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: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 1657.1 | ||
Character | \(\chi\) | \(=\) | 2100.1657 |
Dual form | 2100.2.ce.e.493.1 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.258819 | + | 0.965926i | −0.149429 | + | 0.557678i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.94431 | + | 1.79435i | −0.734879 | + | 0.678199i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.81503 | − | 4.87578i | −0.848764 | − | 1.47010i | −0.882311 | − | 0.470666i | \(-0.844014\pi\) |
0.0335471 | − | 0.999437i | \(-0.489320\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.322009 | + | 0.322009i | 0.0893093 | + | 0.0893093i | 0.750350 | − | 0.661041i | \(-0.229885\pi\) |
−0.661041 | + | 0.750350i | \(0.729885\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.182069 | + | 0.0487852i | 0.0441582 | + | 0.0118322i | 0.280831 | − | 0.959757i | \(-0.409390\pi\) |
−0.236672 | + | 0.971590i | \(0.576057\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.531552 | − | 0.920676i | 0.121946 | − | 0.211217i | −0.798589 | − | 0.601877i | \(-0.794420\pi\) |
0.920535 | + | 0.390660i | \(0.127753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.22998 | − | 2.34247i | −0.268404 | − | 0.511168i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.48218 | + | 5.53156i | 0.309055 | + | 1.15341i | 0.929398 | + | 0.369079i | \(0.120327\pi\) |
−0.620343 | + | 0.784331i | \(0.713007\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.319426i | − | 0.0593159i | −0.999560 | − | 0.0296580i | \(-0.990558\pi\) | ||
0.999560 | − | 0.0296580i | \(-0.00944181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.60261 | − | 2.65732i | 0.826653 | − | 0.477268i | −0.0260526 | − | 0.999661i | \(-0.508294\pi\) |
0.852705 | + | 0.522393i | \(0.174960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.43823 | − | 1.45717i | 0.946674 | − | 0.253660i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.91946 | − | 2.65791i | 1.63075 | − | 0.436958i | 0.676614 | − | 0.736337i | \(-0.263446\pi\) |
0.954134 | + | 0.299380i | \(0.0967797\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.394379 | + | 0.227695i | −0.0631512 | + | 0.0364604i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.68139i | − | 0.887284i | −0.896204 | − | 0.443642i | \(-0.853686\pi\) | ||
0.896204 | − | 0.443642i | \(-0.146314\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.844231 | − | 0.844231i | 0.128744 | − | 0.128744i | −0.639799 | − | 0.768543i | \(-0.720982\pi\) |
0.768543 | + | 0.639799i | \(0.220982\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.23771 | − | 12.0833i | −0.472268 | − | 1.76253i | −0.631590 | − | 0.775302i | \(-0.717598\pi\) |
0.159322 | − | 0.987227i | \(-0.449069\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.560652 | − | 6.97751i | 0.0800931 | − | 0.996787i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0942458 | + | 0.163239i | −0.0131971 | + | 0.0228580i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.320712 | + | 0.0859345i | 0.0440532 | + | 0.0118040i | 0.280778 | − | 0.959773i | \(-0.409407\pi\) |
−0.236725 | + | 0.971577i | \(0.576074\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.751729 | + | 0.751729i | 0.0995689 | + | 0.0995689i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.47674 | + | 7.75395i | 0.582823 | + | 1.00948i | 0.995143 | + | 0.0984394i | \(0.0313850\pi\) |
−0.412321 | + | 0.911039i | \(0.635282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.80767 | + | 5.08511i | 1.12771 | + | 0.651082i | 0.943357 | − | 0.331779i | \(-0.107649\pi\) |
0.184349 | + | 0.982861i | \(0.440982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.58099 | − | 0.581795i | 0.325174 | − | 0.0732993i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.16933 | + | 8.09607i | −0.265026 | + | 0.989092i | 0.697208 | + | 0.716869i | \(0.254425\pi\) |
−0.962234 | + | 0.272223i | \(0.912241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.72669 | −0.689412 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.489937 | 0.0581449 | 0.0290724 | − | 0.999577i | \(-0.490745\pi\) | ||||
0.0290724 | + | 0.999577i | \(0.490745\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.678524 | + | 2.53229i | −0.0794153 | + | 0.296382i | −0.994198 | − | 0.107564i | \(-0.965695\pi\) |
0.914783 | + | 0.403946i | \(0.132362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.2221 | + | 4.42887i | 1.62076 | + | 0.504716i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.2025 | + | 7.04514i | 1.37289 | + | 0.792640i | 0.991291 | − | 0.131687i | \(-0.0420393\pi\) |
0.381602 | + | 0.924327i | \(0.375373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.75762 | − | 4.75762i | −0.522217 | − | 0.522217i | 0.396024 | − | 0.918240i | \(-0.370390\pi\) |
−0.918240 | + | 0.396024i | \(0.870390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.308542 | + | 0.0826735i | 0.0330792 | + | 0.00886353i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.63014 | − | 2.82349i | 0.172795 | − | 0.299289i | −0.766601 | − | 0.642124i | \(-0.778054\pi\) |
0.939396 | + | 0.342834i | \(0.111387\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.20388 | − | 0.0482888i | −0.126201 | − | 0.00506205i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.37553 | + | 5.13354i | 0.142636 | + | 0.532323i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1827 | − | 10.1827i | 1.03390 | − | 1.03390i | 0.0344908 | − | 0.999405i | \(-0.489019\pi\) |
0.999405 | − | 0.0344908i | \(-0.0109810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.63007i | 0.565843i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7539 | − | 7.36347i | 1.26906 | − | 0.732693i | 0.294251 | − | 0.955728i | \(-0.404930\pi\) |
0.974810 | + | 0.223035i | \(0.0715965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9587 | + | 4.27612i | −1.57246 | + | 0.421339i | −0.936581 | − | 0.350451i | \(-0.886028\pi\) |
−0.635877 | + | 0.771790i | \(0.719362\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.4019 | − | 3.05513i | 1.10226 | − | 0.295350i | 0.338577 | − | 0.940939i | \(-0.390055\pi\) |
0.763685 | + | 0.645589i | \(0.223388\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.30183 | − | 1.90631i | 0.316258 | − | 0.182592i | −0.333465 | − | 0.942762i | \(-0.608218\pi\) |
0.649723 | + | 0.760171i | \(0.274885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2694i | 0.974726i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.939611 | + | 0.939611i | −0.0883912 | + | 0.0883912i | −0.749920 | − | 0.661529i | \(-0.769908\pi\) |
0.661529 | + | 0.749920i | \(0.269908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.117864 | − | 0.439873i | −0.0108965 | − | 0.0406663i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.441535 | + | 0.231841i | −0.0404755 | + | 0.0212528i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3488 | + | 17.9247i | −0.940802 | + | 1.62952i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.48780 | + | 1.47045i | 0.494819 | + | 0.132586i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.08221 | − | 9.08221i | −0.805916 | − | 0.805916i | 0.178097 | − | 0.984013i | \(-0.443006\pi\) |
−0.984013 | + | 0.178097i | \(0.943006\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.596961 | + | 1.03397i | 0.0525595 | + | 0.0910358i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.52939 | − | 5.50179i | −0.832586 | − | 0.480694i | 0.0221510 | − | 0.999755i | \(-0.492949\pi\) |
−0.854737 | + | 0.519061i | \(0.826282\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.618509 | + | 2.74386i | 0.0536316 | + | 0.237923i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.165947 | − | 0.619321i | 0.0141778 | − | 0.0529122i | −0.958475 | − | 0.285178i | \(-0.907947\pi\) |
0.972652 | + | 0.232266i | \(0.0746139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3321 | −1.13082 | −0.565408 | − | 0.824812i | \(-0.691281\pi\) | ||||
−0.565408 | + | 0.824812i | \(0.691281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.5095 | 1.05349 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.663580 | − | 2.47651i | 0.0554913 | − | 0.207096i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.59465 | + | 2.34746i | 0.543918 | + | 0.193615i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.1864 | + | 8.76789i | 1.24412 | + | 0.718293i | 0.969930 | − | 0.243382i | \(-0.0782569\pi\) |
0.274190 | + | 0.961676i | \(0.411590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.15912 | − | 15.8641i | −0.745359 | − | 1.29100i | −0.950027 | − | 0.312168i | \(-0.898945\pi\) |
0.204668 | − | 0.978831i | \(-0.434389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.133284 | − | 0.133284i | −0.0107753 | − | 0.0107753i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.50881 | + | 1.74403i | 0.519459 | + | 0.139189i | 0.509016 | − | 0.860757i | \(-0.330009\pi\) |
0.0104428 | + | 0.999945i | \(0.496676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.166013 | + | 0.287542i | −0.0131657 | + | 0.0228036i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.8073 | − | 8.09550i | −1.00936 | − | 0.638015i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.27191 | + | 12.2109i | 0.256276 | + | 0.956434i | 0.967376 | + | 0.253344i | \(0.0815303\pi\) |
−0.711101 | + | 0.703090i | \(0.751803\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.45171 | − | 8.45171i | 0.654013 | − | 0.654013i | −0.299944 | − | 0.953957i | \(-0.596968\pi\) |
0.953957 | + | 0.299944i | \(0.0969679\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.7926i | − | 0.984048i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.920676 | + | 0.531552i | −0.0704058 | + | 0.0406488i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.46758 | − | 0.661185i | 0.187606 | − | 0.0502690i | −0.163793 | − | 0.986495i | \(-0.552373\pi\) |
0.351399 | + | 0.936226i | \(0.385706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.64841 | + | 2.31733i | −0.650054 | + | 0.174181i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.9708 | − | 10.3754i | 1.34320 | − | 0.775496i | 0.355923 | − | 0.934515i | \(-0.384167\pi\) |
0.987275 | + | 0.159019i | \(0.0508332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.3534i | − | 0.843894i | −0.906620 | − | 0.421947i | \(-0.861347\pi\) | ||
0.906620 | − | 0.421947i | \(-0.138653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.19143 | + | 7.19143i | −0.531606 | + | 0.531606i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.274664 | − | 1.02506i | −0.0200854 | − | 0.0749598i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.106038 | + | 2.64363i | −0.00771316 | + | 0.192295i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.7996 | − | 18.7054i | 0.781430 | − | 1.35348i | −0.149679 | − | 0.988735i | \(-0.547824\pi\) |
0.931109 | − | 0.364742i | \(-0.118843\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.3595 | + | 6.52710i | 1.75343 | + | 0.469831i | 0.985354 | − | 0.170524i | \(-0.0545460\pi\) |
0.768079 | + | 0.640355i | \(0.221213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.12836 | + | 5.12836i | 0.365380 | + | 0.365380i | 0.865789 | − | 0.500409i | \(-0.166817\pi\) |
−0.500409 | + | 0.865789i | \(0.666817\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.55338 | + | 11.3508i | 0.464557 | + | 0.804636i | 0.999181 | − | 0.0404537i | \(-0.0128803\pi\) |
−0.534625 | + | 0.845090i | \(0.679547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.25873 | − | 4.19083i | −0.511992 | − | 0.295598i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.573160 | + | 0.621062i | 0.0402280 | + | 0.0435900i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.48218 | − | 5.53156i | 0.103018 | − | 0.384470i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.98535 | −0.414015 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.05363 | −0.623278 | −0.311639 | − | 0.950201i | \(-0.600878\pi\) | ||||
−0.311639 | + | 0.950201i | \(0.600878\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.126805 | + | 0.473243i | −0.00868854 | + | 0.0324261i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.18073 | + | 13.4253i | −0.283807 | + | 0.911369i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.27039 | − | 1.31081i | −0.153419 | − | 0.0885762i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0429186 | + | 0.0743372i | 0.00288702 | + | 0.00500046i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9852 | + | 11.9852i | 0.802591 | + | 0.802591i | 0.983500 | − | 0.180909i | \(-0.0579039\pi\) |
−0.180909 | + | 0.983500i | \(0.557904\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.6308 | − | 4.18826i | −1.03745 | − | 0.277985i | −0.300395 | − | 0.953815i | \(-0.597119\pi\) |
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5466 | + | 21.7313i | −0.829102 | + | 1.43605i | 0.0696420 | + | 0.997572i | \(0.477814\pi\) |
−0.898744 | + | 0.438474i | \(0.855519\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.95891 | + | 12.5912i | −0.523658 | + | 0.828442i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.62271 | − | 6.05603i | −0.106307 | − | 0.396743i | 0.892183 | − | 0.451674i | \(-0.149173\pi\) |
−0.998490 | + | 0.0549305i | \(0.982506\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.96333 | + | 9.96333i | −0.647188 | + | 0.647188i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.6723i | − | 1.33718i | −0.743632 | − | 0.668589i | \(-0.766898\pi\) | ||
0.743632 | − | 0.668589i | \(-0.233102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.23827 | − | 4.17901i | 0.466258 | − | 0.269194i | −0.248414 | − | 0.968654i | \(-0.579909\pi\) |
0.714672 | + | 0.699460i | \(0.246576\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.965926 | + | 0.258819i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.467631 | − | 0.125301i | 0.0297546 | − | 0.00797273i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.82687 | − | 3.36415i | 0.369263 | − | 0.213194i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 10.5554i | − | 0.666251i | −0.942882 | − | 0.333126i | \(-0.891897\pi\) | ||
0.942882 | − | 0.333126i | \(-0.108103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.7983 | − | 22.7983i | 1.43332 | − | 1.43332i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.118451 | − | 0.442064i | −0.00738875 | − | 0.0275752i | 0.962133 | − | 0.272580i | \(-0.0878770\pi\) |
−0.969522 | + | 0.245005i | \(0.921210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.5172 | + | 22.9667i | −0.902058 | + | 1.42708i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.159713 | + | 0.276631i | −0.00988599 | + | 0.0171230i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.0662 | − | 7.52032i | −1.73064 | − | 0.463723i | −0.750307 | − | 0.661089i | \(-0.770094\pi\) |
−0.980330 | + | 0.197367i | \(0.936761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.30537 | + | 2.30537i | 0.141086 | + | 0.141086i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.26094 | − | 12.5763i | −0.442707 | − | 0.766792i | 0.555182 | − | 0.831729i | \(-0.312649\pi\) |
−0.997889 | + | 0.0649371i | \(0.979315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9039 | + | 14.9556i | 1.57355 | + | 0.908489i | 0.995729 | + | 0.0923244i | \(0.0294297\pi\) |
0.577820 | + | 0.816164i | \(0.303904\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.358231 | − | 1.15036i | 0.0216811 | − | 0.0696230i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.84685 | + | 6.89254i | −0.110966 | + | 0.414133i | −0.998954 | − | 0.0457358i | \(-0.985437\pi\) |
0.887987 | + | 0.459868i | \(0.152103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.31463 | −0.318179 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.7558 | 1.77508 | 0.887541 | − | 0.460728i | \(-0.152412\pi\) | ||||
0.887541 | + | 0.460728i | \(0.152412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.213991 | + | 0.798624i | −0.0127204 | + | 0.0474733i | −0.971994 | − | 0.235004i | \(-0.924490\pi\) |
0.959274 | + | 0.282478i | \(0.0911563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1944 | + | 11.0464i | 0.601755 | + | 0.652046i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.6917 | − | 8.48224i | −0.864215 | − | 0.498955i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.20025 | + | 12.4712i | 0.422086 | + | 0.731075i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.9412 | − | 15.9412i | −0.931294 | − | 0.931294i | 0.0664928 | − | 0.997787i | \(-0.478819\pi\) |
−0.997787 | + | 0.0664928i | \(0.978819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.43823 | − | 1.45717i | −0.315558 | − | 0.0845535i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.30394 | + | 2.25849i | −0.0754087 | + | 0.130612i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.126602 | + | 3.15628i | −0.00729720 | + | 0.181925i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.81161 | + | 14.2251i | 0.218971 | + | 0.817213i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0084 | + | 15.0084i | −0.856572 | + | 0.856572i | −0.990933 | − | 0.134360i | \(-0.957102\pi\) |
0.134360 | + | 0.990933i | \(0.457102\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 16.5217i | − | 0.939885i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.6718 | + | 12.5122i | −1.22889 | + | 0.709503i | −0.966799 | − | 0.255539i | \(-0.917747\pi\) |
−0.262096 | + | 0.965042i | \(0.584414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.904959 | + | 0.242483i | −0.0511513 | + | 0.0137060i | −0.284304 | − | 0.958734i | \(-0.591762\pi\) |
0.233153 | + | 0.972440i | \(0.425096\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.9422 | + | 3.46785i | −0.726905 | + | 0.194774i | −0.603251 | − | 0.797552i | \(-0.706128\pi\) |
−0.123655 | + | 0.992325i | \(0.539461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.55745 | + | 0.899195i | −0.0872005 | + | 0.0503452i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8041i | 0.658841i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.141695 | − | 0.141695i | 0.00788409 | − | 0.00788409i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.986780 | + | 3.68271i | 0.0545691 | + | 0.203655i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.9767 | + | 17.6840i | 1.54240 | + | 0.974953i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1822 | + | 19.3681i | −0.614627 | + | 1.06457i | 0.375823 | + | 0.926692i | \(0.377360\pi\) |
−0.990450 | + | 0.137874i | \(0.955973\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.91946 | − | 2.65791i | −0.543583 | − | 0.145653i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.15002 | − | 6.15002i | −0.335013 | − | 0.335013i | 0.519473 | − | 0.854487i | \(-0.326128\pi\) |
−0.854487 | + | 0.519473i | \(0.826128\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.664405 | − | 1.15078i | −0.0360856 | − | 0.0625020i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.9130 | − | 14.9609i | −1.40327 | − | 0.810176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4300 | + | 14.5724i | 0.617161 | + | 0.786837i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.871773 | − | 3.25350i | 0.0467992 | − | 0.174657i | −0.938570 | − | 0.345088i | \(-0.887849\pi\) |
0.985370 | + | 0.170431i | \(0.0545159\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.6071 | −1.15660 | −0.578301 | − | 0.815824i | \(-0.696284\pi\) | ||||
−0.578301 | + | 0.815824i | \(0.696284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.455390 | 0.0243069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.14414 | − | 15.4661i | 0.220570 | − | 0.823179i | −0.763561 | − | 0.645736i | \(-0.776551\pi\) |
0.984131 | − | 0.177443i | \(-0.0567827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.109664 | − | 0.486495i | −0.00580401 | − | 0.0257481i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.16163 | − | 1.24802i | −0.114086 | − | 0.0658678i | 0.441871 | − | 0.897079i | \(-0.354315\pi\) |
−0.555957 | + | 0.831211i | \(0.687648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.93490 | + | 15.4757i | 0.470258 | + | 0.814511i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.6354 | − | 14.6354i | −0.768162 | − | 0.768162i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.95927 | + | 1.86473i | 0.363271 | + | 0.0973382i | 0.435837 | − | 0.900025i | \(-0.356452\pi\) |
−0.0725664 | + | 0.997364i | \(0.523119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.84070 | + | 4.92023i | −0.147881 | + | 0.256137i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.777758 | + | 0.408385i | −0.0403792 | + | 0.0212023i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.82585 | − | 32.9385i | −0.456985 | − | 1.70549i | −0.682185 | − | 0.731179i | \(-0.738970\pi\) |
0.225200 | − | 0.974312i | \(-0.427696\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.102858 | − | 0.102858i | 0.00529746 | − | 0.00529746i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.7567i | − | 0.706632i | −0.935504 | − | 0.353316i | \(-0.885054\pi\) | ||
0.935504 | − | 0.353316i | \(-0.114946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.1234 | − | 6.42209i | 0.569869 | − | 0.329014i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.1114 | + | 3.78113i | −0.721057 | + | 0.193207i | −0.600643 | − | 0.799517i | \(-0.705089\pi\) |
−0.120413 | + | 0.992724i | \(0.538422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.15324 | + | 0.309010i | −0.0586225 | + | 0.0157079i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.89800 | − | 3.98256i | 0.349742 | − | 0.201924i | −0.314829 | − | 0.949148i | \(-0.601947\pi\) |
0.664572 | + | 0.747224i | \(0.268614\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.07943i | 0.0545893i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.78071 | − | 7.78071i | 0.392485 | − | 0.392485i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.89845 | − | 18.2812i | −0.245846 | − | 0.917510i | −0.972956 | − | 0.230989i | \(-0.925804\pi\) |
0.727110 | − | 0.686521i | \(-0.240863\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.81045 | − | 0.112730i | −0.140699 | − | 0.00564356i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.05926 | + | 12.2270i | −0.352523 | + | 0.610587i | −0.986691 | − | 0.162608i | \(-0.948009\pi\) |
0.634168 | + | 0.773195i | \(0.281343\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.33776 | + | 0.626402i | 0.116452 | + | 0.0312033i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.8830 | − | 40.8830i | −2.02649 | − | 2.02649i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.20404 | − | 5.54955i | −0.158429 | − | 0.274408i | 0.775873 | − | 0.630889i | \(-0.217310\pi\) |
−0.934302 | + | 0.356481i | \(0.883976\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.555268 | + | 0.320584i | 0.0273893 | + | 0.0158132i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.6174 | − | 7.04323i | −1.11293 | − | 0.346574i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.45061 | − | 12.8778i | 0.168977 | − | 0.630630i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.0491 | −0.539785 | −0.269893 | − | 0.962890i | \(-0.586988\pi\) | ||||
−0.269893 | + | 0.962890i | \(0.586988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.571065 | −0.0278320 | −0.0139160 | − | 0.999903i | \(-0.504430\pi\) | ||||
−0.0139160 | + | 0.999903i | \(0.504430\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.23771 | + | 12.0833i | −0.157423 | + | 0.587510i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.2492 | + | 5.91699i | −1.27029 | + | 0.286343i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.22038 | + | 1.28194i | 0.107201 | + | 0.0618925i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.04843 | + | 12.2082i | 0.339511 | + | 0.588050i | 0.984341 | − | 0.176276i | \(-0.0564051\pi\) |
−0.644830 | + | 0.764326i | \(0.723072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.3222 | − | 17.3222i | −0.832450 | − | 0.832450i | 0.155402 | − | 0.987851i | \(-0.450333\pi\) |
−0.987851 | + | 0.155402i | \(0.950333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.88062 | + | 1.57571i | 0.281308 | + | 0.0753763i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.4540 | − | 19.8389i | 0.546670 | − | 0.946860i | −0.451830 | − | 0.892104i | \(-0.649229\pi\) |
0.998500 | − | 0.0547558i | \(-0.0174380\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.97429 | + | 5.76238i | −0.189252 | + | 0.274399i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.23331 | + | 15.7989i | 0.201131 | + | 0.750629i | 0.990594 | + | 0.136832i | \(0.0436921\pi\) |
−0.789464 | + | 0.613797i | \(0.789641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.3997 | + | 12.3997i | −0.586484 | + | 0.586484i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 11.7151i | − | 0.552871i | −0.961032 | − | 0.276436i | \(-0.910847\pi\) | ||
0.961032 | − | 0.276436i | \(-0.0891532\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.7012 | + | 15.9933i | −1.30440 | + | 0.753095i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.6941 | − | 4.74111i | 0.831340 | − | 0.222757i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.59999 | − | 0.964614i | 0.168400 | − | 0.0451228i | −0.173634 | − | 0.984810i | \(-0.555551\pi\) |
0.342034 | + | 0.939688i | \(0.388884\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.163239 | − | 0.0942458i | 0.00761932 | − | 0.00439902i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 16.7937i | − | 0.782163i | −0.920356 | − | 0.391081i | \(-0.872101\pi\) | ||
0.920356 | − | 0.391081i | \(-0.127899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.41668 | − | 7.41668i | 0.344682 | − | 0.344682i | −0.513442 | − | 0.858124i | \(-0.671630\pi\) |
0.858124 | + | 0.513442i | \(0.171630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.05853 | + | 22.6108i | 0.280356 | + | 1.04630i | 0.952167 | + | 0.305579i | \(0.0988499\pi\) |
−0.671811 | + | 0.740722i | \(0.734483\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.3093 | − | 19.6338i | −0.476039 | − | 0.906603i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.36921 | + | 5.83564i | −0.155245 | + | 0.268892i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.49282 | − | 1.73975i | −0.298540 | − | 0.0799936i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.234777 | − | 0.234777i | −0.0107497 | − | 0.0107497i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.70212 | − | 2.94816i | −0.0777719 | − | 0.134705i | 0.824516 | − | 0.565838i | \(-0.191447\pi\) |
−0.902288 | + | 0.431133i | \(0.858114\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.05003 | + | 2.33829i | 0.184665 | + | 0.106617i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.1344 | − | 10.2757i | 0.506634 | − | 0.467558i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.63817 | − | 28.5061i | 0.346119 | − | 1.29173i | −0.545181 | − | 0.838318i | \(-0.683539\pi\) |
0.891300 | − | 0.453414i | \(-0.149794\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.6417 | −0.571677 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.14807 | 0.232329 | 0.116164 | − | 0.993230i | \(-0.462940\pi\) | ||||
0.116164 | + | 0.993230i | \(0.462940\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0155833 | − | 0.0581576i | 0.000701835 | − | 0.00261928i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.952588 | + | 0.879116i | −0.0427294 | + | 0.0394338i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.8743 | + | 13.7838i | 1.06876 | + | 0.617049i | 0.927843 | − | 0.372972i | \(-0.121661\pi\) |
0.140918 | + | 0.990021i | \(0.454995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.97626 | + | 10.3512i | 0.267000 | + | 0.462457i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.85759 | − | 7.85759i | −0.350353 | − | 0.350353i | 0.509888 | − | 0.860241i | \(-0.329687\pi\) |
−0.860241 | + | 0.509888i | \(0.829687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.3567 | + | 3.31097i | 0.548781 | + | 0.147046i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.04153 | − | 7.00013i | 0.179138 | − | 0.310275i | −0.762448 | − | 0.647050i | \(-0.776003\pi\) |
0.941585 | + | 0.336774i | \(0.109336\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.22454 | − | 6.14105i | −0.142645 | − | 0.271664i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.275152 | − | 1.02688i | −0.0121482 | − | 0.0453379i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −49.8012 | + | 49.8012i | −2.19025 | + | 2.19025i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.55462i | 0.112135i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.9610 | + | 10.3698i | −0.786887 | + | 0.454309i | −0.838865 | − | 0.544339i | \(-0.816781\pi\) |
0.0519787 | + | 0.998648i | \(0.483447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.0608 | + | 8.85863i | −1.44565 | + | 0.387361i | −0.894508 | − | 0.447051i | \(-0.852474\pi\) |
−0.551141 | + | 0.834412i | \(0.685807\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.967629 | − | 0.259276i | 0.0421506 | − | 0.0112942i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.48268 | + | 4.89748i | −0.368812 | + | 0.212934i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 8.95349i | − | 0.388548i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.82946 | − | 1.82946i | 0.0792428 | − | 0.0792428i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.37072 | + | 20.0438i | 0.231764 | + | 0.864953i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −35.5991 | + | 16.9083i | −1.53336 | + | 0.728292i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.79472 | + | 16.9650i | −0.421108 | + | 0.729380i | −0.996048 | − | 0.0888152i | \(-0.971692\pi\) |
0.574940 | + | 0.818195i | \(0.305025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9666 | + | 2.93848i | 0.470621 | + | 0.126102i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1296 | + | 16.1296i | 0.689650 | + | 0.689650i | 0.962155 | − | 0.272504i | \(-0.0878518\pi\) |
−0.272504 | + | 0.962155i | \(0.587852\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.08511 | − | 8.80767i | −0.217027 | − | 0.375902i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.294088 | − | 0.169792i | −0.0125286 | − | 0.00723337i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.3669 | + | 8.19766i | −1.54648 | + | 0.348600i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.183735 | + | 0.685709i | −0.00778511 | + | 0.0290544i | −0.969709 | − | 0.244263i | \(-0.921454\pi\) |
0.961924 | + | 0.273317i | \(0.0881208\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.543700 | 0.0229961 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06122 | 0.0448048 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.52961 | − | 13.1727i | 0.148755 | − | 0.555163i | −0.850804 | − | 0.525483i | \(-0.823885\pi\) |
0.999559 | − | 0.0296797i | \(-0.00944872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.52610 | − | 0.786646i | −0.106086 | − | 0.0330360i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.7464 | + | 21.7929i | 1.58241 | + | 0.913607i | 0.994506 | + | 0.104678i | \(0.0333813\pi\) |
0.587907 | + | 0.808928i | \(0.299952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.06742 | − | 3.58088i | −0.0865189 | − | 0.149855i | 0.819519 | − | 0.573053i | \(-0.194241\pi\) |
−0.906037 | + | 0.423198i | \(0.860908\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2729 | + | 15.2729i | 0.638035 | + | 0.638035i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.2864 | + | 4.63188i | 0.719643 | + | 0.192828i | 0.600012 | − | 0.799991i | \(-0.295162\pi\) |
0.119631 | + | 0.992818i | \(0.461829\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6094 | + | 21.8401i | −0.524028 | + | 0.907644i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.7871 | + | 0.713458i | 0.737933 | + | 0.0295992i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.483817 | − | 1.80563i | −0.0200377 | − | 0.0747815i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.1491 | + | 22.1491i | −0.914190 | + | 0.914190i | −0.996599 | − | 0.0824083i | \(-0.973739\pi\) |
0.0824083 | + | 0.996599i | \(0.473739\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.65001i | − | 0.232805i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.28093 | + | 3.62630i | −0.258363 | + | 0.149166i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.5732 | − | 11.4075i | 1.74827 | − | 0.468448i | 0.764016 | − | 0.645197i | \(-0.223225\pi\) |
0.984256 | + | 0.176749i | \(0.0565579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.6602 | + | 3.39228i | −0.518146 | + | 0.138837i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.0256 | + | 20.7994i | −1.47196 | + | 0.849839i | −0.999503 | − | 0.0315126i | \(-0.989968\pi\) |
−0.472461 | + | 0.881352i | \(0.656634\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.3940i | − | 0.546353i | −0.961964 | − | 0.273177i | \(-0.911926\pi\) | ||
0.961964 | − | 0.273177i | \(-0.0880744\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.92673 | − | 5.92673i | 0.241355 | − | 0.241355i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0297122 | + | 0.110887i | 0.00120598 | + | 0.00450078i | 0.966526 | − | 0.256568i | \(-0.0825917\pi\) |
−0.965320 | + | 0.261069i | \(0.915925\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.748245 | + | 0.392888i | −0.0303204 | + | 0.0159206i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.84836 | − | 4.93350i | 0.115232 | − | 0.199588i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.6918 | + | 8.22384i | 1.23963 | + | 0.332158i | 0.818322 | − | 0.574760i | \(-0.194905\pi\) |
0.421308 | + | 0.906918i | \(0.361571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.62323 | + | 4.62323i | 0.186124 | + | 0.186124i | 0.794018 | − | 0.607894i | \(-0.207985\pi\) |
−0.607894 | + | 0.794018i | \(0.707985\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.47073 | − | 6.01149i | −0.139501 | − | 0.241622i | 0.787807 | − | 0.615922i | \(-0.211216\pi\) |
−0.927308 | + | 0.374300i | \(0.877883\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.95946 | + | 2.86334i | 0.199016 | + | 0.114902i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.89682 | + | 8.41477i | 0.0759944 | + | 0.337130i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.54912 | − | 5.78140i | 0.0618660 | − | 0.230887i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.93569 | 0.0771811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8796 | 0.791394 | 0.395697 | − | 0.918381i | \(-0.370503\pi\) | ||||
0.395697 | + | 0.918381i | \(0.370503\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.34325 | − | 8.74514i | 0.0931359 | − | 0.347588i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.42736 | − | 2.06629i | 0.0961755 | − | 0.0818693i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.424298 | − | 0.244969i | −0.0167850 | − | 0.00969081i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.4485 | + | 30.2217i | 0.689175 | + | 1.19369i | 0.972105 | + | 0.234545i | \(0.0753600\pi\) |
−0.282931 | + | 0.959140i | \(0.591307\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.88618 | − | 4.88618i | −0.192692 | − | 0.192692i | 0.604166 | − | 0.796858i | \(-0.293506\pi\) |
−0.796858 | + | 0.604166i | \(0.793506\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.77556 | − | 2.08346i | −0.305689 | − | 0.0819091i | 0.102714 | − | 0.994711i | \(-0.467247\pi\) |
−0.408403 | + | 0.912802i | \(0.633914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.2044 | − | 43.6552i | 0.989358 | − | 1.71362i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.8858 | − | 7.51300i | −0.465841 | − | 0.294458i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.88419 | + | 36.8883i | 0.386798 | + | 1.44355i | 0.835312 | + | 0.549775i | \(0.185287\pi\) |
−0.448514 | + | 0.893776i | \(0.648047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.85376 | − | 1.85376i | 0.0723222 | − | 0.0723222i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.6894i | 0.533265i | 0.963798 | + | 0.266633i | \(0.0859110\pi\) | ||||
−0.963798 | + | 0.266633i | \(0.914089\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9368 | + | 11.5105i | −0.775451 | + | 0.447707i | −0.834816 | − | 0.550530i | \(-0.814426\pi\) |
0.0593648 | + | 0.998236i | \(0.481092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0829124 | + | 0.0222163i | −0.00322005 | + | 0.000862810i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.76692 | − | 0.473445i | 0.0684155 | − | 0.0183319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.6789 | + | 8.47484i | −0.567518 | + | 0.327656i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 57.2590i | − | 2.21046i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.2703 | + | 23.2703i | −0.897003 | + | 0.897003i | −0.995170 | − | 0.0981672i | \(-0.968702\pi\) |
0.0981672 | + | 0.995170i | \(0.468702\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.20669 | − | 26.8957i | −0.276976 | − | 1.03369i | −0.954506 | − | 0.298192i | \(-0.903616\pi\) |
0.677530 | − | 0.735495i | \(-0.263050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.52701 | + | 38.0695i | −0.0586012 | + | 1.46097i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.09110 | − | 14.0142i | 0.310051 | − | 0.537025i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.0614 | − | 4.57160i | −0.652838 | − | 0.174927i | −0.0828262 | − | 0.996564i | \(-0.526395\pi\) |
−0.570012 | + | 0.821637i | \(0.693061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.7436 | − | 17.7436i | −0.676959 | − | 0.676959i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0756005 | + | 0.130944i | 0.00288015 | + | 0.00498857i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4671 | + | 12.9714i | 0.854688 | + | 0.493455i | 0.862230 | − | 0.506517i | \(-0.169067\pi\) |
−0.00754165 | + | 0.999972i | \(0.502401\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.1023 | − | 10.9466i | −0.383754 | − | 0.415826i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.277168 | − | 1.03441i | 0.0104985 | − | 0.0391809i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.26966 | 0.237140 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.4364 | −1.67834 | −0.839171 | − | 0.543868i | \(-0.816959\pi\) | ||||
−0.839171 | + | 0.543868i | \(0.816959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.82564 | − | 10.5454i | 0.106571 | − | 0.397728i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.5849 | + | 37.2018i | −0.435695 | + | 1.39912i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.8956 | + | 14.3735i | 0.934975 | + | 0.539808i | 0.888382 | − | 0.459106i | \(-0.151830\pi\) |
0.0465938 | + | 0.998914i | \(0.485163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.04514 | − | 12.2025i | −0.264213 | − | 0.457631i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.5210 | + | 21.5210i | 0.805966 | + | 0.805966i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.9679 | + | 5.35038i | 0.745714 | + | 0.199814i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.2598 | − | 38.5551i | 0.830151 | − | 1.43786i | −0.0677672 | − | 0.997701i | \(-0.521588\pi\) |
0.897918 | − | 0.440162i | \(-0.145079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.3558 | − | 36.9495i | 0.869815 | − | 1.37607i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.16322 | + | 8.07324i | 0.0804509 | + | 0.300247i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.16817 | + | 7.16817i | −0.265853 | + | 0.265853i | −0.827427 | − | 0.561574i | \(-0.810196\pi\) |
0.561574 | + | 0.827427i | \(0.310196\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.194894 | − | 0.112522i | 0.00720842 | − | 0.00416178i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4950 | − | 5.49163i | 0.757002 | − | 0.202838i | 0.140380 | − | 0.990098i | \(-0.455168\pi\) |
0.616622 | + | 0.787260i | \(0.288501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.5814 | − | 12.2135i | 1.67901 | − | 0.449890i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.3345 | − | 14.6269i | 0.931943 | − | 0.538057i | 0.0445173 | − | 0.999009i | \(-0.485825\pi\) |
0.887426 | + | 0.460951i | \(0.152492\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.484127i | 0.0177849i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.9524 | − | 28.9524i | 1.06216 | − | 1.06216i | 0.0642254 | − | 0.997935i | \(-0.479542\pi\) |
0.997935 | − | 0.0642254i | \(-0.0204577\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.74141 | + | 6.49903i | 0.0637149 | + | 0.237787i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.6868 | + | 26.3990i | −0.609723 | + | 0.964599i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5551 | + | 21.7461i | −0.458143 | + | 0.793526i | −0.998863 | − | 0.0476761i | \(-0.984818\pi\) |
0.540720 | + | 0.841203i | \(0.318152\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.1957 | + | 2.73194i | 0.371553 | + | 0.0995574i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.56835 | − | 7.56835i | −0.275076 | − | 0.275076i | 0.556063 | − | 0.831140i | \(-0.312311\pi\) |
−0.831140 | + | 0.556063i | \(0.812311\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.1208 | + | 27.9221i | 0.585149 | + | 1.01351i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.6900 | − | 13.1001i | −0.822513 | − | 0.474878i | 0.0287696 | − | 0.999586i | \(-0.490841\pi\) |
−0.851282 | + | 0.524708i | \(0.824174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.99919 | + | 9.63108i | −0.108578 | + | 0.348668i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.05529 | + | 3.93840i | −0.0381043 | + | 0.142207i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.5978 | −1.13944 | −0.569722 | − | 0.821837i | \(-0.692949\pi\) | ||||
−0.569722 | + | 0.821837i | \(0.692949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.457658 | 0.0164822 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.56418 | + | 5.83759i | −0.0562596 | + | 0.209964i | −0.988334 | − | 0.152304i | \(-0.951331\pi\) |
0.932074 | + | 0.362268i | \(0.117997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.4268 | − | 19.9668i | −0.661058 | − | 0.716305i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.23072 | − | 3.01996i | −0.187410 | − | 0.108201i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.37919 | − | 2.38883i | −0.0493513 | − | 0.0854789i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.225868 | − | 0.225868i | −0.00807187 | − | 0.00807187i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.4494 | + | 7.62300i | 1.01411 | + | 0.271731i | 0.727347 | − | 0.686270i | \(-0.240753\pi\) |
0.286766 | + | 0.958001i | \(0.407420\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.5281 | − | 25.1635i | 0.517216 | − | 0.895844i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.140905 | − | 3.51288i | 0.00501001 | − | 0.124904i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.19870 | + | 4.47360i | 0.0425670 | + | 0.158862i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.2041 | − | 10.2041i | 0.361447 | − | 0.361447i | −0.502898 | − | 0.864346i | \(-0.667733\pi\) |
0.864346 | + | 0.502898i | \(0.167733\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.35794i | − | 0.0834181i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.82349 | + | 1.63014i | −0.0997631 | + | 0.0575982i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.2569 | − | 3.82014i | 0.503117 | − | 0.134810i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.0271 | − | 3.75854i | 0.493776 | − | 0.132307i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.72877 | + | 5.61691i | −0.342045 | + | 0.197480i | −0.661176 | − | 0.750231i | \(-0.729942\pi\) |
0.319131 | + | 0.947711i | \(0.396609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.2294i | 0.429432i | 0.976677 | + | 0.214716i | \(0.0688826\pi\) | ||||
−0.976677 | + | 0.214716i | \(0.931117\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.1504 | + | 21.1504i | −0.741778 | + | 0.741778i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.328510 | − | 1.22602i | −0.0114931 | − | 0.0428929i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.01845 | + | 0.643760i | 0.0355874 | + | 0.0224948i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.28223 | + | 10.8811i | −0.219251 | + | 0.379755i | −0.954579 | − | 0.297957i | \(-0.903695\pi\) |
0.735328 | + | 0.677712i | \(0.237028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.8147 | − | 8.79267i | −1.14385 | − | 0.306493i | −0.363351 | − | 0.931652i | \(-0.618367\pi\) |
−0.780497 | + | 0.625159i | \(0.785034\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.49196 | − | 3.49196i | −0.121427 | − | 0.121427i | 0.643782 | − | 0.765209i | \(-0.277364\pi\) |
−0.765209 | + | 0.643782i | \(0.777364\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.97255 | + | 13.8089i | 0.276898 | + | 0.479602i | 0.970612 | − | 0.240649i | \(-0.0773602\pi\) |
−0.693714 | + | 0.720250i | \(0.744027\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.17968 | − | 3.56784i | −0.214371 | − | 0.123767i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.442477 | − | 1.24304i | 0.0153309 | − | 0.0430687i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.37553 | − | 5.13354i | 0.0475452 | − | 0.177441i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.87527 | 0.0992654 | 0.0496327 | − | 0.998768i | \(-0.484195\pi\) | ||||
0.0496327 | + | 0.998768i | \(0.484195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8980 | 0.996482 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.70137 | + | 28.7419i | −0.265249 | + | 0.989924i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.0418 | − | 53.4204i | −0.413761 | − | 1.83555i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.716027 | − | 0.413398i | −0.0245740 | − | 0.0141878i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.4048 | + | 50.9305i | 1.00798 | + | 1.74588i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.0291 | − | 30.0291i | −1.02818 | − | 1.02818i | −0.999591 | − | 0.0285850i | \(-0.990900\pi\) |
−0.0285850 | − | 0.999591i | \(-0.509100\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.2151 | + | 7.56022i | 0.963810 | + | 0.258252i | 0.706212 | − | 0.708000i | \(-0.250402\pi\) |
0.257598 | + | 0.966252i | \(0.417069\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.4892 | + | 19.8999i | −0.392007 | + | 0.678976i | −0.992714 | − | 0.120493i | \(-0.961553\pi\) |
0.600707 | + | 0.799469i | \(0.294886\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.3085 | + | 6.98800i | −0.453551 | + | 0.238151i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.53355 | − | 16.9194i | −0.154324 | − | 0.575944i | −0.999162 | − | 0.0409229i | \(-0.986970\pi\) |
0.844838 | − | 0.535021i | \(-0.179696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9957 | − | 11.9957i | 0.407395 | − | 0.407395i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 79.3292i | − | 2.69106i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.30555 | + | 1.90846i | −0.112004 | + | 0.0646658i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.9098 | + | 3.72712i | −0.470776 | + | 0.126144i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.4109 | − | 7.34472i | 0.925600 | − | 0.248014i | 0.235622 | − | 0.971845i | \(-0.424287\pi\) |
0.689977 | + | 0.723831i | \(0.257620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.5239 | − | 11.2721i | 0.658524 | − | 0.380199i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.16979i | 0.207865i | 0.994584 | + | 0.103933i | \(0.0331427\pi\) | ||||
−0.994584 | + | 0.103933i | \(0.966857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.783899 | + | 0.783899i | −0.0263803 | + | 0.0263803i | −0.720174 | − | 0.693794i | \(-0.755938\pi\) |
0.693794 | + | 0.720174i | \(0.255938\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.49467 | − | 16.7743i | −0.150916 | − | 0.563227i | −0.999421 | − | 0.0340383i | \(-0.989163\pi\) |
0.848504 | − | 0.529188i | \(-0.177504\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.9552 | + | 1.36198i | 1.13882 | + | 0.0456793i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.81503 | − | 4.87578i | 0.0943072 | − | 0.163345i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.8458 | − | 3.44202i | −0.429868 | − | 0.115183i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.84405 | − | 1.84405i | −0.0615709 | − | 0.0615709i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.848816 | − | 1.47019i | −0.0283096 | − | 0.0490337i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0541994 | + | 0.0312920i | 0.00180564 | + | 0.00104249i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.01597 | − | 0.939194i | −0.100365 | − | 0.0312544i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.63012 | − | 24.7439i | 0.220150 | − | 0.821609i | −0.764140 | − | 0.645050i | \(-0.776837\pi\) |
0.984290 | − | 0.176559i | \(-0.0564967\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.7269 | −0.488462 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6035 | 0.384441 | 0.192220 | − | 0.981352i | \(-0.438431\pi\) | ||||
0.192220 | + | 0.981352i | \(0.438431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.80425 | + | 36.5900i | −0.324473 | + | 1.21095i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.4002 | − | 6.40184i | 0.937856 | − | 0.211407i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.41048 | + | 2.54639i | 0.145488 | + | 0.0839977i | 0.570977 | − | 0.820966i | \(-0.306564\pi\) |
−0.425489 | + | 0.904964i | \(0.639898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.6125 | − | 18.3814i | −0.349694 | − | 0.605688i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.157764 | + | 0.157764i | 0.00519288 | + | 0.00519288i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.9587 | + | 4.27612i | 0.524153 | + | 0.140446i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.2264 | + | 29.8370i | −0.565180 | + | 0.978921i | 0.431853 | + | 0.901944i | \(0.357860\pi\) |
−0.997033 | + | 0.0769766i | \(0.975473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.12601 | − | 4.22509i | −0.200772 | − | 0.138472i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.47680 | − | 24.1717i | −0.212041 | − | 0.791347i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.2281 | + | 24.2281i | −0.791498 | + | 0.791498i | −0.981738 | − | 0.190240i | \(-0.939073\pi\) |
0.190240 | + | 0.981738i | \(0.439073\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 0.936883i | − | 0.0305740i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.74532 | + | 3.89441i | −0.219891 | + | 0.126954i | −0.605900 | − | 0.795541i | \(-0.707187\pi\) |
0.386009 | + | 0.922495i | \(0.373853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.4269 | − | 8.42082i | 1.02340 | − | 0.274220i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.98473 | − | 2.67540i | 0.324460 | − | 0.0869389i | −0.0929124 | − | 0.995674i | \(-0.529618\pi\) |
0.417373 | + | 0.908735i | \(0.362951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.03391 | + | 0.596929i | −0.0335622 | + | 0.0193771i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 13.3987i | − | 0.434484i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.51038 | + | 6.51038i | −0.210892 | + | 0.210892i | −0.804646 | − | 0.593754i | \(-0.797645\pi\) |
0.593754 | + | 0.804646i | \(0.297645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.465457 | − | 1.73711i | −0.0150461 | − | 0.0561528i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.788625 | + | 1.50191i | 0.0254660 | + | 0.0484994i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.37734 | + | 2.38563i | −0.0444304 | + | 0.0769557i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.4019 | − | 3.05513i | −0.367421 | − | 0.0984501i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.7098 | + | 28.7098i | 0.923246 | + | 0.923246i | 0.997257 | − | 0.0740109i | \(-0.0235800\pi\) |
−0.0740109 | + | 0.997257i | \(0.523580\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.100193 | + | 0.173540i | 0.00321867 | + | 0.00557490i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.3528 | + | 30.8032i | 1.71217 | + | 0.988523i | 0.931622 | + | 0.363430i | \(0.118394\pi\) |
0.780550 | + | 0.625093i | \(0.214939\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.9217 | − | 23.9224i | 0.831012 | − | 0.766918i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.36702 | + | 5.10179i | −0.0437349 | + | 0.163221i | −0.984339 | − | 0.176283i | \(-0.943593\pi\) |
0.940605 | + | 0.339504i | \(0.110259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.3556 | −0.586648 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.81263 | −0.121728 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.99952 | + | 29.8546i | −0.255145 | + | 0.952215i | 0.712864 | + | 0.701302i | \(0.247397\pi\) |
−0.968010 | + | 0.250913i | \(0.919269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.3224 | + | 22.4464i | −0.774190 | + | 0.714478i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.92121 | + | 3.41861i | 0.188283 | + | 0.108706i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1694 | − | 22.8100i | −0.418339 | − | 0.724584i | 0.577434 | − | 0.816437i | \(-0.304054\pi\) |
−0.995773 | + | 0.0918537i | \(0.970721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.8140 | − | 15.8140i | −0.501841 | − | 0.501841i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.6007 | − | 2.84044i | −0.335726 | − | 0.0899575i | 0.0870178 | − | 0.996207i | \(-0.472266\pi\) |
−0.422744 | + | 0.906249i | \(0.638933\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.13469 | − | 8.89354i | 0.162454 | − | 0.281379i |
(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.e.1657.1 | 32 | ||
5.2 | odd | 4 | 420.2.bo.a.313.6 | yes | 32 | ||
5.3 | odd | 4 | inner | 2100.2.ce.e.1993.2 | 32 | ||
5.4 | even | 2 | 420.2.bo.a.397.5 | yes | 32 | ||
7.3 | odd | 6 | inner | 2100.2.ce.e.157.2 | 32 | ||
15.2 | even | 4 | 1260.2.dq.c.1153.4 | 32 | |||
15.14 | odd | 2 | 1260.2.dq.c.397.7 | 32 | |||
35.2 | odd | 12 | 2940.2.x.c.1273.3 | 32 | |||
35.3 | even | 12 | inner | 2100.2.ce.e.493.1 | 32 | ||
35.9 | even | 6 | 2940.2.x.c.97.10 | 32 | |||
35.12 | even | 12 | 2940.2.x.c.1273.10 | 32 | |||
35.17 | even | 12 | 420.2.bo.a.73.5 | ✓ | 32 | ||
35.19 | odd | 6 | 2940.2.x.c.97.3 | 32 | |||
35.24 | odd | 6 | 420.2.bo.a.157.6 | yes | 32 | ||
105.17 | odd | 12 | 1260.2.dq.c.73.7 | 32 | |||
105.59 | even | 6 | 1260.2.dq.c.577.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bo.a.73.5 | ✓ | 32 | 35.17 | even | 12 | ||
420.2.bo.a.157.6 | yes | 32 | 35.24 | odd | 6 | ||
420.2.bo.a.313.6 | yes | 32 | 5.2 | odd | 4 | ||
420.2.bo.a.397.5 | yes | 32 | 5.4 | even | 2 | ||
1260.2.dq.c.73.7 | 32 | 105.17 | odd | 12 | |||
1260.2.dq.c.397.7 | 32 | 15.14 | odd | 2 | |||
1260.2.dq.c.577.4 | 32 | 105.59 | even | 6 | |||
1260.2.dq.c.1153.4 | 32 | 15.2 | even | 4 | |||
2100.2.ce.e.157.2 | 32 | 7.3 | odd | 6 | inner | ||
2100.2.ce.e.493.1 | 32 | 35.3 | even | 12 | inner | ||
2100.2.ce.e.1657.1 | 32 | 1.1 | even | 1 | trivial | ||
2100.2.ce.e.1993.2 | 32 | 5.3 | odd | 4 | inner | ||
2940.2.x.c.97.3 | 32 | 35.19 | odd | 6 | |||
2940.2.x.c.97.10 | 32 | 35.9 | even | 6 | |||
2940.2.x.c.1273.3 | 32 | 35.2 | odd | 12 | |||
2940.2.x.c.1273.10 | 32 | 35.12 | even | 12 |