Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [828,2,Mod(73,828)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(828, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("828.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 828.q (of order \(11\), degree \(10\), 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: | \(6.61161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 721.1 | ||
Root | \(2.31834 - 1.48991i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 828.721 |
Dual form | 828.2.q.c.325.1 |
$q$-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 \(\left(\mathbb{Z}/828\mathbb{Z}\right)^\times\).
\(n\) | \(415\) | \(461\) | \(649\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.735636 | − | 0.848969i | −0.328986 | − | 0.379671i | 0.567026 | − | 0.823700i | \(-0.308094\pi\) |
−0.896012 | + | 0.444030i | \(0.853549\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.891451 | + | 0.572901i | 0.336937 | + | 0.216536i | 0.698157 | − | 0.715944i | \(-0.254004\pi\) |
−0.361221 | + | 0.932480i | \(0.617640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.347809 | − | 2.41907i | −0.104868 | − | 0.729376i | −0.972624 | − | 0.232385i | \(-0.925347\pi\) |
0.867756 | − | 0.496991i | \(-0.165562\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00126 | − | 0.643468i | 0.277699 | − | 0.178466i | −0.394377 | − | 0.918949i | \(-0.629039\pi\) |
0.672075 | + | 0.740483i | \(0.265403\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.810376 | − | 0.237948i | 0.196545 | − | 0.0577108i | −0.181978 | − | 0.983303i | \(-0.558250\pi\) |
0.378523 | + | 0.925592i | \(0.376432\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83256 | + | 0.538087i | 0.420417 | + | 0.123446i | 0.485097 | − | 0.874460i | \(-0.338784\pi\) |
−0.0646796 | + | 0.997906i | \(0.520603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.265350 | − | 4.78849i | 0.0553292 | − | 0.998468i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.531986 | − | 3.70004i | 0.106397 | − | 0.740009i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.551701 | − | 0.161994i | 0.102448 | − | 0.0300815i | −0.230107 | − | 0.973165i | \(-0.573908\pi\) |
0.332555 | + | 0.943084i | \(0.392089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.110721 | − | 0.242445i | 0.0198861 | − | 0.0435444i | −0.899428 | − | 0.437068i | \(-0.856017\pi\) |
0.919314 | + | 0.393524i | \(0.128744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.169408 | − | 1.17826i | −0.0286352 | − | 0.199162i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.68252 | − | 6.55798i | 0.934201 | − | 1.07812i | −0.0625874 | − | 0.998039i | \(-0.519935\pi\) |
0.996788 | − | 0.0800854i | \(-0.0255193\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.19380 | + | 3.68585i | 0.498788 | + | 0.575632i | 0.948193 | − | 0.317696i | \(-0.102909\pi\) |
−0.449404 | + | 0.893328i | \(0.648364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.36978 | − | 2.99940i | −0.208889 | − | 0.457404i | 0.775968 | − | 0.630773i | \(-0.217262\pi\) |
−0.984857 | + | 0.173369i | \(0.944535\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.561056 | −0.0818384 | −0.0409192 | − | 0.999162i | \(-0.513029\pi\) | ||||
−0.0409192 | + | 0.999162i | \(0.513029\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.44144 | − | 5.34600i | −0.348777 | − | 0.763714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.21451 | + | 3.35116i | 0.716268 | + | 0.460318i | 0.847337 | − | 0.531056i | \(-0.178204\pi\) |
−0.131069 | + | 0.991373i | \(0.541841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.79785 | + | 2.07483i | −0.242422 | + | 0.279770i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.23668 | − | 0.794765i | 0.161002 | − | 0.103470i | −0.457659 | − | 0.889128i | \(-0.651312\pi\) |
0.618661 | + | 0.785658i | \(0.287676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.69276 | − | 8.08602i | 0.472810 | − | 1.03531i | −0.511568 | − | 0.859243i | \(-0.670935\pi\) |
0.984378 | − | 0.176067i | \(-0.0563374\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.28285 | − | 0.376677i | −0.159117 | − | 0.0467211i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.709022 | − | 4.93135i | 0.0866208 | − | 0.602461i | −0.899561 | − | 0.436795i | \(-0.856114\pi\) |
0.986182 | − | 0.165666i | \(-0.0529773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0399653 | − | 0.277964i | 0.00474300 | − | 0.0329883i | −0.987313 | − | 0.158789i | \(-0.949241\pi\) |
0.992056 | + | 0.125801i | \(0.0401501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.93870 | − | 1.45013i | −0.578031 | − | 0.169725i | −0.0203679 | − | 0.999793i | \(-0.506484\pi\) |
−0.557663 | + | 0.830067i | \(0.688302\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.07583 | − | 2.35574i | 0.122602 | − | 0.268461i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.92920 | + | 3.16780i | −0.554578 | + | 0.356406i | −0.787716 | − | 0.616038i | \(-0.788737\pi\) |
0.233139 | + | 0.972444i | \(0.425100\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.38585 | + | 3.90747i | −0.371645 | + | 0.428901i | −0.910507 | − | 0.413493i | \(-0.864309\pi\) |
0.538863 | + | 0.842394i | \(0.318854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.798152 | − | 0.512941i | −0.0865718 | − | 0.0556363i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.04667 | + | 11.0507i | 0.534946 | + | 1.17137i | 0.963465 | + | 0.267835i | \(0.0863083\pi\) |
−0.428519 | + | 0.903533i | \(0.640964\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.26121 | 0.132211 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.891275 | − | 1.95162i | −0.0914429 | − | 0.200232i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.64165 | + | 3.04863i | 0.268219 | + | 0.309542i | 0.873842 | − | 0.486211i | \(-0.161621\pi\) |
−0.605622 | + | 0.795752i | \(0.707076\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.90660 | − | 9.12470i | 0.786736 | − | 0.907942i | −0.210840 | − | 0.977521i | \(-0.567620\pi\) |
0.997576 | + | 0.0695785i | \(0.0221654\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.41213 | + | 16.7767i | 0.237674 | + | 1.65306i | 0.663444 | + | 0.748226i | \(0.269094\pi\) |
−0.425770 | + | 0.904831i | \(0.639997\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.19217 | + | 11.3693i | −0.501946 | + | 1.09911i | 0.473886 | + | 0.880586i | \(0.342851\pi\) |
−0.975832 | + | 0.218522i | \(0.929876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.535214 | − | 0.157153i | 0.0512642 | − | 0.0150525i | −0.256000 | − | 0.966677i | \(-0.582405\pi\) |
0.307264 | + | 0.951624i | \(0.400586\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.19921 | − | 8.34069i | 0.112812 | − | 0.784626i | −0.852350 | − | 0.522973i | \(-0.824823\pi\) |
0.965162 | − | 0.261654i | \(-0.0842679\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.26048 | + | 3.29731i | −0.397292 | + | 0.307476i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.858731 | + | 0.252146i | 0.0787197 | + | 0.0231142i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.82351 | − | 1.41631i | 0.438501 | − | 0.128756i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.25767 | + | 5.30688i | −0.738588 | + | 0.474662i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.07067 | + | 14.4018i | 0.183742 | + | 1.27796i | 0.847817 | + | 0.530290i | \(0.177917\pi\) |
−0.664074 | + | 0.747667i | \(0.731174\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.54743 | − | 5.49310i | −0.746793 | − | 0.479935i | 0.111070 | − | 0.993813i | \(-0.464572\pi\) |
−0.857863 | + | 0.513878i | \(0.828208\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.32536 | + | 1.52955i | 0.114924 | + | 0.132629i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5603 | −0.902226 | −0.451113 | − | 0.892467i | \(-0.648973\pi\) | ||||
−0.451113 | + | 0.892467i | \(0.648973\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.20115 | −0.525975 | −0.262987 | − | 0.964799i | \(-0.584708\pi\) | ||||
−0.262987 | + | 0.964799i | \(0.584708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.90484 | − | 2.19830i | −0.159291 | − | 0.183831i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.543379 | − | 0.349208i | −0.0451252 | − | 0.0290002i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.91401 | − | 13.3122i | −0.156802 | − | 1.09058i | −0.904479 | − | 0.426518i | \(-0.859740\pi\) |
0.747677 | − | 0.664062i | \(-0.231169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.3689 | + | 9.87699i | −1.25070 | + | 0.803778i | −0.986984 | − | 0.160821i | \(-0.948586\pi\) |
−0.263720 | + | 0.964599i | \(0.584949\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.287279 | + | 0.0843527i | −0.0230748 | + | 0.00677537i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1248 | + | 5.32192i | 1.44652 | + | 0.424735i | 0.908388 | − | 0.418129i | \(-0.137314\pi\) |
0.538127 | + | 0.842864i | \(0.319132\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.97987 | − | 4.11668i | 0.234847 | − | 0.324440i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0147334 | − | 0.102473i | 0.00115401 | − | 0.00802632i | −0.989236 | − | 0.146327i | \(-0.953255\pi\) |
0.990390 | + | 0.138301i | \(0.0441640\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.4318 | + | 4.82480i | −1.27153 | + | 0.373355i | −0.846774 | − | 0.531954i | \(-0.821458\pi\) |
−0.424755 | + | 0.905308i | \(0.639640\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.81193 | + | 10.5367i | −0.370149 | + | 0.810512i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.42048 | − | 9.87965i | −0.107997 | − | 0.751136i | −0.969802 | − | 0.243895i | \(-0.921575\pi\) |
0.861805 | − | 0.507240i | \(-0.169334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.59400 | − | 2.99363i | 0.196088 | − | 0.226297i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.7566 | + | 19.3381i | 1.25245 | + | 1.44540i | 0.847270 | + | 0.531163i | \(0.178245\pi\) |
0.405177 | + | 0.914238i | \(0.367210\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.409057 | + | 0.895711i | 0.0304050 | + | 0.0665776i | 0.924225 | − | 0.381848i | \(-0.124712\pi\) |
−0.893820 | + | 0.448426i | \(0.851985\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.74779 | −0.716672 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.857468 | − | 1.87759i | −0.0627043 | − | 0.137303i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.90200 | + | 2.50766i | 0.282339 | + | 0.181448i | 0.674144 | − | 0.738600i | \(-0.264513\pi\) |
−0.391805 | + | 0.920048i | \(0.628149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2976 | + | 13.0381i | −0.813220 | + | 0.938506i | −0.999028 | − | 0.0440804i | \(-0.985964\pi\) |
0.185808 | + | 0.982586i | \(0.440510\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.22558 | − | 0.787630i | 0.0873187 | − | 0.0561163i | −0.496253 | − | 0.868178i | \(-0.665291\pi\) |
0.583572 | + | 0.812062i | \(0.301655\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.02962 | + | 6.63394i | −0.214764 | + | 0.470268i | −0.986098 | − | 0.166162i | \(-0.946862\pi\) |
0.771334 | + | 0.636430i | \(0.219590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.584621 | + | 0.171660i | 0.0410323 | + | 0.0120482i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.779693 | − | 5.42288i | 0.0544561 | − | 0.378750i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.664288 | − | 4.62023i | 0.0459498 | − | 0.319588i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9625 | − | 7.03603i | −1.64965 | − | 0.484380i | −0.680889 | − | 0.732387i | \(-0.738406\pi\) |
−0.968758 | + | 0.248007i | \(0.920224\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.53874 | + | 3.36937i | −0.104941 | + | 0.229789i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.237599 | − | 0.152696i | 0.0161293 | − | 0.0103657i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.658282 | − | 0.759698i | 0.0442809 | − | 0.0511028i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.31965 | − | 3.41873i | −0.356230 | − | 0.228935i | 0.350269 | − | 0.936649i | \(-0.386090\pi\) |
−0.706499 | + | 0.707714i | \(0.749727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.3131 | + | 22.5824i | 0.684502 | + | 1.49885i | 0.857802 | + | 0.513980i | \(0.171830\pi\) |
−0.173300 | + | 0.984869i | \(0.555443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.33079 | 0.550514 | 0.275257 | − | 0.961371i | \(-0.411237\pi\) | ||||
0.275257 | + | 0.961371i | \(0.411237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.86217 | + | 21.5951i | 0.646092 | + | 1.41474i | 0.894933 | + | 0.446200i | \(0.147223\pi\) |
−0.248841 | + | 0.968544i | \(0.580050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.412733 | + | 0.476319i | 0.0269237 | + | 0.0310716i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.9798 | − | 18.4417i | 1.03365 | − | 1.19289i | 0.0527025 | − | 0.998610i | \(-0.483216\pi\) |
0.980945 | − | 0.194283i | \(-0.0622381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.73814 | + | 12.0890i | 0.111963 | + | 0.778721i | 0.966006 | + | 0.258519i | \(0.0832344\pi\) |
−0.854043 | + | 0.520202i | \(0.825856\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.74258 | + | 6.00541i | −0.175217 | + | 0.383672i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.18110 | − | 0.640429i | 0.138780 | − | 0.0407495i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.55527 | + | 24.7275i | −0.224407 | + | 1.56078i | 0.496677 | + | 0.867936i | \(0.334553\pi\) |
−0.721083 | + | 0.692848i | \(0.756356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6760 | + | 1.02358i | −0.734061 | + | 0.0643520i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.3823 | − | 3.34213i | −0.710005 | − | 0.208476i | −0.0932631 | − | 0.995642i | \(-0.529730\pi\) |
−0.616742 | + | 0.787165i | \(0.711548\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.82276 | − | 2.59060i | 0.548219 | − | 0.160972i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.82837 | + | 5.03099i | −0.482718 | + | 0.310224i | −0.759271 | − | 0.650775i | \(-0.774444\pi\) |
0.276553 | + | 0.960999i | \(0.410808\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.990948 | − | 6.89220i | −0.0608735 | − | 0.423384i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.4123 | + | 6.69157i | 0.634848 | + | 0.407992i | 0.818102 | − | 0.575073i | \(-0.195027\pi\) |
−0.183253 | + | 0.983066i | \(0.558663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.32197 | − | 9.60406i | −0.505523 | − | 0.583405i | 0.444423 | − | 0.895817i | \(-0.353409\pi\) |
−0.949947 | + | 0.312412i | \(0.898863\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.13568 | −0.550902 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8326 | 1.19163 | 0.595813 | − | 0.803123i | \(-0.296830\pi\) | ||||
0.595813 | + | 0.803123i | \(0.296830\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.05300 | − | 10.4477i | −0.540056 | − | 0.623258i | 0.418481 | − | 0.908226i | \(-0.362563\pi\) |
−0.958537 | + | 0.284967i | \(0.908017\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.02597 | − | 3.87266i | −0.358207 | − | 0.230206i | 0.349143 | − | 0.937070i | \(-0.386473\pi\) |
−0.707349 | + | 0.706864i | \(0.750109\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.735495 | + | 5.11548i | 0.0434149 | + | 0.301957i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7012 | + | 8.80524i | −0.805954 | + | 0.517955i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.4859 | − | 5.13434i | 1.02154 | − | 0.299951i | 0.272274 | − | 0.962220i | \(-0.412224\pi\) |
0.749266 | + | 0.662269i | \(0.230406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.58448 | − | 0.465244i | −0.0922518 | − | 0.0270876i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.81556 | − | 4.96525i | −0.162828 | − | 0.287148i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.497267 | − | 3.45857i | 0.0286620 | − | 0.199348i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.58131 | + | 2.81333i | −0.548624 | + | 0.161091i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.61813 | − | 14.4917i | 0.377717 | − | 0.827085i | −0.621335 | − | 0.783545i | \(-0.713409\pi\) |
0.999052 | − | 0.0435395i | \(-0.0138634\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.14594 | − | 28.8357i | −0.235095 | − | 1.63512i | −0.675527 | − | 0.737335i | \(-0.736084\pi\) |
0.440432 | − | 0.897786i | \(-0.354825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6702 | − | 13.4682i | 0.659640 | − | 0.761266i | −0.323078 | − | 0.946372i | \(-0.604718\pi\) |
0.982718 | + | 0.185107i | \(0.0592631\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.6720 | + | 18.0865i | 0.880227 | + | 1.01584i | 0.999735 | + | 0.0230031i | \(0.00732276\pi\) |
−0.119508 | + | 0.992833i | \(0.538132\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.583761 | − | 1.27826i | −0.0326843 | − | 0.0715687i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.61310 | 0.0897551 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.84821 | − | 4.04701i | −0.102520 | − | 0.224488i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.500154 | − | 0.321429i | −0.0275744 | − | 0.0177210i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.23218 | − | 4.88419i | 0.232621 | − | 0.268459i | −0.627423 | − | 0.778679i | \(-0.715890\pi\) |
0.860044 | + | 0.510219i | \(0.170436\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.70815 | + | 3.02574i | −0.257234 | + | 0.165314i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.48662 | + | 7.63463i | −0.189928 | + | 0.415885i | −0.980509 | − | 0.196473i | \(-0.937051\pi\) |
0.790581 | + | 0.612357i | \(0.209779\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.625001 | − | 0.183517i | −0.0338457 | − | 0.00993799i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.94195 | − | 13.5066i | 0.104856 | − | 0.729287i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.15938 | − | 15.0188i | 0.115922 | − | 0.806253i | −0.846050 | − | 0.533104i | \(-0.821026\pi\) |
0.961972 | − | 0.273149i | \(-0.0880653\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.81125 | − | 1.70634i | −0.311069 | − | 0.0913382i | 0.122472 | − | 0.992472i | \(-0.460918\pi\) |
−0.433541 | + | 0.901134i | \(0.642736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6513 | − | 29.8922i | 0.726585 | − | 1.59100i | −0.0778551 | − | 0.996965i | \(-0.524807\pi\) |
0.804440 | − | 0.594034i | \(-0.202466\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.265383 | + | 0.170551i | −0.0140851 | + | 0.00905193i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.97285 | − | 3.43085i | 0.156901 | − | 0.181073i | −0.671856 | − | 0.740681i | \(-0.734503\pi\) |
0.828757 | + | 0.559608i | \(0.189048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9151 | − | 8.30003i | −0.679742 | − | 0.436843i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.40197 | + | 5.25957i | 0.125725 | + | 0.275299i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.9179 | 1.66610 | 0.833050 | − | 0.553198i | \(-0.186593\pi\) | ||||
0.833050 | + | 0.553198i | \(0.186593\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.72860 | + | 5.97479i | 0.141662 | + | 0.310196i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.47685 | + | 1.70437i | 0.0764683 | + | 0.0882491i | 0.792695 | − | 0.609619i | \(-0.208678\pi\) |
−0.716226 | + | 0.697868i | \(0.754132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.448156 | − | 0.517200i | 0.0230812 | − | 0.0266371i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.66978 | + | 25.5239i | 0.188504 | + | 1.31107i | 0.835884 | + | 0.548906i | \(0.184955\pi\) |
−0.647380 | + | 0.762167i | \(0.724135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.68120 | − | 10.2504i | 0.239198 | − | 0.523771i | −0.751519 | − | 0.659712i | \(-0.770678\pi\) |
0.990717 | + | 0.135941i | \(0.0434056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.79137 | + | 0.819620i | −0.142261 | + | 0.0417717i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.09611 | − | 28.4891i | 0.207681 | − | 1.44445i | −0.573016 | − | 0.819544i | \(-0.694227\pi\) |
0.780697 | − | 0.624910i | \(-0.214864\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.924377 | − | 3.94361i | −0.0467477 | − | 0.199437i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.31546 | + | 1.85439i | 0.317765 | + | 0.0933043i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.8529 | − | 9.64649i | 1.64884 | − | 0.484143i | 0.680287 | − | 0.732946i | \(-0.261855\pi\) |
0.968554 | + | 0.248803i | \(0.0800372\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.7957 | + | 15.2926i | −1.18830 | + | 0.763674i | −0.976894 | − | 0.213724i | \(-0.931441\pi\) |
−0.211406 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0451457 | − | 0.313995i | −0.00224887 | − | 0.0156412i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.8406 | − | 11.4655i | −0.884327 | − | 0.568322i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.46621 | − | 1.69210i | −0.0724996 | − | 0.0836690i | 0.718341 | − | 0.695691i | \(-0.244902\pi\) |
−0.790841 | + | 0.612022i | \(0.790356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.55776 | 0.0766523 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.80807 | 0.285107 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.4966 | − | 16.7300i | −0.708205 | − | 0.817312i | 0.281632 | − | 0.959523i | \(-0.409124\pi\) |
−0.989836 | + | 0.142211i | \(0.954579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.06100 | − | 3.89517i | −0.295395 | − | 0.189839i | 0.384546 | − | 0.923106i | \(-0.374358\pi\) |
−0.679941 | + | 0.733267i | \(0.737994\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.449309 | − | 3.12501i | −0.0217947 | − | 0.151585i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.92440 | − | 5.09271i | 0.383489 | − | 0.246453i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4454 | − | 3.65430i | 0.599475 | − | 0.176022i | 0.0321045 | − | 0.999485i | \(-0.489779\pi\) |
0.567370 | + | 0.823463i | \(0.307961\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3167 | + | 4.20377i | 0.688019 | + | 0.202020i | 0.607012 | − | 0.794693i | \(-0.292368\pi\) |
0.0810071 | + | 0.996714i | \(0.474186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.06289 | − | 8.63239i | 0.146518 | − | 0.412943i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0758913 | + | 0.527836i | −0.00362210 | + | 0.0251922i | −0.991552 | − | 0.129707i | \(-0.958596\pi\) |
0.987930 | + | 0.154899i | \(0.0495054\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.4315 | + | 5.41197i | −0.875705 | + | 0.257130i | −0.688540 | − | 0.725198i | \(-0.741748\pi\) |
−0.187165 | + | 0.982328i | \(0.559930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.66916 | − | 12.4137i | 0.268744 | − | 0.588467i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.820060 | − | 5.70365i | −0.0387010 | − | 0.269172i | 0.961278 | − | 0.275579i | \(-0.0888696\pi\) |
−0.999979 | + | 0.00640731i | \(0.997960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.80547 | − | 9.00799i | 0.367545 | − | 0.424170i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.927795 | − | 1.07073i | −0.0434957 | − | 0.0501967i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.55155 | + | 12.1562i | 0.259690 | + | 0.568643i | 0.993901 | − | 0.110279i | \(-0.0351746\pi\) |
−0.734210 | + | 0.678922i | \(0.762447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.9200 | −1.06749 | −0.533745 | − | 0.845645i | \(-0.679216\pi\) | ||||
−0.533745 | + | 0.845645i | \(0.679216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.01092 | + | 10.9724i | 0.232877 | + | 0.509930i | 0.989607 | − | 0.143798i | \(-0.0459314\pi\) |
−0.756730 | + | 0.653728i | \(0.773204\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.16270 | + | 3.96053i | 0.285176 | + | 0.183271i | 0.675406 | − | 0.737446i | \(-0.263968\pi\) |
−0.390230 | + | 0.920717i | \(0.627605\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.45723 | − | 3.98986i | 0.159640 | − | 0.184235i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.77933 | + | 4.35681i | −0.311714 | + | 0.200326i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.96584 | − | 6.49428i | 0.136082 | − | 0.297978i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.9833 | + | 9.68478i | 1.50705 | + | 0.442509i | 0.927936 | − | 0.372739i | \(-0.121581\pi\) |
0.579111 | + | 0.815248i | \(0.303400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.46981 | − | 10.2227i | 0.0670175 | − | 0.466117i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.644898 | − | 4.48537i | 0.0292833 | − | 0.203670i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.9571 | − | 3.21729i | −0.496513 | − | 0.145789i | 0.0238826 | − | 0.999715i | \(-0.492397\pi\) |
−0.520395 | + | 0.853925i | \(0.674215\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4308 | − | 35.9785i | 0.741514 | − | 1.62369i | −0.0395346 | − | 0.999218i | \(-0.512588\pi\) |
0.781048 | − | 0.624471i | \(-0.214685\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.408539 | − | 0.262552i | 0.0183997 | − | 0.0118248i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.194873 | − | 0.224896i | 0.00874125 | − | 0.0100879i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.3299 | + | 6.63865i | 0.462432 | + | 0.297187i | 0.751036 | − | 0.660262i | \(-0.229555\pi\) |
−0.288604 | + | 0.957449i | \(0.593191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.5877 | + | 23.1839i | 0.472084 | + | 1.03372i | 0.984565 | + | 0.175022i | \(0.0559995\pi\) |
−0.512480 | + | 0.858699i | \(0.671273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.5630 | −0.603544 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.83427 | + | 21.5340i | 0.435896 | + | 0.954480i | 0.992333 | + | 0.123590i | \(0.0394408\pi\) |
−0.556437 | + | 0.830890i | \(0.687832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.57183 | − | 4.12211i | −0.158008 | − | 0.182351i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.4685 | − | 14.3894i | 0.549426 | − | 0.634071i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.195140 | + | 1.35723i | 0.00858227 | + | 0.0596910i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.40596 | + | 20.5962i | −0.412083 | + | 0.902335i | 0.583818 | + | 0.811884i | \(0.301558\pi\) |
−0.995901 | + | 0.0904506i | \(0.971169\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.76777 | − | 2.57445i | 0.383388 | − | 0.112573i | −0.0843587 | − | 0.996435i | \(-0.526884\pi\) |
0.467747 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0320363 | − | 0.222818i | 0.00139552 | − | 0.00970609i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8592 | − | 2.54125i | −0.993877 | − | 0.110489i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.56954 | + | 1.63536i | 0.241244 | + | 0.0708355i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.4717 | − | 3.95565i | 0.582432 | − | 0.171018i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0832 | + | 7.76538i | −0.520459 | + | 0.334479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.81852 | − | 33.5135i | −0.207164 | − | 1.44086i | −0.782352 | − | 0.622837i | \(-0.785980\pi\) |
0.575188 | − | 0.818021i | \(-0.304929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.527141 | − | 0.338773i | −0.0225802 | − | 0.0145114i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.24934 | + | 8.36618i | 0.309959 | + | 0.357712i | 0.889260 | − | 0.457402i | \(-0.151220\pi\) |
−0.579301 | + | 0.815114i | \(0.696674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.09819 | 0.0467845 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.20897 | −0.264032 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0341 | + | 11.5799i | 0.425157 | + | 0.490658i | 0.927401 | − | 0.374068i | \(-0.122037\pi\) |
−0.502244 | + | 0.864726i | \(0.667492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.30152 | − | 2.12176i | −0.139639 | − | 0.0897408i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.138018 | + | 0.959933i | 0.00581675 | + | 0.0404564i | 0.992523 | − | 0.122057i | \(-0.0389491\pi\) |
−0.986706 | + | 0.162513i | \(0.948040\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.96317 | + | 5.11762i | −0.335013 | + | 0.215300i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.53852 | − | 0.745376i | 0.106420 | − | 0.0312478i | −0.228089 | − | 0.973640i | \(-0.573248\pi\) |
0.334509 | + | 0.942393i | \(0.391430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9891 | − | 7.33747i | −1.04576 | − | 0.307063i | −0.286658 | − | 0.958033i | \(-0.592544\pi\) |
−0.759104 | + | 0.650970i | \(0.774363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.5764 | − | 3.52921i | −0.732988 | − | 0.147178i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.37205 | + | 23.4531i | −0.140380 | + | 0.976366i | 0.790870 | + | 0.611985i | \(0.209629\pi\) |
−0.931250 | + | 0.364381i | \(0.881280\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.25691 | + | 1.54357i | −0.218093 | + | 0.0640380i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.29303 | − | 13.7798i | 0.260631 | − | 0.570702i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.32866 | − | 16.1962i | −0.0961139 | − | 0.668487i | −0.979737 | − | 0.200288i | \(-0.935812\pi\) |
0.883623 | − | 0.468199i | \(-0.155097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.333359 | − | 0.384717i | 0.0137358 | − | 0.0158520i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.5422 | + | 34.0936i | 1.21315 | + | 1.40006i | 0.891391 | + | 0.453235i | \(0.149730\pi\) |
0.321763 | + | 0.946820i | \(0.395724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.417649 | − | 0.914524i | −0.0171219 | − | 0.0374918i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5788 | 0.513957 | 0.256978 | − | 0.966417i | \(-0.417273\pi\) | ||||
0.256978 | + | 0.966417i | \(0.417273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.2373 | − | 28.9856i | −0.539959 | − | 1.18235i | −0.961315 | − | 0.275451i | \(-0.911173\pi\) |
0.421356 | − | 0.906895i | \(-0.361554\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.75075 | − | 3.05312i | −0.193146 | − | 0.124127i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8020 | − | 15.9283i | 0.560205 | − | 0.646511i | −0.403025 | − | 0.915189i | \(-0.632041\pi\) |
0.963230 | + | 0.268678i | \(0.0865866\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.561761 | + | 0.361022i | −0.0227264 | + | 0.0146054i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.06471 | + | 4.52108i | −0.0833927 | + | 0.182605i | −0.946735 | − | 0.322015i | \(-0.895640\pi\) |
0.863342 | + | 0.504619i | \(0.168367\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.41675 | + | 1.59050i | 0.218070 | + | 0.0640312i | 0.388943 | − | 0.921262i | \(-0.372840\pi\) |
−0.170872 | + | 0.985293i | \(0.554659\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.298014 | + | 2.07273i | −0.0119782 | + | 0.0833101i | −0.994934 | − | 0.100534i | \(-0.967945\pi\) |
0.982955 | + | 0.183844i | \(0.0588541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.83208 | + | 12.7424i | −0.0734005 | + | 0.510512i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.35334 | − | 2.15914i | −0.294134 | − | 0.0863655i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.04452 | − | 6.66657i | 0.121393 | − | 0.265814i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4937 | + | 11.8852i | −0.736223 | + | 0.473142i | −0.854246 | − | 0.519869i | \(-0.825981\pi\) |
0.118023 | + | 0.993011i | \(0.462344\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7035 | − | 12.3524i | 0.424754 | − | 0.490192i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.88448 | − | 3.78173i | −0.233152 | − | 0.149838i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.85869 | + | 4.06996i | 0.0734138 | + | 0.160754i | 0.942781 | − | 0.333413i | \(-0.108200\pi\) |
−0.869367 | + | 0.494167i | \(0.835473\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.7233 | 0.620067 | 0.310034 | − | 0.950726i | \(-0.399660\pi\) | ||||
0.310034 | + | 0.950726i | \(0.399660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.14760 | + | 20.0305i | 0.359629 | + | 0.787478i | 0.999815 | + | 0.0192578i | \(0.00613033\pi\) |
−0.640185 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.35272 | − | 2.71518i | −0.0923523 | − | 0.106580i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.14529 | + | 4.78391i | −0.162218 | + | 0.187209i | −0.831039 | − | 0.556214i | \(-0.812254\pi\) |
0.668822 | + | 0.743423i | \(0.266799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.62433 | + | 11.2974i | 0.0634676 | + | 0.441427i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00751 | − | 4.39583i | 0.0782014 | − | 0.171237i | −0.866493 | − | 0.499189i | \(-0.833631\pi\) |
0.944694 | + | 0.327952i | \(0.106358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.68540 | + | 1.66938i | −0.221136 | + | 0.0649315i | −0.390424 | − | 0.920635i | \(-0.627672\pi\) |
0.169288 | + | 0.985567i | \(0.445853\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.323557 | − | 2.25039i | 0.0125470 | − | 0.0872662i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.629312 | − | 2.68480i | −0.0243671 | − | 0.103956i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.8450 | − | 6.12065i | −0.804712 | − | 0.236285i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.3632 | + | 14.2007i | −1.86426 | + | 0.547397i | −0.865332 | + | 0.501198i | \(0.832893\pi\) |
−0.998932 | + | 0.0461990i | \(0.985289\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.9502 | + | 22.4611i | −1.34324 | + | 0.863251i | −0.997186 | − | 0.0749627i | \(-0.976116\pi\) |
−0.346058 | + | 0.938213i | \(0.612480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.608342 | + | 4.23111i | 0.0233460 | + | 0.162375i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.5235 | − | 23.4722i | −1.39753 | − | 0.898140i | −0.397720 | − | 0.917507i | \(-0.630199\pi\) |
−0.999812 | + | 0.0193668i | \(0.993835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.76852 | + | 8.96535i | 0.296820 | + | 0.342548i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.37743 | 0.281058 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4600 | −0.626168 | −0.313084 | − | 0.949725i | \(-0.601362\pi\) | ||||
−0.313084 | + | 0.949725i | \(0.601362\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.56179 | + | 5.26459i | 0.173039 | + | 0.199697i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.46522 | + | 2.22696i | 0.131255 | + | 0.0843522i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.43218 | + | 9.96101i | 0.0540926 | + | 0.376222i | 0.998829 | + | 0.0483898i | \(0.0154090\pi\) |
−0.944736 | + | 0.327832i | \(0.893682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.9423 | − | 8.96017i | 0.525844 | − | 0.337939i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2759 | − | 3.60453i | 0.461683 | − | 0.135562i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.0074 | + | 9.69186i | 1.23962 | + | 0.363985i | 0.834873 | − | 0.550443i | \(-0.185541\pi\) |
0.404748 | + | 0.914428i | \(0.367359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.13157 | − | 0.594519i | −0.0423775 | − | 0.0222649i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.465022 | + | 3.23430i | −0.0173908 | + | 0.120956i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.8137 | + | 4.05608i | −0.515165 | + | 0.151266i | −0.528973 | − | 0.848638i | \(-0.677423\pi\) |
0.0138079 | + | 0.999905i | \(0.495605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.46109 | + | 16.3375i | −0.277866 | + | 0.608441i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.305888 | − | 2.12750i | −0.0113604 | − | 0.0790132i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.20780 | − | 2.54794i | 0.0818827 | − | 0.0944977i | −0.713330 | − | 0.700829i | \(-0.752814\pi\) |
0.795213 | + | 0.606331i | \(0.207359\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.82374 | − | 2.10471i | −0.0674534 | − | 0.0778453i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.38377 | + | 16.1682i | 0.272726 | + | 0.597186i | 0.995591 | − | 0.0938032i | \(-0.0299024\pi\) |
−0.722865 | + | 0.690989i | \(0.757175\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.1759 | −0.448504 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.4290 | + | 29.4055i | 0.493995 | + | 1.08170i | 0.978375 | + | 0.206840i | \(0.0663181\pi\) |
−0.484380 | + | 0.874858i | \(0.660955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.89559 | − | 3.78886i | −0.216288 | − | 0.139000i | 0.428011 | − | 0.903774i | \(-0.359214\pi\) |
−0.644299 | + | 0.764774i | \(0.722851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.89365 | + | 11.4179i | −0.362475 | + | 0.418319i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.1420 | + | 7.16054i | −0.407121 | + | 0.261641i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.51872 | + | 3.32554i | −0.0554190 | + | 0.121351i | −0.935316 | − | 0.353815i | \(-0.884884\pi\) |
0.879897 | + | 0.475165i | \(0.157612\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.6912 | + | 5.78185i | 0.716635 | + | 0.210423i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.00136 | + | 41.7404i | −0.218123 | + | 1.51708i | 0.526835 | + | 0.849968i | \(0.323379\pi\) |
−0.744958 | + | 0.667112i | \(0.767530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.33621 | + | 30.1590i | −0.157187 | + | 1.09326i | 0.746598 | + | 0.665276i | \(0.231686\pi\) |
−0.903785 | + | 0.427986i | \(0.859223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.567150 | + | 0.166530i | 0.0205322 | + | 0.00602880i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.726826 | − | 1.59153i | 0.0262442 | − | 0.0574667i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.2713 | + | 23.3102i | −1.30798 | + | 0.840586i | −0.994057 | − | 0.108863i | \(-0.965279\pi\) |
−0.313921 | + | 0.949449i | \(0.601643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.4944 | − | 31.7302i | 0.988903 | − | 1.14126i | −0.00106970 | − | 0.999999i | \(-0.500340\pi\) |
0.989973 | − | 0.141256i | \(-0.0451140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.838156 | − | 0.538650i | −0.0301074 | − | 0.0193489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.86952 | + | 8.47306i | 0.138640 | + | 0.303579i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.686315 | −0.0245583 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.81510 | − | 19.3024i | −0.314624 | − | 0.688931i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.2807 | + | 31.4836i | 0.972451 | + | 1.12227i | 0.992472 | + | 0.122469i | \(0.0390812\pi\) |
−0.0200212 | + | 0.999800i | \(0.506373\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.84743 | − | 6.74829i | 0.207911 | − | 0.239942i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50570 | − | 10.4724i | −0.0534689 | − | 0.371884i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.8644 | + | 28.1691i | −0.455680 | + | 0.997800i | 0.532771 | + | 0.846260i | \(0.321151\pi\) |
−0.988451 | + | 0.151541i | \(0.951577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.454666 | + | 0.133502i | −0.0160849 | + | 0.00472296i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.79024 | + | 12.4514i | −0.0631763 | + | 0.439401i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.68704 | + | 0.498558i | −0.200442 | + | 0.0175719i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.0442 | − | 15.5752i | −1.86493 | − | 0.547594i | −0.998863 | − | 0.0476716i | \(-0.984820\pi\) |
−0.866070 | − | 0.499922i | \(-0.833362\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.6152 | + | 8.69581i | −1.03993 | + | 0.305351i | −0.756743 | − | 0.653713i | \(-0.773210\pi\) |
−0.283188 | + | 0.959064i | \(0.591392\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0978350 | + | 0.0628747i | −0.00342701 | + | 0.00220241i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.896261 | − | 6.23363i | −0.0313562 | − | 0.218087i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.317226 | + | 0.203869i | 0.0110713 | + | 0.00711506i | 0.546165 | − | 0.837678i | \(-0.316087\pi\) |
−0.535093 | + | 0.844793i | \(0.679724\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.87193 | + | 3.31438i | 0.100109 | + | 0.115532i | 0.803593 | − | 0.595179i | \(-0.202919\pi\) |
−0.703484 | + | 0.710711i | \(0.748373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.5607 | 1.30611 | 0.653056 | − | 0.757309i | \(-0.273487\pi\) | ||||
0.653056 | + | 0.757309i | \(0.273487\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.6526 | 0.647832 | 0.323916 | − | 0.946086i | \(-0.395000\pi\) | ||||
0.323916 | + | 0.946086i | \(0.395000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.25055 | − | 3.75133i | −0.112625 | − | 0.129976i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.1839 | + | 10.4008i | 0.560067 | + | 0.359933i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.98323 | + | 34.6591i | 0.172040 | + | 1.19657i | 0.874565 | + | 0.484908i | \(0.161147\pi\) |
−0.702525 | + | 0.711659i | \(0.747944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1182 | + | 15.4998i | −0.831663 | + | 0.534477i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4851 | − | 3.66597i | 0.429502 | − | 0.126113i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.11133 | + | 1.50082i | 0.175627 | + | 0.0515688i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.8949 | − | 28.9508i | −1.02478 | − | 0.992421i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.23460 | + | 36.4075i | −0.179229 | + | 1.24657i | 0.679322 | + | 0.733840i | \(0.262274\pi\) |
−0.858551 | + | 0.512728i | \(0.828635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.9111 | − | 8.48905i | 0.987583 | − | 0.289981i | 0.252232 | − | 0.967667i | \(-0.418835\pi\) |
0.735351 | + | 0.677686i | \(0.237017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.89911 | − | 12.9172i | 0.201275 | − | 0.440731i | −0.781898 | − | 0.623406i | \(-0.785748\pi\) |
0.983173 | + | 0.182675i | \(0.0584757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.61465 | − | 11.2302i | −0.0549634 | − | 0.382279i | −0.998673 | − | 0.0515033i | \(-0.983599\pi\) |
0.943709 | − | 0.330776i | \(-0.107310\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.34256 | + | 8.47377i | −0.249655 | + | 0.288117i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.37754 | + | 10.8223i | 0.318111 | + | 0.367120i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.46326 | − | 5.39378i | −0.0834643 | − | 0.182761i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.4016 | −0.351639 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0433 | + | 21.9917i | 0.339138 | + | 0.742608i | 0.999969 | − | 0.00792694i | \(-0.00252325\pi\) |
−0.660831 | + | 0.750535i | \(0.729796\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.9136 | − | 18.5817i | −0.974125 | − | 0.626032i | −0.0462528 | − | 0.998930i | \(-0.514728\pi\) |
−0.927873 | + | 0.372897i | \(0.878364\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.4383 | − | 13.2005i | 0.384930 | − | 0.444233i | −0.529907 | − | 0.848056i | \(-0.677773\pi\) |
0.914837 | + | 0.403823i | \(0.132319\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.1796 | + | 16.8246i | −0.879025 | + | 0.564915i | −0.900501 | − | 0.434854i | \(-0.856800\pi\) |
0.0214758 | + | 0.999769i | \(0.493164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.40492 | + | 14.0248i | −0.214814 | + | 0.470377i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.02817 | − | 0.301897i | −0.0344063 | − | 0.0101026i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.09073 | − | 28.4517i | 0.136738 | − | 0.951034i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0218102 | − | 0.151693i | 0.000727411 | − | 0.00505926i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.02312 | + | 1.47492i | 0.167344 | + | 0.0491367i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.459513 | − | 1.00619i | 0.0152747 | − | 0.0334470i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.4322 | + | 19.5576i | −1.01049 | + | 0.649400i | −0.937519 | − | 0.347935i | \(-0.886883\pi\) |
−0.0729669 | + | 0.997334i | \(0.523247\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.76824 | − | 8.96503i | 0.257373 | − | 0.297025i | −0.612327 | − | 0.790604i | \(-0.709766\pi\) |
0.869700 | + | 0.493580i | \(0.164312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6301 | + | 6.83153i | 0.351804 | + | 0.226091i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.47262 | − | 9.79366i | −0.147699 | − | 0.323415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.62999 | 0.284677 | 0.142338 | − | 0.989818i | \(-0.454538\pi\) | ||||
0.142338 | + | 0.989818i | \(0.454538\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.138846 | − | 0.304030i | −0.00457017 | − | 0.0100073i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.2418 | − | 24.5143i | −0.698425 | − | 0.806026i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.92062 | − | 9.14089i | 0.259867 | − | 0.299903i | −0.610790 | − | 0.791792i | \(-0.709148\pi\) |
0.870658 | + | 0.491890i | \(0.163694\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.59746 | − | 11.1105i | −0.0523545 | − | 0.364134i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.963234 | + | 2.10919i | −0.0315011 | + | 0.0689779i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.7156 | − | 4.61451i | 0.513405 | − | 0.150749i | −0.0147599 | − | 0.999891i | \(-0.504698\pi\) |
0.528165 | + | 0.849142i | \(0.322880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.06149 | − | 28.2483i | 0.132401 | − | 0.920867i | −0.810012 | − | 0.586414i | \(-0.800539\pi\) |
0.942412 | − | 0.334453i | \(-0.108552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.4971 | − | 14.3154i | 0.602348 | − | 0.466175i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.35603 | + | 0.985419i | 0.109056 | + | 0.0320218i | 0.335805 | − | 0.941931i | \(-0.390992\pi\) |
−0.226749 | + | 0.973953i | \(0.572810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.87802 | + | 1.72594i | −0.190809 | + | 0.0560265i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.2661 | + | 20.7362i | −1.04520 | + | 0.671710i | −0.946268 | − | 0.323384i | \(-0.895180\pi\) |
−0.0989337 | + | 0.995094i | \(0.531543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.741522 | − | 5.15740i | −0.0239951 | − | 0.166890i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.41397 | − | 6.04999i | −0.303993 | − | 0.195364i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2542 | + | 23.3745i | 0.653360 | + | 0.754018i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.3799 | 0.623861 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.1290 | −1.77283 | −0.886415 | − | 0.462892i | \(-0.846812\pi\) | ||||
−0.886415 | + | 0.462892i | \(0.846812\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.79907 | + | 2.07624i | 0.0577350 | + | 0.0666297i | 0.783882 | − | 0.620909i | \(-0.213236\pi\) |
−0.726147 | + | 0.687539i | \(0.758691\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.52802 | − | 3.55264i | −0.177220 | − | 0.113893i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.75026 | + | 46.9491i | 0.215960 | + | 1.50203i | 0.752744 | + | 0.658314i | \(0.228730\pi\) |
−0.536784 | + | 0.843720i | \(0.680361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.9770 | − | 16.0518i | 0.798269 | − | 0.513016i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.1583 | + | 6.50627i | −0.706741 | + | 0.207518i | −0.615300 | − | 0.788293i | \(-0.710965\pi\) |
−0.0914405 | + | 0.995811i | \(0.529147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.57025 | − | 0.461068i | −0.0500324 | − | 0.0146908i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.7261 | + | 5.76328i | −0.468261 | + | 0.183262i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.83205 | − | 40.5628i | 0.185261 | − | 1.28852i | −0.658819 | − | 0.752302i | \(-0.728944\pi\) |
0.844080 | − | 0.536218i | \(-0.180147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.86071 | − | 2.30811i | 0.249201 | − | 0.0731721i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.74303 | − | 12.5755i | 0.181884 | − | 0.398269i | −0.796626 | − | 0.604473i | \(-0.793384\pi\) |
0.978509 | + | 0.206204i | \(0.0661110\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 828.2.q.c.721.1 | 20 | ||
3.2 | odd | 2 | 276.2.i.a.169.2 | yes | 20 | ||
23.3 | even | 11 | inner | 828.2.q.c.325.1 | 20 | ||
69.26 | odd | 22 | 276.2.i.a.49.2 | ✓ | 20 | ||
69.53 | even | 22 | 6348.2.a.t.1.6 | 10 | |||
69.62 | odd | 22 | 6348.2.a.s.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.49.2 | ✓ | 20 | 69.26 | odd | 22 | ||
276.2.i.a.169.2 | yes | 20 | 3.2 | odd | 2 | ||
828.2.q.c.325.1 | 20 | 23.3 | even | 11 | inner | ||
828.2.q.c.721.1 | 20 | 1.1 | even | 1 | trivial | ||
6348.2.a.s.1.5 | 10 | 69.62 | odd | 22 | |||
6348.2.a.t.1.6 | 10 | 69.53 | even | 22 |