Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 2x^{8} - 8x^{7} + 16x^{6} + 17x^{5} - 36x^{4} - 4x^{3} + 17x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.446506\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | −1.84294 | −1.06402 | −0.532012 | − | 0.846737i | \(-0.678564\pi\) | ||||
−0.532012 | + | 0.846737i | \(0.678564\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.84294 | −0.752378 | ||||||||
\(7\) | −0.0938987 | −0.0354904 | −0.0177452 | − | 0.999843i | \(-0.505649\pi\) | ||||
−0.0177452 | + | 0.999843i | \(0.505649\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.396437 | 0.132146 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.43048 | −1.03433 | −0.517164 | − | 0.855886i | \(-0.673012\pi\) | ||||
−0.517164 | + | 0.855886i | \(0.673012\pi\) | |||||||
\(12\) | −1.84294 | −0.532012 | ||||||||
\(13\) | −3.36264 | −0.932628 | −0.466314 | − | 0.884619i | \(-0.654418\pi\) | ||||
−0.466314 | + | 0.884619i | \(0.654418\pi\) | |||||||
\(14\) | −0.0938987 | −0.0250955 | ||||||||
\(15\) | −1.84294 | −0.475846 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.56387 | 0.621831 | 0.310915 | − | 0.950438i | \(-0.399364\pi\) | ||||
0.310915 | + | 0.950438i | \(0.399364\pi\) | |||||||
\(18\) | 0.396437 | 0.0934411 | ||||||||
\(19\) | 5.98130 | 1.37220 | 0.686102 | − | 0.727505i | \(-0.259320\pi\) | ||||
0.686102 | + | 0.727505i | \(0.259320\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.173050 | 0.0377626 | ||||||||
\(22\) | −3.43048 | −0.731380 | ||||||||
\(23\) | −2.45511 | −0.511925 | −0.255963 | − | 0.966687i | \(-0.582392\pi\) | ||||
−0.255963 | + | 0.966687i | \(0.582392\pi\) | |||||||
\(24\) | −1.84294 | −0.376189 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.36264 | −0.659468 | ||||||||
\(27\) | 4.79822 | 0.923417 | ||||||||
\(28\) | −0.0938987 | −0.0177452 | ||||||||
\(29\) | 5.77350 | 1.07211 | 0.536056 | − | 0.844183i | \(-0.319914\pi\) | ||||
0.536056 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(30\) | −1.84294 | −0.336474 | ||||||||
\(31\) | −2.23011 | −0.400540 | −0.200270 | − | 0.979741i | \(-0.564182\pi\) | ||||
−0.200270 | + | 0.979741i | \(0.564182\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.32217 | 1.10055 | ||||||||
\(34\) | 2.56387 | 0.439701 | ||||||||
\(35\) | −0.0938987 | −0.0158718 | ||||||||
\(36\) | 0.396437 | 0.0660728 | ||||||||
\(37\) | 0.381184 | 0.0626663 | 0.0313332 | − | 0.999509i | \(-0.490025\pi\) | ||||
0.0313332 | + | 0.999509i | \(0.490025\pi\) | |||||||
\(38\) | 5.98130 | 0.970295 | ||||||||
\(39\) | 6.19715 | 0.992338 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −12.2166 | −1.90791 | −0.953955 | − | 0.299949i | \(-0.903030\pi\) | ||||
−0.953955 | + | 0.299949i | \(0.903030\pi\) | |||||||
\(42\) | 0.173050 | 0.0267022 | ||||||||
\(43\) | −3.15848 | −0.481663 | −0.240832 | − | 0.970567i | \(-0.577420\pi\) | ||||
−0.240832 | + | 0.970567i | \(0.577420\pi\) | |||||||
\(44\) | −3.43048 | −0.517164 | ||||||||
\(45\) | 0.396437 | 0.0590973 | ||||||||
\(46\) | −2.45511 | −0.361986 | ||||||||
\(47\) | 10.4007 | 1.51710 | 0.758551 | − | 0.651613i | \(-0.225907\pi\) | ||||
0.758551 | + | 0.651613i | \(0.225907\pi\) | |||||||
\(48\) | −1.84294 | −0.266006 | ||||||||
\(49\) | −6.99118 | −0.998740 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.72507 | −0.661642 | ||||||||
\(52\) | −3.36264 | −0.466314 | ||||||||
\(53\) | −7.89272 | −1.08415 | −0.542074 | − | 0.840331i | \(-0.682361\pi\) | ||||
−0.542074 | + | 0.840331i | \(0.682361\pi\) | |||||||
\(54\) | 4.79822 | 0.652955 | ||||||||
\(55\) | −3.43048 | −0.462565 | ||||||||
\(56\) | −0.0938987 | −0.0125477 | ||||||||
\(57\) | −11.0232 | −1.46006 | ||||||||
\(58\) | 5.77350 | 0.758097 | ||||||||
\(59\) | −12.0849 | −1.57332 | −0.786658 | − | 0.617388i | \(-0.788191\pi\) | ||||
−0.786658 | + | 0.617388i | \(0.788191\pi\) | |||||||
\(60\) | −1.84294 | −0.237923 | ||||||||
\(61\) | 0.457926 | 0.0586314 | 0.0293157 | − | 0.999570i | \(-0.490667\pi\) | ||||
0.0293157 | + | 0.999570i | \(0.490667\pi\) | |||||||
\(62\) | −2.23011 | −0.283225 | ||||||||
\(63\) | −0.0372249 | −0.00468990 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.36264 | −0.417084 | ||||||||
\(66\) | 6.32217 | 0.778205 | ||||||||
\(67\) | −10.7784 | −1.31679 | −0.658395 | − | 0.752672i | \(-0.728764\pi\) | ||||
−0.658395 | + | 0.752672i | \(0.728764\pi\) | |||||||
\(68\) | 2.56387 | 0.310915 | ||||||||
\(69\) | 4.52462 | 0.544701 | ||||||||
\(70\) | −0.0938987 | −0.0112230 | ||||||||
\(71\) | −4.78946 | −0.568404 | −0.284202 | − | 0.958764i | \(-0.591729\pi\) | ||||
−0.284202 | + | 0.958764i | \(0.591729\pi\) | |||||||
\(72\) | 0.396437 | 0.0467205 | ||||||||
\(73\) | −15.6224 | −1.82846 | −0.914232 | − | 0.405190i | \(-0.867205\pi\) | ||||
−0.914232 | + | 0.405190i | \(0.867205\pi\) | |||||||
\(74\) | 0.381184 | 0.0443118 | ||||||||
\(75\) | −1.84294 | −0.212805 | ||||||||
\(76\) | 5.98130 | 0.686102 | ||||||||
\(77\) | 0.322117 | 0.0367087 | ||||||||
\(78\) | 6.19715 | 0.701689 | ||||||||
\(79\) | 8.50067 | 0.956400 | 0.478200 | − | 0.878251i | \(-0.341289\pi\) | ||||
0.478200 | + | 0.878251i | \(0.341289\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −10.0321 | −1.11468 | ||||||||
\(82\) | −12.2166 | −1.34910 | ||||||||
\(83\) | 3.35560 | 0.368325 | 0.184163 | − | 0.982896i | \(-0.441043\pi\) | ||||
0.184163 | + | 0.982896i | \(0.441043\pi\) | |||||||
\(84\) | 0.173050 | 0.0188813 | ||||||||
\(85\) | 2.56387 | 0.278091 | ||||||||
\(86\) | −3.15848 | −0.340587 | ||||||||
\(87\) | −10.6402 | −1.14075 | ||||||||
\(88\) | −3.43048 | −0.365690 | ||||||||
\(89\) | −7.15936 | −0.758891 | −0.379446 | − | 0.925214i | \(-0.623885\pi\) | ||||
−0.379446 | + | 0.925214i | \(0.623885\pi\) | |||||||
\(90\) | 0.396437 | 0.0417881 | ||||||||
\(91\) | 0.315747 | 0.0330993 | ||||||||
\(92\) | −2.45511 | −0.255963 | ||||||||
\(93\) | 4.10997 | 0.426184 | ||||||||
\(94\) | 10.4007 | 1.07275 | ||||||||
\(95\) | 5.98130 | 0.613668 | ||||||||
\(96\) | −1.84294 | −0.188095 | ||||||||
\(97\) | 6.47511 | 0.657448 | 0.328724 | − | 0.944426i | \(-0.393381\pi\) | ||||
0.328724 | + | 0.944426i | \(0.393381\pi\) | |||||||
\(98\) | −6.99118 | −0.706216 | ||||||||
\(99\) | −1.35997 | −0.136682 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.55210 | −0.253944 | −0.126972 | − | 0.991906i | \(-0.540526\pi\) | ||||
−0.126972 | + | 0.991906i | \(0.540526\pi\) | |||||||
\(102\) | −4.72507 | −0.467852 | ||||||||
\(103\) | −3.93006 | −0.387240 | −0.193620 | − | 0.981077i | \(-0.562023\pi\) | ||||
−0.193620 | + | 0.981077i | \(0.562023\pi\) | |||||||
\(104\) | −3.36264 | −0.329734 | ||||||||
\(105\) | 0.173050 | 0.0168879 | ||||||||
\(106\) | −7.89272 | −0.766608 | ||||||||
\(107\) | 18.5937 | 1.79752 | 0.898759 | − | 0.438443i | \(-0.144470\pi\) | ||||
0.898759 | + | 0.438443i | \(0.144470\pi\) | |||||||
\(108\) | 4.79822 | 0.461709 | ||||||||
\(109\) | −6.58120 | −0.630365 | −0.315183 | − | 0.949031i | \(-0.602066\pi\) | ||||
−0.315183 | + | 0.949031i | \(0.602066\pi\) | |||||||
\(110\) | −3.43048 | −0.327083 | ||||||||
\(111\) | −0.702501 | −0.0666784 | ||||||||
\(112\) | −0.0938987 | −0.00887259 | ||||||||
\(113\) | 9.12255 | 0.858177 | 0.429089 | − | 0.903262i | \(-0.358835\pi\) | ||||
0.429089 | + | 0.903262i | \(0.358835\pi\) | |||||||
\(114\) | −11.0232 | −1.03242 | ||||||||
\(115\) | −2.45511 | −0.228940 | ||||||||
\(116\) | 5.77350 | 0.536056 | ||||||||
\(117\) | −1.33307 | −0.123243 | ||||||||
\(118\) | −12.0849 | −1.11250 | ||||||||
\(119\) | −0.240744 | −0.0220690 | ||||||||
\(120\) | −1.84294 | −0.168237 | ||||||||
\(121\) | 0.768168 | 0.0698334 | ||||||||
\(122\) | 0.457926 | 0.0414587 | ||||||||
\(123\) | 22.5145 | 2.03006 | ||||||||
\(124\) | −2.23011 | −0.200270 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.0372249 | −0.00331626 | ||||||||
\(127\) | 21.8559 | 1.93940 | 0.969701 | − | 0.244297i | \(-0.0785571\pi\) | ||||
0.969701 | + | 0.244297i | \(0.0785571\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.82089 | 0.512501 | ||||||||
\(130\) | −3.36264 | −0.294923 | ||||||||
\(131\) | −9.46857 | −0.827273 | −0.413636 | − | 0.910442i | \(-0.635742\pi\) | ||||
−0.413636 | + | 0.910442i | \(0.635742\pi\) | |||||||
\(132\) | 6.32217 | 0.550274 | ||||||||
\(133\) | −0.561636 | −0.0487000 | ||||||||
\(134\) | −10.7784 | −0.931112 | ||||||||
\(135\) | 4.79822 | 0.412965 | ||||||||
\(136\) | 2.56387 | 0.219850 | ||||||||
\(137\) | −15.5435 | −1.32797 | −0.663986 | − | 0.747745i | \(-0.731137\pi\) | ||||
−0.663986 | + | 0.747745i | \(0.731137\pi\) | |||||||
\(138\) | 4.52462 | 0.385162 | ||||||||
\(139\) | −16.9704 | −1.43941 | −0.719705 | − | 0.694280i | \(-0.755723\pi\) | ||||
−0.719705 | + | 0.694280i | \(0.755723\pi\) | |||||||
\(140\) | −0.0938987 | −0.00793589 | ||||||||
\(141\) | −19.1680 | −1.61423 | ||||||||
\(142\) | −4.78946 | −0.401923 | ||||||||
\(143\) | 11.5355 | 0.964643 | ||||||||
\(144\) | 0.396437 | 0.0330364 | ||||||||
\(145\) | 5.77350 | 0.479463 | ||||||||
\(146\) | −15.6224 | −1.29292 | ||||||||
\(147\) | 12.8843 | 1.06268 | ||||||||
\(148\) | 0.381184 | 0.0313332 | ||||||||
\(149\) | −4.19924 | −0.344015 | −0.172007 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172007 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(150\) | −1.84294 | −0.150476 | ||||||||
\(151\) | 0.915926 | 0.0745370 | 0.0372685 | − | 0.999305i | \(-0.488134\pi\) | ||||
0.0372685 | + | 0.999305i | \(0.488134\pi\) | |||||||
\(152\) | 5.98130 | 0.485147 | ||||||||
\(153\) | 1.01641 | 0.0821722 | ||||||||
\(154\) | 0.322117 | 0.0259569 | ||||||||
\(155\) | −2.23011 | −0.179127 | ||||||||
\(156\) | 6.19715 | 0.496169 | ||||||||
\(157\) | −18.3891 | −1.46761 | −0.733807 | − | 0.679358i | \(-0.762258\pi\) | ||||
−0.733807 | + | 0.679358i | \(0.762258\pi\) | |||||||
\(158\) | 8.50067 | 0.676277 | ||||||||
\(159\) | 14.5458 | 1.15356 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.230531 | 0.0181684 | ||||||||
\(162\) | −10.0321 | −0.788200 | ||||||||
\(163\) | −18.4734 | −1.44695 | −0.723473 | − | 0.690352i | \(-0.757456\pi\) | ||||
−0.723473 | + | 0.690352i | \(0.757456\pi\) | |||||||
\(164\) | −12.2166 | −0.953955 | ||||||||
\(165\) | 6.32217 | 0.492180 | ||||||||
\(166\) | 3.35560 | 0.260445 | ||||||||
\(167\) | −21.8788 | −1.69303 | −0.846514 | − | 0.532366i | \(-0.821303\pi\) | ||||
−0.846514 | + | 0.532366i | \(0.821303\pi\) | |||||||
\(168\) | 0.173050 | 0.0133511 | ||||||||
\(169\) | −1.69266 | −0.130205 | ||||||||
\(170\) | 2.56387 | 0.196640 | ||||||||
\(171\) | 2.37121 | 0.181331 | ||||||||
\(172\) | −3.15848 | −0.240832 | ||||||||
\(173\) | 0.872010 | 0.0662977 | 0.0331488 | − | 0.999450i | \(-0.489446\pi\) | ||||
0.0331488 | + | 0.999450i | \(0.489446\pi\) | |||||||
\(174\) | −10.6402 | −0.806633 | ||||||||
\(175\) | −0.0938987 | −0.00709807 | ||||||||
\(176\) | −3.43048 | −0.258582 | ||||||||
\(177\) | 22.2717 | 1.67405 | ||||||||
\(178\) | −7.15936 | −0.536617 | ||||||||
\(179\) | −10.6354 | −0.794927 | −0.397463 | − | 0.917618i | \(-0.630109\pi\) | ||||
−0.397463 | + | 0.917618i | \(0.630109\pi\) | |||||||
\(180\) | 0.396437 | 0.0295487 | ||||||||
\(181\) | 6.54024 | 0.486132 | 0.243066 | − | 0.970010i | \(-0.421847\pi\) | ||||
0.243066 | + | 0.970010i | \(0.421847\pi\) | |||||||
\(182\) | 0.315747 | 0.0234047 | ||||||||
\(183\) | −0.843932 | −0.0623852 | ||||||||
\(184\) | −2.45511 | −0.180993 | ||||||||
\(185\) | 0.381184 | 0.0280252 | ||||||||
\(186\) | 4.10997 | 0.301358 | ||||||||
\(187\) | −8.79531 | −0.643177 | ||||||||
\(188\) | 10.4007 | 0.758551 | ||||||||
\(189\) | −0.450546 | −0.0327724 | ||||||||
\(190\) | 5.98130 | 0.433929 | ||||||||
\(191\) | 8.47937 | 0.613546 | 0.306773 | − | 0.951783i | \(-0.400751\pi\) | ||||
0.306773 | + | 0.951783i | \(0.400751\pi\) | |||||||
\(192\) | −1.84294 | −0.133003 | ||||||||
\(193\) | −8.23319 | −0.592638 | −0.296319 | − | 0.955089i | \(-0.595759\pi\) | ||||
−0.296319 | + | 0.955089i | \(0.595759\pi\) | |||||||
\(194\) | 6.47511 | 0.464886 | ||||||||
\(195\) | 6.19715 | 0.443787 | ||||||||
\(196\) | −6.99118 | −0.499370 | ||||||||
\(197\) | −0.175702 | −0.0125183 | −0.00625914 | − | 0.999980i | \(-0.501992\pi\) | ||||
−0.00625914 | + | 0.999980i | \(0.501992\pi\) | |||||||
\(198\) | −1.35997 | −0.0966487 | ||||||||
\(199\) | 5.73441 | 0.406502 | 0.203251 | − | 0.979127i | \(-0.434849\pi\) | ||||
0.203251 | + | 0.979127i | \(0.434849\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 19.8640 | 1.40110 | ||||||||
\(202\) | −2.55210 | −0.179565 | ||||||||
\(203\) | −0.542124 | −0.0380496 | ||||||||
\(204\) | −4.72507 | −0.330821 | ||||||||
\(205\) | −12.2166 | −0.853244 | ||||||||
\(206\) | −3.93006 | −0.273820 | ||||||||
\(207\) | −0.973296 | −0.0676487 | ||||||||
\(208\) | −3.36264 | −0.233157 | ||||||||
\(209\) | −20.5187 | −1.41931 | ||||||||
\(210\) | 0.173050 | 0.0119416 | ||||||||
\(211\) | −1.51538 | −0.104323 | −0.0521616 | − | 0.998639i | \(-0.516611\pi\) | ||||
−0.0521616 | + | 0.998639i | \(0.516611\pi\) | |||||||
\(212\) | −7.89272 | −0.542074 | ||||||||
\(213\) | 8.82670 | 0.604795 | ||||||||
\(214\) | 18.5937 | 1.27104 | ||||||||
\(215\) | −3.15848 | −0.215406 | ||||||||
\(216\) | 4.79822 | 0.326477 | ||||||||
\(217\) | 0.209405 | 0.0142153 | ||||||||
\(218\) | −6.58120 | −0.445735 | ||||||||
\(219\) | 28.7912 | 1.94553 | ||||||||
\(220\) | −3.43048 | −0.231283 | ||||||||
\(221\) | −8.62138 | −0.579937 | ||||||||
\(222\) | −0.702501 | −0.0471488 | ||||||||
\(223\) | 15.7565 | 1.05514 | 0.527568 | − | 0.849513i | \(-0.323104\pi\) | ||||
0.527568 | + | 0.849513i | \(0.323104\pi\) | |||||||
\(224\) | −0.0938987 | −0.00627387 | ||||||||
\(225\) | 0.396437 | 0.0264291 | ||||||||
\(226\) | 9.12255 | 0.606823 | ||||||||
\(227\) | 0.499976 | 0.0331846 | 0.0165923 | − | 0.999862i | \(-0.494718\pi\) | ||||
0.0165923 | + | 0.999862i | \(0.494718\pi\) | |||||||
\(228\) | −11.0232 | −0.730028 | ||||||||
\(229\) | −7.06065 | −0.466581 | −0.233291 | − | 0.972407i | \(-0.574949\pi\) | ||||
−0.233291 | + | 0.972407i | \(0.574949\pi\) | |||||||
\(230\) | −2.45511 | −0.161885 | ||||||||
\(231\) | −0.593643 | −0.0390589 | ||||||||
\(232\) | 5.77350 | 0.379049 | ||||||||
\(233\) | 0.634346 | 0.0415574 | 0.0207787 | − | 0.999784i | \(-0.493385\pi\) | ||||
0.0207787 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(234\) | −1.33307 | −0.0871458 | ||||||||
\(235\) | 10.4007 | 0.678469 | ||||||||
\(236\) | −12.0849 | −0.786658 | ||||||||
\(237\) | −15.6662 | −1.01763 | ||||||||
\(238\) | −0.240744 | −0.0156051 | ||||||||
\(239\) | 15.8886 | 1.02775 | 0.513876 | − | 0.857865i | \(-0.328209\pi\) | ||||
0.513876 | + | 0.857865i | \(0.328209\pi\) | |||||||
\(240\) | −1.84294 | −0.118961 | ||||||||
\(241\) | −18.6749 | −1.20295 | −0.601477 | − | 0.798890i | \(-0.705421\pi\) | ||||
−0.601477 | + | 0.798890i | \(0.705421\pi\) | |||||||
\(242\) | 0.768168 | 0.0493797 | ||||||||
\(243\) | 4.09402 | 0.262632 | ||||||||
\(244\) | 0.457926 | 0.0293157 | ||||||||
\(245\) | −6.99118 | −0.446650 | ||||||||
\(246\) | 22.5145 | 1.43547 | ||||||||
\(247\) | −20.1129 | −1.27976 | ||||||||
\(248\) | −2.23011 | −0.141612 | ||||||||
\(249\) | −6.18418 | −0.391907 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −4.78389 | −0.301956 | −0.150978 | − | 0.988537i | \(-0.548242\pi\) | ||||
−0.150978 | + | 0.988537i | \(0.548242\pi\) | |||||||
\(252\) | −0.0372249 | −0.00234495 | ||||||||
\(253\) | 8.42219 | 0.529499 | ||||||||
\(254\) | 21.8559 | 1.37136 | ||||||||
\(255\) | −4.72507 | −0.295895 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.924873 | −0.0576920 | −0.0288460 | − | 0.999584i | \(-0.509183\pi\) | ||||
−0.0288460 | + | 0.999584i | \(0.509183\pi\) | |||||||
\(258\) | 5.82089 | 0.362393 | ||||||||
\(259\) | −0.0357927 | −0.00222405 | ||||||||
\(260\) | −3.36264 | −0.208542 | ||||||||
\(261\) | 2.28883 | 0.141675 | ||||||||
\(262\) | −9.46857 | −0.584970 | ||||||||
\(263\) | −7.75351 | −0.478102 | −0.239051 | − | 0.971007i | \(-0.576836\pi\) | ||||
−0.239051 | + | 0.971007i | \(0.576836\pi\) | |||||||
\(264\) | 6.32217 | 0.389103 | ||||||||
\(265\) | −7.89272 | −0.484846 | ||||||||
\(266\) | −0.561636 | −0.0344361 | ||||||||
\(267\) | 13.1943 | 0.807478 | ||||||||
\(268\) | −10.7784 | −0.658395 | ||||||||
\(269\) | 29.8572 | 1.82043 | 0.910213 | − | 0.414140i | \(-0.135918\pi\) | ||||
0.910213 | + | 0.414140i | \(0.135918\pi\) | |||||||
\(270\) | 4.79822 | 0.292010 | ||||||||
\(271\) | 7.22166 | 0.438684 | 0.219342 | − | 0.975648i | \(-0.429609\pi\) | ||||
0.219342 | + | 0.975648i | \(0.429609\pi\) | |||||||
\(272\) | 2.56387 | 0.155458 | ||||||||
\(273\) | −0.581904 | −0.0352184 | ||||||||
\(274\) | −15.5435 | −0.939019 | ||||||||
\(275\) | −3.43048 | −0.206866 | ||||||||
\(276\) | 4.52462 | 0.272350 | ||||||||
\(277\) | −27.5920 | −1.65784 | −0.828921 | − | 0.559366i | \(-0.811045\pi\) | ||||
−0.828921 | + | 0.559366i | \(0.811045\pi\) | |||||||
\(278\) | −16.9704 | −1.01782 | ||||||||
\(279\) | −0.884099 | −0.0529296 | ||||||||
\(280\) | −0.0938987 | −0.00561152 | ||||||||
\(281\) | −9.57593 | −0.571252 | −0.285626 | − | 0.958341i | \(-0.592202\pi\) | ||||
−0.285626 | + | 0.958341i | \(0.592202\pi\) | |||||||
\(282\) | −19.1680 | −1.14144 | ||||||||
\(283\) | 4.86749 | 0.289342 | 0.144671 | − | 0.989480i | \(-0.453788\pi\) | ||||
0.144671 | + | 0.989480i | \(0.453788\pi\) | |||||||
\(284\) | −4.78946 | −0.284202 | ||||||||
\(285\) | −11.0232 | −0.652957 | ||||||||
\(286\) | 11.5355 | 0.682105 | ||||||||
\(287\) | 1.14712 | 0.0677124 | ||||||||
\(288\) | 0.396437 | 0.0233603 | ||||||||
\(289\) | −10.4266 | −0.613326 | ||||||||
\(290\) | 5.77350 | 0.339031 | ||||||||
\(291\) | −11.9333 | −0.699540 | ||||||||
\(292\) | −15.6224 | −0.914232 | ||||||||
\(293\) | 8.86662 | 0.517993 | 0.258997 | − | 0.965878i | \(-0.416608\pi\) | ||||
0.258997 | + | 0.965878i | \(0.416608\pi\) | |||||||
\(294\) | 12.8843 | 0.751430 | ||||||||
\(295\) | −12.0849 | −0.703609 | ||||||||
\(296\) | 0.381184 | 0.0221559 | ||||||||
\(297\) | −16.4602 | −0.955116 | ||||||||
\(298\) | −4.19924 | −0.243255 | ||||||||
\(299\) | 8.25564 | 0.477436 | ||||||||
\(300\) | −1.84294 | −0.106402 | ||||||||
\(301\) | 0.296577 | 0.0170944 | ||||||||
\(302\) | 0.915926 | 0.0527056 | ||||||||
\(303\) | 4.70338 | 0.270202 | ||||||||
\(304\) | 5.98130 | 0.343051 | ||||||||
\(305\) | 0.457926 | 0.0262208 | ||||||||
\(306\) | 1.01641 | 0.0581045 | ||||||||
\(307\) | 13.1248 | 0.749074 | 0.374537 | − | 0.927212i | \(-0.377802\pi\) | ||||
0.374537 | + | 0.927212i | \(0.377802\pi\) | |||||||
\(308\) | 0.322117 | 0.0183543 | ||||||||
\(309\) | 7.24287 | 0.412033 | ||||||||
\(310\) | −2.23011 | −0.126662 | ||||||||
\(311\) | −1.50532 | −0.0853591 | −0.0426795 | − | 0.999089i | \(-0.513589\pi\) | ||||
−0.0426795 | + | 0.999089i | \(0.513589\pi\) | |||||||
\(312\) | 6.19715 | 0.350844 | ||||||||
\(313\) | 2.86091 | 0.161708 | 0.0808540 | − | 0.996726i | \(-0.474235\pi\) | ||||
0.0808540 | + | 0.996726i | \(0.474235\pi\) | |||||||
\(314\) | −18.3891 | −1.03776 | ||||||||
\(315\) | −0.0372249 | −0.00209739 | ||||||||
\(316\) | 8.50067 | 0.478200 | ||||||||
\(317\) | −20.5102 | −1.15197 | −0.575984 | − | 0.817461i | \(-0.695381\pi\) | ||||
−0.575984 | + | 0.817461i | \(0.695381\pi\) | |||||||
\(318\) | 14.5458 | 0.815689 | ||||||||
\(319\) | −19.8058 | −1.10891 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −34.2671 | −1.91260 | ||||||||
\(322\) | 0.230531 | 0.0128470 | ||||||||
\(323\) | 15.3353 | 0.853279 | ||||||||
\(324\) | −10.0321 | −0.557342 | ||||||||
\(325\) | −3.36264 | −0.186526 | ||||||||
\(326\) | −18.4734 | −1.02315 | ||||||||
\(327\) | 12.1288 | 0.670723 | ||||||||
\(328\) | −12.2166 | −0.674548 | ||||||||
\(329\) | −0.976615 | −0.0538425 | ||||||||
\(330\) | 6.32217 | 0.348024 | ||||||||
\(331\) | −9.27471 | −0.509784 | −0.254892 | − | 0.966970i | \(-0.582040\pi\) | ||||
−0.254892 | + | 0.966970i | \(0.582040\pi\) | |||||||
\(332\) | 3.35560 | 0.184163 | ||||||||
\(333\) | 0.151116 | 0.00828108 | ||||||||
\(334\) | −21.8788 | −1.19715 | ||||||||
\(335\) | −10.7784 | −0.588887 | ||||||||
\(336\) | 0.173050 | 0.00944064 | ||||||||
\(337\) | 24.6047 | 1.34030 | 0.670152 | − | 0.742223i | \(-0.266229\pi\) | ||||
0.670152 | + | 0.742223i | \(0.266229\pi\) | |||||||
\(338\) | −1.69266 | −0.0920688 | ||||||||
\(339\) | −16.8123 | −0.913120 | ||||||||
\(340\) | 2.56387 | 0.139046 | ||||||||
\(341\) | 7.65035 | 0.414290 | ||||||||
\(342\) | 2.37121 | 0.128220 | ||||||||
\(343\) | 1.31375 | 0.0709360 | ||||||||
\(344\) | −3.15848 | −0.170294 | ||||||||
\(345\) | 4.52462 | 0.243598 | ||||||||
\(346\) | 0.872010 | 0.0468795 | ||||||||
\(347\) | −3.87165 | −0.207841 | −0.103921 | − | 0.994586i | \(-0.533139\pi\) | ||||
−0.103921 | + | 0.994586i | \(0.533139\pi\) | |||||||
\(348\) | −10.6402 | −0.570376 | ||||||||
\(349\) | −12.0503 | −0.645036 | −0.322518 | − | 0.946563i | \(-0.604529\pi\) | ||||
−0.322518 | + | 0.946563i | \(0.604529\pi\) | |||||||
\(350\) | −0.0938987 | −0.00501910 | ||||||||
\(351\) | −16.1347 | −0.861205 | ||||||||
\(352\) | −3.43048 | −0.182845 | ||||||||
\(353\) | 32.0479 | 1.70574 | 0.852868 | − | 0.522126i | \(-0.174861\pi\) | ||||
0.852868 | + | 0.522126i | \(0.174861\pi\) | |||||||
\(354\) | 22.2717 | 1.18373 | ||||||||
\(355\) | −4.78946 | −0.254198 | ||||||||
\(356\) | −7.15936 | −0.379446 | ||||||||
\(357\) | 0.443678 | 0.0234819 | ||||||||
\(358\) | −10.6354 | −0.562098 | ||||||||
\(359\) | −20.4761 | −1.08069 | −0.540344 | − | 0.841444i | \(-0.681706\pi\) | ||||
−0.540344 | + | 0.841444i | \(0.681706\pi\) | |||||||
\(360\) | 0.396437 | 0.0208941 | ||||||||
\(361\) | 16.7759 | 0.882944 | ||||||||
\(362\) | 6.54024 | 0.343747 | ||||||||
\(363\) | −1.41569 | −0.0743044 | ||||||||
\(364\) | 0.315747 | 0.0165497 | ||||||||
\(365\) | −15.6224 | −0.817714 | ||||||||
\(366\) | −0.843932 | −0.0441130 | ||||||||
\(367\) | −1.25272 | −0.0653917 | −0.0326958 | − | 0.999465i | \(-0.510409\pi\) | ||||
−0.0326958 | + | 0.999465i | \(0.510409\pi\) | |||||||
\(368\) | −2.45511 | −0.127981 | ||||||||
\(369\) | −4.84311 | −0.252122 | ||||||||
\(370\) | 0.381184 | 0.0198168 | ||||||||
\(371\) | 0.741116 | 0.0384768 | ||||||||
\(372\) | 4.10997 | 0.213092 | ||||||||
\(373\) | 19.0849 | 0.988179 | 0.494090 | − | 0.869411i | \(-0.335501\pi\) | ||||
0.494090 | + | 0.869411i | \(0.335501\pi\) | |||||||
\(374\) | −8.79531 | −0.454795 | ||||||||
\(375\) | −1.84294 | −0.0951691 | ||||||||
\(376\) | 10.4007 | 0.536377 | ||||||||
\(377\) | −19.4142 | −0.999881 | ||||||||
\(378\) | −0.450546 | −0.0231736 | ||||||||
\(379\) | 19.9070 | 1.02255 | 0.511276 | − | 0.859416i | \(-0.329173\pi\) | ||||
0.511276 | + | 0.859416i | \(0.329173\pi\) | |||||||
\(380\) | 5.98130 | 0.306834 | ||||||||
\(381\) | −40.2792 | −2.06357 | ||||||||
\(382\) | 8.47937 | 0.433842 | ||||||||
\(383\) | −22.4584 | −1.14757 | −0.573786 | − | 0.819005i | \(-0.694526\pi\) | ||||
−0.573786 | + | 0.819005i | \(0.694526\pi\) | |||||||
\(384\) | −1.84294 | −0.0940473 | ||||||||
\(385\) | 0.322117 | 0.0164166 | ||||||||
\(386\) | −8.23319 | −0.419058 | ||||||||
\(387\) | −1.25214 | −0.0636497 | ||||||||
\(388\) | 6.47511 | 0.328724 | ||||||||
\(389\) | 24.0783 | 1.22082 | 0.610409 | − | 0.792087i | \(-0.291005\pi\) | ||||
0.610409 | + | 0.792087i | \(0.291005\pi\) | |||||||
\(390\) | 6.19715 | 0.313805 | ||||||||
\(391\) | −6.29459 | −0.318331 | ||||||||
\(392\) | −6.99118 | −0.353108 | ||||||||
\(393\) | 17.4500 | 0.880238 | ||||||||
\(394\) | −0.175702 | −0.00885176 | ||||||||
\(395\) | 8.50067 | 0.427715 | ||||||||
\(396\) | −1.35997 | −0.0683409 | ||||||||
\(397\) | 39.1825 | 1.96651 | 0.983257 | − | 0.182226i | \(-0.0583303\pi\) | ||||
0.983257 | + | 0.182226i | \(0.0583303\pi\) | |||||||
\(398\) | 5.73441 | 0.287440 | ||||||||
\(399\) | 1.03506 | 0.0518180 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 19.8640 | 0.990725 | ||||||||
\(403\) | 7.49906 | 0.373555 | ||||||||
\(404\) | −2.55210 | −0.126972 | ||||||||
\(405\) | −10.0321 | −0.498501 | ||||||||
\(406\) | −0.542124 | −0.0269051 | ||||||||
\(407\) | −1.30764 | −0.0648175 | ||||||||
\(408\) | −4.72507 | −0.233926 | ||||||||
\(409\) | −27.2597 | −1.34790 | −0.673952 | − | 0.738775i | \(-0.735404\pi\) | ||||
−0.673952 | + | 0.738775i | \(0.735404\pi\) | |||||||
\(410\) | −12.2166 | −0.603334 | ||||||||
\(411\) | 28.6458 | 1.41299 | ||||||||
\(412\) | −3.93006 | −0.193620 | ||||||||
\(413\) | 1.13475 | 0.0558376 | ||||||||
\(414\) | −0.973296 | −0.0478349 | ||||||||
\(415\) | 3.35560 | 0.164720 | ||||||||
\(416\) | −3.36264 | −0.164867 | ||||||||
\(417\) | 31.2755 | 1.53157 | ||||||||
\(418\) | −20.5187 | −1.00360 | ||||||||
\(419\) | 0.625472 | 0.0305563 | 0.0152782 | − | 0.999883i | \(-0.495137\pi\) | ||||
0.0152782 | + | 0.999883i | \(0.495137\pi\) | |||||||
\(420\) | 0.173050 | 0.00844397 | ||||||||
\(421\) | 4.29032 | 0.209097 | 0.104549 | − | 0.994520i | \(-0.466660\pi\) | ||||
0.104549 | + | 0.994520i | \(0.466660\pi\) | |||||||
\(422\) | −1.51538 | −0.0737676 | ||||||||
\(423\) | 4.12324 | 0.200479 | ||||||||
\(424\) | −7.89272 | −0.383304 | ||||||||
\(425\) | 2.56387 | 0.124366 | ||||||||
\(426\) | 8.82670 | 0.427655 | ||||||||
\(427\) | −0.0429987 | −0.00208085 | ||||||||
\(428\) | 18.5937 | 0.898759 | ||||||||
\(429\) | −21.2592 | −1.02640 | ||||||||
\(430\) | −3.15848 | −0.152315 | ||||||||
\(431\) | −29.9833 | −1.44425 | −0.722123 | − | 0.691764i | \(-0.756834\pi\) | ||||
−0.722123 | + | 0.691764i | \(0.756834\pi\) | |||||||
\(432\) | 4.79822 | 0.230854 | ||||||||
\(433\) | 18.0144 | 0.865715 | 0.432857 | − | 0.901462i | \(-0.357505\pi\) | ||||
0.432857 | + | 0.901462i | \(0.357505\pi\) | |||||||
\(434\) | 0.209405 | 0.0100517 | ||||||||
\(435\) | −10.6402 | −0.510160 | ||||||||
\(436\) | −6.58120 | −0.315183 | ||||||||
\(437\) | −14.6847 | −0.702466 | ||||||||
\(438\) | 28.7912 | 1.37570 | ||||||||
\(439\) | 4.45552 | 0.212650 | 0.106325 | − | 0.994331i | \(-0.466092\pi\) | ||||
0.106325 | + | 0.994331i | \(0.466092\pi\) | |||||||
\(440\) | −3.43048 | −0.163542 | ||||||||
\(441\) | −2.77156 | −0.131979 | ||||||||
\(442\) | −8.62138 | −0.410077 | ||||||||
\(443\) | 32.2852 | 1.53392 | 0.766958 | − | 0.641698i | \(-0.221770\pi\) | ||||
0.766958 | + | 0.641698i | \(0.221770\pi\) | |||||||
\(444\) | −0.702501 | −0.0333392 | ||||||||
\(445\) | −7.15936 | −0.339386 | ||||||||
\(446\) | 15.7565 | 0.746094 | ||||||||
\(447\) | 7.73895 | 0.366040 | ||||||||
\(448\) | −0.0938987 | −0.00443630 | ||||||||
\(449\) | 17.7475 | 0.837555 | 0.418778 | − | 0.908089i | \(-0.362459\pi\) | ||||
0.418778 | + | 0.908089i | \(0.362459\pi\) | |||||||
\(450\) | 0.396437 | 0.0186882 | ||||||||
\(451\) | 41.9087 | 1.97340 | ||||||||
\(452\) | 9.12255 | 0.429089 | ||||||||
\(453\) | −1.68800 | −0.0793091 | ||||||||
\(454\) | 0.499976 | 0.0234650 | ||||||||
\(455\) | 0.315747 | 0.0148025 | ||||||||
\(456\) | −11.0232 | −0.516208 | ||||||||
\(457\) | −38.5645 | −1.80397 | −0.901986 | − | 0.431766i | \(-0.857891\pi\) | ||||
−0.901986 | + | 0.431766i | \(0.857891\pi\) | |||||||
\(458\) | −7.06065 | −0.329923 | ||||||||
\(459\) | 12.3020 | 0.574209 | ||||||||
\(460\) | −2.45511 | −0.114470 | ||||||||
\(461\) | 16.0662 | 0.748279 | 0.374139 | − | 0.927373i | \(-0.377938\pi\) | ||||
0.374139 | + | 0.927373i | \(0.377938\pi\) | |||||||
\(462\) | −0.593643 | −0.0276188 | ||||||||
\(463\) | −8.15714 | −0.379095 | −0.189547 | − | 0.981872i | \(-0.560702\pi\) | ||||
−0.189547 | + | 0.981872i | \(0.560702\pi\) | |||||||
\(464\) | 5.77350 | 0.268028 | ||||||||
\(465\) | 4.10997 | 0.190595 | ||||||||
\(466\) | 0.634346 | 0.0293855 | ||||||||
\(467\) | 39.3652 | 1.82161 | 0.910803 | − | 0.412842i | \(-0.135464\pi\) | ||||
0.910803 | + | 0.412842i | \(0.135464\pi\) | |||||||
\(468\) | −1.33307 | −0.0616214 | ||||||||
\(469\) | 1.01208 | 0.0467334 | ||||||||
\(470\) | 10.4007 | 0.479750 | ||||||||
\(471\) | 33.8901 | 1.56157 | ||||||||
\(472\) | −12.0849 | −0.556252 | ||||||||
\(473\) | 10.8351 | 0.498197 | ||||||||
\(474\) | −15.6662 | −0.719575 | ||||||||
\(475\) | 5.98130 | 0.274441 | ||||||||
\(476\) | −0.240744 | −0.0110345 | ||||||||
\(477\) | −3.12896 | −0.143265 | ||||||||
\(478\) | 15.8886 | 0.726730 | ||||||||
\(479\) | −34.6506 | −1.58323 | −0.791614 | − | 0.611021i | \(-0.790759\pi\) | ||||
−0.791614 | + | 0.611021i | \(0.790759\pi\) | |||||||
\(480\) | −1.84294 | −0.0841184 | ||||||||
\(481\) | −1.28179 | −0.0584444 | ||||||||
\(482\) | −18.6749 | −0.850617 | ||||||||
\(483\) | −0.424856 | −0.0193316 | ||||||||
\(484\) | 0.768168 | 0.0349167 | ||||||||
\(485\) | 6.47511 | 0.294020 | ||||||||
\(486\) | 4.09402 | 0.185709 | ||||||||
\(487\) | −7.33397 | −0.332334 | −0.166167 | − | 0.986098i | \(-0.553139\pi\) | ||||
−0.166167 | + | 0.986098i | \(0.553139\pi\) | |||||||
\(488\) | 0.457926 | 0.0207293 | ||||||||
\(489\) | 34.0454 | 1.53958 | ||||||||
\(490\) | −6.99118 | −0.315829 | ||||||||
\(491\) | 28.8677 | 1.30278 | 0.651390 | − | 0.758743i | \(-0.274186\pi\) | ||||
0.651390 | + | 0.758743i | \(0.274186\pi\) | |||||||
\(492\) | 22.5145 | 1.01503 | ||||||||
\(493\) | 14.8025 | 0.666672 | ||||||||
\(494\) | −20.1129 | −0.904924 | ||||||||
\(495\) | −1.35997 | −0.0611260 | ||||||||
\(496\) | −2.23011 | −0.100135 | ||||||||
\(497\) | 0.449724 | 0.0201729 | ||||||||
\(498\) | −6.18418 | −0.277120 | ||||||||
\(499\) | 25.1537 | 1.12603 | 0.563017 | − | 0.826445i | \(-0.309641\pi\) | ||||
0.563017 | + | 0.826445i | \(0.309641\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 40.3213 | 1.80142 | ||||||||
\(502\) | −4.78389 | −0.213515 | ||||||||
\(503\) | 41.8439 | 1.86573 | 0.932864 | − | 0.360230i | \(-0.117302\pi\) | ||||
0.932864 | + | 0.360230i | \(0.117302\pi\) | |||||||
\(504\) | −0.0372249 | −0.00165813 | ||||||||
\(505\) | −2.55210 | −0.113567 | ||||||||
\(506\) | 8.42219 | 0.374412 | ||||||||
\(507\) | 3.11948 | 0.138541 | ||||||||
\(508\) | 21.8559 | 0.969701 | ||||||||
\(509\) | −20.9049 | −0.926595 | −0.463297 | − | 0.886203i | \(-0.653334\pi\) | ||||
−0.463297 | + | 0.886203i | \(0.653334\pi\) | |||||||
\(510\) | −4.72507 | −0.209230 | ||||||||
\(511\) | 1.46692 | 0.0648929 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 28.6996 | 1.26712 | ||||||||
\(514\) | −0.924873 | −0.0407944 | ||||||||
\(515\) | −3.93006 | −0.173179 | ||||||||
\(516\) | 5.82089 | 0.256250 | ||||||||
\(517\) | −35.6795 | −1.56918 | ||||||||
\(518\) | −0.0357927 | −0.00157264 | ||||||||
\(519\) | −1.60706 | −0.0705423 | ||||||||
\(520\) | −3.36264 | −0.147461 | ||||||||
\(521\) | −22.4931 | −0.985440 | −0.492720 | − | 0.870188i | \(-0.663997\pi\) | ||||
−0.492720 | + | 0.870188i | \(0.663997\pi\) | |||||||
\(522\) | 2.28883 | 0.100179 | ||||||||
\(523\) | 28.7738 | 1.25819 | 0.629094 | − | 0.777329i | \(-0.283426\pi\) | ||||
0.629094 | + | 0.777329i | \(0.283426\pi\) | |||||||
\(524\) | −9.46857 | −0.413636 | ||||||||
\(525\) | 0.173050 | 0.00755252 | ||||||||
\(526\) | −7.75351 | −0.338069 | ||||||||
\(527\) | −5.71773 | −0.249068 | ||||||||
\(528\) | 6.32217 | 0.275137 | ||||||||
\(529\) | −16.9724 | −0.737932 | ||||||||
\(530\) | −7.89272 | −0.342838 | ||||||||
\(531\) | −4.79089 | −0.207907 | ||||||||
\(532\) | −0.561636 | −0.0243500 | ||||||||
\(533\) | 41.0800 | 1.77937 | ||||||||
\(534\) | 13.1943 | 0.570973 | ||||||||
\(535\) | 18.5937 | 0.803874 | ||||||||
\(536\) | −10.7784 | −0.465556 | ||||||||
\(537\) | 19.6004 | 0.845821 | ||||||||
\(538\) | 29.8572 | 1.28724 | ||||||||
\(539\) | 23.9831 | 1.03302 | ||||||||
\(540\) | 4.79822 | 0.206482 | ||||||||
\(541\) | −7.75971 | −0.333616 | −0.166808 | − | 0.985989i | \(-0.553346\pi\) | ||||
−0.166808 | + | 0.985989i | \(0.553346\pi\) | |||||||
\(542\) | 7.22166 | 0.310197 | ||||||||
\(543\) | −12.0533 | −0.517256 | ||||||||
\(544\) | 2.56387 | 0.109925 | ||||||||
\(545\) | −6.58120 | −0.281908 | ||||||||
\(546\) | −0.581904 | −0.0249032 | ||||||||
\(547\) | 28.7639 | 1.22985 | 0.614927 | − | 0.788584i | \(-0.289185\pi\) | ||||
0.614927 | + | 0.788584i | \(0.289185\pi\) | |||||||
\(548\) | −15.5435 | −0.663986 | ||||||||
\(549\) | 0.181539 | 0.00774789 | ||||||||
\(550\) | −3.43048 | −0.146276 | ||||||||
\(551\) | 34.5330 | 1.47116 | ||||||||
\(552\) | 4.52462 | 0.192581 | ||||||||
\(553\) | −0.798202 | −0.0339430 | ||||||||
\(554\) | −27.5920 | −1.17227 | ||||||||
\(555\) | −0.702501 | −0.0298195 | ||||||||
\(556\) | −16.9704 | −0.719705 | ||||||||
\(557\) | −18.8940 | −0.800563 | −0.400281 | − | 0.916392i | \(-0.631088\pi\) | ||||
−0.400281 | + | 0.916392i | \(0.631088\pi\) | |||||||
\(558\) | −0.884099 | −0.0374269 | ||||||||
\(559\) | 10.6208 | 0.449213 | ||||||||
\(560\) | −0.0938987 | −0.00396794 | ||||||||
\(561\) | 16.2092 | 0.684355 | ||||||||
\(562\) | −9.57593 | −0.403936 | ||||||||
\(563\) | 35.8955 | 1.51281 | 0.756407 | − | 0.654102i | \(-0.226953\pi\) | ||||
0.756407 | + | 0.654102i | \(0.226953\pi\) | |||||||
\(564\) | −19.1680 | −0.807116 | ||||||||
\(565\) | 9.12255 | 0.383788 | ||||||||
\(566\) | 4.86749 | 0.204596 | ||||||||
\(567\) | 0.942006 | 0.0395605 | ||||||||
\(568\) | −4.78946 | −0.200961 | ||||||||
\(569\) | −37.7436 | −1.58229 | −0.791146 | − | 0.611627i | \(-0.790515\pi\) | ||||
−0.791146 | + | 0.611627i | \(0.790515\pi\) | |||||||
\(570\) | −11.0232 | −0.461711 | ||||||||
\(571\) | −23.7037 | −0.991968 | −0.495984 | − | 0.868332i | \(-0.665193\pi\) | ||||
−0.495984 | + | 0.868332i | \(0.665193\pi\) | |||||||
\(572\) | 11.5355 | 0.482321 | ||||||||
\(573\) | −15.6270 | −0.652827 | ||||||||
\(574\) | 1.14712 | 0.0478799 | ||||||||
\(575\) | −2.45511 | −0.102385 | ||||||||
\(576\) | 0.396437 | 0.0165182 | ||||||||
\(577\) | −24.8378 | −1.03401 | −0.517006 | − | 0.855982i | \(-0.672954\pi\) | ||||
−0.517006 | + | 0.855982i | \(0.672954\pi\) | |||||||
\(578\) | −10.4266 | −0.433687 | ||||||||
\(579\) | 15.1733 | 0.630581 | ||||||||
\(580\) | 5.77350 | 0.239731 | ||||||||
\(581\) | −0.315087 | −0.0130720 | ||||||||
\(582\) | −11.9333 | −0.494649 | ||||||||
\(583\) | 27.0758 | 1.12136 | ||||||||
\(584\) | −15.6224 | −0.646460 | ||||||||
\(585\) | −1.33307 | −0.0551158 | ||||||||
\(586\) | 8.86662 | 0.366277 | ||||||||
\(587\) | −35.6906 | −1.47311 | −0.736554 | − | 0.676379i | \(-0.763548\pi\) | ||||
−0.736554 | + | 0.676379i | \(0.763548\pi\) | |||||||
\(588\) | 12.8843 | 0.531342 | ||||||||
\(589\) | −13.3390 | −0.549623 | ||||||||
\(590\) | −12.0849 | −0.497526 | ||||||||
\(591\) | 0.323809 | 0.0133197 | ||||||||
\(592\) | 0.381184 | 0.0156666 | ||||||||
\(593\) | 2.72379 | 0.111852 | 0.0559262 | − | 0.998435i | \(-0.482189\pi\) | ||||
0.0559262 | + | 0.998435i | \(0.482189\pi\) | |||||||
\(594\) | −16.4602 | −0.675369 | ||||||||
\(595\) | −0.240744 | −0.00986956 | ||||||||
\(596\) | −4.19924 | −0.172007 | ||||||||
\(597\) | −10.5682 | −0.432527 | ||||||||
\(598\) | 8.25564 | 0.337598 | ||||||||
\(599\) | −42.5223 | −1.73741 | −0.868707 | − | 0.495326i | \(-0.835049\pi\) | ||||
−0.868707 | + | 0.495326i | \(0.835049\pi\) | |||||||
\(600\) | −1.84294 | −0.0752378 | ||||||||
\(601\) | −13.2007 | −0.538467 | −0.269234 | − | 0.963075i | \(-0.586770\pi\) | ||||
−0.269234 | + | 0.963075i | \(0.586770\pi\) | |||||||
\(602\) | 0.296577 | 0.0120876 | ||||||||
\(603\) | −4.27295 | −0.174008 | ||||||||
\(604\) | 0.915926 | 0.0372685 | ||||||||
\(605\) | 0.768168 | 0.0312305 | ||||||||
\(606\) | 4.70338 | 0.191062 | ||||||||
\(607\) | −37.9231 | −1.53925 | −0.769625 | − | 0.638496i | \(-0.779557\pi\) | ||||
−0.769625 | + | 0.638496i | \(0.779557\pi\) | |||||||
\(608\) | 5.98130 | 0.242574 | ||||||||
\(609\) | 0.999103 | 0.0404857 | ||||||||
\(610\) | 0.457926 | 0.0185409 | ||||||||
\(611\) | −34.9739 | −1.41489 | ||||||||
\(612\) | 1.01641 | 0.0410861 | ||||||||
\(613\) | −9.78357 | −0.395155 | −0.197577 | − | 0.980287i | \(-0.563307\pi\) | ||||
−0.197577 | + | 0.980287i | \(0.563307\pi\) | |||||||
\(614\) | 13.1248 | 0.529675 | ||||||||
\(615\) | 22.5145 | 0.907871 | ||||||||
\(616\) | 0.322117 | 0.0129785 | ||||||||
\(617\) | −5.73237 | −0.230777 | −0.115388 | − | 0.993320i | \(-0.536811\pi\) | ||||
−0.115388 | + | 0.993320i | \(0.536811\pi\) | |||||||
\(618\) | 7.24287 | 0.291351 | ||||||||
\(619\) | 23.9435 | 0.962370 | 0.481185 | − | 0.876619i | \(-0.340206\pi\) | ||||
0.481185 | + | 0.876619i | \(0.340206\pi\) | |||||||
\(620\) | −2.23011 | −0.0895635 | ||||||||
\(621\) | −11.7801 | −0.472721 | ||||||||
\(622\) | −1.50532 | −0.0603580 | ||||||||
\(623\) | 0.672255 | 0.0269333 | ||||||||
\(624\) | 6.19715 | 0.248084 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.86091 | 0.114345 | ||||||||
\(627\) | 37.8148 | 1.51018 | ||||||||
\(628\) | −18.3891 | −0.733807 | ||||||||
\(629\) | 0.977309 | 0.0389678 | ||||||||
\(630\) | −0.0372249 | −0.00148308 | ||||||||
\(631\) | 31.4731 | 1.25293 | 0.626463 | − | 0.779451i | \(-0.284502\pi\) | ||||
0.626463 | + | 0.779451i | \(0.284502\pi\) | |||||||
\(632\) | 8.50067 | 0.338139 | ||||||||
\(633\) | 2.79276 | 0.111002 | ||||||||
\(634\) | −20.5102 | −0.814564 | ||||||||
\(635\) | 21.8559 | 0.867327 | ||||||||
\(636\) | 14.5458 | 0.576779 | ||||||||
\(637\) | 23.5088 | 0.931453 | ||||||||
\(638\) | −19.8058 | −0.784121 | ||||||||
\(639\) | −1.89872 | −0.0751122 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 18.4384 | 0.728273 | 0.364136 | − | 0.931346i | \(-0.381364\pi\) | ||||
0.364136 | + | 0.931346i | \(0.381364\pi\) | |||||||
\(642\) | −34.2671 | −1.35241 | ||||||||
\(643\) | 44.0100 | 1.73559 | 0.867793 | − | 0.496926i | \(-0.165538\pi\) | ||||
0.867793 | + | 0.496926i | \(0.165538\pi\) | |||||||
\(644\) | 0.230531 | 0.00908421 | ||||||||
\(645\) | 5.82089 | 0.229197 | ||||||||
\(646\) | 15.3353 | 0.603359 | ||||||||
\(647\) | 32.2310 | 1.26713 | 0.633565 | − | 0.773689i | \(-0.281591\pi\) | ||||
0.633565 | + | 0.773689i | \(0.281591\pi\) | |||||||
\(648\) | −10.0321 | −0.394100 | ||||||||
\(649\) | 41.4569 | 1.62732 | ||||||||
\(650\) | −3.36264 | −0.131894 | ||||||||
\(651\) | −0.385921 | −0.0151254 | ||||||||
\(652\) | −18.4734 | −0.723473 | ||||||||
\(653\) | 29.8242 | 1.16711 | 0.583556 | − | 0.812073i | \(-0.301661\pi\) | ||||
0.583556 | + | 0.812073i | \(0.301661\pi\) | |||||||
\(654\) | 12.1288 | 0.474273 | ||||||||
\(655\) | −9.46857 | −0.369968 | ||||||||
\(656\) | −12.2166 | −0.476978 | ||||||||
\(657\) | −6.19330 | −0.241624 | ||||||||
\(658\) | −0.976615 | −0.0380724 | ||||||||
\(659\) | 12.1836 | 0.474607 | 0.237303 | − | 0.971436i | \(-0.423736\pi\) | ||||
0.237303 | + | 0.971436i | \(0.423736\pi\) | |||||||
\(660\) | 6.32217 | 0.246090 | ||||||||
\(661\) | −19.1593 | −0.745212 | −0.372606 | − | 0.927990i | \(-0.621536\pi\) | ||||
−0.372606 | + | 0.927990i | \(0.621536\pi\) | |||||||
\(662\) | −9.27471 | −0.360472 | ||||||||
\(663\) | 15.8887 | 0.617066 | ||||||||
\(664\) | 3.35560 | 0.130223 | ||||||||
\(665\) | −0.561636 | −0.0217793 | ||||||||
\(666\) | 0.151116 | 0.00585561 | ||||||||
\(667\) | −14.1746 | −0.548841 | ||||||||
\(668\) | −21.8788 | −0.846514 | ||||||||
\(669\) | −29.0384 | −1.12269 | ||||||||
\(670\) | −10.7784 | −0.416406 | ||||||||
\(671\) | −1.57091 | −0.0606441 | ||||||||
\(672\) | 0.173050 | 0.00667554 | ||||||||
\(673\) | −17.8746 | −0.689013 | −0.344507 | − | 0.938784i | \(-0.611954\pi\) | ||||
−0.344507 | + | 0.938784i | \(0.611954\pi\) | |||||||
\(674\) | 24.6047 | 0.947739 | ||||||||
\(675\) | 4.79822 | 0.184683 | ||||||||
\(676\) | −1.69266 | −0.0651025 | ||||||||
\(677\) | 29.5856 | 1.13707 | 0.568533 | − | 0.822661i | \(-0.307511\pi\) | ||||
0.568533 | + | 0.822661i | \(0.307511\pi\) | |||||||
\(678\) | −16.8123 | −0.645674 | ||||||||
\(679\) | −0.608004 | −0.0233331 | ||||||||
\(680\) | 2.56387 | 0.0983201 | ||||||||
\(681\) | −0.921427 | −0.0353091 | ||||||||
\(682\) | 7.65035 | 0.292947 | ||||||||
\(683\) | −47.8617 | −1.83138 | −0.915689 | − | 0.401887i | \(-0.868355\pi\) | ||||
−0.915689 | + | 0.401887i | \(0.868355\pi\) | |||||||
\(684\) | 2.37121 | 0.0906654 | ||||||||
\(685\) | −15.5435 | −0.593888 | ||||||||
\(686\) | 1.31375 | 0.0501593 | ||||||||
\(687\) | 13.0124 | 0.496453 | ||||||||
\(688\) | −3.15848 | −0.120416 | ||||||||
\(689\) | 26.5404 | 1.01111 | ||||||||
\(690\) | 4.52462 | 0.172249 | ||||||||
\(691\) | −45.0030 | −1.71199 | −0.855997 | − | 0.516980i | \(-0.827056\pi\) | ||||
−0.855997 | + | 0.516980i | \(0.827056\pi\) | |||||||
\(692\) | 0.872010 | 0.0331488 | ||||||||
\(693\) | 0.127699 | 0.00485089 | ||||||||
\(694\) | −3.87165 | −0.146966 | ||||||||
\(695\) | −16.9704 | −0.643724 | ||||||||
\(696\) | −10.6402 | −0.403317 | ||||||||
\(697\) | −31.3218 | −1.18640 | ||||||||
\(698\) | −12.0503 | −0.456110 | ||||||||
\(699\) | −1.16906 | −0.0442181 | ||||||||
\(700\) | −0.0938987 | −0.00354904 | ||||||||
\(701\) | −25.6734 | −0.969670 | −0.484835 | − | 0.874606i | \(-0.661120\pi\) | ||||
−0.484835 | + | 0.874606i | \(0.661120\pi\) | |||||||
\(702\) | −16.1347 | −0.608964 | ||||||||
\(703\) | 2.27998 | 0.0859910 | ||||||||
\(704\) | −3.43048 | −0.129291 | ||||||||
\(705\) | −19.1680 | −0.721907 | ||||||||
\(706\) | 32.0479 | 1.20614 | ||||||||
\(707\) | 0.239639 | 0.00901255 | ||||||||
\(708\) | 22.2717 | 0.837023 | ||||||||
\(709\) | −26.7446 | −1.00441 | −0.502206 | − | 0.864748i | \(-0.667478\pi\) | ||||
−0.502206 | + | 0.864748i | \(0.667478\pi\) | |||||||
\(710\) | −4.78946 | −0.179745 | ||||||||
\(711\) | 3.36998 | 0.126384 | ||||||||
\(712\) | −7.15936 | −0.268309 | ||||||||
\(713\) | 5.47517 | 0.205047 | ||||||||
\(714\) | 0.443678 | 0.0166042 | ||||||||
\(715\) | 11.5355 | 0.431401 | ||||||||
\(716\) | −10.6354 | −0.397463 | ||||||||
\(717\) | −29.2819 | −1.09355 | ||||||||
\(718\) | −20.4761 | −0.764162 | ||||||||
\(719\) | 9.82982 | 0.366590 | 0.183295 | − | 0.983058i | \(-0.441324\pi\) | ||||
0.183295 | + | 0.983058i | \(0.441324\pi\) | |||||||
\(720\) | 0.396437 | 0.0147743 | ||||||||
\(721\) | 0.369027 | 0.0137433 | ||||||||
\(722\) | 16.7759 | 0.624335 | ||||||||
\(723\) | 34.4167 | 1.27997 | ||||||||
\(724\) | 6.54024 | 0.243066 | ||||||||
\(725\) | 5.77350 | 0.214422 | ||||||||
\(726\) | −1.41569 | −0.0525412 | ||||||||
\(727\) | 23.7186 | 0.879675 | 0.439838 | − | 0.898077i | \(-0.355036\pi\) | ||||
0.439838 | + | 0.898077i | \(0.355036\pi\) | |||||||
\(728\) | 0.315747 | 0.0117024 | ||||||||
\(729\) | 22.5514 | 0.835237 | ||||||||
\(730\) | −15.6224 | −0.578211 | ||||||||
\(731\) | −8.09794 | −0.299513 | ||||||||
\(732\) | −0.843932 | −0.0311926 | ||||||||
\(733\) | 31.9151 | 1.17881 | 0.589405 | − | 0.807838i | \(-0.299362\pi\) | ||||
0.589405 | + | 0.807838i | \(0.299362\pi\) | |||||||
\(734\) | −1.25272 | −0.0462389 | ||||||||
\(735\) | 12.8843 | 0.475246 | ||||||||
\(736\) | −2.45511 | −0.0904965 | ||||||||
\(737\) | 36.9750 | 1.36199 | ||||||||
\(738\) | −4.84311 | −0.178277 | ||||||||
\(739\) | −31.6812 | −1.16541 | −0.582705 | − | 0.812684i | \(-0.698006\pi\) | ||||
−0.582705 | + | 0.812684i | \(0.698006\pi\) | |||||||
\(740\) | 0.381184 | 0.0140126 | ||||||||
\(741\) | 37.0670 | 1.36169 | ||||||||
\(742\) | 0.741116 | 0.0272072 | ||||||||
\(743\) | −21.1940 | −0.777531 | −0.388765 | − | 0.921337i | \(-0.627098\pi\) | ||||
−0.388765 | + | 0.921337i | \(0.627098\pi\) | |||||||
\(744\) | 4.10997 | 0.150679 | ||||||||
\(745\) | −4.19924 | −0.153848 | ||||||||
\(746\) | 19.0849 | 0.698748 | ||||||||
\(747\) | 1.33029 | 0.0486726 | ||||||||
\(748\) | −8.79531 | −0.321588 | ||||||||
\(749\) | −1.74592 | −0.0637946 | ||||||||
\(750\) | −1.84294 | −0.0672947 | ||||||||
\(751\) | 7.00106 | 0.255472 | 0.127736 | − | 0.991808i | \(-0.459229\pi\) | ||||
0.127736 | + | 0.991808i | \(0.459229\pi\) | |||||||
\(752\) | 10.4007 | 0.379276 | ||||||||
\(753\) | 8.81643 | 0.321288 | ||||||||
\(754\) | −19.4142 | −0.707023 | ||||||||
\(755\) | 0.915926 | 0.0333339 | ||||||||
\(756\) | −0.450546 | −0.0163862 | ||||||||
\(757\) | 17.4313 | 0.633551 | 0.316775 | − | 0.948501i | \(-0.397400\pi\) | ||||
0.316775 | + | 0.948501i | \(0.397400\pi\) | |||||||
\(758\) | 19.9070 | 0.723054 | ||||||||
\(759\) | −15.5216 | −0.563399 | ||||||||
\(760\) | 5.98130 | 0.216964 | ||||||||
\(761\) | 21.8929 | 0.793618 | 0.396809 | − | 0.917901i | \(-0.370118\pi\) | ||||
0.396809 | + | 0.917901i | \(0.370118\pi\) | |||||||
\(762\) | −40.2792 | −1.45916 | ||||||||
\(763\) | 0.617966 | 0.0223719 | ||||||||
\(764\) | 8.47937 | 0.306773 | ||||||||
\(765\) | 1.01641 | 0.0367485 | ||||||||
\(766\) | −22.4584 | −0.811455 | ||||||||
\(767\) | 40.6371 | 1.46732 | ||||||||
\(768\) | −1.84294 | −0.0665015 | ||||||||
\(769\) | 5.96382 | 0.215061 | 0.107530 | − | 0.994202i | \(-0.465706\pi\) | ||||
0.107530 | + | 0.994202i | \(0.465706\pi\) | |||||||
\(770\) | 0.322117 | 0.0116083 | ||||||||
\(771\) | 1.70449 | 0.0613856 | ||||||||
\(772\) | −8.23319 | −0.296319 | ||||||||
\(773\) | 1.09252 | 0.0392951 | 0.0196476 | − | 0.999807i | \(-0.493746\pi\) | ||||
0.0196476 | + | 0.999807i | \(0.493746\pi\) | |||||||
\(774\) | −1.25214 | −0.0450071 | ||||||||
\(775\) | −2.23011 | −0.0801080 | ||||||||
\(776\) | 6.47511 | 0.232443 | ||||||||
\(777\) | 0.0659639 | 0.00236644 | ||||||||
\(778\) | 24.0783 | 0.863248 | ||||||||
\(779\) | −73.0711 | −2.61804 | ||||||||
\(780\) | 6.19715 | 0.221894 | ||||||||
\(781\) | 16.4301 | 0.587916 | ||||||||
\(782\) | −6.29459 | −0.225094 | ||||||||
\(783\) | 27.7025 | 0.990006 | ||||||||
\(784\) | −6.99118 | −0.249685 | ||||||||
\(785\) | −18.3891 | −0.656337 | ||||||||
\(786\) | 17.4500 | 0.622422 | ||||||||
\(787\) | 39.9819 | 1.42520 | 0.712600 | − | 0.701571i | \(-0.247518\pi\) | ||||
0.712600 | + | 0.701571i | \(0.247518\pi\) | |||||||
\(788\) | −0.175702 | −0.00625914 | ||||||||
\(789\) | 14.2893 | 0.508712 | ||||||||
\(790\) | 8.50067 | 0.302440 | ||||||||
\(791\) | −0.856595 | −0.0304570 | ||||||||
\(792\) | −1.35997 | −0.0483243 | ||||||||
\(793\) | −1.53984 | −0.0546813 | ||||||||
\(794\) | 39.1825 | 1.39053 | ||||||||
\(795\) | 14.5458 | 0.515887 | ||||||||
\(796\) | 5.73441 | 0.203251 | ||||||||
\(797\) | 32.5813 | 1.15409 | 0.577044 | − | 0.816713i | \(-0.304206\pi\) | ||||
0.577044 | + | 0.816713i | \(0.304206\pi\) | |||||||
\(798\) | 1.03506 | 0.0366408 | ||||||||
\(799\) | 26.6662 | 0.943381 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −2.83824 | −0.100284 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | 53.5923 | 1.89123 | ||||||||
\(804\) | 19.8640 | 0.700548 | ||||||||
\(805\) | 0.230531 | 0.00812517 | ||||||||
\(806\) | 7.49906 | 0.264143 | ||||||||
\(807\) | −55.0251 | −1.93698 | ||||||||
\(808\) | −2.55210 | −0.0897826 | ||||||||
\(809\) | 21.5506 | 0.757680 | 0.378840 | − | 0.925462i | \(-0.376323\pi\) | ||||
0.378840 | + | 0.925462i | \(0.376323\pi\) | |||||||
\(810\) | −10.0321 | −0.352494 | ||||||||
\(811\) | −11.8902 | −0.417521 | −0.208761 | − | 0.977967i | \(-0.566943\pi\) | ||||
−0.208761 | + | 0.977967i | \(0.566943\pi\) | |||||||
\(812\) | −0.542124 | −0.0190248 | ||||||||
\(813\) | −13.3091 | −0.466770 | ||||||||
\(814\) | −1.30764 | −0.0458329 | ||||||||
\(815\) | −18.4734 | −0.647094 | ||||||||
\(816\) | −4.72507 | −0.165411 | ||||||||
\(817\) | −18.8918 | −0.660940 | ||||||||
\(818\) | −27.2597 | −0.953112 | ||||||||
\(819\) | 0.125174 | 0.00437393 | ||||||||
\(820\) | −12.2166 | −0.426622 | ||||||||
\(821\) | 8.87452 | 0.309723 | 0.154861 | − | 0.987936i | \(-0.450507\pi\) | ||||
0.154861 | + | 0.987936i | \(0.450507\pi\) | |||||||
\(822\) | 28.6458 | 0.999138 | ||||||||
\(823\) | 35.1961 | 1.22686 | 0.613430 | − | 0.789749i | \(-0.289789\pi\) | ||||
0.613430 | + | 0.789749i | \(0.289789\pi\) | |||||||
\(824\) | −3.93006 | −0.136910 | ||||||||
\(825\) | 6.32217 | 0.220110 | ||||||||
\(826\) | 1.13475 | 0.0394831 | ||||||||
\(827\) | 22.5418 | 0.783856 | 0.391928 | − | 0.919996i | \(-0.371808\pi\) | ||||
0.391928 | + | 0.919996i | \(0.371808\pi\) | |||||||
\(828\) | −0.973296 | −0.0338244 | ||||||||
\(829\) | −28.9658 | −1.00603 | −0.503013 | − | 0.864279i | \(-0.667775\pi\) | ||||
−0.503013 | + | 0.864279i | \(0.667775\pi\) | |||||||
\(830\) | 3.35560 | 0.116475 | ||||||||
\(831\) | 50.8504 | 1.76398 | ||||||||
\(832\) | −3.36264 | −0.116579 | ||||||||
\(833\) | −17.9245 | −0.621048 | ||||||||
\(834\) | 31.2755 | 1.08298 | ||||||||
\(835\) | −21.8788 | −0.757146 | ||||||||
\(836\) | −20.5187 | −0.709654 | ||||||||
\(837\) | −10.7006 | −0.369866 | ||||||||
\(838\) | 0.625472 | 0.0216066 | ||||||||
\(839\) | 54.4410 | 1.87951 | 0.939756 | − | 0.341847i | \(-0.111052\pi\) | ||||
0.939756 | + | 0.341847i | \(0.111052\pi\) | |||||||
\(840\) | 0.173050 | 0.00597079 | ||||||||
\(841\) | 4.33326 | 0.149423 | ||||||||
\(842\) | 4.29032 | 0.147854 | ||||||||
\(843\) | 17.6479 | 0.607826 | ||||||||
\(844\) | −1.51538 | −0.0521616 | ||||||||
\(845\) | −1.69266 | −0.0582294 | ||||||||
\(846\) | 4.12324 | 0.141760 | ||||||||
\(847\) | −0.0721299 | −0.00247841 | ||||||||
\(848\) | −7.89272 | −0.271037 | ||||||||
\(849\) | −8.97050 | −0.307867 | ||||||||
\(850\) | 2.56387 | 0.0879402 | ||||||||
\(851\) | −0.935849 | −0.0320805 | ||||||||
\(852\) | 8.82670 | 0.302398 | ||||||||
\(853\) | 14.9371 | 0.511438 | 0.255719 | − | 0.966751i | \(-0.417688\pi\) | ||||
0.255719 | + | 0.966751i | \(0.417688\pi\) | |||||||
\(854\) | −0.0429987 | −0.00147138 | ||||||||
\(855\) | 2.37121 | 0.0810936 | ||||||||
\(856\) | 18.5937 | 0.635518 | ||||||||
\(857\) | −3.08893 | −0.105516 | −0.0527579 | − | 0.998607i | \(-0.516801\pi\) | ||||
−0.0527579 | + | 0.998607i | \(0.516801\pi\) | |||||||
\(858\) | −21.2592 | −0.725776 | ||||||||
\(859\) | −3.15191 | −0.107542 | −0.0537709 | − | 0.998553i | \(-0.517124\pi\) | ||||
−0.0537709 | + | 0.998553i | \(0.517124\pi\) | |||||||
\(860\) | −3.15848 | −0.107703 | ||||||||
\(861\) | −2.11408 | −0.0720476 | ||||||||
\(862\) | −29.9833 | −1.02124 | ||||||||
\(863\) | −15.5978 | −0.530957 | −0.265478 | − | 0.964117i | \(-0.585530\pi\) | ||||
−0.265478 | + | 0.964117i | \(0.585530\pi\) | |||||||
\(864\) | 4.79822 | 0.163239 | ||||||||
\(865\) | 0.872010 | 0.0296492 | ||||||||
\(866\) | 18.0144 | 0.612153 | ||||||||
\(867\) | 19.2155 | 0.652594 | ||||||||
\(868\) | 0.209405 | 0.00710766 | ||||||||
\(869\) | −29.1613 | −0.989231 | ||||||||
\(870\) | −10.6402 | −0.360737 | ||||||||
\(871\) | 36.2438 | 1.22808 | ||||||||
\(872\) | −6.58120 | −0.222868 | ||||||||
\(873\) | 2.56697 | 0.0868789 | ||||||||
\(874\) | −14.6847 | −0.496719 | ||||||||
\(875\) | −0.0938987 | −0.00317435 | ||||||||
\(876\) | 28.7912 | 0.972765 | ||||||||
\(877\) | −24.1351 | −0.814984 | −0.407492 | − | 0.913209i | \(-0.633597\pi\) | ||||
−0.407492 | + | 0.913209i | \(0.633597\pi\) | |||||||
\(878\) | 4.45552 | 0.150367 | ||||||||
\(879\) | −16.3407 | −0.551157 | ||||||||
\(880\) | −3.43048 | −0.115641 | ||||||||
\(881\) | 15.7995 | 0.532297 | 0.266149 | − | 0.963932i | \(-0.414249\pi\) | ||||
0.266149 | + | 0.963932i | \(0.414249\pi\) | |||||||
\(882\) | −2.77156 | −0.0933234 | ||||||||
\(883\) | −46.1737 | −1.55387 | −0.776935 | − | 0.629581i | \(-0.783227\pi\) | ||||
−0.776935 | + | 0.629581i | \(0.783227\pi\) | |||||||
\(884\) | −8.62138 | −0.289968 | ||||||||
\(885\) | 22.2717 | 0.748656 | ||||||||
\(886\) | 32.2852 | 1.08464 | ||||||||
\(887\) | −12.5940 | −0.422865 | −0.211432 | − | 0.977393i | \(-0.567813\pi\) | ||||
−0.211432 | + | 0.977393i | \(0.567813\pi\) | |||||||
\(888\) | −0.702501 | −0.0235744 | ||||||||
\(889\) | −2.05224 | −0.0688301 | ||||||||
\(890\) | −7.15936 | −0.239982 | ||||||||
\(891\) | 34.4150 | 1.15295 | ||||||||
\(892\) | 15.7565 | 0.527568 | ||||||||
\(893\) | 62.2099 | 2.08177 | ||||||||
\(894\) | 7.73895 | 0.258829 | ||||||||
\(895\) | −10.6354 | −0.355502 | ||||||||
\(896\) | −0.0938987 | −0.00313693 | ||||||||
\(897\) | −15.2147 | −0.508003 | ||||||||
\(898\) | 17.7475 | 0.592241 | ||||||||
\(899\) | −12.8756 | −0.429424 | ||||||||
\(900\) | 0.396437 | 0.0132146 | ||||||||
\(901\) | −20.2359 | −0.674157 | ||||||||
\(902\) | 41.9087 | 1.39541 | ||||||||
\(903\) | −0.546574 | −0.0181888 | ||||||||
\(904\) | 9.12255 | 0.303411 | ||||||||
\(905\) | 6.54024 | 0.217405 | ||||||||
\(906\) | −1.68800 | −0.0560800 | ||||||||
\(907\) | 50.9973 | 1.69334 | 0.846670 | − | 0.532119i | \(-0.178604\pi\) | ||||
0.846670 | + | 0.532119i | \(0.178604\pi\) | |||||||
\(908\) | 0.499976 | 0.0165923 | ||||||||
\(909\) | −1.01175 | −0.0335575 | ||||||||
\(910\) | 0.315747 | 0.0104669 | ||||||||
\(911\) | 18.6642 | 0.618374 | 0.309187 | − | 0.951001i | \(-0.399943\pi\) | ||||
0.309187 | + | 0.951001i | \(0.399943\pi\) | |||||||
\(912\) | −11.0232 | −0.365014 | ||||||||
\(913\) | −11.5113 | −0.380969 | ||||||||
\(914\) | −38.5645 | −1.27560 | ||||||||
\(915\) | −0.843932 | −0.0278995 | ||||||||
\(916\) | −7.06065 | −0.233291 | ||||||||
\(917\) | 0.889086 | 0.0293602 | ||||||||
\(918\) | 12.3020 | 0.406027 | ||||||||
\(919\) | −10.8445 | −0.357726 | −0.178863 | − | 0.983874i | \(-0.557242\pi\) | ||||
−0.178863 | + | 0.983874i | \(0.557242\pi\) | |||||||
\(920\) | −2.45511 | −0.0809425 | ||||||||
\(921\) | −24.1883 | −0.797032 | ||||||||
\(922\) | 16.0662 | 0.529113 | ||||||||
\(923\) | 16.1052 | 0.530110 | ||||||||
\(924\) | −0.593643 | −0.0195294 | ||||||||
\(925\) | 0.381184 | 0.0125333 | ||||||||
\(926\) | −8.15714 | −0.268060 | ||||||||
\(927\) | −1.55802 | −0.0511721 | ||||||||
\(928\) | 5.77350 | 0.189524 | ||||||||
\(929\) | −11.1726 | −0.366563 | −0.183281 | − | 0.983061i | \(-0.558672\pi\) | ||||
−0.183281 | + | 0.983061i | \(0.558672\pi\) | |||||||
\(930\) | 4.10997 | 0.134771 | ||||||||
\(931\) | −41.8163 | −1.37048 | ||||||||
\(932\) | 0.634346 | 0.0207787 | ||||||||
\(933\) | 2.77423 | 0.0908241 | ||||||||
\(934\) | 39.3652 | 1.28807 | ||||||||
\(935\) | −8.79531 | −0.287637 | ||||||||
\(936\) | −1.33307 | −0.0435729 | ||||||||
\(937\) | 13.5690 | 0.443280 | 0.221640 | − | 0.975129i | \(-0.428859\pi\) | ||||
0.221640 | + | 0.975129i | \(0.428859\pi\) | |||||||
\(938\) | 1.01208 | 0.0330455 | ||||||||
\(939\) | −5.27249 | −0.172061 | ||||||||
\(940\) | 10.4007 | 0.339235 | ||||||||
\(941\) | −19.2211 | −0.626590 | −0.313295 | − | 0.949656i | \(-0.601433\pi\) | ||||
−0.313295 | + | 0.949656i | \(0.601433\pi\) | |||||||
\(942\) | 33.8901 | 1.10420 | ||||||||
\(943\) | 29.9930 | 0.976708 | ||||||||
\(944\) | −12.0849 | −0.393329 | ||||||||
\(945\) | −0.450546 | −0.0146563 | ||||||||
\(946\) | 10.8351 | 0.352279 | ||||||||
\(947\) | 30.5365 | 0.992303 | 0.496152 | − | 0.868236i | \(-0.334746\pi\) | ||||
0.496152 | + | 0.868236i | \(0.334746\pi\) | |||||||
\(948\) | −15.6662 | −0.508816 | ||||||||
\(949\) | 52.5325 | 1.70528 | ||||||||
\(950\) | 5.98130 | 0.194059 | ||||||||
\(951\) | 37.7991 | 1.22572 | ||||||||
\(952\) | −0.240744 | −0.00780257 | ||||||||
\(953\) | −9.22331 | −0.298772 | −0.149386 | − | 0.988779i | \(-0.547730\pi\) | ||||
−0.149386 | + | 0.988779i | \(0.547730\pi\) | |||||||
\(954\) | −3.12896 | −0.101304 | ||||||||
\(955\) | 8.47937 | 0.274386 | ||||||||
\(956\) | 15.8886 | 0.513876 | ||||||||
\(957\) | 36.5010 | 1.17991 | ||||||||
\(958\) | −34.6506 | −1.11951 | ||||||||
\(959\) | 1.45952 | 0.0471302 | ||||||||
\(960\) | −1.84294 | −0.0594807 | ||||||||
\(961\) | −26.0266 | −0.839568 | ||||||||
\(962\) | −1.28179 | −0.0413264 | ||||||||
\(963\) | 7.37122 | 0.237534 | ||||||||
\(964\) | −18.6749 | −0.601477 | ||||||||
\(965\) | −8.23319 | −0.265036 | ||||||||
\(966\) | −0.424856 | −0.0136695 | ||||||||
\(967\) | 5.02030 | 0.161442 | 0.0807210 | − | 0.996737i | \(-0.474278\pi\) | ||||
0.0807210 | + | 0.996737i | \(0.474278\pi\) | |||||||
\(968\) | 0.768168 | 0.0246898 | ||||||||
\(969\) | −28.2621 | −0.907908 | ||||||||
\(970\) | 6.47511 | 0.207903 | ||||||||
\(971\) | 25.2192 | 0.809322 | 0.404661 | − | 0.914467i | \(-0.367389\pi\) | ||||
0.404661 | + | 0.914467i | \(0.367389\pi\) | |||||||
\(972\) | 4.09402 | 0.131316 | ||||||||
\(973\) | 1.59350 | 0.0510852 | ||||||||
\(974\) | −7.33397 | −0.234995 | ||||||||
\(975\) | 6.19715 | 0.198468 | ||||||||
\(976\) | 0.457926 | 0.0146579 | ||||||||
\(977\) | −26.2588 | −0.840093 | −0.420046 | − | 0.907503i | \(-0.637986\pi\) | ||||
−0.420046 | + | 0.907503i | \(0.637986\pi\) | |||||||
\(978\) | 34.0454 | 1.08865 | ||||||||
\(979\) | 24.5600 | 0.784942 | ||||||||
\(980\) | −6.99118 | −0.223325 | ||||||||
\(981\) | −2.60903 | −0.0833000 | ||||||||
\(982\) | 28.8677 | 0.921204 | ||||||||
\(983\) | 12.5753 | 0.401091 | 0.200545 | − | 0.979684i | \(-0.435729\pi\) | ||||
0.200545 | + | 0.979684i | \(0.435729\pi\) | |||||||
\(984\) | 22.5145 | 0.717735 | ||||||||
\(985\) | −0.175702 | −0.00559834 | ||||||||
\(986\) | 14.8025 | 0.471408 | ||||||||
\(987\) | 1.79985 | 0.0572897 | ||||||||
\(988\) | −20.1129 | −0.639878 | ||||||||
\(989\) | 7.75440 | 0.246576 | ||||||||
\(990\) | −1.35997 | −0.0432226 | ||||||||
\(991\) | 5.72805 | 0.181957 | 0.0909787 | − | 0.995853i | \(-0.471000\pi\) | ||||
0.0909787 | + | 0.995853i | \(0.471000\pi\) | |||||||
\(992\) | −2.23011 | −0.0708062 | ||||||||
\(993\) | 17.0928 | 0.542422 | ||||||||
\(994\) | 0.449724 | 0.0142644 | ||||||||
\(995\) | 5.73441 | 0.181793 | ||||||||
\(996\) | −6.18418 | −0.195953 | ||||||||
\(997\) | −4.25870 | −0.134874 | −0.0674372 | − | 0.997724i | \(-0.521482\pi\) | ||||
−0.0674372 | + | 0.997724i | \(0.521482\pi\) | |||||||
\(998\) | 25.1537 | 0.796226 | ||||||||
\(999\) | 1.82901 | 0.0578672 |
(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 | 4010.2.a.h.1.3 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.h.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial |