Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(53,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.g (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.4 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.269 |
Dual form | 324.3.g.d.53.4 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.01910 | − | 2.89778i | 1.00382 | − | 0.579555i | 0.0944434 | − | 0.995530i | \(-0.469893\pi\) |
0.909376 | + | 0.415975i | \(0.136560\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.09808 | − | 5.36603i | 0.442582 | − | 0.766575i | −0.555298 | − | 0.831651i | \(-0.687396\pi\) |
0.997880 | + | 0.0650764i | \(0.0207291\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.984508 | − | 0.568406i | −0.0895007 | − | 0.0516733i | 0.454582 | − | 0.890705i | \(-0.349789\pi\) |
−0.544082 | + | 0.839032i | \(0.683122\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.69615 | + | 9.86603i | 0.438166 | + | 0.758925i | 0.997548 | − | 0.0699846i | \(-0.0222950\pi\) |
−0.559382 | + | 0.828910i | \(0.688962\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 31.2514i | − | 1.83832i | −0.393887 | − | 0.919159i | \(-0.628870\pi\) | ||
0.393887 | − | 0.919159i | \(-0.371130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.9808 | −1.73583 | −0.867915 | − | 0.496713i | \(-0.834540\pi\) | ||||
−0.867915 | + | 0.496713i | \(0.834540\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29.1301 | − | 16.8183i | 1.26653 | − | 0.731229i | 0.292196 | − | 0.956358i | \(-0.405614\pi\) |
0.974329 | + | 0.225130i | \(0.0722806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.29423 | − | 7.43782i | 0.171769 | − | 0.297513i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.1420 | + | 12.7837i | 0.763516 | + | 0.440816i | 0.830557 | − | 0.556934i | \(-0.188022\pi\) |
−0.0670407 | + | 0.997750i | \(0.521356\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.5885 | + | 20.0718i | 0.373821 | + | 0.647477i | 0.990150 | − | 0.140012i | \(-0.0447140\pi\) |
−0.616329 | + | 0.787489i | \(0.711381\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 35.9101i | − | 1.02600i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.80385 | 0.237942 | 0.118971 | − | 0.992898i | \(-0.462040\pi\) | ||||
0.118971 | + | 0.992898i | \(0.462040\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 61.2137 | − | 35.3417i | 1.49302 | − | 0.861994i | 0.493049 | − | 0.870002i | \(-0.335882\pi\) |
0.999968 | + | 0.00800815i | \(0.00254910\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.8827 | − | 51.7583i | 0.694946 | − | 1.20368i | −0.275253 | − | 0.961372i | \(-0.588762\pi\) |
0.970199 | − | 0.242310i | \(-0.0779052\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −52.1600 | − | 30.1146i | −1.10979 | − | 0.640736i | −0.171013 | − | 0.985269i | \(-0.554704\pi\) |
−0.938774 | + | 0.344533i | \(0.888037\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.30385 | + | 9.18653i | 0.108242 | + | 0.187480i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19.7718i | 0.373053i | 0.982450 | + | 0.186526i | \(0.0597229\pi\) | ||||
−0.982450 | + | 0.186526i | \(0.940277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.58846 | −0.119790 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −72.2364 | + | 41.7057i | −1.22435 | + | 0.706876i | −0.965841 | − | 0.259134i | \(-0.916563\pi\) |
−0.258504 | + | 0.966010i | \(0.583230\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.3827 | + | 26.6436i | −0.252175 | + | 0.436780i | −0.964124 | − | 0.265451i | \(-0.914479\pi\) |
0.711949 | + | 0.702231i | \(0.247813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 57.1791 | + | 33.0124i | 0.879678 | + | 0.507883i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.29423 | + | 9.16987i | 0.0790183 | + | 0.136864i | 0.902827 | − | 0.430005i | \(-0.141488\pi\) |
−0.823808 | + | 0.566868i | \(0.808155\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.63342i | − | 0.0511750i | −0.999673 | − | 0.0255875i | \(-0.991854\pi\) | ||
0.999673 | − | 0.0255875i | \(-0.00814564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17.2346 | −0.236091 | −0.118045 | − | 0.993008i | \(-0.537663\pi\) | ||||
−0.118045 | + | 0.993008i | \(0.537663\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.10016 | + | 3.52193i | −0.0792229 | + | 0.0457394i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −56.6865 | + | 98.1840i | −0.717551 | + | 1.24283i | 0.244416 | + | 0.969670i | \(0.421404\pi\) |
−0.961967 | + | 0.273164i | \(0.911930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2313 | − | 5.90705i | −0.123269 | − | 0.0711693i | 0.437098 | − | 0.899414i | \(-0.356006\pi\) |
−0.560367 | + | 0.828245i | \(0.689340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −90.5596 | − | 156.854i | −1.06541 | − | 1.84534i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 111.252i | 1.25003i | 0.780614 | + | 0.625013i | \(0.214906\pi\) | ||||
−0.780614 | + | 0.625013i | \(0.785094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 70.5885 | 0.775697 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −165.534 | + | 95.5709i | −1.74246 | + | 1.00601i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −37.1577 | + | 64.3590i | −0.383069 | + | 0.663495i | −0.991499 | − | 0.130113i | \(-0.958466\pi\) |
0.608430 | + | 0.793607i | \(0.291799\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9607 | + | 8.63759i | 0.148126 | + | 0.0855206i | 0.572231 | − | 0.820092i | \(-0.306078\pi\) |
−0.424105 | + | 0.905613i | \(0.639411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.0000 | + | 96.9948i | 0.543689 | + | 0.941698i | 0.998688 | + | 0.0512055i | \(0.0163063\pi\) |
−0.454999 | + | 0.890492i | \(0.650360\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 141.144i | 1.31910i | 0.751660 | + | 0.659551i | \(0.229254\pi\) | ||||
−0.751660 | + | 0.659551i | \(0.770746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171.708 | 1.57530 | 0.787650 | − | 0.616123i | \(-0.211298\pi\) | ||||
0.787650 | + | 0.616123i | \(0.211298\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.82598 | − | 2.78628i | 0.0427078 | − | 0.0246574i | −0.478494 | − | 0.878091i | \(-0.658817\pi\) |
0.521202 | + | 0.853433i | \(0.325484\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 97.4711 | − | 168.825i | 0.847575 | − | 1.46804i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −167.696 | − | 96.8192i | −1.40921 | − | 0.813607i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.8538 | − | 103.670i | −0.494660 | − | 0.856776i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 95.1140i | 0.760912i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −68.2346 | −0.537281 | −0.268640 | − | 0.963241i | \(-0.586574\pi\) | ||||
−0.268640 | + | 0.963241i | \(0.586574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −133.450 | + | 77.0474i | −1.01870 | + | 0.588148i | −0.913728 | − | 0.406327i | \(-0.866810\pi\) |
−0.104975 | + | 0.994475i | \(0.533476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −102.177 | + | 176.976i | −0.768247 | + | 1.33064i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 66.2328 | + | 38.2395i | 0.483451 | + | 0.279121i | 0.721854 | − | 0.692046i | \(-0.243290\pi\) |
−0.238403 | + | 0.971166i | \(0.576624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −47.0192 | − | 81.4397i | −0.338268 | − | 0.585897i | 0.645839 | − | 0.763474i | \(-0.276508\pi\) |
−0.984107 | + | 0.177576i | \(0.943174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 12.9509i | − | 0.0905658i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 148.177 | 1.02191 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 58.1636 | − | 33.5808i | 0.390360 | − | 0.225374i | −0.291956 | − | 0.956432i | \(-0.594306\pi\) |
0.682316 | + | 0.731057i | \(0.260973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.1769 | + | 40.1436i | −0.153490 | + | 0.265852i | −0.932508 | − | 0.361149i | \(-0.882384\pi\) |
0.779018 | + | 0.627001i | \(0.215718\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 116.327 | + | 67.1615i | 0.750498 | + | 0.433300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 84.7942 | + | 146.868i | 0.540091 | + | 0.935464i | 0.998898 | + | 0.0469288i | \(0.0149434\pi\) |
−0.458808 | + | 0.888536i | \(0.651723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 208.417i | − | 1.29452i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −243.023 | −1.49094 | −0.745469 | − | 0.666540i | \(-0.767775\pi\) | ||||
−0.745469 | + | 0.666540i | \(0.767775\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 97.6215 | − | 56.3618i | 0.584560 | − | 0.337496i | −0.178383 | − | 0.983961i | \(-0.557087\pi\) |
0.762944 | + | 0.646465i | \(0.223753\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.6077 | − | 33.9615i | 0.116022 | − | 0.200956i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 162.677 | + | 93.9214i | 0.940328 | + | 0.542898i | 0.890063 | − | 0.455837i | \(-0.150660\pi\) |
0.0502647 | + | 0.998736i | \(0.483993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.6077 | − | 46.0859i | −0.152044 | − | 0.263348i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.3613i | 0.0914042i | 0.998955 | + | 0.0457021i | \(0.0145525\pi\) | ||||
−0.998955 | + | 0.0457021i | \(0.985448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −227.608 | −1.25750 | −0.628751 | − | 0.777607i | \(-0.716433\pi\) | ||||
−0.628751 | + | 0.777607i | \(0.716433\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 44.1874 | − | 25.5116i | 0.238851 | − | 0.137900i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.7635 | + | 30.7673i | −0.0949919 | + | 0.164531i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −315.720 | − | 182.281i | −1.65299 | − | 0.954352i | −0.975835 | − | 0.218508i | \(-0.929881\pi\) |
−0.677151 | − | 0.735844i | \(-0.736786\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4423 | + | 21.5507i | 0.0644678 | + | 0.111662i | 0.896458 | − | 0.443129i | \(-0.146132\pi\) |
−0.831990 | + | 0.554791i | \(0.812798\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 171.259i | − | 0.869333i | −0.900592 | − | 0.434666i | \(-0.856866\pi\) | ||
0.900592 | − | 0.434666i | \(-0.143134\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 122.431 | 0.615230 | 0.307615 | − | 0.951511i | \(-0.400469\pi\) | ||||
0.307615 | + | 0.951511i | \(0.400469\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 137.195 | − | 79.2096i | 0.675837 | − | 0.390195i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 204.825 | − | 354.767i | 0.999146 | − | 1.73057i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.4698 | + | 18.7465i | 0.155358 | + | 0.0896960i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 186.256 | + | 322.604i | 0.882729 | + | 1.52893i | 0.848295 | + | 0.529524i | \(0.177629\pi\) |
0.0344337 | + | 0.999407i | \(0.489037\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 346.373i | − | 1.61104i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 143.608 | 0.661787 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 308.327 | − | 178.013i | 1.39515 | − | 0.805487i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 160.060 | − | 277.231i | 0.717756 | − | 1.24319i | −0.244131 | − | 0.969742i | \(-0.578503\pi\) |
0.961887 | − | 0.273448i | \(-0.0881640\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.1848 | + | 7.61227i | 0.0580830 | + | 0.0335342i | 0.528760 | − | 0.848771i | \(-0.322657\pi\) |
−0.470677 | + | 0.882305i | \(0.655990\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 89.8538 | + | 155.631i | 0.392375 | + | 0.679613i | 0.992762 | − | 0.120096i | \(-0.0383203\pi\) |
−0.600387 | + | 0.799709i | \(0.704987\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 150.796i | 0.647193i | 0.946195 | + | 0.323596i | \(0.104892\pi\) | ||||
−0.946195 | + | 0.323596i | \(0.895108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −349.061 | −1.48537 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 229.103 | − | 132.272i | 0.958588 | − | 0.553441i | 0.0628500 | − | 0.998023i | \(-0.479981\pi\) |
0.895738 | + | 0.444582i | \(0.146648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −114.225 | + | 197.844i | −0.473963 | + | 0.820927i | −0.999556 | − | 0.0298087i | \(-0.990510\pi\) |
0.525593 | + | 0.850736i | \(0.323844\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 53.2411 | + | 30.7387i | 0.217310 | + | 0.125464i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −187.863 | − | 325.389i | −0.760581 | − | 1.31736i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 47.2783i | − | 0.188360i | −0.995555 | − | 0.0941798i | \(-0.969977\pi\) | ||
0.995555 | − | 0.0941798i | \(-0.0300229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.2384 | −0.151140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3351 | − | 12.8952i | 0.0869069 | − | 0.0501757i | −0.455917 | − | 0.890022i | \(-0.650689\pi\) |
0.542824 | + | 0.839847i | \(0.317355\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.2750 | − | 47.2417i | 0.105309 | − | 0.182400i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 247.017 | + | 142.615i | 0.939228 | + | 0.542263i | 0.889718 | − | 0.456510i | \(-0.150901\pi\) |
0.0495095 | + | 0.998774i | \(0.484234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 57.2942 | + | 99.2365i | 0.216205 | + | 0.374477i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 205.341i | − | 0.763350i | −0.924297 | − | 0.381675i | \(-0.875347\pi\) | ||
0.924297 | − | 0.381675i | \(-0.124653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 282.004 | 1.04060 | 0.520302 | − | 0.853982i | \(-0.325819\pi\) | ||||
0.520302 | + | 0.853982i | \(0.325819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.45541 | + | 4.88173i | −0.0307469 | + | 0.0177518i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.3538 | + | 42.1821i | −0.0879200 | + | 0.152282i | −0.906632 | − | 0.421923i | \(-0.861355\pi\) |
0.818712 | + | 0.574205i | \(0.194689\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −213.659 | − | 123.356i | −0.760353 | − | 0.438990i | 0.0690697 | − | 0.997612i | \(-0.477997\pi\) |
−0.829422 | + | 0.558622i | \(0.811330\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 176.473 | + | 305.660i | 0.623580 | + | 1.08007i | 0.988814 | + | 0.149156i | \(0.0476556\pi\) |
−0.365234 | + | 0.930916i | \(0.619011\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 437.966i | − | 1.52601i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −687.650 | −2.37941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −242.191 | + | 139.829i | −0.826590 | + | 0.477232i | −0.852684 | − | 0.522428i | \(-0.825027\pi\) |
0.0260937 | + | 0.999660i | \(0.491693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −241.708 | + | 418.650i | −0.819348 | + | 1.41915i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 331.859 | + | 191.599i | 1.10990 | + | 0.640798i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −185.158 | − | 320.703i | −0.615142 | − | 1.06546i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 178.302i | 0.584598i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 234.708 | 0.764520 | 0.382260 | − | 0.924055i | \(-0.375146\pi\) | ||||
0.382260 | + | 0.924055i | \(0.375146\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −204.123 | + | 117.850i | −0.656343 | + | 0.378940i | −0.790882 | − | 0.611969i | \(-0.790378\pi\) |
0.134539 | + | 0.990908i | \(0.457045\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 178.835 | − | 309.751i | 0.571357 | − | 0.989619i | −0.425070 | − | 0.905160i | \(-0.639751\pi\) |
0.996427 | − | 0.0844583i | \(-0.0269160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −523.067 | − | 301.993i | −1.65005 | − | 0.952659i | −0.977047 | − | 0.213024i | \(-0.931669\pi\) |
−0.673007 | − | 0.739636i | \(-0.734998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.5326 | − | 25.1713i | −0.0455568 | − | 0.0789068i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1030.69i | 3.19101i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 97.8423 | 0.301053 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −323.191 | + | 186.595i | −0.982344 | + | 0.567157i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.3712 | − | 31.8198i | 0.0555021 | − | 0.0961324i | −0.836939 | − | 0.547295i | \(-0.815657\pi\) |
0.892442 | + | 0.451163i | \(0.148991\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 53.1445 | + | 30.6830i | 0.158640 | + | 0.0915910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −84.1384 | − | 145.732i | −0.249669 | − | 0.432439i | 0.713765 | − | 0.700385i | \(-0.246988\pi\) |
−0.963434 | + | 0.267946i | \(0.913655\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 26.3478i | − | 0.0772663i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 369.338 | 1.07679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 152.947 | − | 88.3041i | 0.440770 | − | 0.254479i | −0.263154 | − | 0.964754i | \(-0.584763\pi\) |
0.703924 | + | 0.710275i | \(0.251430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −65.6077 | + | 113.636i | −0.187988 | + | 0.325604i | −0.944579 | − | 0.328284i | \(-0.893530\pi\) |
0.756592 | + | 0.653888i | \(0.226863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.7952 | − | 6.80994i | −0.0334140 | − | 0.0192916i | 0.483200 | − | 0.875510i | \(-0.339474\pi\) |
−0.516614 | + | 0.856218i | \(0.672808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.5289 | − | 18.2365i | −0.0296588 | − | 0.0513705i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 96.5853i | − | 0.269040i | −0.990911 | − | 0.134520i | \(-0.957051\pi\) | ||
0.990911 | − | 0.134520i | \(-0.0429492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 726.731 | 2.01310 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −86.5023 | + | 49.9421i | −0.236993 | + | 0.136828i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −127.473 | + | 220.790i | −0.347338 | + | 0.601607i | −0.985776 | − | 0.168067i | \(-0.946248\pi\) |
0.638438 | + | 0.769674i | \(0.279581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 106.096 | + | 61.2545i | 0.285973 | + | 0.165106i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 45.5500 | + | 78.8949i | 0.122118 | + | 0.211514i | 0.920603 | − | 0.390501i | \(-0.127698\pi\) |
−0.798485 | + | 0.602015i | \(0.794365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 291.271i | 0.772602i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 193.454 | 0.510432 | 0.255216 | − | 0.966884i | \(-0.417853\pi\) | ||||
0.255216 | + | 0.966884i | \(0.417853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −288.347 | + | 166.477i | −0.752865 | + | 0.434667i | −0.826728 | − | 0.562602i | \(-0.809801\pi\) |
0.0738632 | + | 0.997268i | \(0.476467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.4115 | + | 35.3538i | −0.0530170 | + | 0.0918281i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.6165 | − | 20.5632i | −0.0915590 | − | 0.0528616i | 0.453521 | − | 0.891245i | \(-0.350168\pi\) |
−0.545080 | + | 0.838384i | \(0.683501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −525.594 | − | 910.356i | −1.34423 | − | 2.32828i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 657.060i | 1.66344i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −176.881 | −0.445544 | −0.222772 | − | 0.974871i | \(-0.571510\pi\) | ||||
−0.222772 | + | 0.974871i | \(0.571510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −378.613 | + | 218.593i | −0.944173 | + | 0.545119i | −0.891266 | − | 0.453481i | \(-0.850182\pi\) |
−0.0529071 | + | 0.998599i | \(0.516849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −132.019 | + | 228.664i | −0.327591 | + | 0.567405i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.66746 | − | 5.00416i | −0.0212960 | − | 0.0122952i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 72.9519 | + | 126.356i | 0.178367 | + | 0.308940i | 0.941321 | − | 0.337512i | \(-0.109585\pi\) |
−0.762955 | + | 0.646452i | \(0.776252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 516.830i | 1.25140i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −68.4693 | −0.164986 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 115.555 | − | 66.7156i | 0.275787 | − | 0.159226i | −0.355728 | − | 0.934590i | \(-0.615767\pi\) |
0.631515 | + | 0.775364i | \(0.282434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −144.346 | + | 250.015i | −0.342865 | + | 0.593859i | −0.984963 | − | 0.172763i | \(-0.944731\pi\) |
0.642099 | + | 0.766622i | \(0.278064\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −232.442 | − | 134.201i | −0.546923 | − | 0.315766i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 95.3135 | + | 165.088i | 0.223217 | + | 0.386622i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 669.565i | − | 1.55351i | −0.629800 | − | 0.776757i | \(-0.716863\pi\) | ||
0.629800 | − | 0.776757i | \(-0.283137\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −510.654 | −1.17934 | −0.589669 | − | 0.807645i | \(-0.700742\pi\) | ||||
−0.589669 | + | 0.807645i | \(0.700742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −960.732 | + | 554.679i | −2.19847 | + | 1.26929i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.6499 | + | 66.9437i | −0.0880409 | + | 0.152491i | −0.906683 | − | 0.421813i | \(-0.861394\pi\) |
0.818642 | + | 0.574304i | \(0.194727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 657.617 | + | 379.676i | 1.48446 | + | 0.857055i | 0.999844 | − | 0.0176696i | \(-0.00562472\pi\) |
0.484620 | + | 0.874725i | \(0.338958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 322.385 | + | 558.386i | 0.724460 | + | 1.25480i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 541.149i | − | 1.20523i | −0.798032 | − | 0.602616i | \(-0.794125\pi\) | ||
0.798032 | − | 0.602616i | \(-0.205875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −80.3538 | −0.178168 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 354.290 | − | 204.550i | 0.778660 | − | 0.449560i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.7942 | − | 48.1410i | 0.0608189 | − | 0.105341i | −0.834013 | − | 0.551745i | \(-0.813962\pi\) |
0.894832 | + | 0.446404i | \(0.147295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −217.114 | − | 125.351i | −0.470964 | − | 0.271911i | 0.245679 | − | 0.969351i | \(-0.420989\pi\) |
−0.716643 | + | 0.697440i | \(0.754322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −285.512 | − | 494.520i | −0.616656 | − | 1.06808i | −0.990092 | − | 0.140423i | \(-0.955154\pi\) |
0.373436 | − | 0.927656i | \(-0.378180\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 72.2663i | 0.154746i | 0.997002 | + | 0.0773729i | \(0.0246532\pi\) | ||||
−0.997002 | + | 0.0773729i | \(0.975347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 65.6077 | 0.139888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −58.8395 | + | 33.9710i | −0.124396 | + | 0.0718203i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −141.627 | + | 245.305i | −0.298162 | + | 0.516432i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −612.735 | − | 353.763i | −1.27920 | − | 0.738544i | −0.302496 | − | 0.953151i | \(-0.597820\pi\) |
−0.976701 | + | 0.214606i | \(0.931153\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.1481 | + | 86.8590i | 0.104258 | + | 0.180580i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 430.699i | 0.888039i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 360.908 | 0.741083 | 0.370542 | − | 0.928816i | \(-0.379172\pi\) | ||||
0.370542 | + | 0.928816i | \(0.379172\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 588.914 | − | 340.010i | 1.19942 | − | 0.692484i | 0.238992 | − | 0.971022i | \(-0.423183\pi\) |
0.960425 | + | 0.278538i | \(0.0898498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 399.508 | − | 691.967i | 0.810360 | − | 1.40358i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.4971 | − | 11.2566i | −0.0392295 | − | 0.0226491i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −118.352 | − | 204.992i | −0.237178 | − | 0.410805i | 0.722725 | − | 0.691135i | \(-0.242889\pi\) |
−0.959903 | + | 0.280331i | \(0.909556\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 95.6715i | 0.190202i | 0.995468 | + | 0.0951009i | \(0.0303174\pi\) | ||||
−0.995468 | + | 0.0951009i | \(0.969683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 100.119 | 0.198256 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 376.915 | − | 217.612i | 0.740501 | − | 0.427529i | −0.0817503 | − | 0.996653i | \(-0.526051\pi\) |
0.822252 | + | 0.569124i | \(0.192718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.3942 | + | 92.4815i | −0.104490 | + | 0.180981i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 562.139 | + | 324.551i | 1.09153 | + | 0.630196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.2346 | + | 59.2961i | 0.0662178 | + | 0.114693i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 794.771i | − | 1.52547i | −0.646709 | − | 0.762737i | \(-0.723855\pi\) | ||
0.646709 | − | 0.762737i | \(-0.276145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −594.481 | −1.13667 | −0.568337 | − | 0.822796i | \(-0.692413\pi\) | ||||
−0.568337 | + | 0.822796i | \(0.692413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 627.272 | − | 362.156i | 1.19027 | − | 0.687202i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 301.208 | − | 521.707i | 0.569391 | − | 0.986214i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 697.365 | + | 402.624i | 1.30838 | + | 0.755392i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 409.004 | + | 708.415i | 0.764493 | + | 1.32414i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12.0590i | − | 0.0223728i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 219.508 | 0.405744 | 0.202872 | − | 0.979205i | \(-0.434972\pi\) | ||||
0.202872 | + | 0.979205i | \(0.434972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 861.818 | − | 497.571i | 1.58132 | − | 0.912974i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 292.296 | − | 506.272i | 0.534362 | − | 0.925542i | −0.464832 | − | 0.885399i | \(-0.653885\pi\) |
0.999194 | − | 0.0401434i | \(-0.0127815\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −730.259 | − | 421.615i | −1.32533 | − | 0.765182i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 351.238 | + | 608.363i | 0.635151 | + | 1.10011i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 597.187i | − | 1.07215i | −0.844171 | − | 0.536075i | \(-0.819907\pi\) | ||
0.844171 | − | 0.536075i | \(-0.180093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 680.865 | 1.21801 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −311.957 | + | 180.108i | −0.554097 | + | 0.319908i | −0.750773 | − | 0.660561i | \(-0.770319\pi\) |
0.196676 | + | 0.980469i | \(0.436985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.1481 | − | 27.9693i | 0.0285806 | − | 0.0495031i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −486.466 | − | 280.861i | −0.854949 | − | 0.493605i | 0.00736827 | − | 0.999973i | \(-0.497655\pi\) |
−0.862318 | + | 0.506368i | \(0.830988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0385 | + | 32.9756i | 0.0333423 | + | 0.0577506i | 0.882215 | − | 0.470847i | \(-0.156052\pi\) |
−0.848873 | + | 0.528597i | \(0.822718\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 288.886i | − | 0.502410i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −747.008 | −1.29464 | −0.647320 | − | 0.762218i | \(-0.724110\pi\) | ||||
−0.647320 | + | 0.762218i | \(0.724110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −63.3948 | + | 36.6010i | −0.109113 | + | 0.0629965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.2384 | − | 19.4655i | 0.0192768 | − | 0.0333885i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 519.419 | + | 299.887i | 0.884870 | + | 0.510880i | 0.872261 | − | 0.489040i | \(-0.162653\pi\) |
0.0126092 | + | 0.999921i | \(0.495986\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −382.196 | − | 661.983i | −0.648890 | − | 1.12391i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 212.184i | − | 0.357814i | −0.983866 | − | 0.178907i | \(-0.942744\pi\) | ||
0.983866 | − | 0.178907i | \(-0.0572561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1122.24 | −1.88612 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 281.649 | − | 162.610i | 0.470198 | − | 0.271469i | −0.246124 | − | 0.969238i | \(-0.579157\pi\) |
0.716323 | + | 0.697769i | \(0.245824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −373.738 | + | 647.334i | −0.621861 | + | 1.07709i | 0.367278 | + | 0.930111i | \(0.380290\pi\) |
−0.989139 | + | 0.146983i | \(0.953044\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −600.824 | − | 346.886i | −0.993098 | − | 0.573366i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 61.8634 | + | 107.151i | 0.101917 | + | 0.176525i | 0.912474 | − | 0.409134i | \(-0.134169\pi\) |
−0.810558 | + | 0.585659i | \(0.800836\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 686.149i | − | 1.12299i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −954.008 | −1.55629 | −0.778146 | − | 0.628083i | \(-0.783840\pi\) | ||||
−0.778146 | + | 0.628083i | \(0.783840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 216.613 | − | 125.061i | 0.351074 | − | 0.202693i | −0.314084 | − | 0.949395i | \(-0.601697\pi\) |
0.665158 | + | 0.746702i | \(0.268364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 508.769 | − | 881.214i | 0.821921 | − | 1.42361i | −0.0823287 | − | 0.996605i | \(-0.526236\pi\) |
0.904250 | − | 0.427004i | \(-0.140431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 596.983 | + | 344.668i | 0.958239 | + | 0.553240i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 382.975 | + | 663.332i | 0.612760 | + | 1.06133i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 275.133i | − | 0.437413i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −75.6001 | −0.119810 | −0.0599050 | − | 0.998204i | \(-0.519080\pi\) | ||||
−0.0599050 | + | 0.998204i | \(0.519080\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −342.476 | + | 197.729i | −0.539333 | + | 0.311384i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −60.4230 | + | 104.656i | −0.0948556 | + | 0.164295i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 209.895 | + | 121.183i | 0.327450 | + | 0.189053i | 0.654708 | − | 0.755882i | \(-0.272791\pi\) |
−0.327259 | + | 0.944935i | \(0.606125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 366.592 | + | 634.956i | 0.570128 | + | 0.987490i | 0.996552 | + | 0.0829673i | \(0.0264397\pi\) |
−0.426424 | + | 0.904523i | \(0.640227\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1177.72i | − | 1.82028i | −0.414296 | − | 0.910142i | \(-0.635972\pi\) | ||
0.414296 | − | 0.910142i | \(-0.364028\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 94.8231 | 0.146106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 550.151 | − | 317.630i | 0.842497 | − | 0.486416i | −0.0156151 | − | 0.999878i | \(-0.504971\pi\) |
0.858112 | + | 0.513462i | \(0.171637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −446.533 | + | 773.417i | −0.681729 | + | 1.18079i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 793.616 | + | 458.194i | 1.20427 | + | 0.695287i | 0.961502 | − | 0.274797i | \(-0.0886105\pi\) |
0.242770 | + | 0.970084i | \(0.421944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −206.679 | − | 357.978i | −0.312676 | − | 0.541571i | 0.666265 | − | 0.745715i | \(-0.267892\pi\) |
−0.978941 | + | 0.204145i | \(0.934559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1184.34i | 1.78097i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 859.996 | 1.28935 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.2888 | − | 17.4872i | 0.0451397 | − | 0.0260614i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 366.227 | − | 634.324i | 0.544171 | − | 0.942531i | −0.454488 | − | 0.890753i | \(-0.650178\pi\) |
0.998659 | − | 0.0517784i | \(-0.0164890\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −507.219 | − | 292.843i | −0.749215 | − | 0.432559i | 0.0761952 | − | 0.997093i | \(-0.475723\pi\) |
−0.825410 | + | 0.564533i | \(0.809056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 230.235 | + | 398.778i | 0.339079 | + | 0.587302i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1082.97i | 1.58560i | 0.609480 | + | 0.792801i | \(0.291378\pi\) | ||||
−0.609480 | + | 0.792801i | \(0.708622\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 443.238 | 0.647063 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −195.069 | + | 112.623i | −0.283119 | + | 0.163459i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 89.1788 | − | 154.462i | 0.129058 | − | 0.223534i | −0.794254 | − | 0.607586i | \(-0.792138\pi\) |
0.923312 | + | 0.384051i | \(0.125471\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −471.988 | − | 272.503i | −0.679120 | − | 0.392090i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1104.48 | − | 1913.01i | −1.58462 | − | 2.74464i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 638.090i | − | 0.910257i | −0.890426 | − | 0.455129i | \(-0.849593\pi\) | ||
0.890426 | − | 0.455129i | \(-0.150407\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −290.358 | −0.413026 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 92.6990 | − | 53.5198i | 0.131116 | − | 0.0756999i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −412.423 | + | 714.338i | −0.581697 | + | 1.00753i | 0.413582 | + | 0.910467i | \(0.364278\pi\) |
−0.995278 | + | 0.0970614i | \(0.969056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 675.145 | + | 389.795i | 0.946908 | + | 0.546698i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.5289 | − | 65.0019i | −0.0524879 | − | 0.0909117i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 748.451i | 1.04096i | 0.853874 | + | 0.520480i | \(0.174247\pi\) | ||||
−0.853874 | + | 0.520480i | \(0.825753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 693.969 | 0.962509 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 190.165 | − | 109.792i | 0.262297 | − | 0.151437i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.1788 | + | 22.8264i | −0.0181276 | + | 0.0313980i | −0.874947 | − | 0.484219i | \(-0.839104\pi\) |
0.856819 | + | 0.515617i | \(0.172437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1617.52 | − | 933.876i | −2.21275 | − | 1.27753i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 536.473 | + | 929.199i | 0.731887 | + | 1.26767i | 0.956076 | + | 0.293119i | \(0.0946934\pi\) |
−0.224189 | + | 0.974546i | \(0.571973\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.0371i | − | 0.0163325i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 158.831 | 0.214926 | 0.107463 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107463 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −142.080 | + | 82.0297i | −0.191224 | + | 0.110403i | −0.592556 | − | 0.805530i | \(-0.701881\pi\) |
0.401331 | + | 0.915933i | \(0.368548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 194.619 | − | 337.090i | 0.261234 | − | 0.452470i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 757.382 | + | 437.275i | 1.01119 | + | 0.583811i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −116.198 | − | 201.261i | −0.154724 | − | 0.267991i | 0.778234 | − | 0.627974i | \(-0.216116\pi\) |
−0.932959 | + | 0.359984i | \(0.882782\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 268.646i | 0.355823i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1012.72 | 1.33781 | 0.668905 | − | 0.743348i | \(-0.266763\pi\) | ||||
0.668905 | + | 0.743348i | \(0.266763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −501.427 | + | 289.499i | −0.658905 | + | 0.380419i | −0.791860 | − | 0.610703i | \(-0.790887\pi\) |
0.132954 | + | 0.991122i | \(0.457554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 531.963 | − | 921.388i | 0.697200 | − | 1.20759i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −822.939 | − | 475.124i | −1.07293 | − | 0.619458i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 133.635 | + | 231.462i | 0.173777 | + | 0.300991i | 0.939737 | − | 0.341897i | \(-0.111069\pi\) |
−0.765960 | + | 0.642888i | \(0.777736\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1356.98i | 1.75548i | 0.479140 | + | 0.877739i | \(0.340949\pi\) | ||||
−0.479140 | + | 0.877739i | \(0.659051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 199.054 | 0.256844 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2018.87 | + | 1165.60i | −2.59162 | + | 1.49627i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.06526 | + | 3.57714i | −0.00264438 | + | 0.00458020i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 851.181 | + | 491.430i | 1.08431 | + | 0.626025i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.9404 | − | 50.1262i | −0.0367731 | − | 0.0636928i | 0.847053 | − | 0.531508i | \(-0.178375\pi\) |
−0.883826 | + | 0.467815i | \(0.845041\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 34.5285i | − | 0.0436517i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −350.488 | −0.441978 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −142.793 | + | 82.4418i | −0.179164 | + | 0.103440i | −0.586900 | − | 0.809660i | \(-0.699652\pi\) |
0.407736 | + | 0.913100i | \(0.366318\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −941.123 | + | 1630.07i | −1.17788 | + | 2.04014i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9676 | + | 9.79627i | 0.0211303 | + | 0.0121996i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −603.946 | − | 1046.07i | −0.750244 | − | 1.29946i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 981.255i | 1.21292i | 0.795113 | + | 0.606461i | \(0.207412\pi\) | ||||
−0.795113 | + | 0.606461i | \(0.792588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −289.877 | −0.357432 | −0.178716 | − | 0.983901i | \(-0.557194\pi\) | ||||
−0.178716 | + | 0.983901i | \(0.557194\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1219.76 | + | 704.227i | −1.49663 | + | 0.864082i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −985.554 | + | 1707.03i | −1.20631 | + | 2.08939i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −114.436 | − | 66.0695i | −0.139386 | − | 0.0804745i | 0.428685 | − | 0.903454i | \(-0.358977\pi\) |
−0.568071 | + | 0.822979i | \(0.692310\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −243.096 | − | 421.055i | −0.295378 | − | 0.511610i | 0.679695 | − | 0.733495i | \(-0.262112\pi\) |
−0.975073 | + | 0.221885i | \(0.928779\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 258.192i | − | 0.312203i | −0.987741 | − | 0.156101i | \(-0.950107\pi\) | ||
0.987741 | − | 0.156101i | \(-0.0498927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −376.400 | −0.454041 | −0.227020 | − | 0.973890i | \(-0.572898\pi\) | ||||
−0.227020 | + | 0.973890i | \(0.572898\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 287.092 | − | 165.753i | 0.344648 | − | 0.198983i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 326.648 | − | 565.771i | 0.391195 | − | 0.677570i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −252.519 | − | 145.792i | −0.300976 | − | 0.173768i | 0.341905 | − | 0.939734i | \(-0.388928\pi\) |
−0.642881 | + | 0.765966i | \(0.722261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −93.6556 | − | 162.216i | −0.111362 | − | 0.192885i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 227.275i | − | 0.268964i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −741.727 | −0.875711 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 256.457 | − | 148.065i | 0.301359 | − | 0.173990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −96.7691 | + | 167.609i | −0.113446 | + | 0.196494i | −0.917157 | − | 0.398525i | \(-0.869522\pi\) |
0.803712 | + | 0.595019i | \(0.202855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −165.998 | − | 95.8387i | −0.193696 | − | 0.111830i | 0.400016 | − | 0.916508i | \(-0.369005\pi\) |
−0.593712 | + | 0.804678i | \(0.702338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −598.258 | − | 1036.21i | −0.696458 | − | 1.20630i | −0.969687 | − | 0.244352i | \(-0.921425\pi\) |
0.273228 | − | 0.961949i | \(-0.411909\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 692.323i | 0.802228i | 0.916028 | + | 0.401114i | \(0.131377\pi\) | ||||
−0.916028 | + | 0.401114i | \(0.868623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1088.65 | 1.25856 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 111.617 | − | 64.4419i | 0.128443 | − | 0.0741564i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.3135 | + | 104.466i | −0.0692462 | + | 0.119938i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 510.384 | + | 294.670i | 0.583296 | + | 0.336766i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 513.306 | + | 889.072i | 0.585297 | + | 1.01376i | 0.994838 | + | 0.101473i | \(0.0323555\pi\) |
−0.409541 | + | 0.912292i | \(0.634311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 984.820i | − | 1.11784i | −0.829220 | − | 0.558922i | \(-0.811215\pi\) | ||
0.829220 | − | 0.558922i | \(-0.188785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1038.19 | 1.17576 | 0.587878 | − | 0.808950i | \(-0.299964\pi\) | ||||
0.587878 | + | 0.808950i | \(0.299964\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −146.847 | + | 84.7821i | −0.165555 | + | 0.0955830i | −0.580488 | − | 0.814269i | \(-0.697138\pi\) |
0.414933 | + | 0.909852i | \(0.363805\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −211.396 | + | 366.149i | −0.237791 | + | 0.411866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1720.28 | + | 993.202i | 1.92640 | + | 1.11221i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.4115 | + | 82.1192i | 0.0529738 | + | 0.0917533i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 592.572i | 0.659146i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 617.896 | 0.685789 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1142.39 | + | 659.556i | −1.26230 | + | 0.728792i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −365.981 | + | 633.897i | −0.403507 | + | 0.698894i | −0.994146 | − | 0.108041i | \(-0.965542\pi\) |
0.590640 | + | 0.806936i | \(0.298876\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −853.652 | − | 492.856i | −0.937049 | − | 0.541006i | −0.0480151 | − | 0.998847i | \(-0.515290\pi\) |
−0.889034 | + | 0.457841i | \(0.848623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.71521 | + | 11.6311i | 0.00735510 | + | 0.0127394i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 954.795i | 1.04122i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −839.650 | −0.913656 | −0.456828 | − | 0.889555i | \(-0.651015\pi\) | ||||
−0.456828 | + | 0.889555i | \(0.651015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.8475 | − | 20.6965i | 0.0388380 | − | 0.0224231i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.8057 | − | 65.4815i | 0.0408711 | − | 0.0707908i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −519.360 | − | 299.853i | −0.559053 | − | 0.322769i | 0.193712 | − | 0.981058i | \(-0.437947\pi\) |
−0.752765 | + | 0.658289i | \(0.771280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −174.925 | − | 302.979i | −0.187889 | − | 0.325434i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 205.899i | 0.220212i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1610.24 | 1.71850 | 0.859252 | − | 0.511553i | \(-0.170930\pi\) | ||||
0.859252 | + | 0.511553i | \(0.170930\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 762.189 | − | 440.050i | 0.809978 | − | 0.467641i | −0.0369704 | − | 0.999316i | \(-0.511771\pi\) |
0.846948 | + | 0.531675i | \(0.178437\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1188.77 | − | 2059.02i | 1.26063 | − | 2.18347i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −853.072 | − | 492.522i | −0.900816 | − | 0.520086i | −0.0233509 | − | 0.999727i | \(-0.507434\pi\) |
−0.877465 | + | 0.479641i | \(0.840767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −98.1711 | − | 170.037i | −0.103447 | − | 0.179175i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 845.550i | 0.887251i | 0.896212 | + | 0.443625i | \(0.146308\pi\) | ||||
−0.896212 | + | 0.443625i | \(0.853692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2112.84 | −2.21240 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 410.388 | − | 236.938i | 0.427934 | − | 0.247068i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 211.915 | − | 367.048i | 0.220515 | − | 0.381944i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 124.898 | + | 72.1100i | 0.129428 | + | 0.0747253i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 513.471 | + | 889.358i | 0.530994 | + | 0.919708i | 0.999346 | + | 0.0361664i | \(0.0115146\pi\) |
−0.468352 | + | 0.883542i | \(0.655152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 338.171i | − | 0.348271i | −0.984722 | − | 0.174135i | \(-0.944287\pi\) | ||
0.984722 | − | 0.174135i | \(-0.0557130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −582.677 | −0.598846 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 789.485 | − | 455.809i | 0.808070 | − | 0.466540i | −0.0382151 | − | 0.999270i | \(-0.512167\pi\) |
0.846285 | + | 0.532730i | \(0.178834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.2365 | − | 109.529i | 0.0645930 | − | 0.111878i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −829.618 | − | 478.980i | −0.843966 | − | 0.487264i | 0.0146445 | − | 0.999893i | \(-0.495338\pi\) |
−0.858610 | + | 0.512629i | \(0.828672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −496.269 | − | 859.563i | −0.503827 | − | 0.872653i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2010.30i | − | 2.03266i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1771.18 | 1.78727 | 0.893633 | − | 0.448798i | \(-0.148148\pi\) | ||||
0.893633 | + | 0.448798i | \(0.148148\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 614.492 | − | 354.777i | 0.617580 | − | 0.356560i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 544.325 | − | 942.799i | 0.545963 | − | 0.945635i | −0.452583 | − | 0.891722i | \(-0.649497\pi\) |
0.998546 | − | 0.0539130i | \(-0.0171694\pi\) | |||||||
\(998\) | 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 | 324.3.g.d.269.4 | 8 | ||
3.2 | odd | 2 | inner | 324.3.g.d.269.1 | 8 | ||
4.3 | odd | 2 | 1296.3.q.n.593.4 | 8 | |||
9.2 | odd | 6 | 324.3.c.a.161.1 | ✓ | 4 | ||
9.4 | even | 3 | inner | 324.3.g.d.53.1 | 8 | ||
9.5 | odd | 6 | inner | 324.3.g.d.53.4 | 8 | ||
9.7 | even | 3 | 324.3.c.a.161.4 | yes | 4 | ||
12.11 | even | 2 | 1296.3.q.n.593.1 | 8 | |||
36.7 | odd | 6 | 1296.3.e.f.161.4 | 4 | |||
36.11 | even | 6 | 1296.3.e.f.161.1 | 4 | |||
36.23 | even | 6 | 1296.3.q.n.1025.4 | 8 | |||
36.31 | odd | 6 | 1296.3.q.n.1025.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.3.c.a.161.1 | ✓ | 4 | 9.2 | odd | 6 | ||
324.3.c.a.161.4 | yes | 4 | 9.7 | even | 3 | ||
324.3.g.d.53.1 | 8 | 9.4 | even | 3 | inner | ||
324.3.g.d.53.4 | 8 | 9.5 | odd | 6 | inner | ||
324.3.g.d.269.1 | 8 | 3.2 | odd | 2 | inner | ||
324.3.g.d.269.4 | 8 | 1.1 | even | 1 | trivial | ||
1296.3.e.f.161.1 | 4 | 36.11 | even | 6 | |||
1296.3.e.f.161.4 | 4 | 36.7 | odd | 6 | |||
1296.3.q.n.593.1 | 8 | 12.11 | even | 2 | |||
1296.3.q.n.593.4 | 8 | 4.3 | odd | 2 | |||
1296.3.q.n.1025.1 | 8 | 36.31 | odd | 6 | |||
1296.3.q.n.1025.4 | 8 | 36.23 | even | 6 |