Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, 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("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 22x^{6} + 151x^{4} - 332x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.32381\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 | ||||||||
\(3\) | −0.153561 | −0.0886585 | −0.0443292 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443292 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.32381 | 1.48645 | 0.743227 | − | 0.669039i | \(-0.233294\pi\) | ||||
0.743227 | + | 0.669039i | \(0.233294\pi\) | |||||||
\(6\) | −0.153561 | −0.0626910 | ||||||||
\(7\) | 0.786348 | 0.297212 | 0.148606 | − | 0.988897i | \(-0.452521\pi\) | ||||
0.148606 | + | 0.988897i | \(0.452521\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.97642 | −0.992140 | ||||||||
\(10\) | 3.32381 | 1.05108 | ||||||||
\(11\) | 3.10411 | 0.935926 | 0.467963 | − | 0.883748i | \(-0.344988\pi\) | ||||
0.467963 | + | 0.883748i | \(0.344988\pi\) | |||||||
\(12\) | −0.153561 | −0.0443292 | ||||||||
\(13\) | 0.295907 | 0.0820699 | 0.0410349 | − | 0.999158i | \(-0.486935\pi\) | ||||
0.0410349 | + | 0.999158i | \(0.486935\pi\) | |||||||
\(14\) | 0.786348 | 0.210160 | ||||||||
\(15\) | −0.510408 | −0.131787 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.55304 | 0.861740 | 0.430870 | − | 0.902414i | \(-0.358207\pi\) | ||||
0.430870 | + | 0.902414i | \(0.358207\pi\) | |||||||
\(18\) | −2.97642 | −0.701549 | ||||||||
\(19\) | −2.46686 | −0.565936 | −0.282968 | − | 0.959129i | \(-0.591319\pi\) | ||||
−0.282968 | + | 0.959129i | \(0.591319\pi\) | |||||||
\(20\) | 3.32381 | 0.743227 | ||||||||
\(21\) | −0.120752 | −0.0263503 | ||||||||
\(22\) | 3.10411 | 0.661799 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −0.153561 | −0.0313455 | ||||||||
\(25\) | 6.04772 | 1.20954 | ||||||||
\(26\) | 0.295907 | 0.0580322 | ||||||||
\(27\) | 0.917745 | 0.176620 | ||||||||
\(28\) | 0.786348 | 0.148606 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −0.510408 | −0.0931873 | ||||||||
\(31\) | 5.06950 | 0.910508 | 0.455254 | − | 0.890361i | \(-0.349548\pi\) | ||||
0.455254 | + | 0.890361i | \(0.349548\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.476671 | −0.0829777 | ||||||||
\(34\) | 3.55304 | 0.609342 | ||||||||
\(35\) | 2.61367 | 0.441791 | ||||||||
\(36\) | −2.97642 | −0.496070 | ||||||||
\(37\) | −8.14737 | −1.33942 | −0.669710 | − | 0.742623i | \(-0.733582\pi\) | ||||
−0.669710 | + | 0.742623i | \(0.733582\pi\) | |||||||
\(38\) | −2.46686 | −0.400178 | ||||||||
\(39\) | −0.0454398 | −0.00727619 | ||||||||
\(40\) | 3.32381 | 0.525541 | ||||||||
\(41\) | 3.97376 | 0.620597 | 0.310299 | − | 0.950639i | \(-0.399571\pi\) | ||||
0.310299 | + | 0.950639i | \(0.399571\pi\) | |||||||
\(42\) | −0.120752 | −0.0186325 | ||||||||
\(43\) | 3.63031 | 0.553617 | 0.276809 | − | 0.960925i | \(-0.410723\pi\) | ||||
0.276809 | + | 0.960925i | \(0.410723\pi\) | |||||||
\(44\) | 3.10411 | 0.467963 | ||||||||
\(45\) | −9.89306 | −1.47477 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −1.23639 | −0.180346 | −0.0901728 | − | 0.995926i | \(-0.528742\pi\) | ||||
−0.0901728 | + | 0.995926i | \(0.528742\pi\) | |||||||
\(48\) | −0.153561 | −0.0221646 | ||||||||
\(49\) | −6.38166 | −0.911665 | ||||||||
\(50\) | 6.04772 | 0.855277 | ||||||||
\(51\) | −0.545609 | −0.0764005 | ||||||||
\(52\) | 0.295907 | 0.0410349 | ||||||||
\(53\) | 1.82898 | 0.251230 | 0.125615 | − | 0.992079i | \(-0.459910\pi\) | ||||
0.125615 | + | 0.992079i | \(0.459910\pi\) | |||||||
\(54\) | 0.917745 | 0.124889 | ||||||||
\(55\) | 10.3175 | 1.39121 | ||||||||
\(56\) | 0.786348 | 0.105080 | ||||||||
\(57\) | 0.378813 | 0.0501751 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −3.80630 | −0.495538 | −0.247769 | − | 0.968819i | \(-0.579697\pi\) | ||||
−0.247769 | + | 0.968819i | \(0.579697\pi\) | |||||||
\(60\) | −0.510408 | −0.0658934 | ||||||||
\(61\) | −11.0141 | −1.41021 | −0.705104 | − | 0.709104i | \(-0.749100\pi\) | ||||
−0.705104 | + | 0.709104i | \(0.749100\pi\) | |||||||
\(62\) | 5.06950 | 0.643827 | ||||||||
\(63\) | −2.34050 | −0.294875 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.983540 | 0.121993 | ||||||||
\(66\) | −0.476671 | −0.0586741 | ||||||||
\(67\) | 9.71317 | 1.18665 | 0.593327 | − | 0.804962i | \(-0.297814\pi\) | ||||
0.593327 | + | 0.804962i | \(0.297814\pi\) | |||||||
\(68\) | 3.55304 | 0.430870 | ||||||||
\(69\) | 0.153561 | 0.0184866 | ||||||||
\(70\) | 2.61367 | 0.312394 | ||||||||
\(71\) | 8.09167 | 0.960304 | 0.480152 | − | 0.877185i | \(-0.340581\pi\) | ||||
0.480152 | + | 0.877185i | \(0.340581\pi\) | |||||||
\(72\) | −2.97642 | −0.350774 | ||||||||
\(73\) | −6.05116 | −0.708235 | −0.354117 | − | 0.935201i | \(-0.615219\pi\) | ||||
−0.354117 | + | 0.935201i | \(0.615219\pi\) | |||||||
\(74\) | −8.14737 | −0.947113 | ||||||||
\(75\) | −0.928694 | −0.107236 | ||||||||
\(76\) | −2.46686 | −0.282968 | ||||||||
\(77\) | 2.44091 | 0.278168 | ||||||||
\(78\) | −0.0454398 | −0.00514504 | ||||||||
\(79\) | −6.74311 | −0.758660 | −0.379330 | − | 0.925262i | \(-0.623845\pi\) | ||||
−0.379330 | + | 0.925262i | \(0.623845\pi\) | |||||||
\(80\) | 3.32381 | 0.371613 | ||||||||
\(81\) | 8.78833 | 0.976481 | ||||||||
\(82\) | 3.97376 | 0.438828 | ||||||||
\(83\) | 1.88918 | 0.207364 | 0.103682 | − | 0.994610i | \(-0.466938\pi\) | ||||
0.103682 | + | 0.994610i | \(0.466938\pi\) | |||||||
\(84\) | −0.120752 | −0.0131752 | ||||||||
\(85\) | 11.8096 | 1.28094 | ||||||||
\(86\) | 3.63031 | 0.391467 | ||||||||
\(87\) | 0.153561 | 0.0164635 | ||||||||
\(88\) | 3.10411 | 0.330900 | ||||||||
\(89\) | 0.00146765 | 0.000155570 0 | 7.77851e−5 | − | 1.00000i | \(-0.499975\pi\) | ||||
7.77851e−5 | 1.00000i | \(0.499975\pi\) | ||||||||
\(90\) | −9.89306 | −1.04282 | ||||||||
\(91\) | 0.232686 | 0.0243921 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −0.778477 | −0.0807243 | ||||||||
\(94\) | −1.23639 | −0.127524 | ||||||||
\(95\) | −8.19938 | −0.841238 | ||||||||
\(96\) | −0.153561 | −0.0156727 | ||||||||
\(97\) | −10.1740 | −1.03302 | −0.516508 | − | 0.856282i | \(-0.672769\pi\) | ||||
−0.516508 | + | 0.856282i | \(0.672769\pi\) | |||||||
\(98\) | −6.38166 | −0.644645 | ||||||||
\(99\) | −9.23914 | −0.928569 | ||||||||
\(100\) | 6.04772 | 0.604772 | ||||||||
\(101\) | 8.46165 | 0.841965 | 0.420983 | − | 0.907069i | \(-0.361685\pi\) | ||||
0.420983 | + | 0.907069i | \(0.361685\pi\) | |||||||
\(102\) | −0.545609 | −0.0540233 | ||||||||
\(103\) | −5.60825 | −0.552597 | −0.276299 | − | 0.961072i | \(-0.589108\pi\) | ||||
−0.276299 | + | 0.961072i | \(0.589108\pi\) | |||||||
\(104\) | 0.295907 | 0.0290161 | ||||||||
\(105\) | −0.401358 | −0.0391685 | ||||||||
\(106\) | 1.82898 | 0.177647 | ||||||||
\(107\) | −4.43459 | −0.428708 | −0.214354 | − | 0.976756i | \(-0.568765\pi\) | ||||
−0.214354 | + | 0.976756i | \(0.568765\pi\) | |||||||
\(108\) | 0.917745 | 0.0883100 | ||||||||
\(109\) | −1.63054 | −0.156178 | −0.0780888 | − | 0.996946i | \(-0.524882\pi\) | ||||
−0.0780888 | + | 0.996946i | \(0.524882\pi\) | |||||||
\(110\) | 10.3175 | 0.983734 | ||||||||
\(111\) | 1.25112 | 0.118751 | ||||||||
\(112\) | 0.786348 | 0.0743029 | ||||||||
\(113\) | 15.0343 | 1.41430 | 0.707152 | − | 0.707061i | \(-0.249979\pi\) | ||||
0.707152 | + | 0.707061i | \(0.249979\pi\) | |||||||
\(114\) | 0.378813 | 0.0354791 | ||||||||
\(115\) | −3.32381 | −0.309947 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −0.880744 | −0.0814248 | ||||||||
\(118\) | −3.80630 | −0.350398 | ||||||||
\(119\) | 2.79393 | 0.256119 | ||||||||
\(120\) | −0.510408 | −0.0465936 | ||||||||
\(121\) | −1.36448 | −0.124043 | ||||||||
\(122\) | −11.0141 | −0.997167 | ||||||||
\(123\) | −0.610215 | −0.0550212 | ||||||||
\(124\) | 5.06950 | 0.455254 | ||||||||
\(125\) | 3.48244 | 0.311479 | ||||||||
\(126\) | −2.34050 | −0.208508 | ||||||||
\(127\) | −1.23989 | −0.110023 | −0.0550113 | − | 0.998486i | \(-0.517519\pi\) | ||||
−0.0550113 | + | 0.998486i | \(0.517519\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.557474 | −0.0490829 | ||||||||
\(130\) | 0.983540 | 0.0862622 | ||||||||
\(131\) | 0.713793 | 0.0623644 | 0.0311822 | − | 0.999514i | \(-0.490073\pi\) | ||||
0.0311822 | + | 0.999514i | \(0.490073\pi\) | |||||||
\(132\) | −0.476671 | −0.0414889 | ||||||||
\(133\) | −1.93981 | −0.168203 | ||||||||
\(134\) | 9.71317 | 0.839090 | ||||||||
\(135\) | 3.05041 | 0.262538 | ||||||||
\(136\) | 3.55304 | 0.304671 | ||||||||
\(137\) | −4.22179 | −0.360692 | −0.180346 | − | 0.983603i | \(-0.557722\pi\) | ||||
−0.180346 | + | 0.983603i | \(0.557722\pi\) | |||||||
\(138\) | 0.153561 | 0.0130720 | ||||||||
\(139\) | 8.29267 | 0.703375 | 0.351687 | − | 0.936118i | \(-0.385608\pi\) | ||||
0.351687 | + | 0.936118i | \(0.385608\pi\) | |||||||
\(140\) | 2.61367 | 0.220896 | ||||||||
\(141\) | 0.189861 | 0.0159892 | ||||||||
\(142\) | 8.09167 | 0.679038 | ||||||||
\(143\) | 0.918530 | 0.0768113 | ||||||||
\(144\) | −2.97642 | −0.248035 | ||||||||
\(145\) | −3.32381 | −0.276028 | ||||||||
\(146\) | −6.05116 | −0.500798 | ||||||||
\(147\) | 0.979973 | 0.0808268 | ||||||||
\(148\) | −8.14737 | −0.669710 | ||||||||
\(149\) | −9.09064 | −0.744734 | −0.372367 | − | 0.928086i | \(-0.621454\pi\) | ||||
−0.372367 | + | 0.928086i | \(0.621454\pi\) | |||||||
\(150\) | −0.928694 | −0.0758276 | ||||||||
\(151\) | 4.21232 | 0.342793 | 0.171397 | − | 0.985202i | \(-0.445172\pi\) | ||||
0.171397 | + | 0.985202i | \(0.445172\pi\) | |||||||
\(152\) | −2.46686 | −0.200089 | ||||||||
\(153\) | −10.5753 | −0.854966 | ||||||||
\(154\) | 2.44091 | 0.196694 | ||||||||
\(155\) | 16.8501 | 1.35343 | ||||||||
\(156\) | −0.0454398 | −0.00363810 | ||||||||
\(157\) | −2.04867 | −0.163502 | −0.0817508 | − | 0.996653i | \(-0.526051\pi\) | ||||
−0.0817508 | + | 0.996653i | \(0.526051\pi\) | |||||||
\(158\) | −6.74311 | −0.536453 | ||||||||
\(159\) | −0.280860 | −0.0222737 | ||||||||
\(160\) | 3.32381 | 0.262770 | ||||||||
\(161\) | −0.786348 | −0.0619729 | ||||||||
\(162\) | 8.78833 | 0.690476 | ||||||||
\(163\) | 4.11487 | 0.322301 | 0.161151 | − | 0.986930i | \(-0.448479\pi\) | ||||
0.161151 | + | 0.986930i | \(0.448479\pi\) | |||||||
\(164\) | 3.97376 | 0.310299 | ||||||||
\(165\) | −1.58436 | −0.123343 | ||||||||
\(166\) | 1.88918 | 0.146629 | ||||||||
\(167\) | 7.32062 | 0.566487 | 0.283243 | − | 0.959048i | \(-0.408590\pi\) | ||||
0.283243 | + | 0.959048i | \(0.408590\pi\) | |||||||
\(168\) | −0.120752 | −0.00931625 | ||||||||
\(169\) | −12.9124 | −0.993265 | ||||||||
\(170\) | 11.8096 | 0.905759 | ||||||||
\(171\) | 7.34241 | 0.561488 | ||||||||
\(172\) | 3.63031 | 0.276809 | ||||||||
\(173\) | −4.59322 | −0.349216 | −0.174608 | − | 0.984638i | \(-0.555866\pi\) | ||||
−0.174608 | + | 0.984638i | \(0.555866\pi\) | |||||||
\(174\) | 0.153561 | 0.0116414 | ||||||||
\(175\) | 4.75562 | 0.359491 | ||||||||
\(176\) | 3.10411 | 0.233981 | ||||||||
\(177\) | 0.584499 | 0.0439336 | ||||||||
\(178\) | 0.00146765 | 0.000110005 0 | ||||||||
\(179\) | −2.06511 | −0.154354 | −0.0771768 | − | 0.997017i | \(-0.524591\pi\) | ||||
−0.0771768 | + | 0.997017i | \(0.524591\pi\) | |||||||
\(180\) | −9.89306 | −0.737385 | ||||||||
\(181\) | 8.64537 | 0.642606 | 0.321303 | − | 0.946977i | \(-0.395879\pi\) | ||||
0.321303 | + | 0.946977i | \(0.395879\pi\) | |||||||
\(182\) | 0.232686 | 0.0172478 | ||||||||
\(183\) | 1.69133 | 0.125027 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −27.0803 | −1.99099 | ||||||||
\(186\) | −0.778477 | −0.0570807 | ||||||||
\(187\) | 11.0291 | 0.806524 | ||||||||
\(188\) | −1.23639 | −0.0901728 | ||||||||
\(189\) | 0.721667 | 0.0524935 | ||||||||
\(190\) | −8.19938 | −0.594845 | ||||||||
\(191\) | −17.8459 | −1.29128 | −0.645642 | − | 0.763640i | \(-0.723410\pi\) | ||||
−0.645642 | + | 0.763640i | \(0.723410\pi\) | |||||||
\(192\) | −0.153561 | −0.0110823 | ||||||||
\(193\) | −5.87374 | −0.422801 | −0.211401 | − | 0.977400i | \(-0.567802\pi\) | ||||
−0.211401 | + | 0.977400i | \(0.567802\pi\) | |||||||
\(194\) | −10.1740 | −0.730453 | ||||||||
\(195\) | −0.151033 | −0.0108157 | ||||||||
\(196\) | −6.38166 | −0.455833 | ||||||||
\(197\) | 4.06113 | 0.289343 | 0.144672 | − | 0.989480i | \(-0.453787\pi\) | ||||
0.144672 | + | 0.989480i | \(0.453787\pi\) | |||||||
\(198\) | −9.23914 | −0.656597 | ||||||||
\(199\) | −8.69965 | −0.616702 | −0.308351 | − | 0.951273i | \(-0.599777\pi\) | ||||
−0.308351 | + | 0.951273i | \(0.599777\pi\) | |||||||
\(200\) | 6.04772 | 0.427639 | ||||||||
\(201\) | −1.49156 | −0.105207 | ||||||||
\(202\) | 8.46165 | 0.595359 | ||||||||
\(203\) | −0.786348 | −0.0551908 | ||||||||
\(204\) | −0.545609 | −0.0382003 | ||||||||
\(205\) | 13.2080 | 0.922489 | ||||||||
\(206\) | −5.60825 | −0.390745 | ||||||||
\(207\) | 2.97642 | 0.206875 | ||||||||
\(208\) | 0.295907 | 0.0205175 | ||||||||
\(209\) | −7.65742 | −0.529674 | ||||||||
\(210\) | −0.401358 | −0.0276963 | ||||||||
\(211\) | −7.30620 | −0.502979 | −0.251490 | − | 0.967860i | \(-0.580920\pi\) | ||||
−0.251490 | + | 0.967860i | \(0.580920\pi\) | |||||||
\(212\) | 1.82898 | 0.125615 | ||||||||
\(213\) | −1.24256 | −0.0851391 | ||||||||
\(214\) | −4.43459 | −0.303142 | ||||||||
\(215\) | 12.0665 | 0.822927 | ||||||||
\(216\) | 0.917745 | 0.0624446 | ||||||||
\(217\) | 3.98639 | 0.270614 | ||||||||
\(218\) | −1.63054 | −0.110434 | ||||||||
\(219\) | 0.929222 | 0.0627910 | ||||||||
\(220\) | 10.3175 | 0.695605 | ||||||||
\(221\) | 1.05137 | 0.0707229 | ||||||||
\(222\) | 1.25112 | 0.0839696 | ||||||||
\(223\) | −1.08883 | −0.0729131 | −0.0364566 | − | 0.999335i | \(-0.511607\pi\) | ||||
−0.0364566 | + | 0.999335i | \(0.511607\pi\) | |||||||
\(224\) | 0.786348 | 0.0525401 | ||||||||
\(225\) | −18.0006 | −1.20004 | ||||||||
\(226\) | 15.0343 | 1.00006 | ||||||||
\(227\) | −18.4984 | −1.22778 | −0.613891 | − | 0.789391i | \(-0.710396\pi\) | ||||
−0.613891 | + | 0.789391i | \(0.710396\pi\) | |||||||
\(228\) | 0.378813 | 0.0250875 | ||||||||
\(229\) | −15.2651 | −1.00874 | −0.504372 | − | 0.863486i | \(-0.668276\pi\) | ||||
−0.504372 | + | 0.863486i | \(0.668276\pi\) | |||||||
\(230\) | −3.32381 | −0.219166 | ||||||||
\(231\) | −0.374829 | −0.0246619 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −16.2197 | −1.06259 | −0.531295 | − | 0.847187i | \(-0.678294\pi\) | ||||
−0.531295 | + | 0.847187i | \(0.678294\pi\) | |||||||
\(234\) | −0.880744 | −0.0575760 | ||||||||
\(235\) | −4.10952 | −0.268075 | ||||||||
\(236\) | −3.80630 | −0.247769 | ||||||||
\(237\) | 1.03548 | 0.0672616 | ||||||||
\(238\) | 2.79393 | 0.181104 | ||||||||
\(239\) | −2.01739 | −0.130494 | −0.0652471 | − | 0.997869i | \(-0.520784\pi\) | ||||
−0.0652471 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(240\) | −0.510408 | −0.0329467 | ||||||||
\(241\) | −18.5299 | −1.19362 | −0.596808 | − | 0.802384i | \(-0.703565\pi\) | ||||
−0.596808 | + | 0.802384i | \(0.703565\pi\) | |||||||
\(242\) | −1.36448 | −0.0877118 | ||||||||
\(243\) | −4.10278 | −0.263193 | ||||||||
\(244\) | −11.0141 | −0.705104 | ||||||||
\(245\) | −21.2114 | −1.35515 | ||||||||
\(246\) | −0.610215 | −0.0389059 | ||||||||
\(247\) | −0.729962 | −0.0464463 | ||||||||
\(248\) | 5.06950 | 0.321913 | ||||||||
\(249\) | −0.290104 | −0.0183846 | ||||||||
\(250\) | 3.48244 | 0.220249 | ||||||||
\(251\) | 8.18230 | 0.516462 | 0.258231 | − | 0.966083i | \(-0.416860\pi\) | ||||
0.258231 | + | 0.966083i | \(0.416860\pi\) | |||||||
\(252\) | −2.34050 | −0.147438 | ||||||||
\(253\) | −3.10411 | −0.195154 | ||||||||
\(254\) | −1.23989 | −0.0777977 | ||||||||
\(255\) | −1.81350 | −0.113566 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.1136 | −1.69130 | −0.845650 | − | 0.533738i | \(-0.820787\pi\) | ||||
−0.845650 | + | 0.533738i | \(0.820787\pi\) | |||||||
\(258\) | −0.557474 | −0.0347068 | ||||||||
\(259\) | −6.40667 | −0.398091 | ||||||||
\(260\) | 0.983540 | 0.0609966 | ||||||||
\(261\) | 2.97642 | 0.184236 | ||||||||
\(262\) | 0.713793 | 0.0440983 | ||||||||
\(263\) | 17.4454 | 1.07573 | 0.537865 | − | 0.843031i | \(-0.319231\pi\) | ||||
0.537865 | + | 0.843031i | \(0.319231\pi\) | |||||||
\(264\) | −0.476671 | −0.0293371 | ||||||||
\(265\) | 6.07920 | 0.373442 | ||||||||
\(266\) | −1.93981 | −0.118937 | ||||||||
\(267\) | −0.000225373 0 | −1.37926e−5 0 | ||||||||
\(268\) | 9.71317 | 0.593327 | ||||||||
\(269\) | −20.3410 | −1.24021 | −0.620106 | − | 0.784518i | \(-0.712911\pi\) | ||||
−0.620106 | + | 0.784518i | \(0.712911\pi\) | |||||||
\(270\) | 3.05041 | 0.185642 | ||||||||
\(271\) | 15.9266 | 0.967471 | 0.483736 | − | 0.875214i | \(-0.339280\pi\) | ||||
0.483736 | + | 0.875214i | \(0.339280\pi\) | |||||||
\(272\) | 3.55304 | 0.215435 | ||||||||
\(273\) | −0.0357315 | −0.00216257 | ||||||||
\(274\) | −4.22179 | −0.255048 | ||||||||
\(275\) | 18.7728 | 1.13204 | ||||||||
\(276\) | 0.153561 | 0.00924328 | ||||||||
\(277\) | −12.3405 | −0.741468 | −0.370734 | − | 0.928739i | \(-0.620894\pi\) | ||||
−0.370734 | + | 0.928739i | \(0.620894\pi\) | |||||||
\(278\) | 8.29267 | 0.497361 | ||||||||
\(279\) | −15.0889 | −0.903352 | ||||||||
\(280\) | 2.61367 | 0.156197 | ||||||||
\(281\) | −11.2282 | −0.669820 | −0.334910 | − | 0.942250i | \(-0.608706\pi\) | ||||
−0.334910 | + | 0.942250i | \(0.608706\pi\) | |||||||
\(282\) | 0.189861 | 0.0113060 | ||||||||
\(283\) | −5.58632 | −0.332072 | −0.166036 | − | 0.986120i | \(-0.553097\pi\) | ||||
−0.166036 | + | 0.986120i | \(0.553097\pi\) | |||||||
\(284\) | 8.09167 | 0.480152 | ||||||||
\(285\) | 1.25910 | 0.0745829 | ||||||||
\(286\) | 0.918530 | 0.0543138 | ||||||||
\(287\) | 3.12476 | 0.184449 | ||||||||
\(288\) | −2.97642 | −0.175387 | ||||||||
\(289\) | −4.37588 | −0.257405 | ||||||||
\(290\) | −3.32381 | −0.195181 | ||||||||
\(291\) | 1.56233 | 0.0915857 | ||||||||
\(292\) | −6.05116 | −0.354117 | ||||||||
\(293\) | −0.961095 | −0.0561477 | −0.0280739 | − | 0.999606i | \(-0.508937\pi\) | ||||
−0.0280739 | + | 0.999606i | \(0.508937\pi\) | |||||||
\(294\) | 0.979973 | 0.0571532 | ||||||||
\(295\) | −12.6514 | −0.736594 | ||||||||
\(296\) | −8.14737 | −0.473556 | ||||||||
\(297\) | 2.84878 | 0.165303 | ||||||||
\(298\) | −9.09064 | −0.526606 | ||||||||
\(299\) | −0.295907 | −0.0171128 | ||||||||
\(300\) | −0.928694 | −0.0536182 | ||||||||
\(301\) | 2.85469 | 0.164542 | ||||||||
\(302\) | 4.21232 | 0.242391 | ||||||||
\(303\) | −1.29938 | −0.0746473 | ||||||||
\(304\) | −2.46686 | −0.141484 | ||||||||
\(305\) | −36.6087 | −2.09621 | ||||||||
\(306\) | −10.5753 | −0.604552 | ||||||||
\(307\) | 0.670924 | 0.0382917 | 0.0191458 | − | 0.999817i | \(-0.493905\pi\) | ||||
0.0191458 | + | 0.999817i | \(0.493905\pi\) | |||||||
\(308\) | 2.44091 | 0.139084 | ||||||||
\(309\) | 0.861208 | 0.0489924 | ||||||||
\(310\) | 16.8501 | 0.957019 | ||||||||
\(311\) | −15.4376 | −0.875384 | −0.437692 | − | 0.899125i | \(-0.644204\pi\) | ||||
−0.437692 | + | 0.899125i | \(0.644204\pi\) | |||||||
\(312\) | −0.0454398 | −0.00257252 | ||||||||
\(313\) | 7.43893 | 0.420473 | 0.210237 | − | 0.977651i | \(-0.432577\pi\) | ||||
0.210237 | + | 0.977651i | \(0.432577\pi\) | |||||||
\(314\) | −2.04867 | −0.115613 | ||||||||
\(315\) | −7.77939 | −0.438319 | ||||||||
\(316\) | −6.74311 | −0.379330 | ||||||||
\(317\) | 18.5822 | 1.04368 | 0.521839 | − | 0.853044i | \(-0.325246\pi\) | ||||
0.521839 | + | 0.853044i | \(0.325246\pi\) | |||||||
\(318\) | −0.280860 | −0.0157499 | ||||||||
\(319\) | −3.10411 | −0.173797 | ||||||||
\(320\) | 3.32381 | 0.185807 | ||||||||
\(321\) | 0.680980 | 0.0380086 | ||||||||
\(322\) | −0.786348 | −0.0438215 | ||||||||
\(323\) | −8.76486 | −0.487690 | ||||||||
\(324\) | 8.78833 | 0.488240 | ||||||||
\(325\) | 1.78957 | 0.0992672 | ||||||||
\(326\) | 4.11487 | 0.227902 | ||||||||
\(327\) | 0.250387 | 0.0138465 | ||||||||
\(328\) | 3.97376 | 0.219414 | ||||||||
\(329\) | −0.972231 | −0.0536008 | ||||||||
\(330\) | −1.58436 | −0.0872164 | ||||||||
\(331\) | 11.0559 | 0.607686 | 0.303843 | − | 0.952722i | \(-0.401730\pi\) | ||||
0.303843 | + | 0.952722i | \(0.401730\pi\) | |||||||
\(332\) | 1.88918 | 0.103682 | ||||||||
\(333\) | 24.2500 | 1.32889 | ||||||||
\(334\) | 7.32062 | 0.400567 | ||||||||
\(335\) | 32.2848 | 1.76390 | ||||||||
\(336\) | −0.120752 | −0.00658758 | ||||||||
\(337\) | −29.8194 | −1.62436 | −0.812182 | − | 0.583404i | \(-0.801720\pi\) | ||||
−0.812182 | + | 0.583404i | \(0.801720\pi\) | |||||||
\(338\) | −12.9124 | −0.702344 | ||||||||
\(339\) | −2.30868 | −0.125390 | ||||||||
\(340\) | 11.8096 | 0.640468 | ||||||||
\(341\) | 15.7363 | 0.852168 | ||||||||
\(342\) | 7.34241 | 0.397032 | ||||||||
\(343\) | −10.5226 | −0.568169 | ||||||||
\(344\) | 3.63031 | 0.195733 | ||||||||
\(345\) | 0.510408 | 0.0274794 | ||||||||
\(346\) | −4.59322 | −0.246933 | ||||||||
\(347\) | 6.96245 | 0.373764 | 0.186882 | − | 0.982382i | \(-0.440162\pi\) | ||||
0.186882 | + | 0.982382i | \(0.440162\pi\) | |||||||
\(348\) | 0.153561 | 0.00823173 | ||||||||
\(349\) | 2.23162 | 0.119456 | 0.0597279 | − | 0.998215i | \(-0.480977\pi\) | ||||
0.0597279 | + | 0.998215i | \(0.480977\pi\) | |||||||
\(350\) | 4.75562 | 0.254198 | ||||||||
\(351\) | 0.271567 | 0.0144952 | ||||||||
\(352\) | 3.10411 | 0.165450 | ||||||||
\(353\) | 17.8270 | 0.948833 | 0.474416 | − | 0.880301i | \(-0.342659\pi\) | ||||
0.474416 | + | 0.880301i | \(0.342659\pi\) | |||||||
\(354\) | 0.584499 | 0.0310658 | ||||||||
\(355\) | 26.8952 | 1.42745 | ||||||||
\(356\) | 0.00146765 | 7.77851e−5 0 | ||||||||
\(357\) | −0.429038 | −0.0227071 | ||||||||
\(358\) | −2.06511 | −0.109144 | ||||||||
\(359\) | 13.7562 | 0.726025 | 0.363013 | − | 0.931784i | \(-0.381748\pi\) | ||||
0.363013 | + | 0.931784i | \(0.381748\pi\) | |||||||
\(360\) | −9.89306 | −0.521410 | ||||||||
\(361\) | −12.9146 | −0.679716 | ||||||||
\(362\) | 8.64537 | 0.454391 | ||||||||
\(363\) | 0.209530 | 0.0109975 | ||||||||
\(364\) | 0.232686 | 0.0121961 | ||||||||
\(365\) | −20.1129 | −1.05276 | ||||||||
\(366\) | 1.69133 | 0.0884073 | ||||||||
\(367\) | 13.2990 | 0.694201 | 0.347101 | − | 0.937828i | \(-0.387166\pi\) | ||||
0.347101 | + | 0.937828i | \(0.387166\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −11.8276 | −0.615719 | ||||||||
\(370\) | −27.0803 | −1.40784 | ||||||||
\(371\) | 1.43822 | 0.0746685 | ||||||||
\(372\) | −0.778477 | −0.0403621 | ||||||||
\(373\) | 10.4378 | 0.540448 | 0.270224 | − | 0.962798i | \(-0.412902\pi\) | ||||
0.270224 | + | 0.962798i | \(0.412902\pi\) | |||||||
\(374\) | 11.0291 | 0.570299 | ||||||||
\(375\) | −0.534767 | −0.0276152 | ||||||||
\(376\) | −1.23639 | −0.0637618 | ||||||||
\(377\) | −0.295907 | −0.0152400 | ||||||||
\(378\) | 0.721667 | 0.0371185 | ||||||||
\(379\) | 28.1135 | 1.44410 | 0.722048 | − | 0.691843i | \(-0.243201\pi\) | ||||
0.722048 | + | 0.691843i | \(0.243201\pi\) | |||||||
\(380\) | −8.19938 | −0.420619 | ||||||||
\(381\) | 0.190399 | 0.00975443 | ||||||||
\(382\) | −17.8459 | −0.913075 | ||||||||
\(383\) | −14.0928 | −0.720109 | −0.360054 | − | 0.932931i | \(-0.617242\pi\) | ||||
−0.360054 | + | 0.932931i | \(0.617242\pi\) | |||||||
\(384\) | −0.153561 | −0.00783637 | ||||||||
\(385\) | 8.11314 | 0.413484 | ||||||||
\(386\) | −5.87374 | −0.298966 | ||||||||
\(387\) | −10.8053 | −0.549266 | ||||||||
\(388\) | −10.1740 | −0.516508 | ||||||||
\(389\) | 21.4862 | 1.08940 | 0.544698 | − | 0.838632i | \(-0.316644\pi\) | ||||
0.544698 | + | 0.838632i | \(0.316644\pi\) | |||||||
\(390\) | −0.151033 | −0.00764787 | ||||||||
\(391\) | −3.55304 | −0.179685 | ||||||||
\(392\) | −6.38166 | −0.322322 | ||||||||
\(393\) | −0.109611 | −0.00552913 | ||||||||
\(394\) | 4.06113 | 0.204597 | ||||||||
\(395\) | −22.4128 | −1.12771 | ||||||||
\(396\) | −9.23914 | −0.464284 | ||||||||
\(397\) | 4.59406 | 0.230569 | 0.115285 | − | 0.993333i | \(-0.463222\pi\) | ||||
0.115285 | + | 0.993333i | \(0.463222\pi\) | |||||||
\(398\) | −8.69965 | −0.436074 | ||||||||
\(399\) | 0.297879 | 0.0149126 | ||||||||
\(400\) | 6.04772 | 0.302386 | ||||||||
\(401\) | −8.77930 | −0.438417 | −0.219209 | − | 0.975678i | \(-0.570348\pi\) | ||||
−0.219209 | + | 0.975678i | \(0.570348\pi\) | |||||||
\(402\) | −1.49156 | −0.0743925 | ||||||||
\(403\) | 1.50010 | 0.0747253 | ||||||||
\(404\) | 8.46165 | 0.420983 | ||||||||
\(405\) | 29.2107 | 1.45149 | ||||||||
\(406\) | −0.786348 | −0.0390258 | ||||||||
\(407\) | −25.2904 | −1.25360 | ||||||||
\(408\) | −0.545609 | −0.0270117 | ||||||||
\(409\) | 4.93243 | 0.243893 | 0.121947 | − | 0.992537i | \(-0.461086\pi\) | ||||
0.121947 | + | 0.992537i | \(0.461086\pi\) | |||||||
\(410\) | 13.2080 | 0.652298 | ||||||||
\(411\) | 0.648302 | 0.0319784 | ||||||||
\(412\) | −5.60825 | −0.276299 | ||||||||
\(413\) | −2.99308 | −0.147280 | ||||||||
\(414\) | 2.97642 | 0.146283 | ||||||||
\(415\) | 6.27927 | 0.308237 | ||||||||
\(416\) | 0.295907 | 0.0145080 | ||||||||
\(417\) | −1.27343 | −0.0623601 | ||||||||
\(418\) | −7.65742 | −0.374536 | ||||||||
\(419\) | 38.8184 | 1.89640 | 0.948201 | − | 0.317672i | \(-0.102901\pi\) | ||||
0.948201 | + | 0.317672i | \(0.102901\pi\) | |||||||
\(420\) | −0.401358 | −0.0195843 | ||||||||
\(421\) | 8.44366 | 0.411519 | 0.205759 | − | 0.978603i | \(-0.434034\pi\) | ||||
0.205759 | + | 0.978603i | \(0.434034\pi\) | |||||||
\(422\) | −7.30620 | −0.355660 | ||||||||
\(423\) | 3.68001 | 0.178928 | ||||||||
\(424\) | 1.82898 | 0.0888233 | ||||||||
\(425\) | 21.4878 | 1.04231 | ||||||||
\(426\) | −1.24256 | −0.0602024 | ||||||||
\(427\) | −8.66089 | −0.419130 | ||||||||
\(428\) | −4.43459 | −0.214354 | ||||||||
\(429\) | −0.141050 | −0.00680997 | ||||||||
\(430\) | 12.0665 | 0.581897 | ||||||||
\(431\) | 18.6415 | 0.897931 | 0.448966 | − | 0.893549i | \(-0.351793\pi\) | ||||
0.448966 | + | 0.893549i | \(0.351793\pi\) | |||||||
\(432\) | 0.917745 | 0.0441550 | ||||||||
\(433\) | 29.1526 | 1.40098 | 0.700492 | − | 0.713660i | \(-0.252964\pi\) | ||||
0.700492 | + | 0.713660i | \(0.252964\pi\) | |||||||
\(434\) | 3.98639 | 0.191353 | ||||||||
\(435\) | 0.510408 | 0.0244722 | ||||||||
\(436\) | −1.63054 | −0.0780888 | ||||||||
\(437\) | 2.46686 | 0.118006 | ||||||||
\(438\) | 0.929222 | 0.0443999 | ||||||||
\(439\) | 38.7508 | 1.84948 | 0.924738 | − | 0.380605i | \(-0.124284\pi\) | ||||
0.924738 | + | 0.380605i | \(0.124284\pi\) | |||||||
\(440\) | 10.3175 | 0.491867 | ||||||||
\(441\) | 18.9945 | 0.904499 | ||||||||
\(442\) | 1.05137 | 0.0500086 | ||||||||
\(443\) | −26.1856 | −1.24412 | −0.622059 | − | 0.782971i | \(-0.713704\pi\) | ||||
−0.622059 | + | 0.782971i | \(0.713704\pi\) | |||||||
\(444\) | 1.25112 | 0.0593754 | ||||||||
\(445\) | 0.00487818 | 0.000231248 0 | ||||||||
\(446\) | −1.08883 | −0.0515574 | ||||||||
\(447\) | 1.39597 | 0.0660270 | ||||||||
\(448\) | 0.786348 | 0.0371515 | ||||||||
\(449\) | 29.6785 | 1.40062 | 0.700308 | − | 0.713841i | \(-0.253046\pi\) | ||||
0.700308 | + | 0.713841i | \(0.253046\pi\) | |||||||
\(450\) | −18.0006 | −0.848555 | ||||||||
\(451\) | 12.3350 | 0.580833 | ||||||||
\(452\) | 15.0343 | 0.707152 | ||||||||
\(453\) | −0.646847 | −0.0303915 | ||||||||
\(454\) | −18.4984 | −0.868173 | ||||||||
\(455\) | 0.773405 | 0.0362578 | ||||||||
\(456\) | 0.378813 | 0.0177396 | ||||||||
\(457\) | 25.1917 | 1.17842 | 0.589208 | − | 0.807981i | \(-0.299440\pi\) | ||||
0.589208 | + | 0.807981i | \(0.299440\pi\) | |||||||
\(458\) | −15.2651 | −0.713290 | ||||||||
\(459\) | 3.26079 | 0.152200 | ||||||||
\(460\) | −3.32381 | −0.154974 | ||||||||
\(461\) | −18.7697 | −0.874191 | −0.437096 | − | 0.899415i | \(-0.643993\pi\) | ||||
−0.437096 | + | 0.899415i | \(0.643993\pi\) | |||||||
\(462\) | −0.374829 | −0.0174386 | ||||||||
\(463\) | −18.9529 | −0.880817 | −0.440409 | − | 0.897797i | \(-0.645166\pi\) | ||||
−0.440409 | + | 0.897797i | \(0.645166\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −2.58751 | −0.119993 | ||||||||
\(466\) | −16.2197 | −0.751364 | ||||||||
\(467\) | 2.88750 | 0.133617 | 0.0668087 | − | 0.997766i | \(-0.478718\pi\) | ||||
0.0668087 | + | 0.997766i | \(0.478718\pi\) | |||||||
\(468\) | −0.880744 | −0.0407124 | ||||||||
\(469\) | 7.63794 | 0.352687 | ||||||||
\(470\) | −4.10952 | −0.189558 | ||||||||
\(471\) | 0.314595 | 0.0144958 | ||||||||
\(472\) | −3.80630 | −0.175199 | ||||||||
\(473\) | 11.2689 | 0.518145 | ||||||||
\(474\) | 1.03548 | 0.0475611 | ||||||||
\(475\) | −14.9189 | −0.684526 | ||||||||
\(476\) | 2.79393 | 0.128060 | ||||||||
\(477\) | −5.44382 | −0.249255 | ||||||||
\(478\) | −2.01739 | −0.0922734 | ||||||||
\(479\) | −23.4330 | −1.07068 | −0.535340 | − | 0.844637i | \(-0.679816\pi\) | ||||
−0.535340 | + | 0.844637i | \(0.679816\pi\) | |||||||
\(480\) | −0.510408 | −0.0232968 | ||||||||
\(481\) | −2.41087 | −0.109926 | ||||||||
\(482\) | −18.5299 | −0.844014 | ||||||||
\(483\) | 0.120752 | 0.00549442 | ||||||||
\(484\) | −1.36448 | −0.0620216 | ||||||||
\(485\) | −33.8166 | −1.53553 | ||||||||
\(486\) | −4.10278 | −0.186106 | ||||||||
\(487\) | 8.81070 | 0.399251 | 0.199626 | − | 0.979872i | \(-0.436027\pi\) | ||||
0.199626 | + | 0.979872i | \(0.436027\pi\) | |||||||
\(488\) | −11.0141 | −0.498584 | ||||||||
\(489\) | −0.631883 | −0.0285747 | ||||||||
\(490\) | −21.2114 | −0.958235 | ||||||||
\(491\) | −15.2789 | −0.689528 | −0.344764 | − | 0.938689i | \(-0.612041\pi\) | ||||
−0.344764 | + | 0.938689i | \(0.612041\pi\) | |||||||
\(492\) | −0.610215 | −0.0275106 | ||||||||
\(493\) | −3.55304 | −0.160021 | ||||||||
\(494\) | −0.729962 | −0.0328425 | ||||||||
\(495\) | −30.7092 | −1.38027 | ||||||||
\(496\) | 5.06950 | 0.227627 | ||||||||
\(497\) | 6.36287 | 0.285414 | ||||||||
\(498\) | −0.290104 | −0.0129999 | ||||||||
\(499\) | −34.2517 | −1.53331 | −0.766657 | − | 0.642056i | \(-0.778082\pi\) | ||||
−0.766657 | + | 0.642056i | \(0.778082\pi\) | |||||||
\(500\) | 3.48244 | 0.155739 | ||||||||
\(501\) | −1.12416 | −0.0502238 | ||||||||
\(502\) | 8.18230 | 0.365194 | ||||||||
\(503\) | 34.3060 | 1.52963 | 0.764814 | − | 0.644251i | \(-0.222831\pi\) | ||||
0.764814 | + | 0.644251i | \(0.222831\pi\) | |||||||
\(504\) | −2.34050 | −0.104254 | ||||||||
\(505\) | 28.1249 | 1.25154 | ||||||||
\(506\) | −3.10411 | −0.137995 | ||||||||
\(507\) | 1.98285 | 0.0880613 | ||||||||
\(508\) | −1.23989 | −0.0550113 | ||||||||
\(509\) | −4.95216 | −0.219501 | −0.109750 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109750 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(510\) | −1.81350 | −0.0803032 | ||||||||
\(511\) | −4.75832 | −0.210496 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.26395 | −0.0999557 | ||||||||
\(514\) | −27.1136 | −1.19593 | ||||||||
\(515\) | −18.6408 | −0.821410 | ||||||||
\(516\) | −0.557474 | −0.0245414 | ||||||||
\(517\) | −3.83789 | −0.168790 | ||||||||
\(518\) | −6.40667 | −0.281493 | ||||||||
\(519\) | 0.705339 | 0.0309609 | ||||||||
\(520\) | 0.983540 | 0.0431311 | ||||||||
\(521\) | 5.60142 | 0.245402 | 0.122701 | − | 0.992444i | \(-0.460844\pi\) | ||||
0.122701 | + | 0.992444i | \(0.460844\pi\) | |||||||
\(522\) | 2.97642 | 0.130274 | ||||||||
\(523\) | 17.9744 | 0.785967 | 0.392983 | − | 0.919546i | \(-0.371443\pi\) | ||||
0.392983 | + | 0.919546i | \(0.371443\pi\) | |||||||
\(524\) | 0.713793 | 0.0311822 | ||||||||
\(525\) | −0.730277 | −0.0318719 | ||||||||
\(526\) | 17.4454 | 0.760656 | ||||||||
\(527\) | 18.0121 | 0.784621 | ||||||||
\(528\) | −0.476671 | −0.0207444 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.07920 | 0.264063 | ||||||||
\(531\) | 11.3291 | 0.491643 | ||||||||
\(532\) | −1.93981 | −0.0841015 | ||||||||
\(533\) | 1.17586 | 0.0509323 | ||||||||
\(534\) | −0.000225373 0 | −9.75285e−6 0 | ||||||||
\(535\) | −14.7397 | −0.637255 | ||||||||
\(536\) | 9.71317 | 0.419545 | ||||||||
\(537\) | 0.317120 | 0.0136847 | ||||||||
\(538\) | −20.3410 | −0.876963 | ||||||||
\(539\) | −19.8094 | −0.853251 | ||||||||
\(540\) | 3.05041 | 0.131269 | ||||||||
\(541\) | 42.9108 | 1.84488 | 0.922439 | − | 0.386142i | \(-0.126193\pi\) | ||||
0.922439 | + | 0.386142i | \(0.126193\pi\) | |||||||
\(542\) | 15.9266 | 0.684105 | ||||||||
\(543\) | −1.32759 | −0.0569724 | ||||||||
\(544\) | 3.55304 | 0.152335 | ||||||||
\(545\) | −5.41961 | −0.232151 | ||||||||
\(546\) | −0.0357315 | −0.00152917 | ||||||||
\(547\) | −19.8283 | −0.847796 | −0.423898 | − | 0.905710i | \(-0.639339\pi\) | ||||
−0.423898 | + | 0.905710i | \(0.639339\pi\) | |||||||
\(548\) | −4.22179 | −0.180346 | ||||||||
\(549\) | 32.7825 | 1.39912 | ||||||||
\(550\) | 18.7728 | 0.800476 | ||||||||
\(551\) | 2.46686 | 0.105092 | ||||||||
\(552\) | 0.153561 | 0.00653599 | ||||||||
\(553\) | −5.30244 | −0.225482 | ||||||||
\(554\) | −12.3405 | −0.524297 | ||||||||
\(555\) | 4.15848 | 0.176518 | ||||||||
\(556\) | 8.29267 | 0.351687 | ||||||||
\(557\) | −29.0439 | −1.23063 | −0.615314 | − | 0.788282i | \(-0.710971\pi\) | ||||
−0.615314 | + | 0.788282i | \(0.710971\pi\) | |||||||
\(558\) | −15.0889 | −0.638766 | ||||||||
\(559\) | 1.07424 | 0.0454353 | ||||||||
\(560\) | 2.61367 | 0.110448 | ||||||||
\(561\) | −1.69363 | −0.0715052 | ||||||||
\(562\) | −11.2282 | −0.473634 | ||||||||
\(563\) | 37.5653 | 1.58319 | 0.791595 | − | 0.611046i | \(-0.209251\pi\) | ||||
0.791595 | + | 0.611046i | \(0.209251\pi\) | |||||||
\(564\) | 0.189861 | 0.00799458 | ||||||||
\(565\) | 49.9711 | 2.10230 | ||||||||
\(566\) | −5.58632 | −0.234810 | ||||||||
\(567\) | 6.91068 | 0.290221 | ||||||||
\(568\) | 8.09167 | 0.339519 | ||||||||
\(569\) | 4.17484 | 0.175019 | 0.0875093 | − | 0.996164i | \(-0.472109\pi\) | ||||
0.0875093 | + | 0.996164i | \(0.472109\pi\) | |||||||
\(570\) | 1.25910 | 0.0527381 | ||||||||
\(571\) | 17.1823 | 0.719058 | 0.359529 | − | 0.933134i | \(-0.382937\pi\) | ||||
0.359529 | + | 0.933134i | \(0.382937\pi\) | |||||||
\(572\) | 0.918530 | 0.0384057 | ||||||||
\(573\) | 2.74043 | 0.114483 | ||||||||
\(574\) | 3.12476 | 0.130425 | ||||||||
\(575\) | −6.04772 | −0.252208 | ||||||||
\(576\) | −2.97642 | −0.124017 | ||||||||
\(577\) | 21.9897 | 0.915445 | 0.457723 | − | 0.889095i | \(-0.348665\pi\) | ||||
0.457723 | + | 0.889095i | \(0.348665\pi\) | |||||||
\(578\) | −4.37588 | −0.182013 | ||||||||
\(579\) | 0.901977 | 0.0374849 | ||||||||
\(580\) | −3.32381 | −0.138014 | ||||||||
\(581\) | 1.48555 | 0.0616310 | ||||||||
\(582\) | 1.56233 | 0.0647609 | ||||||||
\(583\) | 5.67737 | 0.235133 | ||||||||
\(584\) | −6.05116 | −0.250399 | ||||||||
\(585\) | −2.92743 | −0.121034 | ||||||||
\(586\) | −0.961095 | −0.0397024 | ||||||||
\(587\) | −22.2732 | −0.919312 | −0.459656 | − | 0.888097i | \(-0.652027\pi\) | ||||
−0.459656 | + | 0.888097i | \(0.652027\pi\) | |||||||
\(588\) | 0.979973 | 0.0404134 | ||||||||
\(589\) | −12.5057 | −0.515290 | ||||||||
\(590\) | −12.6514 | −0.520851 | ||||||||
\(591\) | −0.623630 | −0.0256527 | ||||||||
\(592\) | −8.14737 | −0.334855 | ||||||||
\(593\) | −43.6602 | −1.79291 | −0.896455 | − | 0.443134i | \(-0.853866\pi\) | ||||
−0.896455 | + | 0.443134i | \(0.853866\pi\) | |||||||
\(594\) | 2.84878 | 0.116887 | ||||||||
\(595\) | 9.28649 | 0.380709 | ||||||||
\(596\) | −9.09064 | −0.372367 | ||||||||
\(597\) | 1.33593 | 0.0546758 | ||||||||
\(598\) | −0.295907 | −0.0121005 | ||||||||
\(599\) | 47.3562 | 1.93492 | 0.967460 | − | 0.253023i | \(-0.0814249\pi\) | ||||
0.967460 | + | 0.253023i | \(0.0814249\pi\) | |||||||
\(600\) | −0.928694 | −0.0379138 | ||||||||
\(601\) | 21.6046 | 0.881269 | 0.440634 | − | 0.897687i | \(-0.354754\pi\) | ||||
0.440634 | + | 0.897687i | \(0.354754\pi\) | |||||||
\(602\) | 2.85469 | 0.116348 | ||||||||
\(603\) | −28.9105 | −1.17733 | ||||||||
\(604\) | 4.21232 | 0.171397 | ||||||||
\(605\) | −4.53526 | −0.184384 | ||||||||
\(606\) | −1.29938 | −0.0527836 | ||||||||
\(607\) | 13.9265 | 0.565260 | 0.282630 | − | 0.959229i | \(-0.408793\pi\) | ||||
0.282630 | + | 0.959229i | \(0.408793\pi\) | |||||||
\(608\) | −2.46686 | −0.100044 | ||||||||
\(609\) | 0.120752 | 0.00489313 | ||||||||
\(610\) | −36.6087 | −1.48224 | ||||||||
\(611\) | −0.365856 | −0.0148009 | ||||||||
\(612\) | −10.5753 | −0.427483 | ||||||||
\(613\) | 3.71864 | 0.150195 | 0.0750973 | − | 0.997176i | \(-0.476073\pi\) | ||||
0.0750973 | + | 0.997176i | \(0.476073\pi\) | |||||||
\(614\) | 0.670924 | 0.0270763 | ||||||||
\(615\) | −2.02824 | −0.0817865 | ||||||||
\(616\) | 2.44091 | 0.0983472 | ||||||||
\(617\) | 34.8870 | 1.40450 | 0.702248 | − | 0.711932i | \(-0.252180\pi\) | ||||
0.702248 | + | 0.711932i | \(0.252180\pi\) | |||||||
\(618\) | 0.861208 | 0.0346429 | ||||||||
\(619\) | 20.4341 | 0.821314 | 0.410657 | − | 0.911790i | \(-0.365299\pi\) | ||||
0.410657 | + | 0.911790i | \(0.365299\pi\) | |||||||
\(620\) | 16.8501 | 0.676714 | ||||||||
\(621\) | −0.917745 | −0.0368278 | ||||||||
\(622\) | −15.4376 | −0.618990 | ||||||||
\(623\) | 0.00115408 | 4.62373e−5 0 | ||||||||
\(624\) | −0.0454398 | −0.00181905 | ||||||||
\(625\) | −18.6636 | −0.746546 | ||||||||
\(626\) | 7.43893 | 0.297320 | ||||||||
\(627\) | 1.17588 | 0.0469601 | ||||||||
\(628\) | −2.04867 | −0.0817508 | ||||||||
\(629\) | −28.9480 | −1.15423 | ||||||||
\(630\) | −7.77939 | −0.309938 | ||||||||
\(631\) | 39.6233 | 1.57738 | 0.788690 | − | 0.614792i | \(-0.210760\pi\) | ||||
0.788690 | + | 0.614792i | \(0.210760\pi\) | |||||||
\(632\) | −6.74311 | −0.268227 | ||||||||
\(633\) | 1.12195 | 0.0445934 | ||||||||
\(634\) | 18.5822 | 0.737992 | ||||||||
\(635\) | −4.12116 | −0.163543 | ||||||||
\(636\) | −0.280860 | −0.0111368 | ||||||||
\(637\) | −1.88838 | −0.0748203 | ||||||||
\(638\) | −3.10411 | −0.122893 | ||||||||
\(639\) | −24.0842 | −0.952756 | ||||||||
\(640\) | 3.32381 | 0.131385 | ||||||||
\(641\) | −5.89921 | −0.233005 | −0.116502 | − | 0.993190i | \(-0.537168\pi\) | ||||
−0.116502 | + | 0.993190i | \(0.537168\pi\) | |||||||
\(642\) | 0.680980 | 0.0268761 | ||||||||
\(643\) | 44.5127 | 1.75541 | 0.877704 | − | 0.479203i | \(-0.159074\pi\) | ||||
0.877704 | + | 0.479203i | \(0.159074\pi\) | |||||||
\(644\) | −0.786348 | −0.0309865 | ||||||||
\(645\) | −1.85294 | −0.0729594 | ||||||||
\(646\) | −8.76486 | −0.344849 | ||||||||
\(647\) | −43.8740 | −1.72486 | −0.862432 | − | 0.506173i | \(-0.831060\pi\) | ||||
−0.862432 | + | 0.506173i | \(0.831060\pi\) | |||||||
\(648\) | 8.78833 | 0.345238 | ||||||||
\(649\) | −11.8152 | −0.463787 | ||||||||
\(650\) | 1.78957 | 0.0701925 | ||||||||
\(651\) | −0.612154 | −0.0239922 | ||||||||
\(652\) | 4.11487 | 0.161151 | ||||||||
\(653\) | −3.98325 | −0.155877 | −0.0779383 | − | 0.996958i | \(-0.524834\pi\) | ||||
−0.0779383 | + | 0.996958i | \(0.524834\pi\) | |||||||
\(654\) | 0.250387 | 0.00979092 | ||||||||
\(655\) | 2.37251 | 0.0927017 | ||||||||
\(656\) | 3.97376 | 0.155149 | ||||||||
\(657\) | 18.0108 | 0.702668 | ||||||||
\(658\) | −0.972231 | −0.0379015 | ||||||||
\(659\) | −34.4171 | −1.34070 | −0.670349 | − | 0.742046i | \(-0.733856\pi\) | ||||
−0.670349 | + | 0.742046i | \(0.733856\pi\) | |||||||
\(660\) | −1.58436 | −0.0616713 | ||||||||
\(661\) | 22.2203 | 0.864271 | 0.432135 | − | 0.901809i | \(-0.357760\pi\) | ||||
0.432135 | + | 0.901809i | \(0.357760\pi\) | |||||||
\(662\) | 11.0559 | 0.429699 | ||||||||
\(663\) | −0.161450 | −0.00627018 | ||||||||
\(664\) | 1.88918 | 0.0733143 | ||||||||
\(665\) | −6.44757 | −0.250026 | ||||||||
\(666\) | 24.2500 | 0.939668 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 7.32062 | 0.283243 | ||||||||
\(669\) | 0.167201 | 0.00646436 | ||||||||
\(670\) | 32.2848 | 1.24727 | ||||||||
\(671\) | −34.1889 | −1.31985 | ||||||||
\(672\) | −0.120752 | −0.00465812 | ||||||||
\(673\) | −12.8140 | −0.493945 | −0.246973 | − | 0.969022i | \(-0.579436\pi\) | ||||
−0.246973 | + | 0.969022i | \(0.579436\pi\) | |||||||
\(674\) | −29.8194 | −1.14860 | ||||||||
\(675\) | 5.55027 | 0.213630 | ||||||||
\(676\) | −12.9124 | −0.496632 | ||||||||
\(677\) | −6.97407 | −0.268035 | −0.134018 | − | 0.990979i | \(-0.542788\pi\) | ||||
−0.134018 | + | 0.990979i | \(0.542788\pi\) | |||||||
\(678\) | −2.30868 | −0.0886642 | ||||||||
\(679\) | −8.00033 | −0.307025 | ||||||||
\(680\) | 11.8096 | 0.452879 | ||||||||
\(681\) | 2.84063 | 0.108853 | ||||||||
\(682\) | 15.7363 | 0.602574 | ||||||||
\(683\) | −38.7487 | −1.48268 | −0.741339 | − | 0.671131i | \(-0.765809\pi\) | ||||
−0.741339 | + | 0.671131i | \(0.765809\pi\) | |||||||
\(684\) | 7.34241 | 0.280744 | ||||||||
\(685\) | −14.0324 | −0.536151 | ||||||||
\(686\) | −10.5226 | −0.401756 | ||||||||
\(687\) | 2.34412 | 0.0894338 | ||||||||
\(688\) | 3.63031 | 0.138404 | ||||||||
\(689\) | 0.541209 | 0.0206184 | ||||||||
\(690\) | 0.510408 | 0.0194309 | ||||||||
\(691\) | 22.4378 | 0.853574 | 0.426787 | − | 0.904352i | \(-0.359645\pi\) | ||||
0.426787 | + | 0.904352i | \(0.359645\pi\) | |||||||
\(692\) | −4.59322 | −0.174608 | ||||||||
\(693\) | −7.26518 | −0.275982 | ||||||||
\(694\) | 6.96245 | 0.264291 | ||||||||
\(695\) | 27.5633 | 1.04553 | ||||||||
\(696\) | 0.153561 | 0.00582071 | ||||||||
\(697\) | 14.1189 | 0.534793 | ||||||||
\(698\) | 2.23162 | 0.0844680 | ||||||||
\(699\) | 2.49072 | 0.0942075 | ||||||||
\(700\) | 4.75562 | 0.179745 | ||||||||
\(701\) | −4.06194 | −0.153417 | −0.0767086 | − | 0.997054i | \(-0.524441\pi\) | ||||
−0.0767086 | + | 0.997054i | \(0.524441\pi\) | |||||||
\(702\) | 0.271567 | 0.0102496 | ||||||||
\(703\) | 20.0984 | 0.758026 | ||||||||
\(704\) | 3.10411 | 0.116991 | ||||||||
\(705\) | 0.631062 | 0.0237672 | ||||||||
\(706\) | 17.8270 | 0.670926 | ||||||||
\(707\) | 6.65380 | 0.250242 | ||||||||
\(708\) | 0.584499 | 0.0219668 | ||||||||
\(709\) | −31.5431 | −1.18463 | −0.592313 | − | 0.805708i | \(-0.701785\pi\) | ||||
−0.592313 | + | 0.805708i | \(0.701785\pi\) | |||||||
\(710\) | 26.8952 | 1.00936 | ||||||||
\(711\) | 20.0703 | 0.752696 | ||||||||
\(712\) | 0.00146765 | 5.50024e−5 0 | ||||||||
\(713\) | −5.06950 | −0.189854 | ||||||||
\(714\) | −0.429038 | −0.0160564 | ||||||||
\(715\) | 3.05302 | 0.114176 | ||||||||
\(716\) | −2.06511 | −0.0771768 | ||||||||
\(717\) | 0.309793 | 0.0115694 | ||||||||
\(718\) | 13.7562 | 0.513377 | ||||||||
\(719\) | −46.7672 | −1.74412 | −0.872060 | − | 0.489398i | \(-0.837217\pi\) | ||||
−0.872060 | + | 0.489398i | \(0.837217\pi\) | |||||||
\(720\) | −9.89306 | −0.368692 | ||||||||
\(721\) | −4.41004 | −0.164238 | ||||||||
\(722\) | −12.9146 | −0.480632 | ||||||||
\(723\) | 2.84547 | 0.105824 | ||||||||
\(724\) | 8.64537 | 0.321303 | ||||||||
\(725\) | −6.04772 | −0.224607 | ||||||||
\(726\) | 0.209530 | 0.00777639 | ||||||||
\(727\) | −17.0320 | −0.631681 | −0.315841 | − | 0.948812i | \(-0.602287\pi\) | ||||
−0.315841 | + | 0.948812i | \(0.602287\pi\) | |||||||
\(728\) | 0.232686 | 0.00862392 | ||||||||
\(729\) | −25.7350 | −0.953147 | ||||||||
\(730\) | −20.1129 | −0.744413 | ||||||||
\(731\) | 12.8987 | 0.477074 | ||||||||
\(732\) | 1.69133 | 0.0625134 | ||||||||
\(733\) | 42.5421 | 1.57133 | 0.785663 | − | 0.618654i | \(-0.212322\pi\) | ||||
0.785663 | + | 0.618654i | \(0.212322\pi\) | |||||||
\(734\) | 13.2990 | 0.490875 | ||||||||
\(735\) | 3.25725 | 0.120145 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 30.1508 | 1.11062 | ||||||||
\(738\) | −11.8276 | −0.435379 | ||||||||
\(739\) | 44.4525 | 1.63521 | 0.817607 | − | 0.575777i | \(-0.195300\pi\) | ||||
0.817607 | + | 0.575777i | \(0.195300\pi\) | |||||||
\(740\) | −27.0803 | −0.995493 | ||||||||
\(741\) | 0.112094 | 0.00411786 | ||||||||
\(742\) | 1.43822 | 0.0527986 | ||||||||
\(743\) | 28.4255 | 1.04283 | 0.521416 | − | 0.853303i | \(-0.325404\pi\) | ||||
0.521416 | + | 0.853303i | \(0.325404\pi\) | |||||||
\(744\) | −0.778477 | −0.0285403 | ||||||||
\(745\) | −30.2156 | −1.10701 | ||||||||
\(746\) | 10.4378 | 0.382154 | ||||||||
\(747\) | −5.62298 | −0.205734 | ||||||||
\(748\) | 11.0291 | 0.403262 | ||||||||
\(749\) | −3.48713 | −0.127417 | ||||||||
\(750\) | −0.534767 | −0.0195269 | ||||||||
\(751\) | −22.9163 | −0.836227 | −0.418114 | − | 0.908395i | \(-0.637309\pi\) | ||||
−0.418114 | + | 0.908395i | \(0.637309\pi\) | |||||||
\(752\) | −1.23639 | −0.0450864 | ||||||||
\(753\) | −1.25648 | −0.0457887 | ||||||||
\(754\) | −0.295907 | −0.0107763 | ||||||||
\(755\) | 14.0009 | 0.509546 | ||||||||
\(756\) | 0.721667 | 0.0262468 | ||||||||
\(757\) | −52.0669 | −1.89240 | −0.946201 | − | 0.323579i | \(-0.895114\pi\) | ||||
−0.946201 | + | 0.323579i | \(0.895114\pi\) | |||||||
\(758\) | 28.1135 | 1.02113 | ||||||||
\(759\) | 0.476671 | 0.0173021 | ||||||||
\(760\) | −8.19938 | −0.297423 | ||||||||
\(761\) | 30.5328 | 1.10681 | 0.553407 | − | 0.832911i | \(-0.313327\pi\) | ||||
0.553407 | + | 0.832911i | \(0.313327\pi\) | |||||||
\(762\) | 0.190399 | 0.00689742 | ||||||||
\(763\) | −1.28217 | −0.0464178 | ||||||||
\(764\) | −17.8459 | −0.645642 | ||||||||
\(765\) | −35.1505 | −1.27087 | ||||||||
\(766\) | −14.0928 | −0.509194 | ||||||||
\(767\) | −1.12631 | −0.0406688 | ||||||||
\(768\) | −0.153561 | −0.00554115 | ||||||||
\(769\) | 19.1728 | 0.691388 | 0.345694 | − | 0.938347i | \(-0.387643\pi\) | ||||
0.345694 | + | 0.938347i | \(0.387643\pi\) | |||||||
\(770\) | 8.11314 | 0.292377 | ||||||||
\(771\) | 4.16359 | 0.149948 | ||||||||
\(772\) | −5.87374 | −0.211401 | ||||||||
\(773\) | 9.14339 | 0.328865 | 0.164432 | − | 0.986388i | \(-0.447421\pi\) | ||||
0.164432 | + | 0.986388i | \(0.447421\pi\) | |||||||
\(774\) | −10.8053 | −0.388389 | ||||||||
\(775\) | 30.6589 | 1.10130 | ||||||||
\(776\) | −10.1740 | −0.365227 | ||||||||
\(777\) | 0.983815 | 0.0352941 | ||||||||
\(778\) | 21.4862 | 0.770319 | ||||||||
\(779\) | −9.80271 | −0.351219 | ||||||||
\(780\) | −0.151033 | −0.00540786 | ||||||||
\(781\) | 25.1175 | 0.898773 | ||||||||
\(782\) | −3.55304 | −0.127057 | ||||||||
\(783\) | −0.917745 | −0.0327975 | ||||||||
\(784\) | −6.38166 | −0.227916 | ||||||||
\(785\) | −6.80939 | −0.243037 | ||||||||
\(786\) | −0.109611 | −0.00390968 | ||||||||
\(787\) | −34.4612 | −1.22841 | −0.614205 | − | 0.789147i | \(-0.710523\pi\) | ||||
−0.614205 | + | 0.789147i | \(0.710523\pi\) | |||||||
\(788\) | 4.06113 | 0.144672 | ||||||||
\(789\) | −2.67893 | −0.0953726 | ||||||||
\(790\) | −22.4128 | −0.797413 | ||||||||
\(791\) | 11.8222 | 0.420348 | ||||||||
\(792\) | −9.23914 | −0.328299 | ||||||||
\(793\) | −3.25914 | −0.115736 | ||||||||
\(794\) | 4.59406 | 0.163037 | ||||||||
\(795\) | −0.933527 | −0.0331088 | ||||||||
\(796\) | −8.69965 | −0.308351 | ||||||||
\(797\) | 7.92684 | 0.280783 | 0.140391 | − | 0.990096i | \(-0.455164\pi\) | ||||
0.140391 | + | 0.990096i | \(0.455164\pi\) | |||||||
\(798\) | 0.297879 | 0.0105448 | ||||||||
\(799\) | −4.39294 | −0.155411 | ||||||||
\(800\) | 6.04772 | 0.213819 | ||||||||
\(801\) | −0.00436833 | −0.000154347 0 | ||||||||
\(802\) | −8.77930 | −0.310008 | ||||||||
\(803\) | −18.7835 | −0.662855 | ||||||||
\(804\) | −1.49156 | −0.0526034 | ||||||||
\(805\) | −2.61367 | −0.0921199 | ||||||||
\(806\) | 1.50010 | 0.0528388 | ||||||||
\(807\) | 3.12358 | 0.109955 | ||||||||
\(808\) | 8.46165 | 0.297680 | ||||||||
\(809\) | 45.3458 | 1.59427 | 0.797136 | − | 0.603799i | \(-0.206347\pi\) | ||||
0.797136 | + | 0.603799i | \(0.206347\pi\) | |||||||
\(810\) | 29.2107 | 1.02636 | ||||||||
\(811\) | 3.26357 | 0.114599 | 0.0572997 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0572997 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(812\) | −0.786348 | −0.0275954 | ||||||||
\(813\) | −2.44570 | −0.0857745 | ||||||||
\(814\) | −25.2904 | −0.886427 | ||||||||
\(815\) | 13.6770 | 0.479086 | ||||||||
\(816\) | −0.545609 | −0.0191001 | ||||||||
\(817\) | −8.95547 | −0.313312 | ||||||||
\(818\) | 4.93243 | 0.172459 | ||||||||
\(819\) | −0.692571 | −0.0242004 | ||||||||
\(820\) | 13.2080 | 0.461245 | ||||||||
\(821\) | 3.47757 | 0.121368 | 0.0606840 | − | 0.998157i | \(-0.480672\pi\) | ||||
0.0606840 | + | 0.998157i | \(0.480672\pi\) | |||||||
\(822\) | 0.648302 | 0.0226121 | ||||||||
\(823\) | 3.17799 | 0.110778 | 0.0553889 | − | 0.998465i | \(-0.482360\pi\) | ||||
0.0553889 | + | 0.998465i | \(0.482360\pi\) | |||||||
\(824\) | −5.60825 | −0.195373 | ||||||||
\(825\) | −2.88277 | −0.100365 | ||||||||
\(826\) | −2.99308 | −0.104142 | ||||||||
\(827\) | 5.46969 | 0.190200 | 0.0950999 | − | 0.995468i | \(-0.469683\pi\) | ||||
0.0950999 | + | 0.995468i | \(0.469683\pi\) | |||||||
\(828\) | 2.97642 | 0.103438 | ||||||||
\(829\) | 17.8922 | 0.621423 | 0.310711 | − | 0.950504i | \(-0.399433\pi\) | ||||
0.310711 | + | 0.950504i | \(0.399433\pi\) | |||||||
\(830\) | 6.27927 | 0.217957 | ||||||||
\(831\) | 1.89502 | 0.0657374 | ||||||||
\(832\) | 0.295907 | 0.0102587 | ||||||||
\(833\) | −22.6743 | −0.785618 | ||||||||
\(834\) | −1.27343 | −0.0440953 | ||||||||
\(835\) | 24.3324 | 0.842056 | ||||||||
\(836\) | −7.65742 | −0.264837 | ||||||||
\(837\) | 4.65250 | 0.160814 | ||||||||
\(838\) | 38.8184 | 1.34096 | ||||||||
\(839\) | −39.5344 | −1.36488 | −0.682439 | − | 0.730942i | \(-0.739081\pi\) | ||||
−0.682439 | + | 0.730942i | \(0.739081\pi\) | |||||||
\(840\) | −0.401358 | −0.0138482 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 8.44366 | 0.290988 | ||||||||
\(843\) | 1.72422 | 0.0593852 | ||||||||
\(844\) | −7.30620 | −0.251490 | ||||||||
\(845\) | −42.9185 | −1.47644 | ||||||||
\(846\) | 3.68001 | 0.126521 | ||||||||
\(847\) | −1.07295 | −0.0368671 | ||||||||
\(848\) | 1.82898 | 0.0628076 | ||||||||
\(849\) | 0.857840 | 0.0294410 | ||||||||
\(850\) | 21.4878 | 0.737026 | ||||||||
\(851\) | 8.14737 | 0.279288 | ||||||||
\(852\) | −1.24256 | −0.0425696 | ||||||||
\(853\) | −1.68475 | −0.0576847 | −0.0288424 | − | 0.999584i | \(-0.509182\pi\) | ||||
−0.0288424 | + | 0.999584i | \(0.509182\pi\) | |||||||
\(854\) | −8.66089 | −0.296370 | ||||||||
\(855\) | 24.4048 | 0.834626 | ||||||||
\(856\) | −4.43459 | −0.151571 | ||||||||
\(857\) | 6.31178 | 0.215606 | 0.107803 | − | 0.994172i | \(-0.465618\pi\) | ||||
0.107803 | + | 0.994172i | \(0.465618\pi\) | |||||||
\(858\) | −0.141050 | −0.00481538 | ||||||||
\(859\) | 31.9648 | 1.09062 | 0.545312 | − | 0.838233i | \(-0.316411\pi\) | ||||
0.545312 | + | 0.838233i | \(0.316411\pi\) | |||||||
\(860\) | 12.0665 | 0.411463 | ||||||||
\(861\) | −0.479841 | −0.0163529 | ||||||||
\(862\) | 18.6415 | 0.634933 | ||||||||
\(863\) | 3.06550 | 0.104351 | 0.0521755 | − | 0.998638i | \(-0.483384\pi\) | ||||
0.0521755 | + | 0.998638i | \(0.483384\pi\) | |||||||
\(864\) | 0.917745 | 0.0312223 | ||||||||
\(865\) | −15.2670 | −0.519093 | ||||||||
\(866\) | 29.1526 | 0.990645 | ||||||||
\(867\) | 0.671965 | 0.0228211 | ||||||||
\(868\) | 3.98639 | 0.135307 | ||||||||
\(869\) | −20.9314 | −0.710049 | ||||||||
\(870\) | 0.510408 | 0.0173044 | ||||||||
\(871\) | 2.87420 | 0.0973885 | ||||||||
\(872\) | −1.63054 | −0.0552171 | ||||||||
\(873\) | 30.2822 | 1.02490 | ||||||||
\(874\) | 2.46686 | 0.0834428 | ||||||||
\(875\) | 2.73841 | 0.0925751 | ||||||||
\(876\) | 0.929222 | 0.0313955 | ||||||||
\(877\) | 15.2955 | 0.516493 | 0.258246 | − | 0.966079i | \(-0.416855\pi\) | ||||
0.258246 | + | 0.966079i | \(0.416855\pi\) | |||||||
\(878\) | 38.7508 | 1.30778 | ||||||||
\(879\) | 0.147587 | 0.00497797 | ||||||||
\(880\) | 10.3175 | 0.347803 | ||||||||
\(881\) | 28.3526 | 0.955222 | 0.477611 | − | 0.878571i | \(-0.341503\pi\) | ||||
0.477611 | + | 0.878571i | \(0.341503\pi\) | |||||||
\(882\) | 18.9945 | 0.639578 | ||||||||
\(883\) | −17.4488 | −0.587200 | −0.293600 | − | 0.955928i | \(-0.594853\pi\) | ||||
−0.293600 | + | 0.955928i | \(0.594853\pi\) | |||||||
\(884\) | 1.05137 | 0.0353614 | ||||||||
\(885\) | 1.94276 | 0.0653053 | ||||||||
\(886\) | −26.1856 | −0.879724 | ||||||||
\(887\) | 31.1862 | 1.04713 | 0.523565 | − | 0.851985i | \(-0.324602\pi\) | ||||
0.523565 | + | 0.851985i | \(0.324602\pi\) | |||||||
\(888\) | 1.25112 | 0.0419848 | ||||||||
\(889\) | −0.974986 | −0.0327000 | ||||||||
\(890\) | 0.00487818 | 0.000163517 0 | ||||||||
\(891\) | 27.2800 | 0.913913 | ||||||||
\(892\) | −1.08883 | −0.0364566 | ||||||||
\(893\) | 3.04999 | 0.102064 | ||||||||
\(894\) | 1.39597 | 0.0466881 | ||||||||
\(895\) | −6.86403 | −0.229439 | ||||||||
\(896\) | 0.786348 | 0.0262700 | ||||||||
\(897\) | 0.0454398 | 0.00151719 | ||||||||
\(898\) | 29.6785 | 0.990384 | ||||||||
\(899\) | −5.06950 | −0.169077 | ||||||||
\(900\) | −18.0006 | −0.600019 | ||||||||
\(901\) | 6.49846 | 0.216495 | ||||||||
\(902\) | 12.3350 | 0.410711 | ||||||||
\(903\) | −0.438369 | −0.0145880 | ||||||||
\(904\) | 15.0343 | 0.500032 | ||||||||
\(905\) | 28.7356 | 0.955204 | ||||||||
\(906\) | −0.646847 | −0.0214901 | ||||||||
\(907\) | 54.3335 | 1.80412 | 0.902058 | − | 0.431615i | \(-0.142056\pi\) | ||||
0.902058 | + | 0.431615i | \(0.142056\pi\) | |||||||
\(908\) | −18.4984 | −0.613891 | ||||||||
\(909\) | −25.1854 | −0.835347 | ||||||||
\(910\) | 0.773405 | 0.0256381 | ||||||||
\(911\) | 38.5824 | 1.27829 | 0.639145 | − | 0.769086i | \(-0.279288\pi\) | ||||
0.639145 | + | 0.769086i | \(0.279288\pi\) | |||||||
\(912\) | 0.378813 | 0.0125438 | ||||||||
\(913\) | 5.86422 | 0.194077 | ||||||||
\(914\) | 25.1917 | 0.833266 | ||||||||
\(915\) | 5.62167 | 0.185847 | ||||||||
\(916\) | −15.2651 | −0.504372 | ||||||||
\(917\) | 0.561290 | 0.0185354 | ||||||||
\(918\) | 3.26079 | 0.107622 | ||||||||
\(919\) | 33.3788 | 1.10107 | 0.550533 | − | 0.834814i | \(-0.314425\pi\) | ||||
0.550533 | + | 0.834814i | \(0.314425\pi\) | |||||||
\(920\) | −3.32381 | −0.109583 | ||||||||
\(921\) | −0.103028 | −0.00339488 | ||||||||
\(922\) | −18.7697 | −0.618147 | ||||||||
\(923\) | 2.39438 | 0.0788121 | ||||||||
\(924\) | −0.374829 | −0.0123310 | ||||||||
\(925\) | −49.2731 | −1.62009 | ||||||||
\(926\) | −18.9529 | −0.622832 | ||||||||
\(927\) | 16.6925 | 0.548254 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 16.9343 | 0.555598 | 0.277799 | − | 0.960639i | \(-0.410395\pi\) | ||||
0.277799 | + | 0.960639i | \(0.410395\pi\) | |||||||
\(930\) | −2.58751 | −0.0848478 | ||||||||
\(931\) | 15.7427 | 0.515945 | ||||||||
\(932\) | −16.2197 | −0.531295 | ||||||||
\(933\) | 2.37061 | 0.0776102 | ||||||||
\(934\) | 2.88750 | 0.0944817 | ||||||||
\(935\) | 36.6585 | 1.19886 | ||||||||
\(936\) | −0.880744 | −0.0287880 | ||||||||
\(937\) | 52.8086 | 1.72518 | 0.862590 | − | 0.505903i | \(-0.168841\pi\) | ||||
0.862590 | + | 0.505903i | \(0.168841\pi\) | |||||||
\(938\) | 7.63794 | 0.249387 | ||||||||
\(939\) | −1.14233 | −0.0372785 | ||||||||
\(940\) | −4.10952 | −0.134038 | ||||||||
\(941\) | −24.1667 | −0.787813 | −0.393906 | − | 0.919151i | \(-0.628877\pi\) | ||||
−0.393906 | + | 0.919151i | \(0.628877\pi\) | |||||||
\(942\) | 0.314595 | 0.0102501 | ||||||||
\(943\) | −3.97376 | −0.129403 | ||||||||
\(944\) | −3.80630 | −0.123884 | ||||||||
\(945\) | 2.39868 | 0.0780292 | ||||||||
\(946\) | 11.2689 | 0.366384 | ||||||||
\(947\) | −28.1149 | −0.913610 | −0.456805 | − | 0.889567i | \(-0.651006\pi\) | ||||
−0.456805 | + | 0.889567i | \(0.651006\pi\) | |||||||
\(948\) | 1.03548 | 0.0336308 | ||||||||
\(949\) | −1.79058 | −0.0581248 | ||||||||
\(950\) | −14.9189 | −0.484033 | ||||||||
\(951\) | −2.85349 | −0.0925309 | ||||||||
\(952\) | 2.79393 | 0.0905518 | ||||||||
\(953\) | −56.7197 | −1.83733 | −0.918666 | − | 0.395035i | \(-0.870733\pi\) | ||||
−0.918666 | + | 0.395035i | \(0.870733\pi\) | |||||||
\(954\) | −5.44382 | −0.176250 | ||||||||
\(955\) | −59.3164 | −1.91943 | ||||||||
\(956\) | −2.01739 | −0.0652471 | ||||||||
\(957\) | 0.476671 | 0.0154086 | ||||||||
\(958\) | −23.4330 | −0.757085 | ||||||||
\(959\) | −3.31979 | −0.107202 | ||||||||
\(960\) | −0.510408 | −0.0164733 | ||||||||
\(961\) | −5.30020 | −0.170974 | ||||||||
\(962\) | −2.41087 | −0.0777294 | ||||||||
\(963\) | 13.1992 | 0.425338 | ||||||||
\(964\) | −18.5299 | −0.596808 | ||||||||
\(965\) | −19.5232 | −0.628474 | ||||||||
\(966\) | 0.120752 | 0.00388514 | ||||||||
\(967\) | 8.00698 | 0.257487 | 0.128744 | − | 0.991678i | \(-0.458906\pi\) | ||||
0.128744 | + | 0.991678i | \(0.458906\pi\) | |||||||
\(968\) | −1.36448 | −0.0438559 | ||||||||
\(969\) | 1.34594 | 0.0432378 | ||||||||
\(970\) | −33.8166 | −1.08578 | ||||||||
\(971\) | 26.4919 | 0.850164 | 0.425082 | − | 0.905155i | \(-0.360245\pi\) | ||||
0.425082 | + | 0.905155i | \(0.360245\pi\) | |||||||
\(972\) | −4.10278 | −0.131597 | ||||||||
\(973\) | 6.52092 | 0.209051 | ||||||||
\(974\) | 8.81070 | 0.282313 | ||||||||
\(975\) | −0.274807 | −0.00880088 | ||||||||
\(976\) | −11.0141 | −0.352552 | ||||||||
\(977\) | 51.2302 | 1.63900 | 0.819500 | − | 0.573079i | \(-0.194251\pi\) | ||||
0.819500 | + | 0.573079i | \(0.194251\pi\) | |||||||
\(978\) | −0.631883 | −0.0202054 | ||||||||
\(979\) | 0.00455574 | 0.000145602 0 | ||||||||
\(980\) | −21.2114 | −0.677574 | ||||||||
\(981\) | 4.85317 | 0.154950 | ||||||||
\(982\) | −15.2789 | −0.487570 | ||||||||
\(983\) | 42.4952 | 1.35539 | 0.677693 | − | 0.735345i | \(-0.262980\pi\) | ||||
0.677693 | + | 0.735345i | \(0.262980\pi\) | |||||||
\(984\) | −0.610215 | −0.0194529 | ||||||||
\(985\) | 13.4984 | 0.430095 | ||||||||
\(986\) | −3.55304 | −0.113152 | ||||||||
\(987\) | 0.149297 | 0.00475217 | ||||||||
\(988\) | −0.729962 | −0.0232232 | ||||||||
\(989\) | −3.63031 | −0.115437 | ||||||||
\(990\) | −30.7092 | −0.976002 | ||||||||
\(991\) | 52.0678 | 1.65399 | 0.826994 | − | 0.562210i | \(-0.190049\pi\) | ||||
0.826994 | + | 0.562210i | \(0.190049\pi\) | |||||||
\(992\) | 5.06950 | 0.160957 | ||||||||
\(993\) | −1.69775 | −0.0538765 | ||||||||
\(994\) | 6.36287 | 0.201818 | ||||||||
\(995\) | −28.9160 | −0.916699 | ||||||||
\(996\) | −0.290104 | −0.00919229 | ||||||||
\(997\) | −9.48975 | −0.300543 | −0.150272 | − | 0.988645i | \(-0.548015\pi\) | ||||
−0.150272 | + | 0.988645i | \(0.548015\pi\) | |||||||
\(998\) | −34.2517 | −1.08422 | ||||||||
\(999\) | −7.47721 | −0.236568 |
(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 | 1334.2.a.i.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.i.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial |