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: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.9924270768.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.124036 + 0.214837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.w.226.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.124036 | + | 0.214837i | 0.0438533 | + | 0.0759562i | 0.887119 | − | 0.461541i | \(-0.152703\pi\) |
−0.843266 | + | 0.537497i | \(0.819370\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.96923 | − | 6.87491i | 0.496154 | − | 0.859364i | ||||
\(5\) | 6.21730 | + | 10.7687i | 0.556092 | + | 0.963180i | 0.997818 | + | 0.0660299i | \(0.0210333\pi\) |
−0.441725 | + | 0.897150i | \(0.645633\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.95388 | 0.174739 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.54234 | + | 2.67141i | −0.0487730 | + | 0.0844773i | ||||
\(11\) | 30.1558 | − | 52.2313i | 0.826573 | − | 1.43167i | −0.0741379 | − | 0.997248i | \(-0.523621\pi\) |
0.900711 | − | 0.434419i | \(-0.143046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −36.4269 | −0.777154 | −0.388577 | − | 0.921416i | \(-0.627033\pi\) | ||||
−0.388577 | + | 0.921416i | \(0.627033\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.2634 | − | 54.1498i | −0.488491 | − | 0.846091i | ||||
\(17\) | 24.3731 | − | 42.2154i | 0.347726 | − | 0.602279i | −0.638119 | − | 0.769937i | \(-0.720287\pi\) |
0.985845 | + | 0.167659i | \(0.0536207\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.2750 | − | 43.7776i | −0.305183 | − | 0.528593i | 0.672119 | − | 0.740443i | \(-0.265384\pi\) |
−0.977302 | + | 0.211851i | \(0.932051\pi\) | |||||||
\(20\) | 98.7116 | 1.10363 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.9616 | 0.144992 | ||||||||
\(23\) | 69.3962 | + | 120.198i | 0.629135 | + | 1.08969i | 0.987726 | + | 0.156199i | \(0.0499241\pi\) |
−0.358590 | + | 0.933495i | \(0.616743\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.8097 | + | 25.6511i | −0.118478 | + | 0.205209i | ||||
\(26\) | −4.51824 | − | 7.82583i | −0.0340808 | − | 0.0590297i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 61.1345 | 0.391462 | 0.195731 | − | 0.980658i | \(-0.437292\pi\) | ||||
0.195731 | + | 0.980658i | \(0.437292\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.584676 | + | 1.01269i | −0.00338745 | + | 0.00586724i | −0.867714 | − | 0.497064i | \(-0.834412\pi\) |
0.864327 | + | 0.502931i | \(0.167745\pi\) | |||||||
\(32\) | 23.5711 | − | 40.8264i | 0.130213 | − | 0.225536i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.0925 | 0.0609957 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.7634 | − | 60.2120i | −0.154461 | − | 0.267535i | 0.778401 | − | 0.627767i | \(-0.216031\pi\) |
−0.932863 | + | 0.360232i | \(0.882698\pi\) | |||||||
\(38\) | 6.27001 | − | 10.8600i | 0.0267666 | − | 0.0463611i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.5825 | + | 42.5781i | 0.0971708 | + | 0.168305i | ||||
\(41\) | 308.115 | 1.17365 | 0.586823 | − | 0.809715i | \(-0.300378\pi\) | ||||
0.586823 | + | 0.809715i | \(0.300378\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 174.443 | 0.618657 | 0.309329 | − | 0.950955i | \(-0.399896\pi\) | ||||
0.309329 | + | 0.950955i | \(0.399896\pi\) | |||||||
\(44\) | −239.390 | − | 414.636i | −0.820215 | − | 1.42065i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.2153 | + | 29.8177i | −0.0551794 | + | 0.0955734i | ||||
\(47\) | −194.681 | − | 337.197i | −0.604194 | − | 1.04649i | −0.992178 | − | 0.124829i | \(-0.960162\pi\) |
0.387984 | − | 0.921666i | \(-0.373172\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.34774 | −0.0207825 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −144.587 | + | 250.432i | −0.385588 | + | 0.667858i | ||||
\(53\) | 157.467 | − | 272.742i | 0.408110 | − | 0.706867i | −0.586568 | − | 0.809900i | \(-0.699521\pi\) |
0.994678 | + | 0.103033i | \(0.0328547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 749.950 | 1.83860 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.58287 | + | 13.1339i | 0.0171669 | + | 0.0297339i | ||||
\(59\) | −422.263 | + | 731.381i | −0.931762 | + | 1.61386i | −0.151455 | + | 0.988464i | \(0.548396\pi\) |
−0.780308 | + | 0.625396i | \(0.784938\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −169.269 | − | 293.182i | −0.355290 | − | 0.615380i | 0.631878 | − | 0.775068i | \(-0.282284\pi\) |
−0.987167 | + | 0.159688i | \(0.948951\pi\) | |||||||
\(62\) | −0.290084 | −0.000594204 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −488.520 | −0.954141 | ||||||||
\(65\) | −226.477 | − | 392.270i | −0.432169 | − | 0.748539i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 485.775 | − | 841.387i | 0.885774 | − | 1.53421i | 0.0409498 | − | 0.999161i | \(-0.486962\pi\) |
0.844824 | − | 0.535044i | \(-0.179705\pi\) | |||||||
\(68\) | −193.485 | − | 335.125i | −0.345051 | − | 0.597646i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 98.4698 | 0.164595 | 0.0822973 | − | 0.996608i | \(-0.473774\pi\) | ||||
0.0822973 | + | 0.996608i | \(0.473774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 355.117 | − | 615.082i | 0.569361 | − | 0.986162i | −0.427268 | − | 0.904125i | \(-0.640524\pi\) |
0.996629 | − | 0.0820374i | \(-0.0261427\pi\) | |||||||
\(74\) | 8.62383 | − | 14.9369i | 0.0135473 | − | 0.0234646i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −401.289 | −0.605671 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 243.442 | + | 421.654i | 0.346701 | + | 0.600504i | 0.985661 | − | 0.168736i | \(-0.0539686\pi\) |
−0.638960 | + | 0.769240i | \(0.720635\pi\) | |||||||
\(80\) | 388.748 | − | 673.332i | 0.543292 | − | 0.941010i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 38.2174 | + | 66.1944i | 0.0514683 | + | 0.0891458i | ||||
\(83\) | 605.688 | 0.800999 | 0.400499 | − | 0.916297i | \(-0.368837\pi\) | ||||
0.400499 | + | 0.916297i | \(0.368837\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 606.139 | 0.773470 | ||||||||
\(86\) | 21.6372 | + | 37.4767i | 0.0271302 | + | 0.0469908i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 119.232 | − | 206.517i | 0.144434 | − | 0.250168i | ||||
\(89\) | −109.034 | − | 188.853i | −0.129861 | − | 0.224925i | 0.793762 | − | 0.608229i | \(-0.208120\pi\) |
−0.923622 | + | 0.383303i | \(0.874786\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1101.80 | 1.24859 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 48.2949 | − | 83.6491i | 0.0529919 | − | 0.0917846i | ||||
\(95\) | 314.284 | − | 544.357i | 0.339420 | − | 0.587893i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 782.288 | 0.818859 | 0.409429 | − | 0.912342i | \(-0.365728\pi\) | ||||
0.409429 | + | 0.912342i | \(0.365728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 117.566 | + | 203.631i | 0.117566 | + | 0.203631i | ||||
\(101\) | 155.823 | − | 269.893i | 0.153514 | − | 0.265895i | −0.779003 | − | 0.627021i | \(-0.784274\pi\) |
0.932517 | + | 0.361126i | \(0.117608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −74.6289 | − | 129.261i | −0.0713922 | − | 0.123655i | 0.828119 | − | 0.560552i | \(-0.189411\pi\) |
−0.899512 | + | 0.436897i | \(0.856078\pi\) | |||||||
\(104\) | −144.028 | −0.135799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 78.1265 | 0.0715879 | ||||||||
\(107\) | 425.760 | + | 737.437i | 0.384670 | + | 0.666269i | 0.991723 | − | 0.128393i | \(-0.0409818\pi\) |
−0.607053 | + | 0.794661i | \(0.707648\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −680.939 | + | 1179.42i | −0.598369 | + | 1.03640i | 0.394694 | + | 0.918813i | \(0.370851\pi\) |
−0.993062 | + | 0.117592i | \(0.962483\pi\) | |||||||
\(110\) | 93.0208 | + | 161.117i | 0.0806289 | + | 0.139653i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1048.55 | −0.872917 | −0.436459 | − | 0.899724i | \(-0.643767\pi\) | ||||
−0.436459 | + | 0.899724i | \(0.643767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −862.914 | + | 1494.61i | −0.699715 | + | 1.21194i | ||||
\(116\) | 242.657 | − | 420.294i | 0.194225 | − | 0.336408i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −209.503 | −0.163444 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1153.24 | − | 1997.47i | −0.866446 | − | 1.50073i | ||||
\(122\) | 41.9909 | − | 72.7303i | 0.0311613 | − | 0.0539729i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.64143 | + | 8.03919i | 0.00336139 | + | 0.00582210i | ||||
\(125\) | 1186.02 | 0.848647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 488.408 | 0.341254 | 0.170627 | − | 0.985336i | \(-0.445421\pi\) | ||||
0.170627 | + | 0.985336i | \(0.445421\pi\) | |||||||
\(128\) | −249.163 | − | 431.563i | −0.172056 | − | 0.298009i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 56.1826 | − | 97.3111i | 0.0379041 | − | 0.0656519i | ||||
\(131\) | 927.114 | + | 1605.81i | 0.618338 | + | 1.07099i | 0.989789 | + | 0.142541i | \(0.0455272\pi\) |
−0.371451 | + | 0.928453i | \(0.621139\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 241.014 | 0.155377 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 96.3683 | − | 166.915i | 0.0607611 | − | 0.105241i | ||||
\(137\) | −255.558 | + | 442.639i | −0.159370 | + | 0.276038i | −0.934642 | − | 0.355591i | \(-0.884280\pi\) |
0.775271 | + | 0.631628i | \(0.217613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2266.10 | −1.38279 | −0.691397 | − | 0.722475i | \(-0.743005\pi\) | ||||
−0.691397 | + | 0.722475i | \(0.743005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.2138 | + | 21.1549i | 0.00721802 | + | 0.0125020i | ||||
\(143\) | −1098.48 | + | 1902.62i | −0.642375 | + | 1.11263i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 380.091 | + | 658.338i | 0.217689 | + | 0.377048i | ||||
\(146\) | 176.189 | 0.0998735 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −551.936 | −0.306546 | ||||||||
\(149\) | 753.950 | + | 1305.88i | 0.414537 | + | 0.717999i | 0.995380 | − | 0.0960168i | \(-0.0306102\pi\) |
−0.580843 | + | 0.814016i | \(0.697277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −795.913 | + | 1378.56i | −0.428943 | + | 0.742952i | −0.996780 | − | 0.0801897i | \(-0.974447\pi\) |
0.567836 | + | 0.823142i | \(0.307781\pi\) | |||||||
\(152\) | −99.9344 | − | 173.091i | −0.0533273 | − | 0.0923656i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.5404 | −0.00753494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 582.080 | − | 1008.19i | 0.295892 | − | 0.512500i | −0.679300 | − | 0.733861i | \(-0.737717\pi\) |
0.975192 | + | 0.221361i | \(0.0710498\pi\) | |||||||
\(158\) | −60.3911 | + | 104.601i | −0.0304080 | + | 0.0526682i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 586.195 | 0.289642 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 577.940 | + | 1001.02i | 0.277716 | + | 0.481019i | 0.970817 | − | 0.239822i | \(-0.0770892\pi\) |
−0.693101 | + | 0.720841i | \(0.743756\pi\) | |||||||
\(164\) | 1222.98 | − | 2118.26i | 0.582309 | − | 1.00859i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 75.1271 | + | 130.124i | 0.0351265 | + | 0.0608408i | ||||
\(167\) | −2890.61 | −1.33941 | −0.669707 | − | 0.742626i | \(-0.733580\pi\) | ||||
−0.669707 | + | 0.742626i | \(0.733580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −870.082 | −0.396032 | ||||||||
\(170\) | 75.1830 | + | 130.221i | 0.0339193 | + | 0.0587499i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 692.403 | − | 1199.28i | 0.306949 | − | 0.531651i | ||||
\(173\) | −947.468 | − | 1641.06i | −0.416385 | − | 0.721200i | 0.579188 | − | 0.815194i | \(-0.303370\pi\) |
−0.995573 | + | 0.0939940i | \(0.970037\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3771.09 | −1.61509 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 27.0483 | − | 46.8491i | 0.0113897 | − | 0.0197275i | ||||
\(179\) | −2144.25 | + | 3713.94i | −0.895355 | + | 1.55080i | −0.0619893 | + | 0.998077i | \(0.519744\pi\) |
−0.833365 | + | 0.552723i | \(0.813589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −383.732 | −0.157583 | −0.0787917 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787917 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 274.385 | + | 475.248i | 0.109934 | + | 0.190412i | ||||
\(185\) | 432.269 | − | 748.712i | 0.171790 | − | 0.297548i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1469.98 | − | 2546.07i | −0.574841 | − | 0.995655i | ||||
\(188\) | −3090.93 | −1.19909 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 155.930 | 0.0595388 | ||||||||
\(191\) | 192.655 | + | 333.689i | 0.0729845 | + | 0.126413i | 0.900208 | − | 0.435460i | \(-0.143414\pi\) |
−0.827224 | + | 0.561873i | \(0.810081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −315.112 | + | 545.790i | −0.117525 | + | 0.203559i | −0.918786 | − | 0.394756i | \(-0.870829\pi\) |
0.801262 | + | 0.598314i | \(0.204163\pi\) | |||||||
\(194\) | 97.0318 | + | 168.064i | 0.0359097 | + | 0.0621974i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1250.23 | 0.452158 | 0.226079 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226079 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −546.122 | + | 945.912i | −0.194541 | + | 0.336954i | −0.946750 | − | 0.321970i | \(-0.895655\pi\) |
0.752209 | + | 0.658924i | \(0.228988\pi\) | |||||||
\(200\) | −58.5558 | + | 101.422i | −0.0207026 | + | 0.0358580i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 77.3105 | 0.0269285 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1915.65 | + | 3318.00i | 0.652656 | + | 1.13043i | ||||
\(206\) | 18.5133 | − | 32.0660i | 0.00626158 | − | 0.0108454i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1138.83 | + | 1972.51i | 0.379633 | + | 0.657543i | ||||
\(209\) | −3048.75 | −1.00902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3620.05 | −1.18111 | −0.590556 | − | 0.806997i | \(-0.701091\pi\) | ||||
−0.590556 | + | 0.806997i | \(0.701091\pi\) | |||||||
\(212\) | −1250.05 | − | 2165.15i | −0.404970 | − | 0.701429i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −105.619 | + | 182.937i | −0.0337382 | + | 0.0584362i | ||||
\(215\) | 1084.56 | + | 1878.52i | 0.344030 | + | 0.595878i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −337.844 | −0.104962 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2976.72 | − | 5155.84i | 0.912230 | − | 1.58003i | ||||
\(221\) | −887.835 | + | 1537.78i | −0.270236 | + | 0.468063i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 183.844 | 0.0552069 | 0.0276034 | − | 0.999619i | \(-0.491212\pi\) | ||||
0.0276034 | + | 0.999619i | \(0.491212\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −130.058 | − | 225.268i | −0.0382803 | − | 0.0663035i | ||||
\(227\) | −1139.76 | + | 1974.12i | −0.333253 | + | 0.577211i | −0.983148 | − | 0.182813i | \(-0.941480\pi\) |
0.649895 | + | 0.760024i | \(0.274813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2706.34 | + | 4687.51i | 0.780960 | + | 1.35266i | 0.931383 | + | 0.364040i | \(0.118603\pi\) |
−0.150424 | + | 0.988622i | \(0.548064\pi\) | |||||||
\(230\) | −428.130 | −0.122739 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 241.719 | 0.0684035 | ||||||||
\(233\) | 569.184 | + | 985.856i | 0.160036 | + | 0.277191i | 0.934882 | − | 0.354960i | \(-0.115506\pi\) |
−0.774845 | + | 0.632151i | \(0.782172\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2420.78 | − | 4192.91i | 0.671975 | − | 1.16390i | ||||
\(236\) | 3352.12 | + | 5806.04i | 0.924595 | + | 1.60145i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6226.36 | 1.68515 | 0.842573 | − | 0.538583i | \(-0.181040\pi\) | ||||
0.842573 | + | 0.538583i | \(0.181040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1598.10 | + | 2767.99i | −0.427147 | + | 0.739841i | −0.996618 | − | 0.0821704i | \(-0.973815\pi\) |
0.569471 | + | 0.822012i | \(0.307148\pi\) | |||||||
\(242\) | 286.086 | − | 495.516i | 0.0759931 | − | 0.131624i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2687.47 | −0.705113 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 920.689 | + | 1594.68i | 0.237174 | + | 0.410798i | ||||
\(248\) | −2.31174 | + | 4.00406i | −0.000591919 | + | 0.00102523i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 147.109 | + | 254.801i | 0.0372160 | + | 0.0644600i | ||||
\(251\) | 239.608 | 0.0602546 | 0.0301273 | − | 0.999546i | \(-0.490409\pi\) | ||||
0.0301273 | + | 0.999546i | \(0.490409\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8370.78 | 2.08010 | ||||||||
\(254\) | 60.5802 | + | 104.928i | 0.0149651 | + | 0.0259203i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1892.27 | + | 3277.51i | −0.461980 | + | 0.800173i | ||||
\(257\) | −349.559 | − | 605.453i | −0.0848439 | − | 0.146954i | 0.820481 | − | 0.571674i | \(-0.193706\pi\) |
−0.905325 | + | 0.424720i | \(0.860372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3595.76 | −0.857690 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −229.991 | + | 398.356i | −0.0542324 | + | 0.0939333i | ||||
\(263\) | −459.520 | + | 795.912i | −0.107738 | + | 0.186609i | −0.914854 | − | 0.403785i | \(-0.867694\pi\) |
0.807115 | + | 0.590394i | \(0.201028\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3916.09 | 0.907787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3856.30 | − | 6679.32i | −0.878960 | − | 1.52240i | ||||
\(269\) | 1389.59 | − | 2406.84i | 0.314961 | − | 0.545529i | −0.664468 | − | 0.747317i | \(-0.731342\pi\) |
0.979429 | + | 0.201788i | \(0.0646751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1113.49 | + | 1928.62i | 0.249593 | + | 0.432308i | 0.963413 | − | 0.268021i | \(-0.0863698\pi\) |
−0.713820 | + | 0.700329i | \(0.753036\pi\) | |||||||
\(272\) | −3047.94 | −0.679443 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −126.793 | −0.0279557 | ||||||||
\(275\) | 893.195 | + | 1547.06i | 0.195861 | + | 0.339241i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3653.85 | + | 6328.65i | −0.792557 | + | 1.37275i | 0.131821 | + | 0.991273i | \(0.457917\pi\) |
−0.924379 | + | 0.381476i | \(0.875416\pi\) | |||||||
\(278\) | −281.078 | − | 486.842i | −0.0606402 | − | 0.105032i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2730.61 | −0.579696 | −0.289848 | − | 0.957073i | \(-0.593605\pi\) | ||||
−0.289848 | + | 0.957073i | \(0.593605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −884.926 | + | 1532.74i | −0.185878 | + | 0.321950i | −0.943872 | − | 0.330312i | \(-0.892846\pi\) |
0.757994 | + | 0.652261i | \(0.226179\pi\) | |||||||
\(284\) | 390.849 | − | 676.971i | 0.0816642 | − | 0.141447i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −545.004 | −0.112681 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1268.41 | + | 2196.95i | 0.258174 | + | 0.447170i | ||||
\(290\) | −94.2900 | + | 163.315i | −0.0190928 | + | 0.0330696i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2819.09 | − | 4882.80i | −0.564981 | − | 0.978576i | ||||
\(293\) | 8228.81 | 1.64072 | 0.820362 | − | 0.571844i | \(-0.193772\pi\) | ||||
0.820362 | + | 0.571844i | \(0.193772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10501.4 | −2.07258 | ||||||||
\(296\) | −137.451 | − | 238.071i | −0.0269904 | − | 0.0467487i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −187.034 | + | 323.952i | −0.0363577 | + | 0.0629733i | ||||
\(299\) | −2527.89 | − | 4378.43i | −0.488935 | − | 0.846860i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −394.887 | −0.0752424 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1580.36 | + | 2737.27i | −0.298158 | + | 0.516425i | ||||
\(305\) | 2104.79 | − | 3645.61i | 0.395148 | − | 0.684416i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6019.62 | −1.11908 | −0.559541 | − | 0.828803i | \(-0.689023\pi\) | ||||
−0.559541 | + | 0.828803i | \(0.689023\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.80354 | − | 3.12382i | −0.000330432 | − | 0.000572326i | ||||
\(311\) | −596.857 | + | 1033.79i | −0.108825 | + | 0.188491i | −0.915295 | − | 0.402785i | \(-0.868042\pi\) |
0.806469 | + | 0.591276i | \(0.201376\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4423.02 | − | 7660.89i | −0.798734 | − | 1.38345i | −0.920441 | − | 0.390882i | \(-0.872170\pi\) |
0.121707 | − | 0.992566i | \(-0.461163\pi\) | |||||||
\(314\) | 288.795 | 0.0519034 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3865.11 | 0.688068 | ||||||||
\(317\) | 3040.72 | + | 5266.68i | 0.538750 | + | 0.933142i | 0.998972 | + | 0.0453380i | \(0.0144365\pi\) |
−0.460222 | + | 0.887804i | \(0.652230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1843.56 | − | 3193.13i | 0.323572 | − | 0.560442i | ||||
\(320\) | −3037.28 | − | 5260.72i | −0.530590 | − | 0.919009i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2464.12 | −0.424480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 539.471 | − | 934.391i | 0.0920753 | − | 0.159479i | ||||
\(326\) | −143.371 | + | 248.325i | −0.0243576 | + | 0.0421885i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1218.25 | 0.205082 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1526.65 | − | 2644.23i | −0.253511 | − | 0.439094i | 0.710979 | − | 0.703213i | \(-0.248252\pi\) |
−0.964490 | + | 0.264119i | \(0.914919\pi\) | |||||||
\(332\) | 2404.12 | − | 4164.05i | 0.397419 | − | 0.688349i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −358.539 | − | 621.009i | −0.0587377 | − | 0.101737i | ||||
\(335\) | 12080.8 | 1.97029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3865.80 | 0.624877 | 0.312438 | − | 0.949938i | \(-0.398854\pi\) | ||||
0.312438 | + | 0.949938i | \(0.398854\pi\) | |||||||
\(338\) | −107.921 | − | 186.925i | −0.0173673 | − | 0.0300811i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2405.90 | − | 4167.15i | 0.383760 | − | 0.664692i | ||||
\(341\) | 35.2627 | + | 61.0768i | 0.00559995 | + | 0.00969940i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 689.726 | 0.108103 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 235.040 | − | 407.101i | 0.0365198 | − | 0.0632541i | ||||
\(347\) | −49.7965 | + | 86.2501i | −0.00770380 | + | 0.0133434i | −0.869852 | − | 0.493313i | \(-0.835786\pi\) |
0.862148 | + | 0.506657i | \(0.169119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3607.34 | 0.553285 | 0.276643 | − | 0.960973i | \(-0.410778\pi\) | ||||
0.276643 | + | 0.960973i | \(0.410778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1421.61 | − | 2462.30i | −0.215262 | − | 0.372844i | ||||
\(353\) | −3565.37 | + | 6175.40i | −0.537579 | + | 0.931114i | 0.461455 | + | 0.887164i | \(0.347328\pi\) |
−0.999034 | + | 0.0439501i | \(0.986006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 612.216 | + | 1060.39i | 0.0915298 | + | 0.158534i | ||||
\(356\) | −1731.13 | −0.257724 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1063.85 | −0.157057 | ||||||||
\(359\) | −3250.14 | − | 5629.41i | −0.477816 | − | 0.827602i | 0.521860 | − | 0.853031i | \(-0.325238\pi\) |
−0.999677 | + | 0.0254289i | \(0.991905\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2151.85 | − | 3727.11i | 0.313727 | − | 0.543390i | ||||
\(362\) | −47.5966 | − | 82.4398i | −0.00691056 | − | 0.0119694i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8831.49 | 1.26647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 412.443 | − | 714.372i | 0.0586631 | − | 0.101607i | −0.835202 | − | 0.549943i | \(-0.814650\pi\) |
0.893866 | + | 0.448335i | \(0.147983\pi\) | |||||||
\(368\) | 4339.12 | − | 7515.58i | 0.614654 | − | 1.06461i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 214.468 | 0.0301342 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −666.925 | − | 1155.15i | −0.0925793 | − | 0.160352i | 0.816016 | − | 0.578029i | \(-0.196178\pi\) |
−0.908596 | + | 0.417677i | \(0.862845\pi\) | |||||||
\(374\) | 364.660 | − | 631.610i | 0.0504174 | − | 0.0873255i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −769.746 | − | 1333.24i | −0.105576 | − | 0.182863i | ||||
\(377\) | −2226.94 | −0.304226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1338.29 | −0.181380 | −0.0906902 | − | 0.995879i | \(-0.528907\pi\) | ||||
−0.0906902 | + | 0.995879i | \(0.528907\pi\) | |||||||
\(380\) | −2494.93 | − | 4321.35i | −0.336809 | − | 0.583370i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −47.7924 | + | 82.7788i | −0.00640123 | + | 0.0110873i | ||||
\(383\) | −176.688 | − | 306.032i | −0.0235727 | − | 0.0408290i | 0.853998 | − | 0.520276i | \(-0.174171\pi\) |
−0.877571 | + | 0.479447i | \(0.840837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −156.341 | −0.0206154 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3105.08 | − | 5378.16i | 0.406280 | − | 0.703697i | ||||
\(389\) | 5868.59 | − | 10164.7i | 0.764908 | − | 1.32486i | −0.175387 | − | 0.984500i | \(-0.556118\pi\) |
0.940295 | − | 0.340360i | \(-0.110549\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6765.59 | 0.875066 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 155.073 | + | 268.595i | 0.0198286 | + | 0.0343442i | ||||
\(395\) | −3027.11 | + | 5243.10i | −0.385595 | + | 0.667871i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6640.71 | + | 11502.1i | 0.839516 | + | 1.45408i | 0.890300 | + | 0.455374i | \(0.150495\pi\) |
−0.0507841 | + | 0.998710i | \(0.516172\pi\) | |||||||
\(398\) | −270.955 | −0.0341250 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1852.01 | 0.231501 | ||||||||
\(401\) | −3741.18 | − | 6479.91i | −0.465899 | − | 0.806961i | 0.533343 | − | 0.845899i | \(-0.320936\pi\) |
−0.999242 | + | 0.0389385i | \(0.987602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2979 | − | 36.8891i | 0.00263257 | − | 0.00455975i | ||||
\(404\) | −1236.99 | − | 2142.54i | −0.152333 | − | 0.263849i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4193.27 | −0.510694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6898.30 | + | 11948.2i | −0.833983 | + | 1.44450i | 0.0608735 | + | 0.998145i | \(0.480611\pi\) |
−0.894856 | + | 0.446355i | \(0.852722\pi\) | |||||||
\(410\) | −475.218 | + | 823.102i | −0.0572423 | + | 0.0991466i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1184.88 | −0.141686 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3765.75 | + | 6522.46i | 0.445429 | + | 0.771506i | ||||
\(416\) | −858.622 | + | 1487.18i | −0.101196 | + | 0.175276i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −378.154 | − | 654.982i | −0.0442491 | − | 0.0766417i | ||||
\(419\) | 9497.56 | 1.10737 | 0.553683 | − | 0.832728i | \(-0.313222\pi\) | ||||
0.553683 | + | 0.832728i | \(0.313222\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 624.367 | 0.0722797 | 0.0361399 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361399 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(422\) | −449.016 | − | 777.719i | −0.0517957 | − | 0.0897127i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 622.608 | − | 1078.39i | 0.0713126 | − | 0.123517i | ||||
\(425\) | 721.915 | + | 1250.39i | 0.0823954 | + | 0.142713i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6759.75 | 0.763423 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −269.050 | + | 466.007i | −0.0301738 | + | 0.0522625i | ||||
\(431\) | −6698.64 | + | 11602.4i | −0.748636 | + | 1.29668i | 0.199840 | + | 0.979829i | \(0.435958\pi\) |
−0.948476 | + | 0.316848i | \(0.897376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14057.3 | 1.56016 | 0.780079 | − | 0.625681i | \(-0.215179\pi\) | ||||
0.780079 | + | 0.625681i | \(0.215179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5405.61 | + | 9362.79i | 0.593766 | + | 1.02843i | ||||
\(437\) | 3507.98 | − | 6075.99i | 0.384003 | − | 0.665112i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8184.42 | − | 14175.8i | −0.889798 | − | 1.54117i | −0.840114 | − | 0.542409i | \(-0.817512\pi\) |
−0.0496832 | − | 0.998765i | \(-0.515821\pi\) | |||||||
\(440\) | 2965.22 | 0.321275 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −440.494 | −0.0474031 | ||||||||
\(443\) | −589.354 | − | 1020.79i | −0.0632078 | − | 0.109479i | 0.832690 | − | 0.553740i | \(-0.186800\pi\) |
−0.895898 | + | 0.444261i | \(0.853466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1355.80 | − | 2348.31i | 0.144429 | − | 0.250159i | ||||
\(446\) | 22.8033 | + | 39.4965i | 0.00242101 | + | 0.00419331i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12400.9 | 1.30342 | 0.651709 | − | 0.758469i | \(-0.274052\pi\) | ||||
0.651709 | + | 0.758469i | \(0.274052\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9291.45 | − | 16093.3i | 0.970105 | − | 1.68027i | ||||
\(452\) | −4161.95 | + | 7208.71i | −0.433101 | + | 0.750153i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −565.484 | −0.0584570 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4962.79 | − | 8595.81i | −0.507986 | − | 0.879858i | −0.999957 | − | 0.00924618i | \(-0.997057\pi\) |
0.491971 | − | 0.870611i | \(-0.336277\pi\) | |||||||
\(458\) | −671.366 | + | 1162.84i | −0.0684954 | + | 0.118637i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6850.21 | + | 11864.9i | 0.694332 | + | 1.20262i | ||||
\(461\) | −16010.3 | −1.61751 | −0.808755 | − | 0.588146i | \(-0.799858\pi\) | ||||
−0.808755 | + | 0.588146i | \(0.799858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17372.4 | 1.74377 | 0.871883 | − | 0.489714i | \(-0.162899\pi\) | ||||
0.871883 | + | 0.489714i | \(0.162899\pi\) | |||||||
\(464\) | −1911.27 | − | 3310.42i | −0.191225 | − | 0.331212i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −141.199 | + | 244.563i | −0.0140363 | + | 0.0243115i | ||||
\(467\) | −1054.03 | − | 1825.64i | −0.104443 | − | 0.180900i | 0.809068 | − | 0.587716i | \(-0.199973\pi\) |
−0.913510 | + | 0.406815i | \(0.866639\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1201.05 | 0.117873 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1669.58 | + | 2891.80i | −0.162815 | + | 0.282004i | ||||
\(473\) | 5260.45 | − | 9111.37i | 0.511365 | − | 0.885711i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1497.26 | 0.144629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 772.293 | + | 1337.65i | 0.0738992 | + | 0.127997i | ||||
\(479\) | 1225.02 | − | 2121.80i | 0.116853 | − | 0.202395i | −0.801666 | − | 0.597772i | \(-0.796053\pi\) |
0.918519 | + | 0.395377i | \(0.129386\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1266.32 | + | 2193.34i | 0.120040 | + | 0.207916i | ||||
\(482\) | −792.887 | −0.0749274 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18309.9 | −1.71956 | ||||||||
\(485\) | 4863.72 | + | 8424.21i | 0.455361 | + | 0.788709i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −322.618 | + | 558.791i | −0.0300189 | + | 0.0519943i | −0.880645 | − | 0.473778i | \(-0.842890\pi\) |
0.850626 | + | 0.525772i | \(0.176223\pi\) | |||||||
\(488\) | −669.270 | − | 1159.21i | −0.0620828 | − | 0.107531i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11766.1 | −1.08146 | −0.540731 | − | 0.841196i | \(-0.681852\pi\) | ||||
−0.540731 | + | 0.841196i | \(0.681852\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1490.03 | − | 2580.81i | 0.136121 | − | 0.235769i | ||||
\(494\) | −228.397 | + | 395.595i | −0.0208018 | + | 0.0360297i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 73.1159 | 0.00661896 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.0104 | + | 38.1232i | 0.00197459 | + | 0.00342010i | 0.867011 | − | 0.498289i | \(-0.166038\pi\) |
−0.865036 | + | 0.501709i | \(0.832705\pi\) | |||||||
\(500\) | 4707.59 | − | 8153.78i | 0.421059 | − | 0.729296i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.7200 | + | 51.4765i | 0.00264236 | + | 0.00457671i | ||||
\(503\) | 8290.27 | 0.734880 | 0.367440 | − | 0.930047i | \(-0.380234\pi\) | ||||
0.367440 | + | 0.930047i | \(0.380234\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3875.19 | 0.341473 | ||||||||
\(506\) | 1038.28 | + | 1798.35i | 0.0912195 | + | 0.157997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1938.60 | − | 3357.76i | 0.169314 | − | 0.293261i | ||||
\(509\) | −3457.52 | − | 5988.60i | −0.301084 | − | 0.521493i | 0.675298 | − | 0.737545i | \(-0.264015\pi\) |
−0.976382 | + | 0.216052i | \(0.930682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4925.45 | −0.425148 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 86.7157 | − | 150.196i | 0.00744137 | − | 0.0128888i | ||||
\(515\) | 927.980 | − | 1607.31i | 0.0794014 | − | 0.137527i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23483.0 | −1.99764 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −895.464 | − | 1550.99i | −0.0755167 | − | 0.130799i | ||||
\(521\) | −6699.64 | + | 11604.1i | −0.563371 | + | 0.975788i | 0.433828 | + | 0.900996i | \(0.357163\pi\) |
−0.997199 | + | 0.0747919i | \(0.976171\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4968.50 | − | 8605.69i | −0.415406 | − | 0.719504i | 0.580065 | − | 0.814570i | \(-0.303027\pi\) |
−0.995471 | + | 0.0950662i | \(0.969694\pi\) | |||||||
\(524\) | 14719.7 | 1.22716 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −227.988 | −0.0188988 | ||||||||
\(527\) | 28.5007 | + | 49.3647i | 0.00235581 | + | 0.00408038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3548.17 | + | 6145.60i | −0.291622 | + | 0.505104i | ||||
\(530\) | 485.736 | + | 841.320i | 0.0398095 | + | 0.0689521i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11223.7 | −0.912104 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5294.15 | + | 9169.74i | −0.427825 | + | 0.741014i | ||||
\(536\) | 1920.70 | − | 3326.75i | 0.154779 | − | 0.268085i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 689.435 | 0.0552484 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4643.08 | − | 8042.06i | −0.368987 | − | 0.639103i | 0.620421 | − | 0.784269i | \(-0.286962\pi\) |
−0.989407 | + | 0.145166i | \(0.953628\pi\) | |||||||
\(542\) | −276.226 | + | 478.437i | −0.0218910 | + | 0.0379163i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1149.00 | − | 1990.13i | −0.0905570 | − | 0.156849i | ||||
\(545\) | −16934.4 | −1.33099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16821.6 | −1.31488 | −0.657438 | − | 0.753508i | \(-0.728360\pi\) | ||||
−0.657438 | + | 0.753508i | \(0.728360\pi\) | |||||||
\(548\) | 2028.73 | + | 3513.87i | 0.158144 | + | 0.273914i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −221.577 | + | 383.782i | −0.0171783 | + | 0.0297537i | ||||
\(551\) | −1545.17 | − | 2676.32i | −0.119467 | − | 0.206924i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1812.83 | −0.139025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8994.69 | + | 15579.3i | −0.686079 | + | 1.18832i | ||||
\(557\) | 902.972 | − | 1563.99i | 0.0686897 | − | 0.118974i | −0.829635 | − | 0.558306i | \(-0.811451\pi\) |
0.898325 | + | 0.439332i | \(0.144785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6354.40 | −0.480792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −338.694 | − | 586.635i | −0.0254216 | − | 0.0440315i | ||||
\(563\) | −6107.45 | + | 10578.4i | −0.457190 | + | 0.791877i | −0.998811 | − | 0.0487460i | \(-0.984478\pi\) |
0.541621 | + | 0.840623i | \(0.317811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6519.17 | − | 11291.5i | −0.485423 | − | 0.840776i | ||||
\(566\) | −439.050 | −0.0326054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 389.338 | 0.0287610 | ||||||||
\(569\) | 2141.89 | + | 3709.86i | 0.157808 | + | 0.273331i | 0.934078 | − | 0.357070i | \(-0.116224\pi\) |
−0.776270 | + | 0.630400i | \(0.782891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3179.97 | + | 5507.87i | −0.233060 | + | 0.403673i | −0.958707 | − | 0.284395i | \(-0.908207\pi\) |
0.725647 | + | 0.688067i | \(0.241541\pi\) | |||||||
\(572\) | 8720.25 | + | 15103.9i | 0.637433 | + | 1.10407i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4110.95 | −0.298153 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7234.36 | − | 12530.3i | 0.521959 | − | 0.904059i | −0.477715 | − | 0.878515i | \(-0.658535\pi\) |
0.999674 | − | 0.0255444i | \(-0.00813192\pi\) | |||||||
\(578\) | −314.656 | + | 545.001i | −0.0226436 | + | 0.0392198i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6034.68 | 0.432028 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9497.10 | − | 16449.5i | −0.674665 | − | 1.16855i | ||||
\(584\) | 1404.09 | − | 2431.96i | 0.0994894 | − | 0.172321i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1020.67 | + | 1767.85i | 0.0719513 | + | 0.124623i | ||||
\(587\) | −11132.6 | −0.782777 | −0.391388 | − | 0.920226i | \(-0.628005\pi\) | ||||
−0.391388 | + | 0.920226i | \(0.628005\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.1108 | 0.00413517 | ||||||||
\(590\) | −1302.55 | − | 2256.07i | −0.0908897 | − | 0.157426i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2173.65 | + | 3764.87i | −0.150906 | + | 0.261377i | ||||
\(593\) | 9887.81 | + | 17126.2i | 0.684728 | + | 1.18598i | 0.973522 | + | 0.228592i | \(0.0734123\pi\) |
−0.288794 | + | 0.957391i | \(0.593254\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11970.4 | 0.822696 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 627.098 | − | 1086.17i | 0.0428829 | − | 0.0742753i | ||||
\(599\) | −11945.5 | + | 20690.2i | −0.814825 | + | 1.41132i | 0.0946282 | + | 0.995513i | \(0.469834\pi\) |
−0.909453 | + | 0.415806i | \(0.863500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19395.5 | −1.31641 | −0.658204 | − | 0.752840i | \(-0.728683\pi\) | ||||
−0.658204 | + | 0.752840i | \(0.728683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6318.32 | + | 10943.7i | 0.425644 | + | 0.737237i | ||||
\(605\) | 14340.1 | − | 24837.8i | 0.963648 | − | 1.66909i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7298.36 | + | 12641.1i | 0.488025 | + | 0.845285i | 0.999905 | − | 0.0137724i | \(-0.00438402\pi\) |
−0.511880 | + | 0.859057i | \(0.671051\pi\) | |||||||
\(608\) | −2383.04 | −0.158956 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1044.28 | 0.0693142 | ||||||||
\(611\) | 7091.62 | + | 12283.0i | 0.469552 | + | 0.813288i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −989.898 | + | 1714.55i | −0.0652229 | + | 0.112969i | −0.896793 | − | 0.442451i | \(-0.854109\pi\) |
0.831570 | + | 0.555420i | \(0.187442\pi\) | |||||||
\(614\) | −746.650 | − | 1293.24i | −0.0490755 | − | 0.0850012i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16262.4 | −1.06110 | −0.530551 | − | 0.847653i | \(-0.678015\pi\) | ||||
−0.530551 | + | 0.847653i | \(0.678015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6010.49 | + | 10410.5i | −0.390278 | + | 0.675981i | −0.992486 | − | 0.122358i | \(-0.960954\pi\) |
0.602208 | + | 0.798339i | \(0.294288\pi\) | |||||||
\(620\) | −57.7143 | + | 99.9642i | −0.00373849 | + | 0.00647526i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −296.127 | −0.0190894 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9225.06 | + | 15978.3i | 0.590404 | + | 1.02261i | ||||
\(626\) | 1097.23 | − | 1900.45i | 0.0700543 | − | 0.121338i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4620.82 | − | 8003.49i | −0.293616 | − | 0.508557i | ||||
\(629\) | −3389.16 | −0.214841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25347.6 | 1.59916 | 0.799582 | − | 0.600557i | \(-0.205055\pi\) | ||||
0.799582 | + | 0.600557i | \(0.205055\pi\) | |||||||
\(632\) | 962.542 | + | 1667.17i | 0.0605821 | + | 0.104931i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −754.317 | + | 1306.51i | −0.0472519 | + | 0.0818428i | ||||
\(635\) | 3036.58 | + | 5259.51i | 0.189769 | + | 0.328689i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 914.669 | 0.0567588 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3098.24 | − | 5366.31i | 0.191358 | − | 0.331441i | ||||
\(641\) | −2555.80 | + | 4426.78i | −0.157485 | + | 0.272772i | −0.933961 | − | 0.357374i | \(-0.883672\pi\) |
0.776476 | + | 0.630147i | \(0.217005\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10931.3 | 0.670435 | 0.335217 | − | 0.942141i | \(-0.391190\pi\) | ||||
0.335217 | + | 0.942141i | \(0.391190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −305.639 | − | 529.382i | −0.0186149 | − | 0.0322419i | ||||
\(647\) | 9203.06 | − | 15940.2i | 0.559211 | − | 0.968582i | −0.438352 | − | 0.898804i | \(-0.644437\pi\) |
0.997563 | − | 0.0697783i | \(-0.0222292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25467.3 | + | 44110.7i | 1.54034 | + | 2.66795i | ||||
\(650\) | 267.655 | 0.0161512 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9175.91 | 0.551160 | ||||||||
\(653\) | 9960.71 | + | 17252.5i | 0.596926 | + | 1.03391i | 0.993272 | + | 0.115805i | \(0.0369447\pi\) |
−0.396346 | + | 0.918101i | \(0.629722\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11528.3 | + | 19967.6i | −0.687707 | + | 1.19114i | ||||
\(656\) | −9632.74 | − | 16684.4i | −0.573316 | − | 0.993012i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18858.8 | 1.11477 | 0.557385 | − | 0.830254i | \(-0.311805\pi\) | ||||
0.557385 | + | 0.830254i | \(0.311805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12916.0 | − | 22371.2i | 0.760023 | − | 1.31640i | −0.182815 | − | 0.983147i | \(-0.558521\pi\) |
0.942838 | − | 0.333251i | \(-0.108146\pi\) | |||||||
\(662\) | 378.718 | − | 655.960i | 0.0222346 | − | 0.0385115i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2394.82 | 0.139965 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4242.50 | + | 7348.22i | 0.246282 | + | 0.426573i | ||||
\(668\) | −11473.5 | + | 19872.7i | −0.664555 | + | 1.15104i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1498.46 | + | 2595.41i | 0.0864037 | + | 0.149656i | ||||
\(671\) | −20417.7 | −1.17469 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16275.0 | −0.932178 | −0.466089 | − | 0.884738i | \(-0.654337\pi\) | ||||
−0.466089 | + | 0.884738i | \(0.654337\pi\) | |||||||
\(674\) | 479.498 | + | 830.515i | 0.0274029 | + | 0.0474633i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3453.55 | + | 5981.73i | −0.196493 | + | 0.340335i | ||||
\(677\) | 13135.9 | + | 22752.0i | 0.745720 | + | 1.29163i | 0.949857 | + | 0.312683i | \(0.101228\pi\) |
−0.204137 | + | 0.978942i | \(0.565439\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2396.60 | 0.135155 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.74769 | + | 15.1514i | −0.000491153 | + | 0.000850702i | ||||
\(683\) | −4036.14 | + | 6990.81i | −0.226118 | + | 0.391648i | −0.956654 | − | 0.291226i | \(-0.905937\pi\) |
0.730536 | + | 0.682874i | \(0.239270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6355.51 | −0.354499 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5453.67 | − | 9446.04i | −0.302208 | − | 0.523440i | ||||
\(689\) | −5736.05 | + | 9935.13i | −0.317164 | + | 0.549344i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12242.6 | − | 21204.9i | −0.673997 | − | 1.16740i | −0.976761 | − | 0.214332i | \(-0.931243\pi\) |
0.302763 | − | 0.953066i | \(-0.402091\pi\) | |||||||
\(692\) | −15042.9 | −0.826364 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.7062 | −0.00135135 | ||||||||
\(695\) | −14089.1 | − | 24403.0i | −0.768962 | − | 1.33188i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7509.71 | − | 13007.2i | 0.408107 | − | 0.706862i | ||||
\(698\) | 447.440 | + | 774.989i | 0.0242634 | + | 0.0420254i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −778.448 | −0.0419423 | −0.0209712 | − | 0.999780i | \(-0.506676\pi\) | ||||
−0.0209712 | + | 0.999780i | \(0.506676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1757.29 | + | 3043.72i | −0.0942780 | + | 0.163294i | ||||
\(704\) | −14731.7 | + | 25516.0i | −0.788667 | + | 1.36601i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1768.93 | −0.0942985 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12086.0 | + | 20933.6i | 0.640197 | + | 1.10885i | 0.985389 | + | 0.170322i | \(0.0544806\pi\) |
−0.345192 | + | 0.938532i | \(0.612186\pi\) | |||||||
\(710\) | −151.874 | + | 263.053i | −0.00802777 | + | 0.0139045i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −431.109 | − | 746.703i | −0.0226917 | − | 0.0393032i | ||||
\(713\) | −162.297 | −0.00852466 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27318.3 | −1.42888 | ||||||||
\(716\) | 17022.0 | + | 29483.0i | 0.888467 | + | 1.53887i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 806.269 | − | 1396.50i | 0.0419077 | − | 0.0725862i | ||||
\(719\) | 40.9418 | + | 70.9132i | 0.00212360 | + | 0.00367819i | 0.867085 | − | 0.498160i | \(-0.165991\pi\) |
−0.864962 | + | 0.501838i | \(0.832657\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1067.63 | 0.0550318 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1523.12 | + | 2638.13i | −0.0781856 | + | 0.135421i | ||||
\(725\) | −905.382 | + | 1568.17i | −0.0463794 | + | 0.0803315i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32542.9 | 1.66018 | 0.830088 | − | 0.557632i | \(-0.188290\pi\) | ||||
0.830088 | + | 0.557632i | \(0.188290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1095.42 | + | 1897.33i | 0.0555389 | + | 0.0961962i | ||||
\(731\) | 4251.70 | − | 7364.16i | 0.215123 | − | 0.372604i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2534.47 | − | 4389.83i | −0.127712 | − | 0.221203i | 0.795078 | − | 0.606507i | \(-0.207430\pi\) |
−0.922790 | + | 0.385304i | \(0.874097\pi\) | |||||||
\(734\) | 204.631 | 0.0102903 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6542.98 | 0.327687 | ||||||||
\(737\) | −29297.8 | − | 50745.3i | −1.46431 | − | 2.53627i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19214.2 | − | 33280.0i | 0.956437 | − | 1.65660i | 0.225392 | − | 0.974268i | \(-0.427634\pi\) |
0.731045 | − | 0.682329i | \(-0.239033\pi\) | |||||||
\(740\) | −3431.55 | − | 5943.62i | −0.170468 | − | 0.295259i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21592.9 | −1.06617 | −0.533086 | − | 0.846061i | \(-0.678968\pi\) | ||||
−0.533086 | + | 0.846061i | \(0.678968\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9375.07 | + | 16238.1i | −0.461042 | + | 0.798548i | ||||
\(746\) | 165.445 | − | 286.560i | 0.00811982 | − | 0.0140639i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −23338.7 | −1.14084 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4056.30 | − | 7025.72i | −0.197093 | − | 0.341374i | 0.750492 | − | 0.660880i | \(-0.229817\pi\) |
−0.947585 | + | 0.319505i | \(0.896483\pi\) | |||||||
\(752\) | −12172.8 | + | 21083.9i | −0.590287 | + | 1.02241i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −276.220 | − | 478.428i | −0.0133413 | − | 0.0231078i | ||||
\(755\) | −19793.7 | −0.954129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3108.01 | 0.149224 | 0.0746120 | − | 0.997213i | \(-0.476228\pi\) | ||||
0.0746120 | + | 0.997213i | \(0.476228\pi\) | |||||||
\(758\) | −165.996 | − | 287.513i | −0.00795414 | − | 0.0137770i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1242.64 | − | 2152.32i | 0.0593098 | − | 0.102728i | ||||
\(761\) | 3605.96 | + | 6245.71i | 0.171769 | + | 0.297512i | 0.939038 | − | 0.343812i | \(-0.111718\pi\) |
−0.767269 | + | 0.641325i | \(0.778385\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3058.77 | 0.144846 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.8313 | − | 75.9181i | 0.00206748 | − | 0.00358098i | ||||
\(767\) | 15381.7 | − | 26641.9i | 0.724123 | − | 1.25422i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7533.07 | 0.353250 | 0.176625 | − | 0.984278i | \(-0.443482\pi\) | ||||
0.176625 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2501.50 | + | 4332.73i | 0.116621 | + | 0.201993i | ||||
\(773\) | 12416.3 | − | 21505.7i | 0.577728 | − | 1.00065i | −0.418012 | − | 0.908442i | \(-0.637273\pi\) |
0.995739 | − | 0.0922122i | \(-0.0293938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3178 | − | 29.9952i | −0.000802674 | − | 0.00139027i | ||||
\(776\) | 3093.08 | 0.143086 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2911.66 | 0.134175 | ||||||||
\(779\) | −7787.61 | − | 13488.5i | −0.358177 | − | 0.620381i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2969.43 | − | 5143.20i | 0.136049 | − | 0.235644i | ||||
\(782\) | 839.177 | + | 1453.50i | 0.0383746 | + | 0.0664667i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14475.9 | 0.658173 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18156.6 | − | 31448.1i | 0.822378 | − | 1.42440i | −0.0815287 | − | 0.996671i | \(-0.525980\pi\) |
0.903907 | − | 0.427730i | \(-0.140686\pi\) | |||||||
\(788\) | 4962.45 | − | 8595.21i | 0.224340 | − | 0.388568i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1501.88 | −0.0676386 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6165.94 | + | 10679.7i | 0.276115 | + | 0.478245i | ||||
\(794\) | −1647.37 | + | 2853.34i | −0.0736311 | + | 0.127533i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4335.37 | + | 7509.08i | 0.193044 | + | 0.334362i | ||||
\(797\) | 31665.7 | 1.40735 | 0.703675 | − | 0.710522i | \(-0.251541\pi\) | ||||
0.703675 | + | 0.710522i | \(0.251541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18979.9 | −0.840375 | ||||||||
\(800\) | 698.162 | + | 1209.25i | 0.0308547 | + | 0.0534419i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 928.081 | − | 1607.48i | 0.0408625 | − | 0.0707759i | ||||
\(803\) | −21417.7 | − | 37096.5i | −0.941237 | − | 1.63027i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.5668 | 0.000461788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 616.105 | − | 1067.13i | 0.0268249 | − | 0.0464621i | ||||
\(809\) | 6192.30 | − | 10725.4i | 0.269110 | − | 0.466111i | −0.699523 | − | 0.714610i | \(-0.746604\pi\) |
0.968632 | + | 0.248499i | \(0.0799373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16742.4 | −0.724914 | −0.362457 | − | 0.932000i | \(-0.618062\pi\) | ||||
−0.362457 | + | 0.932000i | \(0.618062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −520.116 | − | 900.868i | −0.0223957 | − | 0.0387904i | ||||
\(815\) | −7186.45 | + | 12447.3i | −0.308872 | + | 0.534982i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4409.04 | − | 7636.67i | −0.188804 | − | 0.327018i | ||||
\(818\) | −3422.55 | −0.146292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30414.6 | 1.29527 | ||||||||
\(821\) | 13228.2 | + | 22911.9i | 0.562322 | + | 0.973970i | 0.997293 | + | 0.0735259i | \(0.0234252\pi\) |
−0.434971 | + | 0.900444i | \(0.643241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11549.3 | + | 20003.9i | −0.489164 | + | 0.847257i | −0.999922 | − | 0.0124673i | \(-0.996031\pi\) |
0.510758 | + | 0.859724i | \(0.329365\pi\) | |||||||
\(824\) | −295.074 | − | 511.083i | −0.0124750 | − | 0.0216073i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20647.6 | −0.868183 | −0.434092 | − | 0.900869i | \(-0.642931\pi\) | ||||
−0.434092 | + | 0.900869i | \(0.642931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11684.3 | + | 20237.7i | −0.489519 | + | 0.847871i | −0.999927 | − | 0.0120609i | \(-0.996161\pi\) |
0.510409 | + | 0.859932i | \(0.329494\pi\) | |||||||
\(830\) | −934.176 | + | 1618.04i | −0.0390671 | + | 0.0676662i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17795.3 | 0.741514 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17971.8 | − | 31128.0i | −0.744838 | − | 1.29010i | ||||
\(836\) | −12101.2 | + | 20959.8i | −0.500631 | + | 0.867119i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1178.04 | + | 2040.42i | 0.0485617 | + | 0.0841113i | ||||
\(839\) | 16735.5 | 0.688645 | 0.344322 | − | 0.938851i | \(-0.388109\pi\) | ||||
0.344322 | + | 0.938851i | \(0.388109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20651.6 | −0.846758 | ||||||||
\(842\) | 77.4439 | + | 134.137i | 0.00316971 | + | 0.00549009i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14368.8 | + | 24887.5i | −0.586013 | + | 1.01500i | ||||
\(845\) | −5409.56 | − | 9369.63i | −0.220230 | − | 0.381450i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19691.9 | −0.797432 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −179.087 | + | 310.188i | −0.00722662 | + | 0.0125169i | ||||
\(851\) | 4824.90 | − | 8356.97i | 0.194354 | − | 0.336631i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10294.5 | 0.413219 | 0.206609 | − | 0.978424i | \(-0.433757\pi\) | ||||
0.206609 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1683.40 | + | 2915.74i | 0.0672168 | + | 0.116423i | ||||
\(857\) | 16394.3 | − | 28395.7i | 0.653463 | − | 1.13183i | −0.328813 | − | 0.944395i | \(-0.606649\pi\) |
0.982277 | − | 0.187437i | \(-0.0600180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2454.88 | − | 4251.98i | −0.0975081 | − | 0.168889i | 0.813145 | − | 0.582062i | \(-0.197754\pi\) |
−0.910653 | + | 0.413173i | \(0.864421\pi\) | |||||||
\(860\) | 17219.5 | 0.682768 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3323.49 | −0.131321 | ||||||||
\(863\) | 8897.48 | + | 15410.9i | 0.350954 | + | 0.607871i | 0.986417 | − | 0.164261i | \(-0.0525239\pi\) |
−0.635463 | + | 0.772132i | \(0.719191\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11781.4 | − | 20406.0i | 0.463097 | − | 0.802108i | ||||
\(866\) | 1743.60 | + | 3020.01i | 0.0684181 | + | 0.118504i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29364.7 | 1.14629 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17695.3 | + | 30649.1i | −0.688383 | + | 1.19231i | ||||
\(872\) | −2692.36 | + | 4663.30i | −0.104558 | + | 0.181100i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1740.46 | 0.0673592 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17336.1 | − | 30027.0i | −0.667501 | − | 1.15615i | −0.978601 | − | 0.205769i | \(-0.934030\pi\) |
0.311099 | − | 0.950377i | \(-0.399303\pi\) | |||||||
\(878\) | 2030.33 | − | 3516.63i | 0.0780412 | − | 0.135171i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −23446.0 | − | 40609.7i | −0.898141 | − | 1.55563i | ||||
\(881\) | 40848.2 | 1.56210 | 0.781051 | − | 0.624467i | \(-0.214684\pi\) | ||||
0.781051 | + | 0.624467i | \(0.214684\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30035.1 | 1.14469 | 0.572345 | − | 0.820013i | \(-0.306034\pi\) | ||||
0.572345 | + | 0.820013i | \(0.306034\pi\) | |||||||
\(884\) | 7048.04 | + | 12207.6i | 0.268158 | + | 0.464463i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 146.202 | − | 253.230i | 0.00554375 | − | 0.00960205i | ||||
\(887\) | −16605.4 | − | 28761.3i | −0.628583 | − | 1.08874i | −0.987836 | − | 0.155498i | \(-0.950302\pi\) |
0.359253 | − | 0.933240i | \(-0.383032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 672.671 | 0.0253348 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 729.721 | − | 1263.91i | 0.0273911 | − | 0.0474428i | ||||
\(893\) | −9841.11 | + | 17045.3i | −0.368780 | + | 0.638745i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −53325.7 | −1.99160 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1538.16 | + | 2664.17i | 0.0571592 | + | 0.0990027i | ||||
\(899\) | −35.7439 | + | 61.9102i | −0.00132606 | + | 0.00229680i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7675.93 | − | 13295.1i | −0.283820 | − | 0.491591i | ||||
\(902\) | 4609.90 | 0.170169 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4145.86 | −0.152532 | ||||||||
\(905\) | −2385.78 | − | 4132.29i | −0.0876310 | − | 0.151781i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1248.92 | + | 2163.18i | −0.0457217 | + | 0.0791923i | −0.887981 | − | 0.459881i | \(-0.847892\pi\) |
0.842259 | + | 0.539073i | \(0.181225\pi\) | |||||||
\(908\) | 9047.93 | + | 15671.5i | 0.330690 | + | 0.572771i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1895.00 | 0.0689180 | 0.0344590 | − | 0.999406i | \(-0.489029\pi\) | ||||
0.0344590 | + | 0.999406i | \(0.489029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18265.0 | − | 31635.9i | 0.662084 | − | 1.14676i | ||||
\(914\) | 1231.13 | − | 2132.38i | 0.0445538 | − | 0.0771694i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 42968.3 | 1.54990 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3135.36 | − | 5430.59i | −0.112542 | − | 0.194928i | 0.804253 | − | 0.594287i | \(-0.202566\pi\) |
−0.916794 | + | 0.399360i | \(0.869233\pi\) | |||||||
\(920\) | −3411.86 | + | 5909.52i | −0.122267 | + | 0.211773i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1985.85 | − | 3439.59i | −0.0709332 | − | 0.122860i | ||||
\(923\) | −3586.95 | −0.127915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2059.34 | 0.0732008 | ||||||||
\(926\) | 2154.80 | + | 3732.23i | 0.0764700 | + | 0.132450i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1441.01 | − | 2495.90i | 0.0509735 | − | 0.0882887i | ||||
\(929\) | 15776.3 | + | 27325.3i | 0.557161 | + | 0.965032i | 0.997732 | + | 0.0673138i | \(0.0214429\pi\) |
−0.440570 | + | 0.897718i | \(0.645224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9036.89 | 0.317611 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 261.476 | − | 452.889i | 0.00916033 | − | 0.0158662i | ||||
\(935\) | 18278.6 | − | 31659.4i | 0.639330 | − | 1.10735i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22030.2 | 0.768084 | 0.384042 | − | 0.923316i | \(-0.374532\pi\) | ||||
0.384042 | + | 0.923316i | \(0.374532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19217.3 | − | 33285.3i | −0.666806 | − | 1.15494i | ||||
\(941\) | 16269.3 | − | 28179.3i | 0.563618 | − | 0.976214i | −0.433559 | − | 0.901125i | \(-0.642742\pi\) |
0.997177 | − | 0.0750892i | \(-0.0239242\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21382.0 | + | 37034.8i | 0.738383 | + | 1.27892i | ||||
\(944\) | 52805.6 | 1.82063 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2609.94 | 0.0897003 | ||||||||
\(947\) | −20355.5 | − | 35256.8i | −0.698485 | − | 1.20981i | −0.968992 | − | 0.247093i | \(-0.920525\pi\) |
0.270507 | − | 0.962718i | \(-0.412809\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12935.8 | + | 22405.5i | −0.442481 | + | 0.766400i | ||||
\(950\) | 185.714 | + | 321.666i | 0.00634248 | + | 0.0109855i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52516.4 | 1.78507 | 0.892536 | − | 0.450976i | \(-0.148924\pi\) | ||||
0.892536 | + | 0.450976i | \(0.148924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2395.59 | + | 4149.29i | −0.0811723 | + | 0.140595i | ||||
\(956\) | 24713.9 | − | 42805.7i | 0.836091 | − | 1.44815i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 607.786 | 0.0204976 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14894.8 | + | 25798.6i | 0.499977 | + | 0.865986i | ||||
\(962\) | −314.139 | + | 544.105i | −0.0105283 | + | 0.0182356i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12686.4 | + | 21973.6i | 0.423862 | + | 0.734150i | ||||
\(965\) | −7836.58 | −0.261418 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14721.6 | 0.489570 | 0.244785 | − | 0.969577i | \(-0.421283\pi\) | ||||
0.244785 | + | 0.969577i | \(0.421283\pi\) | |||||||
\(968\) | −4559.78 | − | 7897.77i | −0.151402 | − | 0.262235i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1206.55 | + | 2089.81i | −0.0399382 | + | 0.0691750i | ||||
\(971\) | −6886.25 | − | 11927.3i | −0.227590 | − | 0.394198i | 0.729503 | − | 0.683978i | \(-0.239751\pi\) |
−0.957093 | + | 0.289779i | \(0.906418\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −160.065 | −0.00526572 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10583.8 | + | 18331.8i | −0.347111 | + | 0.601215i | ||||
\(977\) | 12391.0 | − | 21461.9i | 0.405757 | − | 0.702791i | −0.588653 | − | 0.808386i | \(-0.700341\pi\) |
0.994409 | + | 0.105595i | \(0.0336748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13152.0 | −0.429358 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1459.42 | − | 2527.79i | −0.0474257 | − | 0.0821437i | ||||
\(983\) | −21402.4 | + | 37070.0i | −0.694435 | + | 1.20280i | 0.275936 | + | 0.961176i | \(0.411012\pi\) |
−0.970371 | + | 0.241620i | \(0.922321\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7773.05 | + | 13463.3i | 0.251442 | + | 0.435510i | ||||
\(986\) | 739.271 | 0.0238775 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14617.7 | 0.470700 | ||||||||
\(989\) | 12105.7 | + | 20967.6i | 0.389219 | + | 0.674147i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −224.931 | + | 389.592i | −0.00721006 | + | 0.0124882i | −0.869608 | − | 0.493743i | \(-0.835628\pi\) |
0.862398 | + | 0.506231i | \(0.168962\pi\) | |||||||
\(992\) | 27.5630 | + | 47.7404i | 0.000882182 | + | 0.00152798i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13581.6 | −0.432730 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10736.9 | + | 18596.8i | −0.341063 | + | 0.590739i | −0.984630 | − | 0.174651i | \(-0.944120\pi\) |
0.643567 | + | 0.765390i | \(0.277454\pi\) | |||||||
\(998\) | −5.46017 | + | 9.45729i | −0.000173185 | + | 0.000299965i | ||||
\(999\) | 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.w.361.2 | 6 | ||
3.2 | odd | 2 | 147.4.e.n.67.2 | 6 | |||
7.2 | even | 3 | inner | 441.4.e.w.226.2 | 6 | ||
7.3 | odd | 6 | 441.4.a.s.1.2 | 3 | |||
7.4 | even | 3 | 441.4.a.t.1.2 | 3 | |||
7.5 | odd | 6 | 63.4.e.c.37.2 | 6 | |||
7.6 | odd | 2 | 63.4.e.c.46.2 | 6 | |||
21.2 | odd | 6 | 147.4.e.n.79.2 | 6 | |||
21.5 | even | 6 | 21.4.e.b.16.2 | yes | 6 | ||
21.11 | odd | 6 | 147.4.a.m.1.2 | 3 | |||
21.17 | even | 6 | 147.4.a.l.1.2 | 3 | |||
21.20 | even | 2 | 21.4.e.b.4.2 | ✓ | 6 | ||
84.11 | even | 6 | 2352.4.a.cg.1.3 | 3 | |||
84.47 | odd | 6 | 336.4.q.k.289.3 | 6 | |||
84.59 | odd | 6 | 2352.4.a.ci.1.1 | 3 | |||
84.83 | odd | 2 | 336.4.q.k.193.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.2 | ✓ | 6 | 21.20 | even | 2 | ||
21.4.e.b.16.2 | yes | 6 | 21.5 | even | 6 | ||
63.4.e.c.37.2 | 6 | 7.5 | odd | 6 | |||
63.4.e.c.46.2 | 6 | 7.6 | odd | 2 | |||
147.4.a.l.1.2 | 3 | 21.17 | even | 6 | |||
147.4.a.m.1.2 | 3 | 21.11 | odd | 6 | |||
147.4.e.n.67.2 | 6 | 3.2 | odd | 2 | |||
147.4.e.n.79.2 | 6 | 21.2 | odd | 6 | |||
336.4.q.k.193.3 | 6 | 84.83 | odd | 2 | |||
336.4.q.k.289.3 | 6 | 84.47 | odd | 6 | |||
441.4.a.s.1.2 | 3 | 7.3 | odd | 6 | |||
441.4.a.t.1.2 | 3 | 7.4 | even | 3 | |||
441.4.e.w.226.2 | 6 | 7.2 | even | 3 | inner | ||
441.4.e.w.361.2 | 6 | 1.1 | even | 1 | trivial | ||
2352.4.a.cg.1.3 | 3 | 84.11 | even | 6 | |||
2352.4.a.ci.1.1 | 3 | 84.59 | odd | 6 |