Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 239) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.58869 | −1.62235 | −0.811173 | − | 0.584806i | \(-0.801171\pi\) | ||||
−0.811173 | + | 0.584806i | \(0.801171\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 13.0561 | 1.63201 | ||||||||
\(5\) | 15.1251 | 1.35283 | 0.676413 | − | 0.736522i | \(-0.263533\pi\) | ||||
0.676413 | + | 0.736522i | \(0.263533\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.8403 | −1.39524 | −0.697622 | − | 0.716466i | \(-0.745759\pi\) | ||||
−0.697622 | + | 0.716466i | \(0.745759\pi\) | |||||||
\(8\) | −23.2007 | −1.02534 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −69.4042 | −2.19475 | ||||||||
\(11\) | −0.294915 | −0.00808365 | −0.00404183 | − | 0.999992i | \(-0.501287\pi\) | ||||
−0.00404183 | + | 0.999992i | \(0.501287\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.35456 | 0.0715683 | 0.0357841 | − | 0.999360i | \(-0.488607\pi\) | ||||
0.0357841 | + | 0.999360i | \(0.488607\pi\) | |||||||
\(14\) | 118.573 | 2.26357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.01223 | 0.0314411 | ||||||||
\(17\) | −39.1710 | −0.558845 | −0.279422 | − | 0.960168i | \(-0.590143\pi\) | ||||
−0.279422 | + | 0.960168i | \(0.590143\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.2006 | 0.135241 | 0.0676207 | − | 0.997711i | \(-0.478459\pi\) | ||||
0.0676207 | + | 0.997711i | \(0.478459\pi\) | |||||||
\(20\) | 197.474 | 2.20782 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.35327 | 0.0131145 | ||||||||
\(23\) | −44.6692 | −0.404964 | −0.202482 | − | 0.979286i | \(-0.564901\pi\) | ||||
−0.202482 | + | 0.979286i | \(0.564901\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 103.767 | 0.830140 | ||||||||
\(26\) | −15.3930 | −0.116109 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −337.372 | −2.27705 | ||||||||
\(29\) | −75.9968 | −0.486629 | −0.243315 | − | 0.969947i | \(-0.578235\pi\) | ||||
−0.243315 | + | 0.969947i | \(0.578235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −34.1402 | −0.197799 | −0.0988993 | − | 0.995097i | \(-0.531532\pi\) | ||||
−0.0988993 | + | 0.995097i | \(0.531532\pi\) | |||||||
\(32\) | 176.372 | 0.974327 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 179.744 | 0.906640 | ||||||||
\(35\) | −390.836 | −1.88752 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 114.610 | 0.509237 | 0.254618 | − | 0.967042i | \(-0.418050\pi\) | ||||
0.254618 | + | 0.967042i | \(0.418050\pi\) | |||||||
\(38\) | −51.3959 | −0.219408 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −350.912 | −1.38710 | ||||||||
\(41\) | 364.615 | 1.38886 | 0.694431 | − | 0.719559i | \(-0.255656\pi\) | ||||
0.694431 | + | 0.719559i | \(0.255656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 145.626 | 0.516458 | 0.258229 | − | 0.966084i | \(-0.416861\pi\) | ||||
0.258229 | + | 0.966084i | \(0.416861\pi\) | |||||||
\(44\) | −3.85043 | −0.0131926 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 204.973 | 0.656992 | ||||||||
\(47\) | 322.485 | 1.00083 | 0.500417 | − | 0.865784i | \(-0.333180\pi\) | ||||
0.500417 | + | 0.865784i | \(0.333180\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 324.721 | 0.946708 | ||||||||
\(50\) | −476.157 | −1.34677 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 43.7974 | 0.116800 | ||||||||
\(53\) | 345.906 | 0.896488 | 0.448244 | − | 0.893911i | \(-0.352050\pi\) | ||||
0.448244 | + | 0.893911i | \(0.352050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.46061 | −0.0109358 | ||||||||
\(56\) | 599.513 | 1.43059 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 348.726 | 0.789481 | ||||||||
\(59\) | 701.310 | 1.54750 | 0.773752 | − | 0.633488i | \(-0.218378\pi\) | ||||
0.773752 | + | 0.633488i | \(0.218378\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −357.131 | −0.749606 | −0.374803 | − | 0.927104i | \(-0.622290\pi\) | ||||
−0.374803 | + | 0.927104i | \(0.622290\pi\) | |||||||
\(62\) | 156.659 | 0.320898 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −825.414 | −1.61214 | ||||||||
\(65\) | 50.7379 | 0.0968195 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −748.574 | −1.36497 | −0.682484 | − | 0.730901i | \(-0.739100\pi\) | ||||
−0.682484 | + | 0.730901i | \(0.739100\pi\) | |||||||
\(68\) | −511.419 | −0.912039 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1793.42 | 3.06222 | ||||||||
\(71\) | −730.542 | −1.22112 | −0.610559 | − | 0.791971i | \(-0.709055\pi\) | ||||
−0.610559 | + | 0.791971i | \(0.709055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.7860 | 0.0669956 | 0.0334978 | − | 0.999439i | \(-0.489335\pi\) | ||||
0.0334978 | + | 0.999439i | \(0.489335\pi\) | |||||||
\(74\) | −525.909 | −0.826158 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 146.235 | 0.220715 | ||||||||
\(77\) | 7.62069 | 0.0112787 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 450.983 | 0.642273 | 0.321136 | − | 0.947033i | \(-0.395935\pi\) | ||||
0.321136 | + | 0.947033i | \(0.395935\pi\) | |||||||
\(80\) | 30.4351 | 0.0425344 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1673.11 | −2.25322 | ||||||||
\(83\) | 826.811 | 1.09343 | 0.546713 | − | 0.837320i | \(-0.315879\pi\) | ||||
0.546713 | + | 0.837320i | \(0.315879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −592.464 | −0.756020 | ||||||||
\(86\) | −668.230 | −0.837874 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.84223 | 0.00828845 | ||||||||
\(89\) | −1294.94 | −1.54229 | −0.771143 | − | 0.636662i | \(-0.780315\pi\) | ||||
−0.771143 | + | 0.636662i | \(0.780315\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −86.6828 | −0.0998553 | ||||||||
\(92\) | −583.204 | −0.660904 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1479.78 | −1.62370 | ||||||||
\(95\) | 169.409 | 0.182958 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −533.174 | −0.558099 | −0.279050 | − | 0.960277i | \(-0.590019\pi\) | ||||
−0.279050 | + | 0.960277i | \(0.590019\pi\) | |||||||
\(98\) | −1490.04 | −1.53589 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1354.79 | 1.35479 | ||||||||
\(101\) | −944.073 | −0.930087 | −0.465043 | − | 0.885288i | \(-0.653961\pi\) | ||||
−0.465043 | + | 0.885288i | \(0.653961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 174.838 | 0.167256 | 0.0836279 | − | 0.996497i | \(-0.473349\pi\) | ||||
0.0836279 | + | 0.996497i | \(0.473349\pi\) | |||||||
\(104\) | −77.8281 | −0.0733815 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1587.26 | −1.45441 | ||||||||
\(107\) | 21.1974 | 0.0191517 | 0.00957585 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957585 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −680.020 | −0.597561 | −0.298780 | − | 0.954322i | \(-0.596580\pi\) | ||||
−0.298780 | + | 0.954322i | \(0.596580\pi\) | |||||||
\(110\) | 20.4683 | 0.0177416 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −51.9966 | −0.0438680 | ||||||||
\(113\) | 606.546 | 0.504948 | 0.252474 | − | 0.967604i | \(-0.418756\pi\) | ||||
0.252474 | + | 0.967604i | \(0.418756\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −675.624 | −0.547846 | ||||||||
\(116\) | −992.219 | −0.794183 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3218.09 | −2.51059 | ||||||||
\(119\) | 1012.19 | 0.779725 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.91 | −0.999935 | ||||||||
\(122\) | 1638.76 | 1.21612 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −445.736 | −0.322809 | ||||||||
\(125\) | −321.143 | −0.229791 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.4357 | −0.0156760 | −0.00783798 | − | 0.999969i | \(-0.502495\pi\) | ||||
−0.00783798 | + | 0.999969i | \(0.502495\pi\) | |||||||
\(128\) | 2376.59 | 1.64112 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −232.821 | −0.157075 | ||||||||
\(131\) | 778.644 | 0.519316 | 0.259658 | − | 0.965701i | \(-0.416390\pi\) | ||||
0.259658 | + | 0.965701i | \(0.416390\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −289.426 | −0.188695 | ||||||||
\(134\) | 3434.97 | 2.21445 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 908.794 | 0.573003 | ||||||||
\(137\) | −1685.66 | −1.05121 | −0.525605 | − | 0.850729i | \(-0.676161\pi\) | ||||
−0.525605 | + | 0.850729i | \(0.676161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −336.141 | −0.205116 | −0.102558 | − | 0.994727i | \(-0.532703\pi\) | ||||
−0.102558 | + | 0.994727i | \(0.532703\pi\) | |||||||
\(140\) | −5102.78 | −3.08045 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3352.23 | 1.98108 | ||||||||
\(143\) | −0.989310 | −0.000578533 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1149.46 | −0.658325 | ||||||||
\(146\) | −191.743 | −0.108690 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1496.35 | 0.831078 | ||||||||
\(149\) | −1536.41 | −0.844747 | −0.422373 | − | 0.906422i | \(-0.638803\pi\) | ||||
−0.422373 | + | 0.906422i | \(0.638803\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3415.89 | 1.84093 | 0.920466 | − | 0.390822i | \(-0.127809\pi\) | ||||
0.920466 | + | 0.390822i | \(0.127809\pi\) | |||||||
\(152\) | −259.861 | −0.138668 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −34.9690 | −0.0182979 | ||||||||
\(155\) | −516.372 | −0.267587 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 372.951 | 0.189584 | 0.0947921 | − | 0.995497i | \(-0.469781\pi\) | ||||
0.0947921 | + | 0.995497i | \(0.469781\pi\) | |||||||
\(158\) | −2069.42 | −1.04199 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2667.64 | 1.31810 | ||||||||
\(161\) | 1154.26 | 0.565024 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2075.92 | 0.997536 | 0.498768 | − | 0.866735i | \(-0.333786\pi\) | ||||
0.498768 | + | 0.866735i | \(0.333786\pi\) | |||||||
\(164\) | 4760.44 | 2.26663 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3793.98 | −1.77392 | ||||||||
\(167\) | −182.621 | −0.0846205 | −0.0423102 | − | 0.999105i | \(-0.513472\pi\) | ||||
−0.0423102 | + | 0.999105i | \(0.513472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2185.75 | −0.994878 | ||||||||
\(170\) | 2718.63 | 1.22653 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1901.30 | 0.842863 | ||||||||
\(173\) | 2283.44 | 1.00351 | 0.501753 | − | 0.865011i | \(-0.332689\pi\) | ||||
0.501753 | + | 0.865011i | \(0.332689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2681.38 | −1.15825 | ||||||||
\(176\) | −0.593437 | −0.000254159 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5942.08 | 2.50212 | ||||||||
\(179\) | −3077.36 | −1.28499 | −0.642493 | − | 0.766291i | \(-0.722100\pi\) | ||||
−0.642493 | + | 0.766291i | \(0.722100\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1134.36 | −0.465837 | −0.232918 | − | 0.972496i | \(-0.574827\pi\) | ||||
−0.232918 | + | 0.972496i | \(0.574827\pi\) | |||||||
\(182\) | 397.761 | 0.162000 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1036.36 | 0.415224 | ||||||||
\(185\) | 1733.48 | 0.688909 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.5521 | 0.00451751 | ||||||||
\(188\) | 4210.38 | 1.63337 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −777.367 | −0.296822 | ||||||||
\(191\) | 4440.56 | 1.68224 | 0.841120 | − | 0.540848i | \(-0.181897\pi\) | ||||
0.841120 | + | 0.540848i | \(0.181897\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1205.33 | −0.449541 | −0.224770 | − | 0.974412i | \(-0.572163\pi\) | ||||
−0.224770 | + | 0.974412i | \(0.572163\pi\) | |||||||
\(194\) | 2446.57 | 0.905430 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4239.57 | 1.54503 | ||||||||
\(197\) | −3242.26 | −1.17260 | −0.586298 | − | 0.810095i | \(-0.699415\pi\) | ||||
−0.586298 | + | 0.810095i | \(0.699415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −663.638 | −0.236402 | −0.118201 | − | 0.992990i | \(-0.537713\pi\) | ||||
−0.118201 | + | 0.992990i | \(0.537713\pi\) | |||||||
\(200\) | −2407.48 | −0.851171 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4332.06 | 1.50892 | ||||||||
\(203\) | 1963.78 | 0.678967 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5514.83 | 1.87889 | ||||||||
\(206\) | −802.279 | −0.271347 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.75015 | 0.00225019 | ||||||||
\(209\) | −3.30321 | −0.00109324 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1279.83 | 0.417568 | 0.208784 | − | 0.977962i | \(-0.433049\pi\) | ||||
0.208784 | + | 0.977962i | \(0.433049\pi\) | |||||||
\(212\) | 4516.17 | 1.46308 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −97.2683 | −0.0310707 | ||||||||
\(215\) | 2202.60 | 0.698678 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 882.193 | 0.275978 | ||||||||
\(218\) | 3120.40 | 0.969451 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −58.2379 | −0.0178473 | ||||||||
\(221\) | −131.401 | −0.0399956 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4187.92 | −1.25760 | −0.628798 | − | 0.777569i | \(-0.716453\pi\) | ||||
−0.628798 | + | 0.777569i | \(0.716453\pi\) | |||||||
\(224\) | −4557.50 | −1.35942 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2783.25 | −0.819200 | ||||||||
\(227\) | 4456.98 | 1.30317 | 0.651586 | − | 0.758575i | \(-0.274104\pi\) | ||||
0.651586 | + | 0.758575i | \(0.274104\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6368.11 | −1.83763 | −0.918813 | − | 0.394693i | \(-0.870851\pi\) | ||||
−0.918813 | + | 0.394693i | \(0.870851\pi\) | |||||||
\(230\) | 3100.23 | 0.888796 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1763.18 | 0.498958 | ||||||||
\(233\) | 3358.02 | 0.944168 | 0.472084 | − | 0.881553i | \(-0.343502\pi\) | ||||
0.472084 | + | 0.881553i | \(0.343502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4877.60 | 1.35396 | ||||||||
\(236\) | 9156.34 | 2.52554 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4644.62 | −1.26498 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5178.87 | −1.38423 | −0.692117 | − | 0.721785i | \(-0.743322\pi\) | ||||
−0.692117 | + | 0.721785i | \(0.743322\pi\) | |||||||
\(242\) | 6107.15 | 1.62224 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4662.73 | −1.22336 | ||||||||
\(245\) | 4911.42 | 1.28073 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 37.5730 | 0.00967900 | ||||||||
\(248\) | 792.076 | 0.202810 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1473.63 | 0.372801 | ||||||||
\(251\) | 6252.08 | 1.57222 | 0.786111 | − | 0.618085i | \(-0.212091\pi\) | ||||
0.786111 | + | 0.618085i | \(0.212091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.1736 | 0.00327359 | ||||||||
\(254\) | 102.950 | 0.0254318 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4302.13 | −1.05032 | ||||||||
\(257\) | −5515.39 | −1.33868 | −0.669340 | − | 0.742957i | \(-0.733423\pi\) | ||||
−0.669340 | + | 0.742957i | \(0.733423\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2961.55 | −0.710510 | ||||||||
\(260\) | 662.438 | 0.158010 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3572.96 | −0.842511 | ||||||||
\(263\) | −5472.00 | −1.28296 | −0.641480 | − | 0.767140i | \(-0.721679\pi\) | ||||
−0.641480 | + | 0.767140i | \(0.721679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5231.85 | 1.21279 | ||||||||
\(266\) | 1328.09 | 0.306128 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9773.42 | −2.22764 | ||||||||
\(269\) | −1170.67 | −0.265342 | −0.132671 | − | 0.991160i | \(-0.542355\pi\) | ||||
−0.132671 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1426.98 | −0.319864 | −0.159932 | − | 0.987128i | \(-0.551127\pi\) | ||||
−0.159932 | + | 0.987128i | \(0.551127\pi\) | |||||||
\(272\) | −78.8211 | −0.0175707 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7734.97 | 1.70543 | ||||||||
\(275\) | −30.6026 | −0.00671056 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4834.12 | 1.04857 | 0.524286 | − | 0.851542i | \(-0.324332\pi\) | ||||
0.524286 | + | 0.851542i | \(0.324332\pi\) | |||||||
\(278\) | 1542.45 | 0.332769 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9067.66 | 1.93534 | ||||||||
\(281\) | 5865.40 | 1.24520 | 0.622598 | − | 0.782542i | \(-0.286077\pi\) | ||||
0.622598 | + | 0.782542i | \(0.286077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7932.25 | 1.66616 | 0.833080 | − | 0.553153i | \(-0.186576\pi\) | ||||
0.833080 | + | 0.553153i | \(0.186576\pi\) | |||||||
\(284\) | −9538.00 | −1.99287 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.53963 | 0.000938581 0 | ||||||||
\(287\) | −9421.77 | −1.93780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3378.63 | −0.687692 | ||||||||
\(290\) | 5274.49 | 1.06803 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 545.561 | 0.109337 | ||||||||
\(293\) | 9117.39 | 1.81790 | 0.908948 | − | 0.416910i | \(-0.136887\pi\) | ||||
0.908948 | + | 0.416910i | \(0.136887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10607.4 | 2.09350 | ||||||||
\(296\) | −2659.03 | −0.522138 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7050.09 | 1.37047 | ||||||||
\(299\) | −149.845 | −0.0289826 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3763.01 | −0.720585 | ||||||||
\(302\) | −15674.4 | −2.98663 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 22.5381 | 0.00425214 | ||||||||
\(305\) | −5401.63 | −1.01409 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3145.60 | −0.584784 | −0.292392 | − | 0.956299i | \(-0.594451\pi\) | ||||
−0.292392 | + | 0.956299i | \(0.594451\pi\) | |||||||
\(308\) | 99.4961 | 0.0184069 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2369.47 | 0.434119 | ||||||||
\(311\) | −8439.79 | −1.53883 | −0.769416 | − | 0.638748i | \(-0.779452\pi\) | ||||
−0.769416 | + | 0.638748i | \(0.779452\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4897.13 | 0.884351 | 0.442176 | − | 0.896929i | \(-0.354207\pi\) | ||||
0.442176 | + | 0.896929i | \(0.354207\pi\) | |||||||
\(314\) | −1711.36 | −0.307571 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5888.06 | 1.04819 | ||||||||
\(317\) | −4551.34 | −0.806399 | −0.403200 | − | 0.915112i | \(-0.632102\pi\) | ||||
−0.403200 | + | 0.915112i | \(0.632102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.4126 | 0.00393374 | ||||||||
\(320\) | −12484.4 | −2.18094 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5296.56 | −0.916664 | ||||||||
\(323\) | −438.738 | −0.0755790 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 348.094 | 0.0594117 | ||||||||
\(326\) | −9525.74 | −1.61835 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8459.33 | −1.42405 | ||||||||
\(329\) | −8333.10 | −1.39641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7408.96 | −1.23031 | −0.615156 | − | 0.788405i | \(-0.710907\pi\) | ||||
−0.615156 | + | 0.788405i | \(0.710907\pi\) | |||||||
\(332\) | 10794.9 | 1.78448 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 837.990 | 0.137284 | ||||||||
\(335\) | −11322.2 | −1.84656 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11206.3 | −1.81141 | −0.905707 | − | 0.423904i | \(-0.860659\pi\) | ||||
−0.905707 | + | 0.423904i | \(0.860659\pi\) | |||||||
\(338\) | 10029.7 | 1.61404 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7735.24 | −1.23383 | ||||||||
\(341\) | 10.0684 | 0.00159894 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 472.342 | 0.0743559 | ||||||||
\(344\) | −3378.61 | −0.529542 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10478.0 | −1.62803 | ||||||||
\(347\) | −11731.2 | −1.81489 | −0.907444 | − | 0.420174i | \(-0.861969\pi\) | ||||
−0.907444 | + | 0.420174i | \(0.861969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2945.57 | 0.451784 | 0.225892 | − | 0.974152i | \(-0.427470\pi\) | ||||
0.225892 | + | 0.974152i | \(0.427470\pi\) | |||||||
\(350\) | 12304.0 | 1.87908 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −52.0147 | −0.00787612 | ||||||||
\(353\) | 4349.41 | 0.655795 | 0.327898 | − | 0.944713i | \(-0.393660\pi\) | ||||
0.327898 | + | 0.944713i | \(0.393660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11049.5 | −1.65196 | ||||||||
\(356\) | −16906.8 | −2.51702 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14121.0 | 2.08469 | ||||||||
\(359\) | −4682.08 | −0.688331 | −0.344166 | − | 0.938909i | \(-0.611838\pi\) | ||||
−0.344166 | + | 0.938909i | \(0.611838\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6733.55 | −0.981710 | ||||||||
\(362\) | 5205.23 | 0.755748 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1131.74 | −0.162965 | ||||||||
\(365\) | 632.016 | 0.0906335 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4364.51 | 0.620779 | 0.310389 | − | 0.950610i | \(-0.399541\pi\) | ||||
0.310389 | + | 0.950610i | \(0.399541\pi\) | |||||||
\(368\) | −89.8847 | −0.0127325 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7954.41 | −1.11765 | ||||||||
\(371\) | −8938.32 | −1.25082 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9494.23 | −1.31794 | −0.658971 | − | 0.752168i | \(-0.729008\pi\) | ||||
−0.658971 | + | 0.752168i | \(0.729008\pi\) | |||||||
\(374\) | −53.0090 | −0.00732896 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7481.87 | −1.02619 | ||||||||
\(377\) | −254.936 | −0.0348272 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3268.10 | 0.442931 | 0.221466 | − | 0.975168i | \(-0.428916\pi\) | ||||
0.221466 | + | 0.975168i | \(0.428916\pi\) | |||||||
\(380\) | 2211.82 | 0.298589 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20376.4 | −2.72918 | ||||||||
\(383\) | 1831.46 | 0.244342 | 0.122171 | − | 0.992509i | \(-0.461014\pi\) | ||||
0.122171 | + | 0.992509i | \(0.461014\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 115.263 | 0.0152581 | ||||||||
\(386\) | 5530.87 | 0.729311 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6961.15 | −0.910822 | ||||||||
\(389\) | −15278.4 | −1.99138 | −0.995688 | − | 0.0927692i | \(-0.970428\pi\) | ||||
−0.995688 | + | 0.0927692i | \(0.970428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1749.74 | 0.226312 | ||||||||
\(392\) | −7533.74 | −0.970693 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14877.7 | 1.90236 | ||||||||
\(395\) | 6821.15 | 0.868884 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6226.03 | 0.787092 | 0.393546 | − | 0.919305i | \(-0.371248\pi\) | ||||
0.393546 | + | 0.919305i | \(0.371248\pi\) | |||||||
\(398\) | 3045.23 | 0.383526 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 208.804 | 0.0261005 | ||||||||
\(401\) | −3838.48 | −0.478016 | −0.239008 | − | 0.971018i | \(-0.576822\pi\) | ||||
−0.239008 | + | 0.971018i | \(0.576822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −114.525 | −0.0141561 | ||||||||
\(404\) | −12325.9 | −1.51791 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9011.17 | −1.10152 | ||||||||
\(407\) | −33.8002 | −0.00411649 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −890.762 | −0.107690 | −0.0538452 | − | 0.998549i | \(-0.517148\pi\) | ||||
−0.0538452 | + | 0.998549i | \(0.517148\pi\) | |||||||
\(410\) | −25305.8 | −3.04821 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2282.70 | 0.272963 | ||||||||
\(413\) | −18122.0 | −2.15915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12505.6 | 1.47922 | ||||||||
\(416\) | 591.651 | 0.0697309 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.1574 | 0.00177362 | ||||||||
\(419\) | −14865.7 | −1.73326 | −0.866632 | − | 0.498948i | \(-0.833720\pi\) | ||||
−0.866632 | + | 0.498948i | \(0.833720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3211.47 | 0.371776 | 0.185888 | − | 0.982571i | \(-0.440484\pi\) | ||||
0.185888 | + | 0.982571i | \(0.440484\pi\) | |||||||
\(422\) | −5872.73 | −0.677440 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8025.26 | −0.919201 | ||||||||
\(425\) | −4064.68 | −0.463919 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9228.38 | 1.04588 | ||||||||
\(428\) | 276.755 | 0.0312557 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10107.0 | −1.13350 | ||||||||
\(431\) | 7311.80 | 0.817162 | 0.408581 | − | 0.912722i | \(-0.366024\pi\) | ||||
0.408581 | + | 0.912722i | \(0.366024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15748.5 | −1.74786 | −0.873931 | − | 0.486051i | \(-0.838437\pi\) | ||||
−0.873931 | + | 0.486051i | \(0.838437\pi\) | |||||||
\(434\) | −4048.11 | −0.447731 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8878.39 | −0.975224 | ||||||||
\(437\) | −500.320 | −0.0547679 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9031.99 | −0.981944 | −0.490972 | − | 0.871175i | \(-0.663358\pi\) | ||||
−0.490972 | + | 0.871175i | \(0.663358\pi\) | |||||||
\(440\) | 103.489 | 0.0112128 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 602.961 | 0.0648867 | ||||||||
\(443\) | −8338.56 | −0.894304 | −0.447152 | − | 0.894458i | \(-0.647562\pi\) | ||||
−0.447152 | + | 0.894458i | \(0.647562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19586.1 | −2.08645 | ||||||||
\(446\) | 19217.1 | 2.04026 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 21328.9 | 2.24932 | ||||||||
\(449\) | −2254.14 | −0.236926 | −0.118463 | − | 0.992958i | \(-0.537797\pi\) | ||||
−0.118463 | + | 0.992958i | \(0.537797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −107.531 | −0.0112271 | ||||||||
\(452\) | 7919.11 | 0.824078 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20451.7 | −2.11420 | ||||||||
\(455\) | −1311.08 | −0.135087 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3522.47 | 0.360556 | 0.180278 | − | 0.983616i | \(-0.442300\pi\) | ||||
0.180278 | + | 0.983616i | \(0.442300\pi\) | |||||||
\(458\) | 29221.3 | 2.98127 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8820.99 | −0.894089 | ||||||||
\(461\) | 12960.9 | 1.30943 | 0.654715 | − | 0.755876i | \(-0.272789\pi\) | ||||
0.654715 | + | 0.755876i | \(0.272789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13150.7 | 1.32001 | 0.660003 | − | 0.751263i | \(-0.270555\pi\) | ||||
0.660003 | + | 0.751263i | \(0.270555\pi\) | |||||||
\(464\) | −152.923 | −0.0153002 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15408.9 | −1.53177 | ||||||||
\(467\) | −4317.68 | −0.427834 | −0.213917 | − | 0.976852i | \(-0.568622\pi\) | ||||
−0.213917 | + | 0.976852i | \(0.568622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19343.4 | 1.90446 | ||||||||
\(470\) | −22381.8 | −2.19659 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16270.9 | −1.58671 | ||||||||
\(473\) | −42.9471 | −0.00417487 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1162.25 | 0.112269 | ||||||||
\(476\) | 13215.2 | 1.27252 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1096.70 | 0.104941 | ||||||||
\(479\) | −4948.79 | −0.472058 | −0.236029 | − | 0.971746i | \(-0.575846\pi\) | ||||
−0.236029 | + | 0.971746i | \(0.575846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 384.466 | 0.0364452 | ||||||||
\(482\) | 23764.2 | 2.24571 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17376.5 | −1.63190 | ||||||||
\(485\) | −8064.29 | −0.755011 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9485.80 | 0.882633 | 0.441317 | − | 0.897351i | \(-0.354512\pi\) | ||||
0.441317 | + | 0.897351i | \(0.354512\pi\) | |||||||
\(488\) | 8285.69 | 0.768597 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22537.0 | −2.07779 | ||||||||
\(491\) | −11416.0 | −1.04928 | −0.524638 | − | 0.851325i | \(-0.675799\pi\) | ||||
−0.524638 | + | 0.851325i | \(0.675799\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2976.87 | 0.271950 | ||||||||
\(494\) | −172.411 | −0.0157027 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.6979 | −0.00621901 | ||||||||
\(497\) | 18877.4 | 1.70376 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3525.64 | 0.316292 | 0.158146 | − | 0.987416i | \(-0.449448\pi\) | ||||
0.158146 | + | 0.987416i | \(0.449448\pi\) | |||||||
\(500\) | −4192.87 | −0.375021 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28688.9 | −2.55069 | ||||||||
\(503\) | −1779.64 | −0.157754 | −0.0788770 | − | 0.996884i | \(-0.525133\pi\) | ||||
−0.0788770 | + | 0.996884i | \(0.525133\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14279.2 | −1.25825 | ||||||||
\(506\) | −60.4496 | −0.00531089 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −292.922 | −0.0255833 | ||||||||
\(509\) | 19285.4 | 1.67939 | 0.839696 | − | 0.543056i | \(-0.182733\pi\) | ||||
0.839696 | + | 0.543056i | \(0.182733\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1079.76 | −0.0934753 | ||||||||
\(512\) | 728.382 | 0.0628716 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25308.4 | 2.17180 | ||||||||
\(515\) | 2644.44 | 0.226268 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −95.1056 | −0.00809040 | ||||||||
\(518\) | 13589.6 | 1.15269 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1177.15 | −0.0992724 | ||||||||
\(521\) | 8435.69 | 0.709356 | 0.354678 | − | 0.934989i | \(-0.384591\pi\) | ||||
0.354678 | + | 0.934989i | \(0.384591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1493.58 | −0.124875 | −0.0624375 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624375 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(524\) | 10166.0 | 0.847528 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25109.3 | 2.08140 | ||||||||
\(527\) | 1337.31 | 0.110539 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10171.7 | −0.836004 | ||||||||
\(530\) | −24007.3 | −1.96757 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3778.76 | −0.307951 | ||||||||
\(533\) | 1223.12 | 0.0993985 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 320.612 | 0.0259089 | ||||||||
\(536\) | 17367.4 | 1.39955 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5371.83 | 0.430476 | ||||||||
\(539\) | −95.7650 | −0.00765286 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4187.91 | −0.332814 | −0.166407 | − | 0.986057i | \(-0.553217\pi\) | ||||
−0.166407 | + | 0.986057i | \(0.553217\pi\) | |||||||
\(542\) | 6547.98 | 0.518930 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6908.67 | −0.544497 | ||||||||
\(545\) | −10285.4 | −0.808396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4198.00 | 0.328142 | 0.164071 | − | 0.986449i | \(-0.447537\pi\) | ||||
0.164071 | + | 0.986449i | \(0.447537\pi\) | |||||||
\(548\) | −22008.1 | −1.71558 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 140.426 | 0.0108869 | ||||||||
\(551\) | −851.207 | −0.0658124 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11653.5 | −0.896128 | ||||||||
\(554\) | −22182.3 | −1.70115 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4388.68 | −0.334751 | ||||||||
\(557\) | 3451.57 | 0.262563 | 0.131282 | − | 0.991345i | \(-0.458091\pi\) | ||||
0.131282 | + | 0.991345i | \(0.458091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 488.510 | 0.0369620 | ||||||||
\(560\) | −786.452 | −0.0593458 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26914.5 | −2.02014 | ||||||||
\(563\) | 1630.16 | 0.122030 | 0.0610150 | − | 0.998137i | \(-0.480566\pi\) | ||||
0.0610150 | + | 0.998137i | \(0.480566\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9174.05 | 0.683107 | ||||||||
\(566\) | −36398.6 | −2.70309 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16949.1 | 1.25205 | ||||||||
\(569\) | 17097.3 | 1.25967 | 0.629837 | − | 0.776727i | \(-0.283122\pi\) | ||||
0.629837 | + | 0.776727i | \(0.283122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9042.60 | −0.662734 | −0.331367 | − | 0.943502i | \(-0.607510\pi\) | ||||
−0.331367 | + | 0.943502i | \(0.607510\pi\) | |||||||
\(572\) | −12.9165 | −0.000944171 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 43233.6 | 3.14379 | ||||||||
\(575\) | −4635.21 | −0.336177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20921.9 | −1.50952 | −0.754759 | − | 0.656002i | \(-0.772246\pi\) | ||||
−0.754759 | + | 0.656002i | \(0.772246\pi\) | |||||||
\(578\) | 15503.5 | 1.11568 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15007.4 | −1.07439 | ||||||||
\(581\) | −21365.0 | −1.52560 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −102.013 | −0.00724690 | ||||||||
\(584\) | −969.464 | −0.0686930 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41836.8 | −2.94926 | ||||||||
\(587\) | 6953.22 | 0.488910 | 0.244455 | − | 0.969661i | \(-0.421391\pi\) | ||||
0.244455 | + | 0.969661i | \(0.421391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −382.390 | −0.0267506 | ||||||||
\(590\) | −48673.8 | −3.39639 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 230.622 | 0.0160110 | ||||||||
\(593\) | −8046.53 | −0.557220 | −0.278610 | − | 0.960404i | \(-0.589874\pi\) | ||||
−0.278610 | + | 0.960404i | \(0.589874\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15309.4 | 1.05483 | ||||||||
\(596\) | −20059.4 | −1.37863 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 687.594 | 0.0470198 | ||||||||
\(599\) | −15878.7 | −1.08312 | −0.541558 | − | 0.840663i | \(-0.682166\pi\) | ||||
−0.541558 | + | 0.840663i | \(0.682166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4180.66 | −0.283748 | −0.141874 | − | 0.989885i | \(-0.545313\pi\) | ||||
−0.141874 | + | 0.989885i | \(0.545313\pi\) | |||||||
\(602\) | 17267.3 | 1.16904 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 44598.0 | 3.00442 | ||||||||
\(605\) | −20130.1 | −1.35274 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 782.941 | 0.0523536 | 0.0261768 | − | 0.999657i | \(-0.491667\pi\) | ||||
0.0261768 | + | 0.999657i | \(0.491667\pi\) | |||||||
\(608\) | 1975.47 | 0.131769 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24786.4 | 1.64520 | ||||||||
\(611\) | 1081.79 | 0.0716280 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19886.3 | −1.31028 | −0.655138 | − | 0.755509i | \(-0.727390\pi\) | ||||
−0.655138 | + | 0.755509i | \(0.727390\pi\) | |||||||
\(614\) | 14434.2 | 0.948722 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −176.805 | −0.0115644 | ||||||||
\(617\) | −12249.7 | −0.799280 | −0.399640 | − | 0.916672i | \(-0.630865\pi\) | ||||
−0.399640 | + | 0.916672i | \(0.630865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25619.9 | −1.66357 | −0.831785 | − | 0.555097i | \(-0.812681\pi\) | ||||
−0.831785 | + | 0.555097i | \(0.812681\pi\) | |||||||
\(620\) | −6741.79 | −0.436705 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 38727.6 | 2.49652 | ||||||||
\(623\) | 33461.7 | 2.15187 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17828.2 | −1.14101 | ||||||||
\(626\) | −22471.4 | −1.43472 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4869.27 | 0.309403 | ||||||||
\(629\) | −4489.39 | −0.284584 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19492.8 | −1.22979 | −0.614894 | − | 0.788610i | \(-0.710801\pi\) | ||||
−0.614894 | + | 0.788610i | \(0.710801\pi\) | |||||||
\(632\) | −10463.1 | −0.658545 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 20884.7 | 1.30826 | ||||||||
\(635\) | −339.341 | −0.0212068 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1089.30 | 0.0677543 | ||||||||
\(638\) | −102.844 | −0.00638189 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 35946.1 | 2.22015 | ||||||||
\(641\) | 15937.5 | 0.982047 | 0.491024 | − | 0.871146i | \(-0.336623\pi\) | ||||
0.491024 | + | 0.871146i | \(0.336623\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21204.1 | −1.30048 | −0.650239 | − | 0.759730i | \(-0.725331\pi\) | ||||
−0.650239 | + | 0.759730i | \(0.725331\pi\) | |||||||
\(644\) | 15070.2 | 0.922123 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2013.23 | 0.122615 | ||||||||
\(647\) | −16437.7 | −0.998817 | −0.499408 | − | 0.866367i | \(-0.666449\pi\) | ||||
−0.499408 | + | 0.866367i | \(0.666449\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −206.827 | −0.0125095 | ||||||||
\(650\) | −1597.30 | −0.0963863 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27103.3 | 1.62799 | ||||||||
\(653\) | −8512.52 | −0.510139 | −0.255069 | − | 0.966923i | \(-0.582098\pi\) | ||||
−0.255069 | + | 0.966923i | \(0.582098\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11777.0 | 0.702545 | ||||||||
\(656\) | 733.690 | 0.0436674 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 38238.0 | 2.26546 | ||||||||
\(659\) | 587.889 | 0.0347510 | 0.0173755 | − | 0.999849i | \(-0.494469\pi\) | ||||
0.0173755 | + | 0.999849i | \(0.494469\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3835.60 | 0.225700 | 0.112850 | − | 0.993612i | \(-0.464002\pi\) | ||||
0.112850 | + | 0.993612i | \(0.464002\pi\) | |||||||
\(662\) | 33997.4 | 1.99599 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19182.6 | −1.12113 | ||||||||
\(665\) | −4377.59 | −0.255271 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3394.71 | 0.197067 | ||||||||
\(668\) | −2384.31 | −0.138101 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 51954.2 | 2.99577 | ||||||||
\(671\) | 105.323 | 0.00605955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15030.8 | −0.860912 | −0.430456 | − | 0.902612i | \(-0.641647\pi\) | ||||
−0.430456 | + | 0.902612i | \(0.641647\pi\) | |||||||
\(674\) | 51422.3 | 2.93874 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28537.2 | −1.62365 | ||||||||
\(677\) | −20846.3 | −1.18344 | −0.591720 | − | 0.806144i | \(-0.701551\pi\) | ||||
−0.591720 | + | 0.806144i | \(0.701551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13777.4 | 0.778685 | ||||||||
\(680\) | 13745.6 | 0.775174 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −46.2010 | −0.00259403 | ||||||||
\(683\) | 11132.8 | 0.623697 | 0.311849 | − | 0.950132i | \(-0.399052\pi\) | ||||
0.311849 | + | 0.950132i | \(0.399052\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25495.7 | −1.42210 | ||||||||
\(686\) | −2167.43 | −0.120631 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 293.032 | 0.0162380 | ||||||||
\(689\) | 1160.36 | 0.0641601 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22733.5 | 1.25156 | 0.625778 | − | 0.780001i | \(-0.284782\pi\) | ||||
0.625778 | + | 0.780001i | \(0.284782\pi\) | |||||||
\(692\) | 29812.7 | 1.63773 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 53831.0 | 2.94438 | ||||||||
\(695\) | −5084.16 | −0.277486 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14282.4 | −0.776159 | ||||||||
\(698\) | −13516.3 | −0.732950 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −35008.3 | −1.89027 | ||||||||
\(701\) | 2040.80 | 0.109957 | 0.0549785 | − | 0.998488i | \(-0.482491\pi\) | ||||
0.0549785 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1283.70 | 0.0688699 | ||||||||
\(704\) | 243.427 | 0.0130320 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19958.1 | −1.06393 | ||||||||
\(707\) | 24395.1 | 1.29770 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23191.1 | 1.22844 | 0.614218 | − | 0.789136i | \(-0.289471\pi\) | ||||
0.614218 | + | 0.789136i | \(0.289471\pi\) | |||||||
\(710\) | 50702.7 | 2.68005 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30043.5 | 1.58136 | ||||||||
\(713\) | 1525.01 | 0.0801013 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.9634 | −0.000782655 0 | ||||||||
\(716\) | −40178.2 | −2.09711 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21484.6 | 1.11671 | ||||||||
\(719\) | −27756.3 | −1.43969 | −0.719845 | − | 0.694135i | \(-0.755787\pi\) | ||||
−0.719845 | + | 0.694135i | \(0.755787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4517.88 | −0.233363 | ||||||||
\(722\) | 30898.1 | 1.59267 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14810.3 | −0.760249 | ||||||||
\(725\) | −7885.99 | −0.403970 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14185.6 | −0.723679 | −0.361840 | − | 0.932240i | \(-0.617851\pi\) | ||||
−0.361840 | + | 0.932240i | \(0.617851\pi\) | |||||||
\(728\) | 2011.10 | 0.102385 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2900.12 | −0.147039 | ||||||||
\(731\) | −5704.30 | −0.288620 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14805.4 | 0.746042 | 0.373021 | − | 0.927823i | \(-0.378322\pi\) | ||||
0.373021 | + | 0.927823i | \(0.378322\pi\) | |||||||
\(734\) | −20027.4 | −1.00712 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7878.39 | −0.394567 | ||||||||
\(737\) | 220.766 | 0.0110339 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16831.9 | −0.837853 | −0.418926 | − | 0.908020i | \(-0.637593\pi\) | ||||
−0.418926 | + | 0.908020i | \(0.637593\pi\) | |||||||
\(740\) | 22632.4 | 1.12430 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 41015.2 | 2.02926 | ||||||||
\(743\) | 20561.8 | 1.01526 | 0.507631 | − | 0.861575i | \(-0.330521\pi\) | ||||
0.507631 | + | 0.861575i | \(0.330521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23238.2 | −1.14280 | ||||||||
\(746\) | 43566.1 | 2.13816 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 150.825 | 0.00737261 | ||||||||
\(749\) | −547.747 | −0.0267213 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21060.5 | −1.02332 | −0.511658 | − | 0.859189i | \(-0.670968\pi\) | ||||
−0.511658 | + | 0.859189i | \(0.670968\pi\) | |||||||
\(752\) | 648.914 | 0.0314674 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1169.82 | 0.0565018 | ||||||||
\(755\) | 51665.5 | 2.49046 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23440.4 | −1.12544 | −0.562719 | − | 0.826648i | \(-0.690245\pi\) | ||||
−0.562719 | + | 0.826648i | \(0.690245\pi\) | |||||||
\(758\) | −14996.3 | −0.718588 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3930.41 | −0.187593 | ||||||||
\(761\) | −13575.3 | −0.646656 | −0.323328 | − | 0.946287i | \(-0.604802\pi\) | ||||
−0.323328 | + | 0.946287i | \(0.604802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17571.9 | 0.833744 | ||||||||
\(764\) | 57976.3 | 2.74543 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8403.99 | −0.396408 | ||||||||
\(767\) | 2352.59 | 0.110752 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13313.7 | 0.624323 | 0.312162 | − | 0.950029i | \(-0.398947\pi\) | ||||
0.312162 | + | 0.950029i | \(0.398947\pi\) | |||||||
\(770\) | −528.908 | −0.0247539 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15736.8 | −0.733654 | ||||||||
\(773\) | 7378.75 | 0.343331 | 0.171666 | − | 0.985155i | \(-0.445085\pi\) | ||||
0.171666 | + | 0.985155i | \(0.445085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3542.64 | −0.164201 | ||||||||
\(776\) | 12370.0 | 0.572239 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 70107.8 | 3.23070 | ||||||||
\(779\) | 4083.90 | 0.187832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 215.448 | 0.00987109 | ||||||||
\(782\) | −8029.00 | −0.367156 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 653.413 | 0.0297655 | ||||||||
\(785\) | 5640.91 | 0.256475 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32584.1 | 1.47585 | 0.737927 | − | 0.674880i | \(-0.235805\pi\) | ||||
0.737927 | + | 0.674880i | \(0.235805\pi\) | |||||||
\(788\) | −42331.1 | −1.91369 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −31300.1 | −1.40963 | ||||||||
\(791\) | −15673.3 | −0.704525 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1198.02 | −0.0536480 | ||||||||
\(794\) | −28569.3 | −1.27694 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8664.49 | −0.385810 | ||||||||
\(797\) | 30922.0 | 1.37430 | 0.687148 | − | 0.726517i | \(-0.258862\pi\) | ||||
0.687148 | + | 0.726517i | \(0.258862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12632.1 | −0.559311 | ||||||||
\(800\) | 18301.7 | 0.808827 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17613.6 | 0.775507 | ||||||||
\(803\) | −12.3233 | −0.000541569 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17458.3 | 0.764379 | ||||||||
\(806\) | 525.521 | 0.0229661 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21903.1 | 0.953650 | ||||||||
\(809\) | −39348.2 | −1.71003 | −0.855013 | − | 0.518607i | \(-0.826451\pi\) | ||||
−0.855013 | + | 0.518607i | \(0.826451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20564.7 | −0.890413 | −0.445207 | − | 0.895428i | \(-0.646870\pi\) | ||||
−0.445207 | + | 0.895428i | \(0.646870\pi\) | |||||||
\(812\) | 25639.2 | 1.10808 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 155.098 | 0.00667838 | ||||||||
\(815\) | 31398.4 | 1.34949 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1631.09 | 0.0698465 | ||||||||
\(818\) | 4087.43 | 0.174711 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 72002.0 | 3.06636 | ||||||||
\(821\) | −13125.1 | −0.557939 | −0.278969 | − | 0.960300i | \(-0.589993\pi\) | ||||
−0.278969 | + | 0.960300i | \(0.589993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2653.20 | −0.112375 | −0.0561875 | − | 0.998420i | \(-0.517894\pi\) | ||||
−0.0561875 | + | 0.998420i | \(0.517894\pi\) | |||||||
\(824\) | −4056.37 | −0.171493 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 83156.4 | 3.50288 | ||||||||
\(827\) | 16068.9 | 0.675660 | 0.337830 | − | 0.941207i | \(-0.390307\pi\) | ||||
0.337830 | + | 0.941207i | \(0.390307\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9738.24 | −0.407989 | −0.203995 | − | 0.978972i | \(-0.565392\pi\) | ||||
−0.203995 | + | 0.978972i | \(0.565392\pi\) | |||||||
\(830\) | −57384.2 | −2.39980 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2768.90 | −0.115378 | ||||||||
\(833\) | −12719.6 | −0.529063 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2762.15 | −0.114477 | ||||||||
\(836\) | −43.1270 | −0.00178418 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 68214.1 | 2.81195 | ||||||||
\(839\) | −1386.67 | −0.0570600 | −0.0285300 | − | 0.999593i | \(-0.509083\pi\) | ||||
−0.0285300 | + | 0.999593i | \(0.509083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18613.5 | −0.763192 | ||||||||
\(842\) | −14736.5 | −0.603149 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16709.5 | 0.681475 | ||||||||
\(845\) | −33059.6 | −1.34590 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34391.2 | 1.39515 | ||||||||
\(848\) | 696.043 | 0.0281866 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18651.5 | 0.752638 | ||||||||
\(851\) | −5119.53 | −0.206222 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15525.5 | −0.623192 | −0.311596 | − | 0.950215i | \(-0.600863\pi\) | ||||
−0.311596 | + | 0.950215i | \(0.600863\pi\) | |||||||
\(854\) | −42346.1 | −1.69679 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −491.794 | −0.0196369 | ||||||||
\(857\) | −7278.21 | −0.290104 | −0.145052 | − | 0.989424i | \(-0.546335\pi\) | ||||
−0.145052 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23322.9 | 0.926388 | 0.463194 | − | 0.886257i | \(-0.346703\pi\) | ||||
0.463194 | + | 0.886257i | \(0.346703\pi\) | |||||||
\(860\) | 28757.2 | 1.14025 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33551.6 | −1.32572 | ||||||||
\(863\) | 30197.6 | 1.19112 | 0.595561 | − | 0.803310i | \(-0.296930\pi\) | ||||
0.595561 | + | 0.803310i | \(0.296930\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34537.1 | 1.35757 | ||||||||
\(866\) | 72264.9 | 2.83564 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11518.0 | 0.450397 | ||||||||
\(869\) | −133.002 | −0.00519191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2511.14 | −0.0976884 | ||||||||
\(872\) | 15776.9 | 0.612700 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2295.81 | 0.0888525 | ||||||||
\(875\) | 8298.44 | 0.320615 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46507.4 | −1.79070 | −0.895350 | − | 0.445363i | \(-0.853075\pi\) | ||||
−0.895350 | + | 0.445363i | \(0.853075\pi\) | |||||||
\(878\) | 41445.0 | 1.59305 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.97577 | −0.000343833 0 | ||||||||
\(881\) | 358.878 | 0.0137241 | 0.00686203 | − | 0.999976i | \(-0.497816\pi\) | ||||
0.00686203 | + | 0.999976i | \(0.497816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5590.37 | 0.213059 | 0.106529 | − | 0.994310i | \(-0.466026\pi\) | ||||
0.106529 | + | 0.994310i | \(0.466026\pi\) | |||||||
\(884\) | −1715.59 | −0.0652731 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38263.0 | 1.45087 | ||||||||
\(887\) | −32199.9 | −1.21890 | −0.609451 | − | 0.792823i | \(-0.708610\pi\) | ||||
−0.609451 | + | 0.792823i | \(0.708610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 579.745 | 0.0218718 | ||||||||
\(890\) | 89874.4 | 3.38494 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −54677.7 | −2.05241 | ||||||||
\(893\) | 3612.01 | 0.135354 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46545.2 | −1.73836 | ||||||||
\(896\) | −61411.8 | −2.28976 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10343.6 | 0.384375 | ||||||||
\(899\) | 2594.54 | 0.0962546 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13549.5 | −0.500998 | ||||||||
\(902\) | 493.424 | 0.0182142 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14072.3 | −0.517740 | ||||||||
\(905\) | −17157.3 | −0.630196 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2479.81 | 0.0907835 | 0.0453917 | − | 0.998969i | \(-0.485546\pi\) | ||||
0.0453917 | + | 0.998969i | \(0.485546\pi\) | |||||||
\(908\) | 58190.5 | 2.12679 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6016.15 | 0.219158 | ||||||||
\(911\) | 18543.6 | 0.674399 | 0.337199 | − | 0.941433i | \(-0.390520\pi\) | ||||
0.337199 | + | 0.941433i | \(0.390520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −243.839 | −0.00883887 | ||||||||
\(914\) | −16163.5 | −0.584947 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −83142.4 | −2.99902 | ||||||||
\(917\) | −20120.4 | −0.724573 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18668.1 | −0.670081 | −0.335040 | − | 0.942204i | \(-0.608750\pi\) | ||||
−0.335040 | + | 0.942204i | \(0.608750\pi\) | |||||||
\(920\) | 15674.9 | 0.561726 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −59473.3 | −2.12435 | ||||||||
\(923\) | −2450.65 | −0.0873933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11892.8 | 0.422738 | ||||||||
\(926\) | −60344.3 | −2.14151 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13403.7 | −0.474136 | ||||||||
\(929\) | 5627.24 | 0.198734 | 0.0993669 | − | 0.995051i | \(-0.468318\pi\) | ||||
0.0993669 | + | 0.995051i | \(0.468318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3637.06 | 0.128034 | ||||||||
\(932\) | 43842.5 | 1.54089 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19812.5 | 0.694095 | ||||||||
\(935\) | 174.726 | 0.00611140 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6982.60 | 0.243449 | 0.121724 | − | 0.992564i | \(-0.461158\pi\) | ||||
0.121724 | + | 0.992564i | \(0.461158\pi\) | |||||||
\(938\) | −88760.7 | −3.08970 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 63682.3 | 2.20967 | ||||||||
\(941\) | 11915.5 | 0.412789 | 0.206395 | − | 0.978469i | \(-0.433827\pi\) | ||||
0.206395 | + | 0.978469i | \(0.433827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16287.1 | −0.562439 | ||||||||
\(944\) | 1411.20 | 0.0486552 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 197.071 | 0.00677308 | ||||||||
\(947\) | −56192.9 | −1.92822 | −0.964110 | − | 0.265503i | \(-0.914462\pi\) | ||||
−0.964110 | + | 0.265503i | \(0.914462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 140.174 | 0.00479476 | ||||||||
\(950\) | −5333.23 | −0.182140 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23483.5 | −0.799480 | ||||||||
\(953\) | 16717.7 | 0.568246 | 0.284123 | − | 0.958788i | \(-0.408298\pi\) | ||||
0.284123 | + | 0.958788i | \(0.408298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 67163.8 | 2.27578 | ||||||||
\(956\) | −3120.40 | −0.105566 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22708.5 | 0.765842 | ||||||||
\(959\) | 43558.0 | 1.46670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28625.4 | −0.960876 | ||||||||
\(962\) | −1764.19 | −0.0591267 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −67615.7 | −2.25908 | ||||||||
\(965\) | −18230.6 | −0.608151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53927.3 | 1.79337 | 0.896683 | − | 0.442674i | \(-0.145970\pi\) | ||||
0.896683 | + | 0.442674i | \(0.145970\pi\) | |||||||
\(968\) | 30878.1 | 1.02527 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37004.5 | 1.22489 | ||||||||
\(971\) | −21338.5 | −0.705236 | −0.352618 | − | 0.935767i | \(-0.614708\pi\) | ||||
−0.352618 | + | 0.935767i | \(0.614708\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8685.99 | 0.286187 | ||||||||
\(974\) | −43527.4 | −1.43194 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −718.630 | −0.0235684 | ||||||||
\(977\) | 41274.9 | 1.35159 | 0.675794 | − | 0.737091i | \(-0.263801\pi\) | ||||
0.675794 | + | 0.737091i | \(0.263801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 381.897 | 0.0124673 | ||||||||
\(980\) | 64123.8 | 2.09016 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 52384.2 | 1.70229 | ||||||||
\(983\) | −32718.2 | −1.06160 | −0.530798 | − | 0.847498i | \(-0.678108\pi\) | ||||
−0.530798 | + | 0.847498i | \(0.678108\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49039.4 | −1.58632 | ||||||||
\(986\) | −13659.9 | −0.441197 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 490.555 | 0.0157962 | ||||||||
\(989\) | −6504.97 | −0.209147 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11924.6 | −0.382237 | −0.191118 | − | 0.981567i | \(-0.561211\pi\) | ||||
−0.191118 | + | 0.981567i | \(0.561211\pi\) | |||||||
\(992\) | −6021.37 | −0.192721 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −86622.6 | −2.76409 | ||||||||
\(995\) | −10037.6 | −0.319811 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33617.3 | 1.06787 | 0.533936 | − | 0.845525i | \(-0.320712\pi\) | ||||
0.533936 | + | 0.845525i | \(0.320712\pi\) | |||||||
\(998\) | −16178.1 | −0.513135 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.a.1.2 | 22 | ||
3.2 | odd | 2 | 239.4.a.a.1.21 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
239.4.a.a.1.21 | ✓ | 22 | 3.2 | odd | 2 | ||
2151.4.a.a.1.2 | 22 | 1.1 | even | 1 | trivial |