Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(1,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.a (trivial) |
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: | yes |
Analytic conductor: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1397493.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 27) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.05432\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.40162 | 1.69820 | 0.849101 | − | 0.528230i | \(-0.177144\pi\) | ||||
0.849101 | + | 0.528230i | \(0.177144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.76778 | 1.88389 | ||||||||
\(5\) | −0.0930834 | −0.0416282 | −0.0208141 | − | 0.999783i | \(-0.506626\pi\) | ||||
−0.0208141 | + | 0.999783i | \(0.506626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.579861 | −0.219167 | −0.109583 | − | 0.993978i | \(-0.534952\pi\) | ||||
−0.109583 | + | 0.993978i | \(0.534952\pi\) | |||||||
\(8\) | 4.24555 | 1.50103 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.223551 | −0.0706931 | ||||||||
\(11\) | 3.09308 | 0.932600 | 0.466300 | − | 0.884627i | \(-0.345587\pi\) | ||||
0.466300 | + | 0.884627i | \(0.345587\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.20173 | 1.16535 | 0.582676 | − | 0.812705i | \(-0.302006\pi\) | ||||
0.582676 | + | 0.812705i | \(0.302006\pi\) | |||||||
\(14\) | −1.39261 | −0.372190 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.66063 | 0.665158 | ||||||||
\(17\) | 1.99099 | 0.482885 | 0.241443 | − | 0.970415i | \(-0.422379\pi\) | ||||
0.241443 | + | 0.970415i | \(0.422379\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.84542 | −0.882201 | −0.441100 | − | 0.897458i | \(-0.645412\pi\) | ||||
−0.441100 | + | 0.897458i | \(0.645412\pi\) | |||||||
\(20\) | −0.350718 | −0.0784230 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.42841 | 1.58374 | ||||||||
\(23\) | 4.45282 | 0.928476 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99134 | −0.998267 | ||||||||
\(26\) | 10.0910 | 1.97900 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.18479 | −0.412887 | ||||||||
\(29\) | −6.39951 | −1.18836 | −0.594179 | − | 0.804332i | \(-0.702523\pi\) | ||||
−0.594179 | + | 0.804332i | \(0.702523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65750 | 0.297696 | 0.148848 | − | 0.988860i | \(-0.452444\pi\) | ||||
0.148848 | + | 0.988860i | \(0.452444\pi\) | |||||||
\(32\) | −2.10127 | −0.371456 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.78159 | 0.820037 | ||||||||
\(35\) | 0.0539755 | 0.00912352 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.03009 | 0.662543 | 0.331272 | − | 0.943535i | \(-0.392522\pi\) | ||||
0.331272 | + | 0.943535i | \(0.392522\pi\) | |||||||
\(38\) | −9.23525 | −1.49816 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.395190 | −0.0624850 | ||||||||
\(41\) | 1.09616 | 0.171191 | 0.0855954 | − | 0.996330i | \(-0.472721\pi\) | ||||
0.0855954 | + | 0.996330i | \(0.472721\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.90112 | −1.05241 | −0.526206 | − | 0.850357i | \(-0.676386\pi\) | ||||
−0.526206 | + | 0.850357i | \(0.676386\pi\) | |||||||
\(44\) | 11.6541 | 1.75692 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.6940 | 1.57674 | ||||||||
\(47\) | −3.59319 | −0.524121 | −0.262061 | − | 0.965051i | \(-0.584402\pi\) | ||||
−0.262061 | + | 0.965051i | \(0.584402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66376 | −0.951966 | ||||||||
\(50\) | −11.9873 | −1.69526 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15.8312 | 2.19540 | ||||||||
\(53\) | −5.40034 | −0.741793 | −0.370897 | − | 0.928674i | \(-0.620950\pi\) | ||||
−0.370897 | + | 0.928674i | \(0.620950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.287915 | −0.0388224 | ||||||||
\(56\) | −2.46183 | −0.328976 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.3692 | −2.01807 | ||||||||
\(59\) | 10.2847 | 1.33895 | 0.669474 | − | 0.742835i | \(-0.266520\pi\) | ||||
0.669474 | + | 0.742835i | \(0.266520\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1963 | −1.68962 | −0.844808 | − | 0.535070i | \(-0.820285\pi\) | ||||
−0.844808 | + | 0.535070i | \(0.820285\pi\) | |||||||
\(62\) | 3.98069 | 0.505548 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.3677 | −1.29596 | ||||||||
\(65\) | −0.391112 | −0.0485114 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.83729 | −1.07965 | −0.539824 | − | 0.841778i | \(-0.681509\pi\) | ||||
−0.539824 | + | 0.841778i | \(0.681509\pi\) | |||||||
\(68\) | 7.50161 | 0.909703 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.129629 | 0.0154936 | ||||||||
\(71\) | −1.14495 | −0.135880 | −0.0679401 | − | 0.997689i | \(-0.521643\pi\) | ||||
−0.0679401 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.195472 | 0.0228783 | 0.0114391 | − | 0.999935i | \(-0.496359\pi\) | ||||
0.0114391 | + | 0.999935i | \(0.496359\pi\) | |||||||
\(74\) | 9.67876 | 1.12513 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.4887 | −1.66197 | ||||||||
\(77\) | −1.79356 | −0.204395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.20799 | −0.810963 | −0.405481 | − | 0.914103i | \(-0.632896\pi\) | ||||
−0.405481 | + | 0.914103i | \(0.632896\pi\) | |||||||
\(80\) | −0.247661 | −0.0276893 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.63255 | 0.290717 | ||||||||
\(83\) | 14.9004 | 1.63554 | 0.817768 | − | 0.575548i | \(-0.195211\pi\) | ||||
0.817768 | + | 0.575548i | \(0.195211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.185328 | −0.0201016 | ||||||||
\(86\) | −16.5739 | −1.78721 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.1318 | 1.39986 | ||||||||
\(89\) | 1.55313 | 0.164631 | 0.0823155 | − | 0.996606i | \(-0.473768\pi\) | ||||
0.0823155 | + | 0.996606i | \(0.473768\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.43642 | −0.255406 | ||||||||
\(92\) | 16.7772 | 1.74915 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.62949 | −0.890064 | ||||||||
\(95\) | 0.357945 | 0.0367244 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.29553 | 0.537680 | 0.268840 | − | 0.963185i | \(-0.413360\pi\) | ||||
0.268840 | + | 0.963185i | \(0.413360\pi\) | |||||||
\(98\) | −16.0038 | −1.61663 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.8063 | −1.88063 | ||||||||
\(101\) | 7.26898 | 0.723291 | 0.361645 | − | 0.932316i | \(-0.382215\pi\) | ||||
0.361645 | + | 0.932316i | \(0.382215\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.40137 | 0.630746 | 0.315373 | − | 0.948968i | \(-0.397870\pi\) | ||||
0.315373 | + | 0.948968i | \(0.397870\pi\) | |||||||
\(104\) | 17.8387 | 1.74922 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.9696 | −1.25972 | ||||||||
\(107\) | 5.54365 | 0.535925 | 0.267963 | − | 0.963429i | \(-0.413650\pi\) | ||||
0.267963 | + | 0.963429i | \(0.413650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.23137 | −0.596857 | −0.298428 | − | 0.954432i | \(-0.596462\pi\) | ||||
−0.298428 | + | 0.954432i | \(0.596462\pi\) | |||||||
\(110\) | −0.691462 | −0.0659283 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.54280 | −0.145781 | ||||||||
\(113\) | 11.8440 | 1.11419 | 0.557094 | − | 0.830449i | \(-0.311916\pi\) | ||||
0.557094 | + | 0.830449i | \(0.311916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.414483 | −0.0386508 | ||||||||
\(116\) | −24.1120 | −2.23874 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.6998 | 2.27381 | ||||||||
\(119\) | −1.15450 | −0.105832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.43283 | −0.130258 | ||||||||
\(122\) | −31.6926 | −2.86931 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.24510 | 0.560827 | ||||||||
\(125\) | 0.930028 | 0.0831842 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5294 | 1.02307 | 0.511533 | − | 0.859263i | \(-0.329078\pi\) | ||||
0.511533 | + | 0.859263i | \(0.329078\pi\) | |||||||
\(128\) | −20.6968 | −1.82935 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.939302 | −0.0823822 | ||||||||
\(131\) | 9.01177 | 0.787362 | 0.393681 | − | 0.919247i | \(-0.371201\pi\) | ||||
0.393681 | + | 0.919247i | \(0.371201\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.22981 | 0.193349 | ||||||||
\(134\) | −21.2238 | −1.83346 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.45283 | 0.724824 | ||||||||
\(137\) | −11.5202 | −0.984240 | −0.492120 | − | 0.870527i | \(-0.663778\pi\) | ||||
−0.492120 | + | 0.870527i | \(0.663778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.70383 | 0.144517 | 0.0722587 | − | 0.997386i | \(-0.476979\pi\) | ||||
0.0722587 | + | 0.997386i | \(0.476979\pi\) | |||||||
\(140\) | 0.203368 | 0.0171877 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.74973 | −0.230752 | ||||||||
\(143\) | 12.9963 | 1.08681 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.595688 | 0.0494692 | ||||||||
\(146\) | 0.469450 | 0.0388520 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.1845 | 1.24816 | ||||||||
\(149\) | 21.6528 | 1.77386 | 0.886932 | − | 0.461900i | \(-0.152832\pi\) | ||||
0.886932 | + | 0.461900i | \(0.152832\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.74152 | −0.385860 | −0.192930 | − | 0.981213i | \(-0.561799\pi\) | ||||
−0.192930 | + | 0.981213i | \(0.561799\pi\) | |||||||
\(152\) | −16.3259 | −1.32421 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.30745 | −0.347104 | ||||||||
\(155\) | −0.154286 | −0.0123925 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.209206 | −0.0166964 | −0.00834822 | − | 0.999965i | \(-0.502657\pi\) | ||||
−0.00834822 | + | 0.999965i | \(0.502657\pi\) | |||||||
\(158\) | −17.3109 | −1.37718 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.195593 | 0.0154630 | ||||||||
\(161\) | −2.58202 | −0.203491 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.62384 | 0.440493 | 0.220247 | − | 0.975444i | \(-0.429314\pi\) | ||||
0.220247 | + | 0.975444i | \(0.429314\pi\) | |||||||
\(164\) | 4.13008 | 0.322505 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.7852 | 2.77747 | ||||||||
\(167\) | −16.6805 | −1.29078 | −0.645388 | − | 0.763855i | \(-0.723304\pi\) | ||||
−0.645388 | + | 0.763855i | \(0.723304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.65456 | 0.358043 | ||||||||
\(170\) | −0.445087 | −0.0341366 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −26.0019 | −1.98263 | ||||||||
\(173\) | −19.0021 | −1.44471 | −0.722353 | − | 0.691524i | \(-0.756939\pi\) | ||||
−0.722353 | + | 0.691524i | \(0.756939\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.89428 | 0.218787 | ||||||||
\(176\) | 8.22955 | 0.620326 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.73002 | 0.279577 | ||||||||
\(179\) | −16.2352 | −1.21348 | −0.606739 | − | 0.794901i | \(-0.707523\pi\) | ||||
−0.606739 | + | 0.794901i | \(0.707523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.99158 | −0.222362 | −0.111181 | − | 0.993800i | \(-0.535463\pi\) | ||||
−0.111181 | + | 0.993800i | \(0.535463\pi\) | |||||||
\(182\) | −5.85136 | −0.433732 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.9046 | 1.39367 | ||||||||
\(185\) | −0.375135 | −0.0275805 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.15829 | 0.450338 | ||||||||
\(188\) | −13.5384 | −0.987388 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.859649 | 0.0623655 | ||||||||
\(191\) | 2.25382 | 0.163080 | 0.0815402 | − | 0.996670i | \(-0.474016\pi\) | ||||
0.0815402 | + | 0.996670i | \(0.474016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.880273 | −0.0633634 | −0.0316817 | − | 0.999498i | \(-0.510086\pi\) | ||||
−0.0316817 | + | 0.999498i | \(0.510086\pi\) | |||||||
\(194\) | 12.7179 | 0.913090 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.1076 | −1.79340 | ||||||||
\(197\) | −20.2766 | −1.44464 | −0.722322 | − | 0.691557i | \(-0.756925\pi\) | ||||
−0.722322 | + | 0.691557i | \(0.756925\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.0094 | −1.34754 | −0.673772 | − | 0.738939i | \(-0.735327\pi\) | ||||
−0.673772 | + | 0.738939i | \(0.735327\pi\) | |||||||
\(200\) | −21.1910 | −1.49843 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.4573 | 1.22829 | ||||||||
\(203\) | 3.71083 | 0.260449 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.102034 | −0.00712636 | ||||||||
\(206\) | 15.3737 | 1.07113 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.1793 | 0.775142 | ||||||||
\(209\) | −11.8942 | −0.822740 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1841 | 1.11416 | 0.557079 | − | 0.830460i | \(-0.311922\pi\) | ||||
0.557079 | + | 0.830460i | \(0.311922\pi\) | |||||||
\(212\) | −20.3473 | −1.39746 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.3138 | 0.910110 | ||||||||
\(215\) | 0.642380 | 0.0438100 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.961120 | −0.0652451 | ||||||||
\(218\) | −14.9654 | −1.01358 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.08480 | −0.0731373 | ||||||||
\(221\) | 8.36559 | 0.562731 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4573 | 1.43689 | 0.718443 | − | 0.695585i | \(-0.244855\pi\) | ||||
0.718443 | + | 0.695585i | \(0.244855\pi\) | |||||||
\(224\) | 1.21845 | 0.0814108 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 28.4448 | 1.89212 | ||||||||
\(227\) | 19.1142 | 1.26866 | 0.634329 | − | 0.773064i | \(-0.281277\pi\) | ||||
0.634329 | + | 0.773064i | \(0.281277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.4702 | 1.48487 | 0.742435 | − | 0.669918i | \(-0.233671\pi\) | ||||
0.742435 | + | 0.669918i | \(0.233671\pi\) | |||||||
\(230\) | −0.995432 | −0.0656368 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −27.1694 | −1.78376 | ||||||||
\(233\) | 17.6815 | 1.15835 | 0.579176 | − | 0.815203i | \(-0.303374\pi\) | ||||
0.579176 | + | 0.815203i | \(0.303374\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.334467 | 0.0218182 | ||||||||
\(236\) | 38.7504 | 2.52243 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.77266 | −0.179725 | ||||||||
\(239\) | 15.4203 | 0.997457 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1514 | 0.847159 | 0.423580 | − | 0.905859i | \(-0.360773\pi\) | ||||
0.423580 | + | 0.905859i | \(0.360773\pi\) | |||||||
\(242\) | −3.44113 | −0.221204 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −49.7209 | −3.18305 | ||||||||
\(245\) | 0.620286 | 0.0396286 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.1574 | −1.02807 | ||||||||
\(248\) | 7.03700 | 0.446850 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.23357 | 0.141264 | ||||||||
\(251\) | −17.4166 | −1.09933 | −0.549663 | − | 0.835386i | \(-0.685244\pi\) | ||||
−0.549663 | + | 0.835386i | \(0.685244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7729 | 0.865897 | ||||||||
\(254\) | 27.6892 | 1.73737 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.9704 | −1.81065 | ||||||||
\(257\) | −11.1876 | −0.697862 | −0.348931 | − | 0.937148i | \(-0.613455\pi\) | ||||
−0.348931 | + | 0.937148i | \(0.613455\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.33690 | −0.145208 | ||||||||
\(260\) | −1.47362 | −0.0913903 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.6429 | 1.33710 | ||||||||
\(263\) | 20.7109 | 1.27709 | 0.638544 | − | 0.769585i | \(-0.279537\pi\) | ||||
0.638544 | + | 0.769585i | \(0.279537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.502682 | 0.0308795 | ||||||||
\(266\) | 5.35516 | 0.328346 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −33.2970 | −2.03394 | ||||||||
\(269\) | 28.2449 | 1.72212 | 0.861060 | − | 0.508504i | \(-0.169801\pi\) | ||||
0.861060 | + | 0.508504i | \(0.169801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.2626 | 1.04863 | 0.524316 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524316 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(272\) | 5.29728 | 0.321195 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −27.6672 | −1.67144 | ||||||||
\(275\) | −15.4386 | −0.930984 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.16898 | 0.310574 | 0.155287 | − | 0.987869i | \(-0.450370\pi\) | ||||
0.155287 | + | 0.987869i | \(0.450370\pi\) | |||||||
\(278\) | 4.09197 | 0.245420 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.229155 | 0.0136947 | ||||||||
\(281\) | 3.29644 | 0.196649 | 0.0983246 | − | 0.995154i | \(-0.468652\pi\) | ||||
0.0983246 | + | 0.995154i | \(0.468652\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.13072 | −0.542765 | −0.271382 | − | 0.962472i | \(-0.587481\pi\) | ||||
−0.271382 | + | 0.962472i | \(0.587481\pi\) | |||||||
\(284\) | −4.31391 | −0.255984 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 31.2122 | 1.84562 | ||||||||
\(287\) | −0.635618 | −0.0375194 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0360 | −0.766822 | ||||||||
\(290\) | 1.43062 | 0.0840087 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.736497 | 0.0431002 | ||||||||
\(293\) | 2.82643 | 0.165122 | 0.0825610 | − | 0.996586i | \(-0.473690\pi\) | ||||
0.0825610 | + | 0.996586i | \(0.473690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.957331 | −0.0557380 | ||||||||
\(296\) | 17.1100 | 0.994496 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 52.0017 | 3.01238 | ||||||||
\(299\) | 18.7095 | 1.08200 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00169 | 0.230654 | ||||||||
\(302\) | −11.3873 | −0.655268 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.2312 | −0.586802 | ||||||||
\(305\) | 1.22836 | 0.0703356 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.29446 | 0.359244 | 0.179622 | − | 0.983736i | \(-0.442513\pi\) | ||||
0.179622 | + | 0.983736i | \(0.442513\pi\) | |||||||
\(308\) | −6.75775 | −0.385058 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.370536 | −0.0210450 | ||||||||
\(311\) | 7.37289 | 0.418078 | 0.209039 | − | 0.977907i | \(-0.432966\pi\) | ||||
0.209039 | + | 0.977907i | \(0.432966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.27075 | −0.241397 | −0.120699 | − | 0.992689i | \(-0.538513\pi\) | ||||
−0.120699 | + | 0.992689i | \(0.538513\pi\) | |||||||
\(314\) | −0.502433 | −0.0283539 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.1582 | −1.52777 | ||||||||
\(317\) | −16.1476 | −0.906938 | −0.453469 | − | 0.891272i | \(-0.649814\pi\) | ||||
−0.453469 | + | 0.891272i | \(0.649814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.7942 | −1.10826 | ||||||||
\(320\) | 0.965063 | 0.0539486 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.20102 | −0.345570 | ||||||||
\(323\) | −7.65618 | −0.426001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.9723 | −1.16333 | ||||||||
\(326\) | 13.5063 | 0.748047 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.65378 | 0.256962 | ||||||||
\(329\) | 2.08355 | 0.114870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2282 | 1.05688 | 0.528440 | − | 0.848971i | \(-0.322777\pi\) | ||||
0.528440 | + | 0.848971i | \(0.322777\pi\) | |||||||
\(332\) | 56.1417 | 3.08117 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −40.0602 | −2.19200 | ||||||||
\(335\) | 0.822605 | 0.0449437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.4628 | −1.60494 | −0.802469 | − | 0.596693i | \(-0.796481\pi\) | ||||
−0.802469 | + | 0.596693i | \(0.796481\pi\) | |||||||
\(338\) | 11.1785 | 0.608030 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.698275 | −0.0378693 | ||||||||
\(341\) | 5.12679 | 0.277631 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.92309 | 0.427806 | ||||||||
\(344\) | −29.2990 | −1.57970 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −45.6360 | −2.45340 | ||||||||
\(347\) | −11.3970 | −0.611825 | −0.305912 | − | 0.952060i | \(-0.598961\pi\) | ||||
−0.305912 | + | 0.952060i | \(0.598961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.1616 | 1.50746 | 0.753728 | − | 0.657186i | \(-0.228253\pi\) | ||||
0.753728 | + | 0.657186i | \(0.228253\pi\) | |||||||
\(350\) | 6.95097 | 0.371545 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.49941 | −0.346419 | ||||||||
\(353\) | −28.6541 | −1.52510 | −0.762552 | − | 0.646927i | \(-0.776054\pi\) | ||||
−0.762552 | + | 0.646927i | \(0.776054\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.106576 | 0.00565644 | ||||||||
\(356\) | 5.85184 | 0.310147 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.9909 | −2.06073 | ||||||||
\(359\) | 31.0322 | 1.63782 | 0.818909 | − | 0.573923i | \(-0.194579\pi\) | ||||
0.818909 | + | 0.573923i | \(0.194579\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.21272 | −0.221722 | ||||||||
\(362\) | −7.18464 | −0.377616 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.17992 | −0.481158 | ||||||||
\(365\) | −0.0181952 | −0.000952381 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.1242 | 1.25927 | 0.629637 | − | 0.776889i | \(-0.283204\pi\) | ||||
0.629637 | + | 0.776889i | \(0.283204\pi\) | |||||||
\(368\) | 11.8473 | 0.617583 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.900932 | −0.0468372 | ||||||||
\(371\) | 3.13145 | 0.162577 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.5856 | −0.651658 | −0.325829 | − | 0.945429i | \(-0.605643\pi\) | ||||
−0.325829 | + | 0.945429i | \(0.605643\pi\) | |||||||
\(374\) | 14.7899 | 0.764766 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.2551 | −0.786721 | ||||||||
\(377\) | −26.8890 | −1.38486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.70522 | −0.395790 | −0.197895 | − | 0.980223i | \(-0.563411\pi\) | ||||
−0.197895 | + | 0.980223i | \(0.563411\pi\) | |||||||
\(380\) | 1.34866 | 0.0691848 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.41281 | 0.276944 | ||||||||
\(383\) | 17.8616 | 0.912687 | 0.456343 | − | 0.889804i | \(-0.349159\pi\) | ||||
0.456343 | + | 0.889804i | \(0.349159\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.166951 | 0.00850859 | ||||||||
\(386\) | −2.11408 | −0.107604 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.9524 | 1.01293 | ||||||||
\(389\) | −27.3885 | −1.38865 | −0.694325 | − | 0.719662i | \(-0.744297\pi\) | ||||
−0.694325 | + | 0.719662i | \(0.744297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.86549 | 0.448347 | ||||||||
\(392\) | −28.2913 | −1.42893 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −48.6966 | −2.45330 | ||||||||
\(395\) | 0.670945 | 0.0337589 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.21599 | 0.211594 | 0.105797 | − | 0.994388i | \(-0.466261\pi\) | ||||
0.105797 | + | 0.994388i | \(0.466261\pi\) | |||||||
\(398\) | −45.6535 | −2.28840 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.2801 | −0.664005 | ||||||||
\(401\) | −15.1725 | −0.757678 | −0.378839 | − | 0.925462i | \(-0.623677\pi\) | ||||
−0.378839 | + | 0.925462i | \(0.623677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.96437 | 0.346920 | ||||||||
\(404\) | 27.3880 | 1.36260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.91200 | 0.442295 | ||||||||
\(407\) | 12.4654 | 0.617888 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.70961 | 0.232875 | 0.116438 | − | 0.993198i | \(-0.462852\pi\) | ||||
0.116438 | + | 0.993198i | \(0.462852\pi\) | |||||||
\(410\) | −0.245047 | −0.0121020 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24.1190 | 1.18826 | ||||||||
\(413\) | −5.96367 | −0.293453 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.38698 | −0.0680844 | ||||||||
\(416\) | −8.82898 | −0.432876 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −28.5654 | −1.39718 | ||||||||
\(419\) | −19.7911 | −0.966860 | −0.483430 | − | 0.875383i | \(-0.660609\pi\) | ||||
−0.483430 | + | 0.875383i | \(0.660609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1857 | 1.37369 | 0.686844 | − | 0.726805i | \(-0.258996\pi\) | ||||
0.686844 | + | 0.726805i | \(0.258996\pi\) | |||||||
\(422\) | 38.8680 | 1.89206 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.9274 | −1.11345 | ||||||||
\(425\) | −9.93768 | −0.482048 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.65204 | 0.370308 | ||||||||
\(428\) | 20.8873 | 1.00963 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.54275 | 0.0743982 | ||||||||
\(431\) | 5.19681 | 0.250321 | 0.125161 | − | 0.992136i | \(-0.460055\pi\) | ||||
0.125161 | + | 0.992136i | \(0.460055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3285 | 1.21721 | 0.608605 | − | 0.793473i | \(-0.291730\pi\) | ||||
0.608605 | + | 0.793473i | \(0.291730\pi\) | |||||||
\(434\) | −2.30825 | −0.110799 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.4785 | −1.12441 | ||||||||
\(437\) | −17.1230 | −0.819102 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.6612 | −0.747470 | −0.373735 | − | 0.927536i | \(-0.621923\pi\) | ||||
−0.373735 | + | 0.927536i | \(0.621923\pi\) | |||||||
\(440\) | −1.22236 | −0.0582735 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.0910 | 0.955631 | ||||||||
\(443\) | 18.2538 | 0.867266 | 0.433633 | − | 0.901089i | \(-0.357231\pi\) | ||||
0.433633 | + | 0.901089i | \(0.357231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.144570 | −0.00685329 | ||||||||
\(446\) | 51.5323 | 2.44013 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.01184 | 0.284033 | ||||||||
\(449\) | −28.7216 | −1.35546 | −0.677729 | − | 0.735312i | \(-0.737036\pi\) | ||||
−0.677729 | + | 0.735312i | \(0.737036\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.39050 | 0.159652 | ||||||||
\(452\) | 44.6256 | 2.09901 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 45.9052 | 2.15444 | ||||||||
\(455\) | 0.226791 | 0.0106321 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.3879 | −1.65538 | −0.827688 | − | 0.561188i | \(-0.810344\pi\) | ||||
−0.827688 | + | 0.561188i | \(0.810344\pi\) | |||||||
\(458\) | 53.9648 | 2.52161 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.56168 | −0.0728139 | ||||||||
\(461\) | −2.27673 | −0.106038 | −0.0530189 | − | 0.998594i | \(-0.516884\pi\) | ||||
−0.0530189 | + | 0.998594i | \(0.516884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.3745 | 0.853937 | 0.426968 | − | 0.904267i | \(-0.359582\pi\) | ||||
0.426968 | + | 0.904267i | \(0.359582\pi\) | |||||||
\(464\) | −17.0267 | −0.790446 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 42.4642 | 1.96712 | ||||||||
\(467\) | −4.65870 | −0.215579 | −0.107789 | − | 0.994174i | \(-0.534377\pi\) | ||||
−0.107789 | + | 0.994174i | \(0.534377\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.12440 | 0.236623 | ||||||||
\(470\) | 0.803263 | 0.0370517 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 43.6640 | 2.00980 | ||||||||
\(473\) | −21.3457 | −0.981478 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.1938 | 0.880672 | ||||||||
\(476\) | −4.34989 | −0.199377 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 37.0338 | 1.69388 | ||||||||
\(479\) | 14.1759 | 0.647713 | 0.323857 | − | 0.946106i | \(-0.395020\pi\) | ||||
0.323857 | + | 0.946106i | \(0.395020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9334 | 0.772096 | ||||||||
\(482\) | 31.5848 | 1.43865 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.39861 | −0.245392 | ||||||||
\(485\) | −0.492926 | −0.0223826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4338 | −0.971258 | −0.485629 | − | 0.874165i | \(-0.661409\pi\) | ||||
−0.485629 | + | 0.874165i | \(0.661409\pi\) | |||||||
\(488\) | −56.0256 | −2.53616 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.48969 | 0.0672974 | ||||||||
\(491\) | 14.0879 | 0.635776 | 0.317888 | − | 0.948128i | \(-0.397026\pi\) | ||||
0.317888 | + | 0.948128i | \(0.397026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7413 | −0.573841 | ||||||||
\(494\) | −38.8041 | −1.74588 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.40999 | 0.198015 | ||||||||
\(497\) | 0.663910 | 0.0297804 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9093 | 0.667433 | 0.333717 | − | 0.942673i | \(-0.391697\pi\) | ||||
0.333717 | + | 0.942673i | \(0.391697\pi\) | |||||||
\(500\) | 3.50414 | 0.156710 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −41.8281 | −1.86688 | ||||||||
\(503\) | 15.8631 | 0.707299 | 0.353650 | − | 0.935378i | \(-0.384941\pi\) | ||||
0.353650 | + | 0.935378i | \(0.384941\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.676622 | −0.0301093 | ||||||||
\(506\) | 33.0774 | 1.47047 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 43.4402 | 1.92735 | ||||||||
\(509\) | −33.9267 | −1.50377 | −0.751887 | − | 0.659292i | \(-0.770856\pi\) | ||||
−0.751887 | + | 0.659292i | \(0.770856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.113347 | −0.00501416 | ||||||||
\(512\) | −28.1824 | −1.24550 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.8683 | −1.18511 | ||||||||
\(515\) | −0.595862 | −0.0262568 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.1140 | −0.488795 | ||||||||
\(518\) | −5.61234 | −0.246592 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.66048 | −0.0728170 | ||||||||
\(521\) | 42.7798 | 1.87422 | 0.937108 | − | 0.349039i | \(-0.113492\pi\) | ||||
0.937108 | + | 0.349039i | \(0.113492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.77785 | −0.121467 | −0.0607335 | − | 0.998154i | \(-0.519344\pi\) | ||||
−0.0607335 | + | 0.998154i | \(0.519344\pi\) | |||||||
\(524\) | 33.9544 | 1.48331 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.7397 | 2.16875 | ||||||||
\(527\) | 3.30006 | 0.143753 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.17243 | −0.137932 | ||||||||
\(530\) | 1.20725 | 0.0524396 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.40145 | 0.364249 | ||||||||
\(533\) | 4.60575 | 0.199497 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.516022 | −0.0223096 | ||||||||
\(536\) | −37.5192 | −1.62058 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 67.8335 | 2.92451 | ||||||||
\(539\) | −20.6116 | −0.887803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.59390 | −0.154514 | −0.0772570 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772570 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(542\) | 41.4583 | 1.78079 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.18360 | −0.179370 | ||||||||
\(545\) | 0.580037 | 0.0248461 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.5858 | −1.69257 | −0.846284 | − | 0.532732i | \(-0.821165\pi\) | ||||
−0.846284 | + | 0.532732i | \(0.821165\pi\) | |||||||
\(548\) | −43.4057 | −1.85420 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −37.0777 | −1.58100 | ||||||||
\(551\) | 24.6088 | 1.04837 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.17964 | 0.177736 | ||||||||
\(554\) | 12.4139 | 0.527417 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.41968 | 0.272255 | ||||||||
\(557\) | 11.4346 | 0.484501 | 0.242250 | − | 0.970214i | \(-0.422114\pi\) | ||||
0.242250 | + | 0.970214i | \(0.422114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.9967 | −1.22643 | ||||||||
\(560\) | 0.143609 | 0.00606858 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.91680 | 0.333950 | ||||||||
\(563\) | −14.5108 | −0.611557 | −0.305778 | − | 0.952103i | \(-0.598917\pi\) | ||||
−0.305778 | + | 0.952103i | \(0.598917\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.10248 | −0.0463816 | ||||||||
\(566\) | −21.9285 | −0.921725 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.86093 | −0.203960 | ||||||||
\(569\) | 1.29918 | 0.0544646 | 0.0272323 | − | 0.999629i | \(-0.491331\pi\) | ||||
0.0272323 | + | 0.999629i | \(0.491331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0573 | 0.671978 | 0.335989 | − | 0.941866i | \(-0.390929\pi\) | ||||
0.335989 | + | 0.941866i | \(0.390929\pi\) | |||||||
\(572\) | 48.9673 | 2.04743 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.52651 | −0.0637155 | ||||||||
\(575\) | −22.2255 | −0.926867 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.46033 | −0.352208 | −0.176104 | − | 0.984372i | \(-0.556350\pi\) | ||||
−0.176104 | + | 0.984372i | \(0.556350\pi\) | |||||||
\(578\) | −31.3075 | −1.30222 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.24442 | 0.0931947 | ||||||||
\(581\) | −8.64019 | −0.358456 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.7037 | −0.691796 | ||||||||
\(584\) | 0.829886 | 0.0343409 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.78802 | 0.280411 | ||||||||
\(587\) | 18.3852 | 0.758838 | 0.379419 | − | 0.925225i | \(-0.376124\pi\) | ||||
0.379419 | + | 0.925225i | \(0.376124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.37379 | −0.262627 | ||||||||
\(590\) | −2.29915 | −0.0946544 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.7226 | 0.440696 | ||||||||
\(593\) | −13.5128 | −0.554905 | −0.277452 | − | 0.960739i | \(-0.589490\pi\) | ||||
−0.277452 | + | 0.960739i | \(0.589490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.107464 | 0.00440561 | ||||||||
\(596\) | 81.5830 | 3.34177 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 44.9332 | 1.83746 | ||||||||
\(599\) | −11.0277 | −0.450580 | −0.225290 | − | 0.974292i | \(-0.572333\pi\) | ||||
−0.225290 | + | 0.974292i | \(0.572333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.7979 | 1.05232 | 0.526160 | − | 0.850386i | \(-0.323631\pi\) | ||||
0.526160 | + | 0.850386i | \(0.323631\pi\) | |||||||
\(602\) | 9.61055 | 0.391697 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.8650 | −0.726918 | ||||||||
\(605\) | 0.133373 | 0.00542239 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.7899 | −0.600302 | −0.300151 | − | 0.953892i | \(-0.597037\pi\) | ||||
−0.300151 | + | 0.953892i | \(0.597037\pi\) | |||||||
\(608\) | 8.08027 | 0.327698 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.95005 | 0.119444 | ||||||||
\(611\) | −15.0976 | −0.610785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.2739 | 1.46509 | 0.732545 | − | 0.680719i | \(-0.238332\pi\) | ||||
0.732545 | + | 0.680719i | \(0.238332\pi\) | |||||||
\(614\) | 15.1169 | 0.610069 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.61464 | −0.306803 | ||||||||
\(617\) | 40.3735 | 1.62538 | 0.812689 | − | 0.582698i | \(-0.198003\pi\) | ||||
0.812689 | + | 0.582698i | \(0.198003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.89330 | −0.277065 | −0.138533 | − | 0.990358i | \(-0.544239\pi\) | ||||
−0.138533 | + | 0.990358i | \(0.544239\pi\) | |||||||
\(620\) | −0.581315 | −0.0233462 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.7069 | 0.709981 | ||||||||
\(623\) | −0.900598 | −0.0360817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8701 | 0.994804 | ||||||||
\(626\) | −10.2567 | −0.409941 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.788242 | −0.0314543 | ||||||||
\(629\) | 8.02386 | 0.319932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8191 | 1.18708 | 0.593539 | − | 0.804805i | \(-0.297730\pi\) | ||||
0.593539 | + | 0.804805i | \(0.297730\pi\) | |||||||
\(632\) | −30.6019 | −1.21728 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −38.7804 | −1.54016 | ||||||||
\(635\) | −1.07319 | −0.0425884 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.9993 | −1.10937 | ||||||||
\(638\) | −47.5382 | −1.88206 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.92653 | 0.0761527 | ||||||||
\(641\) | −42.8807 | −1.69369 | −0.846844 | − | 0.531842i | \(-0.821500\pi\) | ||||
−0.846844 | + | 0.531842i | \(0.821500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4133 | −1.08107 | −0.540537 | − | 0.841320i | \(-0.681779\pi\) | ||||
−0.540537 | + | 0.841320i | \(0.681779\pi\) | |||||||
\(644\) | −9.72848 | −0.383356 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.3873 | −0.723437 | ||||||||
\(647\) | 16.1623 | 0.635407 | 0.317703 | − | 0.948190i | \(-0.397088\pi\) | ||||
0.317703 | + | 0.948190i | \(0.397088\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.8113 | 1.24870 | ||||||||
\(650\) | −50.3674 | −1.97557 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.1894 | 0.829842 | ||||||||
\(653\) | −32.2463 | −1.26189 | −0.630947 | − | 0.775826i | \(-0.717334\pi\) | ||||
−0.630947 | + | 0.775826i | \(0.717334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.838847 | −0.0327765 | ||||||||
\(656\) | 2.91647 | 0.113869 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.00391 | 0.195073 | ||||||||
\(659\) | −27.8186 | −1.08366 | −0.541829 | − | 0.840489i | \(-0.682268\pi\) | ||||
−0.541829 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7886 | 1.19754 | 0.598769 | − | 0.800922i | \(-0.295657\pi\) | ||||
0.598769 | + | 0.800922i | \(0.295657\pi\) | |||||||
\(662\) | 46.1789 | 1.79480 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 63.2606 | 2.45499 | ||||||||
\(665\) | −0.207559 | −0.00804877 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.4958 | −1.10336 | ||||||||
\(668\) | −62.8485 | −2.43168 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.97559 | 0.0763236 | ||||||||
\(671\) | −40.8173 | −1.57574 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.1306 | −1.00726 | −0.503631 | − | 0.863919i | \(-0.668003\pi\) | ||||
−0.503631 | + | 0.863919i | \(0.668003\pi\) | |||||||
\(674\) | −70.7584 | −2.72551 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.5374 | 0.674515 | ||||||||
\(677\) | −18.1945 | −0.699271 | −0.349636 | − | 0.936886i | \(-0.613695\pi\) | ||||
−0.349636 | + | 0.936886i | \(0.613695\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.07068 | −0.117842 | ||||||||
\(680\) | −0.786818 | −0.0301731 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.3126 | 0.471474 | ||||||||
\(683\) | −23.4971 | −0.899092 | −0.449546 | − | 0.893257i | \(-0.648414\pi\) | ||||
−0.449546 | + | 0.893257i | \(0.648414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.07234 | 0.0409721 | ||||||||
\(686\) | 19.0283 | 0.726502 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.3613 | −0.700019 | ||||||||
\(689\) | −22.6908 | −0.864449 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.5379 | −1.69430 | −0.847151 | − | 0.531352i | \(-0.821684\pi\) | ||||
−0.847151 | + | 0.531352i | \(0.821684\pi\) | |||||||
\(692\) | −71.5960 | −2.72167 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.3714 | −1.03900 | ||||||||
\(695\) | −0.158599 | −0.00601599 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.18243 | 0.0826655 | ||||||||
\(698\) | 67.6335 | 2.55997 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.9050 | 0.412171 | ||||||||
\(701\) | 25.2567 | 0.953934 | 0.476967 | − | 0.878921i | \(-0.341736\pi\) | ||||
0.476967 | + | 0.878921i | \(0.341736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4974 | −0.584496 | ||||||||
\(704\) | −32.0682 | −1.20862 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −68.8163 | −2.58994 | ||||||||
\(707\) | −4.21500 | −0.158521 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.6840 | −0.589026 | −0.294513 | − | 0.955648i | \(-0.595157\pi\) | ||||
−0.294513 | + | 0.955648i | \(0.595157\pi\) | |||||||
\(710\) | 0.255954 | 0.00960579 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.59387 | 0.247116 | ||||||||
\(713\) | 7.38054 | 0.276403 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.20974 | −0.0452417 | ||||||||
\(716\) | −61.1708 | −2.28606 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 74.5277 | 2.78135 | ||||||||
\(719\) | 53.1607 | 1.98256 | 0.991280 | − | 0.131771i | \(-0.0420664\pi\) | ||||
0.991280 | + | 0.131771i | \(0.0420664\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.71191 | −0.138239 | ||||||||
\(722\) | −10.1174 | −0.376529 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.2716 | −0.418907 | ||||||||
\(725\) | 31.9421 | 1.18630 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.469172 | 0.0174006 | 0.00870032 | − | 0.999962i | \(-0.497231\pi\) | ||||
0.00870032 | + | 0.999962i | \(0.497231\pi\) | |||||||
\(728\) | −10.3440 | −0.383372 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.0436980 | −0.00161734 | ||||||||
\(731\) | −13.7400 | −0.508194 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.4063 | −1.71406 | −0.857028 | − | 0.515271i | \(-0.827691\pi\) | ||||
−0.857028 | + | 0.515271i | \(0.827691\pi\) | |||||||
\(734\) | 57.9372 | 2.13850 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.35657 | −0.344888 | ||||||||
\(737\) | −27.3345 | −1.00688 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8093 | 0.949411 | 0.474706 | − | 0.880145i | \(-0.342555\pi\) | ||||
0.474706 | + | 0.880145i | \(0.342555\pi\) | |||||||
\(740\) | −1.41343 | −0.0519586 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.52055 | 0.276088 | ||||||||
\(743\) | −34.7096 | −1.27337 | −0.636687 | − | 0.771123i | \(-0.719695\pi\) | ||||
−0.636687 | + | 0.771123i | \(0.719695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.01551 | −0.0738427 | ||||||||
\(746\) | −30.2259 | −1.10665 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 23.2031 | 0.848389 | ||||||||
\(749\) | −3.21455 | −0.117457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.9858 | 0.875256 | 0.437628 | − | 0.899156i | \(-0.355819\pi\) | ||||
0.437628 | + | 0.899156i | \(0.355819\pi\) | |||||||
\(752\) | −9.56016 | −0.348623 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −64.5773 | −2.35177 | ||||||||
\(755\) | 0.441357 | 0.0160626 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.78780 | −0.319398 | −0.159699 | − | 0.987166i | \(-0.551052\pi\) | ||||
−0.159699 | + | 0.987166i | \(0.551052\pi\) | |||||||
\(758\) | −18.5050 | −0.672132 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.51967 | 0.0551243 | ||||||||
\(761\) | −13.7539 | −0.498578 | −0.249289 | − | 0.968429i | \(-0.580197\pi\) | ||||
−0.249289 | + | 0.968429i | \(0.580197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.61333 | 0.130811 | ||||||||
\(764\) | 8.49190 | 0.307226 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.8969 | 1.54993 | ||||||||
\(767\) | 43.2134 | 1.56034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.3579 | −1.13080 | −0.565398 | − | 0.824818i | \(-0.691277\pi\) | ||||
−0.565398 | + | 0.824818i | \(0.691277\pi\) | |||||||
\(770\) | 0.400952 | 0.0144493 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.31668 | −0.119370 | ||||||||
\(773\) | −28.1214 | −1.01146 | −0.505729 | − | 0.862693i | \(-0.668776\pi\) | ||||
−0.505729 | + | 0.862693i | \(0.668776\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.27314 | −0.297180 | ||||||||
\(776\) | 22.4824 | 0.807073 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −65.7767 | −2.35821 | ||||||||
\(779\) | −4.21518 | −0.151025 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.54142 | −0.126722 | ||||||||
\(782\) | 21.2916 | 0.761385 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.7298 | −0.633207 | ||||||||
\(785\) | 0.0194736 | 0.000695042 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.2002 | −1.29040 | −0.645198 | − | 0.764015i | \(-0.723225\pi\) | ||||
−0.645198 | + | 0.764015i | \(0.723225\pi\) | |||||||
\(788\) | −76.3977 | −2.72155 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.61136 | 0.0573294 | ||||||||
\(791\) | −6.86787 | −0.244193 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.4474 | −1.96900 | ||||||||
\(794\) | 10.1252 | 0.359330 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −71.6235 | −2.53863 | ||||||||
\(797\) | 29.6001 | 1.04849 | 0.524245 | − | 0.851568i | \(-0.324348\pi\) | ||||
0.524245 | + | 0.851568i | \(0.324348\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.15400 | −0.253090 | ||||||||
\(800\) | 10.4881 | 0.370812 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.4386 | −1.28669 | ||||||||
\(803\) | 0.604612 | 0.0213363 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.240343 | 0.00847097 | ||||||||
\(806\) | 16.7258 | 0.589141 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.8608 | 1.08568 | ||||||||
\(809\) | 5.75943 | 0.202491 | 0.101245 | − | 0.994861i | \(-0.467717\pi\) | ||||
0.101245 | + | 0.994861i | \(0.467717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.4896 | 0.438569 | 0.219284 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(812\) | 13.9816 | 0.490658 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.9372 | 1.04930 | ||||||||
\(815\) | −0.523487 | −0.0183369 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.5377 | 0.928438 | ||||||||
\(818\) | 11.3107 | 0.395470 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.384442 | −0.0134253 | ||||||||
\(821\) | −43.0668 | −1.50304 | −0.751520 | − | 0.659710i | \(-0.770679\pi\) | ||||
−0.751520 | + | 0.659710i | \(0.770679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.2841 | 0.358481 | 0.179240 | − | 0.983805i | \(-0.442636\pi\) | ||||
0.179240 | + | 0.983805i | \(0.442636\pi\) | |||||||
\(824\) | 27.1773 | 0.946767 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.3225 | −0.498343 | ||||||||
\(827\) | −6.09463 | −0.211931 | −0.105965 | − | 0.994370i | \(-0.533793\pi\) | ||||
−0.105965 | + | 0.994370i | \(0.533793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.6979 | −1.17038 | −0.585188 | − | 0.810898i | \(-0.698979\pi\) | ||||
−0.585188 | + | 0.810898i | \(0.698979\pi\) | |||||||
\(830\) | −3.33101 | −0.115621 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −43.5624 | −1.51025 | ||||||||
\(833\) | −13.2675 | −0.459690 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.55268 | 0.0537326 | ||||||||
\(836\) | −44.8148 | −1.54995 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47.5308 | −1.64192 | ||||||||
\(839\) | 42.2262 | 1.45781 | 0.728905 | − | 0.684615i | \(-0.240029\pi\) | ||||
0.728905 | + | 0.684615i | \(0.240029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.9537 | 0.412197 | ||||||||
\(842\) | 67.6914 | 2.33280 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 60.9781 | 2.09895 | ||||||||
\(845\) | −0.433262 | −0.0149047 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.830846 | 0.0285482 | ||||||||
\(848\) | −14.3683 | −0.493409 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −23.8665 | −0.818616 | ||||||||
\(851\) | 17.9453 | 0.615156 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.7296 | −1.22336 | −0.611679 | − | 0.791106i | \(-0.709506\pi\) | ||||
−0.611679 | + | 0.791106i | \(0.709506\pi\) | |||||||
\(854\) | 18.3773 | 0.628858 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.5358 | 0.804439 | ||||||||
\(857\) | −7.90865 | −0.270154 | −0.135077 | − | 0.990835i | \(-0.543128\pi\) | ||||
−0.135077 | + | 0.990835i | \(0.543128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.7191 | −1.52580 | −0.762899 | − | 0.646518i | \(-0.776225\pi\) | ||||
−0.762899 | + | 0.646518i | \(0.776225\pi\) | |||||||
\(860\) | 2.42035 | 0.0825332 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.4808 | 0.425096 | ||||||||
\(863\) | 22.9170 | 0.780103 | 0.390052 | − | 0.920793i | \(-0.372457\pi\) | ||||
0.390052 | + | 0.920793i | \(0.372457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.76878 | 0.0601405 | ||||||||
\(866\) | 60.8294 | 2.06707 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.62129 | −0.122915 | ||||||||
\(869\) | −22.2949 | −0.756304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.1319 | −1.25817 | ||||||||
\(872\) | −26.4556 | −0.895899 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −41.1229 | −1.39100 | ||||||||
\(875\) | −0.539287 | −0.0182312 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.1376 | −0.747535 | −0.373767 | − | 0.927522i | \(-0.621934\pi\) | ||||
−0.373767 | + | 0.927522i | \(0.621934\pi\) | |||||||
\(878\) | −37.6124 | −1.26936 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.766035 | −0.0258230 | ||||||||
\(881\) | −9.86404 | −0.332328 | −0.166164 | − | 0.986098i | \(-0.553138\pi\) | ||||
−0.166164 | + | 0.986098i | \(0.553138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.5731 | 1.60096 | 0.800481 | − | 0.599358i | \(-0.204578\pi\) | ||||
0.800481 | + | 0.599358i | \(0.204578\pi\) | |||||||
\(884\) | 31.5197 | 1.06012 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 43.8388 | 1.47279 | ||||||||
\(887\) | −13.3573 | −0.448494 | −0.224247 | − | 0.974532i | \(-0.571992\pi\) | ||||
−0.224247 | + | 0.974532i | \(0.571992\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.68544 | −0.224222 | ||||||||
\(890\) | −0.347203 | −0.0116383 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 80.8465 | 2.70694 | ||||||||
\(893\) | 13.8174 | 0.462380 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.51123 | 0.0505149 | ||||||||
\(896\) | 12.0013 | 0.400934 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −68.9785 | −2.30184 | ||||||||
\(899\) | −10.6072 | −0.353769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7520 | −0.358201 | ||||||||
\(902\) | 8.14270 | 0.271122 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 50.2842 | 1.67243 | ||||||||
\(905\) | 0.278467 | 0.00925654 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.9606 | 1.22726 | 0.613629 | − | 0.789595i | \(-0.289709\pi\) | ||||
0.613629 | + | 0.789595i | \(0.289709\pi\) | |||||||
\(908\) | 72.0184 | 2.39001 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.544665 | 0.0180555 | ||||||||
\(911\) | 48.4111 | 1.60393 | 0.801966 | − | 0.597370i | \(-0.203788\pi\) | ||||
0.801966 | + | 0.597370i | \(0.203788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.0883 | 1.52530 | ||||||||
\(914\) | −84.9884 | −2.81117 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 84.6627 | 2.79733 | ||||||||
\(917\) | −5.22558 | −0.172564 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.93459 | 0.294725 | 0.147363 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147363 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(920\) | −1.75971 | −0.0580159 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.46784 | −0.180074 | ||||||||
\(923\) | −4.81076 | −0.158348 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.1156 | −0.661395 | ||||||||
\(926\) | 44.1287 | 1.45016 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.4471 | 0.441423 | ||||||||
\(929\) | 6.24415 | 0.204864 | 0.102432 | − | 0.994740i | \(-0.467338\pi\) | ||||
0.102432 | + | 0.994740i | \(0.467338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.6250 | 0.839825 | ||||||||
\(932\) | 66.6200 | 2.18221 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.1884 | −0.366097 | ||||||||
\(935\) | −0.573234 | −0.0187468 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.8424 | 1.49760 | 0.748802 | − | 0.662794i | \(-0.230629\pi\) | ||||
0.748802 | + | 0.662794i | \(0.230629\pi\) | |||||||
\(938\) | 12.3069 | 0.401834 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.26020 | 0.0411032 | ||||||||
\(941\) | 4.35263 | 0.141892 | 0.0709459 | − | 0.997480i | \(-0.477398\pi\) | ||||
0.0709459 | + | 0.997480i | \(0.477398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.88098 | 0.158947 | ||||||||
\(944\) | 27.3637 | 0.890612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.2644 | −1.66675 | ||||||||
\(947\) | −2.01674 | −0.0655351 | −0.0327675 | − | 0.999463i | \(-0.510432\pi\) | ||||
−0.0327675 | + | 0.999463i | \(0.510432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.821322 | 0.0266612 | ||||||||
\(950\) | 46.0962 | 1.49556 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.90147 | −0.158857 | ||||||||
\(953\) | 35.7287 | 1.15737 | 0.578684 | − | 0.815552i | \(-0.303567\pi\) | ||||
0.578684 | + | 0.815552i | \(0.303567\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.209793 | −0.00678874 | ||||||||
\(956\) | 58.1004 | 1.87910 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.0451 | 1.09995 | ||||||||
\(959\) | 6.68014 | 0.215713 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2527 | −0.911377 | ||||||||
\(962\) | 40.6676 | 1.31117 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 49.5518 | 1.59596 | ||||||||
\(965\) | 0.0819388 | 0.00263770 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.693317 | −0.0222956 | −0.0111478 | − | 0.999938i | \(-0.503549\pi\) | ||||
−0.0111478 | + | 0.999938i | \(0.503549\pi\) | |||||||
\(968\) | −6.08317 | −0.195520 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.18382 | −0.0380103 | ||||||||
\(971\) | −47.4942 | −1.52416 | −0.762081 | − | 0.647482i | \(-0.775822\pi\) | ||||
−0.762081 | + | 0.647482i | \(0.775822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.987988 | −0.0316734 | ||||||||
\(974\) | −51.4759 | −1.64939 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.1105 | −1.12386 | ||||||||
\(977\) | 12.6033 | 0.403216 | 0.201608 | − | 0.979466i | \(-0.435383\pi\) | ||||
0.201608 | + | 0.979466i | \(0.435383\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.80395 | 0.153535 | ||||||||
\(980\) | 2.33710 | 0.0746560 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.8337 | 1.07968 | ||||||||
\(983\) | −11.5450 | −0.368229 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.88741 | 0.0601379 | ||||||||
\(986\) | −30.5999 | −0.974498 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −60.8778 | −1.93678 | ||||||||
\(989\) | −30.7294 | −0.977139 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.6935 | 0.593819 | 0.296910 | − | 0.954906i | \(-0.404044\pi\) | ||||
0.296910 | + | 0.954906i | \(0.404044\pi\) | |||||||
\(992\) | −3.48286 | −0.110581 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.59446 | 0.0505732 | ||||||||
\(995\) | 1.76946 | 0.0560958 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.35880 | 0.106374 | 0.0531872 | − | 0.998585i | \(-0.483062\pi\) | ||||
0.0531872 | + | 0.998585i | \(0.483062\pi\) | |||||||
\(998\) | 35.8066 | 1.13344 | ||||||||
\(999\) | 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 | 729.2.a.d.1.6 | 6 | ||
3.2 | odd | 2 | 729.2.a.a.1.1 | 6 | |||
9.2 | odd | 6 | 729.2.c.e.244.6 | 12 | |||
9.4 | even | 3 | 729.2.c.b.487.1 | 12 | |||
9.5 | odd | 6 | 729.2.c.e.487.6 | 12 | |||
9.7 | even | 3 | 729.2.c.b.244.1 | 12 | |||
27.2 | odd | 18 | 243.2.e.d.190.2 | 12 | |||
27.4 | even | 9 | 243.2.e.b.136.2 | 12 | |||
27.5 | odd | 18 | 27.2.e.a.25.1 | yes | 12 | ||
27.7 | even | 9 | 243.2.e.b.109.2 | 12 | |||
27.11 | odd | 18 | 27.2.e.a.13.1 | ✓ | 12 | ||
27.13 | even | 9 | 243.2.e.a.55.1 | 12 | |||
27.14 | odd | 18 | 243.2.e.d.55.2 | 12 | |||
27.16 | even | 9 | 81.2.e.a.10.2 | 12 | |||
27.20 | odd | 18 | 243.2.e.c.109.1 | 12 | |||
27.22 | even | 9 | 81.2.e.a.73.2 | 12 | |||
27.23 | odd | 18 | 243.2.e.c.136.1 | 12 | |||
27.25 | even | 9 | 243.2.e.a.190.1 | 12 | |||
108.11 | even | 18 | 432.2.u.c.337.1 | 12 | |||
108.59 | even | 18 | 432.2.u.c.241.1 | 12 | |||
135.32 | even | 36 | 675.2.u.b.349.1 | 24 | |||
135.38 | even | 36 | 675.2.u.b.499.1 | 24 | |||
135.59 | odd | 18 | 675.2.l.c.376.2 | 12 | |||
135.92 | even | 36 | 675.2.u.b.499.4 | 24 | |||
135.113 | even | 36 | 675.2.u.b.349.4 | 24 | |||
135.119 | odd | 18 | 675.2.l.c.526.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.1 | ✓ | 12 | 27.11 | odd | 18 | ||
27.2.e.a.25.1 | yes | 12 | 27.5 | odd | 18 | ||
81.2.e.a.10.2 | 12 | 27.16 | even | 9 | |||
81.2.e.a.73.2 | 12 | 27.22 | even | 9 | |||
243.2.e.a.55.1 | 12 | 27.13 | even | 9 | |||
243.2.e.a.190.1 | 12 | 27.25 | even | 9 | |||
243.2.e.b.109.2 | 12 | 27.7 | even | 9 | |||
243.2.e.b.136.2 | 12 | 27.4 | even | 9 | |||
243.2.e.c.109.1 | 12 | 27.20 | odd | 18 | |||
243.2.e.c.136.1 | 12 | 27.23 | odd | 18 | |||
243.2.e.d.55.2 | 12 | 27.14 | odd | 18 | |||
243.2.e.d.190.2 | 12 | 27.2 | odd | 18 | |||
432.2.u.c.241.1 | 12 | 108.59 | even | 18 | |||
432.2.u.c.337.1 | 12 | 108.11 | even | 18 | |||
675.2.l.c.376.2 | 12 | 135.59 | odd | 18 | |||
675.2.l.c.526.2 | 12 | 135.119 | odd | 18 | |||
675.2.u.b.349.1 | 24 | 135.32 | even | 36 | |||
675.2.u.b.349.4 | 24 | 135.113 | even | 36 | |||
675.2.u.b.499.1 | 24 | 135.38 | even | 36 | |||
675.2.u.b.499.4 | 24 | 135.92 | even | 36 | |||
729.2.a.a.1.1 | 6 | 3.2 | odd | 2 | |||
729.2.a.d.1.6 | 6 | 1.1 | even | 1 | trivial | ||
729.2.c.b.244.1 | 12 | 9.7 | even | 3 | |||
729.2.c.b.487.1 | 12 | 9.4 | even | 3 | |||
729.2.c.e.244.6 | 12 | 9.2 | odd | 6 | |||
729.2.c.e.487.6 | 12 | 9.5 | odd | 6 |