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: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.145408.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 24x^{2} + 142 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1176) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.25358\) 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 | ||||||||
\(5\) | 11.4452 | 1.02369 | 0.511843 | − | 0.859079i | \(-0.328963\pi\) | ||||
0.511843 | + | 0.859079i | \(0.328963\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 52.5886 | 1.44146 | 0.720730 | − | 0.693216i | \(-0.243807\pi\) | ||||
0.720730 | + | 0.693216i | \(0.243807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.48395 | −0.116998 | −0.0584990 | − | 0.998287i | \(-0.518631\pi\) | ||||
−0.0584990 | + | 0.998287i | \(0.518631\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −34.3355 | −0.591025 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 85.3636 | 1.21786 | 0.608932 | − | 0.793222i | \(-0.291598\pi\) | ||||
0.608932 | + | 0.793222i | \(0.291598\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110.620 | 1.33568 | 0.667839 | − | 0.744306i | \(-0.267220\pi\) | ||||
0.667839 | + | 0.744306i | \(0.267220\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 209.332 | 1.89777 | 0.948884 | − | 0.315624i | \(-0.102214\pi\) | ||||
0.948884 | + | 0.315624i | \(0.102214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.99160 | 0.0479328 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −132.843 | −0.850632 | −0.425316 | − | 0.905045i | \(-0.639837\pi\) | ||||
−0.425316 | + | 0.905045i | \(0.639837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 49.3139 | 0.285711 | 0.142856 | − | 0.989744i | \(-0.454372\pi\) | ||||
0.142856 | + | 0.989744i | \(0.454372\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −157.766 | −0.832228 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 160.351 | 0.712474 | 0.356237 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356237 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.4518 | 0.0675488 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 138.120 | 0.526116 | 0.263058 | − | 0.964780i | \(-0.415269\pi\) | ||||
0.263058 | + | 0.964780i | \(0.415269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 365.073 | 1.29472 | 0.647362 | − | 0.762183i | \(-0.275872\pi\) | ||||
0.647362 | + | 0.762183i | \(0.275872\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 103.006 | 0.341229 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −131.370 | −0.407708 | −0.203854 | − | 0.979001i | \(-0.565347\pi\) | ||||
−0.203854 | + | 0.979001i | \(0.565347\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −256.091 | −0.703135 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −561.227 | −1.45454 | −0.727268 | − | 0.686353i | \(-0.759210\pi\) | ||||
−0.727268 | + | 0.686353i | \(0.759210\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 601.885 | 1.47560 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −331.859 | −0.771154 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 436.354 | 0.962854 | 0.481427 | − | 0.876486i | \(-0.340119\pi\) | ||||
0.481427 | + | 0.876486i | \(0.340119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −291.961 | −0.612816 | −0.306408 | − | 0.951900i | \(-0.599127\pi\) | ||||
−0.306408 | + | 0.951900i | \(0.599127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −62.7646 | −0.119769 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 593.683 | 1.08254 | 0.541268 | − | 0.840850i | \(-0.317944\pi\) | ||||
0.541268 | + | 0.840850i | \(0.317944\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −627.995 | −1.09568 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −775.073 | −1.29555 | −0.647776 | − | 0.761831i | \(-0.724301\pi\) | ||||
−0.647776 | + | 0.761831i | \(0.724301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 330.907 | 0.530544 | 0.265272 | − | 0.964174i | \(-0.414538\pi\) | ||||
0.265272 | + | 0.964174i | \(0.414538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.9748 | −0.0276740 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −243.473 | −0.346745 | −0.173373 | − | 0.984856i | \(-0.555467\pi\) | ||||
−0.173373 | + | 0.984856i | \(0.555467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −332.477 | −0.439688 | −0.219844 | − | 0.975535i | \(-0.570555\pi\) | ||||
−0.219844 | + | 0.975535i | \(0.570555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 976.999 | 1.24671 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 398.529 | 0.491113 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −979.115 | −1.16614 | −0.583068 | − | 0.812424i | \(-0.698148\pi\) | ||||
−0.583068 | + | 0.812424i | \(0.698148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −147.942 | −0.164955 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1266.06 | 1.36731 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 466.790 | 0.488612 | 0.244306 | − | 0.969698i | \(-0.421440\pi\) | ||||
0.244306 | + | 0.969698i | \(0.421440\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 473.298 | 0.480487 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 866.429 | 0.853593 | 0.426796 | − | 0.904348i | \(-0.359642\pi\) | ||||
0.426796 | + | 0.904348i | \(0.359642\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −926.755 | −0.886562 | −0.443281 | − | 0.896383i | \(-0.646186\pi\) | ||||
−0.443281 | + | 0.896383i | \(0.646186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1046.38 | −0.945395 | −0.472698 | − | 0.881225i | \(-0.656720\pi\) | ||||
−0.472698 | + | 0.881225i | \(0.656720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −486.397 | −0.427416 | −0.213708 | − | 0.976898i | \(-0.568554\pi\) | ||||
−0.213708 | + | 0.976898i | \(0.568554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −481.053 | −0.411347 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1955.03 | 1.62755 | 0.813777 | − | 0.581178i | \(-0.197408\pi\) | ||||
0.813777 | + | 0.581178i | \(0.197408\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2395.83 | 1.94272 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −49.3555 | −0.0389993 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1434.56 | 1.07781 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −414.360 | −0.303753 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1362.07 | −0.974618 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1255.53 | −0.877246 | −0.438623 | − | 0.898671i | \(-0.644534\pi\) | ||||
−0.438623 | + | 0.898671i | \(0.644534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1095.22 | −0.747509 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1029.41 | 0.686561 | 0.343281 | − | 0.939233i | \(-0.388462\pi\) | ||||
0.343281 | + | 0.939233i | \(0.388462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −309.019 | −0.197008 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1931.36 | −1.20443 | −0.602217 | − | 0.798332i | \(-0.705716\pi\) | ||||
−0.602217 | + | 0.798332i | \(0.705716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2926.04 | 1.78549 | 0.892747 | − | 0.450559i | \(-0.148775\pi\) | ||||
0.892747 | + | 0.450559i | \(0.148775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 394.110 | 0.235390 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −288.393 | −0.168648 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1520.41 | −0.870780 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 131.809 | 0.0724712 | 0.0362356 | − | 0.999343i | \(-0.488463\pi\) | ||||
0.0362356 | + | 0.999343i | \(0.488463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −177.956 | −0.0959066 | −0.0479533 | − | 0.998850i | \(-0.515270\pi\) | ||||
−0.0479533 | + | 0.998850i | \(0.515270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 768.272 | 0.405955 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 564.406 | 0.292479 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3607.47 | −1.83381 | −0.916903 | − | 0.399111i | \(-0.869319\pi\) | ||||
−0.916903 | + | 0.399111i | \(0.869319\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1683.68 | 0.839777 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1540.88 | −0.740438 | −0.370219 | − | 0.928945i | \(-0.620717\pi\) | ||||
−0.370219 | + | 0.928945i | \(0.620717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1805.66 | −0.851940 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −761.798 | −0.352992 | −0.176496 | − | 0.984301i | \(-0.556476\pi\) | ||||
−0.176496 | + | 0.984301i | \(0.556476\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2166.93 | −0.986311 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 995.576 | 0.445226 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2691.32 | −1.18276 | −0.591379 | − | 0.806394i | \(-0.701416\pi\) | ||||
−0.591379 | + | 0.806394i | \(0.701416\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1309.06 | −0.555904 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1123.25 | −0.469027 | −0.234513 | − | 0.972113i | \(-0.575350\pi\) | ||||
−0.234513 | + | 0.972113i | \(0.575350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4221.85 | 1.73374 | 0.866872 | − | 0.498531i | \(-0.166127\pi\) | ||||
0.866872 | + | 0.498531i | \(0.166127\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 875.882 | 0.353809 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1835.24 | 0.729350 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4489.15 | 1.75550 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3293.81 | −1.24781 | −0.623904 | − | 0.781501i | \(-0.714455\pi\) | ||||
−0.623904 | + | 0.781501i | \(0.714455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4623.91 | −1.72454 | −0.862270 | − | 0.506448i | \(-0.830958\pi\) | ||||
−0.862270 | + | 0.506448i | \(0.830958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 188.294 | 0.0691487 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2644.18 | 0.956293 | 0.478147 | − | 0.878280i | \(-0.341309\pi\) | ||||
0.478147 | + | 0.878280i | \(0.341309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1382.33 | 0.492417 | 0.246209 | − | 0.969217i | \(-0.420815\pi\) | ||||
0.246209 | + | 0.969217i | \(0.420815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1781.05 | −0.625002 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1580.81 | 0.538577 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1883.99 | 0.632590 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5817.33 | 1.92533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4533.28 | −1.47907 | −0.739535 | − | 0.673118i | \(-0.764955\pi\) | ||||
−0.739535 | + | 0.673118i | \(0.764955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2325.22 | 0.747987 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4178.32 | 1.32539 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −992.721 | −0.306310 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −468.129 | −0.142488 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3052.46 | 0.916628 | 0.458314 | − | 0.888790i | \(-0.348453\pi\) | ||||
0.458314 | + | 0.888790i | \(0.348453\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 53.9244 | 0.0159776 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5194.86 | 1.51892 | 0.759461 | − | 0.650553i | \(-0.225463\pi\) | ||||
0.759461 | + | 0.650553i | \(0.225463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5497.05 | 1.58627 | 0.793133 | − | 0.609048i | \(-0.208448\pi\) | ||||
0.793133 | + | 0.609048i | \(0.208448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5457.17 | −1.53438 | −0.767191 | − | 0.641419i | \(-0.778346\pi\) | ||||
−0.767191 | + | 0.641419i | \(0.778346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1503.55 | −0.417365 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 730.420 | 0.200194 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5622.17 | 1.52162 | 0.760812 | − | 0.648972i | \(-0.224801\pi\) | ||||
0.760812 | + | 0.648972i | \(0.224801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4083.02 | 1.09133 | 0.545665 | − | 0.838003i | \(-0.316277\pi\) | ||||
0.545665 | + | 0.838003i | \(0.316277\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −606.632 | −0.156271 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 997.430 | 0.253854 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1751.99 | 0.440576 | 0.220288 | − | 0.975435i | \(-0.429300\pi\) | ||||
0.220288 | + | 0.975435i | \(0.429300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11008.5 | 2.73556 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2931.00 | −0.719789 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3825.26 | −0.928457 | −0.464228 | − | 0.885716i | \(-0.653668\pi\) | ||||
−0.464228 | + | 0.885716i | \(0.653668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1195.59 | −0.283544 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5272.57 | 1.23620 | 0.618099 | − | 0.786100i | \(-0.287903\pi\) | ||||
0.618099 | + | 0.786100i | \(0.287903\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6423.33 | −1.48899 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2937.35 | 0.673268 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4535.04 | −1.02790 | −0.513952 | − | 0.857819i | \(-0.671819\pi\) | ||||
−0.513952 | + | 0.857819i | \(0.671819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1439.10 | 0.322580 | 0.161290 | − | 0.986907i | \(-0.448435\pi\) | ||||
0.161290 | + | 0.986907i | \(0.448435\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 315.090 | 0.0690932 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5984.85 | −1.29818 | −0.649088 | − | 0.760713i | \(-0.724849\pi\) | ||||
−0.649088 | + | 0.760713i | \(0.724849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 443.826 | 0.0952371 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2647.87 | −0.562131 | −0.281066 | − | 0.959689i | \(-0.590688\pi\) | ||||
−0.281066 | + | 0.959689i | \(0.590688\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 400.822 | 0.0841922 | 0.0420961 | − | 0.999114i | \(-0.486596\pi\) | ||||
0.0420961 | + | 0.999114i | \(0.486596\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3798.17 | −0.789419 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2373.94 | 0.483195 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1400.37 | −0.282100 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5307.12 | −1.05817 | −0.529087 | − | 0.848567i | \(-0.677466\pi\) | ||||
−0.529087 | + | 0.848567i | \(0.677466\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4994.14 | 0.985660 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1419.89 | −0.277409 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1147.96 | −0.222035 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2599.29 | −0.492822 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3341.54 | −0.627331 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4130.45 | −0.767873 | −0.383936 | − | 0.923360i | \(-0.625432\pi\) | ||||
−0.383936 | + | 0.923360i | \(0.625432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2780.26 | 0.511857 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7653.87 | 1.39553 | 0.697767 | − | 0.716325i | \(-0.254177\pi\) | ||||
0.697767 | + | 0.716325i | \(0.254177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8546.27 | 1.54333 | 0.771667 | − | 0.636026i | \(-0.219423\pi\) | ||||
0.771667 | + | 0.636026i | \(0.219423\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7643.65 | 1.35429 | 0.677145 | − | 0.735850i | \(-0.263217\pi\) | ||||
0.677145 | + | 0.735850i | \(0.263217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6986.03 | −1.22615 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3139.14 | 0.545824 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9442.88 | 1.62667 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.8576 | −0.00560804 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1459.19 | 0.246769 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7550.18 | −1.25376 | −0.626881 | − | 0.779115i | \(-0.715669\pi\) | ||||
−0.626881 | + | 0.779115i | \(0.715669\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1443.16 | 0.237491 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6794.79 | 1.10818 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9391.92 | 1.51813 | 0.759066 | − | 0.651014i | \(-0.225656\pi\) | ||||
0.759066 | + | 0.651014i | \(0.225656\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5865.08 | −0.939668 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2593.35 | 0.411841 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7187.50 | −1.12163 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1005.66 | −0.155580 | −0.0777902 | − | 0.996970i | \(-0.524786\pi\) | ||||
−0.0777902 | + | 0.996970i | \(0.524786\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3109.75 | −0.476966 | −0.238483 | − | 0.971147i | \(-0.576650\pi\) | ||||
−0.238483 | + | 0.971147i | \(0.576650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 148.067 | 0.0225163 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7449.10 | 1.12316 | 0.561580 | − | 0.827423i | \(-0.310194\pi\) | ||||
0.561580 | + | 0.827423i | \(0.310194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8870.83 | −1.32624 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6427.61 | 0.944948 | 0.472474 | − | 0.881344i | \(-0.343361\pi\) | ||||
0.472474 | + | 0.881344i | \(0.343361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5377.69 | 0.784034 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4303.69 | −0.622273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3787.28 | 0.543111 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10767.3 | 1.53147 | 0.765734 | − | 0.643157i | \(-0.222376\pi\) | ||||
0.765734 | + | 0.643157i | \(0.222376\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1243.08 | 0.175372 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3601.03 | −0.499877 | −0.249938 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249938 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4086.21 | 0.562696 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 728.504 | 0.0995222 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6832.02 | −0.925956 | −0.462978 | − | 0.886370i | \(-0.653219\pi\) | ||||
−0.462978 | + | 0.886370i | \(0.653219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3766.59 | 0.506478 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3339.87 | −0.445586 | −0.222793 | − | 0.974866i | \(-0.571517\pi\) | ||||
−0.222793 | + | 0.974866i | \(0.571517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3285.66 | 0.431575 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4701.31 | 0.612765 | 0.306383 | − | 0.951908i | \(-0.400881\pi\) | ||||
0.306383 | + | 0.951908i | \(0.400881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17869.3 | 2.31123 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3088.22 | −0.396386 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2786.59 | −0.354958 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11715.8 | 1.48110 | 0.740552 | − | 0.671999i | \(-0.234564\pi\) | ||||
0.740552 | + | 0.671999i | \(0.234564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1643.72 | −0.204697 | −0.102349 | − | 0.994749i | \(-0.532636\pi\) | ||||
−0.102349 | + | 0.994749i | \(0.532636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −270.435 | −0.0334276 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 927.058 | 0.113743 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8432.64 | 1.02700 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12206.6 | 1.47574 | 0.737869 | − | 0.674944i | \(-0.235832\pi\) | ||||
0.737869 | + | 0.674944i | \(0.235832\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5794.09 | 0.695380 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3805.25 | −0.450102 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8778.12 | −1.03086 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11189.5 | −1.30464 | −0.652319 | − | 0.757945i | \(-0.726204\pi\) | ||||
−0.652319 | + | 0.757945i | \(0.726204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2718.12 | 0.314663 | 0.157331 | − | 0.987546i | \(-0.449711\pi\) | ||||
0.157331 | + | 0.987546i | \(0.449711\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1182.33 | −0.135903 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 511.464 | 0.0583757 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 865.179 | 0.0973689 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11085.2 | −1.23888 | −0.619439 | − | 0.785045i | \(-0.712640\pi\) | ||||
−0.619439 | + | 0.785045i | \(0.712640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10880.6 | 1.20759 | 0.603795 | − | 0.797140i | \(-0.293655\pi\) | ||||
0.603795 | + | 0.797140i | \(0.293655\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4561.23 | 0.502745 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23156.2 | 2.53481 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14902.3 | −1.62015 | −0.810075 | − | 0.586326i | \(-0.800574\pi\) | ||||
−0.810075 | + | 0.586326i | \(0.800574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12504.3 | 1.34108 | 0.670538 | − | 0.741875i | \(-0.266063\pi\) | ||||
0.670538 | + | 0.741875i | \(0.266063\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11206.1 | −1.19376 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −395.427 | −0.0418413 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1612.21 | −0.169454 | −0.0847268 | − | 0.996404i | \(-0.527002\pi\) | ||||
−0.0847268 | + | 0.996404i | \(0.527002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7263.55 | 0.758375 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 533.869 | 0.0553717 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1275.51 | 0.130560 | 0.0652800 | − | 0.997867i | \(-0.479206\pi\) | ||||
0.0652800 | + | 0.997867i | \(0.479206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2304.82 | −0.234378 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9267.92 | 0.936335 | 0.468167 | − | 0.883640i | \(-0.344914\pi\) | ||||
0.468167 | + | 0.883640i | \(0.344914\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12615.3 | 1.26627 | 0.633136 | − | 0.774041i | \(-0.281767\pi\) | ||||
0.633136 | + | 0.774041i | \(0.281767\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1693.22 | −0.168863 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14407.1 | 1.42758 | 0.713790 | − | 0.700359i | \(-0.246977\pi\) | ||||
0.713790 | + | 0.700359i | \(0.246977\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10822.4 | 1.05875 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19198.7 | 1.86629 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 662.788 | 0.0640228 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5051.04 | −0.484845 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 284.296 | 0.0271186 | 0.0135593 | − | 0.999908i | \(-0.495684\pi\) | ||||
0.0135593 | + | 0.999908i | \(0.495684\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −879.356 | −0.0833580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5342.49 | 0.500185 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10535.7 | −0.980323 | −0.490161 | − | 0.871632i | \(-0.663062\pi\) | ||||
−0.490161 | + | 0.871632i | \(0.663062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4622.65 | 0.427492 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14230.4 | 1.30796 | 0.653982 | − | 0.756510i | \(-0.273097\pi\) | ||||
0.653982 | + | 0.756510i | \(0.273097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11340.0 | −1.03596 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5416.97 | 0.491868 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9796.09 | 0.878824 | 0.439412 | − | 0.898286i | \(-0.355187\pi\) | ||||
0.439412 | + | 0.898286i | \(0.355187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2285.39 | 0.203800 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7285.16 | −0.645784 | −0.322892 | − | 0.946436i | \(-0.604655\pi\) | ||||
−0.322892 | + | 0.946436i | \(0.604655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9916.41 | 0.873811 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6500.78 | 0.569447 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13269.6 | −1.15553 | −0.577764 | − | 0.816204i | \(-0.696075\pi\) | ||||
−0.577764 | + | 0.816204i | \(0.696075\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2986.73 | −0.257051 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10606.9 | −0.907561 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6908.56 | −0.587695 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8073.95 | 0.682865 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14711.8 | 1.23711 | 0.618556 | − | 0.785740i | \(-0.287718\pi\) | ||||
0.618556 | + | 0.785740i | \(0.287718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11004.9 | −0.920093 | −0.460046 | − | 0.887895i | \(-0.652167\pi\) | ||||
−0.460046 | + | 0.887895i | \(0.652167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4209.61 | 0.347958 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31652.8 | 2.60153 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3927.18 | 0.320951 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −757.443 | −0.0615544 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11976.0 | −0.967788 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3369.75 | 0.270793 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8884.91 | −0.706085 | −0.353042 | − | 0.935607i | \(-0.614853\pi\) | ||||
−0.353042 | + | 0.935607i | \(0.614853\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12665.5 | −1.00098 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5566.89 | −0.437540 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13986.6 | −1.09328 | −0.546639 | − | 0.837368i | \(-0.684093\pi\) | ||||
−0.546639 | + | 0.837368i | \(0.684093\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2627.65 | −0.204272 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14695.0 | −1.13617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5505.73 | −0.421090 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11252.8 | −0.856006 | −0.428003 | − | 0.903777i | \(-0.640783\pi\) | ||||
−0.428003 | + | 0.903777i | \(0.640783\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2002.04 | −0.151480 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13467.5 | −1.01354 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13559.4 | 1.01503 | 0.507514 | − | 0.861643i | \(-0.330565\pi\) | ||||
0.507514 | + | 0.861643i | \(0.330565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22375.6 | 1.66610 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17208.6 | −1.26788 | −0.633940 | − | 0.773382i | \(-0.718563\pi\) | ||||
−0.633940 | + | 0.773382i | \(0.718563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12910.3 | −0.946196 | −0.473098 | − | 0.881010i | \(-0.656864\pi\) | ||||
−0.473098 | + | 0.881010i | \(0.656864\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9881.42 | 0.720423 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1254.23 | 0.0909654 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16154.8 | −1.16557 | −0.582783 | − | 0.812628i | \(-0.698036\pi\) | ||||
−0.582783 | + | 0.812628i | \(0.698036\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13871.7 | 0.995664 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29514.1 | −2.09666 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −564.881 | −0.0399230 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3403.75 | −0.239332 | −0.119666 | − | 0.992814i | \(-0.538182\pi\) | ||||
−0.119666 | + | 0.992814i | \(0.538182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5455.09 | 0.381618 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7932.53 | −0.552116 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12884.9 | 0.892272 | 0.446136 | − | 0.894965i | \(-0.352800\pi\) | ||||
0.446136 | + | 0.894965i | \(0.352800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4147.00 | −0.284297 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19002.4 | 1.29619 | 0.648095 | − | 0.761559i | \(-0.275566\pi\) | ||||
0.648095 | + | 0.761559i | \(0.275566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8159.94 | 0.553829 | 0.276914 | − | 0.960895i | \(-0.410688\pi\) | ||||
0.276914 | + | 0.960895i | \(0.410688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5343.15 | 0.360845 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16418.8 | 1.10334 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5304.02 | −0.354668 | −0.177334 | − | 0.984151i | \(-0.556747\pi\) | ||||
−0.177334 | + | 0.984151i | \(0.556747\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 720.425 | 0.0477009 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14871.9 | 0.979886 | 0.489943 | − | 0.871754i | \(-0.337018\pi\) | ||||
0.489943 | + | 0.871754i | \(0.337018\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4742.42 | −0.310948 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6214.11 | −0.405463 | −0.202732 | − | 0.979234i | \(-0.564982\pi\) | ||||
−0.202732 | + | 0.979234i | \(0.564982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26716.2 | −1.73475 | −0.867377 | − | 0.497652i | \(-0.834196\pi\) | ||||
−0.867377 | + | 0.497652i | \(0.834196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5651.96 | −0.365226 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16338.1 | −1.04564 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17452.0 | −1.11159 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13688.1 | 0.867697 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1788.18 | 0.112815 | 0.0564074 | − | 0.998408i | \(-0.482035\pi\) | ||||
0.0564074 | + | 0.998408i | \(0.482035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13599.8 | 0.853942 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14369.7 | −0.898025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6975.65 | −0.431851 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4845.85 | −0.298595 | −0.149298 | − | 0.988792i | \(-0.547701\pi\) | ||||
−0.149298 | + | 0.988792i | \(0.547701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8154.19 | 0.500109 | 0.250054 | − | 0.968232i | \(-0.419551\pi\) | ||||
0.250054 | + | 0.968232i | \(0.419551\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12535.0 | −0.765215 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14514.1 | −0.881928 | −0.440964 | − | 0.897525i | \(-0.645363\pi\) | ||||
−0.440964 | + | 0.897525i | \(0.645363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22947.2 | 1.38792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14194.4 | −0.850641 | −0.425321 | − | 0.905043i | \(-0.639839\pi\) | ||||
−0.425321 | + | 0.905043i | \(0.639839\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11781.7 | 0.702823 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2978.16 | 0.176848 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24762.7 | −1.46376 | −0.731879 | − | 0.681435i | \(-0.761356\pi\) | ||||
−0.731879 | + | 0.681435i | \(0.761356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23482.5 | −1.38179 | −0.690897 | − | 0.722954i | \(-0.742784\pi\) | ||||
−0.690897 | + | 0.722954i | \(0.742784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1404.39 | 0.0822653 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27808.3 | −1.61430 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9157.39 | −0.529216 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15353.8 | −0.883350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12943.0 | 0.741333 | 0.370666 | − | 0.928766i | \(-0.379129\pi\) | ||||
0.370666 | + | 0.928766i | \(0.379129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −161.773 | −0.00922467 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25409.8 | −1.44251 | −0.721255 | − | 0.692669i | \(-0.756435\pi\) | ||||
−0.721255 | + | 0.692669i | \(0.756435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15584.6 | −0.876950 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5747.89 | −0.322016 | −0.161008 | − | 0.986953i | \(-0.551474\pi\) | ||||
−0.161008 | + | 0.986953i | \(0.551474\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22104.7 | −1.23296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16491.1 | −0.915831 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3077.74 | 0.170178 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30578.5 | −1.68344 | −0.841722 | − | 0.539911i | \(-0.818458\pi\) | ||||
−0.841722 | + | 0.539911i | \(0.818458\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33489.0 | 1.82778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11790.4 | 0.640738 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16371.5 | 0.885876 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11378.9 | 0.613088 | 0.306544 | − | 0.951857i | \(-0.400827\pi\) | ||||
0.306544 | + | 0.951857i | \(0.400827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17738.0 | 0.951636 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4510.65 | 0.240966 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16050.7 | 0.850208 | 0.425104 | − | 0.905145i | \(-0.360238\pi\) | ||||
0.425104 | + | 0.905145i | \(0.360238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2191.26 | −0.115582 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10323.0 | 0.542214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3300.70 | −0.172642 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16866.5 | −0.878510 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10628.6 | −0.551296 | −0.275648 | − | 0.961259i | \(-0.588892\pi\) | ||||
−0.275648 | + | 0.961259i | \(0.588892\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12249.1 | −0.630080 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −795.943 | −0.0407732 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16912.8 | 0.862810 | 0.431405 | − | 0.902158i | \(-0.358018\pi\) | ||||
0.431405 | + | 0.902158i | \(0.358018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31163.9 | 1.57680 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32129.7 | −1.61901 | −0.809506 | − | 0.587111i | \(-0.800265\pi\) | ||||
−0.809506 | + | 0.587111i | \(0.800265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31221.0 | 1.56043 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21286.3 | −1.05958 | −0.529791 | − | 0.848128i | \(-0.677730\pi\) | ||||
−0.529791 | + | 0.848128i | \(0.677730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1819.90 | 0.0902234 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16441.2 | −0.811804 | −0.405902 | − | 0.913917i | \(-0.633043\pi\) | ||||
−0.405902 | + | 0.913917i | \(0.633043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1508.57 | 0.0741877 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2992.29 | −0.146563 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −844.181 | −0.0410181 | −0.0205091 | − | 0.999790i | \(-0.506529\pi\) | ||||
−0.0205091 | + | 0.999790i | \(0.506529\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5255.97 | −0.254367 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2036.74 | −0.0981782 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13607.9 | −0.653352 | −0.326676 | − | 0.945136i | \(-0.605929\pi\) | ||||
−0.326676 | + | 0.945136i | \(0.605929\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33025.4 | −1.57938 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23150.7 | 1.10277 | 0.551387 | − | 0.834249i | \(-0.314099\pi\) | ||||
0.551387 | + | 0.834249i | \(0.314099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8792.99 | 0.415570 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2392.94 | −0.112652 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39732.0 | −1.86316 | −0.931581 | − | 0.363534i | \(-0.881570\pi\) | ||||
−0.931581 | + | 0.363534i | \(0.881570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11475.8 | 0.536045 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4151.21 | −0.193155 | −0.0965773 | − | 0.995325i | \(-0.530790\pi\) | ||||
−0.0965773 | + | 0.995325i | \(0.530790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 295.469 | 0.0136949 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15278.8 | 0.702721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40760.0 | −1.86749 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3586.76 | 0.163704 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −41288.1 | −1.87724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1290.94 | −0.0584714 | −0.0292357 | − | 0.999573i | \(-0.509307\pi\) | ||||
−0.0292357 | + | 0.999573i | \(0.509307\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15817.7 | −0.713720 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1601.10 | 0.0716981 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19270.0 | 0.859668 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4469.79 | 0.198655 | 0.0993276 | − | 0.995055i | \(-0.468331\pi\) | ||||
0.0993276 | + | 0.995055i | \(0.468331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11214.2 | −0.496533 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8812.04 | −0.388712 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17401.9 | 0.764759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13605.1 | 0.593460 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29777.8 | 1.29411 | 0.647054 | − | 0.762445i | \(-0.276001\pi\) | ||||
0.647054 | + | 0.762445i | \(0.276001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4083.89 | −0.176825 | −0.0884124 | − | 0.996084i | \(-0.528179\pi\) | ||||
−0.0884124 | + | 0.996084i | \(0.528179\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4317.31 | −0.186242 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17635.7 | −0.757975 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40384.2 | 1.72933 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16909.2 | 0.718799 | 0.359399 | − | 0.933184i | \(-0.382982\pi\) | ||||
0.359399 | + | 0.933184i | \(0.382982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 294.522 | 0.0124743 | 0.00623717 | − | 0.999981i | \(-0.498015\pi\) | ||||
0.00623717 | + | 0.999981i | \(0.498015\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −945.270 | −0.0398910 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43346.8 | 1.82263 | 0.911315 | − | 0.411711i | \(-0.135069\pi\) | ||||
0.911315 | + | 0.411711i | \(0.135069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3542.74 | −0.148425 | −0.0742126 | − | 0.997242i | \(-0.523644\pi\) | ||||
−0.0742126 | + | 0.997242i | \(0.523644\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17954.6 | 0.749503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8718.89 | −0.361353 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1331.48 | −0.0549851 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26513.0 | 1.09098 | 0.545489 | − | 0.838118i | \(-0.316344\pi\) | ||||
0.545489 | + | 0.838118i | \(0.316344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6741.72 | −0.276425 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7943.62 | 0.324547 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24800.8 | −1.00967 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1202.47 | −0.0486084 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33566.6 | 1.35211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31158.3 | 1.25069 | 0.625345 | − | 0.780348i | \(-0.284958\pi\) | ||||
0.625345 | + | 0.780348i | \(0.284958\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11394.5 | 0.455771 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22611.4 | 0.901271 | 0.450635 | − | 0.892708i | \(-0.351197\pi\) | ||||
0.450635 | + | 0.892708i | \(0.351197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17135.6 | 0.680627 | 0.340313 | − | 0.940312i | \(-0.389467\pi\) | ||||
0.340313 | + | 0.940312i | \(0.389467\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31801.8 | 1.25440 | 0.627199 | − | 0.778859i | \(-0.284201\pi\) | ||||
0.627199 | + | 0.778859i | \(0.284201\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30802.5 | −1.21077 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7121.81 | −0.278973 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12803.9 | −0.499820 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3255.72 | −0.126654 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4201.11 | 0.162871 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23693.0 | −0.912265 | −0.456133 | − | 0.889912i | \(-0.650766\pi\) | ||||
−0.456133 | + | 0.889912i | \(0.650766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15921.4 | 0.610938 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35584.4 | −1.36080 | −0.680402 | − | 0.732839i | \(-0.738195\pi\) | ||||
−0.680402 | + | 0.732839i | \(0.738195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31928.8 | −1.21686 | −0.608431 | − | 0.793607i | \(-0.708201\pi\) | ||||
−0.608431 | + | 0.793607i | \(0.708201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14982.4 | −0.569071 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24218.6 | 0.916778 | 0.458389 | − | 0.888752i | \(-0.348427\pi\) | ||||
0.458389 | + | 0.888752i | \(0.348427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4259.68 | 0.160162 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14532.1 | −0.544566 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12855.8 | −0.480136 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3443.89 | 0.128192 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6551.02 | −0.243035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47908.3 | −1.77143 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48319.7 | 1.77481 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37779.4 | 1.38307 | 0.691535 | − | 0.722343i | \(-0.256935\pi\) | ||||
0.691535 | + | 0.722343i | \(0.256935\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7797.86 | 0.284531 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33419.0 | −1.21539 | −0.607695 | − | 0.794170i | \(-0.707906\pi\) | ||||
−0.607695 | + | 0.794170i | \(0.707906\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17484.5 | −0.633792 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10024.6 | 0.362190 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15771.4 | −0.566105 | −0.283053 | − | 0.959104i | \(-0.591347\pi\) | ||||
−0.283053 | + | 0.959104i | \(0.591347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12391.3 | 0.443332 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4250.46 | 0.151577 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 960.759 | 0.0341509 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8340.79 | −0.295521 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44216.4 | −1.56157 | −0.780783 | − | 0.624802i | \(-0.785180\pi\) | ||||
−0.780783 | + | 0.624802i | \(0.785180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22961.6 | −0.805712 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 51379.1 | 1.79709 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8691.91 | 0.303044 | 0.151522 | − | 0.988454i | \(-0.451583\pi\) | ||||
0.151522 | + | 0.988454i | \(0.451583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25638.8 | −0.891045 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11824.1 | −0.409622 | −0.204811 | − | 0.978802i | \(-0.565658\pi\) | ||||
−0.204811 | + | 0.978802i | \(0.565658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28912.9 | 0.998446 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4468.88 | −0.153346 | −0.0766732 | − | 0.997056i | \(-0.524430\pi\) | ||||
−0.0766732 | + | 0.997056i | \(0.524430\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1814.68 | −0.0620726 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22930.9 | −0.781900 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18172.0 | 0.617680 | 0.308840 | − | 0.951114i | \(-0.400059\pi\) | ||||
0.308840 | + | 0.951114i | \(0.400059\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37698.1 | −1.27736 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20958.1 | 0.707920 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27359.1 | −0.918369 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9417.41 | −0.315132 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −52921.4 | −1.76539 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53267.4 | −1.77142 | −0.885710 | − | 0.464239i | \(-0.846328\pi\) | ||||
−0.885710 | + | 0.464239i | \(0.846328\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28328.6 | −0.939161 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14899.8 | −0.492439 | −0.246220 | − | 0.969214i | \(-0.579188\pi\) | ||||
−0.246220 | + | 0.969214i | \(0.579188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 98.5728 | 0.00323780 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50912.6 | 1.66718 | 0.833592 | − | 0.552380i | \(-0.186280\pi\) | ||||
0.833592 | + | 0.552380i | \(0.186280\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51490.3 | −1.68094 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4377.57 | −0.142472 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49617.9 | 1.60993 | 0.804967 | − | 0.593320i | \(-0.202183\pi\) | ||||
0.804967 | + | 0.593320i | \(0.202183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30263.0 | 0.978944 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 76421.4 | 2.45709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16435.7 | 0.526839 | 0.263419 | − | 0.964681i | \(-0.415150\pi\) | ||||
0.263419 | + | 0.964681i | \(0.415150\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22650.5 | 0.723860 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15821.0 | 0.504080 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 634.476 | 0.0201545 | 0.0100773 | − | 0.999949i | \(-0.496792\pi\) | ||||
0.0100773 | + | 0.999949i | \(0.496792\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4329.48 | −0.137116 |
(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.ck.1.4 | 4 | ||
4.3 | odd | 2 | 1176.4.a.bc.1.4 | yes | 4 | ||
7.6 | odd | 2 | 2352.4.a.cr.1.1 | 4 | |||
28.27 | even | 2 | 1176.4.a.bb.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.bb.1.1 | ✓ | 4 | 28.27 | even | 2 | ||
1176.4.a.bc.1.4 | yes | 4 | 4.3 | odd | 2 | ||
2352.4.a.ck.1.4 | 4 | 1.1 | even | 1 | trivial | ||
2352.4.a.cr.1.1 | 4 | 7.6 | odd | 2 |