Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(107,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.p (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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.293 |
Dual form | 475.2.p.b.107.1 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | 0.633975 | + | 2.36603i | 0.366025 | + | 1.36603i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 2.00000i | −0.755929 | + | 0.755929i | −0.975579 | − | 0.219650i | \(-0.929509\pi\) |
0.219650 | + | 0.975579i | \(0.429509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.59808 | + | 1.50000i | −0.866025 | + | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | −3.46410 | − | 3.46410i | −1.00000 | − | 1.00000i | ||||
\(13\) | −2.36603 | − | 0.633975i | −0.656217 | − | 0.175833i | −0.0846790 | − | 0.996408i | \(-0.526986\pi\) |
−0.571538 | + | 0.820575i | \(0.693653\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −1.09808 | − | 4.09808i | −0.266323 | − | 0.993929i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.695113 | − | 0.718900i | \(-0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.33013 | − | 0.500000i | 0.993399 | − | 0.114708i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | − | 3.46410i | −1.30931 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.46410 | + | 5.46410i | −0.305286 | + | 1.13934i | 0.627412 | + | 0.778687i | \(0.284114\pi\) |
−0.932699 | + | 0.360657i | \(0.882553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.46410 | − | 5.46410i | 0.276689 | − | 1.03262i | ||||
\(29\) | −0.866025 | − | 1.50000i | −0.160817 | − | 0.278543i | 0.774345 | − | 0.632764i | \(-0.218080\pi\) |
−0.935162 | + | 0.354221i | \(0.884746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.66025i | 1.55543i | 0.628619 | + | 0.777714i | \(0.283621\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.633975 | − | 2.36603i | −0.110361 | − | 0.411872i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | − | 5.19615i | 0.500000 | − | 0.866025i | ||||
\(37\) | 3.46410 | + | 3.46410i | 0.569495 | + | 0.569495i | 0.931987 | − | 0.362492i | \(-0.118074\pi\) |
−0.362492 | + | 0.931987i | \(0.618074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.00000i | − | 0.960769i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.00000 | − | 5.19615i | −1.40556 | − | 0.811503i | −0.410608 | − | 0.911812i | \(-0.634683\pi\) |
−0.994956 | + | 0.100309i | \(0.968017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9282 | + | 2.92820i | −1.66654 | + | 0.446547i | −0.964173 | − | 0.265273i | \(-0.914538\pi\) |
−0.702362 | + | 0.711820i | \(0.747871\pi\) | |||||||
\(44\) | 1.73205 | − | 1.00000i | 0.261116 | − | 0.150756i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.83013 | − | 1.83013i | −0.996276 | − | 0.266951i | −0.276392 | − | 0.961045i | \(-0.589139\pi\) |
−0.719885 | + | 0.694094i | \(0.755805\pi\) | |||||||
\(48\) | 9.46410 | + | 2.53590i | 1.36603 | + | 0.366025i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.00000 | − | 5.19615i | 1.26025 | − | 0.727607i | ||||
\(52\) | 4.73205 | − | 1.26795i | 0.656217 | − | 0.175833i | ||||
\(53\) | 2.36603 | + | 0.633975i | 0.324999 | + | 0.0870831i | 0.417630 | − | 0.908617i | \(-0.362861\pi\) |
−0.0926309 | + | 0.995701i | \(0.529528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.92820 | + | 9.92820i | 0.520303 | + | 1.31502i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.866025 | + | 1.50000i | −0.112747 | + | 0.195283i | −0.916877 | − | 0.399170i | \(-0.869298\pi\) |
0.804130 | + | 0.594454i | \(0.202632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.19615 | − | 8.19615i | 0.276689 | − | 1.03262i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.633975 | − | 2.36603i | 0.0774523 | − | 0.289056i | −0.916326 | − | 0.400433i | \(-0.868860\pi\) |
0.993778 | + | 0.111377i | \(0.0355262\pi\) | |||||||
\(68\) | 6.00000 | + | 6.00000i | 0.727607 | + | 0.727607i | ||||
\(69\) | −13.8564 | −1.66812 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.50000 | + | 4.33013i | 0.890086 | + | 0.513892i | 0.873971 | − | 0.485979i | \(-0.161537\pi\) |
0.0161155 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.73205 | − | 0.732051i | 0.319762 | − | 0.0856801i | −0.0953678 | − | 0.995442i | \(-0.530403\pi\) |
0.415130 | + | 0.909762i | \(0.363736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.00000 | + | 5.19615i | −0.802955 | + | 0.596040i | ||||
\(77\) | 2.00000 | − | 2.00000i | 0.227921 | − | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.59808 | + | 4.50000i | −0.292306 | + | 0.506290i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) |
0.682048 | + | 0.731307i | \(0.261089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 13.8564 | 1.51186 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | − | 3.00000i | 0.321634 | − | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.06218 | + | 10.5000i | 0.642590 | + | 1.11300i | 0.984853 | + | 0.173394i | \(0.0554733\pi\) |
−0.342263 | + | 0.939604i | \(0.611193\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | − | 3.46410i | 0.628971 | − | 0.363137i | ||||
\(92\) | −2.92820 | − | 10.9282i | −0.305286 | − | 1.13934i | ||||
\(93\) | −20.4904 | + | 5.49038i | −2.12475 | + | 0.569326i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.46410 | + | 2.53590i | −0.960934 | + | 0.257481i | −0.704996 | − | 0.709212i | \(-0.749051\pi\) |
−0.255938 | + | 0.966693i | \(0.582384\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.59808 | − | 1.50000i | 0.261116 | − | 0.150756i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.50000 | + | 9.52628i | 0.547270 | + | 0.947900i | 0.998460 | + | 0.0554722i | \(0.0176664\pi\) |
−0.451190 | + | 0.892428i | \(0.649000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.46410 | − | 3.46410i | 0.341328 | − | 0.341328i | −0.515538 | − | 0.856866i | \(-0.672408\pi\) |
0.856866 | + | 0.515538i | \(0.172408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8564 | + | 13.8564i | 1.33955 | + | 1.33955i | 0.896494 | + | 0.443055i | \(0.146105\pi\) |
0.443055 | + | 0.896494i | \(0.353895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.06218 | − | 10.5000i | 0.580651 | − | 1.00572i | −0.414751 | − | 0.909935i | \(-0.636131\pi\) |
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | + | 10.3923i | −0.569495 | + | 0.986394i | ||||
\(112\) | 2.92820 | + | 10.9282i | 0.276689 | + | 1.03262i | ||||
\(113\) | 12.1244 | − | 12.1244i | 1.14056 | − | 1.14056i | 0.152216 | − | 0.988347i | \(-0.451359\pi\) |
0.988347 | − | 0.152216i | \(-0.0486410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | + | 1.73205i | 0.278543 | + | 0.160817i | ||||
\(117\) | 7.09808 | − | 1.90192i | 0.656217 | − | 0.175833i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.3923 | + | 6.00000i | 0.952661 | + | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.58846 | − | 24.5885i | 0.594061 | − | 2.21707i | ||||
\(124\) | −8.66025 | − | 15.0000i | −0.777714 | − | 1.34704i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.633975 | + | 2.36603i | −0.0562561 | + | 0.209951i | −0.988333 | − | 0.152311i | \(-0.951329\pi\) |
0.932077 | + | 0.362261i | \(0.117995\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.8564 | − | 24.0000i | −1.21999 | − | 2.11308i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00000 | − | 12.1244i | 0.611593 | − | 1.05931i | −0.379379 | − | 0.925241i | \(-0.623862\pi\) |
0.990972 | − | 0.134069i | \(-0.0428042\pi\) | |||||||
\(132\) | 3.46410 | + | 3.46410i | 0.301511 | + | 0.301511i | ||||
\(133\) | −7.66025 | + | 9.66025i | −0.664228 | + | 0.837650i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 17.3205i | − | 1.45865i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.36603 | + | 0.633975i | 0.197857 | + | 0.0530156i | ||||
\(144\) | 12.0000i | 1.00000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.36603 | − | 0.633975i | 0.195146 | − | 0.0522893i | ||||
\(148\) | −9.46410 | − | 2.53590i | −0.777944 | − | 0.208450i | ||||
\(149\) | 6.06218 | + | 3.50000i | 0.496633 | + | 0.286731i | 0.727322 | − | 0.686296i | \(-0.240765\pi\) |
−0.230689 | + | 0.973028i | \(0.574098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.73205i | − | 0.140952i | −0.997513 | − | 0.0704761i | \(-0.977548\pi\) | ||
0.997513 | − | 0.0704761i | \(-0.0224519\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.00000 | + | 9.00000i | 0.727607 | + | 0.727607i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.00000 | + | 10.3923i | 0.480384 | + | 0.832050i | ||||
\(157\) | 1.83013 | + | 6.83013i | 0.146060 | + | 0.545103i | 0.999706 | + | 0.0242497i | \(0.00771967\pi\) |
−0.853646 | + | 0.520854i | \(0.825614\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.00000i | 0.475831i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | − | 13.8564i | −0.630488 | − | 1.09204i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | + | 7.00000i | 0.548282 | + | 0.548282i | 0.925944 | − | 0.377661i | \(-0.123272\pi\) |
−0.377661 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(164\) | 20.7846 | 1.62301 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.26795 | − | 4.73205i | 0.0981169 | − | 0.366177i | −0.899357 | − | 0.437216i | \(-0.855965\pi\) |
0.997474 | + | 0.0710385i | \(0.0226313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.06218 | − | 3.50000i | −0.466321 | − | 0.269231i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.5000 | + | 7.79423i | −0.802955 | + | 0.596040i | ||||
\(172\) | 16.0000 | − | 16.0000i | 1.21999 | − | 1.21999i | ||||
\(173\) | −2.53590 | − | 9.46410i | −0.192801 | − | 0.719542i | −0.992825 | − | 0.119575i | \(-0.961847\pi\) |
0.800024 | − | 0.599967i | \(-0.204820\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.00000 | + | 3.46410i | −0.150756 | + | 0.261116i | ||||
\(177\) | −4.09808 | − | 1.09808i | −0.308030 | − | 0.0825365i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.1244 | −0.906217 | −0.453108 | − | 0.891455i | \(-0.649685\pi\) | ||||
−0.453108 | + | 0.891455i | \(0.649685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00000 | + | 1.73205i | −0.222988 | + | 0.128742i | −0.607333 | − | 0.794447i | \(-0.707761\pi\) |
0.384345 | + | 0.923190i | \(0.374427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.1244 | + | 12.1244i | −0.896258 | + | 0.896258i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.09808 | + | 4.09808i | 0.0802993 | + | 0.299681i | ||||
\(188\) | 13.6603 | − | 3.66025i | 0.996276 | − | 0.266951i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.0000 | 1.66422 | 0.832111 | − | 0.554609i | \(-0.187132\pi\) | ||||
0.832111 | + | 0.554609i | \(0.187132\pi\) | |||||||
\(192\) | −18.9282 | + | 5.07180i | −1.36603 | + | 0.366025i | ||||
\(193\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 1.73205i | 0.0714286 | + | 0.123718i | ||||
\(197\) | 1.00000 | − | 1.00000i | 0.0712470 | − | 0.0712470i | −0.670585 | − | 0.741832i | \(-0.733957\pi\) |
0.741832 | + | 0.670585i | \(0.233957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.79423 | − | 4.50000i | 0.552518 | − | 0.318997i | −0.197619 | − | 0.980279i | \(-0.563321\pi\) |
0.750137 | + | 0.661282i | \(0.229987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.73205 | + | 1.26795i | 0.332125 | + | 0.0889926i | ||||
\(204\) | −10.3923 | + | 18.0000i | −0.727607 | + | 1.26025i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.39230 | − | 16.3923i | −0.305286 | − | 1.13934i | ||||
\(208\) | −6.92820 | + | 6.92820i | −0.480384 | + | 0.480384i | ||||
\(209\) | −4.33013 | + | 0.500000i | −0.299521 | + | 0.0345857i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5000 | − | 11.2583i | −1.34244 | − | 0.775055i | −0.355271 | − | 0.934763i | \(-0.615611\pi\) |
−0.987164 | + | 0.159708i | \(0.948945\pi\) | |||||||
\(212\) | −4.73205 | + | 1.26795i | −0.324999 | + | 0.0870831i | ||||
\(213\) | −5.49038 | + | 20.4904i | −0.376195 | + | 1.40398i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.3205 | − | 17.3205i | −1.17579 | − | 1.17579i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.46410 | + | 6.00000i | 0.234082 | + | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3923i | 0.699062i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.80385 | + | 14.1962i | 0.254724 | + | 0.950645i | 0.968244 | + | 0.250009i | \(0.0804335\pi\) |
−0.713519 | + | 0.700636i | \(0.752900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.92820 | − | 6.92820i | −0.459841 | − | 0.459841i | 0.438762 | − | 0.898603i | \(-0.355417\pi\) |
−0.898603 | + | 0.438762i | \(0.855417\pi\) | |||||||
\(228\) | −16.7321 | − | 13.2679i | −1.10811 | − | 0.878691i | ||||
\(229\) | 9.00000i | 0.594737i | 0.954763 | + | 0.297368i | \(0.0961089\pi\) | ||||
−0.954763 | + | 0.297368i | \(0.903891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | + | 3.46410i | 0.394771 | + | 0.227921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.36603 | + | 0.366025i | −0.0894913 | + | 0.0239791i | −0.303287 | − | 0.952899i | \(-0.598084\pi\) |
0.213796 | + | 0.976878i | \(0.431417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 3.46410i | − | 0.225494i | ||||||
\(237\) | −12.2942 | − | 3.29423i | −0.798596 | − | 0.213983i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.00000i | 0.452792i | 0.974035 | + | 0.226396i | \(0.0726944\pi\) | ||||
−0.974035 | + | 0.226396i | \(0.927306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.50000 | + | 2.59808i | −0.289870 | + | 0.167357i | −0.637883 | − | 0.770133i | \(-0.720190\pi\) |
0.348013 | + | 0.937490i | \(0.386857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.2942 | − | 5.70577i | −1.36603 | − | 0.366025i | ||||
\(244\) | −12.1244 | − | 7.00000i | −0.776182 | − | 0.448129i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.5622 | − | 1.56218i | −0.672055 | − | 0.0993990i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.50000 | − | 11.2583i | −0.410276 | − | 0.710620i | 0.584643 | − | 0.811290i | \(-0.301234\pi\) |
−0.994920 | + | 0.100671i | \(0.967901\pi\) | |||||||
\(252\) | 4.39230 | + | 16.3923i | 0.276689 | + | 1.03262i | ||||
\(253\) | 1.46410 | − | 5.46410i | 0.0920473 | − | 0.343525i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −0.633975 | + | 2.36603i | −0.0395462 | + | 0.147589i | −0.982876 | − | 0.184268i | \(-0.941008\pi\) |
0.943330 | + | 0.331857i | \(0.107675\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.8564 | −0.860995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | + | 2.59808i | 0.278543 | + | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.2942 | − | 3.29423i | 0.758095 | − | 0.203131i | 0.140989 | − | 0.990011i | \(-0.454972\pi\) |
0.617106 | + | 0.786880i | \(0.288305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.0000 | + | 21.0000i | −1.28518 | + | 1.28518i | ||||
\(268\) | 1.26795 | + | 4.73205i | 0.0774523 | + | 0.289056i | ||||
\(269\) | −7.79423 | + | 13.5000i | −0.475223 | + | 0.823110i | −0.999597 | − | 0.0283781i | \(-0.990966\pi\) |
0.524375 | + | 0.851488i | \(0.324299\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50000 | + | 2.59808i | −0.0911185 | + | 0.157822i | −0.907982 | − | 0.419009i | \(-0.862378\pi\) |
0.816864 | + | 0.576831i | \(0.195711\pi\) | |||||||
\(272\) | −16.3923 | − | 4.39230i | −0.993929 | − | 0.266323i | ||||
\(273\) | 12.0000 | + | 12.0000i | 0.726273 | + | 0.726273i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 24.0000 | − | 13.8564i | 1.44463 | − | 0.834058i | ||||
\(277\) | −8.00000 | + | 8.00000i | −0.480673 | + | 0.480673i | −0.905347 | − | 0.424673i | \(-0.860389\pi\) |
0.424673 | + | 0.905347i | \(0.360389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9904 | − | 22.5000i | −0.777714 | − | 1.34704i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | + | 6.92820i | −0.715860 | + | 0.413302i | −0.813227 | − | 0.581947i | \(-0.802291\pi\) |
0.0973670 | + | 0.995249i | \(0.468958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.56218 | − | 2.56218i | 0.568412 | − | 0.152306i | 0.0368441 | − | 0.999321i | \(-0.488270\pi\) |
0.531568 | + | 0.847015i | \(0.321603\pi\) | |||||||
\(284\) | −17.3205 | −1.02778 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.3923 | − | 7.60770i | 1.67594 | − | 0.449068i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.866025 | + | 0.500000i | −0.0509427 | + | 0.0294118i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | − | 20.7846i | −0.703452 | − | 1.21842i | ||||
\(292\) | −4.00000 | + | 4.00000i | −0.234082 | + | 0.234082i | ||||
\(293\) | 10.3923 | − | 10.3923i | 0.607125 | − | 0.607125i | −0.335069 | − | 0.942194i | \(-0.608760\pi\) |
0.942194 | + | 0.335069i | \(0.108760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.92820 | − | 12.0000i | 0.400668 | − | 0.693978i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | − | 27.7128i | 0.922225 | − | 1.59734i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.0526 | + | 19.0526i | −1.09454 | + | 1.09454i | ||||
\(304\) | 6.92820 | − | 16.0000i | 0.397360 | − | 0.917663i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5622 | − | 4.43782i | 0.945253 | − | 0.253280i | 0.246906 | − | 0.969039i | \(-0.420586\pi\) |
0.698347 | + | 0.715759i | \(0.253919\pi\) | |||||||
\(308\) | −1.46410 | + | 5.46410i | −0.0834249 | + | 0.311346i | ||||
\(309\) | 10.3923 | + | 6.00000i | 0.591198 | + | 0.341328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0000 | 1.47432 | 0.737162 | − | 0.675716i | \(-0.236165\pi\) | ||||
0.737162 | + | 0.675716i | \(0.236165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.83013 | − | 6.83013i | 0.103445 | − | 0.386062i | −0.894719 | − | 0.446629i | \(-0.852624\pi\) |
0.998164 | + | 0.0605675i | \(0.0192910\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 10.3923i | − | 0.584613i | ||||||
\(317\) | 6.33975 | − | 23.6603i | 0.356076 | − | 1.32889i | −0.523050 | − | 0.852302i | \(-0.675206\pi\) |
0.879126 | − | 0.476590i | \(-0.158127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.866025 | + | 1.50000i | 0.0484881 | + | 0.0839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | + | 41.5692i | −1.33955 | + | 2.32017i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.80385 | − | 17.1962i | −0.378576 | − | 0.956820i | ||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.6865 | + | 7.68653i | 1.58637 | + | 0.425066i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.3205 | − | 10.0000i | 0.954911 | − | 0.551318i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.7128i | 1.52323i | 0.648027 | + | 0.761617i | \(0.275594\pi\) | ||||
−0.648027 | + | 0.761617i | \(0.724406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.1962 | − | 3.80385i | −0.777944 | − | 0.208450i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −24.0000 | + | 13.8564i | −1.30931 | + | 0.755929i | ||||
\(337\) | −23.6603 | + | 6.33975i | −1.28886 | + | 0.345348i | −0.837226 | − | 0.546857i | \(-0.815824\pi\) |
−0.451630 | + | 0.892205i | \(0.649157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.3731 | + | 21.0000i | 1.97551 | + | 1.14056i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.66025i | − | 0.468979i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.39230 | − | 16.3923i | −0.235791 | − | 0.879985i | −0.977791 | − | 0.209584i | \(-0.932789\pi\) |
0.741999 | − | 0.670401i | \(-0.233878\pi\) | |||||||
\(348\) | −2.19615 | + | 8.19615i | −0.117726 | + | 0.439360i | ||||
\(349\) | 24.0000i | 1.28469i | 0.766415 | + | 0.642345i | \(0.222038\pi\) | ||||
−0.766415 | + | 0.642345i | \(0.777962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.0000 | + | 22.0000i | 1.17094 | + | 1.17094i | 0.981985 | + | 0.188956i | \(0.0605105\pi\) |
0.188956 | + | 0.981985i | \(0.439490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −21.0000 | − | 12.1244i | −1.11300 | − | 0.642590i | ||||
\(357\) | −7.60770 | + | 28.3923i | −0.402642 | + | 1.50268i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.66025 | − | 5.00000i | −0.457071 | − | 0.263890i | 0.253741 | − | 0.967272i | \(-0.418339\pi\) |
−0.710812 | + | 0.703382i | \(0.751672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5000 | − | 4.33013i | 0.973684 | − | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.33975 | − | 23.6603i | −0.332750 | − | 1.24184i | ||||
\(364\) | −6.92820 | + | 12.0000i | −0.363137 | + | 0.628971i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3205 | + | 7.32051i | 1.42612 | + | 0.382127i | 0.887650 | − | 0.460518i | \(-0.152336\pi\) |
0.538469 | + | 0.842646i | \(0.319003\pi\) | |||||||
\(368\) | 16.0000 | + | 16.0000i | 0.834058 | + | 0.834058i | ||||
\(369\) | 31.1769 | 1.62301 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.00000 | + | 3.46410i | −0.311504 | + | 0.179847i | ||||
\(372\) | 30.0000 | − | 30.0000i | 1.55543 | − | 1.55543i | ||||
\(373\) | −10.3923 | + | 10.3923i | −0.538093 | + | 0.538093i | −0.922969 | − | 0.384875i | \(-0.874244\pi\) |
0.384875 | + | 0.922969i | \(0.374244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.09808 | + | 4.09808i | 0.0565538 | + | 0.211062i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5885 | −0.800725 | −0.400363 | − | 0.916357i | \(-0.631116\pi\) | ||||
−0.400363 | + | 0.916357i | \(0.631116\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.633975 | − | 2.36603i | −0.0323946 | − | 0.120898i | 0.947835 | − | 0.318761i | \(-0.103267\pi\) |
−0.980230 | + | 0.197863i | \(0.936600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.0000 | − | 24.0000i | 1.21999 | − | 1.21999i | ||||
\(388\) | 13.8564 | − | 13.8564i | 0.703452 | − | 0.703452i | ||||
\(389\) | 26.8468 | − | 15.5000i | 1.36119 | − | 0.785881i | 0.371404 | − | 0.928471i | \(-0.378876\pi\) |
0.989782 | + | 0.142590i | \(0.0455430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33.1244 | + | 8.87564i | 1.67090 | + | 0.447717i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | 0.732051 | + | 2.73205i | 0.0367406 | + | 0.137118i | 0.981860 | − | 0.189607i | \(-0.0607215\pi\) |
−0.945119 | + | 0.326725i | \(0.894055\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.7128 | − | 12.0000i | −1.38738 | − | 0.600751i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5000 | + | 7.79423i | 0.674158 | + | 0.389225i | 0.797650 | − | 0.603120i | \(-0.206076\pi\) |
−0.123492 | + | 0.992346i | \(0.539409\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.49038 | − | 20.4904i | 0.273495 | − | 1.02070i | ||||
\(404\) | −19.0526 | − | 11.0000i | −0.947900 | − | 0.547270i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.46410 | − | 3.46410i | −0.171709 | − | 0.171709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9904 | + | 22.5000i | 0.642333 | + | 1.11255i | 0.984911 | + | 0.173064i | \(0.0553667\pi\) |
−0.342578 | + | 0.939490i | \(0.611300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.53590 | + | 9.46410i | −0.124935 | + | 0.466263i | ||||
\(413\) | −1.26795 | − | 4.73205i | −0.0623917 | − | 0.232849i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.0000i | 1.12362i | 0.827265 | + | 0.561812i | \(0.189895\pi\) | ||||
−0.827265 | + | 0.561812i | \(0.810105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.50000 | − | 0.866025i | −0.0731055 | − | 0.0422075i | 0.463002 | − | 0.886357i | \(-0.346772\pi\) |
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.4904 | − | 5.49038i | 0.996276 | − | 0.266951i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.1244 | − | 5.12436i | −0.925492 | − | 0.247985i | ||||
\(428\) | −37.8564 | − | 10.1436i | −1.82986 | − | 0.490309i | ||||
\(429\) | 6.00000i | 0.289683i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5000 | − | 7.79423i | 0.650272 | − | 0.375435i | −0.138288 | − | 0.990392i | \(-0.544160\pi\) |
0.788560 | + | 0.614957i | \(0.210827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.1962 | − | 3.80385i | −0.682224 | − | 0.182801i | −0.0989688 | − | 0.995091i | \(-0.531554\pi\) |
−0.583255 | + | 0.812289i | \(0.698221\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.2487i | 1.16130i | ||||||||
\(437\) | −3.60770 | + | 24.3923i | −0.172579 | + | 1.16684i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2583 | − | 19.5000i | 0.537331 | − | 0.930684i | −0.461716 | − | 0.887028i | \(-0.652766\pi\) |
0.999047 | − | 0.0436563i | \(-0.0139007\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.50000 | + | 2.59808i | 0.0714286 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.92820 | + | 10.9282i | −0.139123 | + | 0.519215i | 0.860824 | + | 0.508903i | \(0.169949\pi\) |
−0.999947 | + | 0.0103113i | \(0.996718\pi\) | |||||||
\(444\) | − | 24.0000i | − | 1.13899i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.43782 | + | 16.5622i | −0.209902 | + | 0.783364i | ||||
\(448\) | −16.0000 | − | 16.0000i | −0.755929 | − | 0.755929i | ||||
\(449\) | −19.0526 | −0.899146 | −0.449573 | − | 0.893244i | \(-0.648424\pi\) | ||||
−0.449573 | + | 0.893244i | \(0.648424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 5.19615i | 0.423793 | + | 0.244677i | ||||
\(452\) | −8.87564 | + | 33.1244i | −0.417475 | + | 1.55804i | ||||
\(453\) | 4.09808 | − | 1.09808i | 0.192544 | − | 0.0515921i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000 | − | 1.00000i | 0.0467780 | − | 0.0467780i | −0.683331 | − | 0.730109i | \(-0.739469\pi\) |
0.730109 | + | 0.683331i | \(0.239469\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.500000 | + | 0.866025i | −0.0232873 | + | 0.0403348i | −0.877434 | − | 0.479697i | \(-0.840747\pi\) |
0.854147 | + | 0.520032i | \(0.174080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | + | 4.00000i | 0.185896 | + | 0.185896i | 0.793919 | − | 0.608023i | \(-0.208037\pi\) |
−0.608023 | + | 0.793919i | \(0.708037\pi\) | |||||||
\(464\) | −6.92820 | −0.321634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.00000 | − | 8.00000i | 0.370196 | − | 0.370196i | −0.497353 | − | 0.867548i | \(-0.665694\pi\) |
0.867548 | + | 0.497353i | \(0.165694\pi\) | |||||||
\(468\) | −10.3923 | + | 10.3923i | −0.480384 | + | 0.480384i | ||||
\(469\) | 3.46410 | + | 6.00000i | 0.159957 | + | 0.277054i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.0000 | + | 8.66025i | −0.691164 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.9282 | − | 2.92820i | 0.502479 | − | 0.134639i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −24.0000 | −1.10004 | ||||||||
\(477\) | −7.09808 | + | 1.90192i | −0.324999 | + | 0.0870831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.866025 | + | 0.500000i | −0.0395697 | + | 0.0228456i | −0.519654 | − | 0.854377i | \(-0.673939\pi\) |
0.480085 | + | 0.877222i | \(0.340606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | − | 10.3923i | −0.273576 | − | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.7128 | − | 27.7128i | 1.26098 | − | 1.26098i | ||||
\(484\) | 17.3205 | − | 10.0000i | 0.787296 | − | 0.454545i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5885 | + | 15.5885i | 0.706380 | + | 0.706380i | 0.965772 | − | 0.259392i | \(-0.0835221\pi\) |
−0.259392 | + | 0.965772i | \(0.583522\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.1244 | + | 21.0000i | −0.548282 | + | 0.949653i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.50000 | + | 11.2583i | −0.293341 | + | 0.508081i | −0.974598 | − | 0.223963i | \(-0.928100\pi\) |
0.681257 | + | 0.732045i | \(0.261434\pi\) | |||||||
\(492\) | 13.1769 | + | 49.1769i | 0.594061 | + | 2.21707i | ||||
\(493\) | −5.19615 | + | 5.19615i | −0.234023 | + | 0.234023i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.0000 | + | 17.3205i | 1.34704 | + | 0.777714i | ||||
\(497\) | −23.6603 | + | 6.33975i | −1.06131 | + | 0.284376i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.9808 | − | 15.0000i | −1.16306 | − | 0.671492i | −0.211024 | − | 0.977481i | \(-0.567680\pi\) |
−0.952035 | + | 0.305989i | \(0.901013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | 0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.09808 | + | 4.09808i | −0.0489608 | + | 0.182724i | −0.986076 | − | 0.166297i | \(-0.946819\pi\) |
0.937115 | + | 0.349021i | \(0.113486\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.43782 | − | 16.5622i | 0.197091 | − | 0.735552i | ||||
\(508\) | −1.26795 | − | 4.73205i | −0.0562561 | − | 0.209951i | ||||
\(509\) | −1.73205 | − | 3.00000i | −0.0767718 | − | 0.132973i | 0.825084 | − | 0.565011i | \(-0.191128\pi\) |
−0.901855 | + | 0.432038i | \(0.857795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | + | 6.92820i | −0.176950 | + | 0.306486i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 48.0000 | + | 27.7128i | 2.11308 | + | 1.21999i | ||||
\(517\) | 6.83013 | + | 1.83013i | 0.300389 | + | 0.0804889i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.7846 | − | 12.0000i | 0.912343 | − | 0.526742i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 22.5167i | − | 0.986473i | −0.869895 | − | 0.493236i | \(-0.835814\pi\) | ||
0.869895 | − | 0.493236i | \(-0.164186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.8301 | + | 3.16987i | 0.517295 | + | 0.138609i | 0.508015 | − | 0.861348i | \(-0.330379\pi\) |
0.00928008 | + | 0.999957i | \(0.497046\pi\) | |||||||
\(524\) | 28.0000i | 1.22319i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.4904 | − | 9.50962i | 1.54599 | − | 0.414246i | ||||
\(528\) | −9.46410 | − | 2.53590i | −0.411872 | − | 0.110361i | ||||
\(529\) | −7.79423 | − | 4.50000i | −0.338880 | − | 0.195652i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.19615i | − | 0.225494i | ||||||
\(532\) | 3.60770 | − | 24.3923i | 0.156413 | − | 1.05754i | ||||
\(533\) | 18.0000 | + | 18.0000i | 0.779667 | + | 0.779667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.68653 | − | 28.6865i | −0.331698 | − | 1.23792i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.50000 | + | 2.59808i | 0.0644900 | + | 0.111700i | 0.896468 | − | 0.443109i | \(-0.146125\pi\) |
−0.831978 | + | 0.554809i | \(0.812791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.00000 | − | 6.00000i | −0.257485 | − | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.26795 | + | 4.73205i | −0.0542136 | + | 0.202328i | −0.987720 | − | 0.156232i | \(-0.950065\pi\) |
0.933507 | + | 0.358560i | \(0.116732\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.1865 | − | 10.5000i | −0.776182 | − | 0.448129i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.50000 | − | 6.06218i | −0.191706 | − | 0.258257i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.80385 | − | 14.1962i | −0.161756 | − | 0.603682i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.3205 | − | 7.32051i | −1.15761 | − | 0.310180i | −0.371597 | − | 0.928394i | \(-0.621190\pi\) |
−0.786010 | + | 0.618214i | \(0.787856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.7128 | 1.17213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | + | 5.19615i | −0.379980 | + | 0.219382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.9808 | + | 25.9808i | −1.09496 | + | 1.09496i | −0.0999679 | + | 0.994991i | \(0.531874\pi\) |
−0.994991 | + | 0.0999679i | \(0.968126\pi\) | |||||||
\(564\) | 17.3205 | + | 30.0000i | 0.729325 | + | 1.26323i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.58846 | − | 24.5885i | −0.276689 | − | 1.03262i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.9090 | 1.37962 | 0.689808 | − | 0.723993i | \(-0.257695\pi\) | ||||
0.689808 | + | 0.723993i | \(0.257695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.0000 | −1.63210 | −0.816050 | − | 0.577982i | \(-0.803840\pi\) | ||||
−0.816050 | + | 0.577982i | \(0.803840\pi\) | |||||||
\(572\) | −4.73205 | + | 1.26795i | −0.197857 | + | 0.0530156i | ||||
\(573\) | 14.5814 | + | 54.4186i | 0.609147 | + | 2.27337i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.0000 | − | 20.7846i | −0.500000 | − | 0.866025i | ||||
\(577\) | 20.0000 | − | 20.0000i | 0.832611 | − | 0.832611i | −0.155262 | − | 0.987873i | \(-0.549622\pi\) |
0.987873 | + | 0.155262i | \(0.0496223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.36603 | − | 0.633975i | −0.0979908 | − | 0.0262565i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.732051 | − | 2.73205i | −0.0302150 | − | 0.112764i | 0.949171 | − | 0.314760i | \(-0.101924\pi\) |
−0.979386 | + | 0.201996i | \(0.935257\pi\) | |||||||
\(588\) | −3.46410 | + | 3.46410i | −0.142857 | + | 0.142857i | ||||
\(589\) | 4.33013 | + | 37.5000i | 0.178420 | + | 1.54516i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 1.73205i | 0.123404 | + | 0.0712470i | ||||
\(592\) | 18.9282 | − | 5.07180i | 0.777944 | − | 0.208450i | ||||
\(593\) | 8.78461 | − | 32.7846i | 0.360741 | − | 1.34630i | −0.512363 | − | 0.858769i | \(-0.671230\pi\) |
0.873104 | − | 0.487534i | \(-0.162103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14.0000 | −0.573462 | ||||||||
\(597\) | 15.5885 | + | 15.5885i | 0.637993 | + | 0.637993i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8564 | − | 24.0000i | −0.566157 | − | 0.980613i | −0.996941 | − | 0.0781581i | \(-0.975096\pi\) |
0.430784 | − | 0.902455i | \(-0.358237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.4449i | − | 1.20108i | −0.799594 | − | 0.600541i | \(-0.794952\pi\) | ||
0.799594 | − | 0.600541i | \(-0.205048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.90192 | + | 7.09808i | 0.0774523 | + | 0.289056i | ||||
\(604\) | 1.73205 | + | 3.00000i | 0.0704761 | + | 0.122068i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.19615 | − | 5.19615i | −0.210905 | − | 0.210905i | 0.593747 | − | 0.804652i | \(-0.297648\pi\) |
−0.804652 | + | 0.593747i | \(0.797648\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000i | 0.486265i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | + | 8.66025i | 0.606835 | + | 0.350356i | ||||
\(612\) | −24.5885 | − | 6.58846i | −0.993929 | − | 0.266323i | ||||
\(613\) | 17.7583 | − | 4.75833i | 0.717252 | − | 0.192187i | 0.118307 | − | 0.992977i | \(-0.462253\pi\) |
0.598945 | + | 0.800790i | \(0.295587\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.5885 | + | 6.58846i | 0.989894 | + | 0.265241i | 0.717206 | − | 0.696861i | \(-0.245421\pi\) |
0.272688 | + | 0.962103i | \(0.412087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.0000i | − | 1.20580i | −0.797816 | − | 0.602901i | \(-0.794011\pi\) | ||
0.797816 | − | 0.602901i | \(-0.205989\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.1244 | − | 8.87564i | −1.32710 | − | 0.355595i | ||||
\(624\) | −20.7846 | − | 12.0000i | −0.832050 | − | 0.480384i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.92820 | − | 9.92820i | −0.156877 | − | 0.396494i | ||||
\(628\) | −10.0000 | − | 10.0000i | −0.399043 | − | 0.399043i | ||||
\(629\) | 10.3923 | − | 18.0000i | 0.414368 | − | 0.717707i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.500000 | − | 0.866025i | −0.0199047 | − | 0.0344759i | 0.855901 | − | 0.517139i | \(-0.173003\pi\) |
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.2750 | − | 53.2750i | 0.567380 | − | 2.11749i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.00000 | − | 10.3923i | −0.237915 | − | 0.412082i | ||||
\(637\) | −0.633975 | + | 2.36603i | −0.0251190 | + | 0.0937453i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.9808 | −1.02778 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 6.06218i | −0.414725 | − | 0.239442i | 0.278093 | − | 0.960554i | \(-0.410298\pi\) |
−0.692818 | + | 0.721113i | \(0.743631\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.4186 | − | 8.41858i | 1.23903 | − | 0.331997i | 0.420939 | − | 0.907089i | \(-0.361700\pi\) |
0.818089 | + | 0.575092i | \(0.195034\pi\) | |||||||
\(644\) | 27.7128 | + | 16.0000i | 1.09204 | + | 0.630488i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.00000 | + | 9.00000i | −0.353827 | + | 0.353827i | −0.861531 | − | 0.507705i | \(-0.830494\pi\) |
0.507705 | + | 0.861531i | \(0.330494\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.866025 | − | 1.50000i | 0.0339945 | − | 0.0588802i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.0000 | − | 51.9615i | 1.17579 | − | 2.03653i | ||||
\(652\) | −19.1244 | − | 5.12436i | −0.748968 | − | 0.200685i | ||||
\(653\) | 6.00000 | + | 6.00000i | 0.234798 | + | 0.234798i | 0.814692 | − | 0.579894i | \(-0.196906\pi\) |
−0.579894 | + | 0.814692i | \(0.696906\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.0000 | + | 20.7846i | −1.40556 | + | 0.811503i | ||||
\(657\) | −6.00000 | + | 6.00000i | −0.234082 | + | 0.234082i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.92820 | − | 12.0000i | −0.269884 | − | 0.467454i | 0.698947 | − | 0.715173i | \(-0.253652\pi\) |
−0.968832 | + | 0.247720i | \(0.920319\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.5000 | + | 19.9186i | −1.34189 | + | 0.774743i | −0.987085 | − | 0.160196i | \(-0.948788\pi\) |
−0.354809 | + | 0.934939i | \(0.615454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.5885 | + | 6.58846i | −0.954937 | + | 0.255874i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.46410 | − | 2.53590i | 0.366451 | − | 0.0981904i | ||||
\(668\) | 2.53590 | + | 9.46410i | 0.0981169 | + | 0.366177i | ||||
\(669\) | −31.1769 | + | 18.0000i | −1.20537 | + | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.50000 | − | 6.06218i | −0.135116 | − | 0.234028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.7846 | + | 20.7846i | −0.801188 | + | 0.801188i | −0.983281 | − | 0.182093i | \(-0.941713\pi\) |
0.182093 | + | 0.983281i | \(0.441713\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.0000 | 0.538462 | ||||||||
\(677\) | −17.3205 | − | 17.3205i | −0.665681 | − | 0.665681i | 0.291032 | − | 0.956713i | \(-0.406001\pi\) |
−0.956713 | + | 0.291032i | \(0.906001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8564 | − | 24.0000i | 0.531760 | − | 0.921035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | − | 20.7846i | 0.459841 | − | 0.796468i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1244 | + | 12.1244i | −0.463926 | + | 0.463926i | −0.899940 | − | 0.436014i | \(-0.856390\pi\) |
0.436014 | + | 0.899940i | \(0.356390\pi\) | |||||||
\(684\) | 10.3923 | − | 24.0000i | 0.397360 | − | 0.917663i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.2942 | + | 5.70577i | −0.812425 | + | 0.217689i | ||||
\(688\) | −11.7128 | + | 43.7128i | −0.446547 | + | 1.66654i | ||||
\(689\) | −5.19615 | − | 3.00000i | −0.197958 | − | 0.114291i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.00000 | 0.114125 | 0.0570627 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570627 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(692\) | 13.8564 | + | 13.8564i | 0.526742 | + | 0.526742i | ||||
\(693\) | −2.19615 | + | 8.19615i | −0.0834249 | + | 0.311346i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.4115 | + | 42.5885i | −0.432243 | + | 1.61315i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.73205 | − | 3.00000i | −0.0655122 | − | 0.113470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0000 | − | 17.3205i | 0.377695 | − | 0.654187i | −0.613032 | − | 0.790058i | \(-0.710050\pi\) |
0.990726 | + | 0.135872i | \(0.0433835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7321 | + | 13.2679i | 0.631061 | + | 0.500410i | ||||
\(704\) | − | 8.00000i | − | 0.301511i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.0526 | − | 8.05256i | −1.13024 | − | 0.302848i | ||||
\(708\) | 8.19615 | − | 2.19615i | 0.308030 | − | 0.0825365i | ||||
\(709\) | −44.1673 | + | 25.5000i | −1.65874 | + | 0.957673i | −0.685439 | + | 0.728130i | \(0.740390\pi\) |
−0.973299 | + | 0.229543i | \(0.926277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 15.5885i | − | 0.584613i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −47.3205 | − | 12.6795i | −1.77217 | − | 0.474851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.0000 | − | 12.1244i | 0.784807 | − | 0.453108i | ||||
\(717\) | −16.5622 | + | 4.43782i | −0.618526 | + | 0.165734i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.0429 | + | 18.5000i | 1.19500 | + | 0.689934i | 0.959436 | − | 0.281925i | \(-0.0909730\pi\) |
0.235564 | + | 0.971859i | \(0.424306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8564i | 0.516040i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.00000 | − | 9.00000i | −0.334714 | − | 0.334714i | ||||
\(724\) | 3.46410 | − | 6.00000i | 0.128742 | − | 0.222988i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.56218 | − | 9.56218i | −0.0950259 | − | 0.354642i | 0.901997 | − | 0.431741i | \(-0.142101\pi\) |
−0.997023 | + | 0.0770998i | \(0.975434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | + | 41.5692i | 0.887672 | + | 1.53749i | ||||
\(732\) | 8.87564 | − | 33.1244i | 0.328053 | − | 1.22431i | ||||
\(733\) | 26.0000 | + | 26.0000i | 0.960332 | + | 0.960332i | 0.999243 | − | 0.0389108i | \(-0.0123888\pi\) |
−0.0389108 | + | 0.999243i | \(0.512389\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.633975 | + | 2.36603i | −0.0233528 | + | 0.0871537i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9186 | + | 11.5000i | 0.732717 | + | 0.423034i | 0.819415 | − | 0.573200i | \(-0.194298\pi\) |
−0.0866983 | + | 0.996235i | \(0.527632\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | − | 25.9808i | −0.110208 | − | 0.954427i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.80385 | + | 14.1962i | 0.139550 | + | 0.520806i | 0.999938 | + | 0.0111668i | \(0.00355457\pi\) |
−0.860388 | + | 0.509640i | \(0.829779\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.00000 | − | 6.00000i | −0.219382 | − | 0.219382i | ||||
\(749\) | −55.4256 | −2.02521 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.50000 | + | 4.33013i | −0.273679 | + | 0.158009i | −0.630558 | − | 0.776142i | \(-0.717174\pi\) |
0.356879 | + | 0.934150i | \(0.383841\pi\) | |||||||
\(752\) | −20.0000 | + | 20.0000i | −0.729325 | + | 0.729325i | ||||
\(753\) | 22.5167 | − | 22.5167i | 0.820553 | − | 0.820553i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.22243 | + | 23.2224i | 0.226158 | + | 0.844034i | 0.981937 | + | 0.189207i | \(0.0605917\pi\) |
−0.755779 | + | 0.654827i | \(0.772742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.8564 | 0.502956 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.00000 | 0.290000 | 0.145000 | − | 0.989432i | \(-0.453682\pi\) | ||||
0.145000 | + | 0.989432i | \(0.453682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.87564 | + | 33.1244i | 0.321320 | + | 1.19918i | ||||
\(764\) | −39.8372 | + | 23.0000i | −1.44126 | + | 0.832111i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.00000 | − | 3.00000i | 0.108324 | − | 0.108324i | ||||
\(768\) | 27.7128 | − | 27.7128i | 1.00000 | − | 1.00000i | ||||
\(769\) | −2.59808 | + | 1.50000i | −0.0936890 | + | 0.0540914i | −0.546113 | − | 0.837712i | \(-0.683893\pi\) |
0.452423 | + | 0.891803i | \(0.350560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.4904 | − | 9.50962i | −1.27650 | − | 0.342037i | −0.443982 | − | 0.896035i | \(-0.646435\pi\) |
−0.832518 | + | 0.553998i | \(0.813101\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.78461 | − | 32.7846i | −0.315146 | − | 1.17614i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.5692 | − | 18.0000i | −1.48937 | − | 0.644917i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.50000 | − | 4.33013i | −0.268371 | − | 0.154944i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.46410 | − | 2.00000i | −0.123718 | − | 0.0714286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.3731 | − | 36.3731i | −1.29656 | − | 1.29656i | −0.930651 | − | 0.365909i | \(-0.880758\pi\) |
−0.365909 | − | 0.930651i | \(-0.619242\pi\) | |||||||
\(788\) | −0.732051 | + | 2.73205i | −0.0260782 | + | 0.0973253i | ||||
\(789\) | 15.5885 | + | 27.0000i | 0.554964 | + | 0.961225i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.4974i | 1.72437i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.43782 | − | 16.5622i | −0.157592 | − | 0.588140i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.00000 | + | 15.5885i | −0.318997 | + | 0.552518i | ||||
\(797\) | 29.4449 | + | 29.4449i | 1.04299 | + | 1.04299i | 0.999033 | + | 0.0439572i | \(0.0139965\pi\) |
0.0439572 | + | 0.999033i | \(0.486003\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0000i | 1.06132i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.5000 | − | 18.1865i | −1.11300 | − | 0.642590i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.73205 | + | 0.732051i | −0.0964120 | + | 0.0258335i | ||||
\(804\) | −10.3923 | + | 6.00000i | −0.366508 | + | 0.211604i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.8827 | − | 9.88269i | −1.29833 | − | 0.347887i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.0000i | 0.808637i | 0.914618 | + | 0.404318i | \(0.132491\pi\) | ||||
−0.914618 | + | 0.404318i | \(0.867509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.5000 | − | 6.06218i | 0.368705 | − | 0.212872i | −0.304188 | − | 0.952612i | \(-0.598385\pi\) |
0.672892 | + | 0.739740i | \(0.265052\pi\) | |||||||
\(812\) | −9.46410 | + | 2.53590i | −0.332125 | + | 0.0889926i | ||||
\(813\) | −7.09808 | − | 1.90192i | −0.248940 | − | 0.0667034i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 41.5692i | − | 1.45521i | ||||||
\(817\) | −45.8564 | + | 18.1436i | −1.60431 | + | 0.634764i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.3923 | + | 18.0000i | −0.363137 | + | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.50000 | + | 4.33013i | 0.0872506 | + | 0.151122i | 0.906348 | − | 0.422532i | \(-0.138859\pi\) |
−0.819097 | + | 0.573654i | \(0.805525\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.02628 | + | 15.0263i | −0.140347 | + | 0.523783i | 0.859571 | + | 0.511016i | \(0.170731\pi\) |
−0.999918 | + | 0.0127672i | \(0.995936\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.43782 | + | 16.5622i | −0.154318 | + | 0.575923i | 0.844845 | + | 0.535012i | \(0.179693\pi\) |
−0.999163 | + | 0.0409115i | \(0.986974\pi\) | |||||||
\(828\) | 24.0000 | + | 24.0000i | 0.834058 | + | 0.834058i | ||||
\(829\) | 10.3923 | 0.360940 | 0.180470 | − | 0.983581i | \(-0.442238\pi\) | ||||
0.180470 | + | 0.983581i | \(0.442238\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.0000 | − | 13.8564i | −0.832551 | − | 0.480673i | ||||
\(832\) | 5.07180 | − | 18.9282i | 0.175833 | − | 0.656217i | ||||
\(833\) | −4.09808 | + | 1.09808i | −0.141990 | + | 0.0380461i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.00000 | − | 5.19615i | 0.242100 | − | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.3923 | − | 18.0000i | 0.358782 | − | 0.621429i | −0.628975 | − | 0.777425i | \(-0.716525\pi\) |
0.987758 | + | 0.155996i | \(0.0498587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | − | 22.5167i | 0.448276 | − | 0.776437i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.0000 | − | 24.0000i | −0.826604 | − | 0.826604i | ||||
\(844\) | 45.0333 | 1.55011 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0000 | − | 20.0000i | 0.687208 | − | 0.687208i | ||||
\(848\) | 6.92820 | − | 6.92820i | 0.237915 | − | 0.237915i | ||||
\(849\) | 12.1244 | + | 21.0000i | 0.416107 | + | 0.720718i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0000 | + | 13.8564i | −0.822709 | + | 0.474991i | ||||
\(852\) | −10.9808 | − | 40.9808i | −0.376195 | − | 1.40398i | ||||
\(853\) | −50.5429 | + | 13.5429i | −1.73056 | + | 0.463701i | −0.980311 | − | 0.197458i | \(-0.936732\pi\) |
−0.750246 | + | 0.661159i | \(0.770065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.8564 | − | 10.1436i | 1.29315 | − | 0.346499i | 0.454294 | − | 0.890852i | \(-0.349892\pi\) |
0.838856 | + | 0.544353i | \(0.183225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7224 | − | 8.50000i | 0.502323 | − | 0.290016i | −0.227349 | − | 0.973813i | \(-0.573006\pi\) |
0.729672 | + | 0.683797i | \(0.239673\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.0000 | + | 62.3538i | 1.22688 | + | 2.12501i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.3731 | + | 36.3731i | −1.23815 | + | 1.23815i | −0.277399 | + | 0.960755i | \(0.589472\pi\) |
−0.960755 | + | 0.277399i | \(0.910528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.73205 | − | 1.73205i | −0.0588235 | − | 0.0588235i | ||||
\(868\) | 47.3205 | + | 12.6795i | 1.60616 | + | 0.430370i | ||||
\(869\) | 2.59808 | − | 4.50000i | 0.0881337 | − | 0.152652i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | + | 5.19615i | −0.101651 | + | 0.176065i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.7846 | − | 20.7846i | 0.703452 | − | 0.703452i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | − | 6.92820i | −0.405442 | − | 0.234082i | ||||
\(877\) | 52.0526 | − | 13.9474i | 1.75769 | − | 0.470972i | 0.771450 | − | 0.636290i | \(-0.219532\pi\) |
0.986240 | + | 0.165319i | \(0.0528652\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.1769 | + | 18.0000i | 1.05157 | + | 0.607125i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.0000 | 1.24656 | 0.623281 | − | 0.781998i | \(-0.285799\pi\) | ||||
0.623281 | + | 0.781998i | \(0.285799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.32051 | − | 27.3205i | 0.246355 | − | 0.919408i | −0.726343 | − | 0.687332i | \(-0.758782\pi\) |
0.972698 | − | 0.232076i | \(-0.0745518\pi\) | |||||||
\(884\) | −10.3923 | − | 18.0000i | −0.349531 | − | 0.605406i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.53590 | − | 9.46410i | 0.0851471 | − | 0.317773i | −0.910195 | − | 0.414180i | \(-0.864068\pi\) |
0.995342 | + | 0.0964068i | \(0.0307350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.46410 | − | 6.00000i | −0.116182 | − | 0.201234i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.50000 | − | 7.79423i | 0.150756 | − | 0.261116i | ||||
\(892\) | −20.7846 | − | 20.7846i | −0.695920 | − | 0.695920i | ||||
\(893\) | −30.4904 | − | 4.50962i | −1.02032 | − | 0.150909i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.7846 | + | 8.78461i | 1.09465 | + | 0.293310i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.9904 | − | 7.50000i | 0.433253 | − | 0.250139i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.3923i | − | 0.346218i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 75.7128 | + | 20.2872i | 2.51956 | + | 0.675115i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9282 | + | 5.07180i | −0.628501 | + | 0.168406i | −0.558989 | − | 0.829175i | \(-0.688811\pi\) |
−0.0695114 | + | 0.997581i | \(0.522144\pi\) | |||||||
\(908\) | 18.9282 | + | 5.07180i | 0.628154 | + | 0.168313i | ||||
\(909\) | −28.5788 | − | 16.5000i | −0.947900 | − | 0.547270i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.5167i | 0.746010i | 0.927829 | + | 0.373005i | \(0.121673\pi\) | ||||
−0.927829 | + | 0.373005i | \(0.878327\pi\) | |||||||
\(912\) | 42.2487 | + | 6.24871i | 1.39899 | + | 0.206916i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.00000 | − | 15.5885i | −0.297368 | − | 0.515057i | ||||
\(917\) | 10.2487 | + | 38.2487i | 0.338442 | + | 1.26308i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0000i | 0.461817i | 0.972975 | + | 0.230909i | \(0.0741699\pi\) | ||||
−0.972975 | + | 0.230909i | \(0.925830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.0000 | + | 36.3731i | 0.691974 | + | 1.19853i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.0000 | − | 15.0000i | −0.493731 | − | 0.493731i | ||||
\(924\) | −13.8564 | −0.455842 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.80385 | + | 14.1962i | −0.124935 | + | 0.466263i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.4545 | − | 9.50000i | −0.539854 | − | 0.311685i | 0.205166 | − | 0.978727i | \(-0.434227\pi\) |
−0.745020 | + | 0.667042i | \(0.767560\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.500000 | − | 4.33013i | −0.0163868 | − | 0.141914i | ||||
\(932\) | 2.00000 | − | 2.00000i | 0.0655122 | − | 0.0655122i | ||||
\(933\) | 16.4833 | + | 61.5167i | 0.539640 | + | 2.01397i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.2224 | + | 6.22243i | 0.758644 | + | 0.203278i | 0.617349 | − | 0.786690i | \(-0.288207\pi\) |
0.141295 | + | 0.989968i | \(0.454873\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.3205 | 0.565233 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.5000 | + | 16.4545i | −0.929073 | + | 0.536401i | −0.886518 | − | 0.462693i | \(-0.846883\pi\) |
−0.0425550 | + | 0.999094i | \(0.513550\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.5692 | − | 41.5692i | 1.35368 | − | 1.35368i | ||||
\(944\) | 3.46410 | + | 6.00000i | 0.112747 | + | 0.195283i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.2750 | + | 53.2750i | 0.463875 | + | 1.73120i | 0.660593 | + | 0.750744i | \(0.270305\pi\) |
−0.196718 | + | 0.980460i | \(0.563028\pi\) | |||||||
\(948\) | 24.5885 | − | 6.58846i | 0.798596 | − | 0.213983i | ||||
\(949\) | −6.92820 | −0.224899 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 60.0000 | 1.94563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.53590 | − | 9.46410i | −0.0821458 | − | 0.306572i | 0.912613 | − | 0.408825i | \(-0.134062\pi\) |
−0.994758 | + | 0.102253i | \(0.967395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.00000 | − | 12.1244i | −0.226396 | − | 0.392130i | ||||
\(957\) | −3.00000 | + | 3.00000i | −0.0969762 | + | 0.0969762i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.0000 | −1.41935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56.7846 | − | 15.2154i | −1.82986 | − | 0.490309i | ||||
\(964\) | 5.19615 | − | 9.00000i | 0.167357 | − | 0.289870i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.85641 | + | 21.8564i | 0.188329 | + | 0.702855i | 0.993893 | + | 0.110346i | \(0.0351958\pi\) |
−0.805564 | + | 0.592509i | \(0.798138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.3731 | − | 27.0000i | 1.16847 | − | 0.867365i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0000 | − | 13.8564i | −0.770197 | − | 0.444673i | 0.0627481 | − | 0.998029i | \(-0.480014\pi\) |
−0.832945 | + | 0.553356i | \(0.813347\pi\) | |||||||
\(972\) | 42.5885 | − | 11.4115i | 1.36603 | − | 0.366025i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.0000 | 0.896258 | ||||||||
\(977\) | −24.2487 | − | 24.2487i | −0.775785 | − | 0.775785i | 0.203326 | − | 0.979111i | \(-0.434825\pi\) |
−0.979111 | + | 0.203326i | \(0.934825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.06218 | − | 10.5000i | −0.193748 | − | 0.335581i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.3731i | 1.16130i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.2154 | − | 56.7846i | −0.485296 | − | 1.81115i | −0.578726 | − | 0.815522i | \(-0.696450\pi\) |
0.0934305 | − | 0.995626i | \(-0.470217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34.6410 | + | 34.6410i | 1.10264 | + | 1.10264i | ||||
\(988\) | 19.8564 | − | 7.85641i | 0.631716 | − | 0.249946i | ||||
\(989\) | − | 64.0000i | − | 2.03508i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −65.5692 | + | 17.5692i | −2.08078 | + | 0.557542i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.6147 | + | 10.6147i | 1.25461 | + | 0.336172i | 0.824116 | − | 0.566421i | \(-0.191672\pi\) |
0.430495 | + | 0.902593i | \(0.358339\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 475.2.p.b.293.1 | 4 | ||
5.2 | odd | 4 | inner | 475.2.p.b.407.1 | 4 | ||
5.3 | odd | 4 | 95.2.l.b.27.1 | yes | 4 | ||
5.4 | even | 2 | 95.2.l.b.8.1 | ✓ | 4 | ||
15.8 | even | 4 | 855.2.cj.b.217.1 | 4 | |||
15.14 | odd | 2 | 855.2.cj.b.388.1 | 4 | |||
19.12 | odd | 6 | inner | 475.2.p.b.468.1 | 4 | ||
95.12 | even | 12 | inner | 475.2.p.b.107.1 | 4 | ||
95.69 | odd | 6 | 95.2.l.b.88.1 | yes | 4 | ||
95.88 | even | 12 | 95.2.l.b.12.1 | yes | 4 | ||
285.164 | even | 6 | 855.2.cj.b.658.1 | 4 | |||
285.278 | odd | 12 | 855.2.cj.b.487.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.l.b.8.1 | ✓ | 4 | 5.4 | even | 2 | ||
95.2.l.b.12.1 | yes | 4 | 95.88 | even | 12 | ||
95.2.l.b.27.1 | yes | 4 | 5.3 | odd | 4 | ||
95.2.l.b.88.1 | yes | 4 | 95.69 | odd | 6 | ||
475.2.p.b.107.1 | 4 | 95.12 | even | 12 | inner | ||
475.2.p.b.293.1 | 4 | 1.1 | even | 1 | trivial | ||
475.2.p.b.407.1 | 4 | 5.2 | odd | 4 | inner | ||
475.2.p.b.468.1 | 4 | 19.12 | odd | 6 | inner | ||
855.2.cj.b.217.1 | 4 | 15.8 | even | 4 | |||
855.2.cj.b.388.1 | 4 | 15.14 | odd | 2 | |||
855.2.cj.b.487.1 | 4 | 285.278 | odd | 12 | |||
855.2.cj.b.658.1 | 4 | 285.164 | even | 6 |