Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(609,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.609 |
Dual form | 1520.2.d.d.609.1 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.41421i | 1.39385i | 0.717146 | + | 0.696923i | \(0.245448\pi\) | ||||
−0.717146 | + | 0.696923i | \(0.754552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.12132 | + | 0.707107i | 0.948683 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41421i | 0.912487i | 0.889855 | + | 0.456243i | \(0.150805\pi\) | ||||
−0.889855 | + | 0.456243i | \(0.849195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.82843i | − | 0.507114i | −0.967320 | − | 0.253557i | \(-0.918399\pi\) | ||
0.967320 | − | 0.253557i | \(-0.0816006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.70711 | + | 5.12132i | −0.440773 | + | 1.32232i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000i | 0.242536i | 0.992620 | + | 0.121268i | \(0.0386960\pi\) | ||||
−0.992620 | + | 0.121268i | \(0.961304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.82843 | −1.27187 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.24264i | 1.09317i | 0.837405 | + | 0.546583i | \(0.184072\pi\) | ||||
−0.837405 | + | 0.546583i | \(0.815928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | + | 3.00000i | 0.800000 | + | 0.600000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214i | 0.0797154i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82843 | −0.710921 | −0.355461 | − | 0.934691i | \(-0.615676\pi\) | ||||
−0.355461 | + | 0.934691i | \(0.615676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.41421 | −0.613211 | −0.306605 | − | 0.951837i | \(-0.599193\pi\) | ||||
−0.306605 | + | 0.951837i | \(0.599193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.41421i | − | 0.594338i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.70711 | + | 5.12132i | −0.288554 | + | 0.865661i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.17157i | 0.850201i | 0.905146 | + | 0.425101i | \(0.139761\pi\) | ||||
−0.905146 | + | 0.425101i | \(0.860239\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.41421 | 0.706840 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.07107 | −1.10432 | −0.552158 | − | 0.833740i | \(-0.686195\pi\) | ||||
−0.552158 | + | 0.833740i | \(0.686195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.24264i | 0.341999i | 0.985271 | + | 0.171000i | \(0.0546997\pi\) | ||||
−0.985271 | + | 0.171000i | \(0.945300\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | − | 2.00000i | −0.894427 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.17157 | 0.167368 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41421 | −0.338058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.82843i | 0.251154i | 0.992084 | + | 0.125577i | \(0.0400782\pi\) | ||||
−0.992084 | + | 0.125577i | \(0.959922\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | − | 1.00000i | −0.404520 | − | 0.134840i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.41421i | − | 0.319770i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.4142 | 1.87657 | 0.938285 | − | 0.345862i | \(-0.112413\pi\) | ||||
0.938285 | + | 0.345862i | \(0.112413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.41421 | 0.437145 | 0.218573 | − | 0.975821i | \(-0.429860\pi\) | ||||
0.218573 | + | 0.975821i | \(0.429860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 6.82843i | − | 0.860301i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.29289 | − | 3.87868i | 0.160364 | − | 0.481091i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.07107i | 0.741699i | 0.928693 | + | 0.370849i | \(0.120933\pi\) | ||||
−0.928693 | + | 0.370849i | \(0.879067\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.6569 | −1.52371 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.07107 | −0.364469 | −0.182234 | − | 0.983255i | \(-0.558333\pi\) | ||||
−0.182234 | + | 0.983255i | \(0.558333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.8284i | − | 1.61849i | −0.587468 | − | 0.809247i | \(-0.699875\pi\) | ||
0.587468 | − | 0.809247i | \(-0.300125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.24264 | + | 9.65685i | −0.836308 | + | 1.11508i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.41421i | − | 0.389086i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.828427 | −0.0932053 | −0.0466027 | − | 0.998914i | \(-0.514839\pi\) | ||||
−0.0466027 | + | 0.998914i | \(0.514839\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.48528i | − | 0.272795i | −0.990654 | − | 0.136398i | \(-0.956448\pi\) | ||
0.990654 | − | 0.136398i | \(-0.0435524\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.707107 | + | 2.12132i | −0.0766965 | + | 0.230089i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 9.24264i | − | 0.990915i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.75736 | 0.398279 | 0.199140 | − | 0.979971i | \(-0.436185\pi\) | ||||
0.199140 | + | 0.979971i | \(0.436185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.41421 | 0.462735 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.24264i | − | 0.854722i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.12132 | − | 0.707107i | −0.217643 | − | 0.0725476i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.65685i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.8995 | 1.58206 | 0.791029 | − | 0.611778i | \(-0.209545\pi\) | ||||
0.791029 | + | 0.611778i | \(0.209545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.89949i | − | 0.975426i | −0.873004 | − | 0.487713i | \(-0.837831\pi\) | ||
0.873004 | − | 0.487713i | \(-0.162169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.3640 | − | 4.12132i | −1.20660 | − | 0.402200i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.41421i | 0.233391i | 0.993168 | + | 0.116695i | \(0.0372301\pi\) | ||||
−0.993168 | + | 0.116695i | \(0.962770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.4853 | −1.18505 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0711i | 1.22962i | 0.788674 | + | 0.614811i | \(0.210768\pi\) | ||||
−0.788674 | + | 0.614811i | \(0.789232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.70711 | + | 11.1213i | −0.345689 | + | 1.03707i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.17157i | 0.478112i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.41421 | −0.221311 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 17.0711i | − | 1.53925i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.36396 | + | 9.19239i | 0.569210 | + | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.1716i | − | 0.991317i | −0.868518 | − | 0.495658i | \(-0.834927\pi\) | ||
0.868518 | − | 0.495658i | \(-0.165073\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.41421 | −0.476695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.6569 | −1.89217 | −0.946084 | − | 0.323921i | \(-0.894999\pi\) | ||||
−0.946084 | + | 0.323921i | \(0.894999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.41421i | − | 0.209339i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.292893 | + | 0.878680i | −0.0252082 | + | 0.0756247i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.3137i | 1.39377i | 0.717181 | + | 0.696887i | \(0.245432\pi\) | ||||
−0.717181 | + | 0.696887i | \(0.754568\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.3137 | 1.62651 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.58579i | 0.216234i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.12132 | − | 2.70711i | −0.674439 | − | 0.224813i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.82843i | 0.233285i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6569 | 1.44651 | 0.723253 | − | 0.690583i | \(-0.242646\pi\) | ||||
0.723253 | + | 0.690583i | \(0.242646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1716 | −0.909130 | −0.454565 | − | 0.890714i | \(-0.650205\pi\) | ||||
−0.454565 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.82843i | − | 0.228665i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.24264 | − | 2.41421i | −0.581743 | − | 0.193914i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.343146i | 0.0273860i | 0.999906 | + | 0.0136930i | \(0.00435876\pi\) | ||||
−0.999906 | + | 0.0136930i | \(0.995641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.41421 | −0.350070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.6569 | −0.997500 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.92893i | 0.229412i | 0.993400 | + | 0.114706i | \(0.0365925\pi\) | ||||
−0.993400 | + | 0.114706i | \(0.963407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.41421 | − | 7.24264i | 0.187946 | − | 0.563839i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 23.2132i | − | 1.79629i | −0.439698 | − | 0.898146i | \(-0.644914\pi\) | ||
0.439698 | − | 0.898146i | \(-0.355086\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.65685 | 0.742835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 18.8284i | − | 1.43150i | −0.698357 | − | 0.715749i | \(-0.746085\pi\) | ||
0.698357 | − | 0.715749i | \(-0.253915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.24264 | + | 9.65685i | −0.547492 | + | 0.729990i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 34.7990i | 2.61565i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.9706 | −1.71690 | −0.858450 | − | 0.512897i | \(-0.828572\pi\) | ||||
−0.858450 | + | 0.512897i | \(0.828572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.485281 | 0.0360707 | 0.0180353 | − | 0.999837i | \(-0.494259\pi\) | ||||
0.0180353 | + | 0.999837i | \(0.494259\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.24264i | 0.609314i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.65685 | + | 10.9706i | −0.268857 | + | 0.806572i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.41421i | − | 0.103418i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2426 | 0.813489 | 0.406744 | − | 0.913542i | \(-0.366664\pi\) | ||||
0.406744 | + | 0.913542i | \(0.366664\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 7.65685i | − | 0.551152i | −0.961279 | − | 0.275576i | \(-0.911131\pi\) | ||
0.961279 | − | 0.275576i | \(-0.0888686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.36396 | + | 3.12132i | 0.670567 | + | 0.223522i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.7279i | 1.47680i | 0.674361 | + | 0.738402i | \(0.264419\pi\) | ||||
−0.674361 | + | 0.738402i | \(0.735581\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0711 | 1.13925 | 0.569624 | − | 0.821905i | \(-0.307089\pi\) | ||||
0.569624 | + | 0.821905i | \(0.307089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.6569 | −1.03381 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.24264i | − | 0.648706i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.0000 | − | 5.00000i | −1.04765 | − | 0.349215i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 14.8284i | − | 1.03065i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.41421 | 0.0978232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8995 | 1.71415 | 0.857076 | − | 0.515190i | \(-0.172279\pi\) | ||||
0.857076 | + | 0.515190i | \(0.172279\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 7.41421i | − | 0.508014i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.58579 | + | 4.75736i | −0.108150 | + | 0.324449i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.24264i | − | 0.559547i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 33.3848 | 2.25593 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.82843 | 0.122993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.17157i | 0.212384i | 0.994346 | + | 0.106192i | \(0.0338659\pi\) | ||||
−0.994346 | + | 0.106192i | \(0.966134\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.3137 | − | 8.48528i | −0.754247 | − | 0.565685i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2426i | 1.14443i | 0.820102 | + | 0.572217i | \(0.193917\pi\) | ||||
−0.820102 | + | 0.572217i | \(0.806083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.9706 | 1.78226 | 0.891132 | − | 0.453743i | \(-0.149912\pi\) | ||||
0.891132 | + | 0.453743i | \(0.149912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.24264 | 0.542326 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.34315i | 0.153505i | 0.997050 | + | 0.0767523i | \(0.0244551\pi\) | ||||
−0.997050 | + | 0.0767523i | \(0.975545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.65685 | − | 16.9706i | 0.369012 | − | 1.10704i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2.00000i | − | 0.129914i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.27208 | 0.146969 | 0.0734843 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734843 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.65685 | 0.364390 | 0.182195 | − | 0.983262i | \(-0.441680\pi\) | ||||
0.182195 | + | 0.983262i | \(0.441680\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 21.6569i | − | 1.38929i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.48528 | + | 0.828427i | 0.158779 | + | 0.0529263i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.82843i | 0.116340i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.5563 | 1.73934 | 0.869671 | − | 0.493632i | \(-0.164331\pi\) | ||||
0.869671 | + | 0.493632i | \(0.164331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.41421i | − | 0.466128i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.12132 | − | 1.70711i | −0.320710 | − | 0.106903i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.27208i | 0.204107i | 0.994779 | + | 0.102053i | \(0.0325412\pi\) | ||||
−0.994779 | + | 0.102053i | \(0.967459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4853 | −0.775798 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.8284 | 0.670263 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.34315i | − | 0.267810i | −0.990994 | − | 0.133905i | \(-0.957248\pi\) | ||
0.990994 | − | 0.133905i | \(-0.0427517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.29289 | + | 3.87868i | −0.0794218 | + | 0.238265i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.07107i | 0.555140i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3848 | 1.29903 | 0.649516 | − | 0.760348i | \(-0.274971\pi\) | ||||
0.649516 | + | 0.760348i | \(0.274971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.6569i | 0.644982i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.65685 | − | 4.24264i | −0.341121 | − | 0.255841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3137i | 1.16045i | 0.814457 | + | 0.580224i | \(0.197035\pi\) | ||||
−0.814457 | + | 0.580224i | \(0.802965\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.65685 | 0.578141 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2426 | −0.730335 | −0.365167 | − | 0.930942i | \(-0.618988\pi\) | ||||
−0.365167 | + | 0.930942i | \(0.618988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.4853i | 1.57439i | 0.616706 | + | 0.787193i | \(0.288467\pi\) | ||||
−0.616706 | + | 0.787193i | \(0.711533\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.70711 | − | 5.12132i | 0.101120 | − | 0.303361i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 17.0711i | − | 1.00767i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0000 | 0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.4853 | −1.08363 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.7990i | 1.68245i | 0.540681 | + | 0.841227i | \(0.318166\pi\) | ||||
−0.540681 | + | 0.841227i | \(0.681834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.5772 | + | 10.1924i | 1.78027 | + | 0.593424i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.585786i | − | 0.0339908i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.58579 | 0.554360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.41421 | −0.312070 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.3848i | 2.20515i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.24264 | + | 2.41421i | 0.414712 | + | 0.138237i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.2843i | 1.38598i | 0.720949 | + | 0.692988i | \(0.243706\pi\) | ||||
−0.720949 | + | 0.692988i | \(0.756294\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.8995 | 1.35959 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7574 | −0.836813 | −0.418407 | − | 0.908260i | \(-0.637411\pi\) | ||||
−0.418407 | + | 0.908260i | \(0.637411\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.65685i | 0.263221i | 0.991302 | + | 0.131610i | \(0.0420148\pi\) | ||||
−0.991302 | + | 0.131610i | \(0.957985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.82843 | − | 14.4853i | 0.272051 | − | 0.816153i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 32.7990i | − | 1.84217i | −0.389356 | − | 0.921087i | \(-0.627302\pi\) | ||
0.389356 | − | 0.921087i | \(-0.372698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.41421 | 0.303138 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.82843 | −0.325311 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.00000i | − | 0.0556415i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.48528 | − | 7.31371i | 0.304269 | − | 0.405692i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0711i | 0.667532i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.3137 | 1.06480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3848 | 0.955554 | 0.477777 | − | 0.878481i | \(-0.341443\pi\) | ||||
0.477777 | + | 0.878481i | \(0.341443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 14.6274i | − | 0.801578i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.29289 | + | 12.8787i | −0.234546 | + | 0.703637i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.7279i | − | 0.693334i | −0.937988 | − | 0.346667i | \(-0.887313\pi\) | ||
0.937988 | − | 0.346667i | \(-0.112687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.5563 | −1.71391 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.82843 | 0.261474 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7279i | 1.06521i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.8492 | − | 8.94975i | −1.44551 | − | 0.481838i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.8284i | − | 1.11813i | −0.829124 | − | 0.559064i | \(-0.811160\pi\) | ||
0.829124 | − | 0.559064i | \(-0.188840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.6274 | 0.890045 | 0.445023 | − | 0.895519i | \(-0.353196\pi\) | ||||
0.445023 | + | 0.895519i | \(0.353196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.757359 | 0.0404248 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.1127i | 1.38984i | 0.719088 | + | 0.694919i | \(0.244560\pi\) | ||||
−0.719088 | + | 0.694919i | \(0.755440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.51472 | − | 2.17157i | −0.345765 | − | 0.115255i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 5.82843i | − | 0.308473i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.07107 | 0.425975 | 0.212987 | − | 0.977055i | \(-0.431681\pi\) | ||||
0.212987 | + | 0.977055i | \(0.431681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 21.7279i | − | 1.14042i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.77817 | − | 29.3345i | 0.511813 | − | 1.53544i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 17.4558i | − | 0.911188i | −0.890188 | − | 0.455594i | \(-0.849427\pi\) | ||
0.890188 | − | 0.455594i | \(-0.150573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.0000 | 1.04116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.41421 | −0.229175 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.97056i | − | 0.309144i | −0.987982 | − | 0.154572i | \(-0.950600\pi\) | ||
0.987982 | − | 0.154572i | \(-0.0493999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.1924 | + | 15.3640i | −1.14601 | + | 0.793392i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.00000i | 0.360518i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.3848 | 1.71486 | 0.857430 | − | 0.514600i | \(-0.172060\pi\) | ||||
0.857430 | + | 0.514600i | \(0.172060\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.9706 | 1.38174 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.72792i | 0.241586i | 0.992678 | + | 0.120793i | \(0.0385437\pi\) | ||||
−0.992678 | + | 0.120793i | \(0.961456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.41421 | − | 7.24264i | 0.123040 | − | 0.369119i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 6.34315i | − | 0.322440i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8995 | 0.603328 | 0.301664 | − | 0.953414i | \(-0.402458\pi\) | ||||
0.301664 | + | 0.953414i | \(0.402458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.24264 | −0.265132 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 52.2843i | − | 2.63739i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.75736 | − | 0.585786i | −0.0884223 | − | 0.0294741i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.6274i | − | 1.13564i | −0.823154 | − | 0.567819i | \(-0.807787\pi\) | ||
0.823154 | − | 0.567819i | \(-0.192213\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.82843 | 0.291786 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.8995 | −1.29336 | −0.646680 | − | 0.762762i | \(-0.723843\pi\) | ||||
−0.646680 | + | 0.762762i | \(0.723843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.24264i | 0.310968i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.1213 | − | 6.70711i | −0.999836 | − | 0.333279i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.31371i | − | 0.362527i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.41421 | −0.267716 | −0.133858 | − | 0.991001i | \(-0.542737\pi\) | ||||
−0.133858 | + | 0.991001i | \(0.542737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −39.3848 | −1.94271 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.7990i | 1.71235i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.75736 | − | 5.27208i | 0.0862654 | − | 0.258796i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.65685i | − | 0.472898i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2132 | 0.743214 | 0.371607 | − | 0.928390i | \(-0.378807\pi\) | ||||
0.371607 | + | 0.928390i | \(0.378807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1421 | −0.737983 | −0.368991 | − | 0.929433i | \(-0.620297\pi\) | ||||
−0.368991 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.6274i | 1.10018i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.00000 | + | 4.00000i | −0.145521 | + | 0.194029i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.24264i | 0.398889i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.24264 | −0.301398 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.58579 | 0.124553 | 0.0622765 | − | 0.998059i | \(-0.480164\pi\) | ||||
0.0622765 | + | 0.998059i | \(0.480164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.07107i | 0.435928i | 0.975957 | + | 0.217964i | \(0.0699415\pi\) | ||||
−0.975957 | + | 0.217964i | \(0.930059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.53553 | − | 19.6066i | 0.313355 | − | 0.940065i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.24264i | − | 0.250790i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.27208 | −0.251623 | −0.125811 | − | 0.992054i | \(-0.540153\pi\) | ||||
−0.125811 | + | 0.992054i | \(0.540153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.31371 | −0.157796 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 15.5563i | − | 0.739104i | −0.929210 | − | 0.369552i | \(-0.879511\pi\) | ||
0.929210 | − | 0.369552i | \(-0.120489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.97056 | + | 2.65685i | 0.377841 | + | 0.125947i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 42.6274i | 2.01621i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.9411 | −1.50739 | −0.753697 | − | 0.657222i | \(-0.771732\pi\) | ||||
−0.753697 | + | 0.657222i | \(0.771732\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0000 | 0.470882 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 26.9706i | − | 1.26719i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.36396 | + | 3.12132i | 0.438989 | + | 0.146330i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.31371i | − | 0.295343i | −0.989036 | − | 0.147671i | \(-0.952822\pi\) | ||
0.989036 | − | 0.147671i | \(-0.0471778\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.414214 | −0.0193338 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.7279 | −1.52429 | −0.762146 | − | 0.647406i | \(-0.775854\pi\) | ||||
−0.762146 | + | 0.647406i | \(0.775854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.14214i | − | 0.285449i | −0.989762 | − | 0.142725i | \(-0.954414\pi\) | ||
0.989762 | − | 0.142725i | \(-0.0455863\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.82843 | − | 17.4853i | 0.270287 | − | 0.810861i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.10051i | 0.0971998i | 0.998818 | + | 0.0485999i | \(0.0154759\pi\) | ||||
−0.998818 | + | 0.0485999i | \(0.984524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.6569 | −0.676791 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.828427 | −0.0381719 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.17157i | − | 0.145829i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | − | 3.00000i | −0.183533 | − | 0.137649i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 5.17157i | − | 0.236790i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.4558 | −0.797578 | −0.398789 | − | 0.917043i | \(-0.630569\pi\) | ||||
−0.398789 | + | 0.917043i | \(0.630569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.45584 | 0.431149 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 30.5563i | − | 1.39036i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.41421 | + | 16.2426i | −0.245847 | + | 0.737540i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.8284i | − | 0.581312i | −0.956828 | − | 0.290656i | \(-0.906127\pi\) | ||
0.956828 | − | 0.290656i | \(-0.0938734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.07107 | −0.319765 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.2426 | −1.18431 | −0.592157 | − | 0.805823i | \(-0.701723\pi\) | ||||
−0.592157 | + | 0.805823i | \(0.701723\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.82843i | − | 0.172424i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.48528 | + | 2.82843i | 0.381385 | + | 0.127128i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 7.41421i | − | 0.332573i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.0711 | 1.48046 | 0.740232 | − | 0.672351i | \(-0.234716\pi\) | ||||
0.740232 | + | 0.672351i | \(0.234716\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.0416 | 2.50376 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1005i | 0.584123i | 0.956400 | + | 0.292061i | \(0.0943411\pi\) | ||||
−0.956400 | + | 0.292061i | \(0.905659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.7279 | + | 11.2426i | 1.50087 | + | 0.500291i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.3137i | 1.03540i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.65685 | 0.0734388 | 0.0367194 | − | 0.999326i | \(-0.488309\pi\) | ||||
0.0367194 | + | 0.999326i | \(0.488309\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.3848 | 1.47686 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.414214i | − | 0.0182880i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.00000 | − | 21.0000i | 0.308457 | − | 0.925371i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3137i | 0.497576i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.4558 | 1.99529 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.2132i | 0.971316i | 0.874149 | + | 0.485658i | \(0.161420\pi\) | ||||
−0.874149 | + | 0.485658i | \(0.838580\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.3137 | − | 17.4853i | −1.01749 | − | 0.763120i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.41421i | − | 0.148725i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.48528 | −0.195012 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −40.7696 | −1.76925 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.9289i | 0.560014i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.70711 | + | 5.12132i | −0.0738047 | + | 0.221414i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 55.4558i | − | 2.39310i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.65685 | −0.0713658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0416 | −0.775670 | −0.387835 | − | 0.921729i | \(-0.626777\pi\) | ||||
−0.387835 | + | 0.921729i | \(0.626777\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.17157i | 0.0502770i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.6066 | + | 3.53553i | 0.454337 | + | 0.151446i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.9411i | − | 1.87879i | −0.342841 | − | 0.939393i | \(-0.611389\pi\) | ||
0.342841 | − | 0.939393i | \(-0.388611\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.65685 | −0.412144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.82843 | 0.163096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.00000i | − | 0.0850487i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.4853 | − | 8.82843i | −1.12424 | − | 0.374746i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 20.6863i | − | 0.876506i | −0.898852 | − | 0.438253i | \(-0.855597\pi\) | ||
0.898852 | − | 0.438253i | \(-0.144403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.10051 | 0.173433 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.41421 | 0.144148 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 11.0294i | − | 0.464835i | −0.972616 | − | 0.232418i | \(-0.925336\pi\) | ||
0.972616 | − | 0.232418i | \(-0.0746636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.24264 | + | 27.7279i | −0.388841 | + | 1.16652i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 22.8995i | − | 0.961688i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.9706 | −1.04682 | −0.523410 | − | 0.852081i | \(-0.675340\pi\) | ||||
−0.523410 | + | 0.852081i | \(0.675340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.6985 | 0.489566 | 0.244783 | − | 0.969578i | \(-0.421283\pi\) | ||||
0.244783 | + | 0.969578i | \(0.421283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.1421i | 1.13388i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.7279 | + | 20.9706i | −0.655900 | + | 0.874533i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25.0000i | − | 1.04076i | −0.853934 | − | 0.520382i | \(-0.825790\pi\) | ||
0.853934 | − | 0.520382i | \(-0.174210\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.4853 | 0.768222 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | 0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.58579i | − | 0.107092i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.65685 | + | 10.9706i | −0.151192 | + | 0.453577i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.38478i | − | 0.180979i | −0.995897 | − | 0.0904895i | \(-0.971157\pi\) | ||
0.995897 | − | 0.0904895i | \(-0.0288432\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.41421 | 0.140680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −50.0416 | −2.05844 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.0000i | 1.72473i | 0.506284 | + | 0.862367i | \(0.331019\pi\) | ||||
−0.506284 | + | 0.862367i | \(0.668981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.12132 | − | 1.70711i | −0.209954 | − | 0.0699846i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.7990i | 1.58794i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.44365 | −0.0998449 | −0.0499224 | − | 0.998753i | \(-0.515897\pi\) | ||||
−0.0499224 | + | 0.998753i | \(0.515897\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.5563 | 1.28721 | 0.643605 | − | 0.765358i | \(-0.277438\pi\) | ||||
0.643605 | + | 0.765358i | \(0.277438\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 17.1716i | − | 0.699281i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.0919 | − | 6.36396i | −0.776195 | − | 0.258732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.5147i | − | 0.548546i | −0.961652 | − | 0.274273i | \(-0.911563\pi\) | ||
0.961652 | − | 0.274273i | \(-0.0884371\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.3137 | 0.904197 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.6274 | −0.591762 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.7279i | − | 0.917972i | −0.888443 | − | 0.458986i | \(-0.848213\pi\) | ||
0.888443 | − | 0.458986i | \(-0.151787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.0711 | − | 36.2132i | 0.486752 | − | 1.46026i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.79899i | 0.313976i | 0.987601 | + | 0.156988i | \(0.0501783\pi\) | ||||
−0.987601 | + | 0.156988i | \(0.949822\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.3848 | −1.22127 | −0.610634 | − | 0.791913i | \(-0.709085\pi\) | ||||
−0.610634 | + | 0.791913i | \(0.709085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.17157 | −0.0871422 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.07107i | 0.363425i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.41421i | 0.136351i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.17157 | −0.206204 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.9706 | 1.55139 | 0.775697 | − | 0.631106i | \(-0.217399\pi\) | ||||
0.775697 | + | 0.631106i | \(0.217399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 60.1127i | 2.38927i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.89949 | − | 23.6985i | 0.313482 | − | 0.940446i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.14214i | − | 0.0848745i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.68629 | 0.343624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.2132 | −1.54883 | −0.774414 | − | 0.632679i | \(-0.781955\pi\) | ||||
−0.774414 | + | 0.632679i | \(0.781955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.1716i | 1.22929i | 0.788805 | + | 0.614643i | \(0.210700\pi\) | ||||
−0.788805 | + | 0.614643i | \(0.789300\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.4853 | − | 3.82843i | −0.452233 | − | 0.150744i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.0711i | − | 0.474563i | −0.971441 | − | 0.237281i | \(-0.923744\pi\) | ||
0.971441 | − | 0.237281i | \(-0.0762563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.3848 | −0.800172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8995 | 0.779923 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.2843i | 1.26338i | 0.775221 | + | 0.631691i | \(0.217639\pi\) | ||||
−0.775221 | + | 0.631691i | \(0.782361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.9411 | − | 15.3137i | −1.79507 | − | 0.598356i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 39.1127i | 1.52593i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.89949 | −0.346675 | −0.173338 | − | 0.984862i | \(-0.555455\pi\) | ||||
−0.173338 | + | 0.984862i | \(0.555455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4853 | 1.69138 | 0.845691 | − | 0.533673i | \(-0.179189\pi\) | ||||
0.845691 | + | 0.533673i | \(0.179189\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.41421i | 0.171434i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.70711 | − | 5.12132i | 0.0661988 | − | 0.198596i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20.0711i | − | 0.777155i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.65685 | −0.296031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.82843 | −0.186399 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.0000i | − | 1.07932i | −0.841883 | − | 0.539660i | \(-0.818553\pi\) | ||
0.841883 | − | 0.539660i | \(-0.181447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.24264 | + | 1.65685i | −0.0478293 | + | 0.0637723i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 21.3431i | − | 0.820284i | −0.912022 | − | 0.410142i | \(-0.865479\pi\) | ||
0.912022 | − | 0.410142i | \(-0.134521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.4853 | −0.709400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.6274 | −1.59517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.3137i | 0.892074i | 0.895014 | + | 0.446037i | \(0.147165\pi\) | ||||
−0.895014 | + | 0.446037i | \(0.852835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.5355 | + | 34.6066i | −0.440750 | + | 1.32225i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 65.1127i | 2.48420i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.34315 | 0.127364 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.45584 | −0.283634 | −0.141817 | − | 0.989893i | \(-0.545294\pi\) | ||||
−0.141817 | + | 0.989893i | \(0.545294\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.65685i | 0.366834i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.48528 | − | 2.82843i | −0.321865 | − | 0.107288i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.07107i | − | 0.267836i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.65685 | −0.213962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.9706 | 1.24528 | 0.622640 | − | 0.782508i | \(-0.286060\pi\) | ||||
0.622640 | + | 0.782508i | \(0.286060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.17157i | − | 0.195050i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40.9706 | + | 13.6569i | 1.54304 | + | 0.514347i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.3848i | 1.44361i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6863 | −0.401332 | −0.200666 | − | 0.979660i | \(-0.564311\pi\) | ||||
−0.200666 | + | 0.979660i | \(0.564311\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.34315 | 0.0878748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 17.8995i | − | 0.670341i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.82843 | + | 5.48528i | −0.0683793 | + | 0.205138i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.48528i | 0.204852i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.4142 | 1.13426 | 0.567129 | − | 0.823629i | \(-0.308054\pi\) | ||||
0.567129 | + | 0.823629i | \(0.308054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.8995 | 0.890064 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.6569i | 0.507904i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.3137 | − | 11.4853i | −0.568737 | − | 0.426553i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.78680i | 0.0662686i | 0.999451 | + | 0.0331343i | \(0.0105489\pi\) | ||||
−0.999451 | + | 0.0331343i | \(0.989451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.24264 | −0.0829471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.6274i | 0.392533i | 0.980551 | + | 0.196266i | \(0.0628817\pi\) | ||||
−0.980551 | + | 0.196266i | \(0.937118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.00000 | + | 6.00000i | −0.0737711 | + | 0.221313i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.58579i | − | 0.316262i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.41421 | 0.272736 | 0.136368 | − | 0.990658i | \(-0.456457\pi\) | ||||
0.136368 | + | 0.990658i | \(0.456457\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.41421 | −0.162160 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2426i | 0.522512i | 0.965270 | + | 0.261256i | \(0.0841366\pi\) | ||||
−0.965270 | + | 0.261256i | \(0.915863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.4558 | + | 12.4853i | 1.37228 | + | 0.457425i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.02944i | 0.257194i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.82843 | −0.212966 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7574 | −1.08586 | −0.542931 | − | 0.839777i | \(-0.682685\pi\) | ||||
−0.542931 | + | 0.839777i | \(0.682685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 66.5269i | 2.42438i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.6985 | − | 7.89949i | −0.862476 | − | 0.287492i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 16.3431i | − | 0.594002i | −0.954877 | − | 0.297001i | \(-0.904014\pi\) | ||
0.954877 | − | 0.297001i | \(-0.0959864\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.8995 | 0.649711 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.02944 | −0.146067 | −0.0730335 | − | 0.997329i | \(-0.523268\pi\) | ||||
−0.0730335 | + | 0.997329i | \(0.523268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0711i | 0.437002i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | − | 6.00000i | 0.0723102 | − | 0.216930i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 26.3553i | − | 0.951636i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.7990 | 1.11064 | 0.555320 | − | 0.831637i | \(-0.312596\pi\) | ||||
0.555320 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.89949 | −0.284493 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.00000i | − | 0.323708i | −0.986815 | − | 0.161854i | \(-0.948253\pi\) | ||
0.986815 | − | 0.161854i | \(-0.0517473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.6569 | − | 10.2426i | −0.490569 | − | 0.367927i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 30.1421i | − | 1.08134i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.07107 | 0.253347 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.34315 | 0.155410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.58579i | − | 0.0566714i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.242641 | + | 0.727922i | −0.00866022 | + | 0.0259807i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.7574i | 0.811212i | 0.914048 | + | 0.405606i | \(0.132940\pi\) | ||||
−0.914048 | + | 0.405606i | \(0.867060\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.4853 | 0.373286 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.5563 | −1.12201 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.24264i | − | 0.221683i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.36396 | − | 3.12132i | −0.332105 | − | 0.110702i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.1421i | 1.24480i | 0.782700 | + | 0.622399i | \(0.213842\pi\) | ||||
−0.782700 | + | 0.622399i | \(0.786158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | 0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6274 | −0.375501 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.5563i | 0.690129i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.8492 | − | 8.94975i | −0.946311 | − | 0.315437i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.1421i | 0.849843i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.51472 | 0.299362 | 0.149681 | − | 0.988734i | \(-0.452175\pi\) | ||||
0.149681 | + | 0.988734i | \(0.452175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.0122 | 1.47525 | 0.737624 | − | 0.675212i | \(-0.235948\pi\) | ||||
0.737624 | + | 0.675212i | \(0.235948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.6274i | 1.81065i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.07107 | + | 6.21320i | −0.0725463 | + | 0.217639i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.24264i | − | 0.0784601i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.4853 | −0.436271 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.5980 | −1.80078 | −0.900391 | − | 0.435082i | \(-0.856719\pi\) | ||||
−0.900391 | + | 0.435082i | \(0.856719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 47.5269i | − | 1.65668i | −0.560223 | − | 0.828342i | \(-0.689284\pi\) | ||
0.560223 | − | 0.828342i | \(-0.310716\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.2426 | − | 13.6569i | 0.356603 | − | 0.475471i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.8701i | 1.17778i | 0.808214 | + | 0.588889i | \(0.200434\pi\) | ||||
−0.808214 | + | 0.588889i | \(0.799566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.7696 | −0.895014 | −0.447507 | − | 0.894281i | \(-0.647688\pi\) | ||||
−0.447507 | + | 0.894281i | \(0.647688\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.6274 | −1.61749 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.17157i | 0.0405926i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.4142 | − | 49.2426i | 0.568037 | − | 1.70411i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.41421i | − | 0.0488824i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.9411 | −1.72416 | −0.862080 | − | 0.506773i | \(-0.830838\pi\) | ||||
−0.862080 | + | 0.506773i | \(0.830838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3431 | −0.494591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 29.5563i | − | 1.01797i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.4853 | + | 6.82843i | 0.704715 | + | 0.234905i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 21.7279i | − | 0.746580i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.9411 | −2.19445 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.1127 | −0.929411 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9411i | 0.682771i | 0.939923 | + | 0.341386i | \(0.110896\pi\) | ||||
−0.939923 | + | 0.341386i | \(0.889104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | + | 2.00000i | 0.205196 | + | 0.0683986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0000i | 0.546550i | 0.961936 | + | 0.273275i | \(0.0881068\pi\) | ||||
−0.961936 | + | 0.273275i | \(0.911893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.21320 | 0.177872 | 0.0889361 | − | 0.996037i | \(-0.471653\pi\) | ||||
0.0889361 | + | 0.996037i | \(0.471653\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 41.2132 | 1.40454 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 35.0711i | − | 1.19383i | −0.802303 | − | 0.596917i | \(-0.796392\pi\) | ||
0.802303 | − | 0.596917i | \(-0.203608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3137 | − | 39.9411i | 0.452680 | − | 1.35804i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.6274i | 1.31186i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.17157 | 0.0397429 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1005 | 0.376126 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 21.6569i | − | 0.732973i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.1924 | + | 15.3640i | −0.750240 | + | 0.519397i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 29.4853i | − | 0.995647i | −0.867278 | − | 0.497824i | \(-0.834133\pi\) | ||
0.867278 | − | 0.497824i | \(-0.165867\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −69.5269 | −2.34508 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.2843 | 0.413868 | 0.206934 | − | 0.978355i | \(-0.433652\pi\) | ||||
0.206934 | + | 0.978355i | \(0.433652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.4558i | 0.520131i | 0.965591 | + | 0.260065i | \(0.0837441\pi\) | ||||
−0.965591 | + | 0.260065i | \(0.916256\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.6066 | + | 73.8198i | −0.827142 | + | 2.48143i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 0.928932i | − | 0.0311905i | −0.999878 | − | 0.0155952i | \(-0.995036\pi\) | ||
0.999878 | − | 0.0155952i | \(-0.00496432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.9706 | 0.904564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.4142 | 0.449393 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000i | 0.267710i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −48.7279 | − | 16.2426i | −1.62879 | − | 0.542932i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.1421i | 0.772693i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.0711 | 0.435945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.82843 | −0.0609137 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 13.0711i | − | 0.434978i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.02944 | + | 0.343146i | 0.0342197 | + | 0.0114066i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 8.55635i | − | 0.284109i | −0.989859 | − | 0.142054i | \(-0.954629\pi\) | ||
0.989859 | − | 0.142054i | \(-0.0453708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −44.9706 | −1.49158 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.65685 | 0.319946 | 0.159973 | − | 0.987121i | \(-0.448859\pi\) | ||||
0.159973 | + | 0.987121i | \(0.448859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.51472i | 0.116320i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.82843 | + | 17.4853i | −0.192682 | + | 0.578046i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 52.2843i | − | 1.72658i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.8406 | 1.54513 | 0.772565 | − | 0.634936i | \(-0.218974\pi\) | ||||
0.772565 | + | 0.634936i | \(0.218974\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.6274 | −1.93184 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.61522i | 0.184827i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.5147 | + | 20.6863i | −0.510121 | + | 0.680161i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.0000i | 0.919641i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.4853 | −0.836145 | −0.418072 | − | 0.908414i | \(-0.637294\pi\) | ||||
−0.418072 | + | 0.908414i | \(0.637294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.17157 | −0.0383968 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 35.6274i | − | 1.16639i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.00000 | − | 3.00000i | 0.0327035 | − | 0.0981105i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.3137i | 0.728957i | 0.931212 | + | 0.364479i | \(0.118753\pi\) | ||||
−0.931212 | + | 0.364479i | \(0.881247\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.2426 | −0.366890 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.1421 | 1.86278 | 0.931390 | − | 0.364022i | \(-0.118597\pi\) | ||||
0.931390 | + | 0.364022i | \(0.118597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 37.0711i | − | 1.20720i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.12132 | − | 0.707107i | −0.0690066 | − | 0.0230022i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.2548i | 1.34060i | 0.742089 | + | 0.670301i | \(0.233835\pi\) | ||||
−0.742089 | + | 0.670301i | \(0.766165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.2843 | −0.820762 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 79.1838 | 2.56771 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 19.2132i | − | 0.622377i | −0.950348 | − | 0.311188i | \(-0.899273\pi\) | ||
0.950348 | − | 0.311188i | \(-0.100727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.8492 | + | 7.94975i | 0.771743 | + | 0.257248i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.0711i | 0.422528i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.3848 | −1.27180 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3431 | −0.623972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.82843i | − | 0.220043i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.41421 | − | 16.2426i | 0.174290 | − | 0.522869i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.1421i | − | 1.61246i | −0.591601 | − | 0.806231i | \(-0.701504\pi\) | ||
0.591601 | − | 0.806231i | \(-0.298496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.41421 | 0.0775557 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.5980 | 1.14239 | 0.571197 | − | 0.820813i | \(-0.306479\pi\) | ||||
0.571197 | + | 0.820813i | \(0.306479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 9.65685i | − | 0.309585i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.6569 | + | 13.2426i | 0.565472 | + | 0.424104i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.61522i | − | 0.0516756i | −0.999666 | − | 0.0258378i | \(-0.991775\pi\) | ||
0.999666 | − | 0.0258378i | \(-0.00822534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.31371 | −0.169827 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.1421 | −0.451524 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 53.7990i | − | 1.71592i | −0.513715 | − | 0.857961i | \(-0.671731\pi\) | ||
0.513715 | − | 0.857961i | \(-0.328269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6569 | + | 43.9706i | −0.467006 | + | 1.40102i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.6274i | 1.48417i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.7574 | −0.373862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5269 | −0.334398 | −0.167199 | − | 0.985923i | \(-0.553472\pi\) | ||||
−0.167199 | + | 0.985923i | \(0.553472\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.9706i | 1.33190i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.0919 | + | 11.3640i | 1.08079 | + | 0.360262i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5563i | 0.872718i | 0.899773 | + | 0.436359i | \(0.143732\pi\) | ||||
−0.899773 | + | 0.436359i | \(0.856268\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.14214 | −0.0677742 |
(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 | 1520.2.d.d.609.4 | 4 | ||
4.3 | odd | 2 | 760.2.d.c.609.1 | ✓ | 4 | ||
5.2 | odd | 4 | 7600.2.a.bc.1.2 | 2 | |||
5.3 | odd | 4 | 7600.2.a.x.1.1 | 2 | |||
5.4 | even | 2 | inner | 1520.2.d.d.609.1 | 4 | ||
20.3 | even | 4 | 3800.2.a.p.1.2 | 2 | |||
20.7 | even | 4 | 3800.2.a.l.1.1 | 2 | |||
20.19 | odd | 2 | 760.2.d.c.609.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.c.609.1 | ✓ | 4 | 4.3 | odd | 2 | ||
760.2.d.c.609.4 | yes | 4 | 20.19 | odd | 2 | ||
1520.2.d.d.609.1 | 4 | 5.4 | even | 2 | inner | ||
1520.2.d.d.609.4 | 4 | 1.1 | even | 1 | trivial | ||
3800.2.a.l.1.1 | 2 | 20.7 | even | 4 | |||
3800.2.a.p.1.2 | 2 | 20.3 | even | 4 | |||
7600.2.a.x.1.1 | 2 | 5.3 | odd | 4 | |||
7600.2.a.bc.1.2 | 2 | 5.2 | odd | 4 |