Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.20 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.c.5615.19 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 0.206991 | 0.0925694 | 0.0462847 | − | 0.998928i | \(-0.485262\pi\) | ||||
0.0462847 | + | 0.998928i | \(0.485262\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 6.42190i | − 1.93628i | −0.250418 | − | 0.968138i | \(-0.580568\pi\) | ||||
0.250418 | − | 0.968138i | \(-0.419432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.52336i | − 0.977204i | −0.872507 | − | 0.488602i | \(-0.837507\pi\) | ||||
0.872507 | − | 0.488602i | \(-0.162493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.90616i | 0.947383i | 0.880691 | + | 0.473692i | \(0.157079\pi\) | ||||
−0.880691 | + | 0.473692i | \(0.842921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.48691 | 1.25878 | 0.629392 | − | 0.777088i | \(-0.283304\pi\) | ||||
0.629392 | + | 0.777088i | \(0.283304\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.880512 | 0.183599 | 0.0917997 | − | 0.995777i | \(-0.470738\pi\) | ||||
0.0917997 | + | 0.995777i | \(0.470738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.95715 | −0.991431 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.20814 | −0.595737 | −0.297868 | − | 0.954607i | \(-0.596276\pi\) | ||||
−0.297868 | + | 0.954607i | \(0.596276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0631261i | 0.0113378i | 0.999984 | + | 0.00566890i | \(0.00180448\pi\) | ||||
−0.999984 | + | 0.00566890i | \(0.998196\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.206991i | 0.0349879i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.91837i | − 1.63057i | −0.579060 | − | 0.815285i | \(-0.696580\pi\) | ||||
0.579060 | − | 0.815285i | \(-0.303420\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 5.94221i | − 0.928017i | −0.885831 | − | 0.464009i | \(-0.846411\pi\) | ||||
0.885831 | − | 0.464009i | \(-0.153589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.13960 | 0.173788 | 0.0868938 | − | 0.996218i | \(-0.472306\pi\) | ||||
0.0868938 | + | 0.996218i | \(0.472306\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.81266 | −0.993729 | −0.496864 | − | 0.867828i | \(-0.665515\pi\) | ||||
−0.496864 | + | 0.867828i | \(0.665515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.6324 | −1.73520 | −0.867598 | − | 0.497265i | \(-0.834338\pi\) | ||||
−0.867598 | + | 0.497265i | \(0.834338\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.32928i | − 0.179240i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.23338i | 0.551139i | 0.961281 | + | 0.275570i | \(0.0888664\pi\) | ||||
−0.961281 | + | 0.275570i | \(0.911134\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3006i | 1.57493i | 0.616359 | + | 0.787465i | \(0.288607\pi\) | ||||
−0.616359 | + | 0.787465i | \(0.711393\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.729305i | − 0.0904591i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.74666 | 0.702067 | 0.351033 | − | 0.936363i | \(-0.385830\pi\) | ||||
0.351033 | + | 0.936363i | \(0.385830\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1795 | 1.20809 | 0.604043 | − | 0.796952i | \(-0.293556\pi\) | ||||
0.604043 | + | 0.796952i | \(0.293556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.27618 | 0.968653 | 0.484327 | − | 0.874887i | \(-0.339065\pi\) | ||||
0.484327 | + | 0.874887i | \(0.339065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.42190 | 0.731843 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 4.86426i | − 0.547272i | −0.961833 | − | 0.273636i | \(-0.911774\pi\) | ||||
0.961833 | − | 0.273636i | \(-0.0882264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.51539i | − 0.824921i | −0.910976 | − | 0.412460i | \(-0.864669\pi\) | ||||
0.910976 | − | 0.412460i | \(-0.135331\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.808542i | 0.0876987i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.44682i | 0.471362i | 0.971830 | + | 0.235681i | \(0.0757320\pi\) | ||||
−0.971830 | + | 0.235681i | \(0.924268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.52336 | 0.369348 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.13574 | 0.116525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.3929 | −1.76599 | −0.882993 | − | 0.469387i | \(-0.844475\pi\) | ||||
−0.882993 | + | 0.469387i | \(0.844475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.0273 | −1.89329 | −0.946643 | − | 0.322284i | \(-0.895550\pi\) | ||||
−0.946643 | + | 0.322284i | \(0.895550\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7903i | 1.06320i | 0.846995 | + | 0.531601i | \(0.178409\pi\) | ||||
−0.846995 | + | 0.531601i | \(0.821591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.97087i | − 0.480553i | −0.970705 | − | 0.240276i | \(-0.922762\pi\) | ||||
0.970705 | − | 0.240276i | \(-0.0772380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.84810i | − 0.272798i | −0.990654 | − | 0.136399i | \(-0.956447\pi\) | ||||
0.990654 | − | 0.136399i | \(-0.0435530\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.88561i | − 0.271455i | −0.990746 | − | 0.135728i | \(-0.956663\pi\) | ||||
0.990746 | − | 0.135728i | \(-0.0433372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.182258 | 0.0169957 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.90616 | −0.358077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −30.2408 | −2.74916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.06105 | −0.184345 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 7.23082i | − 0.641631i | −0.947142 | − | 0.320816i | \(-0.896043\pi\) | ||||
0.947142 | − | 0.320816i | \(-0.103957\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 12.8026i | − 1.11857i | −0.828975 | − | 0.559286i | \(-0.811076\pi\) | ||||
0.828975 | − | 0.559286i | \(-0.188924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.48691i | 0.475776i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.363873i | 0.0310878i | 0.999879 | + | 0.0155439i | \(0.00494798\pi\) | ||||
−0.999879 | + | 0.0155439i | \(0.995052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.32338 | 0.790799 | 0.395399 | − | 0.918509i | \(-0.370606\pi\) | ||||
0.395399 | + | 0.918509i | \(0.370606\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.6266 | −1.89214 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.664057 | −0.0551470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.82519 | −0.395295 | −0.197648 | − | 0.980273i | \(-0.563330\pi\) | ||||
−0.197648 | + | 0.980273i | \(0.563330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.7969i | 1.04140i | 0.853740 | + | 0.520700i | \(0.174329\pi\) | ||||
−0.853740 | + | 0.520700i | \(0.825671\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0130666i | 0.00104953i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5455i | 1.24067i | 0.784337 | + | 0.620335i | \(0.213003\pi\) | ||||
−0.784337 | + | 0.620335i | \(0.786997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.880512i | 0.0693940i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.4630 | −1.44613 | −0.723067 | − | 0.690778i | \(-0.757268\pi\) | ||||
−0.723067 | + | 0.690778i | \(0.757268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.5320 | −0.969754 | −0.484877 | − | 0.874582i | \(-0.661136\pi\) | ||||
−0.484877 | + | 0.874582i | \(0.661136\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.585951 | 0.0450731 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.49171 | 0.417527 | 0.208763 | − | 0.977966i | \(-0.433056\pi\) | ||||
0.208763 | + | 0.977966i | \(0.433056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.95715i | − 0.374726i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 14.5830i | − 1.08998i | −0.838441 | − | 0.544992i | \(-0.816533\pi\) | ||||
0.838441 | − | 0.544992i | \(-0.183467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2753i | 1.28407i | 0.766677 | + | 0.642033i | \(0.221909\pi\) | ||||
−0.766677 | + | 0.642033i | \(0.778091\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 2.05302i | − 0.150941i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.0850 | 1.83440 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.29828 | 0.528085 | 0.264042 | − | 0.964511i | \(-0.414944\pi\) | ||||
0.264042 | + | 0.964511i | \(0.414944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.1106 | 0.871742 | 0.435871 | − | 0.900009i | \(-0.356440\pi\) | ||||
0.435871 | + | 0.900009i | \(0.356440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3925 | −1.23917 | −0.619584 | − | 0.784931i | \(-0.712699\pi\) | ||||
−0.619584 | + | 0.784931i | \(0.712699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.07583i | 0.218040i | 0.994040 | + | 0.109020i | \(0.0347712\pi\) | ||||
−0.994040 | + | 0.109020i | \(0.965229\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3.20814i | − 0.225167i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.22999i | − 0.0859060i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 35.2364i | − 2.43735i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.57154 | −0.658932 | −0.329466 | − | 0.944167i | \(-0.606869\pi\) | ||||
−0.329466 | + | 0.944167i | \(0.606869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.235888 | 0.0160874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0631261 | −0.00428528 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.7628 | 0.925786 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 26.5694i | − 1.77922i | −0.456722 | − | 0.889610i | \(-0.650976\pi\) | ||||
0.456722 | − | 0.889610i | \(-0.349024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 20.7345i | − 1.37620i | −0.725616 | − | 0.688100i | \(-0.758445\pi\) | ||||
0.725616 | − | 0.688100i | \(-0.241555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 19.2625i | − 1.27290i | −0.771316 | − | 0.636452i | \(-0.780401\pi\) | ||||
0.771316 | − | 0.636452i | \(-0.219599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 25.0038i | − 1.63805i | −0.573756 | − | 0.819027i | \(-0.694514\pi\) | ||||
0.573756 | − | 0.819027i | \(-0.305486\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.41016 | −0.0919889 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0439 | −0.973107 | −0.486553 | − | 0.873651i | \(-0.661746\pi\) | ||||
−0.486553 | + | 0.873651i | \(0.661746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.23274 | −0.208239 | −0.104120 | − | 0.994565i | \(-0.533203\pi\) | ||||
−0.104120 | + | 0.994565i | \(0.533203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.206991 | −0.0132242 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 19.3324i | − 1.23009i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 10.4258i | − 0.658071i | −0.944318 | − | 0.329036i | \(-0.893276\pi\) | ||||
0.944318 | − | 0.329036i | \(-0.106724\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.65456i | − 0.355499i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 8.12452i | − 0.506794i | −0.967362 | − | 0.253397i | \(-0.918452\pi\) | ||||
0.967362 | − | 0.253397i | \(-0.0815479\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.91837 | 0.616297 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.7639 | −0.910382 | −0.455191 | − | 0.890394i | \(-0.650429\pi\) | ||||
−0.455191 | + | 0.890394i | \(0.650429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.61480 | −0.160626 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.8961 | 1.63989 | 0.819943 | − | 0.572445i | \(-0.194005\pi\) | ||||
0.819943 | + | 0.572445i | \(0.194005\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5914i | 1.06860i | 0.845295 | + | 0.534301i | \(0.179425\pi\) | ||||
−0.845295 | + | 0.534301i | \(0.820575\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 31.8343i | 1.91968i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 24.8383i | − 1.49239i | −0.665729 | − | 0.746194i | \(-0.731879\pi\) | ||||
0.665729 | − | 0.746194i | \(-0.268121\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 4.13370i | − 0.246596i | −0.992370 | − | 0.123298i | \(-0.960653\pi\) | ||||
0.992370 | − | 0.123298i | \(-0.0393471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.9297 | 1.42247 | 0.711236 | − | 0.702954i | \(-0.248136\pi\) | ||||
0.711236 | + | 0.702954i | \(0.248136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.94221 | 0.350758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.74190 | 0.102465 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.0225 | −0.702360 | −0.351180 | − | 0.936308i | \(-0.614219\pi\) | ||||
−0.351180 | + | 0.936308i | \(0.614219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.876273i | 0.0510186i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3.10236i | − 0.179414i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.13960i | 0.0656855i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.54612i | 0.145790i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.82060 | 0.332199 | 0.166100 | − | 0.986109i | \(-0.446883\pi\) | ||||
0.166100 | + | 0.986109i | \(0.446883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.7884 | −0.725161 | −0.362580 | − | 0.931952i | \(-0.618104\pi\) | ||||
−0.362580 | + | 0.931952i | \(0.618104\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.74881 | 0.0988483 | 0.0494242 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494242 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.5938 | −1.71832 | −0.859159 | − | 0.511709i | \(-0.829013\pi\) | ||||
−0.859159 | + | 0.511709i | \(0.829013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6024i | 1.15351i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.4328i | 1.19255i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.4658i | 0.968830i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 6.81266i | − 0.375594i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7269 | 1.13925 | 0.569627 | − | 0.821904i | \(-0.307088\pi\) | ||||
0.569627 | + | 0.821904i | \(0.307088\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.18951 | 0.0649899 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9716 | 1.08792 | 0.543961 | − | 0.839110i | \(-0.316924\pi\) | ||||
0.543961 | + | 0.839110i | \(0.316924\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.405390 | 0.0219531 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6443i | 0.571414i | 0.958317 | + | 0.285707i | \(0.0922284\pi\) | ||||
−0.958317 | + | 0.285707i | \(0.907772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 21.1575i | − 1.13254i | −0.824221 | − | 0.566268i | \(-0.808387\pi\) | ||||
0.824221 | − | 0.566268i | \(-0.191613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 7.85498i | − 0.418079i | −0.977907 | − | 0.209039i | \(-0.932966\pi\) | ||||
0.977907 | − | 0.209039i | \(-0.0670337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.10707 | 0.111832 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.0102 | 1.16165 | 0.580826 | − | 0.814028i | \(-0.302730\pi\) | ||||
0.580826 | + | 0.814028i | \(0.302730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.1062 | 0.584537 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.71310 | 0.0896676 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 5.61196i | − 0.292942i | −0.989215 | − | 0.146471i | \(-0.953209\pi\) | ||||
0.989215 | − | 0.146471i | \(-0.0467915\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 12.6324i | − 0.655843i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 21.5334i | − 1.11496i | −0.830192 | − | 0.557478i | \(-0.811769\pi\) | ||||
0.830192 | − | 0.557478i | \(-0.188231\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.3034i | 0.582156i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.2973 | −1.86447 | −0.932233 | − | 0.361858i | \(-0.882143\pi\) | ||||
−0.932233 | + | 0.361858i | \(0.882143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4362 | 0.635462 | 0.317731 | − | 0.948181i | \(-0.397079\pi\) | ||||
0.317731 | + | 0.948181i | \(0.397079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.32928 | 0.0677463 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.47648 | −0.277669 | −0.138834 | − | 0.990316i | \(-0.544336\pi\) | ||||
−0.138834 | + | 0.990316i | \(0.544336\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.43942i | 0.173939i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.00686i | − 0.0506606i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 9.58947i | − 0.481282i | −0.970614 | − | 0.240641i | \(-0.922642\pi\) | ||||
0.970614 | − | 0.240641i | \(-0.0773576\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 1.76702i | − 0.0882408i | −0.999026 | − | 0.0441204i | \(-0.985951\pi\) | ||||
0.999026 | − | 0.0441204i | \(-0.0140485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.222416 | 0.0110793 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −63.6948 | −3.15723 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.87490 | −0.290495 | −0.145248 | − | 0.989395i | \(-0.546398\pi\) | ||||
−0.145248 | + | 0.989395i | \(0.546398\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.23338 | −0.208311 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1.55562i | − 0.0763624i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.9459i | 0.925567i | 0.886471 | + | 0.462783i | \(0.153149\pi\) | ||||
−0.886471 | + | 0.462783i | \(0.846851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.2598i | 1.23109i | 0.788103 | + | 0.615544i | \(0.211064\pi\) | ||||
−0.788103 | + | 0.615544i | \(0.788936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 19.3634i | − 0.939265i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.3006 | −0.595268 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.5774 | −1.81004 | −0.905020 | − | 0.425369i | \(-0.860144\pi\) | ||||
−0.905020 | + | 0.425369i | \(0.860144\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1040 | 1.01419 | 0.507097 | − | 0.861889i | \(-0.330719\pi\) | ||||
0.507097 | + | 0.861889i | \(0.330719\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.83129 | 0.231112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.88405i | 0.137648i | 0.997629 | + | 0.0688240i | \(0.0219247\pi\) | ||||
−0.997629 | + | 0.0688240i | \(0.978075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 34.5978i | − 1.64379i | −0.569640 | − | 0.821895i | \(-0.692917\pi\) | ||||
0.569640 | − | 0.821895i | \(-0.307083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.920453i | 0.0436337i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.8661i | 0.701575i | 0.936455 | + | 0.350787i | \(0.114086\pi\) | ||||
−0.936455 | + | 0.350787i | \(0.885914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.1603 | −1.79690 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.729305 | 0.0341903 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0037 | 0.514730 | 0.257365 | − | 0.966314i | \(-0.417146\pi\) | ||||
0.257365 | + | 0.966314i | \(0.417146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.9687 | −1.53551 | −0.767753 | − | 0.640746i | \(-0.778625\pi\) | ||||
−0.767753 | + | 0.640746i | \(0.778625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 12.3348i | − 0.573245i | −0.958044 | − | 0.286622i | \(-0.907468\pi\) | ||||
0.958044 | − | 0.286622i | \(-0.0925325\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 33.5264i | − 1.55142i | −0.631091 | − | 0.775709i | \(-0.717393\pi\) | ||||
0.631091 | − | 0.775709i | \(-0.282607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.74666i | 0.265356i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.31840i | − 0.336501i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.1995 | −1.24800 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.65791 | −0.441281 | −0.220641 | − | 0.975355i | \(-0.570815\pi\) | ||||
−0.220641 | + | 0.975355i | \(0.570815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.9460 | −1.59340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.60019 | −0.163476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1008i | 1.13742i | 0.822537 | + | 0.568712i | \(0.192558\pi\) | ||||
−0.822537 | + | 0.568712i | \(0.807442\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5524i | 0.476224i | 0.971238 | + | 0.238112i | \(0.0765285\pi\) | ||||
−0.971238 | + | 0.238112i | \(0.923471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 12.5315i | − 0.564391i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.1795i | 0.456613i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.6619 | 0.522059 | 0.261029 | − | 0.965331i | \(-0.415938\pi\) | ||||
0.261029 | + | 0.965331i | \(0.415938\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.0202 | 1.29394 | 0.646972 | − | 0.762513i | \(-0.276035\pi\) | ||||
0.646972 | + | 0.762513i | \(0.276035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.93849 | −0.175260 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.0894 | 0.979096 | 0.489548 | − | 0.871976i | \(-0.337162\pi\) | ||||
0.489548 | + | 0.871976i | \(0.337162\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.27618i | 0.366116i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.23350i | 0.0984199i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.7502i | 1.92413i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.5460i | 0.637273i | 0.947877 | + | 0.318636i | \(0.103225\pi\) | ||||
−0.947877 | + | 0.318636i | \(0.896775\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.6350 | −1.38330 | −0.691651 | − | 0.722232i | \(-0.743116\pi\) | ||||
−0.691651 | + | 0.722232i | \(0.743116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.246581 | −0.0107412 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2247 | −0.966291 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.9365 | −0.906862 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1.02893i | − 0.0444844i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.42190i | 0.276611i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.7160i | 0.976639i | 0.872665 | + | 0.488319i | \(0.162390\pi\) | ||||
−0.872665 | + | 0.488319i | \(0.837610\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 0.589532i | − 0.0252528i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.2601 | 0.951774 | 0.475887 | − | 0.879506i | \(-0.342127\pi\) | ||||
0.475887 | + | 0.879506i | \(0.342127\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.6028 | −0.749904 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.86426 | 0.206849 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.99670 | −0.126974 | −0.0634872 | − | 0.997983i | \(-0.520222\pi\) | ||||
−0.0634872 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 4.01522i | − 0.169826i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 13.4913i | − 0.568589i | −0.958737 | − | 0.284295i | \(-0.908241\pi\) | ||||
0.958737 | − | 0.284295i | \(-0.0917594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 0.597296i | − 0.0251284i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 40.7445i | − 1.70810i | −0.520191 | − | 0.854050i | \(-0.674139\pi\) | ||||
0.520191 | − | 0.854050i | \(-0.325861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.0110 | −0.753739 | −0.376869 | − | 0.926266i | \(-0.622999\pi\) | ||||
−0.376869 | + | 0.926266i | \(0.622999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.36483 | −0.182026 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3495 | 1.22184 | 0.610919 | − | 0.791693i | \(-0.290800\pi\) | ||||
0.610919 | + | 0.791693i | \(0.290800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.51539 | 0.311791 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 81.1242i | 3.35982i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 11.1732i | − 0.461168i | −0.973052 | − | 0.230584i | \(-0.925936\pi\) | ||||
0.973052 | − | 0.230584i | \(-0.0740637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.346368i | 0.0142718i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 29.9792i | − 1.23110i | −0.788099 | − | 0.615549i | \(-0.788934\pi\) | ||||
0.788099 | − | 0.615549i | \(-0.211066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.808542 | −0.0331470 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.38388 | −0.260838 | −0.130419 | − | 0.991459i | \(-0.541632\pi\) | ||||
−0.130419 | + | 0.991459i | \(0.541632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.5445 | −0.960402 | −0.480201 | − | 0.877159i | \(-0.659436\pi\) | ||||
−0.480201 | + | 0.877159i | \(0.659436\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.25958 | −0.254488 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 33.9599i | − 1.37839i | −0.724577 | − | 0.689194i | \(-0.757965\pi\) | ||||
0.724577 | − | 0.689194i | \(-0.242035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0034i | 0.971076i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20.6042i | − 0.832197i | −0.909320 | − | 0.416098i | \(-0.863397\pi\) | ||||
0.909320 | − | 0.416098i | \(-0.136603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.4489i | 1.50764i | 0.657083 | + | 0.753818i | \(0.271790\pi\) | ||||
−0.657083 | + | 0.753818i | \(0.728210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.2766 | −0.573825 | −0.286913 | − | 0.957957i | \(-0.592629\pi\) | ||||
−0.286913 | + | 0.957957i | \(0.592629\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.44682 | −0.178158 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3592 | 0.974366 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.7427 | 1.54477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 7.00448i | − 0.278844i | −0.990233 | − | 0.139422i | \(-0.955476\pi\) | ||||
0.990233 | − | 0.139422i | \(-0.0445244\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.49672i | − 0.0593954i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.52336i | 0.139601i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.23092i | 0.364599i | 0.983243 | + | 0.182300i | \(0.0583541\pi\) | ||||
−0.983243 | + | 0.182300i | \(0.941646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.48603 | −0.0586031 | −0.0293016 | − | 0.999571i | \(-0.509328\pi\) | ||||
−0.0293016 | + | 0.999571i | \(0.509328\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.2654 | 0.639457 | 0.319729 | − | 0.947509i | \(-0.396408\pi\) | ||||
0.319729 | + | 0.947509i | \(0.396408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.1863 | 1.06716 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.92310 | −0.270922 | −0.135461 | − | 0.990783i | \(-0.543252\pi\) | ||||
−0.135461 | + | 0.990783i | \(0.543252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 2.65003i | − 0.103545i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.3057i | 0.440407i | 0.975454 | + | 0.220203i | \(0.0706721\pi\) | ||||
−0.975454 | + | 0.220203i | \(0.929328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9877i | 0.738536i | 0.929323 | + | 0.369268i | \(0.120392\pi\) | ||||
−0.929323 | + | 0.369268i | \(0.879608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.13574i | 0.0440422i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.82481 | −0.109377 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 78.9932 | 3.04950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6164 | 0.679061 | 0.339531 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339531 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.42579 | 0.285396 | 0.142698 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142698 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 17.3929i | − 0.667480i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.8832i | 0.875600i | 0.899072 | + | 0.437800i | \(0.144242\pi\) | ||||
−0.899072 | + | 0.437800i | \(0.855758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0753186i | 0.00287778i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.5086i | 1.69564i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.6439 | −1.27987 | −0.639936 | − | 0.768428i | \(-0.721039\pi\) | ||||
−0.639936 | + | 0.768428i | \(0.721039\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.92986 | 0.0732038 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.2112 | 0.879188 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.4474 | −1.33883 | −0.669414 | − | 0.742890i | \(-0.733455\pi\) | ||||
−0.669414 | + | 0.742890i | \(0.733455\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 54.4212i | − 2.05253i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 19.0273i | − 0.715595i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.71118i | 0.327155i | 0.986530 | + | 0.163578i | \(0.0523034\pi\) | ||||
−0.986530 | + | 0.163578i | \(0.947697\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0555833i | 0.00208161i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.68352 | −0.175154 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.821108 | −0.0306222 | −0.0153111 | − | 0.999883i | \(-0.504874\pi\) | ||||
−0.0153111 | + | 0.999883i | \(0.504874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7903 | −0.401853 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.9032 | 0.590632 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 28.0509i | − 1.04035i | −0.854059 | − | 0.520176i | \(-0.825866\pi\) | ||||
0.854059 | − | 0.520176i | \(-0.174134\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.45147i | 0.164643i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 21.9677i | − 0.811395i | −0.914007 | − | 0.405697i | \(-0.867029\pi\) | ||||
0.914007 | − | 0.405697i | \(-0.132971\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 36.9045i | − 1.35939i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.6044 | 0.684374 | 0.342187 | − | 0.939632i | \(-0.388832\pi\) | ||||
0.342187 | + | 0.939632i | \(0.388832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.0849 | 1.06702 | 0.533512 | − | 0.845793i | \(-0.320872\pi\) | ||||
0.533512 | + | 0.845793i | \(0.320872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.998774 | −0.0365922 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.97087 | 0.181632 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.4693i | 0.527991i | 0.964524 | + | 0.263995i | \(0.0850403\pi\) | ||||
−0.964524 | + | 0.263995i | \(0.914960\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.64886i | 0.0964018i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 13.6988i | − 0.497891i | −0.968517 | − | 0.248946i | \(-0.919916\pi\) | ||||
0.968517 | − | 0.248946i | \(-0.0800840\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.5579i | 1.68772i | 0.536562 | + | 0.843861i | \(0.319723\pi\) | ||||
−0.536562 | + | 0.843861i | \(0.680277\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.84810 | 0.103108 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.9157 | 0.538575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.6427 | 1.82622 | 0.913111 | − | 0.407711i | \(-0.133673\pi\) | ||||
0.913111 | + | 0.407711i | \(0.133673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.66928 | 0.239877 | 0.119939 | − | 0.992781i | \(-0.461730\pi\) | ||||
0.119939 | + | 0.992781i | \(0.461730\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 0.312926i | − 0.0112406i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 32.6044i | − 1.16817i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 65.3718i | − 2.33919i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.21779i | 0.114848i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.759732 | 0.0270815 | 0.0135408 | − | 0.999908i | \(-0.495690\pi\) | ||||
0.0135408 | + | 0.999908i | \(0.495690\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.88561 | 0.102600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.3394 | 1.53903 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.1758 | 0.927194 | 0.463597 | − | 0.886046i | \(-0.346559\pi\) | ||||
0.463597 | + | 0.886046i | \(0.346559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 26.6114i | − 0.941442i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 53.1488i | − 1.87558i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.182258i | 0.00642376i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.6876i | 0.516388i | 0.966093 | + | 0.258194i | \(0.0831273\pi\) | ||||
−0.966093 | + | 0.258194i | \(0.916873\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.13912 | 0.145344 | 0.0726721 | − | 0.997356i | \(-0.476847\pi\) | ||||
0.0726721 | + | 0.997356i | \(0.476847\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.82168 | −0.133868 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.25289 | 0.218761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.7760 | 1.07409 | 0.537045 | − | 0.843554i | \(-0.319540\pi\) | ||||
0.537045 | + | 0.843554i | \(0.319540\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.3750i | 0.989090i | 0.869152 | + | 0.494545i | \(0.164665\pi\) | ||||
−0.869152 | + | 0.494545i | \(0.835335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.2522i | 0.912880i | 0.889754 | + | 0.456440i | \(0.150876\pi\) | ||||
−0.889754 | + | 0.456440i | \(0.849124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 8.40833i | − 0.292033i | −0.989282 | − | 0.146017i | \(-0.953355\pi\) | ||||
0.989282 | − | 0.146017i | \(-0.0466453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.90616i | − 0.135340i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.59401 | −0.0897695 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.3099 | 0.355936 | 0.177968 | − | 0.984036i | \(-0.443048\pi\) | ||||
0.177968 | + | 0.984036i | \(0.443048\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.7078 | −0.645098 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.121287 | 0.00417239 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 30.2408i | − 1.03909i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.73324i | − 0.299372i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.6992i | 1.46199i | 0.682382 | + | 0.730996i | \(0.260944\pi\) | ||||
−0.682382 | + | 0.730996i | \(0.739056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.06990i | 0.173185i | 0.996244 | + | 0.0865923i | \(0.0275977\pi\) | ||||
−0.996244 | + | 0.0865923i | \(0.972402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.9220 | −0.372654 | −0.186327 | − | 0.982488i | \(-0.559658\pi\) | ||||
−0.186327 | + | 0.982488i | \(0.559658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.1030 | 1.29704 | 0.648520 | − | 0.761197i | \(-0.275388\pi\) | ||||
0.648520 | + | 0.761197i | \(0.275388\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.13674 | 0.0386502 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.2378 | −1.05967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 20.2476i | − 0.686062i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.06105i | − 0.0696760i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.1674i | 0.883610i | 0.897111 | + | 0.441805i | \(0.145662\pi\) | ||||
−0.897111 | + | 0.441805i | \(0.854338\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.2903i | 0.986817i | 0.869798 | + | 0.493408i | \(0.164249\pi\) | ||||
−0.869798 | + | 0.493408i | \(0.835751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.0887 | 1.65197 | 0.825983 | − | 0.563696i | \(-0.190621\pi\) | ||||
0.825983 | + | 0.563696i | \(0.190621\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.0617 | 0.673606 | 0.336803 | − | 0.941575i | \(-0.390654\pi\) | ||||
0.336803 | + | 0.941575i | \(0.390654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.23082 | 0.242514 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −37.3805 | −1.25089 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 3.01855i | − 0.100899i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 0.202518i | − 0.00675434i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 49.3443i | − 1.64390i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.57585i | 0.118865i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.0142 | −0.564948 | −0.282474 | − | 0.959275i | \(-0.591155\pi\) | ||||
−0.282474 | + | 0.959275i | \(0.591155\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.54462 | 0.283096 | 0.141548 | − | 0.989931i | \(-0.454792\pi\) | ||||
0.141548 | + | 0.989931i | \(0.454792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.2631 | −1.59727 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.8026 | 0.422780 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.49841i | 0.214363i | 0.994239 | + | 0.107181i | \(0.0341826\pi\) | ||||
−0.994239 | + | 0.107181i | \(0.965817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 35.8660i | − 1.18055i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.1669i | 1.61660i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 16.9216i | − 0.555181i | −0.960699 | − | 0.277591i | \(-0.910464\pi\) | ||||
0.960699 | − | 0.277591i | \(-0.0895358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.48691 | −0.179826 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.19237 | 0.169809 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.4249 | 0.471240 | 0.235620 | − | 0.971845i | \(-0.424288\pi\) | ||||
0.235620 | + | 0.971845i | \(0.424288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.5364 | −1.90823 | −0.954116 | − | 0.299436i | \(-0.903201\pi\) | ||||
−0.954116 | + | 0.299436i | \(0.903201\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 5.23218i | − 0.170383i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.3006i | 0.497201i | 0.968606 | + | 0.248601i | \(0.0799707\pi\) | ||||
−0.968606 | + | 0.248601i | \(0.920029\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 29.1599i | − 0.946571i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.9133i | 0.483089i | 0.970390 | + | 0.241544i | \(0.0776539\pi\) | ||||
−0.970390 | + | 0.241544i | \(0.922346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.51068 | 0.0488845 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.363873 | −0.0117501 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9960 | 0.999871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.50680 | 0.0806966 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.1896i | 0.874358i | 0.899375 | + | 0.437179i | \(0.144022\pi\) | ||||
−0.899375 | + | 0.437179i | \(0.855978\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.0892i | 1.12607i | 0.826434 | + | 0.563034i | \(0.190366\pi\) | ||||
−0.826434 | + | 0.563034i | \(0.809634\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.32338i | 0.298894i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.0438i | 1.02517i | 0.858636 | + | 0.512586i | \(0.171312\pi\) | ||||
−0.858636 | + | 0.512586i | \(0.828688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.5570 | 0.912687 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.5719 | −1.38973 | −0.694864 | − | 0.719142i | \(-0.744535\pi\) | ||||
−0.694864 | + | 0.719142i | \(0.744535\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.60011 | −0.114709 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.00343 | 0.0319073 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.2929i | 0.485794i | 0.970052 | + | 0.242897i | \(0.0780978\pi\) | ||||
−0.970052 | + | 0.242897i | \(0.921902\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.636670i | 0.0201838i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.8050i | 0.943933i | 0.881616 | + | 0.471967i | \(0.156456\pi\) | ||||
−0.881616 | + | 0.471967i | \(0.843544\pi\) | |||||||
\(998\) | 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 | 6048.2.j.c.5615.20 | 32 | ||
3.2 | odd | 2 | inner | 6048.2.j.c.5615.13 | 32 | ||
4.3 | odd | 2 | 1512.2.j.c.323.9 | ✓ | 32 | ||
8.3 | odd | 2 | inner | 6048.2.j.c.5615.14 | 32 | ||
8.5 | even | 2 | 1512.2.j.c.323.23 | yes | 32 | ||
12.11 | even | 2 | 1512.2.j.c.323.24 | yes | 32 | ||
24.5 | odd | 2 | 1512.2.j.c.323.10 | yes | 32 | ||
24.11 | even | 2 | inner | 6048.2.j.c.5615.19 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.9 | ✓ | 32 | 4.3 | odd | 2 | ||
1512.2.j.c.323.10 | yes | 32 | 24.5 | odd | 2 | ||
1512.2.j.c.323.23 | yes | 32 | 8.5 | even | 2 | ||
1512.2.j.c.323.24 | yes | 32 | 12.11 | even | 2 | ||
6048.2.j.c.5615.13 | 32 | 3.2 | odd | 2 | inner | ||
6048.2.j.c.5615.14 | 32 | 8.3 | odd | 2 | inner | ||
6048.2.j.c.5615.19 | 32 | 24.11 | even | 2 | inner | ||
6048.2.j.c.5615.20 | 32 | 1.1 | even | 1 | trivial |