Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.14296 | −1.23724 | −0.618620 | − | 0.785691i | \(-0.712308\pi\) | ||||
−0.618620 | + | 0.785691i | \(0.712308\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.14296 | 0.874860 | ||||||||
\(7\) | 0.736597 | 0.278407 | 0.139204 | − | 0.990264i | \(-0.455546\pi\) | ||||
0.139204 | + | 0.990264i | \(0.455546\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.59228 | 0.530761 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.15712 | −0.951908 | −0.475954 | − | 0.879470i | \(-0.657897\pi\) | ||||
−0.475954 | + | 0.879470i | \(0.657897\pi\) | |||||||
\(12\) | −2.14296 | −0.618620 | ||||||||
\(13\) | −4.66538 | −1.29394 | −0.646972 | − | 0.762514i | \(-0.723965\pi\) | ||||
−0.646972 | + | 0.762514i | \(0.723965\pi\) | |||||||
\(14\) | −0.736597 | −0.196864 | ||||||||
\(15\) | 2.14296 | 0.553310 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.14164 | 0.761959 | 0.380980 | − | 0.924583i | \(-0.375587\pi\) | ||||
0.380980 | + | 0.924583i | \(0.375587\pi\) | |||||||
\(18\) | −1.59228 | −0.375305 | ||||||||
\(19\) | −4.01979 | −0.922204 | −0.461102 | − | 0.887347i | \(-0.652546\pi\) | ||||
−0.461102 | + | 0.887347i | \(0.652546\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.57850 | −0.344457 | ||||||||
\(22\) | 3.15712 | 0.673101 | ||||||||
\(23\) | −7.10860 | −1.48225 | −0.741123 | − | 0.671369i | \(-0.765707\pi\) | ||||
−0.741123 | + | 0.671369i | \(0.765707\pi\) | |||||||
\(24\) | 2.14296 | 0.437430 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.66538 | 0.914957 | ||||||||
\(27\) | 3.01668 | 0.580561 | ||||||||
\(28\) | 0.736597 | 0.139204 | ||||||||
\(29\) | −2.80984 | −0.521773 | −0.260887 | − | 0.965369i | \(-0.584015\pi\) | ||||
−0.260887 | + | 0.965369i | \(0.584015\pi\) | |||||||
\(30\) | −2.14296 | −0.391249 | ||||||||
\(31\) | −5.72133 | −1.02758 | −0.513791 | − | 0.857916i | \(-0.671759\pi\) | ||||
−0.513791 | + | 0.857916i | \(0.671759\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.76559 | 1.17774 | ||||||||
\(34\) | −3.14164 | −0.538787 | ||||||||
\(35\) | −0.736597 | −0.124508 | ||||||||
\(36\) | 1.59228 | 0.265381 | ||||||||
\(37\) | −7.97212 | −1.31061 | −0.655304 | − | 0.755365i | \(-0.727460\pi\) | ||||
−0.655304 | + | 0.755365i | \(0.727460\pi\) | |||||||
\(38\) | 4.01979 | 0.652097 | ||||||||
\(39\) | 9.99774 | 1.60092 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.3736 | −1.62008 | −0.810039 | − | 0.586376i | \(-0.800554\pi\) | ||||
−0.810039 | + | 0.586376i | \(0.800554\pi\) | |||||||
\(42\) | 1.57850 | 0.243568 | ||||||||
\(43\) | 10.0395 | 1.53101 | 0.765507 | − | 0.643428i | \(-0.222488\pi\) | ||||
0.765507 | + | 0.643428i | \(0.222488\pi\) | |||||||
\(44\) | −3.15712 | −0.475954 | ||||||||
\(45\) | −1.59228 | −0.237364 | ||||||||
\(46\) | 7.10860 | 1.04811 | ||||||||
\(47\) | −8.43542 | −1.23043 | −0.615217 | − | 0.788358i | \(-0.710931\pi\) | ||||
−0.615217 | + | 0.788358i | \(0.710931\pi\) | |||||||
\(48\) | −2.14296 | −0.309310 | ||||||||
\(49\) | −6.45743 | −0.922489 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −6.73241 | −0.942726 | ||||||||
\(52\) | −4.66538 | −0.646972 | ||||||||
\(53\) | 7.83253 | 1.07588 | 0.537940 | − | 0.842983i | \(-0.319203\pi\) | ||||
0.537940 | + | 0.842983i | \(0.319203\pi\) | |||||||
\(54\) | −3.01668 | −0.410518 | ||||||||
\(55\) | 3.15712 | 0.425706 | ||||||||
\(56\) | −0.736597 | −0.0984319 | ||||||||
\(57\) | 8.61426 | 1.14099 | ||||||||
\(58\) | 2.80984 | 0.368949 | ||||||||
\(59\) | 2.06051 | 0.268256 | 0.134128 | − | 0.990964i | \(-0.457177\pi\) | ||||
0.134128 | + | 0.990964i | \(0.457177\pi\) | |||||||
\(60\) | 2.14296 | 0.276655 | ||||||||
\(61\) | 4.47293 | 0.572700 | 0.286350 | − | 0.958125i | \(-0.407558\pi\) | ||||
0.286350 | + | 0.958125i | \(0.407558\pi\) | |||||||
\(62\) | 5.72133 | 0.726610 | ||||||||
\(63\) | 1.17287 | 0.147768 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.66538 | 0.578670 | ||||||||
\(66\) | −6.76559 | −0.832787 | ||||||||
\(67\) | −8.16901 | −0.998003 | −0.499002 | − | 0.866601i | \(-0.666300\pi\) | ||||
−0.499002 | + | 0.866601i | \(0.666300\pi\) | |||||||
\(68\) | 3.14164 | 0.380980 | ||||||||
\(69\) | 15.2335 | 1.83389 | ||||||||
\(70\) | 0.736597 | 0.0880401 | ||||||||
\(71\) | 9.31937 | 1.10601 | 0.553003 | − | 0.833179i | \(-0.313482\pi\) | ||||
0.553003 | + | 0.833179i | \(0.313482\pi\) | |||||||
\(72\) | −1.59228 | −0.187652 | ||||||||
\(73\) | −8.97252 | −1.05015 | −0.525077 | − | 0.851055i | \(-0.675963\pi\) | ||||
−0.525077 | + | 0.851055i | \(0.675963\pi\) | |||||||
\(74\) | 7.97212 | 0.926740 | ||||||||
\(75\) | −2.14296 | −0.247448 | ||||||||
\(76\) | −4.01979 | −0.461102 | ||||||||
\(77\) | −2.32553 | −0.265018 | ||||||||
\(78\) | −9.99774 | −1.13202 | ||||||||
\(79\) | −15.5710 | −1.75187 | −0.875937 | − | 0.482425i | \(-0.839756\pi\) | ||||
−0.875937 | + | 0.482425i | \(0.839756\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.2415 | −1.24905 | ||||||||
\(82\) | 10.3736 | 1.14557 | ||||||||
\(83\) | 15.7876 | 1.73291 | 0.866455 | − | 0.499255i | \(-0.166393\pi\) | ||||
0.866455 | + | 0.499255i | \(0.166393\pi\) | |||||||
\(84\) | −1.57850 | −0.172228 | ||||||||
\(85\) | −3.14164 | −0.340759 | ||||||||
\(86\) | −10.0395 | −1.08259 | ||||||||
\(87\) | 6.02137 | 0.645558 | ||||||||
\(88\) | 3.15712 | 0.336550 | ||||||||
\(89\) | −6.08980 | −0.645517 | −0.322759 | − | 0.946481i | \(-0.604610\pi\) | ||||
−0.322759 | + | 0.946481i | \(0.604610\pi\) | |||||||
\(90\) | 1.59228 | 0.167841 | ||||||||
\(91\) | −3.43651 | −0.360244 | ||||||||
\(92\) | −7.10860 | −0.741123 | ||||||||
\(93\) | 12.2606 | 1.27136 | ||||||||
\(94\) | 8.43542 | 0.870048 | ||||||||
\(95\) | 4.01979 | 0.412422 | ||||||||
\(96\) | 2.14296 | 0.218715 | ||||||||
\(97\) | −17.7555 | −1.80280 | −0.901399 | − | 0.432990i | \(-0.857459\pi\) | ||||
−0.901399 | + | 0.432990i | \(0.857459\pi\) | |||||||
\(98\) | 6.45743 | 0.652298 | ||||||||
\(99\) | −5.02703 | −0.505236 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.1340 | −1.40638 | −0.703192 | − | 0.711000i | \(-0.748242\pi\) | ||||
−0.703192 | + | 0.711000i | \(0.748242\pi\) | |||||||
\(102\) | 6.73241 | 0.666608 | ||||||||
\(103\) | 5.56725 | 0.548558 | 0.274279 | − | 0.961650i | \(-0.411561\pi\) | ||||
0.274279 | + | 0.961650i | \(0.411561\pi\) | |||||||
\(104\) | 4.66538 | 0.457478 | ||||||||
\(105\) | 1.57850 | 0.154046 | ||||||||
\(106\) | −7.83253 | −0.760763 | ||||||||
\(107\) | −12.2074 | −1.18013 | −0.590067 | − | 0.807354i | \(-0.700899\pi\) | ||||
−0.590067 | + | 0.807354i | \(0.700899\pi\) | |||||||
\(108\) | 3.01668 | 0.290280 | ||||||||
\(109\) | −3.43406 | −0.328923 | −0.164461 | − | 0.986384i | \(-0.552589\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552589\pi\) | |||||||
\(110\) | −3.15712 | −0.301020 | ||||||||
\(111\) | 17.0839 | 1.62154 | ||||||||
\(112\) | 0.736597 | 0.0696018 | ||||||||
\(113\) | 17.4959 | 1.64587 | 0.822937 | − | 0.568133i | \(-0.192334\pi\) | ||||
0.822937 | + | 0.568133i | \(0.192334\pi\) | |||||||
\(114\) | −8.61426 | −0.806800 | ||||||||
\(115\) | 7.10860 | 0.662881 | ||||||||
\(116\) | −2.80984 | −0.260887 | ||||||||
\(117\) | −7.42861 | −0.686776 | ||||||||
\(118\) | −2.06051 | −0.189686 | ||||||||
\(119\) | 2.31412 | 0.212135 | ||||||||
\(120\) | −2.14296 | −0.195625 | ||||||||
\(121\) | −1.03258 | −0.0938712 | ||||||||
\(122\) | −4.47293 | −0.404960 | ||||||||
\(123\) | 22.2301 | 2.00442 | ||||||||
\(124\) | −5.72133 | −0.513791 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.17287 | −0.104488 | ||||||||
\(127\) | 10.1949 | 0.904652 | 0.452326 | − | 0.891853i | \(-0.350594\pi\) | ||||
0.452326 | + | 0.891853i | \(0.350594\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −21.5143 | −1.89423 | ||||||||
\(130\) | −4.66538 | −0.409181 | ||||||||
\(131\) | 15.1027 | 1.31953 | 0.659764 | − | 0.751473i | \(-0.270656\pi\) | ||||
0.659764 | + | 0.751473i | \(0.270656\pi\) | |||||||
\(132\) | 6.76559 | 0.588869 | ||||||||
\(133\) | −2.96097 | −0.256748 | ||||||||
\(134\) | 8.16901 | 0.705695 | ||||||||
\(135\) | −3.01668 | −0.259635 | ||||||||
\(136\) | −3.14164 | −0.269393 | ||||||||
\(137\) | −14.6783 | −1.25405 | −0.627026 | − | 0.778998i | \(-0.715728\pi\) | ||||
−0.627026 | + | 0.778998i | \(0.715728\pi\) | |||||||
\(138\) | −15.2335 | −1.29676 | ||||||||
\(139\) | 1.17572 | 0.0997236 | 0.0498618 | − | 0.998756i | \(-0.484122\pi\) | ||||
0.0498618 | + | 0.998756i | \(0.484122\pi\) | |||||||
\(140\) | −0.736597 | −0.0622538 | ||||||||
\(141\) | 18.0768 | 1.52234 | ||||||||
\(142\) | −9.31937 | −0.782064 | ||||||||
\(143\) | 14.7292 | 1.23172 | ||||||||
\(144\) | 1.59228 | 0.132690 | ||||||||
\(145\) | 2.80984 | 0.233344 | ||||||||
\(146\) | 8.97252 | 0.742571 | ||||||||
\(147\) | 13.8380 | 1.14134 | ||||||||
\(148\) | −7.97212 | −0.655304 | ||||||||
\(149\) | −4.18473 | −0.342826 | −0.171413 | − | 0.985199i | \(-0.554833\pi\) | ||||
−0.171413 | + | 0.985199i | \(0.554833\pi\) | |||||||
\(150\) | 2.14296 | 0.174972 | ||||||||
\(151\) | −15.7280 | −1.27993 | −0.639963 | − | 0.768406i | \(-0.721050\pi\) | ||||
−0.639963 | + | 0.768406i | \(0.721050\pi\) | |||||||
\(152\) | 4.01979 | 0.326048 | ||||||||
\(153\) | 5.00238 | 0.404418 | ||||||||
\(154\) | 2.32553 | 0.187396 | ||||||||
\(155\) | 5.72133 | 0.459548 | ||||||||
\(156\) | 9.99774 | 0.800460 | ||||||||
\(157\) | 6.05642 | 0.483355 | 0.241678 | − | 0.970357i | \(-0.422302\pi\) | ||||
0.241678 | + | 0.970357i | \(0.422302\pi\) | |||||||
\(158\) | 15.5710 | 1.23876 | ||||||||
\(159\) | −16.7848 | −1.33112 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −5.23617 | −0.412668 | ||||||||
\(162\) | 11.2415 | 0.883214 | ||||||||
\(163\) | −21.4761 | −1.68214 | −0.841068 | − | 0.540929i | \(-0.818073\pi\) | ||||
−0.841068 | + | 0.540929i | \(0.818073\pi\) | |||||||
\(164\) | −10.3736 | −0.810039 | ||||||||
\(165\) | −6.76559 | −0.526700 | ||||||||
\(166\) | −15.7876 | −1.22535 | ||||||||
\(167\) | 5.52017 | 0.427164 | 0.213582 | − | 0.976925i | \(-0.431487\pi\) | ||||
0.213582 | + | 0.976925i | \(0.431487\pi\) | |||||||
\(168\) | 1.57850 | 0.121784 | ||||||||
\(169\) | 8.76580 | 0.674293 | ||||||||
\(170\) | 3.14164 | 0.240953 | ||||||||
\(171\) | −6.40065 | −0.489470 | ||||||||
\(172\) | 10.0395 | 0.765507 | ||||||||
\(173\) | 12.1974 | 0.927351 | 0.463676 | − | 0.886005i | \(-0.346530\pi\) | ||||
0.463676 | + | 0.886005i | \(0.346530\pi\) | |||||||
\(174\) | −6.02137 | −0.456479 | ||||||||
\(175\) | 0.736597 | 0.0556815 | ||||||||
\(176\) | −3.15712 | −0.237977 | ||||||||
\(177\) | −4.41560 | −0.331897 | ||||||||
\(178\) | 6.08980 | 0.456450 | ||||||||
\(179\) | −6.54798 | −0.489419 | −0.244709 | − | 0.969596i | \(-0.578693\pi\) | ||||
−0.244709 | + | 0.969596i | \(0.578693\pi\) | |||||||
\(180\) | −1.59228 | −0.118682 | ||||||||
\(181\) | −13.3931 | −0.995504 | −0.497752 | − | 0.867319i | \(-0.665841\pi\) | ||||
−0.497752 | + | 0.867319i | \(0.665841\pi\) | |||||||
\(182\) | 3.43651 | 0.254731 | ||||||||
\(183\) | −9.58532 | −0.708567 | ||||||||
\(184\) | 7.10860 | 0.524053 | ||||||||
\(185\) | 7.97212 | 0.586122 | ||||||||
\(186\) | −12.2606 | −0.898990 | ||||||||
\(187\) | −9.91854 | −0.725315 | ||||||||
\(188\) | −8.43542 | −0.615217 | ||||||||
\(189\) | 2.22208 | 0.161632 | ||||||||
\(190\) | −4.01979 | −0.291626 | ||||||||
\(191\) | −7.17995 | −0.519523 | −0.259762 | − | 0.965673i | \(-0.583644\pi\) | ||||
−0.259762 | + | 0.965673i | \(0.583644\pi\) | |||||||
\(192\) | −2.14296 | −0.154655 | ||||||||
\(193\) | 14.3466 | 1.03269 | 0.516347 | − | 0.856380i | \(-0.327292\pi\) | ||||
0.516347 | + | 0.856380i | \(0.327292\pi\) | |||||||
\(194\) | 17.7555 | 1.27477 | ||||||||
\(195\) | −9.99774 | −0.715953 | ||||||||
\(196\) | −6.45743 | −0.461245 | ||||||||
\(197\) | −20.7117 | −1.47565 | −0.737825 | − | 0.674993i | \(-0.764147\pi\) | ||||
−0.737825 | + | 0.674993i | \(0.764147\pi\) | |||||||
\(198\) | 5.02703 | 0.357256 | ||||||||
\(199\) | −2.30944 | −0.163712 | −0.0818558 | − | 0.996644i | \(-0.526085\pi\) | ||||
−0.0818558 | + | 0.996644i | \(0.526085\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 17.5059 | 1.23477 | ||||||||
\(202\) | 14.1340 | 0.994463 | ||||||||
\(203\) | −2.06972 | −0.145266 | ||||||||
\(204\) | −6.73241 | −0.471363 | ||||||||
\(205\) | 10.3736 | 0.724521 | ||||||||
\(206\) | −5.56725 | −0.387889 | ||||||||
\(207\) | −11.3189 | −0.786719 | ||||||||
\(208\) | −4.66538 | −0.323486 | ||||||||
\(209\) | 12.6910 | 0.877853 | ||||||||
\(210\) | −1.57850 | −0.108927 | ||||||||
\(211\) | −12.0649 | −0.830579 | −0.415290 | − | 0.909689i | \(-0.636320\pi\) | ||||
−0.415290 | + | 0.909689i | \(0.636320\pi\) | |||||||
\(212\) | 7.83253 | 0.537940 | ||||||||
\(213\) | −19.9711 | −1.36839 | ||||||||
\(214\) | 12.2074 | 0.834481 | ||||||||
\(215\) | −10.0395 | −0.684690 | ||||||||
\(216\) | −3.01668 | −0.205259 | ||||||||
\(217\) | −4.21431 | −0.286086 | ||||||||
\(218\) | 3.43406 | 0.232584 | ||||||||
\(219\) | 19.2278 | 1.29929 | ||||||||
\(220\) | 3.15712 | 0.212853 | ||||||||
\(221\) | −14.6569 | −0.985933 | ||||||||
\(222\) | −17.0839 | −1.14660 | ||||||||
\(223\) | 8.86581 | 0.593699 | 0.296849 | − | 0.954924i | \(-0.404064\pi\) | ||||
0.296849 | + | 0.954924i | \(0.404064\pi\) | |||||||
\(224\) | −0.736597 | −0.0492159 | ||||||||
\(225\) | 1.59228 | 0.106152 | ||||||||
\(226\) | −17.4959 | −1.16381 | ||||||||
\(227\) | −5.87659 | −0.390043 | −0.195022 | − | 0.980799i | \(-0.562478\pi\) | ||||
−0.195022 | + | 0.980799i | \(0.562478\pi\) | |||||||
\(228\) | 8.61426 | 0.570493 | ||||||||
\(229\) | −6.27352 | −0.414566 | −0.207283 | − | 0.978281i | \(-0.566462\pi\) | ||||
−0.207283 | + | 0.978281i | \(0.566462\pi\) | |||||||
\(230\) | −7.10860 | −0.468727 | ||||||||
\(231\) | 4.98351 | 0.327891 | ||||||||
\(232\) | 2.80984 | 0.184475 | ||||||||
\(233\) | −15.2330 | −0.997948 | −0.498974 | − | 0.866617i | \(-0.666290\pi\) | ||||
−0.498974 | + | 0.866617i | \(0.666290\pi\) | |||||||
\(234\) | 7.42861 | 0.485624 | ||||||||
\(235\) | 8.43542 | 0.550266 | ||||||||
\(236\) | 2.06051 | 0.134128 | ||||||||
\(237\) | 33.3680 | 2.16749 | ||||||||
\(238\) | −2.31412 | −0.150002 | ||||||||
\(239\) | −23.8799 | −1.54466 | −0.772330 | − | 0.635222i | \(-0.780909\pi\) | ||||
−0.772330 | + | 0.635222i | \(0.780909\pi\) | |||||||
\(240\) | 2.14296 | 0.138328 | ||||||||
\(241\) | −16.3410 | −1.05262 | −0.526308 | − | 0.850294i | \(-0.676424\pi\) | ||||
−0.526308 | + | 0.850294i | \(0.676424\pi\) | |||||||
\(242\) | 1.03258 | 0.0663769 | ||||||||
\(243\) | 15.0400 | 0.964818 | ||||||||
\(244\) | 4.47293 | 0.286350 | ||||||||
\(245\) | 6.45743 | 0.412550 | ||||||||
\(246\) | −22.2301 | −1.41734 | ||||||||
\(247\) | 18.7539 | 1.19328 | ||||||||
\(248\) | 5.72133 | 0.363305 | ||||||||
\(249\) | −33.8322 | −2.14403 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −7.09340 | −0.447732 | −0.223866 | − | 0.974620i | \(-0.571868\pi\) | ||||
−0.223866 | + | 0.974620i | \(0.571868\pi\) | |||||||
\(252\) | 1.17287 | 0.0738839 | ||||||||
\(253\) | 22.4427 | 1.41096 | ||||||||
\(254\) | −10.1949 | −0.639686 | ||||||||
\(255\) | 6.73241 | 0.421600 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.3092 | 1.51636 | 0.758182 | − | 0.652043i | \(-0.226088\pi\) | ||||
0.758182 | + | 0.652043i | \(0.226088\pi\) | |||||||
\(258\) | 21.5143 | 1.33942 | ||||||||
\(259\) | −5.87224 | −0.364883 | ||||||||
\(260\) | 4.66538 | 0.289335 | ||||||||
\(261\) | −4.47405 | −0.276937 | ||||||||
\(262\) | −15.1027 | −0.933047 | ||||||||
\(263\) | −0.431138 | −0.0265851 | −0.0132925 | − | 0.999912i | \(-0.504231\pi\) | ||||
−0.0132925 | + | 0.999912i | \(0.504231\pi\) | |||||||
\(264\) | −6.76559 | −0.416393 | ||||||||
\(265\) | −7.83253 | −0.481148 | ||||||||
\(266\) | 2.96097 | 0.181548 | ||||||||
\(267\) | 13.0502 | 0.798660 | ||||||||
\(268\) | −8.16901 | −0.499002 | ||||||||
\(269\) | 7.22774 | 0.440683 | 0.220342 | − | 0.975423i | \(-0.429283\pi\) | ||||
0.220342 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(270\) | 3.01668 | 0.183589 | ||||||||
\(271\) | −9.52488 | −0.578595 | −0.289298 | − | 0.957239i | \(-0.593422\pi\) | ||||
−0.289298 | + | 0.957239i | \(0.593422\pi\) | |||||||
\(272\) | 3.14164 | 0.190490 | ||||||||
\(273\) | 7.36430 | 0.445708 | ||||||||
\(274\) | 14.6783 | 0.886749 | ||||||||
\(275\) | −3.15712 | −0.190382 | ||||||||
\(276\) | 15.2335 | 0.916947 | ||||||||
\(277\) | 19.9210 | 1.19694 | 0.598468 | − | 0.801147i | \(-0.295776\pi\) | ||||
0.598468 | + | 0.801147i | \(0.295776\pi\) | |||||||
\(278\) | −1.17572 | −0.0705152 | ||||||||
\(279\) | −9.10998 | −0.545400 | ||||||||
\(280\) | 0.736597 | 0.0440201 | ||||||||
\(281\) | 26.6999 | 1.59278 | 0.796391 | − | 0.604782i | \(-0.206740\pi\) | ||||
0.796391 | + | 0.604782i | \(0.206740\pi\) | |||||||
\(282\) | −18.0768 | −1.07646 | ||||||||
\(283\) | 7.84636 | 0.466418 | 0.233209 | − | 0.972427i | \(-0.425077\pi\) | ||||
0.233209 | + | 0.972427i | \(0.425077\pi\) | |||||||
\(284\) | 9.31937 | 0.553003 | ||||||||
\(285\) | −8.61426 | −0.510265 | ||||||||
\(286\) | −14.7292 | −0.870955 | ||||||||
\(287\) | −7.64113 | −0.451041 | ||||||||
\(288\) | −1.59228 | −0.0938262 | ||||||||
\(289\) | −7.13011 | −0.419418 | ||||||||
\(290\) | −2.80984 | −0.164999 | ||||||||
\(291\) | 38.0493 | 2.23049 | ||||||||
\(292\) | −8.97252 | −0.525077 | ||||||||
\(293\) | −3.76786 | −0.220121 | −0.110060 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110060 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(294\) | −13.8380 | −0.807049 | ||||||||
\(295\) | −2.06051 | −0.119968 | ||||||||
\(296\) | 7.97212 | 0.463370 | ||||||||
\(297\) | −9.52403 | −0.552640 | ||||||||
\(298\) | 4.18473 | 0.242415 | ||||||||
\(299\) | 33.1644 | 1.91794 | ||||||||
\(300\) | −2.14296 | −0.123724 | ||||||||
\(301\) | 7.39508 | 0.426246 | ||||||||
\(302\) | 15.7280 | 0.905044 | ||||||||
\(303\) | 30.2886 | 1.74003 | ||||||||
\(304\) | −4.01979 | −0.230551 | ||||||||
\(305\) | −4.47293 | −0.256119 | ||||||||
\(306\) | −5.00238 | −0.285967 | ||||||||
\(307\) | 9.59769 | 0.547769 | 0.273885 | − | 0.961763i | \(-0.411691\pi\) | ||||
0.273885 | + | 0.961763i | \(0.411691\pi\) | |||||||
\(308\) | −2.32553 | −0.132509 | ||||||||
\(309\) | −11.9304 | −0.678697 | ||||||||
\(310\) | −5.72133 | −0.324950 | ||||||||
\(311\) | 4.00013 | 0.226827 | 0.113413 | − | 0.993548i | \(-0.463822\pi\) | ||||
0.113413 | + | 0.993548i | \(0.463822\pi\) | |||||||
\(312\) | −9.99774 | −0.566010 | ||||||||
\(313\) | −6.13589 | −0.346821 | −0.173410 | − | 0.984850i | \(-0.555479\pi\) | ||||
−0.173410 | + | 0.984850i | \(0.555479\pi\) | |||||||
\(314\) | −6.05642 | −0.341784 | ||||||||
\(315\) | −1.17287 | −0.0660838 | ||||||||
\(316\) | −15.5710 | −0.875937 | ||||||||
\(317\) | −14.6446 | −0.822520 | −0.411260 | − | 0.911518i | \(-0.634911\pi\) | ||||
−0.411260 | + | 0.911518i | \(0.634911\pi\) | |||||||
\(318\) | 16.7848 | 0.941245 | ||||||||
\(319\) | 8.87099 | 0.496680 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 26.1600 | 1.46011 | ||||||||
\(322\) | 5.23617 | 0.291801 | ||||||||
\(323\) | −12.6287 | −0.702682 | ||||||||
\(324\) | −11.2415 | −0.624527 | ||||||||
\(325\) | −4.66538 | −0.258789 | ||||||||
\(326\) | 21.4761 | 1.18945 | ||||||||
\(327\) | 7.35905 | 0.406956 | ||||||||
\(328\) | 10.3736 | 0.572784 | ||||||||
\(329\) | −6.21351 | −0.342562 | ||||||||
\(330\) | 6.76559 | 0.372433 | ||||||||
\(331\) | 28.6390 | 1.57414 | 0.787071 | − | 0.616863i | \(-0.211597\pi\) | ||||
0.787071 | + | 0.616863i | \(0.211597\pi\) | |||||||
\(332\) | 15.7876 | 0.866455 | ||||||||
\(333\) | −12.6939 | −0.695620 | ||||||||
\(334\) | −5.52017 | −0.302050 | ||||||||
\(335\) | 8.16901 | 0.446321 | ||||||||
\(336\) | −1.57850 | −0.0861141 | ||||||||
\(337\) | 14.7214 | 0.801927 | 0.400963 | − | 0.916094i | \(-0.368675\pi\) | ||||
0.400963 | + | 0.916094i | \(0.368675\pi\) | |||||||
\(338\) | −8.76580 | −0.476797 | ||||||||
\(339\) | −37.4930 | −2.03634 | ||||||||
\(340\) | −3.14164 | −0.170379 | ||||||||
\(341\) | 18.0629 | 0.978163 | ||||||||
\(342\) | 6.40065 | 0.346108 | ||||||||
\(343\) | −9.91269 | −0.535235 | ||||||||
\(344\) | −10.0395 | −0.541295 | ||||||||
\(345\) | −15.2335 | −0.820142 | ||||||||
\(346\) | −12.1974 | −0.655736 | ||||||||
\(347\) | 32.0717 | 1.72170 | 0.860849 | − | 0.508860i | \(-0.169933\pi\) | ||||
0.860849 | + | 0.508860i | \(0.169933\pi\) | |||||||
\(348\) | 6.02137 | 0.322779 | ||||||||
\(349\) | −5.43075 | −0.290701 | −0.145351 | − | 0.989380i | \(-0.546431\pi\) | ||||
−0.145351 | + | 0.989380i | \(0.546431\pi\) | |||||||
\(350\) | −0.736597 | −0.0393727 | ||||||||
\(351\) | −14.0740 | −0.751213 | ||||||||
\(352\) | 3.15712 | 0.168275 | ||||||||
\(353\) | −1.82256 | −0.0970050 | −0.0485025 | − | 0.998823i | \(-0.515445\pi\) | ||||
−0.0485025 | + | 0.998823i | \(0.515445\pi\) | |||||||
\(354\) | 4.41560 | 0.234686 | ||||||||
\(355\) | −9.31937 | −0.494621 | ||||||||
\(356\) | −6.08980 | −0.322759 | ||||||||
\(357\) | −4.95907 | −0.262462 | ||||||||
\(358\) | 6.54798 | 0.346071 | ||||||||
\(359\) | −25.8553 | −1.36459 | −0.682296 | − | 0.731076i | \(-0.739019\pi\) | ||||
−0.682296 | + | 0.731076i | \(0.739019\pi\) | |||||||
\(360\) | 1.59228 | 0.0839207 | ||||||||
\(361\) | −2.84126 | −0.149540 | ||||||||
\(362\) | 13.3931 | 0.703928 | ||||||||
\(363\) | 2.21279 | 0.116141 | ||||||||
\(364\) | −3.43651 | −0.180122 | ||||||||
\(365\) | 8.97252 | 0.469643 | ||||||||
\(366\) | 9.58532 | 0.501033 | ||||||||
\(367\) | −8.23813 | −0.430027 | −0.215013 | − | 0.976611i | \(-0.568980\pi\) | ||||
−0.215013 | + | 0.976611i | \(0.568980\pi\) | |||||||
\(368\) | −7.10860 | −0.370562 | ||||||||
\(369\) | −16.5176 | −0.859874 | ||||||||
\(370\) | −7.97212 | −0.414451 | ||||||||
\(371\) | 5.76942 | 0.299533 | ||||||||
\(372\) | 12.2606 | 0.635682 | ||||||||
\(373\) | −18.7443 | −0.970543 | −0.485271 | − | 0.874364i | \(-0.661279\pi\) | ||||
−0.485271 | + | 0.874364i | \(0.661279\pi\) | |||||||
\(374\) | 9.91854 | 0.512875 | ||||||||
\(375\) | 2.14296 | 0.110662 | ||||||||
\(376\) | 8.43542 | 0.435024 | ||||||||
\(377\) | 13.1090 | 0.675146 | ||||||||
\(378\) | −2.22208 | −0.114291 | ||||||||
\(379\) | 21.3593 | 1.09715 | 0.548577 | − | 0.836100i | \(-0.315170\pi\) | ||||
0.548577 | + | 0.836100i | \(0.315170\pi\) | |||||||
\(380\) | 4.01979 | 0.206211 | ||||||||
\(381\) | −21.8473 | −1.11927 | ||||||||
\(382\) | 7.17995 | 0.367358 | ||||||||
\(383\) | 24.9272 | 1.27372 | 0.636860 | − | 0.770979i | \(-0.280233\pi\) | ||||
0.636860 | + | 0.770979i | \(0.280233\pi\) | |||||||
\(384\) | 2.14296 | 0.109358 | ||||||||
\(385\) | 2.32553 | 0.118520 | ||||||||
\(386\) | −14.3466 | −0.730225 | ||||||||
\(387\) | 15.9858 | 0.812603 | ||||||||
\(388\) | −17.7555 | −0.901399 | ||||||||
\(389\) | 2.11348 | 0.107158 | 0.0535788 | − | 0.998564i | \(-0.482937\pi\) | ||||
0.0535788 | + | 0.998564i | \(0.482937\pi\) | |||||||
\(390\) | 9.99774 | 0.506255 | ||||||||
\(391\) | −22.3327 | −1.12941 | ||||||||
\(392\) | 6.45743 | 0.326149 | ||||||||
\(393\) | −32.3645 | −1.63257 | ||||||||
\(394\) | 20.7117 | 1.04344 | ||||||||
\(395\) | 15.5710 | 0.783462 | ||||||||
\(396\) | −5.02703 | −0.252618 | ||||||||
\(397\) | −13.0699 | −0.655959 | −0.327979 | − | 0.944685i | \(-0.606368\pi\) | ||||
−0.327979 | + | 0.944685i | \(0.606368\pi\) | |||||||
\(398\) | 2.30944 | 0.115762 | ||||||||
\(399\) | 6.34524 | 0.317659 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 29.6893 | 1.48261 | 0.741307 | − | 0.671166i | \(-0.234206\pi\) | ||||
0.741307 | + | 0.671166i | \(0.234206\pi\) | |||||||
\(402\) | −17.5059 | −0.873113 | ||||||||
\(403\) | 26.6922 | 1.32963 | ||||||||
\(404\) | −14.1340 | −0.703192 | ||||||||
\(405\) | 11.2415 | 0.558594 | ||||||||
\(406\) | 2.06972 | 0.102718 | ||||||||
\(407\) | 25.1690 | 1.24758 | ||||||||
\(408\) | 6.73241 | 0.333304 | ||||||||
\(409\) | −4.03673 | −0.199603 | −0.0998017 | − | 0.995007i | \(-0.531821\pi\) | ||||
−0.0998017 | + | 0.995007i | \(0.531821\pi\) | |||||||
\(410\) | −10.3736 | −0.512313 | ||||||||
\(411\) | 31.4550 | 1.55156 | ||||||||
\(412\) | 5.56725 | 0.274279 | ||||||||
\(413\) | 1.51777 | 0.0746844 | ||||||||
\(414\) | 11.3189 | 0.556294 | ||||||||
\(415\) | −15.7876 | −0.774981 | ||||||||
\(416\) | 4.66538 | 0.228739 | ||||||||
\(417\) | −2.51953 | −0.123382 | ||||||||
\(418\) | −12.6910 | −0.620736 | ||||||||
\(419\) | 39.1232 | 1.91129 | 0.955647 | − | 0.294516i | \(-0.0951583\pi\) | ||||
0.955647 | + | 0.294516i | \(0.0951583\pi\) | |||||||
\(420\) | 1.57850 | 0.0770228 | ||||||||
\(421\) | 9.80007 | 0.477626 | 0.238813 | − | 0.971066i | \(-0.423242\pi\) | ||||
0.238813 | + | 0.971066i | \(0.423242\pi\) | |||||||
\(422\) | 12.0649 | 0.587308 | ||||||||
\(423\) | −13.4316 | −0.653066 | ||||||||
\(424\) | −7.83253 | −0.380381 | ||||||||
\(425\) | 3.14164 | 0.152392 | ||||||||
\(426\) | 19.9711 | 0.967601 | ||||||||
\(427\) | 3.29475 | 0.159444 | ||||||||
\(428\) | −12.2074 | −0.590067 | ||||||||
\(429\) | −31.5641 | −1.52393 | ||||||||
\(430\) | 10.0395 | 0.484149 | ||||||||
\(431\) | 9.30372 | 0.448145 | 0.224072 | − | 0.974573i | \(-0.428065\pi\) | ||||
0.224072 | + | 0.974573i | \(0.428065\pi\) | |||||||
\(432\) | 3.01668 | 0.145140 | ||||||||
\(433\) | 11.2128 | 0.538851 | 0.269426 | − | 0.963021i | \(-0.413166\pi\) | ||||
0.269426 | + | 0.963021i | \(0.413166\pi\) | |||||||
\(434\) | 4.21431 | 0.202293 | ||||||||
\(435\) | −6.02137 | −0.288703 | ||||||||
\(436\) | −3.43406 | −0.164461 | ||||||||
\(437\) | 28.5751 | 1.36693 | ||||||||
\(438\) | −19.2278 | −0.918738 | ||||||||
\(439\) | 25.9606 | 1.23903 | 0.619516 | − | 0.784984i | \(-0.287329\pi\) | ||||
0.619516 | + | 0.784984i | \(0.287329\pi\) | |||||||
\(440\) | −3.15712 | −0.150510 | ||||||||
\(441\) | −10.2821 | −0.489622 | ||||||||
\(442\) | 14.6569 | 0.697160 | ||||||||
\(443\) | −3.75852 | −0.178573 | −0.0892864 | − | 0.996006i | \(-0.528459\pi\) | ||||
−0.0892864 | + | 0.996006i | \(0.528459\pi\) | |||||||
\(444\) | 17.0839 | 0.810768 | ||||||||
\(445\) | 6.08980 | 0.288684 | ||||||||
\(446\) | −8.86581 | −0.419808 | ||||||||
\(447\) | 8.96772 | 0.424158 | ||||||||
\(448\) | 0.736597 | 0.0348009 | ||||||||
\(449\) | −40.5643 | −1.91435 | −0.957173 | − | 0.289516i | \(-0.906506\pi\) | ||||
−0.957173 | + | 0.289516i | \(0.906506\pi\) | |||||||
\(450\) | −1.59228 | −0.0750610 | ||||||||
\(451\) | 32.7506 | 1.54216 | ||||||||
\(452\) | 17.4959 | 0.822937 | ||||||||
\(453\) | 33.7045 | 1.58357 | ||||||||
\(454\) | 5.87659 | 0.275802 | ||||||||
\(455\) | 3.43651 | 0.161106 | ||||||||
\(456\) | −8.61426 | −0.403400 | ||||||||
\(457\) | 10.9802 | 0.513632 | 0.256816 | − | 0.966460i | \(-0.417327\pi\) | ||||
0.256816 | + | 0.966460i | \(0.417327\pi\) | |||||||
\(458\) | 6.27352 | 0.293142 | ||||||||
\(459\) | 9.47732 | 0.442364 | ||||||||
\(460\) | 7.10860 | 0.331440 | ||||||||
\(461\) | 5.09029 | 0.237078 | 0.118539 | − | 0.992949i | \(-0.462179\pi\) | ||||
0.118539 | + | 0.992949i | \(0.462179\pi\) | |||||||
\(462\) | −4.98351 | −0.231854 | ||||||||
\(463\) | 12.7025 | 0.590334 | 0.295167 | − | 0.955446i | \(-0.404625\pi\) | ||||
0.295167 | + | 0.955446i | \(0.404625\pi\) | |||||||
\(464\) | −2.80984 | −0.130443 | ||||||||
\(465\) | −12.2606 | −0.568571 | ||||||||
\(466\) | 15.2330 | 0.705655 | ||||||||
\(467\) | 9.88392 | 0.457373 | 0.228687 | − | 0.973500i | \(-0.426557\pi\) | ||||
0.228687 | + | 0.973500i | \(0.426557\pi\) | |||||||
\(468\) | −7.42861 | −0.343388 | ||||||||
\(469\) | −6.01726 | −0.277851 | ||||||||
\(470\) | −8.43542 | −0.389097 | ||||||||
\(471\) | −12.9787 | −0.598026 | ||||||||
\(472\) | −2.06051 | −0.0948428 | ||||||||
\(473\) | −31.6960 | −1.45738 | ||||||||
\(474\) | −33.3680 | −1.53265 | ||||||||
\(475\) | −4.01979 | −0.184441 | ||||||||
\(476\) | 2.31412 | 0.106068 | ||||||||
\(477\) | 12.4716 | 0.571036 | ||||||||
\(478\) | 23.8799 | 1.09224 | ||||||||
\(479\) | −4.77224 | −0.218049 | −0.109025 | − | 0.994039i | \(-0.534773\pi\) | ||||
−0.109025 | + | 0.994039i | \(0.534773\pi\) | |||||||
\(480\) | −2.14296 | −0.0978124 | ||||||||
\(481\) | 37.1930 | 1.69585 | ||||||||
\(482\) | 16.3410 | 0.744313 | ||||||||
\(483\) | 11.2209 | 0.510569 | ||||||||
\(484\) | −1.03258 | −0.0469356 | ||||||||
\(485\) | 17.7555 | 0.806236 | ||||||||
\(486\) | −15.0400 | −0.682229 | ||||||||
\(487\) | 0.963447 | 0.0436580 | 0.0218290 | − | 0.999762i | \(-0.493051\pi\) | ||||
0.0218290 | + | 0.999762i | \(0.493051\pi\) | |||||||
\(488\) | −4.47293 | −0.202480 | ||||||||
\(489\) | 46.0224 | 2.08121 | ||||||||
\(490\) | −6.45743 | −0.291717 | ||||||||
\(491\) | 31.5297 | 1.42292 | 0.711459 | − | 0.702728i | \(-0.248035\pi\) | ||||
0.711459 | + | 0.702728i | \(0.248035\pi\) | |||||||
\(492\) | 22.2301 | 1.00221 | ||||||||
\(493\) | −8.82749 | −0.397570 | ||||||||
\(494\) | −18.7539 | −0.843777 | ||||||||
\(495\) | 5.02703 | 0.225948 | ||||||||
\(496\) | −5.72133 | −0.256895 | ||||||||
\(497\) | 6.86462 | 0.307920 | ||||||||
\(498\) | 33.8322 | 1.51605 | ||||||||
\(499\) | 28.3383 | 1.26860 | 0.634298 | − | 0.773089i | \(-0.281289\pi\) | ||||
0.634298 | + | 0.773089i | \(0.281289\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −11.8295 | −0.528504 | ||||||||
\(502\) | 7.09340 | 0.316594 | ||||||||
\(503\) | −19.2281 | −0.857338 | −0.428669 | − | 0.903462i | \(-0.641017\pi\) | ||||
−0.428669 | + | 0.903462i | \(0.641017\pi\) | |||||||
\(504\) | −1.17287 | −0.0522438 | ||||||||
\(505\) | 14.1340 | 0.628954 | ||||||||
\(506\) | −22.4427 | −0.997701 | ||||||||
\(507\) | −18.7848 | −0.834261 | ||||||||
\(508\) | 10.1949 | 0.452326 | ||||||||
\(509\) | 29.6406 | 1.31380 | 0.656899 | − | 0.753979i | \(-0.271868\pi\) | ||||
0.656899 | + | 0.753979i | \(0.271868\pi\) | |||||||
\(510\) | −6.73241 | −0.298116 | ||||||||
\(511\) | −6.60913 | −0.292371 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −12.1264 | −0.535395 | ||||||||
\(514\) | −24.3092 | −1.07223 | ||||||||
\(515\) | −5.56725 | −0.245323 | ||||||||
\(516\) | −21.5143 | −0.947115 | ||||||||
\(517\) | 26.6317 | 1.17126 | ||||||||
\(518\) | 5.87224 | 0.258011 | ||||||||
\(519\) | −26.1386 | −1.14736 | ||||||||
\(520\) | −4.66538 | −0.204591 | ||||||||
\(521\) | −7.06813 | −0.309660 | −0.154830 | − | 0.987941i | \(-0.549483\pi\) | ||||
−0.154830 | + | 0.987941i | \(0.549483\pi\) | |||||||
\(522\) | 4.47405 | 0.195824 | ||||||||
\(523\) | 28.9340 | 1.26520 | 0.632598 | − | 0.774481i | \(-0.281989\pi\) | ||||
0.632598 | + | 0.774481i | \(0.281989\pi\) | |||||||
\(524\) | 15.1027 | 0.659764 | ||||||||
\(525\) | −1.57850 | −0.0688913 | ||||||||
\(526\) | 0.431138 | 0.0187985 | ||||||||
\(527\) | −17.9744 | −0.782975 | ||||||||
\(528\) | 6.76559 | 0.294435 | ||||||||
\(529\) | 27.5323 | 1.19705 | ||||||||
\(530\) | 7.83253 | 0.340223 | ||||||||
\(531\) | 3.28092 | 0.142380 | ||||||||
\(532\) | −2.96097 | −0.128374 | ||||||||
\(533\) | 48.3966 | 2.09629 | ||||||||
\(534\) | −13.0502 | −0.564738 | ||||||||
\(535\) | 12.2074 | 0.527772 | ||||||||
\(536\) | 8.16901 | 0.352847 | ||||||||
\(537\) | 14.0321 | 0.605528 | ||||||||
\(538\) | −7.22774 | −0.311610 | ||||||||
\(539\) | 20.3869 | 0.878125 | ||||||||
\(540\) | −3.01668 | −0.129817 | ||||||||
\(541\) | 2.18518 | 0.0939482 | 0.0469741 | − | 0.998896i | \(-0.485042\pi\) | ||||
0.0469741 | + | 0.998896i | \(0.485042\pi\) | |||||||
\(542\) | 9.52488 | 0.409128 | ||||||||
\(543\) | 28.7010 | 1.23168 | ||||||||
\(544\) | −3.14164 | −0.134697 | ||||||||
\(545\) | 3.43406 | 0.147099 | ||||||||
\(546\) | −7.36430 | −0.315163 | ||||||||
\(547\) | −25.6177 | −1.09533 | −0.547667 | − | 0.836697i | \(-0.684484\pi\) | ||||
−0.547667 | + | 0.836697i | \(0.684484\pi\) | |||||||
\(548\) | −14.6783 | −0.627026 | ||||||||
\(549\) | 7.12218 | 0.303967 | ||||||||
\(550\) | 3.15712 | 0.134620 | ||||||||
\(551\) | 11.2950 | 0.481181 | ||||||||
\(552\) | −15.2335 | −0.648379 | ||||||||
\(553\) | −11.4695 | −0.487735 | ||||||||
\(554\) | −19.9210 | −0.846362 | ||||||||
\(555\) | −17.0839 | −0.725173 | ||||||||
\(556\) | 1.17572 | 0.0498618 | ||||||||
\(557\) | −20.9176 | −0.886306 | −0.443153 | − | 0.896446i | \(-0.646140\pi\) | ||||
−0.443153 | + | 0.896446i | \(0.646140\pi\) | |||||||
\(558\) | 9.10998 | 0.385656 | ||||||||
\(559\) | −46.8383 | −1.98105 | ||||||||
\(560\) | −0.736597 | −0.0311269 | ||||||||
\(561\) | 21.2550 | 0.897388 | ||||||||
\(562\) | −26.6999 | −1.12627 | ||||||||
\(563\) | 33.7960 | 1.42433 | 0.712167 | − | 0.702010i | \(-0.247714\pi\) | ||||
0.712167 | + | 0.702010i | \(0.247714\pi\) | |||||||
\(564\) | 18.0768 | 0.761170 | ||||||||
\(565\) | −17.4959 | −0.736057 | ||||||||
\(566\) | −7.84636 | −0.329807 | ||||||||
\(567\) | −8.28044 | −0.347746 | ||||||||
\(568\) | −9.31937 | −0.391032 | ||||||||
\(569\) | 18.9228 | 0.793285 | 0.396642 | − | 0.917973i | \(-0.370175\pi\) | ||||
0.396642 | + | 0.917973i | \(0.370175\pi\) | |||||||
\(570\) | 8.61426 | 0.360812 | ||||||||
\(571\) | −46.6961 | −1.95417 | −0.977084 | − | 0.212852i | \(-0.931725\pi\) | ||||
−0.977084 | + | 0.212852i | \(0.931725\pi\) | |||||||
\(572\) | 14.7292 | 0.615858 | ||||||||
\(573\) | 15.3864 | 0.642774 | ||||||||
\(574\) | 7.64113 | 0.318934 | ||||||||
\(575\) | −7.10860 | −0.296449 | ||||||||
\(576\) | 1.59228 | 0.0663452 | ||||||||
\(577\) | −20.2305 | −0.842209 | −0.421104 | − | 0.907012i | \(-0.638357\pi\) | ||||
−0.421104 | + | 0.907012i | \(0.638357\pi\) | |||||||
\(578\) | 7.13011 | 0.296573 | ||||||||
\(579\) | −30.7443 | −1.27769 | ||||||||
\(580\) | 2.80984 | 0.116672 | ||||||||
\(581\) | 11.6291 | 0.482455 | ||||||||
\(582\) | −38.0493 | −1.57720 | ||||||||
\(583\) | −24.7283 | −1.02414 | ||||||||
\(584\) | 8.97252 | 0.371286 | ||||||||
\(585\) | 7.42861 | 0.307135 | ||||||||
\(586\) | 3.76786 | 0.155649 | ||||||||
\(587\) | 32.3018 | 1.33324 | 0.666619 | − | 0.745399i | \(-0.267741\pi\) | ||||
0.666619 | + | 0.745399i | \(0.267741\pi\) | |||||||
\(588\) | 13.8380 | 0.570670 | ||||||||
\(589\) | 22.9986 | 0.947639 | ||||||||
\(590\) | 2.06051 | 0.0848300 | ||||||||
\(591\) | 44.3844 | 1.82573 | ||||||||
\(592\) | −7.97212 | −0.327652 | ||||||||
\(593\) | 4.03651 | 0.165760 | 0.0828799 | − | 0.996560i | \(-0.473588\pi\) | ||||
0.0828799 | + | 0.996560i | \(0.473588\pi\) | |||||||
\(594\) | 9.52403 | 0.390776 | ||||||||
\(595\) | −2.31412 | −0.0948697 | ||||||||
\(596\) | −4.18473 | −0.171413 | ||||||||
\(597\) | 4.94903 | 0.202550 | ||||||||
\(598\) | −33.1644 | −1.35619 | ||||||||
\(599\) | 17.7830 | 0.726594 | 0.363297 | − | 0.931673i | \(-0.381651\pi\) | ||||
0.363297 | + | 0.931673i | \(0.381651\pi\) | |||||||
\(600\) | 2.14296 | 0.0874860 | ||||||||
\(601\) | 1.00000 | 0.0407909 | ||||||||
\(602\) | −7.39508 | −0.301401 | ||||||||
\(603\) | −13.0074 | −0.529701 | ||||||||
\(604\) | −15.7280 | −0.639963 | ||||||||
\(605\) | 1.03258 | 0.0419805 | ||||||||
\(606\) | −30.2886 | −1.23039 | ||||||||
\(607\) | −41.7377 | −1.69408 | −0.847040 | − | 0.531529i | \(-0.821618\pi\) | ||||
−0.847040 | + | 0.531529i | \(0.821618\pi\) | |||||||
\(608\) | 4.01979 | 0.163024 | ||||||||
\(609\) | 4.43532 | 0.179728 | ||||||||
\(610\) | 4.47293 | 0.181104 | ||||||||
\(611\) | 39.3545 | 1.59211 | ||||||||
\(612\) | 5.00238 | 0.202209 | ||||||||
\(613\) | 16.3315 | 0.659623 | 0.329812 | − | 0.944047i | \(-0.393015\pi\) | ||||
0.329812 | + | 0.944047i | \(0.393015\pi\) | |||||||
\(614\) | −9.59769 | −0.387331 | ||||||||
\(615\) | −22.2301 | −0.896405 | ||||||||
\(616\) | 2.32553 | 0.0936981 | ||||||||
\(617\) | −28.9374 | −1.16497 | −0.582487 | − | 0.812840i | \(-0.697920\pi\) | ||||
−0.582487 | + | 0.812840i | \(0.697920\pi\) | |||||||
\(618\) | 11.9304 | 0.479912 | ||||||||
\(619\) | −4.64048 | −0.186517 | −0.0932583 | − | 0.995642i | \(-0.529728\pi\) | ||||
−0.0932583 | + | 0.995642i | \(0.529728\pi\) | |||||||
\(620\) | 5.72133 | 0.229774 | ||||||||
\(621\) | −21.4444 | −0.860534 | ||||||||
\(622\) | −4.00013 | −0.160391 | ||||||||
\(623\) | −4.48573 | −0.179717 | ||||||||
\(624\) | 9.99774 | 0.400230 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 6.13589 | 0.245239 | ||||||||
\(627\) | −27.1963 | −1.08611 | ||||||||
\(628\) | 6.05642 | 0.241678 | ||||||||
\(629\) | −25.0455 | −0.998630 | ||||||||
\(630\) | 1.17287 | 0.0467283 | ||||||||
\(631\) | −38.8504 | −1.54661 | −0.773305 | − | 0.634035i | \(-0.781398\pi\) | ||||
−0.773305 | + | 0.634035i | \(0.781398\pi\) | |||||||
\(632\) | 15.5710 | 0.619381 | ||||||||
\(633\) | 25.8545 | 1.02763 | ||||||||
\(634\) | 14.6446 | 0.581609 | ||||||||
\(635\) | −10.1949 | −0.404573 | ||||||||
\(636\) | −16.7848 | −0.665561 | ||||||||
\(637\) | 30.1264 | 1.19365 | ||||||||
\(638\) | −8.87099 | −0.351206 | ||||||||
\(639\) | 14.8391 | 0.587025 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −19.3171 | −0.762978 | −0.381489 | − | 0.924373i | \(-0.624589\pi\) | ||||
−0.381489 | + | 0.924373i | \(0.624589\pi\) | |||||||
\(642\) | −26.1600 | −1.03245 | ||||||||
\(643\) | 3.88125 | 0.153062 | 0.0765309 | − | 0.997067i | \(-0.475616\pi\) | ||||
0.0765309 | + | 0.997067i | \(0.475616\pi\) | |||||||
\(644\) | −5.23617 | −0.206334 | ||||||||
\(645\) | 21.5143 | 0.847126 | ||||||||
\(646\) | 12.6287 | 0.496871 | ||||||||
\(647\) | 7.09591 | 0.278969 | 0.139485 | − | 0.990224i | \(-0.455455\pi\) | ||||
0.139485 | + | 0.990224i | \(0.455455\pi\) | |||||||
\(648\) | 11.2415 | 0.441607 | ||||||||
\(649\) | −6.50529 | −0.255355 | ||||||||
\(650\) | 4.66538 | 0.182991 | ||||||||
\(651\) | 9.03111 | 0.353957 | ||||||||
\(652\) | −21.4761 | −0.841068 | ||||||||
\(653\) | 44.8000 | 1.75316 | 0.876581 | − | 0.481255i | \(-0.159819\pi\) | ||||
0.876581 | + | 0.481255i | \(0.159819\pi\) | |||||||
\(654\) | −7.35905 | −0.287762 | ||||||||
\(655\) | −15.1027 | −0.590111 | ||||||||
\(656\) | −10.3736 | −0.405019 | ||||||||
\(657\) | −14.2868 | −0.557381 | ||||||||
\(658\) | 6.21351 | 0.242228 | ||||||||
\(659\) | 18.1165 | 0.705720 | 0.352860 | − | 0.935676i | \(-0.385209\pi\) | ||||
0.352860 | + | 0.935676i | \(0.385209\pi\) | |||||||
\(660\) | −6.76559 | −0.263350 | ||||||||
\(661\) | 15.1010 | 0.587359 | 0.293680 | − | 0.955904i | \(-0.405120\pi\) | ||||
0.293680 | + | 0.955904i | \(0.405120\pi\) | |||||||
\(662\) | −28.6390 | −1.11309 | ||||||||
\(663\) | 31.4093 | 1.21984 | ||||||||
\(664\) | −15.7876 | −0.612676 | ||||||||
\(665\) | 2.96097 | 0.114821 | ||||||||
\(666\) | 12.6939 | 0.491878 | ||||||||
\(667\) | 19.9740 | 0.773397 | ||||||||
\(668\) | 5.52017 | 0.213582 | ||||||||
\(669\) | −18.9991 | −0.734547 | ||||||||
\(670\) | −8.16901 | −0.315596 | ||||||||
\(671\) | −14.1216 | −0.545158 | ||||||||
\(672\) | 1.57850 | 0.0608919 | ||||||||
\(673\) | 11.5445 | 0.445006 | 0.222503 | − | 0.974932i | \(-0.428577\pi\) | ||||
0.222503 | + | 0.974932i | \(0.428577\pi\) | |||||||
\(674\) | −14.7214 | −0.567048 | ||||||||
\(675\) | 3.01668 | 0.116112 | ||||||||
\(676\) | 8.76580 | 0.337146 | ||||||||
\(677\) | 5.22090 | 0.200656 | 0.100328 | − | 0.994954i | \(-0.468011\pi\) | ||||
0.100328 | + | 0.994954i | \(0.468011\pi\) | |||||||
\(678\) | 37.4930 | 1.43991 | ||||||||
\(679\) | −13.0786 | −0.501912 | ||||||||
\(680\) | 3.14164 | 0.120476 | ||||||||
\(681\) | 12.5933 | 0.482577 | ||||||||
\(682\) | −18.0629 | −0.691665 | ||||||||
\(683\) | 40.5236 | 1.55059 | 0.775295 | − | 0.631599i | \(-0.217601\pi\) | ||||
0.775295 | + | 0.631599i | \(0.217601\pi\) | |||||||
\(684\) | −6.40065 | −0.244735 | ||||||||
\(685\) | 14.6783 | 0.560829 | ||||||||
\(686\) | 9.91269 | 0.378468 | ||||||||
\(687\) | 13.4439 | 0.512917 | ||||||||
\(688\) | 10.0395 | 0.382753 | ||||||||
\(689\) | −36.5418 | −1.39213 | ||||||||
\(690\) | 15.2335 | 0.579928 | ||||||||
\(691\) | 18.8301 | 0.716332 | 0.358166 | − | 0.933658i | \(-0.383402\pi\) | ||||
0.358166 | + | 0.933658i | \(0.383402\pi\) | |||||||
\(692\) | 12.1974 | 0.463676 | ||||||||
\(693\) | −3.70290 | −0.140661 | ||||||||
\(694\) | −32.0717 | −1.21742 | ||||||||
\(695\) | −1.17572 | −0.0445978 | ||||||||
\(696\) | −6.02137 | −0.228239 | ||||||||
\(697\) | −32.5900 | −1.23443 | ||||||||
\(698\) | 5.43075 | 0.205557 | ||||||||
\(699\) | 32.6437 | 1.23470 | ||||||||
\(700\) | 0.736597 | 0.0278407 | ||||||||
\(701\) | −38.9301 | −1.47037 | −0.735186 | − | 0.677866i | \(-0.762905\pi\) | ||||
−0.735186 | + | 0.677866i | \(0.762905\pi\) | |||||||
\(702\) | 14.0740 | 0.531188 | ||||||||
\(703\) | 32.0463 | 1.20865 | ||||||||
\(704\) | −3.15712 | −0.118988 | ||||||||
\(705\) | −18.0768 | −0.680811 | ||||||||
\(706\) | 1.82256 | 0.0685929 | ||||||||
\(707\) | −10.4110 | −0.391547 | ||||||||
\(708\) | −4.41560 | −0.165948 | ||||||||
\(709\) | 15.8921 | 0.596841 | 0.298421 | − | 0.954434i | \(-0.403540\pi\) | ||||
0.298421 | + | 0.954434i | \(0.403540\pi\) | |||||||
\(710\) | 9.31937 | 0.349750 | ||||||||
\(711\) | −24.7934 | −0.929827 | ||||||||
\(712\) | 6.08980 | 0.228225 | ||||||||
\(713\) | 40.6707 | 1.52313 | ||||||||
\(714\) | 4.95907 | 0.185589 | ||||||||
\(715\) | −14.7292 | −0.550840 | ||||||||
\(716\) | −6.54798 | −0.244709 | ||||||||
\(717\) | 51.1736 | 1.91111 | ||||||||
\(718\) | 25.8553 | 0.964913 | ||||||||
\(719\) | −20.8768 | −0.778572 | −0.389286 | − | 0.921117i | \(-0.627278\pi\) | ||||
−0.389286 | + | 0.921117i | \(0.627278\pi\) | |||||||
\(720\) | −1.59228 | −0.0593409 | ||||||||
\(721\) | 4.10082 | 0.152723 | ||||||||
\(722\) | 2.84126 | 0.105741 | ||||||||
\(723\) | 35.0182 | 1.30234 | ||||||||
\(724\) | −13.3931 | −0.497752 | ||||||||
\(725\) | −2.80984 | −0.104355 | ||||||||
\(726\) | −2.21279 | −0.0821242 | ||||||||
\(727\) | −3.27559 | −0.121485 | −0.0607425 | − | 0.998153i | \(-0.519347\pi\) | ||||
−0.0607425 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(728\) | 3.43651 | 0.127365 | ||||||||
\(729\) | 1.49427 | 0.0553432 | ||||||||
\(730\) | −8.97252 | −0.332088 | ||||||||
\(731\) | 31.5406 | 1.16657 | ||||||||
\(732\) | −9.58532 | −0.354284 | ||||||||
\(733\) | −47.3900 | −1.75039 | −0.875196 | − | 0.483769i | \(-0.839267\pi\) | ||||
−0.875196 | + | 0.483769i | \(0.839267\pi\) | |||||||
\(734\) | 8.23813 | 0.304075 | ||||||||
\(735\) | −13.8380 | −0.510423 | ||||||||
\(736\) | 7.10860 | 0.262027 | ||||||||
\(737\) | 25.7905 | 0.950007 | ||||||||
\(738\) | 16.5176 | 0.608023 | ||||||||
\(739\) | −49.8496 | −1.83375 | −0.916874 | − | 0.399176i | \(-0.869296\pi\) | ||||
−0.916874 | + | 0.399176i | \(0.869296\pi\) | |||||||
\(740\) | 7.97212 | 0.293061 | ||||||||
\(741\) | −40.1888 | −1.47637 | ||||||||
\(742\) | −5.76942 | −0.211802 | ||||||||
\(743\) | 9.39024 | 0.344494 | 0.172247 | − | 0.985054i | \(-0.444897\pi\) | ||||
0.172247 | + | 0.985054i | \(0.444897\pi\) | |||||||
\(744\) | −12.2606 | −0.449495 | ||||||||
\(745\) | 4.18473 | 0.153317 | ||||||||
\(746\) | 18.7443 | 0.686277 | ||||||||
\(747\) | 25.1383 | 0.919762 | ||||||||
\(748\) | −9.91854 | −0.362658 | ||||||||
\(749\) | −8.99193 | −0.328558 | ||||||||
\(750\) | −2.14296 | −0.0782499 | ||||||||
\(751\) | 3.92141 | 0.143094 | 0.0715472 | − | 0.997437i | \(-0.477206\pi\) | ||||
0.0715472 | + | 0.997437i | \(0.477206\pi\) | |||||||
\(752\) | −8.43542 | −0.307608 | ||||||||
\(753\) | 15.2009 | 0.553951 | ||||||||
\(754\) | −13.1090 | −0.477400 | ||||||||
\(755\) | 15.7280 | 0.572400 | ||||||||
\(756\) | 2.22208 | 0.0808162 | ||||||||
\(757\) | 35.4154 | 1.28719 | 0.643597 | − | 0.765365i | \(-0.277441\pi\) | ||||
0.643597 | + | 0.765365i | \(0.277441\pi\) | |||||||
\(758\) | −21.3593 | −0.775805 | ||||||||
\(759\) | −48.0939 | −1.74570 | ||||||||
\(760\) | −4.01979 | −0.145813 | ||||||||
\(761\) | 47.8165 | 1.73335 | 0.866673 | − | 0.498877i | \(-0.166254\pi\) | ||||
0.866673 | + | 0.498877i | \(0.166254\pi\) | |||||||
\(762\) | 21.8473 | 0.791445 | ||||||||
\(763\) | −2.52951 | −0.0915746 | ||||||||
\(764\) | −7.17995 | −0.259762 | ||||||||
\(765\) | −5.00238 | −0.180861 | ||||||||
\(766\) | −24.9272 | −0.900656 | ||||||||
\(767\) | −9.61308 | −0.347108 | ||||||||
\(768\) | −2.14296 | −0.0773275 | ||||||||
\(769\) | −26.8548 | −0.968410 | −0.484205 | − | 0.874955i | \(-0.660891\pi\) | ||||
−0.484205 | + | 0.874955i | \(0.660891\pi\) | |||||||
\(770\) | −2.32553 | −0.0838061 | ||||||||
\(771\) | −52.0936 | −1.87611 | ||||||||
\(772\) | 14.3466 | 0.516347 | ||||||||
\(773\) | −46.8908 | −1.68654 | −0.843272 | − | 0.537488i | \(-0.819373\pi\) | ||||
−0.843272 | + | 0.537488i | \(0.819373\pi\) | |||||||
\(774\) | −15.9858 | −0.574597 | ||||||||
\(775\) | −5.72133 | −0.205516 | ||||||||
\(776\) | 17.7555 | 0.637385 | ||||||||
\(777\) | 12.5840 | 0.451448 | ||||||||
\(778\) | −2.11348 | −0.0757718 | ||||||||
\(779\) | 41.6996 | 1.49404 | ||||||||
\(780\) | −9.99774 | −0.357976 | ||||||||
\(781\) | −29.4224 | −1.05282 | ||||||||
\(782\) | 22.3327 | 0.798615 | ||||||||
\(783\) | −8.47638 | −0.302921 | ||||||||
\(784\) | −6.45743 | −0.230622 | ||||||||
\(785\) | −6.05642 | −0.216163 | ||||||||
\(786\) | 32.3645 | 1.15440 | ||||||||
\(787\) | −20.9834 | −0.747978 | −0.373989 | − | 0.927433i | \(-0.622010\pi\) | ||||
−0.373989 | + | 0.927433i | \(0.622010\pi\) | |||||||
\(788\) | −20.7117 | −0.737825 | ||||||||
\(789\) | 0.923911 | 0.0328921 | ||||||||
\(790\) | −15.5710 | −0.553991 | ||||||||
\(791\) | 12.8874 | 0.458223 | ||||||||
\(792\) | 5.02703 | 0.178628 | ||||||||
\(793\) | −20.8679 | −0.741042 | ||||||||
\(794\) | 13.0699 | 0.463833 | ||||||||
\(795\) | 16.7848 | 0.595296 | ||||||||
\(796\) | −2.30944 | −0.0818558 | ||||||||
\(797\) | 21.7525 | 0.770514 | 0.385257 | − | 0.922809i | \(-0.374113\pi\) | ||||
0.385257 | + | 0.922809i | \(0.374113\pi\) | |||||||
\(798\) | −6.34524 | −0.224619 | ||||||||
\(799\) | −26.5011 | −0.937540 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −9.69669 | −0.342616 | ||||||||
\(802\) | −29.6893 | −1.04837 | ||||||||
\(803\) | 28.3273 | 0.999650 | ||||||||
\(804\) | 17.5059 | 0.617384 | ||||||||
\(805\) | 5.23617 | 0.184551 | ||||||||
\(806\) | −26.6922 | −0.940193 | ||||||||
\(807\) | −15.4888 | −0.545230 | ||||||||
\(808\) | 14.1340 | 0.497232 | ||||||||
\(809\) | −2.18991 | −0.0769932 | −0.0384966 | − | 0.999259i | \(-0.512257\pi\) | ||||
−0.0384966 | + | 0.999259i | \(0.512257\pi\) | |||||||
\(810\) | −11.2415 | −0.394985 | ||||||||
\(811\) | 10.7749 | 0.378359 | 0.189180 | − | 0.981943i | \(-0.439417\pi\) | ||||
0.189180 | + | 0.981943i | \(0.439417\pi\) | |||||||
\(812\) | −2.06972 | −0.0726328 | ||||||||
\(813\) | 20.4114 | 0.715861 | ||||||||
\(814\) | −25.1690 | −0.882171 | ||||||||
\(815\) | 21.4761 | 0.752274 | ||||||||
\(816\) | −6.73241 | −0.235682 | ||||||||
\(817\) | −40.3568 | −1.41191 | ||||||||
\(818\) | 4.03673 | 0.141141 | ||||||||
\(819\) | −5.47189 | −0.191203 | ||||||||
\(820\) | 10.3736 | 0.362260 | ||||||||
\(821\) | −46.2372 | −1.61369 | −0.806845 | − | 0.590763i | \(-0.798827\pi\) | ||||
−0.806845 | + | 0.590763i | \(0.798827\pi\) | |||||||
\(822\) | −31.4550 | −1.09712 | ||||||||
\(823\) | −18.1597 | −0.633006 | −0.316503 | − | 0.948591i | \(-0.602509\pi\) | ||||
−0.316503 | + | 0.948591i | \(0.602509\pi\) | |||||||
\(824\) | −5.56725 | −0.193945 | ||||||||
\(825\) | 6.76559 | 0.235548 | ||||||||
\(826\) | −1.51777 | −0.0528099 | ||||||||
\(827\) | −3.22987 | −0.112313 | −0.0561567 | − | 0.998422i | \(-0.517885\pi\) | ||||
−0.0561567 | + | 0.998422i | \(0.517885\pi\) | |||||||
\(828\) | −11.3189 | −0.393359 | ||||||||
\(829\) | 2.96612 | 0.103018 | 0.0515088 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515088 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(830\) | 15.7876 | 0.547994 | ||||||||
\(831\) | −42.6899 | −1.48090 | ||||||||
\(832\) | −4.66538 | −0.161743 | ||||||||
\(833\) | −20.2869 | −0.702899 | ||||||||
\(834\) | 2.51953 | 0.0872442 | ||||||||
\(835\) | −5.52017 | −0.191033 | ||||||||
\(836\) | 12.6910 | 0.438927 | ||||||||
\(837\) | −17.2594 | −0.596573 | ||||||||
\(838\) | −39.1232 | −1.35149 | ||||||||
\(839\) | 46.7222 | 1.61303 | 0.806514 | − | 0.591214i | \(-0.201351\pi\) | ||||
0.806514 | + | 0.591214i | \(0.201351\pi\) | |||||||
\(840\) | −1.57850 | −0.0544634 | ||||||||
\(841\) | −21.1048 | −0.727753 | ||||||||
\(842\) | −9.80007 | −0.337733 | ||||||||
\(843\) | −57.2169 | −1.97065 | ||||||||
\(844\) | −12.0649 | −0.415290 | ||||||||
\(845\) | −8.76580 | −0.301553 | ||||||||
\(846\) | 13.4316 | 0.461788 | ||||||||
\(847\) | −0.760597 | −0.0261344 | ||||||||
\(848\) | 7.83253 | 0.268970 | ||||||||
\(849\) | −16.8145 | −0.577071 | ||||||||
\(850\) | −3.14164 | −0.107757 | ||||||||
\(851\) | 56.6706 | 1.94264 | ||||||||
\(852\) | −19.9711 | −0.684197 | ||||||||
\(853\) | −21.2710 | −0.728306 | −0.364153 | − | 0.931339i | \(-0.618641\pi\) | ||||
−0.364153 | + | 0.931339i | \(0.618641\pi\) | |||||||
\(854\) | −3.29475 | −0.112744 | ||||||||
\(855\) | 6.40065 | 0.218898 | ||||||||
\(856\) | 12.2074 | 0.417240 | ||||||||
\(857\) | −20.0645 | −0.685391 | −0.342696 | − | 0.939447i | \(-0.611340\pi\) | ||||
−0.342696 | + | 0.939447i | \(0.611340\pi\) | |||||||
\(858\) | 31.5641 | 1.07758 | ||||||||
\(859\) | −8.78364 | −0.299694 | −0.149847 | − | 0.988709i | \(-0.547878\pi\) | ||||
−0.149847 | + | 0.988709i | \(0.547878\pi\) | |||||||
\(860\) | −10.0395 | −0.342345 | ||||||||
\(861\) | 16.3746 | 0.558046 | ||||||||
\(862\) | −9.30372 | −0.316886 | ||||||||
\(863\) | 15.1021 | 0.514083 | 0.257041 | − | 0.966400i | \(-0.417252\pi\) | ||||
0.257041 | + | 0.966400i | \(0.417252\pi\) | |||||||
\(864\) | −3.01668 | −0.102630 | ||||||||
\(865\) | −12.1974 | −0.414724 | ||||||||
\(866\) | −11.2128 | −0.381025 | ||||||||
\(867\) | 15.2795 | 0.518920 | ||||||||
\(868\) | −4.21431 | −0.143043 | ||||||||
\(869\) | 49.1595 | 1.66762 | ||||||||
\(870\) | 6.02137 | 0.204144 | ||||||||
\(871\) | 38.1116 | 1.29136 | ||||||||
\(872\) | 3.43406 | 0.116292 | ||||||||
\(873\) | −28.2718 | −0.956855 | ||||||||
\(874\) | −28.5751 | −0.966568 | ||||||||
\(875\) | −0.736597 | −0.0249015 | ||||||||
\(876\) | 19.2278 | 0.649646 | ||||||||
\(877\) | −36.3730 | −1.22823 | −0.614115 | − | 0.789217i | \(-0.710487\pi\) | ||||
−0.614115 | + | 0.789217i | \(0.710487\pi\) | |||||||
\(878\) | −25.9606 | −0.876128 | ||||||||
\(879\) | 8.07439 | 0.272342 | ||||||||
\(880\) | 3.15712 | 0.106427 | ||||||||
\(881\) | −46.5628 | −1.56874 | −0.784371 | − | 0.620292i | \(-0.787014\pi\) | ||||
−0.784371 | + | 0.620292i | \(0.787014\pi\) | |||||||
\(882\) | 10.2821 | 0.346215 | ||||||||
\(883\) | −26.4906 | −0.891480 | −0.445740 | − | 0.895163i | \(-0.647059\pi\) | ||||
−0.445740 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(884\) | −14.6569 | −0.492967 | ||||||||
\(885\) | 4.41560 | 0.148429 | ||||||||
\(886\) | 3.75852 | 0.126270 | ||||||||
\(887\) | −37.8911 | −1.27226 | −0.636129 | − | 0.771582i | \(-0.719466\pi\) | ||||
−0.636129 | + | 0.771582i | \(0.719466\pi\) | |||||||
\(888\) | −17.0839 | −0.573300 | ||||||||
\(889\) | 7.50954 | 0.251862 | ||||||||
\(890\) | −6.08980 | −0.204131 | ||||||||
\(891\) | 35.4907 | 1.18898 | ||||||||
\(892\) | 8.86581 | 0.296849 | ||||||||
\(893\) | 33.9087 | 1.13471 | ||||||||
\(894\) | −8.96772 | −0.299925 | ||||||||
\(895\) | 6.54798 | 0.218875 | ||||||||
\(896\) | −0.736597 | −0.0246080 | ||||||||
\(897\) | −71.0700 | −2.37296 | ||||||||
\(898\) | 40.5643 | 1.35365 | ||||||||
\(899\) | 16.0760 | 0.536164 | ||||||||
\(900\) | 1.59228 | 0.0530761 | ||||||||
\(901\) | 24.6070 | 0.819777 | ||||||||
\(902\) | −32.7506 | −1.09048 | ||||||||
\(903\) | −15.8474 | −0.527368 | ||||||||
\(904\) | −17.4959 | −0.581904 | ||||||||
\(905\) | 13.3931 | 0.445203 | ||||||||
\(906\) | −33.7045 | −1.11976 | ||||||||
\(907\) | −27.8282 | −0.924019 | −0.462009 | − | 0.886875i | \(-0.652871\pi\) | ||||
−0.462009 | + | 0.886875i | \(0.652871\pi\) | |||||||
\(908\) | −5.87659 | −0.195022 | ||||||||
\(909\) | −22.5053 | −0.746454 | ||||||||
\(910\) | −3.43651 | −0.113919 | ||||||||
\(911\) | 9.80608 | 0.324890 | 0.162445 | − | 0.986718i | \(-0.448062\pi\) | ||||
0.162445 | + | 0.986718i | \(0.448062\pi\) | |||||||
\(912\) | 8.61426 | 0.285247 | ||||||||
\(913\) | −49.8433 | −1.64957 | ||||||||
\(914\) | −10.9802 | −0.363193 | ||||||||
\(915\) | 9.58532 | 0.316881 | ||||||||
\(916\) | −6.27352 | −0.207283 | ||||||||
\(917\) | 11.1246 | 0.367366 | ||||||||
\(918\) | −9.47732 | −0.312798 | ||||||||
\(919\) | 3.59770 | 0.118677 | 0.0593386 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593386 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(920\) | −7.10860 | −0.234364 | ||||||||
\(921\) | −20.5675 | −0.677722 | ||||||||
\(922\) | −5.09029 | −0.167640 | ||||||||
\(923\) | −43.4785 | −1.43111 | ||||||||
\(924\) | 4.98351 | 0.163945 | ||||||||
\(925\) | −7.97212 | −0.262122 | ||||||||
\(926\) | −12.7025 | −0.417429 | ||||||||
\(927\) | 8.86465 | 0.291153 | ||||||||
\(928\) | 2.80984 | 0.0922374 | ||||||||
\(929\) | −21.9392 | −0.719801 | −0.359901 | − | 0.932991i | \(-0.617189\pi\) | ||||
−0.359901 | + | 0.932991i | \(0.617189\pi\) | |||||||
\(930\) | 12.2606 | 0.402041 | ||||||||
\(931\) | 25.9575 | 0.850723 | ||||||||
\(932\) | −15.2330 | −0.498974 | ||||||||
\(933\) | −8.57213 | −0.280639 | ||||||||
\(934\) | −9.88392 | −0.323412 | ||||||||
\(935\) | 9.91854 | 0.324371 | ||||||||
\(936\) | 7.42861 | 0.242812 | ||||||||
\(937\) | 43.5668 | 1.42327 | 0.711633 | − | 0.702552i | \(-0.247956\pi\) | ||||
0.711633 | + | 0.702552i | \(0.247956\pi\) | |||||||
\(938\) | 6.01726 | 0.196471 | ||||||||
\(939\) | 13.1490 | 0.429100 | ||||||||
\(940\) | 8.43542 | 0.275133 | ||||||||
\(941\) | 23.9417 | 0.780478 | 0.390239 | − | 0.920714i | \(-0.372392\pi\) | ||||
0.390239 | + | 0.920714i | \(0.372392\pi\) | |||||||
\(942\) | 12.9787 | 0.422868 | ||||||||
\(943\) | 73.7415 | 2.40135 | ||||||||
\(944\) | 2.06051 | 0.0670640 | ||||||||
\(945\) | −2.22208 | −0.0722842 | ||||||||
\(946\) | 31.6960 | 1.03053 | ||||||||
\(947\) | −56.2049 | −1.82641 | −0.913206 | − | 0.407498i | \(-0.866401\pi\) | ||||
−0.913206 | + | 0.407498i | \(0.866401\pi\) | |||||||
\(948\) | 33.3680 | 1.08374 | ||||||||
\(949\) | 41.8602 | 1.35884 | ||||||||
\(950\) | 4.01979 | 0.130419 | ||||||||
\(951\) | 31.3827 | 1.01765 | ||||||||
\(952\) | −2.31412 | −0.0750011 | ||||||||
\(953\) | 13.3214 | 0.431524 | 0.215762 | − | 0.976446i | \(-0.430776\pi\) | ||||
0.215762 | + | 0.976446i | \(0.430776\pi\) | |||||||
\(954\) | −12.4716 | −0.403783 | ||||||||
\(955\) | 7.17995 | 0.232338 | ||||||||
\(956\) | −23.8799 | −0.772330 | ||||||||
\(957\) | −19.0102 | −0.614512 | ||||||||
\(958\) | 4.77224 | 0.154184 | ||||||||
\(959\) | −10.8120 | −0.349137 | ||||||||
\(960\) | 2.14296 | 0.0691638 | ||||||||
\(961\) | 1.73361 | 0.0559229 | ||||||||
\(962\) | −37.1930 | −1.19915 | ||||||||
\(963\) | −19.4376 | −0.626369 | ||||||||
\(964\) | −16.3410 | −0.526308 | ||||||||
\(965\) | −14.3466 | −0.461835 | ||||||||
\(966\) | −11.2209 | −0.361027 | ||||||||
\(967\) | 4.92304 | 0.158314 | 0.0791572 | − | 0.996862i | \(-0.474777\pi\) | ||||
0.0791572 | + | 0.996862i | \(0.474777\pi\) | |||||||
\(968\) | 1.03258 | 0.0331885 | ||||||||
\(969\) | 27.0629 | 0.869386 | ||||||||
\(970\) | −17.7555 | −0.570095 | ||||||||
\(971\) | 24.1991 | 0.776585 | 0.388292 | − | 0.921536i | \(-0.373065\pi\) | ||||
0.388292 | + | 0.921536i | \(0.373065\pi\) | |||||||
\(972\) | 15.0400 | 0.482409 | ||||||||
\(973\) | 0.866034 | 0.0277638 | ||||||||
\(974\) | −0.963447 | −0.0308708 | ||||||||
\(975\) | 9.99774 | 0.320184 | ||||||||
\(976\) | 4.47293 | 0.143175 | ||||||||
\(977\) | 11.4315 | 0.365728 | 0.182864 | − | 0.983138i | \(-0.441463\pi\) | ||||
0.182864 | + | 0.983138i | \(0.441463\pi\) | |||||||
\(978\) | −46.0224 | −1.47163 | ||||||||
\(979\) | 19.2262 | 0.614473 | ||||||||
\(980\) | 6.45743 | 0.206275 | ||||||||
\(981\) | −5.46799 | −0.174580 | ||||||||
\(982\) | −31.5297 | −1.00615 | ||||||||
\(983\) | 21.0272 | 0.670663 | 0.335332 | − | 0.942100i | \(-0.391152\pi\) | ||||
0.335332 | + | 0.942100i | \(0.391152\pi\) | |||||||
\(984\) | −22.2301 | −0.708671 | ||||||||
\(985\) | 20.7117 | 0.659930 | ||||||||
\(986\) | 8.82749 | 0.281124 | ||||||||
\(987\) | 13.3153 | 0.423831 | ||||||||
\(988\) | 18.7539 | 0.596640 | ||||||||
\(989\) | −71.3670 | −2.26934 | ||||||||
\(990\) | −5.02703 | −0.159770 | ||||||||
\(991\) | −8.97600 | −0.285132 | −0.142566 | − | 0.989785i | \(-0.545535\pi\) | ||||
−0.142566 | + | 0.989785i | \(0.545535\pi\) | |||||||
\(992\) | 5.72133 | 0.181652 | ||||||||
\(993\) | −61.3722 | −1.94759 | ||||||||
\(994\) | −6.86462 | −0.217733 | ||||||||
\(995\) | 2.30944 | 0.0732141 | ||||||||
\(996\) | −33.8322 | −1.07201 | ||||||||
\(997\) | 43.9438 | 1.39172 | 0.695858 | − | 0.718180i | \(-0.255024\pi\) | ||||
0.695858 | + | 0.718180i | \(0.255024\pi\) | |||||||
\(998\) | −28.3383 | −0.897033 | ||||||||
\(999\) | −24.0493 | −0.760888 |
(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 | 6010.2.a.e.1.2 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.e.1.2 | ✓ | 21 | 1.1 | even | 1 | trivial |