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 | 5615.25 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.c.5615.26 |
$q$-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 | ||||||||
\(5\) | 2.09311 | 0.936069 | 0.468035 | − | 0.883710i | \(-0.344962\pi\) | ||||
0.468035 | + | 0.883710i | \(0.344962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.961211i | 0.289816i | 0.989445 | + | 0.144908i | \(0.0462886\pi\) | ||||
−0.989445 | + | 0.144908i | \(0.953711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.60210i | − 1.27639i | −0.769874 | − | 0.638196i | \(-0.779681\pi\) | ||||
0.769874 | − | 0.638196i | \(-0.220319\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.28066i | 0.795677i | 0.917455 | + | 0.397839i | \(0.130240\pi\) | ||||
−0.917455 | + | 0.397839i | \(0.869760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.66977 | −0.841904 | −0.420952 | − | 0.907083i | \(-0.638304\pi\) | ||||
−0.420952 | + | 0.907083i | \(0.638304\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.40322 | −0.501105 | −0.250553 | − | 0.968103i | \(-0.580612\pi\) | ||||
−0.250553 | + | 0.968103i | \(0.580612\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.618872 | −0.123774 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.31771 | 1.73026 | 0.865128 | − | 0.501552i | \(-0.167237\pi\) | ||||
0.865128 | + | 0.501552i | \(0.167237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.84927i | 0.332138i | 0.986114 | + | 0.166069i | \(0.0531075\pi\) | ||||
−0.986114 | + | 0.166069i | \(0.946892\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.09311i | − 0.353801i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.29364i | − 0.377072i | −0.982066 | − | 0.188536i | \(-0.939626\pi\) | ||||
0.982066 | − | 0.188536i | \(-0.0603742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.314406i | − 0.0491020i | −0.999699 | − | 0.0245510i | \(-0.992184\pi\) | ||||
0.999699 | − | 0.0245510i | \(-0.00781561\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.64261 | 1.31799 | 0.658993 | − | 0.752149i | \(-0.270983\pi\) | ||||
0.658993 | + | 0.752149i | \(0.270983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.34305 | −0.341769 | −0.170884 | − | 0.985291i | \(-0.554662\pi\) | ||||
−0.170884 | + | 0.985291i | \(0.554662\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.73354 | 1.06228 | 0.531142 | − | 0.847283i | \(-0.321763\pi\) | ||||
0.531142 | + | 0.847283i | \(0.321763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.01192i | 0.271288i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 7.99530i | − 1.04090i | −0.853892 | − | 0.520450i | \(-0.825764\pi\) | ||||
0.853892 | − | 0.520450i | \(-0.174236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 10.6321i | − 1.36130i | −0.732610 | − | 0.680649i | \(-0.761698\pi\) | ||||
0.732610 | − | 0.680649i | \(-0.238302\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 9.63272i | − 1.19479i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.12203 | −0.503586 | −0.251793 | − | 0.967781i | \(-0.581020\pi\) | ||||
−0.251793 | + | 0.967781i | \(0.581020\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.79440 | 0.806347 | 0.403174 | − | 0.915124i | \(-0.367907\pi\) | ||||
0.403174 | + | 0.915124i | \(0.367907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0267 | 1.87579 | 0.937894 | − | 0.346922i | \(-0.112773\pi\) | ||||
0.937894 | + | 0.346922i | \(0.112773\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.961211 | 0.109540 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.26231i | 0.142021i | 0.997476 | + | 0.0710106i | \(0.0226224\pi\) | ||||
−0.997476 | + | 0.0710106i | \(0.977378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.99495i | 0.328738i | 0.986399 | + | 0.164369i | \(0.0525589\pi\) | ||||
−0.986399 | + | 0.164369i | \(0.947441\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.86680i | 0.744809i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 12.8990i | − 1.36729i | −0.729815 | − | 0.683645i | \(-0.760394\pi\) | ||||
0.729815 | − | 0.683645i | \(-0.239606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.60210 | −0.482431 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.68126 | −0.788080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.98346 | 0.505994 | 0.252997 | − | 0.967467i | \(-0.418584\pi\) | ||||
0.252997 | + | 0.967467i | \(0.418584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.18764 | −0.317182 | −0.158591 | − | 0.987344i | \(-0.550695\pi\) | ||||
−0.158591 | + | 0.987344i | \(0.550695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 0.535425i | − 0.0527570i | −0.999652 | − | 0.0263785i | \(-0.991602\pi\) | ||||
0.999652 | − | 0.0263785i | \(-0.00839750\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 9.70673i | − 0.938385i | −0.883096 | − | 0.469193i | \(-0.844545\pi\) | ||||
0.883096 | − | 0.469193i | \(-0.155455\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 8.03576i | − 0.769686i | −0.922982 | − | 0.384843i | \(-0.874256\pi\) | ||||
0.922982 | − | 0.384843i | \(-0.125744\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 12.7809i | − 1.20233i | −0.799126 | − | 0.601163i | \(-0.794704\pi\) | ||||
0.799126 | − | 0.601163i | \(-0.205296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.03021 | −0.469069 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.28066 | 0.300738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0761 | 0.916007 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7609 | −1.05193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 16.6260i | − 1.47532i | −0.675175 | − | 0.737658i | \(-0.735932\pi\) | ||||
0.675175 | − | 0.737658i | \(-0.264068\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 14.5603i | − 1.27214i | −0.771632 | − | 0.636069i | \(-0.780560\pi\) | ||||
0.771632 | − | 0.636069i | \(-0.219440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.66977i | 0.318210i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.2672i | 1.47524i | 0.675216 | + | 0.737620i | \(0.264050\pi\) | ||||
−0.675216 | + | 0.737620i | \(0.735950\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5580 | −1.23480 | −0.617398 | − | 0.786651i | \(-0.711813\pi\) | ||||
−0.617398 | + | 0.786651i | \(0.711813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.42358 | 0.369919 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.5030 | 1.61964 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.1739 | 1.65271 | 0.826356 | − | 0.563148i | \(-0.190410\pi\) | ||||
0.826356 | + | 0.563148i | \(0.190410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9560i | 0.972966i | 0.873690 | + | 0.486483i | \(0.161720\pi\) | ||||
−0.873690 | + | 0.486483i | \(0.838280\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.87073i | 0.310905i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.1011i | 1.76386i | 0.471381 | + | 0.881930i | \(0.343756\pi\) | ||||
−0.471381 | + | 0.881930i | \(0.656244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.40322i | 0.189400i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2054 | −0.877674 | −0.438837 | − | 0.898567i | \(-0.644609\pi\) | ||||
−0.438837 | + | 0.898567i | \(0.644609\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.76628 | 0.136679 | 0.0683395 | − | 0.997662i | \(-0.478230\pi\) | ||||
0.0683395 | + | 0.997662i | \(0.478230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.17930 | −0.629177 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.37240 | −0.332428 | −0.166214 | − | 0.986090i | \(-0.553154\pi\) | ||||
−0.166214 | + | 0.986090i | \(0.553154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.618872i | 0.0467823i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 17.0068i | − 1.27115i | −0.772041 | − | 0.635573i | \(-0.780764\pi\) | ||||
0.772041 | − | 0.635573i | \(-0.219236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.50624i | − 0.632264i | −0.948715 | − | 0.316132i | \(-0.897616\pi\) | ||||
0.948715 | − | 0.316132i | \(-0.102384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 4.80085i | − 0.352965i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.15341 | −0.230600 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.725194 | −0.0524732 | −0.0262366 | − | 0.999656i | \(-0.508352\pi\) | ||||
−0.0262366 | + | 0.999656i | \(0.508352\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7648 | −1.13478 | −0.567388 | − | 0.823450i | \(-0.692046\pi\) | ||||
−0.567388 | + | 0.823450i | \(0.692046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.76032 | −0.410406 | −0.205203 | − | 0.978719i | \(-0.565785\pi\) | ||||
−0.205203 | + | 0.978719i | \(0.565785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7773i | 0.834872i | 0.908706 | + | 0.417436i | \(0.137071\pi\) | ||||
−0.908706 | + | 0.417436i | \(0.862929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.31771i | − 0.653975i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.658088i | − 0.0459629i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 3.52742i | − 0.243997i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9971 | −1.37666 | −0.688328 | − | 0.725399i | \(-0.741655\pi\) | ||||
−0.688328 | + | 0.725399i | \(0.741655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0900 | 1.23373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.84927 | 0.125537 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.0979 | 1.01560 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 6.84047i | − 0.458071i | −0.973418 | − | 0.229036i | \(-0.926443\pi\) | ||||
0.973418 | − | 0.229036i | \(-0.0735573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 13.9061i | − 0.922981i | −0.887145 | − | 0.461490i | \(-0.847315\pi\) | ||||
0.887145 | − | 0.461490i | \(-0.152685\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.87934i | 0.256354i | 0.991751 | + | 0.128177i | \(0.0409126\pi\) | ||||
−0.991751 | + | 0.128177i | \(0.959087\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 21.8307i | − 1.43017i | −0.699035 | − | 0.715087i | \(-0.746387\pi\) | ||||
0.699035 | − | 0.715087i | \(-0.253613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.90427 | −0.319919 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.8956 | 1.80441 | 0.902207 | − | 0.431303i | \(-0.141946\pi\) | ||||
0.902207 | + | 0.431303i | \(0.141946\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.17606 | −0.397835 | −0.198918 | − | 0.980016i | \(-0.563743\pi\) | ||||
−0.198918 | + | 0.980016i | \(0.563743\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.09311 | −0.133724 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.8887i | 1.07460i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.6366i | 1.17633i | 0.808740 | + | 0.588167i | \(0.200150\pi\) | ||||
−0.808740 | + | 0.588167i | \(0.799850\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.31000i | − 0.145228i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 8.25845i | − 0.515148i | −0.966259 | − | 0.257574i | \(-0.917077\pi\) | ||||
0.966259 | − | 0.257574i | \(-0.0829231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.29364 | −0.142520 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.34158 | 0.576027 | 0.288013 | − | 0.957626i | \(-0.407005\pi\) | ||||
0.288013 | + | 0.957626i | \(0.407005\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1872 | 0.994371 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.9972 | 0.731484 | 0.365742 | − | 0.930716i | \(-0.380815\pi\) | ||||
0.365742 | + | 0.930716i | \(0.380815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7030i | 1.43986i | 0.694049 | + | 0.719928i | \(0.255825\pi\) | ||||
−0.694049 | + | 0.719928i | \(0.744175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 0.594866i | − 0.0358718i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 13.7688i | − 0.827284i | −0.910440 | − | 0.413642i | \(-0.864256\pi\) | ||||
0.910440 | − | 0.413642i | \(-0.135744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 8.69078i | − 0.518448i | −0.965817 | − | 0.259224i | \(-0.916533\pi\) | ||||
0.965817 | − | 0.259224i | \(-0.0834669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.7518 | 1.94689 | 0.973447 | − | 0.228913i | \(-0.0735170\pi\) | ||||
0.973447 | + | 0.228913i | \(0.0735170\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.314406 | −0.0185588 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.23727 | 0.366898 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.3629 | 0.722249 | 0.361124 | − | 0.932518i | \(-0.382393\pi\) | ||||
0.361124 | + | 0.932518i | \(0.382393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 16.7351i | − 0.974354i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.0598i | 0.639607i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.64261i | − 0.498152i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 22.2542i | − 1.27427i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2600 | −0.870935 | −0.435468 | − | 0.900204i | \(-0.643417\pi\) | ||||
−0.435468 | + | 0.900204i | \(0.643417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.12076 | 0.290372 | 0.145186 | − | 0.989404i | \(-0.453622\pi\) | ||||
0.145186 | + | 0.989404i | \(0.453622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7058 | −0.661649 | −0.330825 | − | 0.943692i | \(-0.607327\pi\) | ||||
−0.330825 | + | 0.943692i | \(0.607327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.5302 | −1.04076 | −0.520379 | − | 0.853935i | \(-0.674209\pi\) | ||||
−0.520379 | + | 0.853935i | \(0.674209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.95628i | 0.501456i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 12.0393i | − 0.669883i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.84811i | 0.157985i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.34305i | 0.129176i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.4688 | 1.12507 | 0.562534 | − | 0.826774i | \(-0.309826\pi\) | ||||
0.562534 | + | 0.826774i | \(0.309826\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.62789 | −0.471392 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.9419 | −1.08631 | −0.543153 | − | 0.839634i | \(-0.682769\pi\) | ||||
−0.543153 | + | 0.839634i | \(0.682769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.77754 | −0.0962590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 10.1743i | − 0.546187i | −0.961987 | − | 0.273094i | \(-0.911953\pi\) | ||||
0.961987 | − | 0.273094i | \(-0.0880469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.9386i | 1.70963i | 0.518930 | + | 0.854817i | \(0.326331\pi\) | ||||
−0.518930 | + | 0.854817i | \(0.673669\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.3932i | 1.29832i | 0.760653 | + | 0.649159i | \(0.224879\pi\) | ||||
−0.760653 | + | 0.649159i | \(0.775121\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.2215 | 0.754797 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.59571 | 0.453664 | 0.226832 | − | 0.973934i | \(-0.427163\pi\) | ||||
0.226832 | + | 0.973934i | \(0.427163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.53276 | −0.291198 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.5458 | 1.75587 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 29.1285i | − 1.52050i | −0.649632 | − | 0.760249i | \(-0.725077\pi\) | ||||
0.649632 | − | 0.760249i | \(-0.274923\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 7.73354i | − 0.401505i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.56533i | 0.236384i | 0.992991 | + | 0.118192i | \(0.0377098\pi\) | ||||
−0.992991 | + | 0.118192i | \(0.962290\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 42.8810i | − 2.20848i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5673 | −0.799641 | −0.399820 | − | 0.916593i | \(-0.630928\pi\) | ||||
−0.399820 | + | 0.916593i | \(0.630928\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.08947 | −0.157865 | −0.0789323 | − | 0.996880i | \(-0.525151\pi\) | ||||
−0.0789323 | + | 0.996880i | \(0.525151\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.01192 | 0.102537 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.6022 | −1.55160 | −0.775798 | − | 0.630982i | \(-0.782652\pi\) | ||||
−0.775798 | + | 0.630982i | \(0.782652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 7.88413i | − 0.398718i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.64216i | 0.132942i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 0.403742i | − 0.0202632i | −0.999949 | − | 0.0101316i | \(-0.996775\pi\) | ||||
0.999949 | − | 0.0101316i | \(-0.00322505\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 30.3779i | − 1.51700i | −0.651672 | − | 0.758501i | \(-0.725932\pi\) | ||||
0.651672 | − | 0.758501i | \(-0.274068\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.51051 | 0.423939 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.20467 | 0.109281 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8549 | −0.882869 | −0.441434 | − | 0.897293i | \(-0.645530\pi\) | ||||
−0.441434 | + | 0.897293i | \(0.645530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.99530 | −0.393423 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.26877i | 0.307722i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 31.1609i | − 1.52231i | −0.648569 | − | 0.761156i | \(-0.724632\pi\) | ||||
0.648569 | − | 0.761156i | \(-0.275368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.19292i | 0.350562i | 0.984518 | + | 0.175281i | \(0.0560833\pi\) | ||||
−0.984518 | + | 0.175281i | \(0.943917\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 2.03031i | − 0.0984844i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.6321 | −0.514522 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7598 | 1.24081 | 0.620404 | − | 0.784283i | \(-0.286969\pi\) | ||||
0.620404 | + | 0.784283i | \(0.286969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.66449 | −0.176104 | −0.0880521 | − | 0.996116i | \(-0.528064\pi\) | ||||
−0.0880521 | + | 0.996116i | \(0.528064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.81926 | 0.421882 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.4350i | 1.88213i | 0.338227 | + | 0.941064i | \(0.390173\pi\) | ||||
−0.338227 | + | 0.941064i | \(0.609827\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.1437i | 1.71724i | 0.512612 | + | 0.858620i | \(0.328678\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 26.9990i | − 1.27988i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.9465i | 1.17730i | 0.808389 | + | 0.588649i | \(0.200340\pi\) | ||||
−0.808389 | + | 0.588649i | \(0.799660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.302210 | 0.0142305 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.63272 | −0.451589 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1856 | 0.710354 | 0.355177 | − | 0.934799i | \(-0.384421\pi\) | ||||
0.355177 | + | 0.934799i | \(0.384421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.29479 | −0.432902 | −0.216451 | − | 0.976294i | \(-0.569448\pi\) | ||||
−0.216451 | + | 0.976294i | \(0.569448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.13438i | − 0.0991930i | −0.998769 | − | 0.0495965i | \(-0.984206\pi\) | ||||
0.998769 | − | 0.0495965i | \(-0.0157935\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 41.6077i | − 1.92538i | −0.270612 | − | 0.962688i | \(-0.587226\pi\) | ||||
0.270612 | − | 0.962688i | \(-0.412774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.12203i | 0.190338i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.30736i | 0.381973i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.27112 | 0.104206 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.9442 | 1.87079 | 0.935394 | − | 0.353608i | \(-0.115045\pi\) | ||||
0.935394 | + | 0.353608i | \(0.115045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5556 | −0.481292 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4310 | 0.473645 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.2039i | 0.643639i | 0.946801 | + | 0.321820i | \(0.104294\pi\) | ||||
−0.946801 | + | 0.321820i | \(0.895706\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.3013i | 1.77364i | 0.462113 | + | 0.886821i | \(0.347091\pi\) | ||||
−0.462113 | + | 0.886821i | \(0.652909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.5682i | 1.37672i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6.79440i | − 0.304771i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.3257 | 1.44710 | 0.723548 | − | 0.690274i | \(-0.242510\pi\) | ||||
0.723548 | + | 0.690274i | \(0.242510\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.7861 | −0.882217 | −0.441108 | − | 0.897454i | \(-0.645415\pi\) | ||||
−0.441108 | + | 0.897454i | \(0.645415\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.67210 | −0.296904 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.7174 | −1.49450 | −0.747248 | − | 0.664545i | \(-0.768625\pi\) | ||||
−0.747248 | + | 0.664545i | \(0.768625\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 16.0267i | − 0.708981i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.12070i | − 0.0493842i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2.25216i | − 0.0990500i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4958i | 1.24842i | 0.781255 | + | 0.624212i | \(0.214580\pi\) | ||||
−0.781255 | + | 0.624212i | \(0.785420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.42637 | 0.193552 | 0.0967758 | − | 0.995306i | \(-0.469147\pi\) | ||||
0.0967758 | + | 0.995306i | \(0.469147\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.06682 | −0.264275 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2246 | −0.748894 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.44693 | −0.0626734 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 20.3173i | − 0.878394i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 0.961211i | − 0.0414023i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 33.7548i | − 1.45123i | −0.688101 | − | 0.725615i | \(-0.741555\pi\) | ||||
0.688101 | − | 0.725615i | \(-0.258445\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 16.8198i | − 0.720480i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6641 | 0.626992 | 0.313496 | − | 0.949589i | \(-0.398500\pi\) | ||||
0.313496 | + | 0.949589i | \(0.398500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.1939 | −1.45671 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.26231 | 0.0536790 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.4373 | 0.654099 | 0.327050 | − | 0.945007i | \(-0.393946\pi\) | ||||
0.327050 | + | 0.945007i | \(0.393946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 39.7741i | − 1.68227i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 26.9472i | − 1.13569i | −0.823135 | − | 0.567845i | \(-0.807777\pi\) | ||||
0.823135 | − | 0.567845i | \(-0.192223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 26.7519i | − 1.12546i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.63013i | 0.152183i | 0.997101 | + | 0.0760915i | \(0.0242441\pi\) | ||||
−0.997101 | + | 0.0760915i | \(0.975756\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2293 | 0.679174 | 0.339587 | − | 0.940575i | \(-0.389713\pi\) | ||||
0.339587 | + | 0.940575i | \(0.389713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.48728 | 0.0620240 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.1511 | 1.75477 | 0.877386 | − | 0.479786i | \(-0.159286\pi\) | ||||
0.877386 | + | 0.479786i | \(0.159286\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.99495 | 0.124251 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.43356i | 0.307867i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 22.7097i | − 0.937328i | −0.883377 | − | 0.468664i | \(-0.844736\pi\) | ||||
0.883377 | − | 0.468664i | \(-0.155264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 6.78640i | − 0.279629i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.8921i | 0.940068i | 0.882648 | + | 0.470034i | \(0.155758\pi\) | ||||
−0.882648 | + | 0.470034i | \(0.844242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.86680 | 0.281511 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.0216 | 1.26751 | 0.633755 | − | 0.773534i | \(-0.281513\pi\) | ||||
0.633755 | + | 0.773534i | \(0.281513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.3657 | −1.48339 | −0.741693 | − | 0.670739i | \(-0.765977\pi\) | ||||
−0.741693 | + | 0.670739i | \(0.765977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.0904 | 0.857446 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 27.1019i | − 1.10003i | −0.835154 | − | 0.550016i | \(-0.814622\pi\) | ||||
0.835154 | − | 0.550016i | \(-0.185378\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.7829i | 0.436231i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 21.7164i | − 0.877118i | −0.898702 | − | 0.438559i | \(-0.855489\pi\) | ||||
0.898702 | − | 0.438559i | \(-0.144511\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 15.0335i | − 0.605224i | −0.953114 | − | 0.302612i | \(-0.902141\pi\) | ||||
0.953114 | − | 0.302612i | \(-0.0978587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.2249 | 0.491359 | 0.245680 | − | 0.969351i | \(-0.420989\pi\) | ||||
0.245680 | + | 0.969351i | \(0.420989\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.8990 | −0.516787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.5226 | −0.860906 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.52465 | 0.300028 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 0.290118i | − 0.0115494i | −0.999983 | − | 0.00577472i | \(-0.998162\pi\) | ||||
0.999983 | − | 0.00577472i | \(-0.00183816\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 34.8000i | − 1.38100i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.60210i | 0.182342i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.2612i | 1.27424i | 0.770764 | + | 0.637120i | \(0.219875\pi\) | ||||
−0.770764 | + | 0.637120i | \(0.780125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.2641 | 0.996317 | 0.498159 | − | 0.867086i | \(-0.334010\pi\) | ||||
0.498159 | + | 0.867086i | \(0.334010\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.6735 | 0.616188 | 0.308094 | − | 0.951356i | \(-0.400309\pi\) | ||||
0.308094 | + | 0.951356i | \(0.400309\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.68517 | 0.301669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.4580 | −0.683183 | −0.341591 | − | 0.939849i | \(-0.610966\pi\) | ||||
−0.341591 | + | 0.939849i | \(0.610966\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 30.4763i | − 1.19081i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.8692i | 1.35831i | 0.733995 | + | 0.679155i | \(0.237653\pi\) | ||||
−0.733995 | + | 0.679155i | \(0.762347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7607i | 0.535230i | 0.963526 | + | 0.267615i | \(0.0862355\pi\) | ||||
−0.963526 | + | 0.267615i | \(0.913765\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.68126i | 0.297866i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.3925 | −0.867040 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2197 | 0.394526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.50938 | −0.328013 | −0.164006 | − | 0.986459i | \(-0.552442\pi\) | ||||
−0.164006 | + | 0.986459i | \(0.552442\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.14515 | 0.120878 | 0.0604390 | − | 0.998172i | \(-0.480750\pi\) | ||||
0.0604390 | + | 0.998172i | \(0.480750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 4.98346i | − 0.191248i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9.12590i | − 0.349193i | −0.984640 | − | 0.174596i | \(-0.944138\pi\) | ||||
0.984640 | − | 0.174596i | \(-0.0558621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.1423i | 1.38093i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 35.5905i | − 1.35589i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6298 | 0.594586 | 0.297293 | − | 0.954786i | \(-0.403916\pi\) | ||||
0.297293 | + | 0.954786i | \(0.403916\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.4716 | −1.15585 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.03146 | 0.0390693 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.4853 | 1.90680 | 0.953402 | − | 0.301701i | \(-0.0975546\pi\) | ||||
0.953402 | + | 0.301701i | \(0.0975546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.41714i | 0.317458i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.18764i | 0.119884i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7706i | 1.08050i | 0.841504 | + | 0.540251i | \(0.181671\pi\) | ||||
−0.841504 | + | 0.540251i | \(0.818329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.44419i | − 0.166436i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.25907 | 0.346270 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.582170 | 0.0217113 | 0.0108556 | − | 0.999941i | \(-0.496544\pi\) | ||||
0.0108556 | + | 0.999941i | \(0.496544\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.535425 | −0.0199403 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.76647 | −0.214161 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6.92907i | − 0.256985i | −0.991710 | − | 0.128492i | \(-0.958986\pi\) | ||||
0.991710 | − | 0.128492i | \(-0.0410138\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.3535i | 1.04869i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.86770i | − 0.0689850i | −0.999405 | − | 0.0344925i | \(-0.989019\pi\) | ||||
0.999405 | − | 0.0344925i | \(-0.0109815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 3.96214i | − 0.145947i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.7036 | 1.42373 | 0.711867 | − | 0.702314i | \(-0.247850\pi\) | ||||
0.711867 | + | 0.702314i | \(0.247850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.3088 | 0.855118 | 0.427559 | − | 0.903987i | \(-0.359374\pi\) | ||||
0.427559 | + | 0.903987i | \(0.359374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.2263 | 1.54705 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.70673 | −0.354676 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 26.6345i | − 0.971908i | −0.873984 | − | 0.485954i | \(-0.838472\pi\) | ||||
0.873984 | − | 0.485954i | \(-0.161528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.0253i | 0.910764i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.4285i | 0.960562i | 0.877115 | + | 0.480281i | \(0.159465\pi\) | ||||
−0.877115 | + | 0.480281i | \(0.840535\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.2617i | 0.480736i | 0.970682 | + | 0.240368i | \(0.0772681\pi\) | ||||
−0.970682 | + | 0.240368i | \(0.922732\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.03576 | −0.290914 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.7951 | −1.32860 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.34986 | −0.156860 | −0.0784300 | − | 0.996920i | \(-0.524991\pi\) | ||||
−0.0784300 | + | 0.996920i | \(0.524991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.8861 | 1.25477 | 0.627383 | − | 0.778711i | \(-0.284126\pi\) | ||||
0.627383 | + | 0.778711i | \(0.284126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.14446i | − 0.0411102i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.15380i | 0.0413391i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.53085i | 0.233692i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.2601i | 1.65109i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.9317 | −0.460964 | −0.230482 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230482 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.7809 | −0.454437 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.9299 | −1.73755 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.1981 | 0.396656 | 0.198328 | − | 0.980136i | \(-0.436449\pi\) | ||||
0.198328 | + | 0.980136i | \(0.436449\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 7.68675i | − 0.271938i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.4051i | 0.543633i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.03021i | 0.177291i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 23.6434i | − 0.831258i | −0.909534 | − | 0.415629i | \(-0.863561\pi\) | ||||
0.909534 | − | 0.415629i | \(-0.136439\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.8213 | −1.22274 | −0.611371 | − | 0.791344i | \(-0.709382\pi\) | ||||
−0.611371 | + | 0.791344i | \(0.709382\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.4542 | −0.821564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.7164 | −1.10962 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.361884 | −0.0126298 | −0.00631491 | − | 0.999980i | \(-0.502010\pi\) | ||||
−0.00631491 | + | 0.999980i | \(0.502010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.2033i | 1.71512i | 0.514386 | + | 0.857559i | \(0.328020\pi\) | ||||
−0.514386 | + | 0.857559i | \(0.671980\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 16.2920i | − 0.566529i | −0.959042 | − | 0.283264i | \(-0.908583\pi\) | ||||
0.959042 | − | 0.283264i | \(-0.0914174\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.40526i | 0.222464i | 0.993794 | + | 0.111232i | \(0.0354796\pi\) | ||||
−0.993794 | + | 0.111232i | \(0.964520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.28066i | − 0.113668i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.69703 | 0.127941 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.3877 | −0.807432 | −0.403716 | − | 0.914884i | \(-0.632282\pi\) | ||||
−0.403716 | + | 0.914884i | \(0.632282\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.8197 | 1.99378 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.1202 | −0.588953 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 10.0761i | − 0.346218i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.51211i | 0.188953i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 22.3667i | − 0.765821i | −0.923786 | − | 0.382910i | \(-0.874922\pi\) | ||||
0.923786 | − | 0.382910i | \(-0.125078\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.7703i | 1.18773i | 0.804564 | + | 0.593866i | \(0.202399\pi\) | ||||
−0.804564 | + | 0.593866i | \(0.797601\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.1287 | −0.550305 | −0.275152 | − | 0.961401i | \(-0.588728\pi\) | ||||
−0.275152 | + | 0.961401i | \(0.588728\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.3951 | −1.17082 | −0.585412 | − | 0.810736i | \(-0.699067\pi\) | ||||
−0.585412 | + | 0.810736i | \(0.699067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.15194 | −0.311175 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.21335 | −0.0411600 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9700i | 0.642774i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.7609i | 0.397592i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 14.0555i | − 0.474620i | −0.971434 | − | 0.237310i | \(-0.923734\pi\) | ||||
0.971434 | − | 0.237310i | \(-0.0762658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 41.1209i | − 1.38540i | −0.721226 | − | 0.692700i | \(-0.756421\pi\) | ||||
0.721226 | − | 0.692700i | \(-0.243579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8276 | 0.633598 | 0.316799 | − | 0.948493i | \(-0.397392\pi\) | ||||
0.316799 | + | 0.948493i | \(0.397392\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.8728 | −0.365071 | −0.182536 | − | 0.983199i | \(-0.558430\pi\) | ||||
−0.182536 | + | 0.983199i | \(0.558430\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.6260 | −0.557617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.59846 | 0.287736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 35.5971i | − 1.18988i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.2310i | 0.574684i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.3711i | 0.845235i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 17.8045i | − 0.591843i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.4589 | −0.513304 | −0.256652 | − | 0.966504i | \(-0.582619\pi\) | ||||
−0.256652 | + | 0.966504i | \(0.582619\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.9492 | −0.793473 | −0.396737 | − | 0.917933i | \(-0.629857\pi\) | ||||
−0.396737 | + | 0.917933i | \(0.629857\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.87878 | −0.0952736 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.5603 | −0.480823 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.4853i | 0.807694i | 0.914826 | + | 0.403847i | \(0.132327\pi\) | ||||
−0.914826 | + | 0.403847i | \(0.867673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 31.2685i | − 1.02922i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.41947i | 0.0466719i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.7122i | 1.17168i | 0.810428 | + | 0.585839i | \(0.199235\pi\) | ||||
−0.810428 | + | 0.585839i | \(0.800765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.66977 | 0.120272 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.60044 | −0.215857 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.263959 | 0.00862315 | 0.00431157 | − | 0.999991i | \(-0.498628\pi\) | ||||
0.00431157 | + | 0.999991i | \(0.498628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.9124 | −1.33371 | −0.666853 | − | 0.745189i | \(-0.732359\pi\) | ||||
−0.666853 | + | 0.745189i | \(0.732359\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.755586i | 0.0246053i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.3236i | 1.40783i | 0.710286 | + | 0.703913i | \(0.248566\pi\) | ||||
−0.710286 | + | 0.703913i | \(0.751434\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 73.7566i | − 2.39424i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.0756i | 1.68690i | 0.537211 | + | 0.843448i | \(0.319478\pi\) | ||||
−0.537211 | + | 0.843448i | \(0.680522\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.51791 | −0.0491185 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.2672 | 0.557588 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.5802 | 0.889684 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.9976 | −1.06223 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3116i | 0.556705i | 0.960479 | + | 0.278352i | \(0.0897883\pi\) | ||||
−0.960479 | + | 0.278352i | \(0.910212\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 8.86074i | − 0.284355i | −0.989841 | − | 0.142177i | \(-0.954590\pi\) | ||||
0.989841 | − | 0.142177i | \(-0.0454103\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.5580i | 0.466709i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 8.48509i | − 0.271462i | −0.990746 | − | 0.135731i | \(-0.956662\pi\) | ||||
0.990746 | − | 0.135731i | \(-0.0433383\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.3986 | 0.396262 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.6181 | −1.39120 | −0.695600 | − | 0.718429i | \(-0.744862\pi\) | ||||
−0.695600 | + | 0.718429i | \(0.744862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0570 | −0.384168 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.7700 | −0.660449 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.0937i | 1.62304i | 0.584322 | + | 0.811522i | \(0.301361\pi\) | ||||
−0.584322 | + | 0.811522i | \(0.698639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.6513i | 0.781498i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.59455i | 0.0504998i | 0.999681 | + | 0.0252499i | \(0.00803815\pi\) | ||||
−0.999681 | + | 0.0252499i | \(0.991962\pi\) | |||||||
\(998\) | 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.5615.25 | 32 | ||
3.2 | odd | 2 | inner | 6048.2.j.c.5615.8 | 32 | ||
4.3 | odd | 2 | 1512.2.j.c.323.8 | yes | 32 | ||
8.3 | odd | 2 | inner | 6048.2.j.c.5615.7 | 32 | ||
8.5 | even | 2 | 1512.2.j.c.323.26 | yes | 32 | ||
12.11 | even | 2 | 1512.2.j.c.323.25 | yes | 32 | ||
24.5 | odd | 2 | 1512.2.j.c.323.7 | ✓ | 32 | ||
24.11 | even | 2 | inner | 6048.2.j.c.5615.26 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.7 | ✓ | 32 | 24.5 | odd | 2 | ||
1512.2.j.c.323.8 | yes | 32 | 4.3 | odd | 2 | ||
1512.2.j.c.323.25 | yes | 32 | 12.11 | even | 2 | ||
1512.2.j.c.323.26 | yes | 32 | 8.5 | even | 2 | ||
6048.2.j.c.5615.7 | 32 | 8.3 | odd | 2 | inner | ||
6048.2.j.c.5615.8 | 32 | 3.2 | odd | 2 | inner | ||
6048.2.j.c.5615.25 | 32 | 1.1 | even | 1 | trivial | ||
6048.2.j.c.5615.26 | 32 | 24.11 | even | 2 | inner |