \(-0.228041\pi\) | ||||
0.754168 | + | 0.656682i | \(0.228041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.9409i | 0.152245i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 59.6159i | 0.669841i | 0.942246 | + | 0.334921i | \(0.108710\pi\) | ||||
−0.942246 | + | 0.334921i | \(0.891290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 56.1246i | 0.616753i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 6.92217i | − 0.0728649i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −138.481 | −1.42764 | −0.713820 | − | 0.700329i | \(-0.753037\pi\) | ||||
−0.713820 | + | 0.700329i | \(0.753037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 137.234 | 1.35876 | 0.679378 | − | 0.733789i | \(-0.262250\pi\) | ||||
0.679378 | + | 0.733789i | \(0.262250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 69.7312 | 0.677002 | 0.338501 | − | 0.940966i | \(-0.390080\pi\) | ||||
0.338501 | + | 0.940966i | \(0.390080\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 102.077 | 0.953994 | 0.476997 | − | 0.878905i | \(-0.341725\pi\) | ||||
0.476997 | + | 0.878905i | \(0.341725\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 172.600i | − 1.58349i | −0.610853 | − | 0.791744i | \(-0.709173\pi\) | ||||
0.610853 | − | 0.791744i | \(-0.290827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 72.7981i | − 0.644231i | −0.946700 | − | 0.322116i | \(-0.895606\pi\) | ||||
0.946700 | − | 0.322116i | \(-0.104394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 21.3367i | − 0.185536i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 259.591i | 2.18144i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 78.7879 | 0.651140 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 25.8118 | 0.206495 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −88.0992 | −0.693695 | −0.346847 | − | 0.937922i | \(-0.612748\pi\) | ||||
−0.346847 | + | 0.937922i | \(0.612748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −43.4038 | −0.331327 | −0.165663 | − | 0.986182i | \(-0.552976\pi\) | ||||
−0.165663 | + | 0.986182i | \(0.552976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 138.857i | − 1.04404i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 152.154i | − 1.11062i | −0.831645 | − | 0.555308i | \(-0.812600\pi\) | ||||
0.831645 | − | 0.555308i | \(-0.187400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 104.000i | − 0.748201i | −0.927388 | − | 0.374101i | \(-0.877951\pi\) | ||||
0.927388 | − | 0.374101i | \(-0.122049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 76.1930i | 0.532818i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.07721 | 0.0281187 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.4437 | 0.130495 | 0.0652473 | − | 0.997869i | \(-0.479216\pi\) | ||||
0.0652473 | + | 0.997869i | \(0.479216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.5254 | −0.142552 | −0.0712762 | − | 0.997457i | \(-0.522707\pi\) | ||||
−0.0712762 | + | 0.997457i | \(0.522707\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.5958 | −0.0877151 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 272.808i | 1.73763i | 0.495134 | + | 0.868817i | \(0.335119\pi\) | ||||
−0.495134 | + | 0.868817i | \(0.664881\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 428.009i | − 2.65844i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 24.1445i | − 0.148126i | −0.997254 | − | 0.0740628i | \(-0.976403\pi\) | ||||
0.997254 | − | 0.0740628i | \(-0.0235965\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 207.823i | 1.24445i | 0.782839 | + | 0.622224i | \(0.213771\pi\) | ||||
−0.782839 | + | 0.622224i | \(0.786229\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 139.942 | 0.828061 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 302.257 | 1.74715 | 0.873575 | − | 0.486689i | \(-0.161796\pi\) | ||||
0.873575 | + | 0.486689i | \(0.161796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 257.488 | 1.47136 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.9997 | −0.0614511 | −0.0307256 | − | 0.999528i | \(-0.509782\pi\) | ||||
−0.0307256 | + | 0.999528i | \(0.509782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 196.011i | 1.08293i | 0.840723 | + | 0.541466i | \(0.182130\pi\) | ||||
−0.840723 | + | 0.541466i | \(0.817870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.798110i | 0.00431411i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 352.413i | 1.88456i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 267.896i | 1.40260i | 0.712868 | + | 0.701298i | \(0.247396\pi\) | ||||
−0.712868 | + | 0.701298i | \(0.752604\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −33.9996 | −0.176164 | −0.0880819 | − | 0.996113i | \(-0.528074\pi\) | ||||
−0.0880819 | + | 0.996113i | \(0.528074\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 114.706 | 0.582265 | 0.291133 | − | 0.956683i | \(-0.405968\pi\) | ||||
0.291133 | + | 0.956683i | \(0.405968\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −189.845 | −0.953996 | −0.476998 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476998 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 81.7880 | 0.402897 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0744i | 0.0540216i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 188.509i | − 0.901955i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 373.875i | − 1.77192i | −0.463764 | − | 0.885959i | \(-0.653501\pi\) | ||||
0.463764 | − | 0.885959i | \(-0.346499\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33.2880i | 0.154828i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −272.730 | −1.25682 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −134.400 | −0.608144 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 97.7546 | 0.438362 | 0.219181 | − | 0.975684i | \(-0.429662\pi\) | ||||
0.219181 | + | 0.975684i | \(0.429662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 103.347 | 0.455271 | 0.227636 | − | 0.973746i | \(-0.426900\pi\) | ||||
0.227636 | + | 0.973746i | \(0.426900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 126.850i | 0.553931i | 0.960880 | + | 0.276966i | \(0.0893288\pi\) | ||||
−0.960880 | + | 0.276966i | \(0.910671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 380.942i | 1.63494i | 0.575968 | + | 0.817472i | \(0.304625\pi\) | ||||
−0.575968 | + | 0.817472i | \(0.695375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.3096i | 0.0438705i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 266.998i | 1.11715i | 0.829456 | + | 0.558573i | \(0.188651\pi\) | ||||
−0.829456 | + | 0.558573i | \(0.811349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 341.231 | 1.41590 | 0.707949 | − | 0.706264i | \(-0.249621\pi\) | ||||
0.707949 | + | 0.706264i | \(0.249621\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.8326 | −0.125847 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 71.8914 | 0.291058 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −52.9627 | −0.211007 | −0.105503 | − | 0.994419i | \(-0.533645\pi\) | ||||
−0.105503 | + | 0.994419i | \(0.533645\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 581.053i | − 2.29665i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 120.664i | − 0.469508i | −0.972055 | − | 0.234754i | \(-0.924572\pi\) | ||||
0.972055 | − | 0.234754i | \(-0.0754285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0100i | 0.0618145i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 441.123i | − 1.67728i | −0.544690 | − | 0.838638i | \(-0.683353\pi\) | ||||
0.544690 | − | 0.838638i | \(-0.316647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.6327 | −0.134463 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 455.412 | 1.69298 | 0.846490 | − | 0.532404i | \(-0.178711\pi\) | ||||
0.846490 | + | 0.532404i | \(0.178711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −304.415 | −1.12330 | −0.561652 | − | 0.827374i | \(-0.689834\pi\) | ||||
−0.561652 | + | 0.827374i | \(0.689834\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 349.558 | 1.27112 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 541.056i | − 1.95327i | −0.214906 | − | 0.976635i | \(-0.568945\pi\) | ||||
0.214906 | − | 0.976635i | \(-0.431055\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 276.414i | 0.983680i | 0.870686 | + | 0.491840i | \(0.163675\pi\) | ||||
−0.870686 | + | 0.491840i | \(0.836325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 231.990i | − 0.819753i | −0.912141 | − | 0.409876i | \(-0.865572\pi\) | ||||
0.912141 | − | 0.409876i | \(-0.134428\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 222.151i | 0.774046i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −332.636 | −1.15099 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 548.289 | 1.87129 | 0.935646 | − | 0.352939i | \(-0.114818\pi\) | ||||
0.935646 | + | 0.352939i | \(0.114818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −35.2243 | −0.119405 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 221.596 | 0.741123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 667.751i | 2.21844i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 30.4446i | − 0.0998183i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 437.740i | 1.42586i | 0.701233 | + | 0.712932i | \(0.252633\pi\) | ||||
−0.701233 | + | 0.712932i | \(0.747367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 349.215i | − 1.12288i | −0.827519 | − | 0.561438i | \(-0.810248\pi\) | ||||
0.827519 | − | 0.561438i | \(-0.189752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −304.558 | −0.973030 | −0.486515 | − | 0.873672i | \(-0.661732\pi\) | ||||
−0.486515 | + | 0.873672i | \(0.661732\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −387.488 | −1.22236 | −0.611180 | − | 0.791491i | \(-0.709305\pi\) | ||||
−0.611180 | + | 0.791491i | \(0.709305\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 111.033 | 0.348066 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 332.518 | 1.02947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 133.311i | 0.410187i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 206.808i | 0.628597i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 293.690i | 0.887282i | 0.896205 | + | 0.443641i | \(0.146314\pi\) | ||||
−0.896205 | + | 0.443641i | \(0.853686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 29.1357i | − 0.0869722i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 415.845 | 1.23396 | 0.616980 | − | 0.786978i | \(-0.288356\pi\) | ||||
0.616980 | + | 0.786978i | \(0.288356\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −370.250 | −1.08578 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −108.323 | −0.315809 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −202.882 | −0.584676 | −0.292338 | − | 0.956315i | \(-0.594433\pi\) | ||||
−0.292338 | + | 0.956315i | \(0.594433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3532i | 0.0353960i | 0.999843 | + | 0.0176980i | \(0.00563374\pi\) | ||||
−0.999843 | + | 0.0176980i | \(0.994366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.3361i | 0.0717738i | 0.999356 | + | 0.0358869i | \(0.0114256\pi\) | ||||
−0.999356 | + | 0.0358869i | \(0.988574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 55.8555i | − 0.157340i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 264.158i | − 0.735816i | −0.929862 | − | 0.367908i | \(-0.880074\pi\) | ||||
0.929862 | − | 0.367908i | \(-0.119926\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 183.134 | 0.507296 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.01244 | −0.0109930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −417.797 | −1.13841 | −0.569206 | − | 0.822195i | \(-0.692749\pi\) | ||||
−0.569206 | + | 0.822195i | \(0.692749\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −714.787 | −1.92665 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 529.014i | 1.41827i | 0.705074 | + | 0.709134i | \(0.250914\pi\) | ||||
−0.705074 | + | 0.709134i | \(0.749086\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 42.3446i | 0.112320i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 280.329i | − 0.739654i | −0.929101 | − | 0.369827i | \(-0.879417\pi\) | ||||
0.929101 | − | 0.369827i | \(-0.120583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 57.2283i | − 0.149421i | −0.997205 | − | 0.0747105i | \(-0.976197\pi\) | ||||
0.997205 | − | 0.0747105i | \(-0.0238033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −76.3840 | −0.198400 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −279.589 | −0.718738 | −0.359369 | − | 0.933196i | \(-0.617008\pi\) | ||||
−0.359369 | + | 0.933196i | \(0.617008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1024.94 | 2.62133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.4039 | 0.0845668 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 458.764i | − 1.15558i | −0.816187 | − | 0.577788i | \(-0.803916\pi\) | ||||
0.816187 | − | 0.577788i | \(-0.196084\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 620.518i | − 1.54743i | −0.633537 | − | 0.773713i | \(-0.718397\pi\) | ||||
0.633537 | − | 0.773713i | \(-0.281603\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 141.202i | − 0.350378i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.7346i | 0.0534020i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 645.114 | 1.57730 | 0.788648 | − | 0.614845i | \(-0.210782\pi\) | ||||
0.788648 | + | 0.614845i | \(0.210782\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −706.594 | −1.71088 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −64.9787 | −0.156575 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −586.059 | −1.39871 | −0.699355 | − | 0.714775i | \(-0.746529\pi\) | ||||
−0.699355 | + | 0.714775i | \(0.746529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 59.0014i | 0.140146i | 0.997542 | + | 0.0700729i | \(0.0223232\pi\) | ||||
−0.997542 | + | 0.0700729i | \(0.977677\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 616.599i | 1.45082i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 610.713i | − 1.43024i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.3336i | 0.0332565i | 0.999862 | + | 0.0166283i | \(0.00529318\pi\) | ||||
−0.999862 | + | 0.0166283i | \(0.994707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −224.980 | −0.519585 | −0.259792 | − | 0.965665i | \(-0.583654\pi\) | ||||
−0.259792 | + | 0.965665i | \(0.583654\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −548.249 | −1.25457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −223.743 | −0.509666 | −0.254833 | − | 0.966985i | \(-0.582020\pi\) | ||||
−0.254833 | + | 0.966985i | \(0.582020\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −107.058 | −0.241665 | −0.120833 | − | 0.992673i | \(-0.538556\pi\) | ||||
−0.120833 | + | 0.992673i | \(0.538556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 30.9426i | − 0.0695340i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 381.815i | − 0.850367i | −0.905107 | − | 0.425184i | \(-0.860209\pi\) | ||||
0.905107 | − | 0.425184i | \(-0.139791\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 301.586i | 0.668705i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 29.1305i | − 0.0640231i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −349.194 | −0.764101 | −0.382051 | − | 0.924141i | \(-0.624782\pi\) | ||||
−0.382051 | + | 0.924141i | \(0.624782\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.02277 | 0.00872619 | 0.00436309 | − | 0.999990i | \(-0.498611\pi\) | ||||
0.00436309 | + | 0.999990i | \(0.498611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 851.739 | 1.83961 | 0.919804 | − | 0.392377i | \(-0.128347\pi\) | ||||
0.919804 | + | 0.392377i | \(0.128347\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −503.521 | −1.07820 | −0.539101 | − | 0.842241i | \(-0.681236\pi\) | ||||
−0.539101 | + | 0.842241i | \(0.681236\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 584.457i | − 1.24618i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 906.518i | 1.91653i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 329.823i | − 0.694365i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 286.856i | − 0.598863i | −0.954118 | − | 0.299432i | \(-0.903203\pi\) | ||||
0.954118 | − | 0.299432i | \(-0.0967971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.28892 | −0.0172327 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 71.8763 | 0.148199 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −873.195 | −1.79301 | −0.896504 | − | 0.443036i | \(-0.853901\pi\) | ||||
−0.896504 | + | 0.443036i | \(0.853901\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −441.288 | −0.898754 | −0.449377 | − | 0.893342i | \(-0.648354\pi\) | ||||
−0.449377 | + | 0.893342i | \(0.648354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 195.855i | 0.397272i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1120.45i | − 2.25443i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 897.749i | 1.79910i | 0.436823 | + | 0.899548i | \(0.356104\pi\) | ||||
−0.436823 | + | 0.899548i | \(0.643896\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 638.356i | − 1.26910i | −0.772883 | − | 0.634549i | \(-0.781186\pi\) | ||||
0.772883 | − | 0.634549i | \(-0.218814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −71.2292 | −0.141048 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −684.754 | −1.34529 | −0.672647 | − | 0.739964i | \(-0.734843\pi\) | ||||
−0.672647 | + | 0.739964i | \(0.734843\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −80.4889 | −0.157512 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.1928 | −0.0702773 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 280.757i | 0.543050i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 568.644i | 1.09145i | 0.837965 | + | 0.545723i | \(0.183745\pi\) | ||||
−0.837965 | + | 0.545723i | \(0.816255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 972.143i | 1.85878i | 0.369097 | + | 0.929391i | \(0.379667\pi\) | ||||
−0.369097 | + | 0.929391i | \(0.620333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 653.099i | − 1.23928i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1160.90 | −2.19452 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −115.016 | −0.215789 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −52.9815 | −0.0990309 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −839.653 | −1.55780 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 213.997i | − 0.395558i | −0.980247 | − | 0.197779i | \(-0.936627\pi\) | ||||
0.980247 | − | 0.197779i | \(-0.0633728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 89.5853i | 0.164377i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 525.720i | − 0.961097i | −0.876968 | − | 0.480549i | \(-0.840438\pi\) | ||||
0.876968 | − | 0.480549i | \(-0.159562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 104.764i | − 0.190135i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 670.076 | 1.21171 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −171.281 | −0.307506 | −0.153753 | − | 0.988109i | \(-0.549136\pi\) | ||||
−0.153753 | + | 0.988109i | \(0.549136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −345.718 | −0.618458 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 887.405 | 1.57621 | 0.788104 | − | 0.615543i | \(-0.211063\pi\) | ||||
0.788104 | + | 0.615543i | \(0.211063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.7847i | 0.0668755i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 812.458i | 1.42787i | 0.700212 | + | 0.713935i | \(0.253089\pi\) | ||||
−0.700212 | + | 0.713935i | \(0.746911\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 528.085i | − 0.924842i | −0.886660 | − | 0.462421i | \(-0.846981\pi\) | ||||
0.886660 | − | 0.462421i | \(-0.153019\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1016.64i | − 1.76806i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 603.116 | 1.04526 | 0.522631 | − | 0.852559i | \(-0.324951\pi\) | ||||
0.522631 | + | 0.852559i | \(0.324951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1303.46 | −2.24348 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −970.373 | −1.66445 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 496.885 | 0.846481 | 0.423241 | − | 0.906017i | \(-0.360892\pi\) | ||||
0.423241 | + | 0.906017i | \(0.360892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 349.347i | 0.593120i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 963.674i | 1.62508i | 0.582904 | + | 0.812541i | \(0.301916\pi\) | ||||
−0.582904 | + | 0.812541i | \(0.698084\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 134.737i | − 0.226448i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 305.820i | − 0.510551i | −0.966868 | − | 0.255276i | \(-0.917834\pi\) | ||||
0.966868 | − | 0.255276i | \(-0.0821662\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 148.888 | 0.247733 | 0.123867 | − | 0.992299i | \(-0.460470\pi\) | ||||
0.123867 | + | 0.992299i | \(0.460470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.8936 | −0.0675927 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 257.812 | 0.424731 | 0.212366 | − | 0.977190i | \(-0.431883\pi\) | ||||
0.212366 | + | 0.977190i | \(0.431883\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −107.072 | −0.175241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 516.885i | − 0.843206i | −0.906781 | − | 0.421603i | \(-0.861468\pi\) | ||||
0.906781 | − | 0.421603i | \(-0.138532\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 922.184i | 1.49463i | 0.664472 | + | 0.747313i | \(0.268656\pi\) | ||||
−0.664472 | + | 0.747313i | \(0.731344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 517.202i | 0.835545i | 0.908552 | + | 0.417772i | \(0.137189\pi\) | ||||
−0.908552 | + | 0.417772i | \(0.862811\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 620.704i | − 0.996314i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 604.868 | 0.967789 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −38.3385 | −0.0609516 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 500.632 | 0.793395 | 0.396698 | − | 0.917949i | \(-0.370156\pi\) | ||||
0.396698 | + | 0.917949i | \(0.370156\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 45.7264 | 0.0720101 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 320.218i | − 0.502697i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 171.491i | − 0.267537i | −0.991013 | − | 0.133769i | \(-0.957292\pi\) | ||||
0.991013 | − | 0.133769i | \(-0.0427079\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 614.941i | − 0.956362i | −0.878261 | − | 0.478181i | \(-0.841296\pi\) | ||||
0.878261 | − | 0.478181i | \(-0.158704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 448.046i | 0.692497i | 0.938143 | + | 0.346249i | \(0.112545\pi\) | ||||
−0.938143 | + | 0.346249i | \(0.887455\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −959.250 | −1.47804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 749.334 | 1.14753 | 0.573763 | − | 0.819021i | \(-0.305483\pi\) | ||||
0.573763 | + | 0.819021i | \(0.305483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5280 | 0.0343939 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 504.555 | 0.765637 | 0.382819 | − | 0.923824i | \(-0.374953\pi\) | ||||
0.382819 | + | 0.923824i | \(0.374953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 670.255i | 1.01400i | 0.861945 | + | 0.507001i | \(0.169246\pi\) | ||||
−0.861945 | + | 0.507001i | \(0.830754\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 72.0717i | 0.108378i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 322.922i | − 0.484142i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 829.086i | − 1.23560i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 458.749 | 0.681648 | 0.340824 | − | 0.940127i | \(-0.389294\pi\) | ||||
0.340824 | + | 0.940127i | \(0.389294\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 260.944 | 0.385442 | 0.192721 | − | 0.981254i | \(-0.438269\pi\) | ||||
0.192721 | + | 0.981254i | \(0.438269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1441.83 | 2.12346 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 831.346 | 1.21720 | 0.608599 | − | 0.793478i | \(-0.291732\pi\) | ||||
0.608599 | + | 0.793478i | \(0.291732\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 78.9732i | 0.115289i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 370.070i | − 0.537112i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 693.675i | − 1.00387i | −0.864905 | − | 0.501936i | \(-0.832621\pi\) | ||||
0.864905 | − | 0.501936i | \(-0.167379\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.9795i | 0.0776683i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −531.979 | −0.763240 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −652.155 | −0.930321 | −0.465161 | − | 0.885226i | \(-0.654003\pi\) | ||||
−0.465161 | + | 0.885226i | \(0.654003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.5076 | 0.0291715 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1428.85 | −2.02100 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0968i | 0.0537332i | 0.999639 | + | 0.0268666i | \(0.00855293\pi\) | ||||
−0.999639 | + | 0.0268666i | \(0.991447\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1076.82i | 1.51026i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 39.5467i | − 0.0553101i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 529.843i | − 0.736917i | −0.929644 | − | 0.368458i | \(-0.879886\pi\) | ||||
0.929644 | − | 0.368458i | \(-0.120114\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −726.022 | −1.00696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 194.268 | 0.267956 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 918.579 | 1.26352 | 0.631760 | − | 0.775164i | \(-0.282333\pi\) | ||||
0.631760 | + | 0.775164i | \(0.282333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1599.04 | −2.18747 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1004.73i | 1.37070i | 0.728212 | + | 0.685352i | \(0.240352\pi\) | ||||
−0.728212 | + | 0.685352i | \(0.759648\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 793.441i | − 1.07658i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 461.471i | 0.624454i | 0.950008 | + | 0.312227i | \(0.101075\pi\) | ||||
−0.950008 | + | 0.312227i | \(0.898925\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 335.450i | 0.451481i | 0.974187 | + | 0.225740i | \(0.0724801\pi\) | ||||
−0.974187 | + | 0.225740i | \(0.927520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0919 | −0.0135462 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1062.80 | −1.41896 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −230.848 | −0.307387 | −0.153694 | − | 0.988119i | \(-0.549117\pi\) | ||||
−0.153694 | + | 0.988119i | \(0.549117\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.1724 | 0.0147979 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 115.377i | − 0.152414i | −0.997092 | − | 0.0762069i | \(-0.975719\pi\) | ||||
0.997092 | − | 0.0762069i | \(-0.0242810\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 121.617i | 0.159812i | 0.996802 | + | 0.0799061i | \(0.0254621\pi\) | ||||
−0.996802 | + | 0.0799061i | \(0.974538\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1797.06i | 2.35526i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 365.829i | − 0.476961i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 873.135 | 1.13542 | 0.567708 | − | 0.823230i | \(-0.307830\pi\) | ||||
0.567708 | + | 0.823230i | \(0.307830\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −559.288 | −0.723529 | −0.361765 | − | 0.932269i | \(-0.617826\pi\) | ||||
−0.361765 | + | 0.932269i | \(0.617826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −647.807 | −0.835880 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 284.559 | 0.365288 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1521.09i | − 1.94762i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 141.597i | − 0.180378i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 502.213i | − 0.638136i | −0.947732 | − | 0.319068i | \(-0.896630\pi\) | ||||
0.947732 | − | 0.319068i | \(-0.103370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 757.954i | 0.958222i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 316.188 | 0.398724 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 655.828 | 0.822871 | 0.411436 | − | 0.911439i | \(-0.365028\pi\) | ||||
0.411436 | + | 0.911439i | \(0.365028\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −495.237 | −0.619822 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −109.269 | −0.136076 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 222.151i | 0.275964i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 272.193i | − 0.336456i | −0.985748 | − | 0.168228i | \(-0.946195\pi\) | ||||
0.985748 | − | 0.168228i | \(-0.0538045\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 483.162i | − 0.595760i | −0.954603 | − | 0.297880i | \(-0.903720\pi\) | ||||
0.954603 | − | 0.297880i | \(-0.0962796\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.5318i | 0.0153764i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 855.340 | 1.04693 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −695.215 | −0.846791 | −0.423395 | − | 0.905945i | \(-0.639162\pi\) | ||||
−0.423395 | + | 0.905945i | \(0.639162\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1496.48 | −1.81832 | −0.909161 | − | 0.416446i | \(-0.863276\pi\) | ||||
−0.909161 | + | 0.416446i | \(0.863276\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −347.515 | −0.420212 | −0.210106 | − | 0.977679i | \(-0.567381\pi\) | ||||
−0.210106 | + | 0.977679i | \(0.567381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1014.09i | 1.22327i | 0.791140 | + | 0.611635i | \(0.209488\pi\) | ||||
−0.791140 | + | 0.611635i | \(0.790512\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1481.09i | − 1.77803i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 107.867i | − 0.129182i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 207.818i | 0.247697i | 0.992301 | + | 0.123848i | \(0.0395237\pi\) | ||||
−0.992301 | + | 0.123848i | \(0.960476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −779.293 | −0.926627 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −72.6347 | −0.0859583 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −820.318 | −0.968498 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.2118 | 0.0742795 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 184.331i | 0.216098i | 0.994146 | + | 0.108049i | \(0.0344603\pi\) | ||||
−0.994146 | + | 0.108049i | \(0.965540\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 246.050i | 0.287106i | 0.989643 | + | 0.143553i | \(0.0458528\pi\) | ||||
−0.989643 | + | 0.143553i | \(0.954147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 677.137i | − 0.788286i | −0.919049 | − | 0.394143i | \(-0.871042\pi\) | ||||
0.919049 | − | 0.394143i | \(-0.128958\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 766.243i | 0.887882i | 0.896056 | + | 0.443941i | \(0.146420\pi\) | ||||
−0.896056 | + | 0.443941i | \(0.853580\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −156.881 | −0.181366 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 909.675 | 1.04681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 302.594 | 0.347410 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −268.746 | −0.307138 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 917.942i | − 1.04668i | −0.852123 | − | 0.523342i | \(-0.824685\pi\) | ||||
0.852123 | − | 0.523342i | \(-0.175315\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1051.56i | − 1.19360i | −0.802389 | − | 0.596801i | \(-0.796438\pi\) | ||||
0.802389 | − | 0.596801i | \(-0.203562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 232.927i | 0.263790i | 0.991264 | + | 0.131895i | \(0.0421062\pi\) | ||||
−0.991264 | + | 0.131895i | \(0.957894\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 905.279i | 1.02061i | 0.859994 | + | 0.510304i | \(0.170467\pi\) | ||||
−0.859994 | + | 0.510304i | \(0.829533\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 917.264 | 1.03179 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 264.906 | 0.296648 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.70924 | 0.00637904 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −205.768 | −0.228886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1711.68i | − 1.89975i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 101.736i | − 0.112416i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1253.87i | 1.38244i | 0.722644 | + | 0.691221i | \(0.242927\pi\) | ||||
−0.722644 | + | 0.691221i | \(0.757073\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 533.926i | 0.586087i | 0.956099 | + | 0.293044i | \(0.0946681\pi\) | ||||
−0.956099 | + | 0.293044i | \(0.905332\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1769.54 | −1.93816 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 451.908 | 0.492811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 145.848 | 0.158703 | 0.0793516 | − | 0.996847i | \(-0.474715\pi\) | ||||
0.0793516 | + | 0.996847i | \(0.474715\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 580.098 | 0.628492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.0279i | 0.0411112i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 916.827i | − 0.986897i | −0.869775 | − | 0.493449i | \(-0.835736\pi\) | ||||
0.869775 | − | 0.493449i | \(-0.164264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 792.249i | 0.850966i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 182.914i | − 0.195630i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 282.716 | 0.301725 | 0.150862 | − | 0.988555i | \(-0.451795\pi\) | ||||
0.150862 | + | 0.988555i | \(0.451795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1669.95 | −1.77465 | −0.887327 | − | 0.461140i | \(-0.847440\pi\) | ||||
−0.887327 | + | 0.461140i | \(0.847440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 877.116 | 0.930134 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 833.418 | 0.880062 | 0.440031 | − | 0.897983i | \(-0.354968\pi\) | ||||
0.440031 | + | 0.897983i | \(0.354968\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 41.6720i | − 0.0439114i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 978.132i | 1.02637i | 0.858278 | + | 0.513186i | \(0.171535\pi\) | ||||
−0.858278 | + | 0.513186i | \(0.828465\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 139.047i | − 0.145599i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1584.19i | 1.65192i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −274.846 | −0.286000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.6469 | 0.0182870 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 743.175 | 0.768537 | 0.384268 | − | 0.923221i | \(-0.374454\pi\) | ||||
0.384268 | + | 0.923221i | \(0.374454\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 562.344 | 0.579139 | 0.289569 | − | 0.957157i | \(-0.406488\pi\) | ||||
0.289569 | + | 0.957157i | \(0.406488\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1082.82i | 1.11287i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 116.016i | − 0.118747i | −0.998236 | − | 0.0593734i | \(-0.981090\pi\) | ||||
0.998236 | − | 0.0593734i | \(-0.0189103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 842.649i | − 0.860724i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1088.69i | − 1.10752i | −0.832676 | − | 0.553760i | \(-0.813192\pi\) | ||||
0.832676 | − | 0.553760i | \(-0.186808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59.5364 | −0.0604430 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2636.47 | 2.66579 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 938.958 | 0.947486 | 0.473743 | − | 0.880663i | \(-0.342903\pi\) | ||||
0.473743 | + | 0.880663i | \(0.342903\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 98.5360 | 0.0990312 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 970.068i | 0.972987i | 0.873684 | + | 0.486494i | \(0.161724\pi\) | ||||
−0.873684 | + | 0.486494i | \(0.838276\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.h.j.161.5 | yes | 12 | |
3.2 | odd | 2 | 1728.3.h.i.161.7 | yes | 12 | ||
4.3 | odd | 2 | 1728.3.h.i.161.5 | ✓ | 12 | ||
8.3 | odd | 2 | inner | 1728.3.h.j.161.8 | yes | 12 | |
8.5 | even | 2 | 1728.3.h.i.161.8 | yes | 12 | ||
12.11 | even | 2 | inner | 1728.3.h.j.161.7 | yes | 12 | |
24.5 | odd | 2 | inner | 1728.3.h.j.161.6 | yes | 12 | |
24.11 | even | 2 | 1728.3.h.i.161.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.h.i.161.5 | ✓ | 12 | 4.3 | odd | 2 | ||
1728.3.h.i.161.6 | yes | 12 | 24.11 | even | 2 | ||
1728.3.h.i.161.7 | yes | 12 | 3.2 | odd | 2 | ||
1728.3.h.i.161.8 | yes | 12 | 8.5 | even | 2 | ||
1728.3.h.j.161.5 | yes | 12 | 1.1 | even | 1 | trivial | |
1728.3.h.j.161.6 | yes | 12 | 24.5 | odd | 2 | inner | |
1728.3.h.j.161.7 | yes | 12 | 12.11 | even | 2 | inner | |
1728.3.h.j.161.8 | yes | 12 | 8.3 | odd | 2 | inner |