Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(215,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.l (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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.215 |
Dual form | 1134.2.l.d.269.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 1.73205i | −0.832050 | − | 0.480384i | 0.0225039 | − | 0.999747i | \(-0.492836\pi\) |
−0.854554 | + | 0.519362i | \(0.826170\pi\) | |||||||
\(14\) | 1.73205 | + | 2.00000i | 0.462910 | + | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 1.73205 | − | 3.00000i | 0.339683 | − | 0.588348i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | + | 1.73205i | −0.377964 | + | 0.327327i | ||||
\(29\) | 7.79423 | − | 4.50000i | 1.44735 | − | 0.835629i | 0.449029 | − | 0.893517i | \(-0.351770\pi\) |
0.998323 | + | 0.0578882i | \(0.0184367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | − | 6.92820i | 0.657596 | − | 1.13899i | −0.323640 | − | 0.946180i | \(-0.604907\pi\) |
0.981236 | − | 0.192809i | \(-0.0617599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.19615 | + | 9.00000i | −0.811503 | + | 1.40556i | 0.100309 | + | 0.994956i | \(0.468017\pi\) |
−0.911812 | + | 0.410608i | \(0.865317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | − | 3.46410i | −0.304997 | − | 0.528271i | 0.672264 | − | 0.740312i | \(-0.265322\pi\) |
−0.977261 | + | 0.212041i | \(0.931989\pi\) | |||||||
\(44\) | −2.59808 | − | 1.50000i | −0.391675 | − | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.3923 | 1.51587 | 0.757937 | − | 0.652328i | \(-0.226208\pi\) | ||||
0.757937 | + | 0.652328i | \(0.226208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 4.33013 | + | 2.50000i | 0.612372 | + | 0.353553i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.00000 | + | 1.73205i | 0.416025 | + | 0.240192i | ||||
\(53\) | 5.19615 | − | 3.00000i | 0.713746 | − | 0.412082i | −0.0987002 | − | 0.995117i | \(-0.531468\pi\) |
0.812447 | + | 0.583036i | \(0.198135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.73205 | − | 2.00000i | −0.231455 | − | 0.267261i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.50000 | + | 7.79423i | 0.590879 | + | 1.02343i | ||||
\(59\) | 5.19615 | 0.676481 | 0.338241 | − | 0.941060i | \(-0.390168\pi\) | ||||
0.338241 | + | 0.941060i | \(0.390168\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8564i | 1.77413i | 0.461644 | + | 0.887066i | \(0.347260\pi\) | ||||
−0.461644 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(62\) | 1.73205 | 0.219971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | − | 2.59808i | 0.526685 | − | 0.304082i | −0.212980 | − | 0.977056i | \(-0.568317\pi\) |
0.739666 | + | 0.672975i | \(0.234984\pi\) | |||||||
\(74\) | 6.92820 | + | 4.00000i | 0.805387 | + | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.79423 | − | 1.50000i | 0.888235 | − | 0.170941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0000 | −1.46261 | −0.731307 | − | 0.682048i | \(-0.761089\pi\) | ||||
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.00000 | − | 5.19615i | −0.993884 | − | 0.573819i | ||||
\(83\) | 2.59808 | + | 4.50000i | 0.285176 | + | 0.493939i | 0.972652 | − | 0.232268i | \(-0.0746146\pi\) |
−0.687476 | + | 0.726207i | \(0.741281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.46410 | − | 2.00000i | 0.373544 | − | 0.215666i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | 5.19615 | − | 9.00000i | 0.550791 | − | 0.953998i | −0.447427 | − | 0.894321i | \(-0.647659\pi\) |
0.998218 | − | 0.0596775i | \(-0.0190072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.00000 | + | 1.73205i | −0.943456 | + | 0.181568i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.3923i | 1.07188i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.50000 | + | 4.33013i | −0.761510 | + | 0.439658i | −0.829837 | − | 0.558005i | \(-0.811567\pi\) |
0.0683279 | + | 0.997663i | \(0.478234\pi\) | |||||||
\(98\) | 6.92820 | + | 1.00000i | 0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.50000 | + | 4.33013i | −0.250000 | + | 0.433013i | ||||
\(101\) | −2.59808 | + | 4.50000i | −0.258518 | + | 0.447767i | −0.965845 | − | 0.259120i | \(-0.916568\pi\) |
0.707327 | + | 0.706887i | \(0.249901\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0000 | − | 8.66025i | 1.47799 | − | 0.853320i | 0.478303 | − | 0.878195i | \(-0.341252\pi\) |
0.999691 | + | 0.0248745i | \(0.00791862\pi\) | |||||||
\(104\) | −1.73205 | + | 3.00000i | −0.169842 | + | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | −10.3923 | − | 6.00000i | −1.00466 | − | 0.580042i | −0.0950377 | − | 0.995474i | \(-0.530297\pi\) |
−0.909624 | + | 0.415432i | \(0.863630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | + | 6.92820i | 0.383131 | + | 0.663602i | 0.991508 | − | 0.130046i | \(-0.0415126\pi\) |
−0.608377 | + | 0.793648i | \(0.708179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | − | 1.73205i | 0.188982 | − | 0.163663i | ||||
\(113\) | 10.3923 | + | 6.00000i | 0.977626 | + | 0.564433i | 0.901553 | − | 0.432670i | \(-0.142428\pi\) |
0.0760733 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.79423 | + | 4.50000i | −0.723676 | + | 0.417815i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.19615i | 0.478345i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | −13.8564 | −1.25450 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.73205i | 0.155543i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.79423 | − | 13.5000i | −0.680985 | − | 1.17950i | −0.974681 | − | 0.223602i | \(-0.928219\pi\) |
0.293696 | − | 0.955899i | \(-0.405115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | − | 6.00000i | −0.887875 | − | 0.512615i | −0.0146279 | − | 0.999893i | \(-0.504656\pi\) |
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | − | 3.46410i | −0.508913 | − | 0.293821i | 0.223474 | − | 0.974710i | \(-0.428260\pi\) |
−0.732387 | + | 0.680889i | \(0.761594\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | −5.19615 | − | 9.00000i | −0.434524 | − | 0.752618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.59808 | + | 4.50000i | 0.215018 | + | 0.372423i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | + | 6.92820i | −0.328798 | + | 0.569495i | ||||
\(149\) | −12.9904 | + | 7.50000i | −1.06421 | + | 0.614424i | −0.926595 | − | 0.376061i | \(-0.877278\pi\) |
−0.137619 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5000 | − | 19.9186i | 0.935857 | − | 1.62095i | 0.162758 | − | 0.986666i | \(-0.447961\pi\) |
0.773099 | − | 0.634285i | \(-0.218706\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.50000 | + | 7.79423i | 0.120873 | + | 0.628077i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3923i | 0.829396i | 0.909959 | + | 0.414698i | \(0.136113\pi\) | ||||
−0.909959 | + | 0.414698i | \(0.863887\pi\) | |||||||
\(158\) | − | 13.0000i | − | 1.03422i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000 | − | 8.66025i | 0.391630 | − | 0.678323i | −0.601035 | − | 0.799223i | \(-0.705245\pi\) |
0.992665 | + | 0.120900i | \(0.0385779\pi\) | |||||||
\(164\) | 5.19615 | − | 9.00000i | 0.405751 | − | 0.702782i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | + | 2.59808i | −0.349268 | + | 0.201650i | ||||
\(167\) | −5.19615 | + | 9.00000i | −0.402090 | + | 0.696441i | −0.993978 | − | 0.109580i | \(-0.965050\pi\) |
0.591888 | + | 0.806020i | \(0.298383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | −25.9808 | −1.97528 | −0.987640 | − | 0.156737i | \(-0.949903\pi\) | ||||
−0.987640 | + | 0.156737i | \(0.949903\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | − | 12.9904i | −0.188982 | − | 0.981981i | ||||
\(176\) | 2.59808 | + | 1.50000i | 0.195837 | + | 0.113067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.00000 | + | 5.19615i | 0.674579 | + | 0.389468i | ||||
\(179\) | 7.79423 | − | 4.50000i | 0.582568 | − | 0.336346i | −0.179585 | − | 0.983742i | \(-0.557476\pi\) |
0.762153 | + | 0.647397i | \(0.224142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7846i | 1.54491i | 0.635071 | + | 0.772454i | \(0.280971\pi\) | ||||
−0.635071 | + | 0.772454i | \(0.719029\pi\) | |||||||
\(182\) | −1.73205 | − | 9.00000i | −0.128388 | − | 0.667124i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −10.3923 | −0.757937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.00000i | − | 0.434145i | −0.976156 | − | 0.217072i | \(-0.930349\pi\) | ||
0.976156 | − | 0.217072i | \(-0.0696508\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | −0.791797 | −0.395899 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395899 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(194\) | −4.33013 | − | 7.50000i | −0.310885 | − | 0.538469i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | 15.0000i | 1.06871i | 0.845262 | + | 0.534353i | \(0.179445\pi\) | ||||
−0.845262 | + | 0.534353i | \(0.820555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | − | 0.866025i | 0.106332 | − | 0.0613909i | −0.445891 | − | 0.895087i | \(-0.647113\pi\) |
0.552223 | + | 0.833696i | \(0.313780\pi\) | |||||||
\(200\) | −4.33013 | − | 2.50000i | −0.306186 | − | 0.176777i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.50000 | − | 2.59808i | −0.316619 | − | 0.182800i | ||||
\(203\) | 7.79423 | − | 22.5000i | 0.547048 | − | 1.57919i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.66025 | + | 15.0000i | 0.603388 | + | 1.04510i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | − | 1.73205i | −0.208013 | − | 0.120096i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | − | 1.73205i | 0.0688428 | − | 0.119239i | −0.829549 | − | 0.558433i | \(-0.811403\pi\) |
0.898392 | + | 0.439194i | \(0.144736\pi\) | |||||||
\(212\) | −5.19615 | + | 3.00000i | −0.356873 | + | 0.206041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | − | 3.46410i | −0.203653 | − | 0.235159i | ||||
\(218\) | −6.92820 | + | 4.00000i | −0.469237 | + | 0.270914i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50000 | − | 2.59808i | 0.301342 | − | 0.173980i | −0.341703 | − | 0.939808i | \(-0.611004\pi\) |
0.643046 | + | 0.765828i | \(0.277671\pi\) | |||||||
\(224\) | 1.73205 | + | 2.00000i | 0.115728 | + | 0.133631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | + | 10.3923i | −0.399114 | + | 0.691286i | ||||
\(227\) | −12.9904 | + | 22.5000i | −0.862202 | + | 1.49338i | 0.00759708 | + | 0.999971i | \(0.497582\pi\) |
−0.869799 | + | 0.493406i | \(0.835752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00000 | + | 3.46410i | −0.396491 | + | 0.228914i | −0.684969 | − | 0.728572i | \(-0.740184\pi\) |
0.288478 | + | 0.957487i | \(0.406851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.50000 | − | 7.79423i | −0.295439 | − | 0.511716i | ||||
\(233\) | 15.5885 | + | 9.00000i | 1.02123 | + | 0.589610i | 0.914461 | − | 0.404674i | \(-0.132615\pi\) |
0.106773 | + | 0.994283i | \(0.465948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.19615 | −0.338241 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923 | + | 6.00000i | 0.672222 | + | 0.388108i | 0.796918 | − | 0.604087i | \(-0.206462\pi\) |
−0.124696 | + | 0.992195i | \(0.539796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5000 | + | 6.06218i | 0.676364 | + | 0.390499i | 0.798484 | − | 0.602016i | \(-0.205636\pi\) |
−0.122119 | + | 0.992515i | \(0.538969\pi\) | |||||||
\(242\) | 1.73205 | − | 1.00000i | 0.111340 | − | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 13.8564i | − | 0.887066i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.73205 | −0.109985 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.9808 | −1.63989 | −0.819946 | − | 0.572441i | \(-0.805996\pi\) | ||||
−0.819946 | + | 0.572441i | \(0.805996\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000i | 0.501965i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.3923 | − | 18.0000i | −0.648254 | − | 1.12281i | −0.983540 | − | 0.180693i | \(-0.942166\pi\) |
0.335285 | − | 0.942117i | \(-0.391167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 20.7846i | −0.248548 | − | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.5000 | − | 7.79423i | 0.834033 | − | 0.481529i | ||||
\(263\) | −20.7846 | − | 12.0000i | −1.28163 | − | 0.739952i | −0.304487 | − | 0.952517i | \(-0.598485\pi\) |
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00000 | −0.122169 | ||||||||
\(269\) | −7.79423 | − | 13.5000i | −0.475223 | − | 0.823110i | 0.524375 | − | 0.851488i | \(-0.324299\pi\) |
−0.999597 | + | 0.0283781i | \(0.990966\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00000 | + | 1.73205i | 0.182237 | + | 0.105215i | 0.588343 | − | 0.808611i | \(-0.299780\pi\) |
−0.406106 | + | 0.913826i | \(0.633114\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | − | 10.3923i | 0.362473 | − | 0.627822i | ||||
\(275\) | 12.9904 | − | 7.50000i | 0.783349 | − | 0.452267i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 3.46410 | − | 6.00000i | 0.207763 | − | 0.359856i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.19615 | + | 3.00000i | −0.309976 | + | 0.178965i | −0.646916 | − | 0.762561i | \(-0.723942\pi\) |
0.336939 | + | 0.941526i | \(0.390608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.92820i | 0.411839i | 0.978569 | + | 0.205919i | \(0.0660185\pi\) | ||||
−0.978569 | + | 0.205919i | \(0.933982\pi\) | |||||||
\(284\) | − | 12.0000i | − | 0.712069i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.00000 | − | 5.19615i | 0.532181 | − | 0.307255i | ||||
\(287\) | 5.19615 | + | 27.0000i | 0.306719 | + | 1.59376i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.50000 | + | 2.59808i | −0.263343 | + | 0.152041i | ||||
\(293\) | −2.59808 | + | 4.50000i | −0.151781 | + | 0.262893i | −0.931882 | − | 0.362761i | \(-0.881834\pi\) |
0.780101 | + | 0.625653i | \(0.215168\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.92820 | − | 4.00000i | −0.402694 | − | 0.232495i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.50000 | − | 12.9904i | −0.434463 | − | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0000 | − | 3.46410i | −0.576390 | − | 0.199667i | ||||
\(302\) | 19.9186 | + | 11.5000i | 1.14619 | + | 0.661751i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.3205i | − | 0.988534i | −0.869310 | − | 0.494267i | \(-0.835437\pi\) | ||
0.869310 | − | 0.494267i | \(-0.164563\pi\) | |||||||
\(308\) | −7.79423 | + | 1.50000i | −0.444117 | + | 0.0854704i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.1769 | −1.76788 | −0.883940 | − | 0.467600i | \(-0.845119\pi\) | ||||
−0.883940 | + | 0.467600i | \(0.845119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7846i | 1.17482i | 0.809291 | + | 0.587408i | \(0.199852\pi\) | ||||
−0.809291 | + | 0.587408i | \(0.800148\pi\) | |||||||
\(314\) | −10.3923 | −0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0000 | 0.731307 | ||||||||
\(317\) | − | 9.00000i | − | 0.505490i | −0.967533 | − | 0.252745i | \(-0.918667\pi\) | ||
0.967533 | − | 0.252745i | \(-0.0813334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.0000 | 1.51171 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0000 | + | 8.66025i | −0.832050 | + | 0.480384i | ||||
\(326\) | 8.66025 | + | 5.00000i | 0.479647 | + | 0.276924i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.00000 | + | 5.19615i | 0.496942 | + | 0.286910i | ||||
\(329\) | 20.7846 | − | 18.0000i | 1.14589 | − | 0.992372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0000 | 1.53902 | 0.769510 | − | 0.638635i | \(-0.220501\pi\) | ||||
0.769510 | + | 0.638635i | \(0.220501\pi\) | |||||||
\(332\) | −2.59808 | − | 4.50000i | −0.142588 | − | 0.246970i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.00000 | − | 5.19615i | −0.492458 | − | 0.284321i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.50000 | + | 11.2583i | −0.354078 | + | 0.613280i | −0.986960 | − | 0.160968i | \(-0.948538\pi\) |
0.632882 | + | 0.774248i | \(0.281872\pi\) | |||||||
\(338\) | 0.866025 | − | 0.500000i | 0.0471056 | − | 0.0271964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.59808 | − | 4.50000i | 0.140694 | − | 0.243689i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −3.46410 | + | 2.00000i | −0.186772 | + | 0.107833i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 25.9808i | − | 1.39673i | ||||||
\(347\) | 3.00000i | 0.161048i | 0.996753 | + | 0.0805242i | \(0.0256594\pi\) | ||||
−0.996753 | + | 0.0805242i | \(0.974341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | + | 13.8564i | −1.28469 | + | 0.741716i | −0.977702 | − | 0.209997i | \(-0.932655\pi\) |
−0.306988 | + | 0.951713i | \(0.599321\pi\) | |||||||
\(350\) | 12.9904 | − | 2.50000i | 0.694365 | − | 0.133631i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | + | 2.59808i | −0.0799503 | + | 0.138478i | ||||
\(353\) | 5.19615 | − | 9.00000i | 0.276563 | − | 0.479022i | −0.693965 | − | 0.720009i | \(-0.744138\pi\) |
0.970528 | + | 0.240987i | \(0.0774711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.19615 | + | 9.00000i | −0.275396 | + | 0.476999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.50000 | + | 7.79423i | 0.237832 | + | 0.411938i | ||||
\(359\) | 10.3923 | + | 6.00000i | 0.548485 | + | 0.316668i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | − | 16.4545i | −0.500000 | − | 0.866025i | ||||
\(362\) | −20.7846 | −1.09241 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.00000 | − | 1.73205i | 0.471728 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.00000 | − | 5.19615i | −0.469796 | − | 0.271237i | 0.246358 | − | 0.969179i | \(-0.420766\pi\) |
−0.716154 | + | 0.697942i | \(0.754099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.19615 | − | 15.0000i | 0.269771 | − | 0.778761i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 10.3923i | − | 0.535942i | ||||||
\(377\) | −31.1769 | −1.60569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.00000 | 0.306987 | ||||||||
\(383\) | −10.3923 | − | 18.0000i | −0.531022 | − | 0.919757i | −0.999345 | − | 0.0361995i | \(-0.988475\pi\) |
0.468323 | − | 0.883558i | \(-0.344859\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11.0000i | − | 0.559885i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.50000 | − | 4.33013i | 0.380755 | − | 0.219829i | ||||
\(389\) | 7.79423 | + | 4.50000i | 0.395183 | + | 0.228159i | 0.684403 | − | 0.729103i | \(-0.260063\pi\) |
−0.289220 | + | 0.957263i | \(0.593396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.92820 | − | 1.00000i | −0.349927 | − | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.0000 | + | 12.1244i | 1.05396 | + | 0.608504i | 0.923755 | − | 0.382983i | \(-0.125103\pi\) |
0.130204 | + | 0.991487i | \(0.458437\pi\) | |||||||
\(398\) | 0.866025 | + | 1.50000i | 0.0434099 | + | 0.0751882i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.50000 | − | 4.33013i | 0.125000 | − | 0.216506i | ||||
\(401\) | −25.9808 | + | 15.0000i | −1.29742 | + | 0.749064i | −0.979957 | − | 0.199207i | \(-0.936163\pi\) |
−0.317460 | + | 0.948272i | \(0.602830\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | + | 5.19615i | −0.149441 | + | 0.258839i | ||||
\(404\) | 2.59808 | − | 4.50000i | 0.129259 | − | 0.223883i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.5000 | + | 7.79423i | 1.11666 | + | 0.386821i | ||||
\(407\) | 20.7846 | − | 12.0000i | 1.03025 | − | 0.594818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.92820i | 0.342578i | 0.985221 | + | 0.171289i | \(0.0547931\pi\) | ||||
−0.985221 | + | 0.171289i | \(0.945207\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.0000 | + | 8.66025i | −0.738997 | + | 0.426660i | ||||
\(413\) | 10.3923 | − | 9.00000i | 0.511372 | − | 0.442861i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.73205 | − | 3.00000i | 0.0849208 | − | 0.147087i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.5885 | + | 27.0000i | −0.761546 | + | 1.31904i | 0.180508 | + | 0.983574i | \(0.442226\pi\) |
−0.942053 | + | 0.335463i | \(0.891107\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | 1.73205 | + | 1.00000i | 0.0843149 | + | 0.0486792i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.0000 | + | 27.7128i | 1.16144 | + | 1.34112i | ||||
\(428\) | 10.3923 | + | 6.00000i | 0.502331 | + | 0.290021i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5885 | − | 9.00000i | 0.750870 | − | 0.433515i | −0.0751385 | − | 0.997173i | \(-0.523940\pi\) |
0.826008 | + | 0.563658i | \(0.190607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1244i | 0.582659i | 0.956623 | + | 0.291330i | \(0.0940977\pi\) | ||||
−0.956623 | + | 0.291330i | \(0.905902\pi\) | |||||||
\(434\) | 3.46410 | − | 3.00000i | 0.166282 | − | 0.144005i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | − | 6.92820i | −0.191565 | − | 0.331801i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.5885i | − | 0.743996i | −0.928233 | − | 0.371998i | \(-0.878673\pi\) | ||
0.928233 | − | 0.371998i | \(-0.121327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.0000i | 1.28281i | 0.767203 | + | 0.641404i | \(0.221648\pi\) | ||||
−0.767203 | + | 0.641404i | \(0.778352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.59808 | + | 4.50000i | 0.123022 | + | 0.213081i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00000 | + | 1.73205i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | 30.0000i | 1.41579i | 0.706319 | + | 0.707894i | \(0.250354\pi\) | ||||
−0.706319 | + | 0.707894i | \(0.749646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.0000 | + | 15.5885i | −1.27138 | + | 0.734032i | ||||
\(452\) | −10.3923 | − | 6.00000i | −0.488813 | − | 0.282216i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.5000 | − | 12.9904i | −1.05598 | − | 0.609669i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | −3.46410 | − | 6.00000i | −0.161867 | − | 0.280362i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.79423 | + | 13.5000i | 0.363013 | + | 0.628758i | 0.988455 | − | 0.151513i | \(-0.0484146\pi\) |
−0.625442 | + | 0.780271i | \(0.715081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.50000 | + | 4.33013i | −0.116185 | + | 0.201238i | −0.918253 | − | 0.395995i | \(-0.870400\pi\) |
0.802068 | + | 0.597233i | \(0.203733\pi\) | |||||||
\(464\) | 7.79423 | − | 4.50000i | 0.361838 | − | 0.208907i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | −2.59808 | + | 4.50000i | −0.120225 | + | 0.208235i | −0.919856 | − | 0.392256i | \(-0.871695\pi\) |
0.799632 | + | 0.600491i | \(0.205028\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | − | 3.46410i | 0.184703 | − | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 5.19615i | − | 0.239172i | ||||||
\(473\) | − | 12.0000i | − | 0.551761i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.00000 | + | 10.3923i | −0.274434 | + | 0.475333i | ||||
\(479\) | 5.19615 | − | 9.00000i | 0.237418 | − | 0.411220i | −0.722554 | − | 0.691314i | \(-0.757032\pi\) |
0.959973 | + | 0.280094i | \(0.0903655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | + | 13.8564i | −1.09431 | + | 0.631798i | ||||
\(482\) | −6.06218 | + | 10.5000i | −0.276125 | + | 0.478262i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.50000 | + | 9.52628i | 0.249229 | + | 0.431677i | 0.963312 | − | 0.268384i | \(-0.0864896\pi\) |
−0.714083 | + | 0.700061i | \(0.753156\pi\) | |||||||
\(488\) | 13.8564 | 0.627250 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.1769 | + | 18.0000i | 1.40699 | + | 0.812329i | 0.995097 | − | 0.0989017i | \(-0.0315329\pi\) |
0.411897 | + | 0.911230i | \(0.364866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.73205i | − | 0.0777714i | ||||||
\(497\) | 20.7846 | + | 24.0000i | 0.932317 | + | 1.07655i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | − | 13.8564i | −0.358129 | − | 0.620298i | 0.629519 | − | 0.776985i | \(-0.283252\pi\) |
−0.987648 | + | 0.156687i | \(0.949919\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 25.9808i | − | 1.15958i | ||||||
\(503\) | 31.1769 | 1.39011 | 0.695055 | − | 0.718957i | \(-0.255380\pi\) | ||||
0.695055 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | 2.59808 | + | 4.50000i | 0.115158 | + | 0.199459i | 0.917843 | − | 0.396944i | \(-0.129929\pi\) |
−0.802685 | + | 0.596403i | \(0.796596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.50000 | − | 12.9904i | 0.199068 | − | 0.574661i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0000 | − | 10.3923i | 0.793946 | − | 0.458385i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.0000 | + | 15.5885i | 1.18746 | + | 0.685580i | ||||
\(518\) | 20.7846 | − | 4.00000i | 0.913223 | − | 0.175750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3923 | − | 18.0000i | −0.455295 | − | 0.788594i | 0.543410 | − | 0.839467i | \(-0.317133\pi\) |
−0.998705 | + | 0.0508731i | \(0.983800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0000 | + | 19.0526i | 1.44299 | + | 0.833110i | 0.998048 | − | 0.0624496i | \(-0.0198913\pi\) |
0.444941 | + | 0.895560i | \(0.353225\pi\) | |||||||
\(524\) | 7.79423 | + | 13.5000i | 0.340492 | + | 0.589750i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | − | 20.7846i | 0.523225 | − | 0.906252i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.1769 | − | 18.0000i | 1.35042 | − | 0.779667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 2.00000i | − | 0.0863868i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.5000 | − | 7.79423i | 0.582026 | − | 0.336033i | ||||
\(539\) | 12.9904 | − | 16.5000i | 0.559535 | − | 0.710705i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0000 | + | 32.9090i | −0.816874 | + | 1.41487i | 0.0911008 | + | 0.995842i | \(0.470961\pi\) |
−0.907975 | + | 0.419025i | \(0.862372\pi\) | |||||||
\(542\) | −1.73205 | + | 3.00000i | −0.0743980 | + | 0.128861i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.00000 | − | 12.1244i | −0.299298 | − | 0.518400i | 0.676677 | − | 0.736280i | \(-0.263419\pi\) |
−0.975976 | + | 0.217880i | \(0.930086\pi\) | |||||||
\(548\) | 10.3923 | + | 6.00000i | 0.443937 | + | 0.256307i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.50000 | + | 12.9904i | 0.319801 | + | 0.553912i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.0000 | + | 22.5167i | −1.10563 | + | 0.957506i | ||||
\(554\) | −12.1244 | − | 7.00000i | −0.515115 | − | 0.297402i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.00000 | + | 3.46410i | 0.254457 | + | 0.146911i | ||||
\(557\) | −18.1865 | + | 10.5000i | −0.770588 | + | 0.444899i | −0.833084 | − | 0.553146i | \(-0.813427\pi\) |
0.0624962 | + | 0.998045i | \(0.480094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8564i | 0.586064i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | 31.1769 | 1.31395 | 0.656975 | − | 0.753912i | \(-0.271836\pi\) | ||||
0.656975 | + | 0.753912i | \(0.271836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.92820 | −0.291214 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | − | 12.0000i | − | 0.503066i | −0.967849 | − | 0.251533i | \(-0.919065\pi\) | ||
0.967849 | − | 0.251533i | \(-0.0809347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 5.19615 | + | 9.00000i | 0.217262 | + | 0.376309i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27.0000 | + | 5.19615i | −1.12696 | + | 0.216883i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.50000 | + | 4.33013i | −0.312229 | + | 0.180266i | −0.647924 | − | 0.761705i | \(-0.724362\pi\) |
0.335694 | + | 0.941971i | \(0.391029\pi\) | |||||||
\(578\) | 14.7224 | + | 8.50000i | 0.612372 | + | 0.353553i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.9904 | + | 4.50000i | 0.538932 | + | 0.186691i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | 0.745484 | ||||||||
\(584\) | −2.59808 | − | 4.50000i | −0.107509 | − | 0.186211i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | − | 2.59808i | −0.185893 | − | 0.107326i | ||||
\(587\) | 5.19615 | + | 9.00000i | 0.214468 | + | 0.371470i | 0.953108 | − | 0.302631i | \(-0.0978648\pi\) |
−0.738640 | + | 0.674100i | \(0.764532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | − | 6.92820i | 0.164399 | − | 0.284747i | ||||
\(593\) | 10.3923 | − | 18.0000i | 0.426761 | − | 0.739171i | −0.569822 | − | 0.821768i | \(-0.692988\pi\) |
0.996583 | + | 0.0825966i | \(0.0263213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.9904 | − | 7.50000i | 0.532107 | − | 0.307212i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0000i | 1.22577i | 0.790173 | + | 0.612883i | \(0.209990\pi\) | ||||
−0.790173 | + | 0.612883i | \(0.790010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0000 | − | 17.3205i | 1.22373 | − | 0.706518i | 0.258015 | − | 0.966141i | \(-0.416931\pi\) |
0.965710 | + | 0.259623i | \(0.0835982\pi\) | |||||||
\(602\) | 3.46410 | − | 10.0000i | 0.141186 | − | 0.407570i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.5000 | + | 19.9186i | −0.467928 | + | 0.810476i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50000 | − | 2.59808i | 0.182649 | − | 0.105453i | −0.405887 | − | 0.913923i | \(-0.633038\pi\) |
0.588537 | + | 0.808470i | \(0.299704\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.1769 | − | 18.0000i | −1.26128 | − | 0.728202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.00000 | + | 8.66025i | 0.201948 | + | 0.349784i | 0.949156 | − | 0.314806i | \(-0.101939\pi\) |
−0.747208 | + | 0.664590i | \(0.768606\pi\) | |||||||
\(614\) | 17.3205 | 0.698999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50000 | − | 7.79423i | −0.0604367 | − | 0.314038i | ||||
\(617\) | 15.5885 | + | 9.00000i | 0.627568 | + | 0.362326i | 0.779809 | − | 0.626017i | \(-0.215316\pi\) |
−0.152242 | + | 0.988343i | \(0.548649\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.0000 | − | 17.3205i | −1.20580 | − | 0.696170i | −0.243962 | − | 0.969785i | \(-0.578447\pi\) |
−0.961839 | + | 0.273615i | \(0.911781\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 31.1769i | − | 1.25008i | ||||||
\(623\) | −5.19615 | − | 27.0000i | −0.208179 | − | 1.08173i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −20.7846 | −0.830720 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 10.3923i | − | 0.414698i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0000 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(632\) | 13.0000i | 0.517112i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | 0.357436 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0000 | + | 19.0526i | −0.594322 | + | 0.754890i | ||||
\(638\) | 27.0000i | 1.06894i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.3731 | + | 21.0000i | 1.43665 | + | 0.829450i | 0.997615 | − | 0.0690201i | \(-0.0219873\pi\) |
0.439034 | + | 0.898470i | \(0.355321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.00000 | + | 1.73205i | 0.118308 | + | 0.0683054i | 0.557986 | − | 0.829850i | \(-0.311574\pi\) |
−0.439678 | + | 0.898155i | \(0.644907\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.19615 | − | 9.00000i | −0.204282 | − | 0.353827i | 0.745622 | − | 0.666369i | \(-0.232153\pi\) |
−0.949904 | + | 0.312543i | \(0.898819\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | + | 7.79423i | 0.529921 | + | 0.305950i | ||||
\(650\) | −8.66025 | − | 15.0000i | −0.339683 | − | 0.588348i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.00000 | + | 8.66025i | −0.195815 | + | 0.339162i | ||||
\(653\) | 25.9808 | − | 15.0000i | 1.01671 | − | 0.586995i | 0.103558 | − | 0.994623i | \(-0.466977\pi\) |
0.913148 | + | 0.407628i | \(0.133644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.19615 | + | 9.00000i | −0.202876 | + | 0.351391i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.0000 | + | 20.7846i | 0.701713 | + | 0.810268i | ||||
\(659\) | −12.9904 | + | 7.50000i | −0.506033 | + | 0.292159i | −0.731202 | − | 0.682161i | \(-0.761040\pi\) |
0.225168 | + | 0.974320i | \(0.427707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.3923i | 0.404214i | 0.979363 | + | 0.202107i | \(0.0647788\pi\) | ||||
−0.979363 | + | 0.202107i | \(0.935221\pi\) | |||||||
\(662\) | 28.0000i | 1.08825i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.50000 | − | 2.59808i | 0.174634 | − | 0.100825i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 5.19615 | − | 9.00000i | 0.201045 | − | 0.348220i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.7846 | + | 36.0000i | −0.802381 | + | 1.38976i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0000 | + | 22.5167i | 0.501113 | + | 0.867953i | 0.999999 | + | 0.00128586i | \(0.000409302\pi\) |
−0.498886 | + | 0.866668i | \(0.666257\pi\) | |||||||
\(674\) | −11.2583 | − | 6.50000i | −0.433655 | − | 0.250371i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | + | 0.866025i | 0.0192308 | + | 0.0333087i | ||||
\(677\) | 15.5885 | 0.599113 | 0.299557 | − | 0.954079i | \(-0.403161\pi\) | ||||
0.299557 | + | 0.954079i | \(0.403161\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.50000 | + | 21.6506i | −0.287824 | + | 0.830875i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.50000 | + | 2.59808i | 0.172314 | + | 0.0994855i | ||||
\(683\) | 18.1865 | − | 10.5000i | 0.695888 | − | 0.401771i | −0.109926 | − | 0.993940i | \(-0.535061\pi\) |
0.805814 | + | 0.592168i | \(0.201728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.5885 | − | 10.0000i | 0.595170 | − | 0.381802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | −20.7846 | −0.791831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13.8564i | − | 0.527123i | −0.964643 | − | 0.263561i | \(-0.915103\pi\) | ||
0.964643 | − | 0.263561i | \(-0.0848971\pi\) | |||||||
\(692\) | 25.9808 | 0.987640 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.00000 | −0.113878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −13.8564 | − | 24.0000i | −0.524473 | − | 0.908413i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.50000 | + | 12.9904i | 0.0944911 | + | 0.490990i | ||||
\(701\) | − | 6.00000i | − | 0.226617i | −0.993560 | − | 0.113308i | \(-0.963855\pi\) | ||
0.993560 | − | 0.113308i | \(-0.0361448\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.59808 | − | 1.50000i | −0.0979187 | − | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00000 | + | 5.19615i | 0.338719 | + | 0.195560i | ||||
\(707\) | 2.59808 | + | 13.5000i | 0.0977107 | + | 0.507720i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | 0.150223 | 0.0751116 | − | 0.997175i | \(-0.476069\pi\) | ||||
0.0751116 | + | 0.997175i | \(0.476069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.00000 | − | 5.19615i | −0.337289 | − | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.79423 | + | 4.50000i | −0.291284 | + | 0.168173i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.00000 | + | 10.3923i | −0.223918 | + | 0.387837i | ||||
\(719\) | 5.19615 | − | 9.00000i | 0.193784 | − | 0.335643i | −0.752717 | − | 0.658344i | \(-0.771257\pi\) |
0.946501 | + | 0.322700i | \(0.104591\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | − | 43.3013i | 0.558629 | − | 1.61262i | ||||
\(722\) | 16.4545 | − | 9.50000i | 0.612372 | − | 0.353553i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 20.7846i | − | 0.772454i | ||||||
\(725\) | − | 45.0000i | − | 1.67126i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.0000 | + | 12.1244i | −0.778847 | + | 0.449667i | −0.836021 | − | 0.548697i | \(-0.815124\pi\) |
0.0571746 | + | 0.998364i | \(0.481791\pi\) | |||||||
\(728\) | 1.73205 | + | 9.00000i | 0.0641941 | + | 0.333562i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0000 | + | 6.92820i | −0.443230 | + | 0.255899i | −0.704967 | − | 0.709240i | \(-0.749038\pi\) |
0.261737 | + | 0.965139i | \(0.415705\pi\) | |||||||
\(734\) | 5.19615 | − | 9.00000i | 0.191793 | − | 0.332196i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.19615 | + | 3.00000i | 0.191403 | + | 0.110506i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.0000 | − | 22.5167i | −0.478213 | − | 0.828289i | 0.521475 | − | 0.853266i | \(-0.325382\pi\) |
−0.999688 | + | 0.0249776i | \(0.992049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.0000 | + | 5.19615i | 0.550667 | + | 0.190757i | ||||
\(743\) | 5.19615 | + | 3.00000i | 0.190628 | + | 0.110059i | 0.592277 | − | 0.805735i | \(-0.298229\pi\) |
−0.401648 | + | 0.915794i | \(0.631563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.46410 | + | 2.00000i | −0.126830 | + | 0.0732252i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.1769 | + | 6.00000i | −1.13918 | + | 0.219235i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00000 | − | 3.46410i | −0.0729810 | − | 0.126407i | 0.827225 | − | 0.561870i | \(-0.189918\pi\) |
−0.900207 | + | 0.435463i | \(0.856585\pi\) | |||||||
\(752\) | 10.3923 | 0.378968 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 31.1769i | − | 1.13540i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | − | 26.0000i | − | 0.944363i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.7846 | + | 36.0000i | 0.753442 | + | 1.30500i | 0.946145 | + | 0.323742i | \(0.104941\pi\) |
−0.192704 | + | 0.981257i | \(0.561726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0000 | + | 6.92820i | 0.724049 | + | 0.250818i | ||||
\(764\) | 6.00000i | 0.217072i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | − | 10.3923i | 0.650366 | − | 0.375489i | ||||
\(767\) | −15.5885 | − | 9.00000i | −0.562867 | − | 0.324971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5000 | + | 7.79423i | 0.486822 | + | 0.281067i | 0.723255 | − | 0.690581i | \(-0.242645\pi\) |
−0.236433 | + | 0.971648i | \(0.575978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.0000 | 0.395899 | ||||||||
\(773\) | 20.7846 | + | 36.0000i | 0.747570 | + | 1.29483i | 0.948984 | + | 0.315324i | \(0.102113\pi\) |
−0.201414 | + | 0.979506i | \(0.564554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.50000 | − | 4.33013i | −0.269408 | − | 0.155543i | ||||
\(776\) | 4.33013 | + | 7.50000i | 0.155443 | + | 0.269234i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.50000 | + | 7.79423i | −0.161333 | + | 0.279437i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | + | 31.1769i | −0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.2487i | − | 0.864373i | −0.901784 | − | 0.432187i | \(-0.857742\pi\) | ||
0.901784 | − | 0.432187i | \(-0.142258\pi\) | |||||||
\(788\) | − | 15.0000i | − | 0.534353i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.1769 | − | 6.00000i | 1.10852 | − | 0.213335i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | − | 41.5692i | 0.852265 | − | 1.47617i | ||||
\(794\) | −12.1244 | + | 21.0000i | −0.430277 | + | 0.745262i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.50000 | + | 0.866025i | −0.0531661 | + | 0.0306955i | ||||
\(797\) | −7.79423 | + | 13.5000i | −0.276086 | + | 0.478195i | −0.970408 | − | 0.241469i | \(-0.922371\pi\) |
0.694323 | + | 0.719664i | \(0.255704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.33013 | + | 2.50000i | 0.153093 | + | 0.0883883i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.0000 | − | 25.9808i | −0.529668 | − | 0.917413i | ||||
\(803\) | 15.5885 | 0.550105 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.19615 | − | 3.00000i | −0.183027 | − | 0.105670i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.50000 | + | 2.59808i | 0.158309 | + | 0.0914000i | ||||
\(809\) | −5.19615 | + | 3.00000i | −0.182687 | + | 0.105474i | −0.588555 | − | 0.808458i | \(-0.700303\pi\) |
0.405868 | + | 0.913932i | \(0.366969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.3923i | − | 0.364923i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182462i | \(-0.0584065\pi\) | |||||||
\(812\) | −7.79423 | + | 22.5000i | −0.273524 | + | 0.789595i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.92820 | −0.242239 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.0000i | 1.15171i | 0.817553 | + | 0.575854i | \(0.195330\pi\) | ||||
−0.817553 | + | 0.575854i | \(0.804670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0000 | 0.383436 | 0.191718 | − | 0.981450i | \(-0.438594\pi\) | ||||
0.191718 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(824\) | −8.66025 | − | 15.0000i | −0.301694 | − | 0.522550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.00000 | + | 10.3923i | 0.313150 | + | 0.361595i | ||||
\(827\) | − | 3.00000i | − | 0.104320i | −0.998639 | − | 0.0521601i | \(-0.983389\pi\) | ||
0.998639 | − | 0.0521601i | \(-0.0166106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.0000 | + | 15.5885i | −0.937749 | + | 0.541409i | −0.889254 | − | 0.457414i | \(-0.848776\pi\) |
−0.0484949 | + | 0.998823i | \(0.515442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.00000 | + | 1.73205i | 0.104006 | + | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.0000 | − | 15.5885i | −0.932700 | − | 0.538494i | ||||
\(839\) | −10.3923 | − | 18.0000i | −0.358782 | − | 0.621429i | 0.628975 | − | 0.777425i | \(-0.283475\pi\) |
−0.987758 | + | 0.155996i | \(0.950141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0000 | − | 45.0333i | 0.896552 | − | 1.55287i | ||||
\(842\) | −8.66025 | + | 5.00000i | −0.298452 | + | 0.172311i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.00000 | + | 1.73205i | −0.0344214 | + | 0.0596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | − | 1.73205i | −0.171802 | − | 0.0595140i | ||||
\(848\) | 5.19615 | − | 3.00000i | 0.178437 | − | 0.103020i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.00000 | − | 5.19615i | 0.308154 | − | 0.177913i | −0.337946 | − | 0.941165i | \(-0.609732\pi\) |
0.646100 | + | 0.763253i | \(0.276399\pi\) | |||||||
\(854\) | −27.7128 | + | 24.0000i | −0.948313 | + | 0.821263i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | −5.19615 | + | 9.00000i | −0.177497 | + | 0.307434i | −0.941023 | − | 0.338344i | \(-0.890133\pi\) |
0.763525 | + | 0.645778i | \(0.223467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.0000 | − | 24.2487i | 1.43302 | − | 0.827355i | 0.435671 | − | 0.900106i | \(-0.356511\pi\) |
0.997350 | + | 0.0727505i | \(0.0231777\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.00000 | + | 15.5885i | 0.306541 | + | 0.530945i | ||||
\(863\) | −5.19615 | − | 3.00000i | −0.176879 | − | 0.102121i | 0.408946 | − | 0.912558i | \(-0.365896\pi\) |
−0.585826 | + | 0.810437i | \(0.699230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.1244 | −0.412002 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.00000 | + | 3.46410i | 0.101827 | + | 0.117579i | ||||
\(869\) | −33.7750 | − | 19.5000i | −1.14574 | − | 0.661492i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | − | 3.46410i | −0.203302 | − | 0.117377i | ||||
\(872\) | 6.92820 | − | 4.00000i | 0.234619 | − | 0.135457i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00000 | − | 1.73205i | −0.0337676 | − | 0.0584872i | 0.848648 | − | 0.528958i | \(-0.177417\pi\) |
−0.882415 | + | 0.470471i | \(0.844084\pi\) | |||||||
\(878\) | 15.5885 | 0.526085 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1769 | −1.05038 | −0.525188 | − | 0.850986i | \(-0.676005\pi\) | ||||
−0.525188 | + | 0.850986i | \(0.676005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.0000 | −0.907083 | ||||||||
\(887\) | −15.5885 | − | 27.0000i | −0.523409 | − | 0.906571i | −0.999629 | − | 0.0272449i | \(-0.991327\pi\) |
0.476220 | − | 0.879326i | \(-0.342007\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0000 | − | 13.8564i | 0.536623 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.50000 | + | 2.59808i | −0.150671 | + | 0.0869900i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.73205 | − | 2.00000i | −0.0578638 | − | 0.0668153i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.0000 | −1.00111 | ||||||||
\(899\) | −7.79423 | − | 13.5000i | −0.259952 | − | 0.450250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −15.5885 | − | 27.0000i | −0.519039 | − | 0.899002i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | − | 10.3923i | 0.199557 | − | 0.345643i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.0000 | + | 19.0526i | −0.365249 | + | 0.632630i | −0.988816 | − | 0.149140i | \(-0.952349\pi\) |
0.623567 | + | 0.781770i | \(0.285683\pi\) | |||||||
\(908\) | 12.9904 | − | 22.5000i | 0.431101 | − | 0.746689i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.1769 | + | 18.0000i | −1.03294 | + | 0.596367i | −0.917825 | − | 0.396986i | \(-0.870056\pi\) |
−0.115113 | + | 0.993352i | \(0.536723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5885i | 0.515903i | ||||||||
\(914\) | 22.0000i | 0.727695i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.00000 | − | 3.46410i | 0.198246 | − | 0.114457i | ||||
\(917\) | −38.9711 | − | 13.5000i | −1.28694 | − | 0.445809i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.5000 | − | 30.3109i | 0.577272 | − | 0.999864i | −0.418519 | − | 0.908208i | \(-0.637451\pi\) |
0.995791 | − | 0.0916559i | \(-0.0292160\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.5000 | + | 7.79423i | −0.444599 | + | 0.256689i | ||||
\(923\) | 20.7846 | − | 36.0000i | 0.684134 | − | 1.18495i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | − | 34.6410i | −0.657596 | − | 1.13899i | ||||
\(926\) | −4.33013 | − | 2.50000i | −0.142297 | − | 0.0821551i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.50000 | + | 7.79423i | 0.147720 | + | 0.255858i | ||||
\(929\) | −41.5692 | −1.36384 | −0.681921 | − | 0.731426i | \(-0.738855\pi\) | ||||
−0.681921 | + | 0.731426i | \(0.738855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.5885 | − | 9.00000i | −0.510617 | − | 0.294805i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.50000 | − | 2.59808i | −0.147244 | − | 0.0850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 34.6410i | − | 1.13167i | −0.824518 | − | 0.565836i | \(-0.808553\pi\) | ||
0.824518 | − | 0.565836i | \(-0.191447\pi\) | |||||||
\(938\) | 3.46410 | + | 4.00000i | 0.113107 | + | 0.130605i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.19615 | 0.169390 | 0.0846949 | − | 0.996407i | \(-0.473008\pi\) | ||||
0.0846949 | + | 0.996407i | \(0.473008\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 5.19615 | 0.169120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | 9.00000i | 0.292461i | 0.989251 | + | 0.146230i | \(0.0467141\pi\) | ||||
−0.989251 | + | 0.146230i | \(0.953286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | −0.584305 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.0000i | − | 0.583077i | −0.956559 | − | 0.291539i | \(-0.905833\pi\) | ||
0.956559 | − | 0.291539i | \(-0.0941672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.3923 | − | 6.00000i | −0.336111 | − | 0.194054i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.00000 | + | 5.19615i | 0.290777 | + | 0.167880i | ||||
\(959\) | −31.1769 | + | 6.00000i | −1.00676 | + | 0.193750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | −13.8564 | − | 24.0000i | −0.446748 | − | 0.773791i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.5000 | − | 6.06218i | −0.338182 | − | 0.195250i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0000 | + | 48.4974i | −0.900419 | + | 1.55957i | −0.0734686 | + | 0.997298i | \(0.523407\pi\) |
−0.826951 | + | 0.562274i | \(0.809926\pi\) | |||||||
\(968\) | −1.73205 | + | 1.00000i | −0.0556702 | + | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5885 | + | 27.0000i | −0.500257 | + | 0.866471i | 0.499743 | + | 0.866174i | \(0.333428\pi\) |
−1.00000 | 0.000297246i | \(0.999905\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.0000 | + | 3.46410i | −0.577054 | + | 0.111054i | ||||
\(974\) | −9.52628 | + | 5.50000i | −0.305242 | + | 0.176231i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.8564i | 0.443533i | ||||||||
\(977\) | − | 18.0000i | − | 0.575871i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) | ||
0.957650 | − | 0.287936i | \(-0.0929689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0000 | − | 15.5885i | 0.862924 | − | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.0000 | + | 31.1769i | −0.574403 | + | 0.994895i | ||||
\(983\) | 10.3923 | − | 18.0000i | 0.331463 | − | 0.574111i | −0.651336 | − | 0.758790i | \(-0.725791\pi\) |
0.982799 | + | 0.184679i | \(0.0591244\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | + | 6.92820i | 0.127064 | + | 0.220082i | 0.922538 | − | 0.385906i | \(-0.126111\pi\) |
−0.795474 | + | 0.605988i | \(0.792778\pi\) | |||||||
\(992\) | 1.73205 | 0.0549927 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −24.0000 | + | 20.7846i | −0.761234 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0000 | − | 19.0526i | −1.04512 | − | 0.603401i | −0.123841 | − | 0.992302i | \(-0.539521\pi\) |
−0.921279 | + | 0.388901i | \(0.872855\pi\) | |||||||
\(998\) | 13.8564 | − | 8.00000i | 0.438617 | − | 0.253236i | ||||
\(999\) | 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 | 1134.2.l.d.215.2 | 4 | ||
3.2 | odd | 2 | inner | 1134.2.l.d.215.1 | 4 | ||
7.3 | odd | 6 | 1134.2.t.a.1025.1 | 4 | |||
9.2 | odd | 6 | 1134.2.t.a.593.1 | 4 | |||
9.4 | even | 3 | 378.2.k.a.215.1 | ✓ | 4 | ||
9.5 | odd | 6 | 378.2.k.a.215.2 | yes | 4 | ||
9.7 | even | 3 | 1134.2.t.a.593.2 | 4 | |||
21.17 | even | 6 | 1134.2.t.a.1025.2 | 4 | |||
63.5 | even | 6 | 2646.2.d.c.2645.1 | 4 | |||
63.23 | odd | 6 | 2646.2.d.c.2645.2 | 4 | |||
63.31 | odd | 6 | 378.2.k.a.269.2 | yes | 4 | ||
63.38 | even | 6 | inner | 1134.2.l.d.269.1 | 4 | ||
63.40 | odd | 6 | 2646.2.d.c.2645.3 | 4 | |||
63.52 | odd | 6 | inner | 1134.2.l.d.269.2 | 4 | ||
63.58 | even | 3 | 2646.2.d.c.2645.4 | 4 | |||
63.59 | even | 6 | 378.2.k.a.269.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.a.215.1 | ✓ | 4 | 9.4 | even | 3 | ||
378.2.k.a.215.2 | yes | 4 | 9.5 | odd | 6 | ||
378.2.k.a.269.1 | yes | 4 | 63.59 | even | 6 | ||
378.2.k.a.269.2 | yes | 4 | 63.31 | odd | 6 | ||
1134.2.l.d.215.1 | 4 | 3.2 | odd | 2 | inner | ||
1134.2.l.d.215.2 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.l.d.269.1 | 4 | 63.38 | even | 6 | inner | ||
1134.2.l.d.269.2 | 4 | 63.52 | odd | 6 | inner | ||
1134.2.t.a.593.1 | 4 | 9.2 | odd | 6 | |||
1134.2.t.a.593.2 | 4 | 9.7 | even | 3 | |||
1134.2.t.a.1025.1 | 4 | 7.3 | odd | 6 | |||
1134.2.t.a.1025.2 | 4 | 21.17 | even | 6 | |||
2646.2.d.c.2645.1 | 4 | 63.5 | even | 6 | |||
2646.2.d.c.2645.2 | 4 | 63.23 | odd | 6 | |||
2646.2.d.c.2645.3 | 4 | 63.40 | odd | 6 | |||
2646.2.d.c.2645.4 | 4 | 63.58 | even | 3 |