Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\), degree \(4\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 1993.2 | ||
Character | \(\chi\) | \(=\) | 2100.1993 |
Dual form | 2100.2.ce.c.157.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.48036 | + | 0.920762i | 0.937489 | + | 0.348015i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.65754 | + | 2.87094i | 0.499766 | + | 0.865620i | 1.00000 | 0.000270562i | \(-8.61226e-5\pi\) | |
−0.500234 | + | 0.865890i | \(0.666753\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.05702 | + | 1.05702i | −0.293163 | + | 0.293163i | −0.838329 | − | 0.545165i | \(-0.816467\pi\) |
0.545165 | + | 0.838329i | \(0.316467\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.858003 | + | 3.20211i | −0.208096 | + | 0.776626i | 0.780387 | + | 0.625297i | \(0.215022\pi\) |
−0.988483 | + | 0.151329i | \(0.951645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.10280 | + | 1.91011i | −0.253001 | + | 0.438210i | −0.964351 | − | 0.264628i | \(-0.914751\pi\) |
0.711350 | + | 0.702838i | \(0.248084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.15754 | − | 1.53135i | −0.470813 | − | 0.334169i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.83153 | + | 1.83050i | −1.42447 | + | 0.381687i | −0.887069 | − | 0.461638i | \(-0.847262\pi\) |
−0.537405 | + | 0.843324i | \(0.680595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56249 | − | 0.902106i | 0.280632 | − | 0.162023i | −0.353077 | − | 0.935594i | \(-0.614865\pi\) |
0.633710 | + | 0.773571i | \(0.281531\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.858003 | − | 3.20211i | −0.149359 | − | 0.557416i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.448288 | + | 1.67303i | 0.0736980 | + | 0.275045i | 0.992935 | − | 0.118660i | \(-0.0378599\pi\) |
−0.919237 | + | 0.393705i | \(0.871193\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.29457 | − | 0.747423i | 0.207298 | − | 0.119683i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.33066i | 0.207813i | 0.994587 | + | 0.103907i | \(0.0331343\pi\) | ||||
−0.994587 | + | 0.103907i | \(0.966866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.84446 | − | 6.84446i | −1.04377 | − | 1.04377i | −0.998997 | − | 0.0447733i | \(-0.985743\pi\) |
−0.0447733 | − | 0.998997i | \(-0.514257\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.17799 | + | 1.11949i | −0.609423 | + | 0.163294i | −0.550315 | − | 0.834957i | \(-0.685492\pi\) |
−0.0591082 | + | 0.998252i | \(0.518826\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.30439 | + | 4.56765i | 0.757771 | + | 0.652521i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.65754 | − | 2.87094i | 0.232101 | − | 0.402011i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.797308 | − | 2.97559i | 0.109519 | − | 0.408729i | −0.889300 | − | 0.457324i | \(-0.848808\pi\) |
0.998819 | + | 0.0485954i | \(0.0154745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.55960 | − | 1.55960i | 0.206574 | − | 0.206574i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.665328 | + | 1.15238i | 0.0866183 | + | 0.150027i | 0.906080 | − | 0.423107i | \(-0.139061\pi\) |
−0.819461 | + | 0.573134i | \(0.805727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.62499 | − | 2.67024i | −0.592169 | − | 0.341889i | 0.173786 | − | 0.984783i | \(-0.444400\pi\) |
−0.765955 | + | 0.642895i | \(0.777733\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.68768 | + | 2.03758i | 0.212627 | + | 0.256712i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.13045 | − | 0.570853i | −0.260276 | − | 0.0697408i | 0.126321 | − | 0.991989i | \(-0.459683\pi\) |
−0.386597 | + | 0.922249i | \(0.626350\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.07253 | 0.851432 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.98969 | 0.592167 | 0.296084 | − | 0.955162i | \(-0.404319\pi\) | ||||
0.296084 | + | 0.955162i | \(0.404319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2580 | − | 2.74861i | −1.20060 | − | 0.321701i | −0.397535 | − | 0.917587i | \(-0.630134\pi\) |
−0.803069 | + | 0.595886i | \(0.796801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.46784 | + | 8.64716i | 0.167276 | + | 0.985435i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.8000 | + | 7.96745i | 1.55262 | + | 0.896408i | 0.997927 | + | 0.0643564i | \(0.0204995\pi\) |
0.554698 | + | 0.832052i | \(0.312834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.1150 | + | 10.1150i | −1.11026 | + | 1.11026i | −0.117151 | + | 0.993114i | \(0.537376\pi\) |
−0.993114 | + | 0.117151i | \(0.962624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.87094 | + | 4.97261i | −0.304319 | + | 0.527095i | −0.977109 | − | 0.212738i | \(-0.931762\pi\) |
0.672791 | + | 0.739833i | \(0.265095\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.59504 | + | 1.64852i | −0.376863 | + | 0.172812i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.74273 | + | 0.466964i | −0.180713 | + | 0.0484220i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.53553 | − | 3.53553i | −0.358979 | − | 0.358979i | 0.504457 | − | 0.863437i | \(-0.331693\pi\) |
−0.863437 | + | 0.504457i | \(0.831693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.31507i | 0.333177i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2774 | + | 9.39774i | −1.61966 | + | 0.935110i | −0.632651 | + | 0.774437i | \(0.718033\pi\) |
−0.987008 | + | 0.160673i | \(0.948633\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.57134 | + | 9.59638i | 0.253362 | + | 0.945559i | 0.968994 | + | 0.247082i | \(0.0794719\pi\) |
−0.715633 | + | 0.698477i | \(0.753861\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.86463 | + | 18.1550i | 0.470281 | + | 1.75511i | 0.638757 | + | 0.769409i | \(0.279449\pi\) |
−0.168475 | + | 0.985706i | \(0.553884\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0897 | − | 7.55734i | 1.25377 | − | 0.723862i | 0.281910 | − | 0.959441i | \(-0.409032\pi\) |
0.971855 | + | 0.235579i | \(0.0756986\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.73205i | − | 0.164399i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.34847 | − | 7.34847i | −0.691286 | − | 0.691286i | 0.271229 | − | 0.962515i | \(-0.412570\pi\) |
−0.962515 | + | 0.271229i | \(0.912570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.44391 | + | 0.386895i | −0.133490 | + | 0.0357684i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.07654 | + | 7.15238i | −0.465366 | + | 0.655658i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.00515410 | − | 0.00892716i | 0.000468554 | − | 0.000811560i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.344399 | − | 1.28531i | 0.0310534 | − | 0.115893i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.83640 | + | 7.83640i | −0.695368 | + | 0.695368i | −0.963408 | − | 0.268040i | \(-0.913624\pi\) |
0.268040 | + | 0.963408i | \(0.413624\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.83976 | + | 8.38272i | 0.426117 | + | 0.738057i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3048 | + | 6.52681i | 0.987702 | + | 0.570250i | 0.904586 | − | 0.426290i | \(-0.140180\pi\) |
0.0831152 | + | 0.996540i | \(0.473513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.49411 | + | 3.72235i | −0.389689 | + | 0.322769i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.40216 | + | 2.51930i | 0.803281 | + | 0.215238i | 0.637024 | − | 0.770844i | \(-0.280165\pi\) |
0.166257 | + | 0.986082i | \(0.446832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.22383 | −0.782355 | −0.391177 | − | 0.920315i | \(-0.627932\pi\) | ||||
−0.391177 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.32538 | 0.364263 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.78666 | − | 1.28258i | −0.400281 | − | 0.107255i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.94146 | − | 5.78489i | −0.325086 | − | 0.477129i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.41665 | − | 1.97261i | −0.279903 | − | 0.161602i | 0.353476 | − | 0.935443i | \(-0.384999\pi\) |
−0.633380 | + | 0.773841i | \(0.718333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.84246 | + | 3.19124i | 0.149938 | + | 0.259700i | 0.931204 | − | 0.364498i | \(-0.118759\pi\) |
−0.781267 | + | 0.624198i | \(0.785426\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.34411 | + | 2.34411i | −0.189510 | + | 0.189510i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.97483 | − | 7.37015i | 0.157608 | − | 0.588202i | −0.841260 | − | 0.540631i | \(-0.818185\pi\) |
0.998868 | − | 0.0475707i | \(-0.0151479\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.54028 | + | 2.66784i | −0.122152 | + | 0.211574i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.6301 | − | 1.74991i | −1.46826 | − | 0.137912i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.2574 | − | 4.62412i | 1.35171 | − | 0.362189i | 0.490943 | − | 0.871192i | \(-0.336652\pi\) |
0.860765 | + | 0.509003i | \(0.169986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5344 | + | 14.5344i | 1.12471 | + | 1.12471i | 0.991024 | + | 0.133681i | \(0.0426796\pi\) |
0.133681 | + | 0.991024i | \(0.457320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7654i | 0.828110i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.91011 | + | 1.10280i | −0.146070 | + | 0.0843335i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.163092 | − | 0.608669i | −0.0123997 | − | 0.0462763i | 0.959449 | − | 0.281883i | \(-0.0909590\pi\) |
−0.971849 | + | 0.235607i | \(0.924292\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.344399 | − | 1.28531i | −0.0258866 | − | 0.0966101i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.3843 | + | 8.30476i | −1.07513 | + | 0.620727i | −0.929579 | − | 0.368624i | \(-0.879829\pi\) |
−0.145552 | + | 0.989351i | \(0.546496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.6606i | − | 1.16404i | −0.813173 | − | 0.582022i | \(-0.802262\pi\) | ||
0.813173 | − | 0.582022i | \(-0.197738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.77629 | + | 3.77629i | 0.279151 | + | 0.279151i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.6152 | + | 2.84434i | −0.776262 | + | 0.207999i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.10280 | − | 2.40496i | −0.0802172 | − | 0.174935i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.47776 | + | 14.6839i | −0.613429 | + | 1.06249i | 0.377229 | + | 0.926120i | \(0.376877\pi\) |
−0.990658 | + | 0.136370i | \(0.956456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.466964 | + | 1.74273i | −0.0336128 | + | 0.125445i | −0.980694 | − | 0.195550i | \(-0.937351\pi\) |
0.947081 | + | 0.320995i | \(0.104017\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.11110 | − | 6.11110i | 0.435398 | − | 0.435398i | −0.455062 | − | 0.890460i | \(-0.650383\pi\) |
0.890460 | + | 0.455062i | \(0.150383\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.40667 | + | 16.2928i | 0.666821 | + | 1.15497i | 0.978788 | + | 0.204875i | \(0.0656788\pi\) |
−0.311967 | + | 0.950093i | \(0.600988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.91011 | + | 1.10280i | 0.134729 | + | 0.0777858i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.83153 | − | 1.83050i | −0.474825 | − | 0.127229i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.31174 | −0.505764 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.69524 | 0.323233 | 0.161617 | − | 0.986854i | \(-0.448329\pi\) | ||||
0.161617 | + | 0.986854i | \(0.448329\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.81967 | − | 1.29143i | −0.330238 | − | 0.0884871i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.70617 | − | 0.798865i | 0.319476 | − | 0.0542305i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.19704 | + | 5.30992i | 0.621479 | + | 0.358811i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47776 | − | 4.29161i | −0.166672 | − | 0.288685i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.56268 | + | 7.56268i | −0.506434 | + | 0.506434i | −0.913430 | − | 0.406996i | \(-0.866576\pi\) |
0.406996 | + | 0.913430i | \(0.366576\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.61761 | + | 6.03701i | −0.107365 | + | 0.400690i | −0.998603 | − | 0.0528454i | \(-0.983171\pi\) |
0.891238 | + | 0.453536i | \(0.149838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.51000 | − | 13.0077i | 0.496275 | − | 0.859573i | −0.503716 | − | 0.863869i | \(-0.668034\pi\) |
0.999991 | + | 0.00429607i | \(0.00136748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.820225 | − | 8.73242i | 0.0539668 | − | 0.574551i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.5844 | − | 4.17583i | 1.02097 | − | 0.273568i | 0.290763 | − | 0.956795i | \(-0.406091\pi\) |
0.730206 | + | 0.683227i | \(0.239424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.2677 | − | 11.2677i | −0.731914 | − | 0.731914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.6404i | − | 1.65854i | −0.558846 | − | 0.829271i | \(-0.688756\pi\) | ||
0.558846 | − | 0.829271i | \(-0.311244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | + | 4.33013i | −0.483117 | + | 0.278928i | −0.721715 | − | 0.692191i | \(-0.756646\pi\) |
0.238597 | + | 0.971119i | \(0.423312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.853338 | − | 3.18470i | −0.0542966 | − | 0.202638i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.3883 | − | 7.15238i | 0.785076 | − | 0.453264i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.239219i | − | 0.0150994i | −0.999972 | − | 0.00754969i | \(-0.997597\pi\) | ||
0.999972 | − | 0.00754969i | \(-0.00240316\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.5788 | − | 16.5788i | −1.04230 | − | 1.04230i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.63045 | − | 2.31252i | 0.538353 | − | 0.144251i | 0.0206102 | − | 0.999788i | \(-0.493439\pi\) |
0.517743 | + | 0.855536i | \(0.326772\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.428549 | + | 4.56249i | −0.0266287 | + | 0.283500i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.859222 | − | 3.20666i | 0.0529819 | − | 0.197731i | −0.934362 | − | 0.356325i | \(-0.884029\pi\) |
0.987344 | + | 0.158594i | \(0.0506961\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.06012 | − | 4.06012i | 0.248475 | − | 0.248475i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4783 | − | 21.6131i | −0.760816 | − | 1.31777i | −0.942431 | − | 0.334402i | \(-0.891466\pi\) |
0.181615 | − | 0.983370i | \(-0.441867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.0702 | + | 14.4743i | 1.52291 | + | 0.879250i | 0.999633 | + | 0.0270851i | \(0.00862250\pi\) |
0.523273 | + | 0.852165i | \(0.324711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.89921 | − | 0.661884i | 0.235991 | − | 0.0400591i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.72549 | − | 0.462343i | −0.103675 | − | 0.0277795i | 0.206609 | − | 0.978424i | \(-0.433757\pi\) |
−0.310283 | + | 0.950644i | \(0.600424\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.80421 | 0.108015 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.05479 | 0.122578 | 0.0612892 | − | 0.998120i | \(-0.480479\pi\) | ||||
0.0612892 | + | 0.998120i | \(0.480479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.8828 | + | 6.13143i | 1.36024 | + | 0.364476i | 0.863905 | − | 0.503654i | \(-0.168011\pi\) |
0.496337 | + | 0.868130i | \(0.334678\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.22522 | + | 3.30051i | −0.0723223 | + | 0.194823i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.20508 | + | 3.00515i | 0.306181 | + | 0.176774i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.50000 | + | 4.33013i | 0.146553 | + | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.1305 | + | 18.1305i | −1.05920 | + | 1.05920i | −0.0610633 | + | 0.998134i | \(0.519449\pi\) |
−0.998134 | + | 0.0610633i | \(0.980551\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.858003 | − | 3.20211i | 0.0497864 | − | 0.185805i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.28617 | − | 9.15591i | 0.305707 | − | 0.529500i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6746 | − | 23.2789i | −0.615275 | − | 1.34177i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.1550 | − | 4.86463i | 1.04298 | − | 0.279466i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6572 | − | 18.6572i | −1.06482 | − | 1.06482i | −0.997748 | − | 0.0670748i | \(-0.978633\pi\) |
−0.0670748 | − | 0.997748i | \(-0.521367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 9.93490i | − | 0.565177i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.42975 | − | 4.86692i | 0.478007 | − | 0.275978i | −0.241578 | − | 0.970381i | \(-0.577665\pi\) |
0.719586 | + | 0.694404i | \(0.244332\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.29860 | − | 12.3106i | −0.186448 | − | 0.695833i | −0.994316 | − | 0.106470i | \(-0.966045\pi\) |
0.807868 | − | 0.589364i | \(-0.200621\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.97314 | + | 18.5600i | 0.279319 | + | 1.04243i | 0.952891 | + | 0.303312i | \(0.0980925\pi\) |
−0.673572 | + | 0.739122i | \(0.735241\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 18.7955i | − | 1.04906i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.17018 | − | 5.17018i | −0.287677 | − | 0.287677i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.5997 | + | 3.91197i | −0.807363 | + | 0.216332i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3937 | − | 1.07020i | −0.628156 | − | 0.0590019i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.462297 | − | 0.800723i | 0.0254102 | − | 0.0440117i | −0.853041 | − | 0.521844i | \(-0.825244\pi\) |
0.878451 | + | 0.477833i | \(0.158577\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.448288 | + | 1.67303i | −0.0245660 | + | 0.0916816i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7455 | − | 21.7455i | 1.18455 | − | 1.18455i | 0.206001 | − | 0.978552i | \(-0.433955\pi\) |
0.978552 | − | 0.206001i | \(-0.0660451\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.19615 | + | 9.00000i | 0.282216 | + | 0.488813i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.17978 | + | 2.99054i | 0.280501 | + | 0.161947i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.95110 | + | 16.2135i | 0.483314 | + | 0.875447i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.3778 | − | 3.31661i | −0.664473 | − | 0.178045i | −0.0892090 | − | 0.996013i | \(-0.528434\pi\) |
−0.575264 | + | 0.817968i | \(0.695101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0347 | −1.01890 | −0.509452 | − | 0.860499i | \(-0.670152\pi\) | ||||
−0.509452 | + | 0.860499i | \(0.670152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.49485 | 0.0797890 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.9930 | + | 7.23275i | 1.43669 | + | 0.384961i | 0.891374 | − | 0.453268i | \(-0.149742\pi\) |
0.545318 | + | 0.838229i | \(0.316409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.75474 | − | 5.59476i | 0.357499 | − | 0.296106i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.98795 | − | 3.45714i | −0.316032 | − | 0.182461i | 0.333591 | − | 0.942718i | \(-0.391740\pi\) |
−0.649622 | + | 0.760257i | \(0.725073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.06765 | + | 12.2415i | 0.371981 | + | 0.644291i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.00728899 | + | 0.00728899i | −0.000382573 | + | 0.000382573i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.94248 | − | 7.24942i | 0.101396 | − | 0.378417i | −0.896515 | − | 0.443013i | \(-0.853909\pi\) |
0.997911 | + | 0.0645966i | \(0.0205761\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.665328 | + | 1.15238i | −0.0346356 | + | 0.0599906i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.71742 | − | 6.64642i | 0.244917 | − | 0.345065i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.6606 | − | 4.46420i | 0.862654 | − | 0.231148i | 0.199746 | − | 0.979848i | \(-0.435988\pi\) |
0.662909 | + | 0.748700i | \(0.269322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 31.4401i | − | 1.61497i | −0.589890 | − | 0.807484i | \(-0.700829\pi\) | ||
0.589890 | − | 0.807484i | \(-0.299171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.59759 | − | 5.54117i | 0.491700 | − | 0.283883i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.261487 | − | 0.975883i | −0.0133614 | − | 0.0498653i | 0.958923 | − | 0.283665i | \(-0.0915505\pi\) |
−0.972285 | + | 0.233800i | \(0.924884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.50525 | − | 9.34971i | −0.127349 | − | 0.475272i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.8640 | + | 16.0873i | −1.41276 | + | 0.815658i | −0.995648 | − | 0.0931970i | \(-0.970291\pi\) |
−0.417113 | + | 0.908855i | \(0.636958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 23.4459i | − | 1.18571i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.23030 | − | 9.23030i | −0.465607 | − | 0.465607i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.2623 | − | 3.82158i | 0.715805 | − | 0.191799i | 0.117506 | − | 0.993072i | \(-0.462510\pi\) |
0.598299 | + | 0.801273i | \(0.295843\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.30439 | − | 2.43235i | 0.265552 | − | 0.121770i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.7722 | + | 22.1221i | −0.637814 | + | 1.10473i | 0.348098 | + | 0.937458i | \(0.386828\pi\) |
−0.985911 | + | 0.167268i | \(0.946506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.698040 | + | 2.60512i | −0.0347718 | + | 0.129770i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.06012 | + | 4.06012i | −0.201252 | + | 0.201252i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.51000 | − | 13.0077i | −0.371346 | − | 0.643190i | 0.618427 | − | 0.785842i | \(-0.287770\pi\) |
−0.989773 | + | 0.142653i | \(0.954437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.42975 | − | 4.86692i | −0.415809 | − | 0.240067i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.589184 | + | 3.47093i | 0.0289919 | + | 0.170793i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.90953 | + | 2.38730i | 0.436302 | + | 0.116907i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.0131 | −1.95477 | −0.977383 | − | 0.211477i | \(-0.932173\pi\) | ||||
−0.977383 | + | 0.211477i | \(0.932173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0103 | 0.975243 | 0.487621 | − | 0.873055i | \(-0.337865\pi\) | ||||
0.487621 | + | 0.873055i | \(0.337865\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.17799 | − | 1.11949i | −0.203141 | − | 0.0544315i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.01299 | − | 10.8817i | −0.436169 | − | 0.526601i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.29161 | + | 2.47776i | 0.207201 | + | 0.119627i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.7654 | + | 34.2347i | 0.952068 | + | 1.64903i | 0.740940 | + | 0.671571i | \(0.234380\pi\) |
0.211127 | + | 0.977459i | \(0.432287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6886 | − | 17.6886i | 0.850058 | − | 0.850058i | −0.140082 | − | 0.990140i | \(-0.544737\pi\) |
0.990140 | + | 0.140082i | \(0.0447365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.03737 | − | 15.0677i | 0.193134 | − | 0.720785i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.674255 | + | 1.16784i | −0.0321804 | + | 0.0557381i | −0.881667 | − | 0.471872i | \(-0.843578\pi\) |
0.849487 | + | 0.527610i | \(0.176912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.30992 | + | 6.60790i | 0.109996 | + | 0.314662i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.7013 | − | 6.35073i | 1.12608 | − | 0.301733i | 0.352739 | − | 0.935722i | \(-0.385250\pi\) |
0.773342 | + | 0.633989i | \(0.218584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.78969 | + | 2.78969i | 0.131948 | + | 0.131948i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.9555i | − | 0.800180i | −0.916476 | − | 0.400090i | \(-0.868979\pi\) | ||
0.916476 | − | 0.400090i | \(-0.131021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.82022 | + | 2.20561i | −0.179887 | + | 0.103858i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.953730 | − | 3.55937i | −0.0448101 | − | 0.167234i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.54340 | − | 5.76004i | −0.0721972 | − | 0.269443i | 0.920386 | − | 0.391011i | \(-0.127875\pi\) |
−0.992583 | + | 0.121568i | \(0.961208\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.87094 | − | 1.65754i | 0.134004 | − | 0.0773671i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 16.5534i | − | 0.770970i | −0.922714 | − | 0.385485i | \(-0.874034\pi\) | ||
0.922714 | − | 0.385485i | \(-0.125966\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.82028 | + | 9.82028i | 0.456387 | + | 0.456387i | 0.897468 | − | 0.441080i | \(-0.145405\pi\) |
−0.441080 | + | 0.897468i | \(0.645405\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.01289 | + | 1.87910i | −0.324518 | + | 0.0869543i | −0.417400 | − | 0.908723i | \(-0.637059\pi\) |
0.0928822 | + | 0.995677i | \(0.470392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.75868 | − | 3.37756i | −0.219735 | − | 0.155961i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.81507 | + | 6.60790i | −0.175789 | + | 0.304476i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.30507 | − | 30.9949i | 0.381867 | − | 1.42515i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.17829 | − | 2.17829i | 0.0997368 | − | 0.0997368i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.8009 | − | 30.8321i | −0.813345 | − | 1.40875i | −0.910510 | − | 0.413487i | \(-0.864311\pi\) |
0.0971653 | − | 0.995268i | \(-0.469022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.24227 | − | 1.29457i | −0.102239 | − | 0.0590275i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.5424 | + | 6.51211i | 0.798208 | + | 0.296311i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0418 | + | 4.29840i | 0.726925 | + | 0.194779i | 0.603259 | − | 0.797545i | \(-0.293868\pi\) |
0.123666 | + | 0.992324i | \(0.460535\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.8662 | −0.807939 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.8801 | 1.93515 | 0.967576 | − | 0.252579i | \(-0.0812788\pi\) | ||||
0.967576 | + | 0.252579i | \(0.0812788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.3762 | + | 4.59432i | 0.555150 | + | 0.206083i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9270 | − | 10.3502i | −0.802524 | − | 0.463337i | 0.0418292 | − | 0.999125i | \(-0.486681\pi\) |
−0.844353 | + | 0.535788i | \(0.820015\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.2774 | − | 17.8009i | −0.459159 | − | 0.795287i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | + | 25.4558i | −1.13502 | + | 1.13502i | −0.145690 | + | 0.989330i | \(0.546540\pi\) |
−0.989330 | + | 0.145690i | \(0.953460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.78630 | − | 10.3986i | 0.123744 | − | 0.461819i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.329235 | − | 0.570251i | 0.0145931 | − | 0.0252759i | −0.858637 | − | 0.512585i | \(-0.828688\pi\) |
0.873230 | + | 0.487309i | \(0.162021\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.9127 | − | 16.2627i | −1.01360 | − | 0.719420i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.13045 | − | 0.570853i | 0.0940618 | − | 0.0252038i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1392 | − | 10.1392i | −0.445920 | − | 0.445920i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.630141i | 0.0276601i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.2500 | + | 12.2687i | −0.930978 | + | 0.537501i | −0.887121 | − | 0.461537i | \(-0.847298\pi\) |
−0.0438574 | + | 0.999038i | \(0.513965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.20073 | − | 19.4094i | −0.227412 | − | 0.848713i | −0.981424 | − | 0.191852i | \(-0.938551\pi\) |
0.754012 | − | 0.656861i | \(-0.228116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.54802 | + | 5.77729i | 0.0674328 | + | 0.251663i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.4005 | − | 13.5103i | 1.01741 | − | 0.587405i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.33066i | 0.0577455i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.40652 | − | 1.40652i | −0.0609233 | − | 0.0609233i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.0436 | − | 4.29886i | 0.692331 | − | 0.185510i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.32120 | + | 22.7996i | −0.186127 | + | 0.982049i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.94781 | + | 8.56987i | −0.212723 | + | 0.368447i | −0.952566 | − | 0.304333i | \(-0.901567\pi\) |
0.739843 | + | 0.672780i | \(0.234900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.05327 | + | 15.1270i | −0.173942 | + | 0.649162i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.99293 | + | 7.99293i | −0.341753 | + | 0.341753i | −0.857026 | − | 0.515273i | \(-0.827691\pi\) |
0.515273 | + | 0.857026i | \(0.327691\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.67024 | − | 4.62499i | −0.113963 | − | 0.197390i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.8929 | + | 32.4687i | 1.14360 | + | 1.38071i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.636032 | − | 0.170424i | −0.0269496 | − | 0.00722111i | 0.245319 | − | 0.969442i | \(-0.421107\pi\) |
−0.272269 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.4694 | 0.611991 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.9897 | 0.463985 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.7403 | + | 9.30864i | 1.46413 | + | 0.392312i | 0.900914 | − | 0.433997i | \(-0.142897\pi\) |
0.563216 | + | 0.826310i | \(0.309564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.442778 | + | 2.60844i | 0.0185949 | + | 0.109544i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.7095 | + | 9.64723i | 0.700498 | + | 0.404433i | 0.807533 | − | 0.589822i | \(-0.200802\pi\) |
−0.107035 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.35017 | − | 10.9988i | −0.265746 | − | 0.460286i | 0.702013 | − | 0.712165i | \(-0.252285\pi\) |
−0.967759 | + | 0.251878i | \(0.918952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.9894 | − | 11.9894i | 0.500863 | − | 0.500863i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.324865 | + | 1.21241i | −0.0135243 | + | 0.0504733i | −0.972358 | − | 0.233494i | \(-0.924984\pi\) |
0.958834 | + | 0.283967i | \(0.0916507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.902106 | − | 1.56249i | 0.0374902 | − | 0.0649350i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.4024 | + | 15.7753i | −1.42725 | + | 0.654472i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.86430 | − | 2.64313i | 0.408538 | − | 0.109467i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.70500 | − | 3.70500i | −0.152922 | − | 0.152922i | 0.626500 | − | 0.779422i | \(-0.284487\pi\) |
−0.779422 | + | 0.626500i | \(0.784487\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.97938i | 0.163968i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.48454 | + | 4.32120i | −0.307873 | + | 0.177750i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.9473 | + | 44.5881i | 0.490619 | + | 1.83101i | 0.553302 | + | 0.832981i | \(0.313368\pi\) |
−0.0626829 | + | 0.998033i | \(0.519966\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.86925 | − | 18.1723i | −0.199285 | − | 0.743742i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.50005 | − | 4.90751i | 0.347303 | − | 0.200515i | −0.316194 | − | 0.948695i | \(-0.602405\pi\) |
0.663497 | + | 0.748179i | \(0.269072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26.0708i | − | 1.06345i | −0.846917 | − | 0.531725i | \(-0.821544\pi\) | ||
0.846917 | − | 0.531725i | \(-0.178456\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.55960 | − | 1.55960i | −0.0635118 | − | 0.0635118i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.8402 | + | 5.58411i | −0.845877 | + | 0.226652i | −0.655628 | − | 0.755084i | \(-0.727596\pi\) |
−0.190249 | + | 0.981736i | \(0.560929\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.23289 | − | 5.59952i | 0.130789 | − | 0.226533i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.77493 | − | 29.0164i | 0.314026 | − | 1.17196i | −0.610866 | − | 0.791734i | \(-0.709179\pi\) |
0.924893 | − | 0.380228i | \(-0.124155\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.34744 | − | 2.34744i | 0.0945043 | − | 0.0945043i | −0.658274 | − | 0.752778i | \(-0.728713\pi\) |
0.752778 | + | 0.658274i | \(0.228713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9463 | + | 29.3518i | 0.681128 | + | 1.17975i | 0.974637 | + | 0.223792i | \(0.0718436\pi\) |
−0.293509 | + | 0.955956i | \(0.594823\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.12499 | + | 3.53626i | 0.245787 | + | 0.141905i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.6995 | + | 9.69041i | −0.468732 | + | 0.388238i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.06260 | + | 1.89242i | 0.282053 | + | 0.0755759i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.74187 | −0.228943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5341 | 1.41459 | 0.707295 | − | 0.706918i | \(-0.249915\pi\) | ||||
0.707295 | + | 0.706918i | \(0.249915\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.53525 | − | 1.21522i | −0.180260 | − | 0.0483005i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4349 | + | 0.778753i | −0.413446 | + | 0.0308553i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.32120 | + | 2.49485i | 0.170944 | + | 0.0986946i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.83053 | − | 3.17058i | −0.0723017 | − | 0.125230i | 0.827608 | − | 0.561307i | \(-0.189701\pi\) |
−0.899910 | + | 0.436076i | \(0.856368\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.3417 | + | 22.3417i | −0.881072 | + | 0.881072i | −0.993644 | − | 0.112572i | \(-0.964091\pi\) |
0.112572 | + | 0.993644i | \(0.464091\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.39585 | − | 27.6017i | 0.290761 | − | 1.08513i | −0.653765 | − | 0.756697i | \(-0.726812\pi\) |
0.944526 | − | 0.328436i | \(-0.106522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.20561 | + | 3.82022i | −0.0865777 | + | 0.149957i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.75258 | − | 0.446403i | −0.186268 | − | 0.0174959i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.8399 | − | 3.44044i | 0.502464 | − | 0.134635i | 0.00132058 | − | 0.999999i | \(-0.499580\pi\) |
0.501143 | + | 0.865364i | \(0.332913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.50936 | − | 7.50936i | −0.292968 | − | 0.292968i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 33.9452i | − | 1.32232i | −0.750246 | − | 0.661159i | \(-0.770065\pi\) | ||
0.750246 | − | 0.661159i | \(-0.229935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5941 | + | 11.3126i | −0.762121 | + | 0.440011i | −0.830057 | − | 0.557679i | \(-0.811692\pi\) |
0.0679359 | + | 0.997690i | \(0.478359\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.28258 | + | 4.78666i | 0.0498114 | + | 0.185899i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.26235 | − | 5.34762i | 0.358103 | − | 0.206751i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 17.7040i | − | 0.683457i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8025 | − | 12.8025i | −0.493499 | − | 0.493499i | 0.415907 | − | 0.909407i | \(-0.363464\pi\) |
−0.909407 | + | 0.415907i | \(0.863464\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.9712 | − | 5.08332i | 0.729123 | − | 0.195368i | 0.124884 | − | 0.992171i | \(-0.460144\pi\) |
0.604239 | + | 0.796803i | \(0.293477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.51402 | − | 12.0248i | −0.211609 | − | 0.461469i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.12499 | − | 5.41264i | 0.119750 | − | 0.207413i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.9338 | − | 48.2696i | 0.494898 | − | 1.84699i | −0.0356996 | − | 0.999363i | \(-0.511366\pi\) |
0.530598 | − | 0.847624i | \(-0.321967\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.6207 | + | 10.6207i | −0.405207 | + | 0.405207i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.30248 | + | 3.98801i | 0.0877176 | + | 0.151931i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7774 | − | 8.53172i | −0.562158 | − | 0.324562i | 0.191853 | − | 0.981424i | \(-0.438550\pi\) |
−0.754011 | + | 0.656862i | \(0.771884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.05239 | + | 8.22258i | −0.115951 | + | 0.312350i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.26091 | − | 1.14171i | −0.161393 | − | 0.0432452i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.1342 | −0.610251 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.55474 | −0.0964910 | −0.0482455 | − | 0.998836i | \(-0.515363\pi\) | ||||
−0.0482455 | + | 0.998836i | \(0.515363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.69005 | − | 0.988747i | −0.139173 | − | 0.0372913i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.0269 | + | 8.32222i | −1.84384 | + | 0.312989i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.19526 | + | 0.690084i | 0.0448889 | + | 0.0259166i | 0.522277 | − | 0.852776i | \(-0.325083\pi\) |
−0.477388 | + | 0.878693i | \(0.658416\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.96745 | + | 13.8000i | 0.298803 | + | 0.517542i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.02292 | + | 9.02292i | −0.337911 | + | 0.337911i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.63624 | + | 24.7668i | −0.247835 | + | 0.924932i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.86148 | − | 10.1524i | 0.218596 | − | 0.378620i | −0.735783 | − | 0.677218i | \(-0.763186\pi\) |
0.954379 | + | 0.298598i | \(0.0965189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.45812 | + | 26.1701i | −0.0915453 | + | 0.974625i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.36516 | − | 2.24144i | 0.311104 | − | 0.0833600i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.00149 | − | 2.00149i | −0.0742311 | − | 0.0742311i | 0.669016 | − | 0.743248i | \(-0.266716\pi\) |
−0.743248 | + | 0.669016i | \(0.766716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.7893 | − | 16.0442i | 1.02782 | − | 0.593415i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.55183 | + | 9.52354i | 0.0942538 | + | 0.351760i | 0.996905 | − | 0.0786123i | \(-0.0250489\pi\) |
−0.902651 | + | 0.430372i | \(0.858382\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.89242 | − | 7.06260i | −0.0697081 | − | 0.260154i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.74678 | + | 4.47261i | −0.284970 | + | 0.164527i | −0.635671 | − | 0.771960i | \(-0.719277\pi\) |
0.350701 | + | 0.936487i | \(0.385943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.29704i | 0.121120i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.47577 | − | 7.47577i | −0.274259 | − | 0.274259i | 0.556553 | − | 0.830812i | \(-0.312124\pi\) |
−0.830812 | + | 0.556553i | \(0.812124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.8173 | + | 3.70234i | −0.505550 | + | 0.135462i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.65043 | + | 49.5103i | −0.169923 | + | 1.80907i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.4520 | + | 25.0316i | −0.527361 | + | 0.913415i | 0.472131 | + | 0.881528i | \(0.343485\pi\) |
−0.999491 | + | 0.0318869i | \(0.989848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.0619145 | + | 0.231068i | −0.00225629 | + | 0.00842059i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.6945 | − | 21.6945i | 0.788499 | − | 0.788499i | −0.192749 | − | 0.981248i | \(-0.561740\pi\) |
0.981248 | + | 0.192749i | \(0.0617403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.7230 | + | 20.3048i | 0.425516 | + | 0.737016i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.3476 | − | 18.6759i | −1.17260 | − | 0.677000i | −0.218308 | − | 0.975880i | \(-0.570054\pi\) |
−0.954291 | + | 0.298880i | \(0.903387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.4257 | − | 6.69244i | 1.42731 | − | 0.242283i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.92135 | − | 0.514823i | −0.0693758 | − | 0.0185892i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.0886 | −0.940780 | −0.470390 | − | 0.882459i | \(-0.655887\pi\) | ||||
−0.470390 | + | 0.882459i | \(0.655887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.93490 | −0.321783 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.1822 | + | 6.21166i | 0.833806 | + | 0.223418i | 0.650374 | − | 0.759614i | \(-0.274612\pi\) |
0.183433 | + | 0.983032i | \(0.441279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.59481 | − | 4.29611i | 0.0572134 | − | 0.154122i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.54170 | − | 1.46745i | −0.0910659 | − | 0.0525769i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.27059 | + | 14.3251i | 0.295945 | + | 0.512592i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.4006 | + | 38.8156i | −0.370742 | + | 1.38363i | 0.488726 | + | 0.872437i | \(0.337462\pi\) |
−0.859468 | + | 0.511190i | \(0.829205\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.65989 | + | 2.87501i | −0.0590936 | + | 0.102353i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.4607 | − | 24.9931i | −0.407495 | − | 0.888651i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.71117 | − | 2.06620i | 0.273832 | − | 0.0733729i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.3503 | + | 13.3503i | 0.472890 | + | 0.472890i | 0.902849 | − | 0.429958i | \(-0.141472\pi\) |
−0.429958 | + | 0.902849i | \(0.641472\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 14.3389i | − | 0.507275i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.97261 | + | 2.87094i | −0.175698 | + | 0.101440i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.11185 | − | 34.0059i | −0.321550 | − | 1.20004i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.45924 | + | 24.1062i | 0.227376 | + | 0.848579i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.9931 | − | 14.4297i | 0.878709 | − | 0.507323i | 0.00847656 | − | 0.999964i | \(-0.497302\pi\) |
0.870233 | + | 0.492641i | \(0.163968\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.76257i | 0.272581i | 0.990669 | + | 0.136290i | \(0.0435180\pi\) | ||||
−0.990669 | + | 0.136290i | \(0.956482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.4697 | − | 20.4697i | −0.717905 | − | 0.717905i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.6218 | − | 5.52559i | 0.721465 | − | 0.193316i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.93766 | − | 0.369859i | −0.137593 | − | 0.0129239i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6575 | + | 18.4594i | −0.371951 | + | 0.644237i | −0.989866 | − | 0.142008i | \(-0.954644\pi\) |
0.617915 | + | 0.786245i | \(0.287978\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.23853 | + | 30.7466i | −0.287177 | + | 1.07176i | 0.660056 | + | 0.751216i | \(0.270532\pi\) |
−0.947234 | + | 0.320544i | \(0.896134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.00913 | − | 2.00913i | 0.0698643 | − | 0.0698643i | −0.671311 | − | 0.741176i | \(-0.734269\pi\) |
0.741176 | + | 0.671311i | \(0.234269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.374614 | − | 0.648851i | −0.0130109 | − | 0.0225355i | 0.859447 | − | 0.511225i | \(-0.170808\pi\) |
−0.872458 | + | 0.488690i | \(0.837475\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.54703 | + | 0.893179i | 0.0536659 | + | 0.0309840i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.1773 | + | 13.0662i | −0.664454 | + | 0.452717i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.74273 | − | 0.466964i | −0.0602377 | − | 0.0161407i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.6446 | 1.74845 | 0.874223 | − | 0.485525i | \(-0.161372\pi\) | ||||
0.874223 | + | 0.485525i | \(0.161372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.98477 | − | 0.531818i | −0.0683592 | − | 0.0183168i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0210038 | − | 0.0173969i | 0.000721700 | − | 0.000597764i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.5162 | − | 11.8450i | −0.704113 | − | 0.406520i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.12499 | − | 10.6088i | −0.209962 | − | 0.363665i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.4071 | + | 33.4071i | −1.14384 | + | 1.14384i | −0.156095 | + | 0.987742i | \(0.549891\pi\) |
−0.987742 | + | 0.156095i | \(0.950109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.07957 | + | 22.6892i | −0.207674 | + | 0.775050i | 0.780944 | + | 0.624601i | \(0.214738\pi\) |
−0.988618 | + | 0.150449i | \(0.951928\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.6719 | + | 35.8047i | −0.705315 | + | 1.22164i | 0.261263 | + | 0.965268i | \(0.415861\pi\) |
−0.966578 | + | 0.256373i | \(0.917472\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.03770 | − | 2.87094i | 0.0694447 | − | 0.0978412i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.5954 | + | 10.0737i | −1.27976 | + | 0.342911i | −0.833763 | − | 0.552122i | \(-0.813818\pi\) |
−0.445999 | + | 0.895033i | \(0.647152\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.24993 | − | 4.24993i | −0.144335 | − | 0.144335i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.8253i | 1.79198i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.85532 | − | 1.64852i | 0.0967489 | − | 0.0558580i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.29410 | − | 4.82963i | −0.0437985 | − | 0.163458i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.35411 | − | 5.05359i | −0.0457249 | − | 0.170648i | 0.939288 | − | 0.343131i | \(-0.111488\pi\) |
−0.985012 | + | 0.172484i | \(0.944821\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.2053 | − | 12.8202i | 0.748966 | − | 0.432415i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.31978i | − | 0.111846i | −0.998435 | − | 0.0559231i | \(-0.982190\pi\) | ||
0.998435 | − | 0.0559231i | \(-0.0178102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.5455 | − | 17.5455i | −0.590452 | − | 0.590452i | 0.347302 | − | 0.937753i | \(-0.387098\pi\) |
−0.937753 | + | 0.347302i | \(0.887098\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.8120 | − | 14.9548i | 1.87398 | − | 0.502132i | 0.874119 | − | 0.485712i | \(-0.161440\pi\) |
0.999865 | − | 0.0164202i | \(-0.00522693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.6526 | + | 12.2217i | −0.893899 | + | 0.409901i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.65754 | + | 2.87094i | −0.0555295 | + | 0.0961799i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.46916 | − | 9.21502i | 0.0826272 | − | 0.308369i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.47577 | + | 7.47577i | −0.249609 | + | 0.249609i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.84409 | + | 5.10614i | 0.294639 | + | 0.170110i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.28588 | + | 25.2484i | 0.142625 | + | 0.840216i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.1562 | + | 7.27649i | 0.901708 | + | 0.241612i | 0.679750 | − | 0.733444i | \(-0.262088\pi\) |
0.221958 | + | 0.975056i | \(0.428755\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.7955 | −0.623407 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0309 | 0.497997 | 0.248998 | − | 0.968504i | \(-0.419899\pi\) | ||||
0.248998 | + | 0.968504i | \(0.419899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.8055 | − | 12.2735i | −1.51594 | − | 0.406195i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.0303 | + | 26.5978i | 0.727504 | + | 0.878338i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8423 | + | 15.4974i | 0.885445 | + | 0.511212i | 0.872450 | − | 0.488704i | \(-0.162530\pi\) |
0.0129952 | + | 0.999916i | \(0.495863\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.1926 | + | 22.8503i | 0.434712 | + | 0.752943i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.27418 | + | 5.27418i | −0.173602 | + | 0.173602i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.57134 | + | 9.59638i | −0.0844540 | + | 0.315186i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.4528 | − | 40.6214i | 0.769461 | − | 1.33275i | −0.168395 | − | 0.985720i | \(-0.553858\pi\) |
0.937856 | − | 0.347025i | \(-0.112808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.5744 | + | 5.09477i | −0.477658 | + | 0.166974i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.40216 | + | 2.51930i | −0.307813 | + | 0.0824782i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.1331 | + | 30.1331i | 0.984405 | + | 0.984405i | 0.999880 | − | 0.0154751i | \(-0.00492607\pi\) |
−0.0154751 | + | 0.999880i | \(0.504926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.7448i | 0.415911i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.1952 | − | 7.61824i | 0.430151 | − | 0.248348i | −0.269260 | − | 0.963067i | \(-0.586779\pi\) |
0.699411 | + | 0.714720i | \(0.253446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.43577 | − | 9.09042i | −0.0793196 | − | 0.296025i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.94535 | − | 29.6525i | −0.258189 | − | 0.963575i | −0.966288 | − | 0.257462i | \(-0.917114\pi\) |
0.708099 | − | 0.706113i | \(-0.249553\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.7482 | − | 7.93751i | 0.446284 | − | 0.257662i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 19.2147i | − | 0.623080i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.7672 | − | 25.7672i | −0.834682 | − | 0.834682i | 0.153471 | − | 0.988153i | \(-0.450955\pi\) |
−0.988153 | + | 0.153471i | \(0.950955\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.0011 | + | 14.9059i | 0.678161 | + | 0.481338i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.8724 | + | 24.0277i | −0.447497 | + | 0.775088i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.86463 | + | 18.1550i | −0.156760 | + | 0.585038i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.47070 | − | 1.47070i | 0.0472945 | − | 0.0472945i | −0.683064 | − | 0.730359i | \(-0.739353\pi\) |
0.730359 | + | 0.683064i | \(0.239353\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.65587 | + | 6.33216i | 0.117444 | + | 0.203418i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.6833 | + | 11.3641i | 0.631666 | + | 0.364692i | 0.781397 | − | 0.624034i | \(-0.214508\pi\) |
−0.149731 | + | 0.988727i | \(0.547841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8784 | − | 8.49295i | −0.733449 | − | 0.272271i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54.4651 | − | 14.5939i | −1.74249 | − | 0.466900i | −0.759495 | − | 0.650513i | \(-0.774554\pi\) |
−0.982999 | + | 0.183613i | \(0.941221\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.0347 | −0.608352 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.1147 | 0.482575 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.7045 | − | 5.54775i | −0.660370 | − | 0.176946i | −0.0869571 | − | 0.996212i | \(-0.527714\pi\) |
−0.573413 | + | 0.819266i | \(0.694381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.7285 | + | 3.98264i | 0.341492 | + | 0.126769i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 59.2870 | + | 34.2294i | 1.88522 | + | 1.08843i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9922 | + | 50.2160i | 0.920969 | + | 1.59516i | 0.797919 | + | 0.602764i | \(0.205934\pi\) |
0.123050 | + | 0.992401i | \(0.460733\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.653787 | + | 0.653787i | −0.0207473 | + | 0.0207473i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.7747 | + | 40.2116i | −0.341237 | + | 1.27352i | 0.555709 | + | 0.831377i | \(0.312447\pi\) |
−0.896947 | + | 0.442138i | \(0.854220\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.866025 | − | 1.50000i | 0.0273998 | − | 0.0474579i |
(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 | 2100.2.ce.c.1993.2 | yes | 24 | |
5.2 | odd | 4 | inner | 2100.2.ce.c.1657.1 | yes | 24 | |
5.3 | odd | 4 | inner | 2100.2.ce.c.1657.6 | yes | 24 | |
5.4 | even | 2 | inner | 2100.2.ce.c.1993.5 | yes | 24 | |
7.3 | odd | 6 | inner | 2100.2.ce.c.493.1 | yes | 24 | |
35.3 | even | 12 | inner | 2100.2.ce.c.157.5 | yes | 24 | |
35.17 | even | 12 | inner | 2100.2.ce.c.157.2 | ✓ | 24 | |
35.24 | odd | 6 | inner | 2100.2.ce.c.493.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.ce.c.157.2 | ✓ | 24 | 35.17 | even | 12 | inner | |
2100.2.ce.c.157.5 | yes | 24 | 35.3 | even | 12 | inner | |
2100.2.ce.c.493.1 | yes | 24 | 7.3 | odd | 6 | inner | |
2100.2.ce.c.493.6 | yes | 24 | 35.24 | odd | 6 | inner | |
2100.2.ce.c.1657.1 | yes | 24 | 5.2 | odd | 4 | inner | |
2100.2.ce.c.1657.6 | yes | 24 | 5.3 | odd | 4 | inner | |
2100.2.ce.c.1993.2 | yes | 24 | 1.1 | even | 1 | trivial | |
2100.2.ce.c.1993.5 | yes | 24 | 5.4 | even | 2 | inner |