Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, 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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-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 | ||||||||
\(3\) | −1.27492 | −0.245358 | −0.122679 | − | 0.992446i | \(-0.539149\pi\) | ||||
−0.122679 | + | 0.992446i | \(0.539149\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.8248 | −1.77318 | −0.886590 | − | 0.462556i | \(-0.846932\pi\) | ||||
−0.886590 | + | 0.462556i | \(0.846932\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.3746 | −0.939799 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35.4502 | −0.756316 | −0.378158 | − | 0.925741i | \(-0.623442\pi\) | ||||
−0.378158 | + | 0.925741i | \(0.623442\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.2749 | 0.435064 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 65.1478 | 0.929451 | 0.464726 | − | 0.885455i | \(-0.346153\pi\) | ||||
0.464726 | + | 0.885455i | \(0.346153\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 83.0997 | 1.00339 | 0.501694 | − | 0.865045i | \(-0.332710\pi\) | ||||
0.501694 | + | 0.865045i | \(0.332710\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.92442 | −0.0927366 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 70.7733 | 0.641619 | 0.320810 | − | 0.947144i | \(-0.396045\pi\) | ||||
0.320810 | + | 0.947144i | \(0.396045\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 268.021 | 2.14417 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 66.7733 | 0.475945 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 243.196 | 1.55725 | 0.778627 | − | 0.627487i | \(-0.215916\pi\) | ||||
0.778627 | + | 0.627487i | \(0.215916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 69.4743 | 0.402514 | 0.201257 | − | 0.979538i | \(-0.435497\pi\) | ||||
0.201257 | + | 0.979538i | \(0.435497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.0241 | −0.0739782 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −138.773 | −0.670199 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −131.674 | −0.585054 | −0.292527 | − | 0.956257i | \(-0.594496\pi\) | ||||
−0.292527 | + | 0.956257i | \(0.594496\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 45.1960 | 0.185568 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −482.646 | −1.83846 | −0.919228 | − | 0.393726i | \(-0.871186\pi\) | ||||
−0.919228 | + | 0.393726i | \(0.871186\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −498.296 | −1.76719 | −0.883597 | − | 0.468247i | \(-0.844886\pi\) | ||||
−0.883597 | + | 0.468247i | \(0.844886\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 503.045 | 1.66643 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 504.839 | 1.56677 | 0.783386 | − | 0.621535i | \(-0.213491\pi\) | ||||
0.783386 | + | 0.621535i | \(0.213491\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −83.0581 | −0.228048 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −573.286 | −1.48579 | −0.742895 | − | 0.669408i | \(-0.766548\pi\) | ||||
−0.742895 | + | 0.669408i | \(0.766548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −218.072 | −0.534634 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −105.945 | −0.246189 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −262.615 | −0.579485 | −0.289743 | − | 0.957105i | \(-0.593570\pi\) | ||||
−0.289743 | + | 0.957105i | \(0.593570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 884.585 | 1.85671 | 0.928356 | − | 0.371691i | \(-0.121222\pi\) | ||||
0.928356 | + | 0.371691i | \(0.121222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −177.622 | −0.355211 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 702.791 | 1.34108 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −396.478 | −0.722947 | −0.361473 | − | 0.932382i | \(-0.617726\pi\) | ||||
−0.361473 | + | 0.932382i | \(0.617726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −90.2300 | −0.157426 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 414.629 | 0.693062 | 0.346531 | − | 0.938039i | \(-0.387360\pi\) | ||||
0.346531 | + | 0.938039i | \(0.387360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −205.547 | −0.329553 | −0.164777 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164777 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −341.704 | −0.526088 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −232.254 | −0.330767 | −0.165384 | − | 0.986229i | \(-0.552886\pi\) | ||||
−0.165384 | + | 0.986229i | \(0.552886\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 599.983 | 0.823023 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 584.453 | 0.772917 | 0.386458 | − | 0.922307i | \(-0.373698\pi\) | ||||
0.386458 | + | 0.922307i | \(0.373698\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1291.54 | −1.64808 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −310.055 | −0.382085 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −629.715 | −0.749996 | −0.374998 | − | 0.927026i | \(-0.622357\pi\) | ||||
−0.374998 | + | 0.927026i | \(0.622357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −248.151 | −0.285861 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −88.5739 | −0.0987601 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1647.43 | −1.77919 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 320.120 | 0.335086 | 0.167543 | − | 0.985865i | \(-0.446417\pi\) | ||||
0.167543 | + | 0.985865i | \(0.446417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −279.120 | −0.283360 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −311.836 | −0.307216 | −0.153608 | − | 0.988132i | \(-0.549089\pi\) | ||||
−0.153608 | + | 0.988132i | \(0.549089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −110.434 | −0.105644 | −0.0528221 | − | 0.998604i | \(-0.516822\pi\) | ||||
−0.0528221 | + | 0.998604i | \(0.516822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 176.924 | 0.164439 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −408.762 | −0.369314 | −0.184657 | − | 0.982803i | \(-0.559117\pi\) | ||||
−0.184657 | + | 0.982803i | \(0.559117\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1400.23 | −1.23044 | −0.615221 | − | 0.788355i | \(-0.710933\pi\) | ||||
−0.615221 | + | 0.788355i | \(0.710933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 167.873 | 0.143548 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1113.23 | −0.926763 | −0.463381 | − | 0.886159i | \(-0.653364\pi\) | ||||
−0.463381 | + | 0.886159i | \(0.653364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1403.06 | −1.13771 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 899.533 | 0.710785 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 456.035 | 0.351300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 615.334 | 0.451080 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2835.35 | −2.02881 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1574.44 | 1.10007 | 0.550035 | − | 0.835141i | \(-0.314614\pi\) | ||||
0.550035 | + | 0.835141i | \(0.314614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 635.286 | 0.433595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2128.09 | 1.41933 | 0.709664 | − | 0.704540i | \(-0.248847\pi\) | ||||
0.709664 | + | 0.704540i | \(0.248847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 581.698 | 0.379245 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1323.76 | −0.843936 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −406.841 | −0.253714 | −0.126857 | − | 0.991921i | \(-0.540489\pi\) | ||||
−0.126857 | + | 0.991921i | \(0.540489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −159.814 | −0.0975197 | −0.0487599 | − | 0.998811i | \(-0.515527\pi\) | ||||
−0.0487599 | + | 0.998811i | \(0.515527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −643.628 | −0.384420 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −389.952 | −0.228038 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4821.30 | −2.76129 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −62.4709 | −0.0350511 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1106.69 | −0.608479 | −0.304240 | − | 0.952596i | \(-0.598402\pi\) | ||||
−0.304240 | + | 0.952596i | \(0.598402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2950.54 | 1.59014 | 0.795070 | − | 0.606517i | \(-0.207434\pi\) | ||||
0.795070 | + | 0.606517i | \(0.207434\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1653.10 | −0.873498 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1377.31 | −0.713730 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3439.07 | −1.74820 | −0.874101 | − | 0.485744i | \(-0.838549\pi\) | ||||
−0.874101 | + | 0.485744i | \(0.838549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 730.892 | 0.364550 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 495.413 | 0.242509 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3347.56 | −1.60860 | −0.804298 | − | 0.594226i | \(-0.797459\pi\) | ||||
−0.804298 | + | 0.594226i | \(0.797459\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 278.024 | 0.131177 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −424.145 | −0.196535 | −0.0982673 | − | 0.995160i | \(-0.531330\pi\) | ||||
−0.0982673 | + | 0.995160i | \(0.531330\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −940.286 | −0.427986 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2108.62 | −0.942984 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −326.762 | −0.143603 | −0.0718014 | − | 0.997419i | \(-0.522875\pi\) | ||||
−0.0718014 | + | 0.997419i | \(0.522875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1876.15 | 0.810419 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 334.813 | 0.142181 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3982.89 | −1.66310 | −0.831550 | − | 0.555450i | \(-0.812546\pi\) | ||||
−0.831550 | + | 0.555450i | \(0.812546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 704.346 | 0.289247 | 0.144623 | − | 0.989487i | \(-0.453803\pi\) | ||||
0.144623 | + | 0.989487i | \(0.453803\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1127.77 | −0.455559 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2610.40 | 1.03741 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 716.626 | 0.280240 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 467.413 | 0.179890 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3296.18 | 1.24871 | 0.624355 | − | 0.781141i | \(-0.285362\pi\) | ||||
0.624355 | + | 0.781141i | \(0.285362\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1754.99 | 0.654544 | 0.327272 | − | 0.944930i | \(-0.393871\pi\) | ||||
0.327272 | + | 0.944930i | \(0.393871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −896.000 | −0.329046 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −917.890 | −0.331964 | −0.165982 | − | 0.986129i | \(-0.553079\pi\) | ||||
−0.165982 | + | 0.986129i | \(0.553079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5300.55 | −1.88817 | −0.944085 | − | 0.329701i | \(-0.893052\pi\) | ||||
−0.944085 | + | 0.329701i | \(0.893052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 505.476 | 0.177381 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1702.37 | 0.588587 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9568.34 | 3.25991 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1795.84 | −0.602994 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 914.096 | 0.302533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3649.87 | −1.19084 | −0.595420 | − | 0.803415i | \(-0.703014\pi\) | ||||
−0.595420 | + | 0.803415i | \(0.703014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −528.617 | −0.170048 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9878.59 | 3.13355 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 486.320 | 0.152136 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 262.055 | 0.0808585 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2309.50 | −0.702959 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1529.82 | 0.459392 | 0.229696 | − | 0.973262i | \(-0.426227\pi\) | ||||
0.229696 | + | 0.973262i | \(0.426227\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6800.92 | −2.01509 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 256.195 | 0.0749085 | 0.0374542 | − | 0.999298i | \(-0.488075\pi\) | ||||
0.0374542 | + | 0.999298i | \(0.488075\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −591.724 | −0.170752 | −0.0853760 | − | 0.996349i | \(-0.527209\pi\) | ||||
−0.0853760 | + | 0.996349i | \(0.527209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −98.1686 | −0.0279611 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1648.22 | 0.463426 | 0.231713 | − | 0.972784i | \(-0.425567\pi\) | ||||
0.231713 | + | 0.972784i | \(0.425567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10008.3 | −2.77817 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 296.105 | 0.0811564 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1427.79 | −0.386428 | −0.193214 | − | 0.981157i | \(-0.561891\pi\) | ||||
−0.193214 | + | 0.981157i | \(0.561891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1971.21 | 0.526874 | 0.263437 | − | 0.964677i | \(-0.415144\pi\) | ||||
0.263437 | + | 0.964677i | \(0.415144\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2567.81 | −0.677880 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −971.413 | −0.253311 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2945.90 | −0.758878 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −745.130 | −0.189641 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4442.18 | 1.11708 | 0.558542 | − | 0.829476i | \(-0.311361\pi\) | ||||
0.558542 | + | 0.829476i | \(0.311361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 778.506 | 0.193456 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1646.61 | 0.404371 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7113.32 | 1.72652 | 0.863262 | − | 0.504757i | \(-0.168418\pi\) | ||||
0.863262 | + | 0.504757i | \(0.168418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −921.715 | −0.221130 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6171.00 | −1.46351 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1000.42 | −0.234557 | −0.117279 | − | 0.993099i | \(-0.537417\pi\) | ||||
−0.117279 | + | 0.993099i | \(0.537417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11365.2 | 2.63457 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 802.835 | 0.184018 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 187.128 | 0.0424141 | 0.0212071 | − | 0.999775i | \(-0.493249\pi\) | ||||
0.0212071 | + | 0.999775i | \(0.493249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 605.814 | 0.135795 | 0.0678977 | − | 0.997692i | \(-0.478371\pi\) | ||||
0.0678977 | + | 0.997692i | \(0.478371\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 316.372 | 0.0701382 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2948.23 | 0.646490 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1454.30 | −0.315452 | −0.157726 | − | 0.987483i | \(-0.550416\pi\) | ||||
−0.157726 | + | 0.987483i | \(0.550416\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1762.88 | −0.378283 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5940.16 | −1.26107 | −0.630535 | − | 0.776161i | \(-0.717164\pi\) | ||||
−0.630535 | + | 0.776161i | \(0.717164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4483.67 | −0.941790 | −0.470895 | − | 0.882189i | \(-0.656069\pi\) | ||||
−0.470895 | + | 0.882189i | \(0.656069\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2100.34 | 0.436538 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3378.52 | −0.694871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −668.758 | −0.136120 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −408.127 | −0.0822159 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3239.72 | 0.645961 | 0.322980 | − | 0.946406i | \(-0.395315\pi\) | ||||
0.322980 | + | 0.946406i | \(0.395315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5206.29 | 1.02753 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 734.506 | 0.143503 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2508.92 | −0.485267 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3488.07 | −0.667937 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 397.565 | 0.0753778 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17536.7 | −3.29229 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1296.15 | −0.240961 | −0.120481 | − | 0.992716i | \(-0.538444\pi\) | ||||
−0.120481 | + | 0.992716i | \(0.538444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 140.794 | 0.0259206 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4513.53 | −0.822954 | −0.411477 | − | 0.911420i | \(-0.634987\pi\) | ||||
−0.411477 | + | 0.911420i | \(0.634987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6918.74 | −1.24943 | −0.624713 | − | 0.780855i | \(-0.714784\pi\) | ||||
−0.624713 | + | 0.780855i | \(0.714784\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3521.31 | 0.629853 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3844.49 | 0.681161 | 0.340580 | − | 0.940215i | \(-0.389376\pi\) | ||||
0.340580 | + | 0.940215i | \(0.389376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2675.16 | 0.469530 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 521.138 | 0.0906140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5413.76 | 0.932600 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9501.38 | −1.62167 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1785.18 | 0.301899 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3533.87 | 0.592184 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7497.78 | −1.24506 | −0.622530 | − | 0.782596i | \(-0.713895\pi\) | ||||
−0.622530 | + | 0.782596i | \(0.713895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3341.16 | 0.549834 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7860.07 | 1.28191 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9372.82 | −1.51504 | −0.757522 | − | 0.652809i | \(-0.773590\pi\) | ||||
−0.757522 | + | 0.652809i | \(0.773590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1419.28 | 0.227389 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 764.217 | 0.121363 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1788.79 | 0.279145 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8942.10 | 1.38339 | 0.691696 | − | 0.722189i | \(-0.256864\pi\) | ||||
0.691696 | + | 0.722189i | \(0.256864\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6516.32 | 0.999457 | 0.499728 | − | 0.866182i | \(-0.333433\pi\) | ||||
0.499728 | + | 0.866182i | \(0.333433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2367.12 | −0.359965 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11607.3 | 1.75012 | 0.875060 | − | 0.484014i | \(-0.160822\pi\) | ||||
0.875060 | + | 0.484014i | \(0.160822\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8219.91 | −1.22892 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −581.407 | −0.0861941 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7431.08 | 1.09247 | 0.546236 | − | 0.837631i | \(-0.316060\pi\) | ||||
0.546236 | + | 0.837631i | \(0.316060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.5550 | 0.00678743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −154.265 | −0.0223053 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4074.91 | 0.584357 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4233.75 | −0.602179 | −0.301090 | − | 0.953596i | \(-0.597350\pi\) | ||||
−0.301090 | + | 0.953596i | \(0.597350\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12246.9 | 1.72778 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4013.00 | −0.561576 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5807.15 | −0.806120 | −0.403060 | − | 0.915173i | \(-0.632053\pi\) | ||||
−0.403060 | + | 0.915173i | \(0.632053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3614.84 | 0.497785 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8621.34 | −1.17778 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11312.8 | −1.53324 | −0.766622 | − | 0.642098i | \(-0.778064\pi\) | ||||
−0.766622 | + | 0.642098i | \(0.778064\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2007.28 | −0.269911 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13099.0 | −1.74759 | −0.873794 | − | 0.486296i | \(-0.838348\pi\) | ||||
−0.873794 | + | 0.486296i | \(0.838348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1526.51 | −0.202073 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12644.0 | 1.66081 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −62.8377 | −0.00819022 | −0.00409511 | − | 0.999992i | \(-0.501304\pi\) | ||||
−0.00409511 | + | 0.999992i | \(0.501304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4610.73 | 0.596354 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2713.14 | −0.348244 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4604.38 | 0.586510 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −276.394 | −0.0349416 | −0.0174708 | − | 0.999847i | \(-0.505561\pi\) | ||||
−0.0174708 | + | 0.999847i | \(0.505561\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −741.616 | −0.0930508 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7970.49 | −0.992587 | −0.496293 | − | 0.868155i | \(-0.665306\pi\) | ||||
−0.496293 | + | 0.868155i | \(0.665306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2462.87 | −0.304428 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11894.5 | −1.45937 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1448.41 | −0.176400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 908.394 | 0.109822 | 0.0549110 | − | 0.998491i | \(-0.482512\pi\) | ||||
0.0549110 | + | 0.998491i | \(0.482512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 518.689 | 0.0622507 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1838.31 | −0.219025 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11586.6 | −1.37052 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 203.750 | 0.0239272 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.0397 | 0.00420204 | 0.00210102 | − | 0.999998i | \(-0.499331\pi\) | ||||
0.00210102 | + | 0.999998i | \(0.499331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8332.89 | −0.964656 | −0.482328 | − | 0.875991i | \(-0.660209\pi\) | ||||
−0.482328 | + | 0.875991i | \(0.660209\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12810.1 | −1.47245 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17461.0 | 1.99290 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6192.09 | 0.701771 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 497.156 | 0.0559509 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11169.9 | 1.24834 | 0.624171 | − | 0.781288i | \(-0.285437\pi\) | ||||
0.624171 | + | 0.781288i | \(0.285437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10710.9 | −1.18875 | −0.594377 | − | 0.804186i | \(-0.702601\pi\) | ||||
−0.594377 | + | 0.804186i | \(0.702601\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6146.76 | 0.677505 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5881.23 | 0.643793 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3900.57 | −0.424064 | −0.212032 | − | 0.977263i | \(-0.568008\pi\) | ||||
−0.212032 | + | 0.977263i | \(0.568008\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1243.35 | −0.134257 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3396.29 | −0.364250 | −0.182125 | − | 0.983275i | \(-0.558298\pi\) | ||||
−0.182125 | + | 0.983275i | \(0.558298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12483.9 | 1.32988 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1410.94 | 0.149295 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17354.1 | 1.82403 | 0.912014 | − | 0.410160i | \(-0.134527\pi\) | ||||
0.912014 | + | 0.410160i | \(0.134527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5309.11 | −0.554315 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3761.69 | −0.390154 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4919.54 | 0.506882 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3040.01 | −0.311172 | −0.155586 | − | 0.987822i | \(-0.549727\pi\) | ||||
−0.155586 | + | 0.987822i | \(0.549727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4350.13 | 0.442368 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8808.45 | 0.889914 | 0.444957 | − | 0.895552i | \(-0.353219\pi\) | ||||
0.444957 | + | 0.895552i | \(0.353219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9797.22 | −0.983402 | −0.491701 | − | 0.870764i | \(-0.663625\pi\) | ||||
−0.491701 | + | 0.870764i | \(0.663625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1755.96 | 0.175119 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5800.53 | 0.574768 | 0.287384 | − | 0.957815i | \(-0.407214\pi\) | ||||
0.287384 | + | 0.957815i | \(0.407214\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2775.34 | −0.273248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4384.53 | 0.428935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5481.25 | −0.532829 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22272.4 | 2.15143 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14546.9 | 1.39634 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19752.6 | 1.88418 | 0.942089 | − | 0.335363i | \(-0.108859\pi\) | ||||
0.942089 | + | 0.335363i | \(0.108859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4667.85 | 0.442486 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −631.610 | −0.0595016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6346.31 | −0.594167 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1315.06 | 0.122363 | 0.0611817 | − | 0.998127i | \(-0.480513\pi\) | ||||
0.0611817 | + | 0.998127i | \(0.480513\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4267.86 | 0.394682 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 751.005 | 0.0690273 | 0.0345136 | − | 0.999404i | \(-0.489012\pi\) | ||||
0.0345136 | + | 0.999404i | \(0.489012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15843.7 | 1.44739 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5533.49 | 0.502449 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2902.40 | 0.261953 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7619.81 | −0.683586 | −0.341793 | − | 0.939775i | \(-0.611034\pi\) | ||||
−0.341793 | + | 0.939775i | \(0.611034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 540.749 | 0.0482213 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9779.34 | −0.866877 | −0.433439 | − | 0.901183i | \(-0.642700\pi\) | ||||
−0.433439 | + | 0.901183i | \(0.642700\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6182.06 | 0.544749 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1198.79 | 0.105010 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 184.110 | 0.0160325 | 0.00801625 | − | 0.999968i | \(-0.497448\pi\) | ||||
0.00801625 | + | 0.999968i | \(0.497448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1438.83 | −0.124559 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5548.84 | 0.477558 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2189.32 | 0.187326 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5553.23 | 0.472400 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 416.595 | 0.0352341 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20360.9 | −1.71215 | −0.856073 | − | 0.516855i | \(-0.827102\pi\) | ||||
−0.856073 | + | 0.516855i | \(0.827102\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12075.6 | 1.00961 | 0.504806 | − | 0.863233i | \(-0.331564\pi\) | ||||
0.504806 | + | 0.863233i | \(0.331564\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2391.93 | −0.198843 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4526.10 | 0.374118 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7158.15 | −0.588325 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6663.76 | 0.544600 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17109.9 | 1.39045 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8103.61 | 0.654859 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5077.85 | 0.408055 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2616.08 | −0.207900 | −0.103950 | − | 0.994583i | \(-0.533148\pi\) | ||||
−0.103950 | + | 0.994583i | \(0.533148\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −897.983 | −0.0709690 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27759.3 | 2.18179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13719.3 | 1.07239 | 0.536195 | − | 0.844094i | \(-0.319861\pi\) | ||||
0.536195 | + | 0.844094i | \(0.319861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22446.0 | −1.74494 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20209.5 | 1.56253 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1625.78 | −0.125018 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3328.04 | −0.254536 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10510.1 | 0.799510 | 0.399755 | − | 0.916622i | \(-0.369095\pi\) | ||||
0.399755 | + | 0.916622i | \(0.369095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17664.7 | 1.33656 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −913.639 | −0.0687591 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7040.40 | −0.527029 | −0.263515 | − | 0.964655i | \(-0.584882\pi\) | ||||
−0.263515 | + | 0.964655i | \(0.584882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22069.6 | 1.64332 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4199.88 | 0.311073 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11806.9 | −0.869900 | −0.434950 | − | 0.900455i | \(-0.643234\pi\) | ||||
−0.434950 | + | 0.900455i | \(0.643234\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16432.1 | 1.20431 | 0.602155 | − | 0.798379i | \(-0.294309\pi\) | ||||
0.602155 | + | 0.798379i | \(0.294309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4202.36 | −0.306381 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18968.7 | 1.37574 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9781.38 | 0.705727 | 0.352863 | − | 0.935675i | \(-0.385208\pi\) | ||||
0.352863 | + | 0.935675i | \(0.385208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2237.47 | −0.160598 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4091.17 | 0.292135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6306.14 | −0.447982 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17833.0 | −1.26035 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8510.75 | −0.598426 | −0.299213 | − | 0.954186i | \(-0.596724\pi\) | ||||
−0.299213 | + | 0.954186i | \(0.596724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5773.29 | 0.403878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1170.23 | 0.0814501 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12400.7 | 0.858746 | 0.429373 | − | 0.903127i | \(-0.358735\pi\) | ||||
0.429373 | + | 0.903127i | \(0.358735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9040.78 | −0.622917 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6757.76 | 0.463278 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1568.75 | −0.107007 | −0.0535037 | − | 0.998568i | \(-0.517039\pi\) | ||||
−0.0535037 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3991.41 | −0.270903 | −0.135452 | − | 0.990784i | \(-0.543249\pi\) | ||||
−0.135452 | + | 0.990784i | \(0.543249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10060.5 | 0.679425 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2398.79 | −0.161198 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9689.34 | −0.647905 | −0.323952 | − | 0.946073i | \(-0.605012\pi\) | ||||
−0.323952 | + | 0.946073i | \(0.605012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2170.38 | −0.144414 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17896.6 | −1.18498 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5475.09 | −0.360745 | −0.180373 | − | 0.983598i | \(-0.557730\pi\) | ||||
−0.180373 | + | 0.983598i | \(0.557730\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12198.8 | −0.799845 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12908.8 | 0.842282 | 0.421141 | − | 0.906995i | \(-0.361630\pi\) | ||||
0.421141 | + | 0.906995i | \(0.361630\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13016.6 | 0.845206 | 0.422603 | − | 0.906315i | \(-0.361116\pi\) | ||||
0.422603 | + | 0.906315i | \(0.361116\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4725.76 | 0.305376 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4408.01 | −0.283472 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22707.5 | 1.45328 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1165.40 | −0.0742288 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8578.25 | −0.543779 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16555.5 | 1.04447 | 0.522236 | − | 0.852801i | \(-0.325098\pi\) | ||||
0.522236 | + | 0.852801i | \(0.325098\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4653.28 | 0.292182 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31212.9 | −1.95062 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1737.06 | −0.108045 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10521.0 | −0.651339 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27993.2 | −1.72491 | −0.862454 | − | 0.506136i | \(-0.831074\pi\) | ||||
−0.862454 | + | 0.506136i | \(0.831074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25489.3 | −1.56330 | −0.781648 | − | 0.623720i | \(-0.785621\pi\) | ||||
−0.781648 | + | 0.623720i | \(0.785621\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12594.4 | −0.768842 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21121.0 | 1.28339 | 0.641693 | − | 0.766962i | \(-0.278232\pi\) | ||||
0.641693 | + | 0.766962i | \(0.278232\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2888.77 | −0.174721 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −620.017 | −0.0373278 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11406.7 | −0.683583 | −0.341792 | − | 0.939776i | \(-0.611034\pi\) | ||||
−0.341792 | + | 0.939776i | \(0.611034\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42188.9 | −2.51672 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5215.66 | 0.309714 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27601.4 | −1.63156 | −0.815779 | − | 0.578364i | \(-0.803691\pi\) | ||||
−0.815779 | + | 0.578364i | \(0.803691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26538.2 | −1.56160 | −0.780799 | − | 0.624782i | \(-0.785188\pi\) | ||||
−0.780799 | + | 0.624782i | \(0.785188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2944.42 | 0.172477 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11532.0 | −0.672470 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17211.8 | 0.999164 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1950.39 | −0.112715 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9730.43 | 0.559820 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16791.6 | 0.961767 | 0.480883 | − | 0.876785i | \(-0.340316\pi\) | ||||
0.480883 | + | 0.876785i | \(0.340316\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17896.6 | 1.02051 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6405.21 | 0.363622 | 0.181811 | − | 0.983333i | \(-0.441804\pi\) | ||||
0.181811 | + | 0.983333i | \(0.441804\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2240.84 | 0.126650 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −326.627 | −0.0183794 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6951.93 | −0.389470 | −0.194735 | − | 0.980856i | \(-0.562385\pi\) | ||||
−0.194735 | + | 0.980856i | \(0.562385\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8065.53 | 0.449880 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 754.399 | 0.0418953 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20323.1 | 1.12373 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14914.5 | 0.821090 | 0.410545 | − | 0.911840i | \(-0.365338\pi\) | ||||
0.410545 | + | 0.911840i | \(0.365338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1953.84 | −0.107100 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3168.27 | 0.172920 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31443.4 | −1.70875 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2101.34 | −0.113705 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10125.3 | −0.545544 | −0.272772 | − | 0.962079i | \(-0.587941\pi\) | ||||
−0.272772 | + | 0.962079i | \(0.587941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10942.0 | −0.587036 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12759.8 | 0.681646 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2182.85 | −0.116117 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29376.9 | −1.55609 | −0.778047 | − | 0.628206i | \(-0.783790\pi\) | ||||
−0.778047 | + | 0.628206i | \(0.783790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5893.35 | 0.310855 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4916.92 | 0.258261 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7730.70 | 0.404352 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1820.32 | 0.0948132 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34057.4 | 1.76652 | 0.883260 | − | 0.468883i | \(-0.155343\pi\) | ||||
0.883260 | + | 0.468883i | \(0.155343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −773.035 | −0.0399297 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2513.12 | −0.129273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 65181.6 | 3.33901 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13915.1 | −0.709880 | −0.354940 | − | 0.934889i | \(-0.615499\pi\) | ||||
−0.354940 | + | 0.934889i | \(0.615499\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12925.8 | −0.656699 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32462.9 | −1.64252 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11153.8 | −0.562039 | −0.281020 | − | 0.959702i | \(-0.590673\pi\) | ||||
−0.281020 | + | 0.959702i | \(0.590673\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1238.47 | 0.0621520 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4361.25 | −0.217977 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18406.4 | −0.916226 | −0.458113 | − | 0.888894i | \(-0.651474\pi\) | ||||
−0.458113 | + | 0.888894i | \(0.651474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3755.77 | 0.186197 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7902.81 | 0.390210 | 0.195105 | − | 0.980782i | \(-0.437495\pi\) | ||||
0.195105 | + | 0.980782i | \(0.437495\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21939.8 | 1.07894 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14830.3 | −0.726387 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2861.34 | −0.139587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23322.6 | 1.13323 | 0.566615 | − | 0.823983i | \(-0.308253\pi\) | ||||
0.566615 | + | 0.823983i | \(0.308253\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5663.41 | −0.274085 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −58493.7 | −2.81961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9085.76 | −0.436232 | −0.218116 | − | 0.975923i | \(-0.569991\pi\) | ||||
−0.218116 | + | 0.975923i | \(0.569991\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −992.531 | −0.0474658 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38562.4 | −1.83691 | −0.918453 | − | 0.395529i | \(-0.870561\pi\) | ||||
−0.918453 | + | 0.395529i | \(0.870561\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9801.64 | −0.465063 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32772.3 | 1.54887 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9309.76 | 0.438274 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8816.49 | 0.413434 | 0.206717 | − | 0.978401i | \(-0.433722\pi\) | ||||
0.206717 | + | 0.978401i | \(0.433722\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9068.89 | −0.423616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10849.6 | 0.504829 | 0.252414 | − | 0.967619i | \(-0.418775\pi\) | ||||
0.252414 | + | 0.967619i | \(0.418775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18620.5 | 0.863058 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1175.11 | 0.0542559 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40107.7 | −1.84468 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4560.92 | 0.208966 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16239.0 | 0.741168 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 68178.7 | 3.09988 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33817.6 | −1.53173 | −0.765863 | − | 0.643004i | \(-0.777688\pi\) | ||||
−0.765863 | + | 0.643004i | \(0.777688\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1275.45 | 0.0575505 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7792.63 | −0.350283 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31358.7 | −1.40426 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14489.8 | −0.646413 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35828.3 | −1.59235 | −0.796175 | − | 0.605066i | \(-0.793147\pi\) | ||||
−0.796175 | + | 0.605066i | \(0.793147\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32889.2 | 1.45624 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15978.8 | 0.704846 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2261.01 | −0.0993641 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9821.44 | −0.430013 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −238.573 | −0.0104066 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8838.88 | −0.384127 | −0.192063 | − | 0.981383i | \(-0.561518\pi\) | ||||
−0.192063 | + | 0.981383i | \(0.561518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16690.4 | 0.722662 | 0.361331 | − | 0.932438i | \(-0.382323\pi\) | ||||
0.361331 | + | 0.932438i | \(0.382323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −772.363 | −0.0333185 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66364.6 | 2.85233 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41408.2 | −1.77318 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6296.73 | 0.268652 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46102.2 | −1.95978 | −0.979889 | − | 0.199544i | \(-0.936054\pi\) | ||||
−0.979889 | + | 0.199544i | \(0.936054\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5544.15 | 0.234820 | 0.117410 | − | 0.993084i | \(-0.462541\pi\) | ||||
0.117410 | + | 0.993084i | \(0.462541\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3758.75 | −0.158622 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39002.0 | −1.63994 | −0.819972 | − | 0.572404i | \(-0.806011\pi\) | ||||
−0.819972 | + | 0.572404i | \(0.806011\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30509.4 | 1.27821 | 0.639106 | − | 0.769119i | \(-0.279305\pi\) | ||||
0.639106 | + | 0.769119i | \(0.279305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1854.11 | 0.0773987 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3192.24 | 0.132779 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8408.56 | 0.348491 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4639.02 | 0.191575 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17283.7 | −0.711204 | −0.355602 | − | 0.934638i | \(-0.615724\pi\) | ||||
−0.355602 | + | 0.934638i | \(0.615724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34755.3 | 1.42504 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7573.22 | 0.309413 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18640.9 | 0.758897 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5716.31 | 0.231076 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9318.97 | −0.375382 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9478.08 | −0.380450 | −0.190225 | − | 0.981741i | \(-0.560922\pi\) | ||||
−0.190225 | + | 0.981741i | \(0.560922\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 41802.9 | 1.67208 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4723.97 | 0.188294 | 0.0941469 | − | 0.995558i | \(-0.469988\pi\) | ||||
0.0941469 | + | 0.995558i | \(0.469988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6148.17 | 0.244206 | 0.122103 | − | 0.992517i | \(-0.461036\pi\) | ||||
0.122103 | + | 0.992517i | \(0.461036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4307.34 | 0.170492 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8098.18 | −0.319427 | −0.159713 | − | 0.987163i | \(-0.551057\pi\) | ||||
−0.159713 | + | 0.987163i | \(0.551057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6477.98 | 0.254634 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 852.611 | 0.0333981 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2554.80 | −0.0997302 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14055.2 | 0.546776 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8122.92 | −0.314913 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19847.5 | −0.766819 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44807.6 | 1.72525 | 0.862626 | − | 0.505843i | \(-0.168818\pi\) | ||||
0.862626 | + | 0.505843i | \(0.168818\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4130.38 | −0.158492 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20014.9 | −0.765404 | −0.382702 | − | 0.923872i | \(-0.625006\pi\) | ||||
−0.382702 | + | 0.923872i | \(0.625006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38695.5 | 1.47475 | 0.737377 | − | 0.675481i | \(-0.236064\pi\) | ||||
0.737377 | + | 0.675481i | \(0.236064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6637.58 | −0.252113 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39223.3 | 1.48477 | 0.742384 | − | 0.669974i | \(-0.233695\pi\) | ||||
0.742384 | + | 0.669974i | \(0.233695\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11021.1 | 0.415788 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6599.82 | 0.248151 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41951.9 | 1.57208 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 78959.7 | 2.94898 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3198.67 | 0.119064 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16895.9 | 0.626817 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37348.3 | −1.38097 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4447.00 | 0.163884 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13963.5 | −0.512886 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45745.8 | −1.67471 | −0.837357 | − | 0.546657i | \(-0.815900\pi\) | ||||
−0.837357 | + | 0.546657i | \(0.815900\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7912.70 | 0.288721 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17363.7 | −0.631487 | −0.315744 | − | 0.948845i | \(-0.602254\pi\) | ||||
−0.315744 | + | 0.948845i | \(0.602254\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6428.99 | 0.233043 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22357.8 | 0.807788 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14896.6 | 0.536456 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42719.1 | 1.53338 | 0.766688 | − | 0.642020i | \(-0.221904\pi\) | ||||
0.766688 | + | 0.642020i | \(0.221904\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1652.48 | 0.0591217 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14698.7 | −0.524174 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35291.3 | −1.25445 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2802.21 | 0.0992843 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8459.95 | −0.298775 | −0.149388 | − | 0.988779i | \(-0.547730\pi\) | ||||
−0.149388 | + | 0.988779i | \(0.547730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4071.88 | 0.143341 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5754.38 | 0.201918 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14206.9 | −0.496916 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28780.9 | −1.00345 | −0.501724 | − | 0.865028i | \(-0.667301\pi\) | ||||
−0.501724 | + | 0.865028i | \(0.667301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8820.81 | 0.306556 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48285.4 | −1.67275 | −0.836376 | − | 0.548156i | \(-0.815330\pi\) | ||||
−0.836376 | + | 0.548156i | \(0.815330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34158.4 | −1.17959 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9266.34 | −0.318978 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10090.3 | −0.346240 | −0.173120 | − | 0.984901i | \(-0.555385\pi\) | ||||
−0.173120 | + | 0.984901i | \(0.555385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7286.66 | 0.249247 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4901.40 | −0.167128 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2555.53 | 0.0868644 | 0.0434322 | − | 0.999056i | \(-0.486171\pi\) | ||||
0.0434322 | + | 0.999056i | \(0.486171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −65346.0 | −2.21419 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3410.60 | −0.115203 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2847.89 | −0.0958948 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24964.3 | −0.837982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10372.2 | 0.347081 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34792.2 | −1.16062 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41632.4 | 1.38450 | 0.692248 | − | 0.721660i | \(-0.256620\pi\) | ||||
0.692248 | + | 0.721660i | \(0.256620\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6902.10 | −0.228821 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26258.7 | 0.867849 | 0.433924 | − | 0.900949i | \(-0.357129\pi\) | ||||
0.433924 | + | 0.900949i | \(0.357129\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1118.70 | −0.0368590 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12113.5 | 0.397889 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56691.6 | −1.85642 | −0.928211 | − | 0.372053i | \(-0.878654\pi\) | ||||
−0.928211 | + | 0.372053i | \(0.878654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6926.87 | −0.226132 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35530.4 | 1.15637 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38106.9 | −1.23644 | −0.618220 | − | 0.786005i | \(-0.712146\pi\) | ||||
−0.618220 | + | 0.786005i | \(0.712146\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18196.9 | 0.588632 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4505.39 | −0.145297 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35266.0 | −1.13387 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37420.5 | −1.19950 | −0.599748 | − | 0.800189i | \(-0.704732\pi\) | ||||
−0.599748 | + | 0.800189i | \(0.704732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9559.05 | 0.305486 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 105082. | 3.34807 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47293.6 | −1.50231 | −0.751156 | − | 0.660125i | \(-0.770503\pi\) | ||||
−0.751156 | + | 0.660125i | \(0.770503\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8792.28 | −0.278454 |
(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 | 1232.4.a.o.1.1 | 2 | ||
4.3 | odd | 2 | 154.4.a.h.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 1386.4.a.s.1.2 | 2 | |||
28.27 | even | 2 | 1078.4.a.o.1.1 | 2 | |||
44.43 | even | 2 | 1694.4.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.4.a.h.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1078.4.a.o.1.1 | 2 | 28.27 | even | 2 | |||
1232.4.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1386.4.a.s.1.2 | 2 | 12.11 | even | 2 | |||
1694.4.a.h.1.2 | 2 | 44.43 | even | 2 |