Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (of order \(6\), degree \(2\), 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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 863.7 | ||
Root | \(-0.115299 + 1.50155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.863 |
Dual form | 2592.2.s.j.1727.7 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | 2.35218 | + | 1.35803i | 1.05193 | + | 0.607330i | 0.923188 | − | 0.384349i | \(-0.125574\pi\) |
0.128738 | + | 0.991679i | \(0.458907\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.67803 | − | 2.12351i | 1.39017 | − | 0.802613i | 0.396833 | − | 0.917891i | \(-0.370109\pi\) |
0.993333 | + | 0.115278i | \(0.0367759\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09921 | + | 1.90389i | 0.331425 | + | 0.574045i | 0.982791 | − | 0.184719i | \(-0.0591374\pi\) |
−0.651367 | + | 0.758763i | \(0.725804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.25749 | + | 2.17803i | −0.348765 | + | 0.604078i | −0.986030 | − | 0.166566i | \(-0.946732\pi\) |
0.637266 | + | 0.770644i | \(0.280065\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.93806i | − | 1.92526i | −0.270818 | − | 0.962631i | \(-0.587294\pi\) | ||
0.270818 | − | 0.962631i | \(-0.412706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.13799i | 1.17874i | 0.807865 | + | 0.589368i | \(0.200623\pi\) | ||||
−0.807865 | + | 0.589368i | \(0.799377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.868614 | − | 1.50448i | 0.181119 | − | 0.313707i | −0.761143 | − | 0.648584i | \(-0.775362\pi\) |
0.942262 | + | 0.334877i | \(0.108695\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.18849 | + | 2.05853i | 0.237699 | + | 0.411707i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.230858 | − | 0.133286i | 0.0428692 | − | 0.0247506i | −0.478412 | − | 0.878135i | \(-0.658788\pi\) |
0.521281 | + | 0.853385i | \(0.325454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.69251 | + | 5.01862i | 1.56122 | + | 0.901371i | 0.997134 | + | 0.0756553i | \(0.0241049\pi\) |
0.564086 | + | 0.825716i | \(0.309228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.5352 | 1.94980 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.24703 | 1.52020 | 0.760101 | − | 0.649805i | \(-0.225149\pi\) | ||||
0.760101 | + | 0.649805i | \(0.225149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.18363 | − | 1.26072i | −0.341026 | − | 0.196891i | 0.319700 | − | 0.947519i | \(-0.396418\pi\) |
−0.660725 | + | 0.750628i | \(0.729751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.14214 | + | 0.659412i | −0.174174 | + | 0.100559i | −0.584553 | − | 0.811356i | \(-0.698730\pi\) |
0.410379 | + | 0.911915i | \(0.365397\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.860601 | − | 1.49061i | −0.125532 | − | 0.217427i | 0.796409 | − | 0.604758i | \(-0.206730\pi\) |
−0.921941 | + | 0.387331i | \(0.873397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.51862 | − | 9.55853i | 0.788375 | − | 1.36550i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.306989i | − | 0.0421682i | −0.999778 | − | 0.0210841i | \(-0.993288\pi\) | ||
0.999778 | − | 0.0210841i | \(-0.00671177\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.97105i | 0.805137i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.83153 | + | 10.1005i | −0.759200 | + | 1.31497i | 0.184058 | + | 0.982915i | \(0.441076\pi\) |
−0.943259 | + | 0.332058i | \(0.892257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.64214 | − | 8.04041i | −0.594365 | − | 1.02947i | −0.993636 | − | 0.112637i | \(-0.964070\pi\) |
0.399272 | − | 0.916833i | \(-0.369263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.91567 | + | 3.41542i | −0.733749 | + | 0.423630i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.59895 | − | 3.23255i | −0.684020 | − | 0.394919i | 0.117348 | − | 0.993091i | \(-0.462561\pi\) |
−0.801368 | + | 0.598172i | \(0.795894\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.46463 | −1.12325 | −0.561623 | − | 0.827393i | \(-0.689823\pi\) | ||||
−0.561623 | + | 0.827393i | \(0.689823\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.62301 | 0.775165 | 0.387582 | − | 0.921835i | \(-0.373310\pi\) | ||||
0.387582 | + | 0.921835i | \(0.373310\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.08587 | + | 4.66838i | 0.921471 | + | 0.532012i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.83464 | + | 5.67803i | −1.10648 | + | 0.638829i | −0.937916 | − | 0.346861i | \(-0.887247\pi\) |
−0.168567 | + | 0.985690i | \(0.553914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.41148 | − | 11.1050i | −0.703751 | − | 1.21893i | −0.967140 | − | 0.254243i | \(-0.918174\pi\) |
0.263389 | − | 0.964690i | \(-0.415160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.7801 | − | 18.6717i | 1.16927 | − | 2.02523i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.42422i | 0.998965i | 0.866324 | + | 0.499483i | \(0.166477\pi\) | ||||
−0.866324 | + | 0.499483i | \(0.833523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.6812i | 1.11969i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.97754 | + | 12.0855i | −0.715881 | + | 1.23994i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.12766 | − | 7.14932i | −0.419101 | − | 0.725903i | 0.576749 | − | 0.816922i | \(-0.304321\pi\) |
−0.995849 | + | 0.0910182i | \(0.970988\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.61883 | + | 4.97608i | −0.857605 | + | 0.495139i | −0.863210 | − | 0.504846i | \(-0.831549\pi\) |
0.00560428 | + | 0.999984i | \(0.498216\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4641 | + | 8.92820i | 1.52372 | + | 0.879722i | 0.999606 | + | 0.0280760i | \(0.00893804\pi\) |
0.524117 | + | 0.851646i | \(0.324395\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.9160 | 1.53866 | 0.769329 | − | 0.638852i | \(-0.220591\pi\) | ||||
0.769329 | + | 0.638852i | \(0.220591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.435890 | −0.0417507 | −0.0208754 | − | 0.999782i | \(-0.506645\pi\) | ||||
−0.0208754 | + | 0.999782i | \(0.506645\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.82122 | + | 5.67028i | 0.923902 | + | 0.533415i | 0.884878 | − | 0.465823i | \(-0.154242\pi\) |
0.0390244 | + | 0.999238i | \(0.487575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.08627 | − | 2.35921i | 0.381047 | − | 0.219997i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.8566 | − | 29.1964i | −1.54524 | − | 2.67643i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.08347 | − | 5.34072i | 0.280315 | − | 0.485520i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 7.12426i | − | 0.637213i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.39331i | − | 0.833522i | −0.909016 | − | 0.416761i | \(-0.863165\pi\) | ||
0.909016 | − | 0.416761i | \(-0.136835\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50759 | − | 7.80737i | 0.393830 | − | 0.682133i | −0.599121 | − | 0.800658i | \(-0.704483\pi\) |
0.992951 | + | 0.118525i | \(0.0378167\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9106 | + | 18.8977i | 0.946068 | + | 1.63864i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0488813 | − | 0.0282216i | 0.00417621 | − | 0.00241114i | −0.497910 | − | 0.867228i | \(-0.665899\pi\) |
0.502087 | + | 0.864817i | \(0.332566\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.2052 | + | 9.35607i | 1.37451 | + | 0.793571i | 0.991492 | − | 0.130171i | \(-0.0415527\pi\) |
0.383014 | + | 0.923742i | \(0.374886\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.52898 | −0.462357 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.724025 | 0.0601270 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.5329 | − | 8.96792i | −1.27250 | − | 0.734680i | −0.297045 | − | 0.954863i | \(-0.596001\pi\) |
−0.975459 | + | 0.220183i | \(0.929335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.54319 | + | 0.890960i | −0.125583 | + | 0.0725053i | −0.561475 | − | 0.827493i | \(-0.689766\pi\) |
0.435893 | + | 0.899999i | \(0.356433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6309 | + | 23.6094i | 1.09486 | + | 1.89635i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.50415 | − | 9.53346i | 0.439279 | − | 0.760853i | −0.558355 | − | 0.829602i | \(-0.688567\pi\) |
0.997634 | + | 0.0687488i | \(0.0219007\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.37806i | − | 0.581472i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.1835i | 1.81587i | 0.419107 | + | 0.907937i | \(0.362343\pi\) | ||||
−0.419107 | + | 0.907937i | \(0.637657\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.40176 | − | 2.42791i | 0.108471 | − | 0.187878i | −0.806680 | − | 0.590989i | \(-0.798738\pi\) |
0.915151 | + | 0.403111i | \(0.132071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.33745 | + | 5.78063i | 0.256727 | + | 0.444664i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.2303 | + | 8.79324i | −1.15794 | + | 0.668538i | −0.950810 | − | 0.309775i | \(-0.899746\pi\) |
−0.207132 | + | 0.978313i | \(0.566413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.74265 | + | 5.04757i | 0.660882 | + | 0.381560i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.54074 | −0.339391 | −0.169696 | − | 0.985497i | \(-0.554278\pi\) | ||||
−0.169696 | + | 0.985497i | \(0.554278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.34777 | 0.248838 | 0.124419 | − | 0.992230i | \(-0.460293\pi\) | ||||
0.124419 | + | 0.992230i | \(0.460293\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.7507 | + | 12.5577i | 1.59914 | + | 0.923264i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.1132 | − | 8.72560i | 1.10519 | − | 0.638079i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.16390 | − | 5.48003i | −0.228932 | − | 0.396521i | 0.728560 | − | 0.684982i | \(-0.240190\pi\) |
−0.957492 | + | 0.288461i | \(0.906857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.20384 | + | 9.01331i | −0.374581 | + | 0.648793i | −0.990264 | − | 0.139201i | \(-0.955547\pi\) |
0.615684 | + | 0.787993i | \(0.288880\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0477i | − | 1.28584i | −0.765932 | − | 0.642922i | \(-0.777722\pi\) | ||
0.765932 | − | 0.642922i | \(-0.222278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.913624i | 0.0647651i | 0.999476 | + | 0.0323825i | \(0.0103095\pi\) | ||||
−0.999476 | + | 0.0323825i | \(0.989691\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.566068 | − | 0.980459i | 0.0397302 | − | 0.0688148i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.42419 | − | 5.93087i | −0.239156 | − | 0.414230i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.78217 | + | 5.64774i | −0.676647 | + | 0.390662i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.82735 | + | 2.78707i | 0.332329 | + | 0.191870i | 0.656875 | − | 0.754000i | \(-0.271878\pi\) |
−0.324546 | + | 0.945870i | \(0.605211\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.58201 | −0.244291 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42.6284 | 2.89381 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.2894 | + | 9.98201i | 1.16301 | + | 0.671463i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.98553 | + | 4.03310i | −0.467785 | + | 0.270076i | −0.715312 | − | 0.698805i | \(-0.753716\pi\) |
0.247527 | + | 0.968881i | \(0.420382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.1675 | + | 22.8069i | 0.873960 | + | 1.51374i | 0.857866 | + | 0.513873i | \(0.171790\pi\) |
0.0160945 | + | 0.999870i | \(0.494877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.90013 | + | 17.1475i | −0.654219 | + | 1.13314i | 0.327870 | + | 0.944723i | \(0.393669\pi\) |
−0.982089 | + | 0.188417i | \(0.939664\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.08515i | 0.464164i | 0.972696 | + | 0.232082i | \(0.0745537\pi\) | ||||
−0.972696 | + | 0.232082i | \(0.925446\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.67489i | − | 0.304956i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50268 | + | 12.9950i | −0.485308 | + | 0.840578i | −0.999857 | − | 0.0168829i | \(-0.994626\pi\) |
0.514550 | + | 0.857461i | \(0.327959\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.50037 | − | 2.59871i | −0.0966472 | − | 0.167398i | 0.813648 | − | 0.581358i | \(-0.197479\pi\) |
−0.910295 | + | 0.413960i | \(0.864145\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.9616 | − | 14.9889i | 1.65862 | − | 0.957607i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1907 | − | 6.46096i | −0.712048 | − | 0.411101i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.6594 | 1.49337 | 0.746685 | − | 0.665177i | \(-0.231644\pi\) | ||||
0.746685 | + | 0.665177i | \(0.231644\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.81916 | 0.240109 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.3321 | − | 10.5841i | −1.14353 | − | 0.660215i | −0.196225 | − | 0.980559i | \(-0.562868\pi\) |
−0.947301 | + | 0.320344i | \(0.896202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34.0109 | − | 19.6362i | 2.11333 | − | 1.22013i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.59783 | − | 4.49957i | −0.160189 | − | 0.277456i | 0.774747 | − | 0.632271i | \(-0.217877\pi\) |
−0.934936 | + | 0.354815i | \(0.884544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.416901 | − | 0.722093i | 0.0256100 | − | 0.0443578i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.25487i | − | 0.137482i | −0.997635 | − | 0.0687408i | \(-0.978102\pi\) | ||
0.997635 | − | 0.0687408i | \(-0.0218982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7038i | 0.650212i | 0.945678 | + | 0.325106i | \(0.105400\pi\) | ||||
−0.945678 | + | 0.325106i | \(0.894600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.61281 | + | 4.52553i | −0.157559 | + | 0.272900i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.56585 | − | 6.17624i | −0.214251 | − | 0.371094i | 0.738789 | − | 0.673936i | \(-0.235398\pi\) |
−0.953041 | + | 0.302842i | \(0.902064\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.47068 | − | 2.58115i | 0.266698 | − | 0.153978i | −0.360688 | − | 0.932687i | \(-0.617458\pi\) |
0.627386 | + | 0.778708i | \(0.284125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.3561 | − | 7.71113i | −0.793936 | − | 0.458379i | 0.0474105 | − | 0.998875i | \(-0.484903\pi\) |
−0.841346 | + | 0.540496i | \(0.818236\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7086 | −0.632110 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −46.0127 | −2.70663 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.2214 | − | 10.5201i | −1.06450 | − | 0.614592i | −0.137830 | − | 0.990456i | \(-0.544013\pi\) |
−0.926675 | + | 0.375864i | \(0.877346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.4336 | + | 15.8388i | −1.59725 | + | 0.922170i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.18454 | + | 3.78374i | 0.126335 | + | 0.218819i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.80054 | + | 4.85068i | −0.161421 | + | 0.279589i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 25.2166i | − | 1.44390i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.54319i | 0.0880744i | 0.999030 | + | 0.0440372i | \(0.0140220\pi\) | ||||
−0.999030 | + | 0.0440372i | \(0.985978\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.48218 | − | 9.49541i | 0.310866 | − | 0.538435i | −0.667684 | − | 0.744445i | \(-0.732714\pi\) |
0.978550 | + | 0.206009i | \(0.0660477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.43954 | − | 14.6177i | −0.477031 | − | 0.826241i | 0.522623 | − | 0.852564i | \(-0.324954\pi\) |
−0.999654 | + | 0.0263226i | \(0.991620\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.93192 | − | 4.00214i | 0.389335 | − | 0.224783i | −0.292537 | − | 0.956254i | \(-0.594499\pi\) |
0.681872 | + | 0.731471i | \(0.261166\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.507523 | + | 0.293019i | 0.0284158 | + | 0.0164059i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.7856 | 2.26937 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.97807 | −0.331604 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.33064 | − | 3.65500i | −0.349020 | − | 0.201507i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.83464 | + | 5.67803i | −0.540561 | + | 0.312093i | −0.745306 | − | 0.666722i | \(-0.767697\pi\) |
0.204745 | + | 0.978815i | \(0.434363\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.77981 | − | 15.2071i | −0.479692 | − | 0.830852i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2956 | − | 21.2966i | 0.669784 | − | 1.16010i | −0.308180 | − | 0.951328i | \(-0.599720\pi\) |
0.977964 | − | 0.208772i | \(-0.0669467\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.0661i | 1.19495i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.1463i | − | 0.925812i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.60189 | − | 14.8989i | 0.461773 | − | 0.799815i | −0.537276 | − | 0.843407i | \(-0.680547\pi\) |
0.999049 | + | 0.0435914i | \(0.0138800\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8015 | − | 18.7088i | −0.578194 | − | 1.00146i | −0.995687 | − | 0.0927805i | \(-0.970425\pi\) |
0.417493 | − | 0.908680i | \(-0.362909\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.0675 | − | 11.5860i | 1.06808 | − | 0.616658i | 0.140426 | − | 0.990091i | \(-0.455153\pi\) |
0.927657 | + | 0.373433i | \(0.121819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.2625 | − | 12.8533i | −1.18157 | − | 0.682180i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.26471 | 0.172305 | 0.0861524 | − | 0.996282i | \(-0.472543\pi\) | ||||
0.0861524 | + | 0.996282i | \(0.472543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.39892 | −0.389417 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5785 | + | 8.99425i | 0.815416 | + | 0.470781i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.22841 | + | 3.01862i | −0.272921 | + | 0.157571i | −0.630214 | − | 0.776421i | \(-0.717033\pi\) |
0.357294 | + | 0.933992i | \(0.383700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.651895 | − | 1.12912i | −0.0338447 | − | 0.0586208i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.60209 | − | 6.23900i | 0.186509 | − | 0.323043i | −0.757575 | − | 0.652748i | \(-0.773616\pi\) |
0.944084 | + | 0.329705i | \(0.106949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.670421i | 0.0345285i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0971502i | 0.00499027i | 0.999997 | + | 0.00249514i | \(0.000794227\pi\) | ||||
−0.999997 | + | 0.00249514i | \(0.999206\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.53976 | − | 4.39899i | 0.129776 | − | 0.224778i | −0.793814 | − | 0.608161i | \(-0.791908\pi\) |
0.923590 | + | 0.383383i | \(0.125241\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.6796 | + | 21.9617i | 0.646213 | + | 1.11927i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.84234 | + | 5.68248i | −0.499026 | + | 0.288113i | −0.728311 | − | 0.685246i | \(-0.759695\pi\) |
0.229285 | + | 0.973359i | \(0.426361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.9427 | − | 6.89511i | −0.603967 | − | 0.348701i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.8438 | −1.55192 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6693 | 0.535476 | 0.267738 | − | 0.963492i | \(-0.413724\pi\) | ||||
0.267738 | + | 0.963492i | \(0.413724\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.6353 | − | 17.6873i | −1.52986 | − | 0.883263i | −0.999367 | − | 0.0355709i | \(-0.988675\pi\) |
−0.530489 | − | 0.847692i | \(-0.677992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.8615 | + | 12.6217i | −1.08900 | + | 0.628732i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1644 | + | 17.6053i | 0.503833 | + | 0.872664i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.25833 | + | 16.0359i | −0.457795 | + | 0.792924i | −0.998844 | − | 0.0480668i | \(-0.984694\pi\) |
0.541049 | + | 0.840991i | \(0.318027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 49.5333i | 2.43738i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 34.8279i | − | 1.70964i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.11495 | − | 5.39525i | 0.152175 | − | 0.263575i | −0.779852 | − | 0.625964i | \(-0.784706\pi\) |
0.932027 | + | 0.362389i | \(0.118039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.63117 | + | 11.4855i | 0.323184 | + | 0.559770i | 0.981143 | − | 0.193283i | \(-0.0619136\pi\) |
−0.657960 | + | 0.753053i | \(0.728580\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.3407 | − | 9.43434i | 0.792643 | − | 0.457633i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.1479 | − | 19.7153i | −1.65253 | − | 0.954089i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.6333 | −1.66823 | −0.834114 | − | 0.551592i | \(-0.814021\pi\) | ||||
−0.834114 | + | 0.551592i | \(0.814021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.67288 | −0.272621 | −0.136311 | − | 0.990666i | \(-0.543525\pi\) | ||||
−0.136311 | + | 0.990666i | \(0.543525\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.73002 | + | 4.46293i | 0.369777 | + | 0.213491i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.4771 | − | 10.0904i | 0.834137 | − | 0.481589i | −0.0211298 | − | 0.999777i | \(-0.506726\pi\) |
0.855267 | + | 0.518187i | \(0.173393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.16349 | − | 12.4075i | −0.340347 | − | 0.589499i | 0.644150 | − | 0.764899i | \(-0.277211\pi\) |
−0.984497 | + | 0.175400i | \(0.943878\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.7984 | + | 22.1674i | −0.606701 | + | 1.05084i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.4094i | 1.10476i | 0.833593 | + | 0.552379i | \(0.186280\pi\) | ||||
−0.833593 | + | 0.552379i | \(0.813720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.54319i | − | 0.261019i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.5054 | + | 25.1240i | −0.680022 | + | 1.17783i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.786939 | + | 1.36302i | 0.0368115 | + | 0.0637593i | 0.883844 | − | 0.467781i | \(-0.154947\pi\) |
−0.847033 | + | 0.531541i | \(0.821613\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.10140 | + | 2.36794i | −0.191021 | + | 0.110286i | −0.592461 | − | 0.805599i | \(-0.701843\pi\) |
0.401439 | + | 0.915886i | \(0.368510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.54824 | + | 2.04858i | 0.164901 | + | 0.0952054i | 0.580179 | − | 0.814489i | \(-0.302983\pi\) |
−0.415279 | + | 0.909694i | \(0.636316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −41.3565 | −1.91375 | −0.956874 | − | 0.290502i | \(-0.906178\pi\) | ||||
−0.956874 | + | 0.290502i | \(0.906178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.4575 | −1.26787 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.51090 | − | 1.44967i | −0.115451 | − | 0.0666558i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.5767 | + | 6.10647i | −0.485293 | + | 0.280184i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.03763 | − | 3.52927i | −0.0931016 | − | 0.161257i | 0.815713 | − | 0.578457i | \(-0.196345\pi\) |
−0.908815 | + | 0.417200i | \(0.863011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.6280 | + | 20.1403i | −0.530193 | + | 0.918320i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 22.4220i | − | 1.01813i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.4449i | − | 1.06239i | −0.847249 | − | 0.531195i | \(-0.821743\pi\) | ||
0.847249 | − | 0.531195i | \(-0.178257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.12020 | + | 10.6005i | −0.276201 | + | 0.478393i | −0.970437 | − | 0.241353i | \(-0.922409\pi\) |
0.694237 | + | 0.719747i | \(0.255742\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.05803 | − | 1.83256i | −0.0476513 | − | 0.0825344i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.8112 | + | 20.0983i | −1.56150 | + | 0.901531i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.1385 | + | 10.4723i | 0.811993 | + | 0.468804i | 0.847647 | − | 0.530560i | \(-0.178018\pi\) |
−0.0356548 | + | 0.999364i | \(0.511352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.1123 | −1.47641 | −0.738203 | − | 0.674578i | \(-0.764325\pi\) | ||||
−0.738203 | + | 0.674578i | \(0.764325\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0307 | −1.20285 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.04353 | + | 5.22128i | 0.400847 | + | 0.231429i | 0.686850 | − | 0.726800i | \(-0.258993\pi\) |
−0.286002 | + | 0.958229i | \(0.592326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.3597 | − | 14.0641i | 1.07761 | − | 0.622157i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.2495 | + | 42.0014i | 1.06856 | + | 1.85080i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.89197 | − | 3.27698i | 0.0832086 | − | 0.144121i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.4658i | 1.20330i | 0.798760 | + | 0.601649i | \(0.205489\pi\) | ||||
−0.798760 | + | 0.601649i | \(0.794511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.4140i | 0.499098i | 0.968362 | + | 0.249549i | \(0.0802823\pi\) | ||||
−0.968362 | + | 0.249549i | \(0.919718\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.8381 | − | 69.0016i | 1.73537 | − | 3.00576i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.99102 | + | 17.3050i | 0.434392 | + | 0.752389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.49178 | − | 3.17068i | 0.237875 | − | 0.137337i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.4373 | + | 21.6144i | 1.61856 | + | 0.934473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.2645 | 1.04515 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.4658 | −0.750915 | −0.375458 | − | 0.926840i | \(-0.622514\pi\) | ||||
−0.375458 | + | 0.926840i | \(0.622514\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.02529 | − | 0.591952i | −0.0439187 | − | 0.0253565i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6998 | + | 11.3737i | −0.842303 | + | 0.486304i | −0.858046 | − | 0.513572i | \(-0.828322\pi\) |
0.0157437 | + | 0.999876i | \(0.494988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.684821 | + | 1.18614i | 0.0291743 | + | 0.0505314i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.1148 | + | 41.7680i | −1.02546 | + | 1.77616i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.8213i | 1.56017i | 0.625674 | + | 0.780085i | \(0.284824\pi\) | ||||
−0.625674 | + | 0.780085i | \(0.715176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.31681i | − | 0.140286i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.41299 | − | 4.17943i | 0.101696 | − | 0.176142i | −0.810688 | − | 0.585479i | \(-0.800907\pi\) |
0.912383 | + | 0.409337i | \(0.134240\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.4008 | + | 26.6750i | 0.647918 | + | 1.12223i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.1950 | + | 7.61816i | −0.553165 | + | 0.319370i | −0.750397 | − | 0.660987i | \(-0.770138\pi\) |
0.197233 | + | 0.980357i | \(0.436805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.64237 | − | 4.98967i | −0.361672 | − | 0.208811i | 0.308142 | − | 0.951340i | \(-0.400293\pi\) |
−0.669814 | + | 0.742529i | \(0.733626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.12937 | 0.172207 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.1236 | −0.587974 | −0.293987 | − | 0.955809i | \(-0.594982\pi\) | ||||
−0.293987 | + | 0.955809i | \(0.594982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −47.1633 | − | 27.2297i | −1.95666 | − | 1.12968i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.584474 | − | 0.337446i | 0.0242064 | − | 0.0139756i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.6504 | − | 21.9112i | −0.522139 | − | 0.904371i | −0.999668 | − | 0.0257553i | \(-0.991801\pi\) |
0.477529 | − | 0.878616i | \(-0.341532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.7856 | + | 44.6620i | −1.06248 | + | 1.84027i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 29.9811i | − | 1.23118i | −0.788068 | − | 0.615588i | \(-0.788919\pi\) | ||
0.788068 | − | 0.615588i | \(-0.211081\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 91.5670i | − | 3.75388i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.05626 | + | 10.4898i | −0.247452 | + | 0.428600i | −0.962818 | − | 0.270150i | \(-0.912927\pi\) |
0.715366 | + | 0.698750i | \(0.246260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.19251 | − | 5.52959i | −0.130225 | − | 0.225556i | 0.793538 | − | 0.608520i | \(-0.208237\pi\) |
−0.923763 | + | 0.382964i | \(0.874903\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.5057 | − | 8.37489i | 0.589742 | − | 0.340488i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.7050 | − | 15.4181i | −1.08392 | − | 0.625802i | −0.151969 | − | 0.988385i | \(-0.548561\pi\) |
−0.931951 | + | 0.362583i | \(0.881895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.32878 | 0.175124 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.7839 | −0.556728 | −0.278364 | − | 0.960476i | \(-0.589792\pi\) | ||||
−0.278364 | + | 0.960476i | \(0.589792\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.6496 | + | 15.3862i | 1.07287 | + | 0.619424i | 0.928965 | − | 0.370167i | \(-0.120700\pi\) |
0.143909 | + | 0.989591i | \(0.454033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.2973 | − | 16.3374i | 1.13736 | − | 0.656657i | 0.191587 | − | 0.981476i | \(-0.438636\pi\) |
0.945776 | + | 0.324818i | \(0.105303\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.0125 | + | 34.6626i | 0.801782 | + | 1.38873i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6174 | − | 27.0502i | 0.624697 | − | 1.08201i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 73.4034i | − | 2.92679i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.1436i | − | 0.403810i | −0.979405 | − | 0.201905i | \(-0.935287\pi\) | ||
0.979405 | − | 0.201905i | \(-0.0647132\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.7564 | − | 22.0947i | 0.506222 | − | 0.876803i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.8792 | + | 24.0395i | 0.549914 | + | 0.952479i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.5666 | − | 21.6891i | 1.48379 | − | 0.856666i | 0.483959 | − | 0.875091i | \(-0.339198\pi\) |
0.999830 | + | 0.0184242i | \(0.00586495\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2487 | − | 14.0000i | −0.956276 | − | 0.552106i | −0.0612510 | − | 0.998122i | \(-0.519509\pi\) |
−0.895025 | + | 0.446016i | \(0.852842\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.4413 | −0.685687 | −0.342844 | − | 0.939392i | \(-0.611390\pi\) | ||||
−0.342844 | + | 0.939392i | \(0.611390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.6403 | −1.00647 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.7870 | − | 11.4241i | −0.774327 | − | 0.447058i | 0.0600892 | − | 0.998193i | \(-0.480861\pi\) |
−0.834416 | + | 0.551135i | \(0.814195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.2053 | − | 12.2429i | 0.828559 | − | 0.478369i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0517 | − | 26.0703i | −0.586331 | − | 1.01555i | −0.994708 | − | 0.102741i | \(-0.967239\pi\) |
0.408378 | − | 0.912813i | \(-0.366095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.17500 | − | 15.8916i | 0.356866 | − | 0.618110i | −0.630569 | − | 0.776133i | \(-0.717179\pi\) |
0.987435 | + | 0.158023i | \(0.0505119\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 59.2676i | 2.29830i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 0.463096i | − | 0.0179311i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2054 | − | 17.6762i | 0.393974 | − | 0.682383i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.145944 | − | 0.252783i | −0.00562574 | − | 0.00974406i | 0.863199 | − | 0.504864i | \(-0.168457\pi\) |
−0.868825 | + | 0.495120i | \(0.835124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.1176 | + | 12.1922i | −0.811614 | + | 0.468586i | −0.847516 | − | 0.530770i | \(-0.821903\pi\) |
0.0359018 | + | 0.999355i | \(0.488570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.3634 | − | 17.5303i | −1.16524 | − | 0.672751i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.4127 | −1.01065 | −0.505326 | − | 0.862928i | \(-0.668628\pi\) | ||||
−0.505326 | + | 0.862928i | \(0.668628\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.153303 | 0.00585742 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.668633 | + | 0.386035i | 0.0254729 | + | 0.0147068i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0056 | + | 12.7050i | −0.837133 | + | 0.483319i | −0.856289 | − | 0.516497i | \(-0.827236\pi\) |
0.0191555 | + | 0.999817i | \(0.493902\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.4117 | + | 44.0143i | 0.963919 | + | 1.66956i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0077 | + | 17.3338i | −0.379067 | + | 0.656563i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.37948i | − | 0.0898719i | −0.998990 | − | 0.0449359i | \(-0.985692\pi\) | ||
0.998990 | − | 0.0449359i | \(-0.0143084\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.5111i | 1.79192i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.1336 | + | 36.6044i | −0.794809 | + | 1.37665i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.9001 | − | 37.9321i | −0.822477 | − | 1.42457i | −0.903833 | − | 0.427886i | \(-0.859258\pi\) |
0.0813562 | − | 0.996685i | \(-0.474075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.1009 | − | 8.71849i | 0.565532 | − | 0.326510i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.0052 | − | 7.50853i | −0.486365 | − | 0.280803i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.1749 | 1.16263 | 0.581314 | − | 0.813680i | \(-0.302539\pi\) | ||||
0.581314 | + | 0.813680i | \(0.302539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 75.8367 | 2.82430 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.548746 | + | 0.316819i | 0.0203799 | + | 0.0117664i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.8114 | + | 12.0155i | −0.771853 | + | 0.445629i | −0.833535 | − | 0.552466i | \(-0.813687\pi\) |
0.0616823 | + | 0.998096i | \(0.480353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.23445 | + | 9.06633i | 0.193603 | + | 0.335330i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.32611 | + | 10.9572i | −0.233660 | + | 0.404712i | −0.958883 | − | 0.283803i | \(-0.908404\pi\) |
0.725222 | + | 0.688515i | \(0.241737\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 14.2130i | − | 0.523544i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.4097i | 1.00828i | 0.863621 | + | 0.504141i | \(0.168191\pi\) | ||||
−0.863621 | + | 0.504141i | \(0.831809\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2005 | − | 22.8639i | 0.484278 | − | 0.838794i | −0.515559 | − | 0.856854i | \(-0.672416\pi\) |
0.999837 | + | 0.0180598i | \(0.00574894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.3574 | − | 42.1883i | −0.892387 | − | 1.54566i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 58.5396 | − | 33.7979i | 2.13899 | − | 1.23495i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.6599 | − | 20.0109i | −1.26476 | − | 0.730207i | −0.290765 | − | 0.956794i | \(-0.593910\pi\) |
−0.973991 | + | 0.226587i | \(0.927243\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.83980 | −0.176139 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.3671 | −1.83062 | −0.915311 | − | 0.402748i | \(-0.868055\pi\) | ||||
−0.915311 | + | 0.402748i | \(0.868055\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.3409 | + | 24.4455i | 1.53486 | + | 0.886150i | 0.999128 | + | 0.0417602i | \(0.0132965\pi\) |
0.535729 | + | 0.844390i | \(0.320037\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.60322 | + | 0.925619i | −0.0580404 | + | 0.0335097i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.6662 | − | 25.4025i | −0.529564 | − | 0.917232i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.74703 | + | 9.95414i | −0.207243 | + | 0.358956i | −0.950845 | − | 0.309667i | \(-0.899782\pi\) |
0.743602 | + | 0.668623i | \(0.233116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.8866i | 1.14688i | 0.819247 | + | 0.573441i | \(0.194392\pi\) | ||||
−0.819247 | + | 0.573441i | \(0.805608\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.8584i | 0.857020i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.47756 | − | 11.2195i | 0.232083 | − | 0.401979i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.4036 | − | 18.0196i | −0.372271 | − | 0.644793i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.8935 | − | 14.9496i | 0.924178 | − | 0.533574i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4161 | + | 7.74579i | 0.478232 | + | 0.276108i | 0.719680 | − | 0.694306i | \(-0.244289\pi\) |
−0.241447 | + | 0.970414i | \(0.577622\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.1637 | 1.71250 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.3497 | 0.829173 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.99393 | − | 2.30589i | −0.141472 | − | 0.0816790i | 0.427593 | − | 0.903971i | \(-0.359362\pi\) |
−0.569065 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.8325 | + | 6.83150i | −0.418604 | + | 0.241681i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.28009 | + | 12.6095i | 0.256909 | + | 0.444979i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.0196 | − | 17.3545i | 0.353145 | − | 0.611666i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.23050i | 0.324527i | 0.986747 | + | 0.162263i | \(0.0518795\pi\) | ||||
−0.986747 | + | 0.162263i | \(0.948121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14.4920i | − | 0.508884i | −0.967088 | − | 0.254442i | \(-0.918108\pi\) | ||
0.967088 | − | 0.254442i | \(-0.0818919\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.4839 | + | 54.5318i | −1.10283 | + | 1.91017i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.38805 | − | 5.86828i | −0.118533 | − | 0.205305i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.64787 | + | 3.83815i | −0.232012 | + | 0.133952i | −0.611500 | − | 0.791244i | \(-0.709434\pi\) |
0.379488 | + | 0.925197i | \(0.376100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.1619 | − | 10.4858i | −0.633083 | − | 0.365511i | 0.148862 | − | 0.988858i | \(-0.452439\pi\) |
−0.781945 | + | 0.623347i | \(0.785772\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.2620 | −0.774127 | −0.387064 | − | 0.922053i | \(-0.626511\pi\) | ||||
−0.387064 | + | 0.922053i | \(0.626511\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1198 | 0.837716 | 0.418858 | − | 0.908052i | \(-0.362431\pi\) | ||||
0.418858 | + | 0.908052i | \(0.362431\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −75.8762 | − | 43.8071i | −2.62895 | − | 1.51783i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.59437 | − | 3.80726i | 0.228207 | − | 0.131756i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1238 | + | 27.9273i | 0.556657 | + | 0.964158i | 0.997773 | + | 0.0667076i | \(0.0212495\pi\) |
−0.441116 | + | 0.897450i | \(0.645417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4645 | + | 25.0532i | −0.498775 | + | 0.863903i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.1294i | 0.623671i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 26.1911i | − | 0.899938i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.03210 | − | 13.9120i | 0.275337 | − | 0.476897i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4714 | + | 26.7972i | 0.529730 | + | 0.917520i | 0.999399 | + | 0.0346769i | \(0.0110402\pi\) |
−0.469668 | + | 0.882843i | \(0.655626\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.22025 | − | 0.704509i | 0.0416828 | − | 0.0240656i | −0.479014 | − | 0.877807i | \(-0.659006\pi\) |
0.520697 | + | 0.853742i | \(0.325672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9478 | − | 7.47543i | −0.441774 | − | 0.255059i | 0.262576 | − | 0.964911i | \(-0.415428\pi\) |
−0.704350 | + | 0.709853i | \(0.748761\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.6593 | 1.52022 | 0.760109 | − | 0.649795i | \(-0.225145\pi\) | ||||
0.760109 | + | 0.649795i | \(0.225145\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.7660 | −1.62409 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.6207 | − | 12.4827i | −0.733432 | − | 0.423447i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0812 | − | 8.12980i | 0.477124 | − | 0.275468i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.1285 | − | 26.2033i | −0.511435 | − | 0.885832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.4364 | − | 25.0046i | 0.487482 | − | 0.844344i | −0.512414 | − | 0.858739i | \(-0.671249\pi\) |
0.999896 | + | 0.0143943i | \(0.00458201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 14.1962i | − | 0.478283i | −0.970985 | − | 0.239142i | \(-0.923134\pi\) | ||
0.970985 | − | 0.239142i | \(-0.0768660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8730i | 1.13992i | 0.821673 | + | 0.569959i | \(0.193041\pi\) | ||||
−0.821673 | + | 0.569959i | \(0.806959\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.8373 | + | 27.4310i | −0.531765 | + | 0.921044i | 0.467547 | + | 0.883968i | \(0.345138\pi\) |
−0.999312 | + | 0.0370762i | \(0.988196\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.9468 | − | 34.5489i | −0.668995 | − | 1.15873i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.65871 | − | 4.42176i | 0.256289 | − | 0.147969i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.6806 | − | 6.16647i | −0.357014 | − | 0.206122i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.67564 | 0.0892377 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.43690 | −0.0811848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.87456 | + | 4.54638i | 0.261759 | + | 0.151127i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.2072 | + | 12.2440i | −0.704174 | + | 0.406555i | −0.808900 | − | 0.587946i | \(-0.799937\pi\) |
0.104726 | + | 0.994501i | \(0.466603\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.29162 | − | 10.8974i | −0.208451 | − | 0.361047i | 0.742776 | − | 0.669540i | \(-0.233509\pi\) |
−0.951227 | + | 0.308493i | \(0.900175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0951 | − | 24.4135i | 0.466481 | − | 0.807969i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 38.2877i | − | 1.26437i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.2890i | − | 0.768232i | −0.923285 | − | 0.384116i | \(-0.874506\pi\) | ||
0.923285 | − | 0.384116i | \(-0.125494\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.9017 | − | 20.6143i | 0.391748 | − | 0.678528i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.9900 | + | 19.0353i | 0.361350 | + | 0.625877i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.3620 | + | 18.1069i | −1.02895 | + | 0.594067i | −0.916685 | − | 0.399611i | \(-0.869145\pi\) |
−0.112269 | + | 0.993678i | \(0.535812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.1116 | + | 28.3546i | 1.60957 | + | 0.929285i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 47.3985 | 1.55010 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.31254 | −0.0755474 | −0.0377737 | − | 0.999286i | \(-0.512027\pi\) | ||||
−0.0377737 | + | 0.999286i | \(0.512027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.97067 | + | 2.86982i | 0.162039 | + | 0.0935533i | 0.578827 | − | 0.815451i | \(-0.303511\pi\) |
−0.416788 | + | 0.909004i | \(0.636844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.79346 | + | 2.19016i | −0.123532 | + | 0.0713213i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.67639 | − | 8.09975i | −0.151962 | − | 0.263207i | 0.779986 | − | 0.625796i | \(-0.215226\pi\) |
−0.931949 | + | 0.362590i | \(0.881893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.32836 | + | 14.4251i | −0.270350 | + | 0.468260i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 47.4501i | − | 1.53706i | −0.639814 | − | 0.768530i | \(-0.720988\pi\) | ||
0.639814 | − | 0.768530i | \(-0.279012\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 17.1867i | − | 0.556148i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.119858 | − | 0.207600i | 0.00387042 | − | 0.00670376i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.8731 | + | 60.4020i | 1.12494 | + | 1.94845i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.4807 | + | 14.1339i | −0.788062 | + | 0.454988i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.35617 | + | 3.66974i | 0.204401 | + | 0.118011i | 0.598707 | − | 0.800968i | \(-0.295682\pi\) |
−0.394306 | + | 0.918979i | \(0.629015\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.9568 | −1.28228 | −0.641138 | − | 0.767425i | \(-0.721537\pi\) | ||||
−0.641138 | + | 0.767425i | \(0.721537\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 79.4710 | 2.54772 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.03700 | + | 4.06281i | 0.225133 | + | 0.129981i | 0.608325 | − | 0.793688i | \(-0.291842\pi\) |
−0.383192 | + | 0.923669i | \(0.625175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.9427 | + | 10.3592i | −0.573450 | + | 0.331082i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.20579 | + | 10.7487i | 0.197934 | + | 0.342832i | 0.947858 | − | 0.318692i | \(-0.103243\pi\) |
−0.749924 | + | 0.661524i | \(0.769910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.5093 | − | 42.4514i | 0.780931 | − | 1.35261i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.29110i | 0.0728527i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.6327i | 0.973080i | 0.873658 | + | 0.486540i | \(0.161741\pi\) | ||||
−0.873658 | + | 0.486540i | \(0.838259\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.24073 | + | 2.14901i | −0.0393338 | + | 0.0681281i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.5182 | − | 45.9308i | −0.839839 | − | 1.45464i | −0.890029 | − | 0.455904i | \(-0.849316\pi\) |
0.0501902 | − | 0.998740i | \(-0.484017\pi\) | |||||||
\(998\) | 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 | 2592.2.s.j.863.7 | 16 | ||
3.2 | odd | 2 | inner | 2592.2.s.j.863.2 | 16 | ||
4.3 | odd | 2 | 2592.2.s.i.863.7 | 16 | |||
9.2 | odd | 6 | 2592.2.s.i.1727.7 | 16 | |||
9.4 | even | 3 | 2592.2.c.b.2591.4 | yes | 16 | ||
9.5 | odd | 6 | 2592.2.c.b.2591.14 | yes | 16 | ||
9.7 | even | 3 | 2592.2.s.i.1727.2 | 16 | |||
12.11 | even | 2 | 2592.2.s.i.863.2 | 16 | |||
36.7 | odd | 6 | inner | 2592.2.s.j.1727.2 | 16 | ||
36.11 | even | 6 | inner | 2592.2.s.j.1727.7 | 16 | ||
36.23 | even | 6 | 2592.2.c.b.2591.13 | yes | 16 | ||
36.31 | odd | 6 | 2592.2.c.b.2591.3 | ✓ | 16 | ||
72.5 | odd | 6 | 5184.2.c.l.5183.4 | 16 | |||
72.13 | even | 6 | 5184.2.c.l.5183.14 | 16 | |||
72.59 | even | 6 | 5184.2.c.l.5183.3 | 16 | |||
72.67 | odd | 6 | 5184.2.c.l.5183.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2592.2.c.b.2591.3 | ✓ | 16 | 36.31 | odd | 6 | ||
2592.2.c.b.2591.4 | yes | 16 | 9.4 | even | 3 | ||
2592.2.c.b.2591.13 | yes | 16 | 36.23 | even | 6 | ||
2592.2.c.b.2591.14 | yes | 16 | 9.5 | odd | 6 | ||
2592.2.s.i.863.2 | 16 | 12.11 | even | 2 | |||
2592.2.s.i.863.7 | 16 | 4.3 | odd | 2 | |||
2592.2.s.i.1727.2 | 16 | 9.7 | even | 3 | |||
2592.2.s.i.1727.7 | 16 | 9.2 | odd | 6 | |||
2592.2.s.j.863.2 | 16 | 3.2 | odd | 2 | inner | ||
2592.2.s.j.863.7 | 16 | 1.1 | even | 1 | trivial | ||
2592.2.s.j.1727.2 | 16 | 36.7 | odd | 6 | inner | ||
2592.2.s.j.1727.7 | 16 | 36.11 | even | 6 | inner | ||
5184.2.c.l.5183.3 | 16 | 72.59 | even | 6 | |||
5184.2.c.l.5183.4 | 16 | 72.5 | odd | 6 | |||
5184.2.c.l.5183.13 | 16 | 72.67 | odd | 6 | |||
5184.2.c.l.5183.14 | 16 | 72.13 | even | 6 |