Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,4,Mod(1,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2254.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.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: | \(132.990305153\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{11} - 234 x^{9} - 105 x^{8} + 18997 x^{7} + 16513 x^{6} - 621598 x^{5} - 743169 x^{4} + \cdots - 12103441 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | no (minimal twist has level 322) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(7.30492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 7.30492 | 1.40583 | 0.702917 | − | 0.711272i | \(-0.251881\pi\) | ||||
0.702917 | + | 0.711272i | \(0.251881\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 7.55338 | 0.675595 | 0.337797 | − | 0.941219i | \(-0.390318\pi\) | ||||
0.337797 | + | 0.941219i | \(0.390318\pi\) | |||||||
\(6\) | −14.6098 | −0.994074 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 26.3619 | 0.976367 | ||||||||
\(10\) | −15.1068 | −0.477717 | ||||||||
\(11\) | 56.3122 | 1.54352 | 0.771762 | − | 0.635911i | \(-0.219376\pi\) | ||||
0.771762 | + | 0.635911i | \(0.219376\pi\) | |||||||
\(12\) | 29.2197 | 0.702917 | ||||||||
\(13\) | 65.8379 | 1.40463 | 0.702313 | − | 0.711868i | \(-0.252151\pi\) | ||||
0.702313 | + | 0.711868i | \(0.252151\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 55.1768 | 0.949773 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −108.835 | −1.55272 | −0.776361 | − | 0.630289i | \(-0.782936\pi\) | ||||
−0.776361 | + | 0.630289i | \(0.782936\pi\) | |||||||
\(18\) | −52.7238 | −0.690396 | ||||||||
\(19\) | 92.3659 | 1.11527 | 0.557637 | − | 0.830085i | \(-0.311708\pi\) | ||||
0.557637 | + | 0.830085i | \(0.311708\pi\) | |||||||
\(20\) | 30.2135 | 0.337797 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −112.624 | −1.09144 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −58.4394 | −0.497037 | ||||||||
\(25\) | −67.9465 | −0.543572 | ||||||||
\(26\) | −131.676 | −0.993221 | ||||||||
\(27\) | −4.66115 | −0.0332236 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 58.1564 | 0.372392 | 0.186196 | − | 0.982513i | \(-0.440384\pi\) | ||||
0.186196 | + | 0.982513i | \(0.440384\pi\) | |||||||
\(30\) | −110.354 | −0.671591 | ||||||||
\(31\) | 234.881 | 1.36083 | 0.680417 | − | 0.732825i | \(-0.261799\pi\) | ||||
0.680417 | + | 0.732825i | \(0.261799\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 411.356 | 2.16994 | ||||||||
\(34\) | 217.669 | 1.09794 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 105.448 | 0.488184 | ||||||||
\(37\) | −122.911 | −0.546122 | −0.273061 | − | 0.961997i | \(-0.588036\pi\) | ||||
−0.273061 | + | 0.961997i | \(0.588036\pi\) | |||||||
\(38\) | −184.732 | −0.788617 | ||||||||
\(39\) | 480.941 | 1.97467 | ||||||||
\(40\) | −60.4270 | −0.238859 | ||||||||
\(41\) | 359.331 | 1.36873 | 0.684366 | − | 0.729139i | \(-0.260079\pi\) | ||||
0.684366 | + | 0.729139i | \(0.260079\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.0320 | −0.117147 | −0.0585736 | − | 0.998283i | \(-0.518655\pi\) | ||||
−0.0585736 | + | 0.998283i | \(0.518655\pi\) | |||||||
\(44\) | 225.249 | 0.771762 | ||||||||
\(45\) | 199.121 | 0.659628 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −147.849 | −0.458852 | −0.229426 | − | 0.973326i | \(-0.573685\pi\) | ||||
−0.229426 | + | 0.973326i | \(0.573685\pi\) | |||||||
\(48\) | 116.879 | 0.351458 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 135.893 | 0.384363 | ||||||||
\(51\) | −795.028 | −2.18287 | ||||||||
\(52\) | 263.352 | 0.702313 | ||||||||
\(53\) | 640.721 | 1.66056 | 0.830281 | − | 0.557345i | \(-0.188180\pi\) | ||||
0.830281 | + | 0.557345i | \(0.188180\pi\) | |||||||
\(54\) | 9.32230 | 0.0234927 | ||||||||
\(55\) | 425.347 | 1.04280 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 674.726 | 1.56789 | ||||||||
\(58\) | −116.313 | −0.263321 | ||||||||
\(59\) | −402.029 | −0.887115 | −0.443557 | − | 0.896246i | \(-0.646284\pi\) | ||||
−0.443557 | + | 0.896246i | \(0.646284\pi\) | |||||||
\(60\) | 220.707 | 0.474887 | ||||||||
\(61\) | −240.394 | −0.504580 | −0.252290 | − | 0.967652i | \(-0.581184\pi\) | ||||
−0.252290 | + | 0.967652i | \(0.581184\pi\) | |||||||
\(62\) | −469.762 | −0.962255 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 497.298 | 0.948958 | ||||||||
\(66\) | −822.713 | −1.53438 | ||||||||
\(67\) | 112.885 | 0.205838 | 0.102919 | − | 0.994690i | \(-0.467182\pi\) | ||||
0.102919 | + | 0.994690i | \(0.467182\pi\) | |||||||
\(68\) | −435.338 | −0.776361 | ||||||||
\(69\) | 168.013 | 0.293137 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 171.363 | 0.286437 | 0.143219 | − | 0.989691i | \(-0.454255\pi\) | ||||
0.143219 | + | 0.989691i | \(0.454255\pi\) | |||||||
\(72\) | −210.895 | −0.345198 | ||||||||
\(73\) | 361.719 | 0.579946 | 0.289973 | − | 0.957035i | \(-0.406354\pi\) | ||||
0.289973 | + | 0.957035i | \(0.406354\pi\) | |||||||
\(74\) | 245.823 | 0.386166 | ||||||||
\(75\) | −496.344 | −0.764172 | ||||||||
\(76\) | 369.464 | 0.557637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −961.881 | −1.39630 | ||||||||
\(79\) | −842.316 | −1.19959 | −0.599797 | − | 0.800152i | \(-0.704752\pi\) | ||||
−0.599797 | + | 0.800152i | \(0.704752\pi\) | |||||||
\(80\) | 120.854 | 0.168899 | ||||||||
\(81\) | −745.821 | −1.02307 | ||||||||
\(82\) | −718.661 | −0.967840 | ||||||||
\(83\) | 1374.29 | 1.81744 | 0.908721 | − | 0.417404i | \(-0.137060\pi\) | ||||
0.908721 | + | 0.417404i | \(0.137060\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −822.069 | −1.04901 | ||||||||
\(86\) | 66.0640 | 0.0828356 | ||||||||
\(87\) | 424.828 | 0.523521 | ||||||||
\(88\) | −450.498 | −0.545718 | ||||||||
\(89\) | −1241.11 | −1.47818 | −0.739088 | − | 0.673608i | \(-0.764743\pi\) | ||||
−0.739088 | + | 0.673608i | \(0.764743\pi\) | |||||||
\(90\) | −398.243 | −0.466428 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 1715.79 | 1.91311 | ||||||||
\(94\) | 295.699 | 0.324457 | ||||||||
\(95\) | 697.674 | 0.753472 | ||||||||
\(96\) | −233.758 | −0.248519 | ||||||||
\(97\) | −997.907 | −1.04456 | −0.522279 | − | 0.852775i | \(-0.674918\pi\) | ||||
−0.522279 | + | 0.852775i | \(0.674918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1484.50 | 1.50705 | ||||||||
\(100\) | −271.786 | −0.271786 | ||||||||
\(101\) | −946.648 | −0.932624 | −0.466312 | − | 0.884620i | \(-0.654418\pi\) | ||||
−0.466312 | + | 0.884620i | \(0.654418\pi\) | |||||||
\(102\) | 1590.06 | 1.54352 | ||||||||
\(103\) | −422.213 | −0.403902 | −0.201951 | − | 0.979396i | \(-0.564728\pi\) | ||||
−0.201951 | + | 0.979396i | \(0.564728\pi\) | |||||||
\(104\) | −526.703 | −0.496610 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1281.44 | −1.17419 | ||||||||
\(107\) | 588.846 | 0.532018 | 0.266009 | − | 0.963971i | \(-0.414295\pi\) | ||||
0.266009 | + | 0.963971i | \(0.414295\pi\) | |||||||
\(108\) | −18.6446 | −0.0166118 | ||||||||
\(109\) | 106.854 | 0.0938969 | 0.0469484 | − | 0.998897i | \(-0.485050\pi\) | ||||
0.0469484 | + | 0.998897i | \(0.485050\pi\) | |||||||
\(110\) | −850.694 | −0.737368 | ||||||||
\(111\) | −897.858 | −0.767756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 21.1869 | 0.0176380 | 0.00881901 | − | 0.999961i | \(-0.497193\pi\) | ||||
0.00881901 | + | 0.999961i | \(0.497193\pi\) | |||||||
\(114\) | −1349.45 | −1.10866 | ||||||||
\(115\) | 173.728 | 0.140871 | ||||||||
\(116\) | 232.625 | 0.186196 | ||||||||
\(117\) | 1735.61 | 1.37143 | ||||||||
\(118\) | 804.059 | 0.627285 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −441.415 | −0.335796 | ||||||||
\(121\) | 1840.06 | 1.38247 | ||||||||
\(122\) | 480.789 | 0.356792 | ||||||||
\(123\) | 2624.88 | 1.92421 | ||||||||
\(124\) | 939.524 | 0.680417 | ||||||||
\(125\) | −1457.40 | −1.04283 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2173.95 | 1.51895 | 0.759475 | − | 0.650536i | \(-0.225456\pi\) | ||||
0.759475 | + | 0.650536i | \(0.225456\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −241.296 | −0.164689 | ||||||||
\(130\) | −994.597 | −0.671015 | ||||||||
\(131\) | 2455.77 | 1.63788 | 0.818939 | − | 0.573881i | \(-0.194563\pi\) | ||||
0.818939 | + | 0.573881i | \(0.194563\pi\) | |||||||
\(132\) | 1645.43 | 1.08497 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −225.770 | −0.145549 | ||||||||
\(135\) | −35.2074 | −0.0224457 | ||||||||
\(136\) | 870.677 | 0.548970 | ||||||||
\(137\) | 1021.29 | 0.636896 | 0.318448 | − | 0.947940i | \(-0.396838\pi\) | ||||
0.318448 | + | 0.947940i | \(0.396838\pi\) | |||||||
\(138\) | −336.027 | −0.207279 | ||||||||
\(139\) | −418.904 | −0.255619 | −0.127809 | − | 0.991799i | \(-0.540795\pi\) | ||||
−0.127809 | + | 0.991799i | \(0.540795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1080.03 | −0.645069 | ||||||||
\(142\) | −342.726 | −0.202542 | ||||||||
\(143\) | 3707.48 | 2.16807 | ||||||||
\(144\) | 421.791 | 0.244092 | ||||||||
\(145\) | 439.277 | 0.251586 | ||||||||
\(146\) | −723.438 | −0.410083 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −491.645 | −0.273061 | ||||||||
\(149\) | 984.319 | 0.541199 | 0.270599 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270599 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(150\) | 992.688 | 0.540351 | ||||||||
\(151\) | 2004.99 | 1.08056 | 0.540278 | − | 0.841486i | \(-0.318319\pi\) | ||||
0.540278 | + | 0.841486i | \(0.318319\pi\) | |||||||
\(152\) | −738.927 | −0.394309 | ||||||||
\(153\) | −2869.09 | −1.51603 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1774.14 | 0.919372 | ||||||||
\(156\) | 1923.76 | 0.987335 | ||||||||
\(157\) | 385.868 | 0.196150 | 0.0980752 | − | 0.995179i | \(-0.468731\pi\) | ||||
0.0980752 | + | 0.995179i | \(0.468731\pi\) | |||||||
\(158\) | 1684.63 | 0.848242 | ||||||||
\(159\) | 4680.42 | 2.33447 | ||||||||
\(160\) | −241.708 | −0.119429 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1491.64 | 0.723423 | ||||||||
\(163\) | −2397.38 | −1.15201 | −0.576003 | − | 0.817448i | \(-0.695388\pi\) | ||||
−0.576003 | + | 0.817448i | \(0.695388\pi\) | |||||||
\(164\) | 1437.32 | 0.684366 | ||||||||
\(165\) | 3107.13 | 1.46600 | ||||||||
\(166\) | −2748.58 | −1.28513 | ||||||||
\(167\) | −3438.93 | −1.59349 | −0.796743 | − | 0.604318i | \(-0.793446\pi\) | ||||
−0.796743 | + | 0.604318i | \(0.793446\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2137.63 | 0.972975 | ||||||||
\(170\) | 1644.14 | 0.741762 | ||||||||
\(171\) | 2434.94 | 1.08892 | ||||||||
\(172\) | −132.128 | −0.0585736 | ||||||||
\(173\) | −2008.99 | −0.882894 | −0.441447 | − | 0.897287i | \(-0.645535\pi\) | ||||
−0.441447 | + | 0.897287i | \(0.645535\pi\) | |||||||
\(174\) | −849.656 | −0.370185 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 900.995 | 0.385881 | ||||||||
\(177\) | −2936.79 | −1.24714 | ||||||||
\(178\) | 2482.23 | 1.04523 | ||||||||
\(179\) | 4012.23 | 1.67535 | 0.837677 | − | 0.546166i | \(-0.183913\pi\) | ||||
0.837677 | + | 0.546166i | \(0.183913\pi\) | |||||||
\(180\) | 796.486 | 0.329814 | ||||||||
\(181\) | −2231.44 | −0.916361 | −0.458181 | − | 0.888859i | \(-0.651499\pi\) | ||||
−0.458181 | + | 0.888859i | \(0.651499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1756.06 | −0.709355 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | −928.395 | −0.368957 | ||||||||
\(186\) | −3431.57 | −1.35277 | ||||||||
\(187\) | −6128.71 | −2.39666 | ||||||||
\(188\) | −591.397 | −0.229426 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1395.35 | −0.532785 | ||||||||
\(191\) | 130.667 | 0.0495011 | 0.0247505 | − | 0.999694i | \(-0.492121\pi\) | ||||
0.0247505 | + | 0.999694i | \(0.492121\pi\) | |||||||
\(192\) | 467.515 | 0.175729 | ||||||||
\(193\) | −3443.32 | −1.28423 | −0.642113 | − | 0.766610i | \(-0.721942\pi\) | ||||
−0.642113 | + | 0.766610i | \(0.721942\pi\) | |||||||
\(194\) | 1995.81 | 0.738614 | ||||||||
\(195\) | 3632.73 | 1.33408 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2976.33 | −1.07642 | −0.538211 | − | 0.842810i | \(-0.680900\pi\) | ||||
−0.538211 | + | 0.842810i | \(0.680900\pi\) | |||||||
\(198\) | −2968.99 | −1.06564 | ||||||||
\(199\) | 902.959 | 0.321653 | 0.160827 | − | 0.986983i | \(-0.448584\pi\) | ||||
0.160827 | + | 0.986983i | \(0.448584\pi\) | |||||||
\(200\) | 543.572 | 0.192182 | ||||||||
\(201\) | 824.618 | 0.289374 | ||||||||
\(202\) | 1893.30 | 0.659465 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3180.11 | −1.09143 | ||||||||
\(205\) | 2714.16 | 0.924708 | ||||||||
\(206\) | 844.426 | 0.285602 | ||||||||
\(207\) | 606.324 | 0.203587 | ||||||||
\(208\) | 1053.41 | 0.351157 | ||||||||
\(209\) | 5201.33 | 1.72145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2439.95 | −0.796081 | −0.398041 | − | 0.917368i | \(-0.630310\pi\) | ||||
−0.398041 | + | 0.917368i | \(0.630310\pi\) | |||||||
\(212\) | 2562.88 | 0.830281 | ||||||||
\(213\) | 1251.79 | 0.402683 | ||||||||
\(214\) | −1177.69 | −0.376194 | ||||||||
\(215\) | −249.503 | −0.0791440 | ||||||||
\(216\) | 37.2892 | 0.0117463 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −213.708 | −0.0663951 | ||||||||
\(219\) | 2642.33 | 0.815307 | ||||||||
\(220\) | 1701.39 | 0.521398 | ||||||||
\(221\) | −7165.44 | −2.18099 | ||||||||
\(222\) | 1795.72 | 0.542885 | ||||||||
\(223\) | 5414.35 | 1.62588 | 0.812941 | − | 0.582346i | \(-0.197865\pi\) | ||||
0.812941 | + | 0.582346i | \(0.197865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1791.20 | −0.530726 | ||||||||
\(226\) | −42.3738 | −0.0124720 | ||||||||
\(227\) | −4479.54 | −1.30977 | −0.654884 | − | 0.755729i | \(-0.727283\pi\) | ||||
−0.654884 | + | 0.755729i | \(0.727283\pi\) | |||||||
\(228\) | 2698.90 | 0.783944 | ||||||||
\(229\) | 3627.89 | 1.04689 | 0.523445 | − | 0.852059i | \(-0.324646\pi\) | ||||
0.523445 | + | 0.852059i | \(0.324646\pi\) | |||||||
\(230\) | −347.455 | −0.0996110 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −465.251 | −0.131660 | ||||||||
\(233\) | −3682.73 | −1.03547 | −0.517734 | − | 0.855542i | \(-0.673224\pi\) | ||||
−0.517734 | + | 0.855542i | \(0.673224\pi\) | |||||||
\(234\) | −3471.23 | −0.969748 | ||||||||
\(235\) | −1116.76 | −0.309998 | ||||||||
\(236\) | −1608.12 | −0.443557 | ||||||||
\(237\) | −6153.06 | −1.68643 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1289.59 | 0.349025 | 0.174512 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174512 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(240\) | 882.829 | 0.237443 | ||||||||
\(241\) | 664.153 | 0.177518 | 0.0887590 | − | 0.996053i | \(-0.471710\pi\) | ||||
0.0887590 | + | 0.996053i | \(0.471710\pi\) | |||||||
\(242\) | −3680.13 | −0.977552 | ||||||||
\(243\) | −5322.32 | −1.40505 | ||||||||
\(244\) | −961.578 | −0.252290 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5249.77 | −1.36062 | ||||||||
\(247\) | 6081.17 | 1.56654 | ||||||||
\(248\) | −1879.05 | −0.481128 | ||||||||
\(249\) | 10039.1 | 2.55502 | ||||||||
\(250\) | 2914.80 | 0.737391 | ||||||||
\(251\) | −4771.08 | −1.19979 | −0.599896 | − | 0.800078i | \(-0.704791\pi\) | ||||
−0.599896 | + | 0.800078i | \(0.704791\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1295.18 | 0.321847 | ||||||||
\(254\) | −4347.90 | −1.07406 | ||||||||
\(255\) | −6005.15 | −1.47473 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 2134.29 | 0.518028 | 0.259014 | − | 0.965874i | \(-0.416602\pi\) | ||||
0.259014 | + | 0.965874i | \(0.416602\pi\) | |||||||
\(258\) | 482.592 | 0.116453 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1989.19 | 0.474479 | ||||||||
\(261\) | 1533.11 | 0.363591 | ||||||||
\(262\) | −4911.55 | −1.15815 | ||||||||
\(263\) | 6810.24 | 1.59672 | 0.798360 | − | 0.602180i | \(-0.205701\pi\) | ||||
0.798360 | + | 0.602180i | \(0.205701\pi\) | |||||||
\(264\) | −3290.85 | −0.767189 | ||||||||
\(265\) | 4839.61 | 1.12187 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9066.24 | −2.07807 | ||||||||
\(268\) | 451.541 | 0.102919 | ||||||||
\(269\) | 6693.13 | 1.51705 | 0.758526 | − | 0.651643i | \(-0.225920\pi\) | ||||
0.758526 | + | 0.651643i | \(0.225920\pi\) | |||||||
\(270\) | 70.4148 | 0.0158715 | ||||||||
\(271\) | 8641.37 | 1.93699 | 0.968497 | − | 0.249024i | \(-0.0801097\pi\) | ||||
0.968497 | + | 0.249024i | \(0.0801097\pi\) | |||||||
\(272\) | −1741.35 | −0.388180 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2042.58 | −0.450353 | ||||||||
\(275\) | −3826.22 | −0.839017 | ||||||||
\(276\) | 672.053 | 0.146568 | ||||||||
\(277\) | −7493.58 | −1.62544 | −0.812718 | − | 0.582658i | \(-0.802013\pi\) | ||||
−0.812718 | + | 0.582658i | \(0.802013\pi\) | |||||||
\(278\) | 837.808 | 0.180750 | ||||||||
\(279\) | 6191.91 | 1.32867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1976.73 | 0.419651 | 0.209825 | − | 0.977739i | \(-0.432710\pi\) | ||||
0.209825 | + | 0.977739i | \(0.432710\pi\) | |||||||
\(282\) | 2160.06 | 0.456133 | ||||||||
\(283\) | −6154.61 | −1.29277 | −0.646384 | − | 0.763012i | \(-0.723720\pi\) | ||||
−0.646384 | + | 0.763012i | \(0.723720\pi\) | |||||||
\(284\) | 685.452 | 0.143219 | ||||||||
\(285\) | 5096.46 | 1.05926 | ||||||||
\(286\) | −7414.95 | −1.53306 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −843.581 | −0.172599 | ||||||||
\(289\) | 6931.97 | 1.41094 | ||||||||
\(290\) | −878.554 | −0.177898 | ||||||||
\(291\) | −7289.63 | −1.46847 | ||||||||
\(292\) | 1446.88 | 0.289973 | ||||||||
\(293\) | 1905.58 | 0.379950 | 0.189975 | − | 0.981789i | \(-0.439159\pi\) | ||||
0.189975 | + | 0.981789i | \(0.439159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3036.68 | −0.599330 | ||||||||
\(296\) | 983.291 | 0.193083 | ||||||||
\(297\) | −262.479 | −0.0512815 | ||||||||
\(298\) | −1968.64 | −0.382685 | ||||||||
\(299\) | 1514.27 | 0.292885 | ||||||||
\(300\) | −1985.38 | −0.382086 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4009.99 | −0.764069 | ||||||||
\(303\) | −6915.20 | −1.31111 | ||||||||
\(304\) | 1477.85 | 0.278818 | ||||||||
\(305\) | −1815.79 | −0.340891 | ||||||||
\(306\) | 5738.18 | 1.07199 | ||||||||
\(307\) | −643.667 | −0.119661 | −0.0598307 | − | 0.998209i | \(-0.519056\pi\) | ||||
−0.0598307 | + | 0.998209i | \(0.519056\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3084.23 | −0.567818 | ||||||||
\(310\) | −3548.29 | −0.650094 | ||||||||
\(311\) | 5131.05 | 0.935547 | 0.467773 | − | 0.883848i | \(-0.345056\pi\) | ||||
0.467773 | + | 0.883848i | \(0.345056\pi\) | |||||||
\(312\) | −3847.53 | −0.698151 | ||||||||
\(313\) | −4845.93 | −0.875106 | −0.437553 | − | 0.899193i | \(-0.644155\pi\) | ||||
−0.437553 | + | 0.899193i | \(0.644155\pi\) | |||||||
\(314\) | −771.736 | −0.138699 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3369.27 | −0.599797 | ||||||||
\(317\) | 2149.07 | 0.380769 | 0.190384 | − | 0.981710i | \(-0.439027\pi\) | ||||
0.190384 | + | 0.981710i | \(0.439027\pi\) | |||||||
\(318\) | −9360.84 | −1.65072 | ||||||||
\(319\) | 3274.91 | 0.574796 | ||||||||
\(320\) | 483.416 | 0.0844493 | ||||||||
\(321\) | 4301.48 | 0.747929 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10052.6 | −1.73171 | ||||||||
\(324\) | −2983.28 | −0.511537 | ||||||||
\(325\) | −4473.45 | −0.763516 | ||||||||
\(326\) | 4794.75 | 0.814591 | ||||||||
\(327\) | 780.561 | 0.132003 | ||||||||
\(328\) | −2874.64 | −0.483920 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6214.26 | −1.03662 | ||||||||
\(331\) | 733.344 | 0.121777 | 0.0608886 | − | 0.998145i | \(-0.480607\pi\) | ||||
0.0608886 | + | 0.998145i | \(0.480607\pi\) | |||||||
\(332\) | 5497.15 | 0.908721 | ||||||||
\(333\) | −3240.18 | −0.533215 | ||||||||
\(334\) | 6877.86 | 1.12677 | ||||||||
\(335\) | 852.665 | 0.139063 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1922.41 | −0.310743 | −0.155372 | − | 0.987856i | \(-0.549657\pi\) | ||||
−0.155372 | + | 0.987856i | \(0.549657\pi\) | |||||||
\(338\) | −4275.25 | −0.687997 | ||||||||
\(339\) | 154.769 | 0.0247961 | ||||||||
\(340\) | −3288.27 | −0.524505 | ||||||||
\(341\) | 13226.7 | 2.10048 | ||||||||
\(342\) | −4869.88 | −0.769980 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 264.256 | 0.0414178 | ||||||||
\(345\) | 1269.07 | 0.198041 | ||||||||
\(346\) | 4017.98 | 0.624300 | ||||||||
\(347\) | 11309.5 | 1.74964 | 0.874821 | − | 0.484446i | \(-0.160979\pi\) | ||||
0.874821 | + | 0.484446i | \(0.160979\pi\) | |||||||
\(348\) | 1699.31 | 0.261760 | ||||||||
\(349\) | −5202.37 | −0.797927 | −0.398963 | − | 0.916967i | \(-0.630630\pi\) | ||||
−0.398963 | + | 0.916967i | \(0.630630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −306.880 | −0.0466668 | ||||||||
\(352\) | −1801.99 | −0.272859 | ||||||||
\(353\) | −6302.68 | −0.950306 | −0.475153 | − | 0.879903i | \(-0.657607\pi\) | ||||
−0.475153 | + | 0.879903i | \(0.657607\pi\) | |||||||
\(354\) | 5873.59 | 0.881858 | ||||||||
\(355\) | 1294.37 | 0.193515 | ||||||||
\(356\) | −4964.45 | −0.739088 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8024.47 | −1.18465 | ||||||||
\(359\) | −12797.9 | −1.88147 | −0.940733 | − | 0.339148i | \(-0.889861\pi\) | ||||
−0.940733 | + | 0.339148i | \(0.889861\pi\) | |||||||
\(360\) | −1592.97 | −0.233214 | ||||||||
\(361\) | 1672.46 | 0.243834 | ||||||||
\(362\) | 4462.87 | 0.647965 | ||||||||
\(363\) | 13441.5 | 1.94352 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2732.20 | 0.391808 | ||||||||
\(366\) | 3512.13 | 0.501590 | ||||||||
\(367\) | 7794.73 | 1.10867 | 0.554335 | − | 0.832294i | \(-0.312973\pi\) | ||||
0.554335 | + | 0.832294i | \(0.312973\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 9472.64 | 1.33639 | ||||||||
\(370\) | 1856.79 | 0.260892 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6863.15 | 0.956553 | ||||||||
\(373\) | 9352.02 | 1.29820 | 0.649101 | − | 0.760703i | \(-0.275145\pi\) | ||||
0.649101 | + | 0.760703i | \(0.275145\pi\) | |||||||
\(374\) | 12257.4 | 1.69470 | ||||||||
\(375\) | −10646.2 | −1.46604 | ||||||||
\(376\) | 1182.79 | 0.162229 | ||||||||
\(377\) | 3828.89 | 0.523072 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −671.508 | −0.0910107 | −0.0455054 | − | 0.998964i | \(-0.514490\pi\) | ||||
−0.0455054 | + | 0.998964i | \(0.514490\pi\) | |||||||
\(380\) | 2790.70 | 0.376736 | ||||||||
\(381\) | 15880.5 | 2.13539 | ||||||||
\(382\) | −261.333 | −0.0350026 | ||||||||
\(383\) | −5923.13 | −0.790230 | −0.395115 | − | 0.918632i | \(-0.629295\pi\) | ||||
−0.395115 | + | 0.918632i | \(0.629295\pi\) | |||||||
\(384\) | −935.030 | −0.124259 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6886.64 | 0.908085 | ||||||||
\(387\) | −870.787 | −0.114379 | ||||||||
\(388\) | −3991.63 | −0.522279 | ||||||||
\(389\) | −3452.45 | −0.449991 | −0.224995 | − | 0.974360i | \(-0.572237\pi\) | ||||
−0.224995 | + | 0.974360i | \(0.572237\pi\) | |||||||
\(390\) | −7265.45 | −0.943335 | ||||||||
\(391\) | −2503.20 | −0.323765 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17939.2 | 2.30258 | ||||||||
\(394\) | 5952.67 | 0.761145 | ||||||||
\(395\) | −6362.33 | −0.810440 | ||||||||
\(396\) | 5937.99 | 0.753523 | ||||||||
\(397\) | 2462.71 | 0.311334 | 0.155667 | − | 0.987810i | \(-0.450247\pi\) | ||||
0.155667 | + | 0.987810i | \(0.450247\pi\) | |||||||
\(398\) | −1805.92 | −0.227443 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1087.14 | −0.135893 | ||||||||
\(401\) | −12628.0 | −1.57260 | −0.786301 | − | 0.617843i | \(-0.788007\pi\) | ||||
−0.786301 | + | 0.617843i | \(0.788007\pi\) | |||||||
\(402\) | −1649.24 | −0.204618 | ||||||||
\(403\) | 15464.1 | 1.91146 | ||||||||
\(404\) | −3786.59 | −0.466312 | ||||||||
\(405\) | −5633.47 | −0.691183 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6921.41 | −0.842952 | ||||||||
\(408\) | 6360.23 | 0.771760 | ||||||||
\(409\) | −9857.74 | −1.19177 | −0.595885 | − | 0.803070i | \(-0.703199\pi\) | ||||
−0.595885 | + | 0.803070i | \(0.703199\pi\) | |||||||
\(410\) | −5428.32 | −0.653867 | ||||||||
\(411\) | 7460.45 | 0.895370 | ||||||||
\(412\) | −1688.85 | −0.201951 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1212.65 | −0.143958 | ||||||||
\(415\) | 10380.5 | 1.22785 | ||||||||
\(416\) | −2106.81 | −0.248305 | ||||||||
\(417\) | −3060.06 | −0.359357 | ||||||||
\(418\) | −10402.7 | −1.21725 | ||||||||
\(419\) | 15594.0 | 1.81818 | 0.909090 | − | 0.416599i | \(-0.136778\pi\) | ||||
0.909090 | + | 0.416599i | \(0.136778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2429.98 | −0.281306 | −0.140653 | − | 0.990059i | \(-0.544920\pi\) | ||||
−0.140653 | + | 0.990059i | \(0.544920\pi\) | |||||||
\(422\) | 4879.90 | 0.562914 | ||||||||
\(423\) | −3897.59 | −0.448008 | ||||||||
\(424\) | −5125.77 | −0.587097 | ||||||||
\(425\) | 7394.93 | 0.844016 | ||||||||
\(426\) | −2503.59 | −0.284740 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2355.39 | 0.266009 | ||||||||
\(429\) | 27082.8 | 3.04795 | ||||||||
\(430\) | 499.006 | 0.0559633 | ||||||||
\(431\) | −4540.29 | −0.507420 | −0.253710 | − | 0.967280i | \(-0.581651\pi\) | ||||
−0.253710 | + | 0.967280i | \(0.581651\pi\) | |||||||
\(432\) | −74.5784 | −0.00830591 | ||||||||
\(433\) | 15322.6 | 1.70060 | 0.850299 | − | 0.526300i | \(-0.176421\pi\) | ||||
0.850299 | + | 0.526300i | \(0.176421\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3208.88 | 0.353688 | ||||||||
\(436\) | 427.416 | 0.0469484 | ||||||||
\(437\) | 2124.42 | 0.232551 | ||||||||
\(438\) | −5284.66 | −0.576509 | ||||||||
\(439\) | 5141.79 | 0.559008 | 0.279504 | − | 0.960145i | \(-0.409830\pi\) | ||||
0.279504 | + | 0.960145i | \(0.409830\pi\) | |||||||
\(440\) | −3402.78 | −0.368684 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14330.9 | 1.54220 | ||||||||
\(443\) | −7538.33 | −0.808480 | −0.404240 | − | 0.914653i | \(-0.632464\pi\) | ||||
−0.404240 | + | 0.914653i | \(0.632464\pi\) | |||||||
\(444\) | −3591.43 | −0.383878 | ||||||||
\(445\) | −9374.60 | −0.998648 | ||||||||
\(446\) | −10828.7 | −1.14967 | ||||||||
\(447\) | 7190.38 | 0.760835 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7253.14 | −0.762354 | −0.381177 | − | 0.924502i | \(-0.624481\pi\) | ||||
−0.381177 | + | 0.924502i | \(0.624481\pi\) | |||||||
\(450\) | 3582.40 | 0.375280 | ||||||||
\(451\) | 20234.7 | 2.11267 | ||||||||
\(452\) | 84.7476 | 0.00881901 | ||||||||
\(453\) | 14646.3 | 1.51908 | ||||||||
\(454\) | 8959.08 | 0.926146 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5397.81 | −0.554332 | ||||||||
\(457\) | −14113.4 | −1.44464 | −0.722319 | − | 0.691561i | \(-0.756924\pi\) | ||||
−0.722319 | + | 0.691561i | \(0.756924\pi\) | |||||||
\(458\) | −7255.79 | −0.740264 | ||||||||
\(459\) | 507.294 | 0.0515871 | ||||||||
\(460\) | 694.911 | 0.0704356 | ||||||||
\(461\) | −1996.06 | −0.201662 | −0.100831 | − | 0.994904i | \(-0.532150\pi\) | ||||
−0.100831 | + | 0.994904i | \(0.532150\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8301.53 | 0.833271 | 0.416636 | − | 0.909074i | \(-0.363209\pi\) | ||||
0.416636 | + | 0.909074i | \(0.363209\pi\) | |||||||
\(464\) | 930.502 | 0.0930980 | ||||||||
\(465\) | 12960.0 | 1.29248 | ||||||||
\(466\) | 7365.47 | 0.732186 | ||||||||
\(467\) | 4517.84 | 0.447668 | 0.223834 | − | 0.974627i | \(-0.428143\pi\) | ||||
0.223834 | + | 0.974627i | \(0.428143\pi\) | |||||||
\(468\) | 6942.45 | 0.685716 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2233.52 | 0.219202 | ||||||||
\(471\) | 2818.74 | 0.275755 | ||||||||
\(472\) | 3216.24 | 0.313642 | ||||||||
\(473\) | −1860.10 | −0.180820 | ||||||||
\(474\) | 12306.1 | 1.19249 | ||||||||
\(475\) | −6275.94 | −0.606231 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16890.6 | 1.62132 | ||||||||
\(478\) | −2579.19 | −0.246798 | ||||||||
\(479\) | 16515.6 | 1.57540 | 0.787702 | − | 0.616056i | \(-0.211271\pi\) | ||||
0.787702 | + | 0.616056i | \(0.211271\pi\) | |||||||
\(480\) | −1765.66 | −0.167898 | ||||||||
\(481\) | −8092.22 | −0.767097 | ||||||||
\(482\) | −1328.31 | −0.125524 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7360.25 | 0.691233 | ||||||||
\(485\) | −7537.57 | −0.705697 | ||||||||
\(486\) | 10644.6 | 0.993519 | ||||||||
\(487\) | 9053.08 | 0.842370 | 0.421185 | − | 0.906975i | \(-0.361614\pi\) | ||||
0.421185 | + | 0.906975i | \(0.361614\pi\) | |||||||
\(488\) | 1923.16 | 0.178396 | ||||||||
\(489\) | −17512.6 | −1.61953 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7398.88 | −0.680055 | −0.340027 | − | 0.940416i | \(-0.610436\pi\) | ||||
−0.340027 | + | 0.940416i | \(0.610436\pi\) | |||||||
\(492\) | 10499.5 | 0.962105 | ||||||||
\(493\) | −6329.42 | −0.578221 | ||||||||
\(494\) | −12162.3 | −1.10771 | ||||||||
\(495\) | 11213.0 | 1.01815 | ||||||||
\(496\) | 3758.09 | 0.340209 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −20078.1 | −1.80667 | ||||||||
\(499\) | −717.821 | −0.0643970 | −0.0321985 | − | 0.999481i | \(-0.510251\pi\) | ||||
−0.0321985 | + | 0.999481i | \(0.510251\pi\) | |||||||
\(500\) | −5829.59 | −0.521414 | ||||||||
\(501\) | −25121.1 | −2.24018 | ||||||||
\(502\) | 9542.15 | 0.848381 | ||||||||
\(503\) | 1927.68 | 0.170877 | 0.0854385 | − | 0.996343i | \(-0.472771\pi\) | ||||
0.0854385 | + | 0.996343i | \(0.472771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7150.39 | −0.630076 | ||||||||
\(506\) | −2590.36 | −0.227580 | ||||||||
\(507\) | 15615.2 | 1.36784 | ||||||||
\(508\) | 8695.79 | 0.759475 | ||||||||
\(509\) | 7804.87 | 0.679656 | 0.339828 | − | 0.940488i | \(-0.389631\pi\) | ||||
0.339828 | + | 0.940488i | \(0.389631\pi\) | |||||||
\(510\) | 12010.3 | 1.04279 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −430.531 | −0.0370534 | ||||||||
\(514\) | −4268.58 | −0.366301 | ||||||||
\(515\) | −3189.13 | −0.272874 | ||||||||
\(516\) | −965.185 | −0.0823447 | ||||||||
\(517\) | −8325.72 | −0.708249 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14675.5 | −1.24120 | ||||||||
\(520\) | −3978.39 | −0.335507 | ||||||||
\(521\) | 21406.8 | 1.80010 | 0.900049 | − | 0.435789i | \(-0.143531\pi\) | ||||
0.900049 | + | 0.435789i | \(0.143531\pi\) | |||||||
\(522\) | −3066.23 | −0.257098 | ||||||||
\(523\) | −11327.8 | −0.947098 | −0.473549 | − | 0.880768i | \(-0.657027\pi\) | ||||
−0.473549 | + | 0.880768i | \(0.657027\pi\) | |||||||
\(524\) | 9823.10 | 0.818939 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13620.5 | −1.12905 | ||||||||
\(527\) | −25563.2 | −2.11300 | ||||||||
\(528\) | 6581.70 | 0.542484 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −9679.21 | −0.793279 | ||||||||
\(531\) | −10598.3 | −0.866150 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23657.6 | 1.92256 | ||||||||
\(534\) | 18132.5 | 1.46942 | ||||||||
\(535\) | 4447.78 | 0.359428 | ||||||||
\(536\) | −903.082 | −0.0727746 | ||||||||
\(537\) | 29309.1 | 2.35527 | ||||||||
\(538\) | −13386.3 | −1.07272 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −140.830 | −0.0112229 | ||||||||
\(541\) | −8508.86 | −0.676201 | −0.338100 | − | 0.941110i | \(-0.609784\pi\) | ||||
−0.338100 | + | 0.941110i | \(0.609784\pi\) | |||||||
\(542\) | −17282.7 | −1.36966 | ||||||||
\(543\) | −16300.5 | −1.28825 | ||||||||
\(544\) | 3482.71 | 0.274485 | ||||||||
\(545\) | 807.109 | 0.0634362 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7097.86 | 0.554813 | 0.277406 | − | 0.960753i | \(-0.410525\pi\) | ||||
0.277406 | + | 0.960753i | \(0.410525\pi\) | |||||||
\(548\) | 4085.16 | 0.318448 | ||||||||
\(549\) | −6337.26 | −0.492655 | ||||||||
\(550\) | 7652.43 | 0.593274 | ||||||||
\(551\) | 5371.66 | 0.415319 | ||||||||
\(552\) | −1344.11 | −0.103639 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14987.2 | 1.14936 | ||||||||
\(555\) | −6781.86 | −0.518692 | ||||||||
\(556\) | −1675.62 | −0.127809 | ||||||||
\(557\) | 269.957 | 0.0205358 | 0.0102679 | − | 0.999947i | \(-0.496732\pi\) | ||||
0.0102679 | + | 0.999947i | \(0.496732\pi\) | |||||||
\(558\) | −12383.8 | −0.939514 | ||||||||
\(559\) | −2174.76 | −0.164548 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44769.8 | −3.36931 | ||||||||
\(562\) | −3953.46 | −0.296738 | ||||||||
\(563\) | 22749.5 | 1.70298 | 0.851491 | − | 0.524370i | \(-0.175699\pi\) | ||||
0.851491 | + | 0.524370i | \(0.175699\pi\) | |||||||
\(564\) | −4320.11 | −0.322535 | ||||||||
\(565\) | 160.033 | 0.0119161 | ||||||||
\(566\) | 12309.2 | 0.914126 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1370.90 | −0.101271 | ||||||||
\(569\) | −93.7196 | −0.00690498 | −0.00345249 | − | 0.999994i | \(-0.501099\pi\) | ||||
−0.00345249 | + | 0.999994i | \(0.501099\pi\) | |||||||
\(570\) | −10192.9 | −0.749007 | ||||||||
\(571\) | 3511.92 | 0.257389 | 0.128695 | − | 0.991684i | \(-0.458921\pi\) | ||||
0.128695 | + | 0.991684i | \(0.458921\pi\) | |||||||
\(572\) | 14829.9 | 1.08404 | ||||||||
\(573\) | 954.510 | 0.0695903 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1562.77 | −0.113343 | ||||||||
\(576\) | 1687.16 | 0.122046 | ||||||||
\(577\) | 3643.87 | 0.262905 | 0.131453 | − | 0.991322i | \(-0.458036\pi\) | ||||
0.131453 | + | 0.991322i | \(0.458036\pi\) | |||||||
\(578\) | −13863.9 | −0.997688 | ||||||||
\(579\) | −25153.2 | −1.80541 | ||||||||
\(580\) | 1757.11 | 0.125793 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14579.3 | 1.03837 | ||||||||
\(583\) | 36080.4 | 2.56312 | ||||||||
\(584\) | −2893.75 | −0.205042 | ||||||||
\(585\) | 13109.7 | 0.926531 | ||||||||
\(586\) | −3811.16 | −0.268665 | ||||||||
\(587\) | −12611.0 | −0.886730 | −0.443365 | − | 0.896341i | \(-0.646216\pi\) | ||||
−0.443365 | + | 0.896341i | \(0.646216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21695.0 | 1.51770 | ||||||||
\(590\) | 6073.36 | 0.423790 | ||||||||
\(591\) | −21741.9 | −1.51327 | ||||||||
\(592\) | −1966.58 | −0.136530 | ||||||||
\(593\) | 516.853 | 0.0357919 | 0.0178959 | − | 0.999840i | \(-0.494303\pi\) | ||||
0.0178959 | + | 0.999840i | \(0.494303\pi\) | |||||||
\(594\) | 524.959 | 0.0362615 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3937.28 | 0.270599 | ||||||||
\(597\) | 6596.04 | 0.452191 | ||||||||
\(598\) | −3028.54 | −0.207101 | ||||||||
\(599\) | −6239.98 | −0.425640 | −0.212820 | − | 0.977091i | \(-0.568265\pi\) | ||||
−0.212820 | + | 0.977091i | \(0.568265\pi\) | |||||||
\(600\) | 3970.75 | 0.270176 | ||||||||
\(601\) | 22085.1 | 1.49895 | 0.749477 | − | 0.662031i | \(-0.230305\pi\) | ||||
0.749477 | + | 0.662031i | \(0.230305\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2975.87 | 0.200973 | ||||||||
\(604\) | 8019.97 | 0.540278 | ||||||||
\(605\) | 13898.7 | 0.933987 | ||||||||
\(606\) | 13830.4 | 0.927098 | ||||||||
\(607\) | −23388.3 | −1.56393 | −0.781963 | − | 0.623325i | \(-0.785782\pi\) | ||||
−0.781963 | + | 0.623325i | \(0.785782\pi\) | |||||||
\(608\) | −2955.71 | −0.197154 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3631.58 | 0.241046 | ||||||||
\(611\) | −9734.09 | −0.644516 | ||||||||
\(612\) | −11476.4 | −0.758013 | ||||||||
\(613\) | 23195.2 | 1.52830 | 0.764149 | − | 0.645039i | \(-0.223159\pi\) | ||||
0.764149 | + | 0.645039i | \(0.223159\pi\) | |||||||
\(614\) | 1287.33 | 0.0846134 | ||||||||
\(615\) | 19826.7 | 1.29999 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4370.58 | −0.285175 | −0.142588 | − | 0.989782i | \(-0.545542\pi\) | ||||
−0.142588 | + | 0.989782i | \(0.545542\pi\) | |||||||
\(618\) | 6168.47 | 0.401508 | ||||||||
\(619\) | −5754.61 | −0.373663 | −0.186831 | − | 0.982392i | \(-0.559822\pi\) | ||||
−0.186831 | + | 0.982392i | \(0.559822\pi\) | |||||||
\(620\) | 7096.58 | 0.459686 | ||||||||
\(621\) | −107.206 | −0.00692761 | ||||||||
\(622\) | −10262.1 | −0.661531 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7695.05 | 0.493668 | ||||||||
\(625\) | −2514.96 | −0.160957 | ||||||||
\(626\) | 9691.86 | 0.618793 | ||||||||
\(627\) | 37995.3 | 2.42007 | ||||||||
\(628\) | 1543.47 | 0.0980752 | ||||||||
\(629\) | 13377.0 | 0.847975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10487.6 | −0.661658 | −0.330829 | − | 0.943691i | \(-0.607328\pi\) | ||||
−0.330829 | + | 0.943691i | \(0.607328\pi\) | |||||||
\(632\) | 6738.53 | 0.424121 | ||||||||
\(633\) | −17823.7 | −1.11916 | ||||||||
\(634\) | −4298.14 | −0.269244 | ||||||||
\(635\) | 16420.7 | 1.02619 | ||||||||
\(636\) | 18721.7 | 1.16724 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6549.82 | −0.406442 | ||||||||
\(639\) | 4517.46 | 0.279668 | ||||||||
\(640\) | −966.832 | −0.0597147 | ||||||||
\(641\) | 22643.5 | 1.39526 | 0.697631 | − | 0.716457i | \(-0.254237\pi\) | ||||
0.697631 | + | 0.716457i | \(0.254237\pi\) | |||||||
\(642\) | −8602.96 | −0.528865 | ||||||||
\(643\) | 8247.48 | 0.505830 | 0.252915 | − | 0.967488i | \(-0.418611\pi\) | ||||
0.252915 | + | 0.967488i | \(0.418611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1822.60 | −0.111263 | ||||||||
\(646\) | 20105.2 | 1.22450 | ||||||||
\(647\) | −3358.18 | −0.204055 | −0.102027 | − | 0.994782i | \(-0.532533\pi\) | ||||
−0.102027 | + | 0.994782i | \(0.532533\pi\) | |||||||
\(648\) | 5966.57 | 0.361711 | ||||||||
\(649\) | −22639.2 | −1.36928 | ||||||||
\(650\) | 8946.91 | 0.539887 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9589.50 | −0.576003 | ||||||||
\(653\) | −11243.5 | −0.673802 | −0.336901 | − | 0.941540i | \(-0.609379\pi\) | ||||
−0.336901 | + | 0.941540i | \(0.609379\pi\) | |||||||
\(654\) | −1561.12 | −0.0933405 | ||||||||
\(655\) | 18549.4 | 1.10654 | ||||||||
\(656\) | 5749.29 | 0.342183 | ||||||||
\(657\) | 9535.61 | 0.566240 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28375.7 | 1.67733 | 0.838664 | − | 0.544650i | \(-0.183337\pi\) | ||||
0.838664 | + | 0.544650i | \(0.183337\pi\) | |||||||
\(660\) | 12428.5 | 0.732999 | ||||||||
\(661\) | 26521.0 | 1.56058 | 0.780292 | − | 0.625415i | \(-0.215070\pi\) | ||||
0.780292 | + | 0.625415i | \(0.215070\pi\) | |||||||
\(662\) | −1466.69 | −0.0861094 | ||||||||
\(663\) | −52343.0 | −3.06611 | ||||||||
\(664\) | −10994.3 | −0.642563 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6480.36 | 0.377040 | ||||||||
\(667\) | 1337.60 | 0.0776491 | ||||||||
\(668\) | −13755.7 | −0.796743 | ||||||||
\(669\) | 39551.4 | 2.28572 | ||||||||
\(670\) | −1705.33 | −0.0983323 | ||||||||
\(671\) | −13537.1 | −0.778831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11574.0 | −0.662921 | −0.331460 | − | 0.943469i | \(-0.607541\pi\) | ||||
−0.331460 | + | 0.943469i | \(0.607541\pi\) | |||||||
\(674\) | 3844.82 | 0.219729 | ||||||||
\(675\) | 316.709 | 0.0180594 | ||||||||
\(676\) | 8550.51 | 0.486488 | ||||||||
\(677\) | −19964.6 | −1.13338 | −0.566692 | − | 0.823930i | \(-0.691777\pi\) | ||||
−0.566692 | + | 0.823930i | \(0.691777\pi\) | |||||||
\(678\) | −309.537 | −0.0175335 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6576.55 | 0.370881 | ||||||||
\(681\) | −32722.7 | −1.84132 | ||||||||
\(682\) | −26453.3 | −1.48526 | ||||||||
\(683\) | 30955.7 | 1.73424 | 0.867120 | − | 0.498099i | \(-0.165968\pi\) | ||||
0.867120 | + | 0.498099i | \(0.165968\pi\) | |||||||
\(684\) | 9739.77 | 0.544458 | ||||||||
\(685\) | 7714.19 | 0.430283 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26501.5 | 1.47175 | ||||||||
\(688\) | −528.512 | −0.0292868 | ||||||||
\(689\) | 42183.7 | 2.33247 | ||||||||
\(690\) | −2538.13 | −0.140036 | ||||||||
\(691\) | 10356.0 | 0.570133 | 0.285066 | − | 0.958508i | \(-0.407984\pi\) | ||||
0.285066 | + | 0.958508i | \(0.407984\pi\) | |||||||
\(692\) | −8035.96 | −0.441447 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22619.0 | −1.23718 | ||||||||
\(695\) | −3164.14 | −0.172694 | ||||||||
\(696\) | −3398.62 | −0.185093 | ||||||||
\(697\) | −39107.6 | −2.12526 | ||||||||
\(698\) | 10404.7 | 0.564220 | ||||||||
\(699\) | −26902.1 | −1.45569 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −736.621 | −0.0396887 | −0.0198444 | − | 0.999803i | \(-0.506317\pi\) | ||||
−0.0198444 | + | 0.999803i | \(0.506317\pi\) | |||||||
\(702\) | 613.760 | 0.0329984 | ||||||||
\(703\) | −11352.8 | −0.609075 | ||||||||
\(704\) | 3603.98 | 0.192941 | ||||||||
\(705\) | −8157.86 | −0.435805 | ||||||||
\(706\) | 12605.4 | 0.671968 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11747.2 | −0.623568 | ||||||||
\(709\) | −32277.6 | −1.70975 | −0.854873 | − | 0.518838i | \(-0.826365\pi\) | ||||
−0.854873 | + | 0.518838i | \(0.826365\pi\) | |||||||
\(710\) | −2588.74 | −0.136836 | ||||||||
\(711\) | −22205.1 | −1.17125 | ||||||||
\(712\) | 9928.91 | 0.522614 | ||||||||
\(713\) | 5402.26 | 0.283754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28004.0 | 1.46474 | ||||||||
\(716\) | 16048.9 | 0.837677 | ||||||||
\(717\) | 9420.39 | 0.490671 | ||||||||
\(718\) | 25595.8 | 1.33040 | ||||||||
\(719\) | −34790.7 | −1.80455 | −0.902277 | − | 0.431156i | \(-0.858106\pi\) | ||||
−0.902277 | + | 0.431156i | \(0.858106\pi\) | |||||||
\(720\) | 3185.94 | 0.164907 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3344.92 | −0.172417 | ||||||||
\(723\) | 4851.59 | 0.249561 | ||||||||
\(724\) | −8925.75 | −0.458181 | ||||||||
\(725\) | −3951.52 | −0.202422 | ||||||||
\(726\) | −26883.0 | −1.37427 | ||||||||
\(727\) | −21693.3 | −1.10668 | −0.553341 | − | 0.832955i | \(-0.686647\pi\) | ||||
−0.553341 | + | 0.832955i | \(0.686647\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18741.9 | −0.952189 | ||||||||
\(730\) | −5464.40 | −0.277050 | ||||||||
\(731\) | 3595.02 | 0.181897 | ||||||||
\(732\) | −7024.25 | −0.354677 | ||||||||
\(733\) | −18264.6 | −0.920352 | −0.460176 | − | 0.887828i | \(-0.652214\pi\) | ||||
−0.460176 | + | 0.887828i | \(0.652214\pi\) | |||||||
\(734\) | −15589.5 | −0.783948 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 6356.82 | 0.317715 | ||||||||
\(738\) | −18945.3 | −0.944967 | ||||||||
\(739\) | 10487.5 | 0.522040 | 0.261020 | − | 0.965333i | \(-0.415941\pi\) | ||||
0.261020 | + | 0.965333i | \(0.415941\pi\) | |||||||
\(740\) | −3713.58 | −0.184478 | ||||||||
\(741\) | 44422.5 | 2.20230 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6519.14 | 0.321889 | 0.160945 | − | 0.986963i | \(-0.448546\pi\) | ||||
0.160945 | + | 0.986963i | \(0.448546\pi\) | |||||||
\(744\) | −13726.3 | −0.676385 | ||||||||
\(745\) | 7434.93 | 0.365631 | ||||||||
\(746\) | −18704.0 | −0.917967 | ||||||||
\(747\) | 36228.9 | 1.77449 | ||||||||
\(748\) | −24514.9 | −1.19833 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 21292.4 | 1.03665 | ||||||||
\(751\) | −24410.9 | −1.18611 | −0.593053 | − | 0.805164i | \(-0.702077\pi\) | ||||
−0.593053 | + | 0.805164i | \(0.702077\pi\) | |||||||
\(752\) | −2365.59 | −0.114713 | ||||||||
\(753\) | −34852.4 | −1.68671 | ||||||||
\(754\) | −7657.78 | −0.369867 | ||||||||
\(755\) | 15144.5 | 0.730018 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36222.9 | −1.73916 | −0.869580 | − | 0.493793i | \(-0.835610\pi\) | ||||
−0.869580 | + | 0.493793i | \(0.835610\pi\) | |||||||
\(758\) | 1343.02 | 0.0643543 | ||||||||
\(759\) | 9461.19 | 0.452463 | ||||||||
\(760\) | −5581.39 | −0.266393 | ||||||||
\(761\) | −10363.5 | −0.493660 | −0.246830 | − | 0.969059i | \(-0.579389\pi\) | ||||
−0.246830 | + | 0.969059i | \(0.579389\pi\) | |||||||
\(762\) | −31761.1 | −1.50995 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 522.667 | 0.0247505 | ||||||||
\(765\) | −21671.3 | −1.02422 | ||||||||
\(766\) | 11846.3 | 0.558777 | ||||||||
\(767\) | −26468.8 | −1.24607 | ||||||||
\(768\) | 1870.06 | 0.0878646 | ||||||||
\(769\) | 3915.55 | 0.183613 | 0.0918065 | − | 0.995777i | \(-0.470736\pi\) | ||||
0.0918065 | + | 0.995777i | \(0.470736\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15590.8 | 0.728262 | ||||||||
\(772\) | −13773.3 | −0.642113 | ||||||||
\(773\) | −28820.3 | −1.34100 | −0.670500 | − | 0.741910i | \(-0.733920\pi\) | ||||
−0.670500 | + | 0.741910i | \(0.733920\pi\) | |||||||
\(774\) | 1741.57 | 0.0808780 | ||||||||
\(775\) | −15959.3 | −0.739711 | ||||||||
\(776\) | 7983.25 | 0.369307 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6904.91 | 0.318191 | ||||||||
\(779\) | 33189.9 | 1.52651 | ||||||||
\(780\) | 14530.9 | 0.667038 | ||||||||
\(781\) | 9649.82 | 0.442123 | ||||||||
\(782\) | 5006.39 | 0.228936 | ||||||||
\(783\) | −271.075 | −0.0123722 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2914.61 | 0.132518 | ||||||||
\(786\) | −35878.5 | −1.62817 | ||||||||
\(787\) | −23146.5 | −1.04839 | −0.524196 | − | 0.851598i | \(-0.675634\pi\) | ||||
−0.524196 | + | 0.851598i | \(0.675634\pi\) | |||||||
\(788\) | −11905.3 | −0.538211 | ||||||||
\(789\) | 49748.3 | 2.24472 | ||||||||
\(790\) | 12724.7 | 0.573067 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −11876.0 | −0.532821 | ||||||||
\(793\) | −15827.1 | −0.708746 | ||||||||
\(794\) | −4925.42 | −0.220147 | ||||||||
\(795\) | 35353.0 | 1.57716 | ||||||||
\(796\) | 3611.83 | 0.160827 | ||||||||
\(797\) | −8804.30 | −0.391298 | −0.195649 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195649 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16091.1 | 0.712469 | ||||||||
\(800\) | 2174.29 | 0.0960909 | ||||||||
\(801\) | −32718.1 | −1.44324 | ||||||||
\(802\) | 25256.1 | 1.11200 | ||||||||
\(803\) | 20369.2 | 0.895160 | ||||||||
\(804\) | 3298.47 | 0.144687 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30928.1 | −1.35161 | ||||||||
\(807\) | 48892.8 | 2.13272 | ||||||||
\(808\) | 7573.19 | 0.329732 | ||||||||
\(809\) | −16308.6 | −0.708752 | −0.354376 | − | 0.935103i | \(-0.615307\pi\) | ||||
−0.354376 | + | 0.935103i | \(0.615307\pi\) | |||||||
\(810\) | 11266.9 | 0.488740 | ||||||||
\(811\) | −8308.25 | −0.359731 | −0.179866 | − | 0.983691i | \(-0.557566\pi\) | ||||
−0.179866 | + | 0.983691i | \(0.557566\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 63124.5 | 2.72309 | ||||||||
\(814\) | 13842.8 | 0.596057 | ||||||||
\(815\) | −18108.3 | −0.778289 | ||||||||
\(816\) | −12720.5 | −0.545717 | ||||||||
\(817\) | −3051.03 | −0.130651 | ||||||||
\(818\) | 19715.5 | 0.842709 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10856.6 | 0.462354 | ||||||||
\(821\) | 28618.8 | 1.21657 | 0.608284 | − | 0.793720i | \(-0.291858\pi\) | ||||
0.608284 | + | 0.793720i | \(0.291858\pi\) | |||||||
\(822\) | −14920.9 | −0.633122 | ||||||||
\(823\) | 1464.41 | 0.0620244 | 0.0310122 | − | 0.999519i | \(-0.490127\pi\) | ||||
0.0310122 | + | 0.999519i | \(0.490127\pi\) | |||||||
\(824\) | 3377.70 | 0.142801 | ||||||||
\(825\) | −27950.2 | −1.17952 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38045.8 | −1.59974 | −0.799869 | − | 0.600175i | \(-0.795098\pi\) | ||||
−0.799869 | + | 0.600175i | \(0.795098\pi\) | |||||||
\(828\) | 2425.30 | 0.101793 | ||||||||
\(829\) | −23247.3 | −0.973961 | −0.486980 | − | 0.873413i | \(-0.661902\pi\) | ||||
−0.486980 | + | 0.873413i | \(0.661902\pi\) | |||||||
\(830\) | −20761.0 | −0.868224 | ||||||||
\(831\) | −54740.0 | −2.28509 | ||||||||
\(832\) | 4213.62 | 0.175578 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6120.12 | 0.254104 | ||||||||
\(835\) | −25975.5 | −1.07655 | ||||||||
\(836\) | 20805.3 | 0.860725 | ||||||||
\(837\) | −1094.81 | −0.0452119 | ||||||||
\(838\) | −31188.0 | −1.28565 | ||||||||
\(839\) | −10511.6 | −0.432539 | −0.216270 | − | 0.976334i | \(-0.569389\pi\) | ||||
−0.216270 | + | 0.976334i | \(0.569389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21006.8 | −0.861324 | ||||||||
\(842\) | 4859.96 | 0.198914 | ||||||||
\(843\) | 14439.9 | 0.589959 | ||||||||
\(844\) | −9759.80 | −0.398041 | ||||||||
\(845\) | 16146.3 | 0.657337 | ||||||||
\(846\) | 7795.18 | 0.316790 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10251.5 | 0.415141 | ||||||||
\(849\) | −44959.0 | −1.81742 | ||||||||
\(850\) | −14789.9 | −0.596809 | ||||||||
\(851\) | −2826.96 | −0.113874 | ||||||||
\(852\) | 5007.17 | 0.201341 | ||||||||
\(853\) | −10457.1 | −0.419748 | −0.209874 | − | 0.977728i | \(-0.567305\pi\) | ||||
−0.209874 | + | 0.977728i | \(0.567305\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18392.0 | 0.735666 | ||||||||
\(856\) | −4710.77 | −0.188097 | ||||||||
\(857\) | 17615.4 | 0.702135 | 0.351067 | − | 0.936350i | \(-0.385819\pi\) | ||||
0.351067 | + | 0.936350i | \(0.385819\pi\) | |||||||
\(858\) | −54165.7 | −2.15523 | ||||||||
\(859\) | 16600.7 | 0.659381 | 0.329691 | − | 0.944089i | \(-0.393056\pi\) | ||||
0.329691 | + | 0.944089i | \(0.393056\pi\) | |||||||
\(860\) | −998.012 | −0.0395720 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9080.57 | 0.358800 | ||||||||
\(863\) | −11013.9 | −0.434436 | −0.217218 | − | 0.976123i | \(-0.569698\pi\) | ||||
−0.217218 | + | 0.976123i | \(0.569698\pi\) | |||||||
\(864\) | 149.157 | 0.00587317 | ||||||||
\(865\) | −15174.7 | −0.596478 | ||||||||
\(866\) | −30645.3 | −1.20250 | ||||||||
\(867\) | 50637.5 | 1.98355 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47432.7 | −1.85160 | ||||||||
\(870\) | −6417.77 | −0.250095 | ||||||||
\(871\) | 7432.13 | 0.289125 | ||||||||
\(872\) | −854.832 | −0.0331976 | ||||||||
\(873\) | −26306.7 | −1.01987 | ||||||||
\(874\) | −4248.83 | −0.164438 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10569.3 | 0.407653 | ||||||||
\(877\) | 22076.0 | 0.850003 | 0.425002 | − | 0.905193i | \(-0.360274\pi\) | ||||
0.425002 | + | 0.905193i | \(0.360274\pi\) | |||||||
\(878\) | −10283.6 | −0.395278 | ||||||||
\(879\) | 13920.1 | 0.534146 | ||||||||
\(880\) | 6805.55 | 0.260699 | ||||||||
\(881\) | −9443.65 | −0.361140 | −0.180570 | − | 0.983562i | \(-0.557794\pi\) | ||||
−0.180570 | + | 0.983562i | \(0.557794\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31677.0 | 1.20727 | 0.603633 | − | 0.797262i | \(-0.293719\pi\) | ||||
0.603633 | + | 0.797262i | \(0.293719\pi\) | |||||||
\(884\) | −28661.8 | −1.09050 | ||||||||
\(885\) | −22182.7 | −0.842558 | ||||||||
\(886\) | 15076.7 | 0.571682 | ||||||||
\(887\) | 96.4492 | 0.00365101 | 0.00182551 | − | 0.999998i | \(-0.499419\pi\) | ||||
0.00182551 | + | 0.999998i | \(0.499419\pi\) | |||||||
\(888\) | 7182.86 | 0.271443 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18749.2 | 0.706151 | ||||||||
\(891\) | −41998.8 | −1.57914 | ||||||||
\(892\) | 21657.4 | 0.812941 | ||||||||
\(893\) | −13656.2 | −0.511745 | ||||||||
\(894\) | −14380.8 | −0.537992 | ||||||||
\(895\) | 30305.9 | 1.13186 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11061.6 | 0.411747 | ||||||||
\(898\) | 14506.3 | 0.539065 | ||||||||
\(899\) | 13659.8 | 0.506764 | ||||||||
\(900\) | −7164.80 | −0.265363 | ||||||||
\(901\) | −69732.6 | −2.57839 | ||||||||
\(902\) | −40469.4 | −1.49388 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −169.495 | −0.00623598 | ||||||||
\(905\) | −16854.9 | −0.619088 | ||||||||
\(906\) | −29292.6 | −1.07415 | ||||||||
\(907\) | −34721.3 | −1.27112 | −0.635559 | − | 0.772053i | \(-0.719230\pi\) | ||||
−0.635559 | + | 0.772053i | \(0.719230\pi\) | |||||||
\(908\) | −17918.2 | −0.654884 | ||||||||
\(909\) | −24955.5 | −0.910584 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23562.8 | 0.856938 | 0.428469 | − | 0.903557i | \(-0.359053\pi\) | ||||
0.428469 | + | 0.903557i | \(0.359053\pi\) | |||||||
\(912\) | 10795.6 | 0.391972 | ||||||||
\(913\) | 77389.2 | 2.80527 | ||||||||
\(914\) | 28226.9 | 1.02151 | ||||||||
\(915\) | −13264.2 | −0.479236 | ||||||||
\(916\) | 14511.6 | 0.523445 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1014.59 | −0.0364776 | ||||||||
\(919\) | −26368.7 | −0.946487 | −0.473244 | − | 0.880932i | \(-0.656917\pi\) | ||||
−0.473244 | + | 0.880932i | \(0.656917\pi\) | |||||||
\(920\) | −1389.82 | −0.0498055 | ||||||||
\(921\) | −4701.94 | −0.168224 | ||||||||
\(922\) | 3992.13 | 0.142596 | ||||||||
\(923\) | 11282.2 | 0.402337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8351.39 | 0.296856 | ||||||||
\(926\) | −16603.1 | −0.589212 | ||||||||
\(927\) | −11130.3 | −0.394356 | ||||||||
\(928\) | −1861.00 | −0.0658302 | ||||||||
\(929\) | 36036.3 | 1.27267 | 0.636336 | − | 0.771412i | \(-0.280449\pi\) | ||||
0.636336 | + | 0.771412i | \(0.280449\pi\) | |||||||
\(930\) | −25920.0 | −0.913924 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14730.9 | −0.517734 | ||||||||
\(933\) | 37481.9 | 1.31522 | ||||||||
\(934\) | −9035.68 | −0.316549 | ||||||||
\(935\) | −46292.5 | −1.61917 | ||||||||
\(936\) | −13884.9 | −0.484874 | ||||||||
\(937\) | −13236.3 | −0.461483 | −0.230742 | − | 0.973015i | \(-0.574115\pi\) | ||||
−0.230742 | + | 0.973015i | \(0.574115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35399.2 | −1.23025 | ||||||||
\(940\) | −4467.05 | −0.154999 | ||||||||
\(941\) | 14141.9 | 0.489918 | 0.244959 | − | 0.969533i | \(-0.421225\pi\) | ||||
0.244959 | + | 0.969533i | \(0.421225\pi\) | |||||||
\(942\) | −5637.47 | −0.194988 | ||||||||
\(943\) | 8264.60 | 0.285400 | ||||||||
\(944\) | −6432.47 | −0.221779 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3720.21 | 0.127859 | ||||||||
\(947\) | 48138.7 | 1.65185 | 0.825923 | − | 0.563782i | \(-0.190654\pi\) | ||||
0.825923 | + | 0.563782i | \(0.190654\pi\) | |||||||
\(948\) | −24612.2 | −0.843215 | ||||||||
\(949\) | 23814.8 | 0.814607 | ||||||||
\(950\) | 12551.9 | 0.428670 | ||||||||
\(951\) | 15698.8 | 0.535298 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35613.3 | −1.21052 | −0.605262 | − | 0.796027i | \(-0.706932\pi\) | ||||
−0.605262 | + | 0.796027i | \(0.706932\pi\) | |||||||
\(954\) | −33781.3 | −1.14645 | ||||||||
\(955\) | 986.974 | 0.0334427 | ||||||||
\(956\) | 5158.38 | 0.174512 | ||||||||
\(957\) | 23923.0 | 0.808067 | ||||||||
\(958\) | −33031.3 | −1.11398 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3531.32 | 0.118722 | ||||||||
\(961\) | 25378.0 | 0.851869 | ||||||||
\(962\) | 16184.4 | 0.542419 | ||||||||
\(963\) | 15523.1 | 0.519445 | ||||||||
\(964\) | 2656.61 | 0.0887590 | ||||||||
\(965\) | −26008.7 | −0.867616 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19501.2 | −0.648518 | −0.324259 | − | 0.945968i | \(-0.605115\pi\) | ||||
−0.324259 | + | 0.945968i | \(0.605115\pi\) | |||||||
\(968\) | −14720.5 | −0.488776 | ||||||||
\(969\) | −73433.5 | −2.43449 | ||||||||
\(970\) | 15075.1 | 0.499003 | ||||||||
\(971\) | 8769.76 | 0.289840 | 0.144920 | − | 0.989443i | \(-0.453707\pi\) | ||||
0.144920 | + | 0.989443i | \(0.453707\pi\) | |||||||
\(972\) | −21289.3 | −0.702524 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18106.2 | −0.595646 | ||||||||
\(975\) | −32678.2 | −1.07338 | ||||||||
\(976\) | −3846.31 | −0.126145 | ||||||||
\(977\) | −4744.61 | −0.155367 | −0.0776835 | − | 0.996978i | \(-0.524752\pi\) | ||||
−0.0776835 | + | 0.996978i | \(0.524752\pi\) | |||||||
\(978\) | 35025.3 | 1.14518 | ||||||||
\(979\) | −69889.8 | −2.28160 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2816.88 | 0.0916779 | ||||||||
\(982\) | 14797.8 | 0.480871 | ||||||||
\(983\) | 55524.2 | 1.80157 | 0.900787 | − | 0.434262i | \(-0.142991\pi\) | ||||
0.900787 | + | 0.434262i | \(0.142991\pi\) | |||||||
\(984\) | −20999.1 | −0.680311 | ||||||||
\(985\) | −22481.4 | −0.727225 | ||||||||
\(986\) | 12658.8 | 0.408864 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24324.7 | 0.783271 | ||||||||
\(989\) | −759.736 | −0.0244269 | ||||||||
\(990\) | −22425.9 | −0.719942 | ||||||||
\(991\) | −16769.6 | −0.537543 | −0.268771 | − | 0.963204i | \(-0.586618\pi\) | ||||
−0.268771 | + | 0.963204i | \(0.586618\pi\) | |||||||
\(992\) | −7516.19 | −0.240564 | ||||||||
\(993\) | 5357.02 | 0.171198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6820.39 | 0.217307 | ||||||||
\(996\) | 40156.3 | 1.27751 | ||||||||
\(997\) | −14619.4 | −0.464394 | −0.232197 | − | 0.972669i | \(-0.574591\pi\) | ||||
−0.232197 | + | 0.972669i | \(0.574591\pi\) | |||||||
\(998\) | 1435.64 | 0.0455356 | ||||||||
\(999\) | 572.908 | 0.0181441 |
(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 | 2254.4.a.u.1.9 | 11 | ||
7.3 | odd | 6 | 322.4.e.d.93.9 | ✓ | 22 | ||
7.5 | odd | 6 | 322.4.e.d.277.9 | yes | 22 | ||
7.6 | odd | 2 | 2254.4.a.r.1.3 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.e.d.93.9 | ✓ | 22 | 7.3 | odd | 6 | ||
322.4.e.d.277.9 | yes | 22 | 7.5 | odd | 6 | ||
2254.4.a.r.1.3 | 11 | 7.6 | odd | 2 | |||
2254.4.a.u.1.9 | 11 | 1.1 | even | 1 | trivial |