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: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 493.2 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.493 |
Dual form | 2100.2.ce.b.1657.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(7\) | −1.15539 | + | 2.38014i | −0.436698 | + | 0.899608i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.36603 | + | 2.36603i | −0.411872 | + | 0.713384i | −0.995094 | − | 0.0989291i | \(-0.968458\pi\) |
0.583222 | + | 0.812313i | \(0.301792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.707107 | + | 0.707107i | −0.196116 | + | 0.196116i | −0.798333 | − | 0.602217i | \(-0.794284\pi\) |
0.602217 | + | 0.798333i | \(0.294284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.50266 | − | 1.74238i | 1.57713 | − | 0.422590i | 0.639092 | − | 0.769130i | \(-0.279310\pi\) |
0.938035 | + | 0.346540i | \(0.112644\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.23205 | + | 7.33013i | 0.970899 | + | 1.68165i | 0.692853 | + | 0.721079i | \(0.256353\pi\) |
0.278046 | + | 0.960568i | \(0.410313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.59808 | − | 0.500000i | −0.566947 | − | 0.109109i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.93185 | − | 7.20977i | 0.402819 | − | 1.50334i | −0.405224 | − | 0.914217i | \(-0.632807\pi\) |
0.808043 | − | 0.589123i | \(-0.200527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.92820i | 1.28654i | 0.765641 | + | 0.643268i | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.73205 | − | 1.00000i | −0.311086 | − | 0.179605i | 0.336327 | − | 0.941745i | \(-0.390815\pi\) |
−0.647412 | + | 0.762140i | \(0.724149\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.63896 | − | 0.707107i | −0.459384 | − | 0.123091i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8147 | − | 2.89778i | −1.77792 | − | 0.476392i | −0.787717 | − | 0.616038i | \(-0.788737\pi\) |
−0.990201 | + | 0.139646i | \(0.955403\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.866025 | − | 0.500000i | −0.138675 | − | 0.0800641i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.19615i | − | 0.655329i | −0.944794 | − | 0.327664i | \(-0.893738\pi\) | ||
0.944794 | − | 0.327664i | \(-0.106262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.378937 | − | 0.378937i | −0.0577874 | − | 0.0577874i | 0.677623 | − | 0.735410i | \(-0.263010\pi\) |
−0.735410 | + | 0.677623i | \(0.763010\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.63896 | + | 9.84873i | −0.384932 | + | 1.43658i | 0.453343 | + | 0.891336i | \(0.350231\pi\) |
−0.838275 | + | 0.545248i | \(0.816435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.33013 | − | 5.50000i | −0.618590 | − | 0.785714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.36603 | + | 5.83013i | 0.471338 | + | 0.816381i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.43451 | + | 2.26002i | −1.15857 | + | 0.310438i | −0.786394 | − | 0.617725i | \(-0.788055\pi\) |
−0.372175 | + | 0.928163i | \(0.621388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.98502 | + | 5.98502i | −0.792736 | + | 0.792736i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.63397 | + | 8.02628i | −0.603292 | + | 1.04493i | 0.389027 | + | 0.921226i | \(0.372811\pi\) |
−0.992319 | + | 0.123706i | \(0.960522\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.42820 | + | 4.86603i | −1.07912 | + | 0.623031i | −0.930659 | − | 0.365887i | \(-0.880766\pi\) |
−0.148462 | + | 0.988918i | \(0.547432\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.189469 | − | 2.63896i | −0.0238708 | − | 0.332478i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.81173 | + | 6.76148i | 0.221338 | + | 0.826046i | 0.983838 | + | 0.179058i | \(0.0573050\pi\) |
−0.762500 | + | 0.646988i | \(0.776028\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.46410 | 0.898572 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.98382 | − | 14.8678i | −0.466271 | − | 1.74015i | −0.652641 | − | 0.757668i | \(-0.726339\pi\) |
0.186370 | − | 0.982480i | \(-0.440328\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.05317 | − | 5.98502i | −0.461902 | − | 0.682057i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.96410 | − | 1.13397i | 0.220979 | − | 0.127582i | −0.385425 | − | 0.922739i | \(-0.625945\pi\) |
0.606403 | + | 0.795157i | \(0.292612\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.34607 | + | 3.34607i | −0.367278 | + | 0.367278i | −0.866484 | − | 0.499205i | \(-0.833625\pi\) |
0.499205 | + | 0.866484i | \(0.333625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.69213 | + | 1.79315i | −0.717472 | + | 0.192246i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.63397 | + | 6.29423i | 0.385201 | + | 0.667187i | 0.991797 | − | 0.127823i | \(-0.0407989\pi\) |
−0.606596 | + | 0.795010i | \(0.707466\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.866025 | − | 2.50000i | −0.0907841 | − | 0.262071i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.517638 | − | 1.93185i | 0.0536766 | − | 0.200324i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50026 | + | 2.50026i | 0.253863 | + | 0.253863i | 0.822552 | − | 0.568690i | \(-0.192549\pi\) |
−0.568690 | + | 0.822552i | \(0.692549\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.73205i | − | 0.274581i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.83013 | + | 3.36603i | 0.580119 | + | 0.334932i | 0.761181 | − | 0.648540i | \(-0.224620\pi\) |
−0.181061 | + | 0.983472i | \(0.557953\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.50146 | − | 1.20616i | −0.443542 | − | 0.118847i | 0.0301341 | − | 0.999546i | \(-0.490407\pi\) |
−0.473676 | + | 0.880699i | \(0.657073\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.2301 | + | 3.81294i | 1.37567 | + | 0.368610i | 0.869547 | − | 0.493850i | \(-0.164411\pi\) |
0.506125 | + | 0.862460i | \(0.331077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0622 | + | 6.96410i | 1.15535 | + | 0.667040i | 0.950185 | − | 0.311688i | \(-0.100894\pi\) |
0.205163 | + | 0.978728i | \(0.434228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11.1962i | − | 1.06269i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.03579 | − | 6.03579i | −0.567800 | − | 0.567800i | 0.363712 | − | 0.931511i | \(-0.381509\pi\) |
−0.931511 | + | 0.363712i | \(0.881509\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.258819 | − | 0.965926i | 0.0239278 | − | 0.0892999i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.36603 | + | 17.4904i | −0.308563 | + | 1.60334i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.76795 | + | 3.06218i | 0.160723 | + | 0.278380i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.05317 | − | 1.08604i | 0.365462 | − | 0.0979253i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0507680 | + | 0.0507680i | −0.00450493 | + | 0.00450493i | −0.709356 | − | 0.704851i | \(-0.751014\pi\) |
0.704851 | + | 0.709356i | \(0.251014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.267949 | − | 0.464102i | 0.0235916 | − | 0.0408619i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6603 | − | 8.46410i | 1.28087 | − | 0.739512i | 0.303864 | − | 0.952715i | \(-0.401723\pi\) |
0.977008 | + | 0.213203i | \(0.0683897\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.3364 | + | 1.60368i | −1.93681 | + | 0.139057i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.55291 | − | 5.79555i | −0.132674 | − | 0.495148i | 0.867322 | − | 0.497747i | \(-0.165839\pi\) |
−0.999997 | + | 0.00259945i | \(0.999173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8564 | −1.42974 | −0.714871 | − | 0.699256i | \(-0.753515\pi\) | ||||
−0.714871 | + | 0.699256i | \(0.753515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.1962 | −0.858671 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.707107 | − | 2.63896i | −0.0591312 | − | 0.220681i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.19187 | − | 5.60609i | 0.345740 | − | 0.462382i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.90192 | + | 4.56218i | −0.647351 | + | 0.373748i | −0.787441 | − | 0.616391i | \(-0.788594\pi\) |
0.140090 | + | 0.990139i | \(0.455261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.33013 | − | 9.23205i | 0.433760 | − | 0.751294i | −0.563434 | − | 0.826161i | \(-0.690520\pi\) |
0.997193 | + | 0.0748675i | \(0.0238534\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.76028 | + | 4.76028i | −0.384846 | + | 0.384846i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4183 | + | 3.32748i | −0.991091 | + | 0.265562i | −0.717709 | − | 0.696343i | \(-0.754809\pi\) |
−0.273382 | + | 0.961905i | \(0.588142\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.36603 | − | 7.56218i | −0.346248 | − | 0.599720i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.9282 | + | 12.9282i | 1.17651 | + | 1.01889i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.776457 | − | 2.89778i | 0.0608168 | − | 0.226971i | −0.928828 | − | 0.370512i | \(-0.879182\pi\) |
0.989644 | + | 0.143541i | \(0.0458488\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.240237 | − | 0.240237i | −0.0185901 | − | 0.0185901i | 0.697751 | − | 0.716341i | \(-0.254184\pi\) |
−0.716341 | + | 0.697751i | \(0.754184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000i | 0.923077i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.33013 | − | 4.23205i | −0.560549 | − | 0.323633i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1087 | + | 3.24453i | 0.920611 | + | 0.246677i | 0.687847 | − | 0.725856i | \(-0.258556\pi\) |
0.232765 | + | 0.972533i | \(0.425223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.95215 | − | 2.39872i | −0.672885 | − | 0.180299i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.19615 | + | 4.73205i | 0.612609 | + | 0.353690i | 0.773986 | − | 0.633203i | \(-0.218260\pi\) |
−0.161377 | + | 0.986893i | \(0.551593\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.39230i | − | 0.475136i | −0.971371 | − | 0.237568i | \(-0.923650\pi\) | ||
0.971371 | − | 0.237568i | \(-0.0763503\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.88160 | − | 6.88160i | −0.508702 | − | 0.508702i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.76028 | + | 17.7656i | −0.348106 | + | 1.29915i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50000 | − | 0.866025i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0981 | + | 20.9545i | 0.875386 | + | 1.51621i | 0.856351 | + | 0.516394i | \(0.172726\pi\) |
0.0190352 | + | 0.999819i | \(0.493941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8666 | − | 3.44760i | 0.926160 | − | 0.248164i | 0.235943 | − | 0.971767i | \(-0.424182\pi\) |
0.690216 | + | 0.723603i | \(0.257515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.58630 | − | 3.58630i | 0.255513 | − | 0.255513i | −0.567713 | − | 0.823226i | \(-0.692172\pi\) |
0.823226 | + | 0.567713i | \(0.192172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.23205 | − | 7.33013i | 0.300002 | − | 0.519619i | −0.676134 | − | 0.736779i | \(-0.736346\pi\) |
0.976136 | + | 0.217160i | \(0.0696793\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.06218 | + | 3.50000i | −0.427593 | + | 0.246871i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.4901 | − | 8.00481i | −1.15738 | − | 0.561827i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.93185 | + | 7.20977i | 0.134273 | + | 0.501114i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.1244 | −1.59955 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.7321 | −1.08304 | −0.541520 | − | 0.840688i | \(-0.682151\pi\) | ||||
−0.541520 | + | 0.840688i | \(0.682151\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.07055 | − | 7.72741i | −0.141872 | − | 0.529473i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.38134 | − | 2.96713i | 0.297425 | − | 0.201422i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.3301 | − | 7.69615i | 0.900767 | − | 0.520058i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.36603 | + | 5.83013i | −0.226423 | + | 0.392177i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.947343 | + | 0.947343i | −0.0634388 | + | 0.0634388i | −0.738114 | − | 0.674676i | \(-0.764284\pi\) |
0.674676 | + | 0.738114i | \(0.264284\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.3843 | − | 3.58630i | 0.888345 | − | 0.238031i | 0.214341 | − | 0.976759i | \(-0.431240\pi\) |
0.674004 | + | 0.738728i | \(0.264573\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.86603 | − | 10.1603i | −0.387638 | − | 0.671408i | 0.604493 | − | 0.796610i | \(-0.293376\pi\) |
−0.992131 | + | 0.125202i | \(0.960042\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.73205 | − | 5.46410i | 0.311346 | − | 0.359511i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.77766 | + | 10.3664i | −0.181971 | + | 0.679123i | 0.813288 | + | 0.581861i | \(0.197675\pi\) |
−0.995259 | + | 0.0972622i | \(0.968991\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.60368 | + | 1.60368i | 0.104170 | + | 0.104170i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3205i | 1.50848i | 0.656600 | + | 0.754239i | \(0.271994\pi\) | ||||
−0.656600 | + | 0.754239i | \(0.728006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.69615 | − | 5.59808i | −0.624584 | − | 0.360604i | 0.154068 | − | 0.988060i | \(-0.450763\pi\) |
−0.778652 | + | 0.627457i | \(0.784096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.965926 | + | 0.258819i | 0.0619642 | + | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.17569 | − | 2.19067i | −0.520207 | − | 0.139389i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.09808 | − | 2.36603i | −0.259705 | − | 0.149941i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 10.5885i | − | 0.668337i | −0.942513 | − | 0.334169i | \(-0.891544\pi\) | ||
0.942513 | − | 0.334169i | \(-0.108456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.4195 | + | 14.4195i | 0.906549 | + | 0.906549i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.56892 | − | 20.7835i | 0.347380 | − | 1.29644i | −0.542428 | − | 0.840103i | \(-0.682495\pi\) |
0.889807 | − | 0.456336i | \(-0.150839\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.3923 | − | 22.3923i | 1.20498 | − | 1.39139i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.46410 | − | 6.00000i | −0.214423 | − | 0.371391i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.76268 | − | 2.34795i | 0.540330 | − | 0.144781i | 0.0216758 | − | 0.999765i | \(-0.493100\pi\) |
0.518654 | + | 0.854984i | \(0.326433\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.13922 | + | 5.13922i | −0.314515 | + | 0.314515i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.29423 | − | 7.43782i | 0.261824 | − | 0.453492i | −0.704903 | − | 0.709304i | \(-0.749009\pi\) |
0.966727 | + | 0.255812i | \(0.0823428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9282 | − | 7.46410i | 0.785332 | − | 0.453412i | −0.0529843 | − | 0.998595i | \(-0.516873\pi\) |
0.838317 | + | 0.545183i | \(0.183540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.19067 | − | 1.48356i | 0.132585 | − | 0.0897894i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.48597 | − | 20.4739i | −0.329620 | − | 1.23016i | −0.909585 | − | 0.415517i | \(-0.863601\pi\) |
0.579966 | − | 0.814641i | \(-0.303066\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.87564 | −0.529477 | −0.264738 | − | 0.964320i | \(-0.585286\pi\) | ||||
−0.264738 | + | 0.964320i | \(0.585286\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.89967 | − | 7.08965i | −0.112923 | − | 0.421436i | 0.886200 | − | 0.463303i | \(-0.153336\pi\) |
−0.999123 | + | 0.0418674i | \(0.986669\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.98743 | + | 4.84821i | 0.589539 | + | 0.286181i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.5263 | − | 14.1603i | 1.44272 | − | 0.832956i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.76795 | + | 3.06218i | −0.103639 | + | 0.179508i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5911 | + | 11.5911i | −0.677160 | + | 0.677160i | −0.959357 | − | 0.282197i | \(-0.908937\pi\) |
0.282197 | + | 0.959357i | \(0.408937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.63896 | − | 0.707107i | 0.153128 | − | 0.0410305i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.73205 | + | 6.46410i | 0.215830 | + | 0.373829i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.33975 | − | 0.464102i | 0.0772217 | − | 0.0267504i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.74238 | + | 6.50266i | −0.100097 | + | 0.373568i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.79315 | − | 1.79315i | −0.102341 | − | 0.102341i | 0.654083 | − | 0.756423i | \(-0.273055\pi\) |
−0.756423 | + | 0.654083i | \(0.773055\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.66025i | − | 0.265113i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.19615 | + | 3.00000i | 0.294647 | + | 0.170114i | 0.640036 | − | 0.768345i | \(-0.278920\pi\) |
−0.345389 | + | 0.938460i | \(0.612253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.44949 | − | 0.656339i | −0.138453 | − | 0.0370985i | 0.188927 | − | 0.981991i | \(-0.439499\pi\) |
−0.327380 | + | 0.944893i | \(0.606166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.31079 | − | 0.619174i | −0.129787 | − | 0.0347763i | 0.193341 | − | 0.981132i | \(-0.438068\pi\) |
−0.323128 | + | 0.946355i | \(0.604734\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.3923 | − | 9.46410i | −0.917793 | − | 0.529888i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.7321i | 0.822263i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.2915 | + | 40.2915i | 2.24188 | + | 2.24188i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.60488 | + | 13.4536i | −0.199351 | + | 0.743986i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.3923 | − | 17.6603i | −1.12426 | − | 0.973641i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.66987 | + | 11.5526i | 0.366609 | + | 0.634986i | 0.989033 | − | 0.147694i | \(-0.0471852\pi\) |
−0.622424 | + | 0.782681i | \(0.713852\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.8147 | − | 2.89778i | 0.592639 | − | 0.158797i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.656339 | + | 0.656339i | −0.0357531 | + | 0.0357531i | −0.724757 | − | 0.689004i | \(-0.758048\pi\) |
0.689004 | + | 0.724757i | \(0.258048\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.26795 | − | 7.39230i | 0.231803 | − | 0.401495i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.73205 | − | 2.73205i | 0.256255 | − | 0.147949i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0938 | − | 3.95164i | 0.976972 | − | 0.213368i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.19239 | + | 34.3065i | 0.493473 | + | 1.84167i | 0.538418 | + | 0.842678i | \(0.319022\pi\) |
−0.0449449 | + | 0.998989i | \(0.514311\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9282 | 0.692031 | 0.346015 | − | 0.938229i | \(-0.387534\pi\) | ||||
0.346015 | + | 0.938229i | \(0.387534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.01790 | + | 11.2629i | 0.160626 | + | 0.599466i | 0.998558 | + | 0.0536901i | \(0.0170983\pi\) |
−0.837931 | + | 0.545776i | \(0.816235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.7656 | + | 1.27551i | −0.940255 | + | 0.0675073i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.2942 | + | 14.0263i | −1.28220 | + | 0.740279i | −0.977250 | − | 0.212090i | \(-0.931973\pi\) |
−0.304950 | + | 0.952368i | \(0.598640\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26.3205 | + | 45.5885i | −1.38529 | + | 2.39939i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.50026 | + | 2.50026i | −0.131229 | + | 0.131229i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.20977 | − | 1.93185i | 0.376347 | − | 0.100842i | −0.0656868 | − | 0.997840i | \(-0.520924\pi\) |
0.442034 | + | 0.896998i | \(0.354257\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.09808 | + | 3.63397i | 0.109221 | + | 0.189177i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.36603 | − | 22.6865i | 0.226673 | − | 1.17783i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.89589 | − | 14.5397i | 0.201721 | − | 0.752835i | −0.788702 | − | 0.614775i | \(-0.789247\pi\) |
0.990424 | − | 0.138060i | \(-0.0440866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.89898 | − | 4.89898i | −0.252310 | − | 0.252310i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.4449i | − | 1.20428i | −0.798390 | − | 0.602141i | \(-0.794315\pi\) | ||
0.798390 | − | 0.602141i | \(-0.205685\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0621778 | − | 0.0358984i | −0.00318547 | − | 0.00183913i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.7004 | + | 7.69024i | 1.46652 | + | 0.392953i | 0.901737 | − | 0.432286i | \(-0.142293\pi\) |
0.564784 | + | 0.825239i | \(0.308960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.517638 | + | 0.138701i | 0.0263130 | + | 0.00705055i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.4186 | + | 8.90192i | 0.781753 | + | 0.451345i | 0.837051 | − | 0.547124i | \(-0.184278\pi\) |
−0.0552980 | + | 0.998470i | \(0.517611\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 50.2487i | − | 2.54119i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.9700 | + | 11.9700i | 0.603809 | + | 0.603809i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.69161 | + | 6.31319i | −0.0848997 | + | 0.316850i | −0.995295 | − | 0.0968891i | \(-0.969111\pi\) |
0.910395 | + | 0.413739i | \(0.135777\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.33013 | − | 21.1603i | −0.366965 | − | 1.05934i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.2942 | + | 23.0263i | 0.663882 | + | 1.14988i | 0.979587 | + | 0.201020i | \(0.0644257\pi\) |
−0.315705 | + | 0.948857i | \(0.602241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.93185 | − | 0.517638i | 0.0962324 | − | 0.0257854i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.6293 | − | 21.6293i | 1.07212 | − | 1.07212i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.79423 | + | 10.0359i | −0.286506 | + | 0.496243i | −0.972973 | − | 0.230918i | \(-0.925827\pi\) |
0.686467 | + | 0.727161i | \(0.259161\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.19615 | − | 3.00000i | 0.256307 | − | 0.147979i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.7496 | − | 20.3030i | −0.676573 | − | 0.999047i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.36276 | − | 16.2820i | −0.213645 | − | 0.797335i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.0525589 | −0.00256767 | −0.00128383 | − | 0.999999i | \(-0.500409\pi\) | ||||
−0.00128383 | + | 0.999999i | \(0.500409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.3923 | −1.52997 | −0.764984 | − | 0.644050i | \(-0.777253\pi\) | ||||
−0.764984 | + | 0.644050i | \(0.777253\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.63896 | − | 9.84873i | −0.128311 | − | 0.478861i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.84392 | − | 25.6825i | −0.0892335 | − | 1.24286i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.36603 | − | 1.36603i | 0.114233 | − | 0.0659523i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.53590 | + | 9.58846i | −0.266655 | + | 0.461860i | −0.967996 | − | 0.250966i | \(-0.919252\pi\) |
0.701341 | + | 0.712826i | \(0.252585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.5921 | + | 21.5921i | −1.03765 | + | 1.03765i | −0.0383892 | + | 0.999263i | \(0.512223\pi\) |
−0.999263 | + | 0.0383892i | \(0.987777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 61.0242 | − | 16.3514i | 2.91918 | − | 0.782193i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.89230 | + | 11.9378i | 0.328952 | + | 0.569761i | 0.982304 | − | 0.187293i | \(-0.0599713\pi\) |
−0.653352 | + | 0.757054i | \(0.726638\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.50000 | + | 2.59808i | 0.309524 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.99863 | − | 22.3872i | 0.285003 | − | 1.06365i | −0.663834 | − | 0.747880i | \(-0.731072\pi\) |
0.948837 | − | 0.315767i | \(-0.102262\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.45189 | − | 6.45189i | −0.305164 | − | 0.305164i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3397i | 0.487963i | 0.969780 | + | 0.243981i | \(0.0784536\pi\) | ||||
−0.969780 | + | 0.243981i | \(0.921546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.92820 | + | 5.73205i | 0.467501 | + | 0.269912i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.2970 | + | 2.75908i | 0.483796 | + | 0.129633i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5749 | + | 4.17329i | 0.728565 | + | 0.195218i | 0.603990 | − | 0.796992i | \(-0.293577\pi\) |
0.124575 | + | 0.992210i | \(0.460243\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.83013 | − | 3.36603i | −0.272127 | − | 0.157113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.7128i | − | 0.824968i | −0.910965 | − | 0.412484i | \(-0.864661\pi\) | ||
0.910965 | − | 0.412484i | \(-0.135339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0962 | + | 22.0962i | 1.02690 | + | 1.02690i | 0.999628 | + | 0.0272682i | \(0.00868082\pi\) |
0.0272682 | + | 0.999628i | \(0.491319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.20977 | − | 26.9072i | 0.333628 | − | 1.24512i | −0.571720 | − | 0.820449i | \(-0.693724\pi\) |
0.905349 | − | 0.424669i | \(-0.139610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.1865 | − | 3.50000i | −0.839776 | − | 0.161615i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.42820 | − | 11.1340i | −0.296196 | − | 0.513026i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.41421 | − | 0.378937i | 0.0650256 | − | 0.0174236i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.17449 | − | 6.17449i | 0.282711 | − | 0.282711i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.2224 | − | 22.9019i | 0.604148 | − | 1.04642i | −0.388037 | − | 0.921644i | \(-0.626847\pi\) |
0.992185 | − | 0.124772i | \(-0.0398199\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.69615 | − | 5.59808i | 0.442106 | − | 0.255250i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.62398 | + | 17.7656i | −0.392405 | + | 0.808363i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.55343 | + | 24.4577i | 0.296964 | + | 1.10829i | 0.939645 | + | 0.342151i | \(0.111156\pi\) |
−0.642681 | + | 0.766134i | \(0.722178\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.00000 | 0.135665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3923 | 0.649516 | 0.324758 | − | 0.945797i | \(-0.394717\pi\) | ||||
0.324758 | + | 0.945797i | \(0.394717\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0716 | + | 45.0518i | 0.543677 | + | 2.02903i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.24316 | − | 19.0411i | 0.414612 | − | 0.854111i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.03590 | − | 0.598076i | 0.0463732 | − | 0.0267736i | −0.476634 | − | 0.879102i | \(-0.658143\pi\) |
0.523007 | + | 0.852328i | \(0.324810\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.169873 | − | 0.294229i | 0.00758937 | − | 0.0131452i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6969 | − | 14.6969i | 0.655304 | − | 0.655304i | −0.298961 | − | 0.954265i | \(-0.596640\pi\) |
0.954265 | + | 0.298961i | \(0.0966401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.5911 | + | 3.10583i | −0.514779 | + | 0.137935i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.7321 | − | 18.5885i | −0.475690 | − | 0.823919i | 0.523922 | − | 0.851766i | \(-0.324468\pi\) |
−0.999612 | + | 0.0278471i | \(0.991135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.9904 | + | 7.69615i | 1.76907 | + | 0.340458i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.19067 | − | 8.17569i | 0.0967205 | − | 0.360966i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.6975 | − | 19.6975i | −0.866293 | − | 0.866293i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.5359i | 0.550265i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.3205 | + | 18.6603i | 1.41599 | + | 0.817521i | 0.995943 | − | 0.0899832i | \(-0.0286813\pi\) |
0.420044 | + | 0.907504i | \(0.362015\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.6622 | + | 5.00052i | 0.816040 | + | 0.218657i | 0.642614 | − | 0.766190i | \(-0.277850\pi\) |
0.173426 | + | 0.984847i | \(0.444516\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.0053 | − | 3.48477i | −0.566521 | − | 0.151799i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.3301 | − | 16.3564i | −1.23174 | − | 0.711148i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.26795i | − | 0.402195i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.96713 | + | 2.96713i | 0.128521 | + | 0.128521i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.44949 | + | 9.14162i | −0.105703 | + | 0.394490i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.9282 | − | 2.73205i | 0.815295 | − | 0.117678i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1603 | + | 33.1865i | 0.823764 | + | 1.42680i | 0.902861 | + | 0.429934i | \(0.141463\pi\) |
−0.0790969 | + | 0.996867i | \(0.525204\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.17449 | − | 1.65445i | 0.264973 | − | 0.0709993i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3538 | + | 20.3538i | −0.870265 | + | 0.870265i | −0.992501 | − | 0.122236i | \(-0.960994\pi\) |
0.122236 | + | 0.992501i | \(0.460994\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.86603 | − | 8.42820i | 0.207677 | − | 0.359707i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −50.7846 | + | 29.3205i | −2.16350 | + | 1.24910i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.429705 | + | 5.98502i | 0.0182729 | + | 0.254509i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.13681 | + | 4.24264i | 0.0481683 | + | 0.179766i | 0.985819 | − | 0.167813i | \(-0.0536704\pi\) |
−0.937651 | + | 0.347579i | \(0.887004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.535898 | 0.0226661 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.3923 | −0.776524 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.2277 | + | 38.1702i | 0.431045 | + | 1.60868i | 0.750358 | + | 0.661031i | \(0.229881\pi\) |
−0.319314 | + | 0.947649i | \(0.603452\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.48356 | + | 2.19067i | 0.0623038 | + | 0.0919995i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.4186 | − | 19.2942i | 1.40098 | − | 0.808856i | 0.406487 | − | 0.913657i | \(-0.366754\pi\) |
0.994493 | + | 0.104801i | \(0.0334204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.4545 | − | 23.3038i | 0.563053 | − | 0.975236i | −0.434175 | − | 0.900828i | \(-0.642960\pi\) |
0.997228 | − | 0.0744073i | \(-0.0237065\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.1093 | + | 17.1093i | −0.714750 | + | 0.714750i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.65926 | + | 2.58819i | −0.402120 | + | 0.107748i | −0.454210 | − | 0.890895i | \(-0.650078\pi\) |
0.0520899 | + | 0.998642i | \(0.483412\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.66025 | + | 11.5359i | 0.276791 | + | 0.479416i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.09808 | − | 11.8301i | −0.170017 | − | 0.490796i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.17449 | − | 23.0435i | 0.255721 | − | 0.954365i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.0101 | + | 21.0101i | 0.867181 | + | 0.867181i | 0.992159 | − | 0.124979i | \(-0.0398862\pi\) |
−0.124979 | + | 0.992159i | \(0.539886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 16.9282i | − | 0.697514i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.39230 | + | 2.53590i | 0.180675 | + | 0.104313i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.9783 | − | 9.10446i | −1.39532 | − | 0.373875i | −0.518659 | − | 0.854981i | \(-0.673568\pi\) |
−0.876662 | + | 0.481106i | \(0.840235\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.17569 | + | 2.19067i | 0.334609 | + | 0.0896582i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.9545 | + | 6.90192i | 0.488447 | + | 0.282005i | 0.723930 | − | 0.689874i | \(-0.242334\pi\) |
−0.235483 | + | 0.971878i | \(0.575667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.5167i | − | 0.510565i | −0.966866 | − | 0.255283i | \(-0.917831\pi\) | ||
0.966866 | − | 0.255283i | \(-0.0821685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.94975 | − | 4.94975i | −0.201569 | − | 0.201569i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.79435 | − | 14.1607i | 0.154008 | − | 0.574766i | −0.845180 | − | 0.534481i | \(-0.820507\pi\) |
0.999188 | − | 0.0402844i | \(-0.0128264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.46410 | − | 18.0000i | 0.140372 | − | 0.729397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.09808 | − | 8.83013i | −0.206246 | − | 0.357229i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.9072 | − | 7.20977i | 1.08677 | − | 0.291200i | 0.329405 | − | 0.944189i | \(-0.393152\pi\) |
0.757367 | + | 0.652989i | \(0.226485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.14110 | + | 4.14110i | −0.166715 | + | 0.166715i | −0.785534 | − | 0.618819i | \(-0.787611\pi\) |
0.618819 | + | 0.785534i | \(0.287611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1962 | − | 33.2487i | 0.771559 | − | 1.33638i | −0.165150 | − | 0.986268i | \(-0.552811\pi\) |
0.936709 | − | 0.350110i | \(-0.113856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.46410 | + | 3.73205i | −0.259395 | + | 0.149762i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.1798 | + | 1.37705i | −0.768423 | + | 0.0551703i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.98502 | − | 22.3364i | −0.239019 | − | 0.892030i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −75.3731 | −3.00532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.8038 | −1.06704 | −0.533522 | − | 0.845786i | \(-0.679132\pi\) | ||||
−0.533522 | + | 0.845786i | \(0.679132\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.07175 | − | 15.1960i | −0.161838 | − | 0.603987i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.95095 | + | 0.827225i | 0.275407 | + | 0.0327759i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.92820 | − | 4.00000i | 0.274075 | − | 0.158238i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.5885 | − | 39.1244i | 0.892190 | − | 1.54532i | 0.0549467 | − | 0.998489i | \(-0.482501\pi\) |
0.837244 | − | 0.546830i | \(-0.184166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.5486 | + | 33.5486i | −1.32303 | + | 1.32303i | −0.411714 | + | 0.911313i | \(0.635070\pi\) |
−0.911313 | + | 0.411714i | \(0.864930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.3065 | + | 9.19239i | −1.34873 | + | 0.361390i | −0.859664 | − | 0.510859i | \(-0.829327\pi\) |
−0.489062 | + | 0.872249i | \(0.662661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.6603 | − | 21.9282i | −0.496958 | − | 0.860757i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | + | 3.46410i | 0.156772 | + | 0.135769i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.152304 | − | 0.568406i | 0.00596011 | − | 0.0222434i | −0.962882 | − | 0.269924i | \(-0.913002\pi\) |
0.968842 | + | 0.247680i | \(0.0796682\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.8840 | + | 10.8840i | 0.424625 | + | 0.424625i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.66025i | − | 0.220492i | −0.993904 | − | 0.110246i | \(-0.964836\pi\) | ||
0.993904 | − | 0.110246i | \(-0.0351639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.37564 | + | 0.794229i | 0.0535064 | + | 0.0308919i | 0.526515 | − | 0.850166i | \(-0.323499\pi\) |
−0.473008 | + | 0.881058i | \(0.656832\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.50266 | − | 1.74238i | −0.252542 | − | 0.0676685i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 49.9507 | + | 13.3843i | 1.93410 | + | 0.518241i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.16025 | − | 0.669873i | −0.0448580 | − | 0.0258988i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 26.5885i | − | 1.02644i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.29581 | − | 8.29581i | −0.319780 | − | 0.319780i | 0.528903 | − | 0.848683i | \(-0.322604\pi\) |
−0.848683 | + | 0.528903i | \(0.822604\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.896575 | + | 3.34607i | −0.0344582 | + | 0.128600i | −0.981012 | − | 0.193945i | \(-0.937872\pi\) |
0.946554 | + | 0.322545i | \(0.104538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.83975 | + | 3.06218i | −0.339238 | + | 0.117516i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.92820 | + | 12.0000i | 0.265489 | + | 0.459841i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.8840 | − | 2.91636i | 0.416465 | − | 0.111591i | −0.0445009 | − | 0.999009i | \(-0.514170\pi\) |
0.460966 | + | 0.887418i | \(0.347503\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.29581 | − | 8.29581i | 0.316505 | − | 0.316505i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.36603 | − | 7.56218i | 0.166332 | − | 0.288096i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4737 | + | 6.62436i | −0.436481 | + | 0.252002i | −0.702104 | − | 0.712075i | \(-0.747756\pi\) |
0.265623 | + | 0.964077i | \(0.414422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.50266 | + | 3.15660i | 0.247016 | + | 0.119909i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.31130 | − | 27.2862i | −0.276935 | − | 1.03354i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.7321 | −0.405923 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3397 | −0.692683 | −0.346341 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346341 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.5271 | − | 91.5363i | −0.925056 | − | 3.45236i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.7477 | + | 9.98743i | −0.554645 | + | 0.375616i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.45448 | − | 2.57180i | 0.167292 | − | 0.0965859i | −0.414017 | − | 0.910269i | \(-0.635874\pi\) |
0.581308 | + | 0.813684i | \(0.302541\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.13397 | + | 1.96410i | −0.0425274 | + | 0.0736596i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.5558 | + | 10.5558i | −0.395319 | + | 0.395319i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.5259 | + | 6.03579i | −0.841244 | + | 0.225411i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.75833 | − | 8.24167i | −0.177456 | − | 0.307362i | 0.763553 | − | 0.645746i | \(-0.223453\pi\) |
−0.941008 | + | 0.338383i | \(0.890120\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.07180 | − | 9.32051i | 0.300609 | − | 0.347114i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.89778 | − | 10.8147i | 0.107770 | − | 0.402201i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.568406 | + | 0.568406i | 0.0210810 | + | 0.0210810i | 0.717569 | − | 0.696488i | \(-0.245255\pi\) |
−0.696488 | + | 0.717569i | \(0.745255\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.12436 | − | 1.80385i | −0.115558 | − | 0.0667177i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.9031 | + | 4.26122i | 0.587394 | + | 0.157392i | 0.540262 | − | 0.841497i | \(-0.318325\pi\) |
0.0471323 | + | 0.998889i | \(0.484992\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.4727 | − | 4.94975i | −0.680451 | − | 0.182326i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.0359 | + | 14.4545i | 0.920960 | + | 0.531717i | 0.883941 | − | 0.467598i | \(-0.154880\pi\) |
0.0370191 | + | 0.999315i | \(0.488214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 8.46410i | − | 0.310937i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.1160 | + | 24.1160i | 0.884729 | + | 0.884729i | 0.994011 | − | 0.109282i | \(-0.0348552\pi\) |
−0.109282 | + | 0.994011i | \(0.534855\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.22474 | − | 4.57081i | 0.0448111 | − | 0.167237i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.5167 | + | 29.4641i | −0.932358 | + | 1.07659i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0621778 | − | 0.107695i | −0.00226890 | − | 0.00392985i | 0.864889 | − | 0.501964i | \(-0.167389\pi\) |
−0.867158 | + | 0.498034i | \(0.834056\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.2277 | − | 2.74049i | 0.372717 | − | 0.0998692i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.74479 | + | 5.74479i | −0.208798 | + | 0.208798i | −0.803756 | − | 0.594959i | \(-0.797168\pi\) |
0.594959 | + | 0.803756i | \(0.297168\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.1962 | + | 17.6603i | −0.370097 | + | 0.641027i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.4904 | − | 11.8301i | 0.742776 | − | 0.428842i | −0.0803019 | − | 0.996771i | \(-0.525588\pi\) |
0.823078 | + | 0.567929i | \(0.192255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.5121 | + | 20.6634i | −1.10461 | + | 0.748065i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.39872 | − | 8.95215i | −0.0866128 | − | 0.323243i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.3205 | 0.768837 | 0.384419 | − | 0.923159i | \(-0.374402\pi\) | ||||
0.384419 | + | 0.923159i | \(0.374402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.5167 | 0.774904 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.832204 | + | 3.10583i | 0.0299323 | + | 0.111709i | 0.979276 | − | 0.202532i | \(-0.0649169\pi\) |
−0.949343 | + | 0.314240i | \(0.898250\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.6484 | + | 12.9360i | 0.956006 | + | 0.464075i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.7583 | − | 17.7583i | 1.10203 | − | 0.636258i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.9282 | − | 18.9282i | 0.391042 | − | 0.677304i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.89898 | − | 4.89898i | 0.175075 | − | 0.175075i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.397520 | + | 0.106515i | −0.0141700 | + | 0.00379685i | −0.265897 | − | 0.964001i | \(-0.585668\pi\) |
0.251727 | + | 0.967798i | \(0.419001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.53590 | + | 7.85641i | 0.161482 | + | 0.279695i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.3397 | − | 7.39230i | 0.758754 | − | 0.262840i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.51884 | − | 9.40044i | 0.0894466 | − | 0.333819i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.9759 | − | 29.9759i | −1.06180 | − | 1.06180i | −0.997960 | − | 0.0638402i | \(-0.979665\pi\) |
−0.0638402 | − | 0.997960i | \(-0.520335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.6410i | 2.42834i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.29423 | − | 3.63397i | −0.222396 | − | 0.128400i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40.6197 | + | 10.8840i | 1.43344 | + | 0.384088i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.29581 | + | 2.22286i | 0.292026 | + | 0.0782482i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.5692 | + | 25.7321i | 1.56697 | + | 0.904691i | 0.996520 | + | 0.0833589i | \(0.0265648\pi\) |
0.570451 | + | 0.821332i | \(0.306769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1436i | 0.953140i | 0.879136 | + | 0.476570i | \(0.158120\pi\) | ||||
−0.879136 | + | 0.476570i | \(0.841880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.5558 | + | 10.5558i | 0.370209 | + | 0.370209i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.17398 | − | 4.38134i | 0.0410723 | − | 0.153284i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.00000 | + | 1.73205i | 0.0698857 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.8301 | + | 44.7391i | 0.901478 | + | 1.56141i | 0.825577 | + | 0.564290i | \(0.190850\pi\) |
0.0759008 | + | 0.997115i | \(0.475817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.309587 | − | 0.0829536i | 0.0107915 | − | 0.00289158i | −0.253419 | − | 0.967357i | \(-0.581555\pi\) |
0.264211 | + | 0.964465i | \(0.414889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.2784 | + | 10.2784i | −0.357416 | + | 0.357416i | −0.862860 | − | 0.505444i | \(-0.831329\pi\) |
0.505444 | + | 0.862860i | \(0.331329\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.7224 | + | 39.3564i | −0.789183 | + | 1.36690i | 0.137286 | + | 0.990532i | \(0.456162\pi\) |
−0.926468 | + | 0.376373i | \(0.877171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.3564 | − | 10.5981i | 0.636777 | − | 0.367643i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.7405 | − | 28.2199i | −1.30763 | − | 0.977762i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.517638 | + | 1.93185i | 0.0178922 | + | 0.0667746i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.9615 | −1.79391 | −0.896956 | − | 0.442121i | \(-0.854226\pi\) | ||||
−0.896956 | + | 0.442121i | \(0.854226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.29719 | − | 8.57321i | −0.0791193 | − | 0.295277i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.33109 | + | 0.669942i | −0.320620 | + | 0.0230195i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.35641 | − | 3.66987i | 0.218151 | − | 0.125950i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.7846 | + | 72.3731i | −1.43236 | + | 2.48092i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.5563 | + | 15.5563i | −0.532639 | + | 0.532639i | −0.921357 | − | 0.388718i | \(-0.872918\pi\) |
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.8014 | + | 6.37756i | −0.813040 | + | 0.217853i | −0.641301 | − | 0.767289i | \(-0.721605\pi\) |
−0.171739 | + | 0.985143i | \(0.554938\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.464102 | + | 0.803848i | 0.0158349 | + | 0.0274269i | 0.873834 | − | 0.486224i | \(-0.161626\pi\) |
−0.857999 | + | 0.513651i | \(0.828293\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.09808 | + | 10.9019i | −0.0715022 | + | 0.371537i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.5403 | − | 43.0691i | 0.392838 | − | 1.46609i | −0.432594 | − | 0.901589i | \(-0.642402\pi\) |
0.825432 | − | 0.564502i | \(-0.190932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.0256 | + | 20.0256i | 0.680106 | + | 0.680106i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.19615i | 0.210190i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.06218 | − | 3.50000i | −0.205409 | − | 0.118593i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.41542 | − | 0.915158i | −0.115594 | − | 0.0309734i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.1583 | + | 2.72191i | 0.343022 | + | 0.0919124i | 0.426217 | − | 0.904621i | \(-0.359846\pi\) |
−0.0831954 | + | 0.996533i | \(0.526513\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.1962 | − | 8.19615i | −0.478824 | − | 0.276449i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 20.0000i | − | 0.673817i | −0.941537 | − | 0.336909i | \(-0.890619\pi\) | ||
0.941537 | − | 0.336909i | \(-0.109381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.226633 | + | 0.226633i | 0.00762682 | + | 0.00762682i | 0.710910 | − | 0.703283i | \(-0.248283\pi\) |
−0.703283 | + | 0.710910i | \(0.748283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.30701 | + | 16.0740i | −0.144615 | + | 0.539712i | 0.855157 | + | 0.518369i | \(0.173461\pi\) |
−0.999772 | + | 0.0213425i | \(0.993206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0621778 | − | 0.179492i | −0.00208538 | − | 0.00601997i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.36603 | + | 2.36603i | 0.0457636 | + | 0.0792648i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −83.3606 | + | 22.3364i | −2.78956 | + | 0.747460i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.27792 | + | 5.27792i | −0.176225 | + | 0.176225i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.92820 | − | 12.0000i | 0.231069 | − | 0.400222i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.9090 | + | 29.3923i | −1.69602 | + | 0.979200i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.795040 | + | 1.17398i | 0.0264573 | + | 0.0390675i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.22406 | − | 15.7644i | −0.140258 | − | 0.523448i | −0.999921 | − | 0.0125871i | \(-0.995993\pi\) |
0.859663 | − | 0.510861i | \(-0.170673\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.73205 | −0.223288 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.71281 | −0.321800 | −0.160900 | − | 0.986971i | \(-0.551440\pi\) | ||||
−0.160900 | + | 0.986971i | \(0.551440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.34607 | − | 12.4877i | −0.110739 | − | 0.413282i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.20736 | + | 44.6728i | 0.105917 | + | 1.47523i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3923 | − | 6.00000i | 0.342811 | − | 0.197922i | −0.318704 | − | 0.947854i | \(-0.603247\pi\) |
0.661514 | + | 0.749933i | \(0.269914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.26795 | − | 2.19615i | 0.0417803 | − | 0.0723657i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.65685 | − | 5.65685i | 0.186198 | − | 0.186198i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.50146 | − | 1.20616i | 0.147847 | − | 0.0396156i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.09808 | − | 10.5622i | −0.200071 | − | 0.346534i | 0.748480 | − | 0.663158i | \(-0.230784\pi\) |
−0.948551 | + | 0.316624i | \(0.897451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.9904 | − | 55.0167i | 0.720706 | − | 1.80310i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.55291 | + | 5.79555i | −0.0508401 | + | 0.189738i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.8685 | + | 11.8685i | 0.387727 | + | 0.387727i | 0.873876 | − | 0.486149i | \(-0.161599\pi\) |
−0.486149 | + | 0.873876i | \(0.661599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2.53590i | − | 0.0827559i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.124356 | − | 0.0717968i | −0.00405388 | − | 0.00234051i | 0.497972 | − | 0.867193i | \(-0.334078\pi\) |
−0.502026 | + | 0.864853i | \(0.667412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.2533 | − | 8.10634i | −0.985183 | − | 0.263979i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.5288 | + | 8.44812i | 1.02455 | + | 0.274527i | 0.731696 | − | 0.681631i | \(-0.238729\pi\) |
0.292852 | + | 0.956158i | \(0.405396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.3301 | + | 7.69615i | 0.432714 | + | 0.249828i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2.39230i | − | 0.0775758i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.41233 | − | 2.41233i | −0.0781429 | − | 0.0781429i | 0.666955 | − | 0.745098i | \(-0.267597\pi\) |
−0.745098 | + | 0.666955i | \(0.767597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.89898 | − | 18.2832i | 0.158362 | − | 0.591013i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.5885 | + | 3.00000i | 0.503378 | + | 0.0968751i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5000 | − | 23.3827i | −0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.2301 | + | 3.81294i | −0.458558 | + | 0.122870i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.50026 | + | 2.50026i | −0.0804029 | + | 0.0804029i | −0.746164 | − | 0.665762i | \(-0.768107\pi\) |
0.665762 | + | 0.746164i | \(0.268107\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.4904 | + | 49.3468i | −0.915243 | + | 1.58525i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.22243 | + | 0.705771i | −0.0392297 | + | 0.0226493i | −0.519487 | − | 0.854479i | \(-0.673877\pi\) |
0.480257 | + | 0.877128i | \(0.340543\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.4758 | − | 40.1206i | 0.624365 | − | 1.28621i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.36396 | + | 23.7506i | 0.203601 | + | 0.759850i | 0.989871 | + | 0.141967i | \(0.0453427\pi\) |
−0.786270 | + | 0.617883i | \(0.787991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.8564 | −0.634614 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.9282 | −0.444693 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.642736 | + | 2.39872i | 0.0205001 | + | 0.0765073i | 0.975418 | − | 0.220362i | \(-0.0707240\pi\) |
−0.954918 | + | 0.296870i | \(0.904057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.7806 | − | 24.2683i | 0.374980 | − | 0.772467i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.46410 | + | 2.00000i | −0.110152 | + | 0.0635963i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.6603 | + | 18.4641i | −0.338634 | + | 0.586532i | −0.984176 | − | 0.177193i | \(-0.943298\pi\) |
0.645542 | + | 0.763725i | \(0.276632\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.43262 | + | 9.43262i | −0.299335 | + | 0.299335i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.6687 | − | 9.02150i | 1.06630 | − | 0.285714i | 0.317327 | − | 0.948316i | \(-0.397215\pi\) |
0.748971 | + | 0.662602i | \(0.230548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.59808 | + | 9.69615i | 0.177115 | + | 0.306773i |
(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.b.493.2 | yes | 8 | |
5.2 | odd | 4 | 2100.2.ce.a.157.2 | yes | 8 | ||
5.3 | odd | 4 | 2100.2.ce.a.157.1 | ✓ | 8 | ||
5.4 | even | 2 | inner | 2100.2.ce.b.493.1 | yes | 8 | |
7.5 | odd | 6 | 2100.2.ce.a.1993.2 | yes | 8 | ||
35.12 | even | 12 | inner | 2100.2.ce.b.1657.2 | yes | 8 | |
35.19 | odd | 6 | 2100.2.ce.a.1993.1 | yes | 8 | ||
35.33 | even | 12 | inner | 2100.2.ce.b.1657.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.ce.a.157.1 | ✓ | 8 | 5.3 | odd | 4 | ||
2100.2.ce.a.157.2 | yes | 8 | 5.2 | odd | 4 | ||
2100.2.ce.a.1993.1 | yes | 8 | 35.19 | odd | 6 | ||
2100.2.ce.a.1993.2 | yes | 8 | 7.5 | odd | 6 | ||
2100.2.ce.b.493.1 | yes | 8 | 5.4 | even | 2 | inner | |
2100.2.ce.b.493.2 | yes | 8 | 1.1 | even | 1 | trivial | |
2100.2.ce.b.1657.1 | yes | 8 | 35.33 | even | 12 | inner | |
2100.2.ce.b.1657.2 | yes | 8 | 35.12 | even | 12 | inner |