Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(31,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bb (of order \(6\), degree \(2\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 30x^{5} - 5x^{4} + 114x^{3} + 300x^{2} + 116x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(3.14556 + 0.349646i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.31 |
Dual form | 912.2.bb.h.559.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73843 | − | 3.01105i | −0.777450 | − | 1.34658i | −0.933407 | − | 0.358819i | \(-0.883180\pi\) |
0.155957 | − | 0.987764i | \(-0.450154\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.36658i | 1.27245i | 0.771505 | + | 0.636223i | \(0.219504\pi\) | ||||
−0.771505 | + | 0.636223i | \(0.780496\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.43134i | 0.733078i | 0.930403 | + | 0.366539i | \(0.119457\pi\) | ||||
−0.930403 | + | 0.366539i | \(0.880543\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.02115 | − | 2.89896i | −1.39262 | − | 0.804027i | −0.399011 | − | 0.916946i | \(-0.630647\pi\) |
−0.993604 | + | 0.112919i | \(0.963980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73843 | − | 3.01105i | 0.448861 | − | 0.777450i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.67711 | + | 4.63689i | 0.649295 | + | 1.12461i | 0.983292 | + | 0.182037i | \(0.0582692\pi\) |
−0.333997 | + | 0.942574i | \(0.608397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.84404 | − | 3.30325i | −0.652467 | − | 0.757817i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.91554 | + | 1.68329i | −0.636223 | + | 0.367324i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.30585 | + | 0.753935i | 0.272289 | + | 0.157206i | 0.629928 | − | 0.776654i | \(-0.283085\pi\) |
−0.357638 | + | 0.933860i | \(0.616418\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.54429 | + | 6.13888i | −0.708857 | + | 1.22778i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.21121 | − | 2.43134i | −0.782002 | − | 0.451489i | 0.0551373 | − | 0.998479i | \(-0.482440\pi\) |
−0.837139 | + | 0.546990i | \(0.815774\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.5654 | −1.89761 | −0.948804 | − | 0.315866i | \(-0.897705\pi\) | ||||
−0.948804 | + | 0.315866i | \(0.897705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.10560 | + | 1.21567i | −0.366539 | + | 0.211621i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.1369 | − | 5.85256i | 1.71346 | − | 0.989264i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.46521i | 1.39167i | 0.718201 | + | 0.695836i | \(0.244966\pi\) | ||||
−0.718201 | + | 0.695836i | \(0.755034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.79792i | − | 0.928410i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.41146 | + | 1.96961i | −0.532780 | + | 0.307601i | −0.742148 | − | 0.670236i | \(-0.766193\pi\) |
0.209368 | + | 0.977837i | \(0.432859\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.02523 | + | 5.21072i | −1.37633 | + | 0.794627i | −0.991716 | − | 0.128448i | \(-0.959000\pi\) |
−0.384619 | + | 0.923076i | \(0.625667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.47686 | 0.518300 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.63084 | + | 5.56037i | 1.40480 | + | 0.811063i | 0.994881 | − | 0.101058i | \(-0.0322228\pi\) |
0.409921 | + | 0.912121i | \(0.365556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.33385 | −0.619121 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.67711 | + | 4.63689i | −0.374871 | + | 0.649295i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.41554 | − | 2.54931i | −0.606521 | − | 0.350175i | 0.165081 | − | 0.986280i | \(-0.447211\pi\) |
−0.771603 | + | 0.636105i | \(0.780545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.32090 | − | 4.22672i | 0.987150 | − | 0.569931i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.43868 | − | 4.11463i | 0.190558 | − | 0.544996i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.58247 | + | 9.66912i | 0.726775 | + | 1.25881i | 0.958239 | + | 0.285968i | \(0.0923152\pi\) |
−0.231464 | + | 0.972844i | \(0.574351\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.80994 | + | 4.86695i | −0.359776 | + | 0.623150i | −0.987923 | − | 0.154945i | \(-0.950480\pi\) |
0.628148 | + | 0.778094i | \(0.283813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.91554 | − | 1.68329i | −0.367324 | − | 0.212074i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.1586i | 2.50036i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.03818 | − | 5.26229i | 0.371173 | − | 0.642890i | −0.618573 | − | 0.785727i | \(-0.712289\pi\) |
0.989746 | + | 0.142837i | \(0.0456223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.50787i | 0.181526i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.15397 | − | 10.6590i | −0.730342 | − | 1.26499i | −0.956737 | − | 0.290954i | \(-0.906027\pi\) |
0.226395 | − | 0.974036i | \(-0.427306\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.97686 | − | 6.88813i | −0.465457 | − | 0.806194i | 0.533766 | − | 0.845633i | \(-0.320777\pi\) |
−0.999222 | + | 0.0394382i | \(0.987443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.08857 | −0.818518 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.18531 | −0.932802 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.19415 | + | 2.06832i | 0.134352 | + | 0.232704i | 0.925350 | − | 0.379115i | \(-0.123771\pi\) |
−0.790998 | + | 0.611819i | \(0.790438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.59111i | 0.613704i | 0.951757 | + | 0.306852i | \(0.0992757\pi\) | ||||
−0.951757 | + | 0.306852i | \(0.900724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.30795 | − | 16.1218i | 1.00959 | − | 1.74866i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.86269i | − | 0.521335i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.04638 | − | 2.91353i | −0.534915 | − | 0.308833i | 0.208101 | − | 0.978107i | \(-0.433272\pi\) |
−0.743016 | + | 0.669274i | \(0.766605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.75958 | − | 16.9041i | 1.02308 | − | 1.77203i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.28272 | − | 9.14993i | −0.547792 | − | 0.948804i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00209 | + | 14.3060i | −0.513204 | + | 1.46777i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.47885 | − | 1.43117i | 0.251689 | − | 0.145313i | −0.368848 | − | 0.929490i | \(-0.620248\pi\) |
0.620538 | + | 0.784177i | \(0.286914\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.10560 | − | 1.21567i | −0.211621 | − | 0.122180i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.24254 | − | 16.0086i | 0.919667 | − | 1.59291i | 0.119747 | − | 0.992804i | \(-0.461792\pi\) |
0.799920 | − | 0.600106i | \(-0.204875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.83108 | 0.377488 | 0.188744 | − | 0.982026i | \(-0.439558\pi\) | ||||
0.188744 | + | 0.982026i | \(0.439558\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.1369 | + | 5.85256i | 0.989264 | + | 0.571152i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.17714 | 0.597167 | 0.298583 | − | 0.954384i | \(-0.403486\pi\) | ||||
0.298583 | + | 0.954384i | \(0.403486\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.30994 | + | 1.33364i | −0.221252 | + | 0.127740i | −0.606530 | − | 0.795061i | \(-0.707439\pi\) |
0.385278 | + | 0.922801i | \(0.374106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.33108 | + | 4.23260i | −0.695836 | + | 0.401741i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.29368i | − | 0.497987i | −0.968505 | − | 0.248994i | \(-0.919900\pi\) | ||
0.968505 | − | 0.248994i | \(-0.0800998\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.24266i | − | 0.488880i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.02115 | − | 2.89896i | 0.464205 | − | 0.268009i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.6105 | + | 9.01270i | −1.43101 | + | 0.826193i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.08857 | 0.462597 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41146 | − | 1.96961i | −0.307601 | − | 0.177593i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.26167 | 0.649504 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | + | 1.73205i | −0.0887357 | + | 0.153695i | −0.906977 | − | 0.421180i | \(-0.861616\pi\) |
0.818241 | + | 0.574875i | \(0.194949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.02523 | − | 5.21072i | −0.794627 | − | 0.458778i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.03133 | − | 4.63689i | 0.701701 | − | 0.405127i | −0.106280 | − | 0.994336i | \(-0.533894\pi\) |
0.807981 | + | 0.589209i | \(0.200561\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.1206 | − | 9.57467i | 0.964283 | − | 0.830229i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.73843 | + | 3.01105i | 0.149620 | + | 0.259150i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.23644 | − | 0.713859i | −0.104874 | − | 0.0605488i | 0.446646 | − | 0.894711i | \(-0.352618\pi\) |
−0.551519 | + | 0.834162i | \(0.685952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.1207i | 0.936534i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.04837 | − | 12.2081i | 0.589414 | − | 1.02090i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.9069i | 1.40404i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.16692 | − | 3.75322i | −0.178725 | − | 0.309561i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.10361 | + | 15.7679i | 0.745797 | + | 1.29176i | 0.949821 | + | 0.312793i | \(0.101265\pi\) |
−0.204024 | + | 0.978966i | \(0.565402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.04628 | −0.0851447 | −0.0425724 | − | 0.999093i | \(-0.513555\pi\) | ||||
−0.0425724 | + | 0.999093i | \(0.513555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.35422 | −0.432863 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.3673 | + | 31.8131i | 1.47530 | + | 2.55529i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.85422 | − | 15.3360i | −0.706644 | − | 1.22394i | −0.966095 | − | 0.258187i | \(-0.916875\pi\) |
0.259451 | − | 0.965756i | \(-0.416458\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 5.09863i | − | 0.404348i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.53818 | + | 4.39626i | −0.200037 | + | 0.346474i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6934i | 0.915895i | 0.888979 | + | 0.457948i | \(0.151415\pi\) | ||||
−0.888979 | + | 0.457948i | \(0.848585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.32090 | + | 4.22672i | 0.569931 | + | 0.329050i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.69415 | − | 13.3267i | 0.595391 | − | 1.03125i | −0.398101 | − | 0.917342i | \(-0.630331\pi\) |
0.993492 | − | 0.113906i | \(-0.0363361\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3079 | + | 17.8539i | 0.792919 | + | 1.37338i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.28272 | − | 0.811383i | 0.327507 | − | 0.0620480i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.42242 | − | 4.86269i | 0.640345 | − | 0.369703i | −0.144403 | − | 0.989519i | \(-0.546126\pi\) |
0.784747 | + | 0.619816i | \(0.212793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.6670 | − | 11.9321i | −1.56228 | − | 0.901983i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.58247 | + | 9.66912i | −0.419604 | + | 0.726775i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.4047 | −1.07666 | −0.538328 | − | 0.842735i | \(-0.680944\pi\) | ||||
−0.538328 | + | 0.842735i | \(0.680944\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.12065 | + | 4.68846i | 0.603603 | + | 0.348490i | 0.770458 | − | 0.637491i | \(-0.220028\pi\) |
−0.166855 | + | 0.985982i | \(0.553361\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.61987 | −0.415433 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.4892 | − | 14.7162i | 1.87400 | − | 1.08196i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.2739 | + | 6.50898i | −0.824428 | + | 0.475983i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.36658i | − | 0.244883i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.9024i | 1.58480i | 0.610001 | + | 0.792401i | \(0.291169\pi\) | ||||
−0.610001 | + | 0.792401i | \(0.708831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.79773 | + | 5.07937i | −0.633275 | + | 0.365621i | −0.782019 | − | 0.623254i | \(-0.785810\pi\) |
0.148745 | + | 0.988876i | \(0.452477\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.4578 | + | 10.0793i | −1.25018 | + | 0.721793i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.52314 | −0.179766 | −0.0898831 | − | 0.995952i | \(-0.528649\pi\) | ||||
−0.0898831 | + | 0.995952i | \(0.528649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0472 | + | 9.26483i | 1.13755 | + | 0.656766i | 0.945823 | − | 0.324682i | \(-0.105257\pi\) |
0.191729 | + | 0.981448i | \(0.438591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.07636 | 0.428594 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.18531 | − | 14.1774i | 0.574496 | − | 0.995056i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8612 | + | 6.84805i | 0.828420 | + | 0.478289i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.30585 | + | 0.753935i | −0.0907631 | + | 0.0524021i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.03133 | − | 6.91483i | 0.555539 | − | 0.478309i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.81402 | + | 6.60608i | 0.262568 | + | 0.454781i | 0.966924 | − | 0.255066i | \(-0.0820973\pi\) |
−0.704356 | + | 0.709847i | \(0.748764\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.15397 | − | 10.6590i | 0.421663 | − | 0.730342i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.3795 | + | 18.1170i | 2.14006 | + | 1.23557i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 35.5694i | − | 2.41461i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.97686 | − | 6.88813i | 0.268731 | − | 0.465457i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 31.0434i | − | 2.08820i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.71728 | − | 2.97442i | −0.114998 | − | 0.199182i | 0.802781 | − | 0.596274i | \(-0.203353\pi\) |
−0.917779 | + | 0.397092i | \(0.870019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.54429 | − | 6.13888i | −0.236286 | − | 0.409259i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.4729 | 0.761482 | 0.380741 | − | 0.924682i | \(-0.375669\pi\) | ||||
0.380741 | + | 0.924682i | \(0.375669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.13485 | 0.273238 | 0.136619 | − | 0.990624i | \(-0.456376\pi\) | ||||
0.136619 | + | 0.990624i | \(0.456376\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.09265 | − | 7.08868i | −0.269277 | − | 0.466401i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.20025 | − | 3.81094i | −0.144143 | − | 0.249663i | 0.784910 | − | 0.619610i | \(-0.212709\pi\) |
−0.929053 | + | 0.369947i | \(0.879376\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 38.6652i | − | 2.52224i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.19415 | + | 2.06832i | −0.0775681 | + | 0.134352i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.09898i | − | 0.459195i | −0.973286 | − | 0.229598i | \(-0.926259\pi\) | ||
0.973286 | − | 0.229598i | \(-0.0737410\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.09134 | + | 4.09418i | 0.456793 | + | 0.263730i | 0.710695 | − | 0.703500i | \(-0.248381\pi\) |
−0.253902 | + | 0.967230i | \(0.581714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.53410 | + | 13.0494i | 0.481336 | + | 0.833698i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.70433 | + | 24.8309i | 0.299330 | + | 1.57995i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.84205 | + | 2.79556i | −0.306852 | + | 0.177161i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.66217 | − | 5.00111i | −0.546751 | − | 0.315667i | 0.201059 | − | 0.979579i | \(-0.435562\pi\) |
−0.747811 | + | 0.663912i | \(0.768895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.83308 | + | 3.17498i | −0.115244 | + | 0.199609i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.6159 | 1.16577 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.204332 | − | 0.117971i | −0.0127459 | − | 0.00735885i | 0.493614 | − | 0.869681i | \(-0.335676\pi\) |
−0.506359 | + | 0.862323i | \(0.669009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.4988 | −1.77083 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.21121 | − | 2.43134i | 0.260667 | − | 0.150496i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.01096 | + | 2.89308i | −0.308989 | + | 0.178395i | −0.646474 | − | 0.762936i | \(-0.723757\pi\) |
0.337485 | + | 0.941331i | \(0.390424\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.7272i | 1.08898i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.82706i | − | 0.356610i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.79567 | − | 5.07818i | 0.536281 | − | 0.309622i | −0.207289 | − | 0.978280i | \(-0.566464\pi\) |
0.743570 | + | 0.668658i | \(0.233131\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0082 | + | 6.35557i | −0.668698 | + | 0.386073i | −0.795583 | − | 0.605844i | \(-0.792835\pi\) |
0.126885 | + | 0.991917i | \(0.459502\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.5192 | 1.18135 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.9257 | − | 8.61737i | −0.900055 | − | 0.519647i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.39646 | −0.204073 | −0.102037 | − | 0.994781i | \(-0.532536\pi\) | ||||
−0.102037 | + | 0.994781i | \(0.532536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.28272 | − | 9.14993i | 0.316268 | − | 0.547792i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4770 | − | 14.1318i | −1.46017 | − | 0.843031i | −0.461154 | − | 0.887320i | \(-0.652565\pi\) |
−0.999019 | + | 0.0442884i | \(0.985898\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6622 | + | 10.1973i | −1.04991 | + | 0.606164i | −0.922623 | − | 0.385702i | \(-0.873959\pi\) |
−0.127284 | + | 0.991866i | \(0.540626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.8904 | + | 2.82107i | −0.882032 | + | 0.167105i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.63084 | − | 11.4849i | −0.391406 | − | 0.677935i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.83385 | + | 10.1045i | −0.343168 | + | 0.594384i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.47885 | + | 1.43117i | 0.145313 | + | 0.0838965i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.51388i | 0.146862i | 0.997300 | + | 0.0734311i | \(0.0233949\pi\) | ||||
−0.997300 | + | 0.0734311i | \(0.976605\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.4095 | − | 33.6182i | 1.13006 | − | 1.95733i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.43134i | − | 0.141081i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.37126 | − | 7.57124i | −0.252796 | − | 0.437856i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.5423 | − | 30.3841i | −1.01112 | − | 1.75131i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.4851 | 1.06194 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.5395 | 1.11883 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.84404 | + | 8.39012i | 0.276464 | + | 0.478849i | 0.970503 | − | 0.241088i | \(-0.0775041\pi\) |
−0.694040 | + | 0.719937i | \(0.744171\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.91554 | + | 3.31782i | 0.108971 | + | 0.188744i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.56560i | − | 0.372301i | −0.982521 | − | 0.186151i | \(-0.940399\pi\) | ||
0.982521 | − | 0.186151i | \(-0.0596012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.5975 | − | 21.8195i | 0.712053 | − | 1.23331i | −0.252032 | − | 0.967719i | \(-0.581099\pi\) |
0.964085 | − | 0.265594i | \(-0.0855680\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.7051i | 0.659509i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.02321 | + | 4.63220i | 0.450628 | + | 0.260170i | 0.708096 | − | 0.706117i | \(-0.249555\pi\) |
−0.257467 | + | 0.966287i | \(0.582888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.91143 | − | 10.2389i | 0.330977 | − | 0.573268i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.08857 | + | 5.34956i | 0.172387 | + | 0.298583i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.70301 | − | 22.0307i | 0.428607 | − | 1.22582i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 35.5928 | − | 20.5495i | 1.97433 | − | 1.13988i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.30994 | − | 1.33364i | −0.127740 | − | 0.0737506i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.7194 | + | 32.4230i | −1.03203 | + | 1.78754i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9879 | −0.933737 | −0.466868 | − | 0.884327i | \(-0.654618\pi\) | ||||
−0.466868 | + | 0.884327i | \(0.654618\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.33108 | − | 4.23260i | −0.401741 | − | 0.231945i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.1267 | −1.15427 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.01298 | + | 1.73955i | −0.164128 | + | 0.0947591i | −0.579814 | − | 0.814749i | \(-0.696875\pi\) |
0.415686 | + | 0.909508i | \(0.363541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.58446 | − | 2.64684i | 0.248994 | − | 0.143756i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 25.6882i | − | 1.39109i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.97580i | 0.484648i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.54027 | − | 2.62133i | 0.244440 | − | 0.141128i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.9790 | − | 8.64812i | 0.804114 | − | 0.464255i | −0.0407937 | − | 0.999168i | \(-0.512989\pi\) |
0.844908 | + | 0.534912i | \(0.179655\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.3259 | −1.67684 | −0.838418 | − | 0.545028i | \(-0.816519\pi\) | ||||
−0.838418 | + | 0.545028i | \(0.816519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.02115 | + | 2.89896i | 0.268009 | + | 0.154735i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.408665 | −0.0217510 | −0.0108755 | − | 0.999941i | \(-0.503462\pi\) | ||||
−0.0108755 | + | 0.999941i | \(0.503462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.3965 | + | 37.0599i | −1.13561 | + | 1.96693i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.6105 | − | 9.01270i | −0.826193 | − | 0.477003i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.0545 | + | 8.11437i | −0.741768 | + | 0.428260i | −0.822712 | − | 0.568459i | \(-0.807540\pi\) |
0.0809437 | + | 0.996719i | \(0.474207\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.82292 | + | 18.7891i | −0.148575 | + | 0.988901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.54429 | + | 4.40683i | 0.133540 | + | 0.231299i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.8270 | + | 23.9491i | −0.723738 | + | 1.25355i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.15185 | + | 2.97442i | 0.268924 | + | 0.155264i | 0.628399 | − | 0.777891i | \(-0.283711\pi\) |
−0.359474 | + | 0.933155i | \(0.617044\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 3.93921i | − | 0.205067i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.58247 | − | 14.8653i | 0.445579 | − | 0.771766i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.8930i | 1.13358i | 0.823863 | + | 0.566788i | \(0.191814\pi\) | ||||
−0.823863 | + | 0.566788i | \(0.808186\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.63084 | + | 6.28879i | 0.187496 | + | 0.324752i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0967 | + | 24.4163i | 0.726019 | + | 1.25750i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.94158 | 0.407931 | 0.203966 | − | 0.978978i | \(-0.434617\pi\) | ||||
0.203966 | + | 0.978978i | \(0.434617\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.00000 | −0.102463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.0143 | + | 26.0055i | 0.767195 | + | 1.32882i | 0.939078 | + | 0.343703i | \(0.111681\pi\) |
−0.171883 | + | 0.985117i | \(0.554985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.2296 | + | 24.6464i | 0.725207 | + | 1.25610i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 10.4214i | − | 0.529751i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.3462 | + | 31.7765i | −0.930187 | + | 1.61113i | −0.147188 | + | 0.989109i | \(0.547022\pi\) |
−0.782999 | + | 0.622023i | \(0.786311\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.07347i | 0.408293i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.03133 | + | 4.63689i | 0.405127 | + | 0.233900i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.15188 | − | 7.19127i | 0.208904 | − | 0.361832i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.3291 | − | 26.5508i | −0.769345 | − | 1.33254i | −0.937918 | − | 0.346856i | \(-0.887249\pi\) |
0.168573 | − | 0.985689i | \(-0.446084\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.8522 | + | 4.84343i | 0.693479 | + | 0.242475i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8066 | + | 7.97126i | −0.689470 | + | 0.398066i | −0.803414 | − | 0.595421i | \(-0.796985\pi\) |
0.113943 | + | 0.993487i | \(0.463652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 53.0506 | + | 30.6288i | 2.64264 | + | 1.52573i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.73843 | + | 3.01105i | −0.0863833 | + | 0.149620i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.5818 | −1.02020 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.69006 | + | 3.86251i | 0.330802 | + | 0.190989i | 0.656197 | − | 0.754589i | \(-0.272164\pi\) |
−0.325395 | + | 0.945578i | \(0.605497\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.5518 | + | 18.7938i | −1.60177 | + | 0.924783i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.8351 | − | 9.71976i | 0.826404 | − | 0.477124i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.42772i | − | 0.0699157i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.5693i | 1.10258i | 0.834313 | + | 0.551292i | \(0.185865\pi\) | ||||
−0.834313 | + | 0.551292i | \(0.814135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.2174 | + | 20.3328i | −1.71639 | + | 0.990960i | −0.791118 | + | 0.611663i | \(0.790501\pi\) |
−0.925275 | + | 0.379297i | \(0.876166\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.63084 | + | 5.56037i | −0.468267 | + | 0.270354i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.9538 | −1.84103 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3850 | − | 9.45987i | −0.792925 | − | 0.457795i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.0967 | 0.680597 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0313 | + | 24.3030i | −0.675866 | + | 1.17063i | 0.300350 | + | 0.953829i | \(0.402897\pi\) |
−0.976215 | + | 0.216804i | \(0.930437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.6711 | + | 9.04772i | 0.753105 | + | 0.434806i | 0.826815 | − | 0.562474i | \(-0.190150\pi\) |
−0.0737094 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.6418 | + | 8.45345i | −0.702020 | + | 0.405312i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.22346 | − | 6.45778i | −0.0585260 | − | 0.308918i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.65806 | − | 13.2641i | −0.365499 | − | 0.633063i | 0.623357 | − | 0.781937i | \(-0.285768\pi\) |
−0.988856 | + | 0.148874i | \(0.952435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.16692 | − | 3.75322i | 0.103187 | − | 0.178725i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2194 | + | 13.9831i | 1.15070 | + | 0.664355i | 0.949057 | − | 0.315104i | \(-0.102039\pi\) |
0.201640 | + | 0.979460i | \(0.435373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.2599i | 0.960410i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.10361 | + | 15.7679i | −0.430586 | + | 0.745797i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.03148i | 0.284643i | 0.989820 | + | 0.142322i | \(0.0454567\pi\) | ||||
−0.989820 | + | 0.142322i | \(0.954543\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.78879 | − | 8.29443i | −0.225495 | − | 0.390569i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.523138 | − | 0.906101i | −0.0245792 | − | 0.0425724i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −67.8654 | −3.18158 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.5573 | −1.14874 | −0.574370 | − | 0.818596i | \(-0.694753\pi\) | ||||
−0.574370 | + | 0.818596i | \(0.694753\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.67711 | − | 4.63689i | −0.124957 | − | 0.216432i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.74939 | − | 16.8864i | −0.454074 | − | 0.786480i | 0.544560 | − | 0.838722i | \(-0.316697\pi\) |
−0.998634 | + | 0.0522419i | \(0.983363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.2072i | − | 0.660267i | −0.943934 | − | 0.330133i | \(-0.892906\pi\) | ||
0.943934 | − | 0.330133i | \(-0.107094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.3673 | + | 31.8131i | −0.851762 | + | 1.47530i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 16.9572i | − | 0.784684i | −0.919819 | − | 0.392342i | \(-0.871665\pi\) | ||
0.919819 | − | 0.392342i | \(-0.128335\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.7159 | + | 10.2283i | 0.818044 | + | 0.472298i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.85422 | − | 15.3360i | 0.407981 | − | 0.706644i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.6690 | − | 21.9434i | −0.582523 | − | 1.00896i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.3583 | − | 5.75154i | 1.39294 | − | 0.263899i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.41554 | − | 2.54931i | 0.202174 | − | 0.116725i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.2645 | − | 12.8544i | −1.01729 | − | 0.587332i | −0.103972 | − | 0.994580i | \(-0.533155\pi\) |
−0.913318 | + | 0.407248i | \(0.866488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5403 | − | 42.5051i | 1.11894 | − | 1.93806i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.07636 | −0.230983 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.61863 | − | 4.97597i | −0.391352 | − | 0.225947i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.4607 | 0.881850 | 0.440925 | − | 0.897544i | \(-0.354650\pi\) | ||||
0.440925 | + | 0.897544i | \(0.354650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.1268 | + | 5.84668i | −0.457948 | + | 0.264396i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1119 | − | 20.2719i | 1.58458 | − | 0.914856i | 0.590398 | − | 0.807112i | \(-0.298971\pi\) |
0.994179 | − | 0.107744i | \(-0.0343627\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 26.0359i | − | 1.17260i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.45345i | 0.379954i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 35.8843 | − | 20.7178i | 1.60963 | − | 0.929322i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.51908 | + | 3.76379i | −0.291834 | + | 0.168491i | −0.638769 | − | 0.769399i | \(-0.720556\pi\) |
0.346934 | + | 0.937889i | \(0.387223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.3883 | 0.687498 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.19084 | − | 0.687530i | −0.0530968 | − | 0.0306554i | 0.473217 | − | 0.880946i | \(-0.343093\pi\) |
−0.526313 | + | 0.850291i | \(0.676426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −64.2701 | −2.85998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3079 | + | 17.8539i | −0.457792 | + | 0.792919i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0830 | + | 16.2138i | 1.24476 | + | 0.718662i | 0.970059 | − | 0.242868i | \(-0.0780883\pi\) |
0.274700 | + | 0.961530i | \(0.411422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.1894 | − | 13.3884i | 1.02584 | − | 0.592269i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.84404 | + | 3.30325i | 0.125567 | + | 0.145842i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.66008 | − | 11.5356i | −0.293478 | − | 0.508319i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.5192 | + | 23.4159i | −0.594572 | + | 1.02983i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.42242 | + | 4.86269i | 0.369703 | + | 0.213448i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.05664i | − | 0.133914i | −0.997756 | − | 0.0669568i | \(-0.978671\pi\) | ||
0.997756 | − | 0.0669568i | \(-0.0213290\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2031 | + | 17.6723i | −0.446151 | + | 0.772756i | −0.998132 | − | 0.0611006i | \(-0.980539\pi\) |
0.551980 | + | 0.833857i | \(0.313872\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 23.8642i | − | 1.04152i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.2848 | − | 48.9908i | −1.23211 | − | 2.13407i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.3632 | − | 17.9495i | −0.450572 | − | 0.780414i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.1649 | −0.484517 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.8393 | 0.989278 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.7385 | − | 18.5997i | −0.464267 | − | 0.804135i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.20234 | − | 12.4748i | −0.310804 | − | 0.538328i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10.5371i | − | 0.453864i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.20845 | + | 14.2174i | −0.352909 | + | 0.611256i | −0.986758 | − | 0.162201i | \(-0.948141\pi\) |
0.633849 | + | 0.773457i | \(0.281474\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.37692i | 0.402402i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.03133 | + | 4.63689i | 0.344025 | + | 0.198623i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.882218 | + | 1.52805i | −0.0377209 | + | 0.0653345i | −0.884270 | − | 0.466977i | \(-0.845343\pi\) |
0.846549 | + | 0.532311i | \(0.178676\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.80994 | − | 4.86695i | −0.119925 | − | 0.207717i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.94550 | + | 20.8255i | 0.168084 | + | 0.887196i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.96317 | + | 4.02019i | −0.296104 | + | 0.170956i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.4892 | + | 14.7162i | 1.08196 | + | 0.624667i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.388292 | − | 0.672541i | 0.0164525 | − | 0.0284965i | −0.857682 | − | 0.514181i | \(-0.828096\pi\) |
0.874134 | + | 0.485684i | \(0.161429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 60.4227 | 2.55561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.2739 | − | 6.50898i | −0.475983 | − | 0.274809i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.9019 | −1.89239 | −0.946195 | − | 0.323597i | \(-0.895108\pi\) | ||||
−0.946195 | + | 0.323597i | \(0.895108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.9395 | + | 9.20269i | −0.670581 | + | 0.387160i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.91554 | − | 1.68329i | 0.122441 | − | 0.0706915i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 33.7523i | − | 1.41497i | −0.706729 | − | 0.707485i | \(-0.749830\pi\) | ||
0.706729 | − | 0.707485i | \(-0.250170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1007i | 0.883037i | 0.897252 | + | 0.441518i | \(0.145560\pi\) | ||||
−0.897252 | + | 0.441518i | \(0.854440\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.9680 | + | 10.9512i | −0.792401 | + | 0.457493i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.25664 | + | 5.34432i | −0.386029 | + | 0.222874i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.84882 | 0.285120 | 0.142560 | − | 0.989786i | \(-0.454467\pi\) | ||||
0.142560 | + | 0.989786i | \(0.454467\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.79773 | − | 5.07937i | −0.365621 | − | 0.211092i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.8229 | −0.780906 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.19826 | − | 10.7357i | 0.256706 | − | 0.444627i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.4578 | − | 10.0793i | −0.721793 | − | 0.416727i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.3018 | + | 6.52511i | −0.466476 | + | 0.269320i | −0.714763 | − | 0.699366i | \(-0.753466\pi\) |
0.248287 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.0485 | + | 34.9003i | 1.23813 | + | 1.43804i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.26157 | − | 2.18510i | −0.0518940 | − | 0.0898831i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0887 | − | 31.3305i | 0.742813 | − | 1.28659i | −0.208397 | − | 0.978044i | \(-0.566825\pi\) |
0.951210 | − | 0.308545i | \(-0.0998421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 54.2754 | + | 31.3359i | 2.22508 | + | 1.28465i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.5297i | 0.758368i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4449 | + | 23.2872i | −0.549343 | + | 0.951490i | 0.448977 | + | 0.893544i | \(0.351789\pi\) |
−0.998320 | + | 0.0579467i | \(0.981545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.73240i | − | 0.152248i | −0.997098 | − | 0.0761240i | \(-0.975746\pi\) | ||
0.997098 | − | 0.0761240i | \(-0.0242545\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.03818 | + | 5.26229i | 0.123724 | + | 0.214297i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.84613 | − | 15.3219i | −0.359646 | − | 0.622926i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −47.3177 | −1.92057 | −0.960284 | − | 0.279026i | \(-0.909988\pi\) | ||||
−0.960284 | + | 0.279026i | \(0.909988\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.3706 | 0.663371 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.2386 | − | 55.8388i | −1.30423 | − | 2.25900i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.52115 | − | 14.7591i | −0.344166 | − | 0.596113i | 0.641036 | − | 0.767511i | \(-0.278505\pi\) |
−0.985202 | + | 0.171398i | \(0.945172\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.6961i | 0.552280i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.30107 | + | 9.18172i | −0.213413 | + | 0.369642i | −0.952780 | − | 0.303660i | \(-0.901791\pi\) |
0.739367 | + | 0.673302i | \(0.235125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.0642i | 0.927028i | 0.886090 | + | 0.463514i | \(0.153412\pi\) | ||||
−0.886090 | + | 0.463514i | \(0.846588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.30585 | − | 0.753935i | −0.0524021 | − | 0.0302544i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.80862 | − | 16.9890i | 0.392974 | − | 0.680651i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.09751 | + | 8.82915i | 0.203900 | + | 0.353166i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0041 | + | 3.49793i | 0.399525 | + | 0.139694i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −39.2523 | + | 22.6623i | −1.56509 | + | 0.903605i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.71405 | + | 0.989606i | 0.0682352 | + | 0.0393956i | 0.533729 | − | 0.845655i | \(-0.320790\pi\) |
−0.465494 | + | 0.885051i | \(0.654123\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.81402 | + | 6.60608i | −0.151594 | + | 0.262568i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.95372 | 0.275950 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.7609 | + | 12.5637i | 0.862198 | + | 0.497790i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.3079 | 0.486895 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.2425 | − | 12.2644i | 0.839030 | − | 0.484414i | −0.0179044 | − | 0.999840i | \(-0.505699\pi\) |
0.856934 | + | 0.515425i | \(0.172366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.9660 | − | 17.3009i | 1.18174 | − | 0.682280i | 0.225326 | − | 0.974283i | \(-0.427655\pi\) |
0.956417 | + | 0.292003i | \(0.0943218\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.2339i | 1.42671i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.0103i | 1.57297i | 0.617610 | + | 0.786484i | \(0.288101\pi\) | ||||
−0.617610 | + | 0.786484i | \(0.711899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.5089 | + | 13.5729i | −0.922807 | + | 0.532783i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.8040 | − | 17.7847i | 1.20730 | − | 0.697036i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7687 | 0.930140 | 0.465070 | − | 0.885274i | \(-0.346029\pi\) | ||||
0.465070 | + | 0.885274i | \(0.346029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.9238 | − | 16.1218i | −1.09107 | − | 0.629932i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.95372 | 0.310304 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1016 | − | 17.4965i | 0.393503 | − | 0.681568i | −0.599406 | − | 0.800446i | \(-0.704596\pi\) |
0.992909 | + | 0.118878i | \(0.0379296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2836 | + | 11.7107i | 0.788940 | + | 0.455495i | 0.839589 | − | 0.543222i | \(-0.182796\pi\) |
−0.0506490 | + | 0.998717i | \(0.516129\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.8843 | − | 15.5217i | 1.04410 | − | 0.602812i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −48.1623 | − | 16.8399i | −1.86765 | − | 0.653025i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.66615 | − | 6.34996i | −0.141954 | − | 0.245871i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.71728 | − | 2.97442i | 0.0663940 | − | 0.114998i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.8332 | − | 6.83192i | −0.456817 | − | 0.263743i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 43.0646i | − | 1.66002i | −0.557750 | − | 0.830009i | \(-0.688335\pi\) | ||
0.557750 | − | 0.830009i | \(-0.311665\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.54429 | − | 6.13888i | 0.136420 | − | 0.236286i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.2557i | 0.740057i | 0.929020 | + | 0.370028i | \(0.120652\pi\) | ||||
−0.929020 | + | 0.370028i | \(0.879348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.81813 | + | 8.34525i | 0.184903 | + | 0.320261i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.73644 | + | 9.93581i | 0.219821 | + | 0.380741i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.5654 | −1.28435 | −0.642173 | − | 0.766560i | \(-0.721967\pi\) | ||||
−0.642173 | + | 0.766560i | \(0.721967\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.8612 | 0.797064 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.06742 | + | 3.58088i | 0.0788771 | + | 0.136619i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.7807 | + | 25.6010i | 0.563101 | + | 0.975319i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.1717i | 0.577159i | 0.957456 | + | 0.288580i | \(0.0931830\pi\) | ||||
−0.957456 | + | 0.288580i | \(0.906817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.09265 | − | 7.08868i | 0.155467 | − | 0.269277i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.96398i | 0.188295i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.2657 | − | 10.5457i | −0.691863 | − | 0.399447i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.20025 | − | 3.81094i | 0.0832211 | − | 0.144143i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.6158 | + | 27.0473i | 0.589800 | + | 1.02156i | 0.994258 | + | 0.107007i | \(0.0341269\pi\) |
−0.404458 | + | 0.914557i | \(0.632540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.9627 | − | 24.0754i | 1.05463 | − | 0.908019i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33.4851 | − | 19.3326i | 1.26112 | − | 0.728109i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 53.8941 | + | 31.1157i | 2.02689 | + | 1.17023i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.61248 | + | 6.25700i | −0.135670 | + | 0.234987i | −0.925853 | − | 0.377884i | \(-0.876652\pi\) |
0.790183 | + | 0.612870i | \(0.209985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.38829 | −0.0895679 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.7969 | − | 7.96565i | −0.516698 | − | 0.298316i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −49.0124 | −1.83296 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.14790 | − | 3.54949i | 0.229598 | − | 0.132558i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.7051 | − | 7.33530i | 0.473821 | − | 0.273560i | −0.244017 | − | 0.969771i | \(-0.578465\pi\) |
0.717838 | + | 0.696211i | \(0.245132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8976i | 0.480333i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.18837i | 0.304529i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.8515 | − | 17.2347i | 1.10866 | − | 0.640082i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.2064 | + | 14.5529i | −0.934852 | + | 0.539737i | −0.888343 | − | 0.459181i | \(-0.848143\pi\) |
−0.0465091 | + | 0.998918i | \(0.514810\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.3231 | − | 27.8994i | −1.78729 | − | 1.03189i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.2194 | −0.783758 | −0.391879 | − | 0.920017i | \(-0.628175\pi\) | ||||
−0.391879 | + | 0.920017i | \(0.628175\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.53410 | + | 13.0494i | −0.277899 | + | 0.481336i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.7944 | + | 7.38686i | 0.471289 | + | 0.272099i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.07225 | + | 1.19641i | −0.0762290 | + | 0.0440108i | −0.537630 | − | 0.843181i | \(-0.680680\pi\) |
0.461401 | + | 0.887192i | \(0.347347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.1520 | + | 16.4895i | −0.703566 | + | 0.605757i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.71607 | − | 9.90052i | −0.209702 | − | 0.363215i | 0.741919 | − | 0.670490i | \(-0.233916\pi\) |
−0.951621 | + | 0.307275i | \(0.900583\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.6520 | − | 54.8229i | 1.15964 | − | 2.00856i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.84205 | − | 2.79556i | −0.177161 | − | 0.102284i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.7958i | 0.759863i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2195 | + | 38.4853i | −0.810801 | + | 1.40435i | 0.101503 | + | 0.994835i | \(0.467635\pi\) |
−0.912304 | + | 0.409514i | \(0.865698\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 10.0022i | − | 0.364501i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.81888 | + | 3.15039i | 0.0661958 | + | 0.114654i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.6289 | + | 30.5341i | 0.640732 | + | 1.10978i | 0.985270 | + | 0.171008i | \(0.0547025\pi\) |
−0.344537 | + | 0.938773i | \(0.611964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.66615 | −0.133073 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0983 | 1.01856 | 0.509282 | − | 0.860600i | \(-0.329911\pi\) | ||||
0.509282 | + | 0.860600i | \(0.329911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.48981 | − | 7.77659i | −0.162542 | − | 0.281531i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.30795 | + | 16.1218i | 0.336530 | + | 0.582886i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 64.7334i | − | 2.33739i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.36515 | − | 5.82862i | 0.121351 | − | 0.210185i | −0.798950 | − | 0.601398i | \(-0.794611\pi\) |
0.920301 | + | 0.391212i | \(0.127944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 0.235943i | − | 0.00849727i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.5383 | + | 8.97107i | 0.558875 | + | 0.322667i | 0.752694 | − | 0.658371i | \(-0.228754\pi\) |
−0.193819 | + | 0.981037i | \(0.562087\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.4469 | − | 64.8599i | 1.34513 | − | 2.32984i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.2494 | − | 24.6807i | −0.511194 | − | 0.885414i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.2084 | + | 5.66727i | 0.580727 | + | 0.203051i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.9157 | − | 14.9624i | 0.927336 | − | 0.535398i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.21121 | + | 2.43134i | 0.150496 | + | 0.0868891i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.7849 | + | 53.3210i | −1.09876 | + | 1.90311i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.7441 | −0.596861 | −0.298431 | − | 0.954431i | \(-0.596463\pi\) | ||||
−0.298431 | + | 0.954431i | \(0.596463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.01096 | − | 2.89308i | −0.178395 | − | 0.102996i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.8216 | 0.633662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.2182 | − | 16.2918i | 1.00206 | − | 0.578539i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.3522 | + | 8.86362i | −0.544488 | + | 0.314360i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8.30004i | − | 0.294002i | −0.989136 | − | 0.147001i | \(-0.953038\pi\) | ||
0.989136 | − | 0.147001i | \(-0.0469621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59.5429i | 2.10648i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.04638 | − | 2.91353i | 0.178305 | − | 0.102944i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.7474 | − | 9.66912i | 0.591003 | − | 0.341216i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.6498 | 0.622074 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.79567 | + | 5.07818i | 0.309622 | + | 0.178760i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.29972 | 0.116012 | 0.0580060 | − | 0.998316i | \(-0.481526\pi\) | ||||
0.0580060 | + | 0.998316i | \(0.481526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.44279 | − | 11.1592i | 0.226237 | − | 0.391854i | −0.730453 | − | 0.682963i | \(-0.760691\pi\) |
0.956690 | + | 0.291109i | \(0.0940243\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.0082 | − | 6.35557i | −0.386073 | − | 0.222899i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.2093 | − | 20.3281i | 1.23333 | − | 0.712063i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.8804 | + | 14.9931i | 1.50019 | + | 0.524543i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.75958 | + | 16.9041i | 0.341027 | + | 0.590677i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.00817 | + | 13.8706i | −0.279487 | + | 0.484086i | −0.971257 | − | 0.238032i | \(-0.923498\pi\) |
0.691770 | + | 0.722118i | \(0.256831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.6825 | + | 17.1372i | 1.03467 | + | 0.597366i | 0.918319 | − | 0.395842i | \(-0.129547\pi\) |
0.116350 | + | 0.993208i | \(0.462881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 17.2347i | − | 0.600037i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.865154 | + | 1.49849i | −0.0300844 | + | 0.0521076i | −0.880676 | − | 0.473720i | \(-0.842911\pi\) |
0.850591 | + | 0.525827i | \(0.176244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.4144i | 1.02161i | 0.859698 | + | 0.510803i | \(0.170652\pi\) | ||||
−0.859698 | + | 0.510803i | \(0.829348\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.69823 | − | 2.94142i | −0.0589109 | − | 0.102037i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.6022 | − | 20.0956i | −0.401992 | − | 0.696271i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −53.5030 | −1.85155 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.5654 | 0.365195 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.5894 | − | 32.1979i | −0.641779 | − | 1.11159i | −0.985035 | − | 0.172352i | \(-0.944863\pi\) |
0.343256 | − | 0.939242i | \(-0.388470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.67714 | − | 4.63694i | −0.0923152 | − | 0.159895i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 28.2636i | − | 0.973449i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.8393 | − | 62.0755i | 1.23291 | − | 2.13546i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.1311i | 0.588631i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6622 | − | 10.1973i | −0.606164 | − | 0.349969i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.38222 | + | 11.0543i | −0.218780 | + | 0.378937i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.5967 | − | 28.7464i | −0.568261 | − | 0.984258i | −0.996738 | − | 0.0807048i | \(-0.974283\pi\) |
0.428477 | − | 0.903553i | \(-0.359050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.88832 | − | 11.4849i | −0.338173 | − | 0.392777i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5371 | − | 11.2797i | 0.667375 | − | 0.385309i | −0.127707 | − | 0.991812i | \(-0.540762\pi\) |
0.795081 | + | 0.606503i | \(0.207428\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.4006 | − | 7.15951i | −0.423104 | − | 0.244279i | 0.273300 | − | 0.961929i | \(-0.411885\pi\) |
−0.696404 | + | 0.717649i | \(0.745218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.63084 | − | 11.4849i | 0.225978 | − | 0.391406i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.0001 | −1.05525 | −0.527627 | − | 0.849476i | \(-0.676918\pi\) | ||||
−0.527627 | + | 0.849476i | \(0.676918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.2836 | − | 16.9069i | −0.995672 | − | 0.574852i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.6677 | −0.396256 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.02880 | + | 2.90338i | −0.170590 | + | 0.0984904i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.5103 | + | 17.6151i | −1.03380 | + | 0.596866i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.86233i | 0.0968753i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.4470i | 0.826459i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.5764 | − | 19.9627i | 1.16756 | − | 0.674093i | 0.214458 | − | 0.976733i | \(-0.431201\pi\) |
0.953105 | + | 0.302640i | \(0.0978681\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.17708 | + | 1.25694i | −0.0734311 | + | 0.0423955i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.5857 | −0.592479 | −0.296239 | − | 0.955114i | \(-0.595733\pi\) | ||||
−0.296239 | + | 0.955114i | \(0.595733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.6874 | − | 25.8003i | −1.50385 | − | 0.868249i | −0.999990 | − | 0.00446371i | \(-0.998579\pi\) |
−0.503861 | − | 0.863785i | \(-0.668088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.8189 | 1.30488 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8360 | + | 29.1608i | −0.565297 | + | 0.979122i | 0.431725 | + | 0.902005i | \(0.357905\pi\) |
−0.997022 | + | 0.0771174i | \(0.975428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.83108 | − | 3.36658i | −0.195568 | − | 0.112911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.10560 | − | 1.21567i | 0.0705404 | − | 0.0407265i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.02317 | − | 47.6269i | −0.301949 | − | 1.59377i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.0415 | + | 43.3732i | 0.837047 | + | 1.44981i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.37126 | − | 7.57124i | 0.145952 | − | 0.252796i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.4933 | + | 25.6882i | 1.48393 | + | 0.856749i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 27.2992i | − | 0.909468i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.5423 | − | 30.3841i | 0.583771 | − | 1.01112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 32.6023i | − | 1.08374i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.788790 | + | 1.36622i | 0.0261913 | + | 0.0453647i | 0.878824 | − | 0.477146i | \(-0.158329\pi\) |
−0.852633 | + | 0.522511i | \(0.824995\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.24254 | + | 16.0086i | 0.306556 | + | 0.530970i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.05186 | 0.167376 | 0.0836879 | − | 0.996492i | \(-0.473330\pi\) | ||||
0.0836879 | + | 0.996492i | \(0.473330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5939 | −0.449893 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.76976 | + | 16.9217i | 0.322978 | + | 0.559415i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.6105 | + | 27.0381i | 0.515503 | + | 0.892877i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 15.7897i | − | 0.520853i | −0.965494 | − | 0.260426i | \(-0.916137\pi\) | ||
0.965494 | − | 0.260426i | \(-0.0838631\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.84404 | + | 8.39012i | −0.159616 | + | 0.276464i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 71.3605i | 2.34886i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.9669 | − | 30.0031i | −1.70866 | − | 0.986496i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.91554 | + | 3.31782i | −0.0629147 | + | 0.108971i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.3039 | + | 29.9712i | 0.567721 | + | 0.983322i | 0.996791 | + | 0.0800507i | \(0.0255082\pi\) |
−0.429069 | + | 0.903272i | \(0.641158\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.3256 | + | 14.3158i | 0.403956 | + | 0.469181i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.68598 | − | 3.28280i | 0.186151 | − | 0.107474i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.1977 | + | 22.6308i | 1.28190 | + | 0.740107i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6370 | − | 39.2085i | 0.739520 | − | 1.28089i | −0.213192 | − | 0.977010i | \(-0.568386\pi\) |
0.952712 | − | 0.303876i | \(-0.0982807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.1950 | 0.822208 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.0830 | − | 21.4099i | −1.20887 | − | 0.697943i | −0.246360 | − | 0.969178i | \(-0.579234\pi\) |
−0.962513 | + | 0.271236i | \(0.912568\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.93982 | −0.193427 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.1369 | + | 5.85256i | −0.329755 | + | 0.190384i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.4252 | − | 16.9887i | 0.956191 | − | 0.552057i | 0.0611923 | − | 0.998126i | \(-0.480510\pi\) |
0.894999 | + | 0.446069i | \(0.147176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.1151i | 1.49696i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.26441i | 0.300419i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.4648 | − | 18.7435i | 1.05164 | − | 0.607163i | 0.128530 | − | 0.991706i | \(-0.458974\pi\) |
0.923107 | + | 0.384543i | \(0.125641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65.9492 | − | 38.0758i | 2.13407 | − | 1.23210i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.8229 | 0.382179 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.4933 | − | 10.0997i | −0.564887 | − | 0.326137i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 80.6284 | 2.60091 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.08857 | + | 5.34956i | −0.0995278 | + | 0.172387i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.5885 | + | 17.6603i | 0.984679 | + | 0.568504i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.7557 | + | 21.2209i | −1.18198 | + | 0.682418i | −0.956472 | − | 0.291823i | \(-0.905738\pi\) |
−0.225510 | + | 0.974241i | \(0.572405\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.9306 | − | 4.34432i | 0.736638 | − | 0.139560i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.76568 | + | 4.79030i | 0.0887549 | + | 0.153728i | 0.906985 | − | 0.421163i | \(-0.138378\pi\) |
−0.818230 | + | 0.574891i | \(0.805045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.40326 | − | 4.16257i | 0.0770451 | − | 0.133446i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 35.5928 | + | 20.5495i | 1.13988 | + | 0.658110i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.1102i | 0.483419i | 0.970349 | + | 0.241709i | \(0.0777081\pi\) | ||||
−0.970349 | + | 0.241709i | \(0.922292\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.08379 | − | 12.2695i | 0.226399 | − | 0.392134i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.66729i | − | 0.0851599i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.01709 | + | 15.6181i | 0.287601 | + | 0.498139i | 0.973237 | − | 0.229806i | \(-0.0738091\pi\) |
−0.685636 | + | 0.727945i | \(0.740476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.38630 | + | 7.59730i | 0.139759 | + | 0.242070i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −37.4388 | −1.19169 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.7142 | −0.499682 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8741 | + | 18.8344i | 0.345426 | + | 0.598295i | 0.985431 | − | 0.170076i | \(-0.0544012\pi\) |
−0.640005 | + | 0.768370i | \(0.721068\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.49393 | − | 14.7119i | −0.269547 | − | 0.466868i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 64.4251i | − | 2.04241i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0995 | + | 19.2249i | −0.351525 | + | 0.608859i | −0.986517 | − | 0.163660i | \(-0.947670\pi\) |
0.634992 | + | 0.772519i | \(0.281003\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.46521i | − | 0.267827i |
(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 | 912.2.bb.h.31.1 | yes | 8 | |
3.2 | odd | 2 | 2736.2.bm.r.1855.4 | 8 | |||
4.3 | odd | 2 | 912.2.bb.g.31.1 | ✓ | 8 | ||
12.11 | even | 2 | 2736.2.bm.s.1855.4 | 8 | |||
19.8 | odd | 6 | 912.2.bb.g.559.1 | yes | 8 | ||
57.8 | even | 6 | 2736.2.bm.s.559.4 | 8 | |||
76.27 | even | 6 | inner | 912.2.bb.h.559.1 | yes | 8 | |
228.179 | odd | 6 | 2736.2.bm.r.559.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.bb.g.31.1 | ✓ | 8 | 4.3 | odd | 2 | ||
912.2.bb.g.559.1 | yes | 8 | 19.8 | odd | 6 | ||
912.2.bb.h.31.1 | yes | 8 | 1.1 | even | 1 | trivial | |
912.2.bb.h.559.1 | yes | 8 | 76.27 | even | 6 | inner | |
2736.2.bm.r.559.4 | 8 | 228.179 | odd | 6 | |||
2736.2.bm.r.1855.4 | 8 | 3.2 | odd | 2 | |||
2736.2.bm.s.559.4 | 8 | 57.8 | even | 6 | |||
2736.2.bm.s.1855.4 | 8 | 12.11 | even | 2 |