Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.u.226.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.207107 | − | 0.358719i | −0.0732233 | − | 0.126826i | 0.827089 | − | 0.562071i | \(-0.189995\pi\) |
−0.900312 | + | 0.435245i | \(0.856662\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.91421 | − | 6.77962i | 0.489277 | − | 0.847452i | ||||
\(5\) | −0.0502525 | − | 0.0870399i | −0.00449472 | − | 0.00778509i | 0.863769 | − | 0.503887i | \(-0.168097\pi\) |
−0.868264 | + | 0.496102i | \(0.834764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.55635 | −0.289752 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0208153 | + | 0.0360531i | −0.000658237 | + | 0.00114010i | ||||
\(11\) | −21.9706 | + | 38.0541i | −0.602216 | + | 1.04307i | 0.390269 | + | 0.920701i | \(0.372382\pi\) |
−0.992485 | + | 0.122368i | \(0.960951\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.6447 | −0.355108 | −0.177554 | − | 0.984111i | \(-0.556818\pi\) | ||||
−0.177554 | + | 0.984111i | \(0.556818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −29.9558 | − | 51.8850i | −0.468060 | − | 0.810704i | ||||
\(17\) | −60.8198 | + | 105.343i | −0.867704 | + | 1.50291i | −0.00336718 | + | 0.999994i | \(0.501072\pi\) |
−0.864337 | + | 0.502913i | \(0.832262\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 63.5563 | + | 110.083i | 0.767412 | + | 1.32920i | 0.938962 | + | 0.344021i | \(0.111789\pi\) |
−0.171550 | + | 0.985175i | \(0.554878\pi\) | |||||||
\(20\) | −0.786797 | −0.00879665 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.2010 | 0.176385 | ||||||||
\(23\) | 26.7990 | + | 46.4172i | 0.242955 | + | 0.420811i | 0.961555 | − | 0.274613i | \(-0.0885498\pi\) |
−0.718599 | + | 0.695424i | \(0.755216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.4949 | − | 108.244i | 0.499960 | − | 0.865955i | ||||
\(26\) | 3.44722 | + | 5.97076i | 0.0260021 | + | 0.0450370i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −235.681 | −1.50913 | −0.754567 | − | 0.656223i | \(-0.772153\pi\) | ||||
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.35534 | − | 16.2039i | 0.0542022 | − | 0.0938810i | −0.837651 | − | 0.546205i | \(-0.816072\pi\) |
0.891853 | + | 0.452324i | \(0.149405\pi\) | |||||||
\(32\) | −38.6335 | + | 66.9152i | −0.213422 | + | 0.369658i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 50.3848 | 0.254145 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 95.9411 | + | 166.175i | 0.426287 | + | 0.738351i | 0.996540 | − | 0.0831185i | \(-0.0264880\pi\) |
−0.570253 | + | 0.821469i | \(0.693155\pi\) | |||||||
\(38\) | 26.3259 | − | 45.5978i | 0.112385 | − | 0.194656i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.329473 | + | 0.570664i | 0.00130236 | + | 0.00225575i | ||||
\(41\) | 319.713 | 1.21782 | 0.608912 | − | 0.793238i | \(-0.291606\pi\) | ||||
0.608912 | + | 0.793238i | \(0.291606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −218.579 | −0.775184 | −0.387592 | − | 0.921831i | \(-0.626693\pi\) | ||||
−0.387592 | + | 0.921831i | \(0.626693\pi\) | |||||||
\(44\) | 171.995 | + | 297.904i | 0.589300 | + | 1.02070i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.1005 | − | 19.2266i | 0.0355800 | − | 0.0616264i | ||||
\(47\) | 200.777 | + | 347.755i | 0.623113 | + | 1.07926i | 0.988903 | + | 0.148565i | \(0.0474655\pi\) |
−0.365790 | + | 0.930697i | \(0.619201\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −51.7725 | −0.146435 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −65.1508 | + | 112.844i | −0.173746 | + | 0.300937i | ||||
\(53\) | 321.558 | − | 556.956i | 0.833386 | − | 1.44347i | −0.0619521 | − | 0.998079i | \(-0.519733\pi\) |
0.895338 | − | 0.445387i | \(-0.146934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.41631 | 0.0108272 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 48.8112 | + | 84.5434i | 0.110504 | + | 0.191398i | ||||
\(59\) | −5.80613 | + | 10.0565i | −0.0128118 | + | 0.0221906i | −0.872360 | − | 0.488864i | \(-0.837412\pi\) |
0.859548 | + | 0.511054i | \(0.170745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.12132 | + | 10.6024i | 0.0128484 | + | 0.0222541i | 0.872378 | − | 0.488832i | \(-0.162577\pi\) |
−0.859530 | + | 0.511086i | \(0.829243\pi\) | |||||||
\(62\) | −7.75022 | −0.0158755 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −447.288 | −0.873610 | ||||||||
\(65\) | 0.836436 | + | 1.44875i | 0.00159611 | + | 0.00276454i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −334.524 | + | 579.412i | −0.609979 | + | 1.05651i | 0.381264 | + | 0.924466i | \(0.375489\pi\) |
−0.991243 | + | 0.132049i | \(0.957844\pi\) | |||||||
\(68\) | 476.123 | + | 824.670i | 0.849095 | + | 1.47068i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −822.098 | −1.37416 | −0.687078 | − | 0.726584i | \(-0.741107\pi\) | ||||
−0.687078 | + | 0.726584i | \(0.741107\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −257.550 | + | 446.089i | −0.412930 | + | 0.715217i | −0.995209 | − | 0.0977730i | \(-0.968828\pi\) |
0.582278 | + | 0.812990i | \(0.302161\pi\) | |||||||
\(74\) | 39.7401 | − | 68.8319i | 0.0624283 | − | 0.108129i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 995.092 | 1.50191 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 402.877 | + | 697.804i | 0.573762 | + | 0.993786i | 0.996175 | + | 0.0873819i | \(0.0278500\pi\) |
−0.422413 | + | 0.906404i | \(0.638817\pi\) | |||||||
\(80\) | −3.01071 | + | 5.21471i | −0.00420760 | + | 0.00728778i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −66.2147 | − | 114.687i | −0.0891730 | − | 0.154452i | ||||
\(83\) | 394.863 | 0.522191 | 0.261095 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261095 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.2254 | 0.0156004 | ||||||||
\(86\) | 45.2691 | + | 78.4084i | 0.0567616 | + | 0.0983139i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 144.047 | − | 249.496i | 0.174493 | − | 0.302232i | ||||
\(89\) | 336.709 | + | 583.197i | 0.401024 | + | 0.694593i | 0.993850 | − | 0.110737i | \(-0.0353212\pi\) |
−0.592826 | + | 0.805331i | \(0.701988\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 419.588 | 0.475490 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 83.1644 | − | 144.045i | 0.0912527 | − | 0.158054i | ||||
\(95\) | 6.38773 | − | 11.0639i | 0.00689861 | − | 0.0119487i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1091.11 | −1.14212 | −0.571061 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571061 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −489.237 | − | 847.384i | −0.489237 | − | 0.847384i | ||||
\(101\) | −685.395 | + | 1187.14i | −0.675242 | + | 1.16955i | 0.301157 | + | 0.953575i | \(0.402627\pi\) |
−0.976398 | + | 0.215978i | \(0.930706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 706.978 | + | 1224.52i | 0.676316 | + | 1.17141i | 0.976082 | + | 0.217401i | \(0.0697581\pi\) |
−0.299766 | + | 0.954013i | \(0.596909\pi\) | |||||||
\(104\) | 109.128 | 0.102893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −266.388 | −0.244093 | ||||||||
\(107\) | −171.770 | − | 297.514i | −0.155192 | − | 0.268801i | 0.777937 | − | 0.628343i | \(-0.216266\pi\) |
−0.933129 | + | 0.359542i | \(0.882933\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 158.828 | − | 275.099i | 0.139569 | − | 0.241740i | −0.787765 | − | 0.615976i | \(-0.788762\pi\) |
0.927333 | + | 0.374236i | \(0.122095\pi\) | |||||||
\(110\) | −0.914647 | − | 1.58421i | −0.000792801 | − | 0.00137317i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −798.373 | −0.664643 | −0.332321 | − | 0.943166i | \(-0.607832\pi\) | ||||
−0.332321 | + | 0.943166i | \(0.607832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.69343 | − | 4.66516i | 0.00218404 | − | 0.00378286i | ||||
\(116\) | −922.507 | + | 1597.83i | −0.738384 | + | 1.27892i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.80996 | 0.00375248 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −299.911 | − | 519.462i | −0.225328 | − | 0.390279i | ||||
\(122\) | 2.53553 | − | 4.39167i | 0.00188161 | − | 0.00325904i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −73.2376 | − | 126.851i | −0.0530398 | − | 0.0918676i | ||||
\(125\) | −25.1253 | −0.0179782 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1071.40 | 0.748593 | 0.374297 | − | 0.927309i | \(-0.377884\pi\) | ||||
0.374297 | + | 0.927309i | \(0.377884\pi\) | |||||||
\(128\) | 401.705 | + | 695.773i | 0.277391 | + | 0.480455i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.346463 | − | 0.600092i | 0.000233745 | − | 0.000404858i | ||||
\(131\) | −1257.51 | − | 2178.07i | −0.838695 | − | 1.45266i | −0.890986 | − | 0.454031i | \(-0.849986\pi\) |
0.0522910 | − | 0.998632i | \(-0.483348\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 277.129 | 0.178659 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 398.756 | − | 690.665i | 0.251419 | − | 0.435471i | ||||
\(137\) | 125.532 | − | 217.428i | 0.0782841 | − | 0.135592i | −0.824226 | − | 0.566262i | \(-0.808389\pi\) |
0.902510 | + | 0.430670i | \(0.141723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 886.067 | 0.540685 | 0.270343 | − | 0.962764i | \(-0.412863\pi\) | ||||
0.270343 | + | 0.962764i | \(0.412863\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 170.262 | + | 294.902i | 0.100620 | + | 0.174279i | ||||
\(143\) | 365.693 | − | 633.398i | 0.213851 | − | 0.370401i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.8436 | + | 20.5137i | 0.00678314 | + | 0.0117487i | ||||
\(146\) | 213.361 | 0.120945 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1502.14 | 0.834289 | ||||||||
\(149\) | 291.313 | + | 504.569i | 0.160170 | + | 0.277422i | 0.934929 | − | 0.354834i | \(-0.115463\pi\) |
−0.774760 | + | 0.632256i | \(0.782129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1405.88 | − | 2435.06i | 0.757676 | − | 1.31233i | −0.186357 | − | 0.982482i | \(-0.559668\pi\) |
0.944033 | − | 0.329851i | \(-0.106999\pi\) | |||||||
\(152\) | −416.698 | − | 721.741i | −0.222359 | − | 0.385138i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.88052 | −0.000974496 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 845.672 | − | 1464.75i | 0.429885 | − | 0.744583i | −0.566978 | − | 0.823733i | \(-0.691887\pi\) |
0.996863 | + | 0.0791504i | \(0.0252207\pi\) | |||||||
\(158\) | 166.877 | − | 289.040i | 0.0840256 | − | 0.145537i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.76573 | 0.00383709 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3616 | + | 35.2674i | 0.00978432 | + | 0.0169469i | 0.870876 | − | 0.491503i | \(-0.163552\pi\) |
−0.861092 | + | 0.508450i | \(0.830219\pi\) | |||||||
\(164\) | 1251.42 | − | 2167.53i | 0.595852 | − | 1.03205i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −81.7788 | − | 141.645i | −0.0382365 | − | 0.0662276i | ||||
\(167\) | −2900.47 | −1.34398 | −0.671990 | − | 0.740560i | \(-0.734560\pi\) | ||||
−0.671990 | + | 0.740560i | \(0.734560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1919.96 | −0.873899 | ||||||||
\(170\) | −2.53196 | − | 4.38549i | −0.00114231 | − | 0.00197854i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −855.563 | + | 1481.88i | −0.379280 | + | 0.656932i | ||||
\(173\) | −1073.07 | − | 1858.62i | −0.471585 | − | 0.816810i | 0.527886 | − | 0.849315i | \(-0.322985\pi\) |
−0.999472 | + | 0.0325052i | \(0.989651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2632.59 | 1.12749 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 139.470 | − | 241.568i | 0.0587286 | − | 0.101721i | ||||
\(179\) | 601.770 | − | 1042.30i | 0.251276 | − | 0.435222i | −0.712602 | − | 0.701569i | \(-0.752483\pi\) |
0.963877 | + | 0.266347i | \(0.0858166\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2990.47 | −1.22807 | −0.614033 | − | 0.789280i | \(-0.710454\pi\) | ||||
−0.614033 | + | 0.789280i | \(0.710454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −175.704 | − | 304.327i | −0.0703969 | − | 0.121931i | ||||
\(185\) | 9.64257 | − | 16.7014i | 0.00383209 | − | 0.00663737i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2672.49 | − | 4628.89i | −1.04509 | − | 1.81015i | ||||
\(188\) | 3143.53 | 1.21950 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.29177 | −0.00202056 | ||||||||
\(191\) | −1403.70 | − | 2431.29i | −0.531772 | − | 0.921057i | −0.999312 | − | 0.0370847i | \(-0.988193\pi\) |
0.467540 | − | 0.883972i | \(-0.345140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1668.18 | + | 2889.38i | −0.622169 | + | 1.07763i | 0.366913 | + | 0.930255i | \(0.380415\pi\) |
−0.989081 | + | 0.147372i | \(0.952919\pi\) | |||||||
\(194\) | 225.977 | + | 391.404i | 0.0836299 | + | 0.144851i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4226.65 | 1.52861 | 0.764305 | − | 0.644855i | \(-0.223082\pi\) | ||||
0.764305 | + | 0.644855i | \(0.223082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2192.85 | + | 3798.12i | −0.781140 | + | 1.35297i | 0.150139 | + | 0.988665i | \(0.452028\pi\) |
−0.931278 | + | 0.364309i | \(0.881305\pi\) | |||||||
\(200\) | −409.739 | + | 709.688i | −0.144865 | + | 0.250913i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 567.800 | 0.197774 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0664 | − | 27.8278i | −0.00547378 | − | 0.00948086i | ||||
\(206\) | 292.840 | − | 507.213i | 0.0990442 | − | 0.171550i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 498.605 | + | 863.609i | 0.166212 | + | 0.287887i | ||||
\(209\) | −5585.48 | −1.84859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2291.56 | 0.747665 | 0.373833 | − | 0.927496i | \(-0.378043\pi\) | ||||
0.373833 | + | 0.927496i | \(0.378043\pi\) | |||||||
\(212\) | −2517.30 | − | 4360.09i | −0.815513 | − | 1.41251i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −71.1493 | + | 123.234i | −0.0227274 | + | 0.0393650i | ||||
\(215\) | 10.9841 | + | 19.0251i | 0.00348424 | + | 0.00603488i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −131.578 | −0.0408788 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.2864 | − | 29.9409i | 0.00529748 | − | 0.00917551i | ||||
\(221\) | 1012.33 | − | 1753.40i | 0.308128 | − | 0.533694i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −217.970 | −0.0654544 | −0.0327272 | − | 0.999464i | \(-0.510419\pi\) | ||||
−0.0327272 | + | 0.999464i | \(0.510419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 165.349 | + | 286.392i | 0.0486674 | + | 0.0842943i | ||||
\(227\) | 917.680 | − | 1589.47i | 0.268320 | − | 0.464743i | −0.700108 | − | 0.714037i | \(-0.746865\pi\) |
0.968428 | + | 0.249293i | \(0.0801983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1387.00 | − | 2402.36i | −0.400244 | − | 0.693243i | 0.593511 | − | 0.804826i | \(-0.297741\pi\) |
−0.993755 | + | 0.111583i | \(0.964408\pi\) | |||||||
\(230\) | −2.23131 | −0.000639689 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1545.21 | 0.437275 | ||||||||
\(233\) | −494.356 | − | 856.250i | −0.138997 | − | 0.240750i | 0.788120 | − | 0.615522i | \(-0.211055\pi\) |
−0.927117 | + | 0.374771i | \(0.877721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.1791 | − | 34.9512i | 0.00560144 | − | 0.00970197i | ||||
\(236\) | 45.4529 | + | 78.7267i | 0.0125370 | + | 0.0217147i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 837.928 | 0.226783 | 0.113391 | − | 0.993550i | \(-0.463829\pi\) | ||||
0.113391 | + | 0.993550i | \(0.463829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1727.49 | − | 2992.11i | 0.461733 | − | 0.799745i | −0.537315 | − | 0.843382i | \(-0.680561\pi\) |
0.999047 | + | 0.0436371i | \(0.0138945\pi\) | |||||||
\(242\) | −124.227 | + | 215.168i | −0.0329985 | + | 0.0571551i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 95.8406 | 0.0251458 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1057.87 | − | 1832.29i | −0.272514 | − | 0.472008i | ||||
\(248\) | −61.3369 | + | 106.239i | −0.0157052 | + | 0.0272022i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.20361 | + | 9.01292i | 0.00131642 | + | 0.00228011i | ||||
\(251\) | −5635.01 | −1.41705 | −0.708523 | − | 0.705688i | \(-0.750638\pi\) | ||||
−0.708523 | + | 0.705688i | \(0.750638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2355.16 | −0.585246 | ||||||||
\(254\) | −221.894 | − | 384.332i | −0.0548145 | − | 0.0949414i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1622.76 | + | 2810.71i | −0.396182 | + | 0.686208i | ||||
\(257\) | −1135.58 | − | 1966.88i | −0.275624 | − | 0.477395i | 0.694668 | − | 0.719330i | \(-0.255551\pi\) |
−0.970292 | + | 0.241935i | \(0.922218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.0960 | 0.00312376 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −520.877 | + | 902.186i | −0.122824 | + | 0.212737i | ||||
\(263\) | 81.9336 | − | 141.913i | 0.0192101 | − | 0.0332728i | −0.856261 | − | 0.516544i | \(-0.827218\pi\) |
0.875471 | + | 0.483271i | \(0.160552\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −64.6365 | −0.0149834 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2618.80 | + | 4535.89i | 0.596897 | + | 1.03386i | ||||
\(269\) | −2583.55 | + | 4474.84i | −0.585582 | + | 1.01426i | 0.409220 | + | 0.912436i | \(0.365801\pi\) |
−0.994803 | + | 0.101823i | \(0.967533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 811.136 | + | 1404.93i | 0.181819 | + | 0.314920i | 0.942500 | − | 0.334206i | \(-0.108468\pi\) |
−0.760681 | + | 0.649126i | \(0.775135\pi\) | |||||||
\(272\) | 7287.63 | 1.62455 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −103.994 | −0.0229289 | ||||||||
\(275\) | 2746.10 | + | 4756.38i | 0.602167 | + | 1.04298i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2306.18 | − | 3994.43i | 0.500235 | − | 0.866433i | −0.499765 | − | 0.866161i | \(-0.666580\pi\) |
1.00000 | 0.000271708i | \(-8.64874e-5\pi\) | ||||||||
\(278\) | −183.511 | − | 317.850i | −0.0395908 | − | 0.0685732i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2125.22 | 0.451174 | 0.225587 | − | 0.974223i | \(-0.427570\pi\) | ||||
0.225587 | + | 0.974223i | \(0.427570\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1285.77 | + | 2227.02i | −0.270075 | + | 0.467783i | −0.968881 | − | 0.247528i | \(-0.920382\pi\) |
0.698806 | + | 0.715311i | \(0.253715\pi\) | |||||||
\(284\) | −3217.87 | + | 5573.51i | −0.672342 | + | 1.16453i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −302.950 | −0.0626356 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4941.60 | − | 8559.10i | −1.00582 | − | 1.74213i | ||||
\(290\) | 4.90577 | − | 8.49704i | 0.000993368 | − | 0.00172056i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2016.21 | + | 3492.18i | 0.404075 | + | 0.699878i | ||||
\(293\) | 3324.96 | 0.662957 | 0.331478 | − | 0.943463i | \(-0.392453\pi\) | ||||
0.331478 | + | 0.943463i | \(0.392453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.16709 | 0.000230341 | ||||||||
\(296\) | −629.024 | − | 1089.50i | −0.123518 | − | 0.213939i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 120.666 | − | 208.999i | 0.0234563 | − | 0.0406275i | ||||
\(299\) | −446.060 | − | 772.599i | −0.0862753 | − | 0.149433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1164.67 | −0.221918 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3807.77 | − | 6595.25i | 0.718390 | − | 1.24429i | ||||
\(305\) | 0.615224 | − | 1.06560i | 0.000115500 | − | 0.000200052i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 887.096 | 0.164916 | 0.0824580 | − | 0.996595i | \(-0.473723\pi\) | ||||
0.0824580 | + | 0.996595i | \(0.473723\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.389468 | + | 0.674578i | 7.13558e−5 | + | 0.000123592i | ||||
\(311\) | 2255.41 | − | 3906.48i | 0.411230 | − | 0.712271i | −0.583794 | − | 0.811902i | \(-0.698433\pi\) |
0.995025 | + | 0.0996300i | \(0.0317659\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1857.89 | + | 3217.96i | 0.335509 | + | 0.581118i | 0.983582 | − | 0.180459i | \(-0.0577584\pi\) |
−0.648074 | + | 0.761578i | \(0.724425\pi\) | |||||||
\(314\) | −700.577 | −0.125910 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6307.79 | 1.12291 | ||||||||
\(317\) | 3477.26 | + | 6022.79i | 0.616096 | + | 1.06711i | 0.990191 | + | 0.139719i | \(0.0446200\pi\) |
−0.374095 | + | 0.927390i | \(0.622047\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5178.05 | − | 8968.64i | 0.908825 | − | 1.57413i | ||||
\(320\) | 22.4774 | + | 38.9320i | 0.00392664 | + | 0.00680113i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15461.9 | −2.66355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1040.21 | + | 1801.69i | −0.177539 | + | 0.307507i | ||||
\(326\) | 8.43406 | − | 14.6082i | 0.00143288 | − | 0.00248182i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2096.15 | −0.352867 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4931.59 | + | 8541.76i | 0.818926 | + | 1.41842i | 0.906474 | + | 0.422262i | \(0.138764\pi\) |
−0.0875478 | + | 0.996160i | \(0.527903\pi\) | |||||||
\(332\) | 1545.58 | − | 2677.02i | 0.255496 | − | 0.442532i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 600.706 | + | 1040.45i | 0.0984107 | + | 0.170452i | ||||
\(335\) | 67.2427 | 0.0109668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5945.06 | −0.960974 | −0.480487 | − | 0.877002i | \(-0.659540\pi\) | ||||
−0.480487 | + | 0.877002i | \(0.659540\pi\) | |||||||
\(338\) | 397.636 | + | 688.725i | 0.0639897 | + | 0.110833i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 47.8528 | − | 82.8835i | 0.00763289 | − | 0.0132206i | ||||
\(341\) | 411.084 | + | 712.019i | 0.0652829 | + | 0.113073i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1433.08 | 0.224612 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −444.482 | + | 769.865i | −0.0690621 | + | 0.119619i | ||||
\(347\) | 584.786 | − | 1012.88i | 0.0904697 | − | 0.156698i | −0.817239 | − | 0.576299i | \(-0.804497\pi\) |
0.907709 | + | 0.419601i | \(0.137830\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9176.66 | 1.40749 | 0.703747 | − | 0.710451i | \(-0.251509\pi\) | ||||
0.703747 | + | 0.710451i | \(0.251509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1697.60 | − | 2940.33i | −0.257052 | − | 0.445228i | ||||
\(353\) | −5293.60 | + | 9168.78i | −0.798158 | + | 1.38245i | 0.122656 | + | 0.992449i | \(0.460859\pi\) |
−0.920814 | + | 0.390001i | \(0.872474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 41.3125 | + | 71.5553i | 0.00617645 | + | 0.0106979i | ||||
\(356\) | 5271.81 | 0.784846 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −498.522 | −0.0735970 | ||||||||
\(359\) | 4307.61 | + | 7460.99i | 0.633278 | + | 1.09687i | 0.986877 | + | 0.161472i | \(0.0516243\pi\) |
−0.353599 | + | 0.935397i | \(0.615042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4649.32 | + | 8052.86i | −0.677842 | + | 1.17406i | ||||
\(362\) | 619.347 | + | 1072.74i | 0.0899230 | + | 0.155751i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 51.7701 | 0.00742403 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4148.89 | − | 7186.10i | 0.590110 | − | 1.02210i | −0.404107 | − | 0.914712i | \(-0.632418\pi\) |
0.994217 | − | 0.107389i | \(-0.0342492\pi\) | |||||||
\(368\) | 1605.57 | − | 2780.93i | 0.227436 | − | 0.393930i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.98817 | −0.00112239 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2561.93 | + | 4437.39i | 0.355634 | + | 0.615977i | 0.987226 | − | 0.159324i | \(-0.0509315\pi\) |
−0.631592 | + | 0.775301i | \(0.717598\pi\) | |||||||
\(374\) | −1106.98 | + | 1917.35i | −0.153050 | + | 0.265090i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1316.36 | − | 2280.01i | −0.180548 | − | 0.312719i | ||||
\(377\) | 3922.83 | 0.535905 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1502.49 | −0.203635 | −0.101817 | − | 0.994803i | \(-0.532466\pi\) | ||||
−0.101817 | + | 0.994803i | \(0.532466\pi\) | |||||||
\(380\) | −50.0059 | − | 86.6128i | −0.00675066 | − | 0.0116925i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −581.434 | + | 1007.07i | −0.0778763 | + | 0.134886i | ||||
\(383\) | 5436.47 | + | 9416.24i | 0.725301 | + | 1.25626i | 0.958850 | + | 0.283914i | \(0.0916330\pi\) |
−0.233548 | + | 0.972345i | \(0.575034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1381.97 | 0.182229 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4270.85 | + | 7397.33i | −0.558814 | + | 0.967894i | ||||
\(389\) | 2309.50 | − | 4000.16i | 0.301018 | − | 0.521379i | −0.675349 | − | 0.737499i | \(-0.736007\pi\) |
0.976367 | + | 0.216120i | \(0.0693402\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6519.64 | −0.843254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −875.367 | − | 1516.18i | −0.111930 | − | 0.193868i | ||||
\(395\) | 40.4912 | − | 70.1328i | 0.00515781 | − | 0.00893358i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4803.48 | + | 8319.86i | 0.607253 | + | 1.05179i | 0.991691 | + | 0.128642i | \(0.0410620\pi\) |
−0.384438 | + | 0.923151i | \(0.625605\pi\) | |||||||
\(398\) | 1816.61 | 0.228791 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7488.36 | −0.936044 | ||||||||
\(401\) | −5250.52 | − | 9094.17i | −0.653862 | − | 1.13252i | −0.982178 | − | 0.187954i | \(-0.939814\pi\) |
0.328316 | − | 0.944568i | \(-0.393519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −155.716 | + | 269.709i | −0.0192476 | + | 0.0333378i | ||||
\(404\) | 5365.57 | + | 9293.44i | 0.660760 | + | 1.14447i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8431.52 | −1.02687 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6033.47 | + | 10450.3i | −0.729427 | + | 1.26340i | 0.227699 | + | 0.973732i | \(0.426880\pi\) |
−0.957126 | + | 0.289673i | \(0.906453\pi\) | |||||||
\(410\) | −6.65491 | + | 11.5266i | −0.000801616 | + | 0.00138844i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11069.0 | 1.32362 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.8429 | − | 34.3688i | −0.00234710 | − | 0.00406530i | ||||
\(416\) | 643.042 | − | 1113.78i | 0.0757878 | − | 0.131268i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1156.79 | + | 2003.62i | 0.135360 | + | 0.234450i | ||||
\(419\) | −6366.31 | −0.742278 | −0.371139 | − | 0.928577i | \(-0.621033\pi\) | ||||
−0.371139 | + | 0.928577i | \(0.621033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4731.84 | −0.547781 | −0.273890 | − | 0.961761i | \(-0.588311\pi\) | ||||
−0.273890 | + | 0.961761i | \(0.588311\pi\) | |||||||
\(422\) | −474.597 | − | 822.026i | −0.0547465 | − | 0.0948237i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2108.25 | + | 3651.60i | −0.241476 | + | 0.418248i | ||||
\(425\) | 7601.86 | + | 13166.8i | 0.867634 | + | 1.50279i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2689.37 | −0.303728 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.54978 | − | 7.88044i | 0.000510255 | − | 0.000883788i | ||||
\(431\) | 1876.39 | − | 3250.01i | 0.209704 | − | 0.363219i | −0.741917 | − | 0.670492i | \(-0.766083\pi\) |
0.951621 | + | 0.307273i | \(0.0994165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11709.2 | −1.29956 | −0.649780 | − | 0.760122i | \(-0.725139\pi\) | ||||
−0.649780 | + | 0.760122i | \(0.725139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1243.38 | − | 2153.59i | −0.136576 | − | 0.236556i | ||||
\(437\) | −3406.49 | + | 5900.22i | −0.372894 | + | 0.645871i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7462.36 | − | 12925.2i | −0.811296 | − | 1.40521i | −0.911957 | − | 0.410285i | \(-0.865429\pi\) |
0.100661 | − | 0.994921i | \(-0.467904\pi\) | |||||||
\(440\) | −28.9548 | −0.00313720 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −838.638 | −0.0902487 | ||||||||
\(443\) | −4258.83 | − | 7376.51i | −0.456756 | − | 0.791125i | 0.542031 | − | 0.840359i | \(-0.317656\pi\) |
−0.998787 | + | 0.0492333i | \(0.984322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.8410 | − | 58.6143i | 0.00360498 | − | 0.00624401i | ||||
\(446\) | 45.1430 | + | 78.1900i | 0.00479279 | + | 0.00830135i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5965.73 | 0.627038 | 0.313519 | − | 0.949582i | \(-0.398492\pi\) | ||||
0.313519 | + | 0.949582i | \(0.398492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7024.27 | + | 12166.4i | −0.733392 | + | 1.27027i | ||||
\(452\) | −3125.00 | + | 5412.67i | −0.325194 | + | 0.563253i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −760.231 | −0.0785890 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6930.28 | + | 12003.6i | 0.709376 | + | 1.22868i | 0.965089 | + | 0.261923i | \(0.0843567\pi\) |
−0.255712 | + | 0.966753i | \(0.582310\pi\) | |||||||
\(458\) | −574.516 | + | 995.091i | −0.0586143 | + | 0.101523i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.0854 | − | 36.5209i | −0.00213719 | − | 0.00370173i | ||||
\(461\) | −149.312 | −0.0150850 | −0.00754249 | − | 0.999972i | \(-0.502401\pi\) | ||||
−0.00754249 | + | 0.999972i | \(0.502401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5403.95 | 0.542425 | 0.271213 | − | 0.962519i | \(-0.412575\pi\) | ||||
0.271213 | + | 0.962519i | \(0.412575\pi\) | |||||||
\(464\) | 7060.03 | + | 12228.3i | 0.706366 | + | 1.22346i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −204.769 | + | 354.670i | −0.0203557 | + | 0.0352571i | ||||
\(467\) | −1852.33 | − | 3208.33i | −0.183545 | − | 0.317909i | 0.759540 | − | 0.650460i | \(-0.225424\pi\) |
−0.943085 | + | 0.332551i | \(0.892091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.7169 | −0.00164062 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 38.0670 | − | 65.9340i | 0.00371224 | − | 0.00642979i | ||||
\(473\) | 4802.30 | − | 8317.82i | 0.466828 | − | 0.808570i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15887.8 | 1.53470 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −173.540 | − | 300.581i | −0.0166058 | − | 0.0287620i | ||||
\(479\) | 5335.88 | − | 9242.02i | 0.508982 | − | 0.881583i | −0.490963 | − | 0.871180i | \(-0.663355\pi\) |
0.999946 | − | 0.0104033i | \(-0.00331152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1596.91 | − | 2765.92i | −0.151378 | − | 0.262194i | ||||
\(482\) | −1431.10 | −0.135238 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4695.67 | −0.440990 | ||||||||
\(485\) | 54.8312 | + | 94.9705i | 0.00513352 | + | 0.00889152i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2926.96 | + | 5069.65i | −0.272348 | + | 0.471720i | −0.969463 | − | 0.245239i | \(-0.921133\pi\) |
0.697115 | + | 0.716959i | \(0.254467\pi\) | |||||||
\(488\) | −40.1335 | − | 69.5133i | −0.00372287 | − | 0.00644819i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4065.31 | −0.373656 | −0.186828 | − | 0.982393i | \(-0.559821\pi\) | ||||
−0.186828 | + | 0.982393i | \(0.559821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14334.1 | − | 24827.4i | 1.30948 | − | 2.26809i | ||||
\(494\) | −438.186 | + | 758.960i | −0.0399087 | + | 0.0691239i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1120.99 | −0.101480 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2405.59 | − | 4166.61i | −0.215810 | − | 0.373794i | 0.737713 | − | 0.675115i | \(-0.235906\pi\) |
−0.953523 | + | 0.301321i | \(0.902572\pi\) | |||||||
\(500\) | −98.3456 | + | 170.340i | −0.00879630 | + | 0.0152356i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1167.05 | + | 2021.39i | 0.103761 | + | 0.179719i | ||||
\(503\) | 17001.2 | 1.50705 | 0.753526 | − | 0.657418i | \(-0.228351\pi\) | ||||
0.753526 | + | 0.657418i | \(0.228351\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 137.771 | 0.0121401 | ||||||||
\(506\) | 487.769 | + | 844.840i | 0.0428537 | + | 0.0742248i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4193.69 | − | 7263.68i | 0.366269 | − | 0.634397i | ||||
\(509\) | −6898.61 | − | 11948.7i | −0.600738 | − | 1.04051i | −0.992710 | − | 0.120531i | \(-0.961540\pi\) |
0.391972 | − | 0.919977i | \(-0.371793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7771.61 | 0.670820 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −470.372 | + | 814.708i | −0.0403642 | + | 0.0699129i | ||||
\(515\) | 71.0548 | − | 123.071i | 0.00607971 | − | 0.0105304i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17644.7 | −1.50099 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.48397 | − | 9.49851i | −0.000462477 | − | 0.000801033i | ||||
\(521\) | −1968.31 | + | 3409.21i | −0.165515 | + | 0.286680i | −0.936838 | − | 0.349764i | \(-0.886262\pi\) |
0.771323 | + | 0.636443i | \(0.219595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8729.63 | + | 15120.2i | 0.729866 | + | 1.26417i | 0.956939 | + | 0.290288i | \(0.0937510\pi\) |
−0.227073 | + | 0.973878i | \(0.572916\pi\) | |||||||
\(524\) | −19688.6 | −1.64142 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −67.8760 | −0.00562649 | ||||||||
\(527\) | 1137.98 | + | 1971.04i | 0.0940630 | + | 0.162922i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4647.13 | − | 8049.06i | 0.381945 | − | 0.661549i | ||||
\(530\) | 13.3867 | + | 23.1864i | 0.00109713 | + | 0.00190029i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5321.51 | −0.432458 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.2637 | + | 29.9016i | −0.00139509 | + | 0.00241637i | ||||
\(536\) | 2193.26 | − | 3798.83i | 0.176743 | − | 0.306128i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2140.28 | 0.171513 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9550.66 | − | 16542.2i | −0.758992 | − | 1.31461i | −0.943365 | − | 0.331757i | \(-0.892359\pi\) |
0.184373 | − | 0.982856i | \(-0.440975\pi\) | |||||||
\(542\) | 335.983 | − | 581.940i | 0.0266268 | − | 0.0461190i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4699.37 | − | 8139.54i | −0.370374 | − | 0.641507i | ||||
\(545\) | −31.9261 | −0.00250929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15413.5 | 1.20481 | 0.602407 | − | 0.798189i | \(-0.294208\pi\) | ||||
0.602407 | + | 0.798189i | \(0.294208\pi\) | |||||||
\(548\) | −982.718 | − | 1702.12i | −0.0766052 | − | 0.132684i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1137.47 | − | 1970.16i | 0.0881853 | − | 0.152741i | ||||
\(551\) | −14979.0 | − | 25944.5i | −1.15813 | − | 2.00594i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1910.51 | −0.146516 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3468.26 | − | 6007.20i | 0.264545 | − | 0.458205i | ||||
\(557\) | −10246.4 | + | 17747.3i | −0.779453 | + | 1.35005i | 0.152804 | + | 0.988257i | \(0.451170\pi\) |
−0.932257 | + | 0.361796i | \(0.882164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3638.17 | 0.275274 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −440.147 | − | 762.357i | −0.0330364 | − | 0.0572208i | ||||
\(563\) | 3571.24 | − | 6185.57i | 0.267336 | − | 0.463039i | −0.700837 | − | 0.713321i | \(-0.747190\pi\) |
0.968173 | + | 0.250282i | \(0.0805234\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.1203 | + | 69.4904i | 0.00298739 | + | 0.00517430i | ||||
\(566\) | 1065.17 | 0.0791030 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5389.96 | 0.398165 | ||||||||
\(569\) | 2048.96 | + | 3548.90i | 0.150961 | + | 0.261472i | 0.931581 | − | 0.363534i | \(-0.118430\pi\) |
−0.780620 | + | 0.625006i | \(0.785097\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1419.24 | − | 2458.20i | 0.104016 | − | 0.180162i | −0.809320 | − | 0.587369i | \(-0.800164\pi\) |
0.913336 | + | 0.407207i | \(0.133497\pi\) | |||||||
\(572\) | −2862.80 | − | 4958.51i | −0.209265 | − | 0.362458i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6699.21 | 0.485872 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7732.23 | + | 13392.6i | −0.557881 | + | 0.966277i | 0.439793 | + | 0.898099i | \(0.355052\pi\) |
−0.997673 | + | 0.0681781i | \(0.978281\pi\) | |||||||
\(578\) | −2046.88 | + | 3545.29i | −0.147299 | + | 0.255129i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 185.433 | 0.0132753 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14129.6 | + | 24473.3i | 1.00376 | + | 1.73856i | ||||
\(584\) | 1688.59 | − | 2924.72i | 0.119648 | − | 0.207236i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −688.622 | − | 1192.73i | −0.0485439 | − | 0.0840805i | ||||
\(587\) | 14003.6 | 0.984652 | 0.492326 | − | 0.870411i | \(-0.336147\pi\) | ||||
0.492326 | + | 0.870411i | \(0.336147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2378.36 | 0.166382 | ||||||||
\(590\) | −0.241713 | − | 0.418658i | −1.68664e−5 | − | 2.92134e-5i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5747.99 | − | 9955.82i | 0.399056 | − | 0.691185i | ||||
\(593\) | −3252.25 | − | 5633.06i | −0.225217 | − | 0.390088i | 0.731167 | − | 0.682198i | \(-0.238976\pi\) |
−0.956385 | + | 0.292110i | \(0.905643\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4561.04 | 0.313469 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −184.764 | + | 320.021i | −0.0126347 | + | 0.0218840i | ||||
\(599\) | −6308.05 | + | 10925.9i | −0.430284 | + | 0.745273i | −0.996898 | − | 0.0787104i | \(-0.974920\pi\) |
0.566614 | + | 0.823983i | \(0.308253\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8270.87 | −0.561358 | −0.280679 | − | 0.959802i | \(-0.590560\pi\) | ||||
−0.280679 | + | 0.959802i | \(0.590560\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11005.8 | − | 19062.7i | −0.741426 | − | 1.28419i | ||||
\(605\) | −30.1426 | + | 52.2085i | −0.00202557 | + | 0.00350839i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1905.92 | + | 3301.15i | 0.127445 | + | 0.220740i | 0.922686 | − | 0.385553i | \(-0.125989\pi\) |
−0.795241 | + | 0.606293i | \(0.792656\pi\) | |||||||
\(608\) | −9821.62 | −0.655130 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.509668 | −3.38293e−5 | ||||||||
\(611\) | −3341.86 | − | 5788.27i | −0.221272 | − | 0.383254i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5679.63 | + | 9837.42i | −0.374222 | + | 0.648172i | −0.990210 | − | 0.139583i | \(-0.955424\pi\) |
0.615988 | + | 0.787756i | \(0.288757\pi\) | |||||||
\(614\) | −183.724 | − | 318.219i | −0.0120757 | − | 0.0209157i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18272.2 | 1.19224 | 0.596118 | − | 0.802896i | \(-0.296709\pi\) | ||||
0.596118 | + | 0.802896i | \(0.296709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14800.1 | − | 25634.6i | 0.961013 | − | 1.66452i | 0.241048 | − | 0.970513i | \(-0.422509\pi\) |
0.719965 | − | 0.694010i | \(-0.244158\pi\) | |||||||
\(620\) | −7.36075 | + | 12.7492i | −0.000476798 | + | 0.000825838i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1868.44 | −0.120447 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7810.61 | − | 13528.4i | −0.499879 | − | 0.865815i | ||||
\(626\) | 769.564 | − | 1332.92i | 0.0491341 | − | 0.0851028i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6620.28 | − | 11466.7i | −0.420665 | − | 0.728614i | ||||
\(629\) | −23340.5 | −1.47956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7185.41 | 0.453322 | 0.226661 | − | 0.973974i | \(-0.427219\pi\) | ||||
0.226661 | + | 0.973974i | \(0.427219\pi\) | |||||||
\(632\) | −2641.40 | − | 4575.05i | −0.166249 | − | 0.287952i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1440.33 | − | 2494.72i | 0.0902252 | − | 0.156275i | ||||
\(635\) | −53.8405 | − | 93.2545i | −0.00336472 | − | 0.00582786i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4289.64 | −0.266189 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.3733 | − | 69.9287i | 0.00249359 | − | 0.00431902i | ||||
\(641\) | −116.491 | + | 201.768i | −0.00717803 | + | 0.0124327i | −0.869592 | − | 0.493771i | \(-0.835618\pi\) |
0.862414 | + | 0.506203i | \(0.168952\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1837.96 | 0.112725 | 0.0563624 | − | 0.998410i | \(-0.482050\pi\) | ||||
0.0563624 | + | 0.998410i | \(0.482050\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3202.27 | + | 5546.50i | 0.195034 | + | 0.337808i | ||||
\(647\) | 9297.35 | − | 16103.5i | 0.564941 | − | 0.978506i | −0.432114 | − | 0.901819i | \(-0.642232\pi\) |
0.997055 | − | 0.0766874i | \(-0.0244343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −255.128 | − | 441.895i | −0.0154309 | − | 0.0267271i | ||||
\(650\) | 861.736 | 0.0520001 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 318.799 | 0.0191490 | ||||||||
\(653\) | −14432.3 | − | 24997.6i | −0.864902 | − | 1.49805i | −0.867144 | − | 0.498057i | \(-0.834047\pi\) |
0.00224162 | − | 0.999997i | \(-0.499286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −126.386 | + | 218.907i | −0.00753940 | + | 0.0130586i | ||||
\(656\) | −9577.27 | − | 16588.3i | −0.570014 | − | 0.987294i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29066.3 | 1.71815 | 0.859076 | − | 0.511847i | \(-0.171039\pi\) | ||||
0.859076 | + | 0.511847i | \(0.171039\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1989.75 | + | 3446.36i | −0.117084 | + | 0.202795i | −0.918611 | − | 0.395163i | \(-0.870688\pi\) |
0.801527 | + | 0.597959i | \(0.204021\pi\) | |||||||
\(662\) | 2042.73 | − | 3538.11i | 0.119929 | − | 0.207723i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2588.86 | −0.151306 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6316.02 | − | 10939.7i | −0.366653 | − | 0.635061i | ||||
\(668\) | −11353.0 | + | 19664.0i | −0.657578 | + | 1.13896i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.9264 | − | 24.1213i | −0.000803022 | − | 0.00139087i | ||||
\(671\) | −537.955 | −0.0309501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −184.229 | −0.0105520 | −0.00527601 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527601 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(674\) | 1231.26 | + | 2132.61i | 0.0703657 | + | 0.121877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7515.11 | + | 13016.6i | −0.427578 | + | 0.740587i | ||||
\(677\) | 8341.73 | + | 14448.3i | 0.473558 | + | 0.820227i | 0.999542 | − | 0.0302680i | \(-0.00963607\pi\) |
−0.525984 | + | 0.850495i | \(0.676303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −80.1540 | −0.00452024 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 170.277 | − | 294.928i | 0.00956045 | − | 0.0165592i | ||||
\(683\) | 8904.11 | − | 15422.4i | 0.498838 | − | 0.864013i | −0.501161 | − | 0.865354i | \(-0.667094\pi\) |
0.999999 | + | 0.00134107i | \(0.000426875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.2332 | −0.00140746 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6547.71 | + | 11341.0i | 0.362833 | + | 0.628445i | ||||
\(689\) | −5352.23 | + | 9270.34i | −0.295942 | + | 0.512586i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10072.8 | − | 17446.7i | −0.554542 | − | 0.960495i | −0.997939 | − | 0.0641695i | \(-0.979560\pi\) |
0.443397 | − | 0.896325i | \(-0.353773\pi\) | |||||||
\(692\) | −16801.0 | −0.922943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −484.453 | −0.0264980 | ||||||||
\(695\) | −44.5271 | − | 77.1232i | −0.00243023 | − | 0.00420928i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19444.9 | + | 33679.5i | −1.05671 | + | 1.83028i | ||||
\(698\) | −1900.55 | − | 3291.85i | −0.103061 | − | 0.178507i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2719.67 | 0.146534 | 0.0732672 | − | 0.997312i | \(-0.476657\pi\) | ||||
0.0732672 | + | 0.997312i | \(0.476657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12195.3 | + | 21122.9i | −0.654276 | + | 1.13324i | ||||
\(704\) | 9827.18 | − | 17021.2i | 0.526102 | − | 0.911235i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4385.36 | 0.233775 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 312.854 | + | 541.879i | 0.0165719 | + | 0.0287034i | 0.874192 | − | 0.485580i | \(-0.161391\pi\) |
−0.857621 | + | 0.514283i | \(0.828058\pi\) | |||||||
\(710\) | 17.1122 | − | 29.6392i | 0.000904520 | − | 0.00156667i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2207.58 | − | 3823.65i | −0.116198 | − | 0.201260i | ||||
\(713\) | 1002.85 | 0.0526749 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −73.5079 | −0.00384481 | ||||||||
\(716\) | −4710.91 | − | 8159.53i | −0.245887 | − | 0.425888i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1784.27 | − | 3090.44i | 0.0927414 | − | 0.160633i | ||||
\(719\) | 4788.77 | + | 8294.39i | 0.248388 | + | 0.430221i | 0.963079 | − | 0.269220i | \(-0.0867659\pi\) |
−0.714691 | + | 0.699441i | \(0.753433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3851.62 | 0.198535 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11705.3 | + | 20274.2i | −0.600864 | + | 1.04073i | ||||
\(725\) | −14728.9 | + | 25511.2i | −0.754506 | + | 1.30684i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16741.2 | 0.854053 | 0.427027 | − | 0.904239i | \(-0.359561\pi\) | ||||
0.427027 | + | 0.904239i | \(0.359561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.7219 | − | 18.5710i | −0.000543612 | − | 0.000941564i | ||||
\(731\) | 13293.9 | − | 23025.7i | 0.672631 | − | 1.16503i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3248.02 | − | 5625.74i | −0.163668 | − | 0.283481i | 0.772514 | − | 0.634998i | \(-0.218999\pi\) |
−0.936181 | + | 0.351517i | \(0.885666\pi\) | |||||||
\(734\) | −3437.06 | −0.172839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4141.36 | −0.207408 | ||||||||
\(737\) | −14699.4 | − | 25460.0i | −0.734678 | − | 1.27250i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −249.640 | + | 432.389i | −0.0124265 | + | 0.0215233i | −0.872172 | − | 0.489200i | \(-0.837289\pi\) |
0.859745 | + | 0.510723i | \(0.170622\pi\) | |||||||
\(740\) | −75.4861 | − | 130.746i | −0.00374990 | − | 0.00649502i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6367.30 | 0.314393 | 0.157196 | − | 0.987567i | \(-0.449754\pi\) | ||||
0.157196 | + | 0.987567i | \(0.449754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.2784 | − | 50.7117i | 0.00143984 | − | 0.00249387i | ||||
\(746\) | 1061.19 | − | 1838.03i | 0.0520814 | − | 0.0902077i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −41842.8 | −2.04535 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −248.049 | − | 429.634i | −0.0120525 | − | 0.0208756i | 0.859936 | − | 0.510401i | \(-0.170503\pi\) |
−0.871989 | + | 0.489526i | \(0.837170\pi\) | |||||||
\(752\) | 12028.9 | − | 20834.6i | 0.583308 | − | 1.01032i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −812.446 | − | 1407.20i | −0.0392407 | − | 0.0679670i | ||||
\(755\) | −282.597 | −0.0136222 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13025.9 | 0.625408 | 0.312704 | − | 0.949851i | \(-0.398765\pi\) | ||||
0.312704 | + | 0.949851i | \(0.398765\pi\) | |||||||
\(758\) | 311.175 | + | 538.971i | 0.0149108 | + | 0.0258263i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −41.8802 | + | 72.5387i | −0.00199889 | + | 0.00346218i | ||||
\(761\) | 12737.3 | + | 22061.6i | 0.606736 | + | 1.05090i | 0.991775 | + | 0.127997i | \(0.0408548\pi\) |
−0.385039 | + | 0.922900i | \(0.625812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21977.6 | −1.04074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2251.86 | − | 3900.33i | 0.106218 | − | 0.183975i | ||||
\(767\) | 96.6411 | − | 167.387i | 0.00454955 | − | 0.00788006i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29054.0 | 1.36244 | 0.681218 | − | 0.732080i | \(-0.261450\pi\) | ||||
0.681218 | + | 0.732080i | \(0.261450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13059.3 | + | 22619.3i | 0.608825 | + | 1.05452i | ||||
\(773\) | −948.677 | + | 1643.16i | −0.0441417 | + | 0.0764557i | −0.887252 | − | 0.461285i | \(-0.847389\pi\) |
0.843110 | + | 0.537740i | \(0.180722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1169.32 | − | 2025.33i | −0.0541978 | − | 0.0938734i | ||||
\(776\) | 7153.72 | 0.330933 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1913.25 | −0.0881662 | ||||||||
\(779\) | 20319.8 | + | 35194.9i | 0.934572 | + | 1.61873i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18061.9 | − | 31284.2i | 0.827538 | − | 1.43334i | ||||
\(782\) | 1350.26 | + | 2338.72i | 0.0617458 | + | 0.106947i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −169.989 | −0.00772886 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21325.1 | − | 36936.2i | 0.965895 | − | 1.67298i | 0.258702 | − | 0.965957i | \(-0.416705\pi\) |
0.707192 | − | 0.707021i | \(-0.249961\pi\) | |||||||
\(788\) | 16544.0 | − | 28655.0i | 0.747913 | − | 1.29542i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.5440 | −0.00151069 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −101.887 | − | 176.474i | −0.00456258 | − | 0.00790262i | ||||
\(794\) | 1989.66 | − | 3446.20i | 0.0889302 | − | 0.154032i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17166.5 | + | 29733.3i | 0.764387 | + | 1.32396i | ||||
\(797\) | 36822.8 | 1.63655 | 0.818275 | − | 0.574828i | \(-0.194931\pi\) | ||||
0.818275 | + | 0.574828i | \(0.194931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48844.8 | −2.16271 | ||||||||
\(800\) | 4828.80 | + | 8363.73i | 0.213405 | + | 0.369628i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2174.84 | + | 3766.93i | −0.0957559 | + | 0.165854i | ||||
\(803\) | −11317.0 | − | 19601.7i | −0.497347 | − | 0.861429i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 129.000 | 0.00563750 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4493.69 | − | 7783.30i | 0.195653 | − | 0.338881i | ||||
\(809\) | 2540.97 | − | 4401.09i | 0.110427 | − | 0.191266i | −0.805515 | − | 0.592575i | \(-0.798111\pi\) |
0.915943 | + | 0.401309i | \(0.131445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11873.4 | −0.514097 | −0.257048 | − | 0.966399i | \(-0.582750\pi\) | ||||
−0.257048 | + | 0.966399i | \(0.582750\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1746.23 | + | 3024.55i | 0.0751906 | + | 0.130234i | ||||
\(815\) | 2.04645 | − | 3.54455i | 8.79557e−5 | − | 0.000152344i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13892.1 | − | 24061.8i | −0.594886 | − | 1.03037i | ||||
\(818\) | 4998.29 | 0.213644 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −251.549 | −0.0107128 | ||||||||
\(821\) | 8484.72 | + | 14696.0i | 0.360681 | + | 0.624717i | 0.988073 | − | 0.153986i | \(-0.0492111\pi\) |
−0.627392 | + | 0.778703i | \(0.715878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1997.97 | + | 3460.58i | −0.0846231 | + | 0.146572i | −0.905231 | − | 0.424921i | \(-0.860302\pi\) |
0.820607 | + | 0.571492i | \(0.193635\pi\) | |||||||
\(824\) | −4635.19 | − | 8028.39i | −0.195964 | − | 0.339420i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13589.7 | 0.571417 | 0.285708 | − | 0.958317i | \(-0.407771\pi\) | ||||
0.285708 | + | 0.958317i | \(0.407771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15323.0 | + | 26540.2i | −0.641966 | + | 1.11192i | 0.343028 | + | 0.939325i | \(0.388547\pi\) |
−0.984993 | + | 0.172592i | \(0.944786\pi\) | |||||||
\(830\) | −8.21918 | + | 14.2360i | −0.000343725 | + | 0.000595350i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7444.96 | 0.310226 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 145.756 | + | 252.456i | 0.00604082 | + | 0.0104630i | ||||
\(836\) | −21862.7 | + | 37867.4i | −0.904472 | + | 1.56659i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1318.51 | + | 2283.72i | 0.0543521 | + | 0.0941405i | ||||
\(839\) | −7497.57 | −0.308516 | −0.154258 | − | 0.988031i | \(-0.549299\pi\) | ||||
−0.154258 | + | 0.988031i | \(0.549299\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31156.6 | 1.27749 | ||||||||
\(842\) | 979.996 | + | 1697.40i | 0.0401103 | + | 0.0694731i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8969.65 | − | 15535.9i | 0.365815 | − | 0.633610i | ||||
\(845\) | 96.4826 | + | 167.113i | 0.00392793 | + | 0.00680338i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −38530.2 | −1.56030 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3148.79 | − | 5453.87i | 0.127062 | − | 0.220078i | ||||
\(851\) | −5142.25 | + | 8906.64i | −0.207138 | + | 0.358773i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10347.6 | 0.415352 | 0.207676 | − | 0.978198i | \(-0.433410\pi\) | ||||
0.207676 | + | 0.978198i | \(0.433410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1126.18 | + | 1950.60i | 0.0449674 | + | 0.0778858i | ||||
\(857\) | −774.999 | + | 1342.34i | −0.0308909 | + | 0.0535045i | −0.881058 | − | 0.473009i | \(-0.843168\pi\) |
0.850167 | + | 0.526514i | \(0.176501\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7593.76 | + | 13152.8i | 0.301625 | + | 0.522430i | 0.976504 | − | 0.215499i | \(-0.0691377\pi\) |
−0.674879 | + | 0.737928i | \(0.735804\pi\) | |||||||
\(860\) | 171.977 | 0.00681903 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1554.45 | −0.0614210 | ||||||||
\(863\) | 20775.1 | + | 35983.5i | 0.819459 | + | 1.41934i | 0.906082 | + | 0.423103i | \(0.139059\pi\) |
−0.0866230 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −107.849 | + | 186.801i | −0.00423929 | + | 0.00734267i | ||||
\(866\) | 2425.06 | + | 4200.33i | 0.0951581 | + | 0.164819i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35405.8 | −1.38212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5568.04 | − | 9644.12i | 0.216608 | − | 0.375176i | ||||
\(872\) | −1041.33 | + | 1803.64i | −0.0404404 | + | 0.0700449i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2822.03 | 0.109218 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13918.7 | − | 24107.9i | −0.535919 | − | 0.928239i | −0.999118 | − | 0.0419846i | \(-0.986632\pi\) |
0.463199 | − | 0.886254i | \(-0.346701\pi\) | |||||||
\(878\) | −3091.01 | + | 5353.79i | −0.118812 | + | 0.205788i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −132.294 | − | 229.140i | −0.00506777 | − | 0.00877763i | ||||
\(881\) | −2587.85 | −0.0989635 | −0.0494817 | − | 0.998775i | \(-0.515757\pi\) | ||||
−0.0494817 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16382.0 | −0.624346 | −0.312173 | − | 0.950025i | \(-0.601057\pi\) | ||||
−0.312173 | + | 0.950025i | \(0.601057\pi\) | |||||||
\(884\) | −7924.91 | − | 13726.4i | −0.301520 | − | 0.522248i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1764.06 | + | 3055.45i | −0.0668904 | + | 0.115858i | ||||
\(887\) | 11490.1 | + | 19901.4i | 0.434948 | + | 0.753352i | 0.997291 | − | 0.0735516i | \(-0.0234334\pi\) |
−0.562343 | + | 0.826904i | \(0.690100\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −28.0348 | −0.00105587 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −853.180 | + | 1477.75i | −0.0320253 | + | 0.0554695i | ||||
\(893\) | −25521.3 | + | 44204.1i | −0.956368 | + | 1.65648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −120.962 | −0.00451766 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1235.54 | − | 2140.02i | −0.0459138 | − | 0.0795251i | ||||
\(899\) | −2204.88 | + | 3818.96i | −0.0817984 | + | 0.141679i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39114.2 | + | 67747.9i | 1.44626 | + | 2.50500i | ||||
\(902\) | 5819.10 | 0.214806 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5234.42 | 0.192582 | ||||||||
\(905\) | 150.279 | + | 260.290i | 0.00551982 | + | 0.00956060i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11357.7 | − | 19672.1i | 0.415795 | − | 0.720178i | −0.579716 | − | 0.814818i | \(-0.696837\pi\) |
0.995512 | + | 0.0946400i | \(0.0301700\pi\) | |||||||
\(908\) | −7183.99 | − | 12443.0i | −0.262565 | − | 0.454776i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34922.3 | −1.27006 | −0.635031 | − | 0.772487i | \(-0.719013\pi\) | ||||
−0.635031 | + | 0.772487i | \(0.719013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8675.36 | + | 15026.2i | −0.314472 | + | 0.544681i | ||||
\(914\) | 2870.62 | − | 4972.06i | 0.103886 | − | 0.179935i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21716.1 | −0.783320 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5851.32 | − | 10134.8i | −0.210030 | − | 0.363782i | 0.741694 | − | 0.670739i | \(-0.234023\pi\) |
−0.951724 | + | 0.306956i | \(0.900689\pi\) | |||||||
\(920\) | −17.6591 | + | 30.5864i | −0.000632829 | + | 0.00109609i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.9236 | + | 53.5613i | 0.00110457 | + | 0.00191317i | ||||
\(923\) | 13683.5 | 0.487973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23983.3 | 0.852505 | ||||||||
\(926\) | −1119.20 | − | 1938.50i | −0.0397182 | − | 0.0687939i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9105.19 | − | 15770.7i | 0.322083 | − | 0.557863i | ||||
\(929\) | 26548.2 | + | 45982.9i | 0.937588 | + | 1.62395i | 0.769952 | + | 0.638102i | \(0.220280\pi\) |
0.167637 | + | 0.985849i | \(0.446386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7740.06 | −0.272032 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −767.259 | + | 1328.93i | −0.0268795 | + | 0.0465567i | ||||
\(935\) | −268.599 | + | 465.227i | −0.00939478 | + | 0.0162722i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39020.6 | 1.36046 | 0.680229 | − | 0.733000i | \(-0.261880\pi\) | ||||
0.680229 | + | 0.733000i | \(0.261880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −157.970 | − | 273.613i | −0.00548131 | − | 0.00949390i | ||||
\(941\) | −15371.9 | + | 26624.9i | −0.532528 | + | 0.922366i | 0.466750 | + | 0.884389i | \(0.345425\pi\) |
−0.999279 | + | 0.0379770i | \(0.987909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8567.98 | + | 14840.2i | 0.295877 | + | 0.512474i | ||||
\(944\) | 695.710 | 0.0239867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3978.35 | −0.136731 | ||||||||
\(947\) | 8150.14 | + | 14116.5i | 0.279666 | + | 0.484396i | 0.971302 | − | 0.237851i | \(-0.0764429\pi\) |
−0.691636 | + | 0.722247i | \(0.743110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4286.83 | − | 7425.01i | 0.146635 | − | 0.253979i | ||||
\(950\) | −3290.47 | − | 5699.26i | −0.112376 | − | 0.194641i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11512.7 | 0.391325 | 0.195663 | − | 0.980671i | \(-0.437314\pi\) | ||||
0.195663 | + | 0.980671i | \(0.437314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −141.079 | + | 244.357i | −0.00478034 | + | 0.00827979i | ||||
\(956\) | 3279.83 | − | 5680.83i | 0.110959 | − | 0.192187i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4420.39 | −0.149078 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14720.5 | + | 25496.6i | 0.494124 | + | 0.855848i | ||||
\(962\) | −661.461 | + | 1145.68i | −0.0221688 | + | 0.0383974i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13523.6 | − | 23423.5i | −0.451830 | − | 0.782593i | ||||
\(965\) | 335.322 | 0.0111859 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18178.4 | −0.604528 | −0.302264 | − | 0.953224i | \(-0.597742\pi\) | ||||
−0.302264 | + | 0.953224i | \(0.597742\pi\) | |||||||
\(968\) | 1966.32 | + | 3405.77i | 0.0652893 | + | 0.113084i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.7118 | − | 39.3381i | 0.000751787 | − | 0.00130213i | ||||
\(971\) | 14138.3 | + | 24488.3i | 0.467271 | + | 0.809338i | 0.999301 | − | 0.0373880i | \(-0.0119037\pi\) |
−0.532029 | + | 0.846726i | \(0.678570\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2424.77 | 0.0797688 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 366.739 | − | 635.210i | 0.0120277 | − | 0.0208326i | ||||
\(977\) | −6973.53 | + | 12078.5i | −0.228355 | + | 0.395523i | −0.957321 | − | 0.289028i | \(-0.906668\pi\) |
0.728966 | + | 0.684550i | \(0.240001\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29590.8 | −0.966011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 841.954 | + | 1458.31i | 0.0273603 | + | 0.0473894i | ||||
\(983\) | −13288.4 | + | 23016.2i | −0.431164 | + | 0.746797i | −0.996974 | − | 0.0777381i | \(-0.975230\pi\) |
0.565810 | + | 0.824536i | \(0.308564\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −212.400 | − | 367.887i | −0.00687068 | − | 0.0119004i | ||||
\(986\) | −11874.7 | −0.383539 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16563.0 | −0.533339 | ||||||||
\(989\) | −5857.69 | − | 10145.8i | −0.188335 | − | 0.326206i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8124.96 | + | 14072.8i | −0.260442 | + | 0.451099i | −0.966359 | − | 0.257195i | \(-0.917202\pi\) |
0.705917 | + | 0.708294i | \(0.250535\pi\) | |||||||
\(992\) | 722.859 | + | 1252.03i | 0.0231359 | + | 0.0400725i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 440.784 | 0.0140440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9407.05 | + | 16293.5i | −0.298821 | + | 0.517573i | −0.975866 | − | 0.218368i | \(-0.929927\pi\) |
0.677046 | + | 0.735941i | \(0.263260\pi\) | |||||||
\(998\) | −996.429 | + | 1725.87i | −0.0316046 | + | 0.0547408i | ||||
\(999\) | 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 | 441.4.e.u.361.1 | 4 | ||
3.2 | odd | 2 | 147.4.e.j.67.2 | 4 | |||
7.2 | even | 3 | inner | 441.4.e.u.226.1 | 4 | ||
7.3 | odd | 6 | 441.4.a.n.1.2 | 2 | |||
7.4 | even | 3 | 441.4.a.o.1.2 | 2 | |||
7.5 | odd | 6 | 441.4.e.v.226.1 | 4 | |||
7.6 | odd | 2 | 441.4.e.v.361.1 | 4 | |||
21.2 | odd | 6 | 147.4.e.j.79.2 | 4 | |||
21.5 | even | 6 | 147.4.e.k.79.2 | 4 | |||
21.11 | odd | 6 | 147.4.a.k.1.1 | yes | 2 | ||
21.17 | even | 6 | 147.4.a.j.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 147.4.e.k.67.2 | 4 | |||
84.11 | even | 6 | 2352.4.a.bl.1.2 | 2 | |||
84.59 | odd | 6 | 2352.4.a.cf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.j.1.1 | ✓ | 2 | 21.17 | even | 6 | ||
147.4.a.k.1.1 | yes | 2 | 21.11 | odd | 6 | ||
147.4.e.j.67.2 | 4 | 3.2 | odd | 2 | |||
147.4.e.j.79.2 | 4 | 21.2 | odd | 6 | |||
147.4.e.k.67.2 | 4 | 21.20 | even | 2 | |||
147.4.e.k.79.2 | 4 | 21.5 | even | 6 | |||
441.4.a.n.1.2 | 2 | 7.3 | odd | 6 | |||
441.4.a.o.1.2 | 2 | 7.4 | even | 3 | |||
441.4.e.u.226.1 | 4 | 7.2 | even | 3 | inner | ||
441.4.e.u.361.1 | 4 | 1.1 | even | 1 | trivial | ||
441.4.e.v.226.1 | 4 | 7.5 | odd | 6 | |||
441.4.e.v.361.1 | 4 | 7.6 | odd | 2 | |||
2352.4.a.bl.1.2 | 2 | 84.11 | even | 6 | |||
2352.4.a.cf.1.1 | 2 | 84.59 | odd | 6 |