Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 319x^{3} - 666x^{2} + 23460x + 101568 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-5.56964\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 10.3151 | 0.922612 | 0.461306 | − | 0.887241i | \(-0.347381\pi\) | ||||
0.461306 | + | 0.887241i | \(0.347381\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −20.6302 | −0.652386 | ||||||||
\(11\) | −26.5800 | −0.728562 | −0.364281 | − | 0.931289i | \(-0.618685\pi\) | ||||
−0.364281 | + | 0.931289i | \(0.618685\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 51.6261 | 1.10142 | 0.550712 | − | 0.834696i | \(-0.314356\pi\) | ||||
0.550712 | + | 0.834696i | \(0.314356\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | −30.9454 | −0.532671 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −11.0220 | −0.157249 | −0.0786245 | − | 0.996904i | \(-0.525053\pi\) | ||||
−0.0786245 | + | 0.996904i | \(0.525053\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −54.2997 | −0.655642 | −0.327821 | − | 0.944740i | \(-0.606314\pi\) | ||||
−0.327821 | + | 0.944740i | \(0.606314\pi\) | |||||||
\(20\) | 41.2605 | 0.461306 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 53.1601 | 0.515171 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | −18.5983 | −0.148786 | ||||||||
\(26\) | −103.252 | −0.778824 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −310.900 | −1.99078 | −0.995392 | − | 0.0958941i | \(-0.969429\pi\) | ||||
−0.995392 | + | 0.0958941i | \(0.969429\pi\) | |||||||
\(30\) | 61.8907 | 0.376655 | ||||||||
\(31\) | 146.903 | 0.851116 | 0.425558 | − | 0.904931i | \(-0.360078\pi\) | ||||
0.425558 | + | 0.904931i | \(0.360078\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 79.7401 | 0.420635 | ||||||||
\(34\) | 22.0441 | 0.111192 | ||||||||
\(35\) | 72.2058 | 0.348715 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −230.486 | −1.02410 | −0.512049 | − | 0.858956i | \(-0.671113\pi\) | ||||
−0.512049 | + | 0.858956i | \(0.671113\pi\) | |||||||
\(38\) | 108.599 | 0.463609 | ||||||||
\(39\) | −154.878 | −0.635907 | ||||||||
\(40\) | −82.5210 | −0.326193 | ||||||||
\(41\) | 102.366 | 0.389923 | 0.194961 | − | 0.980811i | \(-0.437542\pi\) | ||||
0.194961 | + | 0.980811i | \(0.437542\pi\) | |||||||
\(42\) | 42.0000 | 0.154303 | ||||||||
\(43\) | −224.105 | −0.794783 | −0.397391 | − | 0.917649i | \(-0.630084\pi\) | ||||
−0.397391 | + | 0.917649i | \(0.630084\pi\) | |||||||
\(44\) | −106.320 | −0.364281 | ||||||||
\(45\) | 92.8361 | 0.307537 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 197.357 | 0.612500 | 0.306250 | − | 0.951951i | \(-0.400926\pi\) | ||||
0.306250 | + | 0.951951i | \(0.400926\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 37.1965 | 0.105208 | ||||||||
\(51\) | 33.0661 | 0.0907878 | ||||||||
\(52\) | 206.504 | 0.550712 | ||||||||
\(53\) | −577.290 | −1.49617 | −0.748084 | − | 0.663604i | \(-0.769026\pi\) | ||||
−0.748084 | + | 0.663604i | \(0.769026\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | −274.176 | −0.672180 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 162.899 | 0.378535 | ||||||||
\(58\) | 621.800 | 1.40770 | ||||||||
\(59\) | 360.111 | 0.794618 | 0.397309 | − | 0.917685i | \(-0.369944\pi\) | ||||
0.397309 | + | 0.917685i | \(0.369944\pi\) | |||||||
\(60\) | −123.781 | −0.266335 | ||||||||
\(61\) | −24.5749 | −0.0515819 | −0.0257910 | − | 0.999667i | \(-0.508210\pi\) | ||||
−0.0257910 | + | 0.999667i | \(0.508210\pi\) | |||||||
\(62\) | −293.806 | −0.601830 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 532.529 | 1.01619 | ||||||||
\(66\) | −159.480 | −0.297434 | ||||||||
\(67\) | 69.1973 | 0.126176 | 0.0630880 | − | 0.998008i | \(-0.479905\pi\) | ||||
0.0630880 | + | 0.998008i | \(0.479905\pi\) | |||||||
\(68\) | −44.0881 | −0.0786245 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | −144.412 | −0.246579 | ||||||||
\(71\) | 213.781 | 0.357341 | 0.178670 | − | 0.983909i | \(-0.442820\pi\) | ||||
0.178670 | + | 0.983909i | \(0.442820\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −308.243 | −0.494207 | −0.247103 | − | 0.968989i | \(-0.579479\pi\) | ||||
−0.247103 | + | 0.968989i | \(0.579479\pi\) | |||||||
\(74\) | 460.971 | 0.724146 | ||||||||
\(75\) | 55.7948 | 0.0859017 | ||||||||
\(76\) | −217.199 | −0.327821 | ||||||||
\(77\) | −186.060 | −0.275371 | ||||||||
\(78\) | 309.757 | 0.449654 | ||||||||
\(79\) | 1189.81 | 1.69449 | 0.847244 | − | 0.531203i | \(-0.178260\pi\) | ||||
0.847244 | + | 0.531203i | \(0.178260\pi\) | |||||||
\(80\) | 165.042 | 0.230653 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −204.731 | −0.275717 | ||||||||
\(83\) | −134.809 | −0.178279 | −0.0891395 | − | 0.996019i | \(-0.528412\pi\) | ||||
−0.0891395 | + | 0.996019i | \(0.528412\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | −113.694 | −0.145080 | ||||||||
\(86\) | 448.209 | 0.561996 | ||||||||
\(87\) | 932.700 | 1.14938 | ||||||||
\(88\) | 212.640 | 0.257586 | ||||||||
\(89\) | 165.983 | 0.197687 | 0.0988436 | − | 0.995103i | \(-0.468486\pi\) | ||||
0.0988436 | + | 0.995103i | \(0.468486\pi\) | |||||||
\(90\) | −185.672 | −0.217462 | ||||||||
\(91\) | 361.383 | 0.416299 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −440.710 | −0.491392 | ||||||||
\(94\) | −394.714 | −0.433103 | ||||||||
\(95\) | −560.108 | −0.604903 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 431.667 | 0.451847 | 0.225923 | − | 0.974145i | \(-0.427460\pi\) | ||||
0.225923 | + | 0.974145i | \(0.427460\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | −239.220 | −0.242854 | ||||||||
\(100\) | −74.3931 | −0.0743931 | ||||||||
\(101\) | −1678.66 | −1.65379 | −0.826894 | − | 0.562358i | \(-0.809894\pi\) | ||||
−0.826894 | + | 0.562358i | \(0.809894\pi\) | |||||||
\(102\) | −66.1322 | −0.0641967 | ||||||||
\(103\) | 425.480 | 0.407027 | 0.203513 | − | 0.979072i | \(-0.434764\pi\) | ||||
0.203513 | + | 0.979072i | \(0.434764\pi\) | |||||||
\(104\) | −413.009 | −0.389412 | ||||||||
\(105\) | −216.618 | −0.201331 | ||||||||
\(106\) | 1154.58 | 1.05795 | ||||||||
\(107\) | 318.046 | 0.287352 | 0.143676 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143676 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −572.896 | −0.503427 | −0.251713 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251713 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(110\) | 548.353 | 0.475303 | ||||||||
\(111\) | 691.457 | 0.591263 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | −1079.47 | −0.898652 | −0.449326 | − | 0.893368i | \(-0.648336\pi\) | ||||
−0.449326 | + | 0.893368i | \(0.648336\pi\) | |||||||
\(114\) | −325.798 | −0.267665 | ||||||||
\(115\) | −237.248 | −0.192378 | ||||||||
\(116\) | −1243.60 | −0.995392 | ||||||||
\(117\) | 464.635 | 0.367141 | ||||||||
\(118\) | −720.222 | −0.561880 | ||||||||
\(119\) | −77.1542 | −0.0594346 | ||||||||
\(120\) | 247.563 | 0.188327 | ||||||||
\(121\) | −624.502 | −0.469197 | ||||||||
\(122\) | 49.1498 | 0.0364739 | ||||||||
\(123\) | −307.097 | −0.225122 | ||||||||
\(124\) | 587.613 | 0.425558 | ||||||||
\(125\) | −1481.23 | −1.05988 | ||||||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | −919.985 | −0.642799 | −0.321399 | − | 0.946944i | \(-0.604153\pi\) | ||||
−0.321399 | + | 0.946944i | \(0.604153\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 672.314 | 0.458868 | ||||||||
\(130\) | −1065.06 | −0.718553 | ||||||||
\(131\) | 2582.58 | 1.72245 | 0.861225 | − | 0.508223i | \(-0.169698\pi\) | ||||
0.861225 | + | 0.508223i | \(0.169698\pi\) | |||||||
\(132\) | 318.960 | 0.210318 | ||||||||
\(133\) | −380.098 | −0.247809 | ||||||||
\(134\) | −138.395 | −0.0892199 | ||||||||
\(135\) | −278.508 | −0.177557 | ||||||||
\(136\) | 88.1762 | 0.0555959 | ||||||||
\(137\) | −789.026 | −0.492052 | −0.246026 | − | 0.969263i | \(-0.579125\pi\) | ||||
−0.246026 | + | 0.969263i | \(0.579125\pi\) | |||||||
\(138\) | −138.000 | −0.0851257 | ||||||||
\(139\) | −1504.62 | −0.918133 | −0.459067 | − | 0.888402i | \(-0.651816\pi\) | ||||
−0.459067 | + | 0.888402i | \(0.651816\pi\) | |||||||
\(140\) | 288.823 | 0.174357 | ||||||||
\(141\) | −592.071 | −0.353627 | ||||||||
\(142\) | −427.563 | −0.252678 | ||||||||
\(143\) | −1372.22 | −0.802455 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −3206.97 | −1.83672 | ||||||||
\(146\) | 616.486 | 0.349457 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | −921.943 | −0.512049 | ||||||||
\(149\) | −2635.88 | −1.44926 | −0.724630 | − | 0.689138i | \(-0.757989\pi\) | ||||
−0.724630 | + | 0.689138i | \(0.757989\pi\) | |||||||
\(150\) | −111.590 | −0.0607417 | ||||||||
\(151\) | 116.042 | 0.0625388 | 0.0312694 | − | 0.999511i | \(-0.490045\pi\) | ||||
0.0312694 | + | 0.999511i | \(0.490045\pi\) | |||||||
\(152\) | 434.397 | 0.231804 | ||||||||
\(153\) | −99.1982 | −0.0524164 | ||||||||
\(154\) | 372.120 | 0.194716 | ||||||||
\(155\) | 1515.32 | 0.785250 | ||||||||
\(156\) | −619.513 | −0.317953 | ||||||||
\(157\) | 805.667 | 0.409549 | 0.204775 | − | 0.978809i | \(-0.434354\pi\) | ||||
0.204775 | + | 0.978809i | \(0.434354\pi\) | |||||||
\(158\) | −2379.63 | −1.19818 | ||||||||
\(159\) | 1731.87 | 0.863813 | ||||||||
\(160\) | −330.084 | −0.163096 | ||||||||
\(161\) | −161.000 | −0.0788110 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −2814.39 | −1.35239 | −0.676196 | − | 0.736722i | \(-0.736373\pi\) | ||||
−0.676196 | + | 0.736722i | \(0.736373\pi\) | |||||||
\(164\) | 409.463 | 0.194961 | ||||||||
\(165\) | 822.529 | 0.388084 | ||||||||
\(166\) | 269.617 | 0.126062 | ||||||||
\(167\) | −1809.34 | −0.838390 | −0.419195 | − | 0.907896i | \(-0.637688\pi\) | ||||
−0.419195 | + | 0.907896i | \(0.637688\pi\) | |||||||
\(168\) | 168.000 | 0.0771517 | ||||||||
\(169\) | 468.253 | 0.213133 | ||||||||
\(170\) | 227.387 | 0.102587 | ||||||||
\(171\) | −488.697 | −0.218547 | ||||||||
\(172\) | −896.419 | −0.397391 | ||||||||
\(173\) | −3254.97 | −1.43047 | −0.715233 | − | 0.698886i | \(-0.753680\pi\) | ||||
−0.715233 | + | 0.698886i | \(0.753680\pi\) | |||||||
\(174\) | −1865.40 | −0.812734 | ||||||||
\(175\) | −130.188 | −0.0562359 | ||||||||
\(176\) | −425.281 | −0.182140 | ||||||||
\(177\) | −1080.33 | −0.458773 | ||||||||
\(178\) | −331.966 | −0.139786 | ||||||||
\(179\) | −3954.36 | −1.65119 | −0.825593 | − | 0.564266i | \(-0.809159\pi\) | ||||
−0.825593 | + | 0.564266i | \(0.809159\pi\) | |||||||
\(180\) | 371.344 | 0.153769 | ||||||||
\(181\) | −2310.90 | −0.948995 | −0.474498 | − | 0.880257i | \(-0.657370\pi\) | ||||
−0.474498 | + | 0.880257i | \(0.657370\pi\) | |||||||
\(182\) | −722.765 | −0.294368 | ||||||||
\(183\) | 73.7248 | 0.0297808 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −2377.49 | −0.944845 | ||||||||
\(186\) | 881.419 | 0.347467 | ||||||||
\(187\) | 292.966 | 0.114566 | ||||||||
\(188\) | 789.428 | 0.306250 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 1120.22 | 0.427731 | ||||||||
\(191\) | −2662.01 | −1.00846 | −0.504232 | − | 0.863569i | \(-0.668224\pi\) | ||||
−0.504232 | + | 0.863569i | \(0.668224\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 2792.16 | 1.04137 | 0.520685 | − | 0.853749i | \(-0.325677\pi\) | ||||
0.520685 | + | 0.853749i | \(0.325677\pi\) | |||||||
\(194\) | −863.333 | −0.319504 | ||||||||
\(195\) | −1597.59 | −0.586696 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 917.766 | 0.331919 | 0.165960 | − | 0.986133i | \(-0.446928\pi\) | ||||
0.165960 | + | 0.986133i | \(0.446928\pi\) | |||||||
\(198\) | 478.441 | 0.171724 | ||||||||
\(199\) | 4426.36 | 1.57677 | 0.788383 | − | 0.615184i | \(-0.210918\pi\) | ||||
0.788383 | + | 0.615184i | \(0.210918\pi\) | |||||||
\(200\) | 148.786 | 0.0526039 | ||||||||
\(201\) | −207.592 | −0.0728478 | ||||||||
\(202\) | 3357.31 | 1.16940 | ||||||||
\(203\) | −2176.30 | −0.752445 | ||||||||
\(204\) | 132.264 | 0.0453939 | ||||||||
\(205\) | 1055.91 | 0.359748 | ||||||||
\(206\) | −850.960 | −0.287812 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 826.017 | 0.275356 | ||||||||
\(209\) | 1443.29 | 0.477676 | ||||||||
\(210\) | 433.235 | 0.142362 | ||||||||
\(211\) | 3054.43 | 0.996566 | 0.498283 | − | 0.867014i | \(-0.333964\pi\) | ||||
0.498283 | + | 0.867014i | \(0.333964\pi\) | |||||||
\(212\) | −2309.16 | −0.748084 | ||||||||
\(213\) | −641.344 | −0.206311 | ||||||||
\(214\) | −636.091 | −0.203188 | ||||||||
\(215\) | −2311.67 | −0.733276 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 1028.32 | 0.321692 | ||||||||
\(218\) | 1145.79 | 0.355976 | ||||||||
\(219\) | 924.729 | 0.285330 | ||||||||
\(220\) | −1096.71 | −0.336090 | ||||||||
\(221\) | −569.024 | −0.173198 | ||||||||
\(222\) | −1382.91 | −0.418086 | ||||||||
\(223\) | 273.354 | 0.0820858 | 0.0410429 | − | 0.999157i | \(-0.486932\pi\) | ||||
0.0410429 | + | 0.999157i | \(0.486932\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | −167.384 | −0.0495954 | ||||||||
\(226\) | 2158.93 | 0.635443 | ||||||||
\(227\) | −2755.54 | −0.805690 | −0.402845 | − | 0.915268i | \(-0.631979\pi\) | ||||
−0.402845 | + | 0.915268i | \(0.631979\pi\) | |||||||
\(228\) | 651.596 | 0.189268 | ||||||||
\(229\) | 5096.83 | 1.47078 | 0.735388 | − | 0.677646i | \(-0.237000\pi\) | ||||
0.735388 | + | 0.677646i | \(0.237000\pi\) | |||||||
\(230\) | 474.496 | 0.136032 | ||||||||
\(231\) | 558.181 | 0.158985 | ||||||||
\(232\) | 2487.20 | 0.703848 | ||||||||
\(233\) | −1776.82 | −0.499585 | −0.249793 | − | 0.968299i | \(-0.580362\pi\) | ||||
−0.249793 | + | 0.968299i | \(0.580362\pi\) | |||||||
\(234\) | −929.270 | −0.259608 | ||||||||
\(235\) | 2035.76 | 0.565100 | ||||||||
\(236\) | 1440.44 | 0.397309 | ||||||||
\(237\) | −3569.44 | −0.978314 | ||||||||
\(238\) | 154.308 | 0.0420266 | ||||||||
\(239\) | −3910.70 | −1.05842 | −0.529209 | − | 0.848491i | \(-0.677511\pi\) | ||||
−0.529209 | + | 0.848491i | \(0.677511\pi\) | |||||||
\(240\) | −495.126 | −0.133168 | ||||||||
\(241\) | −3272.18 | −0.874604 | −0.437302 | − | 0.899315i | \(-0.644066\pi\) | ||||
−0.437302 | + | 0.899315i | \(0.644066\pi\) | |||||||
\(242\) | 1249.00 | 0.331773 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −98.2997 | −0.0257910 | ||||||||
\(245\) | 505.441 | 0.131802 | ||||||||
\(246\) | 614.194 | 0.159185 | ||||||||
\(247\) | −2803.28 | −0.722139 | ||||||||
\(248\) | −1175.23 | −0.300915 | ||||||||
\(249\) | 404.426 | 0.102929 | ||||||||
\(250\) | 2962.47 | 0.749452 | ||||||||
\(251\) | −3253.33 | −0.818121 | −0.409060 | − | 0.912507i | \(-0.634143\pi\) | ||||
−0.409060 | + | 0.912507i | \(0.634143\pi\) | |||||||
\(252\) | 252.000 | 0.0629941 | ||||||||
\(253\) | 611.341 | 0.151916 | ||||||||
\(254\) | 1839.97 | 0.454527 | ||||||||
\(255\) | 341.081 | 0.0837620 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1620.58 | −0.393343 | −0.196672 | − | 0.980469i | \(-0.563013\pi\) | ||||
−0.196672 | + | 0.980469i | \(0.563013\pi\) | |||||||
\(258\) | −1344.63 | −0.324469 | ||||||||
\(259\) | −1613.40 | −0.387073 | ||||||||
\(260\) | 2130.12 | 0.508093 | ||||||||
\(261\) | −2798.10 | −0.663594 | ||||||||
\(262\) | −5165.16 | −1.21796 | ||||||||
\(263\) | −2398.45 | −0.562338 | −0.281169 | − | 0.959658i | \(-0.590722\pi\) | ||||
−0.281169 | + | 0.959658i | \(0.590722\pi\) | |||||||
\(264\) | −637.921 | −0.148717 | ||||||||
\(265\) | −5954.82 | −1.38038 | ||||||||
\(266\) | 760.195 | 0.175228 | ||||||||
\(267\) | −497.949 | −0.114135 | ||||||||
\(268\) | 276.789 | 0.0630880 | ||||||||
\(269\) | 4740.44 | 1.07446 | 0.537230 | − | 0.843436i | \(-0.319471\pi\) | ||||
0.537230 | + | 0.843436i | \(0.319471\pi\) | |||||||
\(270\) | 557.017 | 0.125552 | ||||||||
\(271\) | −1727.50 | −0.387225 | −0.193612 | − | 0.981078i | \(-0.562020\pi\) | ||||
−0.193612 | + | 0.981078i | \(0.562020\pi\) | |||||||
\(272\) | −176.352 | −0.0393123 | ||||||||
\(273\) | −1084.15 | −0.240350 | ||||||||
\(274\) | 1578.05 | 0.347933 | ||||||||
\(275\) | 494.343 | 0.108400 | ||||||||
\(276\) | 276.000 | 0.0601929 | ||||||||
\(277\) | 4704.28 | 1.02041 | 0.510203 | − | 0.860054i | \(-0.329570\pi\) | ||||
0.510203 | + | 0.860054i | \(0.329570\pi\) | |||||||
\(278\) | 3009.25 | 0.649218 | ||||||||
\(279\) | 1322.13 | 0.283705 | ||||||||
\(280\) | −577.647 | −0.123289 | ||||||||
\(281\) | −5942.74 | −1.26162 | −0.630808 | − | 0.775939i | \(-0.717276\pi\) | ||||
−0.630808 | + | 0.775939i | \(0.717276\pi\) | |||||||
\(282\) | 1184.14 | 0.250052 | ||||||||
\(283\) | 4459.36 | 0.936684 | 0.468342 | − | 0.883547i | \(-0.344851\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344851\pi\) | |||||||
\(284\) | 855.126 | 0.178670 | ||||||||
\(285\) | 1680.32 | 0.349241 | ||||||||
\(286\) | 2744.45 | 0.567421 | ||||||||
\(287\) | 716.560 | 0.147377 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −4791.51 | −0.975273 | ||||||||
\(290\) | 6413.95 | 1.29876 | ||||||||
\(291\) | −1295.00 | −0.260874 | ||||||||
\(292\) | −1232.97 | −0.247103 | ||||||||
\(293\) | 4888.30 | 0.974668 | 0.487334 | − | 0.873216i | \(-0.337969\pi\) | ||||
0.487334 | + | 0.873216i | \(0.337969\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | 3714.59 | 0.733124 | ||||||||
\(296\) | 1843.89 | 0.362073 | ||||||||
\(297\) | 717.661 | 0.140212 | ||||||||
\(298\) | 5271.76 | 1.02478 | ||||||||
\(299\) | −1187.40 | −0.229663 | ||||||||
\(300\) | 223.179 | 0.0429509 | ||||||||
\(301\) | −1568.73 | −0.300400 | ||||||||
\(302\) | −232.084 | −0.0442216 | ||||||||
\(303\) | 5035.97 | 0.954815 | ||||||||
\(304\) | −868.794 | −0.163910 | ||||||||
\(305\) | −253.493 | −0.0475901 | ||||||||
\(306\) | 198.396 | 0.0370640 | ||||||||
\(307\) | −6956.41 | −1.29324 | −0.646618 | − | 0.762814i | \(-0.723817\pi\) | ||||
−0.646618 | + | 0.762814i | \(0.723817\pi\) | |||||||
\(308\) | −744.241 | −0.137685 | ||||||||
\(309\) | −1276.44 | −0.234997 | ||||||||
\(310\) | −3030.65 | −0.555256 | ||||||||
\(311\) | −444.468 | −0.0810400 | −0.0405200 | − | 0.999179i | \(-0.512901\pi\) | ||||
−0.0405200 | + | 0.999179i | \(0.512901\pi\) | |||||||
\(312\) | 1239.03 | 0.224827 | ||||||||
\(313\) | 8317.74 | 1.50207 | 0.751033 | − | 0.660265i | \(-0.229556\pi\) | ||||
0.751033 | + | 0.660265i | \(0.229556\pi\) | |||||||
\(314\) | −1611.33 | −0.289595 | ||||||||
\(315\) | 649.853 | 0.116238 | ||||||||
\(316\) | 4759.26 | 0.847244 | ||||||||
\(317\) | −2514.32 | −0.445484 | −0.222742 | − | 0.974877i | \(-0.571501\pi\) | ||||
−0.222742 | + | 0.974877i | \(0.571501\pi\) | |||||||
\(318\) | −3463.74 | −0.610808 | ||||||||
\(319\) | 8263.74 | 1.45041 | ||||||||
\(320\) | 660.168 | 0.115327 | ||||||||
\(321\) | −954.137 | −0.165903 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | 598.492 | 0.103099 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −960.156 | −0.163877 | ||||||||
\(326\) | 5628.77 | 0.956285 | ||||||||
\(327\) | 1718.69 | 0.290653 | ||||||||
\(328\) | −818.926 | −0.137859 | ||||||||
\(329\) | 1381.50 | 0.231503 | ||||||||
\(330\) | −1645.06 | −0.274416 | ||||||||
\(331\) | −4260.51 | −0.707489 | −0.353745 | − | 0.935342i | \(-0.615092\pi\) | ||||
−0.353745 | + | 0.935342i | \(0.615092\pi\) | |||||||
\(332\) | −539.234 | −0.0891395 | ||||||||
\(333\) | −2074.37 | −0.341366 | ||||||||
\(334\) | 3618.68 | 0.592831 | ||||||||
\(335\) | 713.778 | 0.116412 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | 8554.60 | 1.38278 | 0.691392 | − | 0.722479i | \(-0.256998\pi\) | ||||
0.691392 | + | 0.722479i | \(0.256998\pi\) | |||||||
\(338\) | −936.507 | −0.150708 | ||||||||
\(339\) | 3238.40 | 0.518837 | ||||||||
\(340\) | −454.774 | −0.0725400 | ||||||||
\(341\) | −3904.69 | −0.620091 | ||||||||
\(342\) | 977.394 | 0.154536 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 1792.84 | 0.280998 | ||||||||
\(345\) | 711.743 | 0.111069 | ||||||||
\(346\) | 6509.94 | 1.01149 | ||||||||
\(347\) | −816.289 | −0.126284 | −0.0631422 | − | 0.998005i | \(-0.520112\pi\) | ||||
−0.0631422 | + | 0.998005i | \(0.520112\pi\) | |||||||
\(348\) | 3730.80 | 0.574690 | ||||||||
\(349\) | −10412.7 | −1.59708 | −0.798538 | − | 0.601945i | \(-0.794393\pi\) | ||||
−0.798538 | + | 0.601945i | \(0.794393\pi\) | |||||||
\(350\) | 260.376 | 0.0397648 | ||||||||
\(351\) | −1393.90 | −0.211969 | ||||||||
\(352\) | 850.561 | 0.128793 | ||||||||
\(353\) | −1557.29 | −0.234805 | −0.117402 | − | 0.993084i | \(-0.537457\pi\) | ||||
−0.117402 | + | 0.993084i | \(0.537457\pi\) | |||||||
\(354\) | 2160.67 | 0.324401 | ||||||||
\(355\) | 2205.18 | 0.329687 | ||||||||
\(356\) | 663.932 | 0.0988436 | ||||||||
\(357\) | 231.463 | 0.0343146 | ||||||||
\(358\) | 7908.71 | 1.16757 | ||||||||
\(359\) | 1154.91 | 0.169788 | 0.0848938 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848938 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(360\) | −742.689 | −0.108731 | ||||||||
\(361\) | −3910.55 | −0.570134 | ||||||||
\(362\) | 4621.81 | 0.671041 | ||||||||
\(363\) | 1873.51 | 0.270891 | ||||||||
\(364\) | 1445.53 | 0.208149 | ||||||||
\(365\) | −3179.56 | −0.455961 | ||||||||
\(366\) | −147.450 | −0.0210582 | ||||||||
\(367\) | 6373.30 | 0.906495 | 0.453248 | − | 0.891385i | \(-0.350265\pi\) | ||||
0.453248 | + | 0.891385i | \(0.350265\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 921.291 | 0.129974 | ||||||||
\(370\) | 4754.98 | 0.668107 | ||||||||
\(371\) | −4041.03 | −0.565498 | ||||||||
\(372\) | −1762.84 | −0.245696 | ||||||||
\(373\) | 8965.73 | 1.24458 | 0.622289 | − | 0.782787i | \(-0.286203\pi\) | ||||
0.622289 | + | 0.782787i | \(0.286203\pi\) | |||||||
\(374\) | −585.932 | −0.0810102 | ||||||||
\(375\) | 4443.70 | 0.611925 | ||||||||
\(376\) | −1578.86 | −0.216551 | ||||||||
\(377\) | −16050.6 | −2.19269 | ||||||||
\(378\) | 378.000 | 0.0514344 | ||||||||
\(379\) | −5837.30 | −0.791139 | −0.395570 | − | 0.918436i | \(-0.629453\pi\) | ||||
−0.395570 | + | 0.918436i | \(0.629453\pi\) | |||||||
\(380\) | −2240.43 | −0.302452 | ||||||||
\(381\) | 2759.95 | 0.371120 | ||||||||
\(382\) | 5324.02 | 0.713091 | ||||||||
\(383\) | 11044.4 | 1.47348 | 0.736741 | − | 0.676175i | \(-0.236364\pi\) | ||||
0.736741 | + | 0.676175i | \(0.236364\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −1919.23 | −0.254060 | ||||||||
\(386\) | −5584.32 | −0.736359 | ||||||||
\(387\) | −2016.94 | −0.264928 | ||||||||
\(388\) | 1726.67 | 0.225923 | ||||||||
\(389\) | 3495.53 | 0.455605 | 0.227803 | − | 0.973707i | \(-0.426846\pi\) | ||||
0.227803 | + | 0.973707i | \(0.426846\pi\) | |||||||
\(390\) | 3195.18 | 0.414857 | ||||||||
\(391\) | 253.507 | 0.0327887 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | −7747.74 | −0.994457 | ||||||||
\(394\) | −1835.53 | −0.234703 | ||||||||
\(395\) | 12273.1 | 1.56336 | ||||||||
\(396\) | −956.881 | −0.121427 | ||||||||
\(397\) | 603.402 | 0.0762818 | 0.0381409 | − | 0.999272i | \(-0.487856\pi\) | ||||
0.0381409 | + | 0.999272i | \(0.487856\pi\) | |||||||
\(398\) | −8852.73 | −1.11494 | ||||||||
\(399\) | 1140.29 | 0.143073 | ||||||||
\(400\) | −297.572 | −0.0371965 | ||||||||
\(401\) | 7929.97 | 0.987541 | 0.493771 | − | 0.869592i | \(-0.335618\pi\) | ||||
0.493771 | + | 0.869592i | \(0.335618\pi\) | |||||||
\(402\) | 415.184 | 0.0515111 | ||||||||
\(403\) | 7584.04 | 0.937439 | ||||||||
\(404\) | −6714.63 | −0.826894 | ||||||||
\(405\) | 835.525 | 0.102512 | ||||||||
\(406\) | 4352.60 | 0.532059 | ||||||||
\(407\) | 6126.32 | 0.746119 | ||||||||
\(408\) | −264.529 | −0.0320983 | ||||||||
\(409\) | −11257.3 | −1.36098 | −0.680488 | − | 0.732760i | \(-0.738232\pi\) | ||||
−0.680488 | + | 0.732760i | \(0.738232\pi\) | |||||||
\(410\) | −2111.83 | −0.254380 | ||||||||
\(411\) | 2367.08 | 0.284086 | ||||||||
\(412\) | 1701.92 | 0.203513 | ||||||||
\(413\) | 2520.78 | 0.300337 | ||||||||
\(414\) | 414.000 | 0.0491473 | ||||||||
\(415\) | −1390.57 | −0.164482 | ||||||||
\(416\) | −1652.03 | −0.194706 | ||||||||
\(417\) | 4513.87 | 0.530084 | ||||||||
\(418\) | −2886.57 | −0.337768 | ||||||||
\(419\) | −5241.74 | −0.611159 | −0.305579 | − | 0.952167i | \(-0.598850\pi\) | ||||
−0.305579 | + | 0.952167i | \(0.598850\pi\) | |||||||
\(420\) | −866.470 | −0.100665 | ||||||||
\(421\) | 8393.67 | 0.971693 | 0.485846 | − | 0.874044i | \(-0.338511\pi\) | ||||
0.485846 | + | 0.874044i | \(0.338511\pi\) | |||||||
\(422\) | −6108.85 | −0.704679 | ||||||||
\(423\) | 1776.21 | 0.204167 | ||||||||
\(424\) | 4618.32 | 0.528975 | ||||||||
\(425\) | 204.991 | 0.0233965 | ||||||||
\(426\) | 1282.69 | 0.145884 | ||||||||
\(427\) | −172.024 | −0.0194961 | ||||||||
\(428\) | 1272.18 | 0.143676 | ||||||||
\(429\) | 4116.67 | 0.463298 | ||||||||
\(430\) | 4623.33 | 0.518505 | ||||||||
\(431\) | −14267.2 | −1.59450 | −0.797249 | − | 0.603651i | \(-0.793712\pi\) | ||||
−0.797249 | + | 0.603651i | \(0.793712\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −5685.40 | −0.630999 | −0.315500 | − | 0.948926i | \(-0.602172\pi\) | ||||
−0.315500 | + | 0.948926i | \(0.602172\pi\) | |||||||
\(434\) | −2056.64 | −0.227470 | ||||||||
\(435\) | 9620.92 | 1.06043 | ||||||||
\(436\) | −2291.58 | −0.251713 | ||||||||
\(437\) | 1248.89 | 0.136711 | ||||||||
\(438\) | −1849.46 | −0.201759 | ||||||||
\(439\) | 5253.99 | 0.571206 | 0.285603 | − | 0.958348i | \(-0.407806\pi\) | ||||
0.285603 | + | 0.958348i | \(0.407806\pi\) | |||||||
\(440\) | 2193.41 | 0.237652 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 1138.05 | 0.122469 | ||||||||
\(443\) | 11033.4 | 1.18333 | 0.591664 | − | 0.806184i | \(-0.298471\pi\) | ||||
0.591664 | + | 0.806184i | \(0.298471\pi\) | |||||||
\(444\) | 2765.83 | 0.295632 | ||||||||
\(445\) | 1712.14 | 0.182389 | ||||||||
\(446\) | −546.708 | −0.0580435 | ||||||||
\(447\) | 7907.64 | 0.836731 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | −14836.1 | −1.55937 | −0.779685 | − | 0.626171i | \(-0.784621\pi\) | ||||
−0.779685 | + | 0.626171i | \(0.784621\pi\) | |||||||
\(450\) | 334.769 | 0.0350692 | ||||||||
\(451\) | −2720.88 | −0.284083 | ||||||||
\(452\) | −4317.87 | −0.449326 | ||||||||
\(453\) | −348.126 | −0.0361068 | ||||||||
\(454\) | 5511.08 | 0.569709 | ||||||||
\(455\) | 3727.71 | 0.384083 | ||||||||
\(456\) | −1303.19 | −0.133832 | ||||||||
\(457\) | −9660.95 | −0.988884 | −0.494442 | − | 0.869211i | \(-0.664628\pi\) | ||||
−0.494442 | + | 0.869211i | \(0.664628\pi\) | |||||||
\(458\) | −10193.7 | −1.04000 | ||||||||
\(459\) | 297.595 | 0.0302626 | ||||||||
\(460\) | −948.991 | −0.0961890 | ||||||||
\(461\) | 11397.9 | 1.15153 | 0.575765 | − | 0.817615i | \(-0.304704\pi\) | ||||
0.575765 | + | 0.817615i | \(0.304704\pi\) | |||||||
\(462\) | −1116.36 | −0.112420 | ||||||||
\(463\) | −85.1822 | −0.00855022 | −0.00427511 | − | 0.999991i | \(-0.501361\pi\) | ||||
−0.00427511 | + | 0.999991i | \(0.501361\pi\) | |||||||
\(464\) | −4974.40 | −0.497696 | ||||||||
\(465\) | −4545.97 | −0.453364 | ||||||||
\(466\) | 3553.64 | 0.353260 | ||||||||
\(467\) | 5205.23 | 0.515780 | 0.257890 | − | 0.966174i | \(-0.416973\pi\) | ||||
0.257890 | + | 0.966174i | \(0.416973\pi\) | |||||||
\(468\) | 1858.54 | 0.183571 | ||||||||
\(469\) | 484.381 | 0.0476901 | ||||||||
\(470\) | −4071.52 | −0.399586 | ||||||||
\(471\) | −2417.00 | −0.236453 | ||||||||
\(472\) | −2880.89 | −0.280940 | ||||||||
\(473\) | 5956.71 | 0.579048 | ||||||||
\(474\) | 7138.89 | 0.691772 | ||||||||
\(475\) | 1009.88 | 0.0975505 | ||||||||
\(476\) | −308.617 | −0.0297173 | ||||||||
\(477\) | −5195.61 | −0.498723 | ||||||||
\(478\) | 7821.40 | 0.748415 | ||||||||
\(479\) | −2379.83 | −0.227009 | −0.113504 | − | 0.993537i | \(-0.536208\pi\) | ||||
−0.113504 | + | 0.993537i | \(0.536208\pi\) | |||||||
\(480\) | 990.252 | 0.0941637 | ||||||||
\(481\) | −11899.1 | −1.12796 | ||||||||
\(482\) | 6544.36 | 0.618439 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | −2498.01 | −0.234599 | ||||||||
\(485\) | 4452.69 | 0.416879 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −17.3278 | −0.00161231 | −0.000806157 | − | 1.00000i | \(-0.500257\pi\) | ||||
−0.000806157 | 1.00000i | \(0.500257\pi\) | ||||||||
\(488\) | 196.599 | 0.0182370 | ||||||||
\(489\) | 8443.16 | 0.780804 | ||||||||
\(490\) | −1010.88 | −0.0931979 | ||||||||
\(491\) | 5073.91 | 0.466359 | 0.233179 | − | 0.972434i | \(-0.425087\pi\) | ||||
0.233179 | + | 0.972434i | \(0.425087\pi\) | |||||||
\(492\) | −1228.39 | −0.112561 | ||||||||
\(493\) | 3426.75 | 0.313049 | ||||||||
\(494\) | 5606.56 | 0.510629 | ||||||||
\(495\) | −2467.59 | −0.224060 | ||||||||
\(496\) | 2350.45 | 0.212779 | ||||||||
\(497\) | 1496.47 | 0.135062 | ||||||||
\(498\) | −808.851 | −0.0727821 | ||||||||
\(499\) | 2523.93 | 0.226426 | 0.113213 | − | 0.993571i | \(-0.463886\pi\) | ||||
0.113213 | + | 0.993571i | \(0.463886\pi\) | |||||||
\(500\) | −5924.93 | −0.529942 | ||||||||
\(501\) | 5428.03 | 0.484045 | ||||||||
\(502\) | 6506.66 | 0.578499 | ||||||||
\(503\) | −17881.7 | −1.58510 | −0.792548 | − | 0.609809i | \(-0.791246\pi\) | ||||
−0.792548 | + | 0.609809i | \(0.791246\pi\) | |||||||
\(504\) | −504.000 | −0.0445435 | ||||||||
\(505\) | −17315.5 | −1.52581 | ||||||||
\(506\) | −1222.68 | −0.107421 | ||||||||
\(507\) | −1404.76 | −0.123052 | ||||||||
\(508\) | −3679.94 | −0.321399 | ||||||||
\(509\) | −14906.1 | −1.29804 | −0.649019 | − | 0.760772i | \(-0.724821\pi\) | ||||
−0.649019 | + | 0.760772i | \(0.724821\pi\) | |||||||
\(510\) | −682.161 | −0.0592286 | ||||||||
\(511\) | −2157.70 | −0.186793 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 1466.09 | 0.126178 | ||||||||
\(514\) | 3241.17 | 0.278136 | ||||||||
\(515\) | 4388.88 | 0.375528 | ||||||||
\(516\) | 2689.26 | 0.229434 | ||||||||
\(517\) | −5245.76 | −0.446244 | ||||||||
\(518\) | 3226.80 | 0.273702 | ||||||||
\(519\) | 9764.91 | 0.825880 | ||||||||
\(520\) | −4260.24 | −0.359276 | ||||||||
\(521\) | 13724.6 | 1.15410 | 0.577049 | − | 0.816710i | \(-0.304204\pi\) | ||||
0.577049 | + | 0.816710i | \(0.304204\pi\) | |||||||
\(522\) | 5596.20 | 0.469232 | ||||||||
\(523\) | −261.061 | −0.0218268 | −0.0109134 | − | 0.999940i | \(-0.503474\pi\) | ||||
−0.0109134 | + | 0.999940i | \(0.503474\pi\) | |||||||
\(524\) | 10330.3 | 0.861225 | ||||||||
\(525\) | 390.564 | 0.0324678 | ||||||||
\(526\) | 4796.91 | 0.397633 | ||||||||
\(527\) | −1619.17 | −0.133837 | ||||||||
\(528\) | 1275.84 | 0.105159 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 11909.6 | 0.976078 | ||||||||
\(531\) | 3241.00 | 0.264873 | ||||||||
\(532\) | −1520.39 | −0.123905 | ||||||||
\(533\) | 5284.74 | 0.429470 | ||||||||
\(534\) | 995.898 | 0.0807055 | ||||||||
\(535\) | 3280.68 | 0.265114 | ||||||||
\(536\) | −553.578 | −0.0446100 | ||||||||
\(537\) | 11863.1 | 0.953313 | ||||||||
\(538\) | −9480.88 | −0.759758 | ||||||||
\(539\) | −1302.42 | −0.104080 | ||||||||
\(540\) | −1114.03 | −0.0887784 | ||||||||
\(541\) | 8406.10 | 0.668034 | 0.334017 | − | 0.942567i | \(-0.391596\pi\) | ||||
0.334017 | + | 0.942567i | \(0.391596\pi\) | |||||||
\(542\) | 3454.99 | 0.273809 | ||||||||
\(543\) | 6932.71 | 0.547903 | ||||||||
\(544\) | 352.705 | 0.0277980 | ||||||||
\(545\) | −5909.49 | −0.464468 | ||||||||
\(546\) | 2168.30 | 0.169953 | ||||||||
\(547\) | 12280.1 | 0.959888 | 0.479944 | − | 0.877299i | \(-0.340657\pi\) | ||||
0.479944 | + | 0.877299i | \(0.340657\pi\) | |||||||
\(548\) | −3156.11 | −0.246026 | ||||||||
\(549\) | −221.174 | −0.0171940 | ||||||||
\(550\) | −988.685 | −0.0766503 | ||||||||
\(551\) | 16881.8 | 1.30524 | ||||||||
\(552\) | −552.000 | −0.0425628 | ||||||||
\(553\) | 8328.70 | 0.640457 | ||||||||
\(554\) | −9408.55 | −0.721536 | ||||||||
\(555\) | 7132.46 | 0.545507 | ||||||||
\(556\) | −6018.50 | −0.459067 | ||||||||
\(557\) | 6430.03 | 0.489137 | 0.244569 | − | 0.969632i | \(-0.421354\pi\) | ||||
0.244569 | + | 0.969632i | \(0.421354\pi\) | |||||||
\(558\) | −2644.26 | −0.200610 | ||||||||
\(559\) | −11569.7 | −0.875392 | ||||||||
\(560\) | 1155.29 | 0.0871787 | ||||||||
\(561\) | −878.898 | −0.0661445 | ||||||||
\(562\) | 11885.5 | 0.892097 | ||||||||
\(563\) | −6302.21 | −0.471770 | −0.235885 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235885 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(564\) | −2368.28 | −0.176813 | ||||||||
\(565\) | −11134.8 | −0.829108 | ||||||||
\(566\) | −8918.73 | −0.662336 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −1710.25 | −0.126339 | ||||||||
\(569\) | 2751.75 | 0.202740 | 0.101370 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101370 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(570\) | −3360.65 | −0.246951 | ||||||||
\(571\) | 15093.6 | 1.10621 | 0.553105 | − | 0.833112i | \(-0.313443\pi\) | ||||
0.553105 | + | 0.833112i | \(0.313443\pi\) | |||||||
\(572\) | −5488.89 | −0.401228 | ||||||||
\(573\) | 7986.04 | 0.582236 | ||||||||
\(574\) | −1433.12 | −0.104211 | ||||||||
\(575\) | 427.760 | 0.0310241 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 20704.9 | 1.49386 | 0.746928 | − | 0.664904i | \(-0.231528\pi\) | ||||
0.746928 | + | 0.664904i | \(0.231528\pi\) | |||||||
\(578\) | 9583.03 | 0.689622 | ||||||||
\(579\) | −8376.49 | −0.601235 | ||||||||
\(580\) | −12827.9 | −0.918361 | ||||||||
\(581\) | −943.660 | −0.0673831 | ||||||||
\(582\) | 2590.00 | 0.184466 | ||||||||
\(583\) | 15344.4 | 1.09005 | ||||||||
\(584\) | 2465.94 | 0.174729 | ||||||||
\(585\) | 4792.76 | 0.338729 | ||||||||
\(586\) | −9776.61 | −0.689194 | ||||||||
\(587\) | −18630.0 | −1.30995 | −0.654976 | − | 0.755650i | \(-0.727321\pi\) | ||||
−0.654976 | + | 0.755650i | \(0.727321\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | −7976.79 | −0.558027 | ||||||||
\(590\) | −7429.17 | −0.518397 | ||||||||
\(591\) | −2753.30 | −0.191634 | ||||||||
\(592\) | −3687.77 | −0.256024 | ||||||||
\(593\) | 9724.26 | 0.673402 | 0.336701 | − | 0.941612i | \(-0.390689\pi\) | ||||
0.336701 | + | 0.941612i | \(0.390689\pi\) | |||||||
\(594\) | −1435.32 | −0.0991447 | ||||||||
\(595\) | −795.855 | −0.0548351 | ||||||||
\(596\) | −10543.5 | −0.724630 | ||||||||
\(597\) | −13279.1 | −0.910347 | ||||||||
\(598\) | 2374.80 | 0.162396 | ||||||||
\(599\) | −11688.9 | −0.797324 | −0.398662 | − | 0.917098i | \(-0.630525\pi\) | ||||
−0.398662 | + | 0.917098i | \(0.630525\pi\) | |||||||
\(600\) | −446.359 | −0.0303709 | ||||||||
\(601\) | −27475.5 | −1.86481 | −0.932405 | − | 0.361416i | \(-0.882293\pi\) | ||||
−0.932405 | + | 0.361416i | \(0.882293\pi\) | |||||||
\(602\) | 3137.47 | 0.212415 | ||||||||
\(603\) | 622.776 | 0.0420587 | ||||||||
\(604\) | 464.168 | 0.0312694 | ||||||||
\(605\) | −6441.81 | −0.432887 | ||||||||
\(606\) | −10071.9 | −0.675156 | ||||||||
\(607\) | 18175.7 | 1.21537 | 0.607685 | − | 0.794178i | \(-0.292098\pi\) | ||||
0.607685 | + | 0.794178i | \(0.292098\pi\) | |||||||
\(608\) | 1737.59 | 0.115902 | ||||||||
\(609\) | 6528.90 | 0.434424 | ||||||||
\(610\) | 506.987 | 0.0336513 | ||||||||
\(611\) | 10188.8 | 0.674621 | ||||||||
\(612\) | −396.793 | −0.0262082 | ||||||||
\(613\) | 13946.9 | 0.918940 | 0.459470 | − | 0.888193i | \(-0.348039\pi\) | ||||
0.459470 | + | 0.888193i | \(0.348039\pi\) | |||||||
\(614\) | 13912.8 | 0.914455 | ||||||||
\(615\) | −3167.74 | −0.207700 | ||||||||
\(616\) | 1488.48 | 0.0973582 | ||||||||
\(617\) | 12686.5 | 0.827780 | 0.413890 | − | 0.910327i | \(-0.364170\pi\) | ||||
0.413890 | + | 0.910327i | \(0.364170\pi\) | |||||||
\(618\) | 2552.88 | 0.166168 | ||||||||
\(619\) | −11200.5 | −0.727282 | −0.363641 | − | 0.931539i | \(-0.618467\pi\) | ||||
−0.363641 | + | 0.931539i | \(0.618467\pi\) | |||||||
\(620\) | 6061.30 | 0.392625 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | 888.935 | 0.0573040 | ||||||||
\(623\) | 1161.88 | 0.0747188 | ||||||||
\(624\) | −2478.05 | −0.158977 | ||||||||
\(625\) | −12954.3 | −0.829076 | ||||||||
\(626\) | −16635.5 | −1.06212 | ||||||||
\(627\) | −4329.86 | −0.275786 | ||||||||
\(628\) | 3222.67 | 0.204775 | ||||||||
\(629\) | 2540.42 | 0.161038 | ||||||||
\(630\) | −1299.71 | −0.0821929 | ||||||||
\(631\) | −17301.2 | −1.09152 | −0.545761 | − | 0.837941i | \(-0.683759\pi\) | ||||
−0.545761 | + | 0.837941i | \(0.683759\pi\) | |||||||
\(632\) | −9518.52 | −0.599092 | ||||||||
\(633\) | −9163.28 | −0.575368 | ||||||||
\(634\) | 5028.65 | 0.315005 | ||||||||
\(635\) | −9489.76 | −0.593054 | ||||||||
\(636\) | 6927.48 | 0.431906 | ||||||||
\(637\) | 2529.68 | 0.157346 | ||||||||
\(638\) | −16527.5 | −1.02559 | ||||||||
\(639\) | 1924.03 | 0.119114 | ||||||||
\(640\) | −1320.34 | −0.0815482 | ||||||||
\(641\) | 23278.1 | 1.43437 | 0.717183 | − | 0.696885i | \(-0.245431\pi\) | ||||
0.717183 | + | 0.696885i | \(0.245431\pi\) | |||||||
\(642\) | 1908.27 | 0.117311 | ||||||||
\(643\) | −3495.34 | −0.214374 | −0.107187 | − | 0.994239i | \(-0.534184\pi\) | ||||
−0.107187 | + | 0.994239i | \(0.534184\pi\) | |||||||
\(644\) | −644.000 | −0.0394055 | ||||||||
\(645\) | 6935.00 | 0.423357 | ||||||||
\(646\) | −1196.98 | −0.0729021 | ||||||||
\(647\) | 28365.2 | 1.72357 | 0.861787 | − | 0.507271i | \(-0.169346\pi\) | ||||
0.861787 | + | 0.507271i | \(0.169346\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | −9571.76 | −0.578928 | ||||||||
\(650\) | 1920.31 | 0.115878 | ||||||||
\(651\) | −3084.97 | −0.185729 | ||||||||
\(652\) | −11257.5 | −0.676196 | ||||||||
\(653\) | 3225.35 | 0.193289 | 0.0966444 | − | 0.995319i | \(-0.469189\pi\) | ||||
0.0966444 | + | 0.995319i | \(0.469189\pi\) | |||||||
\(654\) | −3437.38 | −0.205523 | ||||||||
\(655\) | 26639.6 | 1.58915 | ||||||||
\(656\) | 1637.85 | 0.0974807 | ||||||||
\(657\) | −2774.19 | −0.164736 | ||||||||
\(658\) | −2763.00 | −0.163697 | ||||||||
\(659\) | −1969.27 | −0.116407 | −0.0582033 | − | 0.998305i | \(-0.518537\pi\) | ||||
−0.0582033 | + | 0.998305i | \(0.518537\pi\) | |||||||
\(660\) | 3290.12 | 0.194042 | ||||||||
\(661\) | −17204.2 | −1.01235 | −0.506177 | − | 0.862430i | \(-0.668942\pi\) | ||||
−0.506177 | + | 0.862430i | \(0.668942\pi\) | |||||||
\(662\) | 8521.02 | 0.500270 | ||||||||
\(663\) | 1707.07 | 0.0999958 | ||||||||
\(664\) | 1078.47 | 0.0630311 | ||||||||
\(665\) | −3920.75 | −0.228632 | ||||||||
\(666\) | 4148.74 | 0.241382 | ||||||||
\(667\) | 7150.70 | 0.415107 | ||||||||
\(668\) | −7237.37 | −0.419195 | ||||||||
\(669\) | −820.062 | −0.0473923 | ||||||||
\(670\) | −1427.56 | −0.0823154 | ||||||||
\(671\) | 653.202 | 0.0375806 | ||||||||
\(672\) | 672.000 | 0.0385758 | ||||||||
\(673\) | −20587.6 | −1.17919 | −0.589595 | − | 0.807699i | \(-0.700713\pi\) | ||||
−0.589595 | + | 0.807699i | \(0.700713\pi\) | |||||||
\(674\) | −17109.2 | −0.977777 | ||||||||
\(675\) | 502.153 | 0.0286339 | ||||||||
\(676\) | 1873.01 | 0.106567 | ||||||||
\(677\) | 14983.0 | 0.850584 | 0.425292 | − | 0.905056i | \(-0.360171\pi\) | ||||
0.425292 | + | 0.905056i | \(0.360171\pi\) | |||||||
\(678\) | −6476.80 | −0.366873 | ||||||||
\(679\) | 3021.67 | 0.170782 | ||||||||
\(680\) | 909.548 | 0.0512935 | ||||||||
\(681\) | 8266.62 | 0.465165 | ||||||||
\(682\) | 7809.38 | 0.438470 | ||||||||
\(683\) | 10817.8 | 0.606050 | 0.303025 | − | 0.952983i | \(-0.402003\pi\) | ||||
0.303025 | + | 0.952983i | \(0.402003\pi\) | |||||||
\(684\) | −1954.79 | −0.109274 | ||||||||
\(685\) | −8138.90 | −0.453973 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | −15290.5 | −0.849153 | ||||||||
\(688\) | −3585.68 | −0.198696 | ||||||||
\(689\) | −29803.2 | −1.64791 | ||||||||
\(690\) | −1423.49 | −0.0785380 | ||||||||
\(691\) | −24646.1 | −1.35685 | −0.678425 | − | 0.734670i | \(-0.737337\pi\) | ||||
−0.678425 | + | 0.734670i | \(0.737337\pi\) | |||||||
\(692\) | −13019.9 | −0.715233 | ||||||||
\(693\) | −1674.54 | −0.0917902 | ||||||||
\(694\) | 1632.58 | 0.0892966 | ||||||||
\(695\) | −15520.4 | −0.847081 | ||||||||
\(696\) | −7461.60 | −0.406367 | ||||||||
\(697\) | −1128.28 | −0.0613150 | ||||||||
\(698\) | 20825.4 | 1.12930 | ||||||||
\(699\) | 5330.46 | 0.288436 | ||||||||
\(700\) | −520.752 | −0.0281179 | ||||||||
\(701\) | −29986.4 | −1.61565 | −0.807824 | − | 0.589423i | \(-0.799355\pi\) | ||||
−0.807824 | + | 0.589423i | \(0.799355\pi\) | |||||||
\(702\) | 2787.81 | 0.149885 | ||||||||
\(703\) | 12515.3 | 0.671441 | ||||||||
\(704\) | −1701.12 | −0.0910702 | ||||||||
\(705\) | −6107.29 | −0.326261 | ||||||||
\(706\) | 3114.58 | 0.166032 | ||||||||
\(707\) | −11750.6 | −0.625073 | ||||||||
\(708\) | −4321.33 | −0.229386 | ||||||||
\(709\) | −8413.34 | −0.445655 | −0.222828 | − | 0.974858i | \(-0.571529\pi\) | ||||
−0.222828 | + | 0.974858i | \(0.571529\pi\) | |||||||
\(710\) | −4410.36 | −0.233124 | ||||||||
\(711\) | 10708.3 | 0.564830 | ||||||||
\(712\) | −1327.86 | −0.0698930 | ||||||||
\(713\) | −3378.77 | −0.177470 | ||||||||
\(714\) | −462.925 | −0.0242641 | ||||||||
\(715\) | −14154.6 | −0.740355 | ||||||||
\(716\) | −15817.4 | −0.825593 | ||||||||
\(717\) | 11732.1 | 0.611078 | ||||||||
\(718\) | −2309.82 | −0.120058 | ||||||||
\(719\) | 12474.8 | 0.647055 | 0.323528 | − | 0.946219i | \(-0.395131\pi\) | ||||
0.323528 | + | 0.946219i | \(0.395131\pi\) | |||||||
\(720\) | 1485.38 | 0.0768844 | ||||||||
\(721\) | 2978.36 | 0.153842 | ||||||||
\(722\) | 7821.09 | 0.403145 | ||||||||
\(723\) | 9816.54 | 0.504953 | ||||||||
\(724\) | −9243.62 | −0.474498 | ||||||||
\(725\) | 5782.21 | 0.296201 | ||||||||
\(726\) | −3747.01 | −0.191549 | ||||||||
\(727\) | 2009.59 | 0.102519 | 0.0512597 | − | 0.998685i | \(-0.483676\pi\) | ||||
0.0512597 | + | 0.998685i | \(0.483676\pi\) | |||||||
\(728\) | −2891.06 | −0.147184 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 6359.13 | 0.322413 | ||||||||
\(731\) | 2470.09 | 0.124979 | ||||||||
\(732\) | 294.899 | 0.0148904 | ||||||||
\(733\) | −30858.6 | −1.55496 | −0.777482 | − | 0.628905i | \(-0.783504\pi\) | ||||
−0.777482 | + | 0.628905i | \(0.783504\pi\) | |||||||
\(734\) | −12746.6 | −0.640989 | ||||||||
\(735\) | −1516.32 | −0.0760958 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −1839.27 | −0.0919271 | ||||||||
\(738\) | −1842.58 | −0.0919057 | ||||||||
\(739\) | 27765.2 | 1.38208 | 0.691042 | − | 0.722814i | \(-0.257152\pi\) | ||||
0.691042 | + | 0.722814i | \(0.257152\pi\) | |||||||
\(740\) | −9509.95 | −0.472423 | ||||||||
\(741\) | 8409.84 | 0.416927 | ||||||||
\(742\) | 8082.06 | 0.399868 | ||||||||
\(743\) | 11628.5 | 0.574171 | 0.287085 | − | 0.957905i | \(-0.407314\pi\) | ||||
0.287085 | + | 0.957905i | \(0.407314\pi\) | |||||||
\(744\) | 3525.68 | 0.173733 | ||||||||
\(745\) | −27189.4 | −1.33711 | ||||||||
\(746\) | −17931.5 | −0.880050 | ||||||||
\(747\) | −1213.28 | −0.0594263 | ||||||||
\(748\) | 1171.86 | 0.0572828 | ||||||||
\(749\) | 2226.32 | 0.108609 | ||||||||
\(750\) | −8887.40 | −0.432696 | ||||||||
\(751\) | 25645.6 | 1.24610 | 0.623050 | − | 0.782182i | \(-0.285893\pi\) | ||||
0.623050 | + | 0.782182i | \(0.285893\pi\) | |||||||
\(752\) | 3157.71 | 0.153125 | ||||||||
\(753\) | 9759.98 | 0.472342 | ||||||||
\(754\) | 32101.1 | 1.55047 | ||||||||
\(755\) | 1196.99 | 0.0576991 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | 4553.97 | 0.218649 | 0.109324 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109324 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(758\) | 11674.6 | 0.559420 | ||||||||
\(759\) | −1834.02 | −0.0877086 | ||||||||
\(760\) | 4480.86 | 0.213866 | ||||||||
\(761\) | −874.513 | −0.0416571 | −0.0208286 | − | 0.999783i | \(-0.506630\pi\) | ||||
−0.0208286 | + | 0.999783i | \(0.506630\pi\) | |||||||
\(762\) | −5519.91 | −0.262422 | ||||||||
\(763\) | −4010.27 | −0.190277 | ||||||||
\(764\) | −10648.0 | −0.504232 | ||||||||
\(765\) | −1023.24 | −0.0483600 | ||||||||
\(766\) | −22088.8 | −1.04191 | ||||||||
\(767\) | 18591.1 | 0.875210 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 10434.0 | 0.489286 | 0.244643 | − | 0.969613i | \(-0.421329\pi\) | ||||
0.244643 | + | 0.969613i | \(0.421329\pi\) | |||||||
\(770\) | 3838.47 | 0.179648 | ||||||||
\(771\) | 4861.75 | 0.227097 | ||||||||
\(772\) | 11168.6 | 0.520685 | ||||||||
\(773\) | −7118.89 | −0.331240 | −0.165620 | − | 0.986190i | \(-0.552963\pi\) | ||||
−0.165620 | + | 0.986190i | \(0.552963\pi\) | |||||||
\(774\) | 4033.89 | 0.187332 | ||||||||
\(775\) | −2732.15 | −0.126634 | ||||||||
\(776\) | −3453.33 | −0.159752 | ||||||||
\(777\) | 4840.20 | 0.223476 | ||||||||
\(778\) | −6991.06 | −0.322161 | ||||||||
\(779\) | −5558.42 | −0.255650 | ||||||||
\(780\) | −6390.35 | −0.293348 | ||||||||
\(781\) | −5682.32 | −0.260345 | ||||||||
\(782\) | −507.013 | −0.0231851 | ||||||||
\(783\) | 8394.30 | 0.383126 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 8310.55 | 0.377855 | ||||||||
\(786\) | 15495.5 | 0.703187 | ||||||||
\(787\) | −20000.3 | −0.905890 | −0.452945 | − | 0.891539i | \(-0.649627\pi\) | ||||
−0.452945 | + | 0.891539i | \(0.649627\pi\) | |||||||
\(788\) | 3671.06 | 0.165960 | ||||||||
\(789\) | 7195.36 | 0.324666 | ||||||||
\(790\) | −24546.2 | −1.10546 | ||||||||
\(791\) | −7556.27 | −0.339659 | ||||||||
\(792\) | 1913.76 | 0.0858619 | ||||||||
\(793\) | −1268.71 | −0.0568135 | ||||||||
\(794\) | −1206.80 | −0.0539394 | ||||||||
\(795\) | 17864.4 | 0.796964 | ||||||||
\(796\) | 17705.5 | 0.788383 | ||||||||
\(797\) | −22900.8 | −1.01780 | −0.508900 | − | 0.860826i | \(-0.669948\pi\) | ||||
−0.508900 | + | 0.860826i | \(0.669948\pi\) | |||||||
\(798\) | −2280.59 | −0.101168 | ||||||||
\(799\) | −2175.27 | −0.0963150 | ||||||||
\(800\) | 595.145 | 0.0263019 | ||||||||
\(801\) | 1493.85 | 0.0658958 | ||||||||
\(802\) | −15859.9 | −0.698297 | ||||||||
\(803\) | 8193.11 | 0.360060 | ||||||||
\(804\) | −830.367 | −0.0364239 | ||||||||
\(805\) | −1660.73 | −0.0727121 | ||||||||
\(806\) | −15168.1 | −0.662869 | ||||||||
\(807\) | −14221.3 | −0.620340 | ||||||||
\(808\) | 13429.3 | 0.584702 | ||||||||
\(809\) | −14228.0 | −0.618332 | −0.309166 | − | 0.951008i | \(-0.600050\pi\) | ||||
−0.309166 | + | 0.951008i | \(0.600050\pi\) | |||||||
\(810\) | −1671.05 | −0.0724873 | ||||||||
\(811\) | −6818.47 | −0.295227 | −0.147613 | − | 0.989045i | \(-0.547159\pi\) | ||||
−0.147613 | + | 0.989045i | \(0.547159\pi\) | |||||||
\(812\) | −8705.20 | −0.376223 | ||||||||
\(813\) | 5182.49 | 0.223564 | ||||||||
\(814\) | −12252.6 | −0.527586 | ||||||||
\(815\) | −29030.7 | −1.24773 | ||||||||
\(816\) | 529.057 | 0.0226969 | ||||||||
\(817\) | 12168.8 | 0.521093 | ||||||||
\(818\) | 22514.6 | 0.962355 | ||||||||
\(819\) | 3252.44 | 0.138766 | ||||||||
\(820\) | 4223.66 | 0.179874 | ||||||||
\(821\) | −9205.60 | −0.391325 | −0.195662 | − | 0.980671i | \(-0.562686\pi\) | ||||
−0.195662 | + | 0.980671i | \(0.562686\pi\) | |||||||
\(822\) | −4734.16 | −0.200879 | ||||||||
\(823\) | −8350.74 | −0.353692 | −0.176846 | − | 0.984239i | \(-0.556589\pi\) | ||||
−0.176846 | + | 0.984239i | \(0.556589\pi\) | |||||||
\(824\) | −3403.84 | −0.143906 | ||||||||
\(825\) | −1483.03 | −0.0625847 | ||||||||
\(826\) | −5041.55 | −0.212371 | ||||||||
\(827\) | −45162.5 | −1.89898 | −0.949488 | − | 0.313802i | \(-0.898397\pi\) | ||||
−0.949488 | + | 0.313802i | \(0.898397\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | 27508.8 | 1.15250 | 0.576248 | − | 0.817275i | \(-0.304516\pi\) | ||||
0.576248 | + | 0.817275i | \(0.304516\pi\) | |||||||
\(830\) | 2781.13 | 0.116307 | ||||||||
\(831\) | −14112.8 | −0.589132 | ||||||||
\(832\) | 3304.07 | 0.137678 | ||||||||
\(833\) | −540.079 | −0.0224642 | ||||||||
\(834\) | −9027.74 | −0.374826 | ||||||||
\(835\) | −18663.6 | −0.773509 | ||||||||
\(836\) | 5773.15 | 0.238838 | ||||||||
\(837\) | −3966.39 | −0.163797 | ||||||||
\(838\) | 10483.5 | 0.432155 | ||||||||
\(839\) | 35911.5 | 1.47771 | 0.738857 | − | 0.673862i | \(-0.235366\pi\) | ||||
0.738857 | + | 0.673862i | \(0.235366\pi\) | |||||||
\(840\) | 1732.94 | 0.0711811 | ||||||||
\(841\) | 72269.9 | 2.96322 | ||||||||
\(842\) | −16787.3 | −0.687090 | ||||||||
\(843\) | 17828.2 | 0.728394 | ||||||||
\(844\) | 12217.7 | 0.498283 | ||||||||
\(845\) | 4830.09 | 0.196639 | ||||||||
\(846\) | −3552.43 | −0.144368 | ||||||||
\(847\) | −4371.51 | −0.177340 | ||||||||
\(848\) | −9236.64 | −0.374042 | ||||||||
\(849\) | −13378.1 | −0.540795 | ||||||||
\(850\) | −409.981 | −0.0165438 | ||||||||
\(851\) | 5301.17 | 0.213539 | ||||||||
\(852\) | −2565.38 | −0.103155 | ||||||||
\(853\) | −928.378 | −0.0372650 | −0.0186325 | − | 0.999826i | \(-0.505931\pi\) | ||||
−0.0186325 | + | 0.999826i | \(0.505931\pi\) | |||||||
\(854\) | 344.049 | 0.0137858 | ||||||||
\(855\) | −5040.97 | −0.201634 | ||||||||
\(856\) | −2544.36 | −0.101594 | ||||||||
\(857\) | 28986.8 | 1.15539 | 0.577696 | − | 0.816252i | \(-0.303952\pi\) | ||||
0.577696 | + | 0.816252i | \(0.303952\pi\) | |||||||
\(858\) | −8233.34 | −0.327601 | ||||||||
\(859\) | −42067.7 | −1.67093 | −0.835466 | − | 0.549542i | \(-0.814802\pi\) | ||||
−0.835466 | + | 0.549542i | \(0.814802\pi\) | |||||||
\(860\) | −9246.67 | −0.366638 | ||||||||
\(861\) | −2149.68 | −0.0850881 | ||||||||
\(862\) | 28534.5 | 1.12748 | ||||||||
\(863\) | −19844.8 | −0.782764 | −0.391382 | − | 0.920228i | \(-0.628003\pi\) | ||||
−0.391382 | + | 0.920228i | \(0.628003\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −33575.4 | −1.31977 | ||||||||
\(866\) | 11370.8 | 0.446184 | ||||||||
\(867\) | 14374.5 | 0.563074 | ||||||||
\(868\) | 4113.29 | 0.160846 | ||||||||
\(869\) | −31625.3 | −1.23454 | ||||||||
\(870\) | −19241.8 | −0.749838 | ||||||||
\(871\) | 3572.39 | 0.138973 | ||||||||
\(872\) | 4583.17 | 0.177988 | ||||||||
\(873\) | 3885.00 | 0.150616 | ||||||||
\(874\) | −2497.78 | −0.0966691 | ||||||||
\(875\) | −10368.6 | −0.400599 | ||||||||
\(876\) | 3698.91 | 0.142665 | ||||||||
\(877\) | −13668.2 | −0.526273 | −0.263136 | − | 0.964759i | \(-0.584757\pi\) | ||||
−0.263136 | + | 0.964759i | \(0.584757\pi\) | |||||||
\(878\) | −10508.0 | −0.403904 | ||||||||
\(879\) | −14664.9 | −0.562725 | ||||||||
\(880\) | −4386.82 | −0.168045 | ||||||||
\(881\) | −11477.4 | −0.438916 | −0.219458 | − | 0.975622i | \(-0.570429\pi\) | ||||
−0.219458 | + | 0.975622i | \(0.570429\pi\) | |||||||
\(882\) | −882.000 | −0.0336718 | ||||||||
\(883\) | 5768.82 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(884\) | −2276.10 | −0.0865989 | ||||||||
\(885\) | −11143.8 | −0.423269 | ||||||||
\(886\) | −22066.9 | −0.836740 | ||||||||
\(887\) | 23527.1 | 0.890602 | 0.445301 | − | 0.895381i | \(-0.353097\pi\) | ||||
0.445301 | + | 0.895381i | \(0.353097\pi\) | |||||||
\(888\) | −5531.66 | −0.209043 | ||||||||
\(889\) | −6439.89 | −0.242955 | ||||||||
\(890\) | −3424.27 | −0.128968 | ||||||||
\(891\) | −2152.98 | −0.0809513 | ||||||||
\(892\) | 1093.42 | 0.0410429 | ||||||||
\(893\) | −10716.4 | −0.401580 | ||||||||
\(894\) | −15815.3 | −0.591658 | ||||||||
\(895\) | −40789.7 | −1.52341 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 3562.20 | 0.132596 | ||||||||
\(898\) | 29672.1 | 1.10264 | ||||||||
\(899\) | −45672.2 | −1.69439 | ||||||||
\(900\) | −669.538 | −0.0247977 | ||||||||
\(901\) | 6362.91 | 0.235271 | ||||||||
\(902\) | 5441.77 | 0.200877 | ||||||||
\(903\) | 4706.20 | 0.173436 | ||||||||
\(904\) | 8635.73 | 0.317722 | ||||||||
\(905\) | −23837.3 | −0.875555 | ||||||||
\(906\) | 696.252 | 0.0255314 | ||||||||
\(907\) | −11549.8 | −0.422827 | −0.211413 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211413 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(908\) | −11022.2 | −0.402845 | ||||||||
\(909\) | −15107.9 | −0.551263 | ||||||||
\(910\) | −7455.41 | −0.271587 | ||||||||
\(911\) | −27036.2 | −0.983261 | −0.491630 | − | 0.870804i | \(-0.663599\pi\) | ||||
−0.491630 | + | 0.870804i | \(0.663599\pi\) | |||||||
\(912\) | 2606.38 | 0.0946338 | ||||||||
\(913\) | 3583.21 | 0.129887 | ||||||||
\(914\) | 19321.9 | 0.699247 | ||||||||
\(915\) | 760.480 | 0.0274762 | ||||||||
\(916\) | 20387.3 | 0.735388 | ||||||||
\(917\) | 18078.1 | 0.651025 | ||||||||
\(918\) | −595.189 | −0.0213989 | ||||||||
\(919\) | −2635.88 | −0.0946132 | −0.0473066 | − | 0.998880i | \(-0.515064\pi\) | ||||
−0.0473066 | + | 0.998880i | \(0.515064\pi\) | |||||||
\(920\) | 1897.98 | 0.0680159 | ||||||||
\(921\) | 20869.2 | 0.746650 | ||||||||
\(922\) | −22795.9 | −0.814255 | ||||||||
\(923\) | 11036.7 | 0.393583 | ||||||||
\(924\) | 2232.72 | 0.0794926 | ||||||||
\(925\) | 4286.64 | 0.152372 | ||||||||
\(926\) | 170.364 | 0.00604592 | ||||||||
\(927\) | 3829.32 | 0.135676 | ||||||||
\(928\) | 9948.80 | 0.351924 | ||||||||
\(929\) | −48008.9 | −1.69550 | −0.847751 | − | 0.530395i | \(-0.822044\pi\) | ||||
−0.847751 | + | 0.530395i | \(0.822044\pi\) | |||||||
\(930\) | 9091.94 | 0.320577 | ||||||||
\(931\) | −2660.68 | −0.0936631 | ||||||||
\(932\) | −7107.28 | −0.249793 | ||||||||
\(933\) | 1333.40 | 0.0467885 | ||||||||
\(934\) | −10410.5 | −0.364712 | ||||||||
\(935\) | 3021.98 | 0.105700 | ||||||||
\(936\) | −3717.08 | −0.129804 | ||||||||
\(937\) | −11442.4 | −0.398940 | −0.199470 | − | 0.979904i | \(-0.563922\pi\) | ||||
−0.199470 | + | 0.979904i | \(0.563922\pi\) | |||||||
\(938\) | −968.762 | −0.0337220 | ||||||||
\(939\) | −24953.2 | −0.867218 | ||||||||
\(940\) | 8143.05 | 0.282550 | ||||||||
\(941\) | 53365.5 | 1.84874 | 0.924371 | − | 0.381496i | \(-0.124591\pi\) | ||||
0.924371 | + | 0.381496i | \(0.124591\pi\) | |||||||
\(942\) | 4834.00 | 0.167198 | ||||||||
\(943\) | −2354.41 | −0.0813045 | ||||||||
\(944\) | 5761.77 | 0.198654 | ||||||||
\(945\) | −1949.56 | −0.0671102 | ||||||||
\(946\) | −11913.4 | −0.409449 | ||||||||
\(947\) | 19151.9 | 0.657183 | 0.328592 | − | 0.944472i | \(-0.393426\pi\) | ||||
0.328592 | + | 0.944472i | \(0.393426\pi\) | |||||||
\(948\) | −14277.8 | −0.489157 | ||||||||
\(949\) | −15913.4 | −0.544331 | ||||||||
\(950\) | −2019.76 | −0.0689786 | ||||||||
\(951\) | 7542.97 | 0.257200 | ||||||||
\(952\) | 617.234 | 0.0210133 | ||||||||
\(953\) | −5300.55 | −0.180170 | −0.0900849 | − | 0.995934i | \(-0.528714\pi\) | ||||
−0.0900849 | + | 0.995934i | \(0.528714\pi\) | |||||||
\(954\) | 10391.2 | 0.352650 | ||||||||
\(955\) | −27459.0 | −0.930421 | ||||||||
\(956\) | −15642.8 | −0.529209 | ||||||||
\(957\) | −24791.2 | −0.837394 | ||||||||
\(958\) | 4759.66 | 0.160519 | ||||||||
\(959\) | −5523.18 | −0.185978 | ||||||||
\(960\) | −1980.50 | −0.0665838 | ||||||||
\(961\) | −8210.46 | −0.275602 | ||||||||
\(962\) | 23798.2 | 0.797592 | ||||||||
\(963\) | 2862.41 | 0.0957839 | ||||||||
\(964\) | −13088.7 | −0.437302 | ||||||||
\(965\) | 28801.5 | 0.960780 | ||||||||
\(966\) | −966.000 | −0.0321745 | ||||||||
\(967\) | −23837.0 | −0.792706 | −0.396353 | − | 0.918098i | \(-0.629724\pi\) | ||||
−0.396353 | + | 0.918098i | \(0.629724\pi\) | |||||||
\(968\) | 4996.01 | 0.165886 | ||||||||
\(969\) | −1795.48 | −0.0595243 | ||||||||
\(970\) | −8905.39 | −0.294778 | ||||||||
\(971\) | 4331.23 | 0.143147 | 0.0715735 | − | 0.997435i | \(-0.477198\pi\) | ||||
0.0715735 | + | 0.997435i | \(0.477198\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −10532.4 | −0.347022 | ||||||||
\(974\) | 34.6556 | 0.00114008 | ||||||||
\(975\) | 2880.47 | 0.0946142 | ||||||||
\(976\) | −393.199 | −0.0128955 | ||||||||
\(977\) | 20300.1 | 0.664748 | 0.332374 | − | 0.943148i | \(-0.392150\pi\) | ||||
0.332374 | + | 0.943148i | \(0.392150\pi\) | |||||||
\(978\) | −16886.3 | −0.552112 | ||||||||
\(979\) | −4411.84 | −0.144027 | ||||||||
\(980\) | 2021.76 | 0.0659009 | ||||||||
\(981\) | −5156.06 | −0.167809 | ||||||||
\(982\) | −10147.8 | −0.329765 | ||||||||
\(983\) | 23851.1 | 0.773890 | 0.386945 | − | 0.922103i | \(-0.373530\pi\) | ||||
0.386945 | + | 0.922103i | \(0.373530\pi\) | |||||||
\(984\) | 2456.78 | 0.0795927 | ||||||||
\(985\) | 9466.87 | 0.306233 | ||||||||
\(986\) | −6853.50 | −0.221359 | ||||||||
\(987\) | −4144.50 | −0.133658 | ||||||||
\(988\) | −11213.1 | −0.361070 | ||||||||
\(989\) | 5154.41 | 0.165724 | ||||||||
\(990\) | 4935.17 | 0.158434 | ||||||||
\(991\) | 12071.5 | 0.386948 | 0.193474 | − | 0.981105i | \(-0.438025\pi\) | ||||
0.193474 | + | 0.981105i | \(0.438025\pi\) | |||||||
\(992\) | −4700.90 | −0.150457 | ||||||||
\(993\) | 12781.5 | 0.408469 | ||||||||
\(994\) | −2992.94 | −0.0955033 | ||||||||
\(995\) | 45658.5 | 1.45474 | ||||||||
\(996\) | 1617.70 | 0.0514647 | ||||||||
\(997\) | −21936.7 | −0.696832 | −0.348416 | − | 0.937340i | \(-0.613280\pi\) | ||||
−0.348416 | + | 0.937340i | \(0.613280\pi\) | |||||||
\(998\) | −5047.87 | −0.160108 | ||||||||
\(999\) | 6223.11 | 0.197088 |
(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 | 966.4.a.l.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.l.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial |