Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1345}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 336 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(18.8371\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.8371 | −1.41652 | −0.708258 | − | 0.705954i | \(-0.750518\pi\) | ||||
−0.708258 | + | 0.705954i | \(0.750518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −51.8371 | −1.42086 | −0.710431 | − | 0.703767i | \(-0.751500\pi\) | ||||
−0.710431 | + | 0.703767i | \(0.751500\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.8371 | 0.828575 | 0.414288 | − | 0.910146i | \(-0.364031\pi\) | ||||
0.414288 | + | 0.910146i | \(0.364031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 47.5114 | 0.817825 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 27.3485 | 0.390175 | 0.195088 | − | 0.980786i | \(-0.437501\pi\) | ||||
0.195088 | + | 0.980786i | \(0.437501\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −76.5114 | −0.923837 | −0.461919 | − | 0.886922i | \(-0.652839\pi\) | ||||
−0.461919 | + | 0.886922i | \(0.652839\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −147.348 | −1.33584 | −0.667919 | − | 0.744234i | \(-0.732815\pi\) | ||||
−0.667919 | + | 0.744234i | \(0.732815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 125.814 | 1.00652 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 240.208 | 1.53812 | 0.769061 | − | 0.639175i | \(-0.220724\pi\) | ||||
0.769061 | + | 0.639175i | \(0.220724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 296.674 | 1.71885 | 0.859424 | − | 0.511264i | \(-0.170823\pi\) | ||||
0.859424 | + | 0.511264i | \(0.170823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 155.511 | 0.820335 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −161.534 | −0.717731 | −0.358865 | − | 0.933389i | \(-0.616836\pi\) | ||||
−0.358865 | + | 0.933389i | \(0.616836\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −116.511 | −0.478378 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −102.977 | −0.392252 | −0.196126 | − | 0.980579i | \(-0.562836\pi\) | ||||
−0.196126 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 328.557 | 1.16522 | 0.582610 | − | 0.812752i | \(-0.302032\pi\) | ||||
0.582610 | + | 0.812752i | \(0.302032\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −142.534 | −0.472172 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −67.9546 | −0.210898 | −0.105449 | − | 0.994425i | \(-0.533628\pi\) | ||||
−0.105449 | + | 0.994425i | \(0.533628\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −82.0454 | −0.225268 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −66.4886 | −0.172319 | −0.0861596 | − | 0.996281i | \(-0.527459\pi\) | ||||
−0.0861596 | + | 0.996281i | \(0.527459\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 820.951 | 2.01267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 229.534 | 0.533378 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 461.928 | 1.01929 | 0.509643 | − | 0.860386i | \(-0.329777\pi\) | ||||
0.509643 | + | 0.860386i | \(0.329777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 185.348 | 0.389040 | 0.194520 | − | 0.980899i | \(-0.437685\pi\) | ||||
0.194520 | + | 0.980899i | \(0.437685\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −615.068 | −1.17369 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −545.208 | −0.994146 | −0.497073 | − | 0.867709i | \(-0.665592\pi\) | ||||
−0.497073 | + | 0.867709i | \(0.665592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 442.045 | 0.771247 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 130.742 | 0.218539 | 0.109270 | − | 0.994012i | \(-0.465149\pi\) | ||||
0.109270 | + | 0.994012i | \(0.465149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 181.299 | 0.290678 | 0.145339 | − | 0.989382i | \(-0.453573\pi\) | ||||
0.145339 | + | 0.989382i | \(0.453573\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −377.443 | −0.581112 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 409.697 | 0.583475 | 0.291737 | − | 0.956498i | \(-0.405767\pi\) | ||||
0.291737 | + | 0.956498i | \(0.405767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −347.928 | −0.460121 | −0.230061 | − | 0.973176i | \(-0.573892\pi\) | ||||
−0.230061 | + | 0.973176i | \(0.573892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −433.121 | −0.552689 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −720.625 | −0.888036 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1157.16 | 1.37819 | 0.689093 | − | 0.724673i | \(-0.258009\pi\) | ||||
0.689093 | + | 0.724673i | \(0.258009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −890.023 | −0.992377 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1211.72 | 1.30863 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1618.30 | 1.69395 | 0.846976 | − | 0.531631i | \(-0.178421\pi\) | ||||
0.846976 | + | 0.531631i | \(0.178421\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −466.534 | −0.473621 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 718.742 | 0.708094 | 0.354047 | − | 0.935228i | \(-0.384805\pi\) | ||||
0.354047 | + | 0.935228i | \(0.384805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1611.58 | 1.54169 | 0.770843 | − | 0.637025i | \(-0.219835\pi\) | ||||
0.770843 | + | 0.637025i | \(0.219835\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −934.670 | −0.844467 | −0.422234 | − | 0.906487i | \(-0.638754\pi\) | ||||
−0.422234 | + | 0.906487i | \(0.638754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1197.02 | −1.05187 | −0.525934 | − | 0.850525i | \(-0.676284\pi\) | ||||
−0.525934 | + | 0.850525i | \(0.676284\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 484.602 | 0.414382 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2384.64 | −1.98521 | −0.992604 | − | 0.121400i | \(-0.961262\pi\) | ||||
−0.992604 | + | 0.121400i | \(0.961262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2333.58 | 1.89224 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 349.534 | 0.276192 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1356.09 | 1.01885 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 308.932 | 0.226467 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.8977 | −0.00922883 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2673.92 | 1.86829 | 0.934143 | − | 0.356898i | \(-0.116166\pi\) | ||||
0.934143 | + | 0.356898i | \(0.116166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −985.670 | −0.672740 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 38.8598 | 0.0259176 | 0.0129588 | − | 0.999916i | \(-0.495875\pi\) | ||||
0.0129588 | + | 0.999916i | \(0.495875\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 427.602 | 0.272608 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −768.144 | −0.479029 | −0.239514 | − | 0.970893i | \(-0.576988\pi\) | ||||
−0.239514 | + | 0.970893i | \(0.576988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1052.55 | −0.642274 | −0.321137 | − | 0.947033i | \(-0.604065\pi\) | ||||
−0.321137 | + | 0.947033i | \(0.604065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 203.864 | 0.121762 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2013.20 | −1.17729 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3804.21 | −2.17877 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 360.977 | 0.198473 | 0.0992363 | − | 0.995064i | \(-0.468360\pi\) | ||||
0.0992363 | + | 0.995064i | \(0.468360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1548.39 | −0.834478 | −0.417239 | − | 0.908797i | \(-0.637002\pi\) | ||||
−0.417239 | + | 0.908797i | \(0.637002\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 246.136 | 0.130058 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4698.47 | −2.43477 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −967.068 | −0.491595 | −0.245798 | − | 0.969321i | \(-0.579050\pi\) | ||||
−0.245798 | + | 0.969321i | \(0.579050\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 199.466 | 0.0994885 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1326.50 | 0.637420 | 0.318710 | − | 0.947852i | \(-0.396750\pi\) | ||||
0.318710 | + | 0.947852i | \(0.396750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2462.85 | −1.16202 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1416.70 | −0.656451 | −0.328225 | − | 0.944599i | \(-0.606451\pi\) | ||||
−0.328225 | + | 0.944599i | \(0.606451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −688.678 | −0.313463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −688.602 | −0.307946 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1036.60 | −0.455556 | −0.227778 | − | 0.973713i | \(-0.573146\pi\) | ||||
−0.227778 | + | 0.973713i | \(0.573146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1385.78 | −0.588485 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 767.432 | 0.320450 | 0.160225 | − | 0.987081i | \(-0.448778\pi\) | ||||
0.160225 | + | 0.987081i | \(0.448778\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3957.71 | −1.62527 | −0.812636 | − | 0.582772i | \(-0.801968\pi\) | ||||
−0.812636 | + | 0.582772i | \(0.801968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −556.045 | −0.224612 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2558.23 | 1.01668 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1417.67 | −0.554385 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1805.30 | 0.683909 | 0.341954 | − | 0.939717i | \(-0.388911\pi\) | ||||
0.341954 | + | 0.939717i | \(0.388911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3370.84 | 1.25719 | 0.628597 | − | 0.777731i | \(-0.283630\pi\) | ||||
0.628597 | + | 0.777731i | \(0.283630\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1845.20 | 0.677630 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4612.31 | −1.66809 | −0.834044 | − | 0.551697i | \(-0.813980\pi\) | ||||
−0.834044 | + | 0.551697i | \(0.813980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2229.86 | 0.794326 | 0.397163 | − | 0.917748i | \(-0.369995\pi\) | ||||
0.397163 | + | 0.917748i | \(0.369995\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1635.62 | 0.573971 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1630.86 | 0.555631 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1326.14 | −0.445279 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3966.13 | 1.31265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −912.614 | −0.297758 | −0.148879 | − | 0.988855i | \(-0.547566\pi\) | ||||
−0.148879 | + | 0.988855i | \(0.547566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −392.227 | −0.126174 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5203.39 | −1.65055 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −543.898 | −0.167823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1062.14 | 0.323290 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4319.47 | 1.29710 | 0.648549 | − | 0.761173i | \(-0.275376\pi\) | ||||
0.648549 | + | 0.761173i | \(0.275376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1132.33 | 0.335505 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2061.28 | −0.602697 | −0.301349 | − | 0.953514i | \(-0.597437\pi\) | ||||
−0.301349 | + | 0.953514i | \(0.597437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3474.63 | −1.00266 | −0.501332 | − | 0.865255i | \(-0.667157\pi\) | ||||
−0.501332 | + | 0.865255i | \(0.667157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 776.099 | 0.218214 | 0.109107 | − | 0.994030i | \(-0.465201\pi\) | ||||
0.109107 | + | 0.994030i | \(0.465201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1076.20 | 0.298740 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1229.09 | −0.336869 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2006.80 | −0.543133 | −0.271567 | − | 0.962420i | \(-0.587542\pi\) | ||||
−0.271567 | + | 0.962420i | \(0.587542\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 805.648 | 0.215337 | 0.107669 | − | 0.994187i | \(-0.465661\pi\) | ||||
0.107669 | + | 0.994187i | \(0.465661\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2971.48 | −0.765469 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1043.78 | 0.265651 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1421.78 | −0.357539 | −0.178769 | − | 0.983891i | \(-0.557212\pi\) | ||||
−0.178769 | + | 0.983891i | \(0.557212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7638.12 | 1.89804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1299.36 | 0.319095 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1465.82 | −0.355779 | −0.177890 | − | 0.984050i | \(-0.556927\pi\) | ||||
−0.177890 | + | 0.984050i | \(0.556927\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2161.87 | 0.512708 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6991.39 | −1.63919 | −0.819596 | − | 0.572942i | \(-0.805802\pi\) | ||||
−0.819596 | + | 0.572942i | \(0.805802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1052.99 | 0.244093 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3471.48 | −0.795696 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 808.958 | 0.183357 | 0.0916786 | − | 0.995789i | \(-0.470777\pi\) | ||||
0.0916786 | + | 0.995789i | \(0.470777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6661.77 | −1.49326 | −0.746630 | − | 0.665239i | \(-0.768330\pi\) | ||||
−0.746630 | + | 0.665239i | \(0.768330\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6521.86 | −1.43012 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7531.47 | −1.63365 | −0.816827 | − | 0.576883i | \(-0.804269\pi\) | ||||
−0.816827 | + | 0.576883i | \(0.804269\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2670.07 | 0.572949 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1690.19 | 0.358819 | 0.179410 | − | 0.983774i | \(-0.442581\pi\) | ||||
0.179410 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3178.23 | −0.667584 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3635.16 | −0.755538 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4165.06 | −0.847763 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4854.90 | −0.978004 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2176.53 | −0.433974 | −0.216987 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216987 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7315.61 | −1.44383 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1399.60 | 0.273445 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5722.59 | −1.10684 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2156.23 | −0.408819 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2935.39 | −0.551081 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −623.504 | −0.115913 | −0.0579564 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579564 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4834.74 | −0.890093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −467.992 | −0.0853293 | −0.0426647 | − | 0.999089i | \(-0.513585\pi\) | ||||
−0.0426647 | + | 0.999089i | \(0.513585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3612.81 | 0.652422 | 0.326211 | − | 0.945297i | \(-0.394228\pi\) | ||||
0.326211 | + | 0.945297i | \(0.394228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4531.74 | 0.802927 | 0.401463 | − | 0.915875i | \(-0.368502\pi\) | ||||
0.401463 | + | 0.915875i | \(0.368502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12451.7 | −2.18546 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2804.01 | 0.487553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2092.47 | −0.360459 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4886.27 | 0.833974 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3591.06 | 0.607296 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1237.06 | 0.205422 | 0.102711 | − | 0.994711i | \(-0.467248\pi\) | ||||
0.102711 | + | 0.994711i | \(0.467248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1453.81 | −0.239244 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8634.53 | 1.40822 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1867.83 | −0.301921 | −0.150960 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150960 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7153.93 | 1.14616 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15378.7 | −2.44224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7000.73 | −1.09248 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 63.3637 | 0.00980271 | 0.00490136 | − | 0.999988i | \(-0.498440\pi\) | ||||
0.00490136 | + | 0.999988i | \(0.498440\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1223.79 | 0.187702 | 0.0938508 | − | 0.995586i | \(-0.470082\pi\) | ||||
0.0938508 | + | 0.995586i | \(0.470082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1048.60 | −0.159459 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4515.61 | −0.680855 | −0.340428 | − | 0.940271i | \(-0.610572\pi\) | ||||
−0.340428 | + | 0.940271i | \(0.610572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2070.58 | −0.309564 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2228.49 | −0.327619 | −0.163810 | − | 0.986492i | \(-0.552378\pi\) | ||||
−0.163810 | + | 0.986492i | \(0.552378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1005.01 | −0.146524 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4068.26 | −0.588232 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2871.26 | −0.411749 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1437.34 | 0.204438 | 0.102219 | − | 0.994762i | \(-0.467406\pi\) | ||||
0.102219 | + | 0.994762i | \(0.467406\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −926.795 | −0.130751 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12237.4 | −1.69874 | −0.849370 | − | 0.527798i | \(-0.823018\pi\) | ||||
−0.849370 | + | 0.527798i | \(0.823018\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38.6931 | 0.00532827 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9329.00 | 1.27445 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10647.0 | 1.44301 | 0.721503 | − | 0.692411i | \(-0.243451\pi\) | ||||
0.721503 | + | 0.692411i | \(0.243451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8021.77 | −1.07866 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6714.81 | 0.895851 | 0.447925 | − | 0.894071i | \(-0.352163\pi\) | ||||
0.447925 | + | 0.894071i | \(0.352163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2957.01 | 0.388407 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10653.1 | −1.38852 | −0.694258 | − | 0.719727i | \(-0.744267\pi\) | ||||
−0.694258 | + | 0.719727i | \(0.744267\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4029.76 | −0.521211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −116.580 | −0.0149635 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6488.42 | −0.826501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3221.04 | 0.407203 | 0.203601 | − | 0.979054i | \(-0.434735\pi\) | ||||
0.203601 | + | 0.979054i | \(0.434735\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12485.0 | 1.55479 | 0.777395 | − | 0.629012i | \(-0.216540\pi\) | ||||
0.777395 | + | 0.629012i | \(0.216540\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11522.0 | 1.42419 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1282.81 | −0.157391 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8373.46 | 1.01980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7037.39 | 0.850798 | 0.425399 | − | 0.905006i | \(-0.360134\pi\) | ||||
0.425399 | + | 0.905006i | \(0.360134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2304.43 | 0.276567 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5510.18 | 0.651769 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3157.65 | 0.370817 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1549.66 | 0.180682 | 0.0903410 | − | 0.995911i | \(-0.471204\pi\) | ||||
0.0903410 | + | 0.995911i | \(0.471204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5531.63 | 0.640369 | 0.320184 | − | 0.947355i | \(-0.396255\pi\) | ||||
0.320184 | + | 0.947355i | \(0.396255\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −611.591 | −0.0702992 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3440.83 | 0.392717 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6039.61 | 0.679709 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2029.93 | 0.226864 | 0.113432 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113432 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −327.739 | −0.0363744 | −0.0181872 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181872 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11412.6 | 1.25792 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11273.8 | 1.23410 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7908.68 | −0.859819 | −0.429910 | − | 0.902872i | \(-0.641455\pi\) | ||||
−0.429910 | + | 0.902872i | \(0.641455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2920.82 | 0.313256 | 0.156628 | − | 0.987658i | \(-0.449938\pi\) | ||||
0.156628 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18326.1 | −1.95222 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1082.93 | −0.114588 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10240.2 | −1.07631 | −0.538156 | − | 0.842845i | \(-0.680879\pi\) | ||||
−0.538156 | + | 0.842845i | \(0.680879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5338.05 | 0.557336 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4645.17 | 0.481786 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5892.63 | 0.603163 | 0.301582 | − | 0.953440i | \(-0.402485\pi\) | ||||
0.301582 | + | 0.953440i | \(0.402485\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −738.409 | −0.0750893 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12643.4 | −1.27735 | −0.638677 | − | 0.769475i | \(-0.720518\pi\) | ||||
−0.638677 | + | 0.769475i | \(0.720518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15093.2 | −1.51499 | −0.757494 | − | 0.652842i | \(-0.773577\pi\) | ||||
−0.757494 | + | 0.652842i | \(0.773577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14095.4 | 1.40572 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2820.23 | 0.279454 | 0.139727 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139727 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2901.20 | 0.283823 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17031.4 | −1.65562 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9626.23 | −0.929856 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −598.398 | −0.0574397 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16448.5 | 1.56900 | 0.784500 | − | 0.620129i | \(-0.212920\pi\) | ||||
0.784500 | + | 0.620129i | \(0.212920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6273.52 | −0.594694 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25629.2 | −2.39951 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6331.07 | −0.589093 | −0.294546 | − | 0.955637i | \(-0.595169\pi\) | ||||
−0.294546 | + | 0.955637i | \(0.595169\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3979.50 | −0.368015 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9286.90 | 0.853588 | 0.426794 | − | 0.904349i | \(-0.359643\pi\) | ||||
0.426794 | + | 0.904349i | \(0.359643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6569.33 | 0.600138 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7388.56 | 0.670891 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 243.451 | 0.0218404 | 0.0109202 | − | 0.999940i | \(-0.496524\pi\) | ||||
0.0109202 | + | 0.999940i | \(0.496524\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4250.09 | 0.379002 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8499.30 | −0.753409 | −0.376705 | − | 0.926333i | \(-0.622943\pi\) | ||||
−0.376705 | + | 0.926333i | \(0.622943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11382.8 | −1.00303 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2066.03 | 0.180978 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7683.10 | −0.669052 | −0.334526 | − | 0.942387i | \(-0.608576\pi\) | ||||
−0.334526 | + | 0.942387i | \(0.608576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2065.81 | 0.177793 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25522.8 | −2.18382 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3522.57 | 0.299656 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3109.80 | 0.263015 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21530.6 | −1.81051 | −0.905253 | − | 0.424874i | \(-0.860319\pi\) | ||||
−0.905253 | + | 0.424874i | \(0.860319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16847.1 | 1.40855 | 0.704274 | − | 0.709929i | \(-0.251273\pi\) | ||||
0.704274 | + | 0.709929i | \(0.251273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8113.59 | 0.670652 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9544.58 | 0.784464 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4157.35 | 0.339762 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3999.34 | −0.325011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14802.5 | 1.19620 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2302.30 | −0.185012 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17440.0 | 1.38596 | 0.692981 | − | 0.720955i | \(-0.256297\pi\) | ||||
0.692981 | + | 0.720955i | \(0.256297\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11873.1 | 0.938351 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18957.3 | 1.48999 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11520.7 | −0.900530 | −0.450265 | − | 0.892895i | \(-0.648671\pi\) | ||||
−0.450265 | + | 0.892895i | \(0.648671\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1668.14 | 0.129680 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18378.7 | −1.42098 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7674.70 | −0.586978 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11493.0 | 0.874282 | 0.437141 | − | 0.899393i | \(-0.355991\pi\) | ||||
0.437141 | + | 0.899393i | \(0.355991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12760.2 | 0.965472 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4253.00 | 0.320075 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18111.3 | −1.35577 | −0.677886 | − | 0.735167i | \(-0.737104\pi\) | ||||
−0.677886 | + | 0.735167i | \(0.737104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37765.9 | 2.81208 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4417.61 | 0.325476 | 0.162738 | − | 0.986669i | \(-0.447967\pi\) | ||||
0.162738 | + | 0.986669i | \(0.447967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13219.7 | −0.968878 | −0.484439 | − | 0.874825i | \(-0.660976\pi\) | ||||
−0.484439 | + | 0.874825i | \(0.660976\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5415.89 | −0.394855 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18538.6 | −1.34454 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17496.4 | −1.26236 | −0.631182 | − | 0.775634i | \(-0.717430\pi\) | ||||
−0.631182 | + | 0.775634i | \(0.717430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10112.5 | −0.725841 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3446.58 | 0.244842 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5535.61 | −0.391230 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4280.53 | 0.300982 | 0.150491 | − | 0.988611i | \(-0.451915\pi\) | ||||
0.150491 | + | 0.988611i | \(0.451915\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22699.0 | −1.58794 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13836.9 | 0.963072 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1590.93 | −0.110172 | −0.0550858 | − | 0.998482i | \(-0.517543\pi\) | ||||
−0.0550858 | + | 0.998482i | \(0.517543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6689.59 | −0.458604 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13922.8 | 0.949703 | 0.474851 | − | 0.880066i | \(-0.342502\pi\) | ||||
0.474851 | + | 0.880066i | \(0.342502\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12559.7 | 0.852446 | 0.426223 | − | 0.904618i | \(-0.359844\pi\) | ||||
0.426223 | + | 0.904618i | \(0.359844\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4906.87 | −0.331382 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21476.5 | −1.44321 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7678.37 | −0.513436 | −0.256718 | − | 0.966486i | \(-0.582641\pi\) | ||||
−0.256718 | + | 0.966486i | \(0.582641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2639.16 | −0.174745 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6158.37 | 0.405766 | 0.202883 | − | 0.979203i | \(-0.434969\pi\) | ||||
0.202883 | + | 0.979203i | \(0.434969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4892.59 | −0.320794 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8813.12 | 0.575045 | 0.287523 | − | 0.957774i | \(-0.407168\pi\) | ||||
0.287523 | + | 0.957774i | \(0.407168\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23189.9 | −1.50579 | −0.752894 | − | 0.658142i | \(-0.771342\pi\) | ||||
−0.752894 | + | 0.658142i | \(0.771342\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3978.41 | 0.257082 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15522.5 | −0.993442 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11898.4 | −0.757856 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4417.71 | −0.280041 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7936.94 | −0.500736 | −0.250368 | − | 0.968151i | \(-0.580552\pi\) | ||||
−0.250368 | + | 0.968151i | \(0.580552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2737.84 | 0.171911 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42347.3 | −2.64646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1176.68 | 0.0728463 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32114.6 | 1.97886 | 0.989432 | − | 0.144996i | \(-0.0463169\pi\) | ||||
0.989432 | + | 0.144996i | \(0.0463169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24786.7 | 1.52021 | 0.760104 | − | 0.649802i | \(-0.225148\pi\) | ||||
0.760104 | + | 0.649802i | \(0.225148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15610.2 | 0.952946 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7545.59 | −0.458497 | −0.229249 | − | 0.973368i | \(-0.573627\pi\) | ||||
−0.229249 | + | 0.973368i | \(0.573627\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23945.0 | −1.44827 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4888.99 | −0.292988 | −0.146494 | − | 0.989212i | \(-0.546799\pi\) | ||||
−0.146494 | + | 0.989212i | \(0.546799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −615.428 | −0.0367126 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1631.69 | 0.0968926 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25895.9 | −1.53075 | −0.765374 | − | 0.643586i | \(-0.777446\pi\) | ||||
−0.765374 | + | 0.643586i | \(0.777446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8183.37 | 0.481537 | 0.240769 | − | 0.970583i | \(-0.422601\pi\) | ||||
0.240769 | + | 0.970583i | \(0.422601\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3186.41 | −0.186651 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35394.3 | −2.05468 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12958.4 | −0.748880 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9607.93 | −0.552772 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4635.02 | −0.265478 | −0.132739 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132739 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3396.99 | −0.193704 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24385.8 | −1.38437 | −0.692187 | − | 0.721718i | \(-0.743353\pi\) | ||||
−0.692187 | + | 0.721718i | \(0.743353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6183.85 | 0.347967 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18393.4 | 1.03046 | 0.515230 | − | 0.857052i | \(-0.327706\pi\) | ||||
0.515230 | + | 0.857052i | \(0.327706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12165.2 | 0.678552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10423.9 | 0.578889 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2582.23 | −0.142779 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14898.9 | 0.820231 | 0.410116 | − | 0.912034i | \(-0.365488\pi\) | ||||
0.410116 | + | 0.912034i | \(0.365488\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16669.3 | 0.909791 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2816.27 | −0.153047 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2328.30 | −0.125986 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5725.70 | −0.308497 | −0.154249 | − | 0.988032i | \(-0.549296\pi\) | ||||
−0.154249 | + | 0.988032i | \(0.549296\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12359.2 | 0.663067 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3228.61 | −0.172477 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23456.8 | −1.24251 | −0.621255 | − | 0.783609i | \(-0.713377\pi\) | ||||
−0.621255 | + | 0.783609i | \(0.713377\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3687.27 | 0.194492 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43714.5 | −2.29610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31883.4 | 1.66765 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6020.39 | 0.313578 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8459.00 | 0.438759 | 0.219379 | − | 0.975640i | \(-0.429597\pi\) | ||||
0.219379 | + | 0.975640i | \(0.429597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2416.94 | −0.124325 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30221.7 | 1.54814 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11822.2 | 0.603111 | 0.301555 | − | 0.953449i | \(-0.402494\pi\) | ||||
0.301555 | + | 0.953449i | \(0.402494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8985.53 | 0.454640 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5028.95 | 0.253409 | 0.126704 | − | 0.991941i | \(-0.459560\pi\) | ||||
0.126704 | + | 0.991941i | \(0.459560\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28262.0 | 1.41254 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17743.9 | 0.883247 | 0.441624 | − | 0.897200i | \(-0.354403\pi\) | ||||
0.441624 | + | 0.897200i | \(0.354403\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8914.44 | 0.441944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13202.3 | 0.651877 | 0.325938 | − | 0.945391i | \(-0.394320\pi\) | ||||
0.325938 | + | 0.945391i | \(0.394320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5716.84 | −0.281139 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3131.35 | −0.153374 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15601.0 | −0.758040 | −0.379020 | − | 0.925388i | \(-0.623739\pi\) | ||||
−0.379020 | + | 0.925388i | \(0.623739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4265.35 | 0.206425 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24522.0 | 1.18205 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2948.08 | 0.141545 | 0.0707725 | − | 0.997492i | \(-0.477454\pi\) | ||||
0.0707725 | + | 0.997492i | \(0.477454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22914.4 | −1.09583 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1697.03 | 0.0808375 | 0.0404187 | − | 0.999183i | \(-0.487131\pi\) | ||||
0.0404187 | + | 0.999183i | \(0.487131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3898.09 | −0.184230 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17940.0 | 0.844556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −96.7799 | −0.00453833 | −0.00226916 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226916 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4397.45 | 0.205409 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36326.8 | 1.69028 | 0.845138 | − | 0.534548i | \(-0.179518\pi\) | ||||
0.845138 | + | 0.534548i | \(0.179518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37325.9 | 1.73005 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7878.93 | 0.362377 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6777.31 | −0.310514 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6485.62 | −0.296012 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15315.6 | 0.696352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7096.46 | −0.321425 | −0.160713 | − | 0.987001i | \(-0.551379\pi\) | ||||
−0.160713 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20974.2 | 0.946388 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7198.40 | 0.322349 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3158.97 | −0.140927 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40289.6 | 1.79063 | 0.895314 | − | 0.445436i | \(-0.146951\pi\) | ||||
0.895314 | + | 0.445436i | \(0.146951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1858.45 | −0.0822871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10414.4 | 0.459396 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9398.03 | −0.413013 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2426.88 | −0.105861 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11566.0 | −0.502642 | −0.251321 | − | 0.967904i | \(-0.580865\pi\) | ||||
−0.251321 | + | 0.967904i | \(0.580865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18014.2 | −0.779981 | −0.389991 | − | 0.920819i | \(-0.627522\pi\) | ||||
−0.389991 | + | 0.920819i | \(0.627522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19985.3 | 0.862134 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21007.9 | −0.902915 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25138.3 | −1.07647 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16792.4 | −0.713837 | −0.356918 | − | 0.934136i | \(-0.616173\pi\) | ||||
−0.356918 | + | 0.934136i | \(0.616173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8819.03 | 0.373526 | 0.186763 | − | 0.982405i | \(-0.440200\pi\) | ||||
0.186763 | + | 0.982405i | \(0.440200\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19565.6 | 0.825680 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8250.13 | −0.346898 | −0.173449 | − | 0.984843i | \(-0.555491\pi\) | ||||
−0.173449 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21550.5 | −0.902871 | −0.451435 | − | 0.892304i | \(-0.649088\pi\) | ||||
−0.451435 | + | 0.892304i | \(0.649088\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22594.4 | 0.943190 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22436.4 | 0.929873 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8010.20 | −0.330792 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30130.4 | −1.23983 | −0.619916 | − | 0.784669i | \(-0.712833\pi\) | ||||
−0.619916 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33311.0 | 1.36582 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5070.57 | −0.207164 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10906.7 | 0.444025 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9534.69 | 0.385430 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23801.8 | 0.958772 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40738.6 | −1.63525 | −0.817623 | − | 0.575754i | \(-0.804709\pi\) | ||||
−0.817623 | + | 0.575754i | \(0.804709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10905.5 | 0.436210 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36508.2 | −1.45519 | −0.727594 | − | 0.686008i | \(-0.759362\pi\) | ||||
−0.727594 | + | 0.686008i | \(0.759362\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21980.8 | 0.873081 | 0.436541 | − | 0.899685i | \(-0.356204\pi\) | ||||
0.436541 | + | 0.899685i | \(0.356204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23426.1 | 0.924024 | 0.462012 | − | 0.886874i | \(-0.347128\pi\) | ||||
0.462012 | + | 0.886874i | \(0.347128\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16416.7 | 0.645301 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12495.2 | 0.489456 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21237.5 | −0.829037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21174.3 | −0.823725 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14564.7 | 0.564651 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 307.401 | 0.0118360 | 0.00591802 | − | 0.999982i | \(-0.498116\pi\) | ||||
0.00591802 | + | 0.999982i | \(0.498116\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6529.60 | 0.250555 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19941.7 | −0.762605 | −0.381302 | − | 0.924450i | \(-0.624524\pi\) | ||||
−0.381302 | + | 0.924450i | \(0.624524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37524.1 | 1.43011 | 0.715056 | − | 0.699068i | \(-0.246401\pi\) | ||||
0.715056 | + | 0.699068i | \(0.246401\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21946.8 | 0.833598 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2880.20 | 0.109028 | 0.0545140 | − | 0.998513i | \(-0.482639\pi\) | ||||
0.0545140 | + | 0.998513i | \(0.482639\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4198.81 | −0.157874 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5199.30 | 0.194835 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12153.9 | −0.453922 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17167.8 | 0.639036 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 71263.6 | 2.64380 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1818.36 | −0.0672347 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 62678.7 | 2.30222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18319.2 | −0.670651 | −0.335326 | − | 0.942102i | \(-0.608846\pi\) | ||||
−0.335326 | + | 0.942102i | \(0.608846\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6468.68 | 0.236031 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46150.7 | −1.67842 | −0.839210 | − | 0.543807i | \(-0.816982\pi\) | ||||
−0.839210 | + | 0.543807i | \(0.816982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18035.6 | 0.653769 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8806.16 | 0.318167 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47264.3 | −1.69652 | −0.848261 | − | 0.529578i | \(-0.822350\pi\) | ||||
−0.848261 | + | 0.529578i | \(0.822350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1870.51 | 0.0669223 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5077.66 | 0.181076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20323.3 | −0.722407 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14504.2 | 0.513895 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53271.5 | −1.88136 | −0.940678 | − | 0.339301i | \(-0.889810\pi\) | ||||
−0.940678 | + | 0.339301i | \(0.889810\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1403.98 | 0.0492649 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22451.8 | 0.785295 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17197.8 | 0.599602 | 0.299801 | − | 0.954002i | \(-0.403080\pi\) | ||||
0.299801 | + | 0.954002i | \(0.403080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10838.4 | −0.376676 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28834.9 | 0.998926 | 0.499463 | − | 0.866335i | \(-0.333531\pi\) | ||||
0.499463 | + | 0.866335i | \(0.333531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15173.5 | 0.523986 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51841.2 | 1.77890 | 0.889448 | − | 0.457037i | \(-0.151089\pi\) | ||||
0.889448 | + | 0.457037i | \(0.151089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7041.14 | 0.240848 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13595.2 | −0.463570 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5887.31 | −0.200114 | −0.100057 | − | 0.994982i | \(-0.531903\pi\) | ||||
−0.100057 | + | 0.994982i | \(0.531903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28590.7 | −0.968767 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37355.1 | 1.26178 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58224.6 | 1.95444 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8412.03 | −0.281489 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −53384.4 | −1.78083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36620.0 | 1.21781 | 0.608904 | − | 0.793244i | \(-0.291609\pi\) | ||||
0.608904 | + | 0.793244i | \(0.291609\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6277.41 | 0.208111 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42364.9 | 1.40016 | 0.700079 | − | 0.714065i | \(-0.253148\pi\) | ||||
0.700079 | + | 0.714065i | \(0.253148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14658.8 | −0.481495 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5022.32 | 0.164461 | 0.0822304 | − | 0.996613i | \(-0.473796\pi\) | ||||
0.0822304 | + | 0.996613i | \(0.473796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59983.8 | −1.95821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10773.2 | −0.350623 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28292.8 | −0.918005 | −0.459003 | − | 0.888435i | \(-0.651793\pi\) | ||||
−0.459003 | + | 0.888435i | \(0.651793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 73045.7 | 2.36287 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48412.3 | −1.55655 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36401.1 | −1.16682 | −0.583410 | − | 0.812178i | \(-0.698282\pi\) | ||||
−0.583410 | + | 0.812178i | \(0.698282\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3711.17 | −0.118601 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35314.6 | −1.12517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2357.19 | −0.0748777 | −0.0374389 | − | 0.999299i | \(-0.511920\pi\) | ||||
−0.0374389 | + | 0.999299i | \(0.511920\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4361.42 | 0.138127 |
(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 | 2352.4.a.bq.1.1 | 2 | ||
4.3 | odd | 2 | 294.4.a.n.1.1 | 2 | |||
7.2 | even | 3 | 336.4.q.j.193.2 | 4 | |||
7.4 | even | 3 | 336.4.q.j.289.2 | 4 | |||
7.6 | odd | 2 | 2352.4.a.ca.1.2 | 2 | |||
12.11 | even | 2 | 882.4.a.v.1.2 | 2 | |||
28.3 | even | 6 | 294.4.e.l.79.1 | 4 | |||
28.11 | odd | 6 | 42.4.e.c.37.2 | yes | 4 | ||
28.19 | even | 6 | 294.4.e.l.67.1 | 4 | |||
28.23 | odd | 6 | 42.4.e.c.25.2 | ✓ | 4 | ||
28.27 | even | 2 | 294.4.a.m.1.2 | 2 | |||
84.11 | even | 6 | 126.4.g.g.37.1 | 4 | |||
84.23 | even | 6 | 126.4.g.g.109.1 | 4 | |||
84.47 | odd | 6 | 882.4.g.bf.361.2 | 4 | |||
84.59 | odd | 6 | 882.4.g.bf.667.2 | 4 | |||
84.83 | odd | 2 | 882.4.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.c.25.2 | ✓ | 4 | 28.23 | odd | 6 | ||
42.4.e.c.37.2 | yes | 4 | 28.11 | odd | 6 | ||
126.4.g.g.37.1 | 4 | 84.11 | even | 6 | |||
126.4.g.g.109.1 | 4 | 84.23 | even | 6 | |||
294.4.a.m.1.2 | 2 | 28.27 | even | 2 | |||
294.4.a.n.1.1 | 2 | 4.3 | odd | 2 | |||
294.4.e.l.67.1 | 4 | 28.19 | even | 6 | |||
294.4.e.l.79.1 | 4 | 28.3 | even | 6 | |||
336.4.q.j.193.2 | 4 | 7.2 | even | 3 | |||
336.4.q.j.289.2 | 4 | 7.4 | even | 3 | |||
882.4.a.v.1.2 | 2 | 12.11 | even | 2 | |||
882.4.a.z.1.1 | 2 | 84.83 | odd | 2 | |||
882.4.g.bf.361.2 | 4 | 84.47 | odd | 6 | |||
882.4.g.bf.667.2 | 4 | 84.59 | odd | 6 | |||
2352.4.a.bq.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.ca.1.2 | 2 | 7.6 | odd | 2 |