Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.24285\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.24285 | 1.58594 | 0.792968 | − | 0.609263i | \(-0.208535\pi\) | ||||
0.792968 | + | 0.609263i | \(0.208535\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.03039 | 1.51519 | ||||||||
\(5\) | 3.33222 | 1.49021 | 0.745107 | − | 0.666945i | \(-0.232398\pi\) | ||||
0.745107 | + | 0.666945i | \(0.232398\pi\) | |||||||
\(6\) | −2.24285 | −0.915641 | ||||||||
\(7\) | 0.336371 | 0.127136 | 0.0635682 | − | 0.997977i | \(-0.479752\pi\) | ||||
0.0635682 | + | 0.997977i | \(0.479752\pi\) | |||||||
\(8\) | 2.31101 | 0.817066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.47368 | 2.36338 | ||||||||
\(11\) | 5.35570 | 1.61480 | 0.807402 | − | 0.590001i | \(-0.200873\pi\) | ||||
0.807402 | + | 0.590001i | \(0.200873\pi\) | |||||||
\(12\) | −3.03039 | −0.874798 | ||||||||
\(13\) | −2.46960 | −0.684944 | −0.342472 | − | 0.939528i | \(-0.611264\pi\) | ||||
−0.342472 | + | 0.939528i | \(0.611264\pi\) | |||||||
\(14\) | 0.754431 | 0.201630 | ||||||||
\(15\) | −3.33222 | −0.860376 | ||||||||
\(16\) | −0.877521 | −0.219380 | ||||||||
\(17\) | 3.61233 | 0.876118 | 0.438059 | − | 0.898946i | \(-0.355666\pi\) | ||||
0.438059 | + | 0.898946i | \(0.355666\pi\) | |||||||
\(18\) | 2.24285 | 0.528645 | ||||||||
\(19\) | −5.53686 | −1.27024 | −0.635121 | − | 0.772413i | \(-0.719050\pi\) | ||||
−0.635121 | + | 0.772413i | \(0.719050\pi\) | |||||||
\(20\) | 10.0979 | 2.25796 | ||||||||
\(21\) | −0.336371 | −0.0734022 | ||||||||
\(22\) | 12.0120 | 2.56098 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.31101 | −0.471733 | ||||||||
\(25\) | 6.10369 | 1.22074 | ||||||||
\(26\) | −5.53895 | −1.08628 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.01934 | 0.192636 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −7.47368 | −1.36450 | ||||||||
\(31\) | 8.47832 | 1.52275 | 0.761376 | − | 0.648311i | \(-0.224524\pi\) | ||||
0.761376 | + | 0.648311i | \(0.224524\pi\) | |||||||
\(32\) | −6.59017 | −1.16499 | ||||||||
\(33\) | −5.35570 | −0.932308 | ||||||||
\(34\) | 8.10192 | 1.38947 | ||||||||
\(35\) | 1.12086 | 0.189460 | ||||||||
\(36\) | 3.03039 | 0.505065 | ||||||||
\(37\) | 9.55887 | 1.57147 | 0.785734 | − | 0.618565i | \(-0.212285\pi\) | ||||
0.785734 | + | 0.618565i | \(0.212285\pi\) | |||||||
\(38\) | −12.4184 | −2.01452 | ||||||||
\(39\) | 2.46960 | 0.395453 | ||||||||
\(40\) | 7.70079 | 1.21760 | ||||||||
\(41\) | −11.0317 | −1.72287 | −0.861434 | − | 0.507870i | \(-0.830433\pi\) | ||||
−0.861434 | + | 0.507870i | \(0.830433\pi\) | |||||||
\(42\) | −0.754431 | −0.116411 | ||||||||
\(43\) | 3.41828 | 0.521282 | 0.260641 | − | 0.965436i | \(-0.416066\pi\) | ||||
0.260641 | + | 0.965436i | \(0.416066\pi\) | |||||||
\(44\) | 16.2299 | 2.44674 | ||||||||
\(45\) | 3.33222 | 0.496738 | ||||||||
\(46\) | 2.24285 | 0.330691 | ||||||||
\(47\) | −9.57079 | −1.39604 | −0.698022 | − | 0.716077i | \(-0.745936\pi\) | ||||
−0.698022 | + | 0.716077i | \(0.745936\pi\) | |||||||
\(48\) | 0.877521 | 0.126659 | ||||||||
\(49\) | −6.88685 | −0.983836 | ||||||||
\(50\) | 13.6897 | 1.93601 | ||||||||
\(51\) | −3.61233 | −0.505827 | ||||||||
\(52\) | −7.48385 | −1.03782 | ||||||||
\(53\) | −6.66459 | −0.915452 | −0.457726 | − | 0.889093i | \(-0.651336\pi\) | ||||
−0.457726 | + | 0.889093i | \(0.651336\pi\) | |||||||
\(54\) | −2.24285 | −0.305214 | ||||||||
\(55\) | 17.8464 | 2.40640 | ||||||||
\(56\) | 0.777358 | 0.103879 | ||||||||
\(57\) | 5.53686 | 0.733375 | ||||||||
\(58\) | −2.24285 | −0.294501 | ||||||||
\(59\) | −1.21308 | −0.157930 | −0.0789650 | − | 0.996877i | \(-0.525162\pi\) | ||||
−0.0789650 | + | 0.996877i | \(0.525162\pi\) | |||||||
\(60\) | −10.0979 | −1.30364 | ||||||||
\(61\) | 7.12445 | 0.912193 | 0.456096 | − | 0.889930i | \(-0.349247\pi\) | ||||
0.456096 | + | 0.889930i | \(0.349247\pi\) | |||||||
\(62\) | 19.0156 | 2.41499 | ||||||||
\(63\) | 0.336371 | 0.0423788 | ||||||||
\(64\) | −13.0257 | −1.62822 | ||||||||
\(65\) | −8.22926 | −1.02071 | ||||||||
\(66\) | −12.0120 | −1.47858 | ||||||||
\(67\) | 5.16723 | 0.631278 | 0.315639 | − | 0.948879i | \(-0.397781\pi\) | ||||
0.315639 | + | 0.948879i | \(0.397781\pi\) | |||||||
\(68\) | 10.9468 | 1.32749 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 2.51393 | 0.300472 | ||||||||
\(71\) | 2.09303 | 0.248397 | 0.124199 | − | 0.992257i | \(-0.460364\pi\) | ||||
0.124199 | + | 0.992257i | \(0.460364\pi\) | |||||||
\(72\) | 2.31101 | 0.272355 | ||||||||
\(73\) | −10.2973 | −1.20520 | −0.602602 | − | 0.798042i | \(-0.705869\pi\) | ||||
−0.602602 | + | 0.798042i | \(0.705869\pi\) | |||||||
\(74\) | 21.4391 | 2.49225 | ||||||||
\(75\) | −6.10369 | −0.704793 | ||||||||
\(76\) | −16.7788 | −1.92466 | ||||||||
\(77\) | 1.80150 | 0.205300 | ||||||||
\(78\) | 5.53895 | 0.627163 | ||||||||
\(79\) | −3.62841 | −0.408229 | −0.204114 | − | 0.978947i | \(-0.565431\pi\) | ||||
−0.204114 | + | 0.978947i | \(0.565431\pi\) | |||||||
\(80\) | −2.92409 | −0.326924 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −24.7426 | −2.73236 | ||||||||
\(83\) | 12.6742 | 1.39117 | 0.695587 | − | 0.718442i | \(-0.255144\pi\) | ||||
0.695587 | + | 0.718442i | \(0.255144\pi\) | |||||||
\(84\) | −1.01934 | −0.111219 | ||||||||
\(85\) | 12.0371 | 1.30560 | ||||||||
\(86\) | 7.66669 | 0.826721 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 12.3771 | 1.31940 | ||||||||
\(89\) | 11.8040 | 1.25122 | 0.625611 | − | 0.780135i | \(-0.284850\pi\) | ||||
0.625611 | + | 0.780135i | \(0.284850\pi\) | |||||||
\(90\) | 7.47368 | 0.787795 | ||||||||
\(91\) | −0.830703 | −0.0870814 | ||||||||
\(92\) | 3.03039 | 0.315940 | ||||||||
\(93\) | −8.47832 | −0.879161 | ||||||||
\(94\) | −21.4659 | −2.21404 | ||||||||
\(95\) | −18.4500 | −1.89293 | ||||||||
\(96\) | 6.59017 | 0.672607 | ||||||||
\(97\) | −3.01739 | −0.306369 | −0.153185 | − | 0.988198i | \(-0.548953\pi\) | ||||
−0.153185 | + | 0.988198i | \(0.548953\pi\) | |||||||
\(98\) | −15.4462 | −1.56030 | ||||||||
\(99\) | 5.35570 | 0.538268 | ||||||||
\(100\) | 18.4966 | 1.84966 | ||||||||
\(101\) | −16.5824 | −1.65001 | −0.825007 | − | 0.565122i | \(-0.808829\pi\) | ||||
−0.825007 | + | 0.565122i | \(0.808829\pi\) | |||||||
\(102\) | −8.10192 | −0.802210 | ||||||||
\(103\) | 6.41290 | 0.631882 | 0.315941 | − | 0.948779i | \(-0.397680\pi\) | ||||
0.315941 | + | 0.948779i | \(0.397680\pi\) | |||||||
\(104\) | −5.70728 | −0.559644 | ||||||||
\(105\) | −1.12086 | −0.109385 | ||||||||
\(106\) | −14.9477 | −1.45185 | ||||||||
\(107\) | 13.1923 | 1.27535 | 0.637673 | − | 0.770307i | \(-0.279897\pi\) | ||||
0.637673 | + | 0.770307i | \(0.279897\pi\) | |||||||
\(108\) | −3.03039 | −0.291599 | ||||||||
\(109\) | −10.5087 | −1.00655 | −0.503274 | − | 0.864127i | \(-0.667871\pi\) | ||||
−0.503274 | + | 0.864127i | \(0.667871\pi\) | |||||||
\(110\) | 40.0268 | 3.81640 | ||||||||
\(111\) | −9.55887 | −0.907287 | ||||||||
\(112\) | −0.295173 | −0.0278912 | ||||||||
\(113\) | 3.10892 | 0.292462 | 0.146231 | − | 0.989250i | \(-0.453286\pi\) | ||||
0.146231 | + | 0.989250i | \(0.453286\pi\) | |||||||
\(114\) | 12.4184 | 1.16309 | ||||||||
\(115\) | 3.33222 | 0.310731 | ||||||||
\(116\) | −3.03039 | −0.281365 | ||||||||
\(117\) | −2.46960 | −0.228315 | ||||||||
\(118\) | −2.72077 | −0.250467 | ||||||||
\(119\) | 1.21508 | 0.111387 | ||||||||
\(120\) | −7.70079 | −0.702983 | ||||||||
\(121\) | 17.6835 | 1.60759 | ||||||||
\(122\) | 15.9791 | 1.44668 | ||||||||
\(123\) | 11.0317 | 0.994698 | ||||||||
\(124\) | 25.6926 | 2.30726 | ||||||||
\(125\) | 3.67774 | 0.328947 | ||||||||
\(126\) | 0.754431 | 0.0672101 | ||||||||
\(127\) | 14.8180 | 1.31489 | 0.657443 | − | 0.753504i | \(-0.271638\pi\) | ||||
0.657443 | + | 0.753504i | \(0.271638\pi\) | |||||||
\(128\) | −16.0345 | −1.41726 | ||||||||
\(129\) | −3.41828 | −0.300963 | ||||||||
\(130\) | −18.4570 | −1.61879 | ||||||||
\(131\) | 2.63363 | 0.230102 | 0.115051 | − | 0.993360i | \(-0.463297\pi\) | ||||
0.115051 | + | 0.993360i | \(0.463297\pi\) | |||||||
\(132\) | −16.2299 | −1.41263 | ||||||||
\(133\) | −1.86244 | −0.161494 | ||||||||
\(134\) | 11.5893 | 1.00117 | ||||||||
\(135\) | −3.33222 | −0.286792 | ||||||||
\(136\) | 8.34813 | 0.715846 | ||||||||
\(137\) | −11.2822 | −0.963901 | −0.481951 | − | 0.876198i | \(-0.660072\pi\) | ||||
−0.481951 | + | 0.876198i | \(0.660072\pi\) | |||||||
\(138\) | −2.24285 | −0.190924 | ||||||||
\(139\) | 3.55731 | 0.301727 | 0.150863 | − | 0.988555i | \(-0.451795\pi\) | ||||
0.150863 | + | 0.988555i | \(0.451795\pi\) | |||||||
\(140\) | 3.39665 | 0.287069 | ||||||||
\(141\) | 9.57079 | 0.806006 | ||||||||
\(142\) | 4.69437 | 0.393942 | ||||||||
\(143\) | −13.2264 | −1.10605 | ||||||||
\(144\) | −0.877521 | −0.0731268 | ||||||||
\(145\) | −3.33222 | −0.276726 | ||||||||
\(146\) | −23.0952 | −1.91138 | ||||||||
\(147\) | 6.88685 | 0.568018 | ||||||||
\(148\) | 28.9671 | 2.38108 | ||||||||
\(149\) | 14.5948 | 1.19565 | 0.597827 | − | 0.801625i | \(-0.296031\pi\) | ||||
0.597827 | + | 0.801625i | \(0.296031\pi\) | |||||||
\(150\) | −13.6897 | −1.11776 | ||||||||
\(151\) | 18.5847 | 1.51240 | 0.756202 | − | 0.654338i | \(-0.227053\pi\) | ||||
0.756202 | + | 0.654338i | \(0.227053\pi\) | |||||||
\(152\) | −12.7957 | −1.03787 | ||||||||
\(153\) | 3.61233 | 0.292039 | ||||||||
\(154\) | 4.04051 | 0.325593 | ||||||||
\(155\) | 28.2516 | 2.26923 | ||||||||
\(156\) | 7.48385 | 0.599188 | ||||||||
\(157\) | −9.26130 | −0.739132 | −0.369566 | − | 0.929204i | \(-0.620494\pi\) | ||||
−0.369566 | + | 0.929204i | \(0.620494\pi\) | |||||||
\(158\) | −8.13800 | −0.647425 | ||||||||
\(159\) | 6.66459 | 0.528536 | ||||||||
\(160\) | −21.9599 | −1.73608 | ||||||||
\(161\) | 0.336371 | 0.0265098 | ||||||||
\(162\) | 2.24285 | 0.176215 | ||||||||
\(163\) | −21.2102 | −1.66131 | −0.830655 | − | 0.556788i | \(-0.812034\pi\) | ||||
−0.830655 | + | 0.556788i | \(0.812034\pi\) | |||||||
\(164\) | −33.4304 | −2.61048 | ||||||||
\(165\) | −17.8464 | −1.38934 | ||||||||
\(166\) | 28.4264 | 2.20631 | ||||||||
\(167\) | −21.3627 | −1.65310 | −0.826549 | − | 0.562865i | \(-0.809699\pi\) | ||||
−0.826549 | + | 0.562865i | \(0.809699\pi\) | |||||||
\(168\) | −0.777358 | −0.0599744 | ||||||||
\(169\) | −6.90107 | −0.530851 | ||||||||
\(170\) | 26.9974 | 2.07060 | ||||||||
\(171\) | −5.53686 | −0.423414 | ||||||||
\(172\) | 10.3587 | 0.789844 | ||||||||
\(173\) | −10.6746 | −0.811578 | −0.405789 | − | 0.913967i | \(-0.633003\pi\) | ||||
−0.405789 | + | 0.913967i | \(0.633003\pi\) | |||||||
\(174\) | 2.24285 | 0.170030 | ||||||||
\(175\) | 2.05311 | 0.155200 | ||||||||
\(176\) | −4.69974 | −0.354256 | ||||||||
\(177\) | 1.21308 | 0.0911810 | ||||||||
\(178\) | 26.4746 | 1.98436 | ||||||||
\(179\) | −2.48471 | −0.185716 | −0.0928579 | − | 0.995679i | \(-0.529600\pi\) | ||||
−0.0928579 | + | 0.995679i | \(0.529600\pi\) | |||||||
\(180\) | 10.0979 | 0.752655 | ||||||||
\(181\) | −10.3160 | −0.766784 | −0.383392 | − | 0.923586i | \(-0.625244\pi\) | ||||
−0.383392 | + | 0.923586i | \(0.625244\pi\) | |||||||
\(182\) | −1.86315 | −0.138106 | ||||||||
\(183\) | −7.12445 | −0.526655 | ||||||||
\(184\) | 2.31101 | 0.170370 | ||||||||
\(185\) | 31.8522 | 2.34182 | ||||||||
\(186\) | −19.0156 | −1.39429 | ||||||||
\(187\) | 19.3466 | 1.41476 | ||||||||
\(188\) | −29.0032 | −2.11528 | ||||||||
\(189\) | −0.336371 | −0.0244674 | ||||||||
\(190\) | −41.3807 | −3.00207 | ||||||||
\(191\) | −21.4183 | −1.54977 | −0.774886 | − | 0.632101i | \(-0.782193\pi\) | ||||
−0.774886 | + | 0.632101i | \(0.782193\pi\) | |||||||
\(192\) | 13.0257 | 0.940052 | ||||||||
\(193\) | −13.7870 | −0.992409 | −0.496204 | − | 0.868206i | \(-0.665273\pi\) | ||||
−0.496204 | + | 0.868206i | \(0.665273\pi\) | |||||||
\(194\) | −6.76756 | −0.485882 | ||||||||
\(195\) | 8.22926 | 0.589309 | ||||||||
\(196\) | −20.8698 | −1.49070 | ||||||||
\(197\) | −15.4879 | −1.10347 | −0.551735 | − | 0.834019i | \(-0.686034\pi\) | ||||
−0.551735 | + | 0.834019i | \(0.686034\pi\) | |||||||
\(198\) | 12.0120 | 0.853659 | ||||||||
\(199\) | 4.97074 | 0.352367 | 0.176183 | − | 0.984357i | \(-0.443625\pi\) | ||||
0.176183 | + | 0.984357i | \(0.443625\pi\) | |||||||
\(200\) | 14.1057 | 0.997423 | ||||||||
\(201\) | −5.16723 | −0.364468 | ||||||||
\(202\) | −37.1920 | −2.61682 | ||||||||
\(203\) | −0.336371 | −0.0236086 | ||||||||
\(204\) | −10.9468 | −0.766427 | ||||||||
\(205\) | −36.7602 | −2.56744 | ||||||||
\(206\) | 14.3832 | 1.00212 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 2.16713 | 0.150263 | ||||||||
\(209\) | −29.6537 | −2.05119 | ||||||||
\(210\) | −2.51393 | −0.173478 | ||||||||
\(211\) | −26.1099 | −1.79748 | −0.898739 | − | 0.438484i | \(-0.855516\pi\) | ||||
−0.898739 | + | 0.438484i | \(0.855516\pi\) | |||||||
\(212\) | −20.1963 | −1.38709 | ||||||||
\(213\) | −2.09303 | −0.143412 | ||||||||
\(214\) | 29.5883 | 2.02262 | ||||||||
\(215\) | 11.3905 | 0.776823 | ||||||||
\(216\) | −2.31101 | −0.157244 | ||||||||
\(217\) | 2.85186 | 0.193597 | ||||||||
\(218\) | −23.5694 | −1.59632 | ||||||||
\(219\) | 10.2973 | 0.695824 | ||||||||
\(220\) | 54.0814 | 3.64617 | ||||||||
\(221\) | −8.92101 | −0.600092 | ||||||||
\(222\) | −21.4391 | −1.43890 | ||||||||
\(223\) | −8.28206 | −0.554608 | −0.277304 | − | 0.960782i | \(-0.589441\pi\) | ||||
−0.277304 | + | 0.960782i | \(0.589441\pi\) | |||||||
\(224\) | −2.21675 | −0.148113 | ||||||||
\(225\) | 6.10369 | 0.406913 | ||||||||
\(226\) | 6.97284 | 0.463826 | ||||||||
\(227\) | −15.0362 | −0.997985 | −0.498992 | − | 0.866606i | \(-0.666296\pi\) | ||||
−0.498992 | + | 0.866606i | \(0.666296\pi\) | |||||||
\(228\) | 16.7788 | 1.11121 | ||||||||
\(229\) | −9.35622 | −0.618277 | −0.309138 | − | 0.951017i | \(-0.600041\pi\) | ||||
−0.309138 | + | 0.951017i | \(0.600041\pi\) | |||||||
\(230\) | 7.47368 | 0.492800 | ||||||||
\(231\) | −1.80150 | −0.118530 | ||||||||
\(232\) | −2.31101 | −0.151725 | ||||||||
\(233\) | 1.51916 | 0.0995233 | 0.0497616 | − | 0.998761i | \(-0.484154\pi\) | ||||
0.0497616 | + | 0.998761i | \(0.484154\pi\) | |||||||
\(234\) | −5.53895 | −0.362093 | ||||||||
\(235\) | −31.8920 | −2.08040 | ||||||||
\(236\) | −3.67612 | −0.239295 | ||||||||
\(237\) | 3.62841 | 0.235691 | ||||||||
\(238\) | 2.72525 | 0.176652 | ||||||||
\(239\) | −13.1287 | −0.849225 | −0.424612 | − | 0.905375i | \(-0.639590\pi\) | ||||
−0.424612 | + | 0.905375i | \(0.639590\pi\) | |||||||
\(240\) | 2.92409 | 0.188749 | ||||||||
\(241\) | 26.0253 | 1.67644 | 0.838218 | − | 0.545335i | \(-0.183598\pi\) | ||||
0.838218 | + | 0.545335i | \(0.183598\pi\) | |||||||
\(242\) | 39.6616 | 2.54954 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 21.5899 | 1.38215 | ||||||||
\(245\) | −22.9485 | −1.46613 | ||||||||
\(246\) | 24.7426 | 1.57753 | ||||||||
\(247\) | 13.6738 | 0.870045 | ||||||||
\(248\) | 19.5935 | 1.24419 | ||||||||
\(249\) | −12.6742 | −0.803195 | ||||||||
\(250\) | 8.24863 | 0.521689 | ||||||||
\(251\) | 24.1425 | 1.52386 | 0.761932 | − | 0.647657i | \(-0.224251\pi\) | ||||
0.761932 | + | 0.647657i | \(0.224251\pi\) | |||||||
\(252\) | 1.01934 | 0.0642121 | ||||||||
\(253\) | 5.35570 | 0.336710 | ||||||||
\(254\) | 33.2346 | 2.08533 | ||||||||
\(255\) | −12.0371 | −0.753791 | ||||||||
\(256\) | −9.91149 | −0.619468 | ||||||||
\(257\) | 23.1679 | 1.44518 | 0.722588 | − | 0.691279i | \(-0.242952\pi\) | ||||
0.722588 | + | 0.691279i | \(0.242952\pi\) | |||||||
\(258\) | −7.66669 | −0.477308 | ||||||||
\(259\) | 3.21533 | 0.199791 | ||||||||
\(260\) | −24.9378 | −1.54658 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 5.90685 | 0.364927 | ||||||||
\(263\) | 11.8107 | 0.728277 | 0.364138 | − | 0.931345i | \(-0.381364\pi\) | ||||
0.364138 | + | 0.931345i | \(0.381364\pi\) | |||||||
\(264\) | −12.3771 | −0.761757 | ||||||||
\(265\) | −22.2079 | −1.36422 | ||||||||
\(266\) | −4.17718 | −0.256119 | ||||||||
\(267\) | −11.8040 | −0.722393 | ||||||||
\(268\) | 15.6587 | 0.956508 | ||||||||
\(269\) | −8.58123 | −0.523207 | −0.261603 | − | 0.965175i | \(-0.584251\pi\) | ||||
−0.261603 | + | 0.965175i | \(0.584251\pi\) | |||||||
\(270\) | −7.47368 | −0.454834 | ||||||||
\(271\) | −11.0288 | −0.669952 | −0.334976 | − | 0.942227i | \(-0.608728\pi\) | ||||
−0.334976 | + | 0.942227i | \(0.608728\pi\) | |||||||
\(272\) | −3.16990 | −0.192203 | ||||||||
\(273\) | 0.830703 | 0.0502764 | ||||||||
\(274\) | −25.3043 | −1.52869 | ||||||||
\(275\) | 32.6895 | 1.97125 | ||||||||
\(276\) | −3.03039 | −0.182408 | ||||||||
\(277\) | 9.78001 | 0.587624 | 0.293812 | − | 0.955863i | \(-0.405076\pi\) | ||||
0.293812 | + | 0.955863i | \(0.405076\pi\) | |||||||
\(278\) | 7.97851 | 0.478520 | ||||||||
\(279\) | 8.47832 | 0.507584 | ||||||||
\(280\) | 2.59033 | 0.154802 | ||||||||
\(281\) | −2.79284 | −0.166607 | −0.0833034 | − | 0.996524i | \(-0.526547\pi\) | ||||
−0.0833034 | + | 0.996524i | \(0.526547\pi\) | |||||||
\(282\) | 21.4659 | 1.27827 | ||||||||
\(283\) | −22.6337 | −1.34544 | −0.672718 | − | 0.739899i | \(-0.734873\pi\) | ||||
−0.672718 | + | 0.739899i | \(0.734873\pi\) | |||||||
\(284\) | 6.34270 | 0.376370 | ||||||||
\(285\) | 18.4500 | 1.09289 | ||||||||
\(286\) | −29.6650 | −1.75413 | ||||||||
\(287\) | −3.71076 | −0.219039 | ||||||||
\(288\) | −6.59017 | −0.388330 | ||||||||
\(289\) | −3.95108 | −0.232417 | ||||||||
\(290\) | −7.47368 | −0.438870 | ||||||||
\(291\) | 3.01739 | 0.176882 | ||||||||
\(292\) | −31.2047 | −1.82612 | ||||||||
\(293\) | 26.9534 | 1.57463 | 0.787316 | − | 0.616550i | \(-0.211470\pi\) | ||||
0.787316 | + | 0.616550i | \(0.211470\pi\) | |||||||
\(294\) | 15.4462 | 0.900841 | ||||||||
\(295\) | −4.04226 | −0.235350 | ||||||||
\(296\) | 22.0906 | 1.28399 | ||||||||
\(297\) | −5.35570 | −0.310769 | ||||||||
\(298\) | 32.7340 | 1.89623 | ||||||||
\(299\) | −2.46960 | −0.142821 | ||||||||
\(300\) | −18.4966 | −1.06790 | ||||||||
\(301\) | 1.14981 | 0.0662740 | ||||||||
\(302\) | 41.6828 | 2.39858 | ||||||||
\(303\) | 16.5824 | 0.952636 | ||||||||
\(304\) | 4.85871 | 0.278666 | ||||||||
\(305\) | 23.7402 | 1.35936 | ||||||||
\(306\) | 8.10192 | 0.463156 | ||||||||
\(307\) | 10.5081 | 0.599727 | 0.299863 | − | 0.953982i | \(-0.403059\pi\) | ||||
0.299863 | + | 0.953982i | \(0.403059\pi\) | |||||||
\(308\) | 5.45926 | 0.311070 | ||||||||
\(309\) | −6.41290 | −0.364817 | ||||||||
\(310\) | 63.3643 | 3.59885 | ||||||||
\(311\) | 31.8702 | 1.80719 | 0.903596 | − | 0.428385i | \(-0.140917\pi\) | ||||
0.903596 | + | 0.428385i | \(0.140917\pi\) | |||||||
\(312\) | 5.70728 | 0.323111 | ||||||||
\(313\) | −21.3092 | −1.20446 | −0.602232 | − | 0.798321i | \(-0.705722\pi\) | ||||
−0.602232 | + | 0.798321i | \(0.705722\pi\) | |||||||
\(314\) | −20.7717 | −1.17222 | ||||||||
\(315\) | 1.12086 | 0.0631535 | ||||||||
\(316\) | −10.9955 | −0.618546 | ||||||||
\(317\) | 13.6193 | 0.764935 | 0.382467 | − | 0.923969i | \(-0.375074\pi\) | ||||
0.382467 | + | 0.923969i | \(0.375074\pi\) | |||||||
\(318\) | 14.9477 | 0.838225 | ||||||||
\(319\) | −5.35570 | −0.299862 | ||||||||
\(320\) | −43.4046 | −2.42639 | ||||||||
\(321\) | −13.1923 | −0.736321 | ||||||||
\(322\) | 0.754431 | 0.0420428 | ||||||||
\(323\) | −20.0009 | −1.11288 | ||||||||
\(324\) | 3.03039 | 0.168355 | ||||||||
\(325\) | −15.0737 | −0.836138 | ||||||||
\(326\) | −47.5713 | −2.63473 | ||||||||
\(327\) | 10.5087 | 0.581131 | ||||||||
\(328\) | −25.4945 | −1.40770 | ||||||||
\(329\) | −3.21934 | −0.177488 | ||||||||
\(330\) | −40.0268 | −2.20340 | ||||||||
\(331\) | −8.92149 | −0.490370 | −0.245185 | − | 0.969476i | \(-0.578849\pi\) | ||||
−0.245185 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(332\) | 38.4078 | 2.10790 | ||||||||
\(333\) | 9.55887 | 0.523823 | ||||||||
\(334\) | −47.9135 | −2.62171 | ||||||||
\(335\) | 17.2183 | 0.940739 | ||||||||
\(336\) | 0.295173 | 0.0161030 | ||||||||
\(337\) | 6.68953 | 0.364402 | 0.182201 | − | 0.983261i | \(-0.441678\pi\) | ||||
0.182201 | + | 0.983261i | \(0.441678\pi\) | |||||||
\(338\) | −15.4781 | −0.841896 | ||||||||
\(339\) | −3.10892 | −0.168853 | ||||||||
\(340\) | 36.4770 | 1.97824 | ||||||||
\(341\) | 45.4074 | 2.45895 | ||||||||
\(342\) | −12.4184 | −0.671508 | ||||||||
\(343\) | −4.67114 | −0.252218 | ||||||||
\(344\) | 7.89968 | 0.425922 | ||||||||
\(345\) | −3.33222 | −0.179401 | ||||||||
\(346\) | −23.9416 | −1.28711 | ||||||||
\(347\) | −10.4807 | −0.562635 | −0.281317 | − | 0.959615i | \(-0.590771\pi\) | ||||
−0.281317 | + | 0.959615i | \(0.590771\pi\) | |||||||
\(348\) | 3.03039 | 0.162446 | ||||||||
\(349\) | −21.7281 | −1.16308 | −0.581538 | − | 0.813519i | \(-0.697549\pi\) | ||||
−0.581538 | + | 0.813519i | \(0.697549\pi\) | |||||||
\(350\) | 4.60482 | 0.246138 | ||||||||
\(351\) | 2.46960 | 0.131818 | ||||||||
\(352\) | −35.2950 | −1.88123 | ||||||||
\(353\) | −24.6326 | −1.31106 | −0.655530 | − | 0.755169i | \(-0.727555\pi\) | ||||
−0.655530 | + | 0.755169i | \(0.727555\pi\) | |||||||
\(354\) | 2.72077 | 0.144607 | ||||||||
\(355\) | 6.97445 | 0.370165 | ||||||||
\(356\) | 35.7707 | 1.89584 | ||||||||
\(357\) | −1.21508 | −0.0643091 | ||||||||
\(358\) | −5.57284 | −0.294534 | ||||||||
\(359\) | −5.00818 | −0.264322 | −0.132161 | − | 0.991228i | \(-0.542192\pi\) | ||||
−0.132161 | + | 0.991228i | \(0.542192\pi\) | |||||||
\(360\) | 7.70079 | 0.405868 | ||||||||
\(361\) | 11.6568 | 0.613515 | ||||||||
\(362\) | −23.1373 | −1.21607 | ||||||||
\(363\) | −17.6835 | −0.928145 | ||||||||
\(364\) | −2.51735 | −0.131945 | ||||||||
\(365\) | −34.3127 | −1.79601 | ||||||||
\(366\) | −15.9791 | −0.835241 | ||||||||
\(367\) | −5.98074 | −0.312192 | −0.156096 | − | 0.987742i | \(-0.549891\pi\) | ||||
−0.156096 | + | 0.987742i | \(0.549891\pi\) | |||||||
\(368\) | −0.877521 | −0.0457440 | ||||||||
\(369\) | −11.0317 | −0.574289 | ||||||||
\(370\) | 71.4399 | 3.71398 | ||||||||
\(371\) | −2.24178 | −0.116387 | ||||||||
\(372\) | −25.6926 | −1.33210 | ||||||||
\(373\) | 25.9060 | 1.34136 | 0.670680 | − | 0.741747i | \(-0.266002\pi\) | ||||
0.670680 | + | 0.741747i | \(0.266002\pi\) | |||||||
\(374\) | 43.3915 | 2.24372 | ||||||||
\(375\) | −3.67774 | −0.189918 | ||||||||
\(376\) | −22.1182 | −1.14066 | ||||||||
\(377\) | 2.46960 | 0.127191 | ||||||||
\(378\) | −0.754431 | −0.0388038 | ||||||||
\(379\) | 34.7368 | 1.78431 | 0.892155 | − | 0.451729i | \(-0.149193\pi\) | ||||
0.892155 | + | 0.451729i | \(0.149193\pi\) | |||||||
\(380\) | −55.9107 | −2.86816 | ||||||||
\(381\) | −14.8180 | −0.759150 | ||||||||
\(382\) | −48.0380 | −2.45784 | ||||||||
\(383\) | −22.0435 | −1.12637 | −0.563184 | − | 0.826331i | \(-0.690424\pi\) | ||||
−0.563184 | + | 0.826331i | \(0.690424\pi\) | |||||||
\(384\) | 16.0345 | 0.818256 | ||||||||
\(385\) | 6.00301 | 0.305942 | ||||||||
\(386\) | −30.9222 | −1.57390 | ||||||||
\(387\) | 3.41828 | 0.173761 | ||||||||
\(388\) | −9.14386 | −0.464209 | ||||||||
\(389\) | −10.7238 | −0.543716 | −0.271858 | − | 0.962337i | \(-0.587638\pi\) | ||||
−0.271858 | + | 0.962337i | \(0.587638\pi\) | |||||||
\(390\) | 18.4570 | 0.934607 | ||||||||
\(391\) | 3.61233 | 0.182683 | ||||||||
\(392\) | −15.9156 | −0.803859 | ||||||||
\(393\) | −2.63363 | −0.132849 | ||||||||
\(394\) | −34.7372 | −1.75003 | ||||||||
\(395\) | −12.0907 | −0.608348 | ||||||||
\(396\) | 16.2299 | 0.815581 | ||||||||
\(397\) | −7.85754 | −0.394358 | −0.197179 | − | 0.980367i | \(-0.563178\pi\) | ||||
−0.197179 | + | 0.980367i | \(0.563178\pi\) | |||||||
\(398\) | 11.1486 | 0.558831 | ||||||||
\(399\) | 1.86244 | 0.0932386 | ||||||||
\(400\) | −5.35612 | −0.267806 | ||||||||
\(401\) | 15.0606 | 0.752089 | 0.376044 | − | 0.926602i | \(-0.377284\pi\) | ||||
0.376044 | + | 0.926602i | \(0.377284\pi\) | |||||||
\(402\) | −11.5893 | −0.578023 | ||||||||
\(403\) | −20.9381 | −1.04300 | ||||||||
\(404\) | −50.2512 | −2.50009 | ||||||||
\(405\) | 3.33222 | 0.165579 | ||||||||
\(406\) | −0.754431 | −0.0374418 | ||||||||
\(407\) | 51.1944 | 2.53761 | ||||||||
\(408\) | −8.34813 | −0.413294 | ||||||||
\(409\) | 29.3347 | 1.45051 | 0.725253 | − | 0.688483i | \(-0.241723\pi\) | ||||
0.725253 | + | 0.688483i | \(0.241723\pi\) | |||||||
\(410\) | −82.4476 | −4.07180 | ||||||||
\(411\) | 11.2822 | 0.556509 | ||||||||
\(412\) | 19.4336 | 0.957424 | ||||||||
\(413\) | −0.408047 | −0.0200787 | ||||||||
\(414\) | 2.24285 | 0.110230 | ||||||||
\(415\) | 42.2332 | 2.07315 | ||||||||
\(416\) | 16.2751 | 0.797952 | ||||||||
\(417\) | −3.55731 | −0.174202 | ||||||||
\(418\) | −66.5090 | −3.25306 | ||||||||
\(419\) | −28.4982 | −1.39223 | −0.696114 | − | 0.717931i | \(-0.745089\pi\) | ||||
−0.696114 | + | 0.717931i | \(0.745089\pi\) | |||||||
\(420\) | −3.39665 | −0.165740 | ||||||||
\(421\) | 13.1838 | 0.642540 | 0.321270 | − | 0.946988i | \(-0.395890\pi\) | ||||
0.321270 | + | 0.946988i | \(0.395890\pi\) | |||||||
\(422\) | −58.5606 | −2.85069 | ||||||||
\(423\) | −9.57079 | −0.465348 | ||||||||
\(424\) | −15.4019 | −0.747984 | ||||||||
\(425\) | 22.0485 | 1.06951 | ||||||||
\(426\) | −4.69437 | −0.227443 | ||||||||
\(427\) | 2.39646 | 0.115973 | ||||||||
\(428\) | 39.9777 | 1.93240 | ||||||||
\(429\) | 13.2264 | 0.638579 | ||||||||
\(430\) | 25.5471 | 1.23199 | ||||||||
\(431\) | 21.0595 | 1.01440 | 0.507200 | − | 0.861829i | \(-0.330681\pi\) | ||||
0.507200 | + | 0.861829i | \(0.330681\pi\) | |||||||
\(432\) | 0.877521 | 0.0422198 | ||||||||
\(433\) | −29.6426 | −1.42453 | −0.712267 | − | 0.701909i | \(-0.752331\pi\) | ||||
−0.712267 | + | 0.701909i | \(0.752331\pi\) | |||||||
\(434\) | 6.39631 | 0.307033 | ||||||||
\(435\) | 3.33222 | 0.159768 | ||||||||
\(436\) | −31.8454 | −1.52512 | ||||||||
\(437\) | −5.53686 | −0.264864 | ||||||||
\(438\) | 23.0952 | 1.10353 | ||||||||
\(439\) | 18.1064 | 0.864171 | 0.432086 | − | 0.901833i | \(-0.357778\pi\) | ||||
0.432086 | + | 0.901833i | \(0.357778\pi\) | |||||||
\(440\) | 41.2432 | 1.96619 | ||||||||
\(441\) | −6.88685 | −0.327945 | ||||||||
\(442\) | −20.0085 | −0.951708 | ||||||||
\(443\) | 20.7008 | 0.983527 | 0.491763 | − | 0.870729i | \(-0.336353\pi\) | ||||
0.491763 | + | 0.870729i | \(0.336353\pi\) | |||||||
\(444\) | −28.9671 | −1.37472 | ||||||||
\(445\) | 39.3335 | 1.86459 | ||||||||
\(446\) | −18.5754 | −0.879573 | ||||||||
\(447\) | −14.5948 | −0.690311 | ||||||||
\(448\) | −4.38149 | −0.207006 | ||||||||
\(449\) | −13.6101 | −0.642301 | −0.321150 | − | 0.947028i | \(-0.604069\pi\) | ||||
−0.321150 | + | 0.947028i | \(0.604069\pi\) | |||||||
\(450\) | 13.6897 | 0.645338 | ||||||||
\(451\) | −59.0827 | −2.78209 | ||||||||
\(452\) | 9.42122 | 0.443137 | ||||||||
\(453\) | −18.5847 | −0.873187 | ||||||||
\(454\) | −33.7239 | −1.58274 | ||||||||
\(455\) | −2.76809 | −0.129770 | ||||||||
\(456\) | 12.7957 | 0.599215 | ||||||||
\(457\) | 4.36067 | 0.203984 | 0.101992 | − | 0.994785i | \(-0.467478\pi\) | ||||
0.101992 | + | 0.994785i | \(0.467478\pi\) | |||||||
\(458\) | −20.9846 | −0.980548 | ||||||||
\(459\) | −3.61233 | −0.168609 | ||||||||
\(460\) | 10.0979 | 0.470818 | ||||||||
\(461\) | 1.61989 | 0.0754459 | 0.0377230 | − | 0.999288i | \(-0.487990\pi\) | ||||
0.0377230 | + | 0.999288i | \(0.487990\pi\) | |||||||
\(462\) | −4.04051 | −0.187981 | ||||||||
\(463\) | −0.152373 | −0.00708136 | −0.00354068 | − | 0.999994i | \(-0.501127\pi\) | ||||
−0.00354068 | + | 0.999994i | \(0.501127\pi\) | |||||||
\(464\) | 0.877521 | 0.0407379 | ||||||||
\(465\) | −28.2516 | −1.31014 | ||||||||
\(466\) | 3.40725 | 0.157838 | ||||||||
\(467\) | 25.7057 | 1.18952 | 0.594758 | − | 0.803904i | \(-0.297248\pi\) | ||||
0.594758 | + | 0.803904i | \(0.297248\pi\) | |||||||
\(468\) | −7.48385 | −0.345941 | ||||||||
\(469\) | 1.73811 | 0.0802584 | ||||||||
\(470\) | −71.5290 | −3.29939 | ||||||||
\(471\) | 9.26130 | 0.426738 | ||||||||
\(472\) | −2.80345 | −0.129039 | ||||||||
\(473\) | 18.3073 | 0.841769 | ||||||||
\(474\) | 8.13800 | 0.373791 | ||||||||
\(475\) | −33.7953 | −1.55063 | ||||||||
\(476\) | 3.68218 | 0.168772 | ||||||||
\(477\) | −6.66459 | −0.305151 | ||||||||
\(478\) | −29.4457 | −1.34682 | ||||||||
\(479\) | 5.89195 | 0.269210 | 0.134605 | − | 0.990899i | \(-0.457023\pi\) | ||||
0.134605 | + | 0.990899i | \(0.457023\pi\) | |||||||
\(480\) | 21.9599 | 1.00233 | ||||||||
\(481\) | −23.6066 | −1.07637 | ||||||||
\(482\) | 58.3709 | 2.65872 | ||||||||
\(483\) | −0.336371 | −0.0153054 | ||||||||
\(484\) | 53.5880 | 2.43582 | ||||||||
\(485\) | −10.0546 | −0.456556 | ||||||||
\(486\) | −2.24285 | −0.101738 | ||||||||
\(487\) | −31.3733 | −1.42166 | −0.710831 | − | 0.703363i | \(-0.751681\pi\) | ||||
−0.710831 | + | 0.703363i | \(0.751681\pi\) | |||||||
\(488\) | 16.4647 | 0.745321 | ||||||||
\(489\) | 21.2102 | 0.959158 | ||||||||
\(490\) | −51.4701 | −2.32518 | ||||||||
\(491\) | 2.87963 | 0.129956 | 0.0649778 | − | 0.997887i | \(-0.479302\pi\) | ||||
0.0649778 | + | 0.997887i | \(0.479302\pi\) | |||||||
\(492\) | 33.4304 | 1.50716 | ||||||||
\(493\) | −3.61233 | −0.162691 | ||||||||
\(494\) | 30.6684 | 1.37984 | ||||||||
\(495\) | 17.8464 | 0.802135 | ||||||||
\(496\) | −7.43991 | −0.334062 | ||||||||
\(497\) | 0.704036 | 0.0315804 | ||||||||
\(498\) | −28.4264 | −1.27382 | ||||||||
\(499\) | 43.8494 | 1.96297 | 0.981484 | − | 0.191542i | \(-0.0613489\pi\) | ||||
0.981484 | + | 0.191542i | \(0.0613489\pi\) | |||||||
\(500\) | 11.1450 | 0.498419 | ||||||||
\(501\) | 21.3627 | 0.954416 | ||||||||
\(502\) | 54.1482 | 2.41675 | ||||||||
\(503\) | −41.9172 | −1.86900 | −0.934498 | − | 0.355969i | \(-0.884151\pi\) | ||||
−0.934498 | + | 0.355969i | \(0.884151\pi\) | |||||||
\(504\) | 0.777358 | 0.0346263 | ||||||||
\(505\) | −55.2563 | −2.45887 | ||||||||
\(506\) | 12.0120 | 0.534001 | ||||||||
\(507\) | 6.90107 | 0.306487 | ||||||||
\(508\) | 44.9044 | 1.99231 | ||||||||
\(509\) | −15.4761 | −0.685966 | −0.342983 | − | 0.939342i | \(-0.611437\pi\) | ||||
−0.342983 | + | 0.939342i | \(0.611437\pi\) | |||||||
\(510\) | −26.9974 | −1.19546 | ||||||||
\(511\) | −3.46370 | −0.153225 | ||||||||
\(512\) | 9.83894 | 0.434824 | ||||||||
\(513\) | 5.53686 | 0.244458 | ||||||||
\(514\) | 51.9623 | 2.29196 | ||||||||
\(515\) | 21.3692 | 0.941640 | ||||||||
\(516\) | −10.3587 | −0.456017 | ||||||||
\(517\) | −51.2583 | −2.25434 | ||||||||
\(518\) | 7.21151 | 0.316856 | ||||||||
\(519\) | 10.6746 | 0.468565 | ||||||||
\(520\) | −19.0179 | −0.833990 | ||||||||
\(521\) | 1.20679 | 0.0528705 | 0.0264352 | − | 0.999651i | \(-0.491584\pi\) | ||||
0.0264352 | + | 0.999651i | \(0.491584\pi\) | |||||||
\(522\) | −2.24285 | −0.0981670 | ||||||||
\(523\) | −8.84819 | −0.386905 | −0.193452 | − | 0.981110i | \(-0.561968\pi\) | ||||
−0.193452 | + | 0.981110i | \(0.561968\pi\) | |||||||
\(524\) | 7.98094 | 0.348649 | ||||||||
\(525\) | −2.05311 | −0.0896049 | ||||||||
\(526\) | 26.4896 | 1.15500 | ||||||||
\(527\) | 30.6265 | 1.33411 | ||||||||
\(528\) | 4.69974 | 0.204530 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −49.8090 | −2.16357 | ||||||||
\(531\) | −1.21308 | −0.0526434 | ||||||||
\(532\) | −5.64392 | −0.244695 | ||||||||
\(533\) | 27.2440 | 1.18007 | ||||||||
\(534\) | −26.4746 | −1.14567 | ||||||||
\(535\) | 43.9596 | 1.90054 | ||||||||
\(536\) | 11.9415 | 0.515795 | ||||||||
\(537\) | 2.48471 | 0.107223 | ||||||||
\(538\) | −19.2464 | −0.829772 | ||||||||
\(539\) | −36.8839 | −1.58870 | ||||||||
\(540\) | −10.0979 | −0.434545 | ||||||||
\(541\) | 22.1794 | 0.953567 | 0.476783 | − | 0.879021i | \(-0.341803\pi\) | ||||
0.476783 | + | 0.879021i | \(0.341803\pi\) | |||||||
\(542\) | −24.7360 | −1.06250 | ||||||||
\(543\) | 10.3160 | 0.442703 | ||||||||
\(544\) | −23.8059 | −1.02067 | ||||||||
\(545\) | −35.0172 | −1.49997 | ||||||||
\(546\) | 1.86315 | 0.0797353 | ||||||||
\(547\) | 22.7728 | 0.973697 | 0.486848 | − | 0.873486i | \(-0.338146\pi\) | ||||
0.486848 | + | 0.873486i | \(0.338146\pi\) | |||||||
\(548\) | −34.1894 | −1.46050 | ||||||||
\(549\) | 7.12445 | 0.304064 | ||||||||
\(550\) | 73.3178 | 3.12628 | ||||||||
\(551\) | 5.53686 | 0.235878 | ||||||||
\(552\) | −2.31101 | −0.0983631 | ||||||||
\(553\) | −1.22049 | −0.0519007 | ||||||||
\(554\) | 21.9351 | 0.931934 | ||||||||
\(555\) | −31.8522 | −1.35205 | ||||||||
\(556\) | 10.7800 | 0.457175 | ||||||||
\(557\) | 0.846399 | 0.0358631 | 0.0179315 | − | 0.999839i | \(-0.494292\pi\) | ||||
0.0179315 | + | 0.999839i | \(0.494292\pi\) | |||||||
\(558\) | 19.0156 | 0.804996 | ||||||||
\(559\) | −8.44179 | −0.357049 | ||||||||
\(560\) | −0.983582 | −0.0415639 | ||||||||
\(561\) | −19.3466 | −0.816812 | ||||||||
\(562\) | −6.26393 | −0.264228 | ||||||||
\(563\) | −40.0831 | −1.68930 | −0.844650 | − | 0.535318i | \(-0.820192\pi\) | ||||
−0.844650 | + | 0.535318i | \(0.820192\pi\) | |||||||
\(564\) | 29.0032 | 1.22126 | ||||||||
\(565\) | 10.3596 | 0.435831 | ||||||||
\(566\) | −50.7641 | −2.13378 | ||||||||
\(567\) | 0.336371 | 0.0141263 | ||||||||
\(568\) | 4.83702 | 0.202957 | ||||||||
\(569\) | 23.3038 | 0.976945 | 0.488472 | − | 0.872579i | \(-0.337554\pi\) | ||||
0.488472 | + | 0.872579i | \(0.337554\pi\) | |||||||
\(570\) | 41.3807 | 1.73325 | ||||||||
\(571\) | −0.411433 | −0.0172179 | −0.00860896 | − | 0.999963i | \(-0.502740\pi\) | ||||
−0.00860896 | + | 0.999963i | \(0.502740\pi\) | |||||||
\(572\) | −40.0813 | −1.67588 | ||||||||
\(573\) | 21.4183 | 0.894761 | ||||||||
\(574\) | −8.32269 | −0.347382 | ||||||||
\(575\) | 6.10369 | 0.254541 | ||||||||
\(576\) | −13.0257 | −0.542739 | ||||||||
\(577\) | −13.5456 | −0.563910 | −0.281955 | − | 0.959428i | \(-0.590983\pi\) | ||||
−0.281955 | + | 0.959428i | \(0.590983\pi\) | |||||||
\(578\) | −8.86169 | −0.368598 | ||||||||
\(579\) | 13.7870 | 0.572968 | ||||||||
\(580\) | −10.0979 | −0.419293 | ||||||||
\(581\) | 4.26324 | 0.176869 | ||||||||
\(582\) | 6.76756 | 0.280524 | ||||||||
\(583\) | −35.6936 | −1.47828 | ||||||||
\(584\) | −23.7971 | −0.984730 | ||||||||
\(585\) | −8.22926 | −0.340238 | ||||||||
\(586\) | 60.4524 | 2.49727 | ||||||||
\(587\) | 33.9417 | 1.40092 | 0.700461 | − | 0.713690i | \(-0.252978\pi\) | ||||
0.700461 | + | 0.713690i | \(0.252978\pi\) | |||||||
\(588\) | 20.8698 | 0.860658 | ||||||||
\(589\) | −46.9433 | −1.93426 | ||||||||
\(590\) | −9.06620 | −0.373250 | ||||||||
\(591\) | 15.4879 | 0.637089 | ||||||||
\(592\) | −8.38811 | −0.344749 | ||||||||
\(593\) | −35.4814 | −1.45705 | −0.728524 | − | 0.685021i | \(-0.759793\pi\) | ||||
−0.728524 | + | 0.685021i | \(0.759793\pi\) | |||||||
\(594\) | −12.0120 | −0.492860 | ||||||||
\(595\) | 4.04893 | 0.165990 | ||||||||
\(596\) | 44.2280 | 1.81165 | ||||||||
\(597\) | −4.97074 | −0.203439 | ||||||||
\(598\) | −5.53895 | −0.226505 | ||||||||
\(599\) | 39.5554 | 1.61619 | 0.808094 | − | 0.589054i | \(-0.200499\pi\) | ||||
0.808094 | + | 0.589054i | \(0.200499\pi\) | |||||||
\(600\) | −14.1057 | −0.575862 | ||||||||
\(601\) | 15.7875 | 0.643984 | 0.321992 | − | 0.946742i | \(-0.395648\pi\) | ||||
0.321992 | + | 0.946742i | \(0.395648\pi\) | |||||||
\(602\) | 2.57886 | 0.105106 | ||||||||
\(603\) | 5.16723 | 0.210426 | ||||||||
\(604\) | 56.3190 | 2.29159 | ||||||||
\(605\) | 58.9254 | 2.39566 | ||||||||
\(606\) | 37.1920 | 1.51082 | ||||||||
\(607\) | 23.3376 | 0.947244 | 0.473622 | − | 0.880728i | \(-0.342946\pi\) | ||||
0.473622 | + | 0.880728i | \(0.342946\pi\) | |||||||
\(608\) | 36.4888 | 1.47982 | ||||||||
\(609\) | 0.336371 | 0.0136305 | ||||||||
\(610\) | 53.2459 | 2.15586 | ||||||||
\(611\) | 23.6360 | 0.956212 | ||||||||
\(612\) | 10.9468 | 0.442497 | ||||||||
\(613\) | −37.7636 | −1.52526 | −0.762628 | − | 0.646837i | \(-0.776091\pi\) | ||||
−0.762628 | + | 0.646837i | \(0.776091\pi\) | |||||||
\(614\) | 23.5680 | 0.951129 | ||||||||
\(615\) | 36.7602 | 1.48231 | ||||||||
\(616\) | 4.16329 | 0.167744 | ||||||||
\(617\) | −19.3263 | −0.778046 | −0.389023 | − | 0.921228i | \(-0.627187\pi\) | ||||
−0.389023 | + | 0.921228i | \(0.627187\pi\) | |||||||
\(618\) | −14.3832 | −0.578577 | ||||||||
\(619\) | 40.2999 | 1.61979 | 0.809894 | − | 0.586576i | \(-0.199524\pi\) | ||||
0.809894 | + | 0.586576i | \(0.199524\pi\) | |||||||
\(620\) | 85.6134 | 3.43832 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 71.4801 | 2.86609 | ||||||||
\(623\) | 3.97053 | 0.159076 | ||||||||
\(624\) | −2.16713 | −0.0867546 | ||||||||
\(625\) | −18.2634 | −0.730537 | ||||||||
\(626\) | −47.7933 | −1.91020 | ||||||||
\(627\) | 29.6537 | 1.18426 | ||||||||
\(628\) | −28.0653 | −1.11993 | ||||||||
\(629\) | 34.5298 | 1.37679 | ||||||||
\(630\) | 2.51393 | 0.100157 | ||||||||
\(631\) | −4.24160 | −0.168855 | −0.0844276 | − | 0.996430i | \(-0.526906\pi\) | ||||
−0.0844276 | + | 0.996430i | \(0.526906\pi\) | |||||||
\(632\) | −8.38530 | −0.333549 | ||||||||
\(633\) | 26.1099 | 1.03777 | ||||||||
\(634\) | 30.5460 | 1.21314 | ||||||||
\(635\) | 49.3769 | 1.95946 | ||||||||
\(636\) | 20.1963 | 0.800835 | ||||||||
\(637\) | 17.0078 | 0.673873 | ||||||||
\(638\) | −12.0120 | −0.475562 | ||||||||
\(639\) | 2.09303 | 0.0827991 | ||||||||
\(640\) | −53.4304 | −2.11202 | ||||||||
\(641\) | 14.6358 | 0.578080 | 0.289040 | − | 0.957317i | \(-0.406664\pi\) | ||||
0.289040 | + | 0.957317i | \(0.406664\pi\) | |||||||
\(642\) | −29.5883 | −1.16776 | ||||||||
\(643\) | −7.97033 | −0.314319 | −0.157159 | − | 0.987573i | \(-0.550234\pi\) | ||||
−0.157159 | + | 0.987573i | \(0.550234\pi\) | |||||||
\(644\) | 1.01934 | 0.0401675 | ||||||||
\(645\) | −11.3905 | −0.448499 | ||||||||
\(646\) | −44.8592 | −1.76496 | ||||||||
\(647\) | −0.258751 | −0.0101726 | −0.00508628 | − | 0.999987i | \(-0.501619\pi\) | ||||
−0.00508628 | + | 0.999987i | \(0.501619\pi\) | |||||||
\(648\) | 2.31101 | 0.0907851 | ||||||||
\(649\) | −6.49691 | −0.255026 | ||||||||
\(650\) | −33.8081 | −1.32606 | ||||||||
\(651\) | −2.85186 | −0.111773 | ||||||||
\(652\) | −64.2751 | −2.51721 | ||||||||
\(653\) | 25.8829 | 1.01288 | 0.506438 | − | 0.862276i | \(-0.330962\pi\) | ||||
0.506438 | + | 0.862276i | \(0.330962\pi\) | |||||||
\(654\) | 23.5694 | 0.921637 | ||||||||
\(655\) | 8.77585 | 0.342901 | ||||||||
\(656\) | 9.68058 | 0.377963 | ||||||||
\(657\) | −10.2973 | −0.401734 | ||||||||
\(658\) | −7.22051 | −0.281485 | ||||||||
\(659\) | −2.80499 | −0.109267 | −0.0546335 | − | 0.998506i | \(-0.517399\pi\) | ||||
−0.0546335 | + | 0.998506i | \(0.517399\pi\) | |||||||
\(660\) | −54.0814 | −2.10512 | ||||||||
\(661\) | 33.3102 | 1.29562 | 0.647809 | − | 0.761803i | \(-0.275685\pi\) | ||||
0.647809 | + | 0.761803i | \(0.275685\pi\) | |||||||
\(662\) | −20.0096 | −0.777695 | ||||||||
\(663\) | 8.92101 | 0.346463 | ||||||||
\(664\) | 29.2902 | 1.13668 | ||||||||
\(665\) | −6.20606 | −0.240661 | ||||||||
\(666\) | 21.4391 | 0.830749 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −64.7374 | −2.50476 | ||||||||
\(669\) | 8.28206 | 0.320203 | ||||||||
\(670\) | 38.6182 | 1.49195 | ||||||||
\(671\) | 38.1564 | 1.47301 | ||||||||
\(672\) | 2.21675 | 0.0855128 | ||||||||
\(673\) | −0.265368 | −0.0102292 | −0.00511459 | − | 0.999987i | \(-0.501628\pi\) | ||||
−0.00511459 | + | 0.999987i | \(0.501628\pi\) | |||||||
\(674\) | 15.0036 | 0.577918 | ||||||||
\(675\) | −6.10369 | −0.234931 | ||||||||
\(676\) | −20.9129 | −0.804343 | ||||||||
\(677\) | 16.0535 | 0.616987 | 0.308494 | − | 0.951226i | \(-0.400175\pi\) | ||||
0.308494 | + | 0.951226i | \(0.400175\pi\) | |||||||
\(678\) | −6.97284 | −0.267790 | ||||||||
\(679\) | −1.01496 | −0.0389507 | ||||||||
\(680\) | 27.8178 | 1.06676 | ||||||||
\(681\) | 15.0362 | 0.576187 | ||||||||
\(682\) | 101.842 | 3.89973 | ||||||||
\(683\) | 32.7737 | 1.25405 | 0.627025 | − | 0.778999i | \(-0.284272\pi\) | ||||
0.627025 | + | 0.778999i | \(0.284272\pi\) | |||||||
\(684\) | −16.7788 | −0.641555 | ||||||||
\(685\) | −37.5947 | −1.43642 | ||||||||
\(686\) | −10.4767 | −0.400001 | ||||||||
\(687\) | 9.35622 | 0.356962 | ||||||||
\(688\) | −2.99961 | −0.114359 | ||||||||
\(689\) | 16.4589 | 0.627034 | ||||||||
\(690\) | −7.47368 | −0.284518 | ||||||||
\(691\) | 45.9477 | 1.74793 | 0.873966 | − | 0.485986i | \(-0.161540\pi\) | ||||
0.873966 | + | 0.485986i | \(0.161540\pi\) | |||||||
\(692\) | −32.3483 | −1.22970 | ||||||||
\(693\) | 1.80150 | 0.0684335 | ||||||||
\(694\) | −23.5067 | −0.892303 | ||||||||
\(695\) | 11.8537 | 0.449638 | ||||||||
\(696\) | 2.31101 | 0.0875986 | ||||||||
\(697\) | −39.8503 | −1.50944 | ||||||||
\(698\) | −48.7328 | −1.84457 | ||||||||
\(699\) | −1.51916 | −0.0574598 | ||||||||
\(700\) | 6.22171 | 0.235159 | ||||||||
\(701\) | −11.1726 | −0.421984 | −0.210992 | − | 0.977488i | \(-0.567669\pi\) | ||||
−0.210992 | + | 0.977488i | \(0.567669\pi\) | |||||||
\(702\) | 5.53895 | 0.209054 | ||||||||
\(703\) | −52.9261 | −1.99614 | ||||||||
\(704\) | −69.7620 | −2.62925 | ||||||||
\(705\) | 31.8920 | 1.20112 | ||||||||
\(706\) | −55.2473 | −2.07926 | ||||||||
\(707\) | −5.57786 | −0.209777 | ||||||||
\(708\) | 3.67612 | 0.138157 | ||||||||
\(709\) | −0.376876 | −0.0141539 | −0.00707693 | − | 0.999975i | \(-0.502253\pi\) | ||||
−0.00707693 | + | 0.999975i | \(0.502253\pi\) | |||||||
\(710\) | 15.6427 | 0.587059 | ||||||||
\(711\) | −3.62841 | −0.136076 | ||||||||
\(712\) | 27.2792 | 1.02233 | ||||||||
\(713\) | 8.47832 | 0.317516 | ||||||||
\(714\) | −2.72525 | −0.101990 | ||||||||
\(715\) | −44.0734 | −1.64825 | ||||||||
\(716\) | −7.52963 | −0.281396 | ||||||||
\(717\) | 13.1287 | 0.490300 | ||||||||
\(718\) | −11.2326 | −0.419198 | ||||||||
\(719\) | 33.2548 | 1.24020 | 0.620098 | − | 0.784525i | \(-0.287093\pi\) | ||||
0.620098 | + | 0.784525i | \(0.287093\pi\) | |||||||
\(720\) | −2.92409 | −0.108975 | ||||||||
\(721\) | 2.15712 | 0.0803352 | ||||||||
\(722\) | 26.1444 | 0.972995 | ||||||||
\(723\) | −26.0253 | −0.967891 | ||||||||
\(724\) | −31.2616 | −1.16183 | ||||||||
\(725\) | −6.10369 | −0.226685 | ||||||||
\(726\) | −39.6616 | −1.47198 | ||||||||
\(727\) | −10.5234 | −0.390293 | −0.195146 | − | 0.980774i | \(-0.562518\pi\) | ||||
−0.195146 | + | 0.980774i | \(0.562518\pi\) | |||||||
\(728\) | −1.91976 | −0.0711512 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −76.9584 | −2.84836 | ||||||||
\(731\) | 12.3479 | 0.456705 | ||||||||
\(732\) | −21.5899 | −0.797984 | ||||||||
\(733\) | −17.1253 | −0.632536 | −0.316268 | − | 0.948670i | \(-0.602430\pi\) | ||||
−0.316268 | + | 0.948670i | \(0.602430\pi\) | |||||||
\(734\) | −13.4139 | −0.495117 | ||||||||
\(735\) | 22.9485 | 0.846469 | ||||||||
\(736\) | −6.59017 | −0.242917 | ||||||||
\(737\) | 27.6741 | 1.01939 | ||||||||
\(738\) | −24.7426 | −0.910786 | ||||||||
\(739\) | 20.9535 | 0.770788 | 0.385394 | − | 0.922752i | \(-0.374065\pi\) | ||||
0.385394 | + | 0.922752i | \(0.374065\pi\) | |||||||
\(740\) | 96.5247 | 3.54832 | ||||||||
\(741\) | −13.6738 | −0.502321 | ||||||||
\(742\) | −5.02798 | −0.184583 | ||||||||
\(743\) | 15.7655 | 0.578381 | 0.289190 | − | 0.957272i | \(-0.406614\pi\) | ||||
0.289190 | + | 0.957272i | \(0.406614\pi\) | |||||||
\(744\) | −19.5935 | −0.718332 | ||||||||
\(745\) | 48.6332 | 1.78178 | ||||||||
\(746\) | 58.1033 | 2.12731 | ||||||||
\(747\) | 12.6742 | 0.463725 | ||||||||
\(748\) | 58.6276 | 2.14364 | ||||||||
\(749\) | 4.43750 | 0.162143 | ||||||||
\(750\) | −8.24863 | −0.301197 | ||||||||
\(751\) | 40.8709 | 1.49140 | 0.745700 | − | 0.666282i | \(-0.232115\pi\) | ||||
0.745700 | + | 0.666282i | \(0.232115\pi\) | |||||||
\(752\) | 8.39858 | 0.306265 | ||||||||
\(753\) | −24.1425 | −0.879803 | ||||||||
\(754\) | 5.53895 | 0.201717 | ||||||||
\(755\) | 61.9284 | 2.25381 | ||||||||
\(756\) | −1.01934 | −0.0370729 | ||||||||
\(757\) | 37.3932 | 1.35908 | 0.679539 | − | 0.733639i | \(-0.262180\pi\) | ||||
0.679539 | + | 0.733639i | \(0.262180\pi\) | |||||||
\(758\) | 77.9096 | 2.82980 | ||||||||
\(759\) | −5.35570 | −0.194400 | ||||||||
\(760\) | −42.6382 | −1.54665 | ||||||||
\(761\) | −12.0596 | −0.437161 | −0.218581 | − | 0.975819i | \(-0.570143\pi\) | ||||
−0.218581 | + | 0.975819i | \(0.570143\pi\) | |||||||
\(762\) | −33.2346 | −1.20396 | ||||||||
\(763\) | −3.53482 | −0.127969 | ||||||||
\(764\) | −64.9057 | −2.34820 | ||||||||
\(765\) | 12.0371 | 0.435201 | ||||||||
\(766\) | −49.4402 | −1.78635 | ||||||||
\(767\) | 2.99583 | 0.108173 | ||||||||
\(768\) | 9.91149 | 0.357650 | ||||||||
\(769\) | 27.8157 | 1.00306 | 0.501531 | − | 0.865140i | \(-0.332770\pi\) | ||||
0.501531 | + | 0.865140i | \(0.332770\pi\) | |||||||
\(770\) | 13.4639 | 0.485204 | ||||||||
\(771\) | −23.1679 | −0.834373 | ||||||||
\(772\) | −41.7799 | −1.50369 | ||||||||
\(773\) | −12.1443 | −0.436801 | −0.218401 | − | 0.975859i | \(-0.570084\pi\) | ||||
−0.218401 | + | 0.975859i | \(0.570084\pi\) | |||||||
\(774\) | 7.66669 | 0.275574 | ||||||||
\(775\) | 51.7491 | 1.85888 | ||||||||
\(776\) | −6.97321 | −0.250324 | ||||||||
\(777\) | −3.21533 | −0.115349 | ||||||||
\(778\) | −24.0518 | −0.862299 | ||||||||
\(779\) | 61.0811 | 2.18846 | ||||||||
\(780\) | 24.9378 | 0.892918 | ||||||||
\(781\) | 11.2097 | 0.401113 | ||||||||
\(782\) | 8.10192 | 0.289724 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 6.04336 | 0.215834 | ||||||||
\(785\) | −30.8607 | −1.10147 | ||||||||
\(786\) | −5.90685 | −0.210690 | ||||||||
\(787\) | −18.7378 | −0.667929 | −0.333964 | − | 0.942586i | \(-0.608387\pi\) | ||||
−0.333964 | + | 0.942586i | \(0.608387\pi\) | |||||||
\(788\) | −46.9345 | −1.67197 | ||||||||
\(789\) | −11.8107 | −0.420471 | ||||||||
\(790\) | −27.1176 | −0.964801 | ||||||||
\(791\) | 1.04575 | 0.0371826 | ||||||||
\(792\) | 12.3771 | 0.439800 | ||||||||
\(793\) | −17.5946 | −0.624801 | ||||||||
\(794\) | −17.6233 | −0.625427 | ||||||||
\(795\) | 22.2079 | 0.787632 | ||||||||
\(796\) | 15.0633 | 0.533904 | ||||||||
\(797\) | 26.9033 | 0.952964 | 0.476482 | − | 0.879184i | \(-0.341912\pi\) | ||||
0.476482 | + | 0.879184i | \(0.341912\pi\) | |||||||
\(798\) | 4.17718 | 0.147871 | ||||||||
\(799\) | −34.5728 | −1.22310 | ||||||||
\(800\) | −40.2244 | −1.42215 | ||||||||
\(801\) | 11.8040 | 0.417074 | ||||||||
\(802\) | 33.7786 | 1.19277 | ||||||||
\(803\) | −55.1490 | −1.94617 | ||||||||
\(804\) | −15.6587 | −0.552240 | ||||||||
\(805\) | 1.12086 | 0.0395052 | ||||||||
\(806\) | −46.9610 | −1.65413 | ||||||||
\(807\) | 8.58123 | 0.302073 | ||||||||
\(808\) | −38.3222 | −1.34817 | ||||||||
\(809\) | −25.3753 | −0.892147 | −0.446073 | − | 0.894996i | \(-0.647178\pi\) | ||||
−0.446073 | + | 0.894996i | \(0.647178\pi\) | |||||||
\(810\) | 7.47368 | 0.262598 | ||||||||
\(811\) | −26.9252 | −0.945471 | −0.472736 | − | 0.881204i | \(-0.656733\pi\) | ||||
−0.472736 | + | 0.881204i | \(0.656733\pi\) | |||||||
\(812\) | −1.01934 | −0.0357717 | ||||||||
\(813\) | 11.0288 | 0.386797 | ||||||||
\(814\) | 114.822 | 4.02449 | ||||||||
\(815\) | −70.6770 | −2.47571 | ||||||||
\(816\) | 3.16990 | 0.110969 | ||||||||
\(817\) | −18.9265 | −0.662155 | ||||||||
\(818\) | 65.7933 | 2.30041 | ||||||||
\(819\) | −0.830703 | −0.0290271 | ||||||||
\(820\) | −111.398 | −3.89017 | ||||||||
\(821\) | −24.9489 | −0.870722 | −0.435361 | − | 0.900256i | \(-0.643379\pi\) | ||||
−0.435361 | + | 0.900256i | \(0.643379\pi\) | |||||||
\(822\) | 25.3043 | 0.882587 | ||||||||
\(823\) | 21.2224 | 0.739765 | 0.369882 | − | 0.929079i | \(-0.379398\pi\) | ||||
0.369882 | + | 0.929079i | \(0.379398\pi\) | |||||||
\(824\) | 14.8203 | 0.516289 | ||||||||
\(825\) | −32.6895 | −1.13810 | ||||||||
\(826\) | −0.915189 | −0.0318435 | ||||||||
\(827\) | 13.9717 | 0.485844 | 0.242922 | − | 0.970046i | \(-0.421894\pi\) | ||||
0.242922 | + | 0.970046i | \(0.421894\pi\) | |||||||
\(828\) | 3.03039 | 0.105313 | ||||||||
\(829\) | 5.62458 | 0.195350 | 0.0976748 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976748 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(830\) | 94.7229 | 3.28788 | ||||||||
\(831\) | −9.78001 | −0.339265 | ||||||||
\(832\) | 32.1684 | 1.11524 | ||||||||
\(833\) | −24.8776 | −0.861957 | ||||||||
\(834\) | −7.97851 | −0.276273 | ||||||||
\(835\) | −71.1853 | −2.46347 | ||||||||
\(836\) | −89.8624 | −3.10796 | ||||||||
\(837\) | −8.47832 | −0.293054 | ||||||||
\(838\) | −63.9173 | −2.20799 | ||||||||
\(839\) | 47.4932 | 1.63965 | 0.819824 | − | 0.572616i | \(-0.194071\pi\) | ||||
0.819824 | + | 0.572616i | \(0.194071\pi\) | |||||||
\(840\) | −2.59033 | −0.0893748 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 29.5693 | 1.01903 | ||||||||
\(843\) | 2.79284 | 0.0961905 | ||||||||
\(844\) | −79.1231 | −2.72353 | ||||||||
\(845\) | −22.9959 | −0.791082 | ||||||||
\(846\) | −21.4659 | −0.738012 | ||||||||
\(847\) | 5.94823 | 0.204384 | ||||||||
\(848\) | 5.84832 | 0.200832 | ||||||||
\(849\) | 22.6337 | 0.776788 | ||||||||
\(850\) | 49.4516 | 1.69618 | ||||||||
\(851\) | 9.55887 | 0.327674 | ||||||||
\(852\) | −6.34270 | −0.217297 | ||||||||
\(853\) | −10.5035 | −0.359634 | −0.179817 | − | 0.983700i | \(-0.557550\pi\) | ||||
−0.179817 | + | 0.983700i | \(0.557550\pi\) | |||||||
\(854\) | 5.37491 | 0.183926 | ||||||||
\(855\) | −18.4500 | −0.630978 | ||||||||
\(856\) | 30.4875 | 1.04204 | ||||||||
\(857\) | −21.3106 | −0.727956 | −0.363978 | − | 0.931407i | \(-0.618582\pi\) | ||||
−0.363978 | + | 0.931407i | \(0.618582\pi\) | |||||||
\(858\) | 29.6650 | 1.01275 | ||||||||
\(859\) | −21.9655 | −0.749452 | −0.374726 | − | 0.927136i | \(-0.622263\pi\) | ||||
−0.374726 | + | 0.927136i | \(0.622263\pi\) | |||||||
\(860\) | 34.5175 | 1.17704 | ||||||||
\(861\) | 3.71076 | 0.126462 | ||||||||
\(862\) | 47.2333 | 1.60877 | ||||||||
\(863\) | 50.0442 | 1.70353 | 0.851763 | − | 0.523928i | \(-0.175534\pi\) | ||||
0.851763 | + | 0.523928i | \(0.175534\pi\) | |||||||
\(864\) | 6.59017 | 0.224202 | ||||||||
\(865\) | −35.5702 | −1.20942 | ||||||||
\(866\) | −66.4841 | −2.25922 | ||||||||
\(867\) | 3.95108 | 0.134186 | ||||||||
\(868\) | 8.64226 | 0.293337 | ||||||||
\(869\) | −19.4327 | −0.659209 | ||||||||
\(870\) | 7.47368 | 0.253381 | ||||||||
\(871\) | −12.7610 | −0.432390 | ||||||||
\(872\) | −24.2857 | −0.822416 | ||||||||
\(873\) | −3.01739 | −0.102123 | ||||||||
\(874\) | −12.4184 | −0.420057 | ||||||||
\(875\) | 1.23709 | 0.0418211 | ||||||||
\(876\) | 31.2047 | 1.05431 | ||||||||
\(877\) | −26.3344 | −0.889248 | −0.444624 | − | 0.895717i | \(-0.646663\pi\) | ||||
−0.444624 | + | 0.895717i | \(0.646663\pi\) | |||||||
\(878\) | 40.6100 | 1.37052 | ||||||||
\(879\) | −26.9534 | −0.909114 | ||||||||
\(880\) | −15.6606 | −0.527918 | ||||||||
\(881\) | 53.3563 | 1.79762 | 0.898809 | − | 0.438340i | \(-0.144433\pi\) | ||||
0.898809 | + | 0.438340i | \(0.144433\pi\) | |||||||
\(882\) | −15.4462 | −0.520101 | ||||||||
\(883\) | 2.46924 | 0.0830966 | 0.0415483 | − | 0.999136i | \(-0.486771\pi\) | ||||
0.0415483 | + | 0.999136i | \(0.486771\pi\) | |||||||
\(884\) | −27.0341 | −0.909256 | ||||||||
\(885\) | 4.04226 | 0.135879 | ||||||||
\(886\) | 46.4289 | 1.55981 | ||||||||
\(887\) | 53.9526 | 1.81155 | 0.905776 | − | 0.423757i | \(-0.139289\pi\) | ||||
0.905776 | + | 0.423757i | \(0.139289\pi\) | |||||||
\(888\) | −22.0906 | −0.741313 | ||||||||
\(889\) | 4.98436 | 0.167170 | ||||||||
\(890\) | 88.2193 | 2.95712 | ||||||||
\(891\) | 5.35570 | 0.179423 | ||||||||
\(892\) | −25.0979 | −0.840339 | ||||||||
\(893\) | 52.9921 | 1.77331 | ||||||||
\(894\) | −32.7340 | −1.09479 | ||||||||
\(895\) | −8.27960 | −0.276756 | ||||||||
\(896\) | −5.39354 | −0.180186 | ||||||||
\(897\) | 2.46960 | 0.0824576 | ||||||||
\(898\) | −30.5255 | −1.01865 | ||||||||
\(899\) | −8.47832 | −0.282768 | ||||||||
\(900\) | 18.4966 | 0.616552 | ||||||||
\(901\) | −24.0747 | −0.802044 | ||||||||
\(902\) | −132.514 | −4.41222 | ||||||||
\(903\) | −1.14981 | −0.0382633 | ||||||||
\(904\) | 7.18474 | 0.238961 | ||||||||
\(905\) | −34.3753 | −1.14267 | ||||||||
\(906\) | −41.6828 | −1.38482 | ||||||||
\(907\) | 4.54378 | 0.150874 | 0.0754368 | − | 0.997151i | \(-0.475965\pi\) | ||||
0.0754368 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(908\) | −45.5654 | −1.51214 | ||||||||
\(909\) | −16.5824 | −0.550005 | ||||||||
\(910\) | −6.20841 | −0.205807 | ||||||||
\(911\) | −14.6485 | −0.485327 | −0.242664 | − | 0.970110i | \(-0.578021\pi\) | ||||
−0.242664 | + | 0.970110i | \(0.578021\pi\) | |||||||
\(912\) | −4.85871 | −0.160888 | ||||||||
\(913\) | 67.8792 | 2.24647 | ||||||||
\(914\) | 9.78035 | 0.323505 | ||||||||
\(915\) | −23.7402 | −0.784828 | ||||||||
\(916\) | −28.3530 | −0.936809 | ||||||||
\(917\) | 0.885879 | 0.0292543 | ||||||||
\(918\) | −8.10192 | −0.267403 | ||||||||
\(919\) | 14.7669 | 0.487114 | 0.243557 | − | 0.969887i | \(-0.421686\pi\) | ||||
0.243557 | + | 0.969887i | \(0.421686\pi\) | |||||||
\(920\) | 7.70079 | 0.253888 | ||||||||
\(921\) | −10.5081 | −0.346252 | ||||||||
\(922\) | 3.63318 | 0.119652 | ||||||||
\(923\) | −5.16896 | −0.170138 | ||||||||
\(924\) | −5.45926 | −0.179596 | ||||||||
\(925\) | 58.3444 | 1.91835 | ||||||||
\(926\) | −0.341750 | −0.0112306 | ||||||||
\(927\) | 6.41290 | 0.210627 | ||||||||
\(928\) | 6.59017 | 0.216333 | ||||||||
\(929\) | −27.7957 | −0.911947 | −0.455973 | − | 0.889993i | \(-0.650709\pi\) | ||||
−0.455973 | + | 0.889993i | \(0.650709\pi\) | |||||||
\(930\) | −63.3643 | −2.07780 | ||||||||
\(931\) | 38.1315 | 1.24971 | ||||||||
\(932\) | 4.60364 | 0.150797 | ||||||||
\(933\) | −31.8702 | −1.04338 | ||||||||
\(934\) | 57.6541 | 1.88650 | ||||||||
\(935\) | 64.4670 | 2.10830 | ||||||||
\(936\) | −5.70728 | −0.186548 | ||||||||
\(937\) | 7.42265 | 0.242487 | 0.121244 | − | 0.992623i | \(-0.461312\pi\) | ||||
0.121244 | + | 0.992623i | \(0.461312\pi\) | |||||||
\(938\) | 3.89832 | 0.127285 | ||||||||
\(939\) | 21.3092 | 0.695398 | ||||||||
\(940\) | −96.6451 | −3.15222 | ||||||||
\(941\) | 42.6205 | 1.38939 | 0.694695 | − | 0.719305i | \(-0.255539\pi\) | ||||
0.694695 | + | 0.719305i | \(0.255539\pi\) | |||||||
\(942\) | 20.7717 | 0.676780 | ||||||||
\(943\) | −11.0317 | −0.359243 | ||||||||
\(944\) | 1.06451 | 0.0346468 | ||||||||
\(945\) | −1.12086 | −0.0364617 | ||||||||
\(946\) | 41.0605 | 1.33499 | ||||||||
\(947\) | 18.8970 | 0.614069 | 0.307035 | − | 0.951698i | \(-0.400663\pi\) | ||||
0.307035 | + | 0.951698i | \(0.400663\pi\) | |||||||
\(948\) | 10.9955 | 0.357117 | ||||||||
\(949\) | 25.4301 | 0.825497 | ||||||||
\(950\) | −75.7978 | −2.45920 | ||||||||
\(951\) | −13.6193 | −0.441635 | ||||||||
\(952\) | 2.80807 | 0.0910101 | ||||||||
\(953\) | −4.93984 | −0.160017 | −0.0800086 | − | 0.996794i | \(-0.525495\pi\) | ||||
−0.0800086 | + | 0.996794i | \(0.525495\pi\) | |||||||
\(954\) | −14.9477 | −0.483950 | ||||||||
\(955\) | −71.3704 | −2.30949 | ||||||||
\(956\) | −39.7851 | −1.28674 | ||||||||
\(957\) | 5.35570 | 0.173125 | ||||||||
\(958\) | 13.2148 | 0.426950 | ||||||||
\(959\) | −3.79500 | −0.122547 | ||||||||
\(960\) | 43.4046 | 1.40088 | ||||||||
\(961\) | 40.8820 | 1.31877 | ||||||||
\(962\) | −52.9461 | −1.70705 | ||||||||
\(963\) | 13.1923 | 0.425115 | ||||||||
\(964\) | 78.8667 | 2.54013 | ||||||||
\(965\) | −45.9413 | −1.47890 | ||||||||
\(966\) | −0.754431 | −0.0242734 | ||||||||
\(967\) | 35.7015 | 1.14808 | 0.574041 | − | 0.818827i | \(-0.305375\pi\) | ||||
0.574041 | + | 0.818827i | \(0.305375\pi\) | |||||||
\(968\) | 40.8668 | 1.31351 | ||||||||
\(969\) | 20.0009 | 0.642523 | ||||||||
\(970\) | −22.5510 | −0.724069 | ||||||||
\(971\) | 57.8911 | 1.85781 | 0.928906 | − | 0.370315i | \(-0.120750\pi\) | ||||
0.928906 | + | 0.370315i | \(0.120750\pi\) | |||||||
\(972\) | −3.03039 | −0.0971998 | ||||||||
\(973\) | 1.19658 | 0.0383605 | ||||||||
\(974\) | −70.3658 | −2.25467 | ||||||||
\(975\) | 15.0737 | 0.482744 | ||||||||
\(976\) | −6.25186 | −0.200117 | ||||||||
\(977\) | −24.1856 | −0.773766 | −0.386883 | − | 0.922129i | \(-0.626448\pi\) | ||||
−0.386883 | + | 0.922129i | \(0.626448\pi\) | |||||||
\(978\) | 47.5713 | 1.52116 | ||||||||
\(979\) | 63.2187 | 2.02048 | ||||||||
\(980\) | −69.5429 | −2.22147 | ||||||||
\(981\) | −10.5087 | −0.335516 | ||||||||
\(982\) | 6.45858 | 0.206101 | ||||||||
\(983\) | −30.1771 | −0.962500 | −0.481250 | − | 0.876583i | \(-0.659817\pi\) | ||||
−0.481250 | + | 0.876583i | \(0.659817\pi\) | |||||||
\(984\) | 25.4945 | 0.812733 | ||||||||
\(985\) | −51.6092 | −1.64441 | ||||||||
\(986\) | −8.10192 | −0.258018 | ||||||||
\(987\) | 3.21934 | 0.102473 | ||||||||
\(988\) | 41.4370 | 1.31829 | ||||||||
\(989\) | 3.41828 | 0.108695 | ||||||||
\(990\) | 40.0268 | 1.27213 | ||||||||
\(991\) | 24.1655 | 0.767642 | 0.383821 | − | 0.923407i | \(-0.374608\pi\) | ||||
0.383821 | + | 0.923407i | \(0.374608\pi\) | |||||||
\(992\) | −55.8736 | −1.77399 | ||||||||
\(993\) | 8.92149 | 0.283115 | ||||||||
\(994\) | 1.57905 | 0.0500844 | ||||||||
\(995\) | 16.5636 | 0.525102 | ||||||||
\(996\) | −38.4078 | −1.21700 | ||||||||
\(997\) | −33.3183 | −1.05520 | −0.527600 | − | 0.849493i | \(-0.676908\pi\) | ||||
−0.527600 | + | 0.849493i | \(0.676908\pi\) | |||||||
\(998\) | 98.3478 | 3.11314 | ||||||||
\(999\) | −9.55887 | −0.302429 |
(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 | 2001.2.a.l.1.9 | ✓ | 11 | |
3.2 | odd | 2 | 6003.2.a.m.1.3 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.l.1.9 | ✓ | 11 | 1.1 | even | 1 | trivial | |
6003.2.a.m.1.3 | 11 | 3.2 | odd | 2 |