Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82745 | −1.29220 | −0.646100 | − | 0.763253i | \(-0.723601\pi\) | ||||
−0.646100 | + | 0.763253i | \(0.723601\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.33956 | 0.669782 | ||||||||
\(5\) | 3.12821 | 1.39898 | 0.699489 | − | 0.714643i | \(-0.253411\pi\) | ||||
0.699489 | + | 0.714643i | \(0.253411\pi\) | |||||||
\(6\) | 1.82745 | 0.746052 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.20691 | 0.426708 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.71664 | −1.80776 | ||||||||
\(11\) | 5.32117 | 1.60439 | 0.802196 | − | 0.597060i | \(-0.203665\pi\) | ||||
0.802196 | + | 0.597060i | \(0.203665\pi\) | |||||||
\(12\) | −1.33956 | −0.386699 | ||||||||
\(13\) | −6.23012 | −1.72793 | −0.863963 | − | 0.503555i | \(-0.832025\pi\) | ||||
−0.863963 | + | 0.503555i | \(0.832025\pi\) | |||||||
\(14\) | 1.82745 | 0.488406 | ||||||||
\(15\) | −3.12821 | −0.807700 | ||||||||
\(16\) | −4.88470 | −1.22117 | ||||||||
\(17\) | 3.42890 | 0.831630 | 0.415815 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415815 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(18\) | −1.82745 | −0.430734 | ||||||||
\(19\) | 3.00445 | 0.689268 | 0.344634 | − | 0.938737i | \(-0.388003\pi\) | ||||
0.344634 | + | 0.938737i | \(0.388003\pi\) | |||||||
\(20\) | 4.19044 | 0.937010 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −9.72416 | −2.07320 | ||||||||
\(23\) | −3.54138 | −0.738430 | −0.369215 | − | 0.929344i | \(-0.620373\pi\) | ||||
−0.369215 | + | 0.929344i | \(0.620373\pi\) | |||||||
\(24\) | −1.20691 | −0.246360 | ||||||||
\(25\) | 4.78570 | 0.957139 | ||||||||
\(26\) | 11.3852 | 2.23283 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.33956 | −0.253154 | ||||||||
\(29\) | 9.68026 | 1.79758 | 0.898789 | − | 0.438381i | \(-0.144448\pi\) | ||||
0.898789 | + | 0.438381i | \(0.144448\pi\) | |||||||
\(30\) | 5.71664 | 1.04371 | ||||||||
\(31\) | −7.96130 | −1.42989 | −0.714946 | − | 0.699180i | \(-0.753549\pi\) | ||||
−0.714946 | + | 0.699180i | \(0.753549\pi\) | |||||||
\(32\) | 6.51270 | 1.15129 | ||||||||
\(33\) | −5.32117 | −0.926296 | ||||||||
\(34\) | −6.26613 | −1.07463 | ||||||||
\(35\) | −3.12821 | −0.528764 | ||||||||
\(36\) | 1.33956 | 0.223261 | ||||||||
\(37\) | 3.64886 | 0.599869 | 0.299935 | − | 0.953960i | \(-0.403035\pi\) | ||||
0.299935 | + | 0.953960i | \(0.403035\pi\) | |||||||
\(38\) | −5.49047 | −0.890672 | ||||||||
\(39\) | 6.23012 | 0.997618 | ||||||||
\(40\) | 3.77547 | 0.596955 | ||||||||
\(41\) | 0.294773 | 0.0460357 | 0.0230179 | − | 0.999735i | \(-0.492673\pi\) | ||||
0.0230179 | + | 0.999735i | \(0.492673\pi\) | |||||||
\(42\) | −1.82745 | −0.281981 | ||||||||
\(43\) | −6.81775 | −1.03970 | −0.519849 | − | 0.854258i | \(-0.674012\pi\) | ||||
−0.519849 | + | 0.854258i | \(0.674012\pi\) | |||||||
\(44\) | 7.12805 | 1.07459 | ||||||||
\(45\) | 3.12821 | 0.466326 | ||||||||
\(46\) | 6.47169 | 0.954199 | ||||||||
\(47\) | −6.75725 | −0.985647 | −0.492823 | − | 0.870129i | \(-0.664035\pi\) | ||||
−0.492823 | + | 0.870129i | \(0.664035\pi\) | |||||||
\(48\) | 4.88470 | 0.705045 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.74561 | −1.23682 | ||||||||
\(51\) | −3.42890 | −0.480142 | ||||||||
\(52\) | −8.34565 | −1.15733 | ||||||||
\(53\) | 13.0827 | 1.79705 | 0.898526 | − | 0.438921i | \(-0.144639\pi\) | ||||
0.898526 | + | 0.438921i | \(0.144639\pi\) | |||||||
\(54\) | 1.82745 | 0.248684 | ||||||||
\(55\) | 16.6457 | 2.24451 | ||||||||
\(56\) | −1.20691 | −0.161280 | ||||||||
\(57\) | −3.00445 | −0.397949 | ||||||||
\(58\) | −17.6902 | −2.32283 | ||||||||
\(59\) | 7.44207 | 0.968875 | 0.484438 | − | 0.874826i | \(-0.339024\pi\) | ||||
0.484438 | + | 0.874826i | \(0.339024\pi\) | |||||||
\(60\) | −4.19044 | −0.540983 | ||||||||
\(61\) | 5.24370 | 0.671387 | 0.335694 | − | 0.941971i | \(-0.391029\pi\) | ||||
0.335694 | + | 0.941971i | \(0.391029\pi\) | |||||||
\(62\) | 14.5489 | 1.84771 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −2.13223 | −0.266529 | ||||||||
\(65\) | −19.4891 | −2.41733 | ||||||||
\(66\) | 9.72416 | 1.19696 | ||||||||
\(67\) | −1.88125 | −0.229831 | −0.114916 | − | 0.993375i | \(-0.536660\pi\) | ||||
−0.114916 | + | 0.993375i | \(0.536660\pi\) | |||||||
\(68\) | 4.59323 | 0.557011 | ||||||||
\(69\) | 3.54138 | 0.426333 | ||||||||
\(70\) | 5.71664 | 0.683269 | ||||||||
\(71\) | 12.6404 | 1.50014 | 0.750070 | − | 0.661359i | \(-0.230020\pi\) | ||||
0.750070 | + | 0.661359i | \(0.230020\pi\) | |||||||
\(72\) | 1.20691 | 0.142236 | ||||||||
\(73\) | 4.58132 | 0.536203 | 0.268102 | − | 0.963391i | \(-0.413604\pi\) | ||||
0.268102 | + | 0.963391i | \(0.413604\pi\) | |||||||
\(74\) | −6.66811 | −0.775152 | ||||||||
\(75\) | −4.78570 | −0.552604 | ||||||||
\(76\) | 4.02465 | 0.461659 | ||||||||
\(77\) | −5.32117 | −0.606403 | ||||||||
\(78\) | −11.3852 | −1.28912 | ||||||||
\(79\) | 8.40838 | 0.946017 | 0.473009 | − | 0.881058i | \(-0.343168\pi\) | ||||
0.473009 | + | 0.881058i | \(0.343168\pi\) | |||||||
\(80\) | −15.2804 | −1.70840 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.538681 | −0.0594874 | ||||||||
\(83\) | 11.1938 | 1.22868 | 0.614338 | − | 0.789043i | \(-0.289423\pi\) | ||||
0.614338 | + | 0.789043i | \(0.289423\pi\) | |||||||
\(84\) | 1.33956 | 0.146158 | ||||||||
\(85\) | 10.7263 | 1.16343 | ||||||||
\(86\) | 12.4591 | 1.34350 | ||||||||
\(87\) | −9.68026 | −1.03783 | ||||||||
\(88\) | 6.42218 | 0.684607 | ||||||||
\(89\) | −3.49270 | −0.370226 | −0.185113 | − | 0.982717i | \(-0.559265\pi\) | ||||
−0.185113 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(90\) | −5.71664 | −0.602587 | ||||||||
\(91\) | 6.23012 | 0.653095 | ||||||||
\(92\) | −4.74391 | −0.494587 | ||||||||
\(93\) | 7.96130 | 0.825548 | ||||||||
\(94\) | 12.3485 | 1.27365 | ||||||||
\(95\) | 9.39855 | 0.964271 | ||||||||
\(96\) | −6.51270 | −0.664700 | ||||||||
\(97\) | −12.4927 | −1.26844 | −0.634222 | − | 0.773151i | \(-0.718680\pi\) | ||||
−0.634222 | + | 0.773151i | \(0.718680\pi\) | |||||||
\(98\) | −1.82745 | −0.184600 | ||||||||
\(99\) | 5.32117 | 0.534798 | ||||||||
\(100\) | 6.41075 | 0.641075 | ||||||||
\(101\) | −6.14241 | −0.611193 | −0.305597 | − | 0.952161i | \(-0.598856\pi\) | ||||
−0.305597 | + | 0.952161i | \(0.598856\pi\) | |||||||
\(102\) | 6.26613 | 0.620439 | ||||||||
\(103\) | 6.42298 | 0.632875 | 0.316438 | − | 0.948613i | \(-0.397513\pi\) | ||||
0.316438 | + | 0.948613i | \(0.397513\pi\) | |||||||
\(104\) | −7.51921 | −0.737319 | ||||||||
\(105\) | 3.12821 | 0.305282 | ||||||||
\(106\) | −23.9080 | −2.32215 | ||||||||
\(107\) | −9.48484 | −0.916934 | −0.458467 | − | 0.888711i | \(-0.651601\pi\) | ||||
−0.458467 | + | 0.888711i | \(0.651601\pi\) | |||||||
\(108\) | −1.33956 | −0.128900 | ||||||||
\(109\) | −10.5245 | −1.00806 | −0.504032 | − | 0.863685i | \(-0.668151\pi\) | ||||
−0.504032 | + | 0.863685i | \(0.668151\pi\) | |||||||
\(110\) | −30.4192 | −2.90036 | ||||||||
\(111\) | −3.64886 | −0.346335 | ||||||||
\(112\) | 4.88470 | 0.461560 | ||||||||
\(113\) | −8.33553 | −0.784140 | −0.392070 | − | 0.919935i | \(-0.628241\pi\) | ||||
−0.392070 | + | 0.919935i | \(0.628241\pi\) | |||||||
\(114\) | 5.49047 | 0.514230 | ||||||||
\(115\) | −11.0782 | −1.03305 | ||||||||
\(116\) | 12.9673 | 1.20399 | ||||||||
\(117\) | −6.23012 | −0.575975 | ||||||||
\(118\) | −13.6000 | −1.25198 | ||||||||
\(119\) | −3.42890 | −0.314326 | ||||||||
\(120\) | −3.77547 | −0.344652 | ||||||||
\(121\) | 17.3148 | 1.57408 | ||||||||
\(122\) | −9.58259 | −0.867567 | ||||||||
\(123\) | −0.294773 | −0.0265787 | ||||||||
\(124\) | −10.6647 | −0.957716 | ||||||||
\(125\) | −0.670390 | −0.0599615 | ||||||||
\(126\) | 1.82745 | 0.162802 | ||||||||
\(127\) | 12.3902 | 1.09945 | 0.549726 | − | 0.835345i | \(-0.314732\pi\) | ||||
0.549726 | + | 0.835345i | \(0.314732\pi\) | |||||||
\(128\) | −9.12887 | −0.806886 | ||||||||
\(129\) | 6.81775 | 0.600270 | ||||||||
\(130\) | 35.6154 | 3.12367 | ||||||||
\(131\) | −2.82551 | −0.246866 | −0.123433 | − | 0.992353i | \(-0.539390\pi\) | ||||
−0.123433 | + | 0.992353i | \(0.539390\pi\) | |||||||
\(132\) | −7.12805 | −0.620417 | ||||||||
\(133\) | −3.00445 | −0.260519 | ||||||||
\(134\) | 3.43789 | 0.296988 | ||||||||
\(135\) | −3.12821 | −0.269233 | ||||||||
\(136\) | 4.13838 | 0.354863 | ||||||||
\(137\) | 13.7223 | 1.17238 | 0.586188 | − | 0.810175i | \(-0.300628\pi\) | ||||
0.586188 | + | 0.810175i | \(0.300628\pi\) | |||||||
\(138\) | −6.47169 | −0.550907 | ||||||||
\(139\) | −8.46681 | −0.718145 | −0.359073 | − | 0.933310i | \(-0.616907\pi\) | ||||
−0.359073 | + | 0.933310i | \(0.616907\pi\) | |||||||
\(140\) | −4.19044 | −0.354157 | ||||||||
\(141\) | 6.75725 | 0.569063 | ||||||||
\(142\) | −23.0997 | −1.93848 | ||||||||
\(143\) | −33.1515 | −2.77227 | ||||||||
\(144\) | −4.88470 | −0.407058 | ||||||||
\(145\) | 30.2819 | 2.51477 | ||||||||
\(146\) | −8.37213 | −0.692882 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 4.88789 | 0.401782 | ||||||||
\(149\) | 19.5588 | 1.60232 | 0.801161 | − | 0.598449i | \(-0.204216\pi\) | ||||
0.801161 | + | 0.598449i | \(0.204216\pi\) | |||||||
\(150\) | 8.74561 | 0.714076 | ||||||||
\(151\) | −15.4440 | −1.25681 | −0.628407 | − | 0.777885i | \(-0.716293\pi\) | ||||
−0.628407 | + | 0.777885i | \(0.716293\pi\) | |||||||
\(152\) | 3.62610 | 0.294116 | ||||||||
\(153\) | 3.42890 | 0.277210 | ||||||||
\(154\) | 9.72416 | 0.783595 | ||||||||
\(155\) | −24.9046 | −2.00039 | ||||||||
\(156\) | 8.34565 | 0.668187 | ||||||||
\(157\) | −19.4360 | −1.55116 | −0.775582 | − | 0.631246i | \(-0.782544\pi\) | ||||
−0.775582 | + | 0.631246i | \(0.782544\pi\) | |||||||
\(158\) | −15.3659 | −1.22244 | ||||||||
\(159\) | −13.0827 | −1.03753 | ||||||||
\(160\) | 20.3731 | 1.61063 | ||||||||
\(161\) | 3.54138 | 0.279100 | ||||||||
\(162\) | −1.82745 | −0.143578 | ||||||||
\(163\) | 5.76187 | 0.451304 | 0.225652 | − | 0.974208i | \(-0.427549\pi\) | ||||
0.225652 | + | 0.974208i | \(0.427549\pi\) | |||||||
\(164\) | 0.394867 | 0.0308339 | ||||||||
\(165\) | −16.6457 | −1.29587 | ||||||||
\(166\) | −20.4560 | −1.58769 | ||||||||
\(167\) | 7.03899 | 0.544693 | 0.272347 | − | 0.962199i | \(-0.412200\pi\) | ||||
0.272347 | + | 0.962199i | \(0.412200\pi\) | |||||||
\(168\) | 1.20691 | 0.0931152 | ||||||||
\(169\) | 25.8145 | 1.98573 | ||||||||
\(170\) | −19.6018 | −1.50339 | ||||||||
\(171\) | 3.00445 | 0.229756 | ||||||||
\(172\) | −9.13282 | −0.696371 | ||||||||
\(173\) | −10.5039 | −0.798600 | −0.399300 | − | 0.916820i | \(-0.630747\pi\) | ||||
−0.399300 | + | 0.916820i | \(0.630747\pi\) | |||||||
\(174\) | 17.6902 | 1.34109 | ||||||||
\(175\) | −4.78570 | −0.361765 | ||||||||
\(176\) | −25.9923 | −1.95924 | ||||||||
\(177\) | −7.44207 | −0.559380 | ||||||||
\(178\) | 6.38273 | 0.478406 | ||||||||
\(179\) | −4.17244 | −0.311863 | −0.155931 | − | 0.987768i | \(-0.549838\pi\) | ||||
−0.155931 | + | 0.987768i | \(0.549838\pi\) | |||||||
\(180\) | 4.19044 | 0.312337 | ||||||||
\(181\) | 4.66313 | 0.346607 | 0.173304 | − | 0.984868i | \(-0.444556\pi\) | ||||
0.173304 | + | 0.984868i | \(0.444556\pi\) | |||||||
\(182\) | −11.3852 | −0.843929 | ||||||||
\(183\) | −5.24370 | −0.387626 | ||||||||
\(184\) | −4.27414 | −0.315094 | ||||||||
\(185\) | 11.4144 | 0.839204 | ||||||||
\(186\) | −14.5489 | −1.06677 | ||||||||
\(187\) | 18.2457 | 1.33426 | ||||||||
\(188\) | −9.05178 | −0.660169 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −17.1754 | −1.24603 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 2.13223 | 0.153880 | ||||||||
\(193\) | −3.70861 | −0.266952 | −0.133476 | − | 0.991052i | \(-0.542614\pi\) | ||||
−0.133476 | + | 0.991052i | \(0.542614\pi\) | |||||||
\(194\) | 22.8298 | 1.63908 | ||||||||
\(195\) | 19.4891 | 1.39565 | ||||||||
\(196\) | 1.33956 | 0.0956832 | ||||||||
\(197\) | 3.25792 | 0.232117 | 0.116059 | − | 0.993242i | \(-0.462974\pi\) | ||||
0.116059 | + | 0.993242i | \(0.462974\pi\) | |||||||
\(198\) | −9.72416 | −0.691066 | ||||||||
\(199\) | −9.02179 | −0.639538 | −0.319769 | − | 0.947496i | \(-0.603605\pi\) | ||||
−0.319769 | + | 0.947496i | \(0.603605\pi\) | |||||||
\(200\) | 5.77591 | 0.408419 | ||||||||
\(201\) | 1.88125 | 0.132693 | ||||||||
\(202\) | 11.2249 | 0.789784 | ||||||||
\(203\) | −9.68026 | −0.679421 | ||||||||
\(204\) | −4.59323 | −0.321590 | ||||||||
\(205\) | 0.922110 | 0.0644030 | ||||||||
\(206\) | −11.7377 | −0.817802 | ||||||||
\(207\) | −3.54138 | −0.246143 | ||||||||
\(208\) | 30.4323 | 2.11010 | ||||||||
\(209\) | 15.9872 | 1.10586 | ||||||||
\(210\) | −5.71664 | −0.394486 | ||||||||
\(211\) | 2.27137 | 0.156368 | 0.0781839 | − | 0.996939i | \(-0.475088\pi\) | ||||
0.0781839 | + | 0.996939i | \(0.475088\pi\) | |||||||
\(212\) | 17.5252 | 1.20363 | ||||||||
\(213\) | −12.6404 | −0.866106 | ||||||||
\(214\) | 17.3330 | 1.18486 | ||||||||
\(215\) | −21.3274 | −1.45451 | ||||||||
\(216\) | −1.20691 | −0.0821199 | ||||||||
\(217\) | 7.96130 | 0.540448 | ||||||||
\(218\) | 19.2330 | 1.30262 | ||||||||
\(219\) | −4.58132 | −0.309577 | ||||||||
\(220\) | 22.2980 | 1.50333 | ||||||||
\(221\) | −21.3625 | −1.43699 | ||||||||
\(222\) | 6.66811 | 0.447534 | ||||||||
\(223\) | 0.511803 | 0.0342729 | 0.0171364 | − | 0.999853i | \(-0.494545\pi\) | ||||
0.0171364 | + | 0.999853i | \(0.494545\pi\) | |||||||
\(224\) | −6.51270 | −0.435148 | ||||||||
\(225\) | 4.78570 | 0.319046 | ||||||||
\(226\) | 15.2327 | 1.01327 | ||||||||
\(227\) | −17.3747 | −1.15320 | −0.576600 | − | 0.817026i | \(-0.695621\pi\) | ||||
−0.576600 | + | 0.817026i | \(0.695621\pi\) | |||||||
\(228\) | −4.02465 | −0.266539 | ||||||||
\(229\) | 21.6297 | 1.42933 | 0.714664 | − | 0.699468i | \(-0.246579\pi\) | ||||
0.714664 | + | 0.699468i | \(0.246579\pi\) | |||||||
\(230\) | 20.2448 | 1.33490 | ||||||||
\(231\) | 5.32117 | 0.350107 | ||||||||
\(232\) | 11.6832 | 0.767040 | ||||||||
\(233\) | 13.5171 | 0.885535 | 0.442768 | − | 0.896636i | \(-0.353997\pi\) | ||||
0.442768 | + | 0.896636i | \(0.353997\pi\) | |||||||
\(234\) | 11.3852 | 0.744276 | ||||||||
\(235\) | −21.1381 | −1.37890 | ||||||||
\(236\) | 9.96913 | 0.648935 | ||||||||
\(237\) | −8.40838 | −0.546183 | ||||||||
\(238\) | 6.26613 | 0.406173 | ||||||||
\(239\) | 17.1086 | 1.10666 | 0.553331 | − | 0.832962i | \(-0.313357\pi\) | ||||
0.553331 | + | 0.832962i | \(0.313357\pi\) | |||||||
\(240\) | 15.2804 | 0.986343 | ||||||||
\(241\) | 21.6264 | 1.39308 | 0.696541 | − | 0.717517i | \(-0.254721\pi\) | ||||
0.696541 | + | 0.717517i | \(0.254721\pi\) | |||||||
\(242\) | −31.6419 | −2.03402 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.02428 | 0.449683 | ||||||||
\(245\) | 3.12821 | 0.199854 | ||||||||
\(246\) | 0.538681 | 0.0343451 | ||||||||
\(247\) | −18.7181 | −1.19100 | ||||||||
\(248\) | −9.60858 | −0.610146 | ||||||||
\(249\) | −11.1938 | −0.709376 | ||||||||
\(250\) | 1.22510 | 0.0774823 | ||||||||
\(251\) | 7.73773 | 0.488401 | 0.244201 | − | 0.969725i | \(-0.421474\pi\) | ||||
0.244201 | + | 0.969725i | \(0.421474\pi\) | |||||||
\(252\) | −1.33956 | −0.0843846 | ||||||||
\(253\) | −18.8443 | −1.18473 | ||||||||
\(254\) | −22.6424 | −1.42071 | ||||||||
\(255\) | −10.7263 | −0.671707 | ||||||||
\(256\) | 20.9470 | 1.30919 | ||||||||
\(257\) | 25.9076 | 1.61607 | 0.808037 | − | 0.589132i | \(-0.200530\pi\) | ||||
0.808037 | + | 0.589132i | \(0.200530\pi\) | |||||||
\(258\) | −12.4591 | −0.775669 | ||||||||
\(259\) | −3.64886 | −0.226729 | ||||||||
\(260\) | −26.1070 | −1.61908 | ||||||||
\(261\) | 9.68026 | 0.599193 | ||||||||
\(262\) | 5.16346 | 0.319000 | ||||||||
\(263\) | 20.7483 | 1.27940 | 0.639699 | − | 0.768626i | \(-0.279059\pi\) | ||||
0.639699 | + | 0.768626i | \(0.279059\pi\) | |||||||
\(264\) | −6.42218 | −0.395258 | ||||||||
\(265\) | 40.9255 | 2.51404 | ||||||||
\(266\) | 5.49047 | 0.336643 | ||||||||
\(267\) | 3.49270 | 0.213750 | ||||||||
\(268\) | −2.52006 | −0.153937 | ||||||||
\(269\) | −7.05197 | −0.429966 | −0.214983 | − | 0.976618i | \(-0.568970\pi\) | ||||
−0.214983 | + | 0.976618i | \(0.568970\pi\) | |||||||
\(270\) | 5.71664 | 0.347904 | ||||||||
\(271\) | 23.2104 | 1.40993 | 0.704964 | − | 0.709243i | \(-0.250963\pi\) | ||||
0.704964 | + | 0.709243i | \(0.250963\pi\) | |||||||
\(272\) | −16.7491 | −1.01556 | ||||||||
\(273\) | −6.23012 | −0.377064 | ||||||||
\(274\) | −25.0768 | −1.51495 | ||||||||
\(275\) | 25.4655 | 1.53563 | ||||||||
\(276\) | 4.74391 | 0.285550 | ||||||||
\(277\) | −2.12246 | −0.127526 | −0.0637632 | − | 0.997965i | \(-0.520310\pi\) | ||||
−0.0637632 | + | 0.997965i | \(0.520310\pi\) | |||||||
\(278\) | 15.4727 | 0.927988 | ||||||||
\(279\) | −7.96130 | −0.476630 | ||||||||
\(280\) | −3.77547 | −0.225628 | ||||||||
\(281\) | −10.5544 | −0.629625 | −0.314812 | − | 0.949154i | \(-0.601942\pi\) | ||||
−0.314812 | + | 0.949154i | \(0.601942\pi\) | |||||||
\(282\) | −12.3485 | −0.735344 | ||||||||
\(283\) | −31.5098 | −1.87306 | −0.936532 | − | 0.350583i | \(-0.885984\pi\) | ||||
−0.936532 | + | 0.350583i | \(0.885984\pi\) | |||||||
\(284\) | 16.9326 | 1.00477 | ||||||||
\(285\) | −9.39855 | −0.556722 | ||||||||
\(286\) | 60.5827 | 3.58233 | ||||||||
\(287\) | −0.294773 | −0.0173999 | ||||||||
\(288\) | 6.51270 | 0.383765 | ||||||||
\(289\) | −5.24267 | −0.308392 | ||||||||
\(290\) | −55.3385 | −3.24959 | ||||||||
\(291\) | 12.4927 | 0.732337 | ||||||||
\(292\) | 6.13698 | 0.359139 | ||||||||
\(293\) | −21.2010 | −1.23858 | −0.619289 | − | 0.785163i | \(-0.712579\pi\) | ||||
−0.619289 | + | 0.785163i | \(0.712579\pi\) | |||||||
\(294\) | 1.82745 | 0.106579 | ||||||||
\(295\) | 23.2804 | 1.35543 | ||||||||
\(296\) | 4.40386 | 0.255969 | ||||||||
\(297\) | −5.32117 | −0.308765 | ||||||||
\(298\) | −35.7427 | −2.07052 | ||||||||
\(299\) | 22.0633 | 1.27595 | ||||||||
\(300\) | −6.41075 | −0.370125 | ||||||||
\(301\) | 6.81775 | 0.392969 | ||||||||
\(302\) | 28.2231 | 1.62406 | ||||||||
\(303\) | 6.14241 | 0.352873 | ||||||||
\(304\) | −14.6758 | −0.841716 | ||||||||
\(305\) | 16.4034 | 0.939256 | ||||||||
\(306\) | −6.26613 | −0.358211 | ||||||||
\(307\) | −3.93876 | −0.224797 | −0.112399 | − | 0.993663i | \(-0.535853\pi\) | ||||
−0.112399 | + | 0.993663i | \(0.535853\pi\) | |||||||
\(308\) | −7.12805 | −0.406158 | ||||||||
\(309\) | −6.42298 | −0.365391 | ||||||||
\(310\) | 45.5119 | 2.58490 | ||||||||
\(311\) | −7.83859 | −0.444486 | −0.222243 | − | 0.974991i | \(-0.571338\pi\) | ||||
−0.222243 | + | 0.974991i | \(0.571338\pi\) | |||||||
\(312\) | 7.51921 | 0.425691 | ||||||||
\(313\) | 5.71415 | 0.322983 | 0.161491 | − | 0.986874i | \(-0.448370\pi\) | ||||
0.161491 | + | 0.986874i | \(0.448370\pi\) | |||||||
\(314\) | 35.5183 | 2.00442 | ||||||||
\(315\) | −3.12821 | −0.176255 | ||||||||
\(316\) | 11.2636 | 0.633625 | ||||||||
\(317\) | 15.6031 | 0.876356 | 0.438178 | − | 0.898888i | \(-0.355624\pi\) | ||||
0.438178 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(318\) | 23.9080 | 1.34069 | ||||||||
\(319\) | 51.5103 | 2.88402 | ||||||||
\(320\) | −6.67006 | −0.372868 | ||||||||
\(321\) | 9.48484 | 0.529392 | ||||||||
\(322\) | −6.47169 | −0.360653 | ||||||||
\(323\) | 10.3019 | 0.573216 | ||||||||
\(324\) | 1.33956 | 0.0744202 | ||||||||
\(325\) | −29.8155 | −1.65387 | ||||||||
\(326\) | −10.5295 | −0.583176 | ||||||||
\(327\) | 10.5245 | 0.582006 | ||||||||
\(328\) | 0.355764 | 0.0196438 | ||||||||
\(329\) | 6.75725 | 0.372539 | ||||||||
\(330\) | 30.4192 | 1.67452 | ||||||||
\(331\) | −22.3680 | −1.22946 | −0.614729 | − | 0.788738i | \(-0.710735\pi\) | ||||
−0.614729 | + | 0.788738i | \(0.710735\pi\) | |||||||
\(332\) | 14.9948 | 0.822945 | ||||||||
\(333\) | 3.64886 | 0.199956 | ||||||||
\(334\) | −12.8634 | −0.703853 | ||||||||
\(335\) | −5.88495 | −0.321529 | ||||||||
\(336\) | −4.88470 | −0.266482 | ||||||||
\(337\) | −30.9508 | −1.68600 | −0.843000 | − | 0.537914i | \(-0.819213\pi\) | ||||
−0.843000 | + | 0.537914i | \(0.819213\pi\) | |||||||
\(338\) | −47.1746 | −2.56596 | ||||||||
\(339\) | 8.33553 | 0.452724 | ||||||||
\(340\) | 14.3686 | 0.779246 | ||||||||
\(341\) | −42.3634 | −2.29411 | ||||||||
\(342\) | −5.49047 | −0.296891 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.22842 | −0.443647 | ||||||||
\(345\) | 11.0782 | 0.596430 | ||||||||
\(346\) | 19.1954 | 1.03195 | ||||||||
\(347\) | 20.6092 | 1.10636 | 0.553179 | − | 0.833062i | \(-0.313415\pi\) | ||||
0.553179 | + | 0.833062i | \(0.313415\pi\) | |||||||
\(348\) | −12.9673 | −0.695122 | ||||||||
\(349\) | −13.3692 | −0.715636 | −0.357818 | − | 0.933791i | \(-0.616479\pi\) | ||||
−0.357818 | + | 0.933791i | \(0.616479\pi\) | |||||||
\(350\) | 8.74561 | 0.467472 | ||||||||
\(351\) | 6.23012 | 0.332539 | ||||||||
\(352\) | 34.6552 | 1.84713 | ||||||||
\(353\) | 14.2895 | 0.760554 | 0.380277 | − | 0.924873i | \(-0.375829\pi\) | ||||
0.380277 | + | 0.924873i | \(0.375829\pi\) | |||||||
\(354\) | 13.6000 | 0.722831 | ||||||||
\(355\) | 39.5418 | 2.09866 | ||||||||
\(356\) | −4.67870 | −0.247971 | ||||||||
\(357\) | 3.42890 | 0.181476 | ||||||||
\(358\) | 7.62491 | 0.402989 | ||||||||
\(359\) | 0.666146 | 0.0351579 | 0.0175789 | − | 0.999845i | \(-0.494404\pi\) | ||||
0.0175789 | + | 0.999845i | \(0.494404\pi\) | |||||||
\(360\) | 3.77547 | 0.198985 | ||||||||
\(361\) | −9.97328 | −0.524910 | ||||||||
\(362\) | −8.52162 | −0.447886 | ||||||||
\(363\) | −17.3148 | −0.908793 | ||||||||
\(364\) | 8.34565 | 0.437431 | ||||||||
\(365\) | 14.3313 | 0.750136 | ||||||||
\(366\) | 9.58259 | 0.500890 | ||||||||
\(367\) | 29.4696 | 1.53830 | 0.769150 | − | 0.639068i | \(-0.220680\pi\) | ||||
0.769150 | + | 0.639068i | \(0.220680\pi\) | |||||||
\(368\) | 17.2986 | 0.901751 | ||||||||
\(369\) | 0.294773 | 0.0153452 | ||||||||
\(370\) | −20.8592 | −1.08442 | ||||||||
\(371\) | −13.0827 | −0.679222 | ||||||||
\(372\) | 10.6647 | 0.552937 | ||||||||
\(373\) | 31.2192 | 1.61647 | 0.808233 | − | 0.588862i | \(-0.200424\pi\) | ||||
0.808233 | + | 0.588862i | \(0.200424\pi\) | |||||||
\(374\) | −33.3431 | −1.72413 | ||||||||
\(375\) | 0.670390 | 0.0346188 | ||||||||
\(376\) | −8.15541 | −0.420583 | ||||||||
\(377\) | −60.3092 | −3.10608 | ||||||||
\(378\) | −1.82745 | −0.0939938 | ||||||||
\(379\) | −7.11163 | −0.365300 | −0.182650 | − | 0.983178i | \(-0.558467\pi\) | ||||
−0.182650 | + | 0.983178i | \(0.558467\pi\) | |||||||
\(380\) | 12.5900 | 0.645851 | ||||||||
\(381\) | −12.3902 | −0.634769 | ||||||||
\(382\) | −1.82745 | −0.0935003 | ||||||||
\(383\) | −23.0648 | −1.17855 | −0.589277 | − | 0.807931i | \(-0.700587\pi\) | ||||
−0.589277 | + | 0.807931i | \(0.700587\pi\) | |||||||
\(384\) | 9.12887 | 0.465856 | ||||||||
\(385\) | −16.6457 | −0.848345 | ||||||||
\(386\) | 6.77729 | 0.344955 | ||||||||
\(387\) | −6.81775 | −0.346566 | ||||||||
\(388\) | −16.7348 | −0.849582 | ||||||||
\(389\) | −1.55520 | −0.0788520 | −0.0394260 | − | 0.999222i | \(-0.512553\pi\) | ||||
−0.0394260 | + | 0.999222i | \(0.512553\pi\) | |||||||
\(390\) | −35.6154 | −1.80345 | ||||||||
\(391\) | −12.1430 | −0.614100 | ||||||||
\(392\) | 1.20691 | 0.0609582 | ||||||||
\(393\) | 2.82551 | 0.142528 | ||||||||
\(394\) | −5.95368 | −0.299942 | ||||||||
\(395\) | 26.3032 | 1.32346 | ||||||||
\(396\) | 7.12805 | 0.358198 | ||||||||
\(397\) | 33.9256 | 1.70268 | 0.851339 | − | 0.524615i | \(-0.175791\pi\) | ||||
0.851339 | + | 0.524615i | \(0.175791\pi\) | |||||||
\(398\) | 16.4868 | 0.826411 | ||||||||
\(399\) | 3.00445 | 0.150411 | ||||||||
\(400\) | −23.3767 | −1.16883 | ||||||||
\(401\) | 23.1948 | 1.15830 | 0.579148 | − | 0.815223i | \(-0.303385\pi\) | ||||
0.579148 | + | 0.815223i | \(0.303385\pi\) | |||||||
\(402\) | −3.43789 | −0.171466 | ||||||||
\(403\) | 49.5999 | 2.47075 | ||||||||
\(404\) | −8.22816 | −0.409366 | ||||||||
\(405\) | 3.12821 | 0.155442 | ||||||||
\(406\) | 17.6902 | 0.877948 | ||||||||
\(407\) | 19.4162 | 0.962426 | ||||||||
\(408\) | −4.13838 | −0.204880 | ||||||||
\(409\) | 17.2077 | 0.850864 | 0.425432 | − | 0.904990i | \(-0.360122\pi\) | ||||
0.425432 | + | 0.904990i | \(0.360122\pi\) | |||||||
\(410\) | −1.68511 | −0.0832216 | ||||||||
\(411\) | −13.7223 | −0.676872 | ||||||||
\(412\) | 8.60400 | 0.423889 | ||||||||
\(413\) | −7.44207 | −0.366200 | ||||||||
\(414\) | 6.47169 | 0.318066 | ||||||||
\(415\) | 35.0164 | 1.71889 | ||||||||
\(416\) | −40.5749 | −1.98935 | ||||||||
\(417\) | 8.46681 | 0.414621 | ||||||||
\(418\) | −29.2157 | −1.42899 | ||||||||
\(419\) | 24.1906 | 1.18179 | 0.590895 | − | 0.806749i | \(-0.298775\pi\) | ||||
0.590895 | + | 0.806749i | \(0.298775\pi\) | |||||||
\(420\) | 4.19044 | 0.204472 | ||||||||
\(421\) | 18.9170 | 0.921959 | 0.460979 | − | 0.887411i | \(-0.347498\pi\) | ||||
0.460979 | + | 0.887411i | \(0.347498\pi\) | |||||||
\(422\) | −4.15082 | −0.202059 | ||||||||
\(423\) | −6.75725 | −0.328549 | ||||||||
\(424\) | 15.7897 | 0.766816 | ||||||||
\(425\) | 16.4097 | 0.795985 | ||||||||
\(426\) | 23.0997 | 1.11918 | ||||||||
\(427\) | −5.24370 | −0.253761 | ||||||||
\(428\) | −12.7055 | −0.614146 | ||||||||
\(429\) | 33.1515 | 1.60057 | ||||||||
\(430\) | 38.9746 | 1.87952 | ||||||||
\(431\) | 13.7526 | 0.662440 | 0.331220 | − | 0.943553i | \(-0.392540\pi\) | ||||
0.331220 | + | 0.943553i | \(0.392540\pi\) | |||||||
\(432\) | 4.88470 | 0.235015 | ||||||||
\(433\) | 17.7825 | 0.854574 | 0.427287 | − | 0.904116i | \(-0.359469\pi\) | ||||
0.427287 | + | 0.904116i | \(0.359469\pi\) | |||||||
\(434\) | −14.5489 | −0.698367 | ||||||||
\(435\) | −30.2819 | −1.45190 | ||||||||
\(436\) | −14.0983 | −0.675184 | ||||||||
\(437\) | −10.6399 | −0.508976 | ||||||||
\(438\) | 8.37213 | 0.400036 | ||||||||
\(439\) | −12.7244 | −0.607303 | −0.303651 | − | 0.952783i | \(-0.598206\pi\) | ||||
−0.303651 | + | 0.952783i | \(0.598206\pi\) | |||||||
\(440\) | 20.0899 | 0.957750 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 39.0388 | 1.85688 | ||||||||
\(443\) | 34.8267 | 1.65466 | 0.827332 | − | 0.561713i | \(-0.189857\pi\) | ||||
0.827332 | + | 0.561713i | \(0.189857\pi\) | |||||||
\(444\) | −4.88789 | −0.231969 | ||||||||
\(445\) | −10.9259 | −0.517938 | ||||||||
\(446\) | −0.935293 | −0.0442874 | ||||||||
\(447\) | −19.5588 | −0.925101 | ||||||||
\(448\) | 2.13223 | 0.100738 | ||||||||
\(449\) | 20.1055 | 0.948838 | 0.474419 | − | 0.880299i | \(-0.342658\pi\) | ||||
0.474419 | + | 0.880299i | \(0.342658\pi\) | |||||||
\(450\) | −8.74561 | −0.412272 | ||||||||
\(451\) | 1.56853 | 0.0738594 | ||||||||
\(452\) | −11.1660 | −0.525203 | ||||||||
\(453\) | 15.4440 | 0.725622 | ||||||||
\(454\) | 31.7514 | 1.49017 | ||||||||
\(455\) | 19.4891 | 0.913665 | ||||||||
\(456\) | −3.62610 | −0.169808 | ||||||||
\(457\) | 3.08405 | 0.144266 | 0.0721328 | − | 0.997395i | \(-0.477019\pi\) | ||||
0.0721328 | + | 0.997395i | \(0.477019\pi\) | |||||||
\(458\) | −39.5271 | −1.84698 | ||||||||
\(459\) | −3.42890 | −0.160047 | ||||||||
\(460\) | −14.8400 | −0.691916 | ||||||||
\(461\) | 39.0986 | 1.82101 | 0.910503 | − | 0.413503i | \(-0.135695\pi\) | ||||
0.910503 | + | 0.413503i | \(0.135695\pi\) | |||||||
\(462\) | −9.72416 | −0.452409 | ||||||||
\(463\) | 30.5919 | 1.42173 | 0.710863 | − | 0.703330i | \(-0.248304\pi\) | ||||
0.710863 | + | 0.703330i | \(0.248304\pi\) | |||||||
\(464\) | −47.2851 | −2.19516 | ||||||||
\(465\) | 24.9046 | 1.15492 | ||||||||
\(466\) | −24.7018 | −1.14429 | ||||||||
\(467\) | 28.0040 | 1.29587 | 0.647935 | − | 0.761695i | \(-0.275633\pi\) | ||||
0.647935 | + | 0.761695i | \(0.275633\pi\) | |||||||
\(468\) | −8.34565 | −0.385778 | ||||||||
\(469\) | 1.88125 | 0.0868681 | ||||||||
\(470\) | 38.6288 | 1.78181 | ||||||||
\(471\) | 19.4360 | 0.895565 | ||||||||
\(472\) | 8.98192 | 0.413426 | ||||||||
\(473\) | −36.2784 | −1.66808 | ||||||||
\(474\) | 15.3659 | 0.705778 | ||||||||
\(475\) | 14.3784 | 0.659725 | ||||||||
\(476\) | −4.59323 | −0.210530 | ||||||||
\(477\) | 13.0827 | 0.599017 | ||||||||
\(478\) | −31.2650 | −1.43003 | ||||||||
\(479\) | −1.49664 | −0.0683833 | −0.0341917 | − | 0.999415i | \(-0.510886\pi\) | ||||
−0.0341917 | + | 0.999415i | \(0.510886\pi\) | |||||||
\(480\) | −20.3731 | −0.929900 | ||||||||
\(481\) | −22.7329 | −1.03653 | ||||||||
\(482\) | −39.5212 | −1.80014 | ||||||||
\(483\) | −3.54138 | −0.161139 | ||||||||
\(484\) | 23.1943 | 1.05429 | ||||||||
\(485\) | −39.0799 | −1.77453 | ||||||||
\(486\) | 1.82745 | 0.0828947 | ||||||||
\(487\) | −16.1889 | −0.733590 | −0.366795 | − | 0.930302i | \(-0.619545\pi\) | ||||
−0.366795 | + | 0.930302i | \(0.619545\pi\) | |||||||
\(488\) | 6.32868 | 0.286486 | ||||||||
\(489\) | −5.76187 | −0.260561 | ||||||||
\(490\) | −5.71664 | −0.258251 | ||||||||
\(491\) | −19.9786 | −0.901621 | −0.450810 | − | 0.892620i | \(-0.648865\pi\) | ||||
−0.450810 | + | 0.892620i | \(0.648865\pi\) | |||||||
\(492\) | −0.394867 | −0.0178020 | ||||||||
\(493\) | 33.1926 | 1.49492 | ||||||||
\(494\) | 34.2063 | 1.53902 | ||||||||
\(495\) | 16.6457 | 0.748170 | ||||||||
\(496\) | 38.8885 | 1.74615 | ||||||||
\(497\) | −12.6404 | −0.566999 | ||||||||
\(498\) | 20.4560 | 0.916656 | ||||||||
\(499\) | −6.36633 | −0.284996 | −0.142498 | − | 0.989795i | \(-0.545513\pi\) | ||||
−0.142498 | + | 0.989795i | \(0.545513\pi\) | |||||||
\(500\) | −0.898030 | −0.0401611 | ||||||||
\(501\) | −7.03899 | −0.314479 | ||||||||
\(502\) | −14.1403 | −0.631112 | ||||||||
\(503\) | 26.1278 | 1.16498 | 0.582490 | − | 0.812838i | \(-0.302079\pi\) | ||||
0.582490 | + | 0.812838i | \(0.302079\pi\) | |||||||
\(504\) | −1.20691 | −0.0537601 | ||||||||
\(505\) | −19.2148 | −0.855046 | ||||||||
\(506\) | 34.4370 | 1.53091 | ||||||||
\(507\) | −25.8145 | −1.14646 | ||||||||
\(508\) | 16.5975 | 0.736394 | ||||||||
\(509\) | −10.3430 | −0.458447 | −0.229224 | − | 0.973374i | \(-0.573619\pi\) | ||||
−0.229224 | + | 0.973374i | \(0.573619\pi\) | |||||||
\(510\) | 19.6018 | 0.867981 | ||||||||
\(511\) | −4.58132 | −0.202666 | ||||||||
\(512\) | −20.0218 | −0.884846 | ||||||||
\(513\) | −3.00445 | −0.132650 | ||||||||
\(514\) | −47.3448 | −2.08829 | ||||||||
\(515\) | 20.0924 | 0.885379 | ||||||||
\(516\) | 9.13282 | 0.402050 | ||||||||
\(517\) | −35.9565 | −1.58136 | ||||||||
\(518\) | 6.66811 | 0.292980 | ||||||||
\(519\) | 10.5039 | 0.461072 | ||||||||
\(520\) | −23.5217 | −1.03149 | ||||||||
\(521\) | 29.5916 | 1.29643 | 0.648215 | − | 0.761457i | \(-0.275516\pi\) | ||||
0.648215 | + | 0.761457i | \(0.275516\pi\) | |||||||
\(522\) | −17.6902 | −0.774277 | ||||||||
\(523\) | −29.9079 | −1.30778 | −0.653890 | − | 0.756590i | \(-0.726864\pi\) | ||||
−0.653890 | + | 0.756590i | \(0.726864\pi\) | |||||||
\(524\) | −3.78495 | −0.165346 | ||||||||
\(525\) | 4.78570 | 0.208865 | ||||||||
\(526\) | −37.9165 | −1.65324 | ||||||||
\(527\) | −27.2985 | −1.18914 | ||||||||
\(528\) | 25.9923 | 1.13117 | ||||||||
\(529\) | −10.4586 | −0.454722 | ||||||||
\(530\) | −74.7893 | −3.24864 | ||||||||
\(531\) | 7.44207 | 0.322958 | ||||||||
\(532\) | −4.02465 | −0.174491 | ||||||||
\(533\) | −1.83647 | −0.0795463 | ||||||||
\(534\) | −6.38273 | −0.276208 | ||||||||
\(535\) | −29.6706 | −1.28277 | ||||||||
\(536\) | −2.27050 | −0.0980708 | ||||||||
\(537\) | 4.17244 | 0.180054 | ||||||||
\(538\) | 12.8871 | 0.555603 | ||||||||
\(539\) | 5.32117 | 0.229199 | ||||||||
\(540\) | −4.19044 | −0.180328 | ||||||||
\(541\) | 21.5157 | 0.925030 | 0.462515 | − | 0.886611i | \(-0.346947\pi\) | ||||
0.462515 | + | 0.886611i | \(0.346947\pi\) | |||||||
\(542\) | −42.4157 | −1.82191 | ||||||||
\(543\) | −4.66313 | −0.200114 | ||||||||
\(544\) | 22.3314 | 0.957450 | ||||||||
\(545\) | −32.9229 | −1.41026 | ||||||||
\(546\) | 11.3852 | 0.487243 | ||||||||
\(547\) | −36.7028 | −1.56930 | −0.784650 | − | 0.619939i | \(-0.787157\pi\) | ||||
−0.784650 | + | 0.619939i | \(0.787157\pi\) | |||||||
\(548\) | 18.3819 | 0.785237 | ||||||||
\(549\) | 5.24370 | 0.223796 | ||||||||
\(550\) | −46.5368 | −1.98434 | ||||||||
\(551\) | 29.0838 | 1.23901 | ||||||||
\(552\) | 4.27414 | 0.181919 | ||||||||
\(553\) | −8.40838 | −0.357561 | ||||||||
\(554\) | 3.87869 | 0.164790 | ||||||||
\(555\) | −11.4144 | −0.484515 | ||||||||
\(556\) | −11.3418 | −0.481001 | ||||||||
\(557\) | 8.09376 | 0.342944 | 0.171472 | − | 0.985189i | \(-0.445148\pi\) | ||||
0.171472 | + | 0.985189i | \(0.445148\pi\) | |||||||
\(558\) | 14.5489 | 0.615902 | ||||||||
\(559\) | 42.4754 | 1.79652 | ||||||||
\(560\) | 15.2804 | 0.645713 | ||||||||
\(561\) | −18.2457 | −0.770336 | ||||||||
\(562\) | 19.2877 | 0.813601 | ||||||||
\(563\) | 37.0310 | 1.56067 | 0.780334 | − | 0.625362i | \(-0.215049\pi\) | ||||
0.780334 | + | 0.625362i | \(0.215049\pi\) | |||||||
\(564\) | 9.05178 | 0.381149 | ||||||||
\(565\) | −26.0753 | −1.09700 | ||||||||
\(566\) | 57.5825 | 2.42037 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 15.2558 | 0.640121 | ||||||||
\(569\) | 24.5532 | 1.02932 | 0.514661 | − | 0.857394i | \(-0.327918\pi\) | ||||
0.514661 | + | 0.857394i | \(0.327918\pi\) | |||||||
\(570\) | 17.1754 | 0.719396 | ||||||||
\(571\) | −32.3888 | −1.35543 | −0.677715 | − | 0.735325i | \(-0.737030\pi\) | ||||
−0.677715 | + | 0.735325i | \(0.737030\pi\) | |||||||
\(572\) | −44.4086 | −1.85682 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 0.538681 | 0.0224841 | ||||||||
\(575\) | −16.9480 | −0.706780 | ||||||||
\(576\) | −2.13223 | −0.0888429 | ||||||||
\(577\) | 2.67247 | 0.111256 | 0.0556281 | − | 0.998452i | \(-0.482284\pi\) | ||||
0.0556281 | + | 0.998452i | \(0.482284\pi\) | |||||||
\(578\) | 9.58070 | 0.398504 | ||||||||
\(579\) | 3.70861 | 0.154125 | ||||||||
\(580\) | 40.5645 | 1.68435 | ||||||||
\(581\) | −11.1938 | −0.464396 | ||||||||
\(582\) | −22.8298 | −0.946326 | ||||||||
\(583\) | 69.6154 | 2.88318 | ||||||||
\(584\) | 5.52925 | 0.228802 | ||||||||
\(585\) | −19.4891 | −0.805777 | ||||||||
\(586\) | 38.7438 | 1.60049 | ||||||||
\(587\) | −25.6696 | −1.05950 | −0.529750 | − | 0.848154i | \(-0.677714\pi\) | ||||
−0.529750 | + | 0.848154i | \(0.677714\pi\) | |||||||
\(588\) | −1.33956 | −0.0552427 | ||||||||
\(589\) | −23.9193 | −0.985578 | ||||||||
\(590\) | −42.5436 | −1.75149 | ||||||||
\(591\) | −3.25792 | −0.134013 | ||||||||
\(592\) | −17.8236 | −0.732545 | ||||||||
\(593\) | 29.3254 | 1.20425 | 0.602125 | − | 0.798402i | \(-0.294321\pi\) | ||||
0.602125 | + | 0.798402i | \(0.294321\pi\) | |||||||
\(594\) | 9.72416 | 0.398987 | ||||||||
\(595\) | −10.7263 | −0.439736 | ||||||||
\(596\) | 26.2003 | 1.07321 | ||||||||
\(597\) | 9.02179 | 0.369237 | ||||||||
\(598\) | −40.3195 | −1.64879 | ||||||||
\(599\) | −16.7040 | −0.682508 | −0.341254 | − | 0.939971i | \(-0.610852\pi\) | ||||
−0.341254 | + | 0.939971i | \(0.610852\pi\) | |||||||
\(600\) | −5.77591 | −0.235801 | ||||||||
\(601\) | 31.4715 | 1.28375 | 0.641875 | − | 0.766809i | \(-0.278157\pi\) | ||||
0.641875 | + | 0.766809i | \(0.278157\pi\) | |||||||
\(602\) | −12.4591 | −0.507794 | ||||||||
\(603\) | −1.88125 | −0.0766105 | ||||||||
\(604\) | −20.6882 | −0.841792 | ||||||||
\(605\) | 54.1644 | 2.20210 | ||||||||
\(606\) | −11.2249 | −0.455982 | ||||||||
\(607\) | −39.7592 | −1.61377 | −0.806887 | − | 0.590705i | \(-0.798850\pi\) | ||||
−0.806887 | + | 0.590705i | \(0.798850\pi\) | |||||||
\(608\) | 19.5671 | 0.793550 | ||||||||
\(609\) | 9.68026 | 0.392264 | ||||||||
\(610\) | −29.9764 | −1.21371 | ||||||||
\(611\) | 42.0985 | 1.70312 | ||||||||
\(612\) | 4.59323 | 0.185670 | ||||||||
\(613\) | 0.219957 | 0.00888397 | 0.00444199 | − | 0.999990i | \(-0.498586\pi\) | ||||
0.00444199 | + | 0.999990i | \(0.498586\pi\) | |||||||
\(614\) | 7.19788 | 0.290483 | ||||||||
\(615\) | −0.922110 | −0.0371831 | ||||||||
\(616\) | −6.42218 | −0.258757 | ||||||||
\(617\) | −13.7439 | −0.553308 | −0.276654 | − | 0.960970i | \(-0.589226\pi\) | ||||
−0.276654 | + | 0.960970i | \(0.589226\pi\) | |||||||
\(618\) | 11.7377 | 0.472158 | ||||||||
\(619\) | −29.9646 | −1.20438 | −0.602190 | − | 0.798353i | \(-0.705705\pi\) | ||||
−0.602190 | + | 0.798353i | \(0.705705\pi\) | |||||||
\(620\) | −33.3613 | −1.33982 | ||||||||
\(621\) | 3.54138 | 0.142111 | ||||||||
\(622\) | 14.3246 | 0.574365 | ||||||||
\(623\) | 3.49270 | 0.139932 | ||||||||
\(624\) | −30.4323 | −1.21827 | ||||||||
\(625\) | −26.0256 | −1.04102 | ||||||||
\(626\) | −10.4423 | −0.417359 | ||||||||
\(627\) | −15.9872 | −0.638466 | ||||||||
\(628\) | −26.0358 | −1.03894 | ||||||||
\(629\) | 12.5116 | 0.498869 | ||||||||
\(630\) | 5.71664 | 0.227756 | ||||||||
\(631\) | −10.3776 | −0.413128 | −0.206564 | − | 0.978433i | \(-0.566228\pi\) | ||||
−0.206564 | + | 0.978433i | \(0.566228\pi\) | |||||||
\(632\) | 10.1482 | 0.403673 | ||||||||
\(633\) | −2.27137 | −0.0902790 | ||||||||
\(634\) | −28.5138 | −1.13243 | ||||||||
\(635\) | 38.7592 | 1.53811 | ||||||||
\(636\) | −17.5252 | −0.694918 | ||||||||
\(637\) | −6.23012 | −0.246847 | ||||||||
\(638\) | −94.1323 | −3.72673 | ||||||||
\(639\) | 12.6404 | 0.500046 | ||||||||
\(640\) | −28.5570 | −1.12881 | ||||||||
\(641\) | −44.3334 | −1.75107 | −0.875533 | − | 0.483159i | \(-0.839489\pi\) | ||||
−0.875533 | + | 0.483159i | \(0.839489\pi\) | |||||||
\(642\) | −17.3330 | −0.684081 | ||||||||
\(643\) | −29.4003 | −1.15943 | −0.579717 | − | 0.814818i | \(-0.696837\pi\) | ||||
−0.579717 | + | 0.814818i | \(0.696837\pi\) | |||||||
\(644\) | 4.74391 | 0.186936 | ||||||||
\(645\) | 21.3274 | 0.839764 | ||||||||
\(646\) | −18.8263 | −0.740710 | ||||||||
\(647\) | −6.96071 | −0.273654 | −0.136827 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136827 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(648\) | 1.20691 | 0.0474120 | ||||||||
\(649\) | 39.6005 | 1.55446 | ||||||||
\(650\) | 54.4862 | 2.13713 | ||||||||
\(651\) | −7.96130 | −0.312028 | ||||||||
\(652\) | 7.71839 | 0.302276 | ||||||||
\(653\) | 30.7488 | 1.20330 | 0.601648 | − | 0.798762i | \(-0.294511\pi\) | ||||
0.601648 | + | 0.798762i | \(0.294511\pi\) | |||||||
\(654\) | −19.2330 | −0.752069 | ||||||||
\(655\) | −8.83877 | −0.345359 | ||||||||
\(656\) | −1.43987 | −0.0562177 | ||||||||
\(657\) | 4.58132 | 0.178734 | ||||||||
\(658\) | −12.3485 | −0.481396 | ||||||||
\(659\) | 0.138118 | 0.00538029 | 0.00269015 | − | 0.999996i | \(-0.499144\pi\) | ||||
0.00269015 | + | 0.999996i | \(0.499144\pi\) | |||||||
\(660\) | −22.2980 | −0.867949 | ||||||||
\(661\) | 25.7912 | 1.00316 | 0.501581 | − | 0.865111i | \(-0.332752\pi\) | ||||
0.501581 | + | 0.865111i | \(0.332752\pi\) | |||||||
\(662\) | 40.8764 | 1.58871 | ||||||||
\(663\) | 21.3625 | 0.829649 | ||||||||
\(664\) | 13.5099 | 0.524285 | ||||||||
\(665\) | −9.39855 | −0.364460 | ||||||||
\(666\) | −6.66811 | −0.258384 | ||||||||
\(667\) | −34.2815 | −1.32739 | ||||||||
\(668\) | 9.42918 | 0.364826 | ||||||||
\(669\) | −0.511803 | −0.0197874 | ||||||||
\(670\) | 10.7544 | 0.415480 | ||||||||
\(671\) | 27.9026 | 1.07717 | ||||||||
\(672\) | 6.51270 | 0.251233 | ||||||||
\(673\) | 7.16235 | 0.276088 | 0.138044 | − | 0.990426i | \(-0.455918\pi\) | ||||
0.138044 | + | 0.990426i | \(0.455918\pi\) | |||||||
\(674\) | 56.5610 | 2.17865 | ||||||||
\(675\) | −4.78570 | −0.184201 | ||||||||
\(676\) | 34.5801 | 1.33000 | ||||||||
\(677\) | 33.2004 | 1.27600 | 0.637998 | − | 0.770038i | \(-0.279763\pi\) | ||||
0.637998 | + | 0.770038i | \(0.279763\pi\) | |||||||
\(678\) | −15.2327 | −0.585010 | ||||||||
\(679\) | 12.4927 | 0.479427 | ||||||||
\(680\) | 12.9457 | 0.496445 | ||||||||
\(681\) | 17.3747 | 0.665801 | ||||||||
\(682\) | 77.4169 | 2.96445 | ||||||||
\(683\) | −32.3402 | −1.23746 | −0.618732 | − | 0.785602i | \(-0.712353\pi\) | ||||
−0.618732 | + | 0.785602i | \(0.712353\pi\) | |||||||
\(684\) | 4.02465 | 0.153886 | ||||||||
\(685\) | 42.9263 | 1.64013 | ||||||||
\(686\) | 1.82745 | 0.0697723 | ||||||||
\(687\) | −21.6297 | −0.825223 | ||||||||
\(688\) | 33.3026 | 1.26965 | ||||||||
\(689\) | −81.5071 | −3.10517 | ||||||||
\(690\) | −20.2448 | −0.770707 | ||||||||
\(691\) | −0.421706 | −0.0160424 | −0.00802122 | − | 0.999968i | \(-0.502553\pi\) | ||||
−0.00802122 | + | 0.999968i | \(0.502553\pi\) | |||||||
\(692\) | −14.0707 | −0.534888 | ||||||||
\(693\) | −5.32117 | −0.202134 | ||||||||
\(694\) | −37.6622 | −1.42964 | ||||||||
\(695\) | −26.4860 | −1.00467 | ||||||||
\(696\) | −11.6832 | −0.442851 | ||||||||
\(697\) | 1.01074 | 0.0382847 | ||||||||
\(698\) | 24.4315 | 0.924745 | ||||||||
\(699\) | −13.5171 | −0.511264 | ||||||||
\(700\) | −6.41075 | −0.242303 | ||||||||
\(701\) | 23.6163 | 0.891974 | 0.445987 | − | 0.895039i | \(-0.352853\pi\) | ||||
0.445987 | + | 0.895039i | \(0.352853\pi\) | |||||||
\(702\) | −11.3852 | −0.429708 | ||||||||
\(703\) | 10.9628 | 0.413471 | ||||||||
\(704\) | −11.3460 | −0.427617 | ||||||||
\(705\) | 21.1381 | 0.796107 | ||||||||
\(706\) | −26.1133 | −0.982789 | ||||||||
\(707\) | 6.14241 | 0.231009 | ||||||||
\(708\) | −9.96913 | −0.374663 | ||||||||
\(709\) | −39.0828 | −1.46779 | −0.733893 | − | 0.679265i | \(-0.762299\pi\) | ||||
−0.733893 | + | 0.679265i | \(0.762299\pi\) | |||||||
\(710\) | −72.2606 | −2.71189 | ||||||||
\(711\) | 8.40838 | 0.315339 | ||||||||
\(712\) | −4.21539 | −0.157978 | ||||||||
\(713\) | 28.1940 | 1.05587 | ||||||||
\(714\) | −6.26613 | −0.234504 | ||||||||
\(715\) | −103.705 | −3.87835 | ||||||||
\(716\) | −5.58925 | −0.208880 | ||||||||
\(717\) | −17.1086 | −0.638931 | ||||||||
\(718\) | −1.21735 | −0.0454310 | ||||||||
\(719\) | −18.2086 | −0.679066 | −0.339533 | − | 0.940594i | \(-0.610269\pi\) | ||||
−0.339533 | + | 0.940594i | \(0.610269\pi\) | |||||||
\(720\) | −15.2804 | −0.569465 | ||||||||
\(721\) | −6.42298 | −0.239204 | ||||||||
\(722\) | 18.2257 | 0.678289 | ||||||||
\(723\) | −21.6264 | −0.804296 | ||||||||
\(724\) | 6.24656 | 0.232151 | ||||||||
\(725\) | 46.3268 | 1.72053 | ||||||||
\(726\) | 31.6419 | 1.17434 | ||||||||
\(727\) | 22.8951 | 0.849134 | 0.424567 | − | 0.905397i | \(-0.360426\pi\) | ||||
0.424567 | + | 0.905397i | \(0.360426\pi\) | |||||||
\(728\) | 7.51921 | 0.278680 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −26.1898 | −0.969327 | ||||||||
\(731\) | −23.3774 | −0.864643 | ||||||||
\(732\) | −7.02428 | −0.259625 | ||||||||
\(733\) | 52.7136 | 1.94702 | 0.973511 | − | 0.228639i | \(-0.0734275\pi\) | ||||
0.973511 | + | 0.228639i | \(0.0734275\pi\) | |||||||
\(734\) | −53.8542 | −1.98779 | ||||||||
\(735\) | −3.12821 | −0.115386 | ||||||||
\(736\) | −23.0640 | −0.850150 | ||||||||
\(737\) | −10.0105 | −0.368740 | ||||||||
\(738\) | −0.538681 | −0.0198291 | ||||||||
\(739\) | −6.13486 | −0.225674 | −0.112837 | − | 0.993613i | \(-0.535994\pi\) | ||||
−0.112837 | + | 0.993613i | \(0.535994\pi\) | |||||||
\(740\) | 15.2903 | 0.562084 | ||||||||
\(741\) | 18.7181 | 0.687626 | ||||||||
\(742\) | 23.9080 | 0.877691 | ||||||||
\(743\) | 2.51718 | 0.0923465 | 0.0461733 | − | 0.998933i | \(-0.485297\pi\) | ||||
0.0461733 | + | 0.998933i | \(0.485297\pi\) | |||||||
\(744\) | 9.60858 | 0.352268 | ||||||||
\(745\) | 61.1841 | 2.24161 | ||||||||
\(746\) | −57.0514 | −2.08880 | ||||||||
\(747\) | 11.1938 | 0.409558 | ||||||||
\(748\) | 24.4413 | 0.893664 | ||||||||
\(749\) | 9.48484 | 0.346568 | ||||||||
\(750\) | −1.22510 | −0.0447344 | ||||||||
\(751\) | −39.5923 | −1.44475 | −0.722373 | − | 0.691504i | \(-0.756948\pi\) | ||||
−0.722373 | + | 0.691504i | \(0.756948\pi\) | |||||||
\(752\) | 33.0071 | 1.20365 | ||||||||
\(753\) | −7.73773 | −0.281978 | ||||||||
\(754\) | 110.212 | 4.01368 | ||||||||
\(755\) | −48.3120 | −1.75826 | ||||||||
\(756\) | 1.33956 | 0.0487195 | ||||||||
\(757\) | 0.850165 | 0.0308998 | 0.0154499 | − | 0.999881i | \(-0.495082\pi\) | ||||
0.0154499 | + | 0.999881i | \(0.495082\pi\) | |||||||
\(758\) | 12.9961 | 0.472041 | ||||||||
\(759\) | 18.8443 | 0.684005 | ||||||||
\(760\) | 11.3432 | 0.411462 | ||||||||
\(761\) | −26.2249 | −0.950652 | −0.475326 | − | 0.879810i | \(-0.657670\pi\) | ||||
−0.475326 | + | 0.879810i | \(0.657670\pi\) | |||||||
\(762\) | 22.6424 | 0.820249 | ||||||||
\(763\) | 10.5245 | 0.381013 | ||||||||
\(764\) | 1.33956 | 0.0484637 | ||||||||
\(765\) | 10.7263 | 0.387811 | ||||||||
\(766\) | 42.1496 | 1.52293 | ||||||||
\(767\) | −46.3650 | −1.67414 | ||||||||
\(768\) | −20.9470 | −0.755859 | ||||||||
\(769\) | −50.5509 | −1.82291 | −0.911455 | − | 0.411399i | \(-0.865040\pi\) | ||||
−0.911455 | + | 0.411399i | \(0.865040\pi\) | |||||||
\(770\) | 30.4192 | 1.09623 | ||||||||
\(771\) | −25.9076 | −0.933040 | ||||||||
\(772\) | −4.96792 | −0.178799 | ||||||||
\(773\) | 12.6438 | 0.454767 | 0.227384 | − | 0.973805i | \(-0.426983\pi\) | ||||
0.227384 | + | 0.973805i | \(0.426983\pi\) | |||||||
\(774\) | 12.4591 | 0.447833 | ||||||||
\(775\) | −38.1003 | −1.36860 | ||||||||
\(776\) | −15.0776 | −0.541255 | ||||||||
\(777\) | 3.64886 | 0.130902 | ||||||||
\(778\) | 2.84205 | 0.101893 | ||||||||
\(779\) | 0.885629 | 0.0317310 | ||||||||
\(780\) | 26.1070 | 0.934779 | ||||||||
\(781\) | 67.2617 | 2.40681 | ||||||||
\(782\) | 22.1908 | 0.793540 | ||||||||
\(783\) | −9.68026 | −0.345944 | ||||||||
\(784\) | −4.88470 | −0.174453 | ||||||||
\(785\) | −60.8000 | −2.17005 | ||||||||
\(786\) | −5.16346 | −0.184175 | ||||||||
\(787\) | −23.3402 | −0.831989 | −0.415995 | − | 0.909367i | \(-0.636567\pi\) | ||||
−0.415995 | + | 0.909367i | \(0.636567\pi\) | |||||||
\(788\) | 4.36419 | 0.155468 | ||||||||
\(789\) | −20.7483 | −0.738660 | ||||||||
\(790\) | −48.0677 | −1.71017 | ||||||||
\(791\) | 8.33553 | 0.296377 | ||||||||
\(792\) | 6.42218 | 0.228202 | ||||||||
\(793\) | −32.6689 | −1.16011 | ||||||||
\(794\) | −61.9973 | −2.20020 | ||||||||
\(795\) | −40.9255 | −1.45148 | ||||||||
\(796\) | −12.0853 | −0.428351 | ||||||||
\(797\) | 9.55645 | 0.338507 | 0.169253 | − | 0.985573i | \(-0.445864\pi\) | ||||
0.169253 | + | 0.985573i | \(0.445864\pi\) | |||||||
\(798\) | −5.49047 | −0.194361 | ||||||||
\(799\) | −23.1699 | −0.819693 | ||||||||
\(800\) | 31.1678 | 1.10195 | ||||||||
\(801\) | −3.49270 | −0.123409 | ||||||||
\(802\) | −42.3874 | −1.49675 | ||||||||
\(803\) | 24.3780 | 0.860281 | ||||||||
\(804\) | 2.52006 | 0.0888755 | ||||||||
\(805\) | 11.0782 | 0.390455 | ||||||||
\(806\) | −90.6412 | −3.19270 | ||||||||
\(807\) | 7.05197 | 0.248241 | ||||||||
\(808\) | −7.41335 | −0.260801 | ||||||||
\(809\) | −40.8987 | −1.43792 | −0.718961 | − | 0.695050i | \(-0.755382\pi\) | ||||
−0.718961 | + | 0.695050i | \(0.755382\pi\) | |||||||
\(810\) | −5.71664 | −0.200862 | ||||||||
\(811\) | 9.69394 | 0.340400 | 0.170200 | − | 0.985410i | \(-0.445559\pi\) | ||||
0.170200 | + | 0.985410i | \(0.445559\pi\) | |||||||
\(812\) | −12.9673 | −0.455064 | ||||||||
\(813\) | −23.2104 | −0.814023 | ||||||||
\(814\) | −35.4821 | −1.24365 | ||||||||
\(815\) | 18.0243 | 0.631365 | ||||||||
\(816\) | 16.7491 | 0.586336 | ||||||||
\(817\) | −20.4836 | −0.716630 | ||||||||
\(818\) | −31.4461 | −1.09949 | ||||||||
\(819\) | 6.23012 | 0.217698 | ||||||||
\(820\) | 1.23523 | 0.0431360 | ||||||||
\(821\) | 31.3298 | 1.09342 | 0.546708 | − | 0.837323i | \(-0.315881\pi\) | ||||
0.546708 | + | 0.837323i | \(0.315881\pi\) | |||||||
\(822\) | 25.0768 | 0.874654 | ||||||||
\(823\) | −28.0131 | −0.976474 | −0.488237 | − | 0.872711i | \(-0.662360\pi\) | ||||
−0.488237 | + | 0.872711i | \(0.662360\pi\) | |||||||
\(824\) | 7.75197 | 0.270053 | ||||||||
\(825\) | −25.4655 | −0.886595 | ||||||||
\(826\) | 13.6000 | 0.473204 | ||||||||
\(827\) | −37.3982 | −1.30046 | −0.650232 | − | 0.759736i | \(-0.725328\pi\) | ||||
−0.650232 | + | 0.759736i | \(0.725328\pi\) | |||||||
\(828\) | −4.74391 | −0.164862 | ||||||||
\(829\) | 35.5639 | 1.23519 | 0.617594 | − | 0.786497i | \(-0.288108\pi\) | ||||
0.617594 | + | 0.786497i | \(0.288108\pi\) | |||||||
\(830\) | −63.9907 | −2.22115 | ||||||||
\(831\) | 2.12246 | 0.0736274 | ||||||||
\(832\) | 13.2841 | 0.460542 | ||||||||
\(833\) | 3.42890 | 0.118804 | ||||||||
\(834\) | −15.4727 | −0.535774 | ||||||||
\(835\) | 22.0194 | 0.762014 | ||||||||
\(836\) | 21.4159 | 0.740683 | ||||||||
\(837\) | 7.96130 | 0.275183 | ||||||||
\(838\) | −44.2071 | −1.52711 | ||||||||
\(839\) | −7.11969 | −0.245799 | −0.122899 | − | 0.992419i | \(-0.539219\pi\) | ||||
−0.122899 | + | 0.992419i | \(0.539219\pi\) | |||||||
\(840\) | 3.77547 | 0.130266 | ||||||||
\(841\) | 64.7073 | 2.23129 | ||||||||
\(842\) | −34.5699 | −1.19136 | ||||||||
\(843\) | 10.5544 | 0.363514 | ||||||||
\(844\) | 3.04265 | 0.104732 | ||||||||
\(845\) | 80.7530 | 2.77799 | ||||||||
\(846\) | 12.3485 | 0.424551 | ||||||||
\(847\) | −17.3148 | −0.594945 | ||||||||
\(848\) | −63.9052 | −2.19451 | ||||||||
\(849\) | 31.5098 | 1.08141 | ||||||||
\(850\) | −29.9878 | −1.02857 | ||||||||
\(851\) | −12.9220 | −0.442961 | ||||||||
\(852\) | −16.9326 | −0.580102 | ||||||||
\(853\) | −30.3904 | −1.04055 | −0.520273 | − | 0.854000i | \(-0.674170\pi\) | ||||
−0.520273 | + | 0.854000i | \(0.674170\pi\) | |||||||
\(854\) | 9.58259 | 0.327909 | ||||||||
\(855\) | 9.39855 | 0.321424 | ||||||||
\(856\) | −11.4474 | −0.391263 | ||||||||
\(857\) | −0.620340 | −0.0211904 | −0.0105952 | − | 0.999944i | \(-0.503373\pi\) | ||||
−0.0105952 | + | 0.999944i | \(0.503373\pi\) | |||||||
\(858\) | −60.5827 | −2.06826 | ||||||||
\(859\) | −12.7467 | −0.434910 | −0.217455 | − | 0.976070i | \(-0.569776\pi\) | ||||
−0.217455 | + | 0.976070i | \(0.569776\pi\) | |||||||
\(860\) | −28.5694 | −0.974207 | ||||||||
\(861\) | 0.294773 | 0.0100458 | ||||||||
\(862\) | −25.1322 | −0.856006 | ||||||||
\(863\) | −41.9397 | −1.42765 | −0.713823 | − | 0.700327i | \(-0.753038\pi\) | ||||
−0.713823 | + | 0.700327i | \(0.753038\pi\) | |||||||
\(864\) | −6.51270 | −0.221567 | ||||||||
\(865\) | −32.8585 | −1.11722 | ||||||||
\(866\) | −32.4966 | −1.10428 | ||||||||
\(867\) | 5.24267 | 0.178050 | ||||||||
\(868\) | 10.6647 | 0.361982 | ||||||||
\(869\) | 44.7424 | 1.51778 | ||||||||
\(870\) | 55.3385 | 1.87615 | ||||||||
\(871\) | 11.7204 | 0.397132 | ||||||||
\(872\) | −12.7021 | −0.430149 | ||||||||
\(873\) | −12.4927 | −0.422815 | ||||||||
\(874\) | 19.4439 | 0.657699 | ||||||||
\(875\) | 0.670390 | 0.0226633 | ||||||||
\(876\) | −6.13698 | −0.207349 | ||||||||
\(877\) | −37.0536 | −1.25121 | −0.625606 | − | 0.780139i | \(-0.715148\pi\) | ||||
−0.625606 | + | 0.780139i | \(0.715148\pi\) | |||||||
\(878\) | 23.2532 | 0.784757 | ||||||||
\(879\) | 21.2010 | 0.715093 | ||||||||
\(880\) | −81.3093 | −2.74094 | ||||||||
\(881\) | −12.8619 | −0.433328 | −0.216664 | − | 0.976246i | \(-0.569518\pi\) | ||||
−0.216664 | + | 0.976246i | \(0.569518\pi\) | |||||||
\(882\) | −1.82745 | −0.0615334 | ||||||||
\(883\) | 17.5336 | 0.590052 | 0.295026 | − | 0.955489i | \(-0.404672\pi\) | ||||
0.295026 | + | 0.955489i | \(0.404672\pi\) | |||||||
\(884\) | −28.6164 | −0.962473 | ||||||||
\(885\) | −23.2804 | −0.782561 | ||||||||
\(886\) | −63.6439 | −2.13816 | ||||||||
\(887\) | 48.9193 | 1.64255 | 0.821275 | − | 0.570533i | \(-0.193263\pi\) | ||||
0.821275 | + | 0.570533i | \(0.193263\pi\) | |||||||
\(888\) | −4.40386 | −0.147784 | ||||||||
\(889\) | −12.3902 | −0.415554 | ||||||||
\(890\) | 19.9665 | 0.669280 | ||||||||
\(891\) | 5.32117 | 0.178266 | ||||||||
\(892\) | 0.685593 | 0.0229553 | ||||||||
\(893\) | −20.3018 | −0.679375 | ||||||||
\(894\) | 35.7427 | 1.19542 | ||||||||
\(895\) | −13.0523 | −0.436289 | ||||||||
\(896\) | 9.12887 | 0.304974 | ||||||||
\(897\) | −22.0633 | −0.736671 | ||||||||
\(898\) | −36.7418 | −1.22609 | ||||||||
\(899\) | −77.0674 | −2.57034 | ||||||||
\(900\) | 6.41075 | 0.213692 | ||||||||
\(901\) | 44.8593 | 1.49448 | ||||||||
\(902\) | −2.86641 | −0.0954412 | ||||||||
\(903\) | −6.81775 | −0.226881 | ||||||||
\(904\) | −10.0602 | −0.334599 | ||||||||
\(905\) | 14.5872 | 0.484896 | ||||||||
\(906\) | −28.2231 | −0.937649 | ||||||||
\(907\) | −15.8634 | −0.526736 | −0.263368 | − | 0.964696i | \(-0.584833\pi\) | ||||
−0.263368 | + | 0.964696i | \(0.584833\pi\) | |||||||
\(908\) | −23.2746 | −0.772393 | ||||||||
\(909\) | −6.14241 | −0.203731 | ||||||||
\(910\) | −35.6154 | −1.18064 | ||||||||
\(911\) | 22.4983 | 0.745402 | 0.372701 | − | 0.927951i | \(-0.378432\pi\) | ||||
0.372701 | + | 0.927951i | \(0.378432\pi\) | |||||||
\(912\) | 14.6758 | 0.485965 | ||||||||
\(913\) | 59.5639 | 1.97128 | ||||||||
\(914\) | −5.63594 | −0.186420 | ||||||||
\(915\) | −16.4034 | −0.542280 | ||||||||
\(916\) | 28.9743 | 0.957339 | ||||||||
\(917\) | 2.82551 | 0.0933064 | ||||||||
\(918\) | 6.26613 | 0.206813 | ||||||||
\(919\) | 34.5130 | 1.13848 | 0.569240 | − | 0.822172i | \(-0.307238\pi\) | ||||
0.569240 | + | 0.822172i | \(0.307238\pi\) | |||||||
\(920\) | −13.3704 | −0.440809 | ||||||||
\(921\) | 3.93876 | 0.129787 | ||||||||
\(922\) | −71.4507 | −2.35310 | ||||||||
\(923\) | −78.7513 | −2.59213 | ||||||||
\(924\) | 7.12805 | 0.234496 | ||||||||
\(925\) | 17.4623 | 0.574158 | ||||||||
\(926\) | −55.9051 | −1.83716 | ||||||||
\(927\) | 6.42298 | 0.210958 | ||||||||
\(928\) | 63.0446 | 2.06954 | ||||||||
\(929\) | −25.1880 | −0.826393 | −0.413196 | − | 0.910642i | \(-0.635588\pi\) | ||||
−0.413196 | + | 0.910642i | \(0.635588\pi\) | |||||||
\(930\) | −45.5119 | −1.49239 | ||||||||
\(931\) | 3.00445 | 0.0984668 | ||||||||
\(932\) | 18.1070 | 0.593116 | ||||||||
\(933\) | 7.83859 | 0.256624 | ||||||||
\(934\) | −51.1759 | −1.67453 | ||||||||
\(935\) | 57.0765 | 1.86660 | ||||||||
\(936\) | −7.51921 | −0.245773 | ||||||||
\(937\) | −1.46214 | −0.0477661 | −0.0238830 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238830 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(938\) | −3.43789 | −0.112251 | ||||||||
\(939\) | −5.71415 | −0.186474 | ||||||||
\(940\) | −28.3159 | −0.923561 | ||||||||
\(941\) | −30.4128 | −0.991428 | −0.495714 | − | 0.868486i | \(-0.665094\pi\) | ||||
−0.495714 | + | 0.868486i | \(0.665094\pi\) | |||||||
\(942\) | −35.5183 | −1.15725 | ||||||||
\(943\) | −1.04390 | −0.0339942 | ||||||||
\(944\) | −36.3523 | −1.18317 | ||||||||
\(945\) | 3.12821 | 0.101761 | ||||||||
\(946\) | 66.2969 | 2.15550 | ||||||||
\(947\) | 19.6335 | 0.638003 | 0.319001 | − | 0.947754i | \(-0.396653\pi\) | ||||
0.319001 | + | 0.947754i | \(0.396653\pi\) | |||||||
\(948\) | −11.2636 | −0.365824 | ||||||||
\(949\) | −28.5422 | −0.926519 | ||||||||
\(950\) | −26.2757 | −0.852497 | ||||||||
\(951\) | −15.6031 | −0.505965 | ||||||||
\(952\) | −4.13838 | −0.134126 | ||||||||
\(953\) | −11.9892 | −0.388367 | −0.194183 | − | 0.980965i | \(-0.562206\pi\) | ||||
−0.194183 | + | 0.980965i | \(0.562206\pi\) | |||||||
\(954\) | −23.9080 | −0.774050 | ||||||||
\(955\) | 3.12821 | 0.101226 | ||||||||
\(956\) | 22.9180 | 0.741222 | ||||||||
\(957\) | −51.5103 | −1.66509 | ||||||||
\(958\) | 2.73503 | 0.0883650 | ||||||||
\(959\) | −13.7223 | −0.443117 | ||||||||
\(960\) | 6.67006 | 0.215275 | ||||||||
\(961\) | 32.3822 | 1.04459 | ||||||||
\(962\) | 41.5431 | 1.33940 | ||||||||
\(963\) | −9.48484 | −0.305645 | ||||||||
\(964\) | 28.9700 | 0.933061 | ||||||||
\(965\) | −11.6013 | −0.373459 | ||||||||
\(966\) | 6.47169 | 0.208223 | ||||||||
\(967\) | 41.4489 | 1.33291 | 0.666454 | − | 0.745546i | \(-0.267811\pi\) | ||||
0.666454 | + | 0.745546i | \(0.267811\pi\) | |||||||
\(968\) | 20.8975 | 0.671670 | ||||||||
\(969\) | −10.3019 | −0.330946 | ||||||||
\(970\) | 71.4164 | 2.29304 | ||||||||
\(971\) | −1.60436 | −0.0514863 | −0.0257431 | − | 0.999669i | \(-0.508195\pi\) | ||||
−0.0257431 | + | 0.999669i | \(0.508195\pi\) | |||||||
\(972\) | −1.33956 | −0.0429665 | ||||||||
\(973\) | 8.46681 | 0.271433 | ||||||||
\(974\) | 29.5844 | 0.947946 | ||||||||
\(975\) | 29.8155 | 0.954860 | ||||||||
\(976\) | −25.6139 | −0.819881 | ||||||||
\(977\) | 47.0685 | 1.50585 | 0.752927 | − | 0.658104i | \(-0.228641\pi\) | ||||
0.752927 | + | 0.658104i | \(0.228641\pi\) | |||||||
\(978\) | 10.5295 | 0.336697 | ||||||||
\(979\) | −18.5853 | −0.593988 | ||||||||
\(980\) | 4.19044 | 0.133859 | ||||||||
\(981\) | −10.5245 | −0.336022 | ||||||||
\(982\) | 36.5098 | 1.16507 | ||||||||
\(983\) | −45.3101 | −1.44517 | −0.722584 | − | 0.691283i | \(-0.757046\pi\) | ||||
−0.722584 | + | 0.691283i | \(0.757046\pi\) | |||||||
\(984\) | −0.355764 | −0.0113414 | ||||||||
\(985\) | 10.1915 | 0.324727 | ||||||||
\(986\) | −60.6577 | −1.93174 | ||||||||
\(987\) | −6.75725 | −0.215086 | ||||||||
\(988\) | −25.0741 | −0.797713 | ||||||||
\(989\) | 24.1443 | 0.767743 | ||||||||
\(990\) | −30.4192 | −0.966786 | ||||||||
\(991\) | 34.9225 | 1.10935 | 0.554674 | − | 0.832068i | \(-0.312843\pi\) | ||||
0.554674 | + | 0.832068i | \(0.312843\pi\) | |||||||
\(992\) | −51.8496 | −1.64623 | ||||||||
\(993\) | 22.3680 | 0.709828 | ||||||||
\(994\) | 23.0997 | 0.732677 | ||||||||
\(995\) | −28.2220 | −0.894699 | ||||||||
\(996\) | −14.9948 | −0.475127 | ||||||||
\(997\) | −59.9137 | −1.89749 | −0.948743 | − | 0.316050i | \(-0.897643\pi\) | ||||
−0.948743 | + | 0.316050i | \(0.897643\pi\) | |||||||
\(998\) | 11.6341 | 0.368272 | ||||||||
\(999\) | −3.64886 | −0.115445 |
(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 | 4011.2.a.j.1.6 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.j.1.6 | ✓ | 26 | 1.1 | even | 1 | trivial |