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 | 53.4 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.53 |
Dual form | 324.3.g.d.269.4 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0.909376 | − | 0.415975i | \(-0.136560\pi\) |
0.0944434 | + | 0.995530i | \(0.469893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.09808 | + | 5.36603i | 0.442582 | + | 0.766575i | 0.997880 | − | 0.0650764i | \(-0.0207291\pi\) |
−0.555298 | + | 0.831651i | \(0.687396\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.984508 | + | 0.568406i | −0.0895007 | + | 0.0516733i | −0.544082 | − | 0.839032i | \(-0.683122\pi\) |
0.454582 | + | 0.890705i | \(0.349789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.69615 | − | 9.86603i | 0.438166 | − | 0.758925i | −0.559382 | − | 0.828910i | \(-0.688962\pi\) |
0.997548 | + | 0.0699846i | \(0.0222950\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 31.2514i | 1.83832i | 0.393887 | + | 0.919159i | \(0.371130\pi\) | ||||
−0.393887 | + | 0.919159i | \(0.628870\pi\) | |||||||
\(18\) | 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 | 0.974329 | − | 0.225130i | \(-0.0722806\pi\) |
0.292196 | + | 0.956358i | \(0.405614\pi\) | |||||||
\(24\) | 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 | −0.0670407 | − | 0.997750i | \(-0.521356\pi\) |
0.830557 | + | 0.556934i | \(0.188022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.5885 | − | 20.0718i | 0.373821 | − | 0.647477i | −0.616329 | − | 0.787489i | \(-0.711381\pi\) |
0.990150 | + | 0.140012i | \(0.0447140\pi\) | |||||||
\(32\) | 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 | 0.999968 | − | 0.00800815i | \(-0.00254910\pi\) |
0.493049 | + | 0.870002i | \(0.335882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.8827 | + | 51.7583i | 0.694946 | + | 1.20368i | 0.970199 | + | 0.242310i | \(0.0779052\pi\) |
−0.275253 | + | 0.961372i | \(0.588762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −52.1600 | + | 30.1146i | −1.10979 | + | 0.640736i | −0.938774 | − | 0.344533i | \(-0.888037\pi\) |
−0.171013 | + | 0.985269i | \(0.554704\pi\) | |||||||
\(48\) | 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 | \(-0.940277\pi\) | ||
0.982450 | − | 0.186526i | \(-0.0597229\pi\) | |||||||
\(54\) | 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 | −0.258504 | − | 0.966010i | \(-0.583230\pi\) |
−0.965841 | + | 0.259134i | \(0.916563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.3827 | − | 26.6436i | −0.252175 | − | 0.436780i | 0.711949 | − | 0.702231i | \(-0.247813\pi\) |
−0.964124 | + | 0.265451i | \(0.914479\pi\) | |||||||
\(62\) | 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 | −0.823808 | − | 0.566868i | \(-0.808155\pi\) |
0.902827 | + | 0.430005i | \(0.141488\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.63342i | 0.0511750i | 0.999673 | + | 0.0255875i | \(0.00814564\pi\) | ||||
−0.999673 | + | 0.0255875i | \(0.991854\pi\) | |||||||
\(72\) | 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 | −0.961967 | − | 0.273164i | \(-0.911930\pi\) |
0.244416 | − | 0.969670i | \(-0.421404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2313 | + | 5.90705i | −0.123269 | + | 0.0711693i | −0.560367 | − | 0.828245i | \(-0.689340\pi\) |
0.437098 | + | 0.899414i | \(0.356006\pi\) | |||||||
\(84\) | 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 | \(-0.785094\pi\) | ||
0.780614 | − | 0.625013i | \(-0.214906\pi\) | |||||||
\(90\) | 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 | 0.608430 | − | 0.793607i | \(-0.291799\pi\) |
−0.991499 | + | 0.130113i | \(0.958466\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9607 | − | 8.63759i | 0.148126 | − | 0.0855206i | −0.424105 | − | 0.905613i | \(-0.639411\pi\) |
0.572231 | + | 0.820092i | \(0.306078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.0000 | − | 96.9948i | 0.543689 | − | 0.941698i | −0.454999 | − | 0.890492i | \(-0.650360\pi\) |
0.998688 | − | 0.0512055i | \(-0.0163063\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 141.144i | − | 1.31910i | −0.751660 | − | 0.659551i | \(-0.770746\pi\) | ||
0.751660 | − | 0.659551i | \(-0.229254\pi\) | |||||||
\(108\) | 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 | 0.521202 | − | 0.853433i | \(-0.325484\pi\) |
−0.478494 | + | 0.878091i | \(0.658817\pi\) | |||||||
\(114\) | 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 | −0.104975 | − | 0.994475i | \(-0.533476\pi\) |
−0.913728 | + | 0.406327i | \(0.866810\pi\) | |||||||
\(132\) | 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 | −0.238403 | − | 0.971166i | \(-0.576624\pi\) |
0.721854 | + | 0.692046i | \(0.243290\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −47.0192 | + | 81.4397i | −0.338268 | + | 0.585897i | −0.984107 | − | 0.177576i | \(-0.943174\pi\) |
0.645839 | + | 0.763474i | \(0.276508\pi\) | |||||||
\(140\) | 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 | 0.682316 | − | 0.731057i | \(-0.260973\pi\) |
−0.291956 | + | 0.956432i | \(0.594306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.1769 | − | 40.1436i | −0.153490 | − | 0.265852i | 0.779018 | − | 0.627001i | \(-0.215718\pi\) |
−0.932508 | + | 0.361149i | \(0.882384\pi\) | |||||||
\(152\) | 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 | −0.458808 | − | 0.888536i | \(-0.651723\pi\) |
0.998898 | − | 0.0469288i | \(-0.0149434\pi\) | |||||||
\(158\) | 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 | 0.762944 | − | 0.646465i | \(-0.223753\pi\) |
−0.178383 | + | 0.983961i | \(0.557087\pi\) | |||||||
\(168\) | 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 | 0.0502647 | − | 0.998736i | \(-0.483993\pi\) |
0.890063 | + | 0.455837i | \(0.150660\pi\) | |||||||
\(174\) | 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 | \(-0.985448\pi\) | ||
0.998955 | − | 0.0457021i | \(-0.0145525\pi\) | |||||||
\(180\) | 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 | −0.677151 | + | 0.735844i | \(0.736786\pi\) |
−0.975835 | + | 0.218508i | \(0.929881\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4423 | − | 21.5507i | 0.0644678 | − | 0.111662i | −0.831990 | − | 0.554791i | \(-0.812798\pi\) |
0.896458 | + | 0.443129i | \(0.146132\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 171.259i | 0.869333i | 0.900592 | + | 0.434666i | \(0.143134\pi\) | ||||
−0.900592 | + | 0.434666i | \(0.856866\pi\) | |||||||
\(198\) | 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 | 0.0344337 | − | 0.999407i | \(-0.489037\pi\) |
0.848295 | − | 0.529524i | \(-0.177629\pi\) | |||||||
\(212\) | 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 | 0.961887 | + | 0.273448i | \(0.0881640\pi\) |
−0.244131 | + | 0.969742i | \(0.578503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.1848 | − | 7.61227i | 0.0580830 | − | 0.0335342i | −0.470677 | − | 0.882305i | \(-0.655990\pi\) |
0.528760 | + | 0.848771i | \(0.322657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 89.8538 | − | 155.631i | 0.392375 | − | 0.679613i | −0.600387 | − | 0.799709i | \(-0.704987\pi\) |
0.992762 | + | 0.120096i | \(0.0383203\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 150.796i | − | 0.647193i | −0.946195 | − | 0.323596i | \(-0.895108\pi\) | ||
0.946195 | − | 0.323596i | \(-0.104892\pi\) | |||||||
\(234\) | 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 | 0.895738 | − | 0.444582i | \(-0.146648\pi\) |
0.0628500 | + | 0.998023i | \(0.479981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −114.225 | − | 197.844i | −0.473963 | − | 0.820927i | 0.525593 | − | 0.850736i | \(-0.323844\pi\) |
−0.999556 | + | 0.0298087i | \(0.990510\pi\) | |||||||
\(242\) | 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 | \(0.0300229\pi\) | ||||
−0.995555 | + | 0.0941798i | \(0.969977\pi\) | |||||||
\(252\) | 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 | 0.542824 | − | 0.839847i | \(-0.317355\pi\) |
−0.455917 | + | 0.890022i | \(0.650689\pi\) | |||||||
\(258\) | 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 | 0.0495095 | − | 0.998774i | \(-0.484234\pi\) |
0.889718 | + | 0.456510i | \(0.150901\pi\) | |||||||
\(264\) | 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 | \(0.124653\pi\) | ||||
−0.924297 | + | 0.381675i | \(0.875347\pi\) | |||||||
\(270\) | 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 | 0.818712 | − | 0.574205i | \(-0.194689\pi\) |
−0.906632 | + | 0.421923i | \(0.861355\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −213.659 | + | 123.356i | −0.760353 | + | 0.438990i | −0.829422 | − | 0.558622i | \(-0.811330\pi\) |
0.0690697 | + | 0.997612i | \(0.477997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 176.473 | − | 305.660i | 0.623580 | − | 1.08007i | −0.365234 | − | 0.930916i | \(-0.619011\pi\) |
0.988814 | − | 0.149156i | \(-0.0476556\pi\) | |||||||
\(284\) | 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 | 0.0260937 | − | 0.999660i | \(-0.491693\pi\) |
−0.852684 | + | 0.522428i | \(0.825027\pi\) | |||||||
\(294\) | 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 | 0.134539 | − | 0.990908i | \(-0.457045\pi\) |
−0.790882 | + | 0.611969i | \(0.790378\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 178.835 | + | 309.751i | 0.571357 | + | 0.989619i | 0.996427 | + | 0.0844583i | \(0.0269160\pi\) |
−0.425070 | + | 0.905160i | \(0.639751\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −523.067 | + | 301.993i | −1.65005 | + | 0.952659i | −0.673007 | + | 0.739636i | \(0.734998\pi\) |
−0.977047 | + | 0.213024i | \(0.931669\pi\) | |||||||
\(318\) | 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 | 0.892442 | − | 0.451163i | \(-0.148991\pi\) |
−0.836939 | + | 0.547295i | \(0.815657\pi\) | |||||||
\(332\) | 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 | −0.963434 | − | 0.267946i | \(-0.913655\pi\) |
0.713765 | + | 0.700385i | \(0.246988\pi\) | |||||||
\(338\) | 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 | 0.703924 | − | 0.710275i | \(-0.251430\pi\) |
−0.263154 | + | 0.964754i | \(0.584763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −65.6077 | − | 113.636i | −0.187988 | − | 0.325604i | 0.756592 | − | 0.653888i | \(-0.226863\pi\) |
−0.944579 | + | 0.328284i | \(0.893530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.7952 | + | 6.80994i | −0.0334140 | + | 0.0192916i | −0.516614 | − | 0.856218i | \(-0.672808\pi\) |
0.483200 | + | 0.875510i | \(0.339474\pi\) | |||||||
\(354\) | 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 | \(0.0429492\pi\) | ||||
−0.990911 | + | 0.134520i | \(0.957051\pi\) | |||||||
\(360\) | 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 | 0.638438 | − | 0.769674i | \(-0.279581\pi\) |
−0.985776 | + | 0.168067i | \(0.946248\pi\) | |||||||
\(368\) | 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 | −0.798485 | − | 0.602015i | \(-0.794365\pi\) |
0.920603 | + | 0.390501i | \(0.127698\pi\) | |||||||
\(374\) | 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 | 0.0738632 | − | 0.997268i | \(-0.476467\pi\) |
−0.826728 | + | 0.562602i | \(0.809801\pi\) | |||||||
\(384\) | 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 | −0.545080 | − | 0.838384i | \(-0.683501\pi\) |
0.453521 | + | 0.891245i | \(0.350168\pi\) | |||||||
\(390\) | 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 | −0.0529071 | − | 0.998599i | \(-0.516849\pi\) |
−0.891266 | + | 0.453481i | \(0.850182\pi\) | |||||||
\(402\) | 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 | −0.762955 | − | 0.646452i | \(-0.776252\pi\) |
0.941321 | + | 0.337512i | \(0.109585\pi\) | |||||||
\(410\) | 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 | 0.631515 | − | 0.775364i | \(-0.282434\pi\) |
−0.355728 | + | 0.934590i | \(0.615767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −144.346 | − | 250.015i | −0.342865 | − | 0.593859i | 0.642099 | − | 0.766622i | \(-0.278064\pi\) |
−0.984963 | + | 0.172763i | \(0.944731\pi\) | |||||||
\(422\) | 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 | \(0.283137\pi\) | ||||
−0.629800 | + | 0.776757i | \(0.716863\pi\) | |||||||
\(432\) | 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 | 0.818642 | − | 0.574304i | \(-0.194727\pi\) |
−0.906683 | + | 0.421813i | \(0.861394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 657.617 | − | 379.676i | 1.48446 | − | 0.857055i | 0.484620 | − | 0.874725i | \(-0.338958\pi\) |
0.999844 | + | 0.0176696i | \(0.00562472\pi\) | |||||||
\(444\) | 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 | \(0.205875\pi\) | ||||
−0.798032 | + | 0.602616i | \(0.794125\pi\) | |||||||
\(450\) | 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 | 0.894832 | − | 0.446404i | \(-0.147295\pi\) |
−0.834013 | + | 0.551745i | \(0.813962\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −217.114 | + | 125.351i | −0.470964 | + | 0.271911i | −0.716643 | − | 0.697440i | \(-0.754322\pi\) |
0.245679 | + | 0.969351i | \(0.420989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −285.512 | + | 494.520i | −0.616656 | + | 1.06808i | 0.373436 | + | 0.927656i | \(0.378180\pi\) |
−0.990092 | + | 0.140423i | \(0.955154\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 72.2663i | − | 0.154746i | −0.997002 | − | 0.0773729i | \(-0.975347\pi\) | ||
0.997002 | − | 0.0773729i | \(-0.0246532\pi\) | |||||||
\(468\) | 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 | −0.976701 | − | 0.214606i | \(-0.931153\pi\) |
−0.302496 | + | 0.953151i | \(0.597820\pi\) | |||||||
\(480\) | 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 | 0.960425 | − | 0.278538i | \(-0.0898498\pi\) |
0.238992 | + | 0.971022i | \(0.423183\pi\) | |||||||
\(492\) | 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 | −0.959903 | − | 0.280331i | \(-0.909556\pi\) |
0.722725 | + | 0.691135i | \(0.242889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 95.6715i | − | 0.190202i | −0.995468 | − | 0.0951009i | \(-0.969683\pi\) | ||
0.995468 | − | 0.0951009i | \(-0.0303174\pi\) | |||||||
\(504\) | 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 | 0.822252 | − | 0.569124i | \(-0.192718\pi\) |
−0.0817503 | + | 0.996653i | \(0.526051\pi\) | |||||||
\(510\) | 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 | \(0.276145\pi\) | ||||
−0.646709 | + | 0.762737i | \(0.723855\pi\) | |||||||
\(522\) | 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 | 0.999194 | + | 0.0401434i | \(0.0127815\pi\) |
−0.464832 | + | 0.885399i | \(0.653885\pi\) | |||||||
\(548\) | 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 | \(0.180093\pi\) | ||||
−0.844171 | + | 0.536075i | \(0.819907\pi\) | |||||||
\(558\) | 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 | 0.196676 | − | 0.980469i | \(-0.436985\pi\) |
−0.750773 | + | 0.660561i | \(0.770319\pi\) | |||||||
\(564\) | 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 | −0.862318 | − | 0.506368i | \(-0.830988\pi\) |
0.00736827 | + | 0.999973i | \(0.497655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0385 | − | 32.9756i | 0.0333423 | − | 0.0577506i | −0.848873 | − | 0.528597i | \(-0.822718\pi\) |
0.882215 | + | 0.470847i | \(0.156052\pi\) | |||||||
\(572\) | 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 | 0.0126092 | − | 0.999921i | \(-0.495986\pi\) |
0.872261 | + | 0.489040i | \(0.162653\pi\) | |||||||
\(588\) | 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 | \(0.0572561\pi\) | ||||
−0.983866 | + | 0.178907i | \(0.942744\pi\) | |||||||
\(594\) | 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 | 0.716323 | − | 0.697769i | \(-0.245824\pi\) |
−0.246124 | + | 0.969238i | \(0.579157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −373.738 | − | 647.334i | −0.621861 | − | 1.07709i | −0.989139 | − | 0.146983i | \(-0.953044\pi\) |
0.367278 | − | 0.930111i | \(-0.380290\pi\) | |||||||
\(602\) | 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 | −0.810558 | − | 0.585659i | \(-0.800836\pi\) |
0.912474 | + | 0.409134i | \(0.134169\pi\) | |||||||
\(608\) | 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 | 0.665158 | − | 0.746702i | \(-0.268364\pi\) |
−0.314084 | + | 0.949395i | \(0.601697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 508.769 | + | 881.214i | 0.821921 | + | 1.42361i | 0.904250 | + | 0.427004i | \(0.140431\pi\) |
−0.0823287 | + | 0.996605i | \(0.526236\pi\) | |||||||
\(620\) | 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 | −0.327259 | − | 0.944935i | \(-0.606125\pi\) |
0.654708 | + | 0.755882i | \(0.272791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 366.592 | − | 634.956i | 0.570128 | − | 0.987490i | −0.426424 | − | 0.904523i | \(-0.640227\pi\) |
0.996552 | − | 0.0829673i | \(-0.0264397\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1177.72i | 1.82028i | 0.414296 | + | 0.910142i | \(0.364028\pi\) | ||||
−0.414296 | + | 0.910142i | \(0.635972\pi\) | |||||||
\(648\) | 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 | 0.858112 | − | 0.513462i | \(-0.171637\pi\) |
−0.0156151 | + | 0.999878i | \(0.504971\pi\) | |||||||
\(654\) | 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 | 0.242770 | − | 0.970084i | \(-0.421944\pi\) |
0.961502 | + | 0.274797i | \(0.0886105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −206.679 | + | 357.978i | −0.312676 | + | 0.541571i | −0.978941 | − | 0.204145i | \(-0.934559\pi\) |
0.666265 | + | 0.745715i | \(0.267892\pi\) | |||||||
\(662\) | 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 | 0.998659 | + | 0.0517784i | \(0.0164890\pi\) |
−0.454488 | + | 0.890753i | \(0.650178\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −507.219 | + | 292.843i | −0.749215 | + | 0.432559i | −0.825410 | − | 0.564533i | \(-0.809056\pi\) |
0.0761952 | + | 0.997093i | \(0.475723\pi\) | |||||||
\(678\) | 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 | \(-0.708622\pi\) | ||
0.609480 | − | 0.792801i | \(-0.291378\pi\) | |||||||
\(684\) | 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 | 0.923312 | − | 0.384051i | \(-0.125471\pi\) |
−0.794254 | + | 0.607586i | \(0.792138\pi\) | |||||||
\(692\) | 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 | \(0.150407\pi\) | ||||
−0.890426 | + | 0.455129i | \(0.849593\pi\) | |||||||
\(702\) | 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 | −0.995278 | − | 0.0970614i | \(-0.969056\pi\) |
0.413582 | − | 0.910467i | \(-0.364278\pi\) | |||||||
\(710\) | 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 | \(-0.825753\pi\) | ||
0.853874 | − | 0.520480i | \(-0.174247\pi\) | |||||||
\(720\) | 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 | 0.856819 | − | 0.515617i | \(-0.172437\pi\) |
−0.874947 | + | 0.484219i | \(0.839104\pi\) | |||||||
\(728\) | 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 | −0.224189 | − | 0.974546i | \(-0.571973\pi\) |
0.956076 | − | 0.293119i | \(-0.0946934\pi\) | |||||||
\(734\) | 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 | 0.401331 | − | 0.915933i | \(-0.368548\pi\) |
−0.592556 | + | 0.805530i | \(0.701881\pi\) | |||||||
\(744\) | 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 | −0.932959 | − | 0.359984i | \(-0.882782\pi\) |
0.778234 | + | 0.627974i | \(0.216116\pi\) | |||||||
\(752\) | 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 | 0.132954 | − | 0.991122i | \(-0.457554\pi\) |
−0.791860 | + | 0.610703i | \(0.790887\pi\) | |||||||
\(762\) | 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 | −0.765960 | − | 0.642888i | \(-0.777736\pi\) |
0.939737 | + | 0.341897i | \(0.111069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1356.98i | − | 1.75548i | −0.479140 | − | 0.877739i | \(-0.659051\pi\) | ||
0.479140 | − | 0.877739i | \(-0.340949\pi\) | |||||||
\(774\) | 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 | −0.883826 | − | 0.467815i | \(-0.845041\pi\) |
0.847053 | + | 0.531508i | \(0.178375\pi\) | |||||||
\(788\) | 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 | 0.407736 | − | 0.913100i | \(-0.366318\pi\) |
−0.586900 | + | 0.809660i | \(0.699652\pi\) | |||||||
\(798\) | 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 | \(-0.792588\pi\) | ||
0.795113 | − | 0.606461i | \(-0.207412\pi\) | |||||||
\(810\) | 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 | −0.568071 | − | 0.822979i | \(-0.692310\pi\) |
0.428685 | + | 0.903454i | \(0.358977\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −243.096 | + | 421.055i | −0.295378 | + | 0.511610i | −0.975073 | − | 0.221885i | \(-0.928779\pi\) |
0.679695 | + | 0.733495i | \(0.262112\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 258.192i | 0.312203i | 0.987741 | + | 0.156101i | \(0.0498927\pi\) | ||||
−0.987741 | + | 0.156101i | \(0.950107\pi\) | |||||||
\(828\) | 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 | −0.642881 | − | 0.765966i | \(-0.722261\pi\) |
0.341905 | + | 0.939734i | \(0.388928\pi\) | |||||||
\(840\) | 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 | 0.803712 | − | 0.595019i | \(-0.202855\pi\) |
−0.917157 | + | 0.398525i | \(0.869522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −165.998 | + | 95.8387i | −0.193696 | + | 0.111830i | −0.593712 | − | 0.804678i | \(-0.702338\pi\) |
0.400016 | + | 0.916508i | \(0.369005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −598.258 | + | 1036.21i | −0.696458 | + | 1.20630i | 0.273228 | + | 0.961949i | \(0.411909\pi\) |
−0.969687 | + | 0.244352i | \(0.921425\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 692.323i | − | 0.802228i | −0.916028 | − | 0.401114i | \(-0.868623\pi\) | ||
0.916028 | − | 0.401114i | \(-0.131377\pi\) | |||||||
\(864\) | 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 | −0.409541 | − | 0.912292i | \(-0.634311\pi\) |
0.994838 | − | 0.101473i | \(-0.0323555\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 984.820i | 1.11784i | 0.829220 | + | 0.558922i | \(0.188785\pi\) | ||||
−0.829220 | + | 0.558922i | \(0.811215\pi\) | |||||||
\(882\) | 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 | 0.414933 | − | 0.909852i | \(-0.363805\pi\) |
−0.580488 | + | 0.814269i | \(0.697138\pi\) | |||||||
\(888\) | 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 | 0.590640 | − | 0.806936i | \(-0.298876\pi\) |
−0.994146 | + | 0.108041i | \(0.965542\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −853.652 | + | 492.856i | −0.937049 | + | 0.541006i | −0.889034 | − | 0.457841i | \(-0.848623\pi\) |
−0.0480151 | + | 0.998847i | \(0.515290\pi\) | |||||||
\(912\) | 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 | −0.752765 | − | 0.658289i | \(-0.771280\pi\) |
0.193712 | + | 0.981058i | \(0.437947\pi\) | |||||||
\(930\) | 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 | 0.846948 | − | 0.531675i | \(-0.178437\pi\) |
−0.0369704 | + | 0.999316i | \(0.511771\pi\) | |||||||
\(942\) | 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 | −0.877465 | − | 0.479641i | \(-0.840767\pi\) |
−0.0233509 | + | 0.999727i | \(0.507434\pi\) | |||||||
\(948\) | 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 | \(-0.853692\pi\) | ||
0.896212 | − | 0.443625i | \(-0.146308\pi\) | |||||||
\(954\) | 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 | −0.468352 | − | 0.883542i | \(-0.655152\pi\) |
0.999346 | − | 0.0361664i | \(-0.0115146\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 338.171i | 0.348271i | 0.984722 | + | 0.174135i | \(0.0557130\pi\) | ||||
−0.984722 | + | 0.174135i | \(0.944287\pi\) | |||||||
\(972\) | 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 | 0.846285 | − | 0.532730i | \(-0.178834\pi\) |
−0.0382151 | + | 0.999270i | \(0.512167\pi\) | |||||||
\(978\) | 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 | −0.858610 | − | 0.512629i | \(-0.828672\pi\) |
0.0146445 | + | 0.999893i | \(0.495338\pi\) | |||||||
\(984\) | 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 | 0.998546 | + | 0.0539130i | \(0.0171694\pi\) |
−0.452583 | + | 0.891722i | \(0.649497\pi\) | |||||||
\(998\) | 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.53.4 | 8 | ||
3.2 | odd | 2 | inner | 324.3.g.d.53.1 | 8 | ||
4.3 | odd | 2 | 1296.3.q.n.1025.4 | 8 | |||
9.2 | odd | 6 | inner | 324.3.g.d.269.4 | 8 | ||
9.4 | even | 3 | 324.3.c.a.161.1 | ✓ | 4 | ||
9.5 | odd | 6 | 324.3.c.a.161.4 | yes | 4 | ||
9.7 | even | 3 | inner | 324.3.g.d.269.1 | 8 | ||
12.11 | even | 2 | 1296.3.q.n.1025.1 | 8 | |||
36.7 | odd | 6 | 1296.3.q.n.593.1 | 8 | |||
36.11 | even | 6 | 1296.3.q.n.593.4 | 8 | |||
36.23 | even | 6 | 1296.3.e.f.161.4 | 4 | |||
36.31 | odd | 6 | 1296.3.e.f.161.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.3.c.a.161.1 | ✓ | 4 | 9.4 | even | 3 | ||
324.3.c.a.161.4 | yes | 4 | 9.5 | odd | 6 | ||
324.3.g.d.53.1 | 8 | 3.2 | odd | 2 | inner | ||
324.3.g.d.53.4 | 8 | 1.1 | even | 1 | trivial | ||
324.3.g.d.269.1 | 8 | 9.7 | even | 3 | inner | ||
324.3.g.d.269.4 | 8 | 9.2 | odd | 6 | inner | ||
1296.3.e.f.161.1 | 4 | 36.31 | odd | 6 | |||
1296.3.e.f.161.4 | 4 | 36.23 | even | 6 | |||
1296.3.q.n.593.1 | 8 | 36.7 | odd | 6 | |||
1296.3.q.n.593.4 | 8 | 36.11 | even | 6 | |||
1296.3.q.n.1025.1 | 8 | 12.11 | even | 2 | |||
1296.3.q.n.1025.4 | 8 | 4.3 | odd | 2 |