Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.j.199.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.56155i | − 0.552092i | −0.961144 | − | 0.276046i | \(-0.910976\pi\) | ||||
0.961144 | − | 0.276046i | \(-0.0890243\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 5.56155 | 0.695194 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.68466 | 0.318751 | ||||||||
\(7\) | 10.2462i | 0.553243i | 0.960979 | + | 0.276622i | \(0.0892149\pi\) | ||||
−0.960979 | + | 0.276622i | \(0.910785\pi\) | |||||||
\(8\) | − 21.1771i | − 0.935904i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 16.6847i | 0.401371i | ||||||||
\(13\) | − 40.8769i | − 0.872093i | −0.899924 | − | 0.436047i | \(-0.856378\pi\) | ||||
0.899924 | − | 0.436047i | \(-0.143622\pi\) | |||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.4233 | 0.178489 | ||||||||
\(17\) | 98.7083i | 1.40825i | 0.710075 | + | 0.704126i | \(0.248661\pi\) | ||||
−0.710075 | + | 0.704126i | \(0.751339\pi\) | |||||||
\(18\) | 14.0540i | 0.184031i | ||||||||
\(19\) | 39.6458 | 0.478704 | 0.239352 | − | 0.970933i | \(-0.423065\pi\) | ||||
0.239352 | + | 0.970933i | \(0.423065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −30.7386 | −0.319415 | ||||||||
\(22\) | 17.1771i | 0.166462i | ||||||||
\(23\) | 61.6932i | 0.559301i | 0.960102 | + | 0.279650i | \(0.0902185\pi\) | ||||
−0.960102 | + | 0.279650i | \(0.909781\pi\) | |||||||
\(24\) | 63.5312 | 0.540344 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −63.8314 | −0.481476 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 56.9848i | 0.384612i | ||||||||
\(29\) | 149.093 | 0.954684 | 0.477342 | − | 0.878718i | \(-0.341600\pi\) | ||||
0.477342 | + | 0.878718i | \(0.341600\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 54.7386 | 0.317140 | 0.158570 | − | 0.987348i | \(-0.449312\pi\) | ||||
0.158570 | + | 0.987348i | \(0.449312\pi\) | |||||||
\(32\) | − 187.255i | − 1.03445i | ||||||||
\(33\) | − 33.0000i | − 0.174078i | ||||||||
\(34\) | 154.138 | 0.777485 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −50.0540 | −0.231731 | ||||||||
\(37\) | − 44.8939i | − 0.199473i | −0.995014 | − | 0.0997367i | \(-0.968200\pi\) | ||||
0.995014 | − | 0.0997367i | \(-0.0318000\pi\) | |||||||
\(38\) | − 61.9091i | − 0.264289i | ||||||||
\(39\) | 122.631 | 0.503503 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 336.479 | 1.28169 | 0.640844 | − | 0.767671i | \(-0.278585\pi\) | ||||
0.640844 | + | 0.767671i | \(0.278585\pi\) | |||||||
\(42\) | 48.0000i | 0.176347i | ||||||||
\(43\) | − 2.36745i | − 0.00839611i | −0.999991 | − | 0.00419806i | \(-0.998664\pi\) | ||||
0.999991 | − | 0.00419806i | \(-0.00133629\pi\) | |||||||
\(44\) | −61.1771 | −0.209609 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 96.3371 | 0.308786 | ||||||||
\(47\) | 333.295i | 1.03439i | 0.855869 | + | 0.517193i | \(0.173023\pi\) | ||||
−0.855869 | + | 0.517193i | \(0.826977\pi\) | |||||||
\(48\) | 34.2699i | 0.103051i | ||||||||
\(49\) | 238.015 | 0.693922 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −296.125 | −0.813055 | ||||||||
\(52\) | − 227.339i | − 0.606274i | ||||||||
\(53\) | 640.064i | 1.65886i | 0.558610 | + | 0.829430i | \(0.311335\pi\) | ||||
−0.558610 | + | 0.829430i | \(0.688665\pi\) | |||||||
\(54\) | −42.1619 | −0.106250 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 216.985 | 0.517782 | ||||||||
\(57\) | 118.938i | 0.276380i | ||||||||
\(58\) | − 232.816i | − 0.527074i | ||||||||
\(59\) | 370.773 | 0.818144 | 0.409072 | − | 0.912502i | \(-0.365853\pi\) | ||||
0.409072 | + | 0.912502i | \(0.365853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −714.405 | −1.49951 | −0.749756 | − | 0.661715i | \(-0.769829\pi\) | ||||
−0.749756 | + | 0.661715i | \(0.769829\pi\) | |||||||
\(62\) | − 85.4773i | − 0.175091i | ||||||||
\(63\) | − 92.2159i | − 0.184414i | ||||||||
\(64\) | −201.022 | −0.392621 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −51.5312 | −0.0961069 | ||||||||
\(67\) | 404.985i | 0.738459i | 0.929338 | + | 0.369230i | \(0.120378\pi\) | ||||
−0.929338 | + | 0.369230i | \(0.879622\pi\) | |||||||
\(68\) | 548.972i | 0.979009i | ||||||||
\(69\) | −185.080 | −0.322912 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 939.292 | 1.57005 | 0.785024 | − | 0.619465i | \(-0.212651\pi\) | ||||
0.785024 | + | 0.619465i | \(0.212651\pi\) | |||||||
\(72\) | 190.594i | 0.311968i | ||||||||
\(73\) | − 362.570i | − 0.581310i | −0.956828 | − | 0.290655i | \(-0.906127\pi\) | ||||
0.956828 | − | 0.290655i | \(-0.0938732\pi\) | |||||||
\(74\) | −70.1042 | −0.110128 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 220.492 | 0.332792 | ||||||||
\(77\) | − 112.708i | − 0.166809i | ||||||||
\(78\) | − 191.494i | − 0.277980i | ||||||||
\(79\) | −951.835 | −1.35557 | −0.677784 | − | 0.735261i | \(-0.737059\pi\) | ||||
−0.677784 | + | 0.735261i | \(0.737059\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 525.430i | − 0.707610i | ||||||||
\(83\) | 735.221i | 0.972302i | 0.873875 | + | 0.486151i | \(0.161599\pi\) | ||||
−0.873875 | + | 0.486151i | \(0.838401\pi\) | |||||||
\(84\) | −170.955 | −0.222056 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.69690 | −0.00463543 | ||||||||
\(87\) | 447.278i | 0.551187i | ||||||||
\(88\) | 232.948i | 0.282186i | ||||||||
\(89\) | −385.879 | −0.459585 | −0.229793 | − | 0.973240i | \(-0.573805\pi\) | ||||
−0.229793 | + | 0.973240i | \(0.573805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 418.833 | 0.482480 | ||||||||
\(92\) | 343.110i | 0.388823i | ||||||||
\(93\) | 164.216i | 0.183101i | ||||||||
\(94\) | 520.458 | 0.571076 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 561.764 | 0.597238 | ||||||||
\(97\) | 966.345i | 1.01152i | 0.862674 | + | 0.505760i | \(0.168788\pi\) | ||||
−0.862674 | + | 0.505760i | \(0.831212\pi\) | |||||||
\(98\) | − 371.673i | − 0.383109i | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 348.600 | 0.343436 | 0.171718 | − | 0.985146i | \(-0.445068\pi\) | ||||
0.171718 | + | 0.985146i | \(0.445068\pi\) | |||||||
\(102\) | 462.415i | 0.448881i | ||||||||
\(103\) | − 1536.38i | − 1.46975i | −0.678204 | − | 0.734873i | \(-0.737242\pi\) | ||||
0.678204 | − | 0.734873i | \(-0.262758\pi\) | |||||||
\(104\) | −865.653 | −0.816195 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 999.494 | 0.915844 | ||||||||
\(107\) | 779.180i | 0.703983i | 0.936003 | + | 0.351991i | \(0.114495\pi\) | ||||
−0.936003 | + | 0.351991i | \(0.885505\pi\) | |||||||
\(108\) | − 150.162i | − 0.133790i | ||||||||
\(109\) | 1501.79 | 1.31968 | 0.659842 | − | 0.751404i | \(-0.270623\pi\) | ||||
0.659842 | + | 0.751404i | \(0.270623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 134.682 | 0.115166 | ||||||||
\(112\) | 117.045i | 0.0987478i | ||||||||
\(113\) | 170.000i | 0.141524i | 0.997493 | + | 0.0707622i | \(0.0225431\pi\) | ||||
−0.997493 | + | 0.0707622i | \(0.977457\pi\) | |||||||
\(114\) | 185.727 | 0.152587 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 829.187 | 0.663691 | ||||||||
\(117\) | 367.892i | 0.290698i | ||||||||
\(118\) | − 578.981i | − 0.451691i | ||||||||
\(119\) | −1011.39 | −0.779106 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1115.58i | 0.827869i | ||||||||
\(123\) | 1009.44i | 0.739983i | ||||||||
\(124\) | 304.432 | 0.220474 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −144.000 | −0.101814 | ||||||||
\(127\) | 1739.82i | 1.21562i | 0.794082 | + | 0.607811i | \(0.207952\pi\) | ||||
−0.794082 | + | 0.607811i | \(0.792048\pi\) | |||||||
\(128\) | − 1184.13i | − 0.817683i | ||||||||
\(129\) | 7.10235 | 0.00484750 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 312.837 | 0.208647 | 0.104323 | − | 0.994543i | \(-0.466732\pi\) | ||||
0.104323 | + | 0.994543i | \(0.466732\pi\) | |||||||
\(132\) | − 183.531i | − 0.121018i | ||||||||
\(133\) | 406.220i | 0.264840i | ||||||||
\(134\) | 632.405 | 0.407698 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2090.35 | 1.31799 | ||||||||
\(137\) | 716.928i | 0.447090i | 0.974694 | + | 0.223545i | \(0.0717629\pi\) | ||||
−0.974694 | + | 0.223545i | \(0.928237\pi\) | |||||||
\(138\) | 289.011i | 0.178277i | ||||||||
\(139\) | 876.483 | 0.534837 | 0.267418 | − | 0.963581i | \(-0.413829\pi\) | ||||
0.267418 | + | 0.963581i | \(0.413829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −999.886 | −0.597203 | ||||||||
\(142\) | − 1466.75i | − 0.866811i | ||||||||
\(143\) | 449.646i | 0.262946i | ||||||||
\(144\) | −102.810 | −0.0594963 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −566.172 | −0.320937 | ||||||||
\(147\) | 714.045i | 0.400636i | ||||||||
\(148\) | − 249.680i | − 0.138673i | ||||||||
\(149\) | 2376.36 | 1.30657 | 0.653285 | − | 0.757112i | \(-0.273390\pi\) | ||||
0.653285 | + | 0.757112i | \(0.273390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −92.8466 | −0.0500381 | −0.0250190 | − | 0.999687i | \(-0.507965\pi\) | ||||
−0.0250190 | + | 0.999687i | \(0.507965\pi\) | |||||||
\(152\) | − 839.583i | − 0.448021i | ||||||||
\(153\) | − 888.375i | − 0.469417i | ||||||||
\(154\) | −176.000 | −0.0920941 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 682.017 | 0.350032 | ||||||||
\(157\) | 1881.24i | 0.956301i | 0.878278 | + | 0.478150i | \(0.158693\pi\) | ||||
−0.878278 | + | 0.478150i | \(0.841307\pi\) | |||||||
\(158\) | 1486.34i | 0.748398i | ||||||||
\(159\) | −1920.19 | −0.957743 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −632.121 | −0.309429 | ||||||||
\(162\) | − 126.486i | − 0.0613436i | ||||||||
\(163\) | − 2465.49i | − 1.18474i | −0.805667 | − | 0.592369i | \(-0.798193\pi\) | ||||
0.805667 | − | 0.592369i | \(-0.201807\pi\) | |||||||
\(164\) | 1871.35 | 0.891022 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1148.09 | 0.536800 | ||||||||
\(167\) | 1254.30i | 0.581200i | 0.956845 | + | 0.290600i | \(0.0938549\pi\) | ||||
−0.956845 | + | 0.290600i | \(0.906145\pi\) | |||||||
\(168\) | 650.955i | 0.298942i | ||||||||
\(169\) | 526.080 | 0.239454 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −356.813 | −0.159568 | ||||||||
\(172\) | − 13.1667i | − 0.00583693i | ||||||||
\(173\) | − 1206.71i | − 0.530314i | −0.964205 | − | 0.265157i | \(-0.914576\pi\) | ||||
0.964205 | − | 0.265157i | \(-0.0854238\pi\) | |||||||
\(174\) | 698.449 | 0.304306 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −125.656 | −0.0538164 | ||||||||
\(177\) | 1112.32i | 0.472356i | ||||||||
\(178\) | 602.570i | 0.253733i | ||||||||
\(179\) | 1442.29 | 0.602244 | 0.301122 | − | 0.953586i | \(-0.402639\pi\) | ||||
0.301122 | + | 0.953586i | \(0.402639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4261.81 | 1.75015 | 0.875076 | − | 0.483985i | \(-0.160811\pi\) | ||||
0.875076 | + | 0.483985i | \(0.160811\pi\) | |||||||
\(182\) | − 654.030i | − 0.266373i | ||||||||
\(183\) | − 2143.22i | − 0.865744i | ||||||||
\(184\) | 1306.48 | 0.523451 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 256.432 | 0.101089 | ||||||||
\(187\) | − 1085.79i | − 0.424604i | ||||||||
\(188\) | 1853.64i | 0.719099i | ||||||||
\(189\) | 276.648 | 0.106472 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −852.223 | −0.322852 | −0.161426 | − | 0.986885i | \(-0.551609\pi\) | ||||
−0.161426 | + | 0.986885i | \(0.551609\pi\) | |||||||
\(192\) | − 603.065i | − 0.226680i | ||||||||
\(193\) | − 2459.95i | − 0.917468i | −0.888574 | − | 0.458734i | \(-0.848303\pi\) | ||||
0.888574 | − | 0.458734i | \(-0.151697\pi\) | |||||||
\(194\) | 1509.00 | 0.558452 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1323.73 | 0.482410 | ||||||||
\(197\) | − 3477.06i | − 1.25751i | −0.777602 | − | 0.628756i | \(-0.783564\pi\) | ||||
0.777602 | − | 0.628756i | \(-0.216436\pi\) | |||||||
\(198\) | − 154.594i | − 0.0554874i | ||||||||
\(199\) | −3995.04 | −1.42312 | −0.711560 | − | 0.702626i | \(-0.752011\pi\) | ||||
−0.711560 | + | 0.702626i | \(0.752011\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1214.95 | −0.426350 | ||||||||
\(202\) | − 544.358i | − 0.189608i | ||||||||
\(203\) | 1527.64i | 0.528173i | ||||||||
\(204\) | −1646.91 | −0.565231 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2399.14 | −0.811436 | ||||||||
\(207\) | − 555.239i | − 0.186434i | ||||||||
\(208\) | − 466.949i | − 0.155659i | ||||||||
\(209\) | −436.104 | −0.144335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1046.13 | 0.341319 | 0.170660 | − | 0.985330i | \(-0.445410\pi\) | ||||
0.170660 | + | 0.985330i | \(0.445410\pi\) | |||||||
\(212\) | 3559.75i | 1.15323i | ||||||||
\(213\) | 2817.88i | 0.906468i | ||||||||
\(214\) | 1216.73 | 0.388664 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −571.781 | −0.180115 | ||||||||
\(217\) | 560.864i | 0.175456i | ||||||||
\(218\) | − 2345.13i | − 0.728587i | ||||||||
\(219\) | 1087.71 | 0.335619 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4034.89 | 1.22813 | ||||||||
\(222\) | − 210.313i | − 0.0635823i | ||||||||
\(223\) | − 506.265i | − 0.152027i | −0.997107 | − | 0.0760135i | \(-0.975781\pi\) | ||||
0.997107 | − | 0.0760135i | \(-0.0242192\pi\) | |||||||
\(224\) | 1918.65 | 0.572300 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 265.464 | 0.0781345 | ||||||||
\(227\) | 4286.29i | 1.25326i | 0.779315 | + | 0.626632i | \(0.215567\pi\) | ||||
−0.779315 | + | 0.626632i | \(0.784433\pi\) | |||||||
\(228\) | 661.477i | 0.192138i | ||||||||
\(229\) | −5709.37 | −1.64754 | −0.823769 | − | 0.566926i | \(-0.808133\pi\) | ||||
−0.823769 | + | 0.566926i | \(0.808133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 338.125 | 0.0963073 | ||||||||
\(232\) | − 3157.35i | − 0.893492i | ||||||||
\(233\) | 2946.09i | 0.828348i | 0.910198 | + | 0.414174i | \(0.135929\pi\) | ||||
−0.910198 | + | 0.414174i | \(0.864071\pi\) | |||||||
\(234\) | 574.483 | 0.160492 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2062.07 | 0.568769 | ||||||||
\(237\) | − 2855.51i | − 0.782637i | ||||||||
\(238\) | 1579.33i | 0.430139i | ||||||||
\(239\) | 2078.89 | 0.562646 | 0.281323 | − | 0.959613i | \(-0.409227\pi\) | ||||
0.281323 | + | 0.959613i | \(0.409227\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1853.37 | 0.495378 | 0.247689 | − | 0.968840i | \(-0.420329\pi\) | ||||
0.247689 | + | 0.968840i | \(0.420329\pi\) | |||||||
\(242\) | − 188.948i | − 0.0501902i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −3973.20 | −1.04245 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1576.29 | 0.408539 | ||||||||
\(247\) | − 1620.60i | − 0.417475i | ||||||||
\(248\) | − 1159.20i | − 0.296813i | ||||||||
\(249\) | −2205.66 | −0.561359 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2358.39 | −0.593068 | −0.296534 | − | 0.955022i | \(-0.595831\pi\) | ||||
−0.296534 | + | 0.955022i | \(0.595831\pi\) | |||||||
\(252\) | − 512.864i | − 0.128204i | ||||||||
\(253\) | − 678.625i | − 0.168635i | ||||||||
\(254\) | 2716.82 | 0.671135 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3457.26 | −0.844057 | ||||||||
\(257\) | − 5519.25i | − 1.33962i | −0.742534 | − | 0.669809i | \(-0.766376\pi\) | ||||
0.742534 | − | 0.669809i | \(-0.233624\pi\) | |||||||
\(258\) | − 11.0907i | − 0.00267627i | ||||||||
\(259\) | 459.993 | 0.110357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1341.84 | −0.318228 | ||||||||
\(262\) | − 488.512i | − 0.115192i | ||||||||
\(263\) | 2259.65i | 0.529795i | 0.964277 | + | 0.264898i | \(0.0853382\pi\) | ||||
−0.964277 | + | 0.264898i | \(0.914662\pi\) | |||||||
\(264\) | −698.844 | −0.162920 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 634.333 | 0.146216 | ||||||||
\(267\) | − 1157.64i | − 0.265342i | ||||||||
\(268\) | 2252.34i | 0.513373i | ||||||||
\(269\) | −7039.53 | −1.59557 | −0.797783 | − | 0.602944i | \(-0.793994\pi\) | ||||
−0.797783 | + | 0.602944i | \(0.793994\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5155.08 | 1.15553 | 0.577765 | − | 0.816203i | \(-0.303925\pi\) | ||||
0.577765 | + | 0.816203i | \(0.303925\pi\) | |||||||
\(272\) | 1127.57i | 0.251357i | ||||||||
\(273\) | 1256.50i | 0.278560i | ||||||||
\(274\) | 1119.52 | 0.246835 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1029.33 | −0.224487 | ||||||||
\(277\) | − 9074.52i | − 1.96836i | −0.177175 | − | 0.984179i | \(-0.556696\pi\) | ||||
0.177175 | − | 0.984179i | \(-0.443304\pi\) | |||||||
\(278\) | − 1368.67i | − 0.295279i | ||||||||
\(279\) | −492.648 | −0.105713 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3407.79 | −0.723459 | −0.361729 | − | 0.932283i | \(-0.617814\pi\) | ||||
−0.361729 | + | 0.932283i | \(0.617814\pi\) | |||||||
\(282\) | 1561.38i | 0.329711i | ||||||||
\(283\) | − 8827.73i | − 1.85425i | −0.374746 | − | 0.927127i | \(-0.622270\pi\) | ||||
0.374746 | − | 0.927127i | \(-0.377730\pi\) | |||||||
\(284\) | 5223.92 | 1.09149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 702.146 | 0.145170 | ||||||||
\(287\) | 3447.64i | 0.709085i | ||||||||
\(288\) | 1685.29i | 0.344815i | ||||||||
\(289\) | −4830.33 | −0.983174 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2899.03 | −0.584001 | ||||||||
\(292\) | − 2016.45i | − 0.404123i | ||||||||
\(293\) | − 4528.29i | − 0.902886i | −0.892300 | − | 0.451443i | \(-0.850909\pi\) | ||||
0.892300 | − | 0.451443i | \(-0.149091\pi\) | |||||||
\(294\) | 1115.02 | 0.221188 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −950.722 | −0.186688 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | − 3710.81i | − 0.721347i | ||||||||
\(299\) | 2521.83 | 0.487762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.2574 | 0.00464509 | ||||||||
\(302\) | 144.985i | 0.0276256i | ||||||||
\(303\) | 1045.80i | 0.198283i | ||||||||
\(304\) | 452.886 | 0.0854434 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1387.24 | −0.259162 | ||||||||
\(307\) | − 568.106i | − 0.105614i | −0.998605 | − | 0.0528071i | \(-0.983183\pi\) | ||||
0.998605 | − | 0.0528071i | \(-0.0168168\pi\) | |||||||
\(308\) | − 626.833i | − 0.115965i | ||||||||
\(309\) | 4609.14 | 0.848559 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6853.59 | −1.24962 | −0.624809 | − | 0.780778i | \(-0.714823\pi\) | ||||
−0.624809 | + | 0.780778i | \(0.714823\pi\) | |||||||
\(312\) | − 2596.96i | − 0.471230i | ||||||||
\(313\) | − 1138.92i | − 0.205673i | −0.994698 | − | 0.102837i | \(-0.967208\pi\) | ||||
0.994698 | − | 0.102837i | \(-0.0327919\pi\) | |||||||
\(314\) | 2937.65 | 0.527966 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5293.68 | −0.942382 | ||||||||
\(317\) | − 3207.48i | − 0.568297i | −0.958780 | − | 0.284148i | \(-0.908289\pi\) | ||||
0.958780 | − | 0.284148i | \(-0.0917109\pi\) | |||||||
\(318\) | 2998.48i | 0.528763i | ||||||||
\(319\) | −1640.02 | −0.287848 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2337.54 | −0.406445 | ||||||||
\(322\) | 987.091i | 0.170834i | ||||||||
\(323\) | 3913.37i | 0.674136i | ||||||||
\(324\) | 450.486 | 0.0772438 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3850.00 | −0.654085 | ||||||||
\(327\) | 4505.37i | 0.761920i | ||||||||
\(328\) | − 7125.65i | − 1.19954i | ||||||||
\(329\) | −3415.02 | −0.572267 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9135.12 | −1.51695 | −0.758477 | − | 0.651700i | \(-0.774056\pi\) | ||||
−0.758477 | + | 0.651700i | \(0.774056\pi\) | |||||||
\(332\) | 4088.97i | 0.675938i | ||||||||
\(333\) | 404.045i | 0.0664911i | ||||||||
\(334\) | 1958.65 | 0.320876 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −351.136 | −0.0570121 | ||||||||
\(337\) | 3470.05i | 0.560907i | 0.959868 | + | 0.280453i | \(0.0904848\pi\) | ||||
−0.959868 | + | 0.280453i | \(0.909515\pi\) | |||||||
\(338\) | − 821.501i | − 0.132200i | ||||||||
\(339\) | −510.000 | −0.0817091 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −602.125 | −0.0956214 | ||||||||
\(342\) | 557.182i | 0.0880963i | ||||||||
\(343\) | 5953.20i | 0.937151i | ||||||||
\(344\) | −50.1357 | −0.00785795 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1884.34 | −0.292782 | ||||||||
\(347\) | 89.3315i | 0.0138201i | 0.999976 | + | 0.00691004i | \(0.00219955\pi\) | ||||
−0.999976 | + | 0.00691004i | \(0.997800\pi\) | |||||||
\(348\) | 2487.56i | 0.383182i | ||||||||
\(349\) | 149.375 | 0.0229107 | 0.0114554 | − | 0.999934i | \(-0.496354\pi\) | ||||
0.0114554 | + | 0.999934i | \(0.496354\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1103.68 | −0.167834 | ||||||||
\(352\) | 2059.80i | 0.311897i | ||||||||
\(353\) | 7867.64i | 1.18627i | 0.805104 | + | 0.593133i | \(0.202109\pi\) | ||||
−0.805104 | + | 0.593133i | \(0.797891\pi\) | |||||||
\(354\) | 1736.94 | 0.260784 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2146.09 | −0.319501 | ||||||||
\(357\) | − 3034.16i | − 0.449817i | ||||||||
\(358\) | − 2252.21i | − 0.332494i | ||||||||
\(359\) | −4974.22 | −0.731279 | −0.365639 | − | 0.930757i | \(-0.619150\pi\) | ||||
−0.365639 | + | 0.930757i | \(0.619150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5287.21 | −0.770842 | ||||||||
\(362\) | − 6655.04i | − 0.966246i | ||||||||
\(363\) | 363.000i | 0.0524864i | ||||||||
\(364\) | 2329.36 | 0.335417 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3346.74 | −0.477970 | ||||||||
\(367\) | 13266.7i | 1.88696i | 0.331433 | + | 0.943479i | \(0.392468\pi\) | ||||
−0.331433 | + | 0.943479i | \(0.607532\pi\) | |||||||
\(368\) | 704.739i | 0.0998290i | ||||||||
\(369\) | −3028.31 | −0.427229 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6558.23 | −0.917754 | ||||||||
\(372\) | 913.295i | 0.127291i | ||||||||
\(373\) | − 4632.77i | − 0.643099i | −0.946893 | − | 0.321549i | \(-0.895796\pi\) | ||||
0.946893 | − | 0.321549i | \(-0.104204\pi\) | |||||||
\(374\) | −1695.52 | −0.234421 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7058.22 | 0.968085 | ||||||||
\(377\) | − 6094.45i | − 0.832573i | ||||||||
\(378\) | − 432.000i | − 0.0587822i | ||||||||
\(379\) | −6503.31 | −0.881406 | −0.440703 | − | 0.897653i | \(-0.645271\pi\) | ||||
−0.440703 | + | 0.897653i | \(0.645271\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5219.45 | −0.701839 | ||||||||
\(382\) | 1330.79i | 0.178244i | ||||||||
\(383\) | 12734.5i | 1.69897i | 0.527614 | + | 0.849484i | \(0.323087\pi\) | ||||
−0.527614 | + | 0.849484i | \(0.676913\pi\) | |||||||
\(384\) | 3552.39 | 0.472090 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3841.35 | −0.506527 | ||||||||
\(387\) | 21.3071i | 0.00279870i | ||||||||
\(388\) | 5374.38i | 0.703203i | ||||||||
\(389\) | −12024.6 | −1.56728 | −0.783639 | − | 0.621216i | \(-0.786639\pi\) | ||||
−0.783639 | + | 0.621216i | \(0.786639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6089.63 | −0.787636 | ||||||||
\(392\) | − 5040.47i | − 0.649444i | ||||||||
\(393\) | 938.511i | 0.120462i | ||||||||
\(394\) | −5429.61 | −0.694263 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 550.594 | 0.0698696 | ||||||||
\(397\) | 5223.65i | 0.660371i | 0.943916 | + | 0.330186i | \(0.107111\pi\) | ||||
−0.943916 | + | 0.330186i | \(0.892889\pi\) | |||||||
\(398\) | 6238.46i | 0.785693i | ||||||||
\(399\) | −1218.66 | −0.152905 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9648.18 | 1.20151 | 0.600757 | − | 0.799432i | \(-0.294866\pi\) | ||||
0.600757 | + | 0.799432i | \(0.294866\pi\) | |||||||
\(402\) | 1897.22i | 0.235384i | ||||||||
\(403\) | − 2237.55i | − 0.276576i | ||||||||
\(404\) | 1938.76 | 0.238755 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2385.48 | 0.291600 | ||||||||
\(407\) | 493.833i | 0.0601435i | ||||||||
\(408\) | 6271.06i | 0.760941i | ||||||||
\(409\) | 2010.47 | 0.243060 | 0.121530 | − | 0.992588i | \(-0.461220\pi\) | ||||
0.121530 | + | 0.992588i | \(0.461220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2150.78 | −0.258127 | ||||||||
\(412\) | − 8544.65i | − 1.02176i | ||||||||
\(413\) | 3799.02i | 0.452633i | ||||||||
\(414\) | −867.034 | −0.102929 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7654.39 | −0.902133 | ||||||||
\(417\) | 2629.45i | 0.308788i | ||||||||
\(418\) | 681.000i | 0.0796861i | ||||||||
\(419\) | −4435.27 | −0.517129 | −0.258565 | − | 0.965994i | \(-0.583250\pi\) | ||||
−0.258565 | + | 0.965994i | \(0.583250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15217.9 | 1.76170 | 0.880852 | − | 0.473392i | \(-0.156971\pi\) | ||||
0.880852 | + | 0.473392i | \(0.156971\pi\) | |||||||
\(422\) | − 1633.58i | − 0.188440i | ||||||||
\(423\) | − 2999.66i | − 0.344795i | ||||||||
\(424\) | 13554.7 | 1.55253 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4400.26 | 0.500454 | ||||||||
\(427\) | − 7319.95i | − 0.829595i | ||||||||
\(428\) | 4333.45i | 0.489405i | ||||||||
\(429\) | −1348.94 | −0.151812 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5622.11 | −0.628324 | −0.314162 | − | 0.949369i | \(-0.601723\pi\) | ||||
−0.314162 | + | 0.949369i | \(0.601723\pi\) | |||||||
\(432\) | − 308.429i | − 0.0343502i | ||||||||
\(433\) | − 14306.3i | − 1.58780i | −0.608051 | − | 0.793898i | \(-0.708049\pi\) | ||||
0.608051 | − | 0.793898i | \(-0.291951\pi\) | |||||||
\(434\) | 875.818 | 0.0968678 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8352.29 | 0.917436 | ||||||||
\(437\) | 2445.88i | 0.267740i | ||||||||
\(438\) | − 1698.52i | − 0.185293i | ||||||||
\(439\) | −4384.20 | −0.476643 | −0.238322 | − | 0.971186i | \(-0.576597\pi\) | ||||
−0.238322 | + | 0.971186i | \(0.576597\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2142.14 | −0.231307 | ||||||||
\(442\) | − 6300.69i | − 0.678039i | ||||||||
\(443\) | − 10090.0i | − 1.08214i | −0.840977 | − | 0.541071i | \(-0.818019\pi\) | ||||
0.840977 | − | 0.541071i | \(-0.181981\pi\) | |||||||
\(444\) | 749.040 | 0.0800627 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −790.560 | −0.0839330 | ||||||||
\(447\) | 7129.07i | 0.754348i | ||||||||
\(448\) | − 2059.71i | − 0.217215i | ||||||||
\(449\) | −9582.52 | −1.00719 | −0.503594 | − | 0.863941i | \(-0.667989\pi\) | ||||
−0.503594 | + | 0.863941i | \(0.667989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3701.27 | −0.386444 | ||||||||
\(452\) | 945.464i | 0.0983869i | ||||||||
\(453\) | − 278.540i | − 0.0288895i | ||||||||
\(454\) | 6693.27 | 0.691918 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2518.75 | 0.258665 | ||||||||
\(457\) | − 9999.34i | − 1.02352i | −0.859128 | − | 0.511761i | \(-0.828993\pi\) | ||||
0.859128 | − | 0.511761i | \(-0.171007\pi\) | |||||||
\(458\) | 8915.49i | 0.909593i | ||||||||
\(459\) | 2665.12 | 0.271018 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11115.8 | −1.12302 | −0.561512 | − | 0.827468i | \(-0.689780\pi\) | ||||
−0.561512 | + | 0.827468i | \(0.689780\pi\) | |||||||
\(462\) | − 528.000i | − 0.0531705i | ||||||||
\(463\) | − 1567.16i | − 0.157305i | −0.996902 | − | 0.0786524i | \(-0.974938\pi\) | ||||
0.996902 | − | 0.0786524i | \(-0.0250617\pi\) | |||||||
\(464\) | 1703.13 | 0.170401 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4600.48 | 0.457325 | ||||||||
\(467\) | − 12648.8i | − 1.25335i | −0.779281 | − | 0.626675i | \(-0.784415\pi\) | ||||
0.779281 | − | 0.626675i | \(-0.215585\pi\) | |||||||
\(468\) | 2046.05i | 0.202091i | ||||||||
\(469\) | −4149.56 | −0.408548 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5643.72 | −0.552120 | ||||||||
\(472\) | − 7851.88i | − 0.765704i | ||||||||
\(473\) | 26.0420i | 0.00253152i | ||||||||
\(474\) | −4459.02 | −0.432088 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5624.88 | −0.541630 | ||||||||
\(477\) | − 5760.58i | − 0.552953i | ||||||||
\(478\) | − 3246.30i | − 0.310633i | ||||||||
\(479\) | 10719.2 | 1.02249 | 0.511247 | − | 0.859434i | \(-0.329184\pi\) | ||||
0.511247 | + | 0.859434i | \(0.329184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1835.12 | −0.173959 | ||||||||
\(482\) | − 2894.14i | − 0.273494i | ||||||||
\(483\) | − 1896.36i | − 0.178649i | ||||||||
\(484\) | 672.948 | 0.0631995 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 379.457 | 0.0354167 | ||||||||
\(487\) | − 7161.20i | − 0.666335i | −0.942868 | − | 0.333167i | \(-0.891883\pi\) | ||||
0.942868 | − | 0.333167i | \(-0.108117\pi\) | |||||||
\(488\) | 15129.0i | 1.40340i | ||||||||
\(489\) | 7396.48 | 0.684009 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14567.3 | 1.33893 | 0.669463 | − | 0.742845i | \(-0.266524\pi\) | ||||
0.669463 | + | 0.742845i | \(0.266524\pi\) | |||||||
\(492\) | 5614.04i | 0.514432i | ||||||||
\(493\) | 14716.7i | 1.34444i | ||||||||
\(494\) | −2530.65 | −0.230485 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 625.295 | 0.0566060 | ||||||||
\(497\) | 9624.18i | 0.868619i | ||||||||
\(498\) | 3444.26i | 0.309922i | ||||||||
\(499\) | 4638.99 | 0.416172 | 0.208086 | − | 0.978111i | \(-0.433277\pi\) | ||||
0.208086 | + | 0.978111i | \(0.433277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3762.89 | −0.335556 | ||||||||
\(502\) | 3682.75i | 0.327428i | ||||||||
\(503\) | − 12206.3i | − 1.08201i | −0.841019 | − | 0.541006i | \(-0.818044\pi\) | ||||
0.841019 | − | 0.541006i | \(-0.181956\pi\) | |||||||
\(504\) | −1952.86 | −0.172594 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1059.71 | −0.0931024 | ||||||||
\(507\) | 1578.24i | 0.138249i | ||||||||
\(508\) | 9676.09i | 0.845093i | ||||||||
\(509\) | −10018.6 | −0.872427 | −0.436214 | − | 0.899843i | \(-0.643681\pi\) | ||||
−0.436214 | + | 0.899843i | \(0.643681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3714.97 | 0.321606 | ||||||||
\(512\) | − 4074.36i | − 0.351686i | ||||||||
\(513\) | − 1070.44i | − 0.0921267i | ||||||||
\(514\) | −8618.61 | −0.739592 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 39.5001 | 0.00336995 | ||||||||
\(517\) | − 3666.25i | − 0.311879i | ||||||||
\(518\) | − 718.303i | − 0.0609274i | ||||||||
\(519\) | 3620.12 | 0.306177 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1054.72 | 0.0886916 | 0.0443458 | − | 0.999016i | \(-0.485880\pi\) | ||||
0.0443458 | + | 0.999016i | \(0.485880\pi\) | |||||||
\(522\) | 2095.35i | 0.175691i | ||||||||
\(523\) | − 16234.2i | − 1.35730i | −0.734460 | − | 0.678652i | \(-0.762564\pi\) | ||||
0.734460 | − | 0.678652i | \(-0.237436\pi\) | |||||||
\(524\) | 1739.86 | 0.145050 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3528.57 | 0.292496 | ||||||||
\(527\) | 5403.16i | 0.446613i | ||||||||
\(528\) | − 376.969i | − 0.0310709i | ||||||||
\(529\) | 8360.95 | 0.687183 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3336.95 | −0.272715 | ||||||||
\(532\) | 2259.21i | 0.184115i | ||||||||
\(533\) | − 13754.2i | − 1.11775i | ||||||||
\(534\) | −1807.71 | −0.146493 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8576.40 | 0.691127 | ||||||||
\(537\) | 4326.86i | 0.347706i | ||||||||
\(538\) | 10992.6i | 0.880900i | ||||||||
\(539\) | −2618.17 | −0.209225 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 675.936 | 0.0537167 | 0.0268584 | − | 0.999639i | \(-0.491450\pi\) | ||||
0.0268584 | + | 0.999639i | \(0.491450\pi\) | |||||||
\(542\) | − 8049.93i | − 0.637960i | ||||||||
\(543\) | 12785.4i | 1.01045i | ||||||||
\(544\) | 18483.6 | 1.45676 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1962.09 | 0.153791 | ||||||||
\(547\) | − 13058.2i | − 1.02071i | −0.859964 | − | 0.510355i | \(-0.829514\pi\) | ||||
0.859964 | − | 0.510355i | \(-0.170486\pi\) | |||||||
\(548\) | 3987.23i | 0.310814i | ||||||||
\(549\) | 6429.65 | 0.499837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5910.91 | 0.457011 | ||||||||
\(552\) | 3919.44i | 0.302215i | ||||||||
\(553\) | − 9752.70i | − 0.749959i | ||||||||
\(554\) | −14170.3 | −1.08672 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4874.61 | 0.371815 | ||||||||
\(557\) | 6710.48i | 0.510471i | 0.966879 | + | 0.255236i | \(0.0821530\pi\) | ||||
−0.966879 | + | 0.255236i | \(0.917847\pi\) | |||||||
\(558\) | 769.295i | 0.0583636i | ||||||||
\(559\) | −96.7741 | −0.00732219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3257.37 | 0.245145 | ||||||||
\(562\) | 5321.45i | 0.399416i | ||||||||
\(563\) | − 20820.5i | − 1.55858i | −0.626666 | − | 0.779288i | \(-0.715581\pi\) | ||||
0.626666 | − | 0.779288i | \(-0.284419\pi\) | |||||||
\(564\) | −5560.92 | −0.415172 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13785.0 | −1.02372 | ||||||||
\(567\) | 829.943i | 0.0614715i | ||||||||
\(568\) | − 19891.5i | − 1.46941i | ||||||||
\(569\) | −3251.08 | −0.239530 | −0.119765 | − | 0.992802i | \(-0.538214\pi\) | ||||
−0.119765 | + | 0.992802i | \(0.538214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4637.50 | −0.339883 | −0.169941 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169941 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(572\) | 2500.73i | 0.182798i | ||||||||
\(573\) | − 2556.67i | − 0.186399i | ||||||||
\(574\) | 5383.67 | 0.391481 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1809.20 | 0.130874 | ||||||||
\(577\) | − 14462.4i | − 1.04346i | −0.853111 | − | 0.521730i | \(-0.825287\pi\) | ||||
0.853111 | − | 0.521730i | \(-0.174713\pi\) | |||||||
\(578\) | 7542.82i | 0.542803i | ||||||||
\(579\) | 7379.86 | 0.529700 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7533.23 | −0.537920 | ||||||||
\(582\) | 4526.99i | 0.322423i | ||||||||
\(583\) | − 7040.71i | − 0.500165i | ||||||||
\(584\) | −7678.18 | −0.544050 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7071.17 | −0.498476 | ||||||||
\(587\) | 22759.7i | 1.60033i | 0.599779 | + | 0.800166i | \(0.295255\pi\) | ||||
−0.599779 | + | 0.800166i | \(0.704745\pi\) | |||||||
\(588\) | 3971.20i | 0.278520i | ||||||||
\(589\) | 2170.16 | 0.151816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10431.2 | 0.726025 | ||||||||
\(592\) | − 512.836i | − 0.0356038i | ||||||||
\(593\) | − 14956.4i | − 1.03573i | −0.855463 | − | 0.517864i | \(-0.826727\pi\) | ||||
0.855463 | − | 0.517864i | \(-0.173273\pi\) | |||||||
\(594\) | 463.781 | 0.0320356 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13216.2 | 0.908319 | ||||||||
\(597\) | − 11985.1i | − 0.821638i | ||||||||
\(598\) | − 3937.96i | − 0.269290i | ||||||||
\(599\) | −2150.77 | −0.146708 | −0.0733539 | − | 0.997306i | \(-0.523370\pi\) | ||||
−0.0733539 | + | 0.997306i | \(0.523370\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27759.8 | 1.88410 | 0.942050 | − | 0.335472i | \(-0.108896\pi\) | ||||
0.942050 | + | 0.335472i | \(0.108896\pi\) | |||||||
\(602\) | − 37.8792i | − 0.00256452i | ||||||||
\(603\) | − 3644.86i | − 0.246153i | ||||||||
\(604\) | −516.371 | −0.0347862 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1633.07 | 0.109470 | ||||||||
\(607\) | 10991.5i | 0.734974i | 0.930029 | + | 0.367487i | \(0.119782\pi\) | ||||
−0.930029 | + | 0.367487i | \(0.880218\pi\) | |||||||
\(608\) | − 7423.87i | − 0.495194i | ||||||||
\(609\) | −4582.91 | −0.304941 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13624.1 | 0.902081 | ||||||||
\(612\) | − 4940.74i | − 0.326336i | ||||||||
\(613\) | 10646.1i | 0.701457i | 0.936477 | + | 0.350728i | \(0.114066\pi\) | ||||
−0.936477 | + | 0.350728i | \(0.885934\pi\) | |||||||
\(614\) | −887.128 | −0.0583088 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2386.83 | −0.156117 | ||||||||
\(617\) | − 7199.92i | − 0.469786i | −0.972021 | − | 0.234893i | \(-0.924526\pi\) | ||||
0.972021 | − | 0.234893i | \(-0.0754739\pi\) | |||||||
\(618\) | − 7197.41i | − 0.468483i | ||||||||
\(619\) | −12186.9 | −0.791332 | −0.395666 | − | 0.918395i | \(-0.629486\pi\) | ||||
−0.395666 | + | 0.918395i | \(0.629486\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1665.72 | 0.107637 | ||||||||
\(622\) | 10702.2i | 0.689905i | ||||||||
\(623\) | − 3953.80i | − 0.254262i | ||||||||
\(624\) | 1400.85 | 0.0898698 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1778.49 | −0.113551 | ||||||||
\(627\) | − 1308.31i | − 0.0833317i | ||||||||
\(628\) | 10462.6i | 0.664814i | ||||||||
\(629\) | 4431.40 | 0.280909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7370.64 | 0.465009 | 0.232505 | − | 0.972595i | \(-0.425308\pi\) | ||||
0.232505 | + | 0.972595i | \(0.425308\pi\) | |||||||
\(632\) | 20157.1i | 1.26868i | ||||||||
\(633\) | 3138.38i | 0.197061i | ||||||||
\(634\) | −5008.65 | −0.313752 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10679.3 | −0.665818 | ||||||||
\(637\) | − 9729.32i | − 0.605164i | ||||||||
\(638\) | 2560.98i | 0.158919i | ||||||||
\(639\) | −8453.63 | −0.523349 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25014.9 | −1.54139 | −0.770693 | − | 0.637207i | \(-0.780090\pi\) | ||||
−0.770693 | + | 0.637207i | \(0.780090\pi\) | |||||||
\(642\) | 3650.19i | 0.224395i | ||||||||
\(643\) | − 21668.2i | − 1.32894i | −0.747313 | − | 0.664472i | \(-0.768657\pi\) | ||||
0.747313 | − | 0.664472i | \(-0.231343\pi\) | |||||||
\(644\) | −3515.58 | −0.215113 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6110.94 | 0.372185 | ||||||||
\(647\) | 27625.3i | 1.67861i | 0.543661 | + | 0.839305i | \(0.317038\pi\) | ||||
−0.543661 | + | 0.839305i | \(0.682962\pi\) | |||||||
\(648\) | − 1715.34i | − 0.103989i | ||||||||
\(649\) | −4078.50 | −0.246680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1682.59 | −0.101299 | ||||||||
\(652\) | − 13712.0i | − 0.823623i | ||||||||
\(653\) | − 14314.0i | − 0.857810i | −0.903350 | − | 0.428905i | \(-0.858899\pi\) | ||||
0.903350 | − | 0.428905i | \(-0.141101\pi\) | |||||||
\(654\) | 7035.38 | 0.420650 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3843.70 | 0.228767 | ||||||||
\(657\) | 3263.13i | 0.193770i | ||||||||
\(658\) | 5332.73i | 0.315944i | ||||||||
\(659\) | 28327.8 | 1.67450 | 0.837249 | − | 0.546822i | \(-0.184163\pi\) | ||||
0.837249 | + | 0.546822i | \(0.184163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32190.9 | −1.89422 | −0.947112 | − | 0.320905i | \(-0.896013\pi\) | ||||
−0.947112 | + | 0.320905i | \(0.896013\pi\) | |||||||
\(662\) | 14265.0i | 0.837498i | ||||||||
\(663\) | 12104.7i | 0.709059i | ||||||||
\(664\) | 15569.8 | 0.909981 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 630.938 | 0.0367092 | ||||||||
\(667\) | 9198.01i | 0.533955i | ||||||||
\(668\) | 6975.84i | 0.404047i | ||||||||
\(669\) | 1518.80 | 0.0877729 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7858.46 | 0.452120 | ||||||||
\(672\) | 5755.95i | 0.330418i | ||||||||
\(673\) | − 6207.38i | − 0.355538i | −0.984072 | − | 0.177769i | \(-0.943112\pi\) | ||||
0.984072 | − | 0.177769i | \(-0.0568879\pi\) | |||||||
\(674\) | 5418.66 | 0.309672 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2925.82 | 0.166467 | ||||||||
\(677\) | − 28831.1i | − 1.63674i | −0.574695 | − | 0.818368i | \(-0.694879\pi\) | ||||
0.574695 | − | 0.818368i | \(-0.305121\pi\) | |||||||
\(678\) | 796.392i | 0.0451110i | ||||||||
\(679\) | −9901.37 | −0.559617 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12858.9 | −0.723573 | ||||||||
\(682\) | 940.250i | 0.0527918i | ||||||||
\(683\) | 3193.10i | 0.178888i | 0.995992 | + | 0.0894441i | \(0.0285090\pi\) | ||||
−0.995992 | + | 0.0894441i | \(0.971491\pi\) | |||||||
\(684\) | −1984.43 | −0.110931 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9296.24 | 0.517394 | ||||||||
\(687\) | − 17128.1i | − 0.951206i | ||||||||
\(688\) | − 27.0441i | − 0.00149861i | ||||||||
\(689\) | 26163.8 | 1.44668 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7682.49 | 0.422946 | 0.211473 | − | 0.977384i | \(-0.432174\pi\) | ||||
0.211473 | + | 0.977384i | \(0.432174\pi\) | |||||||
\(692\) | − 6711.17i | − 0.368671i | ||||||||
\(693\) | 1014.37i | 0.0556031i | ||||||||
\(694\) | 139.496 | 0.00762996 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9472.05 | 0.515858 | ||||||||
\(697\) | 33213.3i | 1.80494i | ||||||||
\(698\) | − 233.256i | − 0.0126488i | ||||||||
\(699\) | −8838.28 | −0.478247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26551.6 | 1.43058 | 0.715292 | − | 0.698825i | \(-0.246293\pi\) | ||||
0.715292 | + | 0.698825i | \(0.246293\pi\) | |||||||
\(702\) | 1723.45i | 0.0926601i | ||||||||
\(703\) | − 1779.86i | − 0.0954887i | ||||||||
\(704\) | 2211.24 | 0.118380 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12285.7 | 0.654928 | ||||||||
\(707\) | 3571.83i | 0.190004i | ||||||||
\(708\) | 6186.22i | 0.328379i | ||||||||
\(709\) | 16304.6 | 0.863655 | 0.431828 | − | 0.901956i | \(-0.357869\pi\) | ||||
0.431828 | + | 0.901956i | \(0.357869\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8566.52 | 0.451856 | ||||||||
\(712\) | 8171.79i | 0.430127i | ||||||||
\(713\) | 3377.00i | 0.177377i | ||||||||
\(714\) | −4738.00 | −0.248341 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8021.36 | 0.418676 | ||||||||
\(717\) | 6236.68i | 0.324844i | ||||||||
\(718\) | 7767.50i | 0.403733i | ||||||||
\(719\) | 3973.62 | 0.206107 | 0.103053 | − | 0.994676i | \(-0.467139\pi\) | ||||
0.103053 | + | 0.994676i | \(0.467139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15742.1 | 0.813128 | ||||||||
\(722\) | 8256.25i | 0.425576i | ||||||||
\(723\) | 5560.11i | 0.286007i | ||||||||
\(724\) | 23702.3 | 1.21670 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 566.844 | 0.0289773 | ||||||||
\(727\) | 10780.4i | 0.549961i | 0.961450 | + | 0.274980i | \(0.0886714\pi\) | ||||
−0.961450 | + | 0.274980i | \(0.911329\pi\) | |||||||
\(728\) | − 8869.67i | − 0.451555i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 233.687 | 0.0118238 | ||||||||
\(732\) | − 11919.6i | − 0.601860i | ||||||||
\(733\) | − 9211.46i | − 0.464165i | −0.972696 | − | 0.232083i | \(-0.925446\pi\) | ||||
0.972696 | − | 0.232083i | \(-0.0745540\pi\) | |||||||
\(734\) | 20716.6 | 1.04177 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11552.3 | 0.578566 | ||||||||
\(737\) | − 4454.83i | − 0.222654i | ||||||||
\(738\) | 4728.87i | 0.235870i | ||||||||
\(739\) | −11084.7 | −0.551768 | −0.275884 | − | 0.961191i | \(-0.588971\pi\) | ||||
−0.275884 | + | 0.961191i | \(0.588971\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4861.80 | 0.241029 | ||||||||
\(742\) | 10241.0i | 0.506685i | ||||||||
\(743\) | − 27420.4i | − 1.35391i | −0.736024 | − | 0.676955i | \(-0.763299\pi\) | ||||
0.736024 | − | 0.676955i | \(-0.236701\pi\) | |||||||
\(744\) | 3477.61 | 0.171365 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7234.32 | −0.355050 | ||||||||
\(747\) | − 6616.99i | − 0.324101i | ||||||||
\(748\) | − 6038.69i | − 0.295182i | ||||||||
\(749\) | −7983.64 | −0.389474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11290.8 | −0.548614 | −0.274307 | − | 0.961642i | \(-0.588448\pi\) | ||||
−0.274307 | + | 0.961642i | \(0.588448\pi\) | |||||||
\(752\) | 3807.33i | 0.184626i | ||||||||
\(753\) | − 7075.16i | − 0.342408i | ||||||||
\(754\) | −9516.81 | −0.459657 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1538.59 | 0.0740185 | ||||||||
\(757\) | − 3739.19i | − 0.179528i | −0.995963 | − | 0.0897642i | \(-0.971389\pi\) | ||||
0.995963 | − | 0.0897642i | \(-0.0286113\pi\) | |||||||
\(758\) | 10155.3i | 0.486617i | ||||||||
\(759\) | 2035.87 | 0.0973617 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15621.1 | −0.744107 | −0.372053 | − | 0.928211i | \(-0.621346\pi\) | ||||
−0.372053 | + | 0.928211i | \(0.621346\pi\) | |||||||
\(762\) | 8150.45i | 0.387480i | ||||||||
\(763\) | 15387.7i | 0.730106i | ||||||||
\(764\) | −4739.69 | −0.224445 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19885.7 | 0.937987 | ||||||||
\(767\) | − 15156.0i | − 0.713498i | ||||||||
\(768\) | − 10371.8i | − 0.487317i | ||||||||
\(769\) | −40241.7 | −1.88706 | −0.943531 | − | 0.331284i | \(-0.892518\pi\) | ||||
−0.943531 | + | 0.331284i | \(0.892518\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16557.8 | 0.773428 | ||||||||
\(772\) | − 13681.2i | − 0.637818i | ||||||||
\(773\) | 22821.4i | 1.06187i | 0.847412 | + | 0.530936i | \(0.178160\pi\) | ||||
−0.847412 | + | 0.530936i | \(0.821840\pi\) | |||||||
\(774\) | 33.2721 | 0.00154514 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20464.4 | 0.946685 | ||||||||
\(777\) | 1379.98i | 0.0637148i | ||||||||
\(778\) | 18777.0i | 0.865282i | ||||||||
\(779\) | 13340.0 | 0.613549 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10332.2 | −0.473387 | ||||||||
\(782\) | 9509.28i | 0.434848i | ||||||||
\(783\) | − 4025.51i | − 0.183729i | ||||||||
\(784\) | 2718.92 | 0.123857 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1465.53 | 0.0665062 | ||||||||
\(787\) | 29454.3i | 1.33410i | 0.745015 | + | 0.667048i | \(0.232442\pi\) | ||||
−0.745015 | + | 0.667048i | \(0.767558\pi\) | |||||||
\(788\) | − 19337.8i | − 0.874216i | ||||||||
\(789\) | −6778.96 | −0.305878 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1741.86 | −0.0782974 | ||||||||
\(792\) | − 2096.53i | − 0.0940619i | ||||||||
\(793\) | 29202.7i | 1.30771i | ||||||||
\(794\) | 8157.00 | 0.364586 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22218.6 | −0.989344 | ||||||||
\(797\) | 27440.3i | 1.21955i | 0.792573 | + | 0.609777i | \(0.208741\pi\) | ||||
−0.792573 | + | 0.609777i | \(0.791259\pi\) | |||||||
\(798\) | 1903.00i | 0.0844179i | ||||||||
\(799\) | −32899.0 | −1.45668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3472.91 | 0.153195 | ||||||||
\(802\) | − 15066.1i | − 0.663346i | ||||||||
\(803\) | 3988.27i | 0.175272i | ||||||||
\(804\) | −6757.03 | −0.296396 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3494.05 | −0.152695 | ||||||||
\(807\) | − 21118.6i | − 0.921201i | ||||||||
\(808\) | − 7382.34i | − 0.321423i | ||||||||
\(809\) | 5060.18 | 0.219909 | 0.109954 | − | 0.993937i | \(-0.464930\pi\) | ||||
0.109954 | + | 0.993937i | \(0.464930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30480.1 | 1.31973 | 0.659865 | − | 0.751384i | \(-0.270613\pi\) | ||||
0.659865 | + | 0.751384i | \(0.270613\pi\) | |||||||
\(812\) | 8496.03i | 0.367183i | ||||||||
\(813\) | 15465.2i | 0.667146i | ||||||||
\(814\) | 771.146 | 0.0332048 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3382.72 | −0.145121 | ||||||||
\(817\) | − 93.8596i | − 0.00401925i | ||||||||
\(818\) | − 3139.46i | − 0.134192i | ||||||||
\(819\) | −3769.50 | −0.160827 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37909.0 | 1.61149 | 0.805745 | − | 0.592263i | \(-0.201765\pi\) | ||||
0.805745 | + | 0.592263i | \(0.201765\pi\) | |||||||
\(822\) | 3358.56i | 0.142510i | ||||||||
\(823\) | 23636.0i | 1.00109i | 0.865710 | + | 0.500546i | \(0.166867\pi\) | ||||
−0.865710 | + | 0.500546i | \(0.833133\pi\) | |||||||
\(824\) | −32536.0 | −1.37554 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5932.36 | 0.249895 | ||||||||
\(827\) | 42634.3i | 1.79267i | 0.443376 | + | 0.896336i | \(0.353781\pi\) | ||||
−0.443376 | + | 0.896336i | \(0.646219\pi\) | |||||||
\(828\) | − 3087.99i | − 0.129608i | ||||||||
\(829\) | 45152.5 | 1.89169 | 0.945845 | − | 0.324619i | \(-0.105236\pi\) | ||||
0.945845 | + | 0.324619i | \(0.105236\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27223.6 | 1.13643 | ||||||||
\(832\) | 8217.15i | 0.342402i | ||||||||
\(833\) | 23494.1i | 0.977217i | ||||||||
\(834\) | 4106.02 | 0.170480 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2425.42 | −0.100341 | ||||||||
\(837\) | − 1477.94i | − 0.0610337i | ||||||||
\(838\) | 6925.91i | 0.285503i | ||||||||
\(839\) | −30431.5 | −1.25222 | −0.626110 | − | 0.779734i | \(-0.715354\pi\) | ||||
−0.626110 | + | 0.779734i | \(0.715354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2160.34 | −0.0885784 | ||||||||
\(842\) | − 23763.6i | − 0.972623i | ||||||||
\(843\) | − 10223.4i | − 0.417689i | ||||||||
\(844\) | 5818.09 | 0.237283 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4684.13 | −0.190359 | ||||||||
\(847\) | 1239.79i | 0.0502949i | ||||||||
\(848\) | 7311.64i | 0.296088i | ||||||||
\(849\) | 26483.2 | 1.07055 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2769.65 | 0.111566 | ||||||||
\(852\) | 15671.8i | 0.630171i | ||||||||
\(853\) | 10367.2i | 0.416139i | 0.978114 | + | 0.208070i | \(0.0667180\pi\) | ||||
−0.978114 | + | 0.208070i | \(0.933282\pi\) | |||||||
\(854\) | −11430.5 | −0.458013 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16500.8 | 0.658860 | ||||||||
\(857\) | − 12947.1i | − 0.516063i | −0.966136 | − | 0.258032i | \(-0.916926\pi\) | ||||
0.966136 | − | 0.258032i | \(-0.0830739\pi\) | |||||||
\(858\) | 2106.44i | 0.0838142i | ||||||||
\(859\) | 20383.5 | 0.809636 | 0.404818 | − | 0.914397i | \(-0.367335\pi\) | ||||
0.404818 | + | 0.914397i | \(0.367335\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10342.9 | −0.409391 | ||||||||
\(862\) | 8779.22i | 0.346893i | ||||||||
\(863\) | 9056.42i | 0.357224i | 0.983920 | + | 0.178612i | \(0.0571606\pi\) | ||||
−0.983920 | + | 0.178612i | \(0.942839\pi\) | |||||||
\(864\) | −5055.88 | −0.199079 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22340.0 | −0.876610 | ||||||||
\(867\) | − 14491.0i | − 0.567636i | ||||||||
\(868\) | 3119.27i | 0.121976i | ||||||||
\(869\) | 10470.2 | 0.408719 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16554.5 | 0.644005 | ||||||||
\(872\) | − 31803.6i | − 1.23510i | ||||||||
\(873\) | − 8697.10i | − 0.337173i | ||||||||
\(874\) | 3819.37 | 0.147817 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6049.36 | 0.233321 | ||||||||
\(877\) | 2867.88i | 0.110424i | 0.998475 | + | 0.0552118i | \(0.0175834\pi\) | ||||
−0.998475 | + | 0.0552118i | \(0.982417\pi\) | |||||||
\(878\) | 6846.16i | 0.263151i | ||||||||
\(879\) | 13584.9 | 0.521281 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11862.5 | −0.453640 | −0.226820 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226820 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(882\) | 3345.06i | 0.127703i | ||||||||
\(883\) | 33463.8i | 1.27537i | 0.770299 | + | 0.637683i | \(0.220107\pi\) | ||||
−0.770299 | + | 0.637683i | \(0.779893\pi\) | |||||||
\(884\) | 22440.3 | 0.853787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15756.0 | −0.597442 | ||||||||
\(887\) | − 2420.75i | − 0.0916357i | −0.998950 | − | 0.0458178i | \(-0.985411\pi\) | ||||
0.998950 | − | 0.0458178i | \(-0.0145894\pi\) | |||||||
\(888\) | − 2852.17i | − 0.107784i | ||||||||
\(889\) | −17826.5 | −0.672534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | − 2815.62i | − 0.105688i | ||||||||
\(893\) | 13213.8i | 0.495165i | ||||||||
\(894\) | 11132.4 | 0.416470 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12132.9 | 0.452378 | ||||||||
\(897\) | 7565.48i | 0.281610i | ||||||||
\(898\) | 14963.6i | 0.556060i | ||||||||
\(899\) | 8161.14 | 0.302769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63179.7 | −2.33609 | ||||||||
\(902\) | 5779.73i | 0.213352i | ||||||||
\(903\) | 72.7722i | 0.00268185i | ||||||||
\(904\) | 3600.10 | 0.132453 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −434.955 | −0.0159497 | ||||||||
\(907\) | 38154.1i | 1.39679i | 0.715714 | + | 0.698393i | \(0.246101\pi\) | ||||
−0.715714 | + | 0.698393i | \(0.753899\pi\) | |||||||
\(908\) | 23838.4i | 0.871262i | ||||||||
\(909\) | −3137.40 | −0.114479 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35758.0 | −1.30045 | −0.650227 | − | 0.759740i | \(-0.725326\pi\) | ||||
−0.650227 | + | 0.759740i | \(0.725326\pi\) | |||||||
\(912\) | 1358.66i | 0.0493308i | ||||||||
\(913\) | − 8087.44i | − 0.293160i | ||||||||
\(914\) | −15614.5 | −0.565079 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31753.0 | −1.14536 | ||||||||
\(917\) | 3205.39i | 0.115432i | ||||||||
\(918\) | − 4161.73i | − 0.149627i | ||||||||
\(919\) | −17387.5 | −0.624115 | −0.312058 | − | 0.950063i | \(-0.601018\pi\) | ||||
−0.312058 | + | 0.950063i | \(0.601018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1704.32 | 0.0609764 | ||||||||
\(922\) | 17357.9i | 0.620013i | ||||||||
\(923\) | − 38395.3i | − 1.36923i | ||||||||
\(924\) | 1880.50 | 0.0669523 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2447.20 | −0.0868467 | ||||||||
\(927\) | 13827.4i | 0.489915i | ||||||||
\(928\) | − 27918.3i | − 0.987569i | ||||||||
\(929\) | −6955.93 | −0.245658 | −0.122829 | − | 0.992428i | \(-0.539197\pi\) | ||||
−0.122829 | + | 0.992428i | \(0.539197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9436.31 | 0.332183 | ||||||||
\(932\) | 16384.9i | 0.575863i | ||||||||
\(933\) | − 20560.8i | − 0.721467i | ||||||||
\(934\) | −19751.7 | −0.691965 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7790.88 | 0.272065 | ||||||||
\(937\) | 16074.5i | 0.560438i | 0.959936 | + | 0.280219i | \(0.0904070\pi\) | ||||
−0.959936 | + | 0.280219i | \(0.909593\pi\) | |||||||
\(938\) | 6479.76i | 0.225556i | ||||||||
\(939\) | 3416.77 | 0.118746 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −687.126 | −0.0238041 | −0.0119021 | − | 0.999929i | \(-0.503789\pi\) | ||||
−0.0119021 | + | 0.999929i | \(0.503789\pi\) | |||||||
\(942\) | 8812.96i | 0.304821i | ||||||||
\(943\) | 20758.5i | 0.716849i | ||||||||
\(944\) | 4235.44 | 0.146030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.6659 | 0.00139763 | ||||||||
\(947\) | − 35352.0i | − 1.21308i | −0.795053 | − | 0.606540i | \(-0.792557\pi\) | ||||
0.795053 | − | 0.606540i | \(-0.207443\pi\) | |||||||
\(948\) | − 15881.0i | − 0.544085i | ||||||||
\(949\) | −14820.7 | −0.506956 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9622.44 | 0.328106 | ||||||||
\(952\) | 21418.2i | 0.729168i | ||||||||
\(953\) | − 19390.7i | − 0.659103i | −0.944138 | − | 0.329552i | \(-0.893102\pi\) | ||||
0.944138 | − | 0.329552i | \(-0.106898\pi\) | |||||||
\(954\) | −8995.45 | −0.305281 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11561.9 | 0.391148 | ||||||||
\(957\) | − 4920.06i | − 0.166189i | ||||||||
\(958\) | − 16738.7i | − 0.564511i | ||||||||
\(959\) | −7345.80 | −0.247349 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26794.7 | −0.899422 | ||||||||
\(962\) | 2865.64i | 0.0960416i | ||||||||
\(963\) | − 7012.62i | − 0.234661i | ||||||||
\(964\) | 10307.6 | 0.344384 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2961.27 | −0.0986308 | ||||||||
\(967\) | − 28643.6i | − 0.952551i | −0.879296 | − | 0.476275i | \(-0.841987\pi\) | ||||
0.879296 | − | 0.476275i | \(-0.158013\pi\) | |||||||
\(968\) | − 2562.43i | − 0.0850821i | ||||||||
\(969\) | −11740.1 | −0.389213 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19574.8 | −0.646946 | −0.323473 | − | 0.946237i | \(-0.604851\pi\) | ||||
−0.323473 | + | 0.946237i | \(0.604851\pi\) | |||||||
\(972\) | 1351.46i | 0.0445967i | ||||||||
\(973\) | 8980.63i | 0.295895i | ||||||||
\(974\) | −11182.6 | −0.367878 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8160.86 | −0.267646 | ||||||||
\(977\) | − 50095.5i | − 1.64043i | −0.572058 | − | 0.820213i | \(-0.693855\pi\) | ||||
0.572058 | − | 0.820213i | \(-0.306145\pi\) | |||||||
\(978\) | − 11550.0i | − 0.377636i | ||||||||
\(979\) | 4244.67 | 0.138570 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13516.1 | −0.439895 | ||||||||
\(982\) | − 22747.6i | − 0.739211i | ||||||||
\(983\) | 14445.4i | 0.468706i | 0.972152 | + | 0.234353i | \(0.0752971\pi\) | ||||
−0.972152 | + | 0.234353i | \(0.924703\pi\) | |||||||
\(984\) | 21376.9 | 0.692553 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22980.9 | 0.742253 | ||||||||
\(987\) | − 10245.0i | − 0.330399i | ||||||||
\(988\) | − 9013.05i | − 0.290226i | ||||||||
\(989\) | 146.056 | 0.00469595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29120.1 | 0.933430 | 0.466715 | − | 0.884408i | \(-0.345437\pi\) | ||||
0.466715 | + | 0.884408i | \(0.345437\pi\) | |||||||
\(992\) | − 10250.1i | − 0.328064i | ||||||||
\(993\) | − 27405.4i | − 0.875814i | ||||||||
\(994\) | 15028.7 | 0.479558 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12266.9 | −0.390253 | ||||||||
\(997\) | 9137.45i | 0.290257i | 0.989413 | + | 0.145128i | \(0.0463595\pi\) | ||||
−0.989413 | + | 0.145128i | \(0.953640\pi\) | |||||||
\(998\) | − 7244.03i | − 0.229765i | ||||||||
\(999\) | −1212.14 | −0.0383887 |
(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 | 825.4.c.j.199.2 | 4 | ||
5.2 | odd | 4 | 165.4.a.c.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 825.4.a.m.1.1 | 2 | |||
5.4 | even | 2 | inner | 825.4.c.j.199.3 | 4 | ||
15.2 | even | 4 | 495.4.a.d.1.1 | 2 | |||
15.8 | even | 4 | 2475.4.a.n.1.2 | 2 | |||
55.32 | even | 4 | 1815.4.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.c.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
495.4.a.d.1.1 | 2 | 15.2 | even | 4 | |||
825.4.a.m.1.1 | 2 | 5.3 | odd | 4 | |||
825.4.c.j.199.2 | 4 | 1.1 | even | 1 | trivial | ||
825.4.c.j.199.3 | 4 | 5.4 | even | 2 | inner | ||
1815.4.a.n.1.1 | 2 | 55.32 | even | 4 | |||
2475.4.a.n.1.2 | 2 | 15.8 | even | 4 |